Finite Group Databasebeta

← #31764127

Subgroups — #31764127

Order 17152.

7190 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574309C216yesmaximal, complemented
2#22574307C212yesmaximal, complemented
3#22574227C211yesmaximal, characteristic, complemented
4#22574225C213yesmaximal, complemented
5#22574212C213yesmaximal, complemented
6#22574210C211yesmaximal, characteristic, complemented
7#22574053C213yesmaximal, complemented
8#22574051C213yesmaximal, complemented
9#22574018C211yesmaximal, characteristic, complemented
10#22573974C211yesmaximal, characteristic, complemented
11#22573920C216yesmaximal, complemented
12#22573862C212yesmaximal, complemented
13#22573833C213yesmaximal, complemented
14#22573831C211yesmaximal, characteristic, complemented
15#22573824C213yesmaximal, complemented
16#22573807C212yesmaximal, complemented
17#22573806C216yesmaximal, complemented
18#22573623C216yesmaximal, complemented
19#22573504C213yesmaximal, complemented
20#22573502C213yesmaximal, complemented
21C4×#14524090C212yesmaximal, complemented
22C4×#41×D67C211yesmaximal, characteristic, complemented
23C67×#3483C211yesmaximal, characteristic, complemented
24C2×#14524090C2212yes—
25C2×#41×D67C2211yescharacteristic
26#16864132C2216yescomplemented
27#16864129C2216yescomplemented
28#16864128C22112yescomplemented
29#16864126C2213yescomplemented
30#16864125C2211yescharacteristic, complemented
31#16864124C2213yescomplemented
32#16864122C2212yescomplemented
33#16864121C2216yescomplemented
34#16864120C2216yescomplemented
35#16864119C2213yescomplemented
36#16864116C2213yescomplemented
37#16864115C22112yescomplemented
38#16864114C2216yescomplemented
39#16864114C2216yescomplemented
40#16864112C2213yescomplemented
41#16864110C2216yescomplemented
42#16864110C2216yescomplemented
43#16864108C22112yescomplemented
44#16864098C2216yescomplemented
45#16864098C2216yescomplemented
46#16864096C2216yescomplemented
47#16864090C2216yescomplemented
48#16864089C22112yescomplemented
49#16864089C22112yescomplemented
50#16864086C2216yescomplemented
51#16864085C2216yescomplemented
52#16864079C22112yescomplemented
53#16864066C2216yes—
54#16864066C2213yescomplemented
55#16864066C2213yescomplemented
56#16864065C2212yes—
57#16864064C2216yes—
58#16864064C2216yescomplemented
59Q8×D268C2211yescharacteristic, complemented
60D4×Dic134C2213yescomplemented
61#16864058C2212yes—
62#16864055C2216yes—
63#16864053C2212yes—
64#16864053C2212yescomplemented
65#16864052C2216yes—
66#16864052C2216yescomplemented
67#16864051C2213yescomplemented
68#16864050C2213yescomplemented
69#16864045C2216yescomplemented
70#16864023C2216yes—
71#16864020C2216yescomplemented
72#16864013C2216yescomplemented
73#16864010C22112yescomplemented
74#16864000C2216yescomplemented
75#16863999C2216yescomplemented
76#16863996C22112yescomplemented
77#16863980C22112yes—
78#16863978C22112yes—
79#16863975C2216yes—
80#16863962C2216yes—
81#16863959C2216yes—
82#16863953C2213yescomplemented
83#16863951C2213yes—
84#16863951C2213yescomplemented
85#16863950C2213yes—
86#16863950C2213yescomplemented
87#16863949C2213yescomplemented
88#16863944C2213yes—
89#16863944C2213yescomplemented
90#16863943C2213yes—
91#16863943C2213yescomplemented
92#16863943C2216yescomplemented
93#16863942C22112yescomplemented
94#16863942C2213yescomplemented
95#16863933C2211yescharacteristic
96#16863933C2213yescomplemented
97#16863930C2216yescomplemented
98#16863928C2213yes—
99#16863928C2216yescomplemented
100#16863928C2213yescomplemented
101#16863928C2216yescomplemented
102#16863927C2216yescomplemented
103#16863927C2216yescomplemented
104#16863926C22112yescomplemented
105#16863926C2216yescomplemented
106#16863926C2216yescomplemented
107#16863925C2216yes—
108#16863925C2216yescomplemented
109#16863924C2216yes—
110#16863924C2216yescomplemented
111#16863908C2213yes—
112#16863906C2216yes—
113#16863906C2216yes—
114#16863905C2216yes—
115#16863905C2216yes—
116#16863903C2216yes—
117#16863903C2213yes—
118#16863879C2212yescomplemented
119#16863876C2216yes—
120#16863875C2216yes—
121#16863875C2216yescomplemented
