Finite Group Databasebeta

← #31764131

Subgroups — #31764131

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#22574319C212yesmaximal, complemented
2#22574315C216yesmaximal, complemented
3#22574223C213yesmaximal, complemented
4#22574221C211yesmaximal, characteristic, complemented
5#22574216C211yesmaximal, characteristic, complemented
6#22574214C213yesmaximal, complemented
7#22574062C213yesmaximal, complemented
8#22574059C213yesmaximal, complemented
9#22574013C211yesmaximal, characteristic, complemented
10#22573979C211yesmaximal, characteristic, complemented
11#22573927C216yesmaximal, complemented
12#22573866C212yesmaximal, complemented
13#22573835C211yesmaximal, characteristic, complemented
14#22573835C213yesmaximal, complemented
15#22573827C213yesmaximal, complemented
16#22573804C212yesmaximal, complemented
17#22573800C216yesmaximal, complemented
18#22573630C216yesmaximal, complemented
19#22573506C213yesmaximal, complemented
20#22573502C213yesmaximal, complemented
21C4×#14524091C212yesmaximal, complemented
22C4×#41×D67C211yesmaximal, characteristic, complemented
23C67×#3482C211yesmaximal, characteristic, complemented
24C2×#14524091C2212yes—
25C2×#41×D67C2211yescharacteristic
26#16864131C2216yescomplemented
27#16864130C22112yescomplemented
28#16864128C2216yescomplemented
29Q8×Dic134C2211yescharacteristic, complemented
30Q8×Dic134C2213yescomplemented
31#16864125C2212yescomplemented
32#16864123C2216yescomplemented
33#16864121C2213yescomplemented
34#16864120C2213yescomplemented
35#16864119C2216yescomplemented
36#16864117C2216yescomplemented
37#16864117C2216yescomplemented
38#16864113C22112yescomplemented
39#16864111C2216yescomplemented
40#16864111C2213yescomplemented
41#16864111C2213yescomplemented
42#16864109C2216yescomplemented
43#16864109C22112yescomplemented
44#16864109C2216yescomplemented
45#16864099C2216yescomplemented
46#16864097C22112yescomplemented
47#16864094C2216yescomplemented
48#16864094C2216yescomplemented
49#16864093C2216yescomplemented
50#16864091C22112yescomplemented
51#16864080C2216yescomplemented
52#16864078C22112yescomplemented
53#16864068C2212yes—
54#16864068C2211yescharacteristic, complemented
55#16864068C2213yescomplemented
56#16864067C2216yes—
57#16864067C2213yescomplemented
58#16864067C2213yescomplemented
59#16864065C2212yes—
60#16864065C2216yescomplemented
61#16864064C2216yes—
62#16864061C2213yescomplemented
63#16864057C2212yes—
64#16864057C2212yescomplemented
65#16864056C2216yes—
66#16864056C2216yescomplemented
67#16864054C2216yes—
68#16864049C2213yescomplemented
69#16864048C2216yescomplemented
70#16864026C2216yes—
71#16864019C2216yescomplemented
72#16864015C2216yescomplemented
73#16864012C22112yescomplemented
74#16864002C2216yescomplemented
75#16863999C2216yescomplemented
76#16863998C22112yescomplemented
77#16863985C22112yes—
78#16863982C22112yes—
79#16863976C2216yes—
80#16863964C2216yes—
81#16863962C2216yes—
82#16863951C2213yes—
83#16863951C2213yescomplemented
84#16863950C2213yes—
85#16863950C2213yescomplemented
86#16863949C2213yescomplemented
87#16863947C2213yes—
88#16863947C2213yescomplemented
89#16863946C2213yescomplemented
90#16863946C2216yescomplemented
91#16863943C2213yes—
92#16863943C2213yescomplemented
93#16863943C2216yescomplemented
94#16863943C22112yescomplemented
95#16863942C2213yescomplemented
96#16863933C2213yes—
97#16863933C2216yescomplemented
98#16863933C2213yescomplemented
99#16863933C2216yescomplemented
100#16863932C2216yescomplemented
101#16863932C2216yescomplemented
102#16863931C2216yes—
103#16863931C2216yescomplemented
104#16863928C2211yescharacteristic
105#16863928C2213yescomplemented
106#16863926C2216yescomplemented
107#16863926C2216yescomplemented
108#16863924C2216yes—
109#16863924C22112yescomplemented
110#16863924C2216yescomplemented
111#16863909C2216yes—
112#16863909C2216yes—
113#16863908C2216yes—
114#16863908C2213yes—
115#16863905C2216yes—
116#16863905C2216yes—
117#16863903C2213yes—
118#16863878C2216yes—
