Finite Group Databasebeta

← C2×#14543106 #17941466

Subgroups — C2×#14543106 #17941466

Order 4352.

8122 conjugacy classes of subgroups.

The subgroup lattice has 1444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14543106C2132yesmaximal, direct product factor
2C2×#11763556C212yesmaximal, complemented
3C2×#11763549C212yesmaximal, complemented
4C2×#11763524C211yesmaximal, characteristic, complemented
5C2×#11763512C211yesmaximal, characteristic, complemented
6C2×#11763497C211yesmaximal, characteristic, complemented
7C2×#11763482C212yesmaximal, complemented
8C2×#11763479C211yesmaximal, characteristic, complemented
9C2×#11763464C211yesmaximal, characteristic, complemented
10C2×#11763454C211yesmaximal, characteristic, complemented
11C2×#11763454C211yesmaximal, characteristic, complemented
12C2×#11763451C212yesmaximal, complemented
13C2×#11763444C211yesmaximal, characteristic, complemented
14C2×#11763430C211yesmaximal, characteristic, complemented
15C2×#11763412C212yesmaximal, complemented
16C2×#11763396C212yesmaximal, complemented
17C2×#11763388C211yesmaximal, characteristic, complemented
18C2×#11763375C212yesmaximal, complemented
19C2×#11763375C211yesmaximal, characteristic, complemented
20C2×#11763367C212yesmaximal, complemented
21C2×#11763321C211yesmaximal, characteristic, complemented
22C2×#11763319C211yesmaximal, characteristic, complemented
23C2×#121×D17C211yesmaximal, characteristic, complemented
24C2×C17×#540C211yesmaximal, characteristic, complemented
25C22×#63252C2211yescharacteristic, complemented
26C22×#63252C2212yescomplemented
27C22×#63254C2211yescharacteristic, complemented
28C22×#63254C2211yescharacteristic, complemented
29C22×D4×D17C2212yes—
30C22×D4×D17C2211yescharacteristic
31C22×D4×D17C2212yescomplemented
32C22×D4×D17C2211yescharacteristic, complemented
33C23×C4×D17C2211yescharacteristic, complemented
34#11763556C22132yescomplemented
35#11763549C22132yescomplemented
36#11763524C22116yescomplemented
37#11763512C22116yescomplemented
38#11763497C22116yescomplemented
39#11763482C22132yescomplemented
40#11763479C22116yescomplemented
41#11763464C22116yescomplemented
42#11763454C22116yescomplemented
43#11763454C22116yescomplemented
44#11763451C22132yescomplemented
45#11763444C22116yescomplemented
46#11763430C22116yescomplemented
47#11763412C22132yescomplemented
48#11763396C22132yescomplemented
49#11763388C22116yescomplemented
50#11763375C22116yescomplemented
51#11763375C22132yescomplemented
52#11763367C22132yescomplemented
53C2×#10587555C2211yescharacteristic, complemented
54C2×#10587626C2212yescomplemented
55C2×#10587626C2212yescomplemented
56C2×#10587584C2212yescomplemented
57C2×#10587584C2212yescomplemented
58C2×#10587584C2212yescomplemented
59C2×#10587576C2212yescomplemented
60C2×#10587561C2211yescharacteristic, complemented
61C2×#10587571C2212yescomplemented
62C2×#10587571C2212yescomplemented
63C2×#10587571C2212yescomplemented
64C2×#10587571C2212yescomplemented
65#11763321C22116yescomplemented
66#11763319C22116yescomplemented
67C2×#10587580C2212yes—
68C2×#10587580C2212yescomplemented
69C2×#10587572C2211yescharacteristic, complemented
70C2×#10587572C2212yescomplemented
71C2×#10587572C2211yescharacteristic, complemented
72C2×#10587572C2212yescomplemented
73C2×#10587569C2212yescomplemented
74C2×#10587569C2212yescomplemented
75C2×#10587569C2212yescomplemented
76C2×#10587569C2212yescomplemented
77C2×#10587583C2211yescharacteristic, complemented
78C2×#10587583C2211yescharacteristic, complemented
79C2×#10587583C2211yescharacteristic, complemented
80C2×#10587583C2211yescharacteristic, complemented
81C2×#10587610C2211yescharacteristic, complemented
82C2×#10587610C2212yescomplemented
83C2×#10587582C2212yescomplemented
84C2×#10587564C2212yescomplemented
85C2×#10587581C2211yescharacteristic
86C2×#10587581C2211yescharacteristic
87C2×#10587581C2212yescomplemented
88C2×#10587581C2211yescharacteristic, complemented
89C2×#10587581C2211yescharacteristic, complemented
90C2×#10587616C2211yescharacteristic
91C2×#10587616C2212yescomplemented
92C2×#10587616C2212yescomplemented
93C2×#10587616C2212yescomplemented
94C2×#10587570C2212yescomplemented
95C2×#10587570C2212yescomplemented
96C2×#10587625C2212yescomplemented
97C2×#10587625C2212yescomplemented
98C2×#10587625C2212yescomplemented
99C2×#10587625C2212yescomplemented
100C2×#10587624C2211yescharacteristic
101C2×#10587624C2212yescomplemented
102C2×#10587624C2211yescharacteristic, complemented
103C2×#10587624C2211yescharacteristic, complemented
104C2×#10587624C2212yescomplemented
105C2×#10587624C2211yescharacteristic, complemented
106#121×D17C22116yescomplemented
107C2×#10587568C2211yescharacteristic
108C2×#10587568C2212yescomplemented
109C2×#10587568C2211yescharacteristic, complemented
110C2×#10587568C2212yescomplemented
111C2×#10587568C2212yescomplemented
112C2×#10587623C2212yes—
113C2×#10587623C2212yescomplemented
114C2×#10587623C2212yescomplemented
115C2×#10587623C2212yescomplemented
116C2×C4×Dic34C2211yescharacteristic, complemented
117C2×C4×D68C2211yescharacteristic
118C2×C4×D68C2211yescharacteristic, complemented
119C2×C4×D68C2211yescharacteristic, complemented
