Finite Group Databasebeta

← #11884436

Subgroups — #11884436

Order 1152.

1187 conjugacy classes of subgroups.

The subgroup lattice has 959 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596300C211yesmaximal, characteristic, complemented
2C2×C3×#950C211yesmaximal, characteristic, complemented
3C2×#63937C211yesmaximal, characteristic, complemented
4#10595006C211yesmaximal, characteristic, complemented
5C3×#5238C211yesmaximal, characteristic, complemented
6#10591656C211yesmaximal, characteristic, complemented
7#10591621C211yesmaximal, characteristic, complemented
8#10591590C211yesmaximal, characteristic, complemented
9#10591579C211yesmaximal, characteristic, complemented
10#10591486C211yesmaximal, characteristic, complemented
11#10591456C211yesmaximal, characteristic, complemented
12#10591446C211yesmaximal, characteristic, complemented
13#10591164C211yesmaximal, characteristic, complemented
14#10591163C211yesmaximal, characteristic, complemented
15#10591157C211yesmaximal, characteristic, complemented
16#83922—31nomaximal
17#80128—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×D4×C3⋊D3C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic, complemented
21C2×#3796C2211yescharacteristic
22#64156C2211yescharacteristic
23#64155C2211yescharacteristic
24#64148—21no—
25#64146—21no—
26D4×C3⋊Dic3C2211yescharacteristic
27#64139C2211yescharacteristic
28#64138—21no—
29C4×#638C2211yescharacteristic
30C2×#3752—21no—
31C3×#950—24no—
32C2×C3×#216C2211yescharacteristic, complemented
33C2×C3×#215C2211yescharacteristic, complemented
34C2×C3×#215C2211yescharacteristic, complemented
35C2×C3×#214C2211yescharacteristic
36C2×C3×#213C2211yescharacteristic
37C2×C3×#213C2211yescharacteristic
38C3×#930C2211yescharacteristic, complemented
39C22×C3×C3⋊C8C2211yescharacteristic, complemented
40#63979—21no—
41#63970—21no—
42#63937—24no—
43#63916C2211yescharacteristic
44#63914C2211yescharacteristic, complemented
45#63906—21no—
46#63879—21no—
47#63843C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50C2×#3714C2211yescharacteristic
51C2×#3712C2211yescharacteristic
52C3×#835C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic
54C3×#830C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63557C2211yescharacteristic
62#63555C2211yescharacteristic, complemented
63C2×C3×#135—31no—
64#5834—31no—
65#5829—31no—
66#5829—31no—
67#5829—61no—
68C2×#950D311yescharacteristic, complemented
69C2×#914—31no—
70C2×#911—31no—
71#5599—31no—
72C3×#449—31no—
73#5238—31no—
74#5238D311yescharacteristic, complemented
75#5187—31no—
76#5185—31no—
77#5176—31no—
78#5176—31no—
79#5174—31no—
80#5173—31no—
81#5164—31no—
82#5156—31no—
83#5150—31no—
84#5150—31no—
85#5115—31no—
86#5111—31no—
87#5038—31no—
88#4812—31no—
89#4798—31no—
90#4773—31no—
91#4757—31no—
92#4734—31no—
93#4730—31no—
