Finite Group Databasebeta

← C2×#14542461 #17942724

Subgroups — C2×#14542461 #17942724

Order 4352.

11438 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587694C211yesmaximal, characteristic, complemented
2C23×#63256C211yesmaximal, characteristic, complemented
3#14542461C2132yesmaximal, direct product factor
4C2×Q8×C22⋊D17C211yesmaximal, characteristic, complemented
5C2×#11763471C211yesmaximal, characteristic, complemented
6C2×#11763470C211yesmaximal, characteristic, complemented
7C2×#11763462C213yesmaximal, complemented
8C2×#11763461C213yesmaximal, complemented
9C2×#11763455C213yesmaximal, complemented
10C2×#11763450C213yesmaximal, complemented
11C2×#11763389C213yesmaximal, complemented
12C2×#11763384C213yesmaximal, complemented
13C2×#11763318C213yesmaximal, complemented
14C2×C22⋊Q8×D17C213yesmaximal, complemented
15C2×#11763291C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C17C211yesmaximal, characteristic, complemented
17C2×#10587694—216no—
18C2×#10587694C22116yescomplemented
19C22×#63256—216no—
20C22×#63256C2213yes—
21C22×#63256C2213yes—
22C22×#63256C2211yescharacteristic
23C22×#63256C2211yescharacteristic
24C22×#63256C22116yescomplemented
25C22×#63256C2213yescomplemented
26C22×#63252C2213yescomplemented
27C22×#63252C2213yescomplemented
28C22×Q8×D17C2213yescomplemented
29C22×Q8×D17C2211yescharacteristic, complemented
30C23×D68C2213yes—
31C23×C4×D17C2213yes—
32Q8×C22⋊D17C22116yescomplemented
33#11763471C22116yescomplemented
34#11763470C22116yescomplemented
35#11763462C22148yescomplemented
36#11763461C22148yescomplemented
37#11763455C22148yescomplemented
38#11763450C22148yescomplemented
39#11763389C22148yescomplemented
40#11763384C22148yescomplemented
41C2×#10587630C2213yescomplemented
42C2×#10587633C2213yescomplemented
43C2×#10587561C2213yescomplemented
44#11763318C22148yescomplemented
45C2×#10587580C2216yescomplemented
46C2×#10587580C2216yescomplemented
47C2×#10587580C2213yescomplemented
48C2×#10587569C2213yescomplemented
49C2×#10587583C2213yescomplemented
50C2×#10587610C2213yes—
51C2×#10587582C2213yescomplemented
52C2×#10587582C2216yescomplemented
53C2×#10587564C2213yes—
54C2×#10587632C2213yescomplemented
55C2×#10587632C2213yescomplemented
56C22⋊Q8×D17C22148yescomplemented
57C2×#10587581C2216yescomplemented
58C2×#10587581C2213yescomplemented
59C2×#10587616C2213yescomplemented
60C2×#10587570C2213yescomplemented
61C2×#10587570C2216yescomplemented
62C2×#10587625C2211yescharacteristic
63C2×#10587568C2213yes—
64C2×#10587623C2213yes—
65#11763291C22116yescomplemented
66C2×Q8×Dic17C2211yescharacteristic, complemented
67C2×C4×D68C2213yescomplemented
68C2×C4×D68C2213yescomplemented
69C2×#10587579C2213yescomplemented
70C2×C4×C22⋊D17C2213yes—
71C2×C4×C22⋊D17C2213yescomplemented
72C2×#10587558C2213yescomplemented
73C2×C4⋊C4×D17C2213yescomplemented
