Finite Group Databasebeta

← #11884482

Subgroups — #11884482

Order 1152.

1101 conjugacy classes of subgroups.

The subgroup lattice has 925 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595431C211yesmaximal, characteristic, complemented
2C2×#63950C211yesmaximal, characteristic, complemented
3C2×#63794C211yesmaximal, characteristic, complemented
4#10594524C211yesmaximal, characteristic, complemented
5#10592509C211yesmaximal, characteristic, complemented
6C3×#4812C211yesmaximal, characteristic, complemented
7C3×#4798C211yesmaximal, characteristic, complemented
8#10591657C211yesmaximal, characteristic, complemented
9#10591619C211yesmaximal, characteristic, complemented
10#10590964C211yesmaximal, characteristic, complemented
11#10590765C211yesmaximal, characteristic, complemented
12#10590738C211yesmaximal, characteristic, complemented
13#10590595C211yesmaximal, characteristic, complemented
14#10590509C211yesmaximal, characteristic, complemented
15#10590457C211yesmaximal, characteristic, complemented
16#80836—31nomaximal
17#80628—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21C2×#3796C2211yescharacteristic, complemented
22C2×#3755C2211yescharacteristic, complemented
23C2×#3745C2211yescharacteristic
24#64104C2211yescharacteristic, complemented
25C3×#947C2211yescharacteristic
26C3×#946C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic, complemented
29C2×C3×#204C2211yescharacteristic
30C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
31C3×#895C2211yescharacteristic
32C3×#887C2211yescharacteristic, complemented
33#63950—24no—
34#63923—21no—
35#63921—21no—
36#63916C2211yescharacteristic
37#63911—21no—
38#63911C2211yescharacteristic, complemented
39#63910—21no—
40#63910—21no—
41C4×#626C2211yescharacteristic
42#63894C2211yescharacteristic
43#63886—21no—
44#63880—21no—
45#63853—21no—
46C2×#3717C2211yescharacteristic
47C2×#3714C2211yescharacteristic
48C2×#3714C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50C2×#3710C2211yescharacteristic, complemented
51#63794—24no—
52C32×#103C2211yescharacteristic, complemented
53#63647C2211yescharacteristic, complemented
54#63636C2211yescharacteristic
55C3×#821C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#807C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic, complemented
63C2×#919—31no—
64C2×#916—31no—
65C2×#914—31no—
66C2×#908—31no—
67#5676—31no—
68#5630—31no—
69#5599—31no—
70#5577—31no—
71C3×#468—31no—
72C3×#464—31no—
73#5187—31no—
74#5176—31no—
75#5172—31no—
76#5127—31no—
77#5058—31no—
78#5047—31no—
79#5036—31no—
80#5026—31no—
81#4889—31no—
82#4883—31no—
83#4843—31no—
84#4836—31no—
85#4812D311yescharacteristic, complemented
86#4810—31no—
87#4810—31no—
88#4810—61no—
89#4798D311yescharacteristic, complemented
90#4786—31no—
91#4781—31no—
92#4775—31no—
93#4773—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96#3832—22no—
97#3832—41no—
98C2×C4⋊(C3⋊D3)—21no—
99C2×C4⋊(C3⋊D3)—21no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3C2311yescharacteristic