119#16863878C2212yescomplemented
120#16863877C2216yes—
121#16863877C2216yescomplemented
122#16863874C2212yescomplemented
123#16863872C2212yes—
124#16863872C2216yescomplemented
125#41×Dic67C2211yescharacteristic
126C4×#11761629C2216yes—
127C4×#11761629C2211yescharacteristic
128C4×#11761629C2211yescharacteristic
129C4×#11761629C2216yescomplemented
130C4×#11761629C2212yescomplemented
131C4×#11761628C2213yes—
132C4×#11761628C2216yes—
133C4×#11761628C2213yescomplemented
134C4×#11761628C2216yescomplemented
135C4×#11761628C2216yescomplemented
136#16863864C2213yes—
137#16863864C2216yescomplemented
138C4×#11761627C2213yes—
139C4×#11761627C2213yes—
140C4×Q8×D67C2211yescharacteristic
141C4×Q8×D67C2211yescharacteristic
142C4×Q8×D67C2216yescomplemented
143C4×D4×D67C2213yes—
144C4×D4×D67C2213yes—
145#117×D67C2213yes—
146C2×C42×D67C2213yes—
147#557×C67C2211yescharacteristic, complemented
148#556×C67C2213yescomplemented
149#552×C67C2216yescomplemented
150D4×Q8×C67C2211yescharacteristic, complemented
151#548×C67C2212yes—
152#547×C67C2213yescomplemented
153#533×C67C2213yescomplemented
154#529×C67C2216yescomplemented
155C4×#41×C67C2211yescharacteristic
156C4×#41×C67C2213yescomplemented
157C2×C4×Q8×C67C2212yescomplemented
158#14524091—216no—
159C2×#11761629C2311yescharacteristic
160C2×#11761629C2312yes—
161C2×#11761629C2316yes—
162C2×#11761629C2316yes—
163C2×#11761628C2313yes—
164C2×#11761628C2316yes—
165C2×#11761628C2316yes—
166C2×#11761628C2313yes—
167C2×#11761628C2316yes—
168C2×#11761628C2316yes—
169C2×#11761627C2313yes—
170#41×D67—28no—
171C2×Q8×D67C2316yes—
172C2×Q8×D67C2311yescharacteristic
173C2×D4×D67C2313yes—
174C22×C4×D67C2313yes—
175C22×C4×D67C2313yes—
176C22×C4×D67C2313yes—
177#14524043C2316yes—
178#14524043C2313yes—
179#14524042C23112yes—
180#14524042C2316yes—
181#14524042C2313yes—
182#14524042C2313yes—
183#14524041C2313yes—
184#14524040C2316yes—
185#14524040C2313yes—
186#14524039C2316yes—
187#14524039C23112yes—
188#14524039C2313yes—
189#14524038C23112yes—
190#14524038C23112yes—
191#14524038C23112yes—
192#14524038C2316yes—
193#14524038C2316yes—
194#14524036C23112yes—
195#14524036C2316yes—
196#14524036C2312yes—
197#14524034C2316yes—
198#14524034C2316yes—
199#14524034C2311yescharacteristic
200#14524034C2313yes—
201#14524033C23112yes—
202#14524033C2316yes—
203#14524033C2316yes—
204#14524032C2316yes—
205#14524032C2316yes—
206#14524032C2313yes—
207#14524031C23112yes—
208#14524031C2316yes—
209#14524030C2311yescharacteristic
210#14524029C23112yes—
211#14524029C23112yes—
212#14524029C23112yes—
213#14524029C23112yes—
214#14524029C2316yes—
215#14524029C2316yes—
216#14524028C2316yes—
217#14524028C23112yes—
218#14524028C23112yes—
219#14524028C23112yes—
220#14524028C2316yes—
221#14524027C23112yes—
222#14524027C2316yes—
223#14524025C2316yes—
224#14524025C23112yes—
225#14524025C2312yes—
226#14524024C2316yes—
227#14524023C2316yes—
228#14524023C2316yes—
229#14524023C2313yes—
230#14524023C2311yescharacteristic
231#14524021C23112yes—
232#14524021C2316yes—
233#14524021C2316yes—
234#14524020C2316yes—
235#14524020C2316yes—
236#14524019C2316yes—
237#14524019C2313yes—
238#14524019C2316yes—
239#14524019C2313yes—
240#14524018C2316yes—
241#14524018C2316yes—
242#14524018C2316yes—
243#14524018C23112yes—
244#14524018C2316yes—
245#14524018C2313yes—
246#14524018C2313yes—
247#14524018C2316yes—
248#14524017C2316yes—
249#14524017C2316yes—
250#14524017C2316yes—
251#14524017C2316yes—
252#14524017C23112yes—
253#14524016C23112yes—
254#14524016C23112yes—
255#14524016C23112yes—
256#14524016C2316yes—
257#14524016C23112yes—
258#14524016C2316yes—
259#14524015C2316yes—
260#14524015C2316yes—
261#14524014C2316yes—
262#14524014C2313yes—
263#14524014C23112yes—
264#14524014C2311yescharacteristic
265#14524013C2316yes—
266#14524013C23112yes—
267#14524011C2316yes—
268Q8×Dic67C2316yes—
269Q8×Dic67C2312yes—
270Q8×Dic67C2311yescharacteristic
271Q8×Dic67C2316yes—
272Q8×Dic67C2316yes—
273Q8×Dic67C2311yescharacteristic
274C4×Dic134C2316yes—
