Finite Group Databasebeta

← #11884434

Subgroups — #11884434

Order 1152.

1153 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64125C211yesmaximal, characteristic, complemented
2C2×C3×#914C211yesmaximal, characteristic, complemented
3#10595410C211yesmaximal, characteristic, complemented
4#10595246C211yesmaximal, characteristic, complemented
5C3×#5164C211yesmaximal, characteristic, complemented
6#10591604C211yesmaximal, characteristic, complemented
7#10591599C211yesmaximal, characteristic, complemented
8#10591593C211yesmaximal, characteristic, complemented
9#10591481C211yesmaximal, characteristic, complemented
10#10591457C211yesmaximal, characteristic, complemented
11#10591448C211yesmaximal, characteristic, complemented
12#10590883C211yesmaximal, characteristic, complemented
13#10590844C211yesmaximal, characteristic, complemented
14#10590838C211yesmaximal, characteristic, complemented
15#10590736C211yesmaximal, characteristic, complemented
16#83955—31nomaximal
17#79796—31nomaximal
18C2×#3832C2211yescharacteristic, complemented
19C2×#3830C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic
21C2×C3×D3×D4C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic
23C2×#3756C2211yescharacteristic, complemented
24C2×#3753C2211yescharacteristic
25#64125—24no—
26C2×#3744C2211yescharacteristic, complemented
27C2×C8×C3⋊D3C2211yescharacteristic, complemented
28C3×Q8×Dic3C2211yescharacteristic, complemented
29C2×C3×#215C2211yescharacteristic
30C3×D4×Dic3C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×#914—24no—
33C2×C3×D24C2211yescharacteristic
34C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
35#63978—21no—
36#63977—21no—
37#63962—21no—
38C2×(C2×D3)⋊Dic3—21no—
39#63916—21no—
40#63916C2211yescharacteristic
41#63916C2211yescharacteristic, complemented
42#63911—21no—
43#63911C2211yescharacteristic, complemented
44#63909—21no—
45#63909C2211yescharacteristic
46C4×#626—21no—
47C4×#626C2211yescharacteristic
48#63860C2211yescharacteristic
49#63857C2211yescharacteristic
50C2×#3716C2211yescharacteristic, complemented
51C2×#3714C2211yescharacteristic
52C3×#835C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic
54C3×#818C2211yescharacteristic, complemented
55C3×#815C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63564C2211yescharacteristic, complemented
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic, complemented
61#63557C2211yescharacteristic, complemented
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
63C2×C3×AGL(1,ℤ/8)—31no—
64#5834—31no—
65#5806—31no—
66C2×#916—31no—
67C2×#916—31no—
68C2×#916—61no—
69C2×#914D311yescharacteristic, complemented
70#5577—31no—
71#5554—31no—
72C3×#440—31no—
73#5239—31no—
74#5217—31no—
75#5172—31no—
76#5166—31no—
77#5164D311yescharacteristic, complemented
78#5158—31no—
79#5157—31no—
80#5154—31no—
81#5150—31no—
82#5134—31no—
83#5127—31no—
84#5028—31no—
85#5015—31no—
86#4886—31no—
87#4883—31no—
88#4810—31no—
89#4808—31no—
90#4781—31no—
91#4773—31no—
92#4712—31no—
93#4706—31no—
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98C22×C3⋊Dic3—21no—
99#3832—22no—
100#3832—41no—
101#3830—22no—
102#3830—41no—
