Finite Group Databasebeta

← C2×#14543105 #17941463

Subgroups — C2×#14543105 #17941463

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#14543105C2132yesmaximal, direct product factor
2C2×#11763554C212yesmaximal, complemented
3C2×#11763548C212yesmaximal, complemented
4C2×#11763523C211yesmaximal, characteristic, complemented
5C2×#11763509C211yesmaximal, characteristic, complemented
6C2×#11763499C211yesmaximal, characteristic, complemented
7C2×#11763490C212yesmaximal, complemented
8C2×#11763479C211yesmaximal, characteristic, complemented
9C2×#11763459C211yesmaximal, characteristic, complemented
10C2×#11763453C212yesmaximal, complemented
11C2×#11763453C211yesmaximal, characteristic, complemented
12C2×#11763453C211yesmaximal, characteristic, complemented
13C2×#11763424C211yesmaximal, characteristic, complemented
14C2×#11763413C211yesmaximal, characteristic, complemented
15C2×#11763409C212yesmaximal, complemented
16C2×#11763394C212yesmaximal, complemented
17C2×#11763388C211yesmaximal, characteristic, complemented
18C2×#11763376C211yesmaximal, characteristic, complemented
19C2×#11763374C212yesmaximal, complemented
20C2×#11763368C212yesmaximal, complemented
21C2×#11763319C211yesmaximal, characteristic, complemented
22C2×#11763318C211yesmaximal, characteristic, complemented
23C22×#10587624C211yesmaximal, characteristic, complemented
24C2×D42×C17C211yesmaximal, characteristic, complemented
25C22×#63252C2211yescharacteristic, complemented
26C22×#63254C2212yescomplemented
27C22×#63254C2211yescharacteristic, complemented
28C22×#63254C2211yescharacteristic, complemented
29C23×C22⋊D17C2212yescomplemented
30C23×C4×D17C2211yescharacteristic, complemented
31#11763554C22132yescomplemented
32#11763548C22132yescomplemented
33#11763523C22116yescomplemented
34#11763509C22116yescomplemented
35#11763499C22116yescomplemented
36#11763490C22132yescomplemented
37#11763479C22116yescomplemented
38#11763459C22116yescomplemented
39#11763453C22132yescomplemented
40#11763453C22116yescomplemented
41#11763453C22116yescomplemented
42#11763424C22116yescomplemented
43#11763413C22116yescomplemented
44#11763409C22132yescomplemented
45#11763394C22132yescomplemented
46#11763388C22116yescomplemented
47#11763376C22116yescomplemented
48#11763374C22132yescomplemented
49#11763368C22132yescomplemented
50C2×#10587574C2211yescharacteristic, complemented
51C2×#10587626C2212yescomplemented
52C2×#10587626C2212yescomplemented
53C2×#10587565C2212yescomplemented
54C2×#10587565C2212yescomplemented
55C2×#10587565C2212yescomplemented
56C2×#10587556C2211yescharacteristic, complemented
57C2×#10587575C2212yescomplemented
58C2×#10587622C2212yescomplemented
59C2×#10587622C2212yescomplemented
60C2×#10587622C2211yescharacteristic, complemented
61C2×#10587571C2212yescomplemented
62C2×#10587571C2212yescomplemented
63#11763319C22116yescomplemented
64#11763318C22116yescomplemented
65C2×#10587580C2211yescharacteristic, complemented
66C2×#10587615C2212yescomplemented
67C2×#10587615C2212yescomplemented
68C2×#10587569C2211yescharacteristic, complemented
69C2×#10587569C2212yescomplemented
70C2×#10587569C2212yescomplemented
71C2×#10587621C2212yes—
72C2×#10587621C2212yescomplemented
73C2×#10587621C2212yescomplemented
74C2×#10587621C2212yescomplemented
75C2×#10587621C2212yescomplemented
76C2×#10587621C2212yescomplemented
77C2×#10587583C2211yescharacteristic, complemented
78C2×#10587610C2211yescharacteristic, complemented
79C2×#10587610C2212yescomplemented
80C2×#10587610C2211yescharacteristic, complemented
81C2×#10587582C2211yescharacteristic, complemented
82C2×#10587564C2212yescomplemented
83C2×#10587564C2212yescomplemented
84C2×#10587564C2211yescharacteristic, complemented
85C2×#10587570C2212yescomplemented
86C2×#10587570C2212yescomplemented
87C2×#10587570C2211yescharacteristic, complemented
88C2×#10587625C2211yescharacteristic
89C2×#10587625C2212yescomplemented
90C2×#10587625C2212yescomplemented
91C2×#10587625C2212yescomplemented
92C2×#10587625C2212yescomplemented
93C2×#10587625C2212yescomplemented
94C2×#10587625C2212yescomplemented
95C2×#10587625C2212yescomplemented
96C2×#10587625C2212yescomplemented
97C2×#10587624C2211yescharacteristic
98C2×#10587624C2211yescharacteristic
99C2×#10587624C2211yescharacteristic, complemented
100C2×#10587624C2211yescharacteristic, complemented
101C2×#10587624C2211yescharacteristic, complemented
102C2×#10587624C2212yescomplemented
103C2×#10587624C2211yescharacteristic, complemented
104C2×#10587624C2212yescomplemented
105C2×#10587624C2212yescomplemented
106C2×#10587624C2211yescharacteristic, complemented
107C2×#10587624C22116yescomplemented
108C2×#10587568C2211yescharacteristic, complemented
109C2×#10587639C2212yescomplemented
110C2×#10587639C2212yescomplemented
111C2×#10587639C2212yescomplemented
112C2×#10587639C2212yescomplemented
113C2×#10587623C2211yescharacteristic
114C2×#10587623C2212yescomplemented
115C2×C4×Dic34C2211yescharacteristic, complemented
116C2×C4×D68C2211yescharacteristic, complemented
117C2×D4×Dic17C2212yescomplemented
