Finite Group Databasebeta

← #11884405

Subgroups — #11884405

Order 1152.

1096 conjugacy classes of subgroups.

The subgroup lattice has 921 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595410C211yesmaximal, characteristic, complemented
2C2×#63947C211yesmaximal, characteristic, complemented
3C2×#63941C211yesmaximal, characteristic, complemented
4#10594630C211yesmaximal, characteristic, complemented
5#10592507C211yesmaximal, characteristic, complemented
6C3×#4817C211yesmaximal, characteristic, complemented
7C3×#4810C211yesmaximal, characteristic, complemented
8#10591604C211yesmaximal, characteristic, complemented
9#10590968C211yesmaximal, characteristic, complemented
10#10590945C211yesmaximal, characteristic, complemented
11#10590883C211yesmaximal, characteristic, complemented
12#10590728C211yesmaximal, characteristic, complemented
13#10590576C211yesmaximal, characteristic, complemented
14#10590547C211yesmaximal, characteristic, complemented
15#10590506C211yesmaximal, characteristic, complemented
16#80123—31nomaximal
17#79796—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic, complemented
20C2×#3802C2211yescharacteristic
21C2×#3795C2211yescharacteristic
22C2×#3756C2211yescharacteristic, complemented
23C2×#3744C2211yescharacteristic, complemented
24#64106C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27C2×C3×#215C2211yescharacteristic
28C2×C3×D24C2211yescharacteristic
29C3×#895C2211yescharacteristic
30C3×#893C2211yescharacteristic
31#63947—24no—
32#63941—24no—
33#63922—21no—
34D3×(C2×D3)⋊C4—21no—
35#63916—21no—
36#63916C2211yescharacteristic
37#63911—21no—
38#63911C2211yescharacteristic, complemented
39#63909—21no—
40#63909C2211yescharacteristic, complemented
41#63908—21no—
42C4×#626—21no—
43C4×#626C2211yescharacteristic
44#63891—21no—
45#63860C2211yescharacteristic
46C2×#3716C2211yescharacteristic, complemented
47C2×#3714C2211yescharacteristic
48C2×#3714C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50C2×#3712C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52C32×#103C2211yescharacteristic, complemented
53#63647C2211yescharacteristic
54#63636C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×#815C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59C3×#807C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63562C2211yescharacteristic
63#5834—31no—
64C2×#950—31no—
65C2×#916—31no—
66C2×#914—31no—
67C2×#914—31no—
68#5612—31no—
69#5577—31no—
70#5554—31no—
71C3×#449—31no—
72C3×#440—31no—
73#5166—31no—
74#5156—31no—
75#5154—31no—
76#5038—31no—
77#5028—31no—
78#5015—31no—
79#4886—31no—
80#4883—31no—
81#4817D311yescharacteristic, complemented
82#4810D311yescharacteristic, complemented
83#4808—31no—
84#4808—31no—
85#4808—61no—
86#4786—31no—
87#4781—31no—
88#4780—31no—
89#4773—31no—
90#4734—31no—
91#4730—31no—
92#4712—31no—
93#4706—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96#3832—22no—
97#3832—41no—
98C2×C4⋊(C3⋊D3)—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C3×#239—22no—
104C3×#239—41no—
105C2×C3×D12—21no—
106C2×C3×D12—21no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3C2311yescharacteristic
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#626D411yescharacteristic
118C2×#625—21no—
119C2×#625—21no—
120C2×D3×Dic3—21no—
121#3802—22no—
122#3802—41no—
123#3795—22no—
124#3795—41no—
125C2×C32×C8C2311yescharacteristic
126C32×C4⋊C4C2311yescharacteristic
127#3756—22no—
128#3752—21no—
129C4⋊(C3⋊Dic3)—21no—
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131#3744—41no—
132C3×#215—22no—
133C3×#215D414yescomplemented