122#16863873C2216yescomplemented
123#16863872C2212yes—
124#16863872C2212yescomplemented
125#41×Dic67C2211yescharacteristic
126#41×Dic67C2216yescomplemented
127C4×#11761629C2211yescharacteristic
128C4×#11761629C2211yescharacteristic
129C4×#11761628C2213yes—
130C4×#11761628C2216yes—
131C4×#11761628C2213yescomplemented
132C4×#11761628C2216yescomplemented
133#16863864C2213yes—
134C4×#11761627C2216yes—
135C4×#11761627C2213yes—
136C4×#11761627C2213yes—
137C4×#11761627C2216yescomplemented
138C4×#11761627C2216yescomplemented
139C2×C4×Dic134C2216yescomplemented
140C4×Q8×D67C2211yescharacteristic
141C4×Q8×D67C2211yescharacteristic
142C4×Q8×D67C2212yescomplemented
143C4×D4×D67C2213yes—
144C4×D4×D67C2213yes—
145#117×D67C2213yes—
146C2×C42×D67C2213yes—
147Q82×C67C2211yescharacteristic, complemented
148#555×C67C2216yescomplemented
149#555×C67C2213yescomplemented
150#550×C67C2212yes—
151#550×C67C2211yescharacteristic, complemented
152#550×C67C2213yescomplemented
153#532×C67C2213yescomplemented
154#532×C67C2216yescomplemented
155C4×#41×C67C2211yescharacteristic
156C4×#41×C67C2213yescomplemented
157C4×#41×C67C2212yescomplemented
158#14524090—216no—
159C2×#11761629C2311yescharacteristic
160C2×#11761628C2313yes—
161C2×#11761628C2316yes—
162C2×#11761628C2313yes—
163C2×#11761628C2316yes—
164C2×#11761627C2313yes—
165C2×#11761627C2316yes—
166C2×#11761627C2316yes—
167C2×#11761627C2316yes—
168#41×D67—28no—
169C22×Dic134C2316yes—
170C2×Q8×D67C2312yes—
171C2×Q8×D67C2311yescharacteristic
172C2×D4×D67C2313yes—
173C22×C4×D67C2313yes—
174C22×C4×D67C2313yes—
175C22×C4×D67C2313yes—
176#14524043C2313yes—
177#14524043C2313yes—
178#14524042C2316yes—
179#14524042C2313yes—
180#14524042C2313yes—
181#14524041C23112yes—
182#14524041C2313yes—
183#14524039C23112yes—
184#14524039C2316yes—
185#14524039C2313yes—
186#14524038C23112yes—
187#14524038C2316yes—
188#14524038C2312yes—
189#14524037C23112yes—
190#14524036C23112yes—
191#14524036C23112yes—
192#14524036C23112yes—
193#14524036C2316yes—
194#14524036C2316yes—
195#14524035C2316yes—
196#14524035C2316yes—
197#14524034C2316yes—
198#14524034C2316yes—
199#14524034C2313yes—
200#14524034C2311yescharacteristic
201#14524033C23112yes—
202#14524033C2316yes—
203#14524033C2316yes—
204#14524032C23112yes—
205#14524032C2311yescharacteristic
206#14524031C2316yes—
207#14524030C2316yes—
208#14524030C23112yes—
209#14524030C2316yes—
210#14524030C2313yes—
211#14524029C23112yes—
212#14524029C23112yes—
213#14524029C2316yes—
214#14524029C2316yes—
215#14524028C2316yes—
216#14524028C2312yes—
217#14524027C23112yes—
218#14524027C2316yes—
219#14524026C23112yes—
220#14524025C2316yes—
221#14524025C23112yes—
222#14524025C23112yes—
223#14524025C2316yes—
224#14524024C23112yes—
225#14524024C23112yes—
226#14524024C2316yes—
227#14524023C2316yes—
228#14524023C2313yes—
229#14524023C2316yes—
230#14524023C2313yes—
231#14524022C2316yes—
232#14524022C2316yes—
233#14524022C2316yes—
234#14524021C2316yes—
235#14524021C2316yes—
236#14524020C2316yes—
237#14524020C23112yes—
238#14524020C2316yes—
239#14524019C2316yes—
240#14524019C2316yes—
241#14524019C2313yes—
242#14524019C2311yescharacteristic
243#14524018C2316yes—
244#14524018C2313yes—
245#14524018C2311yescharacteristic
246#14524017C2316yes—
247#14524016C2316yes—
248#14524016C23112yes—
249#14524016C2316yes—
250#14524015C2316yes—
251#14524015C23112yes—
252#14524015C23112yes—
253#14524015C23112yes—
254#14524015C23112yes—
255#14524015C2316yes—
256#14524015C23112yes—
257#14524014C2316yes—
258#14524014C2316yes—
259#14524014C2316yes—
260#14524014C2313yes—
261#14524014C2313yes—
262#14524014C2316yes—
263#14524014C2316yes—
264#14524013C2316yes—
265#14524011C2316yes—
266#14524011C23112yes—
267Q8×Dic67C2312yes—
268Q8×Dic67C2311yescharacteristic
269Q8×Dic67C2311yescharacteristic
270Q8×Dic67C2316yes—
271Q8×Dic67C2316yes—
272C4×Dic134C2316yes—
273C4×Dic134C2316yes—
274C4×Dic134C2313yes—
275C4×Dic134C2313yes—
276C4×Dic134C23112yes—
277C4×Dic134C2316yes—
278C4×Dic134C2316yes—
279C4×Dic134C2313yes—
280C4×Dic134C2316yes—
281C4×Dic134C2316yes—
282C4×Dic134C2313yes—
283C4×Dic134C2316yes—