118C2×D4×Dic17C2211yescharacteristic, complemented
119C2×D4×Dic17C2211yescharacteristic, complemented
120C2×D4×Dic17C2212yescomplemented
121C2×C4×C22⋊D17C2212yescomplemented
122C2×C4×C22⋊D17C2211yescharacteristic, complemented
123C2×C4×C22⋊D17C2211yescharacteristic, complemented
124C2×#10587567C2212yescomplemented
125C2×#10587612C2211yescharacteristic, complemented
126C2×#10587578C2211yescharacteristic, complemented
127C2×#10587558C2211yescharacteristic, complemented
128C2×#10587563C2212yescomplemented
129C2×#10587563C2212yescomplemented
130C22×C4⋊Dic17C2211yescharacteristic, complemented
131C2×C4⋊C4×D17C2211yescharacteristic, complemented
132C22×C22⋊Dic17C2212yescomplemented
133C22×C22⋊Dic17C2212yescomplemented
134C22×C22⋊Dic17C2212yescomplemented
135C23×D4×C17C2212yes—
136C23×D4×C17C2211yescharacteristic
137C23×D4×C17C2211yescharacteristic, complemented
138D42×C17C22116yescomplemented
139C2×C17×#127C2211yescharacteristic, complemented
140C2×C17×#121C2211yescharacteristic
141C2×C17×#121C2211yescharacteristic, complemented
142C2×C17×#121C2212yescomplemented
143C2×C17×#120C2212yes—
144C2×C17×#120C2212yescomplemented
145C2×C4×D4×C17C2211yescharacteristic
146C2×C4×D4×C17C2211yescharacteristic, complemented
147C25×C17C2312yes—
148C25×C17C2312yes—
149C24×D17C2311yescharacteristic
150C22×D4×C17—44no—
151C22×D4×C17—44no—
152C22×D4×C17—48no—
153C22×D4×C17C2311yescharacteristic
154C22×D4×C17C2311yescharacteristic
155C22×D4×C17C2312yes—
156C22×D4×C17C2311yescharacteristic
157C22×D4×C17C2311yescharacteristic
158C22×D4×C17C2312yes—
159C22×D4×C17C2312yes—
160C22×D4×C17C2312yes—
161C22×D4×C17C2312yes—
162C22×D4×C17C2312yes—
163C22×D4×C17C2318yes—
164C22×D4×C17C23116yes—
165C22×D4×C17C2318yescomplemented
166C23×C4×C17C2311yescharacteristic
167C23×C4×C17C2311yescharacteristic
168C23×C4×C17C2312yes—
169C22×C22⋊D17—48no—
170C22×C22⋊D17C2311yescharacteristic
171C22×C22⋊D17C2312yes—
172C22×C22⋊D17C2311yescharacteristic
173C22×C22⋊D17C2312yes—
174C22×C22⋊D17C2311yescharacteristic
175C22×C22⋊D17C2312yes—
176C22×C22⋊D17C2311yescharacteristic
177C22×C22⋊D17C2312yes—
178C22×C22⋊D17C2312yes—
179C22×C22⋊D17C2312yes—
180C22×C22⋊D17C2312yes—
181C22×C22⋊D17C2312yes—
182C22×C22⋊D17C2312yes—
183C22×C22⋊D17C23116yescomplemented
184C23×Dic17C2312yes—
185C23×Dic17C2311yescharacteristic
186C23×Dic17C2312yes—
187C23×Dic17C2312yes—
188C23×Dic17C2312yes—
189C23×Dic17C2312yes—
190C2×#63254—44no—
191C2×#63254—44no—
192C2×#63254—48no—
193C2×#63254C23116yescomplemented
194C2×#63254C2318yescomplemented
195C2×#63254C2318yescomplemented
196C2×#63252—44no—
197C2×#63252C2318yescomplemented
198C22×D68C2311yescharacteristic
199C22×D68C2311yescharacteristic
200C22×C4×D17—44no—
201C22×C4×D17C2311yescharacteristic
202C22×C4×D17C2311yescharacteristic
203C22×C4×D17C2311yescharacteristic
204C22×C4×D17C2312yes—
205C22×C4×D17C2311yescharacteristic
206C22×C4×D17C2311yescharacteristic
207C22×C4×D17C2318yescomplemented
208C22×Dic34C2311yescharacteristic
209C22×Dic34C2311yescharacteristic
210C22×Dic34C2312yes—
211C17×#127C2318yescomplemented
212C17×#121C2318yes—
213C17×#121C2318yescomplemented
214C17×#121C23116yescomplemented
215C17×#120C23116yes—
216C17×#120C23116yescomplemented
217C4×D4×C17C2318yes—
218C4×D4×C17C2318yescomplemented
219C2×C4⋊C4×C17C2311yescharacteristic
220C2×C4⋊C4×C17C2311yescharacteristic
221C2×C22⋊C4×C17C2311yescharacteristic
222C2×C22⋊C4×C17C2311yescharacteristic
223C2×C22⋊C4×C17C2312yes—
224C2×C22⋊C4×C17C2312yes—
225C2×C22⋊C4×C17C2312yes—
226C2×C42×C17C2311yescharacteristic
227#10587639C23116yescomplemented
228#10587639C23116yescomplemented
229#10587639C23116yescomplemented
230#10587639C23116yescomplemented
231C2×C22⋊Dic17C2311yescharacteristic
232C2×C22⋊Dic17C2312yes—
233C2×C22⋊Dic17C2311yescharacteristic
234C2×C22⋊Dic17C2312yes—
235C2×C22⋊Dic17C2312yes—
236C2×C22⋊Dic17C2312yes—
237C2×C22⋊Dic17C2312yes—
238C2×C22⋊Dic17C2312yes—
239C2×C22⋊Dic17C2312yes—
240C2×C22⋊Dic17C2312yes—
241C2×C22⋊Dic17C2312yes—
242C2×C22⋊Dic17C2312yes—
243C2×C22⋊Dic17C2312yes—
244C2×C22⋊Dic17C2312yes—
245C2×C22⋊Dic17C2312yes—
246C2×C22⋊Dic17C2312yes—
247C2×C22⋊Dic17C23116yescomplemented
248C2×C22⋊Dic17C23116yescomplemented
249C2×C22⋊Dic17C23116yescomplemented
250#10587626C23116yescomplemented
251#10587626C23116yescomplemented
252#10587625C2318yes—
253#10587625C23116yescomplemented
254#10587625C23116yescomplemented
255#10587625C23116yescomplemented
256#10587625C23116yescomplemented
257#10587625C23116yescomplemented
258#10587625C23116yescomplemented
259#10587625C23116yescomplemented
260#10587625C23116yescomplemented
261#10587624C2318yes—
262#10587624C2318yes—
263#10587624C2318yescomplemented
264#10587624C2318yescomplemented
265#10587624C2318yescomplemented
266#10587624C23116yescomplemented
267#10587624C23116yescomplemented
268#10587624C2318yescomplemented
269#10587624C23116yescomplemented
270#10587624C2318yescomplemented
271#10587623C2318yes—
272#10587623C23116yescomplemented
273#10587622C23116yescomplemented
274#10587622C23116yescomplemented
275#10587622C2318yescomplemented
