Finite Group Databasebeta

← #11887453

Subgroups — #11887453

Order 1152.

907 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5612C211yesmaximal, characteristic, complemented
2#10594946C211yesmaximal, characteristic, complemented
3#10592737C211yesmaximal, characteristic, complemented
4C3×#5035C211yesmaximal, characteristic, complemented
5#10591478C211yesmaximal, characteristic, complemented
6#10591448C211yesmaximal, characteristic, complemented
7#10591432C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10591163C211yesmaximal, characteristic, complemented
10#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
11#10591083C211yesmaximal, characteristic, complemented
12#10590577C211yesmaximal, characteristic, complemented
13#10590545C211yesmaximal, characteristic, complemented
14#10590456C211yesmaximal, characteristic, complemented
15#10590440C211yesmaximal, characteristic, complemented
16#83495—31nomaximal
17#81382—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C32×#121C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22#64139C2211yescharacteristic, complemented
23C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
24C3×#938—21no—
25C3×#937—21no—
26C3×#936C2211yescharacteristic
27C3×C4×#67C2211yescharacteristic
28C3×#926C2211yescharacteristic, complemented
29C3×#897C2211yescharacteristic
30C3×#893C2211yescharacteristic
31C3×#883—21no—
32C3×D3×C22⋊C4—21no—
33#63975—21no—
34#63971—21no—
35#63909C2211yescharacteristic
36#63894C2211yescharacteristic, complemented
37D3×C4⋊Dic3C2211yescharacteristic
38#63880—21no—
39#63869C2211yescharacteristic, complemented
40#63868—21no—
41C2×#3717C2211yescharacteristic, complemented
42C2×#3714C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63659C2211yescharacteristic
45#63636C2211yescharacteristic, complemented
46#63634C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#830C2211yescharacteristic, complemented
50C3×#808C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63566C2211yescharacteristic, complemented
54#63565C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#546—31no—
62#5612D311yescharacteristic, complemented
63#5565—31no—
64#5530—31no—
65C3×#482—31no—
66#5238—31no—
67#5233—31no—
68#5217—31no—
69C2×#832—31no—
70#5057—31no—
71#5056—31no—
72#5048—31no—
73#5044—31no—
74#5038—31no—
75#5038—31no—
76#5038—61no—
77#5035D311yescharacteristic, complemented
78C4×#213—31no—
79D4×C3⋊C8—31no—
80#5009—31no—
81#5002—31no—
82#4884—31no—
83#4872—31no—
84#4871—31no—
85#4864—31no—
86#4787—31no—
87#4773—31no—
88D3×#102—31no—
89#4768—31no—
90#4734—31no—
91#67⋊C8—31no—
92C23×C3×D3—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67D411yescharacteristic
101C3×D3×D4—22no—
102C3×D3×D4—41no—
103C3×#235—22no—
104C3×#235—41no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×#626—21no—
111C2×#624—21no—
112C2×D3×Dic3—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C22⋊C4—21no—
115#3753—41no—
116#3752—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)—41no—
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#217—21no—
122C3×#217—21no—
123C3×#217—21no—
124C3×#217D411yescharacteristic
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136#3724—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139#3722—21no—
140#3722—21no—
141#3717—41no—
142#3714—22no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×D3×D4C2×D311yescharacteristic
148C2×#235C2×D311yescharacteristic
149C3×#124—31no—
150C3×#123—61no—
151C3×C22⋊Q8—31no—
152C3×#121—21no—
153C3×#121—61no—
154C3×#121C2×D311yescharacteristic
155C3×#121C2×D311yescharacteristic
156C3×#120—61no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C3×#117—31no—
160C2×C3×C22⋊C4—61no—
161C2×#215—31no—
162#939—61no—
163#938—21no—
164#937—21no—
165#936C2×D311yescharacteristic
166C2×#213—31no—
167C2×#213—31no—
168C2×#213—31no—