284#14524008C2316yes—
285#14524008C2316yes—
286#14524008C2313yes—
287#14524008C2316yes—
288#14524008C2316yes—
289#14524008C2313yes—
290C4×D268C2313yes—
291C4×D268C2313yes—
292C4×D268C2316yes—
293C4×D268C2316yes—
294C4×D268C2313yes—
295C4×D268C2312yes—
296C4×D268C2316yes—
297C4×D268C2311yescharacteristic
298D4×Dic67C2313yes—
299D4×Dic67C2316yes—
300D4×Dic67C2316yes—
301D4×Dic67C23112yes—
302D4×Dic67C2316yes—
303D4×Dic67C2316yes—
304D4×Dic67C2316yes—
305D4×Dic67C23112yes—
306D4×Dic67C2313yes—
307#14524005C2313yes—
308#14524005C2313yes—
309C4×C22⋊D67C2316yes—
310C4×C22⋊D67C2316yes—
311C4×C22⋊D67C2316yes—
312C4×C22⋊D67C2316yes—
313C4×C22⋊D67C2316yes—
314C4×C22⋊D67C2316yes—
315C4×C22⋊D67C2316yes—
316C4×C22⋊D67C2316yes—
317C4×C22⋊D67C2316yes—
318C4×C22⋊D67C23112yes—
319C4×C22⋊D67C2316yes—
320C4×C22⋊D67C2316yes—
321C4×C22⋊D67C2316yes—
322(C22⋊D67)⋊C4C2316yes—
323(C22⋊D67)⋊C4C23112yes—
324(C22⋊D67)⋊C4C23112yes—
325(C22⋊D67)⋊C4C2316yes—
326(C22⋊D67)⋊C4C23112yes—
327#14524002C2316yes—
328#14524002C2313yes—
329#14524002C2313yes—
330#14524002C2316yes—
331#14524002C2316yes—
332#14524001C2316yes—
333#14524001C2313yes—
334#14524001C2313yes—
335#14524001C2316yes—
336#14524001C2316yes—
337#14524000C2316yes—
338#14524000C2316yes—
339#14524000C2316yes—
340#14524000C2316yes—
341#14524000C2312yes—
342#14524000C2316yes—
343#14523999C23112yes—
344#14523999C23112yes—
345#14523999C2316yes—
346#14523999C23112yes—
347C2×C4⋊Dic67C2316yes—
348C2×Dic67⋊C4C23112yes—
349C4⋊C4×D67C2313yes—
350C4⋊C4×D67C2316yes—
351C4⋊C4×D67C2313yes—
352C22⋊C4×D67C2316yes—
353C2×C4×Dic67C2313yes—
354C2×C4×Dic67C2313yes—
355C2×C4×Dic67C2313yes—
356C2×C4×Dic67C23112yes—
357C42×D67C2311yescharacteristic
358C42×D67C2313yes—
359C42×D67C2313yes—
360C42×D67C2313yes—
361C42×D67C2313yes—
362C42×D67C2313yes—
363C42×D67C2313yes—
364C42×D67C2313yes—
365C42×D67C2316yes—
366C2×#41×C67C2311yescharacteristic
367C2×#41×C67C2312yes—
368C2×#41×C67C2313yes—
369C2×#41×C67C2316yes—
370C4⋊Q8×C67C2316yes—
371C4⋊Q8×C67C2313yes—
372#127×C67C2316yes—
373#127×C67C2313yes—
374#124×C67C23112yes—
375#124×C67C2316yes—
376#121×C67C2316yes—
377#121×C67C2316yes—
378#121×C67C2316yes—
379#121×C67C2316yes—
380#121×C67C23112yes—
381C4×Q8×C67C2312yes—
382C4×Q8×C67C2311yescharacteristic
383C4×Q8×C67C2311yescharacteristic
384C4×Q8×C67C2311yescharacteristic
385C4×Q8×C67C2313yes—
386C4×D4×C67C2313yes—
387C4×D4×C67C2313yes—
388C4×D4×C67C2316yes—
389C4×D4×C67C2313yes—
390C4×D4×C67C2316yes—
391C4×D4×C67C2313yes—
392C4×D4×C67C2316yes—
393C4×D4×C67C2316yes—
394#117×C67C2313yes—
395#117×C67C2316yes—
396#117×C67C2316yes—
397#117×C67C2313yes—
398C2×C42×C67C2313yes—
399C2×C42×C67C2316yes—
400C23×D67C2413yes—
401#11761629—24no—
402#11761628—224no—
403#11761628—212no—
404#11761628—46no—
405#11761628—412no—
406#11761627—224no—
407#11761627—212no—
408#11761627—224no—
409#11761627—412no—
410C2×Dic134—224no—
411C2×Dic134C2416yes—
412C2×Dic134C2413yes—
413C2×Dic134C2416yes—
414C2×Dic134C2416yes—
415C2×Dic134C2413yes—
416Q8×D67—28no—
417Q8×D67#4118yescomplemented
418C2×D268C2413yes—
419C2×D268C2412yes—
420C2×D268C2411yescharacteristic
421C2×D268C2416yes—
422C2×C22⋊D67C2416yes—
423C2×C22⋊D67C2416yes—
424C2×C22⋊D67C2416yes—
425C2×C22⋊D67C24112yes—
426C2×C22⋊D67C2416yes—
427C2×C22⋊D67C2416yes—
428C2×C22⋊D67C2416yes—
429D4×D67—212no—
430C22×Dic67C2413yes—
431C22×Dic67C24112yes—
432C22×Dic67C2413yes—
433C22×Dic67C2413yes—
434C22×Dic67C24112yes—
435C2×C4×D67—212no—
436C2×C4×D67—46no—
437C2×C4×D67—46no—
438C2×C4×D67C2411yescharacteristic
439C2×C4×D67C2411yescharacteristic
440C2×C4×D67C2411yescharacteristic
441C2×C4×D67C2412yes—
442C2×C4×D67C2413yes—
443C2×C4×D67C2413yes—
444C2×C4×D67C2413yes—
445C2×C4×D67C2413yes—
446C2×C4×D67C2416yes—
447C2×C4×D67C2413yes—
448C2×C4×D67C2413yes—
449C2×C4×D67C2413yes—
450C2×C4×D67C2413yes—
451C2×C4×D67C2416yes—
452C2×C4×D67C2413yes—
453C4⋊Dic67C2413yes—
454C4⋊Dic67C2416yes—
455C4⋊Dic67C2413yes—
456C4⋊Dic67C2416yes—
457C4⋊Dic67C2413yes—
458C4⋊Dic67C2411yescharacteristic
459C4⋊Dic67C2412yes—
460C4⋊Dic67C2416yes—
461C4⋊Dic67C2416yes—
462C4⋊Dic67C2416yes—