94C23×C3⋊D3—21no—
95C32×#41—22no—
96C32×#41—41no—
97C2×C32×Q8C2311yescharacteristic
98C2×C32×D4—21no—
99C2×C32×D4C2311yescharacteristic
100C22×C32×C4—21no—
101C22×C32×C4C2311yescharacteristic
102C2×#638—21no—
103C2×#638—21no—
104C2×#638D411yescharacteristic
105C22×C3⋊Dic3—21no—
106D4×C3⋊D3—22no—
107D4×C3⋊D3—41no—
108C2×C4⋊(C3⋊D3)C2311yescharacteristic
109C2×C4×C3⋊D3C2311yescharacteristic
110C2×C3×#67—21no—
111C2×C3×#67—21no—
112C3×#235—22no—
113C3×#235—41no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—21no—
117C2×C3×Dic6C2311yescharacteristic
118C2×#626—21no—
119C2×#626—21no—
120C2×#625—21no—
121C2×#625—21no—
122C2×D3×Dic3—21no—
123#3796—22no—
124#3796—41no—
125#3757—21no—
126#3757D411yescharacteristic
127#3752—21no—
128#3752—21no—
129#3752—21no—
130#3752—21no—
131#3752D411yescharacteristic
132C4⋊(C3⋊Dic3)C2311yescharacteristic
133#3750—21no—
134#3750D411yescharacteristic
135C4×C3⋊Dic3C2311yescharacteristic
136C3×#216—22no—
137C3×#215—22no—
138C3×#215—41no—
139C3×#214D414yescomplemented
140C3×#213—22no—
141C3×#213—22no—
142C3×(C2×D3)⋊C4—21no—
143C3×C4⋊Dic3C2311yescharacteristic
144C2×C3×C3⋊C8—22no—
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148C2×C3×C3⋊C8C2311yescharacteristic
149Dic3⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151Dic32—21no—
152#3717—22no—
153#3714—22no—
154#3714—41no—
155#3712—22no—
156#3268—91noSylow
157C2×C3×#41—21no—
158C2×C3×#41—31no—
159C2×C3×#41C2×D311yescharacteristic
160C2×C3×#41C2×D311yescharacteristic
161C2×#239—31no—
162C2×#237—31no—
163C2×D3×D4—31no—
164C2×D3×D4—31no—
165C2×D3×D4—61no—
166C2×#235C2×D311yescharacteristic, complemented
167C3×#135—64no—
168C2×C3×Q16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×D8—31no—
173C2×C3×D8—31no—
174C22×C3×C8—31no—
175C3×#121—31no—
176#950—24no—
177#947—31no—
178#947—31no—
179#947—61no—
180#946—31no—
181#946—31no—
182#946—61no—
183Q8×Dic3—31no—
184C2×#216C2×D311yescharacteristic, complemented
185C2×#215—31no—
186C2×#215C2×D311yescharacteristic, complemented
187C2×#215C2×D311yescharacteristic, complemented
188#940—31no—
189#940—31no—
190#940—61no—
191#940—61no—
192#939—61no—
193#939—61no—
194#939—61no—
195#939—62no—
196#938—31no—
197#938—61no—
198#937—61no—
199#937—61no—
200#937—62no—
201D4×Dic3—31no—
202D4×Dic3—31no—
203D4×Dic3—61no—
204C2×#214C2×D311yescharacteristic
205C2×#213—31no—
206C2×#213—31no—
207C2×#213C2×D311yescharacteristic
208C2×#213C2×D311yescharacteristic
209#930—31no—
210#930—31no—
211#930—61no—
212#930—61no—
213#930C2×D311yescharacteristic, complemented
214#929—61no—
215#929—61no—
216#929—62no—
217C4×#67—31no—
218C4×#67—31no—
219C4×#67—61no—
220C4×#67—61no—
221C2×(C2×D3)⋊C4—61no—
222C2×(C2×D3)⋊C4—61no—
223C2×(C2×D3)⋊C4—62no—
224C22×C3⋊C8C2×D311yescharacteristic, complemented
225#914—64no—
226#911—64no—
227C2×D24—31no—
