Finite Group Databasebeta

← #11884504

Subgroups — #11884504

Order 1152.

1076 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63807C211yesmaximal, characteristic, complemented
2C2×#63795C211yesmaximal, characteristic, complemented
3#10594003C211yesmaximal, characteristic, complemented
4#10593906C211yesmaximal, characteristic, complemented
5#10592544C211yesmaximal, characteristic, complemented
6C3×#4843C211yesmaximal, characteristic, complemented
7C3×#4836C211yesmaximal, characteristic, complemented
8#10590969C211yesmaximal, characteristic, complemented
9#10590968C211yesmaximal, characteristic, complemented
10#10590962C211yesmaximal, characteristic, complemented
11#10590944C211yesmaximal, characteristic, complemented
12#10590828C211yesmaximal, characteristic, complemented
13#10590826C211yesmaximal, characteristic, complemented
14#10590371C211yesmaximal, characteristic, complemented
15#10590360C211yesmaximal, characteristic, complemented
16#80348—31nomaximal
17#79497—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22C2×#3746C2211yescharacteristic, complemented
23C2×#3744C2211yescharacteristic
24#64084C2211yescharacteristic
25C4×#634C2211yescharacteristic, complemented
26C2×C3×D24C2211yescharacteristic
27C2×C3×D24C2211yescharacteristic
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
29C2×C3×D3×C8C2211yescharacteristic, complemented
30C3×#874C2211yescharacteristic, complemented
31C3×C4×D12C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic
33#63922—21no—
34D3×(C2×D3)⋊C4—21no—
35#63914—21no—
36#63909C2211yescharacteristic
37#63908C2211yescharacteristic
38#63908C2211yescharacteristic, complemented
39#63906—21no—
40#63898—21no—
41#63890—21no—
42#63885—21no—
43#63885—21no—
44#63857C2211yescharacteristic
45C2×#3716C2211yescharacteristic
46C2×#3716C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50#63807—24no—
51#63795—24no—
52C32×C4⋊C8C2211yescharacteristic, complemented
53#63648C2211yescharacteristic
54#63643C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#803C2211yescharacteristic, complemented
60#63575C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63563C2211yescharacteristic
63C2×#912—31no—
64C2×#911—31no—
65C2×#908—31no—
66C2×#904—31no—
67#5718—31no—
68#5554—31no—
69#5553—31no—
70#5550—31no—
71C3×#459—31no—
72C3×#435—31no—
73#5158—31no—
74#5156—31no—
75#5134—31no—
76#5115—31no—
77#5074—31no—
78#5018—31no—
79#4845—31no—
80#4845—31no—
81#4845—61no—
82#4843D311yescharacteristic, complemented
83#4836D311yescharacteristic, complemented
84#4783—31no—
85#4781—31no—
86#4780—31no—
87#4775—31no—
88#4734—31no—
89#4734—31no—
90#4733—31no—
91#4732—31no—
92#4712—31no—
93#4710—31no—
94C22×D32—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×D12—21no—
99C2×C3×D12—21no—
100C2×C3×D12D411yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×#626—21no—
108C2×#626—21no—
109C2×#625—21no—
110C2×#625—21no—
111C2×#625—21no—
112C2×#625—21no—
113C2×#625—21no—
114C2×D3×Dic3—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117D3×D12—22no—
118D3×D12—41no—
119#3795—22no—
120#3795—22no—
121#3795—22no—
122#3795—41no—
123#3795—41no—
124#3795—41no—
125C2×C32×C8C2311yescharacteristic
126C2×C32×C8C2311yescharacteristic
127C32×C42C2311yescharacteristic
128#3752—21no—
129#3752—21no—
130C4⋊(C3⋊Dic3)C2311yescharacteristic
131#3750—21no—
132C4×C3⋊Dic3—21no—
133#3746—22no—
134#3744—22no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×(C2×D3)⋊C4D411yescharacteristic