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4×Dic3—21no—
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×D24—41no—
143Dic3⋊Dic3D411yescharacteristic
144#3722—21no—
145#3722D411yescharacteristic
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3D411yescharacteristic
150#3716—22no—
151#3714—22no—
152#3714—22no—
153#3713—22no—
154#3712—22no—
155D3×C3⋊C8—22no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C2×#239—31no—
159C2×#239—31no—
160C2×#239—61no—
161C2×#239C2×D311yescharacteristic, complemented
162C2×#237—31no—
163C2×D3×D4—31no—
164C2×D3×D4—31no—
165C2×#235—31no—
166C2×C3×SD16—31no—
167C2×C3×SD16—31no—
168C2×C3×D8—31no—
169C3×#121—31no—
170C3×C4×Q8—31no—
171C3×C4×D4—31no—
172#950—64no—
173Q8×Dic3C2×D311yescharacteristic, complemented
174C2×#216—31no—
175C2×#216—31no—
176C2×#216—61no—
177C2×#215C2×D311yescharacteristic
178C2×#215C2×D311yescharacteristic
179#940—31no—
180#940—61no—
181#938—31no—
182#938—61no—
183#938—61no—
184#937—61no—
185#936—31no—
186C2×#214—31no—
187C2×#213—31no—
188C2×#213—31no—
189C2×#213—31no—
190C2×#213—31no—
191#930—31no—
192#930—61no—
193#930—61no—
194C4×#67—31no—
195C4×#67—61no—
196C2×(C2×D3)⋊C4—61no—
197C22×C3⋊C8—31no—
198#916—64no—
199#914—64no—
200#914—64no—
201C2×D24—31no—
202C2×D24—31no—
203C2×D24C2×D311yescharacteristic
204C2×#204—31no—
205C2×#204—31no—
206C2×#204—31no—
207C2×#204—61no—
208C2×ΓL(1,𝔽25)—31no—
209C2×ΓL(1,𝔽25)—31no—
210C2×D3×C8—31no—
211#897—31no—
212#897—31no—
213#897—61no—
214#895—31no—
215#895—31no—
216#895—61no—
217#895—61no—
218#895C2×D311yescharacteristic
219#893C2×D311yescharacteristic
220#886—61no—
221#883—61no—
222#882—61no—
223D3×C22⋊C4—61no—
224#875—31no—
225#874—31no—
226#874—61no—
227C4×D12—31no—
228C4×D12—61no—
229C3×#107—31no—
230C3×#103—21no—
231C3×#103C2×D311yescharacteristic, complemented
232C3×#103C2×D311yescharacteristic, complemented
233C3×#102—31no—
234C3×#102—31no—
235C3×C22⋊C8—31no—
236C3×#97—31no—
237#832—31no—
238#821C2×D311yescharacteristic
239(C2×D3)⋊C8—31no—
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—61no—
242(C2×D3)⋊C8C2×D311yescharacteristic, complemented
243#816—31no—
244#815C2×D311yescharacteristic, complemented
245Dic3⋊C8—31no—
246#810—31no—
247#809—31no—
248#809—31no—
249#809—31no—
250#809—61no—
251#809C2×D311yescharacteristic, complemented
252#807C2×D311yescharacteristic, complemented
253C4⋊(C3⋊C8)—31no—
254C22×C3⋊D3—21no—
255C22×C3⋊D3C2×D411yescharacteristic
256C22×C3×D3—21no—
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×Q8C2×D412yes—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2411yescharacteristic
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3C2×D411yescharacteristic
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—42no—
273C4×C3⋊D3—21no—
274C4×C3⋊D3—21no—
275C4×C3⋊D3—42no—
276#634—21no—
277#634—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—42no—
288C3×D12—81no—
289C3×D12C2×D412yes—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—42no—
293C3×C4×D3—81no—
294#626—41no—
295#626—42no—
296#626—81no—
297#626—81no—
298#626—81no—
299#625—42no—
300#625—42no—
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—91no—
312#466—91no—
313#464—91no—
314#459—91no—
315#452—91no—
316#449—31no—
317#449—91no—
318#447—91no—
319#440—31no—
320#435—91no—
321C23×D3—61no—
322C23×D3—61no—
323C3×#41—62no—
324C3×#41—121no—
325C2×C3×Q8—21no—
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×D4—31no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—61no—
332C2×C3×D4—61no—
333C22×C3×C4—31no—
334C22×C3×C4—61no—
335C22×C3×C4—61no—