74C2×C4⋊C4×D17C2216yescomplemented
75C2×C22⋊C4×D17C2216yes—
76C23×Q8×C17C2211yescharacteristic
77C23×Q8×C17C2211yescharacteristic, complemented
78D4×Q8×C17C22116yescomplemented
79C2×C17×C4⋊Q8C2213yescomplemented
80C2×C17×C22⋊Q8C2213yes—
81C2×C17×C22⋊Q8C2213yescomplemented
82C2×C4×Q8×C17C2211yescharacteristic, complemented
83C2×C4×D4×C17C2213yes—
84C24×D17C2313yes—
85C22×Q8×C17—28no—
86C22×Q8×C17—28no—
87C22×Q8×C17C2318yes—
88C22×Q8×C17C2313yes—
89C22×Q8×C17C2313yes—
90C22×Q8×C17C2311yescharacteristic
91C22×Q8×C17C2318yescomplemented
92C22×D4×C17C2311yescharacteristic
93C23×C4×C17C2313yes—
94C23×C4×C17C2313yes—
95C22×C22⋊D17C2311yescharacteristic
96C22×C22⋊D17C2313yes—
97C22×C22⋊D17C2311yescharacteristic
98C22×C22⋊D17C2313yes—
99C23×Dic17C2311yescharacteristic
100#10587694—2128no—
101C2×#63256—28no—
102C2×#63256—2128no—
103C2×#63256—224no—
104C2×#63256—224no—
105C2×#63256—224no—
106C2×#63256D4116yescomplemented
107C2×#63256C23124yes—
108C2×#63256C2318yes—
109C2×#63256C23124yes—
110C2×#63256C2318yes—
111C2×#63256C23124yescomplemented
112C2×Q8×D17—28no—
113C2×Q8×D17—224no—
114C2×Q8×D17C2318yescomplemented
115C2×Q8×D17C23124yescomplemented
116C2×#63252—224no—
117C2×#63252—224no—
118C2×#63252C23124yescomplemented
119C2×#63252C23124yescomplemented
120C22×D68—224no—
121C22×D68C2313yes—
122C22×D68C2316yes—
123C22×D68C2313yes—
124C22×D68C23124yes—
125C22×D68C2313yes—
126C22×D68C2313yes—
127C22×C4×D17—224no—
128C22×C4×D17C2316yes—
129C22×C4×D17C2313yes—
130C22×C4×D17C2313yes—
131C22×C4×D17C2313yes—
132C22×C4×D17C2313yes—
133C22×C4×D17C23124yes—
134C22×C4×D17C2316yes—
135C22×C4×D17C2313yes—
136C22×Dic34C2313yes—
137C22×Dic34C2313yes—
138C17×C4⋊Q8C23124yescomplemented
139C17×C22⋊Q8C23124yes—
140C17×C22⋊Q8C23124yescomplemented
141C4×Q8×C17C2318yescomplemented
142C4×D4×C17C23124yes—
143C2×C4⋊C4×C17C2313yes—
144C2×C4⋊C4×C17C2313yes—
145C2×C4⋊C4×C17C2316yes—
146C2×C22⋊C4×C17C2313yes—
147C2×C22⋊C4×C17C2313yes—
148C2×C42×C17C2313yes—
149C2×C22⋊Dic17C2313yes—
150C2×C22⋊Dic17C2311yescharacteristic
151#10587633C23124yescomplemented
152#10587632C23124yescomplemented
153#10587632C23124yescomplemented
154Q8×Dic17C2318yescomplemented
155#10587630C23124yescomplemented
156#10587625C2318yes—
157#10587623C23124yes—
158#10587616C23124yescomplemented
159C4×C22⋊D17C23124yes—
160C4×C22⋊D17C23124yescomplemented
161C2×#63227C2316yes—
162C2×#63227C2316yes—
163C2×#63227C2313yes—
164C2×#63227C2313yes—
165C2×#63227C2313yes—
166C2×#63227C2313yes—
167C2×#63227C2311yescharacteristic
168C2×#63227C2313yes—
169C2×C4⋊Dic17C2313yes—
170C2×C4⋊Dic17C2313yes—
171#10587610C23124yes—
172C2×#63225C2313yes—
173C2×#63225C2313yes—
174C2×#63225C2316yes—
175C2×#63225C2311yescharacteristic
176C2×#63225C2313yes—
177C2×C4×Dic17C2313yes—
178#10587583C23124yescomplemented