275C4×Dic134C2316yes—
276C4×Dic134C2313yes—
277C4×Dic134C2313yes—
278C4×Dic134C2316yes—
279C4×Dic134C2313yes—
280C4×Dic134C2316yes—
281C4×Dic134C2311yescharacteristic
282C4×Dic134C2316yes—
283#14524008C2316yes—
284#14524008C2313yes—
285#14524008C23112yes—
286#14524008C2316yes—
287#14524008C2313yes—
288#14524008C2316yes—
289C4×D268C2313yes—
290C4×D268C2313yes—
291C4×D268C2316yes—
292C4×D268C2316yes—
293C4×D268C2316yes—
294C4×D268C2313yes—
295C4×D268C2316yes—
296C4×D268C2316yes—
297C4×D268C2316yes—
298C4×D268C2313yes—
299C4×D268C23112yes—
300D4×Dic67C2313yes—
301D4×Dic67C2313yes—
302#14524005C2313yes—
303#14524005C2316yes—
304#14524005C2316yes—
305#14524005C23112yes—
306#14524005C2316yes—
307#14524005C2316yes—
308#14524005C2316yes—
309#14524005C2313yes—
310#14524005C23112yes—
311C4×C22⋊D67C2316yes—
312C4×C22⋊D67C2316yes—
313C4×C22⋊D67C2316yes—
314C4×C22⋊D67C2316yes—
315C4×C22⋊D67C23112yes—
316C4×C22⋊D67C2316yes—
317C4×C22⋊D67C2316yes—
318C4×C22⋊D67C2316yes—
319C4×C22⋊D67C2312yes—
320C4×C22⋊D67C2316yes—
321C4×C22⋊D67C2316yes—
322C4×C22⋊D67C2316yes—
323C4×C22⋊D67C2316yes—
324(C22⋊D67)⋊C4C2316yes—
325(C22⋊D67)⋊C4C23112yes—
326(C22⋊D67)⋊C4C23112yes—
327(C22⋊D67)⋊C4C2316yes—
328#14524002C2316yes—
329#14524002C2313yes—
330#14524002C2316yes—
331#14524002C2313yes—
332#14524002C2312yes—
333#14524001C23112yes—
334#14524001C2316yes—
335#14524001C23112yes—
336#14524001C2313yes—
337#14524001C2316yes—
338#14524001C2313yes—
339#14524001C2316yes—
340#14524000C2316yes—
341#14524000C2316yes—
342#14524000C2316yes—
343#14524000C2316yes—
344#14524000C23112yes—
345#14524000C2316yes—
346#14524000C2316yes—
347#14523999C2316yes—
348C4⋊C4×D67C2313yes—
349C4⋊C4×D67C23112yes—
350C4⋊C4×D67C2316yes—
351C4⋊C4×D67C2313yes—
352C22⋊C4×D67C2316yes—
353C2×C4×Dic67C2313yes—
354C2×C4×Dic67C2313yes—
355C2×C4×Dic67C2313yes—
356C42×D67C2311yescharacteristic
357C42×D67C2313yes—
358C42×D67C2313yes—
359C42×D67C2313yes—
360C42×D67C2313yes—
361C42×D67C2313yes—
362C42×D67C2313yes—
363C42×D67C2313yes—
364C42×D67C23112yes—
365C42×D67C2316yes—
366C2×#41×C67C2311yescharacteristic
367C2×#41×C67C2313yes—
368C22×Q8×C67C2312yes—
369C4⋊Q8×C67C2313yes—
370C4⋊Q8×C67C2313yes—
371#126×C67C23112yes—
372#125×C67C2316yes—
373#125×C67C2316yes—
374#124×C67C2316yes—
375#123×C67C23112yes—
376C22⋊Q8×C67C2316yes—
377C22⋊Q8×C67C2316yes—
378C22⋊Q8×C67C2316yes—
379#121×C67C2316yes—
380C4×Q8×C67C2311yescharacteristic
381C4×Q8×C67C2312yes—
382C4×Q8×C67C2316yes—
383C4×Q8×C67C2316yes—
384C4×Q8×C67C2311yescharacteristic
385C4×Q8×C67C2313yes—
386C4×Q8×C67C2313yes—
387C4×D4×C67C2316yes—
388C4×D4×C67C2313yes—
389C4×D4×C67C2313yes—
390C4×D4×C67C2313yes—
391C4×D4×C67C2311yescharacteristic
392C4×D4×C67C2316yes—
393#117×C67C2313yes—
394#117×C67C2316yes—
395#117×C67C2313yes—
396#117×C67C2316yes—
397C2×C4⋊C4×C67C2316yes—
398C2×C42×C67C2316yes—
399C2×C42×C67C2313yes—
400C23×D67C2413yes—
401#11761629—24no—
402#11761629—28no—
403#11761629—224no—
404#11761629—412no—
405#11761628—224no—
406#11761628—212no—
407#11761628—224no—
408#11761628—46no—
409#11761628—412no—
410#11761628—412no—
411#11761627—212no—
412C2×Dic134C2416yes—
413C2×Dic134C2411yescharacteristic
414C2×Dic134C2416yes—
415C2×Dic134C2416yes—
416C2×Dic134C2413yes—
417Q8×D67—224no—
418Q8×D67#4118yescomplemented
419C2×D268C2416yes—
420C2×D268C2413yes—
421C2×D268C2416yes—
422C2×D268C2413yes—
423C2×D268C2416yes—
424C2×D268C24112yes—
425C2×D268C2416yes—
426C2×C22⋊D67C2416yes—
427C2×C22⋊D67C2412yes—
428C2×C22⋊D67C2416yes—
429C2×C22⋊D67C24112yes—
430C2×C22⋊D67C2416yes—
431C2×C22⋊D67C2416yes—
432C2×C22⋊D67C2416yes—
433D4×D67—212no—
434C22×Dic67C2413yes—
435C22×Dic67C2413yes—
436C22×Dic67C2413yes—
437C2×C4×D67—212no—
438C2×C4×D67—46no—
439C2×C4×D67—46no—
440C2×C4×D67C2411yescharacteristic
441C2×C4×D67C2411yescharacteristic
442C2×C4×D67C2411yescharacteristic
443C2×C4×D67C2416yes—
444C2×C4×D67C2413yes—
445C2×C4×D67C2413yes—
446C2×C4×D67C2413yes—
447C2×C4×D67C2413yes—
448C2×C4×D67C24112yes—