228C2×D24—31no—
229C2×#204—31no—
230C2×ΓL(1,𝔽25)—31no—
231C2×ΓL(1,𝔽25)—31no—
232#895—31no—
233#887—31no—
234#884—61no—
235#67⋊C4—61no—
236C3×#103—31no—
237C3×#102—31no—
238C3×C22⋊C8—31no—
239#835—31no—
240#835C2×D311yescharacteristic, complemented
241#832—31no—
242#832—31no—
243#832C2×D311yescharacteristic
244#830C2×D311yescharacteristic, complemented
245#821—31no—
246#821—31no—
247#821—31no—
248(C2×D3)⋊C8—31no—
249(C2×D3)⋊C8—31no—
250#818—31no—
251#816—31no—
252#815—31no—
253#815—31no—
254Dic3⋊C8—31no—
255Dic3⋊C8—31no—
256#809—31no—
257#807—31no—
258C23×C32—21no—
259C23×C32C2×D411yescharacteristic
260C22×C3⋊D3—21no—
261C22×C3⋊D3—42no—
262C22×C3⋊D3—42no—
263C22×C3⋊D3—81no—
264C22×C3⋊D3C2×D411yescharacteristic
265C22×C3×D3—21no—
266C22×C3×D3—21no—
267C32×Q8—21no—
268C32×Q8—21no—
269C32×D4—21no—
270C32×D4—42no—
271C32×D4C2×D412yes—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—42no—
276C2×C32×C4C2×D411yescharacteristic
277C2×C32×C4C2411yescharacteristic
278#638—41no—
279#638—42no—
280#638—81no—
281C2×C3⋊Dic3—21no—
282C2×C3⋊Dic3—81no—
283C2×C3⋊Dic3C2×D411yescharacteristic
284C2×C3⋊Dic3C2×D411yescharacteristic
285C2×C3⋊Dic3C2×D411yescharacteristic
286C4⋊(C3⋊D3)—21no—
287C4⋊(C3⋊D3)—21no—
288C4×C3⋊D3—21no—
289C4×C3⋊D3—21no—
290C3×#67—42no—
291C3×#67—81no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C3×D12—21no—
295C3×D12—21no—
296C3×D12—21no—
297C3×D12—21no—
298C3×C4×D3—42no—
299C3×Dic6—21no—
300C3×Dic6C2×D412yes—
301#626—42no—
302#626—81no—
303#625—42no—
304#625—81no—
305D3×Dic3—42no—
306C3×C3⋊C8—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8—21no—
309C3×C3⋊C8C2×D412yes—
310C2×AGL(1,ℤ/8)—91no—
311C2×#135—31no—
312#550—91no—
313#546—91no—
314#496—91no—
315#468—91no—
316#466—91no—
317#464—91no—
318#459—91no—
319#452—91no—
320#449—31no—
321#449—91no—
322#447—91no—
323#440—91no—
324#435—91no—
325C23×D3—61no—
326C23×D3—61no—
327C23×D3—62no—
328C3×#41—22no—
329C3×#41—22no—
330C3×#41—42no—
331C3×#41—41no—
332C3×#41—41no—
333C3×#41—42no—
334C3×#41—62no—
335C3×#41—121no—
336C2×C3×Q8—21no—
337C2×C3×Q8—31no—
338C2×C3×Q8C22×D311yescharacteristic
339C2×C3×Q8C22×D311yescharacteristic
340C2×C3×D4—22no—
341C2×C3×D4—21no—
342C2×C3×D4—21no—
343C2×C3×D4—21no—
344C2×C3×D4—31no—
345C2×C3×D4—31no—
346C2×C3×D4—61no—
347C2×C3×D4—61no—
348C2×C3×D4C22×D311yescharacteristic
349C2×C3×D4C22×D311yescharacteristic
350C22×C3×C4—22no—
351C22×C3×C4—21no—
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—61no—
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C2×#67—21no—
358C2×#67—21no—
359C2×#67—31no—
360C2×#67—31no—
361C2×#67—61no—
362C2×#67—61no—
363C2×#67—61no—
364C2×#67—61no—
365C2×#67—61no—
366C2×#67—61no—
367C2×#67—61no—
368C2×#67—61no—
369C2×#67—61no—
370C2×#67—62no—
371C2×#67—62no—
372C2×#67—61no—
373C2×#67—61no—
374C22×Dic3—61no—
