Finite Group Databasebeta

← #11884433

Subgroups — #11884433

Order 1152.

1169 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64123C211yesmaximal, characteristic, complemented
2C2×C3×#916C211yesmaximal, characteristic, complemented
3#10595410C211yesmaximal, characteristic, complemented
4#10595254C211yesmaximal, characteristic, complemented
5C3×#5164C211yesmaximal, characteristic, complemented
6#10591607C211yesmaximal, characteristic, complemented
7#10591602C211yesmaximal, characteristic, complemented
8#10591588C211yesmaximal, characteristic, complemented
9#10591481C211yesmaximal, characteristic, complemented
10#10591456C211yesmaximal, characteristic, complemented
11#10591452C211yesmaximal, characteristic, complemented
12#10590881C211yesmaximal, characteristic, complemented
13#10590845C211yesmaximal, characteristic, complemented
14#10590832C211yesmaximal, characteristic, complemented
15#10590726C211yesmaximal, characteristic, complemented
16#83922—31nomaximal
17#79796—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×D4×C3⋊D3C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic, complemented
21C2×C3×#237C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic
23C2×#3755C2211yescharacteristic
24C2×#3753C2211yescharacteristic
25#64123—24no—
26C2×#3745C2211yescharacteristic
27C2×#3743C2211yescharacteristic
28C3×Q8×Dic3C2211yescharacteristic, complemented
29C2×C3×#216C2211yescharacteristic, complemented
30C3×D4×Dic3C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×#916—24no—
33C2×C3×#204C2211yescharacteristic, complemented
34C2×C3×D3×C8C2211yescharacteristic, complemented
35#63981—21no—
36#63978—21no—
37#63966—21no—
38C2×#3722—21no—
39#63916—21no—
40#63916C2211yescharacteristic
41#63911—21no—
42#63911C2211yescharacteristic, complemented
43#63909—21no—
44#63909C2211yescharacteristic
45#63909C2211yescharacteristic, complemented
46C4×#626—21no—
47C4×#626C2211yescharacteristic
48#63871C2211yescharacteristic
49#63864C2211yescharacteristic
50C2×#3717C2211yescharacteristic, complemented
51C2×#3714C2211yescharacteristic
52C3×#835C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic
54C3×#818C2211yescharacteristic, complemented
55C3×#815C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61#63557C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×C3×#135—31no—
64#5834—31no—
65#5829—31no—
66C2×#916D311yescharacteristic, complemented
67C2×#914—31no—
68C2×#914—31no—
69C2×#914—61no—
70#5577—31no—
71#5554—31no—
72C3×#440—31no—
73#5238—31no—
74#5238—31no—
75#5187—31no—
76#5185—31no—
77#5176—31no—
78#5174—31no—
79#5164D311yescharacteristic, complemented
80#5156—31no—
81#5150—31no—
82#5115—31no—
83#5111—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—
98#3832—22no—
99#3832—41no—
100D4×C3⋊D3—22no—
101D4×C3⋊D3—41no—
102C2×C4⋊(C3⋊D3)—21no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3—21no—
106C2×C4×C3⋊D3C2311yescharacteristic
107C2×C3×#67—21no—
108C22×C3×Dic3—21no—
109C22×C3×Dic3—21no—
110C3×#239—22no—
111C3×#239—41no—
112C3×#237—22no—
113C3×#237—41no—
114C2×C3×D12—21no—
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119C2×#626—21no—
120C2×#626—21no—
121C2×#626—21no—
122C2×#626—21no—
123C2×#626—21no—
124C2×#626D411yescharacteristic
125C32×SD16D414yescomplemented
126C2×C32×C8C2311yescharacteristic
127#3755—22no—
128#3753—22no—
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130#3745—22no—