336C2×#67—31no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C22×Dic3—61no—
346#239—22no—
347#239—41no—
348#239—62no—
349#239—62no—
350#239—122no—
351#239—121no—
352#239—121no—
353#239—122no—
354#237—62no—
355#237—121no—
356D3×D4—62no—
357D3×D4—62no—
358D3×D4—121no—
359D3×D4—121no—
360#235—62no—
361#235—121no—
362C2×D12—21no—
363C2×D12—21no—
364C2×D12—31no—
365C2×D12—31no—
366C2×D12—31no—
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×D12C22×D311yescharacteristic
376C2×D12C22×D311yescharacteristic
377C2×D12C22×D311yescharacteristic
378C2×C4×D3—21no—
379C2×C4×D3—21no—
380C2×C4×D3—31no—
381C2×C4×D3—31no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3—121no—
387C2×C4×D3C22×D311yescharacteristic
388C2×Dic6—31no—
389C2×Dic6—31no—
390C2×Dic6—61no—
391C3×SD16—34no—
392C3×SD16—62no—
393C3×D8—121no—
394C2×C3×C8—21no—
395C2×C3×C8—31no—
396C2×C3×C8—31no—
397C2×C3×C8C22×D311yescharacteristic
398C2×C3×C8C22×D311yescharacteristic
399C3×C4⋊C4—21no—
400C3×C4⋊C4—31no—
401C3×C4⋊C4—61no—
402C3×C4⋊C4C22×D311yescharacteristic
403C3×C4⋊C4C22×D311yescharacteristic
404C3×C22⋊C4—61no—
405C3×C22⋊C4—61no—
406C3×C42—31no—
407C3×C42—61no—
408#217—31no—
409#217—61no—
410#217—61no—
411#217—61no—
412#216—62no—
413#216—62no—
414#216—122no—
415#215—22no—
416#215D1214yescomplemented
417#214—62no—
418#213—62no—
419#213—62no—
420#213—62no—
421#213—62no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—31no—
425(C2×D3)⋊C4—31no—
426(C2×D3)⋊C4—31no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—121no—
435C4⋊Dic3—21no—
436C4⋊Dic3—31no—
437C4⋊Dic3—61no—
438C4⋊Dic3—61no—
439C4⋊Dic3—121no—
440C4⋊Dic3C22×D311yescharacteristic
441Dic3⋊C4—31no—
442C4×Dic3—21no—
443C4×Dic3C22×D311yescharacteristic
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—61no—
447C2×C3⋊C8—62no—
448C2×C3⋊C8C22×D311yescharacteristic
449C2×C3⋊C8C22×D311yescharacteristic
450D24—41no—
451D24—62no—
452D24—62no—
453#204—62no—
454#204—121no—
455#204—121no—
456#204—122no—
457ΓL(1,𝔽25)—62no—
458ΓL(1,𝔽25)—62no—
459D3×C8—62no—
460C22×C32C22×D411yescharacteristic
461C2×C3⋊D3—21no—
462C2×C3⋊D3—21no—
463C2×C3⋊D3—21no—
464C2×C3⋊D3—41no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3×D3—22no—
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
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—22no—
481C32×C4—41no—
482C32×C4C22×D411yescharacteristic
483C32×C4H(5,𝔽2)11yescharacteristic
484C3⋊Dic3—21no—
485C3⋊Dic3—41no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—21no—
489C3×Dic3—41no—
490C2×#41—31no—
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—31no—
499C2×SD16—91no—
500C2×SD16—91no—
501C2×D8—31no—
502C2×D8—91no—
503C2×D8—91no—
504C2×D8—91no—
505C2×M16—91no—
506C22×C8—91no—
507#127—91no—
508#127—181no—
509#124—91no—
510#123—181no—
511C22⋊Q8—91no—
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—31no—
521C4×D4—91no—
522C4×D4—181no—
523C2×C22⋊C4—181no—
524#107—31no—
525C4⋊C8—91no—
526#103—91no—
527#103D3211yescharacteristic, complemented
528#102—31no—
529#102—31no—
530#102—91no—
531#102—91no—
532C22⋊C8—31no—
533C22⋊C8—91no—
534#97—31no—
535C23×C3—31no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3—61no—
539C22×D3—21no—
540C22×D3—21no—
541C22×D3—21no—
542C22×D3—31no—
543C22×D3—31no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—121no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—241no—
553C22×D3—241no—
554C22×D3D3×D411yescharacteristic
555C3×Q8—21no—
556C3×Q8—21no—
557C3×Q8—22no—
558C3×Q8—41no—
559C3×Q8C2×D1212yes—
560C3×Q8D3×D412yes—
561C3×D4—32no—
562C3×D4—61no—
563C3×D4—61no—