103C2×C4⋊(C3⋊D3)—21no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3—21no—
106C2×C4×C3⋊D3C2311yescharacteristic
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C22×C3×Dic3—21no—
110C3×#239—22no—
111C3×#239—41no—
112C3×D3×D4—22no—
113C3×D3×D4—41no—
114C2×C3×D12—21no—
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3C2311yescharacteristic
119C2×#626—21no—
120C2×#626—21no—
121C2×#626—21no—
122C2×#626—21no—
123C2×#626—21no—
124C2×#626D411yescharacteristic
125C32×SD16D414yescomplemented
126C2×C32×C8C2311yescharacteristic
127#3756—22no—
128#3753—22no—
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130#3744—22no—
131C8×C3⋊D3—22no—
132C3×#217—21no—
133C3×#215—22no—
134C3×#213—22no—
135C3×C4⋊Dic3—21no—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4×Dic3—21no—
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×D24—22no—
143C3×ΓL(1,𝔽25)—22no—
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3D411yescharacteristic
146#3722—21no—
147#3722D411yescharacteristic
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3—21no—
153(C2×D3)⋊Dic3D411yescharacteristic
154#3716—41no—
155#3714—41no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C22×C3×D4—31no—
159C2×#239—31no—
160C2×#239—31no—
161C2×#239—61no—
162C2×#239C2×D311yescharacteristic
163C2×#237—31no—
164C2×#237—31no—
165C2×#237—61no—
166C2×D3×D4C2×D311yescharacteristic
167C3×AGL(1,ℤ/8)—64no—
168C2×C3×SD16—21no—
169C2×C3×SD16—31no—
170C2×C3×SD16C2×D311yescharacteristic
171C2×C3×SD16C2×D311yescharacteristic
172C2×C3×D8—31no—
173C2×C3×D8—31no—
174C2×C3×M16—31no—
175C3×C4×Q8—31no—
176C3×C4×D4—31no—
177#953—61no—
178C2×#217—61no—
179Q8×Dic3C2×D311yescharacteristic, complemented
180C2×#216—31no—
181C2×#216—31no—
182C2×#216—61no—
183C2×#215C2×D311yescharacteristic
184#940—31no—
185#940—61no—
186#939—61no—
187#938—31no—
188#938—31no—
189#938—61no—
190#936—31no—
191#935—61no—
192D4×Dic3C2×D311yescharacteristic
193C2×#214—31no—
194C2×#213—31no—
195C2×#213—31no—
196C2×#213—31no—
197C2×#213—61no—
198C2×#213C2×D311yescharacteristic
199#930—31no—
200#930—61no—
201#930—61no—
202C4×#67—31no—
203C4×#67—61no—
204C2×(C2×D3)⋊C4—61no—
205#924—31no—
206#916—68no—
207#916—64no—
208#916—64no—
209#914—24no—
210C2×D24—31no—
211C2×D24C2×D311yescharacteristic
212C2×#204—31no—
213C2×#204—31no—
214C2×#204—31no—
215C2×#204—61no—
216C2×ΓL(1,𝔽25)C2×D311yescharacteristic
217C2×D3×C8—31no—
218C2×D3×C8—31no—
219C2×D3×C8—61no—
220#897—31no—
221#895—31no—
222#895—31no—
223#895—31no—
224#895—61no—
225#895—61no—
226#886—61no—
227#882—61no—
228#875—31no—
229#874—31no—
230#874—61no—
231C4×D12—31no—
232C4×D12—61no—
233C3×#107—31no—
234C3×#103—31no—
235C3×#102—31no—
236C3×#97—31no—
237#835C2×D311yescharacteristic, complemented
238#832—31no—
239#832—31no—
240#832C2×D311yescharacteristic
241#830—31no—
242#821—31no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8—31no—
245(C2×D3)⋊C8—31no—
246#818C2×D311yescharacteristic, complemented
247#816—31no—
248#815C2×D311yescharacteristic, complemented
249Dic3⋊C8—31no—
250#810—31no—
251#809—31no—
252#809—31no—
253#809—31no—
254C4⋊(C3⋊C8)—31no—
255C23×C32—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3C2×D411yescharacteristic
