Finite Group Databasebeta

← C2×#14542459 #17942727

Subgroups — C2×#14542459 #17942727

Order 4352.

11438 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587697C211yesmaximal, characteristic, complemented
2C22×#41×D17C211yesmaximal, characteristic, complemented
3#14542459C2132yesmaximal, direct product factor
4C2×#11763472C212yesmaximal, complemented
5C2×#11763465C212yesmaximal, complemented
6C2×#11763461C212yesmaximal, complemented
7C2×#11763459C214yesmaximal, complemented
8C2×#11763456C212yesmaximal, complemented
9C2×#11763448C214yesmaximal, complemented
10C2×#11763388C212yesmaximal, complemented
11C2×#11763382C212yesmaximal, complemented
12C2×#11763380C211yesmaximal, characteristic, complemented
13C2×#11763319C212yesmaximal, complemented
14C2×#11763316C211yesmaximal, characteristic, complemented
15C22×#10587583C211yesmaximal, characteristic, complemented
16C2×C22⋊Q8×D17C212yesmaximal, complemented
17C2×#11763290C211yesmaximal, characteristic, complemented
18C2×C17×#537C211yesmaximal, characteristic, complemented
19C2×#10587697—216no—
20C2×#10587697C22116yescomplemented
21C22×#63256C2211yescharacteristic
22C22×#63252C2212yes—
23C22×#63252C2211yescharacteristic
24C22×#63252C2212yescomplemented
25C22×#63254C2212yes—
26C22×#63254C2211yescharacteristic
27C22×#63254C2212yescomplemented
28C22×#63254C2214yescomplemented
29C2×#41×D17—216no—
30C2×#41×D17C22116yescomplemented
31C23×Dic34C2211yescharacteristic, complemented
32C23×Dic34C2212yescomplemented
33C22×Q8×D17C2211yescharacteristic
34C22×Q8×D17C2212yescomplemented
35C22×D4×D17C2212yes—
36C22×D4×D17C2211yescharacteristic
37C23×C4×D17C2212yes—
38C23×C4×D17C2211yescharacteristic
39#11763472C22132yescomplemented
40#11763465C22132yescomplemented
41#11763461C22132yescomplemented
42#11763459C22164yescomplemented
43#11763456C22132yescomplemented
44#11763448C22164yescomplemented
45#11763388C22132yescomplemented
46#11763382C22132yescomplemented
47#11763380C22116yescomplemented
48C2×#10587574C2214yescomplemented
49C2×#10587630C2212yescomplemented
50C2×#10587622C2212yescomplemented
51C2×#10587571C2214yescomplemented
52#11763319C22132yescomplemented
53#11763316C22116yescomplemented
54C2×#10587580C2214yescomplemented
55C2×#10587569C2214yescomplemented
56C2×#10587569C2214yescomplemented
57C2×#10587621C2214yescomplemented
58C2×#10587621C2212yescomplemented
59C2×#10587583C2212yes—
60C2×#10587583C2212yes—
61C2×#10587583C2212yescomplemented
62C2×#10587583C2212yescomplemented
63C2×#10587583C22116yescomplemented
64C2×#10587610C2212yescomplemented
65C2×#10587610C2212yescomplemented
66C2×#10587582C2214yes—
67C2×#10587564C2214yescomplemented
68C2×#10587564C2214yescomplemented
69C2×#10587632C2211yescharacteristic
70C2×#10587632C2211yescharacteristic, complemented
71C22⋊Q8×D17C22132yescomplemented
72C2×#10587570C2214yescomplemented
73C2×#10587625C2214yescomplemented
74C2×#10587624C2211yescharacteristic
75C2×#10587624C2211yescharacteristic, complemented
76C2×#10587624C2214yescomplemented
77C2×#10587623C2212yes—
78C2×#10587623C2214yes—
79#11763290C22116yescomplemented
80C2×#10587573C2212yescomplemented
81C2×D4×Dic17C2214yescomplemented
82C2×#10587579C2212yescomplemented
83C2×C4×C22⋊D17C2212yes—
84C2×C4×C22⋊D17C2214yescomplemented
85C2×C4×C22⋊D17C2212yescomplemented
86C2×#10587567C2214yes—
87C2×#10587612C2211yescharacteristic, complemented
88C2×#10587578C2212yescomplemented
89C22×C4⋊Dic17C2212yescomplemented
90C2×C4⋊C4×D17C2212yescomplemented
91C2×C4⋊C4×D17C2214yescomplemented
92C22×#63227C2212yes—
93C2×C22⋊C4×D17C2214yes—
94C22×#41×C17C2211yescharacteristic