120C2×C4×D68C2211yescharacteristic, complemented
121C2×C4×D68C2211yescharacteristic, complemented
122C2×D4×Dic17C2212yescomplemented
123C2×D4×Dic17C2212yescomplemented
124C2×#10587579C2212yescomplemented
125C2×#10587567C2212yescomplemented
126C2×#10587612C2212yescomplemented
127C2×#10587578C2212yescomplemented
128C2×#10587578C2211yescharacteristic, complemented
129C2×#10587578C2211yescharacteristic, complemented
130C2×C4⋊C4×D17C2211yescharacteristic, complemented
131C2×C4⋊C4×D17C2211yescharacteristic, complemented
132C22×#63227C2212yescomplemented
133C22×#63227C2212yescomplemented
134C2×C22⋊C4×D17C2212yescomplemented
135C17×#540C22116yescomplemented
136C2×C17×#127C2211yescharacteristic, complemented
137C2×C17×#125C2211yescharacteristic, complemented
138C2×C17×#123C2212yescomplemented
139C2×C17×#123C2212yescomplemented
140C2×C17×#121C2212yescomplemented
141C2×C17×#121C2212yescomplemented
142C2×C17×#121C2211yescharacteristic, complemented
143C2×C17×#121C2211yescharacteristic, complemented
144C2×C4×D4×C17C2211yescharacteristic, complemented
145C2×C4×D4×C17C2211yescharacteristic, complemented
146C2×C17×#117C2211yescharacteristic, complemented
147C24×D17C2312yes—
148C24×D17C2311yescharacteristic
149C24×D17C2312yes—
150C22×D4×C17C2311yescharacteristic
151C22×D4×C17C2311yescharacteristic
152C22×D4×C17C2312yes—
153C22×D4×C17C2312yes—
154C22×D4×C17C2312yes—
155C22×D4×C17C2312yes—
156C23×C4×C17C2311yescharacteristic
157C23×C4×C17C2312yes—
158C23×C4×C17C2312yes—
159C22×C22⋊D17C2312yes—
160C22×C22⋊D17C2312yes—
161C22×C22⋊D17C2311yescharacteristic
162C22×C22⋊D17C2312yes—
163C22×C22⋊D17C2312yes—
164C22×C22⋊D17C2312yes—
165C22×C22⋊D17C2312yes—
166C22×C22⋊D17C2311yescharacteristic
167C22×C22⋊D17C2312yes—
168C22×C22⋊D17C2312yes—
169C22×C22⋊D17C2312yes—
170C23×Dic17C2312yes—
171C23×Dic17C2312yes—
172C23×Dic17C2311yescharacteristic
173C2×#63254—44no—
174C2×#63254—44no—
175C2×#63254C2318yescomplemented
176C2×#63254C2318yescomplemented
177C2×D4×D17—44no—
178C2×D4×D17—44no—
179C2×D4×D17—48no—
180C2×D4×D17—48no—
181C2×D4×D17C2318yes—
182C2×D4×D17C23116yes—
183C2×D4×D17C23116yescomplemented
184C2×D4×D17C2318yescomplemented
185C2×#63252—44no—
186C2×#63252—48no—
187C2×#63252C23116yescomplemented
188C2×#63252C2318yescomplemented
189C22×D68C2311yescharacteristic
190C22×D68C2311yescharacteristic
191C22×D68C2311yescharacteristic
192C22×D68C2312yes—
193C22×D68C2311yescharacteristic
194C22×D68C2311yescharacteristic
195C22×D68C2311yescharacteristic
196C22×D68C2312yes—
197C22×C4×D17—44no—
198C22×C4×D17C2312yes—
199C22×C4×D17C2311yescharacteristic
200C22×C4×D17C2311yescharacteristic
201C22×C4×D17C2311yescharacteristic
202C22×C4×D17C2311yescharacteristic
203C22×C4×D17C2311yescharacteristic
204C22×C4×D17C2312yes—
205C22×C4×D17C2312yes—
206C22×C4×D17C2311yescharacteristic
207C22×C4×D17C2318yescomplemented
208C22×Dic34C2311yescharacteristic
209C22×Dic34C2311yescharacteristic
210C22×Dic34C2312yes—
211C17×#127C2318yescomplemented
212C17×#125C2318yescomplemented
213C17×#123C23116yescomplemented
214C17×#123C23116yescomplemented
215C17×#121C2318yescomplemented
216C17×#121C2318yescomplemented
217C17×#121C23116yescomplemented
218C17×#121C23116yescomplemented
219C4×D4×C17C2318yescomplemented
220C4×D4×C17C2318yescomplemented
221C17×#117C2318yescomplemented
222C2×C4⋊C4×C17C2311yescharacteristic
223C2×C4⋊C4×C17C2311yescharacteristic
224C2×C4⋊C4×C17C2311yescharacteristic
225C2×C4⋊C4×C17C2311yescharacteristic
226C2×C4⋊C4×C17C2312yes—
227C2×C4⋊C4×C17C2312yes—
228C2×C22⋊C4×C17C2311yescharacteristic
229C2×C22⋊C4×C17C2311yescharacteristic
230C2×C22⋊C4×C17C2312yes—
231C2×C22⋊C4×C17C2312yes—
232C2×C22⋊C4×C17C2312yes—
233C2×C22⋊C4×C17C2312yes—
234C2×C42×C17C2311yescharacteristic
235C2×C42×C17C2311yescharacteristic
236C2×C22⋊Dic17C2312yes—
237C2×C22⋊Dic17C2312yes—
238C2×C22⋊Dic17C2312yes—
239C2×C22⋊Dic17C2312yes—
240C2×C22⋊Dic17C2312yes—
241#10587626C23116yescomplemented
242#10587626C23116yescomplemented
243#10587625C23116yescomplemented
244#10587625C23116yescomplemented
245#10587625C23116yescomplemented
246#10587625C23116yescomplemented
247#10587624C2318yes—
248#10587624C2318yescomplemented
249#10587624C2318yescomplemented
250#10587624C2318yescomplemented
251#10587624C23116yescomplemented
252#10587624C23116yescomplemented
253#10587623C23116yes—
254#10587623C23116yescomplemented
255#10587623C23116yescomplemented
256#10587623C23116yescomplemented
257D4×Dic17C23116yescomplemented
258D4×Dic17C23116yescomplemented
259#10587616C2318yes—
260#10587616C23116yescomplemented
261#10587616C23116yescomplemented
262#10587616C23116yescomplemented
263C2×#63227C2312yes—
264C2×#63227C2312yes—
265C2×#63227C2311yescharacteristic
266C2×#63227C2311yescharacteristic
267C2×#63227C2312yes—
268C2×#63227C2312yes—
269C2×#63227C2312yes—
270C2×#63227C2312yes—
271C2×#63227C2312yes—
272C2×#63227C2311yescharacteristic
273C2×#63227C2312yes—
274C2×#63227C2312yes—
275C2×#63227C2311yescharacteristic
276C2×#63227C2311yescharacteristic
277C2×#63227C2312yes—
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×#63227C23116yescomplemented
282C2×#63227C23116yescomplemented
283#10587612C23116yescomplemented
284C2×C4⋊Dic17C2311yescharacteristic