449C2×C4×D67C2416yes—
450C2×C4×D67C2413yes—
451C2×C4×D67C2413yes—
452C2×C4×D67C2413yes—
453C2×C4×D67C2413yes—
454C2×C4×D67C2416yes—
455C2×C4×D67C24112yes—
456C2×C4×D67C2413yes—
457C4⋊Dic67C2413yes—
458C4⋊Dic67C2416yes—
459C4⋊Dic67C2413yes—
460C4⋊Dic67C2416yes—
461C4⋊Dic67C2413yes—
462C4⋊Dic67C2416yes—
463C4⋊Dic67C24112yes—
464C4⋊Dic67C2411yescharacteristic
465C4⋊Dic67C2412yes—
466C4⋊Dic67C2412yes—
467Dic67⋊C4C2416yes—
468Dic67⋊C4C2416yes—
469Dic67⋊C4C2416yes—
470Dic67⋊C4C2416yes—
471Dic67⋊C4C2412yes—
472Dic67⋊C4C2416yes—
473Dic67⋊C4C2412yes—
474Dic67⋊C4C2416yes—
475Dic67⋊C4C2416yes—
476Dic67⋊C4C2416yes—
477Dic67⋊C4C2416yes—
478Dic67⋊C4C2416yes—
479C22⋊Dic67C2416yes—
480C22⋊Dic67C2416yes—
481C22⋊Dic67C2412yes—
482C22⋊Dic67C2412yes—
483C22⋊Dic67C2412yes—
484C22⋊Dic67C2416yes—
485(C2×D67)⋊C4C2416yes—
486(C2×D67)⋊C4C2416yes—
487(C2×D67)⋊C4C2412yes—
488(C2×D67)⋊C4C2416yes—
489(C2×D67)⋊C4C2416yes—
490(C2×D67)⋊C4C2416yes—
491(C2×D67)⋊C4C2416yes—
492(C2×D67)⋊C4C24112yes—
493(C2×D67)⋊C4C2416yes—
494(C2×D67)⋊C4C2416yes—
495(C2×D67)⋊C4C2416yes—
496(C2×D67)⋊C4C2416yes—
497(C2×D67)⋊C4C2416yes—
498(C2×D67)⋊C4C24112yes—
499(C2×D67)⋊C4C24112yes—
500C4×Dic67C2413yes—
501C4×Dic67C2411yescharacteristic
502C4×Dic67C2411yescharacteristic
503C4×Dic67C2411yescharacteristic
504C4×Dic67C2412yes—
505C4×Dic67C2413yes—
506C4×Dic67C2413yes—
507C4×Dic67C2413yes—
508C4×Dic67C2413yes—
509C4×Dic67C2413yes—
510C4×Dic67C2413yes—
511C4×Dic67C2413yes—
512C4×Dic67C2413yes—
513C4×Dic67C24112yes—
514C4×Dic67C2416yes—
515C4×Dic67C2416yes—
516C4×Dic67C24112yes—
517#41×C67—24no—
518#41×C67—46no—
519C2×Q8×C67—28no—
520C2×Q8×C67C2416yes—
521C2×Q8×C67C2413yes—
522C2×Q8×C67C2411yescharacteristic
523C2×D4×C67C2411yescharacteristic
524C2×D4×C67C2413yes—
525C2×D4×C67C2416yes—
526C22×C4×C67C2412yes—
527C22×C4×C67C2416yes—
528C22×C4×C67C2413yes—
529C22×C4×C67C2413yes—
530C22×C4×C67C2413yes—
531C22×C4×C67C2416yes—
532C4⋊C4×C67C2413yes—
533C4⋊C4×C67C2416yes—
534C4⋊C4×C67C24112yes—
535C4⋊C4×C67C2411yescharacteristic
536C4⋊C4×C67C2413yes—
537C4⋊C4×C67C2416yes—
538C4⋊C4×C67C2413yes—
539C4⋊C4×C67C2416yes—
540C4⋊C4×C67C2416yes—
541C4⋊C4×C67C2416yes—
542C22⋊C4×C67C2412yes—
543C22⋊C4×C67C2416yes—
544C22⋊C4×C67C2416yes—
545C22⋊C4×C67C2416yes—
546C22⋊C4×C67C24112yes—
547C42×C67C2413yes—
548C42×C67C2411yescharacteristic
549C42×C67C2413yes—
550C42×C67C2416yes—
551C42×C67C2416yes—
552C42×C67C2413yes—
553C42×C67C2416yes—
554C23×C67C2513yes—
555C23×C67C2512yes—
556C22×D67—26no—
557C22×D67—43no—
558C22×D67—43no—
559C22×D67C2513yes—
560C22×D67C2516yes—
561C22×D67C2511yescharacteristic
562Q8×C67—212no—
563Q8×C67—26no—
564Q8×C67C2×#4114yes—
565D4×C67—26no—
566D4×C67—22no—
567D4×C67—46no—
568C2×C4×C67—212no—
569C2×C4×C67—26no—
570C2×C4×C67—26no—
571C2×C4×C67—26no—
572C2×C4×C67—24no—
573C2×C4×C67—46no—
574C2×C4×C67C2512yes—
575C2×C4×C67C2511yescharacteristic
576C2×C4×C67C2513yes—
577C2×C4×C67C2513yes—
578C2×C4×C67C2516yes—
579C2×C4×C67C2516yes—
580C2×C4×C67C2513yes—
581C2×C4×C67C2511yescharacteristic
582C2×C4×C67C2511yescharacteristic
583C22⋊D67—24no—
584C22⋊D67—212no—
585C22⋊D67—212no—
586C22⋊D67—46no—
587C22⋊D67—46no—
588C22⋊D67—412no—
589C22⋊D67—46no—
590C2×Dic67—26no—
591C2×Dic67—43no—
592C2×Dic67—43no—
593C2×Dic67C2511yescharacteristic
594C2×Dic67C2511yescharacteristic
595C2×Dic67C2511yescharacteristic
596C2×Dic67C2513yes—
597C2×Dic67C2516yes—
598C2×Dic67C2512yes—
599C2×Dic67C2513yes—
600C2×Dic67C2512yes—
601C2×Dic67C2513yes—
602D268—212no—
603D268—26no—
604D268—212no—
605D268—26no—
606D268—46no—
607D268—46no—
608D268—412no—
609C4×D67—22no—
610C4×D67—26no—
611C4×D67—212no—
612C4×D67—22no—
613C4×D67—22no—
614C4×D67—26no—
615C4×D67—26no—
616C4×D67—212no—
617C4×D67—26no—
618C4×D67—224no—
619C4×D67—43no—
620C4×D67—43no—
621C4×D67—43no—
622C4×D67—43no—
623C4×D67—46no—
624C4×D67—412no—
625C4×D67C2×#41112yes—
626Dic134—22no—
627Dic134—212no—
628Dic134—46no—
629Dic134—46no—
630Dic134C2×#41112yes—
631C22×C67—23no—
632C22×C67—22no—
633C22×C67—23no—