95C22×#41×C17C2211yescharacteristic, complemented
96C17×#537C22116yescomplemented
97C2×C17×C22⋊Q8C2212yescomplemented
98C2×C17×C22⋊Q8C2212yescomplemented
99C2×C17×#121C2212yescomplemented
100C2×C17×#121C2214yescomplemented
101C2×C17×#121C2212yescomplemented
102C22×C4⋊C4×C17C2211yescharacteristic, complemented
103C24×D17C2312yes—
104C24×D17C2311yescharacteristic
105C2×#41×C17—28no—
106C2×#41×C17—28no—
107C2×#41×C17C2318yes—
108C2×#41×C17C2318yescomplemented
109C22×Q8×C17C2311yescharacteristic
110C22×Q8×C17C2311yescharacteristic
111C22×D4×C17C2312yes—
112C22×D4×C17C2311yescharacteristic
113C22×D4×C17C2312yes—
114C22×D4×C17C2311yescharacteristic
115C22×D4×C17C2314yes—
116C23×C4×C17C2312yes—
117C23×C4×C17C2312yes—
118C23×C4×C17C2312yes—
119C23×C4×C17C2311yescharacteristic
120C22×C22⋊D17C2312yes—
121C22×C22⋊D17C2314yes—
122C22×C22⋊D17C2312yes—
123C22×C22⋊D17C2312yes—
124C22×C22⋊D17C2312yes—
125C22×C22⋊D17C2312yes—
126C23×Dic17C2312yes—
127C23×Dic17C2311yescharacteristic
128C23×Dic17C2314yes—
129C23×Dic17C2312yes—
130#10587697—2128no—
131#41×D17—2128no—
132C2×#63256—28no—
133C2×#63256C2318yes—
134C2×Q8×D17—216no—
135C2×Q8×D17—28no—
136C2×Q8×D17C2318yes—
137C2×Q8×D17C23116yescomplemented
138C2×#63254—216no—
139C2×#63254—232no—
140C2×#63254—216no—
141C2×#63254—28no—
142C2×#63254C23116yes—
143C2×#63254C2318yes—
144C2×#63254C23132yescomplemented
145C2×#63254C23116yescomplemented
146C2×D4×D17—216no—
147C2×D4×D17—28no—
148C2×D4×D17C2318yes—
149C2×D4×D17C23116yes—
150C2×#63252—216no—
151C2×#63252—216no—
152C2×#63252D4116yescomplemented
153C2×#63252C23116yes—
154C2×#63252C2318yes—
155C2×#63252C23116yescomplemented
156C22×D68C2312yes—
157C22×D68C2311yescharacteristic
158C22×C4×D17—28no—
159C22×C4×D17—216no—
160C22×C4×D17C2314yes—
161C22×C4×D17C2312yes—
162C22×C4×D17C2312yes—
163C22×C4×D17C2311yescharacteristic
164C22×C4×D17C2311yescharacteristic
165C22×C4×D17C2311yescharacteristic
166C22×C4×D17C2311yescharacteristic
167C22×C4×D17C23116yes—
168C22×C4×D17C2318yes—
169C22×C4×D17C2314yes—
170C22×C4×D17C2312yes—
171C22×Dic34—28no—
172C22×Dic34—216no—
173C22×Dic34C2312yes—
174C22×Dic34C2314yes—
175C22×Dic34C2312yes—
176C22×Dic34C2312yes—
177C22×Dic34C2311yescharacteristic
178C22×Dic34C23116yescomplemented
179C22×Dic34C2318yescomplemented
180C17×C22⋊Q8C23116yescomplemented
181C17×C22⋊Q8C23116yescomplemented
182C17×#121C23116yescomplemented
183C17×#121C23132yescomplemented
184C17×#121C23116yescomplemented
185C2×C4⋊C4×C17C2312yes—
186C2×C4⋊C4×C17C2312yes—
187C2×C4⋊C4×C17C2314yes—
188C2×C4⋊C4×C17C2318yescomplemented
189C2×C22⋊C4×C17C2314yes—
190C2×C22⋊C4×C17C2314yes—
191C2×C22⋊Dic17C2314yes—
192C2×C22⋊Dic17C2312yes—
193C2×C22⋊Dic17C2312yes—
194C2×C22⋊Dic17C2312yes—
195C2×C22⋊Dic17C2314yes—
196#10587632C2318yes—
197#10587632C2318yescomplemented
198#10587630C23116yescomplemented
199#10587625C23132yescomplemented
200#10587624C2318yes—
201#10587624C23132yescomplemented
202#10587624C2318yescomplemented
203#10587623C23132yes—
204#10587623C23116yes—
205#10587622C23116yescomplemented
206#10587621C23116yescomplemented
207#10587621C23132yescomplemented
208D4×Dic17C23132yescomplemented
209C4×C22⋊D17C23116yes—
210C4×C22⋊D17C23132yescomplemented
211C4×C22⋊D17C23116yescomplemented
212C2×#63227C2312yes—
213C2×#63227C2314yes—
214C2×#63227C2314yes—
215C2×#63227C23116yes—
216C2×#63227C2314yes—
217C2×#63227C2312yes—
218#10587612C2318yescomplemented
219C2×C4⋊Dic17C2311yescharacteristic
220C2×C4⋊Dic17C2314yes—
221C2×C4⋊Dic17C2314yes—
222C2×C4⋊Dic17C2311yescharacteristic
223C2×C4⋊Dic17C23116yescomplemented