169C2×#213—61no—
170#930—31no—
171#930—31no—
172#930—31no—
173#930—61no—
174C4×#67C2×D311yescharacteristic
175#926C2×D311yescharacteristic, complemented
176C2×C4⋊Dic3—31no—
177C22×C3⋊C8—31no—
178C22×C3⋊C8—31no—
179C22×C3⋊C8—31no—
180C22×C3⋊C8—61no—
181C2×D24—31no—
182C2×#204—31no—
183C2×D3×C8—31no—
184#898—61no—
185#897C2×D311yescharacteristic
186#895—31no—
187#893—31no—
188#893C2×D311yescharacteristic
189D3×C4⋊C4—31no—
190#890—31no—
191#884—61no—
192#883—21no—
193#883—61no—
194#883—61no—
195#67⋊C4—61no—
196D3×C22⋊C4—21no—
197#876—61no—
198C4×D12—31no—
199C4×D12—61no—
200#870—31no—
201C3×#107—31no—
202C3×#106—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×C22⋊C8—31no—
206#835—31no—
207#835—31no—
208#835—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—61no—
215#832C2×D311yescharacteristic
216#832C2×D311yescharacteristic
217#830—31no—
218#830C2×D311yescharacteristic, complemented
219#821—31no—
220(C2×D3)⋊C8—31no—
221#816—31no—
222Dic3⋊C8—31no—
223C8×Dic3—31no—
224#810—31no—
225#810—31no—
226#809—31no—
227#809—31no—
228#809—31no—
229#809—31no—
230#809—61no—
231#808C2×D311yescharacteristic, complemented
232#807—31no—
233#807—31no—
234#807—61no—
235#807C2×D311yescharacteristic, complemented
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32—21no—
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—81no—
245C22×C3×D3C2×D411yescharacteristic
246C32×D4—21no—
247C32×D4—21no—
248C32×D4—81no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254#638—81no—
255C2×C3⋊Dic3—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)—21no—
258C3×#67—22no—
259C3×#67—42no—
260C3×#67—42no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12#4112yes—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—42no—
272C3×C4×D3—81no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275#626—42no—
276#624—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—31no—
287#478—91no—
288#466—91no—
289#465—91no—
290#463—91no—
291#449—91no—
292#447—91no—
293C4×D8—91no—
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—21no—
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—41no—
308C2×C3×D4—61no—
309C2×C3×D4—62no—
310C2×C3×D4—61no—
311C2×C3×D4—121no—
312C2×C3×D4C22×D311yescharacteristic
313C2×C3×D4C22×D311yescharacteristic
314C22×C3×C4—21no—
315C22×C3×C4—31no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C2×#67—21no—
321C2×#67—21no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—121no—
326C2×#67#6711yescharacteristic
327C22×Dic3—61no—
328D3×D4—22no—
329D3×D4—41no—
330#235—22no—
331#235—41no—
332C2×D12—31no—
333C2×D12—31no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12C22×D311yescharacteristic
337C2×C4×D3—21no—
338C2×C4×D3—21no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3C22×D311yescharacteristic
343C2×Dic6C22×D311yescharacteristic
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C22⋊C4—21no—
354C3×C22⋊C4—21no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—31no—
357C3×C22⋊C4—41no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C42—31no—
364C3×C42—61no—
365#217—21no—
366#217—21no—
367#217—21no—
368#217#6711yescharacteristic
369#215—121no—
370#213—62no—
371#213—121no—
372#213—121no—
373#213—122no—
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—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—121no—
383(C2×D3)⋊C4#6711yescharacteristic
384C4⋊Dic3—21no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3C22×D311yescharacteristic
391C4⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4#6711yescharacteristic
397C4×Dic3—21no—
398C4×Dic3C22×D311yescharacteristic
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—121no—
406C2×C3⋊C8—121no—
407C2×C3⋊C8—121no—
408C2×C3⋊C8—122no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411D24—62no—
412#204—121no—
413D3×C8—121no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32C22×D411yescharacteristic