285C2×C4⋊Dic17C2311yescharacteristic
286C2×C4⋊Dic17C2312yes—
287C2×C4⋊Dic17C2311yescharacteristic
288C2×C4⋊Dic17C2312yes—
289C2×C4⋊Dic17C2311yescharacteristic
290C2×C4⋊Dic17C2312yes—
291C2×C4⋊Dic17C2311yescharacteristic
292C2×C4⋊Dic17C2311yescharacteristic
293#10587610C23116yescomplemented
294#10587610C2318yescomplemented
295C2×#63225C2312yes—
296C2×#63225C2312yes—
297C2×#63225C2312yes—
298C2×#63225C2312yes—
299C2×C4×Dic17C2312yes—
300C2×C4×Dic17C2312yes—
301C2×C4×Dic17C2312yes—
302#10587584C23116yescomplemented
303#10587584C23116yescomplemented
304#10587584C23116yescomplemented
305#10587583C2318yescomplemented
306#10587583C2318yescomplemented
307#10587583C2318yescomplemented
308#10587583C2318yescomplemented
309#10587582C23116yescomplemented
310#10587581C2318yes—
311#10587581C2318yes—
312#10587581C23116yescomplemented
313#10587581C2318yescomplemented
314#10587581C2318yescomplemented
315#10587580C23116yes—
316#10587580C23116yescomplemented
317#10587579C23116yescomplemented
318#10587578C23116yescomplemented
319#10587578C2318yescomplemented
320#10587578C2318yescomplemented
321C4⋊C4×D17C2318yescomplemented
322C4⋊C4×D17C2318yescomplemented
323#10587576C23116yescomplemented
324#10587572C23116yescomplemented
325#10587572C23116yescomplemented
326#10587572C2318yescomplemented
327#10587572C2318yescomplemented
328#10587571C23116yescomplemented
329#10587571C23116yescomplemented
330#10587571C23116yescomplemented
331#10587571C23116yescomplemented
332#10587570C23116yescomplemented
333#10587570C23116yescomplemented
334#10587569C23116yescomplemented
335#10587569C23116yescomplemented
336#10587569C23116yescomplemented
337#10587569C23116yescomplemented
338#10587568C2318yes—
339#10587568C23116yescomplemented
340#10587568C23116yescomplemented
341#10587568C2318yescomplemented
342#10587568C23116yescomplemented
343#10587567C23116yescomplemented
344C22⋊C4×D17C23116yescomplemented
345#10587564C23116yescomplemented
346#10587561C2318yescomplemented
347C4×D68C2318yes—
348C4×D68C2318yescomplemented
349C4×D68C2318yescomplemented
350C4×D68C2318yescomplemented
351C4×D68C2318yescomplemented
352#10587555C2318yescomplemented
353C4×Dic34C2318yescomplemented
354C24×C17C2411yescharacteristic
355C24×C17C2412yes—
356C24×C17C2412yes—
357C23×D17—24no—
358C23×D17—28no—
359C23×D17—42no—
360C23×D17—42no—
361C23×D17—44no—
362C23×D17—44no—
363C23×D17—44no—
364C23×D17—44no—
365C23×D17—44no—
366C23×D17C2411yescharacteristic
367C23×D17C2411yescharacteristic
368C23×D17C2411yescharacteristic
369C23×D17C2412yes—
370C23×D17C2411yescharacteristic
371C23×D17C2414yes—
372C23×D17C2418yes—
373C23×D17C2418yes—
374C2×D4×C17—24no—
375C2×D4×C17—24no—
376C2×D4×C17—44no—
377C2×D4×C17—44no—
378C2×D4×C17—44no—
379C2×D4×C17—44no—
380C2×D4×C17C2414yes—
381C2×D4×C17C2414yes—
382C2×D4×C17C2418yes—
383C2×D4×C17C2418yes—
384C2×D4×C17C2418yes—
385C2×D4×C17C2418yes—
386C22×C4×C17—24no—
387C22×C4×C17—44no—
388C22×C4×C17—44no—
389C22×C4×C17C2411yescharacteristic
390C22×C4×C17C2411yescharacteristic
391C22×C4×C17C2412yes—
392C22×C4×C17C2411yescharacteristic
393C22×C4×C17C2414yes—
394C22×C4×C17C2411yescharacteristic
395C22×C4×C17C2412yes—
396C22×C4×C17C2411yescharacteristic
397C22×C4×C17C2418yes—
398C22×C4×C17C2418yes—
399C22×C4×C17C2411yescharacteristic
400C2×C22⋊D17—28no—
401C2×C22⋊D17—42no—
402C2×C22⋊D17—42no—
403C2×C22⋊D17—44no—
404C2×C22⋊D17—44no—
405C2×C22⋊D17—44no—
406C2×C22⋊D17—44no—
407C2×C22⋊D17—44no—
408C2×C22⋊D17—44no—
409C2×C22⋊D17—44no—
410C2×C22⋊D17—44no—
411C2×C22⋊D17C2418yes—
412C2×C22⋊D17C2414yes—
413C2×C22⋊D17C2418yes—
414C2×C22⋊D17C2414yes—
415C2×C22⋊D17C2418yes—
416C2×C22⋊D17C2418yes—
417C2×C22⋊D17C2418yes—
418C2×C22⋊D17C2418yes—
419C2×C22⋊D17C2418yes—
420C2×C22⋊D17C2418yes—
421C2×C22⋊D17C2418yes—
422C22×Dic17—42no—
423C22×Dic17—44no—
424C22×Dic17—44no—
425C22×Dic17C2412yes—
426C22×Dic17C2411yescharacteristic
427C22×Dic17C2412yes—
428C22×Dic17C2411yescharacteristic
429C22×Dic17C2412yes—
430C22×Dic17C2411yescharacteristic
431C22×Dic17C2411yescharacteristic
432C22×Dic17C2414yes—
433C22×Dic17C2418yes—
434C22×Dic17C2418yes—
435#63254—416no—
436#63254—416no—
437D4×D17—416no—
438D4×D17—416no—
439D4×D17—432no—
440D4×D17—432no—
441#63252—416no—
442#63252—432no—
443C2×D68—24no—
444C2×D68—24no—
445C2×D68—24no—
446C2×D68—42no—
447C2×D68—44no—
448C2×D68—42no—
449C2×D68—42no—
450C2×D68—44no—
451C2×D68C2414yes—
452C2×D68C2414yes—
453C2×D68C2414yes—
454C2×D68C2414yes—
455C2×D68C2418yes—
456C2×D68C2414yes—
457C2×D68C2414yes—
458C2×D68C2418yes—
459C2×C4×D17—28no—
460C2×C4×D17—24no—
461C2×C4×D17—24no—
462C2×C4×D17—24no—
463C2×C4×D17—24no—
464C2×C4×D17—416no—
465C2×C4×D17—42no—
466C2×C4×D17—42no—
467C2×C4×D17—44no—
468C2×C4×D17—44no—
469C2×C4×D17C2414yes—
470C2×C4×D17C2414yes—
471C2×C4×D17C2414yes—
472C2×C4×D17C2418yes—
473C2×C4×D17C2414yes—
474C2×C4×D17C2414yes—
475C2×C4×D17C2414yes—
476C2×C4×D17C2418yes—
477C2×C4×D17C2418yes—
478C2×Dic34—24no—
479C2×Dic34—42no—
480C2×Dic34—44no—
481C2×Dic34C2414yes—
482C2×Dic34C2418yes—
483C2×Dic34C2414yes—
484C4⋊C4×C17C2414yes—
485C4⋊C4×C17C2414yes—
486C4⋊C4×C17C2418yes—
487C4⋊C4×C17C2418yes—
488C4⋊C4×C17C2414yes—
489C4⋊C4×C17C2414yes—
490C22⋊C4×C17C2418yes—