224#10587610C23116yescomplemented
225#10587610C23116yescomplemented
226C2×#63225C2312yes—
227C2×#63225C2314yes—
228C2×#63225C2314yes—
229C2×#63225C2314yes—
230C2×#63225C2312yes—
231C2×C4×Dic17C2314yes—
232C2×C4×Dic17C2312yes—
233#10587583C23116yes—
234#10587583C23116yes—
235#10587583C23116yescomplemented
236#10587583C23116yescomplemented
237#10587582C23132yes—
238#10587580C23132yescomplemented
239#10587579C23116yescomplemented
240#10587578C23116yescomplemented
241C4⋊C4×D17C23132yescomplemented
242C4⋊C4×D17C23116yescomplemented
243#10587574C23132yescomplemented
244#10587573C23116yescomplemented
245#10587571C23132yescomplemented
246#10587570C23132yescomplemented
247#10587569C23132yescomplemented
248#10587569C23132yescomplemented
249#10587567C23132yes—
250C22⋊C4×D17C23132yes—
251#10587564C23132yescomplemented
252#10587564C23132yescomplemented
253C24×C17C2412yes—
254C24×C17C2412yes—
255C24×C17C2411yescharacteristic
256C23×D17—24no—
257C23×D17—28no—
258C23×D17—28no—
259C23×D17—24no—
260C23×D17—44no—
261C23×D17—42no—
262C23×D17C2411yescharacteristic
263C23×D17C2418yes—
264C23×D17C2414yes—
265C23×D17C2412yes—
266C23×D17C2411yescharacteristic
267#41×C17—232no—
268#41×C17—232no—
269C2×Q8×C17—24no—
270C2×Q8×C17—24no—
271C2×Q8×C17C2414yes—
272C2×Q8×C17C2414yes—
273C2×D4×C17—28no—
274C2×D4×C17—28no—
275C2×D4×C17—24no—
276C2×D4×C17—24no—
277C2×D4×C17—48no—
278C2×D4×C17C2418yes—
279C2×D4×C17C2414yes—
280C2×D4×C17C2418yes—
281C2×D4×C17C2414yes—
282C2×D4×C17C24116yes—
283C22×C4×C17—28no—
284C22×C4×C17—28no—
285C22×C4×C17—44no—
286C22×C4×C17C2×D418yes—
287C22×C4×C17C2418yes—
288C22×C4×C17C2418yes—
289C22×C4×C17C2412yes—
290C22×C4×C17C2412yes—
291C22×C4×C17C2414yes—
292C22×C4×C17C2418yes—
293C22×C4×C17C2411yescharacteristic
294C22×C4×C17C2411yescharacteristic
295C22×C4×C17C2414yes—
296C2×C22⋊D17—28no—
297C2×C22⋊D17—216no—
298C2×C22⋊D17—28no—
299C2×C22⋊D17—28no—
300C2×C22⋊D17—44no—
301C2×C22⋊D17C2×D4116yes—
302C2×C22⋊D17C2418yes—
303C2×C22⋊D17C2418yes—
304C2×C22⋊D17C24116yes—
305C2×C22⋊D17C2418yes—
306C2×C22⋊D17C2418yes—
307C2×C22⋊D17C2418yes—
308C22×Dic17—28no—
309C22×Dic17—24no—
310C22×Dic17—216no—
311C22×Dic17—28no—
312C22×Dic17C2414yes—
313C22×Dic17C2411yescharacteristic
314C22×Dic17C24116yes—
315C22×Dic17C2418yes—
316C22×Dic17C2411yescharacteristic
317C22×Dic17C2418yes—
318C22×Dic17C2414yes—
319C22×Dic17C2412yes—
320C22×Dic17C2412yes—
321C22×Dic17C2412yes—
322#63256—232no—
323Q8×D17—264no—
324Q8×D17—232no—
325#63254—264no—
326#63254—2128no—
327#63254—264no—
328#63254—232no—
329D4×D17—264no—
330D4×D17—232no—
331#63252—264no—
332#63252—264no—
333#63252C2×D4164yescomplemented
334C2×D68—28no—
335C2×D68C2×D418yes—
336C2×D68C2418yes—
337C2×D68C2414yes—
338C2×C4×D17—28no—
339C2×C4×D17—216no—
340C2×C4×D17—24no—
341C2×C4×D17—24no—
342C2×C4×D17—24no—
343C2×C4×D17—24no—
344C2×C4×D17—232no—
345C2×C4×D17—28no—
346C2×C4×D17—264no—
347C2×C4×D17—48no—
348C2×C4×D17C2×D4116yes—
349C2×C4×D17C2414yes—
350C2×C4×D17C2414yes—
351C2×C4×D17C2418yes—
352C2×C4×D17C2414yes—
353C2×C4×D17C2418yes—
354C2×C4×D17C2414yes—
355C2×C4×D17C24116yes—
356C2×C4×D17C24116yes—
357C2×C4×D17C2418yes—
358C2×Dic34—28no—
359C2×Dic34—28no—
360C2×Dic34—232no—
361C2×Dic34—216no—
362C2×Dic34—28no—
363C2×Dic34—264no—
364C2×Dic34C2×D418yes—
365C2×Dic34C2418yes—
366C2×Dic34C24116yes—
367C2×Dic34C2418yes—
368C2×Dic34C2418yes—
369C2×Dic34C2414yes—
370C4⋊C4×C17C24116yes—
371C4⋊C4×C17C2418yes—
372C4⋊C4×C17C2418yes—
373C22⋊C4×C17C24116yes—
374C22⋊C4×C17C24116yes—
375C22⋊Dic17C2418yes—
376C22⋊Dic17C24116yes—
377C22⋊Dic17C2418yes—
378C22⋊Dic17C24116yes—