179#10587582C23148yescomplemented
180#10587582C23124yescomplemented
181#10587581C23148yescomplemented
182#10587581C23124yescomplemented
183#10587580C23148yescomplemented
184#10587580C23124yescomplemented
185#10587580C23148yescomplemented
186#10587579C23124yescomplemented
187C4⋊C4×D17C23148yescomplemented
188C4⋊C4×D17C23124yescomplemented
189#10587570C23148yescomplemented
190#10587570C23124yescomplemented
191#10587569C23124yescomplemented
192#10587568C23124yes—
193C22⋊C4×D17C23148yes—
194#10587564C23124yes—
195#10587561C23124yescomplemented
196C4×D68C23124yescomplemented
197C4×D68C23124yescomplemented
198#10587558C23124yescomplemented
199C24×C17C2411yescharacteristic
200C24×C17C2411yescharacteristic
201C23×D17—212no—
202C23×D17—212no—
203C23×D17—46no—
204C23×D17C2411yescharacteristic
205C23×D17C2413yes—
206C23×D17C24112yes—
207C23×D17C2413yes—
208C2×Q8×C17—232no—
209C2×Q8×C17—232no—
210C2×Q8×C17—212no—
211C2×Q8×C17—212no—
212C2×Q8×C17C2×D418yes—
213C2×Q8×C17C24112yes—
214C2×Q8×C17C24112yes—
215C2×Q8×C17C2414yes—
216C2×D4×C17—24no—
217C2×D4×C17C2414yes—
218C22×C4×C17—212no—
219C22×C4×C17—212no—
220C22×C4×C17C24112yes—
221C22×C4×C17C24112yes—
222C22×C4×C17C2413yes—
223C22×C4×C17C2413yes—
224C22×C4×C17C2413yes—
225C22×C4×C17C2411yescharacteristic
226C22×C4×C17C2413yes—
227C2×C22⋊D17—24no—
228C2×C22⋊D17—212no—
229C2×C22⋊D17—24no—
230C2×C22⋊D17—46no—
231C2×C22⋊D17C24112yes—
232C2×C22⋊D17C2414yes—
233C2×C22⋊D17C2414yes—
234C2×C22⋊D17C24112yes—
235C22×Dic17—24no—
236C22×Dic17C2413yes—
237C22×Dic17C2414yes—
238C22×Dic17C2411yescharacteristic
239C22×Dic17C2413yes—
240C22×Dic17C2411yescharacteristic
241C22×Dic17C2411yescharacteristic
242#63256—232no—
243#63256—296no—
244#63256—296no—
245#63256—296no—
246#63256C2×D4164yescomplemented
247Q8×D17—232no—
248Q8×D17—296no—
249#63252—296no—
250#63252—296no—
251C2×D68—224no—
252C2×D68—212no—
253C2×D68—212no—
254C2×D68—296no—
255C2×D68—46no—
256C2×D68C2×D4124yes—
257C2×D68C24112yes—
258C2×D68C24124yes—
259C2×D68C24112yes—
260C2×D68C24112yes—
261C2×D68C24112yes—
262C2×C4×D17—212no—
263C2×C4×D17—224no—
264C2×C4×D17—212no—
265C2×C4×D17—212no—
266C2×C4×D17—212no—
267C2×C4×D17—296no—
268C2×C4×D17—412no—
269C2×C4×D17C2×D4124yes—
270C2×C4×D17C24112yes—
271C2×C4×D17C24112yes—
272C2×C4×D17C24112yes—
273C2×C4×D17C24112yes—
274C2×C4×D17C24124yes—
275C2×C4×D17C24124yes—
276C2×C4×D17C24112yes—
277C2×Dic34—212no—
278C2×Dic34—212no—
279C2×Dic34C24112yes—
280C2×Dic34C24112yes—
281C4⋊C4×C17C24124yes—
282C4⋊C4×C17C24112yes—
283C4⋊C4×C17C24112yes—
284C22⋊C4×C17C24112yes—
285C22⋊C4×C17C24112yes—
286C42×C17C24112yes—
287C22⋊Dic17C24112yes—
288C22⋊Dic17C2414yes—
289#63227C24112yes—
290#63227C24112yes—
291#63227C2414yes—
292#63227C24112yes—
293#63227C24124yes—
294#63227C24124yes—
295#63227C24112yes—
296#63227C24112yes—
297C4⋊Dic17C24112yes—
