Finite Group Databasebeta

← #11884474

Subgroups — #11884474

Order 1152.

1092 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63806C211yesmaximal, characteristic, complemented
2C2×#63794C211yesmaximal, characteristic, complemented
3#10594003C211yesmaximal, characteristic, complemented
4#10593902C211yesmaximal, characteristic, complemented
5#10592411C211yesmaximal, characteristic, complemented
6C3×#4710C211yesmaximal, characteristic, complemented
7C3×#4706C211yesmaximal, characteristic, complemented
8#10590970C211yesmaximal, characteristic, complemented
9#10590968C211yesmaximal, characteristic, complemented
10#10590967C211yesmaximal, characteristic, complemented
11#10590947C211yesmaximal, characteristic, complemented
12#10590838C211yesmaximal, characteristic, complemented
13#10590832C211yesmaximal, characteristic, complemented
14#10590368C211yesmaximal, characteristic, complemented
15#10590349C211yesmaximal, characteristic, complemented
16#79796—31nomaximal
17#79497—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×#3799C2211yescharacteristic, complemented
21C2×#3795C2211yescharacteristic
22C2×#3745C2211yescharacteristic
23C2×#3745C2211yescharacteristic
24C2×#3744C2211yescharacteristic, complemented
25C2×#3744C2211yescharacteristic, complemented
26#64084C2211yescharacteristic
27#64083C2211yescharacteristic, complemented
28C2×C3×#204C2211yescharacteristic
29C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
30C2×C3×D3×C8C2211yescharacteristic, complemented
31C3×C4×D12C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic, complemented
34#63922—21no—
35D3×(C2×D3)⋊C4—21no—
36#63911—21no—
37#63910—21no—
38#63910—21no—
39#63909C2211yescharacteristic
40#63909C2211yescharacteristic
41#63909C2211yescharacteristic, complemented
42#63906—21no—
43#63894—21no—
44#63890—21no—
45#63857C2211yescharacteristic
46C2×#3719C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic
48C2×#3714C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50#63806—24no—
51#63794—24no—
52C32×#97C2211yescharacteristic, complemented
53C3×#821C2211yescharacteristic
54C3×(C2×D3)⋊C8C2211yescharacteristic
55C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
56C3×#818C2211yescharacteristic, complemented
57C3×#816C2211yescharacteristic, complemented
58C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63564C2211yescharacteristic
61#63564C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63C2×#916—31no—
64C2×#914—31no—
65C2×#908—31no—
66C2×#904—31no—
67#5577—31no—
68#5554—31no—
69#5553—31no—
70#5550—31no—
71C3×#440—31no—
72C3×#435—31no—
73#5134—31no—
74#5115—31no—
75#5028—31no—
76#5015—31no—
77#4886—31no—
78#4883—31no—
79#4845—31no—
80#4843—31no—
81#4810—31no—
82#4808—31no—
83#4781—31no—
84#4773—31no—
85#4734—31no—
86#4734—31no—
87#4733—31no—
88#4732—31no—
89#4712—31no—
90#4712—31no—
91#4712—61no—
92#4710D311yescharacteristic, complemented
93#4706D311yescharacteristic, complemented
94C22×D32—21no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×#634C2311yescharacteristic
101C2×C3×D12D411yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#625—21no—