138C3×C4⋊Dic3D411yescharacteristic
139C3×C4⋊Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×D24—22no—
143C3×D24—22no—
144C3×ΓL(1,𝔽25)—22no—
145C3×D3×C8—22no—
146Dic3⋊Dic3—21no—
147#3722—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151#3716—22no—
152#3716—41no—
153#3716D414yescomplemented
154#3714—22no—
155#3714—41no—
156#3268—91noSylow
157C2×#237—31no—
158C2×#237—31no—
159C2×#237—31no—
160C2×D3×D4—31no—
161C2×#235—31no—
162C2×#235—31no—
163C2×#235—31no—
164C22×D12—31no—
165C2×C3×D8—31no—
166C2×C3×D8—31no—
167C2×C3×M16—31no—
168C22×C3×C8—31no—
169C3×#127—31no—
170C3×C4×D4—31no—
171C3×C4×D4—31no—
172#940—61no—
173#940—61no—
174#939—61no—
175#939—61no—
176#938—31no—
177#938—31no—
178#937—61no—
179D4×Dic3—61no—
180C2×#214—31no—
181C2×#214—31no—
182C2×#214—31no—
183C2×#213—31no—
184C2×#213—31no—
185#930—31no—
186#930—31no—
187#930—31no—
188#930—61no—
189C2×(C2×D3)⋊C4—61no—
190#924—31no—
191#912—64no—
192#911—64no—
193#908—64no—
194C2×Dic12—31no—
195C2×Dic12—31no—
196C2×Dic12—61no—
197#904—64no—
198C2×D24—31no—
199C2×D24—31no—
200C2×D24C2×D311yescharacteristic
201C2×D24C2×D311yescharacteristic
202C2×#204—31no—
203C2×#204—31no—
204C2×#204—31no—
205C2×#204—31no—
206C2×#204—31no—
207C2×#204—61no—
208C2×ΓL(1,𝔽25)C2×D311yescharacteristic
209C2×D3×C8C2×D311yescharacteristic, complemented
210#897—31no—
211#895—31no—
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#874C2×D311yescharacteristic, complemented
224C4×D12C2×D311yescharacteristic
225C4×D12C2×D311yescharacteristic
226C4×Dic6—31no—
227C4×Dic6—31no—
228C4×Dic6—61no—
229C3×C4⋊C8—21no—
230C3×C4⋊C8C2×D311yescharacteristic, complemented
231C3×C4⋊C8C2×D311yescharacteristic, complemented
232C3×#102—31no—
233C3×#102—31no—
234C3×C22⋊C8—31no—
235C3×C22⋊C8—31no—
236C3×#97—31no—
237#832—31no—
238#821—31no—
239#821—31no—
240#821—31no—
241#821—61no—
242#821C2×D311yescharacteristic, complemented
243#821C2×D311yescharacteristic, complemented
244(C2×D3)⋊C8C2×D311yescharacteristic
245(C2×D3)⋊C8C2×D311yescharacteristic, complemented
246#818—31no—
247#816—31no—
248#816—31no—
249#816—31no—
250#816—61no—
251#810—31no—
252#807—31no—
253#803C2×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—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—21no—
271#634—21no—
272#634—21no—
273#634—21no—
274#634C2×D412yes—
275C2×C3×Dic3—21no—
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—41no—
284C3×D12—42no—
285C3×D12—81no—
286C3×D12C2×D412yes—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×C4×D3—81no—
292#626—42no—
293#626—81no—
294#625—42no—
295#625—42no—
296#625—42no—
297#625—81no—
298#625—81no—
299D3×Dic3—42no—
300D3×Dic3—42no—
301D3×Dic3—42no—
302C32×C8—21no—
303C32×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—31no—
315#452—91no—
316#449—91no—
317#449—91no—
318#447—91no—
319#440—91no—
320#435—31no—
321C23×D3—61no—
322C23×D3—61no—
323C2×C3×D4—31no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—61no—
328C2×C3×D4—61no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C22×Dic3—61no—
345C22×Dic3—61no—
346C22×Dic3—61no—
347#237—62no—
348#237—62no—
349#237—62no—
350#237—121no—
351#237—121no—
352#237—121no—
353D3×D4—62no—
354D3×D4—121no—
355#235—62no—
356#235—62no—
357#235—62no—
358#235—121no—
359#235—121no—
360#235—121no—
361C2×D12—21no—
362C2×D12—21no—
363C2×D12—31no—
364C2×D12—31no—
365C2×D12—61no—
366C2×D12—62no—
367C2×D12—61no—
368C2×D12—61no—
