Finite Group Databasebeta

← #11884281

Subgroups — #11884281

Order 1152.

1167 conjugacy classes of subgroups.

The subgroup lattice has 935 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#10594890C211yesmaximal, characteristic, complemented
5C3×#5239C211yesmaximal, characteristic, complemented
6#10591656C211yesmaximal, characteristic, complemented
7#10591629C211yesmaximal, characteristic, complemented
8#10591600C211yesmaximal, characteristic, complemented
9#10591570C211yesmaximal, characteristic, complemented
10#10591497C211yesmaximal, characteristic, complemented
11#10591467C211yesmaximal, characteristic, complemented
12#10591436C211yesmaximal, characteristic, complemented
13#10591177C211yesmaximal, characteristic, complemented
14#10591163C211yesmaximal, characteristic, complemented
15#10591157C211yesmaximal, characteristic, complemented
16#83921—31nomaximal
17#80264—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×#216C2211yescharacteristic, complemented
34C2×C3×#215C2211yescharacteristic, complemented
35C2×C3×#214C2211yescharacteristic
36C2×C3×#214C2211yescharacteristic
37C2×C3×#213C2211yescharacteristic
38C3×#924C2211yescharacteristic, complemented
39C22×C3×C3⋊C8C2211yescharacteristic, complemented
40#63971—21no—
41#63969—21no—
42#63937—24no—
43#63898C2211yescharacteristic, complemented
44D3×Dic3⋊C4—21no—
45#63873C2211yescharacteristic, complemented
46#63871C2211yescharacteristic
47#63850—21no—
48C2×#3717C2211yescharacteristic
49C2×#3717C2211yescharacteristic
50C2×#3714C2211yescharacteristic
51C2×#3712C2211yescharacteristic
52C3×#835C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic
54C3×#830C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63563C2211yescharacteristic, complemented
61#63557C2211yescharacteristic
62#63555C2211yescharacteristic, complemented
63C2×C3×#135—31no—
64#5829—31no—
65#5829—31no—
66#5829—61no—
67#5824—31no—
68C2×#950D311yescharacteristic, complemented
69C2×#914—31no—
70C2×#911—31no—
71#5631—31no—
72C3×#452—31no—
73#5239D311yescharacteristic, complemented
74#5238—31no—
75#5190—31no—
76#5190—31no—
77#5189—31no—
78#5187—31no—
79#5173—31no—
80#5169—31no—
81#5165—31no—
82#5162—31no—
83#5162—31no—
84#5152—31no—
85#5114—31no—
86#5111—31no—
87#5048—31no—
88#4819—31no—
89#4816—31no—
90#4785—31no—
91#4776—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—
111C3×#235—22no—
112C3×#235—41no—
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3—21no—
115C2×C3×Dic6C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#626—21no—
118C2×D3×Dic3—21no—
119C2×D3×Dic3—21no—
120#3796—22no—
121#3796—41no—
122#3757—21no—
123#3757D411yescharacteristic
124#3752—21no—
125#3752—21no—
126#3752—21no—
127#3752—21no—
128#3752D411yescharacteristic
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130#3750—21no—
131#3750D411yescharacteristic
132C4×C3⋊Dic3C2311yescharacteristic
133C3×#217—21no—
134C3×#216—22no—
135C3×#216—41no—
136C3×#215—22no—
137C3×#214—22no—
138C3×#214—22no—
