Finite Group Databasebeta

← #31763615

Subgroups — #31763615

Order 17152.

6644 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574877C218yesmaximal, complemented
2#22574837C214yesmaximal, complemented
3#22574765C214yesmaximal, complemented
4#22574662C214yesmaximal, complemented
5#22574561C214yesmaximal, complemented
6#22574412C214yesmaximal, complemented
7#22574393C214yesmaximal, complemented
8#22574356C212yesmaximal, complemented
9#22574345C212yesmaximal, complemented
10#22573811C214yesmaximal, complemented
11#22573771C218yesmaximal, complemented
12#22573638C214yesmaximal, complemented
13#22573619C214yesmaximal, complemented
14#22573594C214yesmaximal, complemented
15C2×#16863930C212yesmaximal, complemented
16C67×#3444C211yesmaximal, characteristic, complemented
17C67⋊#564C2212yescomplemented
18#16864150C2214yescomplemented
19#16864147C2218yescomplemented
20#16864146C2212yescomplemented
21#16864145C2214yescomplemented
22#16864145C2218yescomplemented
23#16864144C2212yescomplemented
24#16864142C2218yescomplemented
25#16864141C2218yescomplemented
26#16864140C2214yescomplemented
27#16864138C2212yescomplemented
28#16864134C2218yescomplemented
29#16864133C2214yescomplemented
30#16864130C2214yescomplemented
31#16864118C2218yescomplemented
32#16864109C2218yescomplemented
33#16864105C2218yescomplemented
34#16864100C2218yescomplemented
35#16864095C2218yescomplemented
36#16864095C2218yescomplemented
37#16864091C2218yescomplemented
38#16864089C2218yescomplemented
39#16864087C2218yescomplemented
40#16864085C2218yescomplemented
41#16864079C2218yescomplemented
42#16864079C2218yescomplemented
43#16864077C2214yescomplemented
44#16864075C2218yescomplemented
45#16864075C2218yescomplemented
46#16864074C2214yescomplemented
47#16864073C2218yescomplemented
48#16864070C2218yescomplemented
49#16864070C2218yescomplemented
50#16864045C2218yescomplemented
51#16864041C2218yescomplemented
52#16864035C2218yescomplemented
53#16864034C2218yescomplemented
54#16864033C2218yescomplemented
55#16864028C2214yescomplemented
56#16864025C2214yescomplemented
57#16864021C2214yescomplemented
58#16864018C2218yescomplemented
59#16864012C2218yescomplemented
60#16864011C2218yescomplemented
61#16864010C2218yescomplemented
62#16864005C2218yescomplemented
63#16864004C2218yescomplemented
64#16864003C2218yescomplemented
65#16863997C2218yescomplemented
66#16863995C2214yescomplemented
67#16863994C2218yescomplemented
68#16863991C2214yescomplemented
69#16863990C2218yescomplemented
70#16863990C2218yescomplemented
71#16863988C2218yescomplemented
72#16863988C2218yescomplemented
73#16863987C2218yescomplemented
74#16863986C2214yes—
75#16863985C2218yescomplemented
76#16863983C2214yescomplemented
77#16863980C2218yescomplemented
78#16863979C2218yescomplemented
79#16863979C2218yescomplemented
80#16863973C2214yes—
81#16863968C2218yescomplemented
82#16863957C2218yescomplemented
83#16863954C2214yescomplemented
84#16863950C2218yescomplemented
85#16863949C2214yescomplemented
86#16863942C2214yescomplemented
87#16863933C2218yescomplemented
88#16863930C2214yescomplemented
89#16863930C2214yescomplemented
90#16863930C2218yescomplemented
91#16863930C2214yescomplemented
92#16863930C2214yescomplemented
93#16863930C2214yescomplemented
94#16863930C2214yescomplemented
95#16863930C2214yescomplemented
96#16863930C2214yescomplemented
97#16863926C2218yescomplemented
98#16863926C2218yescomplemented
99#16863924C2218yescomplemented
100#16863924C2218yescomplemented
101C2×#14524037C2214yescomplemented
102C2×#14524035C2212yescomplemented
103C2×#14524031C2212yescomplemented
104#16863908C2214yescomplemented