369C2×D12—121no—
370C2×D12D1211yescharacteristic
371C2×D12C22×D311yescharacteristic
372C2×D12C22×D311yescharacteristic
373C2×D12C22×D311yescharacteristic
374C2×C4×D3—21no—
375C2×C4×D3—61no—
376C2×C4×D3—61no—
377C2×C4×D3—61no—
378C2×C4×D3C22×D311yescharacteristic
379C2×C4×D3C22×D311yescharacteristic
380C2×Dic6—31no—
381C2×Dic6—31no—
382C2×Dic6—31no—
383C2×Dic6—31no—
384C2×Dic6—61no—
385C2×Dic6—61no—
386C3×D8—62no—
387C3×D8—62no—
388C3×M16—62no—
389C2×C3×C8—21no—
390C2×C3×C8—21no—
391C2×C3×C8—31no—
392C2×C3×C8—31no—
393C2×C3×C8—62no—
394C2×C3×C8C22×D311yescharacteristic
395C2×C3×C8C22×D311yescharacteristic
396C2×C3×C8C22×D311yescharacteristic
397C2×C3×C8C22×D311yescharacteristic
398C3×C4⋊C4—31no—
399C3×C4⋊C4—31no—
400C3×C22⋊C4—31no—
401C3×C22⋊C4—31no—
402C3×C22⋊C4—61no—
403C3×C42—21no—
404C3×C42C22×D311yescharacteristic
405C3×C42C22×D311yescharacteristic
406#217—61no—
407#217—61no—
408#217—61no—
409#214—34no—
410#214—62no—
411#214—121no—
412#213—62no—
413#213—121no—
414(C2×D3)⋊C4—21no—
415(C2×D3)⋊C4—61no—
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—121no—
425(C2×D3)⋊C4—121no—
426(C2×D3)⋊C4D1211yescharacteristic
427(C2×D3)⋊C4D1211yescharacteristic
428C4⋊Dic3—31no—
429C4⋊Dic3—31no—
430C4⋊Dic3—61no—
431C4⋊Dic3—61no—
432C4⋊Dic3D1211yescharacteristic
433C4⋊Dic3C22×D311yescharacteristic
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—121no—
438C4×Dic3—61no—
439C4×Dic3—61no—
440C4×Dic3—121no—
441C2×C3⋊C8C22×D311yescharacteristic
442C2×C3⋊C8C22×D311yescharacteristic
443Dic12—62no—
444Dic12—62no—
445Dic12—122no—
446D24—22no—
447D24—22no—
448D24—62no—
449D24—121no—
450#204—34no—
451#204—62no—
452#204—62no—
453#204—62no—
454#204—122no—
455#204—121no—
456ΓL(1,𝔽25)—22no—
457D3×C8—22no—
458C22×C32C22×D411yescharacteristic
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3⋊D3—41no—
462C2×C3×D3—22no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
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×C4—21no—
480C32×C4C22×D411yescharacteristic
481C32×C4H(5,𝔽2)11yescharacteristic
482C3⋊Dic3—22no—
483C3⋊Dic3—41no—
484C3⋊Dic3—41no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—41no—
488C2×#41—91no—
489C2×#41—91no—
490C2×#41—91no—
491C22×D4—91no—
492AGL(1,ℤ/8)—184no—
493#135—184no—
494C2×Q16—91no—
495C2×SD16—91no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×SD16—91no—
499C2×D8—31no—
500C2×D8—31no—
501C2×D8—91no—
502C2×D8—91no—
503C2×M16—31no—
504C22×C8—31no—
505#127—31no—
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—31no—
520C4×D4—181no—
521C2×C22⋊C4—181no—
522#107—91no—
523C4⋊C8D3211yescharacteristic, complemented
524#103—91no—
525#103—91no—
526#102—31no—
527#102—31no—
528#102—91no—
529#102—91no—
530C22⋊C8—31no—
531C22⋊C8—31no—
532#97—31no—
533C23×C3—31no—
534C23×C3—31no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—61no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—21no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—121no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—122no—
547C22×D3—122no—
548C22×D3—241no—
549C22×D3—241no—
550C22×D3C2×D1211yescharacteristic
551C22×D3C2×D1211yescharacteristic
552C3×D4—32no—
553C3×D4—61no—
554C3×D4—61no—
555C3×D4—61no—
556C3×D4—61no—
557C3×D4—61no—
558C3×D4—121no—
559C3×D4—122no—
560C3×D4—241no—
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—241no—
572C2×C3×C4C2×D1211yescharacteristic
573C2×C3×C4C2×D1211yescharacteristic
574C2×C3×C4D3×D411yescharacteristic