104C2×C3×D12—21no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#626D411yescharacteristic
116C2×#624—21no—
117C2×#624—21no—
118C2×D3×Dic3—21no—
119D3×D12—22no—
120D3×D12—41no—
121#3799—22no—
122#3799—41no—
123#3796—22no—
124#3796—41no—
125C2×C32×C8C2311yescharacteristic
126C32×C4⋊C4C2311yescharacteristic
127#3755—41no—
128#3752—21no—
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130#3745—22no—
131C3×#216—22no—
132C3×#215—22no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×C4×Dic3—21no—
141C3×C4×Dic3C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C3×#204—22no—
145C3×ΓL(1,𝔽25)—22no—
146Dic3⋊Dic3D411yescharacteristic
147#3722—21no—
148#3722D411yescharacteristic
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3D411yescharacteristic
151#3717D414yescomplemented
152#3714—22no—
153#3714—22no—
154#3713—41no—
155#3710—22no—
156#3268—91noSylow
157C2×#239—31no—
158C2×#239—31no—
159C2×#239—31no—
160C2×#239—31no—
161C2×#239—61no—
162C2×#237—31no—
163C2×D3×D4—31no—
164C2×#235—31no—
165C22×D12—31no—
166C2×C3×Q16—31no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C2×C3×M16—31no—
170C3×#124—31no—
171C3×C22⋊Q8—31no—
172C3×#121—31no—
173C3×C4×Q8—31no—
174#947C2×D311yescharacteristic
175#946C2×D311yescharacteristic
176C2×#216C2×D311yescharacteristic, complemented
177C2×#215—31no—
178C2×#215—31no—
179C2×#215—31no—
180C2×#215—61no—
181C2×#215C2×D311yescharacteristic, complemented
182#940—31no—
183#940—61no—
184#939—61no—
185#938—31no—
186C2×#213—31no—
187C2×#213—31no—
188C2×#213—31no—
189C2×#213—31no—
190C4×#67—31no—
191#919—64no—
192#916—64no—
193#914—64no—
194#908—64no—
195C2×D24—31no—
196C2×D24—31no—
197C2×D24—31no—
198C2×D24—31no—
199C2×D24—61no—
200C2×#204—31no—
201C2×#204C2×D311yescharacteristic
202C2×ΓL(1,𝔽25)C2×D311yescharacteristic
203C2×D3×C8—31no—
204C2×D3×C8—31no—
205#895—31no—
206#895—31no—
207#895—31no—
208#895—61no—
209#895—61no—
210#895—61no—
211#895—61no—
212#895C2×D311yescharacteristic
213#894—61no—
214#893—31no—
215#887C2×D311yescharacteristic, complemented
216#884—61no—
217#884—61no—
218#883—61no—
219#882—61no—
220#882—61no—
221#67⋊C4—61no—
222D3×C22⋊C4—61no—
223D3×C22⋊C4—61no—
224#874—31no—
225#874—61no—
226C4×D12—31no—
227C4×D12—31no—
228C4×D12—61no—
229C3×#107—31no—
230C3×C4⋊C8—31no—
231C3×#103—21no—
232C3×#103C2×D311yescharacteristic, complemented
233C3×#103C2×D311yescharacteristic, complemented
234C3×#102—31no—
235C3×#102—31no—
236#835—31no—
237#830—31no—
238#821—31no—
239#821C2×D311yescharacteristic, complemented
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8—31no—
243(C2×D3)⋊C8—61no—
244#815—31no—
245Dic3⋊C8C2×D311yescharacteristic, complemented
246#810—31no—
247#809—31no—
248#809—31no—
249#809—31no—
250#809—61no—
251#809C2×D311yescharacteristic
252#807C2×D311yescharacteristic, complemented
253#803—31no—
254C22×C3⋊D3—21no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3C2×D411yescharacteristic
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—42no—
261C2×D32—42no—
262C2×D32—81no—
