Finite Group Databasebeta

← #11887399

Subgroups — #11887399

Order 1152.

891 conjugacy classes of subgroups.

The subgroup lattice has 815 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5554C211yesmaximal, characteristic, complemented
2#10593923C211yesmaximal, characteristic, complemented
3#10592708C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic, complemented
5#10591450C211yesmaximal, characteristic, complemented
6#10591447C211yesmaximal, characteristic, complemented
7#10591420C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10590501C211yesmaximal, characteristic, complemented
10#10590499C211yesmaximal, characteristic, complemented
11#10590446C211yesmaximal, characteristic, complemented
12#10590440C211yesmaximal, characteristic, complemented
13#10590348C211yesmaximal, characteristic, complemented
14C3⋊C8×D12C211yesmaximal, characteristic, complemented
15#10590274C211yesmaximal, characteristic, complemented
16#83495—31nomaximal
17#79609—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21#64079C2211yescharacteristic, complemented
22C2×C3×#213C2211yescharacteristic
23C3×#930—21no—
24C2×C3×(C2×D3)⋊C4—21no—
25C3×#897C2211yescharacteristic
26C3×#895C2211yescharacteristic
27C3×#886—21no—
28C3×#882—21no—
29C3×#875C2211yescharacteristic
30C3×C4×D12C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic, complemented
32#63908C2211yescharacteristic
33#63908C2211yescharacteristic, complemented
34#63905—21no—
35D3×C4⋊Dic3C2211yescharacteristic
36#63885—21no—
37#63879—21no—
38#63858—21no—
39#63841C2211yescharacteristic, complemented
40C2×#3715C2211yescharacteristic, complemented
41C2×#3713C2211yescharacteristic
42C2×D3×C3⋊C8C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63659C2211yescharacteristic
45#63659C2211yescharacteristic
46#63635C2211yescharacteristic, complemented
47#63634C2211yescharacteristic, complemented
48C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×#809C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×C4×C3⋊C8C2211yescharacteristic, complemented
53#63566C2211yescharacteristic, complemented
54#63566C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#546—31no—
62#5565—31no—
63#5558—31no—
64#5554D311yescharacteristic, complemented
65C3×C4×D8—31no—
66#5238—31no—
67#5233—31no—
68#5217—31no—
69C2×#832—31no—
70#5158—31no—
71#5156—31no—
72#5057—31no—
73#5056—31no—
74#5048—31no—
75#5044—31no—
76#5038—31no—
77#5035—31no—
78#5016—31no—
79C4×#213D311yescharacteristic, complemented
80D4×C3⋊C8—31no—
81#5009—31no—
82#5009—31no—
83#5009—61no—
84#4885—31no—
85#4884—31no—
86#4778—31no—
87#4775—31no—
88#4772—31no—
89D3×#102—31no—
90#4697—31no—
91C8×D12—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C3×#237—22no—
99C3×#237—41no—
100C3×D3×D4—22no—
101C3×D3×D4—41no—
102C2×C3×D12—21no—
103C2×C3×D12D411yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×#625—21no—
111C2×#625—21no—
112C2×D3×Dic3—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C22⋊C4—21no—
115C32×C42C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119#3750—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#213—22no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×(C2×D3)⋊C4D411yescharacteristic
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3D411yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135Dic3⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140#3715—41no—
141#3713—41no—
142D3×C3⋊C8—41no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#237C2×D311yescharacteristic
148C2×D3×D4C2×D311yescharacteristic
149C2×C3×D8—31no—
150C3×#124—31no—
151C3×#123—61no—
152C3×C22⋊Q8—31no—
153C3×#121—31no—
154C3×#121—61no—
155C3×#120—61no—
156C3×C4×D4—21no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C3×C4×D4C2×D311yescharacteristic