131#3743—22no—
132C3×#217—21no—
133C3×#216—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×#204—22no—
143C3×D3×C8—22no—
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3D411yescharacteristic
146#3722—21no—
147#3722—21no—
148#3722—21no—
149#3722—21no—
150#3722—21no—
151#3722D411yescharacteristic
152(C2×D3)⋊Dic3—21no—
153(C2×D3)⋊Dic3D411yescharacteristic
154#3717—41no—
155#3714—41no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×#239—31no—
160C2×#239—31no—
161C2×#239—61no—
162C2×#239C2×D311yescharacteristic, complemented
163C2×#237C2×D311yescharacteristic
164C2×D3×D4—31no—
165C2×D3×D4—31no—
166C2×D3×D4—61no—
167C3×#135—64no—
168C2×C3×Q16—31no—
169C2×C3×SD16—21no—
170C2×C3×SD16—31no—
171C2×C3×SD16C2×D311yescharacteristic
172C2×C3×SD16C2×D311yescharacteristic
173C2×C3×D8—31no—
174C22×C3×C8—31no—
175C3×C4×Q8—31no—
176C3×C4×D4—31no—
177#947—31no—
178#946—31no—
179Q8×Dic3C2×D311yescharacteristic, complemented
180C2×#216C2×D311yescharacteristic, complemented
181C2×#215—31no—
182C2×#215—31no—
183C2×#215—31no—
184C2×#215—61no—
185#940—31no—
186#940—61no—
187#939—61no—
188#938—31no—
189#938—61no—
190#937—61no—
191D4×Dic3C2×D311yescharacteristic
192C2×#213—31no—
193C2×#213—31no—
194C2×#213—31no—
195C2×#213—61no—
196C2×#213C2×D311yescharacteristic
197#930—31no—
198#930—31no—
199#930—61no—
200#930—61no—
201#929—61no—
202C4×#67—31no—
203C4×#67—61no—
204C2×(C2×D3)⋊C4—61no—
205C2×(C2×D3)⋊C4—61no—
206#916—24no—
207#914—68no—
208#914—64no—
209#914—64no—
210C2×D24—31no—
211C2×D24—31no—
212C2×D24—31no—
213C2×D24—61no—
214C2×#204—31no—
215C2×#204C2×D311yescharacteristic, complemented
216C2×ΓL(1,𝔽25)—31no—
217C2×ΓL(1,𝔽25)—31no—
218C2×ΓL(1,𝔽25)—61no—
219C2×D3×C8C2×D311yescharacteristic, complemented
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#835—31no—
238#835C2×D311yescharacteristic, complemented
239#832—31no—
240#832C2×D311yescharacteristic
241#830—31no—
242#821—31no—
243#821—31no—
244(C2×D3)⋊C8—31no—
245(C2×D3)⋊C8—31no—
246(C2×D3)⋊C8—31no—
247#818C2×D311yescharacteristic, complemented
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⋊D3—21no—
258C22×C3⋊D3—42no—
259C22×C3⋊D3—42no—
260C22×C3⋊D3—81no—
261C22×C3⋊D3C2×D411yescharacteristic
262C22×C3×D3—21no—
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⋊Dic3C2×D411yescharacteristic
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—42no—
277C4×C3⋊D3—21no—
278C4×C3⋊D3—21no—
279C4×C3⋊D3—42no—
280C3×#67—42no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—42no—
285C2×C3×Dic3—81no—
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C2×C3×Dic3C2×D411yescharacteristic
289C3×D12—21no—
290C3×D12—21no—
291C3×D12—42no—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×C4×D3—42no—
295C3×Dic6—21no—
296C3×Dic6—21no—
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)—91no—
308C2×#135—31no—
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—
322C23×D3—61no—
323C23×D3—61no—
324C23×D3—121no—
325C3×#41—62no—
326C3×#41—62no—
327C3×#41—121no—
328C3×#41—121no—
329C2×C3×Q8—21no—
330C2×C3×Q8—31no—
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×Q8C22×D311yescharacteristic
333C2×C3×D4—21no—
334C2×C3×D4—31no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C2×C3×D4C22×D311yescharacteristic
338C2×C3×D4C22×D311yescharacteristic
339C22×C3×C4—31no—
340C22×C3×C4—61no—
341C22×C3×C4—61no—
342C22×C3×C4—61no—
343C2×#67—21no—
344C2×#67—31no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—121no—