139C3×#213D414yescomplemented
140C3×C4⋊Dic3C2311yescharacteristic
141C3×Dic3⋊C4—21no—
142C2×C3×C3⋊C8—22no—
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147#3724—21no—
148#3724—21no—
149Dic3⋊Dic3—21no—
150#3722—21no—
151(C2×D3)⋊Dic3—21no—
152#3717—22no—
153#3717—41no—
154#3714—22no—
155#3712—22no—
156#3267—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×Q16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×D8—31no—
174C22×C3×C8—31no—
175C3×C22⋊Q8—31no—
176#950—24no—
177#947—31no—
178#947—31no—
179#947—61no—
180#946—31no—
181#946—31no—
182#946—31no—
183#946—61no—
184#944—31no—
185#944—31no—
186C2×#216C2×D311yescharacteristic, complemented
187C2×#216C2×D311yescharacteristic, complemented
188C2×#215—31no—
189C2×#215—31no—
190C2×#215C2×D311yescharacteristic, complemented
191#939—61no—
192#939—61no—
193#939—61no—
194#939—62no—
195#937—61no—
196#937—61no—
197#937—62no—
198#935—61no—
199D4×Dic3—31no—
200D4×Dic3—31no—
201D4×Dic3—31no—
202D4×Dic3—61no—
203C2×#214C2×D311yescharacteristic
204C2×#214C2×D311yescharacteristic
205C2×#213—31no—
206C2×#213C2×D311yescharacteristic
207#930—31no—
208#930—31no—
209#930—61no—
210#929—61no—
211#929—61no—
212#929—61no—
213#929—62no—
214C4×#67—31no—
215C4×#67—31no—
216C4×#67—61no—
217C2×(C2×D3)⋊C4—61no—
218C2×(C2×D3)⋊C4—61no—
219C2×(C2×D3)⋊C4—62no—
220#924C2×D311yescharacteristic, complemented
221C2×Dic3⋊C4—61no—
222C22×C3⋊C8C2×D311yescharacteristic, complemented
223#914—64no—
224#911—64no—
225C2×D24—31no—
226C2×#204—31no—
227C2×#204—31no—
228C2×ΓL(1,𝔽25)—31no—
229C2×ΓL(1,𝔽25)—31no—
230#897—31no—
231#894—61no—
232#893—31no—
233D3×C4⋊C4—61no—
234#884—61no—
235#883—61no—
236C3×#103—31no—
237C3×#102—31no—
238C3×C22⋊C8—31no—
239#835—31no—
240#835—31no—
241#835C2×D311yescharacteristic, complemented
242#832—31no—
243#832C2×D311yescharacteristic
244#830C2×D311yescharacteristic, complemented
245#821—31no—
246#821—31no—
247(C2×D3)⋊C8—31no—
248(C2×D3)⋊C8—31no—
249#817—31no—
250#816—31no—
251#816—31no—
252#815—31no—
253#815—31no—
254Dic3⋊C8—31no—
255Dic3⋊C8—31no—
256#809—31no—
257#808—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—
266C32×Q8—21no—
267C32×Q8—21no—
268C32×D4—21no—
269C32×D4—42no—
270C32×D4C2×D412yes—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—42no—
275C2×C32×C4C2×D411yescharacteristic
276C2×C32×C4C2411yescharacteristic
277#638—41no—
278#638—42no—
279#638—81no—
280C2×C3⋊Dic3—21no—
281C2×C3⋊Dic3—81no—
282C2×C3⋊Dic3C2×D411yescharacteristic
283C2×C3⋊Dic3C2×D411yescharacteristic
284C2×C3⋊Dic3C2×D411yescharacteristic
285C4⋊(C3⋊D3)—21no—
286C4⋊(C3⋊D3)—21no—
287C4×C3⋊D3—21no—
288C4×C3⋊D3—21no—
289C3×#67—42no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C3×D12—21no—
294C3×D12C2×D412yes—
295C3×C4×D3—42no—
296C3×Dic6—21no—
297C3×Dic6—21no—
298C3×Dic6—21no—
299C3×Dic6—21no—
300#626—42no—
301D3×Dic3—42no—
302D3×Dic3—42no—
303C3×C3⋊C8—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8—21no—
306C3×C3⋊C8C2×D412yes—
307C2×AGL(1,ℤ/8)—91no—
308C2×#135—31no—
309#547—91no—