463C4⋊Dic67C2416yes—
464Dic67⋊C4C2416yes—
465Dic67⋊C4C24112yes—
466Dic67⋊C4C2416yes—
467Dic67⋊C4C2416yes—
468Dic67⋊C4C2416yes—
469Dic67⋊C4C2416yes—
470Dic67⋊C4C2416yes—
471Dic67⋊C4C2416yes—
472Dic67⋊C4C24112yes—
473Dic67⋊C4C2412yes—
474Dic67⋊C4C2412yes—
475Dic67⋊C4C2416yes—
476Dic67⋊C4C2416yes—
477Dic67⋊C4C2416yes—
478C22⋊Dic67C2416yes—
479C22⋊Dic67C2416yes—
480C22⋊Dic67C2416yes—
481C22⋊Dic67C24112yes—
482C22⋊Dic67C2416yes—
483C22⋊Dic67C2416yes—
484C22⋊Dic67C2416yes—
485C22⋊Dic67C24112yes—
486(C2×D67)⋊C4C2416yes—
487(C2×D67)⋊C4C2416yes—
488(C2×D67)⋊C4C2412yes—
489(C2×D67)⋊C4C2412yes—
490(C2×D67)⋊C4C2412yes—
491(C2×D67)⋊C4C2416yes—
492(C2×D67)⋊C4C2416yes—
493(C2×D67)⋊C4C2412yes—
494(C2×D67)⋊C4C2412yes—
495(C2×D67)⋊C4C2416yes—
496(C2×D67)⋊C4C2416yes—
497(C2×D67)⋊C4C2416yes—
498(C2×D67)⋊C4C24112yes—
499C4×Dic67C2411yescharacteristic
500C4×Dic67C2411yescharacteristic
501C4×Dic67C2411yescharacteristic
502C4×Dic67C2413yes—
503C4×Dic67C2413yes—
504C4×Dic67C2413yes—
505C4×Dic67C2413yes—
506C4×Dic67C2413yes—
507C4×Dic67C2413yes—
508C4×Dic67C2413yes—
509C4×Dic67C2413yes—
510C4×Dic67C2413yes—
511C4×Dic67C2416yes—
512C4×Dic67C2416yes—
513C4×Dic67C2416yes—
514C4×Dic67C24112yes—
515C4×Dic67C24112yes—
516#41×C67—24no—
517#41×C67—28no—
518#41×C67—412no—
519#41×C67—46no—
520C2×Q8×C67C2411yescharacteristic
521C2×Q8×C67C2416yes—
522C2×Q8×C67C2411yescharacteristic
523C2×D4×C67C2413yes—
524C2×D4×C67C2416yes—
525C2×D4×C67C2413yes—
526C2×D4×C67C2416yes—
527C2×D4×C67C24112yes—
528C2×D4×C67C2416yes—
529C22×C4×C67C2413yes—
530C22×C4×C67C2413yes—
531C22×C4×C67C2416yes—
532C22×C4×C67C2416yes—
533C22×C4×C67C2413yes—
534C22×C4×C67C2416yes—
535C4⋊C4×C67C2413yes—
536C4⋊C4×C67C2411yescharacteristic
537C4⋊C4×C67C2412yes—
538C4⋊C4×C67C2413yes—
539C4⋊C4×C67C2416yes—
540C4⋊C4×C67C2413yes—
541C4⋊C4×C67C2416yes—
542C22⋊C4×C67C2416yes—
543C22⋊C4×C67C2416yes—
544C22⋊C4×C67C24112yes—
545C22⋊C4×C67C2416yes—
546C22⋊C4×C67C2416yes—
547C42×C67C2413yes—
548C42×C67C2411yescharacteristic
549C42×C67C2412yes—
550C42×C67C2413yes—
551C42×C67C2416yes—
552C42×C67C2413yes—
553C42×C67C2416yes—
554C23×C67C2513yes—
555C23×C67C2516yes—
556C22×D67—26no—
557C22×D67—43no—
558C22×D67—43no—
559C22×D67C2513yes—
560C22×D67C2512yes—
561C22×D67C2511yescharacteristic
562Q8×C67—22no—
563Q8×C67—46no—
564Q8×C67C2×#4114yes—
565D4×C67—26no—
566D4×C67—212no—
567D4×C67—26no—
568D4×C67—412no—
569D4×C67—46no—
570D4×C67—46no—
571C2×C4×C67—26no—
572C2×C4×C67—212no—
573C2×C4×C67—26no—
574C2×C4×C67—212no—
575C2×C4×C67—26no—
576C2×C4×C67—46no—
577C2×C4×C67C2511yescharacteristic
578C2×C4×C67C2513yes—
579C2×C4×C67C2512yes—
580C2×C4×C67C2512yes—
581C2×C4×C67C2516yes—
582C2×C4×C67C2513yes—
583C2×C4×C67C2513yes—
584C2×C4×C67C2511yescharacteristic
585C2×C4×C67C2511yescharacteristic
586C22⋊D67—212no—
587C22⋊D67—212no—
588C22⋊D67—212no—
589C22⋊D67—412no—
590C22⋊D67—46no—
591C22⋊D67—46no—
592C22⋊D67—46no—
593C2×Dic67—26no—
594C2×Dic67—224no—
595C2×Dic67—43no—
596C2×Dic67—43no—
597C2×Dic67—412no—
598C2×Dic67C2513yes—
599C2×Dic67C2511yescharacteristic
600C2×Dic67C2511yescharacteristic
601C2×Dic67C2511yescharacteristic
602C2×Dic67C2512yes—
603C2×Dic67C2516yes—
604C2×Dic67C2513yes—
605C2×Dic67C2516yes—
606C2×Dic67C2513yes—
607D268—24no—
608D268—26no—
609D268—22no—
610D268—46no—
611C4×D67—22no—
612C4×D67—26no—
613C4×D67—212no—
614C4×D67—22no—
615C4×D67—22no—
616C4×D67—26no—
617C4×D67—26no—
618C4×D67—24no—
619C4×D67—26no—
620C4×D67—43no—
621C4×D67—43no—
622C4×D67—43no—
623C4×D67—43no—
624C4×D67—46no—
625C4×D67C2×#41112yes—
626Dic134—212no—
627Dic134—26no—
628Dic134—212no—
629Dic134—46no—
630Dic134C2×#41112yes—
631C22×C67—26no—
632C22×C67—23no—
633C22×C67—26no—
634C22×C67—23no—
635C22×C67—23no—
636C22×C67—26no—
637C22×C67C2611yescharacteristic
638C2×D67—21no—
639C2×D67—21no—
640C2×D67—22no—
641C2×D67—23no—
642C2×D67—23no—
643C2×D67—23no—
644C2×D67—22no—
645C2×D67—22no—
646C2×D67—412no—
647C2×D67C22×#4112yes—
648C4×C67—22no—
649C4×C67—21no—
650C4×C67—26no—
651C4×C67—23no—
652C4×C67—23no—
653C4×C67—22no—
654C4×C67C22×#4116yes—
655C4×C67#58512yes—
656C4×C67#58512yes—