114C2×#624—21no—
115C2×#624—21no—
116C2×D3×Dic3—21no—
117D3×D12—22no—
118D3×D12—41no—
119#3799—22no—
120#3799—22no—
121#3799—41no—
122#3799—41no—
123#3795—22no—
124#3795—41no—
125C2×C32×C8C2311yescharacteristic
126C2×C32×C8C2311yescharacteristic
127C32×C42C2311yescharacteristic
128#3752—21no—
129#3752—21no—
130#3745—22no—
131#3745—41no—
132#3744—22no—
133#3744—41no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4D411yescharacteristic
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×C4⋊Dic3D411yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C3×C4⋊Dic3C2311yescharacteristic
140C3×Dic3⋊C4—21no—
141C3×C4×Dic3—21no—
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C3×#204D414yescomplemented
145C3×ΓL(1,𝔽25)—22no—
146C3×D3×C8—22no—
147Dic3⋊Dic3—21no—
148#3722—21no—
149#3722—21no—
150#3722—21no—
151(C2×D3)⋊Dic3—21no—
152#3719—22no—
153#3717—22no—
154#3714—22no—
155#3714—22no—
156#3268—91noSylow
157C2×#239—31no—
158C2×#239—31no—
159C2×#237—31no—
160C2×D3×D4—31no—
161C2×#235—31no—
162C2×#235—31no—
163C2×#235—31no—
164C22×D12—31no—
165C2×C3×SD16—31no—
166C2×C3×M16—31no—
167C22×C3×C8—31no—
168C3×C4×Q8—31no—
169C3×C4×D4—31no—
170C3×C4×D4—31no—
171C2×#216—31no—
172C2×#215—31no—
173#940—61no—
174#937—61no—
175C2×#213—31no—
176C2×#213—31no—
177#930—31no—
178#930—31no—
179#930—31no—
180#930—61no—
181C2×(C2×D3)⋊C4—61no—
182#924—31no—
183#916—64no—
184#914—64no—
185#908—64no—
186C2×Dic12—31no—
187#904—64no—
188C2×D24—31no—
189C2×D24—31no—
190C2×D24—31no—
191C2×D24—31no—
192C2×D24—31no—
193C2×D24—31no—
194C2×D24—61no—
195C2×D24—61no—
196C2×#204—31no—
197C2×#204—31no—
198C2×#204—31no—
199C2×#204—31no—
200C2×#204—31no—
201C2×#204—61no—
202C2×#204—61no—
203C2×#204C2×D311yescharacteristic
204C2×ΓL(1,𝔽25)C2×D311yescharacteristic
205C2×D3×C8C2×D311yescharacteristic, complemented
206#897—31no—
207#895—31no—
208#895—31no—
209#895—31no—
210#895—61no—
211#895—61no—
212#894—61no—
213#893—61no—
214#886—61no—
215#884—61no—
216#884—61no—
217#884—61no—
218#882—61no—
219D3×C22⋊C4—61no—
220#875—31no—
221#875—31no—
222#875—61no—
223#874—31no—
224#874—31no—
225#874—61no—
226#874—61no—
227C4×D12—61no—
228C4×D12C2×D311yescharacteristic
229C4×D12C2×D311yescharacteristic
230C4×Dic6C2×D311yescharacteristic, complemented
231C3×#107—31no—
232C3×C4⋊C8—31no—
233C3×#103—31no—
234C3×#102—31no—
235C3×C22⋊C8—31no—
236C3×C22⋊C8—31no—
237C3×#97—21no—
238C3×#97C2×D311yescharacteristic, complemented
239C3×#97C2×D311yescharacteristic, complemented
240#821—31no—
241#821—31no—
242#821—31no—
243#821C2×D311yescharacteristic
244(C2×D3)⋊C8C2×D311yescharacteristic
245(C2×D3)⋊C8C2×D311yescharacteristic, complemented
246#818C2×D311yescharacteristic, complemented
247#816—31no—
248#816C2×D311yescharacteristic, complemented
249#810—31no—
250#809—31no—
251#809—31no—
252#809—31no—
253C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
254C22×C3⋊D3—21no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3C2×D411yescharacteristic
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—42no—
261C2×D32—42no—
