Finite Group Databasebeta

← #11884424

Subgroups — #11884424

Order 1152.

1087 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#904C211yesmaximal, characteristic, complemented
2#10595067C211yesmaximal, characteristic, complemented
3#10595007C211yesmaximal, characteristic, complemented
4C2×#63794C211yesmaximal, characteristic, complemented
5#10592814C211yesmaximal, characteristic, complemented
6C3×#5111C211yesmaximal, characteristic, complemented
7#10591163C211yesmaximal, characteristic, complemented
8#10591163C211yesmaximal, characteristic, complemented
9#10590966C211yesmaximal, characteristic, complemented
10#10590944C211yesmaximal, characteristic, complemented
11#10590881C211yesmaximal, characteristic, complemented
12#10590833C211yesmaximal, characteristic, complemented
13#10590801C211yesmaximal, characteristic, complemented
14#10590766C211yesmaximal, characteristic, complemented
15#10590753C211yesmaximal, characteristic, complemented
16#83922—31nomaximal
17#79497—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic, complemented
20C2×D3×D12C2211yescharacteristic
21C2×#3799C2211yescharacteristic
22C22×C32×C8C2211yescharacteristic, complemented
23#64139C2211yescharacteristic
24#64139C2211yescharacteristic, complemented
25C2×#3745C2211yescharacteristic
26C3×C4×#67C2211yescharacteristic
27C2×C3×Dic12C2211yescharacteristic, complemented
28C3×#904—24no—
29C2×C3×D24C2211yescharacteristic
30C2×C3×#204C2211yescharacteristic
31C2×C3×#204C2211yescharacteristic, complemented
32C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
33#63983—21no—
34#63979—21no—
35#63971—21no—
36#63958—21no—
37D3×(C2×D3)⋊C4—21no—
38#63911C2211yescharacteristic, complemented
39#63908C2211yescharacteristic
40#63906—21no—
41#63904—21no—
42Dic3×D12C2211yescharacteristic
43#63864C2211yescharacteristic
44#63856C2211yescharacteristic
45#63850—21no—
46Dic3×Dic6C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic
48C2×#3717C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50C2×#3714C2211yescharacteristic
51#63794—24no—
52#63648C2211yescharacteristic
53#63648C2211yescharacteristic, complemented
54#63645C2211yescharacteristic, complemented
55C3×#830C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×#815C2211yescharacteristic, complemented
58C3×Dic3⋊C8C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63563C2211yescharacteristic
62#63563C2211yescharacteristic, complemented
63C2×C3×#135—31no—
64#5834—31no—
65#5829—31no—
66C2×#914—31no—
67C2×#908—31no—
68C2×#904D311yescharacteristic, complemented
69#5553—31no—
70#5550—31no—
71C3×#435—31no—
72#5238—31no—
73#5238—31no—
74#5187—31no—
75#5185—31no—
76#5176—31no—
77#5174—31no—
78#5164—31no—
79#5156—31no—
80#5150—31no—
81#5134—31no—
82#5115—31no—
83#5115—31no—
84#5115—61no—
85#5111D311yescharacteristic, complemented
86#4845—31no—
87#4843—31no—
88#4734—31no—
89#4734—31no—
90#4733—31no—
91#4732—31no—
92#4712—31no—
93#4710—31no—
94C22×D32—21no—
