Finite Group Databasebeta

← #11885822

Subgroups — #11885822

Order 1152.

1219 conjugacy classes of subgroups.

The subgroup lattice has 963 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×#63926C211yesmaximal, characteristic, complemented
4#10595070C211yesmaximal, characteristic, complemented
5C3×#5238C211yesmaximal, characteristic, complemented
6#10591652C211yesmaximal, characteristic, complemented
7#10591610C211yesmaximal, characteristic, complemented
8#10591601C211yesmaximal, characteristic, complemented
9#10591570C211yesmaximal, characteristic, complemented
10#10591476C211yesmaximal, characteristic, complemented
11#10591467C211yesmaximal, characteristic, complemented
12#10591435C211yesmaximal, characteristic, complemented
13#10591164C211yesmaximal, characteristic, complemented
14#10591163C211yesmaximal, characteristic, complemented
15#10591148C211yesmaximal, characteristic, complemented
16#83918—31nomaximal
17#80101—31nomaximal
18C2×C32×#41C2211yescharacteristic, complemented
19C2×D4×C3⋊D3C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic, complemented
21C2×#3802C2211yescharacteristic
22#64156C2211yescharacteristic, complemented
23#64155C2211yescharacteristic
24#64148—21no—
25#64146—21no—
26D4×C3⋊Dic3C2211yescharacteristic, complemented
27#64139C2211yescharacteristic, complemented
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, complemented
36C2×C3×#213C2211yescharacteristic
37C2×C3×#213C2211yescharacteristic
38C3×#930C2211yescharacteristic, complemented
39C22×C3×C3⋊C8C2211yescharacteristic, complemented
40#63983—21no—
41#63970—21no—
42#63926—24no—
43D3×(C2×D3)⋊C4—21no—
44#63905—21no—
45#63898C2211yescharacteristic, complemented
46#63871C2211yescharacteristic
47#63863C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50C2×#3714C2211yescharacteristic
51C2×#3710C2211yescharacteristic
52C3×#835C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic, complemented
54C3×#830C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63564C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63557C2211yescharacteristic
62#63553C2211yescharacteristic, complemented
63C2×C3×#135—31no—
64#5829—31no—
65#5829—31no—
66#5829—31no—
67#5829—61no—
68C2×#950D311yescharacteristic, complemented
69C2×D3×D8—31no—
70C2×D3×D8—31no—
71#5612—31no—
72C3×#449—31no—
73#5238—31no—
74#5238D311yescharacteristic, complemented
75#5191—31no—
76#5188—31no—
77#5169—31no—
78#5169—31no—
79#5169—31no—
80#5168—31no—
81#5165—31no—
82#5165—31no—
83#5153—31no—
84Dic3×D8—31no—
85#5115—31no—
86C8×#67—31no—
87#5038—31no—
88#4819—31no—
89#4813—31no—
90#4776—31no—
91#4756—31no—
92#4734—31no—
93#67⋊C8—31no—
94C23×C3⋊D3—21no—
95C22×D32—21no—