276#10587621C23116yes—
277#10587621C23116yescomplemented
278#10587621C23116yescomplemented
279#10587621C23116yescomplemented
280#10587621C23116yescomplemented
281#10587621C23116yescomplemented
282D4×Dic17C2318yescomplemented
283D4×Dic17C23116yescomplemented
284D4×Dic17C23116yescomplemented
285D4×Dic17C2318yescomplemented
286#10587615C23116yescomplemented
287#10587615C23116yescomplemented
288C4×C22⋊D17C2318yescomplemented
289C4×C22⋊D17C23116yescomplemented
290C4×C22⋊D17C2318yescomplemented
291C2×#63227C2311yescharacteristic
292C2×#63227C2311yescharacteristic
293C2×#63227C2312yes—
294C2×#63227C2312yes—
295C2×#63227C2311yescharacteristic
296C2×#63227C2311yescharacteristic
297C2×#63227C2311yescharacteristic
298C2×#63227C2311yescharacteristic
299#10587612C2318yescomplemented
300C2×C4⋊Dic17C2311yescharacteristic
301C2×C4⋊Dic17C2311yescharacteristic
302C2×C4⋊Dic17C2312yes—
303C2×C4⋊Dic17C2311yescharacteristic
304C2×C4⋊Dic17C2311yescharacteristic
305C2×C4⋊Dic17C2312yes—
306C2×C4⋊Dic17C2318yescomplemented
307#10587610C2318yescomplemented
308#10587610C2318yescomplemented
309#10587610C23116yescomplemented
310C2×#63225C2312yes—
311C2×#63225C2311yescharacteristic
312C2×#63225C2312yes—
313C2×#63225C2312yes—
314C2×#63225C2312yes—
315C2×#63225C2311yescharacteristic
316C2×#63225C2311yescharacteristic
317C2×#63225C2312yes—
318C2×#63225C2312yes—
319C2×#63225C2311yescharacteristic
320C2×#63225C2312yes—
321C2×C4×Dic17C2312yes—
322C2×C4×Dic17C2312yes—
323C2×C4×Dic17C2312yes—
324C2×C4×Dic17C2311yescharacteristic
325#10587583C2318yescomplemented
326#10587582C2318yescomplemented
327#10587580C2318yescomplemented
328#10587578C2318yescomplemented
329C4⋊C4×D17C2318yescomplemented
330#10587575C23116yescomplemented
331#10587574C2318yescomplemented
332#10587571C23116yescomplemented
333#10587571C23116yescomplemented
334#10587570C23116yescomplemented
335#10587570C2318yescomplemented
336#10587570C23116yescomplemented
337#10587569C23116yescomplemented
338#10587569C23116yescomplemented
339#10587569C2318yescomplemented
340#10587568C2318yescomplemented
341#10587567C23116yescomplemented
342#10587565C23116yescomplemented
343#10587565C23116yescomplemented
344#10587565C23116yescomplemented
345#10587564C23116yescomplemented
346#10587564C2318yescomplemented
347#10587564C23116yescomplemented
348#10587563C23116yescomplemented
349#10587563C23116yescomplemented
350C4×D68C2318yescomplemented
351#10587558C2318yescomplemented
352#10587556C2318yescomplemented
353C4×Dic34C2318yescomplemented
354C24×C17—28no—
355C24×C17—44no—
356C24×C17—44no—
357C24×C17—44no—
358C24×C17—44no—
359C24×C17—44no—
360C24×C17C2412yes—
361C24×C17C2412yes—
362C24×C17C2411yescharacteristic
363C24×C17C2412yes—
364C24×C17C2411yescharacteristic
365C24×C17C2418yes—
366C24×C17C2418yes—
367C23×D17—24no—
368C23×D17—42no—
369C23×D17—42no—
370C23×D17C2411yescharacteristic
371C23×D17C2411yescharacteristic
372C23×D17C2411yescharacteristic
373C23×D17C2414yes—
374C2×D4×C17—28no—
375C2×D4×C17—24no—
376C2×D4×C17—24no—
377C2×D4×C17—24no—
378C2×D4×C17—24no—
379C2×D4×C17—416no—
380C2×D4×C17—416no—
381C2×D4×C17—44no—
382C2×D4×C17—44no—
383C2×D4×C17—44no—
384C2×D4×C17—44no—
385C2×D4×C17—44no—
386C2×D4×C17—432no—
387C2×D4×C17C2414yes—
388C2×D4×C17C2414yes—
389C2×D4×C17C2418yes—
390C2×D4×C17C2414yes—
391C2×D4×C17C2414yes—
392C2×D4×C17C2418yes—
393C2×D4×C17C2418yes—
394C2×D4×C17C2418yes—
395C2×D4×C17C2418yes—
396C2×D4×C17C2418yes—
397C22×C4×C17—24no—
398C22×C4×C17—24no—
399C22×C4×C17—44no—
400C22×C4×C17C2412yes—
401C22×C4×C17C2411yescharacteristic
402C22×C4×C17C2411yescharacteristic
403C22×C4×C17C2414yes—
404C22×C4×C17C2411yescharacteristic
405C22×C4×C17C2414yes—
406C22×C4×C17C2411yescharacteristic
407C22×C4×C17C2418yes—
408C22×C4×C17C2411yescharacteristic
409C2×C22⋊D17—24no—
410C2×C22⋊D17—42no—
411C2×C22⋊D17—42no—
412C2×C22⋊D17—44no—
413C2×C22⋊D17—44no—
414C2×C22⋊D17—44no—
415C2×C22⋊D17—44no—
416C2×C22⋊D17—44no—
417C2×C22⋊D17—44no—
418C2×C22⋊D17—44no—
419C2×C22⋊D17—432no—
420C2×C22⋊D17—42no—
421C2×C22⋊D17—44no—
422C2×C22⋊D17—44no—
423C2×C22⋊D17C2414yes—
424C2×C22⋊D17C2414yes—
425C2×C22⋊D17C2414yes—
426C2×C22⋊D17C2418yes—
427C2×C22⋊D17C2418yes—
428C2×C22⋊D17C2418yes—
429C2×C22⋊D17C2418yes—
430C2×C22⋊D17C2418yes—
431C2×C22⋊D17C2418yes—
432C2×C22⋊D17C2418yes—
433C2×C22⋊D17C2418yes—
434C2×C22⋊D17C2414yes—
435C2×C22⋊D17C2418yes—
436C22×Dic17—28no—
437C22×Dic17—42no—
438C22×Dic17—44no—
439C22×Dic17—44no—
440C22×Dic17—44no—
441C22×Dic17—44no—
442C22×Dic17C2411yescharacteristic
443C22×Dic17C2411yescharacteristic
444C22×Dic17C2411yescharacteristic
445C22×Dic17C2412yes—
446C22×Dic17C2412yes—
447C22×Dic17C2411yescharacteristic
448C22×Dic17C2412yes—
449C22×Dic17C2418yes—
450C22×Dic17C2411yescharacteristic
451C22×Dic17C2412yes—
452C22×Dic17C2414yes—
453C22×Dic17C2418yes—
454C22×Dic17C2418yes—
455C22×Dic17C2418yes—
456C22×Dic17C2418yes—
457#63254—416no—
458#63254—416no—
459#63254—432no—
460#63252—416no—
461C2×D68—42no—
462C2×D68—42no—
463C2×D68C2414yes—
464C2×D68C2414yes—
465C2×C4×D17—24no—
466C2×C4×D17—24no—