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97C2×#638—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C3×#235—22no—
104C3×#235—22no—
105C3×#235—41no—
106C3×#235—41no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×C3×Dic6C2311yescharacteristic
114C2×#626—21no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#625—21no—
119C2×#624—21no—
120C2×D3×Dic3—21no—
121D3×D12—22no—
122D3×D12—41no—
123#3799—22no—
124#3799—41no—
125C2×C32×C8—22no—
126C2×C32×C8C2311yescharacteristic
127C2×C32×C8C2311yescharacteristic
128#3752—21no—
129#3752—21no—
130C4⋊(C3⋊Dic3)C2311yescharacteristic
131C4⋊(C3⋊Dic3)C2311yescharacteristic
132#3745—22no—
133C3×#217D411yescharacteristic
134C3×(C2×D3)⋊C4D411yescharacteristic
135C3×Dic3⋊C4D411yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×Dic12—22no—
140C3×D24—22no—
141C3×#204—22no—
142C3×#204D414yescomplemented
143C3×ΓL(1,𝔽25)—22no—
144#3724—21no—
145Dic3⋊Dic3—21no—
146#3722—21no—
147#3722—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151Dic32—21no—
152#3717—22no—
153#3717—41no—
154#3714—22no—
155#3714—41no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×#239—31no—
160C2×D3×D4—31no—
161C2×#235—31no—
162C2×#235C2×D311yescharacteristic
163C2×#235C2×D311yescharacteristic, complemented
164C22×D12—31no—
165C3×#135—64no—
166C2×C3×Q16—31no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C2×C3×D8—31no—
170C2×C3×M16—31no—
171C22×C3×C8—21no—
172C22×C3×C8C2×D311yescharacteristic, complemented
173C22×C3×C8C2×D311yescharacteristic, complemented
174C3×C4×D4—31no—
175#947—31no—
176#946—31no—
177Q8×Dic3—31no—
178C2×#215—31no—
179C2×#215—31no—
180#940—31no—
181#940—61no—
182#940—61no—
183#939—61no—
184#938—31no—
185#938—61no—
186#937—61no—
187#937—61no—
188D4×Dic3—31no—
189C2×#213—31no—
190C2×#213—31no—
191#930—31no—
192#930—31no—
193#930—31no—
194#930—31no—
195#930—31no—
196#930—61no—
197#930—61no—
198#930—61no—
199#929—61no—
200C4×#67—61no—
201C4×#67C2×D311yescharacteristic
202C2×(C2×D3)⋊C4—61no—
203#924—31no—
204#914—64no—
205#908—64no—
206C2×Dic12C2×D311yescharacteristic, complemented
207#904—24no—
208C2×D24—31no—
209C2×D24—31no—
210C2×D24—31no—
211C2×D24—31no—
212C2×D24—61no—
213C2×D24C2×D311yescharacteristic
214C2×#204—31no—
215C2×#204—31no—
216C2×#204C2×D311yescharacteristic
217C2×#204C2×D311yescharacteristic, complemented
218C2×ΓL(1,𝔽25)C2×D311yescharacteristic
219#894—61no—
220#893—61no—
221#884—61no—
222#884—61no—
223#884—61no—
224D3×C22⋊C4—61no—
225#875—31no—
226#874—31no—
227C4×D12—31no—
228C4×Dic6—31no—
229C3×C4⋊C8—31no—
230C3×C22⋊C8—31no—
231C3×C22⋊C8—31no—
232C3×#97—31no—
233#835—31no—
234#835—31no—
235#832—31no—
236#832—31no—
237#830C2×D311yescharacteristic, complemented
238#821—31no—
239#821—31no—
240#821—31no—
241#821—31no—
242#821—31no—
243#821—31no—
244#821—61no—
245#821—61no—
246(C2×D3)⋊C8C2×D311yescharacteristic
247#818—31no—
248#818—31no—
249#818—61no—
250#816—31no—
251#816—31no—
252#815C2×D311yescharacteristic, complemented
253Dic3⋊C8C2×D311yescharacteristic, complemented
