Finite Group Databasebeta

← C2×#22573875 #31764138

Subgroups — C2×#22573875 #31764138

Order 17152.

12366 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524089C211yesmaximal, characteristic, complemented
2C23×#11761629C211yesmaximal, characteristic, complemented
3#22573875C2132yesmaximal, direct product factor
4C2×#16864068C211yesmaximal, characteristic, complemented
5C2×#16864065C211yesmaximal, characteristic, complemented
6C2×#16864057C211yesmaximal, characteristic, complemented
7C2×#16864039C213yesmaximal, complemented
8C2×#16864037C213yesmaximal, complemented
9C2×D4×D268C213yesmaximal, complemented
10C2×#16864030C213yesmaximal, complemented
11C2×#16863976C213yesmaximal, complemented
12C2×#16863964C213yesmaximal, complemented
13C2×#16863905C213yesmaximal, complemented
14C2×#121×D67C213yesmaximal, complemented
15C2×#16863878C211yesmaximal, characteristic, complemented
16C2×#548×C67C211yesmaximal, characteristic, complemented
17C2×#14524089—216no—
18C2×#14524089C22116yescomplemented
19C22×#11761629—216no—
20C22×#11761629C2211yescharacteristic
21C22×#11761629C2213yescomplemented
22C22×#11761629C2211yescharacteristic, complemented
23C22×#11761629C2211yescharacteristic, complemented
24C22×#11761629C2213yescomplemented
25C22×#11761629C22116yescomplemented
26C22×#11761628C2213yescomplemented
27C23×D268C2213yescomplemented
28C23×D268C2213yescomplemented
29C22×D4×D67C2213yescomplemented
30C22×D4×D67C2213yescomplemented
31C22×D4×D67C2216yescomplemented
32C23×C4×D67C2213yescomplemented
33#16864068C22116yescomplemented
34#16864065C22116yescomplemented
35#16864057C22116yescomplemented
36#16864039C22148yescomplemented
37#16864037C22148yescomplemented
38D4×D268C22148yescomplemented
39#16864030C22148yescomplemented
40#16863976C22148yescomplemented
41#16863964C22148yescomplemented
42C2×#14524040C2213yescomplemented
43C2×#14524039C2213yescomplemented
44C2×#14524032C2213yescomplemented
45#16863905C22148yescomplemented
46C2×#14524028C2213yescomplemented
47C2×#14524025C2213yescomplemented
48C2×#14524021C2213yescomplemented
49C2×#14524020C2211yescharacteristic, complemented
50C2×#14524019C2213yescomplemented
51C2×#14524018C2213yescomplemented
52C2×#14524018C2216yescomplemented
53C2×#14524018C2213yescomplemented
54C2×#14524017C2213yescomplemented
55C2×#14524017C2213yescomplemented
56C2×#14524016C2216yescomplemented
57C2×#14524016C2216yescomplemented
58C2×#14524016C2213yescomplemented
59C2×#14524015C2213yescomplemented
60C2×#14524014C2213yescomplemented
61#121×D67C22148yescomplemented
62C2×#14524013C2216yescomplemented
63C2×#14524013C2213yescomplemented
64C2×#14524013C2216yescomplemented
65C2×#14524011C2213yescomplemented
66#16863878C22116yescomplemented
67C2×Q8×Dic67C2211yescharacteristic, complemented
68C2×C4×D268C2213yescomplemented
69C2×C4×D268C2213yescomplemented
70C2×#14524005C2213yescomplemented
71C2×C4×C22⋊D67C2213yescomplemented
72C2×C4×C22⋊D67C2213yescomplemented
73C2×#14524000C2213yescomplemented
74C2×C4⋊C4×D67C2213yescomplemented
75C2×C22⋊C4×D67C2216yescomplemented
76C22×#41×C67C2211yescharacteristic, complemented