575C2×C3×C4D3×D411yescharacteristic
576C2×C3×C4C23×D311yescharacteristic
577C2×C3×C4C23×D311yescharacteristic
578#67—122no—
579#67—122no—
580#67—122no—
581#67—122no—
582#67—122no—
583#67—122no—
584#67—122no—
585#67—241no—
586#67—241no—
587#67—241no—
588#67—241no—
589#67—241no—
590C2×Dic3—21no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—121no—
598C2×Dic3—121no—
599C2×Dic3—121no—
600C2×Dic3—122no—
601C2×Dic3—122no—
602C2×Dic3—122no—
603C2×Dic3C2×D1211yescharacteristic
604C2×Dic3C2×D1211yescharacteristic
605D12—21no—
606D12—21no—
607D12—21no—
608D12—21no—
609D12—21no—
610D12—41no—
611D12—42no—
612D12—61no—
613D12—61no—
614D12—61no—
615D12—61no—
616D12—81no—
617D12—121no—
618D12—121no—
619D12—122no—
620D12—241no—
621D12D3×D412yes—
622C4×D3—21no—
623C4×D3—21no—
624C4×D3—21no—
625C4×D3—21no—
626C4×D3—81no—
627C4×D3—122no—
628C4×D3—122no—
629C4×D3—122no—
630Dic6—32no—
631Dic6—32no—
632Dic6—62no—
633Dic6—61no—
634Dic6—61no—
635Dic6—61no—
636Dic6—61no—
637Dic6—61no—
638Dic6—61no—
639Dic6—121no—
640Dic6—121no—
641Dic6—121no—
642C3×C8—21no—
643C3×C8—21no—
644C3×C8—21no—
645C3×C8—21no—
646C3×C8—32no—
647C3×C8—41no—
648C3×C8—41no—
649C3×C8—61no—
650C3⋊C8—21no—
651C3⋊C8D3×D412yes—
652C2×C32D4211yescharacteristic
653C2×C32#57511yescharacteristic
654C2×C32#57611yescharacteristic
655C3⋊D3—81no—
656C3×D3—41no—
657C3×D3—42no—
658C3×D3—41no—
659C3×D3—81no—
660C3×D3—81no—
661C24—181no—
662#41—182no—
663#41—182no—
664#41—182no—
665#41—361no—
666#41—361no—
667#41—361no—
668C2×Q8—91no—
669C2×Q8—91no—
670C2×D4—31no—
671C2×D4—31no—
672C2×D4—31no—
673C2×D4—31no—
674C2×D4—61no—
675C2×D4—61no—
676C2×D4—91no—
677C2×D4—181no—
678C2×D4—182no—
679C2×D4—181no—
680C2×D4—181no—
681C2×D4—181no—
682C2×D4—181no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—361no—
686C22×C4—31no—
687C22×C4—31no—
688C22×C4—61no—
689C22×C4—181no—
690C22×C4—181no—
691C22×C4—181no—
692Q16—182no—
693SD16—94no—
694SD16—182no—
695SD16—182no—
696SD16—361no—
697D8—62no—
698D8—62no—
699D8—182no—
700D8—361no—
701M16—62no—
702C2×C8—31no—
703C2×C8—31no—
704C2×C8—62no—
705C2×C8C2×D3211yescharacteristic
706C2×C8C2×D3211yescharacteristic
707C4⋊C4—31no—
708C4⋊C4—31no—
709C4⋊C4—91no—
710C4⋊C4—181no—
711C4⋊C4—181no—
712C22⋊C4—31no—
713C22⋊C4—31no—
714C22⋊C4—61no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C22⋊C4—181no—
718C22⋊C4—181no—
719C22⋊C4—181no—
720C22⋊C4—181no—
721C42—181no—
722C42C2×D3211yescharacteristic
723C22×C3—21no—
724C22×C3—61no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—61no—
728C22×C3—62no—
729C22×C3—61no—
730C22×C3—61no—
731C22×C3—121no—
732C22×C3—121no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
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—41no—
751C2×D3—41no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—121no—
757C2×D3—121no—
758C2×D3—121no—
759C2×D3—121no—
760C2×D3—121no—
761C2×D3—121no—
762C2×D3—241no—
763C2×D3—241no—
764C2×D3—241no—
765C2×D3—244no—
766C2×D3—244no—
767C3×C4—21no—
768C3×C4—21no—
769C3×C4—21no—
770C3×C4—21no—
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—41no—
774C3×C4—41no—
775C3×C4—61no—
776C3×C4—61no—
777C3×C4—121no—
778C3×C4C2×D3×D411yescharacteristic
779C3×C4C2×D3×D411yescharacteristic
780C3×C4#100911yescharacteristic
781C3×C4#100911yescharacteristic
782Dic3—21no—
783Dic3—21no—
784Dic3—41no—
785Dic3—62no—
786Dic3—62no—
787Dic3—122no—
788Dic3—121no—
789Dic3—121no—
790Dic3—121no—
791Dic3—121no—
792Dic3—241no—