262C2×D32—81no—
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4C2411yescharacteristic
266C2×C3⋊Dic3—21no—
267C4⋊(C3⋊D3)—21no—
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—42no—
274C4⋊(C3⋊D3)—81no—
275#634—21no—
276#634—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—41no—
284C3×D12C2×D412yes—
285C3×C4×D3—21no—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—81no—
290C3×Dic6—21no—
291C3×Dic6C2×D412yes—
292#626—42no—
293#626—42no—
294#626—42no—
295#626—81no—
296#626—81no—
297#626—81no—
298#625—42no—
299#624—42no—
300#624—42no—
301D3×Dic3—42no—
302C32×C8—21no—
303C32×C8C2×D412yes—
304C3×C3⋊C8—21no—
305C3×C3⋊C8—21no—
306C2×AGL(1,ℤ/8)—91no—
307C2×#135—91no—
308#550—91no—
309#546—91no—
310#496—91no—
311#468—91no—
312#466—91no—
313#464—91no—
314#459—91no—
315#452—91no—
316#449—91no—
317#449—91no—
318#447—91no—
319#440—31no—
320#435—31no—
321C23×D3—61no—
322C23×D3—61no—
323C2×C3×Q8—31no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C22×Dic3—61no—
338#239—62no—
339#239—62no—
340#239—121no—
341#239—121no—
342#237—62no—
343#237—121no—
344D3×D4—62no—
345D3×D4—121no—
346#235—62no—
347#235—62no—
348#235—62no—
349#235—121no—
350#235—121no—
351#235—121no—
352C2×D12—31no—
353C2×D12—31no—
354C2×D12—31no—
355C2×D12—31no—
356C2×D12—31no—
357C2×D12—31no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12—61no—
361C2×D12—62no—
362C2×D12—61no—
363C2×D12—61no—
364C2×D12—61no—
365C2×D12—61no—
366C2×D12—61no—
367C2×D12—61no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—121no—
373C2×D12—121no—
374C2×D12—121no—
375C2×D12D1211yescharacteristic
376C2×D12C22×D311yescharacteristic
377C2×C4×D3—21no—
378C2×C4×D3—61no—
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3C22×D311yescharacteristic
384C2×C4×D3C22×D311yescharacteristic
385C2×Dic6—31no—
386C2×Dic6—31no—
387C2×Dic6—61no—
388C2×Dic6C22×D311yescharacteristic
389C3×SD16—34no—
390C3×M16—62no—
391C2×C3×C8—21no—
392C2×C3×C8—21no—
393C2×C3×C8—31no—
394C2×C3×C8—31no—
395C2×C3×C8—62no—
396C2×C3×C8C22×D311yescharacteristic
397C2×C3×C8C22×D311yescharacteristic
398C2×C3×C8C22×D311yescharacteristic
399C2×C3×C8C22×D311yescharacteristic
400C3×C4⋊C4—31no—
401C3×C4⋊C4—31no—
402C3×C4⋊C4—31no—
403C3×C4⋊C4—61no—
404C3×C22⋊C4—31no—
405C3×C22⋊C4—31no—
406C3×C22⋊C4—61no—
407C3×C42—21no—
408C3×C42—61no—
409C3×C42C22×D311yescharacteristic
410C3×C42C22×D311yescharacteristic
411#217—61no—
412#216—62no—
413#215—62no—
414#213—62no—
415#213—62no—
416(C2×D3)⋊C4—21no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—121no—
429(C2×D3)⋊C4—121no—
430(C2×D3)⋊C4D1211yescharacteristic
431(C2×D3)⋊C4D1211yescharacteristic
432C4⋊Dic3—61no—
433C4⋊Dic3D1211yescharacteristic
434C4⋊Dic3C22×D311yescharacteristic
435C4⋊Dic3C22×D311yescharacteristic
436Dic3⋊C4—21no—
437Dic3⋊C4—61no—
438C4×Dic3—21no—
439C2×C3⋊C8C22×D311yescharacteristic
440C2×C3⋊C8C22×D311yescharacteristic
441Dic12—62no—
442D24—62no—
443D24—62no—
444D24—62no—
445D24—62no—
446D24—122no—
447D24—121no—
448D24—121no—
449D24—122no—
450#204—62no—
451#204—62no—
452#204—62no—
453#204—122no—
454#204—121no—
455#204—121no—