634C22×C67—23no—
635C22×C67—22no—
636C22×C67—22no—
637C22×C67C2611yescharacteristic
638C2×D67—21no—
639C2×D67—21no—
640C2×D67—26no—
641C2×D67—23no—
642C2×D67—23no—
643C2×D67—23no—
644C2×D67—26no—
645C2×D67—26no—
646C2×D67—412no—
647C2×D67C22×#4112yes—
648C4×C67—26no—
649C4×C67—21no—
650C4×C67—22no—
651C4×C67—23no—
652C4×C67—23no—
653C4×C67—26no—
654C4×C67C22×#4116yes—
655C4×C67#58512yes—
656C4×C67#58512yes—
657Dic67—22no—
658Dic67—21no—
659Dic67—22no—
660Dic67—26no—
661Dic67—23no—
662Dic67—23no—
663Dic67—21no—
664Dic67—21no—
665Dic67C22×#4116yes—
666#62793—671nomaximal, Sylow
667C2×C67—43no—
668C2×C67—42no—
669C2×C67C23×#4111yescharacteristic
670C2×C67C2×#58511yescharacteristic
671C2×C67C2×#58511yescharacteristic
672D67—22no—
673D67—46no—
674D67—43no—
675#3524—676no—
676#3524—672no—
677#3518—673no—
678#3518—671no—
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—671no—
688#3483—673no—
689#3482—673no—
690#3482D6711yescharacteristic, complemented
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—671no—
705Q82—673no—
706#557—673no—
707#557—676no—
708#557—672no—
709#557C2×D6711yescharacteristic, complemented
710#556—673no—
711#556—6712no—
712#556—676no—
713#556—676no—
714#556—676no—
715#556C2×D6713yescomplemented
716#555—676no—
717#555—673no—
718#555—673no—
719#555—676no—
720#555—6712no—
721#555—676no—
722#553—6712no—
723#553—676no—
724#553—6712no—
725#553—676no—
726#553—676no—
727#553—676no—
728#552—6712no—
729#552—676no—
730#552C2×D6716yescomplemented
731#550—672no—
732#550—676no—
733#550—676no—
734#550—672no—
735#550—671no—
736#550—673no—
737#550—676no—
738#550—673no—
739#550—673no—
740D4×Q8—673no—
741D4×Q8C2×D6711yescharacteristic, complemented
742#548—672no—
743#548—672no—
744#548—676no—
745#548—676no—
746#548—676no—
747#548C2×D6712yes—
748#547—673no—
749#547—676no—
750#547C2×D6713yescomplemented
751#544—676no—
752#542—6712no—
753#542—676no—
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#533C2×D6713yescomplemented
769#532—673no—
770#532—673no—
771#532—673no—
772#532—673no—
773#532—673no—
774#532—6712no—
775#532—676no—
776#532—673no—
777#532—676no—
778#529—676no—
779#529—676no—
780#529—676no—
781#529—676no—
782#529—673no—
783#529—676no—
784#529—673no—
785#529—676no—
786#529—671no—
787#529—676no—
788#529—676no—
789#529—673no—
790#529—676no—
791#529—676no—
792#529—6712no—
793#529C2×D6716yescomplemented
794#525—673no—
795#525—676no—
796#525—676no—
797#525—676no—
798#525—676no—
799#525—676no—
800#525—673no—
801#520—676no—
802#520—672no—
803#520—676no—
804#520—676no—
805#519—672no—
806#519—672no—
807#519—676no—
808C4×#41—671no—
809C4×#41—671no—
810C4×#41—671no—
811C4×#41—676no—
812C4×#41—672no—
813C4×#41—676no—
814C4×#41—673no—
815C4×#41—673no—
816C4×#41—673no—
817C4×#41—676no—
818C4×#41—673no—
819C4×#41—676no—
820C4×#41—676no—
821C4×#41—676no—
822C4×#41—673no—
823C4×#41C2×D6711yescharacteristic
824C4×#41C2×D6713yescomplemented
825C2×C4×Q8—671no—
826C2×C4×Q8—671no—
827C2×C4×Q8—676no—
828C2×C4×Q8C2×D6712yescomplemented
829C2×C4×D4—673no—
830C2×C4×D4—673no—
831C2×#117—673no—
832C22×C42—673no—
8332−1+4—13416no—
834C2×#41—676no—
835C2×#41—671no—
836C2×#41—676no—
837C2×#41—672no—
838C2×#41—673no—
839C2×#41—676no—
840C2×#41—676no—
841C2×#41—673no—
842C2×#41—673no—
843C2×#41—676no—
844C2×#41—676no—
845C2×#41—1348no—
846C2×#41C22×D6711yescharacteristic
847C2×#41C22×D6713yes—
848C22×Q8—671no—
849C22×Q8—676no—
850C22×Q8C22×D6712yes—
851C22×D4—673no—
852C23×C4—673no—
853C23×C4—673no—
854C23×C4—673no—
855C4⋊Q8—673no—
856C4⋊Q8—673no—
857C4⋊Q8—673no—
858C4⋊Q8—6712no—
859C4⋊Q8—676no—
860C4⋊Q8—673no—
861C4⋊Q8—676no—
862C4⋊Q8C22×D6713yes—
863C4⋊Q8C22×D6713yes—
864#127—673no—
865#127—676no—
866#127—6712no—
867#127—673no—
868#127—676no—
869#126—676no—
870#126—676no—
871#126—6712no—
872#126—6712no—
873#126—6712no—
874#126—672no—
875#126—676no—
876#126—6712no—
877#126C22×D67112yes—
878#125—671no—
879#125—673no—
880#125—676no—
881#125—676no—
882#125—676no—
883#125—6712no—