657Dic67—26no—
658Dic67—21no—
659Dic67—26no—
660Dic67—22no—
661Dic67—23no—
662Dic67—21no—
663Dic67—21no—
664Dic67—23no—
665Dic67C22×#4116yes—
666#62793—671nomaximal, Sylow
667C2×C67—43no—
668C2×C67—46no—
669C2×C67C23×#4111yescharacteristic
670C2×C67C2×#58511yescharacteristic
671C2×C67C2×#58511yescharacteristic
672D67—22no—
673D67—42no—
674D67—43no—
675#3524—676no—
676#3524—672no—
677#3518—671no—
678#3518—673no—
679#3517—671no—
680#3517—673no—
681#3506—673no—
682#3506—673no—
683#3502—671no—
684#3497—671no—
685#3493—676no—
686#3487—672no—
687#3483—673no—
688#3483D6711yescharacteristic, complemented
689#3482—671no—
690#3482—673no—
691#3480—676no—
692#3480—672no—
693#3460—676no—
694#3444—673no—
695#3444—673no—
696C4×2−1+4—672no—
697C2×C4×#41—671no—
698C67#6279311yescharacteristic, complemented, Sylow
699C2×2−1+4—672no—
700C22×#41—671no—
701#559—676no—
702#559—6712no—
703#559—676no—
704Q82—673no—
705Q82C2×D6711yescharacteristic, complemented
706#557—676no—
707#557—672no—
708#557—673no—
709#557—671no—
710#556—676no—
711#556—6712no—
712#556—673no—
713#556—673no—
714#556—676no—
715#556—676no—
716#555—673no—
717#555—6712no—
718#555—676no—
719#555—676no—
720#555C2×D6716yescomplemented
721#555C2×D6713yescomplemented
722#553—6712no—
723#553—6712no—
724#553—676no—
725#553—676no—
726#553—676no—
727#553—676no—
728#552—676no—
729#552—6712no—
730#552—676no—
731#550—672no—
732#550—676no—
733#550—673no—
734#550—673no—
735#550—676no—
736#550—676no—
737#550C2×D6712yes—
738#550C2×D6711yescharacteristic, complemented
739#550C2×D6713yescomplemented
740D4×Q8—671no—
741D4×Q8—673no—
742#548—672no—
743#548—672no—
744#548—676no—
745#548—676no—
746#548—672no—
747#548—676no—
748#547—676no—
749#547—673no—
750#547—673no—
751#544—676no—
752#542—676no—
753#542—6712no—
754#542—676no—
755#540—676no—
756#540—6712no—
757#540—676no—
758#538—6712no—
759#538—6712no—
760#537—676no—
761#535—676no—
762#535—676no—
763#533—673no—
764#533—673no—
765#533—673no—
766#533—673no—
767#533—673no—
768#533—673no—
769#532—673no—
770#532—6712no—
771#532—673no—
772#532—673no—
773#532—673no—
774#532—673no—
775#532—676no—
776#532C2×D6713yescomplemented
777#532C2×D6716yescomplemented
778#529—676no—
779#529—676no—
780#529—676no—
781#529—676no—
782#529—671no—
783#529—673no—
784#529—673no—
785#529—676no—
786#529—676no—
787#529—676no—
788#529—673no—
789#529—6712no—
790#529—676no—
791#529—676no—
792#529—676no—
793#529—676no—
794#525—676no—
795#525—673no—
796#525—676no—
797#525—676no—
798#525—676no—
799#525—676no—
800#525—673no—
801#520—672no—
802#520—676no—
803#520—676no—
804#520—676no—
805#519—672no—
806#519—672no—
807#519—676no—
808C4×#41—671no—
809C4×#41—676no—
810C4×#41—671no—
811C4×#41—671no—
812C4×#41—673no—
813C4×#41—673no—
814C4×#41—676no—
815C4×#41—676no—
816C4×#41—676no—
817C4×#41—673no—
818C4×#41—673no—
819C4×#41—676no—
820C4×#41—676no—
821C4×#41—673no—
822C4×#41C2×D6711yescharacteristic
823C4×#41C2×D6712yescomplemented
824C4×#41C2×D6713yescomplemented
825C2×C4×Q8—671no—
826C2×C4×Q8—671no—
827C2×C4×Q8—672no—
828C2×C4×Q8—676no—
829C2×C4×D4—673no—
830C2×C4×D4—673no—
831C2×#117—673no—
832C22×C42—673no—
8332−1+4—13416no—
834C2×#41—671no—
835C2×#41—676no—
836C2×#41—673no—
837C2×#41—676no—
838C2×#41—676no—
839C2×#41—676no—
840C2×#41—673no—
841C2×#41—673no—
842C2×#41—676no—
843C2×#41—1348no—
844C2×#41C22×D6711yescharacteristic
845C2×#41C22×D6712yes—
846C2×#41C22×D6716yes—
847C2×#41C22×D6713yes—
848C22×Q8—671no—
849C22×Q8—672no—
850C22×Q8—676no—
851C22×D4—673no—
852C23×C4—673no—
853C23×C4—673no—
854C23×C4—673no—
855C4⋊Q8—673no—
856C4⋊Q8—6712no—
857C4⋊Q8—673no—
858C4⋊Q8—673no—
859C4⋊Q8—676no—
860C4⋊Q8—673no—
861C4⋊Q8—673no—
862C4⋊Q8C22×D6713yes—
863C4⋊Q8C22×D6716yes—
864#127—673no—
865#127—676no—
866#127—6712no—
867#127C22×D6713yes—
868#127C22×D6716yes—
869#126—672no—
870#126—676no—
871#126—6712no—
872#126—676no—
873#126—676no—
874#126—6712no—
875#126—6712no—
876#126—6712no—
877#126—6712no—
878#125—673no—
879#125—671no—
880#125—676no—
881#125—676no—
882#125—676no—
883#125—6712no—
884#125—676no—
885#125—676no—
886#125—676no—