77C23×Q8×C67C2211yescharacteristic, complemented
78#548×C67C22116yescomplemented
79C2×#124×C67C2213yescomplemented
80C2×C22⋊Q8×C67C2213yescomplemented
81C2×#121×C67C2213yescomplemented
82C2×C4×Q8×C67C2211yescharacteristic, complemented
83C2×C4×D4×C67C2213yescomplemented
84C24×D67C2313yes—
85C24×D67C2316yes—
86#14524089—2128no—
87C2×#11761629—2128no—
88C2×#11761629—224no—
89C2×#11761629—224no—
90C2×#11761629—28no—
91C2×#11761629—28no—
92C2×#11761629D4116yescomplemented
93C2×#11761629C2318yes—
94C2×#11761629C23124yescomplemented
95C2×#11761629C2318yescomplemented
96C2×#11761629C2318yescomplemented
97C2×#11761629C23124yescomplemented
98C2×#11761628—224no—
99C2×#11761628C23124yescomplemented
100C22×Dic134C2311yescharacteristic
101C22×D268—224no—
102C22×D268—224no—
103C22×D268C2316yes—
104C22×D268C2313yes—
105C22×D268C2313yes—
106C22×D268C2313yes—
107C22×D268C2313yes—
108C22×D268C2316yes—
109C22×D268C2313yes—
110C22×D268C23124yescomplemented
111C22×D268C23124yescomplemented
112C22×C22⋊D67C2313yes—
113C22×C22⋊D67C2313yes—
114C22×C22⋊D67C2313yes—
115C22×C22⋊D67C2313yes—
116C22×C22⋊D67C2316yes—
117C2×D4×D67—224no—
118C2×D4×D67—224no—
119C2×D4×D67—424no—
120C2×D4×D67C23124yescomplemented
121C2×D4×D67C23124yescomplemented
122C2×D4×D67C23148yescomplemented
123C23×Dic67C2311yescharacteristic
124C22×C4×D67—224no—
125C22×C4×D67C2313yes—
126C22×C4×D67C2313yes—
127C22×C4×D67C2313yes—
128C22×C4×D67C2313yes—
129C22×C4×D67C2316yes—
130C22×C4×D67C2313yes—
131C22×C4×D67C23124yescomplemented
132#14524040C23124yescomplemented
133#14524039C23124yescomplemented
134#14524032C23124yescomplemented
135#14524028C23124yescomplemented
136#14524025C23124yescomplemented
137#14524021C23124yescomplemented
138#14524020C2318yescomplemented
139#14524019C23124yescomplemented
140#14524018C23124yescomplemented
141#14524018C23148yescomplemented
142#14524018C23124yescomplemented
143#14524017C23124yescomplemented
144#14524017C23124yescomplemented
145#14524016C23148yescomplemented
146#14524016C23148yescomplemented
147#14524016C23124yescomplemented
148#14524015C23124yescomplemented
149#14524014C23124yescomplemented
150#14524013C23148yescomplemented
151#14524013C23124yescomplemented
152#14524013C23148yescomplemented
153#14524011C23124yescomplemented
154Q8×Dic67C2318yescomplemented
155C4×D268C23124yescomplemented
156C4×D268C23124yescomplemented
157#14524005C23124yescomplemented
158C4×C22⋊D67C23124yescomplemented
159C4×C22⋊D67C23124yescomplemented
160#14524000C23124yescomplemented
161C2×C4⋊Dic67C2313yes—
162C2×C4⋊Dic67C2311yescharacteristic
163C2×Dic67⋊C4C2313yes—
164C2×Dic67⋊C4C2311yescharacteristic
165C2×Dic67⋊C4C2311yescharacteristic
166C2×Dic67⋊C4C2313yes—
167C4⋊C4×D67C23124yescomplemented
168C2×C22⋊Dic67C2313yes—
169C2×C22⋊Dic67C2311yescharacteristic
170C2×(C2×D67)⋊C4C2313yes—
171C2×(C2×D67)⋊C4C2316yes—
172C2×(C2×D67)⋊C4C2313yes—
173C2×(C2×D67)⋊C4C2313yes—
174C2×(C2×D67)⋊C4C2313yes—
175C2×(C2×D67)⋊C4C2313yes—
176C2×(C2×D67)⋊C4C2313yes—
177C22⋊C4×D67C23148yescomplemented
178C2×C4×Dic67C2313yes—
179C2×#41×C67—28no—
180C2×#41×C67C2318yescomplemented
181C22×Q8×C67—28no—
182C22×Q8×C67C2313yes—
