Finite Group Databasebeta

← #11887397

Subgroups — #11887397

Order 1152.

941 conjugacy classes of subgroups.

The subgroup lattice has 833 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595254C211yesmaximal, characteristic, complemented
2#10594583C211yesmaximal, characteristic, complemented
3C3⋊D3×#102C211yesmaximal, characteristic, complemented
4C3×#4772C211yesmaximal, characteristic, complemented
5C3×#4756C211yesmaximal, characteristic, complemented
6#10591456C211yesmaximal, characteristic, complemented
7#10591450C211yesmaximal, characteristic, complemented
8#10591411C211yesmaximal, characteristic, complemented
9#10590872C211yesmaximal, characteristic, complemented
10#10590841C211yesmaximal, characteristic, complemented
11#10590826C211yesmaximal, characteristic, complemented
12C8×#626C211yesmaximal, characteristic, complemented
13#10590534C211yesmaximal, characteristic, complemented
14#10590528C211yesmaximal, characteristic, complemented
15#10590424C211yesmaximal, characteristic, complemented
16#79609—31nomaximal
17#78846—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C8×C3⋊D3C2211yescharacteristic
21C4⋊C4×C3⋊D3C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic, complemented
25C3×#893C2211yescharacteristic, complemented
26C3×#892C2211yescharacteristic, complemented
27#63981—21no—
28#63978—21no—
29#63966—21no—
30C2×#3722—21no—
31#63916C2211yescharacteristic
32#63912—21no—
33#63909C2211yescharacteristic
34#63908C2211yescharacteristic, complemented
35#63905—21no—
36C4×#626—21no—
37C4×#626C2211yescharacteristic
38#63871C2211yescharacteristic
39#63869C2211yescharacteristic, complemented
40#63864C2211yescharacteristic
41#63859—21no—
42C2×#3715C2211yescharacteristic, complemented
43C2×#3714C2211yescharacteristic
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63648C2211yescharacteristic
47#63636C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic, complemented
50C3×#816C2211yescharacteristic, complemented
51C3×C8×Dic3C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#807C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63574C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63557C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61#5829—31no—
62#5558—31no—
63#5554—31no—
64#5530—31no—
65C3×C4×D8—31no—
66C3×#416—31no—
67#5238—31no—
68#5158—31no—
69#5156—31no—
70#5115—31no—
71C8×#67—31no—
72#5016—31no—
73#5009—31no—
74#5003—31no—
75#4885—31no—
76#4884—31no—
77#4819—31no—
78#4811—31no—
79#4807—31no—
80#4800—31no—
81#4778—31no—
82#4775—31no—
83#4773—31no—
84#4772D311yescharacteristic, complemented
85D3×#102—31no—
86D3×#102—31no—
87D3×#102—61no—
88#4766—31no—
89#4756D311yescharacteristic, complemented
90#4697—31no—
91C8×D12—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95D4×C3⋊D3—22no—
96D4×C3⋊D3—41no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C3×#237—22no—
104C3×#237—41no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#626—21no—
110C2×#626—21no—
111C2×#626D411yescharacteristic
112C2×#625—21no—
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C8×C3⋊D3—41no—
119C3×#217—21no—
120C3×#213—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4×Dic3—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×D3×C8—41no—