254C23×C32C2×D411yescharacteristic
255C22×C3⋊D3—21no—
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—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4C2×D411yescharacteristic
266C2×C32×C4C2411yescharacteristic
267#638—81no—
268#638—81no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—21no—
275C3×#67—41no—
276C3×#67—42no—
277C3×#67—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×D12C2×D412yes—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—42no—
290C3×C4×D3—42no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6C2×D412yes—
295#626—42no—
296#626—42no—
297#626—42no—
298#626—81no—
299#625—81no—
300#624—42no—
301D3×Dic3—81no—
302C32×C8—21no—
303C32×C8C2×D412yes—
304C3×C3⋊C8—21no—
305C3×C3⋊C8—21no—
306C2×AGL(1,ℤ/8)—91no—
307C2×#135—31no—
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—91no—
320#435—31no—
321C23×D3—61no—
322C23×D3—61no—
323C3×#41—62no—
324C3×#41—62no—
325C3×#41—121no—
326C3×#41—121no—
327C2×C3×Q8—31no—
328C2×C3×Q8—31no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C22×C3×C4—21no—
335C22×C3×C4—31no—
336C22×C3×C4—61no—
337C22×C3×C4—61no—
338C22×C3×C4C22×D311yescharacteristic
339C22×C3×C4C22×D311yescharacteristic
340C2×#67—21no—
341C2×#67—21no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—121no—
353C2×#67—121no—
354C2×#67D1211yescharacteristic
355C22×Dic3—61no—
356#239—62no—
357#239—121no—
358D3×D4—62no—
359D3×D4—121no—
360#235—22no—
361#235—22no—
362#235—41no—
363#235—41no—
364#235—62no—
365#235—121no—
366C2×D12—31no—
367C2×D12—31no—
368C2×D12—31no—
369C2×D12—31no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—62no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—121no—
378C2×D12C22×D311yescharacteristic
379C2×D12C22×D311yescharacteristic
380C2×C4×D3—21no—
381C2×C4×D3—21no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3C22×D311yescharacteristic
386C2×Dic6C22×D311yescharacteristic
387C2×Dic6C22×D311yescharacteristic
388C3×Q16—62no—
389C3×SD16—34no—
390C3×SD16—62no—
391C3×D8—62no—
392C3×M16—62no—
393C2×C3×C8—22no—
394C2×C3×C8—22no—
395C2×C3×C8—21no—
396C2×C3×C8—21no—
397C2×C3×C8—31no—
398C2×C3×C8—31no—
399C2×C3×C8—42no—
400C2×C3×C8C22×D311yescharacteristic
401C2×C3×C8C22×D311yescharacteristic
402C2×C3×C8C22×D311yescharacteristic
403C2×C3×C8C22×D311yescharacteristic
404C3×C4⋊C4—31no—
405C3×C22⋊C4—31no—
406C3×C22⋊C4—31no—
407C3×C42—31no—
408#217—61no—
409#217—61no—
410#217—61no—
411#217D1211yescharacteristic
412#215—62no—
413#215—121no—
414#213—62no—
415#213—121no—
416(C2×D3)⋊C4—61no—
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—121no—
428(C2×D3)⋊C4—121no—
429(C2×D3)⋊C4D1211yescharacteristic
430C4⋊Dic3—31no—
431C4⋊Dic3—31no—
432C4⋊Dic3—31no—
433C4⋊Dic3—31no—
434C4⋊Dic3—61no—
435C4⋊Dic3—61no—
436C4⋊Dic3—61no—
437Dic3⋊C4—61no—
438Dic3⋊C4—61no—
439Dic3⋊C4—61no—
440Dic3⋊C4D1211yescharacteristic
441C4×Dic3—61no—
442C4×Dic3—61no—
443C4×Dic3C22×D311yescharacteristic
444C2×C3⋊C8C22×D311yescharacteristic