160C3×C4×D4C2×D311yescharacteristic
161C2×C3×C22⋊C4—61no—
162C2×#215—31no—
163#939—61no—
164#938—31no—
165#938—31no—
166C2×#214—31no—
167C2×#213—31no—
168C2×#213—31no—
169C2×#213C2×D311yescharacteristic
170#930—21no—
171#930—31no—
172#930—31no—
173#929—61no—
174C4×#67—61no—
175C2×(C2×D3)⋊C4—21no—
176#926—31no—
177C2×C4⋊Dic3—31no—
178C22×C3⋊C8—31no—
179C22×C3⋊C8—31no—
180C2×D3×C8—31no—
181C2×D3×C8—31no—
182#898—61no—
183#897C2×D311yescharacteristic
184#895C2×D311yescharacteristic
185#892—31no—
186D3×C4⋊C4—31no—
187#886—21no—
188#884—61no—
189#883—61no—
190#882—21no—
191#67⋊C4—61no—
192#879—61no—
193#875C2×D311yescharacteristic
194C4×D12C2×D311yescharacteristic
195C4×D12C2×D311yescharacteristic, complemented
196#870—31no—
197#870—31no—
198#870—61no—
199C3×#107—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×C4×C8—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—61no—
214#832—61no—
215#832C2×D311yescharacteristic
216#830—31no—
217#830—31no—
218#821—31no—
219#821—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222#816—31no—
223#816—31no—
224#810—31no—
225#809—31no—
226#809C2×D311yescharacteristic, complemented
227#808—31no—
228#808—31no—
229#808—61no—
230#807—31no—
231#807—31no—
232#807—61no—
233#807C2×D311yescharacteristic, complemented
234C4⋊(C3⋊C8)—31no—
235C4⋊(C3⋊C8)—31no—
236C4⋊(C3⋊C8)—61no—
237C4×C3⋊C8C2×D311yescharacteristic, complemented
238C23×C32—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C22×C3×D3C2×D411yescharacteristic
246C32×D4—21no—
247C32×D4#4112yes—
248C2×C32×C4—21no—
249C2×C32×C4—81no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C3×#67—42no—
256C3×#67—42no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—22no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—81no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—81no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275#625—42no—
276#625—81no—
277D3×Dic3—81no—
278C3⋊(C3⋊C8)—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—91no—
283#546—31no—
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—91no—
296C2×#102—91no—
297C24×C3—61no—
298C23×D3—21no—
299C3×#41—62no—
300C3×#41—121no—
301C2×C3×Q8—31no—
302C2×C3×D4—21no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C2×C3×D4—61no—
307C2×C3×D4—61no—
308C2×C3×D4—62no—
309C2×C3×D4—61no—
310C2×C3×D4—121no—
311C2×C3×D4C22×D311yescharacteristic
312C2×C3×D4C22×D311yescharacteristic
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—41no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C2×#67—21no—
321C2×#67—21no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C22×Dic3—21no—
327C22×Dic3—61no—
328#237—22no—
329#237—41no—
330D3×D4—22no—
331D3×D4—41no—
332C2×D12—21no—
333C2×D12#6711yescharacteristic
334C2×D12C22×D311yescharacteristic
335C2×D12C22×D311yescharacteristic
336C2×C4×D3—21no—
337C2×C4×D3—61no—
338C2×C4×D3C22×D311yescharacteristic
339C2×C4×D3C22×D311yescharacteristic
340C2×Dic6C22×D311yescharacteristic
341C3×D8—62no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C22⋊C4—21no—
351C3×C22⋊C4—21no—
352C3×C22⋊C4—31no—
353C3×C22⋊C4—31no—
354C3×C22⋊C4—41no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C42—21no—
361C3×C42C22×D311yescharacteristic
362C3×C42C22×D311yescharacteristic
363#217—61no—
364#217—61no—
365#217—61no—
366#215—121no—
367#214—121no—
368#213—22no—
369#213—121no—
370#213—121no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4#6711yescharacteristic
380(C2×D3)⋊C4#6711yescharacteristic
381C4⋊Dic3—21no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3#6711yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—121no—
397Dic3⋊C4—121no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—121no—
407C2×C3⋊C8—121no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410D3×C8—121no—
411D3×C8—121no—