884#125—676no—
885#125C22×D6716yes—
886#125C22×D6716yes—
887#124—673no—
888#124—676no—
889#124—676no—
890#124—671no—
891#124—676no—
892#124—676no—
893#124—6712no—
894#124—6712no—
895#124—6712no—
896#124—6712no—
897#124—676no—
898#124—6712no—
899#124C22×D6716yes—
900#123—676no—
901#123—676no—
902#123—676no—
903#123—6712no—
904#123—6712no—
905#123—6712no—
906#123—672no—
907#123—676no—
908#123—6712no—
909#123—676no—
910#123—6712no—
911#123C22×D67112yes—
912C22⋊Q8—673no—
913C22⋊Q8—673no—
914C22⋊Q8—676no—
915C22⋊Q8—676no—
916C22⋊Q8—671no—
917C22⋊Q8—676no—
918C22⋊Q8—676no—
919C22⋊Q8—676no—
920C22⋊Q8—673no—
921C22⋊Q8—676no—
922C22⋊Q8—6712no—
923C22⋊Q8—676no—
924C22⋊Q8—676no—
925C22⋊Q8C22×D6716yes—
926C22⋊Q8C22×D6716yes—
927C22⋊Q8C22×D6716yes—
928#121—671no—
929#121—676no—
930#121—676no—
931#121—673no—
932#121—676no—
933#121—6712no—
934#121—676no—
935#121—676no—
936#121—676no—
937#121—676no—
938#121—6712no—
939#121—673no—
940#121—676no—
941#121—676no—
942#121—676no—
943#121—673no—
944#121—676no—
945#121—676no—
946#121—6712no—
947#121—676no—
948#121—676no—
949#121—6712no—
950#121—6712no—
951#121—6712no—
952#121—6712no—
953#121C22×D6716yes—
954#120—676no—
955#120—676no—
956#120—6712no—
957C4×Q8—671no—
958C4×Q8—671no—
959C4×Q8—676no—
960C4×Q8—676no—
961C4×Q8—672no—
962C4×Q8—676no—
963C4×Q8—673no—
964C4×Q8—673no—
965C4×Q8—676no—
966C4×Q8—6712no—
967C4×Q8—676no—
968C4×Q8—676no—
969C4×Q8—673no—
970C4×Q8—676no—
971C4×Q8—673no—
972C4×Q8—671no—
973C4×Q8—676no—
974C4×Q8—676no—
975C4×Q8—673no—
976C4×Q8—676no—
977C4×Q8—676no—
978C4×Q8C22×D6711yescharacteristic
979C4×Q8C22×D6716yes—
980C4×Q8C22×D6711yescharacteristic
981C4×Q8C22×D6712yes—
982C4×Q8C22×D6716yes—
983C4×Q8C22×D6713yes—
984C4×Q8C22×D6713yes—
985C4×D4—673no—
986C4×D4—673no—
987C4×D4—676no—
988C4×D4—676no—
989C4×D4—672no—
990C4×D4—676no—
991C4×D4—676no—
992C4×D4—676no—
993C4×D4—6712no—
994C4×D4—676no—
995C4×D4—676no—
996C4×D4—676no—
997C4×D4—676no—
998C4×D4—676no—
999C4×D4—676no—
1000C4×D4—673no—
1001C4×D4—673no—
1002C4×D4—6712no—
1003C4×D4—676no—
1004C4×D4—676no—
1005C4×D4—6712no—
1006C4×D4—676no—
1007C4×D4—676no—
1008C4×D4—676no—
1009C4×D4—676no—
1010C4×D4—676no—
1011C4×D4—6712no—
1012C4×D4—6712no—
1013C4×D4—673no—
1014C4×D4—673no—
1015C4×D4—676no—
1016C4×D4—676no—
1017C4×D4—673no—
1018C4×D4—676no—
1019C4×D4—676no—
1020C4×D4—6712no—
1021C4×D4—676no—
1022C4×D4—676no—
1023C4×D4—673no—
1024C4×D4C22×D6713yes—
1025C4×D4C22×D6713yes—
1026C4×D4C22×D6711yescharacteristic
1027C4×D4C22×D6716yes—
1028C4×D4C22×D6716yes—
1029C4×D4C22×D6713yes—
1030#117—673no—
1031#117—672no—
1032#117—676no—
1033#117—676no—
1034#117—673no—
1035#117—673no—
1036#117—673no—
1037#117—676no—
1038#117—6712no—
1039#117—676no—
1040#117—676no—
1041#117—6712no—
1042#117—676no—
1043#117—676no—
1044#117—676no—
1045#117—676no—
1046#117—676no—
1047#117—6712no—
1048#117—676no—
1049#117—676no—
1050#117C22×D6713yes—
1051#117C22×D6716yes—
1052#117C22×D6713yes—
1053#117C22×D6716yes—
1054C2×C4⋊C4—673no—
1055C2×C4⋊C4—673no—
1056C2×C4⋊C4—6712no—
1057C2×C4⋊C4—676no—
1058C2×C4⋊C4C22×D6716yes—
1059C2×C22⋊C4—676no—
1060C2×C42—673no—
1061C2×C42—673no—
1062C2×C42—673no—
1063C2×C42—673no—
1064C2×C42—673no—
1065C2×C42—673no—
1066C2×C42—6712no—
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—46no—
1078#41—2686no—
1079#41—26812no—
1080#41—26812no—
1081#41—26812no—
1082#41—13424no—
1083#41—13412no—
1084#41—13424no—
1085#41—13424no—
1086#41—13412no—
1087#41—1344no—
1088#41—1348no—
1089C2×Q8—28no—
1090C2×Q8—678no—
1091C2×Q8—676no—
1092C2×Q8—676no—
1093C2×Q8—673no—
1094C2×Q8—676no—
1095C2×Q8—671no—
1096C2×Q8—13424no—
1097C2×Q8C23×D6716yes—
1098C2×Q8C23×D6713yes—
1099C2×Q8C23×D6711yescharacteristic
1100C2×D4—676no—
1101C2×D4—676no—
1102C2×D4—6712no—
1103C2×D4—676no—
1104C2×D4—672no—
1105C2×D4—676no—
1106C2×D4—676no—
1107C2×D4—6712no—
1108C2×D4—676no—
1109C2×D4—676no—
1110C2×D4—676no—
1111C2×D4—673no—
1112C2×D4—676no—
1113C2×D4—673no—
1114C2×D4—13412no—
1115C2×D4C23×D6713yes—