887#124—671no—
888#124—6712no—
889#124—673no—
890#124—676no—
891#124—676no—
892#124—6712no—
893#124—676no—
894#124—676no—
895#124—6712no—
896#124—6712no—
897#124—676no—
898#124C22×D6716yes—
899#124C22×D67112yes—
900#123—6712no—
901#123—676no—
902#123—6712no—
903#123—6712no—
904#123—672no—
905#123—676no—
906#123—676no—
907#123—676no—
908#123—6712no—
909#123—676no—
910#123—6712no—
911#123—6712no—
912C22⋊Q8—671no—
913C22⋊Q8—676no—
914C22⋊Q8—676no—
915C22⋊Q8—673no—
916C22⋊Q8—676no—
917C22⋊Q8—676no—
918C22⋊Q8—676no—
919C22⋊Q8—673no—
920C22⋊Q8—676no—
921C22⋊Q8—673no—
922C22⋊Q8—676no—
923C22⋊Q8—676no—
924C22⋊Q8—676no—
925C22⋊Q8—676no—
926C22⋊Q8—676no—
927C22⋊Q8—6712no—
928#121—673no—
929#121—676no—
930#121—676no—
931#121—676no—
932#121—676no—
933#121—676no—
934#121—673no—
935#121—676no—
936#121—6712no—
937#121—6712no—
938#121—676no—
939#121—6712no—
940#121—6712no—
941#121—6712no—
942#121—676no—
943#121—671no—
944#121—673no—
945#121—676no—
946#121—676no—
947#121—676no—
948#121—6712no—
949#121C22×D6716yes—
950#121C22×D6716yes—
951#121C22×D6716yes—
952#121C22×D6716yes—
953#121C22×D67112yes—
954#120—6712no—
955#120—676no—
956#120—676no—
957C4×Q8—671no—
958C4×Q8—671no—
959C4×Q8—672no—
960C4×Q8—676no—
961C4×Q8—676no—
962C4×Q8—673no—
963C4×Q8—673no—
964C4×Q8—676no—
965C4×Q8—676no—
966C4×Q8—676no—
967C4×Q8—676no—
968C4×Q8—673no—
969C4×Q8—676no—
970C4×Q8—676no—
971C4×Q8—673no—
972C4×Q8—676no—
973C4×Q8—676no—
974C4×Q8—6712no—
975C4×Q8—673no—
976C4×Q8—676no—
977C4×Q8—673no—
978C4×Q8—676no—
979C4×Q8—676no—
980C4×Q8C22×D6711yescharacteristic
981C4×Q8C22×D6711yescharacteristic
982C4×Q8C22×D6711yescharacteristic
983C4×Q8C22×D6712yes—
984C4×Q8C22×D6713yes—
985C4×D4—673no—
986C4×D4—673no—
987C4×D4—676no—
988C4×D4—676no—
989C4×D4—6712no—
990C4×D4—6712no—
991C4×D4—676no—
992C4×D4—676no—
993C4×D4—676no—
994C4×D4—676no—
995C4×D4—676no—
996C4×D4—676no—
997C4×D4—676no—
998C4×D4—676no—
999C4×D4—676no—
1000C4×D4—676no—
1001C4×D4—6712no—
1002C4×D4—676no—
1003C4×D4—676no—
1004C4×D4—676no—
1005C4×D4—676no—
1006C4×D4—676no—
1007C4×D4—673no—
1008C4×D4—673no—
1009C4×D4—676no—
1010C4×D4—676no—
1011C4×D4—6712no—
1012C4×D4—6712no—
1013C4×D4—6712no—
1014C4×D4—673no—
1015C4×D4—673no—
1016C4×D4—672no—
1017C4×D4—671no—
1018C4×D4—676no—
1019C4×D4—676no—
1020C4×D4—676no—
1021C4×D4—673no—
1022C4×D4C22×D6713yes—
1023C4×D4C22×D6713yes—
1024C4×D4C22×D6716yes—
1025C4×D4C22×D6713yes—
1026C4×D4C22×D6716yes—
1027C4×D4C22×D6716yes—
1028C4×D4C22×D6716yes—
1029C4×D4C22×D6713yes—
1030#117—673no—
1031#117—676no—
1032#117—676no—
1033#117—676no—
1034#117—673no—
1035#117—673no—
1036#117—673no—
1037#117—676no—
1038#117—676no—
1039#117—676no—
1040#117—676no—
1041#117—6712no—
1042#117—6712no—
1043#117—6712no—
1044#117—676no—
1045#117—672no—
1046#117—676no—
1047#117—676no—
1048#117—676no—
1049#117—676no—
1050#117C22×D6713yes—
1051#117C22×D6716yes—
1052#117C22×D6713yes—
1053#117C22×D6716yes—
1054C2×C4⋊C4—6712no—
1055C2×C4⋊C4—676no—
1056C2×C4⋊C4—673no—
1057C2×C4⋊C4—673no—
1058C2×C4⋊C4—676no—
1059C2×C22⋊C4—676no—
1060C2×C42—6712no—
1061C2×C42—673no—
1062C2×C42—673no—
1063C2×C42—673no—
1064C2×C42—673no—
1065C2×C42—673no—
1066C2×C42—673no—
1067C2×C42—676no—
1068C2×C42—673no—
1069C2×C42—673no—
1070C2×C42—673no—
1071C2×C42—673no—
1072C2×C42—671no—
1073C2×C42C22×D6716yes—
1074C2×C42C22×D6713yes—
1075C24—673no—
1076#41—24no—
1077#41—28no—
1078#41—412no—
1079#41—46no—
1080#41—2686no—
1081#41—26812no—
1082#41—26812no—
1083#41—13424no—
1084#41—13412no—
1085#41—13424no—
1086#41—13412no—
1087#41—13424no—
1088#41—1344no—
1089C2×Q8—678no—
1090C2×Q8—676no—
1091C2×Q8—673no—
1092C2×Q8—676no—
1093C2×Q8—676no—
1094C2×Q8—673no—
1095C2×Q8—13424no—
1096C2×Q8—1348no—
1097C2×Q8C23×D6711yescharacteristic
1098C2×Q8C23×D6716yes—
1099C2×Q8C23×D6711yescharacteristic
1100C2×D4—6712no—
1101C2×D4—676no—
1102C2×D4—676no—
1103C2×D4—676no—
1104C2×D4—676no—
1105C2×D4—676no—
1106C2×D4—676no—
1107C2×D4—676no—
1108C2×D4—672no—
1109C2×D4—673no—
1110C2×D4—671no—
1111C2×D4—13412no—
1112C2×D4C23×D6713yes—
1113C2×D4C23×D6716yes—
1114C2×D4C23×D6713yes—
1115C2×D4C23×D67112yes—