456#204—122no—
457#204D1214yescomplemented
458ΓL(1,𝔽25)—22no—
459D3×C8—22no—
460C22×C32C22×D411yescharacteristic
461C2×C3⋊D3—41no—
462C2×C3⋊D3—41no—
463C2×C3⋊D3—41no—
464C2×C3⋊D3—41no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3×D3—22no—
471C2×C3×D3—21no—
472C2×C3×D3—21no—
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479D32—84no—
480C32×C4—21no—
481C32×C4—21no—
482C32×C4C22×D411yescharacteristic
483C32×C4H(5,𝔽2)11yescharacteristic
484C3⋊Dic3—41no—
485C3×Dic3—21no—
486C3×Dic3—22no—
487C3×Dic3—21no—
488C3×Dic3—41no—
489C3×Dic3—41no—
490C2×#41—91no—
491C2×#41—91no—
492C2×#41—91no—
493C22×D4—91no—
494AGL(1,ℤ/8)—184no—
495#135—184no—
496C2×Q16—91no—
497C2×SD16—31no—
498C2×SD16—91no—
499C2×SD16—91no—
500C2×SD16—91no—
501C2×D8—91no—
502C2×D8—91no—
503C2×D8—91no—
504C2×D8—91no—
505C2×M16—31no—
506C22×C8—31no—
507#127—91no—
508#127—181no—
509#124—91no—
510#123—181no—
511C22⋊Q8—91no—
512#121—91no—
513#121—91no—
514#121—91no—
515#121—181no—
516#121—181no—
517#121—181no—
518#120—181no—
519C4×Q8—31no—
520C4×D4—31no—
521C4×D4—31no—
522C4×D4—181no—
523C2×C22⋊C4—181no—
524#107—31no—
525C4⋊C8—31no—
526#103—31no—
527#103—91no—
528#102—31no—
529#102—91no—
530#102—91no—
531#102—91no—
532C22⋊C8—31no—
533C22⋊C8—31no—
534#97D3211yescharacteristic, complemented
535C23×C3—31no—
536C23×C3—31no—
537C23×C3—61no—
538C22×D3—21no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—121no—
546C22×D3—121no—
547C22×D3—121no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—241no—
553C22×D3—241no—
554C22×D3C2×D1211yescharacteristic
555C22×D3C2×D1211yescharacteristic
556C3×Q8—32no—
557C3×Q8—61no—
558C3×D4—32no—
559C3×D4—61no—
560C3×D4—121no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—31no—
565C2×C3×C4—31no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—241no—
574C2×C3×C4C2×D1211yescharacteristic
575C2×C3×C4C2×D1211yescharacteristic
576C2×C3×C4D3×D411yescharacteristic
577C2×C3×C4D3×D411yescharacteristic
578C2×C3×C4C23×D311yescharacteristic
579C2×C3×C4C23×D311yescharacteristic
580#67—122no—
581#67—122no—
582#67—122no—
583#67—122no—
584#67—122no—
585#67—241no—
586#67—241no—
587#67—241no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—121no—
594C2×Dic3—122no—
595C2×Dic3C2×D1211yescharacteristic
596C2×Dic3C2×D1211yescharacteristic
597D12—21no—
598D12—41no—
599D12—61no—
600D12—61no—
601D12—61no—
602D12—61no—
603D12—61no—
604D12—61no—
605D12—61no—
606D12—61no—
607D12—61no—
608D12—61no—
609D12—61no—
610D12—61no—
611D12—121no—
612D12—121no—
613D12—121no—
614D12—121no—
615D12—121no—
616D12—121no—
617D12—122no—
618D12—122no—
619D12—122no—
620D12—122no—
621D12—122no—
622D12—242no—
623D12—241no—
624D12—241no—
625D12—242no—
626D12—241no—
627D12—241no—
628D12—241no—
629D12C2×D1212yes—
630C4×D3—21no—
631C4×D3—21no—
632C4×D3—21no—
633C4×D3—21no—
634C4×D3—81no—
635C4×D3—122no—
636C4×D3—122no—
637C4×D3—122no—
638C4×D3—122no—
639C4×D3—122no—
640Dic6—21no—
641Dic6—61no—
642Dic6—61no—
643Dic6—61no—
644Dic6—61no—
645Dic6—121no—
646Dic6—121no—
647Dic6C2×D1212yes—
648C3×C8—22no—
649C3×C8—21no—
650C3×C8—21no—
651C3×C8—22no—