96C32×#41—22no—
97C32×#41—41no—
98C2×C32×Q8C2311yescharacteristic
99C2×C32×D4—21no—
100C2×C32×D4C2311yescharacteristic
101C22×C32×C4—21no—
102C22×C32×C4C2311yescharacteristic
103C2×#638—21no—
104C2×#638—21no—
105C2×#638D411yescharacteristic
106C22×C3⋊Dic3—21no—
107D4×C3⋊D3—22no—
108D4×C3⋊D3—41no—
109C2×C4⋊(C3⋊D3)C2311yescharacteristic
110C2×C4×C3⋊D3C2311yescharacteristic
111C2×C3×#67—21no—
112C2×C3×#67—21no—
113C3×#235—22no—
114C3×#235—41no—
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×Dic6C2311yescharacteristic
119C2×#625—21no—
120C2×D3×Dic3—21no—
121#3802—22no—
122#3802—41no—
123#3757—21no—
124#3757D411yescharacteristic
125#3752—21no—
126#3752—21no—
127#3752—21no—
128#3752—21no—
129#3752D411yescharacteristic
130C4⋊(C3⋊Dic3)C2311yescharacteristic
131#3750—21no—
132#3750D411yescharacteristic
133C4×C3⋊Dic3C2311yescharacteristic
134C3×#216—22no—
135C3×#215—22no—
136C3×#215—41no—
137C3×#214—22no—
138C3×#213—22no—
139C3×#213D414yescomplemented
140C3×(C2×D3)⋊C4—21no—
141C3×C4⋊Dic3C2311yescharacteristic
142C2×C3×C3⋊C8—22no—
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147Dic3⋊Dic3—21no—
148#3722—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152#3717—41no—
153#3714—22no—
154#3714—22no—
155#3710—22no—
156#3280—91noSylow
157C2×C3×#41—21no—
158C2×C3×#41—31no—
159C2×C3×#41C2×D311yescharacteristic, complemented
160C2×C3×#41C2×D311yescharacteristic, complemented
161C2×D3×D4—31no—
162C2×D3×D4—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—31no—
180#947—61no—
181#946—31no—
182#946—31no—
183#946—31no—
184#946—61no—
185C2×#216C2×D311yescharacteristic, complemented
186C2×#215—31no—
187C2×#215C2×D311yescharacteristic, complemented
188C2×#215C2×D311yescharacteristic, complemented
189#939—61no—
190#939—61no—
191#939—61no—
192#939—62no—
193#938—61no—
194#937—61no—
195#937—61no—
196#937—61no—
197#937—61no—
198#937—62no—
199#936—31no—
200D4×Dic3—31no—
201D4×Dic3—31no—
202D4×Dic3—31no—
203D4×Dic3—61no—
204C2×#214C2×D311yescharacteristic, complemented
205C2×#213—31no—
206C2×#213—31no—
207C2×#213C2×D311yescharacteristic
208C2×#213C2×D311yescharacteristic
209#930—31no—
210#930—31no—
211#930—61no—
212#930C2×D311yescharacteristic, complemented
213#929—61no—
214#929—61no—
215#929—61no—
216#929—62no—
217C4×#67—31no—
218C4×#67—31no—
219C4×#67—61no—
220C2×(C2×D3)⋊C4—61no—
221C2×(C2×D3)⋊C4—61no—
222C2×(C2×D3)⋊C4—61no—
223C2×(C2×D3)⋊C4—62no—
224C22×C3⋊C8C2×D311yescharacteristic, complemented
225D3×D8—64no—
226D3×D8—64no—
227C2×D24—31no—
228C2×D24—31no—
229C2×#204—31no—
230C2×D3×C8—31no—
231C2×D3×C8—31no—
232#897—31no—
233#893—31no—
234#883—61no—
235D3×C22⋊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, complemented