467C2×C4×D17—24no—
468C2×C4×D17—416no—
469C2×C4×D17—42no—
470C2×C4×D17—42no—
471C2×C4×D17—44no—
472C2×C4×D17C2414yes—
473C2×C4×D17C2414yes—
474C2×C4×D17C2414yes—
475C2×C4×D17C2414yes—
476C2×C4×D17C2414yes—
477C2×C4×D17C2418yes—
478C2×Dic34—24no—
479C2×Dic34—42no—
480C2×Dic34—44no—
481C2×Dic34C2414yes—
482C2×Dic34C2414yes—
483C2×Dic34C2418yes—
484C4⋊C4×C17C2414yes—
485C4⋊C4×C17C2414yes—
486C22⋊C4×C17C2414yes—
487C22⋊C4×C17C2418yes—
488C22⋊C4×C17C2418yes—
489C22⋊C4×C17C2414yes—
490C22⋊C4×C17C2418yes—
491C42×C17C2414yes—
492C22⋊Dic17C2418yes—
493C22⋊Dic17C2418yes—
494C22⋊Dic17C2414yes—
495C22⋊Dic17C2418yes—
496C22⋊Dic17C2418yes—
497C22⋊Dic17C2418yes—
498C22⋊Dic17C2418yes—
499C22⋊Dic17C2418yes—
500C22⋊Dic17C2418yes—
501C22⋊Dic17C2418yes—
502C22⋊Dic17C2418yes—
503C22⋊Dic17C2414yes—
504C22⋊Dic17C2418yes—
505C22⋊Dic17C2418yes—
506C22⋊Dic17C2418yes—
507C22⋊Dic17C2418yes—
508#63227C2414yes—
509#63227C2414yes—
510#63227C2414yes—
511#63227C2414yes—
512#63227C2418yes—
513#63227C2414yes—
514#63227C2414yes—
515#63227C2418yes—
516C4⋊Dic17C2414yes—
517C4⋊Dic17C2414yes—
518C4⋊Dic17C2414yes—
519C4⋊Dic17C2414yes—
520C4⋊Dic17C2418yes—
521C4⋊Dic17C2418yes—
522#63225C2418yes—
523#63225C2418yes—
524#63225C2418yes—
525#63225C2414yes—
526#63225C2414yes—
527#63225C2414yes—
528#63225C2418yes—
529#63225C2418yes—
530#63225C2418yes—
531#63225C2414yes—
532#63225C2418yes—
533C4×Dic17C2418yes—
534C4×Dic17C2414yes—
535C4×Dic17C2418yes—
536C4×Dic17C2418yes—
537C2×#3542—171nomaximal, Sylow
538C23×C17—22no—
539C23×C17—22no—
540C23×C17—24no—
541C23×C17—24no—
542C23×C17—24no—
543C23×C17—22no—
544C23×C17—24no—
545C23×C17—24no—
546C23×C17—22no—
547C23×C17—24no—
548C23×C17—24no—
549C23×C17—24no—
550C23×C17—22no—
551C23×C17—24no—
552C23×C17—216no—
553C23×C17—48no—
554C23×C17—48no—
555C23×C17—48no—
556C23×C17—48no—
557C23×C17—48no—
558C23×C17—816no—
559C23×C17—816no—
560C23×C17H(5,𝔽2)14yes—
561C23×C17C2512yes—
562C23×C17C2514yes—
563C23×C17C2514yes—
564C23×C17C2514yes—
565C23×C17C2512yes—
566C23×C17C2511yescharacteristic
567C22×D17—22no—
568C22×D17—22no—
569C22×D17—22no—
570C22×D17—22no—
571C22×D17—28no—
572C22×D17—22no—
573C22×D17—22no—
574C22×D17—22no—
575C22×D17—22no—
576C22×D17—22no—
577C22×D17—44no—
578C22×D17—44no—
579C22×D17—416no—
580C22×D17C2512yes—
581C22×D17C2512yes—
582C22×D17C2512yes—
583D4×C17—216no—
584D4×C17—28no—
585D4×C17—28no—
586D4×C17—28no—
587D4×C17—28no—
588D4×C17—48no—
589D4×C17—48no—
590D4×C17—48no—
591D4×C17—48no—
592D4×C17—48no—
593C2×C4×C17—24no—
594C2×C4×C17—22no—
595C2×C4×C17—22no—
596C2×C4×C17—22no—
597C2×C4×C17—22no—
598C2×C4×C17—28no—
599C2×C4×C17—28no—
600C2×C4×C17—48no—
601C2×C4×C17H(5,𝔽2)14yes—
602C2×C4×C17C2512yes—
603C2×C4×C17C2512yes—
604C2×C4×C17C2514yes—
605C2×C4×C17C2512yes—
606C2×C4×C17C2512yes—
607C2×C4×C17C2512yes—
608C22⋊D17—28no—
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—44no—
619C22⋊D17—48no—
620C22⋊D17—48no—
621C2×Dic17—24no—
622C2×Dic17—22no—
623C2×Dic17—22no—
624C2×Dic17—22no—
625C2×Dic17—24no—
626C2×Dic17—22no—
627C2×Dic17—24no—
628C2×Dic17—216no—
629C2×Dic17—22no—
630C2×Dic17—24no—
631C2×Dic17—44no—
632C2×Dic17—48no—
633C2×Dic17—48no—
634C2×Dic17—48no—
635C2×Dic17—48no—
636C2×Dic17C2512yes—
637C2×Dic17C2512yes—
638C2×Dic17C2512yes—
639C2×Dic17C2512yes—
640C2×Dic17C2512yes—
641C2×Dic17C2514yes—
642C2×Dic17C2514yes—
643C2×Dic17C2514yes—
644C2×Dic17C2514yes—
645D68—44no—
646D68—44no—
647C4×D17—28no—
648C4×D17—28no—
649C4×D17—28no—
650C4×D17—44no—
651C4×D17—44no—
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×D42D1711yescharacteristic, complemented
669C2×#542—171no—
670C2×#540—171no—
671C2×#540—172no—
672C2×#538—172no—
673C2×#537—171no—
674C2×#535—171no—
675C2×#535—172no—
676C2×#534—172no—
677C2×#525—171no—
678C2×#525—171no—
679C22×#121—171no—
680C22×C17—22no—
681C22×C17—22no—
682C22×C17—28no—
683C22×C17—24no—
684C22×C17—24no—
685C22×C17—24no—
686C22×C17—22no—
687C22×C17—24no—
688C22×C17—24no—
689C22×C17—22no—
690C22×C17—24no—
691C22×C17—24no—
692C22×C17—24no—
693C22×C17—22no—
694C22×C17—24no—
695C22×C17—48no—
696C22×C17—48no—
697C22×C17—44no—
698C22×C17—48no—
699C22×C17—816no—
700C22×C17—816no—
701C22×C17C2×H(5,𝔽2)14yes—
702C22×C17C2×H(5,𝔽2)12yes—
703C22×C17C2×H(5,𝔽2)12yes—
704C22×C17#58512yes—
705C22×C17C2611yescharacteristic
706C2×D17—22no—
707C2×D17—22no—
708C2×D17—22no—
709C2×D17—22no—
710C2×D17—22no—
711C2×D17—22no—
712C2×D17—22no—
713C2×D17—22no—
714C2×D17—22no—
715C2×D17—416no—
716C2×D17—44no—
717C2×D17—44no—
718C2×D17—44no—
719C4×C17—24no—
720C4×C17—22no—
721C4×C17—22no—
722C4×C17—22no—
723C4×C17—22no—
724C4×C17C2×H(5,𝔽2)14yes—
725Dic17—24no—
726Dic17—22no—
727Dic17—22no—
728Dic17—22no—
729Dic17—24no—
730Dic17—22no—
731Dic17—24no—
732Dic17—22no—
733Dic17—24no—
734C22×#41—171no—
735C22×#41—172no—
736C22×#41—171no—
737C22×#41—171no—
738C23×D4—172no—
739C23×D4C2×D1711yescharacteristic
740C23×D4C2×D1712yes—
741C23×D4C2×D1711yescharacteristic, complemented
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—
754D42C2×D17116yescomplemented
755#542—1716no—