652C3×C8—61no—
653C3×C8—61no—
654C3×C8C2×D1212yes—
655C3×C8D3×D412yes—
656C3⋊C8—21no—
657C3⋊C8—21no—
658C2×C32D4211yescharacteristic
659C2×C32#57511yescharacteristic
660C2×C32#57611yescharacteristic
661C3⋊D3—81no—
662C3⋊D3—81no—
663C3⋊D3—81no—
664C3×D3—41no—
665C3×D3—42no—
666C3×D3—41no—
667C24—181no—
668#41—182no—
669#41—182no—
670#41—182no—
671#41—361no—
672#41—361no—
673#41—361no—
674C2×Q8—31no—
675C2×Q8—91no—
676C2×D4—31no—
677C2×D4—31no—
678C2×D4—91no—
679C2×D4—91no—
680C2×D4—91no—
681C2×D4—181no—
682C2×D4—182no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—181no—
686C2×D4—181no—
687C2×D4—181no—
688C2×D4—181no—
689C2×D4—181no—
690C2×D4—181no—
691C2×D4—361no—
692C22×C4—31no—
693C22×C4—31no—
694C22×C4—61no—
695C22×C4—181no—
696C22×C4—181no—
697C22×C4—181no—
698Q16—182no—
699SD16—34no—
700SD16—182no—
701SD16—182no—
702SD16—361no—
703D8—182no—
704D8—182no—
705D8—182no—
706D8—361no—
707M16—62no—
708C2×C8—31no—
709C2×C8—31no—
710C2×C8—62no—
711C2×C8C2×D3211yescharacteristic
712C2×C8C2×D3211yescharacteristic
713C4⋊C4—31no—
714C4⋊C4—31no—
715C4⋊C4—31no—
716C4⋊C4—61no—
717C4⋊C4—181no—
718C22⋊C4—31no—
719C22⋊C4—31no—
720C22⋊C4—61no—
721C22⋊C4—181no—
722C22⋊C4—181no—
723C22⋊C4—181no—
724C22⋊C4—181no—
725C22⋊C4—181no—
726C22⋊C4—181no—
727C42—61no—
728C42C2×D3211yescharacteristic
729C22×C3—21no—
730C22×C3—61no—
731C22×C3—61no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3—62no—
735C22×C3—61no—
736C22×C3—61no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3C22×D1211yescharacteristic
740C22×C3C2×D3×D411yescharacteristic
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—21no—
745C2×D3—21no—
746C2×D3—21no—
747C2×D3—22no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—121no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—121no—
754C2×D3—121no—
755C2×D3—121no—
756C2×D3—121no—
757C2×D3—121no—
758C2×D3—121no—
759C2×D3—121no—
760C2×D3—121no—
761C2×D3—121no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—241no—
769C2×D3—241no—
770C2×D3—241no—
771C2×D3—241no—
772C2×D3—241no—
773C2×D3—241no—
774C2×D3—241no—
775C2×D3—241no—
776C2×D3—241no—
777C2×D3—244no—
778C2×D3—244no—
779C3×C4—21no—
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—21no—
783C3×C4—21no—
784C3×C4—21no—
785C3×C4—41no—
786C3×C4—41no—
787C3×C4—61no—
788C3×C4—61no—
789C3×C4—62no—
790C3×C4—121no—
791C3×C4—121no—
792C3×C4C22×D1211yescharacteristic
793C3×C4C2×D3×D411yescharacteristic
794C3×C4#100911yescharacteristic
795C3×C4#100911yescharacteristic
796Dic3—22no—
797Dic3—21no—
798Dic3—21no—
799Dic3—41no—
800Dic3—41no—
801Dic3—121no—
802Dic3—121no—
803Dic3—241no—
804C32#326811yescharacteristic, complemented, Sylow
805C23—31no—
806C23—31no—
807C23—61no—
808C23—181no—
809C23—181no—
810C23—181no—
811C23—362no—
812C23—362no—
813C23—721no—
814Q8—32no—
815Q8—61no—
816Q8—181no—
817Q8—181no—
818D4—32no—
819D4—61no—
820D4—121no—
821D4—181no—
822D4—181no—
823D4—181no—
824D4—181no—
825D4—181no—
826D4—181no—
827D4—362no—
828D4—362no—
829D4—362no—
830D4—362no—
831D4—362no—
832D4—721no—
833D4—721no—
834D4—721no—
835D4—721no—
836C2×C4—31no—