379C22⋊Dic17C2418yes—
380#63227C2418yes—
381#63227C24116yes—
382#63227C24116yes—
383#63227C24116yes—
384#63227C2418yes—
385C4⋊Dic17C24116yes—
386C4⋊Dic17C24116yes—
387C4⋊Dic17C2414yes—
388C4⋊Dic17C2414yes—
389#63225C24116yes—
390#63225C2418yes—
391#63225C24116yes—
392#63225C24116yes—
393#63225C2418yes—
394C4×Dic17C24116yes—
395C4×Dic17C2418yes—
396C2×#3489—171nomaximal, Sylow
397C23×C17—22no—
398C23×C17—22no—
399C23×C17—24no—
400C23×C17—24no—
401C23×C17—24no—
402C23×C17—24no—
403C23×C17—24no—
404C23×C17—24no—
405C23×C17C22×D414yes—
406C23×C17C2514yes—
407C23×C17C2514yes—
408C23×C17C2512yes—
409C23×C17C2511yescharacteristic
410C22×D17—22no—
411C22×D17—24no—
412C22×D17—24no—
413C22×D17—22no—
414C22×D17—22no—
415C22×D17—28no—
416C22×D17—22no—
417C22×D17—22no—
418C22×D17—216no—
419C22×D17—216no—
420C22×D17—28no—
421C22×D17—48no—
422C22×D17—44no—
423C22×D17—432no—
424C22×D17—416no—
425C22×D17C22×D418yes—
426C22×D172−1+414yescomplemented
427C22×D17C2512yes—
428C22×D17C2514yes—
429C22×D17C2512yes—
430Q8×C17—28no—
431Q8×C17—28no—
432D4×C17—216no—
433D4×C17—216no—
434D4×C17—28no—
435D4×C17—28no—
436D4×C17—416no—
437C2×C4×C17—24no—
438C2×C4×C17—24no—
439C2×C4×C17—28no—
440C2×C4×C17—216no—
441C2×C4×C17—216no—
442C2×C4×C17—48no—
443C2×C4×C17C22×D414yes—
444C2×C4×C17C22×D414yes—
445C2×C4×C17C22×D4116yes—
446C2×C4×C17C2518yes—
447C2×C4×C17C2514yes—
448C2×C4×C17C2514yes—
449C2×C4×C17C2512yes—
450C2×C4×C17C2512yes—
451C22⋊D17—216no—
452C22⋊D17—232no—
453C22⋊D17—216no—
454C22⋊D17—216no—
455C22⋊D17—48no—
456C22⋊D17C22×D4132yes—
457C2×Dic17—28no—
458C2×Dic17—22no—
459C2×Dic17—216no—
460C2×Dic17—22no—
461C2×Dic17—28no—
462C2×Dic17—24no—
463C2×Dic17—24no—
464C2×Dic17—232no—
465C2×Dic17—216no—
466C2×Dic17C22×D418yes—
467C2×Dic17C2514yes—
468C2×Dic17C2514yes—
469C2×Dic17C2518yes—
470C2×Dic17C2512yes—
471C2×Dic17C2512yes—
472C2×Dic17C2514yes—
473D68—216no—
474D68C22×D4116yes—
475C4×D17—216no—
476C4×D17—232no—
477C4×D17—28no—
478C4×D17—28no—
479C4×D17—28no—
480C4×D17—28no—
481C4×D17—216no—
482C4×D17—416no—
483C4×D17C22×D4132yes—
484Dic34—216no—
485Dic34—216no—
486Dic34—232no—
487Dic34—216no—
488Dic34C22×D4116yes—
489C22×2−1+4—171no—
490C23×#41—171no—
491#3489—1732no—
492C2×D4×Q8—172no—
493C2×#548—172no—
494C2×#547—172no—
495C2×#547—174no—
496C2×#546—174no—
497C2×#546—172no—
498C2×#537—172no—
499C2×#537D1711yescharacteristic, complemented
500C2×#536—171no—
501C2×#536—172no—
502C2×#525—171no—
503C2×#525—172no—
504C22×C22⋊Q8—172no—
505C22×C22⋊Q8—171no—
506C2×#520—171no—
507C22×C17—22no—
508C22×C17—22no—
509C22×C17—28no—
510C22×C17—24no—
511C22×C17—24no—
512C22×C17—24no—
513C22×C17—24no—
514C22×C17—24no—
515C22×C17—24no—
516C22×C17—48no—
517C22×C17—48no—
518C22×C17C23×D414yes—
519C22×C17C23×D412yes—
520C22×C17C2×2−1+412yes—
521C22×C17#58512yes—
522C22×C17C2611yescharacteristic
523C2×D17—22no—
524C2×D17—24no—
525C2×D17—24no—
526C2×D17—22no—
527C2×D17—28no—
528C2×D17—216no—
529C2×D17—22no—
530C2×D17—22no—
531C2×D17—22no—
532C2×D17—432no—
533C2×D17—416no—
534C2×D17—44no—
535C2×D17C23×D418yes—
536C2×D17C2×2−1+414yescomplemented
537C4×C17—24no—
538C4×C17—24no—
539C4×C17—28no—
540C4×C17C23×D414yes—
541C4×C17C23×D414yes—
542Dic17—28no—
543Dic17—22no—
544Dic17—22no—
545Dic17—24no—
546Dic17—24no—
547Dic17C23×D418yes—
548C2×2−1+4—1716no—
549C2×2−1+4—3416no—
550C22×#41—1716no—
551C22×#41—171no—
552C22×#41—172no—
553C22×#41—171no—
554C22×#41—172no—
555C22×#41—174no—
556C22×#41—171no—
557C22×#41—172no—
558C22×#41—172no—
559C22×#41—3416no—
560C22×#41C2×D1711yescharacteristic
561C22×#41C2×D1711yescharacteristic, complemented