1116C2×D4C23×D6716yes—
1117C2×D4C23×D6716yes—
1118C22×C4—2686no—
1119C22×C4—2686no—
1120C22×C4—673no—
1121C22×C4—673no—
1122C22×C4—6712no—
1123C22×C4—673no—
1124C22×C4—673no—
1125C22×C4—673no—
1126C22×C4—673no—
1127C22×C4—676no—
1128C22×C4—673no—
1129C22×C4—673no—
1130C22×C4—6712no—
1131C22×C4—671no—
1132C22×C4—671no—
1133C22×C4—673no—
1134C22×C4—673no—
1135C22×C4—673no—
1136C22×C4—676no—
1137C22×C4—671no—
1138C22×C4—672no—
1139C22×C4—673no—
1140C22×C4—13412no—
1141C22×C4C23×D6713yes—
1142C22×C4C23×D6713yes—
1143C22×C4C23×D6716yes—
1144C22×C4C23×D6716yes—
1145C22×C4C23×D6713yes—
1146C22×C4C23×D6716yes—
1147C4⋊C4—676no—
1148C4⋊C4—673no—
1149C4⋊C4—676no—
1150C4⋊C4—676no—
1151C4⋊C4—676no—
1152C4⋊C4—6712no—
1153C4⋊C4—676no—
1154C4⋊C4—676no—
1155C4⋊C4—673no—
1156C4⋊C4—673no—
1157C4⋊C4—676no—
1158C4⋊C4—676no—
1159C4⋊C4—671no—
1160C4⋊C4—676no—
1161C4⋊C4—672no—
1162C4⋊C4—672no—
1163C4⋊C4—676no—
1164C4⋊C4—672no—
1165C4⋊C4—676no—
1166C4⋊C4—676no—
1167C4⋊C4—6712no—
1168C4⋊C4—676no—
1169C4⋊C4—676no—
1170C4⋊C4—676no—
1171C4⋊C4—676no—
1172C4⋊C4C23×D6713yes—
1173C4⋊C4C23×D6713yes—
1174C4⋊C4C23×D6716yes—
1175C4⋊C4C23×D6713yes—
1176C4⋊C4C23×D6711yescharacteristic
1177C4⋊C4C23×D6712yes—
1178C4⋊C4C23×D6716yes—
1179C22⋊C4—676no—
1180C22⋊C4—676no—
1181C22⋊C4—676no—
1182C22⋊C4—676no—
1183C22⋊C4—676no—
1184C22⋊C4—6712no—
1185C22⋊C4—676no—
1186C22⋊C4—6712no—
1187C22⋊C4—676no—
1188C22⋊C4—676no—
1189C22⋊C4—672no—
1190C22⋊C4—676no—
1191C22⋊C4—672no—
1192C22⋊C4—676no—
1193C22⋊C4—672no—
1194C22⋊C4—672no—
1195C22⋊C4—672no—
1196C22⋊C4—676no—
1197C22⋊C4—676no—
1198C22⋊C4—6712no—
1199C22⋊C4—676no—
1200C22⋊C4C23×D6716yes—
1201C22⋊C4C23×D67112yes—
1202C22⋊C4C23×D6716yes—
1203C22⋊C4C23×D6716yes—
1204C22⋊C4C23×D6716yes—
1205C42—671no—
1206C42—671no—
1207C42—673no—
1208C42—673no—
1209C42—673no—
1210C42—673no—
1211C42—673no—
1212C42—673no—
1213C42—673no—
1214C42—673no—
1215C42—6712no—
1216C42—676no—
1217C42—6712no—
1218C42—676no—
1219C42—671no—
1220C42—673no—
1221C42—676no—
1222C42C23×D6713yes—
1223C42C23×D6713yes—
1224C42C23×D6716yes—
1225C42C23×D6716yes—
1226C42C23×D6713yes—
1227C42C23×D6711yescharacteristic
1228C42C23×D6712yes—
1229C23—2683no—
1230C23—2683no—
1231C23—671no—
1232C23—673no—
1233C23—672no—
1234C23—1346no—
1235C23C24×D6713yes—
1236C23C24×D6716yes—
1237Q8—22no—
1238Q8—46no—
1239Q8—2686no—
1240Q8—6712no—
1241Q8—13412no—
1242Q8—13412no—
1243Q8—1346no—
1244Q8#41×D6714yes—
1245D4—26no—
1246D4—212no—
1247D4—26no—
1248D4—46no—
1249D4—412no—
1250D4—46no—
1251D4—2686no—
1252D4—2686no—
1253D4—2686no—
1254D4—2686no—
1255D4—26812no—
1256D4—1344no—
1257D4—13412no—
1258D4—13412no—
1259D4—13412no—
1260D4—1346no—
1261D4—1342no—
1262C2×C4—26no—
1263C2×C4—212no—
1264C2×C4—26no—
1265C2×C4—212no—
1266C2×C4—26no—
1267C2×C4—46no—
1268C2×C4—2683no—
1269C2×C4—2683no—
1270C2×C4—2683no—
1271C2×C4—2683no—
1272C2×C4—2686no—
1273C2×C4—2683no—
1274C2×C4—2683no—
1275C2×C4—26812no—
1276C2×C4—673no—
1277C2×C4—6712no—
1278C2×C4—671no—
1279C2×C4—671no—
1280C2×C4—671no—
1281C2×C4—673no—
1282C2×C4—672no—
1283C2×C4—676no—
1284C2×C4—673no—
1285C2×C4—676no—
1286C2×C4—1346no—
1287C2×C4—1342no—
1288C2×C4—1346no—
1289C2×C4—13424no—
1290C2×C4—1346no—
1291C2×C4—13412no—
1292C2×C4—1342no—
1293C2×C4—1346no—
1294C2×C4—1344no—
1295C2×C4—1342no—
1296C2×C4—1346no—
1297C2×C4C24×D6711yescharacteristic
1298C2×C4C24×D6713yes—
1299C2×C4C24×D6716yes—
1300C2×C4C24×D6713yes—
1301C2×C4C24×D6712yes—
1302C2×C4C24×D6712yes—
1303C2×C4C24×D6713yes—
1304C2×C4C24×D6711yescharacteristic
1305C2×C4C24×D6711yescharacteristic
1306C22—26no—
1307C22—23no—
1308C22—23no—
1309C22—26no—
1310C22—23no—
1311C22—26no—
1312C22—26812no—
1313C22—672no—
1314C22—1342no—
1315C22—1343no—
1316C22—1343no—
1317C22—1342no—
1318C22—1342no—
1319C22—1343no—
1320C22—1341no—
1321C22—1341no—
1322C22C25×D6711yescharacteristic
1323C4—21no—
1324C4—22no—
1325C4—23no—
1326C4—26no—
1327C4—23no—
1328C4—22no—
1329C4—676no—
1330C4—1341no—
1331C4—1346no—
1332C4—1341no—
1333C4—1343no—
1334C4—1342no—
1335C4—1341no—
1336C4—1343no—
1337C4—1346no—
1338C4C2×#41×D6716yes—
1339C4#1686423112yes—
1340C4#1686423212yes—