445C2×C3⋊C8C22×D311yescharacteristic
446Dic12—22no—
447D24—22no—
448D24—62no—
449D24—62no—
450D24—62no—
451D24—122no—
452D24—121no—
453#204—22no—
454#204—62no—
455#204—121no—
456#204#6714yescomplemented
457ΓL(1,𝔽25)—22no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32C22×D411yescharacteristic
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—21no—
469C2×C3×D3—22no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477D32—84no—
478C32×C4—21no—
479C32×C4C22×D411yescharacteristic
480C32×C4H(5,𝔽2)11yescharacteristic
481C3⋊Dic3—41no—
482C3⋊Dic3—41no—
483C3×Dic3—21no—
484C3×Dic3—22no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—41no—
488C2×#41—31no—
489C2×#41—31no—
490C2×#41—91no—
491C22×D4—91no—
492AGL(1,ℤ/8)—184no—
493#135—64no—
494C2×Q16—31no—
495C2×SD16—31no—
496C2×SD16—31no—
497C2×SD16—91no—
498C2×SD16—91no—
499C2×D8—31no—
500C2×D8—91no—
501C2×D8—91no—
502C2×D8—91no—
503C2×M16—31no—
504C22×C8D3211yescharacteristic, complemented
505#127—91no—
506#127—181no—
507#124—91no—
508#123—181no—
509C22⋊Q8—91no—
510#121—91no—
511#121—91no—
512#121—91no—
513#121—181no—
514#121—181no—
515#121—181no—
516#120—181no—
517C4×Q8—91no—
518C4×D4—31no—
519C4×D4—91no—
520C4×D4—181no—
521C2×C22⋊C4—181no—
522#107—91no—
523C4⋊C8—31no—
524#103—91no—
525#103—91no—
526#102—91no—
527#102—91no—
528#102—91no—
529#102—91no—
530C22⋊C8—31no—
531C22⋊C8—31no—
532#97—31no—
533C23×C3—21no—
534C23×C3—31no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3C2×D1211yescharacteristic
538C23×C3D3×D411yescharacteristic
539C22×D3—21no—
540C22×D3—21no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—121no—
546C22×D3—121no—
547C22×D3—122no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—241no—
552C22×D3—241no—
553C22×D3C2×D1211yescharacteristic
554C3×Q8—32no—
555C3×Q8—61no—
556C3×Q8—61no—
557C3×Q8—61no—
558C3×D4—32no—
559C3×D4—61no—
560C3×D4—61no—
561C3×D4—61no—
562C3×D4—121no—
563C3×D4—122no—
564C3×D4—122no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—31no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—122no—
581C2×C3×C4—122no—
582C2×C3×C4C2×D1211yescharacteristic
583C2×C3×C4D3×D411yescharacteristic
584C2×C3×C4C23×D311yescharacteristic
585C2×C3×C4C23×D311yescharacteristic
586#67—41no—
587#67—42no—
588#67—42no—
589#67—122no—
590#67—122no—
591#67—122no—
592#67—241no—
593#67—241no—
594#67—241no—
595#67—241no—
596#67—241no—
597#67—241no—
598#67—241no—
599#67—242no—
600#67—242no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—121no—
608C2×Dic3—121no—
609C2×Dic3—241no—
610C2×Dic3C2×D1211yescharacteristic
611C2×Dic3C2×D1211yescharacteristic
612C2×Dic3C2×D1211yescharacteristic
613D12—21no—
614D12—21no—
615D12—21no—
616D12—61no—
617D12—61no—
618D12—61no—
619D12—61no—
620D12—61no—
621D12—61no—
622D12—61no—
623D12—61no—
624D12—121no—
625D12—121no—
626D12—121no—
627D12—121no—
628D12—122no—
629D12—122no—
630D12—122no—
631D12—241no—
632D12C2×#6712yes—
633C4×D3—21no—
634C4×D3—21no—
635C4×D3—42no—
636C4×D3—42no—