491C22⋊C4×C17C2418yes—
492C22⋊C4×C17C2418yes—
493C22⋊C4×C17C2418yes—
494C22⋊C4×C17C2414yes—
495C22⋊C4×C17C2414yes—
496C42×C17C2414yes—
497C42×C17C2414yes—
498C22⋊Dic17C2418yes—
499C22⋊Dic17C2418yes—
500C22⋊Dic17C2418yes—
501C22⋊Dic17C2418yes—
502C22⋊Dic17C2418yes—
503#63227C2414yes—
504#63227C2414yes—
505#63227C2414yes—
506#63227C2414yes—
507#63227C2414yes—
508#63227C2414yes—
509#63227C2414yes—
510#63227C2418yes—
511#63227C2414yes—
512#63227C2418yes—
513#63227C2418yes—
514#63227C2418yes—
515#63227C2418yes—
516#63227C2418yes—
517#63227C2418yes—
518#63227C2418yes—
519#63227C2418yes—
520#63227C2418yes—
521C4⋊Dic17C2414yes—
522C4⋊Dic17C2414yes—
523C4⋊Dic17C2418yes—
524C4⋊Dic17C2414yes—
525C4⋊Dic17C2414yes—
526C4⋊Dic17C2414yes—
527C4⋊Dic17C2414yes—
528C4⋊Dic17C2418yes—
529C4⋊Dic17C2418yes—
530#63225C2418yes—
531#63225C2418yes—
532#63225C2418yes—
533#63225C2418yes—
534C4×Dic17C2418yes—
535C4×Dic17C2418yes—
536C4×Dic17C2418yes—
537C2×#3542—171nomaximal, Sylow
538C23×C17—22no—
539C23×C17—24no—
540C23×C17—24no—
541C23×C17—24no—
542C23×C17—22no—
543C23×C17—24no—
544C23×C17—24no—
545C23×C17—22no—
546C23×C17—24no—
547C23×C17C2512yes—
548C23×C17C2514yes—
549C23×C17C2514yes—
550C23×C17C2511yescharacteristic
551C22×D17—22no—
552C22×D17—22no—
553C22×D17—22no—
554C22×D17—22no—
555C22×D17—22no—
556C22×D17—22no—
557C22×D17—24no—
558C22×D17—22no—
559C22×D17—24no—
560C22×D17—22no—
561C22×D17—22no—
562C22×D17—22no—
563C22×D17—22no—
564C22×D17—24no—
565C22×D17—28no—
566C22×D17—216no—
567C22×D17—44no—
568C22×D17—44no—
569C22×D17—48no—
570C22×D17—48no—
571C22×D17—48no—
572C22×D17—48no—
573C22×D17—48no—
574C22×D17—416no—
575C22×D17—816no—
576C22×D17—816no—
577C22×D17H(5,𝔽2)14yes—
578C22×D17C2512yes—
579C22×D17C2512yes—
580C22×D17C2512yes—
581C22×D17C2514yes—
582C22×D17C2512yes—
583D4×C17—28no—
584D4×C17—28no—
585D4×C17—48no—
586D4×C17—48no—
587D4×C17—48no—
588D4×C17—48no—
589C2×C4×C17—22no—
590C2×C4×C17—22no—
591C2×C4×C17—24no—
592C2×C4×C17—22no—
593C2×C4×C17—22no—
594C2×C4×C17—24no—
595C2×C4×C17—22no—
596C2×C4×C17—28no—
597C2×C4×C17—48no—
598C2×C4×C17—48no—
599C2×C4×C17H(5,𝔽2)14yes—
600C2×C4×C17C2512yes—
601C2×C4×C17C2512yes—
602C2×C4×C17C2512yes—
603C2×C4×C17C2512yes—
604C2×C4×C17C2512yes—
605C2×C4×C17C2514yes—
606C2×C4×C17C2514yes—
607C2×C4×C17C2512yes—
608C22⋊D17—216no—
609C22⋊D17—44no—
610C22⋊D17—44no—
611C22⋊D17—48no—
612C22⋊D17—48no—
613C22⋊D17—48no—
614C22⋊D17—48no—
615C22⋊D17—48no—
616C22⋊D17—48no—
617C22⋊D17—48no—
618C22⋊D17—48no—
619C2×Dic17—24no—
620C2×Dic17—22no—
621C2×Dic17—24no—
622C2×Dic17—22no—
623C2×Dic17—24no—
624C2×Dic17—22no—
625C2×Dic17—22no—
626C2×Dic17—44no—
627C2×Dic17—48no—
628C2×Dic17—48no—
629C2×Dic17C2514yes—
630C2×Dic17C2512yes—
631C2×Dic17C2514yes—
632C2×Dic17C2512yes—
633C2×Dic17C2512yes—
634C2×Dic17C2512yes—
635C2×Dic17C2514yes—
636D68—28no—
637D68—28no—
638D68—28no—
639D68—44no—
640D68—48no—
641D68—44no—
642D68—44no—
643D68—48no—
644C4×D17—216no—
645C4×D17—28no—
646C4×D17—28no—
647C4×D17—28no—
648C4×D17—28no—
649C4×D17—44no—
650C4×D17—44no—
651C4×D17—48no—
652C4×D17—48no—
653Dic34—28no—
654Dic34—44no—
655Dic34—48no—
656#3542—1732no—
657C2×#562—172no—
658C2×#560—172no—
659C2×#555—171no—
660C2×#553—171no—
661C2×#552—171no—
662C2×#551—172no—
663C2×#550—171no—
664C2×#547—171no—
665C2×#546—172no—
666C2×#546—171no—
667C2×#546—171no—
668C2×D42—171no—
669C2×#542—171no—
670C2×#540—172no—
671C2×#540D1711yescharacteristic, complemented
672C2×#538—172no—
673C2×#537—171no—
674C2×#535—172no—
675C2×#535—171no—
676C2×#534—172no—
677C2×#525—171no—
678C2×#525—171no—
679C22×#121—171no—
680C22×C17—22no—
681C22×C17—24no—
682C22×C17—24no—
683C22×C17—24no—
684C22×C17—22no—
685C22×C17—24no—
686C22×C17—24no—
687C22×C17—22no—
688C22×C17—24no—
689C22×C17—44no—
690C22×C17—48no—
691C22×C17—48no—
692C22×C17C2×H(5,𝔽2)12yes—
693C22×C17C2×H(5,𝔽2)12yes—
694C22×C17#58512yes—
695C22×C17C2611yescharacteristic
696C2×D17—22no—
697C2×D17—22no—
698C2×D17—28no—
699C2×D17—22no—
700C2×D17—22no—
701C2×D17—22no—
702C2×D17—22no—
703C2×D17—24no—
704C2×D17—22no—
705C2×D17—24no—
706C2×D17—22no—
707C2×D17—22no—
708C2×D17—22no—
709C2×D17—22no—
710C2×D17—24no—
711C2×D17—416no—
712C2×D17—44no—
713C2×D17—44no—
714C2×D17—44no—
715C2×D17—48no—
716C2×D17—816no—
717C2×D17—816no—
718C2×D17C2×H(5,𝔽2)14yes—
719C4×C17—22no—
720C4×C17—22no—
721C4×C17—24no—
722C4×C17—22no—
723C4×C17—22no—
724C4×C17—24no—
725C4×C17—22no—
726C4×C17C2×H(5,𝔽2)14yes—
727Dic17—24no—
728Dic17—22no—
729Dic17—24no—
730Dic17—22no—
731Dic17—24no—
732Dic17—22no—
733Dic17—22no—
734C22×#41—171no—
735C22×#41—171no—
736C22×#41—171no—
737C22×#41—172no—
738C23×D4—172no—
739C23×D4—171no—
740C23×D4—172no—
741C23×D4—171no—
742C24×C4—171no—
743#562—1732no—
744#560—1732no—
745#555—1716no—
746#553—1716no—
747#552—1716no—
748#551—1732no—
749#550—1716no—
750#547—1716no—
751#546—1732no—
752#546—1716no—
753#546—1716no—
754D42—1716no—
755#542—1716no—
756#540—1732no—
757#540C2×D17116yescomplemented
758#538—1732no—
759#537—1716no—
760#535—1732no—
761#535—1716no—
762#534—1732no—
763C2×C4⋊Q8—171no—
764C2×#127—172no—
765C2×#127—172no—
766C2×#127C2×D1711yescharacteristic, complemented
767C2×#126—172no—
768C2×#126—172no—
769C2×#126—172no—