105#16863905C2218yescomplemented
106#16863905C2218yescomplemented
107#16863903C2214yescomplemented
108C2×#14524026C2214yescomplemented
109C2×#14524022C2212yescomplemented
110C2×#14524017C2212yes—
111C4×#11761628C2214yescomplemented
112C4×#11761627C2218yescomplemented
113C2×C4×Dic134C2212yescomplemented
114C2×C4×D268C2212yescomplemented
115C2×C4×C22⋊D67C2214yescomplemented
116C4×D4×D67C2218yescomplemented
117C2×#14524000C2214yescomplemented
118C2×#14524000C2214yescomplemented
119#533×C67C2211yescharacteristic, complemented
120#533×C67C2212yescomplemented
121#532×C67C2211yescharacteristic, complemented
122#532×C67C2212yescomplemented
123#529×C67C2214yescomplemented
124#529×C67C2214yescomplemented
125#529×C67C2214yescomplemented
126#525×C67C2214yescomplemented
127#525×C67C2212yescomplemented
128C4×#41×C67C2212yescomplemented
129C4×#41×C67C2214yescomplemented
130C22×C42×C67C2211yescharacteristic, complemented
131C2×#11761628C2314yes—
132C2×#11761627C2318yes—
133C22×Dic134C2312yes—
134C22×D268C2312yes—
135C22×C22⋊D67C2314yes—
136C2×D4×D67C2318yes—
137C22×C4×D67C2314yes—
138C22×C4×D67C2314yes—
139#14524042C2318yes—
140#14524042C2318yes—
141#14524041C2314yes—
142#14524041C2318yes—
143#14524039C2314yes—
144#14524038C2318yes—
145#14524038C2318yes—
146#14524038C2318yes—
147#14524038C2318yes—
148#14524038C2318yes—
149#14524038C2318yes—
150#14524037C2318yes—
151#14524037C2318yes—
152#14524037C2318yes—
153#14524037C2318yes—
154#14524037C2318yes—
155#14524037C2318yes—
156#14524036C2318yes—
157#14524036C2318yes—
158#14524036C2318yes—
159#14524036C2318yes—
160#14524035C2314yes—
161#14524035C2314yes—
162#14524035C2318yes—
163#14524035C2314yes—
164#14524035C2314yes—
165#14524034C2318yes—
166#14524034C2318yes—
167#14524033C2318yes—
168#14524033C2318yes—
169#14524033C2318yes—
170#14524033C2318yes—
171#14524033C2318yes—
172#14524033C2318yes—
173#14524032C2314yes—
174#14524032C2318yes—
175#14524031C2314yes—
176#14524031C2314yes—
177#14524031C2318yes—
178#14524031C2314yes—
179#14524031C2314yes—
180#14524030C2314yes—
181#14524029C2318yes—
182#14524029C2318yes—
183#14524029C2318yes—
184#14524029C2318yes—
185#14524028C2318yes—
186#14524028C2318yes—
187#14524028C2318yes—
188#14524028C2318yes—
189#14524028C2318yes—
190#14524028C2318yes—
191#14524027C2318yes—
192#14524027C2318yes—
193#14524027C2318yes—
194#14524026C2318yes—
195#14524026C2318yes—
196#14524026C2318yes—
197#14524026C2318yes—
198#14524026C2318yes—
199#14524026C2318yes—
200#14524025C2318yes—
201#14524025C2318yes—
202#14524025C2318yes—
203#14524025C2318yes—
204#14524024C2318yes—
205#14524024C2318yes—
206#14524024C2314yes—
207#14524024C2314yes—
208#14524023C2318yes—
209#14524023C2318yes—
210#14524022C2314yes—
211#14524022C2318yes—
212#14524022C2314yes—
213#14524022C2314yes—
214#14524022C2314yes—
215#14524021C2318yes—
216#14524021C2318yes—
217#14524021C2318yes—
218#14524021C2318yes—
219#14524021C2318yes—
220#14524021C2318yes—
221#14524020C2318yes—
222#14524020C2318yes—
223#14524020C2318yes—
224#14524020C2318yes—
225#14524020C2318yes—
226#14524020C2318yes—
227#14524019C2318yes—
228#14524019C2318yes—
229#14524019C2318yes—
230#14524018C2318yes—
231#14524018C2318yes—
232#14524017C2318yes—
233#14524017C2314yes—
234#14524017C2314yes—
235#14524017C2314yes—
236#14524017C2314yes—
237#14524016C2318yes—
238#14524016C2318yes—
239#14524016C2318yes—
240#14524016C2318yes—
241#14524015C2318yes—
242#14524015C2318yes—
243#14524015C2318yes—
244#14524015C2318yes—
245#14524015C2318yes—
246#14524015C2318yes—
247#14524014C2318yes—
248#14524013C2318yes—
249#14524013C2318yes—
250#14524013C2318yes—
251#14524011C2314yes—
252#14524011C2318yes—