263C32×Q8—21no—
264C32×Q8—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2411yescharacteristic
268C2×C3⋊Dic3C2×D411yescharacteristic
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—42no—
273C4⋊(C3⋊D3)—81no—
274C4⋊(C3⋊D3)C2×D412yes—
275C4×C3⋊D3—21no—
276C4×C3⋊D3—21no—
277C4×C3⋊D3—42no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—81no—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×Dic6—21no—
291C3×Dic6C2×D412yes—
292#626—41no—
293#626—42no—
294#626—42no—
295#626—42no—
296#626—42no—
297#626—81no—
298#626—81no—
299#624—42no—
300#624—81no—
301D3×Dic3—42no—
302C32×C8—21no—
303C3⋊(C3⋊C8)—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×AGL(1,ℤ/8)—91no—
307C2×#135—91no—
308#550—91no—
309#546—91no—
310#496—91no—
311#468—31no—
312#466—91no—
313#464—31no—
314#459—91no—
315#452—91no—
316#449—91no—
317#449—91no—
318#447—91no—
319#440—91no—
320#435—91no—
321C23×D3—61no—
322C23×D3—61no—
323C2×C3×Q8—21no—
324C2×C3×Q8—31no—
325C2×C3×Q8C22×D311yescharacteristic
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×D4—31no—
328C2×C3×D4—31no—
329C2×C3×D4—61no—
330C22×C3×C4—31no—
331C2×#67—31no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C22×Dic3—61no—
339#239—62no—
340#239—62no—
341#239—62no—
342#239—62no—
343#239—122no—
344#239—121no—
345#239—121no—
346#239—121no—
347#239—121no—
348#239—122no—
349#237—62no—
350#237—121no—
351D3×D4—62no—
352D3×D4—121no—
353#235—62no—
354#235—121no—
355C2×D12—21no—
356C2×D12—31no—
357C2×D12—31no—
358C2×D12—31no—
359C2×D12—31no—
360C2×D12—31no—
361C2×D12—61no—
362C2×D12—61no—
363C2×D12—62no—
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—61no—
373C2×D12—61no—
374C2×D12—121no—
375C2×D12—121no—
376C2×D12—121no—
377C2×D12C22×D311yescharacteristic
378C2×D12C22×D311yescharacteristic
379C2×C4×D3—31no—
380C2×C4×D3—31no—
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3—61no—
387C2×C4×D3—61no—
388C2×C4×D3—61no—
389C2×C4×D3—121no—
390C2×C4×D3C22×D311yescharacteristic
391C2×Dic6C22×D311yescharacteristic
392C3×Q16—62no—
393C3×SD16—62no—
394C3×SD16—62no—
395C3×M16—62no—
396C2×C3×C8—21no—
397C2×C3×C8—31no—
398C2×C3×C8—31no—
399C2×C3×C8C22×D311yescharacteristic
400C2×C3×C8C22×D311yescharacteristic
401C3×C4⋊C4—21no—
402C3×C4⋊C4—31no—
403C3×C4⋊C4—61no—
404C3×C4⋊C4—61no—
405C3×C4⋊C4C22×D311yescharacteristic
406C3×C4⋊C4C22×D311yescharacteristic
407C3×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409C3×C22⋊C4—61no—
410C3×C22⋊C4—61no—
411C3×C42—31no—
412C3×C42—61no—
413#217—31no—
414#217—61no—
415#216—22no—
416#215—22no—
417#215—34no—
418#215—121no—
419#215—121no—
420#215—122no—
421#213—62no—
422#213—62no—
423#213—121no—
424#213—121no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—21no—
427(C2×D3)⋊C4—21no—
428(C2×D3)⋊C4—21no—
429(C2×D3)⋊C4—31no—
430(C2×D3)⋊C4—31no—
431(C2×D3)⋊C4—31no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—121no—
438C4⋊Dic3—31no—
439C4⋊Dic3C22×D311yescharacteristic
440Dic3⋊C4—21no—
441Dic3⋊C4—21no—
442Dic3⋊C4—31no—
443C4×Dic3—21no—
444C4×Dic3C22×D311yescharacteristic