298C4⋊Dic17C24112yes—
299#63225C2414yes—
300#63225C24112yes—
301#63225C24112yes—
302#63225C24112yes—
303#63225C24124yes—
304C4×Dic17C24112yes—
305C2×#3489—171nomaximal, Sylow
306C23×C17—22no—
307C23×C17—22no—
308C23×C17—22no—
309C23×C17—22no—
310C23×C17—22no—
311C23×C172−1+414yescomplemented
312C23×C17C2512yes—
313C23×C17C2512yes—
314C23×C17C2511yescharacteristic
315C22×D17—26no—
316C22×D17—26no—
317C22×D17—22no—
318C22×D17—26no—
319C22×D17—22no—
320C22×D17—26no—
321C22×D17—224no—
322C22×D17—22no—
323C22×D17—26no—
324C22×D17—224no—
325C22×D17—412no—
326C22×D17—448no—
327C22×D17C22×D4112yes—
328C22×D17C2512yes—
329C22×D17C2516yes—
330C22×D17C2516yes—
331Q8×C17—224no—
332Q8×C17—224no—
333Q8×C17C22×D4116yes—
334D4×C17—28no—
335C2×C4×C17—26no—
336C2×C4×C17—26no—
337C2×C4×C17—22no—
338C2×C4×C17—26no—
339C2×C4×C17—224no—
340C2×C4×C17—224no—
341C2×C4×C17C22×D4112yes—
342C2×C4×C17C2512yes—
343C2×C4×C17C2516yes—
344C2×C4×C17C2516yes—
345C2×C4×C17C2516yes—
346C2×C4×C17C2516yes—
347C22⋊D17—28no—
348C22⋊D17—224no—
349C22⋊D17—28no—
350C22⋊D17—412no—
351C2×Dic17—26no—
352C2×Dic17—22no—
353C2×Dic17—22no—
354C2×Dic17—26no—
355C2×Dic17—28no—
356C2×Dic17C22×D414yes—
357C2×Dic17C2516yes—
358C2×Dic17C2512yes—
359C2×Dic17C2516yes—
360C2×Dic17C2512yes—
361C2×Dic17C2512yes—
362D68—248no—
363D68—224no—
364D68—224no—
365D68—412no—
366D68C22×D4148yes—
367C4×D17—224no—
368C4×D17—248no—
369C4×D17—224no—
370C4×D17—224no—
371C4×D17—224no—
372C4×D17—424no—
373C4×D17C22×D4148yes—
374Dic34—224no—
375Dic34—224no—
376C22×2−1+4—171no—
377C23×#41—171no—
378#3489—1732no—
379C2×D4×Q8—171no—
380C2×D4×Q8D1711yescharacteristic, complemented
381C2×#548—171no—
382C2×#548—171no—
383C2×#547—173no—
384C2×#547—173no—
385C2×#546—173no—
386C2×#546—173no—
387C2×#537—173no—
388C2×#536—173no—
389C2×#525—173no—
390C22×C22⋊Q8—173no—
391C2×#520—171no—
392C22×C17—22no—
393C22×C17—22no—
394C22×C17—28no—
395C22×C17—22no—
396C22×C17—22no—
397C22×C17—22no—
398C22×C17—44no—
399C22×C17C23×D412yes—
400C22×C17C2×2−1+412yes—
401C22×C17C2×2−1+414yescomplemented
402C22×C17#58512yes—
403C22×C17C2611yescharacteristic
404C2×D17—26no—
405C2×D17—26no—
406C2×D17—224no—
407C2×D17—22no—
408C2×D17—26no—
409C2×D17—22no—
410C2×D17—26no—
411C2×D17—22no—
412C2×D17—26no—
413C2×D17—448no—
414C2×D17—44no—
415C2×D17—412no—
416C2×D17C23×D4112yes—
417C4×C17—26no—
418C4×C17—26no—
419C4×C17—22no—
420C4×C17—26no—
421C4×C17C23×D4112yes—
422Dic17—26no—
423Dic17—22no—
424Dic17—22no—
425Dic17—26no—
426Dic17C23×D414yes—
427C2×2−1+4—1716no—
428C2×2−1+4—3416no—
429C22×#41—171no—
430C22×#41—173no—
431C22×#41—173no—
432C22×#41—171no—
433C22×#41—1716no—
434C22×#41—173no—
435C22×#41—173no—
436C22×#41—173no—
437C22×#41—3416no—
438C23×Q8—173no—
439C23×Q8—171no—
440C23×Q8C2×D1711yescharacteristic
441C23×Q8C2×D1711yescharacteristic, complemented