253#14524011C2318yes—
254#14524011C2314yes—
255C4×Dic134C2314yes—
256C4×Dic134C2318yes—
257C4×Dic134C2314yes—
258C4×Dic134C2314yes—
259C4×Dic134C2314yes—
260C4×Dic134C2318yes—
261#14524008C2318yes—
262C4×D268C2318yes—
263C4×D268C2318yes—
264C4×D268C2314yes—
265C4×D268C2314yes—
266C4×D268C2314yes—
267C4×D268C2314yes—
268D4×Dic67C2318yes—
269D4×Dic67C2318yes—
270#14524005C2318yes—
271C4×C22⋊D67C2318yes—
272C4×C22⋊D67C2318yes—
273C4×C22⋊D67C2318yes—
274C4×C22⋊D67C2318yes—
275C4×C22⋊D67C2318yes—
276C4×C22⋊D67C2318yes—
277C4×C22⋊D67C2318yes—
278C4×C22⋊D67C2318yes—
279(C22⋊D67)⋊C4C2318yes—
280(C22⋊D67)⋊C4C2318yes—
281(C22⋊D67)⋊C4C2318yes—
282(C22⋊D67)⋊C4C2318yes—
283#14524002C2314yes—
284#14524001C2318yes—
285#14524000C2318yes—
286#14524000C2318yes—
287#14524000C2318yes—
288#14524000C2318yes—
289#14524000C2318yes—
290#14524000C2318yes—
291#14524000C2318yes—
292#14523999C2318yes—
293#14523999C2318yes—
294C2×C4⋊Dic67C2312yes—
295C2×C4⋊Dic67C2312yes—
296C2×Dic67⋊C4C2314yes—
297C2×Dic67⋊C4C2314yes—
298C2×Dic67⋊C4C2318yes—
299C2×Dic67⋊C4C2314yes—
300C2×Dic67⋊C4C2314yes—
301C4⋊C4×D67C2318yes—
302C2×C22⋊Dic67C2314yes—
303C2×(C2×D67)⋊C4C2314yes—
304C2×(C2×D67)⋊C4C2314yes—
305C2×(C2×D67)⋊C4C2318yes—
306C2×(C2×D67)⋊C4C2314yes—
307C2×(C2×D67)⋊C4C2314yes—
308C22⋊C4×D67C2318yes—
309C22⋊C4×D67C2318yes—
310C2×C4×Dic67C2314yes—
311C2×C4×Dic67C2314yes—
312C42×D67C2318yes—
313C2×#41×C67C2314yes—
314C2×#41×C67C2312yes—
315C23×C4×C67C2311yescharacteristic
316C23×C4×C67C2312yes—
317C4⋊Q8×C67C2311yescharacteristic
318C4⋊Q8×C67C2312yes—
319#127×C67C2311yescharacteristic
320#126×C67C2318yes—
321#125×C67C2314yes—
322#125×C67C2312yes—
323#124×C67C2314yes—
324#124×C67C2312yes—
325#123×C67C2314yes—
326#123×C67C2318yes—
327C22⋊Q8×C67C2314yes—
328C22⋊Q8×C67C2314yes—
329C22⋊Q8×C67C2314yes—
330#121×C67C2314yes—
331#121×C67C2314yes—
332#121×C67C2314yes—
333#120×C67C2314yes—
334C4×Q8×C67C2314yes—
335C4×Q8×C67C2314yes—
336C4×Q8×C67C2314yes—
337C4×D4×C67C2318yes—
338C4×D4×C67C2318yes—
339C4×D4×C67C2314yes—
340C4×D4×C67C2318yes—
341C4×D4×C67C2314yes—
342C4×D4×C67C2314yes—
343#117×C67C2314yes—
344#117×C67C2318yes—
345#117×C67C2312yes—
346#117×C67C2314yes—
347C2×C42×C67C2312yes—
348C2×C42×C67C2311yescharacteristic
349C2×C42×C67C2312yes—
350C2×C42×C67C2312yes—
351C2×C42×C67C2312yes—
352C2×C42×C67C2312yes—
353C2×C42×C67C2311yescharacteristic
354C2×C42×C67C2314yes—
355C23×D67C2414yes—
356C23×D67C2414yes—
357#11761628—48no—
358#11761627—416no—
359C2×Dic134—44no—
360C2×Dic134C2418yes—
361C2×Dic134C2414yes—
362C2×Dic134C2414yes—
363C2×Dic134C2414yes—
364C2×D268—44no—
365C2×D268C2418yes—
366C2×D268C2414yes—
367C2×D268C2414yes—
368C2×D268C2414yes—
369C2×C22⋊D67—48no—
370C2×C22⋊D67C2418yes—
371C2×C22⋊D67C2418yes—
372C2×C22⋊D67C2418yes—
373C2×C22⋊D67C2418yes—
374C2×C22⋊D67C2418yes—
375D4×D67—416no—
376C22×Dic67C2414yes—
377C22×Dic67C2414yes—
378C22×Dic67C2418yes—
379C22×Dic67C2414yes—
380C22×Dic67C2414yes—
381C2×C4×D67—48no—
382C2×C4×D67—48no—
383C2×C4×D67C2418yes—
384C2×C4×D67C2418yes—
385C2×C4×D67C2418yes—
386C2×C4×D67C2418yes—
387C2×C4×D67C2418yes—
388C4⋊Dic67C2418yes—
389C4⋊Dic67C2414yes—
390C4⋊Dic67C2414yes—
391C4⋊Dic67C2414yes—
392C4⋊Dic67C2414yes—
393C4⋊Dic67C2418yes—
394C4⋊Dic67C2418yes—
395Dic67⋊C4C2418yes—
396Dic67⋊C4C2418yes—
397Dic67⋊C4C2418yes—
398Dic67⋊C4C2418yes—
399Dic67⋊C4C2418yes—
400Dic67⋊C4C2418yes—
401Dic67⋊C4C2418yes—
402Dic67⋊C4C2418yes—
403Dic67⋊C4C2418yes—
404Dic67⋊C4C2418yes—
405Dic67⋊C4C2418yes—
406Dic67⋊C4C2418yes—
407Dic67⋊C4C2418yes—
408Dic67⋊C4C2418yes—
409C22⋊Dic67C2418yes—
410C22⋊Dic67C2418yes—
411C22⋊Dic67C2418yes—
412C22⋊Dic67C2418yes—
413C22⋊Dic67C2414yes—