837C2×C4—31no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—181no—
846C2×C4—241no—
847C2×C4—362no—
848C2×C4—362no—
849C2×C4—362no—
850C2×C4D3×D1211yescharacteristic
851C2×C4D3×D1211yescharacteristic
852C2×C4C22×D3211yescharacteristic
853C8—21no—
854C8—61no—
855C8—61no—
856C8D3×D1212yes—
857C2×C3—21no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—122no—
861C2×C3—121no—
862C2×C3—121no—
863C2×C3D4×D1211yescharacteristic
864C2×C3D4×D1211yescharacteristic
865C2×C3#574811yescharacteristic
866C2×C3#575211yescharacteristic
867C2×C3#577411yescharacteristic
868C2×C3#577711yescharacteristic
869D3—41no—
870D3—41no—
871D3—42no—
872D3—241no—
873D3—241no—
874D3—241no—
875D3—241no—
876D3—241no—
877D3—241no—
878D3—481no—
879D3—481no—
880D3—481no—
881C22—61no—
882C22—61no—
883C22—61no—
884C22—61no—
885C22—61no—
886C22—61no—
887C22—62no—
888C22—121no—
889C22—121no—
890C22—361no—
891C22—361no—
892C22—361no—
893C22—361no—
894C22—361no—
895C22—361no—
896C22—361no—
897C22—361no—
898C22—361no—
899C22—724no—
900C22C2×D3×D1211yescharacteristic
901C4—21no—
902C4—21no—
903C4—61no—
904C4—61no—
905C4—62no—
906C4—121no—
907C4—121no—
908C4—361no—
909C4C2×D3×D1211yescharacteristic
910C4#6430811yescharacteristic
911C3—21no—
912C3#7949711yescharacteristic, complemented
913C3#7979611yescharacteristic, complemented
914C2—121no—
915C2—121no—
916C2—122no—
917C2—721no—
918C2—721no—
919C2—721no—
920C2D12211yescharacteristic
921C2#1059471111yescharacteristic
922C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
hypercenter#97D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
1. C2×#63806C2semidirect
2. C2×#63794C2semidirect
3. #10594003C2semidirect
4. #10593902C2semidirect
5. #10592411C2semidirect
6. C3×#4710C2semidirect
7. C3×#4706C2semidirect
8. #10590970C2semidirect
9. #10590968C2semidirect
10. #10590967C2semidirect
11. #10590947C2semidirect
12. #10590838C2semidirect
13. #10590832C2semidirect
14. #10590368C2semidirect
15. #10590349C2semidirect
20. C2×#3799C22semidirect
24. C2×#3744C22semidirect
25. C2×#3744C22semidirect
27. #64083C22semidirect
30. C2×C3×D3×C8C22semidirect
33. C3×C4×Dic6C22semidirect
41. #63909C22semidirect
46. C2×#3719C22semidirect
52. C32×#97C22semidirect
55. C3×(C2×D3)⋊C8C22semidirect
56. C3×#818C22semidirect
57. C3×#816C22semidirect
58. C3×C4⋊(C3⋊C8)C22semidirect
59. #63567C22semidirect
61. #63564C22semidirect
62. #63564C22semidirect
92. #4710D3semidirect
93. #4706D3semidirect
144. C3×#204D4semidirect
205. C2×D3×C8C2×D3semidirect
230. C4×Dic6C2×D3semidirect
238. C3×#97C2×D3semidirect
239. C3×#97C2×D3semidirect
245. (C2×D3)⋊C8C2×D3semidirect
246. #818C2×D3semidirect
248. #816C2×D3semidirect
253. C4⋊(C3⋊C8)C2×D3semidirect
457. #204D12semidirect
534. #97D32semidirect
804. C32#3268semidirect
912. C3#79497semidirect
913. C3#79796semidirect

Maximal subgroups

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

subgroupindex
C2×#638062
C2×#637942
#105940032
#105939022
#105924112
C3×#47102
C3×#47062
#105909702
#105909682
#105909672
#105909472
#105908382
#105908322
#105903682
#105903492
#797963
#794973