442C23×D4—173no—
443C24×C4—173no—
444D4×Q8—1716no—
445D4×Q8C2×D17116yescomplemented
446#548—1716no—
447#548—1716no—
448#547—1748no—
449#547—1748no—
450#546—1748no—
451#546—1748no—
452#537—1748no—
453#536—1748no—
454C2×C4⋊Q8—173no—
455C2×C4⋊Q8C2×D1713yescomplemented
456C2×#124—173no—
457C2×#124—173no—
458#525—1748no—
459C2×#123—173no—
460C2×#123—176no—
461C2×#123—176no—
462C2×#123—173no—
463C2×C22⋊Q8—173no—
464C2×C22⋊Q8—173no—
465C2×C22⋊Q8—173no—
466C2×C22⋊Q8—1748no—
467C2×C22⋊Q8—176no—
468C2×C22⋊Q8—173no—
469C2×C22⋊Q8—173no—
470C2×C22⋊Q8—173no—
471C2×C22⋊Q8C2×D1713yes—
472C2×C22⋊Q8C2×D1713yescomplemented
473C2×#121—171no—
474C2×#121—173no—
475C2×#121—176no—
476C2×#121—173no—
477C2×#121—173no—
478C2×#121—176no—
479C2×#120—173no—
480C2×#120—173no—
481#520—1716no—
482C2×C4×Q8—171no—
483C2×C4×Q8C2×D1711yescharacteristic, complemented
484C2×C4×D4—173no—
485C2×C4×D4—173no—
486C2×C4×D4—173no—
487C2×C4×D4—173no—
488C2×C4×D4—173no—
489C2×C4×D4C2×D1713yes—
490C2×#117—173no—
491C22×C4⋊C4—173no—
492C22×C4⋊C4—176no—
493C22×C22⋊C4—176no—
494C2×C17—24no—
495C2×C17—42no—
496C2×C17#348914yescomplemented
497C2×C17C24×D411yescharacteristic
498C2×C17C22×2−1+411yescharacteristic
499C2×C17C2×#58511yescharacteristic
500D17—212no—
501D17—42no—
502D17—46no—
503C25—173no—
5042−1+4—34128no—
505C2×#41—1716no—
506C2×#41—178no—
507C2×#41—1724no—
508C2×#41—1724no—
509C2×#41—1724no—
510C2×#41—178no—
511C2×#41—1724no—
512C2×#41—1724no—
513C2×#41—3424no—
514C2×#41—3424no—
515C2×#41—3424no—
516C2×#41—3424no—
517C2×#41—3424no—
518C2×#41—34128no—
519C2×#41—348no—
520C22×Q8—28no—
521C22×Q8—28no—
522C22×Q8—1724no—
523C22×Q8—178no—
524C22×Q8—173no—
525C22×Q8—173no—
526C22×Q8—3424no—
527C22×Q8—348no—
528C22×Q8C22×D1713yes—
529C22×Q8C22×D1713yes—
530C22×Q8C22×D1718yes—
531C22×Q8C22×D1711yescharacteristic
532C22×Q8C22×D1718yescomplemented
533C22×D4—171no—
534C22×D4—173no—
535C22×D4—171no—
536C22×D4—173no—
537C22×D4—173no—
538C22×D4—173no—
539C22×D4—176no—
540C22×D4—173no—
541C22×D4—1724no—
542C22×D4—173no—
543C22×D4—3424no—
544C22×D4C22×D1711yescharacteristic
545C23×C4—173no—
546C23×C4—171no—
547C23×C4—176no—
548C23×C4—173no—
549C23×C4—173no—
550C23×C4—173no—
551C23×C4—173no—
552C23×C4—1724no—
553C23×C4—176no—
554C23×C4—3424no—
555C23×C4C22×D1713yes—
556C23×C4C22×D1713yes—
557C4⋊Q8—1724no—
558C4⋊Q8C22×D17124yescomplemented
559#124—1724no—
560#124—1724no—
561#123—1724no—
562#123—1748no—
563#123—1748no—
564#123—1724no—
565C22⋊Q8—1724no—
566C22⋊Q8—1724no—
567C22⋊Q8—1724no—
568C22⋊Q8—1748no—
569C22⋊Q8—1724no—
570C22⋊Q8—1724no—
571C22⋊Q8—1724no—
572C22⋊Q8C22×D17124yes—
573C22⋊Q8C22×D17124yescomplemented
574#121—178no—
575#121—1724no—
576#121—1748no—
577#121—1724no—
578#121—1724no—
579#121—1748no—
580#120—1724no—
581#120—1724no—
582C4×Q8—178no—
583C4×Q8C22×D1718yescomplemented