414C22⋊Dic67C2414yes—
415(C2×D67)⋊C4C2418yes—
416(C2×D67)⋊C4C2418yes—
417(C2×D67)⋊C4C2418yes—
418(C2×D67)⋊C4C2418yes—
419(C2×D67)⋊C4C2418yes—
420(C2×D67)⋊C4C2418yes—
421(C2×D67)⋊C4C2418yes—
422(C2×D67)⋊C4C2418yes—
423(C2×D67)⋊C4C2418yes—
424(C2×D67)⋊C4C2418yes—
425(C2×D67)⋊C4C2418yes—
426(C2×D67)⋊C4C2418yes—
427(C2×D67)⋊C4C2418yes—
428(C2×D67)⋊C4C2418yes—
429C4×Dic67C2418yes—
430C4×Dic67C2418yes—
431C4×Dic67C2418yes—
432C4×Dic67C2414yes—
433C4×Dic67C2418yes—
434C4×Dic67C2414yes—
435C24×C67C2411yescharacteristic
436#41×C67—44no—
437#41×C67—48no—
438C2×Q8×C67C2412yes—
439C2×Q8×C67C2414yes—
440C2×D4×C67C2418yes—
441C2×D4×C67C2414yes—
442C2×D4×C67C2414yes—
443C2×D4×C67C2412yes—
444C22×C4×C67—42no—
445C22×C4×C67—44no—
446C22×C4×C67C2412yes—
447C22×C4×C67C2411yescharacteristic
448C22×C4×C67C2412yes—
449C22×C4×C67C2412yes—
450C22×C4×C67C2414yes—
451C22×C4×C67C2412yes—
452C22×C4×C67C2412yes—
453C22×C4×C67C2412yes—
454C22×C4×C67C2412yes—
455C22×C4×C67C2412yes—
456C22×C4×C67C2411yescharacteristic
457C22×C4×C67C2418yes—
458C4⋊C4×C67C2414yes—
459C4⋊C4×C67C2414yes—
460C4⋊C4×C67C2414yes—
461C4⋊C4×C67C2418yes—
462C4⋊C4×C67C2418yes—
463C4⋊C4×C67C2418yes—
464C22⋊C4×C67C2418yes—
465C22⋊C4×C67C2414yes—
466C22⋊C4×C67C2418yes—
467C22⋊C4×C67C2418yes—
468C22⋊C4×C67C2418yes—
469C42×C67C2411yescharacteristic
470C42×C67C2412yes—
471C42×C67C2411yescharacteristic
472C42×C67C2412yes—
473C42×C67C2412yes—
474C42×C67C2412yes—
475C42×C67C2412yes—
476C42×C67C2411yescharacteristic
477C42×C67C2412yes—
478C42×C67C2411yescharacteristic
479C42×C67C2414yes—
480C42×C67C2418yes—
481C23×C67—24no—
482C23×C67—41no—
483C23×C67C2514yes—
484C23×C67C2511yescharacteristic
485C23×C67C2512yes—
486C22×D67—28no—
487C22×D67—44no—
488C22×D67—44no—
489C22×D67—48no—
490C22×D67—44no—
491C22×D67C2518yes—
492Q8×C67—42no—
493Q8×C67—44no—
494D4×C67—216no—
495D4×C67—44no—
496D4×C67—42no—
497D4×C67—44no—
498C2×C4×C67—24no—
499C2×C4×C67—24no—
500C2×C4×C67—22no—
501C2×C4×C67—24no—
502C2×C4×C67—28no—
503C2×C4×C67—42no—
504C2×C4×C67—42no—
505C2×C4×C67—42no—
506C2×C4×C67—42no—
507C2×C4×C67—41no—
508C2×C4×C67—42no—
509C2×C4×C67—48no—
510C2×C4×C67C2512yes—
511C2×C4×C67C2512yes—
512C2×C4×C67C2512yes—
513C2×C4×C67C2512yes—
514C2×C4×C67C2512yes—
515C2×C4×C67C2511yescharacteristic
516C2×C4×C67C2514yes—
517C2×C4×C67C2518yes—
518C2×C4×C67C2511yescharacteristic
519C22⋊D67—216no—
520C22⋊D67—48no—
521C22⋊D67—48no—
522C22⋊D67—48no—
523C22⋊D67—48no—
524C2×Dic67—28no—
525C2×Dic67—44no—
526C2×Dic67—44no—
527C2×Dic67—44no—
528C2×Dic67—48no—
529C2×Dic67C2518yes—
530C2×Dic67C2518yes—
531C2×Dic67C2518yes—
532D268—48no—
533D268—44no—
534D268—44no—
535D268—44no—
536C4×D67—216no—
537C4×D67—48no—
538C4×D67—48no—
539C4×D67—48no—
540C4×D67—48no—
541Dic134—44no—
542Dic134—44no—
543Dic134—48no—
544Dic134—44no—
545C22×C67—22no—
546C22×C67—22no—
547C22×C67—24no—
548C22×C67—28no—
549C22×C67—22no—
550C22×C67—21no—
551C22×C67—44no—
552C22×C67#58514yes—
553C22×C67C2611yescharacteristic
554C2×D67—28no—
555C2×D67—28no—
556C2×D67—28no—
557C2×D67—88no—
558C2×D67—88no—
559C4×C67—22no—
560C4×C67—22no—
561C4×C67—24no—
562C4×C67—28no—
563C4×C67—22no—
564C4×C67—22no—
565C4×C67—22no—
566C4×C67—21no—
567C4×C67#58512yes—
568Dic67—28no—
569Dic67—28no—
570Dic67—28no—
571#62755—671nomaximal, Sylow
572C2×C67—24no—
573C2×C67—44no—
574C2×C67—41no—
575C2×C67C2×#58512yes—
576C2×C67C2×#58511yescharacteristic
577D67—48no—
578#3566—678no—
579#3564—674no—
580#3560—674no—
581#3553—674no—
582#3545—674no—
583#3535—674no—
584#3534—674no—
585#3531—672no—
586#3529—672no—
587#3481—674no—
588#3475—678no—
589#3461—674no—
590#3459—674no—
591#3455—674no—