375C22×Dic3—61no—
376C22×Dic3—61no—
377C22×Dic3—62no—
378#239—62no—
379#239—121no—
380#237—62no—
381#237—121no—
382D3×D4—62no—
383D3×D4—62no—
384D3×D4—122no—
385D3×D4—121no—
386D3×D4—121no—
387D3×D4—122no—
388#235—22no—
389#235—41no—
390C2×D12—31no—
391C2×D12—31no—
392C2×D12—61no—
393C2×D12—61no—
394C2×D12—61no—
395C2×D12C22×D311yescharacteristic
396C2×D12C22×D311yescharacteristic
397C2×C4×D3—21no—
398C2×C4×D3—31no—
399C2×C4×D3—31no—
400C2×C4×D3—61no—
401C2×C4×D3—61no—
402C2×Dic6C22×D311yescharacteristic
403C3×Q16—62no—
404C3×SD16—34no—
405C3×SD16—62no—
406C3×SD16—121no—
407C3×D8—62no—
408C3×D8—62no—
409C2×C3×C8—31no—
410C2×C3×C8—31no—
411C2×C3×C8—31no—
412C2×C3×C8—31no—
413C2×C3×C8—62no—
414C3×C4⋊C4—31no—
415C3×C22⋊C4—61no—
416#217—31no—
417#217—31no—
418#217—61no—
419#217—61no—
420#217—61no—
421#217—61no—
422#217—62no—
423#216—22no—
424#215—22no—
425#215—41no—
426#215—62no—
427#214#6714yescomplemented
428#213—22no—
429#213—22no—
430#213—62no—
431#213—121no—
432(C2×D3)⋊C4—21no—
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—
442(C2×D3)⋊C4—61no—
443(C2×D3)⋊C4—62no—
444(C2×D3)⋊C4—62no—
445(C2×D3)⋊C4—62no—
446(C2×D3)⋊C4—62no—
447(C2×D3)⋊C4—61no—
448(C2×D3)⋊C4—61no—
449C4⋊Dic3—31no—
450C4⋊Dic3—31no—
451C4⋊Dic3—61no—
452C4⋊Dic3—61no—
453C4⋊Dic3C22×D311yescharacteristic
454Dic3⋊C4—31no—
455Dic3⋊C4—31no—
456Dic3⋊C4—61no—
457Dic3⋊C4—61no—
458Dic3⋊C4—61no—
459Dic3⋊C4—61no—
460Dic3⋊C4—62no—
461C4×Dic3—31no—
462C4×Dic3—31no—
463C4×Dic3—61no—
464C4×Dic3—61no—
465C4×Dic3—61no—
466C2×C3⋊C8—22no—
467C2×C3⋊C8C22×D311yescharacteristic
468C2×C3⋊C8C22×D311yescharacteristic
469C2×C3⋊C8C22×D311yescharacteristic
470C2×C3⋊C8C22×D311yescharacteristic
471D24—62no—
472D24—121no—
473#204—62no—
474ΓL(1,𝔽25)—62no—
475ΓL(1,𝔽25)—62no—
476C22×C32—22no—
477C22×C32—21no—
478C22×C32—21no—
479C22×C32—21no—
480C22×C32—41no—
481C22×C32—41no—
482C22×C32C22×D411yescharacteristic
483C2×C3⋊D3—21no—
484C2×C3⋊D3—21no—
485C2×C3⋊D3—21no—
486C2×C3⋊D3—41no—
487C2×C3⋊D3—41no—
488C2×C3⋊D3—41no—
489C2×C3⋊D3—84no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496C32×C4—21no—
497C32×C4—41no—
498C32×C4C22×D411yescharacteristic
499C32×C4H(5,𝔽2)11yescharacteristic
500C3⋊Dic3—21no—
501C3⋊Dic3—21no—
502C3⋊Dic3—21no—
503C3⋊Dic3—41no—
504C3×Dic3—22no—
505C3×Dic3—41no—
506C2×#41—31no—
507C2×#41—91no—
508C2×#41D3211yescharacteristic
509C22×D4—91no—
510AGL(1,ℤ/8)—184no—
511#135—64no—
512C2×Q16—31no—
513C2×SD16—31no—
514C2×SD16—31no—
515C2×SD16—31no—
516C2×SD16—91no—
517C2×D8—31no—
518C2×D8—31no—
519C2×D8—91no—
520C2×D8—91no—
521C2×M16—91no—
522C22×C8—31no—
523#127—91no—
524#127—181no—
525#124—91no—
526#123—181no—
527C22⋊Q8—91no—
528#121—31no—
529#121—91no—
530#121—91no—
531#121—181no—
532#121—181no—
533#121—181no—
534#120—181no—
535C4×Q8—91no—
536C4×D4—91no—
537C4×D4—91no—
538C4×D4—181no—