310#546—91no—
311#497—91no—
312#470—91no—
313#465—91no—
314#463—91no—
315#461—91no—
316#452—31no—
317#452—91no—
318#450—91no—
319#449—91no—
320#442—91no—
321#435—91no—
322C23×D3—61no—
323C23×D3—61no—
324C23×D3—62no—
325C3×#41—22no—
326C3×#41—22no—
327C3×#41—42no—
328C3×#41—41no—
329C3×#41—41no—
330C3×#41—42no—
331C3×#41—62no—
332C3×#41—121no—
333C2×C3×Q8—21no—
334C2×C3×Q8—31no—
335C2×C3×Q8—31no—
336C2×C3×Q8C22×D311yescharacteristic
337C2×C3×Q8C22×D311yescharacteristic
338C2×C3×D4—22no—
339C2×C3×D4—21no—
340C2×C3×D4—21no—
341C2×C3×D4—21no—
342C2×C3×D4—31no—
343C2×C3×D4—61no—
344C2×C3×D4C22×D311yescharacteristic
345C2×C3×D4C22×D311yescharacteristic
346C22×C3×C4—22no—
347C22×C3×C4—21no—
348C22×C3×C4—21no—
349C22×C3×C4—21no—
350C22×C3×C4—61no—
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C2×#67—21no—
354C2×#67—31no—
355C2×#67—31no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67—62no—
361C2×#67—62no—
362C2×#67—61no—
363C2×#67—61no—
364C22×Dic3—61no—
365C22×Dic3—61no—
366C22×Dic3—61no—
367C22×Dic3—61no—
368C22×Dic3—62no—
369#239—62no—
370#239—121no—
371#237—62no—
372#237—121no—
373D3×D4—62no—
374D3×D4—62no—
375D3×D4—122no—
376D3×D4—121no—
377D3×D4—121no—
378D3×D4—122no—
379#235—22no—
380#235—41no—
381C2×D12—31no—
382C2×D12—31no—
383C2×D12—61no—
384C2×D12—61no—
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×Dic6C22×D311yescharacteristic
393C2×Dic6C22×D311yescharacteristic
394C3×Q16—62no—
395C3×Q16—121no—
396C3×SD16—62no—
397C3×SD16—62no—
398C3×SD16—62no—
399C3×D8—34no—
400C2×C3×C8—31no—
401C2×C3×C8—31no—
402C2×C3×C8—31no—
403C2×C3×C8—31no—
404C2×C3×C8—62no—
405C3×C4⋊C4—31no—
406C3×C4⋊C4—61no—
407C3×C22⋊C4—61no—
408#217—21no—
409#217—31no—
410#217—31no—
411#217—61no—
412#217—61no—
413#217—61no—
414#217—61no—
415#217—62no—
416#216—22no—
417#216—41no—
418#215—22no—
419#215—62no—
420#215—121no—
421#214—22no—
422#214—22no—
423#213—62no—
424#213#6714yescomplemented
425(C2×D3)⋊C4—31no—
426(C2×D3)⋊C4—31no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
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—62no—
438(C2×D3)⋊C4—62no—
439(C2×D3)⋊C4—62no—
440(C2×D3)⋊C4—62no—
441(C2×D3)⋊C4—61no—
442(C2×D3)⋊C4—61no—
443C4⋊Dic3—31no—
444C4⋊Dic3—31no—
445C4⋊Dic3—61no—
446C4⋊Dic3—61no—
447C4⋊Dic3C22×D311yescharacteristic
448Dic3⋊C4—21no—
449Dic3⋊C4—31no—
450Dic3⋊C4—31no—
451Dic3⋊C4—61no—
452Dic3⋊C4—61no—
453Dic3⋊C4—61no—
454Dic3⋊C4—61no—
455Dic3⋊C4—61no—
456Dic3⋊C4—61no—
457Dic3⋊C4—61no—
458Dic3⋊C4—61no—
459Dic3⋊C4—62no—
460C4×Dic3—31no—
461C4×Dic3—31no—
462C4×Dic3—61no—
463C2×C3⋊C8—22no—
464C2×C3⋊C8C22×D311yescharacteristic
465C2×C3⋊C8C22×D311yescharacteristic
466C2×C3⋊C8C22×D311yescharacteristic
467C2×C3⋊C8C22×D311yescharacteristic
468D24—62no—
469#204—62no—
470#204—121no—
471ΓL(1,𝔽25)—62no—
472ΓL(1,𝔽25)—62no—
473C22×C32—22no—
474C22×C32—21no—
475C22×C32—21no—
476C22×C32—21no—
477C22×C32—41no—
478C22×C32—41no—
479C22×C32C22×D411yescharacteristic
480C2×C3⋊D3—21no—
481C2×C3⋊D3—21no—
482C2×C3⋊D3—21no—
483C2×C3⋊D3—41no—