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—
252Dic3⋊C8—31no—
253Dic3⋊C8—31no—
254C8×Dic3—31no—
255C8×Dic3—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—
267C2×D32—42no—
268C2×D32—42no—
269C2×D32—81no—
270C32×Q8—21no—
271C32×Q8—21no—
272C32×D4—21no—
273C32×D4—42no—
274C32×D4C2×D412yes—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4—42no—
279C2×C32×C4C2×D411yescharacteristic
280C2×C32×C4C2411yescharacteristic
281#638—22no—
282#638—42no—
283#638—81no—
284C2×C3⋊Dic3—21no—
285C2×C3⋊Dic3—81no—
286C2×C3⋊Dic3C2×D411yescharacteristic
287C2×C3⋊Dic3C2×D411yescharacteristic
288C2×C3⋊Dic3C2×D411yescharacteristic
289C4⋊(C3⋊D3)—21no—
290C4⋊(C3⋊D3)—21no—
291C4×C3⋊D3—21no—
292C4×C3⋊D3—21no—
293C3×#67—42no—
294C3×#67—81no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C3×D12—21no—
298C3×D12—21no—
299C3×D12—21no—
300C3×D12C2×D412yes—
301C3×C4×D3—42no—
302C3×Dic6—21no—
303C3×Dic6—21no—
304#625—42no—
305D3×Dic3—81no—
306C3×C3⋊C8—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8—21no—
309C3×C3⋊C8C2×D412yes—
310C2×#135—31no—
311C22×D8—91no—
312#546—91no—
313#546—91no—
314#495—91no—
315#467—91no—
316#466—91no—
317#463—91no—
318#463—91no—
319#450—91no—
320#450—91no—
321#449—31no—
322#449—91no—
323C4×D8—91no—
324C8×D4—91no—
325C23×D3—61no—
326C23×D3—61no—
327C23×D3—61no—
328C23×D3—61no—
329C23×D3—62no—
330C3×#41—22no—
331C3×#41—22no—
332C3×#41—42no—
333C3×#41—41no—
334C3×#41—41no—
335C3×#41—42no—
336C3×#41—62no—
337C3×#41—121no—
338C2×C3×Q8—21no—
339C2×C3×Q8—31no—
340C2×C3×Q8C22×D311yescharacteristic
341C2×C3×Q8C22×D311yescharacteristic
342C2×C3×D4—22no—
343C2×C3×D4—21no—
344C2×C3×D4—21no—
345C2×C3×D4—21no—
346C2×C3×D4—31no—
347C2×C3×D4—31no—
348C2×C3×D4—61no—
349C2×C3×D4—61no—
350C2×C3×D4C22×D311yescharacteristic
351C2×C3×D4C22×D311yescharacteristic
352C22×C3×C4—22no—
353C22×C3×C4—21no—
354C22×C3×C4—21no—
355C22×C3×C4—21no—
356C22×C3×C4—61no—
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C2×#67—21no—
360C2×#67—21no—
361C2×#67—31no—
362C2×#67—31no—
363C2×#67—61no—
364C2×#67—61no—
365C2×#67—61no—
366C2×#67—61no—
367C2×#67—61no—
368C2×#67—62no—
369C2×#67—62no—
370C2×#67—61no—
371C2×#67—61no—
372C22×Dic3—61no—
373C22×Dic3—61no—
374C22×Dic3—61no—
375C22×Dic3—62no—
376D3×D4—62no—
377D3×D4—62no—
378D3×D4—62no—
379D3×D4—62no—
380D3×D4—122no—
381D3×D4—121no—
382D3×D4—121no—
383D3×D4—121no—
384D3×D4—121no—
385D3×D4—122no—
386#235—22no—
387#235—41no—
388C2×D12—31no—
389C2×D12—31no—
390C2×D12—61no—
391C2×D12C22×D311yescharacteristic
392C2×D12C22×D311yescharacteristic
393C2×C4×D3—21no—
394C2×C4×D3—31no—
395C2×C4×D3—31no—
396C2×C4×D3—61no—
397C2×C4×D3—61no—
398C2×Dic6C22×D311yescharacteristic