539C2×C22⋊C4—181no—
540#107—91no—
541C4⋊C8—91no—
542#103—31no—
543#103—91no—
544#102—31no—
545#102—91no—
546#102—91no—
547#102—91no—
548C22⋊C8—31no—
549C22⋊C8—91no—
550#97—91no—
551C23×C3—22no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—61no—
556C23×C3—61no—
557C23×C3D3×D411yescharacteristic
558C23×C3D3×D411yescharacteristic
559C22×D3—21no—
560C22×D3—21no—
561C22×D3—31no—
562C22×D3—31no—
563C22×D3—61no—
564C22×D3—62no—
565C22×D3—61no—
566C22×D3—61no—
567C22×D3—122no—
568C22×D3—122no—
569C22×D3—124no—
570C22×D3—122no—
571C22×D3—122no—
572C22×D3—124no—
573C22×D3—241no—
574C22×D3—241no—
575C22×D3—242no—
576C3×Q8—21no—
577C3×Q8—21no—
578C3×Q8—21no—
579C3×Q8—21no—
580C3×Q8—32no—
581C3×Q8—41no—
582C3×Q8—41no—
583C3×Q8—61no—
584C3×D4—22no—
585C3×D4—21no—
586C3×D4—21no—
587C3×D4—22no—
588C3×D4—42no—
589C3×D4—42no—
590C3×D4—44no—
591C3×D4—61no—
592C3×D4—61no—
593C3×D4—61no—
594C3×D4—61no—
595C3×D4—122no—
596C3×D4—241no—
597C3×D4D3×D412yes—
598C3×D4C2×#6712yes—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—22no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—42no—
611C2×C3×C4—42no—
612C2×C3×C4—44no—
613C2×C3×C4—61no—
614C2×C3×C4—61no—
615C2×C3×C4—122no—
616C2×C3×C4D3×D411yescharacteristic
617C2×C3×C4D3×D411yescharacteristic
618C2×C3×C4C23×D311yescharacteristic
619C2×C3×C4C23×D311yescharacteristic
620#67—42no—
621#67—81no—
622#67—122no—
623#67—122no—
624#67—122no—
625#67—121no—
626#67—121no—
627#67—122no—
628#67—122no—
629#67—122no—
630#67—124no—
631#67—241no—
632#67—241no—
633#67—241no—
634#67—241no—
635#67—241no—
636#67—242no—
637C2×Dic3—21no—
638C2×Dic3—21no—
639C2×Dic3—31no—
640C2×Dic3—31no—
641C2×Dic3—31no—
642C2×Dic3—31no—
643C2×Dic3—31no—
644C2×Dic3—31no—
645C2×Dic3—61no—
646C2×Dic3—61no—
647C2×Dic3—61no—
648C2×Dic3—62no—
649C2×Dic3—61no—
650C2×Dic3—61no—
651C2×Dic3—122no—
652C2×Dic3—241no—
653C2×Dic3—241no—
654C2×Dic3—242no—
655D12—21no—
656D12—21no—
657D12—21no—
658D12—21no—
659D12—61no—
660D12—61no—
661D12—61no—
662D12—61no—
663D12—121no—
664D12—121no—
665D12—122no—
666D12—241no—
667C4×D3—42no—
668C4×D3—61no—
669C4×D3—61no—
670C4×D3—61no—
671C4×D3—61no—
672C4×D3—121no—
673C4×D3—121no—
674C4×D3—122no—
675Dic6—21no—
676Dic6C2×#6712yes—
677C3×C8—32no—
678C3×C8—61no—
679C3×C8—61no—
680C3×C8—61no—
681C3⋊C8—21no—
682C3⋊C8—21no—
683C3⋊C8—21no—
684C3⋊C8C2×#6712yes—
685C2×C32—42no—
686C2×C32—41no—
687C2×C32D4211yescharacteristic
688C2×C32#57511yescharacteristic
689C2×C32#57611yescharacteristic
690C3⋊D3—41no—
691C3⋊D3—81no—
692C3×D3—81no—
693C3×D3—81no—
694C24—181no—
695#41—22no—
696#41—41no—
697#41—62no—
698#41—121no—
699#41—182no—
700#41—361no—
701C2×Q8—31no—
702C2×Q8C2×D3211yescharacteristic
703C2×D4—21no—
704C2×D4—31no—
705C2×D4—31no—
706C2×D4—61no—
707C2×D4—61no—
708C2×D4—91no—
709C2×D4—91no—
710C2×D4—181no—
711C2×D4—181no—