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—22no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—84no—
430C2×C3×D3#13512yes—
431C32×C4—21no—
432C32×C4—41no—
433C32×C4C2×#4111yescharacteristic
434C32×C4H(5,𝔽2)11yescharacteristic
435C3⋊Dic3—41no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C2×#41—31no—
443C22×D4—31no—
444C2×SD16—91no—
445C2×D8—91no—
446C2×D8—91no—
447C22×C8—91no—
448C22×C8—91no—
449#126—181no—
450#125—91no—
451#124—31no—
452#123—61no—
453#123—181no—
454C22⋊Q8—31no—
455#121—61no—
456#121—91no—
457#121—91no—
458#121—181no—
459#121D3211yescharacteristic
460#120—61no—
461C4×D4—31no—
462C4×D4—31no—
463C4×D4—91no—
464C4×D4—181no—
465#117—31no—
466C2×C4⋊C4—91no—
467C2×C22⋊C4—61no—
468#107—31no—
469#107—91no—
470#106—31no—
471C4⋊C8—91no—
472#103—91no—
473#103—91no—
474#103—91no—
475#102—31no—
476#102—31no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481#102—91no—
482C22⋊C8—31no—
483C22⋊C8—91no—
484C4×C8—91no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—31no—
489C23×C3—41no—
490C23×C3—61no—
491C23×C3—122no—
492C23×C3—122no—
493C23×C3—241no—
494C23×C3D3×D411yescharacteristic
495C23×C3C2×#6711yescharacteristic
496C22×D3—21no—
497C22×D3—42no—
498C22×D3—42no—
499C22×D3—61no—
500C22×D3—61no—
501C22×D3—81no—
502C22×D3—121no—
503C22×D3C2×#6711yescharacteristic
504C3×Q8—61no—
505C3×Q8—61no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—32no—
511C3×D4—41no—
512C3×D4—41no—
513C3×D4—62no—
514C3×D4—61no—
515C3×D4—81no—
516C3×D4—81no—
517C3×D4—82no—
518C3×D4—122no—
519C3×D4—122no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—31no—
529C2×C3×C4—31no—
530C2×C3×C4—31no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—122no—
540C2×C3×C4—241no—
541C2×C3×C4D3×D411yescharacteristic
542C2×C3×C4C2×#6711yescharacteristic
543C2×C3×C4C23×D311yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545#67—22no—
546#67—42no—
547#67—42no—
548#67—122no—
549#67—241no—
550#67—241no—
551#67—242no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—121no—
558C2×Dic3—241no—
559C2×Dic3C2×#6711yescharacteristic
560C2×Dic3C2×#6711yescharacteristic
561C2×Dic3C2×#6711yescharacteristic
562D12—21no—
563D12—61no—
564D12—61no—
565D12—61no—
566D12—61no—
567D12—121no—
568D12—121no—
569D12—122no—
570D12#23712yes—
571C4×D3—21no—
572C4×D3—21no—
573C4×D3—42no—
574C4×D3—81no—
575C4×D3—241no—
576C4×D3—241no—
577C4×D3—241no—
578Dic6—21no—
579Dic6—21no—
580C3×C8—61no—
581C3×C8—61no—
582C3⋊C8—21no—
583C3⋊C8—21no—
584C3⋊C8—62no—
585C3⋊C8—61no—
586C3⋊C8—61no—
587C3⋊C8—61no—
588C3⋊C8—61no—
589C3⋊C8—121no—
590C2×C32—41no—
591C2×C32—81no—
592C2×C32#54611yescharacteristic
593C2×C32C2×#13511yescharacteristic
594C2×C32#57611yescharacteristic
595C3⋊D3—81no—
596C3×D3—22no—
597C3×D3—42no—
598C24—61no—
599#41—62no—
600#41—121no—
601C2×Q8—31no—
602C2×D4—21no—
603C2×D4—31no—
604C2×D4—31no—
605C2×D4—61no—
606C2×D4—62no—
607C2×D4—61no—
608C2×D4—91no—
609C2×D4—121no—
610C2×D4—181no—
611C2×D4—181no—
612C2×D4C2×D3211yescharacteristic
613C22×C4—31no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—181no—
617C22×C4—181no—
618C22×C4C2×D3211yescharacteristic
619SD16—361no—
620D8—182no—
621D8—361no—
622C2×C8—31no—
623C2×C8—31no—
624C2×C8—91no—
625C2×C8—91no—
626C2×C8—361no—
627C2×C8—361no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—31no—
631C4⋊C4—61no—
632C4⋊C4—91no—
633C4⋊C4—181no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C4⋊C4C2×D3211yescharacteristic
637C22⋊C4—21no—
638C22⋊C4—31no—
639C22⋊C4—31no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—61no—
643C22⋊C4—61no—
644C22⋊C4—61no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C42—31no—
649C42—61no—
650C22×C3—22no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—32no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—61no—
668C22×C3—61no—