399C3×Q16—62no—
400C3×SD16—62no—
401C3×SD16—62no—
402C3×SD16—121no—
403C3×D8—34no—
404C3×D8—62no—
405C2×C3×C8—31no—
406C2×C3×C8—31no—
407C2×C3×C8—31no—
408C2×C3×C8—31no—
409C2×C3×C8—62no—
410C3×C4⋊C4—31no—
411C3×C22⋊C4—61no—
412#217—31no—
413#217—31no—
414#217—61no—
415#217—61no—
416#217—61no—
417#217—61no—
418#217—61no—
419#217—61no—
420#217—62no—
421#216—22no—
422#215—22no—
423#215—41no—
424#215—121no—
425#214—22no—
426#213—22no—
427#213—62no—
428#213—62no—
429#213#6714yescomplemented
430(C2×D3)⋊C4—21no—
431(C2×D3)⋊C4—31no—
432(C2×D3)⋊C4—31no—
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—
442(C2×D3)⋊C4—61no—
443(C2×D3)⋊C4—61no—
444(C2×D3)⋊C4—61no—
445(C2×D3)⋊C4—62no—
446(C2×D3)⋊C4—62no—
447(C2×D3)⋊C4—62no—
448(C2×D3)⋊C4—62no—
449(C2×D3)⋊C4—61no—
450(C2×D3)⋊C4—61no—
451C4⋊Dic3—31no—
452C4⋊Dic3—31no—
453C4⋊Dic3—61no—
454C4⋊Dic3—61no—
455C4⋊Dic3C22×D311yescharacteristic
456Dic3⋊C4—31no—
457Dic3⋊C4—31no—
458Dic3⋊C4—61no—
459Dic3⋊C4—61no—
460Dic3⋊C4—61no—
461Dic3⋊C4—61no—
462Dic3⋊C4—62no—
463C4×Dic3—31no—
464C4×Dic3—31no—
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—62no—
473#204—121no—
474D3×C8—62no—
475D3×C8—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—41no—
486C2×C3⋊D3—41no—
487C2×C3⋊D3—41no—
488C2×C3⋊D3—84no—
489C2×C3⋊D3#13512yescomplemented
490C2×C3×D3—22no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496D32—84no—
497C32×C4—21no—
498C32×C4—41no—
499C32×C4C22×D411yescharacteristic
500C32×C4H(5,𝔽2)11yescharacteristic
501C3⋊Dic3—21no—
502C3⋊Dic3—21no—
503C3⋊Dic3—21no—
504C3⋊Dic3—41no—
505C3×Dic3—41no—
506C3×Dic3—41no—
507C2×#41—31no—
508C2×#41D3211yescharacteristic, complemented
509C22×D4—91no—
510C22×D4—91no—
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×D8—184no—
522C22×C8—31no—
523C22×C8—91no—
524#124—91no—
525#124—91no—
526#123—181no—
527#123—181no—
528C22⋊Q8—91no—
529C22⋊Q8—91no—
530#121—31no—
531#121—91no—
532#121—181no—
533#121—181no—
534#120—181no—
535#120—181no—
536C4×D4—91no—
537C4×D4—91no—
538C4×D4—91no—
539C2×C22⋊C4—181no—
540C2×C22⋊C4—181no—
541#107—91no—
542C4⋊C8—91no—
543#103—31no—
544#103—91no—
545#102—31no—
546#102—91no—
547#102—91no—
548#102—91no—
549C22⋊C8—31no—
550C22⋊C8—91no—
551C4×C8—91no—
552C23×C3—22no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—21no—
556C23×C3—61no—
557C23×C3—61no—
558C23×C3D3×D411yescharacteristic
559C23×C3D3×D411yescharacteristic
560C22×D3—21no—
561C22×D3—21no—
562C22×D3—31no—
563C22×D3—31no—
564C22×D3—61no—
565C22×D3—62no—
566C22×D3—61no—
567C22×D3—61no—
568C22×D3—122no—
569C22×D3—122no—
570C22×D3—122no—
571C22×D3—122no—
572C22×D3—122no—
573C22×D3—122no—
574C22×D3—122no—
575C22×D3—122no—
576C22×D3—124no—
577C22×D3—124no—