445C2×C3⋊C8—31no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—61no—
448C2×C3⋊C8C22×D311yescharacteristic
449C2×C3⋊C8C22×D311yescharacteristic
450D24—62no—
451D24—62no—
452D24—62no—
453D24—62no—
454D24—122no—
455#204—22no—
456#204—34no—
457ΓL(1,𝔽25)—22no—
458D3×C8—62no—
459D3×C8—62no—
460C22×C32C22×D411yescharacteristic
461C2×C3⋊D3—21no—
462C2×C3⋊D3—22no—
463C2×C3⋊D3—21no—
464C2×C3⋊D3—21no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—21no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479D32—84no—
480C32×C4—41no—
481C32×C4—41no—
482C32×C4C22×D411yescharacteristic
483C32×C4H(5,𝔽2)11yescharacteristic
484C3⋊Dic3—21no—
485C3×Dic3—22no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—21no—
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—31no—
497C2×SD16—31no—
498C2×SD16—31no—
499C2×SD16—91no—
500C2×SD16—91no—
501C2×D8—91no—
502C2×D8—91no—
503C2×D8—91no—
504C2×D8—91no—
505C2×M16—31no—
506C22×C8—91no—
507#127—91no—
508#127—181no—
509#124—31no—
510#123—181no—
511C22⋊Q8—31no—
512#121—31no—
513#121—91no—
514#121—91no—
515#121—181no—
516#121—181no—
517#121—181no—
518#120—181no—
519C4×Q8—31no—
520C4×D4—91no—
521C4×D4—91no—
522C4×D4—181no—
523C2×C22⋊C4—181no—
524#107—31no—
525C4⋊C8—31no—
526#103—91no—
527#103D3211yescharacteristic, complemented
528#102—31no—
529#102—31no—
530#102—91no—
531#102—91no—
532C22⋊C8—91no—
533C22⋊C8—91no—
534#97—91no—
535C23×C3—31no—
536C23×C3—61no—
537C23×C3—61no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—31no—
541C22×D3—31no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—121no—
548C22×D3—121no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3—241no—
554C22×D3—241no—
555C22×D3D3×D411yescharacteristic
556C3×Q8—22no—
557C3×Q8—21no—
558C3×Q8—21no—
559C3×Q8—21no—
560C3×Q8—21no—
561C3×Q8—32no—
562C3×Q8—41no—
563C3×Q8—61no—
564C3×D4—61no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—61no—
568C3×D4—241no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—31no—
575C2×C3×C4—31no—
576C2×C3×C4—31no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4C23×D311yescharacteristic
584C2×C3×C4C23×D311yescharacteristic
585#67—121no—
586#67—122no—
587#67—122no—
588#67—122no—
589#67—122no—
590#67—241no—
591#67—241no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—31no—
595C2×Dic3—31no—
596C2×Dic3—61no—
597C2×Dic3—122no—
598C2×Dic3D3×D411yescharacteristic
599C2×Dic3D3×D411yescharacteristic
600C2×Dic3D3×D411yescharacteristic
601D12—21no—
602D12—21no—
603D12—21no—
604D12—21no—
605D12—32no—
606D12—32no—
607D12—62no—
608D12—61no—
609D12—61no—
610D12—61no—
611D12—61no—
612D12—61no—
613D12—61no—
614D12—81no—
615D12—121no—
616D12—121no—
617D12—121no—
618D12—122no—
619D12—122no—
620D12—124no—
621D12—121no—
622D12—122no—
623D12—122no—
624D12—122no—
625D12—122no—
626D12—241no—
627D12—241no—
628D12—241no—
629D12—242no—
630D12—241no—
631C4×D3—21no—
632C4×D3—21no—
633C4×D3—61no—
634C4×D3—61no—
635C4×D3—61no—
636C4×D3—61no—
637C4×D3—121no—
638C4×D3—121no—
639C4×D3—122no—
640C4×D3—122no—