562C23×Q8—171no—
563C23×Q8—172no—
564C23×Q8—171no—
565C23×Q8—172no—
566C23×D4—172no—
567C23×D4—171no—
568C24×C4—172no—
569C24×C4—171no—
570D4×Q8—1732no—
571#548—1732no—
572#547—1732no—
573#547—1764no—
574#546—1732no—
575#546—1764no—
576#537—1732no—
577#537C2×D17116yescomplemented
578#536—1716no—
579#536—1732no—
580C2×C4⋊Q8—172no—
581C2×C4⋊Q8—174no—
582C2×#124—172no—
583C2×#124—174no—
584#525—1716no—
585#525—1732no—
586C2×#123—172no—
587C2×#123—174no—
588C2×#123—174no—
589C2×#123—174no—
590C2×#123—174no—
591C2×C22⋊Q8—171no—
592C2×C22⋊Q8—171no—
593C2×C22⋊Q8—172no—
594C2×C22⋊Q8—172no—
595C2×C22⋊Q8—1732no—
596C2×C22⋊Q8—172no—
597C2×C22⋊Q8—174no—
598C2×C22⋊Q8—172no—
599C2×C22⋊Q8—172no—
600C2×C22⋊Q8—172no—
601C2×C22⋊Q8—1716no—
602C2×C22⋊Q8—174no—
603C2×C22⋊Q8—174no—
604C2×C22⋊Q8C2×D1712yescomplemented
605C2×C22⋊Q8C2×D1712yescomplemented
606C2×#121—171no—
607C2×#121—171no—
608C2×#121—174no—
609C2×#121—174no—
610C2×#121—174no—
611C2×#121C2×D1712yescomplemented
612C2×#121C2×D1714yescomplemented
613C2×#121C2×D1712yescomplemented
614C2×#120—172no—
615C2×#120—174no—
616#520—1716no—
617C2×C4×Q8—172no—
618C2×C4×D4—174no—
619C2×C4×D4—172no—
620C2×C4×D4—174no—
621C2×C4×D4—172no—
622C2×C4×D4—172no—
623C2×C4×D4—174no—
624C2×#117—171no—
625C2×#117—172no—
626C22×C4⋊C4—172no—
627C22×C4⋊C4—172no—
628C22×C4⋊C4—174no—
629C22×C4⋊C4C2×D1711yescharacteristic, complemented
630C22×C22⋊C4—172no—
631C22×C22⋊C4—174no—
632C2×C17—24no—
633C2×C17—44no—
634C2×C17—44no—
635C2×C17#348914yescomplemented
636C2×C17C24×D411yescharacteristic
637C2×C17C22×2−1+411yescharacteristic
638C2×C17C2×#58511yescharacteristic
639D17—24no—
640D17—28no—
641D17—42no—
642C25—172no—
643C25—171no—
6442−1+4—34128no—
645C2×#41—28no—
646C2×#41—28no—
647C2×#41—178no—
648C2×#41—1716no—
649C2×#41—1732no—
650C2×#41—1716no—
651C2×#41—178no—
652C2×#41—1716no—
653C2×#41—178no—
654C2×#41—1716no—
655C2×#41—1716no—
656C2×#41—3416no—
657C2×#41—3416no—
658C2×#41—3416no—
659C2×#41—3416no—
660C2×#41—3432no—
661C2×#41—348no—
662C2×#41—348no—
663C2×#41—34128no—
664C2×#41C22×D1718yes—
665C2×#41C22×D1718yescomplemented
666C22×Q8—1716no—
667C22×Q8—178no—
668C22×Q8—171no—
669C22×Q8—172no—
670C22×Q8—174no—
671C22×Q8—172no—
672C22×Q8—172no—
673C22×Q8—178no—
674C22×Q8—1716no—
675C22×Q8—3416no—
676C22×Q8—3416no—
677C22×Q8—348no—
678C22×Q8—348no—
679C22×Q8C22×D1711yescharacteristic
680C22×Q8C22×D1711yescharacteristic
681C22×D4—172no—
682C22×D4—172no—
683C22×D4—174no—
684C22×D4—172no—
685C22×D4—172no—
686C22×D4—172no—
687C22×D4—1716no—
688C22×D4—178no—
689C22×D4—171no—
690C22×D4—172no—
691C22×D4—3416no—
692C22×D4—348no—
693C22×D4C22×D1712yes—
694C22×D4C22×D1711yescharacteristic
695C22×D4C22×D1712yes—
696C22×D4C22×D1711yescharacteristic
697C22×D4C22×D1714yes—
698C23×C4—172no—
699C23×C4—172no—
700C23×C4—171no—
701C23×C4—174no—
702C23×C4—172no—
703C23×C4—174no—
704C23×C4—172no—
705C23×C4—172no—
706C23×C4—171no—
707C23×C4—171no—
708C23×C4—171no—
709C23×C4—171no—
710C23×C4—1716no—
711C23×C4—178no—
712C23×C4—174no—
713C23×C4—3416no—
714C23×C4—348no—
715C23×C4C22×D1712yes—
716C23×C4C22×D1712yes—
717C23×C4C22×D1712yes—
718C23×C4C22×D1711yescharacteristic
719C4⋊Q8—1716no—
720C4⋊Q8—1732no—
721#124—1716no—
722#124—1732no—
723#123—1716no—
724#123—1732no—
725#123—1732no—
726#123—1732no—
727#123—1732no—
728C22⋊Q8—178no—
729C22⋊Q8—178no—
730C22⋊Q8—1716no—
731C22⋊Q8—1716no—
732C22⋊Q8—1716no—
733C22⋊Q8—1716no—
734C22⋊Q8—1732no—
735C22⋊Q8—1716no—
736C22⋊Q8—1716no—
737C22⋊Q8—1732no—
738C22⋊Q8—1732no—
739C22⋊Q8C22×D17116yescomplemented
740C22⋊Q8C22×D17116yescomplemented