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—81no—
263C22×C3×D3C2×D411yescharacteristic
264C32×Q8—21no—
265C32×Q8C2×D412yes—
266C32×D4—21no—
267C32×D4C2×D412yes—
268C2×C32×C4—21no—
269C2×C32×C4C2411yescharacteristic
270#638—42no—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—42no—
273C2×C3⋊Dic3C2×D411yescharacteristic
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—42no—
277C4×C3⋊D3—21no—
278C4×C3⋊D3—21no—
279C4×C3⋊D3—42no—
280#634—21no—
281#634—21no—
282C3×#67—42no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—81no—
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C2×C3×Dic3C2×D411yescharacteristic
289C3×D12—21no—
290C3×D12—21no—
291C3×D12—21no—
292C3×D12—21no—
293C3×D12—42no—
294C3×C4×D3—21no—
295C3×C4×D3—21no—
296C3×C4×D3—42no—
297#626—41no—
298#626—42no—
299#626—81no—
300#626—81no—
301#626—81no—
302#626—81no—
303C32×C8C2×D412yes—
304C3⋊(C3⋊C8)—21no—
305C3×C3⋊C8—21no—
306C3×C3⋊C8—21no—
307C2×AGL(1,ℤ/8)—31no—
308C2×#135—91no—
309#550—91no—
310#546—91no—
311#496—91no—
312#468—91no—
313#466—91no—
314#464—91no—
315#459—91no—
316#452—91no—
317#449—91no—
318#449—91no—
319#447—91no—
320#440—31no—
321#435—91no—
322C24×C3—61no—
323C23×D3—21no—
324C3×#41—62no—
325C3×#41—121no—
326C2×C3×Q8—21no—
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×D4—21no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C2×C3×D4—62no—
335C2×C3×D4—121no—
336C2×C3×D4C22×D311yescharacteristic
337C2×C3×D4C22×D311yescharacteristic
338C22×C3×C4—31no—
339C22×C3×C4—61no—
340C22×C3×C4—61no—
341C2×#67—21no—
342C2×#67—31no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—121no—
351C22×Dic3—21no—
352C22×Dic3—61no—
353C22×Dic3—61no—
354C22×Dic3—121no—
355#239—22no—
356#239—41no—
357#239—64no—
358#239—62no—
359#239—62no—
360#239—121no—
361#239—121no—
362#239—122no—
363#237—64no—
364#237—62no—
365#237—62no—
366#237—121no—
367#237—121no—
368#237—122no—
369D3×D4—22no—
370D3×D4—41no—
371C2×D12—21no—
372C2×D12—31no—
373C2×D12—31no—
374C2×D12—31no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12—61no—
379C2×D12—61no—
380C2×D12—61no—
381C2×D12—61no—
382C2×D12—61no—
383C2×D12—121no—
384C2×D12C22×D311yescharacteristic
385C2×D12C22×D311yescharacteristic
386C2×C4×D3—21no—
387C2×C4×D3—31no—
388C2×C4×D3—31no—
389C2×C4×D3—61no—
390C2×C4×D3—61no—
391C2×C4×D3—61no—
392C2×C4×D3—121no—
393C2×C4×D3C22×D311yescharacteristic
394C2×Dic6—31no—
395C2×Dic6—31no—
396C2×Dic6—61no—
397C3×SD16—24no—
398C3×SD16—62no—
399C3×SD16D1214yescomplemented
400C3×SD16#6714yescomplemented
401C3×D8—62no—
402C3×D8—62no—
403C3×M16—62no—
404C2×C3×C8—21no—
405C2×C3×C8—31no—
406C2×C3×C8—31no—
407C2×C3×C8C22×D311yescharacteristic
408C2×C3×C8C22×D311yescharacteristic
409C3×C4⋊C4—31no—
410C3×C4⋊C4—31no—
411C3×C4⋊C4—61no—
412C3×C22⋊C4—61no—
413C3×C42—31no—
414C3×C42—61no—
415#217—21no—
416#217—31no—
417#217—61no—
418#217—61no—
419#217—61no—
420#217—61no—
421#217—61no—
422#216—64no—
423#216—62no—
424#216—62no—
425#215—22no—
426#214—121no—
427#213—22no—
428#213—64no—
429#213—62no—
430#213—62no—
431#213—121no—
432(C2×D3)⋊C4—31no—
433(C2×D3)⋊C4—31no—
434(C2×D3)⋊C4—31no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—61no—
439(C2×D3)⋊C4—61no—
440(C2×D3)⋊C4—61no—