770C2×#125—172no—
771C2×#125C2×D1711yescharacteristic, complemented
772C2×#124—172no—
773C2×#124—172no—
774C2×#124—172no—
775C2×#124—172no—
776C2×#124—171no—
777#525—1716no—
778#525—1716no—
779C2×#123—172no—
780C2×#123—172no—
781C2×#123—172no—
782C2×#123—171no—
783C2×#123—171no—
784C2×#123—172no—
785C2×#123—172no—
786C2×#123—172no—
787C2×#123—172no—
788C2×#123—172no—
789C2×#123C2×D1712yescomplemented
790C2×#123C2×D1712yescomplemented
791C2×C22⋊Q8—171no—
792C2×C22⋊Q8—172no—
793C2×C22⋊Q8—172no—
794C2×C22⋊Q8—171no—
795C2×C22⋊Q8—171no—
796C2×C22⋊Q8—171no—
797C2×C22⋊Q8—171no—
798C2×C22⋊Q8—172no—
799C2×#121—171no—
800C2×#121—171no—
801C2×#121—172no—
802C2×#121—171no—
803C2×#121—171no—
804C2×#121—172no—
805C2×#121—172no—
806C2×#121—172no—
807C2×#121—172no—
808C2×#121—172no—
809C2×#121—171no—
810C2×#121—172no—
811C2×#121—172no—
812C2×#121—172no—
813C2×#121—1716no—
814C2×#121—171no—
815C2×#121—171no—
816C2×#121—171no—
817C2×#121—171no—
818C2×#121—172no—
819C2×#121—172no—
820C2×#121—172no—
821C2×#121C2×D1711yescharacteristic, complemented
822C2×#121C2×D1711yescharacteristic, complemented
823C2×#121C2×D1712yescomplemented
824C2×#121C2×D1712yescomplemented
825C2×#120—172no—
826C2×#120—172no—
827C2×#120—172no—
828C2×#120—172no—
829C2×#120—171no—
830C2×#120—171no—
831C2×#120—172no—
832C2×#120—172no—
833C2×#120—172no—
834C2×C4×Q8—171no—
835C2×C4×D4—172no—
836C2×C4×D4—172no—
837C2×C4×D4—172no—
838C2×C4×D4—172no—
839C2×C4×D4—171no—
840C2×C4×D4—171no—
841C2×C4×D4—171no—
842C2×C4×D4—171no—
843C2×C4×D4—171no—
844C2×C4×D4C2×D1711yescharacteristic, complemented
845C2×C4×D4C2×D1711yescharacteristic, complemented
846C2×#117—172no—
847C2×#117—171no—
848C2×#117—172no—
849C2×#117—171no—
850C2×#117C2×D1711yescharacteristic, complemented
851C22×C4⋊C4—171no—
852C22×C4⋊C4—171no—
853C22×C22⋊C4—172no—
854C22×C22⋊C4—172no—
855C22×C22⋊C4—172no—
856C2×C17—42no—
857C2×C17—44no—
858C2×C17—44no—
859C2×C17#354214yescomplemented
860C2×C17C22×H(5,𝔽2)11yescharacteristic
861C2×C17C22×H(5,𝔽2)11yescharacteristic
862C2×C17C2×#58511yescharacteristic
863D17—24no—
864D17—42no—
865D17—42no—
866D17—42no—
867D17—44no—
868C25—172no—
869C25—171no—
870C25—172no—
871C2×#41—178no—
872C2×#41—178no—
873C2×#41—178no—
874C2×#41—1716no—
875C2×#41—684no—
876C2×#41—688no—
877C2×#41—684no—
878C2×#41—684no—
879C22×Q8—171no—
880C22×Q8—171no—
881C22×Q8—172no—
882C22×D4—172no—
883C22×D4—171no—
884C22×D4—172no—
885C22×D4—172no—
886C22×D4—172no—
887C22×D4—172no—
888C22×D4—172no—
889C22×D4—172no—
890C22×D4—171no—
891C22×D4—172no—
892C22×D4—172no—
893C22×D4—1716no—
894C22×D4—178no—
895C22×D4—1716no—
896C22×D4—178no—
897C22×D4—171no—
898C22×D4—171no—
899C22×D4—171no—
900C22×D4—171no—
901C22×D4—172no—
902C22×D4—171no—
903C22×D4—171no—
904C22×D4—172no—
905C22×D4—684no—
906C22×D4—684no—
907C22×D4—688no—
908C22×D4—688no—
909C22×D4C22×D1711yescharacteristic
910C22×D4C22×D1711yescharacteristic
911C22×D4C22×D1712yes—
912C22×D4C22×D1712yes—
913C22×D4C22×D1712yes—
914C22×D4C22×D1712yes—
915C23×C4—172no—
916C23×C4—172no—
917C23×C4—171no—
918C23×C4—172no—
919C23×C4—171no—
920C23×C4—171no—
921C23×C4—171no—
922C23×C4—171no—
923C23×C4—171no—
924C23×C4—172no—
925C23×C4—172no—
926C23×C4—171no—
927C23×C4—178no—
928C23×C4—684no—
929C23×C4C22×D1711yescharacteristic
930C23×C4C22×D1712yes—
931C23×C4C22×D1712yes—
932C4⋊Q8—178no—
933#127—1716no—
934#127—1716no—
935#127C22×D1718yescomplemented
936#126—1716no—
937#126—1716no—
938#126—1716no—
939#125—1716no—
940#125C22×D1718yescomplemented
941#124—1716no—
942#124—1716no—
943#124—1716no—
944#124—1716no—
945#124—178no—
946#123—1716no—
947#123—1716no—
948#123—178no—
949#123—178no—
950#123—1716no—
951#123—1716no—
952#123—1716no—
953#123—1716no—
954#123—1716no—
955#123—1716no—
956#123C22×D17116yescomplemented
957#123C22×D17116yescomplemented
958C22⋊Q8—178no—
959C22⋊Q8—1716no—
960C22⋊Q8—178no—
961C22⋊Q8—178no—
962C22⋊Q8—178no—
963C22⋊Q8—178no—
964C22⋊Q8—1716no—
965C22⋊Q8—1716no—
966#121—1716no—
967#121—178no—
968#121—178no—
969#121—1716no—
970#121—1716no—
971#121—1716no—
972#121—178no—
973#121—178no—
974#121—1716no—
975#121—1716no—
976#121—178no—
977#121—1716no—
978#121—1716no—
979#121—1716no—
980#121—178no—
981#121—178no—
982#121—178no—
983#121—178no—
984#121—1716no—
985#121—1716no—
986#121—1716no—
987#121C22×D1718yescomplemented
988#121C22×D1718yescomplemented
989#121C22×D17116yescomplemented
990#121C22×D17116yescomplemented
991#120—1716no—
992#120—1716no—
993#120—1716no—
994#120—1716no—
995#120—178no—
996#120—178no—
997#120—1716no—
998#120—1716no—
999#120—1716no—
1000C4×Q8—178no—
1001C4×D4—1716no—
1002C4×D4—1716no—
1003C4×D4—1716no—
1004C4×D4—1716no—
1005C4×D4—178no—
1006C4×D4—178no—
1007C4×D4—178no—
1008C4×D4—178no—
1009C4×D4—178no—
1010C4×D4C22×D1718yescomplemented
1011C4×D4C22×D1718yescomplemented
1012#117—1716no—
1013#117—178no—
1014#117—1716no—
1015#117—178no—
1016#117C22×D1718yescomplemented
1017C2×C4⋊C4—171no—
1018C2×C4⋊C4—171no—
1019C2×C4⋊C4—172no—
1020C2×C4⋊C4—172no—
1021C2×C4⋊C4—171no—
1022C2×C4⋊C4—172no—
1023C2×C4⋊C4—172no—
1024C2×C4⋊C4—171no—
1025C2×C4⋊C4—171no—
1026C2×C4⋊C4—172no—
1027C2×C4⋊C4—172no—
1028C2×C4⋊C4—171no—
1029C2×C4⋊C4—172no—
1030C2×C4⋊C4—178no—