353C22×Dic3—21no—
354C22×Dic3—21no—
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—22no—
364#237—41no—
365D3×D4—64no—
366D3×D4—62no—
367D3×D4—62no—
368D3×D4—121no—
369D3×D4—121no—
370D3×D4—122no—
371C2×D12—21no—
372C2×D12—31no—
373C2×D12—31no—
374C2×D12—31no—
375C2×D12—31no—
376C2×D12—31no—
377C2×D12—61no—
378C2×D12—61no—
379C2×D12—61no—
380C2×D12—61no—
381C2×D12—61no—
382C2×D12—61no—
383C2×D12—61no—
384C2×D12—61no—
385C2×D12—61no—
386C2×D12—121no—
387C2×D12C22×D311yescharacteristic
388C2×C4×D3—21no—
389C2×C4×D3—31no—
390C2×C4×D3—31no—
391C2×C4×D3—61no—
392C2×C4×D3—61no—
393C2×C4×D3—61no—
394C2×C4×D3—121no—
395C2×C4×D3C22×D311yescharacteristic
396C2×Dic6C22×D311yescharacteristic
397C3×Q16—62no—
398C3×SD16—24no—
399C3×SD16—62no—
400C3×SD16D1214yescomplemented
401C3×SD16#6714yescomplemented
402C3×D8—62no—
403C2×C3×C8—21no—
404C2×C3×C8—31no—
405C2×C3×C8—31no—
406C2×C3×C8—62no—
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#216—22no—
419#215—64no—
420#215—62no—
421#215—62no—
422#215—121no—
423#213—22no—
424#213—64no—
425#213—62no—
426#213—62no—
427#213—121no—
428(C2×D3)⋊C4—31no—
429(C2×D3)⋊C4—31no—
430(C2×D3)⋊C4—31no—
431(C2×D3)⋊C4—61no—
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—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—64no—
457D24—62no—
458D24—62no—
459D24—121no—
460#204—22no—
461#204—121no—
462ΓL(1,𝔽25)—64no—
463ΓL(1,𝔽25)—62no—
464ΓL(1,𝔽25)—62no—
465D3×C8—22no—
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—41no—
477C2×C3⋊D3—41no—
478C2×C3⋊D3—41no—
479C2×C3⋊D3—84no—
480C2×C3×D3—21no—
481C2×C3×D3—21no—
482C2×C3×D3—21no—
483C2×C3×D3—41no—
484C2×C3×D3—41no—
485C2×C3×D3—41no—
486C32×C4—22no—
487C32×C4C22×D411yescharacteristic
488C32×C4H(5,𝔽2)11yescharacteristic
489C3⋊Dic3—21no—
490C3×Dic3—21no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—41no—
494C3×Dic3—41no—
495C3×Dic3—41no—
496C2×#41—31no—
497C2×#41—31no—
498C2×#41—91no—
499C22×D4—91no—
500AGL(1,ℤ/8)—184no—
501#135—64no—
502C2×Q16—31no—
503C2×SD16—31no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16D3211yescharacteristic
507C2×D8—31no—
508C2×D8—91no—
509C2×D8—91no—
510C2×D8—91no—
511C2×M16—91no—
512C22×C8—31no—
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—
546C22×D3—21no—
547C22×D3—31no—
548C22×D3—31no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—61no—
554C22×D3—121no—
555C22×D3—121no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—124no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—242no—
562C22×D3—241no—
563C22×D3—241no—
564C22×D3—242no—
565C22×D3D3×D411yescharacteristic
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—22no—
569C3×Q8—41no—
570C3×Q8—61no—
571C3×Q8—61no—
572C3×Q8C2×D1212yes—
573C3×Q8C2×#6712yes—
574C3×D4—21no—
575C3×D4—21no—
576C3×D4—22no—
577C3×D4—41no—
578C3×D4—61no—
579C3×D4—61no—
580C3×D4—122no—
581C3×D4—122no—
582C3×D4C2×D1212yes—
583C3×D4C2×#6712yes—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—31no—
588C2×C3×C4—31no—
589C2×C3×C4—31no—
590C2×C3×C4—41no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—122no—
597C2×C3×C4—122no—
598C2×C3×C4—241no—
599C2×C3×C4C23×D311yescharacteristic
600C2×C3×C4C23×D311yescharacteristic
601#67—42no—
602#67—121no—
603#67—122no—
604#67—122no—
605#67—122no—
606#67—124no—
607#67—241no—
608#67—241no—
609#67—241no—
610#67—241no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—31no—
615C2×Dic3—31no—