756#540—1716no—
757#540—1732no—
758#538—1732no—
759#537—1716no—
760#535—1716no—
761#535—1732no—
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×#125—171no—
772C2×#124—172no—
773C2×#124—172no—
774C2×#124—171no—
775C2×#124—172no—
776C2×#124—172no—
777#525—1716no—
778#525—1716no—
779C2×#123—172no—
780C2×#123—172no—
781C2×#123—172no—
782C2×#123—172no—
783C2×#123—172no—
784C2×#123—172no—
785C2×#123—172no—
786C2×#123—172no—
787C2×#123—171no—
788C2×#123—171no—
789C2×#123—172no—
790C2×#123—172no—
791C2×C22⋊Q8—171no—
792C2×C22⋊Q8—171no—
793C2×C22⋊Q8—172no—
794C2×C22⋊Q8—171no—
795C2×C22⋊Q8—171no—
796C2×C22⋊Q8—171no—
797C2×C22⋊Q8—172no—
798C2×C22⋊Q8—172no—
799C2×#121—171no—
800C2×#121—171no—
801C2×#121—171no—
802C2×#121—172no—
803C2×#121—171no—
804C2×#121—172no—
805C2×#121—1716no—
806C2×#121—171no—
807C2×#121—171no—
808C2×#121—171no—
809C2×#121—172no—
810C2×#121—171no—
811C2×#121—172no—
812C2×#121—172no—
813C2×#121—172no—
814C2×#121—172no—
815C2×#121—172no—
816C2×#121—172no—
817C2×#121—172no—
818C2×#121—172no—
819C2×#121—171no—
820C2×#121—172no—
821C2×#121—172no—
822C2×#121C2×D1711yescharacteristic
823C2×#121C2×D1711yescharacteristic, complemented
824C2×#121C2×D1712yescomplemented
825C2×#120—172no—
826C2×#120—172no—
827C2×#120—172no—
828C2×#120—172no—
829C2×#120—171no—
830C2×#120—172no—
831C2×#120—171no—
832C2×#120C2×D1712yes—
833C2×#120C2×D1712yescomplemented
834C2×C4×Q8—171no—
835C2×C4×D4—172no—
836C2×C4×D4—172no—
837C2×C4×D4—171no—
838C2×C4×D4—171no—
839C2×C4×D4—171no—
840C2×C4×D4—171no—
841C2×C4×D4—172no—
842C2×C4×D4—172no—
843C2×C4×D4—171no—
844C2×C4×D4C2×D1711yescharacteristic
845C2×C4×D4C2×D1711yescharacteristic, complemented
846C2×#117—171no—
847C2×#117—171no—
848C2×#117—172no—
849C2×#117—172no—
850C2×#117—171no—
851C22×C4⋊C4—171no—
852C22×C4⋊C4—171no—
853C22×C22⋊C4—172no—
854C22×C22⋊C4—172no—
855C22×C22⋊C4—172no—
856C2×C17—24no—
857C2×C17—44no—
858C2×C17—44no—
859C2×C17—42no—
860C2×C17—44no—
861C2×C17#354214yescomplemented
862C2×C17C22×H(5,𝔽2)11yescharacteristic
863C2×C17C22×H(5,𝔽2)11yescharacteristic
864C2×C17C2×#58511yescharacteristic
865D17—42no—
866D17—42no—
867D17—42no—
868C25—171no—
869C25C22×D1712yes—
870C25C22×D1712yes—
871C2×#41—178no—
872C2×#41—1716no—
873C2×#41—178no—
874C2×#41—178no—
875C2×#41—684no—
876C2×#41—688no—
877C2×#41—684no—
878C2×#41—684no—
879C22×Q8—171no—
880C22×Q8—171no—
881C22×Q8—172no—
882C22×D4—44no—
883C22×D4—44no—
884C22×D4—48no—
885C22×D4—171no—
886C22×D4—171no—
887C22×D4—172no—
888C22×D4—172no—
889C22×D4—171no—
890C22×D4—171no—
891C22×D4—172no—
892C22×D4—172no—
893C22×D4—172no—
894C22×D4—172no—
895C22×D4—172no—
896C22×D4—172no—
897C22×D4—172no—
898C22×D4—1716no—
899C22×D4—171no—
900C22×D4—171no—
901C22×D4—688no—
902C22×D4C22×D1712yes—
903C22×D4C22×D1711yescharacteristic
904C22×D4C22×D1711yescharacteristic
905C22×D4C22×D1711yescharacteristic
906C22×D4C22×D1711yescharacteristic
907C22×D4C22×D1712yes—
908C22×D4C22×D1712yes—
909C22×D4C22×D1712yes—
910C22×D4C22×D1712yes—
911C22×D4C22×D1712yes—
912C22×D4C22×D1718yes—
913C22×D4C22×D17116yes—
914C22×D4C22×D1718yescomplemented
915C23×C4—172no—
916C23×C4—171no—
917C23×C4—172no—
918C23×C4—172no—
919C23×C4—172no—
920C23×C4—172no—
921C23×C4—171no—
922C23×C4—171no—
923C23×C4—171no—
924C23×C4—172no—
925C23×C4—171no—
926C23×C4—171no—
927C23×C4—178no—
928C23×C4—684no—
929C23×C4C22×D1711yescharacteristic
930C23×C4C22×D1711yescharacteristic
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#125—178no—
941#124—1716no—
942#124—1716no—
943#124—178no—
944#124—1716no—
945#124—1716no—
946#123—1716no—
947#123—1716no—
948#123—1716no—
949#123—1716no—
950#123—1716no—
951#123—1716no—
952#123—1716no—
953#123—1716no—
954#123—178no—
955#123—178no—
956#123—1716no—
957#123—1716no—
958C22⋊Q8—178no—
959C22⋊Q8—178no—
960C22⋊Q8—1716no—
961C22⋊Q8—178no—
962C22⋊Q8—178no—
963C22⋊Q8—178no—
964C22⋊Q8—1716no—
965C22⋊Q8—1716no—
966#121—178no—
967#121—178no—
968#121—1716no—
969#121—178no—
970#121—178no—
971#121—1716no—
972#121—178no—
973#121—178no—
974#121—1716no—
975#121—1716no—
976#121—1716no—
977#121—1716no—
978#121—1716no—
979#121—178no—
980#121—1716no—
981#121—178no—
982#121—1716no—
983#121—1716no—
984#121—1716no—
985#121—178no—
986#121—1716no—
987#121—1716no—
988#121C22×D1718yes—
989#121C22×D1718yescomplemented
990#121C22×D17116yescomplemented
991#120—1716no—
992#120—1716no—
993#120—1716no—
994#120—1716no—
995#120—178no—
996#120—1716no—
997#120—178no—
998#120C22×D17116yes—
999#120C22×D17116yescomplemented
1000C4×Q8—178no—
1001C4×D4—1716no—
1002C4×D4—1716no—
1003C4×D4—178no—
1004C4×D4—178no—
1005C4×D4—178no—
1006C4×D4—178no—
1007C4×D4—1716no—
1008C4×D4—1716no—
1009C4×D4—178no—
1010C4×D4C22×D1718yes—
1011C4×D4C22×D1718yescomplemented
1012#117—178no—
1013#117—178no—
1014#117—1716no—
1015#117—1716no—
1016#117—178no—
1017C2×C4⋊C4—171no—
1018C2×C4⋊C4—171no—
1019C2×C4⋊C4—172no—
1020C2×C4⋊C4—178no—
1021C2×C4⋊C4—172no—
1022C2×C4⋊C4—171no—
1023C2×C4⋊C4—171no—
1024C2×C4⋊C4—172no—
1025C2×C4⋊C4—172no—
1026C2×C4⋊C4—171no—
1027C2×C4⋊C4—171no—
1028C2×C4⋊C4—172no—
1029C2×C4⋊C4—171no—