183C22×Q8×C67C2311yescharacteristic
184C22×Q8×C67C2318yescomplemented
185C22×D4×C67C2313yes—
186C22×D4×C67C2313yes—
187C23×C4×C67C2313yes—
188C23×C4×C67C2313yes—
189#124×C67C23124yescomplemented
190C22⋊Q8×C67C23124yescomplemented
191#121×C67C23124yescomplemented
192C4×Q8×C67C2318yescomplemented
193C4×D4×C67C23124yescomplemented
194C2×C4⋊C4×C67C2313yes—
195C2×C4⋊C4×C67C2313yes—
196C2×C22⋊C4×C67C2311yescharacteristic
197C2×C22⋊C4×C67C2313yes—
198C2×C22⋊C4×C67C2316yes—
199C2×C42×C67C2313yes—
200C23×D67—212no—
201C23×D67—212no—
202C23×D67—224no—
203C23×D67—46no—
204C23×D67—412no—
205C23×D67—412no—
206C23×D67C2413yes—
207C23×D67C2413yes—
208C23×D67C24112yes—
209C23×D67C2413yes—
210C23×D67C24124yes—
211#11761629—232no—
212#11761629—232no—
213#11761629—296no—
214#11761629—296no—
215#11761629C2×D4164yescomplemented
216#11761628—296no—
217C2×Dic134—24no—
218C2×Dic134C2414yes—
219C2×D268—212no—
220C2×D268—224no—
221C2×D268—212no—
222C2×D268—212no—
223C2×D268—296no—
224C2×D268—296no—
225C2×D268—412no—
226C2×D268—46no—
227C2×D268C2×D4124yescomplemented
228C2×D268C24124yes—
229C2×D268C24112yes—
230C2×D268C24112yes—
231C2×D268C24112yes—
232C2×D268C24112yes—
233C2×D268C24124yes—
234C2×D268C24112yes—
235C2×C22⋊D67—212no—
236C2×C22⋊D67—212no—
237C2×C22⋊D67—212no—
238C2×C22⋊D67—412no—
239C2×C22⋊D67—46no—
240C2×C22⋊D67C24112yes—
241C2×C22⋊D67C24112yes—
242C2×C22⋊D67C24112yes—
243C2×C22⋊D67C24112yes—
244C2×C22⋊D67C24124yes—
245D4×D67—296no—
246D4×D67—296no—
247D4×D67—496no—
248C22×Dic67—24no—
249C22×Dic67C2411yescharacteristic
250C22×Dic67C2413yes—
251C22×Dic67C2411yescharacteristic
252C22×Dic67C2411yescharacteristic
253C22×Dic67C2414yes—
254C22×Dic67C2411yescharacteristic
255C2×C4×D67—212no—
256C2×C4×D67—212no—
257C2×C4×D67—212no—
258C2×C4×D67—212no—
259C2×C4×D67—296no—
260C2×C4×D67—412no—
261C2×C4×D67C2×D4124yescomplemented
262C2×C4×D67C24112yes—
263C2×C4×D67C24112yes—
264C2×C4×D67C24112yes—
265C2×C4×D67C24112yes—
266C2×C4×D67C24124yes—
267C2×C4×D67C24112yes—
268C4⋊Dic67C24112yes—
269C4⋊Dic67C2414yes—
270Dic67⋊C4C24112yes—
271Dic67⋊C4C2414yes—
272Dic67⋊C4C2414yes—
273Dic67⋊C4C24112yes—
274C22⋊Dic67C24112yes—
275C22⋊Dic67C2414yes—
276(C2×D67)⋊C4C24112yes—
277(C2×D67)⋊C4C24124yes—
278(C2×D67)⋊C4C24112yes—
279(C2×D67)⋊C4C24112yes—
280(C2×D67)⋊C4C24112yes—
281(C2×D67)⋊C4C24112yes—
282(C2×D67)⋊C4C24112yes—
283C4×Dic67C24112yes—
284C24×C67C2413yes—
285C24×C67C2411yescharacteristic
286#41×C67—232no—
287C2×Q8×C67—232no—
288C2×Q8×C67—212no—
289C2×Q8×C67C2×D418yescomplemented
290C2×Q8×C67C24112yes—
291C2×Q8×C67C2414yes—
292C2×D4×C67—212no—
293C2×D4×C67—212no—
294C2×D4×C67C24112yes—
295C2×D4×C67C24112yes—
296C22×C4×C67—212no—
297C22×C4×C67—212no—
298C22×C4×C67C2411yescharacteristic
299C22×C4×C67C2413yes—
300C22×C4×C67C2413yes—
301C22×C4×C67C2411yescharacteristic
302C22×C4×C67C24112yes—
303C22×C4×C67C24112yes—
304C22×C4×C67C2413yes—
305C4⋊C4×C67C24112yes—
306C4⋊C4×C67C24112yes—
307C22⋊C4×C67C2414yes—
308C22⋊C4×C67C24112yes—
309C22⋊C4×C67C24124yes—
310C42×C67C24112yes—
311C23×C67—22no—
312C23×C67—22no—
313C23×C67—26no—
314C23×C67—26no—
315C23×C67—26no—
316C23×C67H(5,𝔽2)14yescomplemented