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3D411yescharacteristic
134#3722—21no—
135#3722—21no—
136#3722—21no—
137#3722—21no—
138#3722D411yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142#3715—41no—
143#3714—41no—
144#3297—91noSylow
145C2×C3×#41—31no—
146C2×#237C2×D311yescharacteristic
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×D3×D4—61no—
150C2×C3×D8—31no—
151C22×C3×C8—31no—
152C3×C4×D4—31no—
153C3×C4×D4—31no—
154C3×#117—31no—
155#947—31no—
156#946—31no—
157C2×#215—31no—
158#939—61no—
159#938—31no—
160#938—31no—
161#937—61no—
162D4×Dic3C2×D311yescharacteristic
163C2×#214—31no—
164C2×#213—31no—
165C2×#213C2×D311yescharacteristic
166#930—31no—
167#930—31no—
168#930—61no—
169#929—61no—
170#929—61no—
171C4×#67—31no—
172C4×#67—61no—
173C2×(C2×D3)⋊C4—61no—
174C2×(C2×D3)⋊C4—61no—
175C2×D24—31no—
176C2×D3×C8—31no—
177C2×D3×C8—31no—
178C2×D3×C8—61no—
179C2×D3×C8C2×D311yescharacteristic, complemented
180#897—31no—
181#895—31no—
182#895—31no—
183#893C2×D311yescharacteristic, complemented
184#892C2×D311yescharacteristic, complemented
185D3×C4⋊C4—31no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4—61no—
188#890—31no—
189#886—61no—
190#884—61no—
191#884—61no—
192#883—61no—
193#882—61no—
194#879—61no—
195#876—61no—
196#875—31no—
197C4×D12—31no—
198C4×D12—61no—
199#870—31no—
200C3×#107—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#102—21no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102C2×D311yescharacteristic
207C3×#102C2×D311yescharacteristic
208C3×C4×C8—31no—
209#835—31no—
210#832—31no—
211#832—31no—
212#832—61no—
213#832C2×D311yescharacteristic
214#830—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—61no—
219#821C2×D311yescharacteristic, complemented
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223#818—31no—
224#816—31no—
225#816C2×D311yescharacteristic, complemented
226Dic3⋊C8—31no—
227C8×Dic3C2×D311yescharacteristic, complemented
228#810C2×D311yescharacteristic, complemented
229#809—31no—
230#809—31no—
231#809—31no—
232#809—61no—
233#808—31no—
234#808—31no—
235#807—31no—
236#807C2×D311yescharacteristic, complemented
237C4⋊(C3⋊C8)—31no—
238C23×C32—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3—42no—
241C22×C3⋊D3—42no—
242C22×C3⋊D3—81no—
243C22×C3⋊D3C2×D411yescharacteristic
244C22×C3×D3—21no—
245C22×C3×D3C2×D411yescharacteristic
246C32×D4—21no—
247C32×D4#4112yes—
248C2×C32×C4—21no—
249C2×C32×C4C2411yescharacteristic
250#638—42no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255C4×C3⋊D3—21no—
256C4×C3⋊D3—21no—
257C4×C3⋊D3—81no—
258C3×#67—42no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—42no—
263C2×C3×Dic3—81no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12—21no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—81no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274#626—22no—
275#626—42no—
276#626—81no—
277#625—81no—
278C32×C8—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—91no—
283#546—91no—
284#488—91no—
285#484—91no—
286#482—91no—
287#478—91no—
288#466—91no—
289#465—91no—
290#463—91no—
291#449—91no—
292#447—91no—
293C4×D8—31no—
294C8×D4—91no—
295#416—31no—
296C2×#102—91no—
297C23×D3—61no—
298C23×D3—61no—
299C23×D3—121no—
300C3×#41—62no—
301C3×#41—121no—
302C2×C3×Q8—31no—
303C2×C3×D4—21no—
304C2×C3×D4—31no—