712C2×D4—181no—
713C2×D4—181no—
714C2×D4—181no—
715C2×D4—182no—
716C2×D4—181no—
717C2×D4—361no—
718C2×D4C2×D3211yescharacteristic
719C22×C4—21no—
720C22×C4—61no—
721C22×C4—91no—
722C22×C4—181no—
723C22×C4—181no—
724C22×C4C2×D3211yescharacteristic
725Q16—62no—
726SD16—34no—
727SD16—62no—
728SD16—121no—
729SD16—182no—
730D8—62no—
731D8—62no—
732D8—182no—
733D8—361no—
734M16—182no—
735C2×C8—31no—
736C2×C8—31no—
737C2×C8—31no—
738C2×C8—31no—
739C2×C8—62no—
740C4⋊C4—31no—
741C4⋊C4—91no—
742C4⋊C4—91no—
743C4⋊C4—181no—
744C4⋊C4—181no—
745C22⋊C4—61no—
746C22⋊C4—91no—
747C22⋊C4—91no—
748C22⋊C4—181no—
749C22⋊C4—181no—
750C22⋊C4—181no—
751C22⋊C4—181no—
752C22⋊C4—181no—
753C22⋊C4—181no—
754C42—91no—
755C42—181no—
756C22×C3—24no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—22no—
763C22×C3—22no—
764C22×C3—21no—
765C22×C3—21no—
766C22×C3—41no—
767C22×C3—41no—
768C22×C3—41no—
769C22×C3—42no—
770C22×C3—42no—
771C22×C3—41no—
772C22×C3—41no—
773C22×C3—41no—
774C22×C3—41no—
775C22×C3—121no—
776C22×C3—121no—
777C22×C3—121no—
778C22×C3—121no—
779C22×C3—121no—
780C22×C3—121no—
781C22×C3C2×D3×D411yescharacteristic
782C22×C3C2×D3×D411yescharacteristic
783C2×D3—41no—
784C2×D3—41no—
785C2×D3—41no—
786C2×D3—41no—
787C2×D3—41no—
788C2×D3—41no—
789C2×D3—62no—
790C2×D3—61no—
791C2×D3—61no—
792C2×D3—61no—
793C2×D3—61no—
794C2×D3—61no—
795C2×D3—61no—
796C2×D3—121no—
797C2×D3—121no—
798C2×D3—122no—
799C2×D3—122no—
800C2×D3—122no—
801C2×D3—121no—
802C2×D3—121no—
803C2×D3—121no—
804C2×D3—121no—
805C2×D3—121no—
806C2×D3—121no—
807C2×D3—248no—
808C2×D3—244no—
809C2×D3—244no—
810C3×C4—21no—
811C3×C4—21no—
812C3×C4—21no—
813C3×C4—21no—
814C3×C4—41no—
815C3×C4—42no—
816C3×C4—41no—
817C3×C4—41no—
818C3×C4—62no—
819C3×C4—121no—
820C3×C4C2×D3×D411yescharacteristic
821C3×C4#100411yescharacteristic
822C3×C4#100411yescharacteristic
823C3×C4C22×#6711yescharacteristic
824Dic3—22no—
825Dic3—41no—
826Dic3—61no—
827Dic3—61no—
828Dic3—61no—
829Dic3—61no—
830Dic3—61no—
831Dic3—61no—
832Dic3—121no—
833Dic3—121no—
834Dic3—121no—
835Dic3—122no—
836Dic3—121no—
837Dic3—121no—
838C32#326811yescharacteristic, complemented, Sylow
839C23—21no—
840C23—61no—
841C23—61no—
842C23—91no—
843C23—181no—
844C23—362no—
845C23—362no—
846C23—721no—
847C23#381111yescharacteristic
848Q8—21no—
849Q8—21no—
850Q8—32no—
851Q8—61no—
852D4—21no—
853D4—42no—
854D4—61no—
855D4—61no—
856D4—61no—
857D4—61no—
858D4—122no—
859D4—181no—
860D4—181no—
861D4—241no—
862D4—362no—
863D4—361no—
864D4—362no—
865D4—362no—
866D4—721no—
867D4—721no—
868D4—721no—
869D4D3×#6712yes—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—42no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—91no—
877C2×C4—91no—
878C2×C4—91no—
879C2×C4—122no—
880C2×C4—181no—
881C2×C4—181no—
882C2×C4—181no—
883C2×C4—362no—
884C2×C4—721no—