616C2×Dic3—42no—
617C2×Dic3—61no—
618C2×Dic3—81no—
619C2×Dic3D3×D411yescharacteristic
620C2×Dic3D3×D411yescharacteristic
621C2×Dic3D3×D411yescharacteristic
622D12—21no—
623D12—21no—
624D12—42no—
625D12—62no—
626D12—62no—
627D12—61no—
628D12—61no—
629D12—61no—
630D12—61no—
631D12—61no—
632D12—61no—
633D12—61no—
634D12—61no—
635D12—121no—
636D12—121no—
637D12—122no—
638D12—122no—
639D12—124no—
640D12—121no—
641D12—122no—
642D12—241no—
643D12—241no—
644D12—241no—
645D12—241no—
646C4×D3—21no—
647C4×D3—21no—
648C4×D3—42no—
649C4×D3—62no—
650C4×D3—62no—
651C4×D3—61no—
652C4×D3—61no—
653C4×D3—61no—
654C4×D3—61no—
655C4×D3—122no—
656C4×D3—122no—
657C4×D3—124no—
658Dic6—21no—
659Dic6—21no—
660C3×C8—22no—
661C3×C8—61no—
662C3×C8—61no—
663C3×C8C2×D1212yes—
664C3×C8C2×#6712yes—
665C3⋊C8—21no—
666C3⋊C8—21no—
667C3⋊C8—62no—
668C3⋊C8—61no—
669C3⋊C8—61no—
670C2×C32—42no—
671C2×C32D4211yescharacteristic
672C2×C32#57511yescharacteristic
673C2×C32#57611yescharacteristic
674C3⋊D3—41no—
675C3⋊D3—81no—
676C3⋊D3—81no—
677C3×D3—41no—
678C3×D3—81no—
679C24—181no—
680#41—62no—
681#41—62no—
682#41—121no—
683#41—121no—
684#41—182no—
685#41—361no—
686C2×Q8—31no—
687C2×Q8C2×D3211yescharacteristic
688C2×D4—31no—
689C2×D4—61no—
690C2×D4—61no—
691C2×D4—91no—
692C2×D4—91no—
693C2×D4—91no—
694C2×D4—181no—
695C2×D4—181no—
696C2×D4—181no—
697C2×D4—181no—
698C2×D4—181no—
699C2×D4—181no—
700C2×D4—181no—
701C2×D4—182no—
702C2×D4—361no—
703C2×D4C2×D3211yescharacteristic
704C22×C4—31no—
705C22×C4—61no—
706C22×C4—61no—
707C22×C4—61no—
708C22×C4—91no—
709C22×C4—181no—
710Q16—62no—
711SD16—62no—
712SD16—182no—
713SD16—361no—
714SD16#62614yescomplemented
715D8—62no—
716D8—182no—
717D8—182no—
718D8—361no—
719M16—182no—
720C2×C8—31no—
721C2×C8—31no—
722C2×C8—62no—
723C2×C8—91no—
724C2×C8C2×D3211yescharacteristic
725C4⋊C4—31no—
726C4⋊C4—31no—
727C4⋊C4—61no—
728C4⋊C4—91no—
729C4⋊C4—181no—
730C22⋊C4—61no—
731C22⋊C4—91no—
732C22⋊C4—91no—
733C22⋊C4—181no—
734C22⋊C4—181no—
735C22⋊C4—181no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C22⋊C4—181no—
739C42—31no—
740C42—61no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—21no—
744C22×C3—42no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—61no—
750C22×C3—61no—
751C22×C3—61no—
752C22×C3—81no—
753C22×C3—81no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3C2×D3×D411yescharacteristic
758C22×C3C2×D3×D411yescharacteristic
759C2×D3—21no—
760C2×D3—21no—
761C2×D3—21no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—62no—
766C2×D3—61no—
767C2×D3—61no—
768C2×D3—61no—
769C2×D3—61no—
770C2×D3—61no—
771C2×D3—61no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—122no—
775C2×D3—122no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—121no—
788C2×D3—241no—
789C2×D3—241no—
790C2×D3—241no—
791C2×D3—241no—
792C2×D3—244no—
793C2×D3—244no—
794C2×D3—248no—
795C3×C4—22no—
796C3×C4—22no—
797C3×C4—21no—
798C3×C4—21no—
799C3×C4—42no—
800C3×C4—61no—
801C3×C4—61no—
802C3×C4—61no—
803C3×C4—121no—
804C3×C4—121no—
805C3×C4—121no—
806C3×C4C22×D1211yescharacteristic
807C3×C4#100411yescharacteristic
808C3×C4#100911yescharacteristic
809C3×C4C22×#6711yescharacteristic
810Dic3—21no—
811Dic3—21no—
812Dic3—21no—
813Dic3—41no—
814Dic3—41no—
815Dic3—41no—
816Dic3—62no—
817Dic3—61no—
818Dic3—61no—
819C32#326811yescharacteristic, complemented, Sylow
820C23—21no—
821C23—31no—
822C23—61no—
823C23—91no—
824C23—181no—
825C23—181no—