484C2×C3⋊D3—41no—
485C2×C3⋊D3—41no—
486C2×C3⋊D3—84no—
487C2×C3×D3—22no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C32×C4—21no—
491C32×C4—41no—
492C32×C4C22×D411yescharacteristic
493C32×C4H(5,𝔽2)11yescharacteristic
494C3⋊Dic3—21no—
495C3⋊Dic3—21no—
496C3⋊Dic3—21no—
497C3⋊Dic3—41no—
498C3×Dic3—41no—
499C3×Dic3—41no—
500C3×Dic3—41no—
501C2×#41—31no—
502C2×#41—91no—
503C2×#41D3211yescharacteristic
504C22×D4—91no—
505AGL(1,ℤ/8)—184no—
506#135—64no—
507C2×Q16—31no—
508C2×Q16—31no—
509C2×SD16—31no—
510C2×SD16—31no—
511C2×SD16—31no—
512C2×SD16—91no—
513C2×SD16—91no—
514C2×D8—31no—
515C2×D8—91no—
516C2×M16—91no—
517C22×C8—31no—
518C4⋊Q8—91no—
519#124—91no—
520#123—181no—
521#123—181no—
522#123—181no—
523C22⋊Q8—31no—
524C22⋊Q8—91no—
525C22⋊Q8—91no—
526#121—91no—
527#121—181no—
528#121—181no—
529#120—181no—
530C4×D4—91no—
531C4×D4—91no—
532C4×D4—91no—
533C2×C4⋊C4—181no—
534C2×C22⋊C4—181no—
535#106—91no—
536C4⋊C8—91no—
537#103—31no—
538#103—91no—
539#103—91no—
540#102—31no—
541#102—91no—
542#102—91no—
543C22⋊C8—31no—
544C22⋊C8—91no—
545#97—91no—
546C23×C3—22no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—61no—
551C23×C3D3×D411yescharacteristic
552C23×C3D3×D411yescharacteristic
553C22×D3—21no—
554C22×D3—31no—
555C22×D3—31no—
556C22×D3—61no—
557C22×D3—62no—
558C22×D3—61no—
559C22×D3—61no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—124no—
563C22×D3—122no—
564C22×D3—122no—
565C22×D3—124no—
566C22×D3—241no—
567C22×D3—241no—
568C22×D3—242no—
569C3×Q8—21no—
570C3×Q8—21no—
571C3×Q8—21no—
572C3×Q8—21no—
573C3×Q8—41no—
574C3×Q8—41no—
575C3×Q8—61no—
576C3×Q8—61no—
577C3×Q8—61no—
578C3×Q8—61no—
579C3×D4—22no—
580C3×D4—21no—
581C3×D4—21no—
582C3×D4—22no—
583C3×D4—32no—
584C3×D4—42no—
585C3×D4—42no—
586C3×D4—44no—
587C3×D4—61no—
588C3×D4—122no—
589C3×D4D3×D412yes—
590C3×D4C2×#6712yes—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—22no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—42no—
603C2×C3×C4—42no—
604C2×C3×C4—44no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—122no—
609C2×C3×C4D3×D411yescharacteristic
610C2×C3×C4D3×D411yescharacteristic
611C2×C3×C4C23×D311yescharacteristic
612C2×C3×C4C23×D311yescharacteristic
613#67—42no—
614#67—122no—
615#67—121no—
616#67—121no—
617#67—122no—
618#67—122no—
619#67—122no—
620#67—124no—
621#67—241no—
622#67—241no—
623#67—242no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—31no—
628C2×Dic3—31no—
629C2×Dic3—31no—
630C2×Dic3—31no—
631C2×Dic3—31no—
632C2×Dic3—31no—
633C2×Dic3—61no—
634C2×Dic3—61no—
635C2×Dic3—61no—
636C2×Dic3—62no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—122no—
640C2×Dic3—122no—
641C2×Dic3—241no—
642C2×Dic3—241no—
643C2×Dic3—242no—
644D12—21no—
645D12—61no—
646D12—61no—
647D12—61no—
648D12—61no—
649D12—121no—
650D12—121no—
651D12—122no—
652D12C2×#6712yes—
653C4×D3—42no—
654C4×D3—61no—
655C4×D3—61no—
656C4×D3—61no—
657C4×D3—61no—
658C4×D3—121no—
659C4×D3—121no—
660C4×D3—122no—
661C4×D3—122no—
662Dic6—21no—
663Dic6—21no—