578C22×D3—241no—
579C22×D3—241no—
580C22×D3—241no—
581C22×D3—241no—
582C22×D3—242no—
583C3×Q8—21no—
584C3×Q8—21no—
585C3×Q8—21no—
586C3×Q8—21no—
587C3×Q8—41no—
588C3×Q8—41no—
589C3×Q8—61no—
590C3×Q8—61no—
591C3×D4—22no—
592C3×D4—21no—
593C3×D4—21no—
594C3×D4—22no—
595C3×D4—32no—
596C3×D4—42no—
597C3×D4—42no—
598C3×D4—44no—
599C3×D4—61no—
600C3×D4—61no—
601C3×D4—61no—
602C3×D4—122no—
603C3×D4—241no—
604C3×D4D3×D412yes—
605C3×D4C2×#6712yes—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—22no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—42no—
618C2×C3×C4—42no—
619C2×C3×C4—44no—
620C2×C3×C4—61no—
621C2×C3×C4—61no—
622C2×C3×C4—122no—
623C2×C3×C4D3×D411yescharacteristic
624C2×C3×C4D3×D411yescharacteristic
625C2×C3×C4C23×D311yescharacteristic
626C2×C3×C4C23×D311yescharacteristic
627#67—42no—
628#67—62no—
629#67—62no—
630#67—81no—
631#67—122no—
632#67—122no—
633#67—122no—
634#67—122no—
635#67—122no—
636#67—124no—
637#67—241no—
638#67—241no—
639#67—242no—
640C2×Dic3—21no—
641C2×Dic3—21no—
642C2×Dic3—31no—
643C2×Dic3—31no—
644C2×Dic3—31no—
645C2×Dic3—31no—
646C2×Dic3—31no—
647C2×Dic3—31no—
648C2×Dic3—61no—
649C2×Dic3—61no—
650C2×Dic3—61no—
651C2×Dic3—62no—
652C2×Dic3—61no—
653C2×Dic3—61no—
654C2×Dic3—241no—
655C2×Dic3—241no—
656C2×Dic3—241no—
657C2×Dic3—242no—
658D12—21no—
659D12—21no—
660D12—21no—
661D12—61no—
662D12—61no—
663D12—61no—
664D12—61no—
665D12—121no—
666D12—121no—
667D12C2×#6712yes—
668C4×D3—42no—
669C4×D3—61no—
670C4×D3—61no—
671C4×D3—61no—
672C4×D3—61no—
673C4×D3—121no—
674C4×D3—121no—
675C4×D3—241no—
676Dic6—21no—
677Dic6—21no—
678C3×C8—32no—
679C3×C8—61no—
680C3×C8—61no—
681C3×C8—61no—
682C3⋊C8—21no—
683C3⋊C8—21no—
684C3⋊C8—21no—
685C3⋊C8C2×#6712yes—
686C2×C32—42no—
687C2×C32—41no—
688C2×C32D4211yescharacteristic
689C2×C32C2×#13511yescharacteristic
690C2×C32#57611yescharacteristic
691C3⋊D3—22no—
692C3⋊D3—81no—
693C3×D3—42no—
694C3×D3—81no—
695C24—181no—
696C24—181no—
697#41—22no—
698#41—41no—
699#41—62no—
700#41—121no—
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—182no—
713C2×D4—182no—
714C2×D4—181no—
715C2×D4—361no—
716C2×D4—361no—
717C2×D4C2×D3211yescharacteristic
718C22×C4—21no—
719C22×C4—61no—
720C22×C4—91no—
721C22×C4—181no—
722C22×C4—181no—
723C22×C4C2×D3211yescharacteristic
724Q16—62no—
725SD16—62no—
726SD16—62no—
727SD16—121no—
728SD16—361no—
729D8—34no—
730D8—62no—
731D8—182no—
732D8—182no—
733C2×C8—31no—
734C2×C8—31no—
735C2×C8—31no—
736C2×C8—31no—
737C2×C8—62no—
738C2×C8—182no—
739C4⋊C4—31no—
740C4⋊C4—91no—
741C4⋊C4—91no—
742C4⋊C4—181no—
743C4⋊C4—181no—
744C22⋊C4—61no—
745C22⋊C4—91no—
746C22⋊C4—91no—
747C22⋊C4—181no—
748C22⋊C4—181no—
749C22⋊C4—181no—
750C22⋊C4—181no—
751C22⋊C4—181no—