441(C2×D3)⋊C4—61no—
442C4⋊Dic3—21no—
443C4⋊Dic3—31no—
444C4⋊Dic3—61no—
445C4⋊Dic3C22×D311yescharacteristic
446C4⋊Dic3C22×D311yescharacteristic
447Dic3⋊C4—31no—
448Dic3⋊C4—61no—
449C4×Dic3—21no—
450C4×Dic3C22×D311yescharacteristic
451C2×C3⋊C8—31no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—61no—
454C2×C3⋊C8C22×D311yescharacteristic
455C2×C3⋊C8C22×D311yescharacteristic
456D24—22no—
457D24—121no—
458#204—64no—
459#204—62no—
460#204—62no—
461#204—121no—
462ΓL(1,𝔽25)—22no—
463D3×C8—64no—
464D3×C8—62no—
465D3×C8—62no—
466C22×C32—22no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32C22×D411yescharacteristic
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—21no—
477C2×C3×D3—21no—
478C2×C3×D3—21no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3—41no—
485C2×C3×D3—84no—
486C32×C4—22no—
487C32×C4C22×D411yescharacteristic
488C32×C4H(5,𝔽2)11yescharacteristic
489C3⋊Dic3—21no—
490C3⋊Dic3—41no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—41no—
495C3×Dic3—41no—
496C2×#41—31no—
497C2×#41—91no—
498C2×#41—91no—
499C22×D4—31no—
500AGL(1,ℤ/8)—64no—
501#135—184no—
502C2×Q16—91no—
503C2×SD16—31no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16D3211yescharacteristic
507C2×D8—31no—
508C2×D8—31no—
509C2×D8—91no—
510C2×D8—91no—
511C2×M16—31no—
512C22×C8—91no—
513#127—91no—
514#127—181no—
515#124—91no—
516#123—181no—
517C22⋊Q8—91no—
518#121—91no—
519#121—91no—
520#121—91no—
521#121—181no—
522#121—181no—
523#121—181no—
524#120—181no—
525C4×Q8—31no—
526C4×D4—31no—
527C4×D4—91no—
528C4×D4—181no—
529C2×C22⋊C4—181no—
530#107—31no—
531C4⋊C8—91no—
532#103—31no—
533#103—91no—
534#102—31no—
535#102—91no—
536#102—91no—
537#102—91no—
538C22⋊C8—91no—
539C22⋊C8—91no—
540#97—31no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—31no—
544C23×C3—41no—
545C23×C3—61no—
546C23×C3—61no—
547C23×C3—122no—
548C23×C3—122no—
549C23×C3—241no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—31no—
553C22×D3—31no—
554C22×D3—42no—
555C22×D3—42no—
556C22×D3—61no—
557C22×D3—61no—
558C22×D3—61no—
559C22×D3—81no—
560C22×D3—121no—
561C22×D3D3×D411yescharacteristic
562C3×Q8—21no—
563C3×Q8—21no—
564C3×Q8—22no—
565C3×Q8—41no—
566C3×Q8C2×D1212yes—
567C3×Q8C2×#6712yes—
568C3×D4—21no—
569C3×D4—21no—
570C3×D4—22no—
571C3×D4—41no—
572C3×D4—61no—
573C3×D4—61no—
574C3×D4—61no—
575C3×D4—61no—
576C3×D4—122no—
577C3×D4—122no—
578C3×D4C2×D1212yes—
579C3×D4C2×#6712yes—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—31no—
584C2×C3×C4—31no—
585C2×C3×C4—31no—
586C2×C3×C4—41no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—122no—
592C2×C3×C4—241no—
593C2×C3×C4C23×D311yescharacteristic
594C2×C3×C4C23×D311yescharacteristic
595#67—42no—
596#67—121no—
597#67—122no—
598#67—122no—
599#67—122no—
600#67—124no—
601#67—241no—
602#67—241no—
603#67—241no—
604#67—241no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—31no—
608C2×Dic3—31no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—81no—
613C2×Dic3—121no—
614C2×Dic3—122no—
615C2×Dic3—122no—
616C2×Dic3—124no—
617C2×Dic3D3×D411yescharacteristic
618C2×Dic3D3×D411yescharacteristic
619C2×Dic3D3×D411yescharacteristic
620D12—21no—
621D12—21no—
622D12—21no—
623D12—21no—
624D12—42no—