317C23×C67C2516yes—
318C23×C67C2512yes—
319C23×C67C2511yescharacteristic
320C22×D67—26no—
321C22×D67—26no—
322C22×D67—26no—
323C22×D67—26no—
324C22×D67—26no—
325C22×D67—26no—
326C22×D67—224no—
327C22×D67—26no—
328C22×D67—26no—
329C22×D67—224no—
330C22×D67—248no—
331C22×D67—412no—
332C22×D67—424no—
333C22×D67—424no—
334C22×D67—448no—
335C22×D67—848no—
336C22×D67C22×D4112yes—
337C22×D67C2516yes—
338C22×D67C2516yes—
339C22×D67C2516yes—
340Q8×C67—224no—
341Q8×C67C22×D4116yescomplemented
342D4×C67—224no—
343D4×C67—224no—
344C2×C4×C67—22no—
345C2×C4×C67—26no—
346C2×C4×C67—26no—
347C2×C4×C67—22no—
348C2×C4×C67—224no—
349C2×C4×C67—224no—
350C2×C4×C67C22×D4112yes—
351C2×C4×C67C2512yes—
352C2×C4×C67C2516yes—
353C2×C4×C67C2516yes—
354C2×C4×C67C2512yes—
355C2×C4×C67C2516yes—
356C22⋊D67—224no—
357C22⋊D67—224no—
358C22⋊D67—224no—
359C22⋊D67—424no—
360C22⋊D67—412no—
361C2×Dic67—22no—
362C2×Dic67—22no—
363C2×Dic67—26no—
364C2×Dic67—22no—
365C2×Dic67—28no—
366C2×Dic67C22×D414yes—
367C2×Dic67C2512yes—
368C2×Dic67C2516yes—
369C2×Dic67C2512yes—
370C2×Dic67C2512yes—
371C2×Dic67C2512yes—
372D268—224no—
373D268—248no—
374D268—224no—
375D268—224no—
376D268—424no—
377D268—412no—
378D268C22×D4148yescomplemented
379C4×D67—224no—
380C4×D67—224no—
381C4×D67—224no—
382C4×D67—224no—
383C4×D67—424no—
384C4×D67C22×D4148yescomplemented
385Dic134—28no—
386C22×C67—22no—
387C22×C67—22no—
388C22×C67—28no—
389C22×C67—26no—
390C22×C67—26no—
391C22×C67—26no—
392C22×C67—412no—
393C22×C67C23×D412yes—
394C22×C67C2×H(5,𝔽2)12yes—
395C22×C67C2×H(5,𝔽2)14yescomplemented
396C22×C67#58512yes—
397C22×C67C2611yescharacteristic
398C2×D67—26no—
399C2×D67—26no—
400C2×D67—224no—
401C2×D67—26no—
402C2×D67—26no—
403C2×D67—26no—
404C2×D67—26no—
405C2×D67—26no—
406C2×D67—26no—
407C2×D67—448no—
408C2×D67—412no—
409C2×D67—412no—
410C2×D67—848no—
411C2×D67C23×D4112yes—
412C4×C67—22no—
413C4×C67—26no—
414C4×C67—26no—
415C4×C67—22no—
416C4×C67C23×D4112yes—
417Dic67—22no—
418Dic67—22no—
419Dic67—26no—
420Dic67—22no—
421Dic67C23×D414yes—
422C2×#3488—671nomaximal, Sylow
423C2×C67—24no—
424C2×C67—46no—
425C2×C67#348814yescomplemented
426C2×C67C24×D411yescharacteristic
427C2×C67C22×H(5,𝔽2)11yescharacteristic
428C2×C67C2×#58511yescharacteristic
429D67—212no—
430D67—46no—
431D67—46no—
432C22×H(5,𝔽2)—671no—
433C23×#41—671no—
434#3488—6732no—
435C2×#550—671no—
436C2×#550—671no—
437C2×#548—671no—
438C2×#548D6711yescharacteristic, complemented
439C2×#546—673no—
440C2×#546—673no—
441C2×D42—673no—
442C2×D42—673no—
443C2×#537—673no—
444C2×#535—673no—
445C2×#525—673no—
446C22×#121—673no—
447C2×#520—671no—
448C67C2×#348811yescharacteristic, complemented, Sylow
449C2×H(5,𝔽2)—6716no—
450C2×H(5,𝔽2)—13416no—
451C22×#41—671no—
452C22×#41—673no—
453C22×#41—673no—
454C22×#41—671no—
455C22×#41—671no—
456C22×#41—6716no—
457C22×#41—673no—
458C22×#41—13416no—
459C22×#41C2×D6711yescharacteristic, complemented
460C23×Q8C2×D6711yescharacteristic, complemented
461C23×D4—676no—
462C23×D4—673no—
463C23×D4—673no—
464C23×D4—673no—
465C23×D4—673no—
466C24×C4—673no—
467#550—6716no—
468#550—6716no—
469#548—6716no—