1116C2×D4C23×D6711yescharacteristic
1117C2×D4C23×D6716yes—
1118C22×C4—2686no—
1119C22×C4—2686no—
1120C22×C4—673no—
1121C22×C4—673no—
1122C22×C4—673no—
1123C22×C4—673no—
1124C22×C4—673no—
1125C22×C4—673no—
1126C22×C4—6712no—
1127C22×C4—676no—
1128C22×C4—673no—
1129C22×C4—673no—
1130C22×C4—671no—
1131C22×C4—671no—
1132C22×C4—673no—
1133C22×C4—673no—
1134C22×C4—673no—
1135C22×C4—6712no—
1136C22×C4—676no—
1137C22×C4—671no—
1138C22×C4—676no—
1139C22×C4—673no—
1140C22×C4—13412no—
1141C22×C4C23×D6713yes—
1142C22×C4C23×D6713yes—
1143C22×C4C23×D6716yes—
1144C22×C4C23×D6713yes—
1145C22×C4C23×D6712yes—
1146C22×C4C23×D6716yes—
1147C4⋊C4—676no—
1148C4⋊C4—673no—
1149C4⋊C4—676no—
1150C4⋊C4—676no—
1151C4⋊C4—676no—
1152C4⋊C4—676no—
1153C4⋊C4—673no—
1154C4⋊C4—671no—
1155C4⋊C4—672no—
1156C4⋊C4—676no—
1157C4⋊C4—676no—
1158C4⋊C4—673no—
1159C4⋊C4—672no—
1160C4⋊C4—676no—
1161C4⋊C4—676no—
1162C4⋊C4—672no—
1163C4⋊C4—676no—
1164C4⋊C4—672no—
1165C4⋊C4—676no—
1166C4⋊C4—6712no—
1167C4⋊C4—676no—
1168C4⋊C4—676no—
1169C4⋊C4C23×D6713yes—
1170C4⋊C4C23×D6716yes—
1171C4⋊C4C23×D67112yes—
1172C4⋊C4C23×D6713yes—
1173C4⋊C4C23×D6713yes—
1174C4⋊C4C23×D6716yes—
1175C4⋊C4C23×D6711yescharacteristic
1176C4⋊C4C23×D6716yes—
1177C4⋊C4C23×D6716yes—
1178C4⋊C4C23×D6716yes—
1179C22⋊C4—676no—
1180C22⋊C4—672no—
1181C22⋊C4—676no—
1182C22⋊C4—672no—
1183C22⋊C4—672no—
1184C22⋊C4—676no—
1185C22⋊C4—676no—
1186C22⋊C4—676no—
1187C22⋊C4—676no—
1188C22⋊C4—672no—
1189C22⋊C4—676no—
1190C22⋊C4—676no—
1191C22⋊C4—6712no—
1192C22⋊C4—676no—
1193C22⋊C4—676no—
1194C22⋊C4—676no—
1195C22⋊C4—676no—
1196C22⋊C4—676no—
1197C22⋊C4—6712no—
1198C22⋊C4—676no—
1199C22⋊C4—6712no—
1200C22⋊C4C23×D6716yes—
1201C22⋊C4C23×D6712yes—
1202C22⋊C4C23×D67112yes—
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—672no—
1222C42C23×D6713yes—
1223C42C23×D6713yes—
1224C42C23×D6716yes—
1225C42C23×D6716yes—
1226C42C23×D6713yes—
1227C42C23×D6711yescharacteristic
1228C42C23×D6716yes—
1229C23—2683no—
1230C23—2683no—
1231C23—671no—
1232C23—673no—
1233C23—676no—
1234C23—1346no—
1235C23C24×D6712yes—
1236C23C24×D6713yes—
1237Q8—212no—
1238Q8—26no—
1239Q8—2686no—
1240Q8—2686no—
1241Q8—6712no—
1242Q8—13412no—
1243Q8—1342no—
1244Q8#41×D6714yes—
1245D4—26no—
1246D4—22no—
1247D4—46no—
1248D4—26812no—
1249D4—2686no—
1250D4—2686no—
1251D4—2686no—
1252D4—2686no—
1253D4—26812no—
1254D4—2686no—
1255D4—13412no—
1256D4—13412no—
1257D4—13412no—
1258D4—1344no—
1259D4—1346no—
1260D4—13412no—
1261D4—1346no—
1262C2×C4—26no—
1263C2×C4—212no—
1264C2×C4—26no—
1265C2×C4—26no—
1266C2×C4—24no—
1267C2×C4—46no—
1268C2×C4—2683no—
1269C2×C4—2683no—
1270C2×C4—2683no—
1271C2×C4—2683no—
1272C2×C4—2686no—
1273C2×C4—26812no—
1274C2×C4—2683no—
1275C2×C4—2683no—
1276C2×C4—673no—
1277C2×C4—6712no—
1278C2×C4—671no—
1279C2×C4—671no—
1280C2×C4—673no—
1281C2×C4—671no—
1282C2×C4—676no—
1283C2×C4—672no—
1284C2×C4—673no—
1285C2×C4—672no—
1286C2×C4—1346no—
1287C2×C4—13424no—
1288C2×C4—1342no—
1289C2×C4—1346no—
1290C2×C4—1346no—
1291C2×C4—13412no—
1292C2×C4—1342no—
1293C2×C4—1346no—
1294C2×C4—1342no—
1295C2×C4—1346no—
1296C2×C4—13412no—
1297C2×C4C24×D6711yescharacteristic
1298C2×C4C24×D6713yes—
1299C2×C4C24×D6716yes—
1300C2×C4C24×D6713yes—
1301C2×C4C24×D6716yes—
1302C2×C4C24×D6712yes—
1303C2×C4C24×D6713yes—
1304C2×C4C24×D6711yescharacteristic
1305C2×C4C24×D6711yescharacteristic
1306C22—22no—
1307C22—23no—
1308C22—23no—
1309C22—22no—
1310C22—23no—
1311C22—22no—
1312C22—26812no—
1313C22—672no—
1314C22—1346no—
1315C22—1343no—
1316C22—1346no—
1317C22—1343no—
1318C22—1343no—
1319C22—1346no—
1320C22—1341no—
1321C22—1341no—
1322C22C25×D6711yescharacteristic
1323C4—21no—
1324C4—26no—
1325C4—23no—
1326C4—26no—
1327C4—23no—
1328C4—22no—
1329C4—676no—
1330C4—1341no—
1331C4—1342no—
1332C4—1341no—
1333C4—1343no—
1334C4—1342no—
1335C4—1341no—
1336C4—1343no—
1337C4—1346no—
1338C4C2×#41×D6716yes—
1339C4#1686423212yes—
1340C4#1686423312yes—
1341C2—43no—
1342C2—42no—
1343C2—2683no—
1344C2—2686no—
1345C2—1342no—
1346C2C22×#41×D6711yescharacteristic