752C22⋊C4—181no—
753C22⋊C4—181no—
754C22⋊C4—181no—
755C22⋊C4—181no—
756C42—91no—
757C22×C3—24no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—22no—
764C22×C3—22no—
765C22×C3—21no—
766C22×C3—21no—
767C22×C3—41no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3—42no—
771C22×C3—42no—
772C22×C3—41no—
773C22×C3—41no—
774C22×C3—41no—
775C22×C3—41no—
776C22×C3—62no—
777C22×C3—121no—
778C22×C3—121no—
779C22×C3—121no—
780C22×C3—121no—
781C22×C3—121no—
782C22×C3C2×D3×D411yescharacteristic
783C22×C3C2×D3×D411yescharacteristic
784C2×D3—22no—
785C2×D3—32no—
786C2×D3—32no—
787C2×D3—41no—
788C2×D3—41no—
789C2×D3—41no—
790C2×D3—41no—
791C2×D3—41no—
792C2×D3—62no—
793C2×D3—61no—
794C2×D3—61no—
795C2×D3—61no—
796C2×D3—61no—
797C2×D3—121no—
798C2×D3—121no—
799C2×D3—122no—
800C2×D3—122no—
801C2×D3—122no—
802C2×D3—121no—
803C2×D3—121no—
804C2×D3—121no—
805C2×D3—121no—
806C2×D3—121no—
807C2×D3—121no—
808C2×D3—244no—
809C2×D3—244no—
810C2×D3—244no—
811C2×D3—244no—
812C2×D3—248no—
813C3×C4—21no—
814C3×C4—21no—
815C3×C4—21no—
816C3×C4—21no—
817C3×C4—41no—
818C3×C4—42no—
819C3×C4—41no—
820C3×C4—41no—
821C3×C4—121no—
822C3×C4—121no—
823C3×C4C2×D3×D411yescharacteristic
824C3×C4#100411yescharacteristic
825C3×C4#100411yescharacteristic
826C3×C4C22×#6711yescharacteristic
827Dic3—41no—
828Dic3—41no—
829Dic3—61no—
830Dic3—61no—
831Dic3—61no—
832Dic3—61no—
833Dic3—61no—
834Dic3—61no—
835Dic3—121no—
836Dic3—121no—
837Dic3—121no—
838Dic3—122no—
839Dic3—121no—
840Dic3—121no—
841C32#328011yescharacteristic, complemented, Sylow
842C23—21no—
843C23—61no—
844C23—61no—
845C23—91no—
846C23—181no—
847C23—362no—
848C23—362no—
849C23—362no—
850C23—362no—
851C23—721no—
852C23—721no—
853C23#381111yescharacteristic
854Q8—21no—
855Q8—21no—
856Q8—61no—
857Q8—61no—
858D4—21no—
859D4—32no—
860D4—42no—
861D4—61no—
862D4—61no—
863D4—61no—
864D4—122no—
865D4—182no—
866D4—181no—
867D4—181no—
868D4—241no—
869D4—362no—
870D4—362no—
871D4—721no—
872D4D3×#6712yes—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—42no—
877C2×C4—61no—
878C2×C4—61no—
879C2×C4—91no—
880C2×C4—91no—
881C2×C4—91no—
882C2×C4—122no—
883C2×C4—181no—
884C2×C4—181no—
885C2×C4—181no—
886C2×C4—721no—
887C2×C4—721no—
888C2×C4#381111yescharacteristic
889C2×C4C22×D3211yescharacteristic
890C8—32no—
891C8—61no—
892C8—61no—
893C8—61no—
894C2×C3—21no—
895C2×C3—21no—
896C2×C3—21no—
897C2×C3—44no—
898C2×C3—42no—
899C2×C3—41no—
900C2×C3—42no—
901C2×C3—41no—
902C2×C3—81no—
903C2×C3—122no—
904C2×C3—241no—
905C2×C3#559011yescharacteristic
906C2×C3D3×#13511yescharacteristic
907C2×C3D3×#13511yescharacteristic
908C2×C3#576911yescharacteristic
909C2×C3#577411yescharacteristic
910C2×C3D4×#6711yescharacteristic