470#548C2×D67116yescomplemented
471#546—6748no—
472#546—6748no—
473D42—6748no—
474D42—6748no—
475#537—6748no—
476#535—6748no—
477C2×#127—673no—
478C2×#127—673no—
479C2×#124—673no—
480C2×#124C2×D6713yescomplemented
481#525—6748no—
482C2×#123—673no—
483C2×#123—673no—
484C2×C22⋊Q8—673no—
485C2×C22⋊Q8—673no—
486C2×C22⋊Q8—671no—
487C2×C22⋊Q8C2×D6713yescomplemented
488C2×#121—673no—
489C2×#121—673no—
490C2×#121—673no—
491C2×#121—673no—
492C2×#121—6748no—
493C2×#121—673no—
494C2×#121—676no—
495C2×#121—673no—
496C2×#121—676no—
497C2×#121—673no—
498C2×#121—676no—
499C2×#121C2×D6713yescomplemented
500C2×#120—673no—
501C2×#120—673no—
502C2×#120—676no—
503C2×#120—676no—
504#520—6716no—
505C2×C4×Q8—671no—
506C2×C4×Q8C2×D6711yescharacteristic, complemented
507C2×C4×D4—673no—
508C2×C4×D4—673no—
509C2×C4×D4—673no—
510C2×C4×D4—673no—
511C2×C4×D4—673no—
512C2×C4×D4C2×D6713yescomplemented
513C2×#117—673no—
514C22×C4⋊C4—673no—
515C22×C22⋊C4—676no—
516C25—676no—
517C25—673no—
518H(5,𝔽2)—134128no—
519C2×#41—28no—
520C2×#41—6716no—
521C2×#41—678no—
522C2×#41—6724no—
523C2×#41—6724no—
524C2×#41—678no—
525C2×#41—678no—
526C2×#41—6724no—
527C2×#41—13424no—
528C2×#41—13424no—
529C2×#41—13424no—
530C2×#41—134128no—
531C2×#41—1348no—
532C2×#41—1348no—
533C2×#41C22×D6718yescomplemented
534C22×Q8—28no—
535C22×Q8—671no—
536C22×Q8C22×D6713yes—
537C22×Q8C22×D6711yescharacteristic
538C22×Q8C22×D6718yescomplemented
539C22×D4—26824no—
540C22×D4—673no—
541C22×D4—676no—
542C22×D4—6748no—
543C22×D4—673no—
544C22×D4—673no—
545C22×D4—673no—
546C22×D4—6724no—
547C22×D4—6724no—
548C22×D4—673no—
549C22×D4—676no—
550C22×D4—673no—
551C22×D4—676no—
552C22×D4—673no—
553C22×D4—673no—
554C22×D4—673no—
555C22×D4—6724no—
556C22×D4—6724no—
557C22×D4—13424no—
558C22×D4—13424no—
559C22×D4—13424no—
560C22×D4—13424no—
561C22×D4C22×D6713yes—
562C22×D4C22×D6713yes—
563C23×C4—676no—
564C23×C4—673no—
565C23×C4—671no—
566C23×C4—673no—
567C23×C4—673no—
568C23×C4—673no—
569C23×C4—673no—
570C23×C4—6724no—
571C23×C4—13424no—
572C23×C4C22×D6713yes—
573C23×C4C22×D6713yes—
574#127—6724no—
575#127—6724no—
576#124—6724no—
577#124C22×D67124yescomplemented
578#123—6724no—
579#123—6724no—
580C22⋊Q8—6724no—
581C22⋊Q8—6724no—
582C22⋊Q8—678no—
583C22⋊Q8C22×D67124yescomplemented
584#121—6724no—
585#121—6724no—
586#121—6724no—
587#121—6724no—
588#121—6724no—
589#121—6748no—
590#121—6724no—
591#121—6748no—
592#121—6724no—
593#121—6748no—
594#121C22×D67124yescomplemented
595#120—6724no—
596#120—6724no—
597#120—6748no—
598#120—6748no—
599C4×Q8—678no—
600C4×Q8C22×D6718yescomplemented
601C4×D4—6724no—
602C4×D4—6724no—
603C4×D4—6724no—
604C4×D4—6724no—
605C4×D4—6724no—
606C4×D4C22×D67124yescomplemented
607#117—6724no—
608C2×C4⋊C4—673no—
609C2×C4⋊C4—673no—
610C2×C4⋊C4—671no—
611C2×C4⋊C4—671no—
612C2×C4⋊C4—671no—
613C2×C4⋊C4—673no—
614C2×C4⋊C4—6724no—
615C2×C4⋊C4C22×D6713yes—
616C2×C4⋊C4C22×D6713yes—
617C2×C22⋊C4—673no—
618C2×C22⋊C4—671no—
619C2×C22⋊C4—673no—
620C2×C22⋊C4—676no—
621C2×C22⋊C4—673no—
622C2×C22⋊C4—673no—
623C2×C22⋊C4—673no—
624C2×C22⋊C4—673no—
625C2×C22⋊C4—673no—
626C2×C22⋊C4—6748no—
627C2×C22⋊C4C22×D6716yes—