592#3444D6711yescharacteristic, complemented
593C2×#529—672no—
594C67#6275511yescharacteristic, complemented, Sylow
595#564—672no—
596#563—674no—
597#563—678no—
598#563—674no—
599#563—672no—
600#563—678no—
601#562—672no—
602#562—674no—
603#562—678no—
604#562—678no—
605H(3,𝔽4)—672no—
606#560—674no—
607#560—678no—
608#559—674no—
609#556—678no—
610#555—678no—
611#554—678no—
612#554—678no—
613#553—678no—
614#553—678no—
615#553—678no—
616#553—678no—
617#552—678no—
618#552—678no—
619#552—678no—
620#552—678no—
621#551—674no—
622#551—678no—
623#551—674no—
624#551—678no—
625#551—678no—
626#551—678no—
627#551—678no—
628#547—678no—
629#546—678no—
630#546—678no—
631#546—678no—
632#546—678no—
633D42—674no—
634#544—674no—
635#543—674no—
636#542—678no—
637#542—678no—
638#542—678no—
639#542—678no—
640#541—678no—
641#541—678no—
642#541—678no—
643#540—678no—
644#539—678no—
645#539—678no—
646#539—678no—
647#539—678no—
648#539—674no—
649#539—674no—
650#539—678no—
651#539—678no—
652#538—678no—
653#538—678no—
654#538—674no—
655#538—674no—
656#538—678no—
657#538—678no—
658#537—674no—
659#536—678no—
660#534—678no—
661#534—674no—
662#533—678no—
663#533—674no—
664#533C2×D6711yescharacteristic, complemented
665#533C2×D6712yescomplemented
666#532—674no—
667#532C2×D6711yescharacteristic, complemented
668#532C2×D6712yescomplemented
669#529—678no—
670#529—678no—
671#529—678no—
672#529—678no—
673#529—678no—
674#529—674no—
675#529—674no—
676#529—674no—
677#529—674no—
678#529—674no—
679#529—674no—
680#529—674no—
681#529—674no—
682#529—678no—
683#529C2×D6714yescomplemented
684#529C2×D6714yescomplemented
685#529C2×D6714yescomplemented
686C2×#126—674no—
687C2×#125—672no—
688C2×#124—672no—
689#525—674no—
690#525—678no—
691#525—678no—
692#525—674no—
693#525C2×D6712yescomplemented
694#525C2×D6714yescomplemented
695C2×#123—674no—
696C2×C22⋊Q8—672no—
697C2×#121—672no—
698C4×#41—678no—
699C4×#41—674no—
700C4×#41C2×D6712yescomplemented
701C4×#41C2×D6714yescomplemented
702C2×C4×Q8—672no—
703C2×C4×D4—674no—
704C2×C4×D4—678no—
705C2×C4×D4—672no—
706C2×#117—674no—
707C2×#117—674no—
708C22×C42C2×D6711yescharacteristic, complemented
709C2×#41—678no—
710C2×#41—674no—
711C2×#41C22×D6712yes—
712C2×#41C22×D6714yes—
713C22×Q8—672no—
714C22×D4—674no—
715C22×D4—678no—
716C22×D4—672no—
717C23×C4—674no—
718C23×C4—674no—
719C23×C4C22×D6711yescharacteristic
720C23×C4C22×D6712yes—
721C4⋊Q8—674no—
722C4⋊Q8—678no—
723C4⋊Q8—678no—
724C4⋊Q8—678no—
725C4⋊Q8C22×D6711yescharacteristic
726C4⋊Q8C22×D6712yes—
727#127—674no—
728#127C22×D6711yescharacteristic
729#126—678no—
730#126—678no—
731#126—678no—
732#126—678no—
733#126—678no—
734#126—678no—
735#126—678no—
736#126—678no—
737#126—678no—
738#126—678no—
739#126—678no—
740#126—678no—
741#126—678no—
742#126—678no—
743#126—678no—
744#126—678no—
745#126C22×D6718yes—
746#125—678no—
747#125—678no—
748#125—678no—
749#125—678no—
750#125—678no—
751#125—678no—
752#125—678no—
753#125—678no—
754#125—674no—
755#125—674no—
756#125—674no—
757#125—674no—
758#125—678no—
759#125C22×D6714yes—
760#125C22×D6712yes—
761#124—678no—
762#124—674no—
763#124—674no—
764#124—678no—
765#124—678no—
766#124—678no—
767#124—678no—
768#124—674no—
769#124—674no—
770#124—674no—
771#124—674no—
772#124—678no—
773#124C22×D6714yes—
774#124C22×D6712yes—
775#123—674no—
776#123—674no—
777#123—678no—
778#123—678no—
779#123—678no—
780#123—678no—
781#123—678no—
782#123—678no—
783#123—678no—
784#123—678no—
785#123—678no—
786#123—678no—
787#123—678no—
788#123—678no—
789#123—678no—
790#123—678no—
791#123—678no—
792#123—678no—
793#123—678no—
794#123—678no—
795#123—678no—
796#123—678no—
797#123—678no—