412C22×C32—22no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32C22×D411yescharacteristic
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—84no—
428C2×C3×D3#13512yes—
429C32×C4—21no—
430C32×C4—21no—
431C32×C4—41no—
432C32×C4C2×#4111yescharacteristic
433C32×C4H(5,𝔽2)11yescharacteristic
434C3⋊Dic3—41no—
435C3⋊Dic3—41no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C2×#41—31no—
441C22×D4—31no—
442C2×SD16—91no—
443C2×D8—31no—
444C2×D8—91no—
445C22×C8—91no—
446C22×C8—91no—
447#126—181no—
448#125—91no—
449#124—31no—
450#123—61no—
451#123—181no—
452C22⋊Q8—31no—
453#121—31no—
454#121—61no—
455#121—91no—
456#121—91no—
457#121—181no—
458#120—61no—
459C4×D4—31no—
460C4×D4—31no—
461C4×D4—181no—
462C4×D4D3211yescharacteristic
463#117—91no—
464C2×C4⋊C4—91no—
465C2×C22⋊C4—61no—
466#107—31no—
467#107—91no—
468#106—91no—
469C4⋊C8—91no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480C22⋊C8—91no—
481C22⋊C8—91no—
482C4×C8—31no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—31no—
486C23×C3—31no—
487C23×C3—41no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3—122no—
491C23×C3—122no—
492C23×C3—241no—
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—42no—
496C22×D3—42no—
497C22×D3—81no—
498C22×D3C2×#6711yescharacteristic
499C22×D3C2×#6711yescharacteristic
500C3×Q8—61no—
501C3×Q8—61no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—22no—
505C3×D4—41no—
506C3×D4—62no—
507C3×D4—61no—
508C3×D4—61no—
509C3×D4—61no—
510C3×D4—61no—
511C3×D4—122no—
512C3×D4—122no—
513C3×D4—241no—
514C3×D4#23512yes—
515C3×D4#23712yes—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—41no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—81no—
531C2×C3×C4—81no—
532C2×C3×C4—82no—
533C2×C3×C4—122no—
534C2×C3×C4—241no—
535C2×C3×C4D3×D411yescharacteristic
536C2×C3×C4D3×D411yescharacteristic
537C2×C3×C4C2×#6711yescharacteristic
538C2×C3×C4C2×#6711yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540C2×C3×C4C23×D311yescharacteristic
541#67—42no—
542#67—42no—
543#67—122no—
544#67—122no—
545#67—241no—
546#67—241no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—42no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—121no—
555C2×Dic3—121no—
556C2×Dic3—241no—
557C2×Dic3C2×#6711yescharacteristic
558C2×Dic3C2×#6711yescharacteristic
559D12—22no—
560D12—21no—
561D12—21no—
562D12—21no—
563D12—21no—
564D12—81no—
565C4×D3—21no—
566C4×D3—21no—
567C4×D3—21no—
568C4×D3—21no—
569C4×D3—81no—
570C4×D3—241no—
571Dic6—21no—
572Dic6—21no—
573C3×C8—61no—
574C3×C8—61no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C3⋊C8—61no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—121no—
582C3⋊C8—121no—
583C2×C32—42no—
584C2×C32#54611yescharacteristic
585C2×C32C2×#13511yescharacteristic
586C2×C32#57611yescharacteristic
587C3×D3—22no—
588C3×D3—41no—
589C3×D3—81no—
590C3×D3—81no—
591C24—61no—
592#41—62no—
593#41—121no—
594C2×Q8—31no—
595C2×D4—31no—
596C2×D4—31no—
597C2×D4—31no—
598C2×D4—61no—
599C2×D4—61no—
600C2×D4—62no—
601C2×D4—61no—
602C2×D4—121no—
603C2×D4—181no—
604C2×D4—181no—
605C2×D4C2×D3211yescharacteristic
606C22×C4—21no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—181no—
612SD16—361no—
613D8—62no—
614D8—361no—
615C2×C8—31no—
616C2×C8—31no—
617C2×C8—91no—
618C2×C8—91no—
619C2×C8—361no—
620C2×C8—361no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—61no—
624C4⋊C4—91no—
625C4⋊C4—91no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4C2×D3211yescharacteristic
630C22⋊C4—21no—
631C22⋊C4—31no—
632C22⋊C4—31no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C42—181no—
642C42C2×D3211yescharacteristic
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—21no—
646C22×C3—32no—
647C22×C3—42no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3—61no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—244no—