628C2×C22⋊C4C22×D6711yescharacteristic
629C2×C22⋊C4C22×D6713yes—
630C2×C42—673no—
631C2×C42C22×D6713yes—
632C24—2686no—
633C24—26812no—
634C24—26812no—
635C24—6724no—
636C24—6712no—
637C24—673no—
638C24—673no—
639C24—673no—
640C24—13412no—
641C24—13424no—
642C24—13412no—
643C24C23×D6713yes—
644C24C23×D6711yescharacteristic
645#41—232no—
646#41—6764no—
647#41—13496no—
648#41—13496no—
649#41—13496no—
650#41—13432no—
651#41—13432no—
652C2×Q8—232no—
653C2×Q8—212no—
654C2×Q8—674no—
655C2×Q8—1344no—
656C2×Q8D4×D6718yescomplemented
657C2×Q8C23×D67112yes—
658C2×Q8C23×D6714yes—
659C2×D4—212no—
660C2×D4—212no—
661C2×D4—26812no—
662C2×D4—2686no—
663C2×D4—26896no—
664C2×D4—26812no—
665C2×D4—2686no—
666C2×D4—6712no—
667C2×D4—6724no—
668C2×D4—6712no—
669C2×D4—6712no—
670C2×D4—6712no—
671C2×D4—6724no—
672C2×D4—6712no—
673C2×D4—6724no—
674C2×D4—6712no—
675C2×D4—6724no—
676C2×D4—6712no—
677C2×D4—6712no—
678C2×D4—6712no—
679C2×D4—13496no—
680C2×D4—13496no—
681C2×D4—13412no—
682C2×D4—13424no—
683C2×D4—13496no—
684C2×D4—13412no—
685C2×D4—13496no—
686C2×D4—13412no—
687C2×D4—13412no—
688C2×D4—13412no—
689C2×D4—13412no—
690C2×D4C23×D67112yes—
691C2×D4C23×D67112yes—
692C22×C4—212no—
693C22×C4—212no—
694C22×C4—26812no—
695C22×C4—6724no—
696C22×C4—671no—
697C22×C4—6724no—
698C22×C4—6712no—
699C22×C4—674no—
700C22×C4—671no—
701C22×C4—673no—
702C22×C4—671no—
703C22×C4—671no—
704C22×C4—6712no—
705C22×C4—6712no—
706C22×C4—6712no—
707C22×C4—6712no—
708C22×C4—13412no—
709C22×C4—13496no—
710C22×C4—13412no—
711C22×C4—1344no—
712C22×C4—13412no—
713C22×C4—13412no—
714C22×C4C23×D67112yes—
715C22×C4C23×D67112yes—
716C22×C4C23×D6711yescharacteristic
717C22×C4C23×D6713yes—
718C22×C4C23×D6713yes—
719C22×C4C23×D6711yescharacteristic
720C22×C4C23×D6713yes—
721C4⋊C4—6712no—
722C4⋊C4—6712no—
723C4⋊C4—674no—
724C4⋊C4—674no—
725C4⋊C4—674no—
726C4⋊C4—6712no—
727C4⋊C4C23×D67112yes—
728C4⋊C4C23×D67112yes—
729C22⋊C4—6712no—
730C22⋊C4—674no—
731C22⋊C4—6712no—
732C22⋊C4—6724no—
733C22⋊C4—6712no—
734C22⋊C4—6712no—
735C22⋊C4—6712no—
736C22⋊C4—6712no—
737C22⋊C4—6712no—
738C22⋊C4C23×D67124yes—
739C22⋊C4C23×D6714yes—
740C22⋊C4C23×D67112yes—
741C42—6712no—
742C42C23×D67112yes—
743C23—22no—
744C23—22no—
745C23—26no—
746C23—26no—
747C23—26no—
748C23—26848no—
749C23—26812no—
750C23—26824no—
751C23—26824no—
752C23—53648no—
753C23—6712no—
754C23—676no—
755C23—676no—
756C23—676no—
757C23—13424no—
758C23—13448no—
759C23—1346no—
760C23—1346no—
761C23—1346no—
762C23—1346no—
763C23—13424no—
764C23—1346no—
765C23—1346no—
766C23—1346no—
767C23—1346no—
768C23#1452408914yescomplemented
769C23C24×D6716yes—
770C23C24×D6712yes—
771C23C24×D6711yescharacteristic
772Q8—224no—
773Q8—1348no—
774Q8C2×D4×D67116yescomplemented
775D4—224no—
776D4—224no—
777D4—26824no—
778D4—26812no—
779D4—26824no—
780D4—26812no—
781D4—6748no—
782D4—13424no—
783D4—13448no—
784D4—13424no—
785D4—13424no—
786D4—13424no—
787D4—13424no—
788D4—13424no—
789C2×C4—22no—
790C2×C4—26no—
791C2×C4—26no—
792C2×C4—22no—
793C2×C4—224no—
794C2×C4—224no—
795C2×C4—26824no—
796C2×C4—674no—
797C2×C4—672no—
798C2×C4—6748no—
799C2×C4—672no—
800C2×C4—676no—