885C2×C4#381111yescharacteristic
886C2×C4C22×D3211yescharacteristic
887C8—32no—
888C8—61no—
889C8—61no—
890C8—61no—
891C2×C3—21no—
892C2×C3—21no—
893C2×C3—21no—
894C2×C3—44no—
895C2×C3—42no—
896C2×C3—41no—
897C2×C3—42no—
898C2×C3—41no—
899C2×C3—81no—
900C2×C3—241no—
901C2×C3—241no—
902C2×C3#559011yescharacteristic
903C2×C3#576811yescharacteristic
904C2×C3#576811yescharacteristic
905C2×C3#576911yescharacteristic
906C2×C3#577411yescharacteristic
907C2×C3D4×#6711yescharacteristic
908D3—81no—
909D3—81no—
910D3—122no—
911D3—121no—
912D3—121no—
913D3—242no—
914D3—241no—
915D3—241no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—22no—
920C22—41no—
921C22—41no—
922C22—121no—
923C22—121no—
924C22—121no—
925C22—121no—
926C22—121no—
927C22—121no—
928C22—181no—
929C22—181no—
930C22—181no—
931C22—361no—
932C22—361no—
933C22—361no—
934C22—724no—
935C22C2×#381111yescharacteristic
936C4—21no—
937C4—41no—
938C4—62no—
939C4—121no—
940C4—181no—
941C4—181no—
942C4—181no—
943C4—361no—
944C4C2×D3×#6711yescharacteristic
945C4#6433011yescharacteristic
946C3—21no—
947C3#8012811yescharacteristic, complemented
948C3#8392211yescharacteristic, complemented
949C2—41no—
950C2—42no—
951C2—241no—
952C2—241no—
953C2—361no—
954C2—721no—
955C2#1059546011yescharacteristic
956C2#1059546111yescharacteristic
957C2#1059552611yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #10596300C2semidirect
2. C2×C3×#950C2semidirect
3. C2×#63937C2semidirect
4. #10595006C2semidirect
5. C3×#5238C2semidirect
6. #10591656C2semidirect
7. #10591621C2semidirect
8. #10591590C2semidirect
9. #10591579C2semidirect
10. #10591486C2semidirect
11. #10591456C2semidirect
12. #10591446C2semidirect
13. #10591164C2semidirect
14. #10591163C2semidirect
15. #10591157C2semidirect
20. C2×C3×#235C22semidirect
32. C2×C3×#216C22semidirect
33. C2×C3×#215C22semidirect
34. C2×C3×#215C22semidirect
38. C3×#930C22semidirect
39. C22×C3×C3⋊C8C22semidirect
44. #63914C22semidirect
47. #63843C22semidirect
52. C3×#835C22semidirect
54. C3×#830C22semidirect
55. #63575C22semidirect
56. #63572C22semidirect
57. #63566C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
62. #63555C22semidirect
68. C2×#950D3semidirect
74. #5238D3semidirect
139. C3×#214D4semidirect
166. C2×#235C2×D3semidirect
184. C2×#216C2×D3semidirect
186. C2×#215C2×D3semidirect
187. C2×#215C2×D3semidirect
213. #930C2×D3semidirect
224. C22×C3⋊C8C2×D3semidirect
240. #835C2×D3semidirect
244. #830C2×D3semidirect
427. #214#67semidirect
838. C32#3268semidirect
947. C3#80128semidirect
948. C3#83922semidirect

Maximal subgroups

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

subgroupindex
#105963002
C2×C3×#9502
C2×#639372
#105950062
C3×#52382
#105916562
#105916212
#105915902
#105915792
#105914862
#105914562
#105914462
#105911642
#105911632
#105911572
#839223
#801283