564C3×D4—61no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—122no—
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—122no—
583C2×C3×C4—241no—
584C2×C3×C4C23×D311yescharacteristic
585C2×C3×C4C23×D311yescharacteristic
586#67—121no—
587#67—122no—
588#67—122no—
589#67—122no—
590#67—122no—
591#67—122no—
592#67—241no—
593#67—241no—
594#67—241no—
595C2×Dic3—21no—
596C2×Dic3—31no—
597C2×Dic3—31no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—121no—
602C2×Dic3—122no—
603C2×Dic3D3×D411yescharacteristic
604C2×Dic3D3×D411yescharacteristic
605C2×Dic3D3×D411yescharacteristic
606D12—21no—
607D12—21no—
608D12—21no—
609D12—21no—
610D12—21no—
611D12—42no—
612D12—62no—
613D12—61no—
614D12—61no—
615D12—61no—
616D12—61no—
617D12—81no—
618D12—121no—
619D12—122no—
620D12—122no—
621D12—124no—
622D12—121no—
623D12—122no—
624D12—241no—
625D12—241no—
626D12—241no—
627D12C2×D1212yes—
628C4×D3—21no—
629C4×D3—21no—
630C4×D3—42no—
631C4×D3—61no—
632C4×D3—61no—
633C4×D3—61no—
634C4×D3—61no—
635C4×D3—81no—
636C4×D3—121no—
637C4×D3—121no—
638C4×D3—122no—
639C4×D3—122no—
640C4×D3—124no—
641C4×D3—122no—
642Dic6—61no—
643Dic6—61no—
644Dic6—61no—
645Dic6—61no—
646Dic6—121no—
647Dic6—121no—
648C3×C8—21no—
649C3×C8—21no—
650C3×C8—32no—
651C3×C8—41no—
652C3×C8—61no—
653C3⋊C8—21no—
654C3⋊C8—61no—
655C3⋊C8—61no—
656C3⋊C8—121no—
657C3⋊C8C2×D1212yes—
658C2×C32D4211yescharacteristic
659C2×C32#57511yescharacteristic
660C2×C32#57611yescharacteristic
661C3⋊D3—41no—
662C3⋊D3—81no—
663C3×D3—42no—
664C3×D3—41no—
665C3×D3—81no—
666C3×D3—81no—
667C24—181no—
668#41—62no—
669#41—121no—
670#41—182no—
671#41—182no—
672#41—361no—
673#41—361no—
674C2×Q8—91no—
675C2×Q8C2×D3211yescharacteristic
676C2×D4—31no—
677C2×D4—31no—
678C2×D4—31no—
679C2×D4—61no—
680C2×D4—61no—
681C2×D4—91no—
682C2×D4—91no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—181no—
686C2×D4—181no—
687C2×D4—181no—
688C2×D4—181no—
689C2×D4—182no—
690C2×D4—181no—
691C2×D4—361no—
692C22×C4—31no—
693C22×C4—61no—
694C22×C4—61no—
695C22×C4—91no—
696C22×C4—181no—
697C22×C4—181no—
698Q16—182no—
699SD16—34no—
700SD16—62no—
701SD16—182no—
702SD16—361no—
703D8—121no—
704D8—182no—
705D8—182no—
706D8—182no—
707M16—182no—
708C2×C8—31no—
709C2×C8—31no—
710C2×C8—91no—
711C2×C8—182no—
712C2×C8C2×D3211yescharacteristic
713C4⋊C4—31no—
714C4⋊C4—61no—
715C4⋊C4—91no—
716C4⋊C4—181no—
717C4⋊C4C2×D3211yescharacteristic
718C22⋊C4—61no—
719C22⋊C4—61no—
720C22⋊C4—91no—
721C22⋊C4—91no—
722C22⋊C4—181no—
723C22⋊C4—181no—
724C22⋊C4—181no—
725C22⋊C4—181no—
726C22⋊C4—181no—
727C42—31no—
728C42—61no—
729C22×C3—21no—
730C22×C3—61no—
731C22×C3—61no—
732C22×C3—61no—
733C22×C3—62no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3C2×D3×D411yescharacteristic
743C22×C3C2×D3×D411yescharacteristic
744C2×D3—21no—
745C2×D3—21no—
746C2×D3—22no—
747C2×D3—21no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—61no—
757C2×D3—61no—
758C2×D3—61no—
759C2×D3—61no—
760C2×D3—61no—
761C2×D3—61no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—122no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—241no—
773C2×D3—241no—
774C2×D3—244no—
775C2×D3—244no—
776C3×C4—22no—
777C3×C4—22no—
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—42no—
781C3×C4—41no—
782C3×C4—41no—
783C3×C4—61no—
784C3×C4—61no—
785C3×C4—61no—
786C3×C4—81no—
787C3×C4—121no—
788C3×C4C22×D1211yescharacteristic
789C3×C4C2×D3×D411yescharacteristic
790C3×C4#100411yescharacteristic
791C3×C4#100911yescharacteristic
792Dic3—21no—
793Dic3—21no—
794Dic3—21no—
795Dic3—41no—
796Dic3—61no—
797Dic3—61no—
798Dic3—121no—
799Dic3—121no—