801C2×C4—672no—
802C2×C4—672no—
803C2×C4—13424no—
804C2×C4—13424no—
805C2×C4—1348no—
806C2×C4—1342no—
807C2×C4—1342no—
808C2×C4—1346no—
809C2×C4—1342no—
810C2×C4—13424no—
811C2×C4—13424no—
812C2×C4C2×D4×D67112yes—
813C2×C4C24×D6712yes—
814C2×C4C24×D6716yes—
815C2×C4C24×D6716yes—
816C2×C4C24×D6712yes—
817C2×C4C24×D6716yes—
818C22—28no—
819C22—22no—
820C22—22no—
821C22—26no—
822C22—26no—
823C22—26no—
824C22—412no—
825C22—26848no—
826C22—26812no—
827C22—26812no—
828C22—53648no—
829C22—6712no—
830C22—1346no—
831C22—1346no—
832C22—1346no—
833C22—1346no—
834C22—1346no—
835C22—1346no—
836C22—13424no—
837C22—1346no—
838C22—1346no—
839C22C22×D4×D6712yes—
840C22C2×#1452408912yes—
841C22C2×#1452408914yescomplemented
842C22#1686423312yes—
843C22C25×D6711yescharacteristic
844C4—22no—
845C4—26no—
846C4—26no—
847C4—22no—
848C4—674no—
849C4—1342no—
850C4—1342no—
851C4—1346no—
852C4—1342no—
853C4C22×D4×D67112yes—
854C2—24no—
855C2—46no—
856C2—2686no—
857C2—2686no—
858C2—13412no—
859C2#2257387514yesdirect product factor
860C2C23×D4×D6711yescharacteristic
861C2C22×#1452408911yescharacteristic
862C2C2×#1686423311yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#548×C67C2
socleC23×C67C25
hypercenterC2×#548D67
hypocenterC67C2×#3488
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#14524089C2semidirect
2. C23×#11761629C2semidirect
3. #22573875C2direct (N × H)
4. C2×#16864068C2semidirect
5. C2×#16864065C2semidirect
6. C2×#16864057C2semidirect
7. C2×#16864039C2semidirect
8. C2×#16864037C2semidirect
9. C2×D4×D268C2semidirect
10. C2×#16864030C2semidirect
11. C2×#16863976C2semidirect
12. C2×#16863964C2semidirect
13. C2×#16863905C2semidirect
14. C2×#121×D67C2semidirect
15. C2×#16863878C2semidirect
16. C2×#548×C67C2semidirect
18. C2×#14524089C22semidirect
21. C22×#11761629C22semidirect
22. C22×#11761629C22semidirect
23. C22×#11761629C22semidirect
24. C22×#11761629C22semidirect
25. C22×#11761629C22semidirect
26. C22×#11761628C22semidirect
27. C23×D268C22semidirect
28. C23×D268C22semidirect
29. C22×D4×D67C22semidirect
30. C22×D4×D67C22semidirect
31. C22×D4×D67C22semidirect
32. C23×C4×D67C22semidirect
33. #16864068C22semidirect
34. #16864065C22semidirect
35. #16864057C22semidirect
36. #16864039C22semidirect
37. #16864037C22semidirect
38. D4×D268C22semidirect
39. #16864030C22semidirect
40. #16863976C22semidirect
41. #16863964C22semidirect
42. C2×#14524040C22semidirect
43. C2×#14524039C22semidirect
44. C2×#14524032C22semidirect
45. #16863905C22semidirect
46. C2×#14524028C22semidirect
47. C2×#14524025C22semidirect
48. C2×#14524021C22semidirect
49. C2×#14524020C22semidirect
50. C2×#14524019C22semidirect
51. C2×#14524018C22semidirect
52. C2×#14524018C22semidirect
53. C2×#14524018C22semidirect
54. C2×#14524017C22semidirect
55. C2×#14524017C22semidirect
56. C2×#14524016C22semidirect
57. C2×#14524016C22semidirect
58. C2×#14524016C22semidirect
59. C2×#14524015C22semidirect
60. C2×#14524014C22semidirect
61. #121×D67C22semidirect
62. C2×#14524013C22semidirect
63. C2×#14524013C22semidirect
64. C2×#14524013C22semidirect
65. C2×#14524011C22semidirect
66. #16863878C22semidirect