664Dic6—21no—
665Dic6—21no—
666C3×C8—32no—
667C3×C8—61no—
668C3×C8—61no—
669C3×C8—61no—
670C3⋊C8—21no—
671C3⋊C8—21no—
672C3⋊C8—21no—
673C3⋊C8C2×#6712yes—
674C2×C32—42no—
675C2×C32—41no—
676C2×C32D4211yescharacteristic
677C2×C32#57511yescharacteristic
678C2×C32#57711yescharacteristic
679C3⋊D3—41no—
680C3⋊D3—81no—
681C3×D3—42no—
682C24—181no—
683#41—22no—
684#41—41no—
685#41—62no—
686#41—121no—
687#41—182no—
688#41—361no—
689C2×Q8—31no—
690C2×Q8—31no—
691C2×Q8C2×D3211yescharacteristic
692C2×D4—21no—
693C2×D4—31no—
694C2×D4—61no—
695C2×D4—91no—
696C2×D4—91no—
697C2×D4—181no—
698C2×D4—181no—
699C2×D4—182no—
700C2×D4—181no—
701C2×D4—361no—
702C2×D4C2×D3211yescharacteristic
703C22×C4—21no—
704C22×C4—61no—
705C22×C4—91no—
706C22×C4—181no—
707C22×C4—181no—
708C22×C4—181no—
709C22×C4C2×D3211yescharacteristic
710Q16—62no—
711Q16—121no—
712SD16—62no—
713SD16—62no—
714SD16—62no—
715SD16—182no—
716SD16—361no—
717D8—34no—
718D8—182no—
719M16—182no—
720C2×C8—31no—
721C2×C8—31no—
722C2×C8—31no—
723C2×C8—31no—
724C2×C8—62no—
725C4⋊C4—31no—
726C4⋊C4—61no—
727C4⋊C4—91no—
728C4⋊C4—91no—
729C4⋊C4—181no—
730C4⋊C4—181no—
731C4⋊C4—181no—
732C4⋊C4—181no—
733C22⋊C4—61no—
734C22⋊C4—91no—
735C22⋊C4—91no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C22⋊C4—181no—
739C22⋊C4—181no—
740C22⋊C4—181no—
741C22⋊C4—181no—
742C22⋊C4—181no—
743C42—91no—
744C22×C3—24no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—22no—
751C22×C3—22no—
752C22×C3—21no—
753C22×C3—21no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—42no—
758C22×C3—42no—
759C22×C3—41no—
760C22×C3—41no—
761C22×C3—41no—
762C22×C3—41no—
763C22×C3—62no—
764C22×C3—121no—
765C22×C3—121no—
766C22×C3C2×D3×D411yescharacteristic
767C22×C3C2×D3×D411yescharacteristic
768C2×D3—22no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—62no—
772C2×D3—61no—
773C2×D3—61no—
774C2×D3—61no—
775C2×D3—61no—
776C2×D3—61no—
777C2×D3—61no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—122no—
781C2×D3—122no—
782C2×D3—122no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—121no—
788C2×D3—121no—
789C2×D3—248no—
790C2×D3—244no—
791C2×D3—244no—
792C3×C4—21no—
793C3×C4—21no—
794C3×C4—21no—
795C3×C4—21no—
796C3×C4—41no—
797C3×C4—42no—
798C3×C4—41no—
799C3×C4—41no—
800C3×C4—121no—
801C3×C4—121no—
802C3×C4—121no—
803C3×C4C2×D3×D411yescharacteristic
804C3×C4#100411yescharacteristic
805C3×C4#100411yescharacteristic
806C3×C4C22×#6711yescharacteristic
807Dic3—41no—
808Dic3—41no—
809Dic3—41no—
810Dic3—61no—
811Dic3—61no—
812Dic3—61no—
813Dic3—61no—
814Dic3—61no—
815Dic3—61no—
816Dic3—121no—
817Dic3—121no—
818Dic3—121no—
819Dic3—122no—
820Dic3—121no—
821Dic3—121no—
822C32#326711yescharacteristic, complemented, Sylow
823C23—21no—
824C23—61no—
825C23—91no—
826C23—181no—
827C23—362no—
828C23—362no—
829C23—721no—
830C23#381111yescharacteristic
831Q8—21no—
832Q8—21no—
833Q8—61no—
834Q8—61no—
835Q8—61no—
836Q8—61no—
837D4—21no—
838D4—32no—
839D4—42no—
840D4—61no—
841D4—122no—
842D4—181no—
843D4—181no—
844D4—362no—