1031C2×C4⋊C4—178no—
1032C2×C4⋊C4C22×D1711yescharacteristic
1033C2×C4⋊C4C22×D1711yescharacteristic
1034C2×C4⋊C4C22×D1712yes—
1035C2×C4⋊C4C22×D1711yescharacteristic
1036C2×C4⋊C4C22×D1711yescharacteristic
1037C2×C4⋊C4C22×D1712yes—
1038C2×C22⋊C4—172no—
1039C2×C22⋊C4—172no—
1040C2×C22⋊C4—172no—
1041C2×C22⋊C4—172no—
1042C2×C22⋊C4—172no—
1043C2×C22⋊C4—171no—
1044C2×C22⋊C4—172no—
1045C2×C22⋊C4—171no—
1046C2×C22⋊C4—172no—
1047C2×C22⋊C4—172no—
1048C2×C22⋊C4—172no—
1049C2×C22⋊C4—172no—
1050C2×C22⋊C4—172no—
1051C2×C22⋊C4—172no—
1052C2×C22⋊C4—1716no—
1053C2×C22⋊C4—1716no—
1054C2×C22⋊C4—171no—
1055C2×C22⋊C4—172no—
1056C2×C22⋊C4—172no—
1057C2×C22⋊C4—171no—
1058C2×C22⋊C4—171no—
1059C2×C22⋊C4—172no—
1060C2×C22⋊C4—171no—
1061C2×C22⋊C4—171no—
1062C2×C22⋊C4—171no—
1063C2×C22⋊C4—1716no—
1064C2×C22⋊C4C22×D1712yes—
1065C2×C22⋊C4C22×D1711yescharacteristic
1066C2×C22⋊C4C22×D1711yescharacteristic
1067C2×C22⋊C4C22×D1712yes—
1068C2×C22⋊C4C22×D1712yes—
1069C2×C22⋊C4C22×D1712yes—
1070C2×C42—172no—
1071C2×C42—172no—
1072C2×C42—172no—
1073C2×C42C22×D1711yescharacteristic
1074C2×C42C22×D1711yescharacteristic
1075C17C2×#354211yescharacteristic, complemented, Sylow
1076C24—171no—
1077C24—172no—
1078C24—171no—
1079C24—171no—
1080C24—171no—
1081C24—178no—
1082C24—174no—
1083C24—178no—
1084C24—344no—
1085C24—348no—
1086C24—682no—
1087C24—682no—
1088C24—684no—
1089C24—684no—
1090C24—684no—
1091C24—684no—
1092C24—684no—
1093C24C23×D1712yes—
1094C24C23×D1711yescharacteristic
1095C24C23×D1712yes—
1096#41—6816no—
1097#41—6832no—
1098#41—6816no—
1099#41—6816no—
1100C2×Q8—174no—
1101C2×Q8—174no—
1102C2×Q8—178no—
1103C2×Q8—344no—
1104C2×Q8—684no—
1105C2×Q8—682no—
1106C2×D4—24no—
1107C2×D4—24no—
1108C2×D4—44no—
1109C2×D4—44no—
1110C2×D4—44no—
1111C2×D4—44no—
1112C2×D4—178no—
1113C2×D4—174no—
1114C2×D4—178no—
1115C2×D4—178no—
1116C2×D4—178no—
1117C2×D4—178no—
1118C2×D4—178no—
1119C2×D4—178no—
1120C2×D4—178no—
1121C2×D4—174no—
1122C2×D4—178no—
1123C2×D4—174no—
1124C2×D4—174no—
1125C2×D4—174no—
1126C2×D4—174no—
1127C2×D4—178no—
1128C2×D4—174no—
1129C2×D4—174no—
1130C2×D4—178no—
1131C2×D4—344no—
1132C2×D4—344no—
1133C2×D4—348no—
1134C2×D4—344no—
1135C2×D4—682no—
1136C2×D4—684no—
1137C2×D4—682no—
1138C2×D4—684no—
1139C2×D4—682no—
1140C2×D4—6816no—
1141C2×D4—6816no—
1142C2×D4—6832no—
1143C2×D4—684no—
1144C2×D4—684no—
1145C2×D4—684no—
1146C2×D4—684no—
1147C2×D4—684no—
1148C2×D4—684no—
1149C2×D4—682no—
1150C2×D4—682no—
1151C2×D4—684no—
1152C2×D4—684no—
1153C2×D4—6832no—
1154C2×D4C23×D1714yes—
1155C2×D4C23×D1714yes—
1156C2×D4C23×D1718yes—
1157C2×D4C23×D1718yes—
1158C2×D4C23×D1718yes—
1159C2×D4C23×D1718yes—
1160C22×C4—24no—
1161C22×C4—44no—
1162C22×C4—44no—
1163C22×C4—171no—
1164C22×C4—172no—
1165C22×C4—171no—
1166C22×C4—172no—
1167C22×C4—172no—
1168C22×C4—171no—
1169C22×C4—171no—
1170C22×C4—178no—
1171C22×C4—178no—
1172C22×C4—174no—
1173C22×C4—178no—
1174C22×C4—174no—
1175C22×C4—174no—
1176C22×C4—174no—
1177C22×C4—174no—
1178C22×C4—174no—
1179C22×C4—178no—
1180C22×C4—178no—
1181C22×C4—174no—
1182C22×C4—348no—
1183C22×C4—344no—
1184C22×C4—344no—
1185C22×C4—344no—
1186C22×C4—344no—
1187C22×C4—6816no—
1188C22×C4—682no—
1189C22×C4—682no—
1190C22×C4—684no—
1191C22×C4—684no—
1192C22×C4—682no—
1193C22×C4—684no—
1194C22×C4—684no—
1195C22×C4C23×D1714yes—
1196C22×C4C23×D1711yescharacteristic
1197C22×C4C23×D1712yes—
1198C22×C4C23×D1711yescharacteristic
1199C22×C4C23×D1711yescharacteristic
1200C22×C4C23×D1711yescharacteristic
1201C22×C4C23×D1711yescharacteristic
1202C22×C4C23×D1712yes—
1203C22×C4C23×D1718yes—
1204C22×C4C23×D1718yes—
1205C22×C4C23×D1711yescharacteristic
1206C4⋊C4—174no—
1207C4⋊C4—174no—
1208C4⋊C4—178no—
1209C4⋊C4—178no—
1210C4⋊C4—174no—
1211C4⋊C4—178no—
1212C4⋊C4—178no—
1213C4⋊C4—174no—
1214C4⋊C4—174no—
1215C4⋊C4—178no—
1216C4⋊C4—178no—
1217C4⋊C4—174no—
1218C4⋊C4—178no—
1219C4⋊C4C23×D1714yes—
1220C4⋊C4C23×D1714yes—
1221C4⋊C4C23×D1718yes—
1222C4⋊C4C23×D1714yes—
1223C4⋊C4C23×D1714yes—
1224C4⋊C4C23×D1718yes—
1225C22⋊C4—178no—
1226C22⋊C4—178no—
1227C22⋊C4—178no—
1228C22⋊C4—178no—
1229C22⋊C4—178no—
1230C22⋊C4—174no—
1231C22⋊C4—178no—
1232C22⋊C4—174no—
1233C22⋊C4—178no—
1234C22⋊C4—178no—
1235C22⋊C4—178no—
1236C22⋊C4—178no—
1237C22⋊C4—178no—
1238C22⋊C4—178no—
1239C22⋊C4—174no—
1240C22⋊C4—178no—
1241C22⋊C4—178no—
1242C22⋊C4—174no—
1243C22⋊C4—174no—
1244C22⋊C4—178no—
1245C22⋊C4—174no—
1246C22⋊C4—174no—
1247C22⋊C4—174no—
1248C22⋊C4C23×D1718yes—
1249C22⋊C4C23×D1714yes—
1250C22⋊C4C23×D1714yes—
1251C22⋊C4C23×D1718yes—
1252C22⋊C4C23×D1718yes—
1253C22⋊C4C23×D1718yes—
1254C42—178no—
1255C42—178no—
1256C42—178no—
1257C42C23×D1714yes—
1258C42C23×D1714yes—
1259C23—24no—
1260C23—22no—
1261C23—24no—
1262C23—22no—
1263C23—24no—
1264C23—24no—
1265C23—24no—
1266C23—22no—
1267C23—24no—
1268C23—174no—
1269C23—172no—
1270C23—174no—
1271C23—172no—
1272C23—172no—
1273C23—172no—
1274C23—348no—
1275C23—3416no—
1276C23—342no—
1277C23—342no—
1278C23—342no—
1279C23—344no—
1280C23—342no—
1281C23—342no—
1282C23—342no—
1283C23—342no—
1284C23—342no—
1285C23—344no—
1286C23—342no—
1287C23—342no—
1288C23—344no—
1289C23—342no—
1290C23—684no—
1291C23—684no—
1292C23—688no—
1293C23—688no—
1294C23—688no—
1295C23—688no—
1296C23—688no—