741#121—178no—
742#121—178no—
743#121—1732no—
744#121—1732no—
745#121—1732no—
746#121C22×D17116yescomplemented
747#121C22×D17132yescomplemented
748#121C22×D17116yescomplemented
749#120—1716no—
750#120—1732no—
751C4×Q8—1716no—
752C4×D4—1732no—
753C4×D4—1732no—
754C4×D4—1716no—
755C4×D4—1716no—
756C4×D4—1716no—
757C4×D4—1732no—
758#117—178no—
759#117—1716no—
760C2×C4⋊C4—171no—
761C2×C4⋊C4—172no—
762C2×C4⋊C4—174no—
763C2×C4⋊C4—174no—
764C2×C4⋊C4—174no—
765C2×C4⋊C4—174no—
766C2×C4⋊C4—1716no—
767C2×C4⋊C4—171no—
768C2×C4⋊C4—174no—
769C2×C4⋊C4—172no—
770C2×C4⋊C4—1716no—
771C2×C4⋊C4—1732no—
772C2×C4⋊C4C22×D1712yes—
773C2×C4⋊C4C22×D1714yes—
774C2×C4⋊C4C22×D1712yes—
775C2×C4⋊C4C22×D1718yescomplemented
776C2×C22⋊C4—174no—
777C2×C22⋊C4—172no—
778C2×C22⋊C4—172no—
779C2×C22⋊C4—174no—
780C2×C22⋊C4—172no—
781C2×C22⋊C4—172no—
782C2×C22⋊C4—174no—
783C2×C22⋊C4—174no—
784C2×C22⋊C4—1716no—
785C2×C22⋊C4—174no—
786C2×C22⋊C4—172no—
787C2×C22⋊C4—1732no—
788C2×C22⋊C4C22×D1714yes—
789C2×C22⋊C4C22×D1714yes—
790C2×C42—174no—
791C2×C42—172no—
792C17C2×#348911yescharacteristic, complemented, Sylow
793C24—171no—
794C24—172no—
795C24—171no—
796C24—178no—
797C24—174no—
798C24—348no—
799C24—344no—
800C24—348no—
801C24—344no—
802C24—682no—
803C24—684no—
804C24C23×D1712yes—
805C24C23×D1712yes—
806C24C23×D1711yescharacteristic
807#41—232no—
808#41—232no—
809#41—1764no—
810#41—3464no—
811#41—3464no—
812#41—3464no—
813#41—3464no—
814#41—34128no—
815#41—3432no—
816#41—3432no—
817C2×Q8—24no—
818C2×Q8—24no—
819C2×Q8—178no—
820C2×Q8—174no—
821C2×Q8—178no—
822C2×Q8—1716no—
823C2×Q8—178no—
824C2×Q8—178no—
825C2×Q8—3416no—
826C2×Q8—348no—
827C2×Q8—3464no—
828C2×Q8—3464no—
829C2×Q8—3432no—
830C2×Q8—348no—
831C2×Q8—348no—
832C2×Q8—3432no—
833C2×Q8C23×D1714yes—
834C2×Q8C23×D1714yes—
835C2×D4—28no—
836C2×D4—28no—
837C2×D4—24no—
838C2×D4—24no—
839C2×D4—48no—
840C2×D4—1716no—
841C2×D4—178no—
842C2×D4—178no—
843C2×D4—1716no—
844C2×D4—178no—
845C2×D4—178no—
846C2×D4—178no—
847C2×D4—178no—
848C2×D4—174no—
849C2×D4—178no—
850C2×D4—348no—
851C2×D4—348no—
852C2×D4—3464no—
853C2×D4—3432no—
854C2×D4—348no—
855C2×D4—348no—
856C2×D4—3416no—
857C2×D4—684no—
858C2×D4C23×D1718yes—
859C2×D4C23×D1714yes—
860C2×D4C23×D1718yes—
861C2×D4C23×D1714yes—
862C2×D4C23×D17116yes—
863C22×C4—28no—
864C22×C4—28no—
865C22×C4—44no—
866C22×C4—172no—
867C22×C4—1716no—
868C22×C4—178no—
869C22×C4—178no—
870C22×C4—174no—
871C22×C4—1716no—
872C22×C4—178no—
873C22×C4—172no—
874C22×C4—172no—
875C22×C4—174no—
876C22×C4—171no—
877C22×C4—171no—
878C22×C4—1716no—
879C22×C4—178no—
880C22×C4—178no—
881C22×C4—174no—
882C22×C4—174no—
883C22×C4—174no—
884C22×C4—174no—
885C22×C4—1716no—
886C22×C4—348no—
887C22×C4—3464no—
888C22×C4—348no—
889C22×C4—3416no—
890C22×C4—348no—
891C22×C4—3416no—
892C22×C4—344no—
893C22×C4—348no—
894C22×C4—344no—
895C22×C4—344no—
896C22×C4—344no—
897C22×C4—344no—
898C22×C4—3432no—
899C22×C4—688no—
900C22×C4D4×D1718yes—
901C22×C4C23×D1718yes—
902C22×C4C23×D1718yes—
903C22×C4C23×D1714yes—
904C22×C4C23×D1712yes—
905C22×C4C23×D1712yes—
906C22×C4C23×D1718yes—
907C22×C4C23×D1714yes—
908C22×C4C23×D1711yescharacteristic
909C22×C4C23×D1711yescharacteristic
910C4⋊C4—174no—
911C4⋊C4—178no—
912C4⋊C4—1716no—
913C4⋊C4—1716no—
914C4⋊C4—1716no—
915C4⋊C4—1716no—
916C4⋊C4—174no—
917C4⋊C4—1716no—
918C4⋊C4—178no—
919C4⋊C4C23×D1718yes—
920C4⋊C4C23×D17116yes—
921C4⋊C4C23×D1718yes—
922C22⋊C4—1716no—
923C22⋊C4—178no—
924C22⋊C4—178no—
925C22⋊C4—1716no—
926C22⋊C4—178no—
927C22⋊C4—178no—
928C22⋊C4—1716no—
929C22⋊C4—1716no—
930C22⋊C4—1716no—
931C22⋊C4—178no—
932C22⋊C4C23×D17116yes—