641C4×D3—122no—
642C4×D3—122no—
643C4×D3—122no—
644C4×D3—124no—
645C4×D3—241no—
646C4×D3—241no—
647Dic6—21no—
648Dic6D3×D412yes—
649C3×C8—21no—
650C3×C8—21no—
651C3×C8—32no—
652C3×C8—41no—
653C3×C8—61no—
654C3⋊C8—21no—
655C3⋊C8—61no—
656C3⋊C8—61no—
657C3⋊C8—121no—
658C3⋊C8D3×D412yes—
659C2×C32D4211yescharacteristic
660C2×C32#57511yescharacteristic
661C2×C32#57611yescharacteristic
662C3⋊D3—42no—
663C3⋊D3—41no—
664C3⋊D3—81no—
665C3×D3—41no—
666C3×D3—81no—
667C3×D3—81no—
668C24—181no—
669#41—182no—
670#41—182no—
671#41—182no—
672#41—361no—
673#41—361no—
674#41—361no—
675C2×Q8—31no—
676C2×Q8C2×D3211yescharacteristic
677C2×D4—31no—
678C2×D4—31no—
679C2×D4—61no—
680C2×D4—91no—
681C2×D4—91no—
682C2×D4—91no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—181no—
686C2×D4—181no—
687C2×D4—181no—
688C2×D4—182no—
689C2×D4—181no—
690C2×D4—181no—
691C2×D4—181no—
692C2×D4—361no—
693C22×C4—31no—
694C22×C4—91no—
695C22×C4—181no—
696C22×C4—181no—
697C22×C4—181no—
698C22×C4—181no—
699Q16—62no—
700SD16—62no—
701SD16—62no—
702SD16—94no—
703SD16—361no—
704D8—182no—
705D8—182no—
706D8—182no—
707D8—361no—
708M16—62no—
709C2×C8—31no—
710C2×C8—31no—
711C2×C8—91no—
712C2×C8—182no—
713C2×C8C2×D3211yescharacteristic
714C4⋊C4—31no—
715C4⋊C4—61no—
716C4⋊C4—61no—
717C4⋊C4—91no—
718C4⋊C4C2×D3211yescharacteristic
719C22⋊C4—61no—
720C22⋊C4—61no—
721C22⋊C4—61no—
722C22⋊C4—61no—
723C22⋊C4—91no—
724C22⋊C4—91no—
725C22⋊C4—181no—
726C22⋊C4—181no—
727C22⋊C4—181no—
728C42—31no—
729C42—61no—
730C22×C3—21no—
731C22×C3—61no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3C2×D3×D411yescharacteristic
741C22×C3C2×D3×D411yescharacteristic
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—21no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—61no—
752C2×D3—61no—
753C2×D3—61no—
754C2×D3—61no—
755C2×D3—61no—
756C2×D3—61no—
757C2×D3—62no—
758C2×D3—62no—
759C2×D3—122no—
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—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—241no—
774C2×D3—241no—
775C2×D3—241no—
776C2×D3—241no—
777C2×D3—241no—
778C2×D3—244no—
779C2×D3—244no—
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—42no—
783C3×C4—41no—
784C3×C4—41no—
785C3×C4—41no—
786C3×C4—41no—
787C3×C4—61no—
788C3×C4—61no—
789C3×C4—61no—
790C3×C4—62no—
791C3×C4—81no—
792C3×C4—121no—
793C3×C4C2×D3×D411yescharacteristic
794C3×C4C2×D3×D411yescharacteristic
795C3×C4#100911yescharacteristic
796C3×C4#100911yescharacteristic
797Dic3—21no—
798Dic3—21no—
799Dic3—22no—
800Dic3—21no—
801Dic3—41no—
802Dic3—61no—
803Dic3—61no—
804Dic3—121no—
805C32#326811yescharacteristic, complemented, Sylow
806C23—31no—
807C23—61no—
808C23—61no—
809C23—91no—
810C23—181no—
811C23—181no—
812C23—362no—
813C23—362no—
814C23—721no—
815Q8—21no—
816Q8—21no—
817Q8—32no—
818Q8—61no—
819D4—61no—
820D4—61no—
821D4—61no—
822D4—61no—
823D4—92no—
824D4—181no—
825D4—181no—
826D4—181no—
827D4—241no—
828D4—362no—
829D4—361no—
830D4—362no—
831D4—362no—
832D4—362no—
833D4—362no—
834D4—721no—
835D4—721no—