1297C23—6816no—
1298C23—13616no—
1299C23—13616no—
1300C23C24×D1714yes—
1301C23C24×D1712yes—
1302C23C24×D1714yes—
1303C23C24×D1711yescharacteristic
1304Q8—348no—
1305Q8—688no—
1306Q8—684no—
1307D4—28no—
1308D4—28no—
1309D4—48no—
1310D4—48no—
1311D4—48no—
1312D4—48no—
1313D4—348no—
1314D4—348no—
1315D4—3416no—
1316D4—348no—
1317D4—688no—
1318D4—684no—
1319D4—684no—
1320D4—688no—
1321D4—684no—
1322D4—688no—
1323D4—688no—
1324D4—688no—
1325D4—688no—
1326D4—688no—
1327D4—688no—
1328D4—684no—
1329D4—684no—
1330D4—688no—
1331D4—688no—
1332C2×C4—22no—
1333C2×C4—24no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—28no—
1340C2×C4—48no—
1341C2×C4—48no—
1342C2×C4—172no—
1343C2×C4—174no—
1344C2×C4—172no—
1345C2×C4—174no—
1346C2×C4—174no—
1347C2×C4—172no—
1348C2×C4—172no—
1349C2×C4—3416no—
1350C2×C4—344no—
1351C2×C4—344no—
1352C2×C4—342no—
1353C2×C4—342no—
1354C2×C4—342no—
1355C2×C4—342no—
1356C2×C4—344no—
1357C2×C4—348no—
1358C2×C4—348no—
1359C2×C4—348no—
1360C2×C4—348no—
1361C2×C4—684no—
1362C2×C4—684no—
1363C2×C4—688no—
1364C2×C4—688no—
1365C2×C4—684no—
1366C2×C4—688no—
1367C2×C4—688no—
1368C2×C4#1058769614yes—
1369C2×C4C24×D1712yes—
1370C2×C4C24×D1714yes—
1371C2×C4C24×D1712yes—
1372C2×C4C24×D1712yes—
1373C2×C4C24×D1712yes—
1374C2×C4C24×D1712yes—
1375C2×C4C24×D1714yes—
1376C2×C4C24×D1712yes—
1377C22—24no—
1378C22—22no—
1379C22—24no—
1380C22—22no—
1381C22—24no—
1382C22—24no—
1383C22—24no—
1384C22—22no—
1385C22—24no—
1386C22—44no—
1387C22—48no—
1388C22—48no—
1389C22—174no—
1390C22—348no—
1391C22—342no—
1392C22—342no—
1393C22—342no—
1394C22—344no—
1395C22—342no—
1396C22—342no—
1397C22—342no—
1398C22—342no—
1399C22—342no—
1400C22—344no—
1401C22—342no—
1402C22—342no—
1403C22—344no—
1404C22—342no—
1405C22—6816no—
1406C22—684no—
1407C22—688no—
1408C22—684no—
1409C22—684no—
1410C22—13616no—
1411C22—13616no—
1412C22H(5,𝔽2)×D1712yes—
1413C22C2×#1058769612yes—
1414C22#1176364412yes—
1415C22C25×D1711yescharacteristic
1416C4—22no—
1417C4—24no—
1418C4—22no—
1419C4—22no—
1420C4—22no—
1421C4—24no—
1422C4—22no—
1423C4—344no—
1424C4—344no—
1425C4—342no—
1426C4—342no—
1427C4—342no—
1428C4—342no—
1429C4—344no—
1430C4C2×#1058769614yes—
1431C2—42no—
1432C2—44no—
1433C2—44no—
1434C2—344no—
1435C2—682no—
1436C2—684no—
1437C2—682no—
1438C2—682no—
1439C2#1454310614yesdirect product factor
1440C2C2×H(5,𝔽2)×D1711yescharacteristic
1441C2C22×#1058769611yescharacteristic
1442C2C2×#1176364411yescharacteristic
subgroupG/H
centerC23C24×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC2×C17×#540C2
socleC23×C17C25
hypercenterC2×#540D17
hypocenterC17C2×#3542
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#540

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14543106C2direct (N × H)
2. C2×#11763556C2semidirect
3. C2×#11763549C2semidirect
4. C2×#11763524C2semidirect
5. C2×#11763512C2semidirect
6. C2×#11763497C2semidirect
7. C2×#11763482C2semidirect
8. C2×#11763479C2semidirect
9. C2×#11763464C2semidirect
10. C2×#11763454C2semidirect
11. C2×#11763454C2semidirect
12. C2×#11763451C2semidirect
13. C2×#11763444C2semidirect
14. C2×#11763430C2semidirect
15. C2×#11763412C2semidirect
16. C2×#11763396C2semidirect
17. C2×#11763388C2semidirect
18. C2×#11763375C2semidirect
19. C2×#11763375C2semidirect
20. C2×#11763367C2semidirect
21. C2×#11763321C2semidirect
22. C2×#11763319C2semidirect
23. C2×#121×D17C2semidirect
24. C2×C17×#540C2semidirect
25. C22×#63252C22semidirect
26. C22×#63252C22semidirect
27. C22×#63254C22semidirect
28. C22×#63254C22semidirect
31. C22×D4×D17C22semidirect
32. C22×D4×D17C22semidirect
33. C23×C4×D17C22semidirect
34. #11763556C22semidirect
35. #11763549C22semidirect
36. #11763524C22semidirect
37. #11763512C22semidirect
38. #11763497C22semidirect
39. #11763482C22semidirect
40. #11763479C22semidirect
41. #11763464C22semidirect
42. #11763454C22semidirect
43. #11763454C22semidirect
44. #11763451C22semidirect
45. #11763444C22semidirect
46. #11763430C22semidirect
47. #11763412C22semidirect
48. #11763396C22semidirect
49. #11763388C22semidirect
50. #11763375C22semidirect
51. #11763375C22semidirect
52. #11763367C22semidirect
53. C2×#10587555C22semidirect
54. C2×#10587626C22semidirect
55. C2×#10587626C22semidirect
56. C2×#10587584C22semidirect
57. C2×#10587584C22semidirect
58. C2×#10587584C22semidirect
59. C2×#10587576C22semidirect
60. C2×#10587561C22semidirect
61. C2×#10587571C22semidirect
62. C2×#10587571C22semidirect
63. C2×#10587571C22semidirect
64. C2×#10587571C22semidirect
65. #11763321C22semidirect
66. #11763319C22semidirect
68. C2×#10587580C22semidirect
69. C2×#10587572C22semidirect
70. C2×#10587572C22semidirect
71. C2×#10587572C22semidirect
72. C2×#10587572C22semidirect
73. C2×#10587569C22semidirect
74. C2×#10587569C22semidirect
75. C2×#10587569C22semidirect
76. C2×#10587569C22semidirect
77. C2×#10587583C22semidirect
78. C2×#10587583C22semidirect
79. C2×#10587583C22semidirect
80. C2×#10587583C22semidirect
81. C2×#10587610C22semidirect
82. C2×#10587610C22semidirect
83. C2×#10587582C22semidirect
84. C2×#10587564C22semidirect
87. C2×#10587581C22semidirect
88. C2×#10587581C22semidirect
89. C2×#10587581C22semidirect
91. C2×#10587616C22semidirect