584C4×D4—1724no—
585C4×D4—1724no—
586C4×D4—1724no—
587C4×D4—1724no—
588C4×D4—1724no—
589C4×D4C22×D17124yes—
590#117—1724no—
591C2×C4⋊C4—173no—
592C2×C4⋊C4—173no—
593C2×C4⋊C4—173no—
594C2×C4⋊C4—173no—
595C2×C4⋊C4—176no—
596C2×C4⋊C4—171no—
597C2×C4⋊C4—173no—
598C2×C4⋊C4—1724no—
599C2×C4⋊C4—1748no—
600C2×C4⋊C4C22×D1713yes—
601C2×C4⋊C4C22×D1716yes—
602C2×C4⋊C4C22×D1713yes—
603C2×C22⋊C4—173no—
604C2×C22⋊C4—171no—
605C2×C22⋊C4—176no—
606C2×C22⋊C4—176no—
607C2×C22⋊C4—173no—
608C2×C22⋊C4—173no—
609C2×C22⋊C4—171no—
610C2×C22⋊C4—173no—
611C2×C22⋊C4—173no—
612C2×C22⋊C4—173no—
613C2×C22⋊C4—1748no—
614C2×C22⋊C4C22×D1713yes—
615C2×C22⋊C4C22×D1713yes—
616C2×C42—173no—
617C2×C42C22×D1713yes—
618C17C2×#348911yescharacteristic, complemented, Sylow
619C24—173no—
620C24—173no—
621C24—171no—
622C24—1712no—
623C24—3412no—
624C24—3412no—
625C24—686no—
626C24C23×D1711yescharacteristic
627C24C23×D1711yescharacteristic
628#41—1764no—
629#41—3496no—
630#41—3496no—
631#41—3496no—
632#41—3496no—
633#41—3496no—
634#41—3432no—
635C2×Q8—232no—
636C2×Q8—232no—
637C2×Q8—212no—
638C2×Q8—212no—
639C2×Q8—1712no—
640C2×Q8—1712no—
641C2×Q8—3412no—
642C2×Q8—3496no—
643C2×Q8—3432no—
644C2×Q8—3412no—
645C2×Q8D4×D1718yes—
646C2×Q8C23×D17112yes—
647C2×Q8C23×D17112yes—
648C2×Q8C23×D1714yes—
649C2×D4—24no—
650C2×D4—174no—
651C2×D4—1712no—
652C2×D4—174no—
653C2×D4—1712no—
654C2×D4—1724no—
655C2×D4—1712no—
656C2×D4—1712no—
657C2×D4—1724no—
658C2×D4—1712no—
659C2×D4—1712no—
660C2×D4—3496no—
661C2×D4—3424no—
662C2×D4—3412no—
663C2×D4—344no—
664C2×D4—3412no—
665C2×D4—344no—
666C2×D4—3412no—
667C2×D4—686no—
668C2×D4—686no—
669C2×D4C23×D1714yes—
670C22×C4—212no—
671C22×C4—212no—
672C22×C4—171no—
673C22×C4—1724no—
674C22×C4—1712no—
675C22×C4—174no—
676C22×C4—171no—
677C22×C4—173no—
678C22×C4—173no—
679C22×C4—171no—
680C22×C4—1724no—
681C22×C4—1712no—
682C22×C4—1712no—
683C22×C4—1712no—
684C22×C4—1712no—
685C22×C4—1724no—
686C22×C4—3412no—
687C22×C4—3496no—
688C22×C4—3412no—
689C22×C4—3424no—
690C22×C4—344no—
691C22×C4—3412no—
692C22×C4—3412no—
693C22×C4—6812no—
694C22×C4C23×D17112yes—
695C22×C4C23×D17112yes—
696C22×C4C23×D1711yescharacteristic
697C22×C4C23×D1713yes—
698C22×C4C23×D1713yes—
699C22×C4C23×D1713yes—
700C22×C4C23×D1713yes—
701C4⋊C4—1712no—
702C4⋊C4—1712no—
703C4⋊C4—1712no—
704C4⋊C4—1712no—
705C4⋊C4—1724no—
706C4⋊C4—174no—
707C4⋊C4—1712no—
708C4⋊C4C23×D17112yes—
709C4⋊C4C23×D17124yes—
710C4⋊C4C23×D17112yes—
711C22⋊C4—1712no—
712C22⋊C4—174no—
713C22⋊C4—1724no—
714C22⋊C4—1724no—
715C22⋊C4—1712no—
716C22⋊C4—1712no—
717C22⋊C4—174no—
718C22⋊C4—1712no—
719C22⋊C4—1712no—
720C22⋊C4—1712no—
721C22⋊C4C23×D17112yes—
722C22⋊C4C23×D17112yes—
723C42—1712no—
724C42C23×D17112yes—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—1712no—
731C23—176no—
732C23—176no—
733C23—172no—
734C23—3424no—