800Dic3—121no—
801Dic3—241no—
802C32#326811yescharacteristic, complemented, Sylow
803C23—31no—
804C23—61no—
805C23—61no—
806C23—61no—
807C23—91no—
808C23—181no—
809C23—362no—
810C23—362no—
811C23—721no—
812Q8—21no—
813Q8—181no—
814Q8—181no—
815Q8D3×D1212yes—
816D4—32no—
817D4—61no—
818D4—61no—
819D4—61no—
820D4—61no—
821D4—61no—
822D4—122no—
823D4—181no—
824D4—181no—
825D4—241no—
826D4—362no—
827D4—361no—
828D4—362no—
829D4—362no—
830D4—362no—
831D4—721no—
832D4—721no—
833D4—721no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—31no—
837C2×C4—31no—
838C2×C4—31no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—91no—
843C2×C4—122no—
844C2×C4—181no—
845C2×C4—181no—
846C2×C4—181no—
847C2×C4—241no—
848C2×C4—362no—
849C2×C4—362no—
850C2×C4C22×D3211yescharacteristic
851C8—21no—
852C8—32no—
853C8—61no—
854C8—181no—
855C2×C3—21no—
856C2×C3—21no—
857C2×C3—21no—
858C2×C3—121no—
859C2×C3—122no—
860C2×C3—241no—
861C2×C3—241no—
862C2×C3D4×D1211yescharacteristic
863C2×C3#559011yescharacteristic
864C2×C3#576811yescharacteristic
865C2×C3#577411yescharacteristic
866C2×C3#577411yescharacteristic
867C2×C3#577711yescharacteristic
868D3—42no—
869D3—41no—
870D3—81no—
871D3—81no—
872D3—121no—
873D3—121no—
874D3—241no—
875D3—242no—
876D3—241no—
877D3—241no—
878C22—61no—
879C22—61no—
880C22—61no—
881C22—62no—
882C22—121no—
883C22—121no—
884C22—121no—
885C22—121no—
886C22—121no—
887C22—121no—
888C22—121no—
889C22—121no—
890C22—181no—
891C22—181no—
892C22—181no—
893C22—361no—
894C22—361no—
895C22—361no—
896C22—724no—
897C22D32×D411yescharacteristic
898C4—22no—
899C4—41no—
900C4—61no—
901C4—61no—
902C4—61no—
903C4—121no—
904C4—181no—
905C4—361no—
906C4C2×D3×D1211yescharacteristic
907C4#6431411yescharacteristic
908C3—21no—
909C3#7979611yescharacteristic, complemented
910C3#8012311yescharacteristic, complemented
911C2—121no—
912C2—122no—
913C2—241no—
914C2—241no—
915C2—361no—
916C2—721no—
917C2#1059427711yescharacteristic
918C2#1059475011yescharacteristic
919C2#1059476311yescharacteristic
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. #10595410C2semidirect
2. C2×#63947C2semidirect
3. C2×#63941C2semidirect
4. #10594630C2semidirect
5. #10592507C2semidirect
6. C3×#4817C2semidirect
7. C3×#4810C2semidirect
8. #10591604C2semidirect
9. #10590968C2semidirect
10. #10590945C2semidirect
11. #10590883C2semidirect
12. #10590728C2semidirect
13. #10590576C2semidirect
14. #10590547C2semidirect
15. #10590506C2semidirect
19. C2×C3×#239C22semidirect
22. C2×#3756C22semidirect
23. C2×#3744C22semidirect
25. C3×Q8×Dic3C22semidirect
38. #63911C22semidirect
40. #63909C22semidirect
46. C2×#3716C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. C32×#103C22semidirect
54. #63636C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×#815C22semidirect
58. C3×#809C22semidirect
59. C3×#807C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63567C22semidirect
81. #4817D3semidirect
82. #4810D3semidirect
133. C3×#215D4semidirect
161. C2×#239C2×D3semidirect
173. Q8×Dic3C2×D3semidirect
231. C3×#103C2×D3semidirect
232. C3×#103C2×D3semidirect
242. (C2×D3)⋊C8C2×D3semidirect
244. #815C2×D3semidirect
251. #809C2×D3semidirect
252. #807C2×D3semidirect
416. #215D12semidirect
527. #103D32semidirect
802. C32#3268semidirect
909. C3#79796semidirect
910. C3#80123semidirect

Maximal subgroups

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

subgroupindex
#105954102
C2×#639472
C2×#639412
#105946302
#105925072
C3×#48172
C3×#48102
#105916042
#105909682
#105909452
#105908832
#105907282
#105905762
#105905472
#105905062
#801233
#797963