933C22⋊C4C23×D17116yes—
934C42—1716no—
935C42—178no—
936C23—22no—
937C23—22no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—24no—
942C23—24no—
943C23—24no—
944C23—178no—
945C23—174no—
946C23—172no—
947C23—174no—
948C23—172no—
949C23—3416no—
950C23—348no—
951C23—3416no—
952C23—342no—
953C23—344no—
954C23—344no—
955C23—342no—
956C23—348no—
957C23—342no—
958C23—342no—
959C23—342no—
960C23—684no—
961C23—688no—
962C23—6816no—
963C23—6832no—
964C23C2×D4×D1714yes—
965C23C24×D1714yes—
966C23C24×D1714yes—
967C23C24×D1712yes—
968C23C24×D1711yescharacteristic
969Q8—28no—
970Q8—28no—
971Q8—1716no—
972Q8—3432no—
973Q8—3416no—
974Q8—3416no—
975Q8—3416no—
976D4—216no—
977D4—216no—
978D4—28no—
979D4—28no—
980D4—416no—
981D4—1732no—
982D4—1716no—
983D4—3416no—
984D4—3416no—
985D4—3416no—
986D4—3432no—
987D4—3416no—
988D4—688no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—28no—
992C2×C4—216no—
993C2×C4—216no—
994C2×C4—48no—
995C2×C4—178no—
996C2×C4—174no—
997C2×C4—1732no—
998C2×C4—174no—
999C2×C4—174no—
1000C2×C4—178no—
1001C2×C4—172no—
1002C2×C4—172no—
1003C2×C4—3416no—
1004C2×C4—3416no—
1005C2×C4—3432no—
1006C2×C4—3416no—
1007C2×C4—3432no—
1008C2×C4—342no—
1009C2×C4—342no—
1010C2×C4—348no—
1011C2×C4—348no—
1012C2×C4—3416no—
1013C2×C4—344no—
1014C2×C4—344no—
1015C2×C4—348no—
1016C2×C4—348no—
1017C2×C4—348no—
1018C2×C4—348no—
1019C2×C4—6816no—
1020C2×C4C2×D4×D1714yes—
1021C2×C4C2×D4×D1714yes—
1022C2×C4C2×D4×D17116yes—
1023C2×C4C24×D1718yes—
1024C2×C4C24×D1714yes—
1025C2×C4C24×D1714yes—
1026C2×C4C24×D1712yes—
1027C2×C4C24×D1712yes—
1028C22—28no—
1029C22—22no—
1030C22—22no—
1031C22—24no—
1032C22—24no—
1033C22—24no—
1034C22—24no—
1035C22—24no—
1036C22—24no—
1037C22—48no—
1038C22—48no—
1039C22—178no—
1040C22—174no—
1041C22—348no—
1042C22—3416no—
1043C22—342no—
1044C22—344no—
1045C22—344no—
1046C22—342no—
1047C22—342no—
1048C22—342no—
1049C22—342no—
1050C22—6816no—
1051C22—6832no—
1052C22—684no—
1053C22C22×D4×D1714yes—
1054C22C22×D4×D1712yes—
1055C222−1+4×D1712yes—
1056C22#1176364412yes—
1057C22C25×D1711yescharacteristic
1058C4—24no—
1059C4—24no—
1060C4—28no—
1061C4—178no—
1062C4—342no—
1063C4—342no—
1064C4—348no—
1065C4—344no—
1066C4—344no—
1067C4C22×D4×D1714yes—
1068C4C22×D4×D1714yes—
1069C2—24no—
1070C2—44no—
1071C2—44no—
1072C2—344no—
1073C2—348no—
1074C2—682no—
1075C2#1454245914yesdirect product factor
1076C2C23×D4×D1711yescharacteristic
1077C2C2×2−1+4×D1711yescharacteristic
1078C2C2×#1176364411yescharacteristic
subgroupG/H
centerC23C24×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC2×C17×#537C2
socleC23×C17C25
hypercenterC2×#537D17
hypocenterC17C2×#3489
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C22×#10587697C2semidirect
2. C22×#41×D17C2semidirect
3. #14542459C2direct (N × H)
4. C2×#11763472C2semidirect
5. C2×#11763465C2semidirect
6. C2×#11763461C2semidirect
7. C2×#11763459C2semidirect
8. C2×#11763456C2semidirect
9. C2×#11763448C2semidirect
10. C2×#11763388C2semidirect
11. C2×#11763382C2semidirect
12. C2×#11763380C2semidirect
13. C2×#11763319C2semidirect
14. C2×#11763316C2semidirect
15. C22×#10587583C2semidirect
16. C2×C22⋊Q8×D17C2semidirect
17. C2×#11763290C2semidirect
18. C2×C17×#537C2semidirect
20. C2×#10587697C22semidirect
24. C22×#63252C22semidirect
27. C22×#63254C22semidirect
28. C22×#63254C22semidirect
30. C2×#41×D17C22semidirect
31. C23×Dic34C22semidirect
32. C23×Dic34C22semidirect
34. C22×Q8×D17C22semidirect
39. #11763472C22semidirect
40. #11763465C22semidirect
41. #11763461C22semidirect
42. #11763459C22semidirect
43. #11763456C22semidirect