836D4—721no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—31no—
840C2×C4—31no—
841C2×C4—31no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—91no—
847C2×C4—181no—
848C2×C4—181no—
849C2×C4—362no—
850C2×C4—362no—
851C2×C4—362no—
852C2×C4—721no—
853C2×C4C22×D3211yescharacteristic
854C8—21no—
855C8—32no—
856C8—61no—
857C8—181no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—21no—
861C2×C3—121no—
862C2×C3—241no—
863C2×C3—241no—
864C2×C3#560911yescharacteristic
865C2×C3#560911yescharacteristic
866C2×C3#576911yescharacteristic
867C2×C3#577411yescharacteristic
868C2×C3#577711yescharacteristic
869C2×C3#577711yescharacteristic
870D3—41no—
871D3—81no—
872D3—81no—
873D3—121no—
874D3—122no—
875D3—121no—
876D3—122no—
877D3—241no—
878D3—242no—
879D3—241no—
880D3—241no—
881D3—481no—
882C22—61no—
883C22—61no—
884C22—61no—
885C22—121no—
886C22—121no—
887C22—121no—
888C22—121no—
889C22—121no—
890C22—121no—
891C22—181no—
892C22—181no—
893C22—181no—
894C22—182no—
895C22—361no—
896C22—361no—
897C22—361no—
898C22—361no—
899C22—361no—
900C22—724no—
901C22D32×D411yescharacteristic
902C4—41no—
903C4—41no—
904C4—61no—
905C4—61no—
906C4—61no—
907C4—62no—
908C4—121no—
909C4—181no—
910C4#6430811yescharacteristic
911C4D32×D411yescharacteristic
912C3—21no—
913C3#8062811yescharacteristic, complemented
914C3#8083611yescharacteristic, complemented
915C2—121no—
916C2—241no—
917C2—241no—
918C2—361no—
919C2—362no—
920C2—721no—
921C2#1059428411yescharacteristic
922C2#1059475511yescharacteristic
923C2#1059476211yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595431C2semidirect
2. C2×#63950C2semidirect
3. C2×#63794C2semidirect
4. #10594524C2semidirect
5. #10592509C2semidirect
6. C3×#4812C2semidirect
7. C3×#4798C2semidirect
8. #10591657C2semidirect
9. #10591619C2semidirect
10. #10590964C2semidirect
11. #10590765C2semidirect
12. #10590738C2semidirect
13. #10590595C2semidirect
14. #10590509C2semidirect
15. #10590457C2semidirect
21. C2×#3796C22semidirect
22. C2×#3755C22semidirect
24. #64104C22semidirect
27. C2×C3×#216C22semidirect
28. C2×C3×#215C22semidirect
32. C3×#887C22semidirect
38. #63911C22semidirect
50. C2×#3710C22semidirect
52. C32×#103C22semidirect
53. #63647C22semidirect
55. C3×#821C22semidirect
56. C3×Dic3⋊C8C22semidirect
58. C3×#807C22semidirect
59. #63565C22semidirect
60. #63564C22semidirect
62. #63554C22semidirect
85. #4812D3semidirect
89. #4798D3semidirect
151. #3717D4semidirect
176. C2×#216C2×D3semidirect
181. C2×#215C2×D3semidirect
215. #887C2×D3semidirect
232. C3×#103C2×D3semidirect
233. C3×#103C2×D3semidirect
239. #821C2×D3semidirect
245. Dic3⋊C8C2×D3semidirect
252. #807C2×D3semidirect
527. #103D32semidirect
805. C32#3268semidirect
913. C3#80628semidirect
914. C3#80836semidirect

Maximal subgroups

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

subgroupindex
#105954312
C2×#639502
C2×#637942
#105945242
#105925092
C3×#48122
C3×#47982
#105916572
#105916192
#105909642
#105907652
#105907382
#105905952
#105905092
#105904572
#808363
#806283