305C2×C3×D4—61no—
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C22×D311yescharacteristic
308C22×C3×C4—31no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C2×#67—21no—
313C2×#67—31no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—121no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323#237—22no—
324#237—41no—
325D3×D4—64no—
326D3×D4—62no—
327D3×D4—62no—
328D3×D4—121no—
329D3×D4—121no—
330D3×D4—122no—
331C2×D12—31no—
332C2×D12—31no—
333C2×D12—31no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12—61no—
337C2×D12C22×D311yescharacteristic
338C2×C4×D3—21no—
339C2×C4×D3—31no—
340C2×C4×D3—31no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—121no—
345C2×C4×D3C22×D311yescharacteristic
346C2×Dic6C22×D311yescharacteristic
347C3×D8—62no—
348C2×C3×C8—21no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C2×C3×C8—121no—
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C22×D311yescharacteristic
354C3×C4⋊C4—21no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C42—31no—
363C3×C42—61no—
364#217—21no—
365#217—31no—
366#217—61no—
367#217—61no—
368#215—121no—
369#214—121no—
370#213—22no—
371#213—121no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3C22×D311yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395Dic3⋊C4—31no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—121no—
403C4×Dic3—21no—
404C4×Dic3C22×D311yescharacteristic
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410D24—121no—
411D3×C8—41no—
412D3×C8—121no—
413D3×C8—121no—
414D3×C8—122no—
415C22×C32—22no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32C22×D411yescharacteristic
419C2×C3⋊D3—21no—
420C2×C3⋊D3—21no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—84no—
425C2×C3⋊D3#13512yes—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C32×C4—41no—
433C32×C4C2×#4111yescharacteristic
434C32×C4H(5,𝔽2)11yescharacteristic
435C3⋊Dic3—21no—
436C3⋊Dic3—41no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C2×#41—31no—
444C22×D4—91no—
445C2×SD16—91no—
446C2×D8—31no—
447C2×D8—91no—
448C22×C8—31no—
449C22×C8—91no—
450#126—181no—
451#125—91no—
452#124—91no—
453#123—181no—
454#123—181no—
455C22⋊Q8—91no—
456#121—91no—
457#121—91no—
458#121—91no—
459#121—181no—
460#121—181no—
461#120—181no—
462C4×D4—31no—
463C4×D4—31no—
464C4×D4—91no—
465C4×D4—181no—
466#117—31no—
467C2×C4⋊C4—91no—
468C2×C22⋊C4—181no—
469#107—31no—
470#107—91no—
471#106—91no—
472C4⋊C8—91no—
473#103—31no—
474#103—31no—
475#103—91no—
476#102—31no—
477#102—31no—
478#102—91no—
479#102—91no—
480#102—91no—
481#102—91no—
482#102D3211yescharacteristic
483C22⋊C8—91no—
484C22⋊C8—91no—
485C4×C8—31no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—31no—
489C23×C3—41no—
490C23×C3—61no—
491C22×D3—21no—
492C22×D3—31no—
493C22×D3—31no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—61no—
497C22×D3—121no—
498C22×D3—122no—
499C22×D3—122no—
500C22×D3—122no—
501C22×D3—122no—
502C22×D3—124no—
503C22×D3—242no—
504C22×D3—241no—
505C22×D3—241no—
506C22×D3—242no—
507C22×D3D3×D411yescharacteristic
508C3×Q8—61no—
509C3×Q8—61no—
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—22no—
513C3×D4—41no—
514C3×D4—61no—
515C3×D4—61no—
516C3×D4—122no—
517C3×D4#23512yes—
518C3×D4#23512yes—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—41no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—122no—