92. C2×#10587616C22semidirect
93. C2×#10587616C22semidirect
94. C2×#10587570C22semidirect
95. C2×#10587570C22semidirect
96. C2×#10587625C22semidirect
97. C2×#10587625C22semidirect
98. C2×#10587625C22semidirect
99. C2×#10587625C22semidirect
101. C2×#10587624C22semidirect
102. C2×#10587624C22semidirect
103. C2×#10587624C22semidirect
104. C2×#10587624C22semidirect
105. C2×#10587624C22semidirect
106. #121×D17C22semidirect
108. C2×#10587568C22semidirect
109. C2×#10587568C22semidirect
110. C2×#10587568C22semidirect
111. C2×#10587568C22semidirect
113. C2×#10587623C22semidirect
114. C2×#10587623C22semidirect
115. C2×#10587623C22semidirect
116. C2×C4×Dic34C22semidirect
118. C2×C4×D68C22semidirect
119. C2×C4×D68C22semidirect
120. C2×C4×D68C22semidirect
121. C2×C4×D68C22semidirect
122. C2×D4×Dic17C22semidirect
123. C2×D4×Dic17C22semidirect
124. C2×#10587579C22semidirect
125. C2×#10587567C22semidirect
126. C2×#10587612C22semidirect
127. C2×#10587578C22semidirect
128. C2×#10587578C22semidirect
129. C2×#10587578C22semidirect
130. C2×C4⋊C4×D17C22semidirect
131. C2×C4⋊C4×D17C22semidirect
132. C22×#63227C22semidirect
133. C22×#63227C22semidirect
134. C2×C22⋊C4×D17C22semidirect
135. C17×#540C22semidirect
136. C2×C17×#127C22semidirect
137. C2×C17×#125C22semidirect
138. C2×C17×#123C22semidirect
139. C2×C17×#123C22semidirect
140. C2×C17×#121C22semidirect
141. C2×C17×#121C22semidirect
142. C2×C17×#121C22semidirect
143. C2×C17×#121C22semidirect
144. C2×C4×D4×C17C22semidirect
145. C2×C4×D4×C17C22semidirect
146. C2×C17×#117C22semidirect
175. C2×#63254C23semidirect
176. C2×#63254C23semidirect
183. C2×D4×D17C23semidirect
184. C2×D4×D17C23semidirect
187. C2×#63252C23semidirect
188. C2×#63252C23semidirect
207. C22×C4×D17C23semidirect
211. C17×#127C23semidirect
212. C17×#125C23semidirect
213. C17×#123C23semidirect
214. C17×#123C23semidirect
215. C17×#121C23semidirect
216. C17×#121C23semidirect
217. C17×#121C23semidirect
218. C17×#121C23semidirect
219. C4×D4×C17C23semidirect
220. C4×D4×C17C23semidirect
221. C17×#117C23semidirect
241. #10587626C23semidirect
242. #10587626C23semidirect
243. #10587625C23semidirect
244. #10587625C23semidirect
245. #10587625C23semidirect
246. #10587625C23semidirect
248. #10587624C23semidirect
249. #10587624C23semidirect
250. #10587624C23semidirect
251. #10587624C23semidirect
252. #10587624C23semidirect
254. #10587623C23semidirect
255. #10587623C23semidirect
256. #10587623C23semidirect
257. D4×Dic17C23semidirect
258. D4×Dic17C23semidirect
260. #10587616C23semidirect
261. #10587616C23semidirect
262. #10587616C23semidirect
281. C2×#63227C23semidirect
282. C2×#63227C23semidirect
283. #10587612C23semidirect
293. #10587610C23semidirect
294. #10587610C23semidirect
302. #10587584C23semidirect
303. #10587584C23semidirect
304. #10587584C23semidirect
305. #10587583C23semidirect
306. #10587583C23semidirect
307. #10587583C23semidirect
308. #10587583C23semidirect
309. #10587582C23semidirect
312. #10587581C23semidirect
313. #10587581C23semidirect
314. #10587581C23semidirect
316. #10587580C23semidirect
317. #10587579C23semidirect
318. #10587578C23semidirect
319. #10587578C23semidirect
320. #10587578C23semidirect
321. C4⋊C4×D17C23semidirect
322. C4⋊C4×D17C23semidirect
323. #10587576C23semidirect
324. #10587572C23semidirect
325. #10587572C23semidirect
326. #10587572C23semidirect
327. #10587572C23semidirect
328. #10587571C23semidirect
329. #10587571C23semidirect
330. #10587571C23semidirect
331. #10587571C23semidirect
332. #10587570C23semidirect
333. #10587570C23semidirect
334. #10587569C23semidirect
335. #10587569C23semidirect
336. #10587569C23semidirect
337. #10587569C23semidirect
339. #10587568C23semidirect
340. #10587568C23semidirect
341. #10587568C23semidirect
342. #10587568C23semidirect
343. #10587567C23semidirect
344. C22⋊C4×D17C23semidirect
345. #10587564C23semidirect
346. #10587561C23semidirect
348. C4×D68C23semidirect
349. C4×D68C23semidirect
350. C4×D68C23semidirect
351. C4×D68C23semidirect
352. #10587555C23semidirect
353. C4×Dic34C23semidirect
671. C2×#540D17semidirect
757. #540C2×D17semidirect
766. C2×#127C2×D17semidirect
771. C2×#125C2×D17semidirect
789. C2×#123C2×D17semidirect
790. C2×#123C2×D17semidirect
821. C2×#121C2×D17semidirect
822. C2×#121C2×D17semidirect
823. C2×#121C2×D17semidirect
824. C2×#121C2×D17semidirect
844. C2×C4×D4C2×D17semidirect
845. C2×C4×D4C2×D17semidirect
850. C2×#117C2×D17semidirect
859. C2×C17#3542semidirect
935. #127C22×D17semidirect
940. #125C22×D17semidirect
956. #123C22×D17semidirect
957. #123C22×D17semidirect
987. #121C22×D17semidirect
988. #121C22×D17semidirect
989. #121C22×D17semidirect
990. #121C22×D17semidirect
1010. C4×D4C22×D17semidirect
1011. C4×D4C22×D17semidirect
1016. #117C22×D17semidirect
1075. C17C2×#3542semidirect
1439. C2#14543106direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145431062
C2×#117635562
C2×#117635492
C2×#117635242
C2×#117635122
C2×#117634972
C2×#117634822
C2×#117634792
C2×#117634642
C2×#117634542
C2×#117634512
C2×#117634442
C2×#117634302
C2×#117634122
C2×#117633962
C2×#117633882
C2×#117633752
C2×#117633672
C2×#117633212
C2×#117633192
C2×#121×D172
C2×C17×#5402
C2×#354217