793Dic3—241no—
794C32#326811yescharacteristic, complemented, Sylow
795C23—31no—
796C23—31no—
797C23—61no—
798C23—61no—
799C23—61no—
800C23—181no—
801C23—362no—
802C23—362no—
803C23—721no—
804Q8—92no—
805Q8—181no—
806Q8—181no—
807Q8—181no—
808D4—32no—
809D4—61no—
810D4—61no—
811D4—61no—
812D4—61no—
813D4—61no—
814D4—121no—
815D4—122no—
816D4—181no—
817D4—181no—
818D4—241no—
819D4—362no—
820D4—362no—
821D4—362no—
822D4—362no—
823D4—721no—
824D4—721no—
825D4—721no—
826C2×C4—31no—
827C2×C4—31no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—181no—
834C2×C4—181no—
835C2×C4—181no—
836C2×C4—241no—
837C2×C4—362no—
838C2×C4—362no—
839C2×C4—362no—
840C2×C4D3×D1211yescharacteristic
841C2×C4D3×D1211yescharacteristic
842C2×C4C22×D3211yescharacteristic
843C8—21no—
844C8—21no—
845C8—32no—
846C8—61no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—122no—
851C2×C3—121no—
852C2×C3—121no—
853C2×C3—241no—
854C2×C3—241no—
855C2×C3D4×D1211yescharacteristic
856C2×C3#560911yescharacteristic
857C2×C3#574811yescharacteristic
858C2×C3#575211yescharacteristic
859C2×C3#575711yescharacteristic
860C2×C3#577311yescharacteristic
861D3—41no—
862D3—41no—
863D3—42no—
864D3—81no—
865D3—81no—
866D3—241no—
867D3—241no—
868D3—481no—
869C22—61no—
870C22—61no—
871C22—62no—
872C22—61no—
873C22—61no—
874C22—61no—
875C22—61no—
876C22—121no—
877C22—121no—
878C22—121no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—361no—
885C22—361no—
886C22—361no—
887C22—724no—
888C22C2×D3×D1211yescharacteristic
889C4—21no—
890C4—21no—
891C4—61no—
892C4—61no—
893C4—121no—
894C4—182no—
895C4—361no—
896C4—361no—
897C4D32×D411yescharacteristic
898C4#6432011yescharacteristic
899C3—21no—
900C3#7949711yescharacteristic, complemented
901C3#8034811yescharacteristic, complemented
902C2—121no—
903C2—121no—
904C2—122no—
905C2—241no—
906C2—241no—
907C2—721no—
908C2#1059462111yescharacteristic
909C2#1059467811yescharacteristic
910C2#1059471211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#63807C2semidirect
2. C2×#63795C2semidirect
3. #10594003C2semidirect
4. #10593906C2semidirect
5. #10592544C2semidirect
6. C3×#4843C2semidirect
7. C3×#4836C2semidirect
8. #10590969C2semidirect
9. #10590968C2semidirect
10. #10590962C2semidirect
11. #10590944C2semidirect
12. #10590828C2semidirect
13. #10590826C2semidirect
14. #10590371C2semidirect
15. #10590360C2semidirect
21. C2×#3795C22semidirect
22. C2×#3746C22semidirect
25. C4×#634C22semidirect
29. C2×C3×D3×C8C22semidirect
30. C3×#874C22semidirect
38. #63908C22semidirect
46. C2×#3716C22semidirect
47. C2×#3716C22semidirect
52. C32×C4⋊C8C22semidirect
54. #63643C22semidirect
55. C3×#821C22semidirect
56. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#803C22semidirect
60. #63575C22semidirect
61. #63567C22semidirect
82. #4843D3semidirect
83. #4836D3semidirect
153. #3716D4semidirect
209. C2×D3×C8C2×D3semidirect
223. #874C2×D3semidirect
230. C3×C4⋊C8C2×D3semidirect
231. C3×C4⋊C8C2×D3semidirect
242. #821C2×D3semidirect
243. #821C2×D3semidirect
245. (C2×D3)⋊C8C2×D3semidirect
253. #803C2×D3semidirect
523. C4⋊C8D32semidirect
794. C32#3268semidirect
900. C3#79497semidirect
901. C3#80348semidirect

Maximal subgroups

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

subgroupindex
C2×#638072
C2×#637952
#105940032
#105939062
#105925442
C3×#48432
C3×#48362
#105909692
#105909682
#105909622
#105909442
#105908282
#105908262
#105903712
#105903602
#803483
#794973