67. C2×Q8×Dic67C22semidirect
68. C2×C4×D268C22semidirect
69. C2×C4×D268C22semidirect
70. C2×#14524005C22semidirect
71. C2×C4×C22⋊D67C22semidirect
72. C2×C4×C22⋊D67C22semidirect
73. C2×#14524000C22semidirect
74. C2×C4⋊C4×D67C22semidirect
75. C2×C22⋊C4×D67C22semidirect
76. C22×#41×C67C22semidirect
77. C23×Q8×C67C22semidirect
78. #548×C67C22semidirect
79. C2×#124×C67C22semidirect
80. C2×C22⋊Q8×C67C22semidirect
81. C2×#121×C67C22semidirect
82. C2×C4×Q8×C67C22semidirect
83. C2×C4×D4×C67C22semidirect
92. C2×#11761629D4semidirect
94. C2×#11761629C23semidirect
95. C2×#11761629C23semidirect
96. C2×#11761629C23semidirect
97. C2×#11761629C23semidirect
99. C2×#11761628C23semidirect
110. C22×D268C23semidirect
111. C22×D268C23semidirect
120. C2×D4×D67C23semidirect
121. C2×D4×D67C23semidirect
122. C2×D4×D67C23semidirect
131. C22×C4×D67C23semidirect
132. #14524040C23semidirect
133. #14524039C23semidirect
134. #14524032C23semidirect
135. #14524028C23semidirect
136. #14524025C23semidirect
137. #14524021C23semidirect
138. #14524020C23semidirect
139. #14524019C23semidirect
140. #14524018C23semidirect
141. #14524018C23semidirect
142. #14524018C23semidirect
143. #14524017C23semidirect
144. #14524017C23semidirect
145. #14524016C23semidirect
146. #14524016C23semidirect
147. #14524016C23semidirect
148. #14524015C23semidirect
149. #14524014C23semidirect
150. #14524013C23semidirect
151. #14524013C23semidirect
152. #14524013C23semidirect
153. #14524011C23semidirect
154. Q8×Dic67C23semidirect
155. C4×D268C23semidirect
156. C4×D268C23semidirect
157. #14524005C23semidirect
158. C4×C22⋊D67C23semidirect
159. C4×C22⋊D67C23semidirect
160. #14524000C23semidirect
167. C4⋊C4×D67C23semidirect
177. C22⋊C4×D67C23semidirect
180. C2×#41×C67C23semidirect
184. C22×Q8×C67C23semidirect
189. #124×C67C23semidirect
190. C22⋊Q8×C67C23semidirect
191. #121×C67C23semidirect
192. C4×Q8×C67C23semidirect
193. C4×D4×C67C23semidirect
215. #11761629C2×D4semidirect
227. C2×D268C2×D4semidirect
261. C2×C4×D67C2×D4semidirect
289. C2×Q8×C67C2×D4semidirect
316. C23×C67H(5,𝔽2)semidirect
341. Q8×C67C22×D4semidirect
378. D268C22×D4semidirect
384. C4×D67C22×D4semidirect
395. C22×C67C2×H(5,𝔽2)semidirect
425. C2×C67#3488semidirect
438. C2×#548D67semidirect
448. C67C2×#3488semidirect
459. C22×#41C2×D67semidirect
460. C23×Q8C2×D67semidirect
470. #548C2×D67semidirect
480. C2×#124C2×D67semidirect
487. C2×C22⋊Q8C2×D67semidirect
499. C2×#121C2×D67semidirect
506. C2×C4×Q8C2×D67semidirect
512. C2×C4×D4C2×D67semidirect
533. C2×#41C22×D67semidirect
538. C22×Q8C22×D67semidirect
577. #124C22×D67semidirect
583. C22⋊Q8C22×D67semidirect
594. #121C22×D67semidirect
600. C4×Q8C22×D67semidirect
606. C4×D4C22×D67semidirect
656. C2×Q8D4×D67semidirect
768. C23#14524089semidirect
774. Q8C2×D4×D67semidirect
841. C22C2×#14524089semidirect
859. C2#22573875direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240892
C23×#117616292
#225738752
C2×#168640682
C2×#168640652
C2×#168640572
C2×#168640392
C2×#168640372
C2×D4×D2682
C2×#168640302
C2×#168639762
C2×#168639642
C2×#168639052
C2×#121×D672
C2×#168638782
C2×#548×C672
C2×#348867