637C4×D3—122no—
638C4×D3—122no—
639C4×D3—241no—
640Dic6—21no—
641Dic6—21no—
642Dic6—21no—
643Dic6C2×#6712yes—
644C3×C8—21no—
645C3×C8—21no—
646C3×C8—22no—
647C3×C8—41no—
648C3×C8—61no—
649C3×C8—61no—
650C3×C8D3×D412yes—
651C3×C8C2×#6712yes—
652C3⋊C8—21no—
653C3⋊C8—21no—
654C2×C32—41no—
655C2×C32D4211yescharacteristic
656C2×C32#57511yescharacteristic
657C2×C32#57611yescharacteristic
658C3⋊D3—81no—
659C3⋊D3—81no—
660C3×D3—41no—
661C3×D3—42no—
662C3×D3—81no—
663C24—181no—
664#41—62no—
665#41—62no—
666#41—121no—
667#41—121no—
668#41—182no—
669#41—361no—
670C2×Q8—31no—
671C2×Q8—31no—
672C2×D4—31no—
673C2×D4—31no—
674C2×D4—31no—
675C2×D4—61no—
676C2×D4—61no—
677C2×D4—91no—
678C2×D4—91no—
679C2×D4—181no—
680C2×D4—181no—
681C2×D4—181no—
682C2×D4—182no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—181no—
686C2×D4—181no—
687C2×D4—361no—
688C22×C4—31no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—181no—
692C22×C4—181no—
693C22×C4C2×D3211yescharacteristic
694Q16—62no—
695SD16—34no—
696SD16—62no—
697SD16—182no—
698SD16—361no—
699D8—62no—
700D8—182no—
701D8—182no—
702D8—361no—
703M16—62no—
704C2×C8—22no—
705C2×C8—31no—
706C2×C8—31no—
707C2×C8C2×D3211yescharacteristic
708C2×C8C2×D3211yescharacteristic
709C4⋊C4—31no—
710C4⋊C4—91no—
711C4⋊C4—91no—
712C4⋊C4—181no—
713C4⋊C4—181no—
714C22⋊C4—31no—
715C22⋊C4—31no—
716C22⋊C4—181no—
717C22⋊C4—181no—
718C22⋊C4—181no—
719C22⋊C4—181no—
720C22⋊C4—181no—
721C22⋊C4—181no—
722C22⋊C4—181no—
723C42—31no—
724C42—181no—
725C22×C3—22no—
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—61no—
736C22×C3—61no—
737C22×C3—61no—
738C22×C3—62no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3C22×D1211yescharacteristic
745C22×C3C2×D3×D411yescharacteristic
746C2×D3—21no—
747C2×D3—21no—
748C2×D3—22no—
749C2×D3—21no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—41no—
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—241no—
768C2×D3—241no—
769C2×D3—241no—
770C2×D3—241no—
771C2×D3—241no—
772C2×D3—241no—
773C2×D3—244no—
774C2×D3—244no—
775C3×C4—21no—
776C3×C4—21no—
777C3×C4—21no—
778C3×C4—21no—
779C3×C4—41no—
780C3×C4—61no—
781C3×C4—61no—
782C3×C4—61no—
783C3×C4—62no—
784C3×C4—121no—
785C3×C4C2×D3×D411yescharacteristic
786C3×C4#100411yescharacteristic
787C3×C4#100911yescharacteristic
788C3×C4C22×#6711yescharacteristic
789Dic3—21no—
790Dic3—21no—
791Dic3—22no—
792Dic3—21no—
793Dic3—41no—
794Dic3—121no—
795Dic3—121no—
796Dic3—121no—
797Dic3—121no—
798Dic3—241no—
799Dic3—241no—
800C32#326811yescharacteristic, complemented, Sylow
801C23—31no—
802C23—61no—
803C23—61no—
804C23—181no—
805C23—181no—
806C23—362no—
807C23—362no—
808C23—721no—
809C23D3×D1211yescharacteristic
810Q8—32no—
811Q8—61no—
812Q8—61no—
813Q8—61no—
814D4—32no—
815D4—61no—
816D4—61no—
817D4—61no—
818D4—121no—
819D4—122no—
820D4—122no—
821D4—181no—
822D4—181no—
823D4—181no—
824D4—181no—
825D4—362no—
826D4—362no—
827D4—362no—
828D4—721no—
829D4—721no—
830D4—721no—
831D4—721no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—31no—