798#123C22×D6718yes—
799#123C22×D6714yes—
800C22⋊Q8—678no—
801C22⋊Q8—678no—
802C22⋊Q8—678no—
803C22⋊Q8—674no—
804C22⋊Q8—674no—
805C22⋊Q8—674no—
806C22⋊Q8—674no—
807C22⋊Q8—678no—
808C22⋊Q8—678no—
809C22⋊Q8—678no—
810C22⋊Q8—678no—
811C22⋊Q8—678no—
812C22⋊Q8—678no—
813C22⋊Q8—678no—
814C22⋊Q8—678no—
815C22⋊Q8—678no—
816C22⋊Q8—678no—
817C22⋊Q8—678no—
818C22⋊Q8—678no—
819C22⋊Q8—678no—
820C22⋊Q8—678no—
821C22⋊Q8—678no—
822C22⋊Q8C22×D6714yes—
823C22⋊Q8C22×D6714yes—
824C22⋊Q8C22×D6714yes—
825#121—678no—
826#121—678no—
827#121—678no—
828#121—678no—
829#121—678no—
830#121—678no—
831#121—678no—
832#121—674no—
833#121—674no—
834#121—674no—
835#121—674no—
836#121—678no—
837#121—678no—
838#121—678no—
839#121—678no—
840#121—678no—
841#121—678no—
842#121—678no—
843#121C22×D6714yes—
844#121C22×D6714yes—
845#121C22×D6714yes—
846#120—678no—
847#120—678no—
848#120—674no—
849#120—674no—
850#120—678no—
851#120—678no—
852#120—678no—
853#120C22×D6714yes—
854C4×Q8—678no—
855C4×Q8—674no—
856C4×Q8—674no—
857C4×Q8—674no—
858C4×Q8—674no—
859C4×Q8—678no—
860C4×Q8—678no—
861C4×Q8C22×D6714yes—
862C4×Q8C22×D6714yes—
863C4×Q8C22×D6714yes—
864C4×D4—678no—
865C4×D4—678no—
866C4×D4—678no—
867C4×D4—678no—
868C4×D4—678no—
869C4×D4—678no—
870C4×D4—678no—
871C4×D4—678no—
872C4×D4—678no—
873C4×D4—678no—
874C4×D4—678no—
875C4×D4—678no—
876C4×D4—678no—
877C4×D4—678no—
878C4×D4—678no—
879C4×D4—678no—
880C4×D4—674no—
881C4×D4—674no—
882C4×D4—674no—
883C4×D4—674no—
884C4×D4—678no—
885C4×D4C22×D6718yes—
886C4×D4C22×D6714yes—
887C4×D4C22×D6718yes—
888C4×D4C22×D6718yes—
889C4×D4C22×D6714yes—
890C4×D4C22×D6714yes—
891#117—674no—
892#117—678no—
893#117—678no—
894#117—678no—
895#117—678no—
896#117—678no—
897#117—678no—
898#117—678no—
899#117—678no—
900#117—678no—
901#117—678no—
902#117C22×D6714yes—
903#117C22×D6712yes—
904#117C22×D6714yes—
905#117C22×D6718yes—
906C2×C4⋊C4—674no—
907C2×C4⋊C4—674no—
908C2×C4⋊C4—678no—
909C2×C4⋊C4—672no—
910C2×C4⋊C4—674no—
911C2×C4⋊C4—672no—
912C2×C4⋊C4—674no—
913C2×C4⋊C4—678no—
914C2×C22⋊C4—674no—
915C2×C22⋊C4—674no—
916C2×C22⋊C4—674no—
917C2×C22⋊C4—678no—
918C2×C22⋊C4—674no—
919C2×C22⋊C4—674no—
920C2×C22⋊C4—678no—
921C2×C22⋊C4—678no—
922C2×C42—674no—
923C2×C42—674no—
924C2×C42—678no—
925C2×C42C22×D6712yes—
926C2×C42C22×D6714yes—
927C2×C42C22×D6712yes—
928C2×C42C22×D6711yescharacteristic
929C2×C42C22×D6712yes—
930C2×C42C22×D6712yes—
931C2×C42C22×D6712yes—
932C2×C42C22×D6711yescharacteristic
933C24—674no—
934C24—674no—
935C24C23×D6711yescharacteristic
936#41—44no—
937#41—48no—
938#41—2688no—
939#41—26816no—
940C2×Q8—2684no—
941C2×Q8—674no—
942C2×Q8—674no—
943C2×Q8—674no—
944C2×Q8—678no—
945C2×Q8C23×D6714yes—
946C2×Q8C23×D6712yes—
947C2×D4—2684no—
948C2×D4—26816no—
949C2×D4—2688no—
950C2×D4—678no—
951C2×D4—678no—
952C2×D4—678no—
953C2×D4—678no—
954C2×D4—678no—
955C2×D4—674no—
956C2×D4—678no—
957C2×D4—674no—
958C2×D4—674no—
959C2×D4C23×D6718yes—
960C2×D4C23×D6714yes—
961C2×D4C23×D6712yes—
962C2×D4C23×D6714yes—
963C22×C4—42no—
964C22×C4—44no—
965C22×C4—2688no—
966C22×C4—2688no—
967C22×C4—674no—
968C22×C4—678no—
969C22×C4—674no—
970C22×C4—674no—
971C22×C4—678no—
972C22×C4—678no—
973C22×C4—678no—
974C22×C4—678no—
975C22×C4—674no—
976C22×C4—678no—
977C22×C4C23×D6712yes—
978C22×C4C23×D6712yes—
979C22×C4C23×D6712yes—
980C22×C4C23×D6714yes—
981C22×C4C23×D6711yescharacteristic
982C22×C4C23×D6712yes—
983C22×C4C23×D6712yes—
984C22×C4C23×D6712yes—
985C22×C4C23×D6711yescharacteristic
986C22×C4C23×D6712yes—
987C22×C4C23×D6712yes—
988C22×C4C23×D6718yes—
989C4⋊C4—678no—
990C4⋊C4—678no—
991C4⋊C4—678no—
992C4⋊C4—678no—
993C4⋊C4—678no—
994C4⋊C4—678no—
995C4⋊C4—678no—
996C4⋊C4—678no—