1030C2×C4⋊C4—172no—
1031C2×C4⋊C4—172no—
1032C2×C4⋊C4—172no—
1033C2×C4⋊C4—171no—
1034C2×C4⋊C4—172no—
1035C2×C4⋊C4—178no—
1036C2×C4⋊C4C22×D1711yescharacteristic
1037C2×C4⋊C4C22×D1711yescharacteristic
1038C2×C22⋊C4—171no—
1039C2×C22⋊C4—172no—
1040C2×C22⋊C4—171no—
1041C2×C22⋊C4—172no—
1042C2×C22⋊C4—172no—
1043C2×C22⋊C4—172no—
1044C2×C22⋊C4—172no—
1045C2×C22⋊C4—172no—
1046C2×C22⋊C4—172no—
1047C2×C22⋊C4—172no—
1048C2×C22⋊C4—172no—
1049C2×C22⋊C4—1716no—
1050C2×C22⋊C4—1716no—
1051C2×C22⋊C4—1716no—
1052C2×C22⋊C4—172no—
1053C2×C22⋊C4—172no—
1054C2×C22⋊C4—172no—
1055C2×C22⋊C4—172no—
1056C2×C22⋊C4—172no—
1057C2×C22⋊C4—171no—
1058C2×C22⋊C4—172no—
1059C2×C22⋊C4—171no—
1060C2×C22⋊C4—171no—
1061C2×C22⋊C4—171no—
1062C2×C22⋊C4—172no—
1063C2×C22⋊C4—171no—
1064C2×C22⋊C4—171no—
1065C2×C22⋊C4C22×D1711yescharacteristic
1066C2×C22⋊C4C22×D1712yes—
1067C2×C22⋊C4C22×D1712yes—
1068C2×C22⋊C4C22×D1711yescharacteristic
1069C2×C22⋊C4C22×D1712yes—
1070C2×C42—172no—
1071C2×C42—172no—
1072C2×C42—171no—
1073C2×C42—172no—
1074C2×C42C22×D1711yescharacteristic
1075C17C2×#354211yescharacteristic, complemented, Sylow
1076C24—28no—
1077C24—44no—
1078C24—44no—
1079C24—44no—
1080C24—44no—
1081C24—44no—
1082C24—171no—
1083C24—171no—
1084C24—171no—
1085C24—174no—
1086C24—344no—
1087C24—682no—
1088C24—682no—
1089C24C23×D1711yescharacteristic
1090C24C23×D1712yes—
1091C24C23×D1712yes—
1092C24C23×D1712yes—
1093C24C23×D1711yescharacteristic
1094C24C23×D1718yes—
1095C24C23×D1718yes—
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—682no—
1105C2×Q8—684no—
1106C2×D4—24no—
1107C2×D4—28no—
1108C2×D4—24no—
1109C2×D4—24no—
1110C2×D4—24no—
1111C2×D4—416no—
1112C2×D4—416no—
1113C2×D4—44no—
1114C2×D4—44no—
1115C2×D4—44no—
1116C2×D4—44no—
1117C2×D4—44no—
1118C2×D4—432no—
1119C2×D4—174no—
1120C2×D4—174no—
1121C2×D4—178no—
1122C2×D4—178no—
1123C2×D4—174no—
1124C2×D4—174no—
1125C2×D4—178no—
1126C2×D4—178no—
1127C2×D4—178no—
1128C2×D4—178no—
1129C2×D4—178no—
1130C2×D4—178no—
1131C2×D4—178no—
1132C2×D4—174no—
1133C2×D4—174no—
1134C2×D4—344no—
1135C2×D4—682no—
1136C2×D4—682no—
1137C2×D4—682no—
1138C2×D4—684no—
1139C2×D4—684no—
1140C2×D4—684no—
1141C2×D4—684no—
1142C2×D4—684no—
1143C2×D4—684no—
1144C2×D4—6832no—
1145C2×D4—682no—
1146C2×D4—682no—
1147C2×D4—684no—
1148C2×D4—684no—
1149C2×D4—684no—
1150C2×D4C23×D1718yes—
1151C2×D4C23×D1714yes—
1152C2×D4C23×D1714yes—
1153C2×D4C23×D1714yes—
1154C2×D4C23×D1714yes—
1155C2×D4C23×D1718yes—
1156C2×D4C23×D1718yes—
1157C2×D4C23×D1718yes—
1158C2×D4C23×D1718yes—
1159C2×D4C23×D1718yes—
1160C22×C4—24no—
1161C22×C4—24no—
1162C22×C4—44no—
1163C22×C4—178no—
1164C22×C4—172no—
1165C22×C4—171no—
1166C22×C4—172no—
1167C22×C4—171no—
1168C22×C4—171no—
1169C22×C4—172no—
1170C22×C4—171no—
1171C22×C4—171no—
1172C22×C4—172no—
1173C22×C4—174no—
1174C22×C4—178no—
1175C22×C4—178no—
1176C22×C4—178no—
1177C22×C4—178no—
1178C22×C4—174no—
1179C22×C4—174no—
1180C22×C4—174no—
1181C22×C4—178no—
1182C22×C4—174no—
1183C22×C4—174no—
1184C22×C4—348no—
1185C22×C4—344no—
1186C22×C4—344no—
1187C22×C4—344no—
1188C22×C4—6816no—
1189C22×C4—682no—
1190C22×C4—682no—
1191C22×C4—684no—
1192C22×C4—684no—
1193C22×C4—682no—
1194C22×C4—684no—
1195C22×C4—684no—
1196C22×C4—684no—
1197C22×C4C23×D1714yes—
1198C22×C4C23×D1714yes—
1199C22×C4C23×D1711yescharacteristic
1200C22×C4C23×D1711yescharacteristic
1201C22×C4C23×D1712yes—
1202C22×C4C23×D1711yescharacteristic
1203C22×C4C23×D1711yescharacteristic
1204C22×C4C23×D1718yes—
1205C22×C4C23×D1711yescharacteristic
1206C4⋊C4—174no—
1207C4⋊C4—174no—
1208C4⋊C4—178no—
1209C4⋊C4—178no—
1210C4⋊C4—174no—
1211C4⋊C4—174no—
1212C4⋊C4—178no—
1213C4⋊C4—178no—
1214C4⋊C4—174no—
1215C4⋊C4—174no—
1216C4⋊C4—178no—
1217C4⋊C4—174no—
1218C4⋊C4—178no—
1219C4⋊C4—178no—
1220C4⋊C4—178no—
1221C4⋊C4—174no—
1222C4⋊C4—178no—
1223C4⋊C4C23×D1714yes—
1224C4⋊C4C23×D1714yes—
1225C22⋊C4—174no—
1226C22⋊C4—178no—
1227C22⋊C4—174no—
1228C22⋊C4—178no—
1229C22⋊C4—178no—
1230C22⋊C4—178no—
1231C22⋊C4—178no—
1232C22⋊C4—178no—
1233C22⋊C4—178no—
1234C22⋊C4—178no—
1235C22⋊C4—178no—
1236C22⋊C4—178no—
1237C22⋊C4—178no—
1238C22⋊C4—178no—
1239C22⋊C4—178no—
1240C22⋊C4—178no—
1241C22⋊C4—174no—
1242C22⋊C4—178no—
1243C22⋊C4—174no—
1244C22⋊C4—174no—
1245C22⋊C4—174no—
1246C22⋊C4—178no—
1247C22⋊C4—174no—
1248C22⋊C4—174no—
1249C22⋊C4C23×D1714yes—
1250C22⋊C4C23×D1718yes—
1251C22⋊C4C23×D1718yes—
1252C22⋊C4C23×D1714yes—
1253C22⋊C4C23×D1718yes—
1254C42—178no—
1255C42—178no—
1256C42—174no—
1257C42—178no—
1258C42C23×D1714yes—
1259C23—22no—
1260C23—22no—
1261C23—22no—
1262C23—24no—
1263C23—24no—
1264C23—24no—
1265C23—24no—
1266C23—22no—
1267C23—24no—
1268C23—24no—
1269C23—24no—
1270C23—24no—
1271C23—22no—
1272C23—24no—
1273C23—216no—
1274C23—48no—
1275C23—48no—
1276C23—48no—
1277C23—48no—
1278C23—48no—
1279C23—816no—
1280C23—816no—
1281C23—172no—
1282C23—172no—
1283C23—172no—
1284C23—342no—
1285C23—342no—
1286C23—342no—
1287C23—342no—
1288C23—348no—
1289C23—342no—
1290C23—342no—
1291C23—342no—
1292C23—342no—
1293C23—342no—
1294C23—684no—
1295C23—684no—
1296C23—6816no—
1297C23#1058769114yes—