826C23—362no—
827C23—362no—
828C23—721no—
829Q8—21no—
830Q8—61no—
831Q8—61no—
832Q8C2×#62612yes—
833D4—21no—
834D4—61no—
835D4—61no—
836D4—122no—
837D4—122no—
838D4—181no—
839D4—181no—
840D4—181no—
841D4—181no—
842D4—362no—
843D4—361no—
844D4—362no—
845D4—362no—
846D4—721no—
847D4—721no—
848D4—721no—
849D4—721no—
850D4C2×#62612yes—
851C2×C4—21no—
852C2×C4—31no—
853C2×C4—31no—
854C2×C4—31no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—91no—
861C2×C4—122no—
862C2×C4—122no—
863C2×C4—181no—
864C2×C4—181no—
865C2×C4—241no—
866C2×C4—362no—
867C2×C4C22×D3211yescharacteristic
868C8—61no—
869C8—61no—
870C8—181no—
871C8C2×#62612yes—
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—42no—
876C2×C3—42no—
877C2×C3—82no—
878C2×C3—121no—
879C2×C3—241no—
880C2×C3D4×D1211yescharacteristic
881C2×C3#576811yescharacteristic
882C2×C3#576911yescharacteristic
883C2×C3#577411yescharacteristic
884C2×C3#577711yescharacteristic
885C2×C3D4×#6711yescharacteristic
886D3—41no—
887D3—81no—
888D3—122no—
889D3—121no—
890D3—121no—
891D3—242no—
892D3—242no—
893D3—241no—
894D3—241no—
895D3—241no—
896D3—241no—
897C22—22no—
898C22—41no—
899C22—41no—
900C22—61no—
901C22—61no—
902C22—61no—
903C22—121no—
904C22—121no—
905C22—121no—
906C22—181no—
907C22—181no—
908C22—181no—
909C22—361no—
910C22—361no—
911C22—361no—
912C22—361no—
913C22—361no—
914C22—361no—
915C22—724no—
916C22D32×D411yescharacteristic
917C4—22no—
918C4—61no—
919C4—61no—
920C4—61no—
921C4—121no—
922C4—121no—
923C4—121no—
924C4—181no—
925C4#6431411yescharacteristic
926C4C22×#62611yescharacteristic
927C3—21no—
928C3#7979611yescharacteristic, complemented
929C3#8392211yescharacteristic, complemented
930C2—42no—
931C2—121no—
932C2—241no—
933C2—361no—
934C2—721no—
935C2—721no—
936C2#1059474611yescharacteristic
937C2#1059475511yescharacteristic
938C2D4×#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×#64123C2semidirect
2. C2×C3×#916C2semidirect
3. #10595410C2semidirect
4. #10595254C2semidirect
5. C3×#5164C2semidirect
6. #10591607C2semidirect
7. #10591602C2semidirect
8. #10591588C2semidirect
9. #10591481C2semidirect
10. #10591456C2semidirect
11. #10591452C2semidirect
12. #10590881C2semidirect
13. #10590845C2semidirect
14. #10590832C2semidirect
15. #10590726C2semidirect
20. C2×C3×#239C22semidirect
28. C3×Q8×Dic3C22semidirect
29. C2×C3×#216C22semidirect
33. C2×C3×#204C22semidirect
34. C2×C3×D3×C8C22semidirect
42. #63911C22semidirect
45. #63909C22semidirect
50. C2×#3717C22semidirect
52. C3×#835C22semidirect
54. C3×#818C22semidirect
55. C3×#815C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63565C22semidirect
59. #63564C22semidirect
60. #63562C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
66. C2×#916D3semidirect
79. #5164D3semidirect
125. C32×SD16D4semidirect
162. C2×#239C2×D3semidirect
179. Q8×Dic3C2×D3semidirect
180. C2×#216C2×D3semidirect
215. C2×#204C2×D3semidirect
219. C2×D3×C8C2×D3semidirect
238. #835C2×D3semidirect
247. #818C2×D3semidirect
248. #815C2×D3semidirect
400. C3×SD16D12semidirect
401. C3×SD16#67semidirect
714. SD16#626semidirect
819. C32#3268semidirect
928. C3#79796semidirect
929. C3#83922semidirect

Maximal subgroups

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

subgroupindex
C2×#641232
C2×C3×#9162
#105954102
#105952542
C3×#51642
#105916072
#105916022
#105915882
#105914812
#105914562
#105914522
#105908812
#105908452
#105908322
#105907262
#839223
#797963