532C2×C3×C4—241no—
533C2×C3×C4—241no—
534C2×C3×C4C23×D311yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536#67—42no—
537#67—62no—
538#67—122no—
539#67—122no—
540#67—122no—
541#67—124no—
542#67—241no—
543#67—241no—
544#67—241no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—31no—
549C2×Dic3—31no—
550C2×Dic3—42no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—81no—
555C2×Dic3—121no—
556C2×Dic3D3×D411yescharacteristic
557C2×Dic3D3×D411yescharacteristic
558C2×Dic3D3×D411yescharacteristic
559D12—21no—
560D12—21no—
561D12—62no—
562D12—62no—
563D12—61no—
564D12—61no—
565D12—61no—
566D12—61no—
567D12—121no—
568D12—122no—
569D12—241no—
570C4×D3—21no—
571C4×D3—21no—
572C4×D3—62no—
573C4×D3—62no—
574C4×D3—61no—
575C4×D3—61no—
576C4×D3—61no—
577C4×D3—61no—
578C4×D3—81no—
579C4×D3—241no—
580C4×D3—241no—
581C4×D3—242no—
582Dic6—21no—
583Dic6—21no—
584C3×C8—21no—
585C3×C8—21no—
586C3×C8—41no—
587C3×C8—61no—
588C3×C8—61no—
589C3⋊C8—21no—
590C3⋊C8—21no—
591C3⋊C8—61no—
592C3⋊C8—61no—
593C3⋊C8—121no—
594C2×C32—42no—
595C2×C32#54611yescharacteristic
596C2×C32C2×#13511yescharacteristic
597C2×C32#57611yescharacteristic
598C3⋊D3—22no—
599C3⋊D3—81no—
600C3×D3—41no—
601C3×D3—81no—
602C24—181no—
603#41—62no—
604#41—121no—
605C2×Q8—31no—
606C2×D4—31no—
607C2×D4—61no—
608C2×D4—91no—
609C2×D4—91no—
610C2×D4—181no—
611C2×D4—181no—
612C2×D4—181no—
613C2×D4—182no—
614C2×D4—181no—
615C2×D4—361no—
616C2×D4C2×D3211yescharacteristic
617C22×C4—31no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—91no—
622C22×C4—181no—
623SD16—361no—
624D8—62no—
625D8—361no—
626C2×C8—31no—
627C2×C8—31no—
628C2×C8—91no—
629C2×C8—121no—
630C2×C8—361no—
631C2×C8C2×D3211yescharacteristic
632C4⋊C4—31no—
633C4⋊C4—31no—
634C4⋊C4—91no—
635C4⋊C4—91no—
636C4⋊C4—181no—
637C4⋊C4—181no—
638C4⋊C4—181no—
639C4⋊C4—181no—
640C4⋊C4C2×D3211yescharacteristic
641C22⋊C4—61no—
642C22⋊C4—61no—
643C22⋊C4—61no—
644C22⋊C4—91no—
645C22⋊C4—91no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C22⋊C4—181no—
652C42—31no—
653C42—61no—
654C22×C3—22no—
655C22×C3—22no—
656C22×C3—21no—
657C22×C3—42no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—61no—
663C22×C3—61no—
664C22×C3—61no—
665C22×C3—81no—
666C22×C3—81no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3C2×D3×D411yescharacteristic
671C22×C3C2×D3×D411yescharacteristic
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—21no—
675C2×D3—32no—
676C2×D3—32no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—62no—
681C2×D3—62no—
682C2×D3—62no—
683C2×D3—61no—
684C2×D3—61no—
685C2×D3—61no—
686C2×D3—61no—
687C2×D3—122no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—121no—
691C2×D3—121no—
692C2×D3—121no—
693C2×D3—121no—
694C2×D3—241no—
695C2×D3—241no—
696C2×D3—244no—
697C2×D3—244no—
698C2×D3—248no—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—61no—
704C3×C4—61no—
705C3×C4—61no—
706C3×C4—81no—
707C3×C4—121no—
708C3×C4—121no—
709C3×C4—121no—
710C3×C4C2×#23511yescharacteristic
711C3×C4C2×#23511yescharacteristic
712C3×C4#100411yescharacteristic
713C3×C4#100911yescharacteristic
714Dic3—21no—
715Dic3—21no—
716Dic3—21no—
717Dic3—41no—
718Dic3—41no—
719Dic3—41no—
720Dic3—62no—
721Dic3—61no—
722Dic3—61no—
723Dic3—121no—