997C4⋊C4—678no—
998C4⋊C4—678no—
999C4⋊C4—674no—
1000C4⋊C4—674no—
1001C4⋊C4—674no—
1002C4⋊C4—674no—
1003C4⋊C4—678no—
1004C4⋊C4—678no—
1005C4⋊C4—678no—
1006C4⋊C4—678no—
1007C4⋊C4—678no—
1008C4⋊C4—678no—
1009C4⋊C4—678no—
1010C4⋊C4C23×D6718yes—
1011C4⋊C4C23×D6718yes—
1012C4⋊C4C23×D6718yes—
1013C4⋊C4C23×D6714yes—
1014C4⋊C4C23×D6714yes—
1015C4⋊C4C23×D6714yes—
1016C22⋊C4—678no—
1017C22⋊C4—678no—
1018C22⋊C4—678no—
1019C22⋊C4—674no—
1020C22⋊C4—678no—
1021C22⋊C4—674no—
1022C22⋊C4—678no—
1023C22⋊C4—678no—
1024C22⋊C4—678no—
1025C22⋊C4—678no—
1026C22⋊C4—678no—
1027C22⋊C4—678no—
1028C22⋊C4—678no—
1029C22⋊C4—678no—
1030C22⋊C4—678no—
1031C22⋊C4—678no—
1032C22⋊C4—678no—
1033C22⋊C4—678no—
1034C22⋊C4—678no—
1035C22⋊C4—678no—
1036C22⋊C4C23×D6718yes—
1037C22⋊C4C23×D6718yes—
1038C22⋊C4C23×D6718yes—
1039C22⋊C4C23×D6718yes—
1040C22⋊C4C23×D6714yes—
1041C42—674no—
1042C42—678no—
1043C42—678no—
1044C42—674no—
1045C42—678no—
1046C42—678no—
1047C42C23×D6712yes—
1048C42C23×D6712yes—
1049C42C23×D6712yes—
1050C42C23×D6712yes—
1051C42C23×D6712yes—
1052C42C23×D6711yescharacteristic
1053C42C23×D6711yescharacteristic
1054C42C23×D6718yes—
1055C42C23×D6714yes—
1056C42C23×D6711yescharacteristic
1057C42C23×D6712yes—
1058C42C23×D6711yescharacteristic
1059C23—24no—
1060C23—41no—
1061C23—2684no—
1062C23—2684no—
1063C23—2684no—
1064C23—2688no—
1065C23—678no—
1066C23—1348no—
1067C23C24×D6711yescharacteristic
1068C23C24×D6714yes—
1069C23C24×D6712yes—
1070Q8—42no—
1071Q8—44no—
1072Q8—2684no—
1073Q8—2684no—
1074Q8—2684no—
1075Q8—2688no—
1076D4—216no—
1077D4—42no—
1078D4—44no—
1079D4—44no—
1080D4—2684no—
1081D4—2684no—
1082D4—2688no—
1083D4—2684no—
1084D4—2688no—
1085D4—2688no—
1086D4—2688no—
1087D4—2688no—
1088D4—13416no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—22no—
1093C2×C4—28no—
1094C2×C4—42no—
1095C2×C4—42no—
1096C2×C4—41no—
1097C2×C4—42no—
1098C2×C4—42no—
1099C2×C4—42no—
1100C2×C4—48no—
1101C2×C4—2688no—
1102C2×C4—2688no—
1103C2×C4—2688no—
1104C2×C4—2688no—
1105C2×C4—2684no—
1106C2×C4—2684no—
1107C2×C4—2684no—
1108C2×C4—2688no—
1109C2×C4—678no—
1110C2×C4—678no—
1111C2×C4—678no—
1112C2×C4—1348no—
1113C2×C4—13416no—
1114C2×C4C24×D6712yes—
1115C2×C4C24×D6714yes—
1116C2×C4C24×D6718yes—
1117C2×C4C24×D6712yes—
1118C2×C4C24×D6712yes—
1119C2×C4C24×D6711yescharacteristic
1120C2×C4C24×D6712yes—
1121C2×C4C24×D6712yes—
1122C2×C4C24×D6711yescharacteristic
1123C22—22no—
1124C22—22no—
1125C22—21no—
1126C22—24no—
1127C22—22no—
1128C22—28no—
1129C22—44no—
1130C22—5368no—
1131C22—5368no—
1132C22—1348no—
1133C22—1348no—
1134C22—1348no—
1135C22#1686423214yes—
1136C22C25×D6711yescharacteristic
1137C4—22no—
1138C4—22no—
1139C4—22no—
1140C4—21no—
1141C4—22no—
1142C4—22no—
1143C4—24no—
1144C4—28no—
1145C4—1348no—
1146C4—1348no—
1147C4—1348no—
1148C4#1686423212yes—
1149C2—24no—
1150C2—41no—
1151C2—44no—
1152C2—2688no—
1153C2C2×#1686423212yes—
1154C2C2×#1686423211yescharacteristic
subgroupG/H
centerC2×C4C24×D67
commutator, socle, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC67×#3444C2
hypercenter#3444D67
hypocenterC67#62755
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #22574877C2semidirect
2. #22574837C2semidirect
3. #22574765C2semidirect
4. #22574662C2semidirect
5. #22574561C2semidirect
6. #22574412C2semidirect
7. #22574393C2semidirect
8. #22574356C2semidirect
9. #22574345C2semidirect
10. #22573811C2semidirect
11. #22573771C2semidirect
12. #22573638C2semidirect
13. #22573619C2semidirect
14. #22573594C2semidirect
15. C2×#16863930C2semidirect
16. C67×#3444C2semidirect
17. C67⋊#564C22semidirect
18. #16864150C22semidirect
19. #16864147C22semidirect
20. #16864146C22semidirect