735C23—346no—
736C23—346no—
737C23—342no—
738C23—346no—
739C23—342no—
740C23—346no—
741C23—3424no—
742C23—342no—
743C23—346no—
744C23—6812no—
745C23—6848no—
746C23#1058769414yescomplemented
747C23C24×D1712yes—
748C23C24×D1712yes—
749C23C24×D1711yescharacteristic
750Q8—224no—
751Q8—224no—
752Q8—3424no—
753Q8—3424no—
754Q8C2×D4×D17116yes—
755D4—28no—
756D4—1748no—
757D4—3448no—
758D4—3424no—
759D4—348no—
760D4—3424no—
761D4—348no—
762D4—3424no—
763D4—6812no—
764D4—6812no—
765C2×C4—26no—
766C2×C4—26no—
767C2×C4—22no—
768C2×C4—26no—
769C2×C4—224no—
770C2×C4—224no—
771C2×C4—174no—
772C2×C4—172no—
773C2×C4—1748no—
774C2×C4—172no—
775C2×C4—176no—
776C2×C4—176no—
777C2×C4—172no—
778C2×C4—3424no—
779C2×C4—3424no—
780C2×C4—3448no—
781C2×C4—348no—
782C2×C4—342no—
783C2×C4—346no—
784C2×C4—342no—
785C2×C4—346no—
786C2×C4—3424no—
787C2×C4—3424no—
788C2×C4—6824no—
789C2×C4C2×D4×D17112yes—
790C2×C4C24×D1712yes—
791C2×C4C24×D1716yes—
792C2×C4C24×D1716yes—
793C2×C4C24×D1716yes—
794C2×C4C24×D1716yes—
795C22—28no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—44no—
802C22—1712no—
803C22—3424no—
804C22—346no—
805C22—346no—
806C22—342no—
807C22—346no—
808C22—342no—
809C22—346no—
810C22—342no—
811C22—346no—
812C22—6848no—
813C22—6812no—
814C22—684no—
815C22C22×D4×D1712yes—
816C22C2×#1058769412yes—
817C22C2×#1058769414yescomplemented
818C22#1176364612yes—
819C22C25×D1711yescharacteristic
820C4—26no—
821C4—26no—
822C4—22no—
823C4—26no—
824C4—174no—
825C4—342no—
826C4—346no—
827C4—342no—
828C4—346no—
829C4C22×D4×D17112yes—
830C2—24no—
831C2—42no—
832C2—3412no—
833C2—686no—
834C2—682no—
835C2#1454246114yesdirect product factor
836C2C23×D4×D1711yescharacteristic
837C2C22×#1058769411yescharacteristic
838C2C2×#1176364611yescharacteristic
subgroupG/H
centerC23C24×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC2×D4×Q8×C17C2
socleC23×C17C25
hypercenterC2×D4×Q8D17
hypocenterC17C2×#3489
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#10587694C2semidirect
2. C23×#63256C2semidirect
3. #14542461C2direct (N × H)
4. C2×Q8×C22⋊D17C2semidirect
5. C2×#11763471C2semidirect
6. C2×#11763470C2semidirect
7. C2×#11763462C2semidirect
8. C2×#11763461C2semidirect
9. C2×#11763455C2semidirect
10. C2×#11763450C2semidirect
11. C2×#11763389C2semidirect
12. C2×#11763384C2semidirect
13. C2×#11763318C2semidirect
14. C2×C22⋊Q8×D17C2semidirect
15. C2×#11763291C2semidirect
16. C2×D4×Q8×C17C2semidirect
18. C2×#10587694C22semidirect
24. C22×#63256C22semidirect
25. C22×#63256C22semidirect
26. C22×#63252C22semidirect
27. C22×#63252C22semidirect
28. C22×Q8×D17C22semidirect
29. C22×Q8×D17C22semidirect
32. Q8×C22⋊D17C22semidirect
33. #11763471C22semidirect
34. #11763470C22semidirect
35. #11763462C22semidirect
36. #11763461C22semidirect
37. #11763455C22semidirect
38. #11763450C22semidirect