625D12—62no—
626D12—61no—
627D12—61no—
628D12—61no—
629D12—61no—
630D12—121no—
631D12—122no—
632D12—122no—
633D12—124no—
634D12—121no—
635D12—122no—
636D12—241no—
637D12—241no—
638D12—241no—
639D12—241no—
640C4×D3—21no—
641C4×D3—21no—
642C4×D3—42no—
643C4×D3—62no—
644C4×D3—62no—
645C4×D3—61no—
646C4×D3—61no—
647C4×D3—61no—
648C4×D3—61no—
649C4×D3—122no—
650C4×D3—122no—
651C4×D3—124no—
652Dic6—62no—
653Dic6—61no—
654Dic6—61no—
655Dic6—61no—
656Dic6—61no—
657Dic6—121no—
658C3×C8—22no—
659C3×C8—61no—
660C3×C8—61no—
661C3×C8C2×D1212yes—
662C3×C8C2×#6712yes—
663C3⋊C8—21no—
664C3⋊C8—21no—
665C3⋊C8—62no—
666C3⋊C8—61no—
667C3⋊C8—61no—
668C2×C32—42no—
669C2×C32D4211yescharacteristic
670C2×C32#57511yescharacteristic
671C2×C32#57611yescharacteristic
672C3⋊D3—41no—
673C3⋊D3—81no—
674C3×D3—41no—
675C3×D3—81no—
676C3×D3—81no—
677C24—61no—
678#41—62no—
679#41—121no—
680#41—182no—
681#41—182no—
682#41—361no—
683#41—361no—
684C2×Q8—91no—
685C2×Q8C2×D3211yescharacteristic
686C2×D4—31no—
687C2×D4—31no—
688C2×D4—61no—
689C2×D4—61no—
690C2×D4—62no—
691C2×D4—91no—
692C2×D4—91no—
693C2×D4—121no—
694C2×D4—181no—
695C2×D4—181no—
696C2×D4—181no—
697C2×D4—181no—
698C2×D4—181no—
699C2×D4—181no—
700C2×D4—181no—
701C2×D4C2×D3211yescharacteristic
702C22×C4—31no—
703C22×C4—61no—
704C22×C4—61no—
705C22×C4—91no—
706C22×C4—181no—
707C22×C4—181no—
708Q16—182no—
709SD16—62no—
710SD16—182no—
711SD16—361no—
712SD16#62614yescomplemented
713D8—62no—
714D8—62no—
715D8—182no—
716D8—361no—
717M16—62no—
718C2×C8—31no—
719C2×C8—31no—
720C2×C8—91no—
721C2×C8—182no—
722C2×C8C2×D3211yescharacteristic
723C4⋊C4—31no—
724C4⋊C4—31no—
725C4⋊C4—61no—
726C4⋊C4—91no—
727C4⋊C4—181no—
728C22⋊C4—61no—
729C22⋊C4—91no—
730C22⋊C4—91no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C22⋊C4—181no—
734C22⋊C4—181no—
735C22⋊C4—181no—
736C22⋊C4—181no—
737C42—31no—
738C42—61no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—21no—
742C22×C3—42no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—61no—
748C22×C3—61no—
749C22×C3—61no—
750C22×C3—81no—
751C22×C3—81no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3—244no—
759C22×C3C2×D3×D411yescharacteristic
760C22×C3C2×D3×D411yescharacteristic
761C2×D3—21no—
762C2×D3—21no—
763C2×D3—21no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—62no—
771C2×D3—61no—
772C2×D3—61no—
773C2×D3—61no—
774C2×D3—61no—
775C2×D3—61no—
776C2×D3—61no—
777C2×D3—84no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—122no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—241no—
788C2×D3—241no—
789C3×C4—22no—
790C3×C4—22no—
791C3×C4—21no—
792C3×C4—21no—
793C3×C4—42no—
794C3×C4—61no—
795C3×C4—61no—
796C3×C4—61no—
797C3×C4—121no—
798C3×C4—121no—
799C3×C4C22×D1211yescharacteristic
800C3×C4#100411yescharacteristic
801C3×C4#100911yescharacteristic
802C3×C4C22×#6711yescharacteristic
803Dic3—21no—
804Dic3—21no—
805Dic3—21no—
806Dic3—41no—
807Dic3—41no—
808Dic3—62no—
809Dic3—61no—
810Dic3—61no—
811Dic3—122no—
812Dic3—121no—
813Dic3—121no—
814C32#326811yescharacteristic, complemented, Sylow
815C23—21no—
816C23—31no—
817C23—61no—
818C23—61no—
819C23—91no—
820C23—122no—
821C23—122no—
822C23—181no—
823C23—241no—
824Q8—21no—