1347C2C2×#1686423211yescharacteristic
1348C2C2×#1686423311yescharacteristic
subgroupG/H
centerC2×C4C24×D67
commutator, socle, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC67×#3482C2
hypercenter#3482D67
hypocenterC67#62793
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ #3482

Complements

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

NH ≅ G/Ntype
1. #22574319C2semidirect
2. #22574315C2semidirect
3. #22574223C2semidirect
4. #22574221C2semidirect
5. #22574216C2semidirect
6. #22574214C2semidirect
7. #22574062C2semidirect
8. #22574059C2semidirect
9. #22574013C2semidirect
10. #22573979C2semidirect
11. #22573927C2semidirect
12. #22573866C2semidirect
13. #22573835C2semidirect
14. #22573835C2semidirect
15. #22573827C2semidirect
16. #22573804C2semidirect
17. #22573800C2semidirect
18. #22573630C2semidirect
19. #22573506C2semidirect
20. #22573502C2semidirect
21. C4×#14524091C2semidirect
22. C4×#41×D67C2semidirect
23. C67×#3482C2semidirect
26. #16864131C22semidirect
27. #16864130C22semidirect
28. #16864128C22semidirect
29. Q8×Dic134C22semidirect
30. Q8×Dic134C22semidirect
31. #16864125C22semidirect
32. #16864123C22semidirect
33. #16864121C22semidirect
34. #16864120C22semidirect
35. #16864119C22semidirect
36. #16864117C22semidirect
37. #16864117C22semidirect
38. #16864113C22semidirect
39. #16864111C22semidirect
40. #16864111C22semidirect
41. #16864111C22semidirect
42. #16864109C22semidirect
43. #16864109C22semidirect
44. #16864109C22semidirect
45. #16864099C22semidirect
46. #16864097C22semidirect
47. #16864094C22semidirect
48. #16864094C22semidirect
49. #16864093C22semidirect
50. #16864091C22semidirect
51. #16864080C22semidirect
52. #16864078C22semidirect
54. #16864068C22semidirect
55. #16864068C22semidirect
57. #16864067C22semidirect
58. #16864067C22semidirect
60. #16864065C22semidirect
62. #16864061C22semidirect
64. #16864057C22semidirect
66. #16864056C22semidirect
68. #16864049C22semidirect
69. #16864048C22semidirect
71. #16864019C22semidirect
72. #16864015C22semidirect
73. #16864012C22semidirect
74. #16864002C22semidirect
75. #16863999C22semidirect
76. #16863998C22semidirect
83. #16863951C22semidirect
85. #16863950C22semidirect
86. #16863949C22semidirect
88. #16863947C22semidirect
89. #16863946C22semidirect
90. #16863946C22semidirect
92. #16863943C22semidirect
93. #16863943C22semidirect
94. #16863943C22semidirect
95. #16863942C22semidirect
97. #16863933C22semidirect
98. #16863933C22semidirect
99. #16863933C22semidirect
100. #16863932C22semidirect
101. #16863932C22semidirect
103. #16863931C22semidirect
105. #16863928C22semidirect
106. #16863926C22semidirect
107. #16863926C22semidirect
109. #16863924C22semidirect
110. #16863924C22semidirect
119. #16863878C22semidirect
121. #16863877C22semidirect
122. #16863874C22semidirect
124. #16863872C22semidirect
129. C4×#11761629C22semidirect
130. C4×#11761629C22semidirect
133. C4×#11761628C22semidirect
134. C4×#11761628C22semidirect
135. C4×#11761628C22semidirect
137. #16863864C22semidirect
142. C4×Q8×D67C22semidirect
147. #557×C67C22semidirect
148. #556×C67C22semidirect
149. #552×C67C22semidirect
150. D4×Q8×C67C22semidirect
152. #547×C67C22semidirect
153. #533×C67C22semidirect
154. #529×C67C22semidirect
156. C4×#41×C67C22semidirect
157. C2×C4×Q8×C67C22semidirect
418. Q8×D67#41semidirect
690. #3482D67semidirect
698. C67#62793semidirect
709. #557C2×D67semidirect
715. #556C2×D67semidirect
730. #552C2×D67semidirect
741. D4×Q8C2×D67semidirect
750. #547C2×D67semidirect
768. #533C2×D67semidirect
793. #529C2×D67semidirect
824. C4×#41C2×D67semidirect
828. C2×C4×Q8C2×D67semidirect

Maximal subgroups

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

subgroupindex
#225743192
#225743152
#225742232
#225742212
#225742162
#225742142
#225740622
#225740592
#225740132
#225739792
#225739272
#225738662
#225738352
#225738272
#225738042
#225738002
#225736302
#225735062
#225735022
C4×#145240912
C4×#41×D672
C67×#34822
#6279367