1298C23C24×D1712yes—
1299C23C24×D1714yes—
1300C23C24×D1714yes—
1301C23C24×D1714yes—
1302C23C24×D1712yes—
1303C23C24×D1711yescharacteristic
1304Q8—348no—
1305Q8—684no—
1306Q8—688no—
1307D4—28no—
1308D4—216no—
1309D4—28no—
1310D4—28no—
1311D4—28no—
1312D4—48no—
1313D4—48no—
1314D4—48no—
1315D4—48no—
1316D4—48no—
1317D4—348no—
1318D4—684no—
1319D4—684no—
1320D4—688no—
1321D4—688no—
1322D4—688no—
1323D4—688no—
1324D4—684no—
1325D4—684no—
1326D4—688no—
1327D4—688no—
1328D4—688no—
1329D4—684no—
1330D4—688no—
1331D4—688no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—28no—
1338C2×C4—28no—
1339C2×C4—48no—
1340C2×C4—174no—
1341C2×C4—172no—
1342C2×C4—174no—
1343C2×C4—172no—
1344C2×C4—172no—
1345C2×C4—174no—
1346C2×C4—172no—
1347C2×C4—172no—
1348C2×C4—174no—
1349C2×C4—342no—
1350C2×C4—344no—
1351C2×C4—342no—
1352C2×C4—342no—
1353C2×C4—344no—
1354C2×C4—3416no—
1355C2×C4—342no—
1356C2×C4—344no—
1357C2×C4—342no—
1358C2×C4—344no—
1359C2×C4—348no—
1360C2×C4—348no—
1361C2×C4—348no—
1362C2×C4—684no—
1363C2×C4—684no—
1364C2×C4—688no—
1365C2×C4—684no—
1366C2×C4—688no—
1367C2×C4—688no—
1368C2×C4—688no—
1369C2×C4—688no—
1370C2×C4#1058769114yes—
1371C2×C4C24×D1712yes—
1372C2×C4C24×D1712yes—
1373C2×C4C24×D1714yes—
1374C2×C4C24×D1712yes—
1375C2×C4C24×D1712yes—
1376C2×C4C24×D1712yes—
1377C22—28no—
1378C22—22no—
1379C22—22no—
1380C22—22no—
1381C22—24no—
1382C22—24no—
1383C22—24no—
1384C22—24no—
1385C22—22no—
1386C22—24no—
1387C22—24no—
1388C22—24no—
1389C22—24no—
1390C22—22no—
1391C22—24no—
1392C22—44no—
1393C22—48no—
1394C22—48no—
1395C22—48no—
1396C22—816no—
1397C22—816no—
1398C22—342no—
1399C22—342no—
1400C22—342no—
1401C22—342no—
1402C22—342no—
1403C22—342no—
1404C22—342no—
1405C22—342no—
1406C22—342no—
1407C22—6816no—
1408C22—684no—
1409C22—684no—
1410C22—684no—
1411C22C2×#1058769114yes—
1412C22C2×#1058769112yes—
1413C22C2×#1058769112yes—
1414C22#1176364412yes—
1415C22C25×D1711yescharacteristic
1416C4—22no—
1417C4—22no—
1418C4—22no—
1419C4—24no—
1420C4—22no—
1421C4—342no—
1422C4—344no—
1423C4—342no—
1424C4—342no—
1425C4—344no—
1426C4—342no—
1427C4—344no—
1428C4—342no—
1429C4—344no—
1430C4C2×#1058769114yes—
1431C2—24no—
1432C2—42no—
1433C2—44no—
1434C2—44no—
1435C2—44no—
1436C2—682no—
1437C2—682no—
1438C2—682no—
1439C2#1454310514yesdirect product factor
1440C2C22×#1058769111yescharacteristic
1441C2C22×#1058769111yescharacteristic
1442C2C2×#1176364411yescharacteristic
subgroupG/H
centerC23C24×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC2×D42×C17C2
socleC23×C17C25
hypercenterC2×D42D17
hypocenterC17C2×#3542
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. #14543105C2direct (N × H)
2. C2×#11763554C2semidirect
3. C2×#11763548C2semidirect
4. C2×#11763523C2semidirect
5. C2×#11763509C2semidirect
6. C2×#11763499C2semidirect
7. C2×#11763490C2semidirect
8. C2×#11763479C2semidirect
9. C2×#11763459C2semidirect
10. C2×#11763453C2semidirect
11. C2×#11763453C2semidirect
12. C2×#11763453C2semidirect
13. C2×#11763424C2semidirect
14. C2×#11763413C2semidirect
15. C2×#11763409C2semidirect
16. C2×#11763394C2semidirect
17. C2×#11763388C2semidirect
18. C2×#11763376C2semidirect
19. C2×#11763374C2semidirect
20. C2×#11763368C2semidirect
21. C2×#11763319C2semidirect
22. C2×#11763318C2semidirect
23. C22×#10587624C2semidirect
24. C2×D42×C17C2semidirect
25. C22×#63252C22semidirect
26. C22×#63254C22semidirect
27. C22×#63254C22semidirect
28. C22×#63254C22semidirect
29. C23×C22⋊D17C22semidirect
30. C23×C4×D17C22semidirect
31. #11763554C22semidirect
32. #11763548C22semidirect
33. #11763523C22semidirect
34. #11763509C22semidirect
35. #11763499C22semidirect
36. #11763490C22semidirect
37. #11763479C22semidirect
38. #11763459C22semidirect
39. #11763453C22semidirect
40. #11763453C22semidirect
41. #11763453C22semidirect
42. #11763424C22semidirect
43. #11763413C22semidirect
44. #11763409C22semidirect
45. #11763394C22semidirect
46. #11763388C22semidirect
47. #11763376C22semidirect
48. #11763374C22semidirect
49. #11763368C22semidirect
50. C2×#10587574C22semidirect
51. C2×#10587626C22semidirect
52. C2×#10587626C22semidirect
53. C2×#10587565C22semidirect
54. C2×#10587565C22semidirect
55. C2×#10587565C22semidirect
56. C2×#10587556C22semidirect
57. C2×#10587575C22semidirect
58. C2×#10587622C22semidirect
59. C2×#10587622C22semidirect
60. C2×#10587622C22semidirect
61. C2×#10587571C22semidirect
62. C2×#10587571C22semidirect
63. #11763319C22semidirect
64. #11763318C22semidirect
65. C2×#10587580C22semidirect
66. C2×#10587615C22semidirect
67. C2×#10587615C22semidirect
68. C2×#10587569C22semidirect
69. C2×#10587569C22semidirect
70. C2×#10587569C22semidirect
72. C2×#10587621C22semidirect
73. C2×#10587621C22semidirect
74. C2×#10587621C22semidirect
75. C2×#10587621C22semidirect
76. C2×#10587621C22semidirect
77. C2×#10587583C22semidirect
78. C2×#10587610C22semidirect
79. C2×#10587610C22semidirect
80. C2×#10587610C22semidirect
81. C2×#10587582C22semidirect
82. C2×#10587564C22semidirect
83. C2×#10587564C22semidirect
84. C2×#10587564C22semidirect