825Q8—181no—
826Q8—181no—
827Q8C2×#62612yes—
828D4—21no—
829D4—61no—
830D4—61no—
831D4—61no—
832D4—61no—
833D4—122no—
834D4—122no—
835D4—181no—
836D4—181no—
837D4—362no—
838D4—361no—
839D4—362no—
840D4—362no—
841D4—721no—
842D4—721no—
843D4—721no—
844D4—721no—
845D4C2×#62612yes—
846C2×C4—21no—
847C2×C4—31no—
848C2×C4—31no—
849C2×C4—31no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—91no—
855C2×C4—122no—
856C2×C4—181no—
857C2×C4—181no—
858C2×C4—181no—
859C2×C4—241no—
860C2×C4—362no—
861C2×C4—362no—
862C2×C4C22×D3211yescharacteristic
863C8—61no—
864C8—61no—
865C8—181no—
866C8C2×#62612yes—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—21no—
870C2×C3—42no—
871C2×C3—42no—
872C2×C3—82no—
873C2×C3—121no—
874C2×C3—241no—
875C2×C3—241no—
876C2×C3D4×D1211yescharacteristic
877C2×C3#577311yescharacteristic
878C2×C3#577411yescharacteristic
879C2×C3#577411yescharacteristic
880C2×C3#577711yescharacteristic
881C2×C3D4×#6711yescharacteristic
882D3—41no—
883D3—81no—
884D3—81no—
885D3—122no—
886D3—121no—
887D3—121no—
888D3—242no—
889D3—241no—
890D3—241no—
891C22—22no—
892C22—41no—
893C22—41no—
894C22—61no—
895C22—61no—
896C22—61no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—181no—
904C22—181no—
905C22—181no—
906C22—244no—
907C22—361no—
908C22—361no—
909C22—361no—
910C22D32×D411yescharacteristic
911C4—22no—
912C4—61no—
913C4—61no—
914C4—61no—
915C4—121no—
916C4—121no—
917C4—181no—
918C4—361no—
919C4#6431411yescharacteristic
920C4C22×#62611yescharacteristic
921C3—21no—
922C3#7979611yescharacteristic, complemented
923C3#8395511yescharacteristic, complemented
924C2—42no—
925C2—121no—
926C2—241no—
927C2—241no—
928C2—361no—
929C2—721no—
930C2#1059474411yescharacteristic
931C2#1059475011yescharacteristic
932C2D4×#62611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#64125C2semidirect
2. C2×C3×#914C2semidirect
3. #10595410C2semidirect
4. #10595246C2semidirect
5. C3×#5164C2semidirect
6. #10591604C2semidirect
7. #10591599C2semidirect
8. #10591593C2semidirect
9. #10591481C2semidirect
10. #10591457C2semidirect
11. #10591448C2semidirect
12. #10590883C2semidirect
13. #10590844C2semidirect
14. #10590838C2semidirect
15. #10590736C2semidirect
18. C2×#3832C22semidirect
23. C2×#3756C22semidirect
26. C2×#3744C22semidirect
27. C2×C8×C3⋊D3C22semidirect
28. C3×Q8×Dic3C22semidirect
41. #63916C22semidirect
43. #63911C22semidirect
50. C2×#3716C22semidirect
52. C3×#835C22semidirect
54. C3×#818C22semidirect
55. C3×#815C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63564C22semidirect
60. #63562C22semidirect
61. #63557C22semidirect
69. C2×#914D3semidirect
77. #5164D3semidirect
125. C32×SD16D4semidirect
179. Q8×Dic3C2×D3semidirect
237. #835C2×D3semidirect
246. #818C2×D3semidirect
248. #815C2×D3semidirect
399. C3×SD16D12semidirect
400. C3×SD16#67semidirect
712. SD16#626semidirect
814. C32#3268semidirect
922. C3#79796semidirect
923. C3#83955semidirect

Maximal subgroups

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

subgroupindex
C2×#641252
C2×C3×#9142
#105954102
#105952462
C3×#51642
#105916042
#105915992
#105915932
#105914812
#105914572
#105914482
#105908832
#105908442
#105908382
#105907362
#839553
#797963