911D3—42no—
912D3—62no—
913D3—62no—
914D3—81no—
915D3—122no—
916D3—242no—
917D3—241no—
918D3—241no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—22no—
923C22—41no—
924C22—41no—
925C22—62no—
926C22—92no—
927C22—121no—
928C22—121no—
929C22—121no—
930C22—121no—
931C22—121no—
932C22—181no—
933C22—181no—
934C22—361no—
935C22—361no—
936C22—361no—
937C22—724no—
938C22—724no—
939C22C2×#381111yescharacteristic
940C4—21no—
941C4—41no—
942C4—121no—
943C4—121no—
944C4—181no—
945C4—181no—
946C4—181no—
947C4—361no—
948C4C2×D3×#6711yescharacteristic
949C4#6433011yescharacteristic
950C3—21no—
951C3#8010111yescharacteristic, complemented
952C3#8391811yescharacteristic, complemented
953C2—41no—
954C2—42no—
955C2—122no—
956C2—182no—
957C2—241no—
958C2—721no—
959C2#1059545911yescharacteristic
960C2#1059546111yescharacteristic
961C2#1059552611yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3280
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×#63926C2semidirect
4. #10595070C2semidirect
5. C3×#5238C2semidirect
6. #10591652C2semidirect
7. #10591610C2semidirect
8. #10591601C2semidirect
9. #10591570C2semidirect
10. #10591476C2semidirect
11. #10591467C2semidirect
12. #10591435C2semidirect
13. #10591164C2semidirect
14. #10591163C2semidirect
15. #10591148C2semidirect
18. C2×C32×#41C22semidirect
20. C2×C3×#235C22semidirect
22. #64156C22semidirect
26. D4×C3⋊Dic3C22semidirect
27. #64139C22semidirect
32. C2×C3×#216C22semidirect
33. C2×C3×#215C22semidirect
34. C2×C3×#215C22semidirect
35. C2×C3×#214C22semidirect
38. C3×#930C22semidirect
39. C22×C3×C3⋊C8C22semidirect
45. #63898C22semidirect
47. #63863C22semidirect
48. C2×#3717C22semidirect
52. C3×#835C22semidirect
53. C3×#832C22semidirect
54. C3×#830C22semidirect
55. #63575C22semidirect
56. #63572C22semidirect
57. #63566C22semidirect
58. #63564C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
62. #63553C22semidirect
68. C2×#950D3semidirect
74. #5238D3semidirect
139. C3×#213D4semidirect
159. C2×C3×#41C2×D3semidirect
160. C2×C3×#41C2×D3semidirect
166. C2×#235C2×D3semidirect
185. C2×#216C2×D3semidirect
187. C2×#215C2×D3semidirect
188. C2×#215C2×D3semidirect
204. C2×#214C2×D3semidirect
212. #930C2×D3semidirect
224. C22×C3⋊C8C2×D3semidirect
240. #835C2×D3semidirect
243. #832C2×D3semidirect
244. #830C2×D3semidirect
429. #213#67semidirect
489. C2×C3⋊D3#135semidirect
508. C2×#41D32semidirect
841. C32#3280semidirect
951. C3#80101semidirect
952. C3#83918semidirect

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×#639262
#105950702
C3×#52382
#105916522
#105916102
#105916012
#105915702
#105914762
#105914672
#105914352
#105911642
#105911632
#105911482
#839183
#801013