835C2×C4—31no—
836C2×C4—31no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—122no—
842C2×C4—122no—
843C2×C4—181no—
844C2×C4—181no—
845C2×C4—362no—
846C2×C4—721no—
847C2×C4D3×D1211yescharacteristic
848C2×C4C22×D3211yescharacteristic
849C8—21no—
850C8—61no—
851C8—61no—
852C8D3×#6712yes—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3—42no—
857C2×C3—41no—
858C2×C3—41no—
859C2×C3—122no—
860C2×C3—121no—
861C2×C3—241no—
862C2×C3D4×D1211yescharacteristic
863C2×C3#574811yescharacteristic
864C2×C3#575211yescharacteristic
865C2×C3#576811yescharacteristic
866C2×C3#576911yescharacteristic
867C2×C3D4×#6711yescharacteristic
868D3—41no—
869D3—42no—
870D3—81no—
871D3—241no—
872D3—241no—
873D3—241no—
874D3—241no—
875D3—481no—
876D3—481no—
877C22—21no—
878C22—21no—
879C22—21no—
880C22—61no—
881C22—61no—
882C22—61no—
883C22—62no—
884C22—121no—
885C22—121no—
886C22—121no—
887C22—121no—
888C22—121no—
889C22—361no—
890C22—361no—
891C22—361no—
892C22—361no—
893C22—361no—
894C22—361no—
895C22—724no—
896C22C2×D3×D1211yescharacteristic
897C4—21no—
898C4—61no—
899C4—61no—
900C4—61no—
901C4—62no—
902C4—121no—
903C4—361no—
904C4—361no—
905C4#6430711yescharacteristic
906C4C2×D3×#6711yescharacteristic
907C3—21no—
908C3#7949711yescharacteristic, complemented
909C3#8392211yescharacteristic, complemented
910C2—41no—
911C2—121no—
912C2—122no—
913C2—241no—
914C2—721no—
915C2—721no—
916C2#1059467611yescharacteristic
917C2#1059468011yescharacteristic
918C2D12×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#904C2semidirect
2. #10595067C2semidirect
3. #10595007C2semidirect
4. C2×#63794C2semidirect
5. #10592814C2semidirect
6. C3×#5111C2semidirect
7. #10591163C2semidirect
8. #10591163C2semidirect
9. #10590966C2semidirect
10. #10590944C2semidirect
11. #10590881C2semidirect
12. #10590833C2semidirect
13. #10590801C2semidirect
14. #10590766C2semidirect
15. #10590753C2semidirect
19. C2×C3×#235C22semidirect
22. C22×C32×C8C22semidirect
24. #64139C22semidirect
27. C2×C3×Dic12C22semidirect
31. C2×C3×#204C22semidirect
38. #63911C22semidirect
46. Dic3×Dic6C22semidirect
48. C2×#3717C22semidirect
53. #63648C22semidirect
54. #63645C22semidirect
55. C3×#830C22semidirect
57. C3×#815C22semidirect
58. C3×Dic3⋊C8C22semidirect
59. #63566C22semidirect
60. #63566C22semidirect
62. #63563C22semidirect
68. C2×#904D3semidirect
85. #5111D3semidirect
142. C3×#204D4semidirect
163. C2×#235C2×D3semidirect
172. C22×C3×C8C2×D3semidirect
173. C22×C3×C8C2×D3semidirect
206. C2×Dic12C2×D3semidirect
217. C2×#204C2×D3semidirect
237. #830C2×D3semidirect
252. #815C2×D3semidirect
253. Dic3⋊C8C2×D3semidirect
456. #204#67semidirect
504. C22×C8D32semidirect
800. C32#3268semidirect
908. C3#79497semidirect
909. C3#83922semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9042
#105950672
#105950072
C2×#637942
#105928142
C3×#51112
#105911632
#105909662
#105909442
#105908812
#105908332
#105908012
#105907662
#105907532
#839223
#794973