85. C2×#10587570C22semidirect
86. C2×#10587570C22semidirect
87. C2×#10587570C22semidirect
89. C2×#10587625C22semidirect
90. C2×#10587625C22semidirect
91. C2×#10587625C22semidirect
92. C2×#10587625C22semidirect
93. C2×#10587625C22semidirect
94. C2×#10587625C22semidirect
95. C2×#10587625C22semidirect
96. C2×#10587625C22semidirect
99. C2×#10587624C22semidirect
100. C2×#10587624C22semidirect
101. C2×#10587624C22semidirect
102. C2×#10587624C22semidirect
103. C2×#10587624C22semidirect
104. C2×#10587624C22semidirect
105. C2×#10587624C22semidirect
106. C2×#10587624C22semidirect
107. C2×#10587624C22semidirect
108. C2×#10587568C22semidirect
109. C2×#10587639C22semidirect
110. C2×#10587639C22semidirect
111. C2×#10587639C22semidirect
112. C2×#10587639C22semidirect
114. C2×#10587623C22semidirect
115. C2×C4×Dic34C22semidirect
116. C2×C4×D68C22semidirect
117. C2×D4×Dic17C22semidirect
118. C2×D4×Dic17C22semidirect
119. C2×D4×Dic17C22semidirect
120. C2×D4×Dic17C22semidirect
121. C2×C4×C22⋊D17C22semidirect
122. C2×C4×C22⋊D17C22semidirect
123. C2×C4×C22⋊D17C22semidirect
124. C2×#10587567C22semidirect
125. C2×#10587612C22semidirect
126. C2×#10587578C22semidirect
127. C2×#10587558C22semidirect
128. C2×#10587563C22semidirect
129. C2×#10587563C22semidirect
130. C22×C4⋊Dic17C22semidirect
131. C2×C4⋊C4×D17C22semidirect
132. C22×C22⋊Dic17C22semidirect
133. C22×C22⋊Dic17C22semidirect
134. C22×C22⋊Dic17C22semidirect
137. C23×D4×C17C22semidirect
138. D42×C17C22semidirect
139. C2×C17×#127C22semidirect
141. C2×C17×#121C22semidirect
142. C2×C17×#121C22semidirect
144. C2×C17×#120C22semidirect
146. C2×C4×D4×C17C22semidirect
165. C22×D4×C17C23semidirect
183. C22×C22⋊D17C23semidirect
193. C2×#63254C23semidirect
194. C2×#63254C23semidirect
195. C2×#63254C23semidirect
197. C2×#63252C23semidirect
207. C22×C4×D17C23semidirect
211. C17×#127C23semidirect
213. C17×#121C23semidirect
214. C17×#121C23semidirect
216. C17×#120C23semidirect
218. C4×D4×C17C23semidirect
227. #10587639C23semidirect
228. #10587639C23semidirect
229. #10587639C23semidirect
230. #10587639C23semidirect
247. C2×C22⋊Dic17C23semidirect
248. C2×C22⋊Dic17C23semidirect
249. C2×C22⋊Dic17C23semidirect
250. #10587626C23semidirect
251. #10587626C23semidirect
253. #10587625C23semidirect
254. #10587625C23semidirect
255. #10587625C23semidirect
256. #10587625C23semidirect
257. #10587625C23semidirect
258. #10587625C23semidirect
259. #10587625C23semidirect
260. #10587625C23semidirect
263. #10587624C23semidirect
264. #10587624C23semidirect
265. #10587624C23semidirect
266. #10587624C23semidirect
267. #10587624C23semidirect
268. #10587624C23semidirect
269. #10587624C23semidirect
270. #10587624C23semidirect
272. #10587623C23semidirect
273. #10587622C23semidirect
274. #10587622C23semidirect
275. #10587622C23semidirect
277. #10587621C23semidirect
278. #10587621C23semidirect
279. #10587621C23semidirect
280. #10587621C23semidirect
281. #10587621C23semidirect
282. D4×Dic17C23semidirect
283. D4×Dic17C23semidirect
284. D4×Dic17C23semidirect
285. D4×Dic17C23semidirect
286. #10587615C23semidirect
287. #10587615C23semidirect
288. C4×C22⋊D17C23semidirect
289. C4×C22⋊D17C23semidirect
290. C4×C22⋊D17C23semidirect
299. #10587612C23semidirect
306. C2×C4⋊Dic17C23semidirect
307. #10587610C23semidirect
308. #10587610C23semidirect
309. #10587610C23semidirect
325. #10587583C23semidirect
326. #10587582C23semidirect
327. #10587580C23semidirect
328. #10587578C23semidirect
329. C4⋊C4×D17C23semidirect
330. #10587575C23semidirect
331. #10587574C23semidirect
332. #10587571C23semidirect
333. #10587571C23semidirect
334. #10587570C23semidirect
335. #10587570C23semidirect
336. #10587570C23semidirect
337. #10587569C23semidirect
338. #10587569C23semidirect
339. #10587569C23semidirect
340. #10587568C23semidirect
341. #10587567C23semidirect
342. #10587565C23semidirect
343. #10587565C23semidirect
344. #10587565C23semidirect
345. #10587564C23semidirect
346. #10587564C23semidirect
347. #10587564C23semidirect
348. #10587563C23semidirect
349. #10587563C23semidirect
350. C4×D68C23semidirect
351. #10587558C23semidirect
352. #10587556C23semidirect
353. C4×Dic34C23semidirect
668. C2×D42D17semidirect
741. C23×D4C2×D17semidirect
754. D42C2×D17semidirect
766. C2×#127C2×D17semidirect
823. C2×#121C2×D17semidirect
824. C2×#121C2×D17semidirect
833. C2×#120C2×D17semidirect
845. C2×C4×D4C2×D17semidirect
861. C2×C17#3542semidirect
914. C22×D4C22×D17semidirect
935. #127C22×D17semidirect
989. #121C22×D17semidirect
990. #121C22×D17semidirect
999. #120C22×D17semidirect
1011. C4×D4C22×D17semidirect
1075. C17C2×#3542semidirect
1439. C2#14543105direct (N × H)

Maximal subgroups

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

subgroupindex
#145431052
C2×#117635542
C2×#117635482
C2×#117635232
C2×#117635092
C2×#117634992
C2×#117634902
C2×#117634792
C2×#117634592
C2×#117634532
C2×#117634242
C2×#117634132
C2×#117634092
C2×#117633942
C2×#117633882
C2×#117633762
C2×#117633742
C2×#117633682
C2×#117633192
C2×#117633182
C22×#105876242
C2×D42×C172
C2×#354217