1341C2—43no—
1342C2—46no—
1343C2—2683no—
1344C2—2682no—
1345C2—1342no—
1346C2C22×#41×D6711yescharacteristic
1347C2C2×#1686423111yescharacteristic
1348C2C2×#1686423211yescharacteristic
subgroupG/H
centerC2×C4C24×D67
commutator, socle, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC67×#3483C2
hypercenter#3483D67
hypocenterC67#62793
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ #3483

Complements

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

NH ≅ G/Ntype
1. #22574309C2semidirect
2. #22574307C2semidirect
3. #22574227C2semidirect
4. #22574225C2semidirect
5. #22574212C2semidirect
6. #22574210C2semidirect
7. #22574053C2semidirect
8. #22574051C2semidirect
9. #22574018C2semidirect
10. #22573974C2semidirect
11. #22573920C2semidirect
12. #22573862C2semidirect
13. #22573833C2semidirect
14. #22573831C2semidirect
15. #22573824C2semidirect
16. #22573807C2semidirect
17. #22573806C2semidirect
18. #22573623C2semidirect
19. #22573504C2semidirect
20. #22573502C2semidirect
21. C4×#14524090C2semidirect
22. C4×#41×D67C2semidirect
23. C67×#3483C2semidirect
26. #16864132C22semidirect
27. #16864129C22semidirect
28. #16864128C22semidirect
29. #16864126C22semidirect
30. #16864125C22semidirect
31. #16864124C22semidirect
32. #16864122C22semidirect
33. #16864121C22semidirect
34. #16864120C22semidirect
35. #16864119C22semidirect
36. #16864116C22semidirect
37. #16864115C22semidirect
38. #16864114C22semidirect
39. #16864114C22semidirect
40. #16864112C22semidirect
41. #16864110C22semidirect
42. #16864110C22semidirect
43. #16864108C22semidirect
44. #16864098C22semidirect
45. #16864098C22semidirect
46. #16864096C22semidirect
47. #16864090C22semidirect
48. #16864089C22semidirect
49. #16864089C22semidirect
50. #16864086C22semidirect
51. #16864085C22semidirect
52. #16864079C22semidirect
54. #16864066C22semidirect
55. #16864066C22semidirect
58. #16864064C22semidirect
59. Q8×D268C22semidirect
60. D4×Dic134C22semidirect
64. #16864053C22semidirect
66. #16864052C22semidirect
67. #16864051C22semidirect
68. #16864050C22semidirect
69. #16864045C22semidirect
71. #16864020C22semidirect
72. #16864013C22semidirect
73. #16864010C22semidirect
74. #16864000C22semidirect
75. #16863999C22semidirect
76. #16863996C22semidirect
82. #16863953C22semidirect
84. #16863951C22semidirect
86. #16863950C22semidirect
87. #16863949C22semidirect
89. #16863944C22semidirect
91. #16863943C22semidirect
92. #16863943C22semidirect
93. #16863942C22semidirect
94. #16863942C22semidirect
96. #16863933C22semidirect
97. #16863930C22semidirect
99. #16863928C22semidirect
100. #16863928C22semidirect
101. #16863928C22semidirect
102. #16863927C22semidirect
103. #16863927C22semidirect
104. #16863926C22semidirect
105. #16863926C22semidirect
106. #16863926C22semidirect
108. #16863925C22semidirect
110. #16863924C22semidirect
118. #16863879C22semidirect
121. #16863875C22semidirect
122. #16863873C22semidirect
124. #16863872C22semidirect
126. #41×Dic67C22semidirect
131. C4×#11761628C22semidirect
132. C4×#11761628C22semidirect
137. C4×#11761627C22semidirect
138. C4×#11761627C22semidirect
139. C2×C4×Dic134C22semidirect
142. C4×Q8×D67C22semidirect
147. Q82×C67C22semidirect
148. #555×C67C22semidirect
149. #555×C67C22semidirect
151. #550×C67C22semidirect
152. #550×C67C22semidirect
153. #532×C67C22semidirect
154. #532×C67C22semidirect
156. C4×#41×C67C22semidirect
157. C4×#41×C67C22semidirect
417. Q8×D67#41semidirect
688. #3483D67semidirect
698. C67#62793semidirect
705. Q82C2×D67semidirect
720. #555C2×D67semidirect
721. #555C2×D67semidirect
738. #550C2×D67semidirect
739. #550C2×D67semidirect
776. #532C2×D67semidirect
777. #532C2×D67semidirect
823. C4×#41C2×D67semidirect
824. C4×#41C2×D67semidirect

Maximal subgroups

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

subgroupindex
#225743092
#225743072
#225742272
#225742252
#225742122
#225742102
#225740532
#225740512
#225740182
#225739742
#225739202
#225738622
#225738332
#225738312
#225738242
#225738072
#225738062
#225736232
#225735042
#225735022
C4×#145240902
C4×#41×D672
C67×#34832
#6279367