44. #11763448C22semidirect
45. #11763388C22semidirect
46. #11763382C22semidirect
47. #11763380C22semidirect
48. C2×#10587574C22semidirect
49. C2×#10587630C22semidirect
50. C2×#10587622C22semidirect
51. C2×#10587571C22semidirect
52. #11763319C22semidirect
53. #11763316C22semidirect
54. C2×#10587580C22semidirect
55. C2×#10587569C22semidirect
56. C2×#10587569C22semidirect
57. C2×#10587621C22semidirect
58. C2×#10587621C22semidirect
61. C2×#10587583C22semidirect
62. C2×#10587583C22semidirect
63. C2×#10587583C22semidirect
64. C2×#10587610C22semidirect
65. C2×#10587610C22semidirect
67. C2×#10587564C22semidirect
68. C2×#10587564C22semidirect
70. C2×#10587632C22semidirect
71. C22⋊Q8×D17C22semidirect
72. C2×#10587570C22semidirect
73. C2×#10587625C22semidirect
75. C2×#10587624C22semidirect
76. C2×#10587624C22semidirect
79. #11763290C22semidirect
80. C2×#10587573C22semidirect
81. C2×D4×Dic17C22semidirect
82. C2×#10587579C22semidirect
84. C2×C4×C22⋊D17C22semidirect
85. C2×C4×C22⋊D17C22semidirect
87. C2×#10587612C22semidirect
88. C2×#10587578C22semidirect
89. C22×C4⋊Dic17C22semidirect
90. C2×C4⋊C4×D17C22semidirect
91. C2×C4⋊C4×D17C22semidirect
95. C22×#41×C17C22semidirect
96. C17×#537C22semidirect
97. C2×C17×C22⋊Q8C22semidirect
98. C2×C17×C22⋊Q8C22semidirect
99. C2×C17×#121C22semidirect
100. C2×C17×#121C22semidirect
101. C2×C17×#121C22semidirect
102. C22×C4⋊C4×C17C22semidirect
108. C2×#41×C17C23semidirect
137. C2×Q8×D17C23semidirect
144. C2×#63254C23semidirect
145. C2×#63254C23semidirect
152. C2×#63252D4semidirect
155. C2×#63252C23semidirect
178. C22×Dic34C23semidirect
179. C22×Dic34C23semidirect
180. C17×C22⋊Q8C23semidirect
181. C17×C22⋊Q8C23semidirect
182. C17×#121C23semidirect
183. C17×#121C23semidirect
184. C17×#121C23semidirect
188. C2×C4⋊C4×C17C23semidirect
197. #10587632C23semidirect
198. #10587630C23semidirect
199. #10587625C23semidirect
201. #10587624C23semidirect
202. #10587624C23semidirect
205. #10587622C23semidirect
206. #10587621C23semidirect
207. #10587621C23semidirect
208. D4×Dic17C23semidirect
210. C4×C22⋊D17C23semidirect
211. C4×C22⋊D17C23semidirect
218. #10587612C23semidirect
223. C2×C4⋊Dic17C23semidirect
224. #10587610C23semidirect
225. #10587610C23semidirect
235. #10587583C23semidirect
236. #10587583C23semidirect
238. #10587580C23semidirect
239. #10587579C23semidirect
240. #10587578C23semidirect
241. C4⋊C4×D17C23semidirect
242. C4⋊C4×D17C23semidirect
243. #10587574C23semidirect
244. #10587573C23semidirect
245. #10587571C23semidirect
246. #10587570C23semidirect
247. #10587569C23semidirect
248. #10587569C23semidirect
251. #10587564C23semidirect
252. #10587564C23semidirect
333. #63252C2×D4semidirect
426. C22×D172−1+4semidirect
499. C2×#537D17semidirect
536. C2×D17C2×2−1+4semidirect
561. C22×#41C2×D17semidirect
577. #537C2×D17semidirect
604. C2×C22⋊Q8C2×D17semidirect
605. C2×C22⋊Q8C2×D17semidirect
611. C2×#121C2×D17semidirect
612. C2×#121C2×D17semidirect
613. C2×#121C2×D17semidirect
629. C22×C4⋊C4C2×D17semidirect
635. C2×C17#3489semidirect
665. C2×#41C22×D17semidirect
739. C22⋊Q8C22×D17semidirect
740. C22⋊Q8C22×D17semidirect
746. #121C22×D17semidirect
747. #121C22×D17semidirect
748. #121C22×D17semidirect
775. C2×C4⋊C4C22×D17semidirect
792. C17C2×#3489semidirect
1075. C2#14542459direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105876972
C22×#41×D172
#145424592
C2×#117634722
C2×#117634652
C2×#117634612
C2×#117634592
C2×#117634562
C2×#117634482
C2×#117633882
C2×#117633822
C2×#117633802
C2×#117633192
C2×#117633162
C22×#105875832
C2×C22⋊Q8×D172
C2×#117632902
C2×C17×#5372
C2×#348917