724Dic3—121no—
725Dic3—241no—
726C32#329711yescharacteristic, complemented, Sylow
727C23—21no—
728C23—31no—
729C23—61no—
730C23—91no—
731C23—181no—
732C23—362no—
733C23—362no—
734C23—721no—
735Q8—61no—
736Q8—61no—
737D4—21no—
738D4—61no—
739D4—61no—
740D4—122no—
741D4—182no—
742D4—181no—
743D4—181no—
744D4—362no—
745D4—362no—
746D4—721no—
747D4—721no—
748D4#379812yes—
749C2×C4—21no—
750C2×C4—31no—
751C2×C4—31no—
752C2×C4—31no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—91no—
759C2×C4—122no—
760C2×C4—181no—
761C2×C4—181no—
762C2×C4—181no—
763C2×C4—241no—
764C2×C4—241no—
765C2×C4—721no—
766C2×C4C22×D3211yescharacteristic
767C8—21no—
768C8—61no—
769C8—61no—
770C8—181no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—21no—
774C2×C3—42no—
775C2×C3—42no—
776C2×C3—82no—
777C2×C3—121no—
778C2×C3—241no—
779C2×C3#549011yescharacteristic
780C2×C3#555011yescharacteristic
781C2×C3#575711yescharacteristic
782C2×C3D3×#13511yescharacteristic
783C2×C3D3×#13511yescharacteristic
784C2×C3#576911yescharacteristic
785D3—41no—
786D3—64no—
787D3—62no—
788D3—62no—
789D3—81no—
790D3—242no—
791D3—241no—
792D3—241no—
793C22—22no—
794C22—41no—
795C22—41no—
796C22—61no—
797C22—61no—
798C22—61no—
799C22—92no—
800C22—121no—
801C22—121no—
802C22—121no—
803C22—181no—
804C22—181no—
805C22—361no—
806C22—361no—
807C22—361no—
808C22—724no—
809C22D32×D411yescharacteristic
810C4—41no—
811C4—61no—
812C4—61no—
813C4—61no—
814C4—121no—
815C4—121no—
816C4—121no—
817C4—181no—
818C4—361no—
819C4C2×#379811yescharacteristic
820C4#6431411yescharacteristic
821C3—21no—
822C3#7884611yescharacteristic, complemented
823C3#7960911yescharacteristic, complemented
824C2—42no—
825C2—121no—
826C2—182no—
827C2—241no—
828C2—721no—
829C2#1059418611yescharacteristic
830C2#1059473411yescharacteristic
831C2#1059474711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595254C2semidirect
2. #10594583C2semidirect
3. C3⋊D3×#102C2semidirect
4. C3×#4772C2semidirect
5. C3×#4756C2semidirect
6. #10591456C2semidirect
7. #10591450C2semidirect
8. #10591411C2semidirect
9. #10590872C2semidirect
10. #10590841C2semidirect
11. #10590826C2semidirect
12. C8×#626C2semidirect
13. #10590534C2semidirect
14. #10590528C2semidirect
15. #10590424C2semidirect
24. C2×C3×D3×C8C22semidirect
25. C3×#893C22semidirect
26. C3×#892C22semidirect
34. #63908C22semidirect
39. #63869C22semidirect
42. C2×#3715C22semidirect
49. C3×#821C22semidirect
50. C3×#816C22semidirect
51. C3×C8×Dic3C22semidirect
52. C3×#810C22semidirect
53. C3×#807C22semidirect
54. #63575C22semidirect
55. #63574C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63566C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
84. #4772D3semidirect
89. #4756D3semidirect
179. C2×D3×C8C2×D3semidirect
183. #893C2×D3semidirect
184. #892C2×D3semidirect
219. #821C2×D3semidirect
225. #816C2×D3semidirect
227. C8×Dic3C2×D3semidirect
228. #810C2×D3semidirect
236. #807C2×D3semidirect
726. C32#3297semidirect
822. C3#78846semidirect
823. C3#79609semidirect

Maximal subgroups

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

subgroupindex
#105952542
#105945832
C3⋊D3×#1022
C3×#47722
C3×#47562
#105914562
#105914502
#105914112
#105908722
#105908412
#105908262
C8×#6262
#105905342
#105905282
#105904242
#796093
#788463