39. #11763389C22semidirect
40. #11763384C22semidirect
41. C2×#10587630C22semidirect
42. C2×#10587633C22semidirect
43. C2×#10587561C22semidirect
44. #11763318C22semidirect
45. C2×#10587580C22semidirect
46. C2×#10587580C22semidirect
47. C2×#10587580C22semidirect
48. C2×#10587569C22semidirect
49. C2×#10587583C22semidirect
51. C2×#10587582C22semidirect
52. C2×#10587582C22semidirect
54. C2×#10587632C22semidirect
55. C2×#10587632C22semidirect
56. C22⋊Q8×D17C22semidirect
57. C2×#10587581C22semidirect
58. C2×#10587581C22semidirect
59. C2×#10587616C22semidirect
60. C2×#10587570C22semidirect
61. C2×#10587570C22semidirect
65. #11763291C22semidirect
66. C2×Q8×Dic17C22semidirect
67. C2×C4×D68C22semidirect
68. C2×C4×D68C22semidirect
69. C2×#10587579C22semidirect
71. C2×C4×C22⋊D17C22semidirect
72. C2×#10587558C22semidirect
73. C2×C4⋊C4×D17C22semidirect
74. C2×C4⋊C4×D17C22semidirect
77. C23×Q8×C17C22semidirect
78. D4×Q8×C17C22semidirect
79. C2×C17×C4⋊Q8C22semidirect
81. C2×C17×C22⋊Q8C22semidirect
82. C2×C4×Q8×C17C22semidirect
91. C22×Q8×C17C23semidirect
106. C2×#63256D4semidirect
111. C2×#63256C23semidirect
114. C2×Q8×D17C23semidirect
115. C2×Q8×D17C23semidirect
118. C2×#63252C23semidirect
119. C2×#63252C23semidirect
138. C17×C4⋊Q8C23semidirect
140. C17×C22⋊Q8C23semidirect
141. C4×Q8×C17C23semidirect
151. #10587633C23semidirect
152. #10587632C23semidirect
153. #10587632C23semidirect
154. Q8×Dic17C23semidirect
155. #10587630C23semidirect
158. #10587616C23semidirect
160. C4×C22⋊D17C23semidirect
178. #10587583C23semidirect
179. #10587582C23semidirect
180. #10587582C23semidirect
181. #10587581C23semidirect
182. #10587581C23semidirect
183. #10587580C23semidirect
184. #10587580C23semidirect
185. #10587580C23semidirect
186. #10587579C23semidirect
187. C4⋊C4×D17C23semidirect
188. C4⋊C4×D17C23semidirect
189. #10587570C23semidirect
190. #10587570C23semidirect
191. #10587569C23semidirect
195. #10587561C23semidirect
196. C4×D68C23semidirect
197. C4×D68C23semidirect
198. #10587558C23semidirect
246. #63256C2×D4semidirect
311. C23×C172−1+4semidirect
380. C2×D4×Q8D17semidirect
401. C22×C17C2×2−1+4semidirect
441. C23×Q8C2×D17semidirect
445. D4×Q8C2×D17semidirect
455. C2×C4⋊Q8C2×D17semidirect
472. C2×C22⋊Q8C2×D17semidirect
483. C2×C4×Q8C2×D17semidirect
496. C2×C17#3489semidirect
532. C22×Q8C22×D17semidirect
558. C4⋊Q8C22×D17semidirect
573. C22⋊Q8C22×D17semidirect
583. C4×Q8C22×D17semidirect
618. C17C2×#3489semidirect
746. C23#10587694semidirect
817. C22C2×#10587694semidirect
835. C2#14542461direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105876942
C23×#632562
#145424612
C2×Q8×C22⋊D172
C2×#117634712
C2×#117634702
C2×#117634622
C2×#117634612
C2×#117634552
C2×#117634502
C2×#117633892
C2×#117633842
C2×#117633182
C2×C22⋊Q8×D172
C2×#117632912
C2×D4×Q8×C172
C2×#348917