845D4—361no—
846D4—362no—
847D4—721no—
848D4D3×#6712yes—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—42no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—91no—
857C2×C4—91no—
858C2×C4—91no—
859C2×C4—122no—
860C2×C4—181no—
861C2×C4—181no—
862C2×C4—181no—
863C2×C4—362no—
864C2×C4—362no—
865C2×C4—721no—
866C2×C4#381111yescharacteristic
867C2×C4C22×D3211yescharacteristic
868C8—32no—
869C8—61no—
870C8—61no—
871C8—61no—
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—44no—
876C2×C3—42no—
877C2×C3—41no—
878C2×C3—42no—
879C2×C3—41no—
880C2×C3—81no—
881C2×C3—122no—
882C2×C3#559011yescharacteristic
883C2×C3#576811yescharacteristic
884C2×C3#576811yescharacteristic
885C2×C3#577011yescharacteristic
886C2×C3#577811yescharacteristic
887C2×C3D4×#6711yescharacteristic
888D3—42no—
889D3—122no—
890D3—121no—
891D3—121no—
892D3—242no—
893D3—241no—
894D3—241no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—22no—
899C22—41no—
900C22—41no—
901C22—62no—
902C22—121no—
903C22—121no—
904C22—181no—
905C22—181no—
906C22—181no—
907C22—361no—
908C22—361no—
909C22—361no—
910C22—724no—
911C22C2×#381111yescharacteristic
912C4—21no—
913C4—41no—
914C4—121no—
915C4—121no—
916C4—121no—
917C4—181no—
918C4—181no—
919C4—181no—
920C4—361no—
921C4C2×D3×#6711yescharacteristic
922C4#6433011yescharacteristic
923C3—21no—
924C3#8026411yescharacteristic, complemented
925C3#8392111yescharacteristic, complemented
926C2—41no—
927C2—42no—
928C2—122no—
929C2—361no—
930C2—721no—
931C2#1059546011yescharacteristic
932C2#1059547311yescharacteristic
933C2#1059552611yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3267
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. #10594890C2semidirect
5. C3×#5239C2semidirect
6. #10591656C2semidirect
7. #10591629C2semidirect
8. #10591600C2semidirect
9. #10591570C2semidirect
10. #10591497C2semidirect
11. #10591467C2semidirect
12. #10591436C2semidirect
13. #10591177C2semidirect
14. #10591163C2semidirect
15. #10591157C2semidirect
20. C2×C3×#235C22semidirect
32. C2×C3×#216C22semidirect
33. C2×C3×#216C22semidirect
34. C2×C3×#215C22semidirect
38. C3×#924C22semidirect
39. C22×C3×C3⋊C8C22semidirect
43. #63898C22semidirect
45. #63873C22semidirect
52. C3×#835C22semidirect
54. C3×#830C22semidirect
55. #63573C22semidirect
56. #63572C22semidirect
57. #63566C22semidirect
58. #63566C22semidirect
60. #63563C22semidirect
62. #63555C22semidirect
68. C2×#950D3semidirect
73. #5239D3semidirect
139. C3×#213D4semidirect
166. C2×#235C2×D3semidirect
186. C2×#216C2×D3semidirect
187. C2×#216C2×D3semidirect
190. C2×#215C2×D3semidirect
220. #924C2×D3semidirect
222. C22×C3⋊C8C2×D3semidirect
241. #835C2×D3semidirect
244. #830C2×D3semidirect
424. #213#67semidirect
822. C32#3267semidirect
924. C3#80264semidirect
925. C3#83921semidirect

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
#105948902
C3×#52392
#105916562
#105916292
#105916002
#105915702
#105914972
#105914672
#105914362
#105911772
#105911632
#105911572
#839213
#802643