21. #16864145C22semidirect
22. #16864145C22semidirect
23. #16864144C22semidirect
24. #16864142C22semidirect
25. #16864141C22semidirect
26. #16864140C22semidirect
27. #16864138C22semidirect
28. #16864134C22semidirect
29. #16864133C22semidirect
30. #16864130C22semidirect
31. #16864118C22semidirect
32. #16864109C22semidirect
33. #16864105C22semidirect
34. #16864100C22semidirect
35. #16864095C22semidirect
36. #16864095C22semidirect
37. #16864091C22semidirect
38. #16864089C22semidirect
39. #16864087C22semidirect
40. #16864085C22semidirect
41. #16864079C22semidirect
42. #16864079C22semidirect
43. #16864077C22semidirect
44. #16864075C22semidirect
45. #16864075C22semidirect
46. #16864074C22semidirect
47. #16864073C22semidirect
48. #16864070C22semidirect
49. #16864070C22semidirect
50. #16864045C22semidirect
51. #16864041C22semidirect
52. #16864035C22semidirect
53. #16864034C22semidirect
54. #16864033C22semidirect
55. #16864028C22semidirect
56. #16864025C22semidirect
57. #16864021C22semidirect
58. #16864018C22semidirect
59. #16864012C22semidirect
60. #16864011C22semidirect
61. #16864010C22semidirect
62. #16864005C22semidirect
63. #16864004C22semidirect
64. #16864003C22semidirect
65. #16863997C22semidirect
66. #16863995C22semidirect
67. #16863994C22semidirect
68. #16863991C22semidirect
69. #16863990C22semidirect
70. #16863990C22semidirect
71. #16863988C22semidirect
72. #16863988C22semidirect
73. #16863987C22semidirect
75. #16863985C22semidirect
76. #16863983C22semidirect
77. #16863980C22semidirect
78. #16863979C22semidirect
79. #16863979C22semidirect
81. #16863968C22semidirect
82. #16863957C22semidirect
83. #16863954C22semidirect
84. #16863950C22semidirect
85. #16863949C22semidirect
86. #16863942C22semidirect
87. #16863933C22semidirect
88. #16863930C22semidirect
89. #16863930C22semidirect
90. #16863930C22semidirect
91. #16863930C22semidirect
92. #16863930C22semidirect
93. #16863930C22semidirect
94. #16863930C22semidirect
95. #16863930C22semidirect
96. #16863930C22semidirect
97. #16863926C22semidirect
98. #16863926C22semidirect
99. #16863924C22semidirect
100. #16863924C22semidirect
101. C2×#14524037C22semidirect
102. C2×#14524035C22semidirect
103. C2×#14524031C22semidirect
104. #16863908C22semidirect
105. #16863905C22semidirect
106. #16863905C22semidirect
107. #16863903C22semidirect
108. C2×#14524026C22semidirect
109. C2×#14524022C22semidirect
111. C4×#11761628C22semidirect
112. C4×#11761627C22semidirect
113. C2×C4×Dic134C22semidirect
114. C2×C4×D268C22semidirect
115. C2×C4×C22⋊D67C22semidirect
116. C4×D4×D67C22semidirect
117. C2×#14524000C22semidirect
118. C2×#14524000C22semidirect
119. #533×C67C22semidirect
120. #533×C67C22semidirect
121. #532×C67C22semidirect
122. #532×C67C22semidirect
123. #529×C67C22semidirect
124. #529×C67C22semidirect
125. #529×C67C22semidirect
126. #525×C67C22semidirect
127. #525×C67C22semidirect
128. C4×#41×C67C22semidirect
129. C4×#41×C67C22semidirect
130. C22×C42×C67C22semidirect
592. #3444D67semidirect
594. C67#62755semidirect
664. #533C2×D67semidirect
665. #533C2×D67semidirect
667. #532C2×D67semidirect
668. #532C2×D67semidirect
683. #529C2×D67semidirect
684. #529C2×D67semidirect
685. #529C2×D67semidirect
693. #525C2×D67semidirect
694. #525C2×D67semidirect
700. C4×#41C2×D67semidirect
701. C4×#41C2×D67semidirect
708. C22×C42C2×D67semidirect

Maximal subgroups

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

subgroupindex
#225748772
#225748372
#225747652
#225746622
#225745612
#225744122
#225743932
#225743562
#225743452
#225738112
#225737712
#225736382
#225736192
#225735942
C2×#168639302
C67×#34442
#6275567