666C22×C3C2×D3×D411yescharacteristic
667C22×C3C22×#6711yescharacteristic
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—21no—
673C2×D3—41no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—84no—
680C2×D3#95012yes—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—41no—
691C3×C4—61no—
692C3×C4—61no—
693C3×C4—81no—
694C3×C4—121no—
695C3×C4—121no—
696C3×C4C2×#23511yescharacteristic
697C3×C4C2×#23711yescharacteristic
698C3×C4#100411yescharacteristic
699C3×C4#100911yescharacteristic
700Dic3—21no—
701Dic3—21no—
702Dic3—41no—
703Dic3—41no—
704Dic3—121no—
705Dic3—121no—
706Dic3—121no—
707Dic3—121no—
708Dic3—241no—
709Dic3—241no—
710C32#329711yescharacteristic, complemented, Sylow
711C23—21no—
712C23—31no—
713C23—31no—
714C23—61no—
715C23—61no—
716C23—122no—
717C23—122no—
718C23—241no—
719Q8—61no—
720Q8—61no—
721D4—21no—
722D4—62no—
723D4—61no—
724D4—61no—
725D4—61no—
726D4—61no—
727D4—122no—
728D4—122no—
729D4—241no—
730D4—362no—
731D4—721no—
732D4#379512yes—
733C2×C4—21no—
734C2×C4—31no—
735C2×C4—31no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—81no—
743C2×C4—122no—
744C2×C4—181no—
745C2×C4—181no—
746C2×C4—241no—
747C2×C4—721no—
748C2×C4D3×#6711yescharacteristic
749C2×C4D3×#6711yescharacteristic
750C2×C4C22×D3211yescharacteristic
751C8—61no—
752C8—61no—
753C8—181no—
754C8—181no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—42no—
759C2×C3—42no—
760C2×C3—62no—
761C2×C3—82no—
762C2×C3—121no—
763C2×C3—241no—
764C2×C3—241no—
765C2×C3#555011yescharacteristic
766C2×C3#575711yescharacteristic
767C2×C3D3×#13511yescharacteristic
768C2×C3#580611yescharacteristic
769C2×C3C2×#95011yescharacteristic
770C2×C3#583511yescharacteristic
771D3—22no—
772D3—41no—
773D3—81no—
774D3—81no—
775C22—22no—
776C22—32no—
777C22—41no—
778C22—41no—
779C22—61no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—61no—
784C22—121no—
785C22—121no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—244no—
791C22C2×D3×#6711yescharacteristic
792C4—21no—
793C4—21no—
794C4—41no—
795C4—61no—
796C4—61no—
797C4—121no—
798C4—121no—
799C4—361no—
800C4—361no—
801C4C2×#379511yescharacteristic
802C4#6430711yescharacteristic
803C3—21no—
804C3#7960911yescharacteristic, complemented
805C3#8349511yescharacteristic, complemented
806C2—42no—
807C2—62no—
808C2—121no—
809C2—241no—
810C2—241no—
811C2#1059488611yescharacteristic
812C2#1059509611yescharacteristic
813C2D3×#95011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5554C2semidirect
2. #10593923C2semidirect
3. #10592708C2semidirect
4. C3×C4×#213C2semidirect
5. #10591450C2semidirect
6. #10591447C2semidirect
7. #10591420C2semidirect
8. D3×#832C2semidirect
9. #10590501C2semidirect
10. #10590499C2semidirect
11. #10590446C2semidirect
12. #10590440C2semidirect
13. #10590348C2semidirect
14. C3⋊C8×D12C2semidirect
15. #10590274C2semidirect
21. #64079C22semidirect
31. C3×C4×D12C22semidirect
33. #63908C22semidirect
39. #63841C22semidirect
40. C2×#3715C22semidirect
43. C2×D3×C3⋊C8C22semidirect
46. #63635C22semidirect
47. #63634C22semidirect
48. C4⋊(C3⋊(C3⋊C8))C22semidirect
50. C3×#809C22semidirect
51. C3×#807C22semidirect
52. C3×C4×C3⋊C8C22semidirect
53. #63566C22semidirect
54. #63566C22semidirect
55. #63565C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
64. #5554D3semidirect
79. C4×#213D3semidirect
195. C4×D12C2×D3semidirect
226. #809C2×D3semidirect
233. #807C2×D3semidirect
237. C4×C3⋊C8C2×D3semidirect
710. C32#3297semidirect
804. C3#79609semidirect
805. C3#83495semidirect

Maximal subgroups

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

subgroupindex
C3×#55542
#105939232
#105927082
C3×C4×#2132
#105914502
#105914472
#105914202
D3×#8322
#105905012
#105904992
#105904462
#105904402
#105903482
C3⋊C8×D122
#105902742
#834953
#796093