669C22×C3—62no—
670C22×C3—81no—
671C22×C3—81no—
672C22×C3—81no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3—244no—
676C22×C3C2×D3×D411yescharacteristic
677C22×C3C22×#6711yescharacteristic
678C2×D3—21no—
679C2×D3—21no—
680C2×D3—22no—
681C2×D3—41no—
682C2×D3—41no—
683C2×D3—84no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—241no—
691C2×D3—241no—
692C2×D3—241no—
693C2×D3#95012yes—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—21no—
698C3×C4—41no—
699C3×C4—41no—
700C3×C4—41no—
701C3×C4—61no—
702C3×C4—61no—
703C3×C4—61no—
704C3×C4—81no—
705C3×C4—121no—
706C3×C4—121no—
707C3×C4—121no—
708C3×C4C2×#23711yescharacteristic
709C3×C4#100411yescharacteristic
710C3×C4D3×#4111yescharacteristic
711C3×C4#100911yescharacteristic
712Dic3—21no—
713Dic3—21no—
714Dic3—21no—
715Dic3—41no—
716Dic3—41no—
717Dic3—41no—
718Dic3—121no—
719Dic3—121no—
720Dic3—241no—
721C32#329711yescharacteristic, complemented, Sylow
722C23—21no—
723C23—31no—
724C23—61no—
725C23—122no—
726C23—122no—
727C23—181no—
728C23—241no—
729C23D3×#6711yescharacteristic
730Q8—61no—
731Q8—61no—
732D4—21no—
733D4—21no—
734D4—32no—
735D4—62no—
736D4—61no—
737D4—81no—
738D4—122no—
739D4—122no—
740D4—181no—
741D4—181no—
742D4—362no—
743D4—721no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—31no—
748C2×C4—31no—
749C2×C4—31no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—122no—
756C2×C4—181no—
757C2×C4—241no—
758C2×C4—721no—
759C2×C4—721no—
760C2×C4D3×#6711yescharacteristic
761C2×C4C22×D3211yescharacteristic
762C8—61no—
763C8—61no—
764C8—181no—
765C8—181no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—42no—
770C2×C3—41no—
771C2×C3—41no—
772C2×C3—62no—
773C2×C3—81no—
774C2×C3—81no—
775C2×C3—122no—
776C2×C3—161no—
777C2×C3#565411yescharacteristic
778C2×C3D3×#13511yescharacteristic
779C2×C3#577411yescharacteristic
780C2×C3#580611yescharacteristic
781C2×C3C2×#95011yescharacteristic
782C2×C3#583511yescharacteristic
783D3—22no—
784D3—42no—
785D3—241no—
786D3—241no—
787D3—481no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—32no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—61no—
796C22—61no—
797C22—62no—
798C22—121no—
799C22—121no—
800C22—244no—
801C22—361no—
802C22—361no—
803C22—361no—
804C22C2×D3×#6711yescharacteristic
805C4—21no—
806C4—41no—
807C4—61no—
808C4—61no—
809C4—61no—
810C4—121no—
811C4—121no—
812C4—121no—
813C4—361no—
814C4D3×#23711yescharacteristic
815C4#6431411yescharacteristic
816C3—21no—
817C3#8138211yescharacteristic, complemented
818C3#8349511yescharacteristic, complemented
819C2—41no—
820C2—62no—
821C2—81no—
822C2—122no—
823C2—721no—
824C2#1059509711yescharacteristic
825C2#1059514811yescharacteristic
826C2D3×#95011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#5612C2semidirect
2. #10594946C2semidirect
3. #10592737C2semidirect
4. C3×#5035C2semidirect
5. #10591478C2semidirect
6. #10591448C2semidirect
7. #10591432C2semidirect
8. D3×#832C2semidirect
9. #10591163C2semidirect
10. #67⋊(C3⋊C8)C2semidirect
11. #10591083C2semidirect
12. #10590577C2semidirect
13. #10590545C2semidirect
14. #10590456C2semidirect
15. #10590440C2semidirect
22. #64139C22semidirect
23. C22×C3⋊(C3⋊C8)C22semidirect
28. C3×#926C22semidirect
36. #63894C22semidirect
39. #63869C22semidirect
41. C2×#3717C22semidirect
45. #63636C22semidirect
46. #63634C22semidirect
49. C3×#830C22semidirect
50. C3×#808C22semidirect
51. C3×#807C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
53. #63566C22semidirect
54. #63565C22semidirect
55. #63565C22semidirect
60. Dic3×C3⋊C8C22semidirect
62. #5612D3semidirect
77. #5035D3semidirect
175. #926C2×D3semidirect
218. #830C2×D3semidirect
231. #808C2×D3semidirect
235. #807C2×D3semidirect
721. C32#3297semidirect
817. C3#81382semidirect
818. C3#83495semidirect

Maximal subgroups

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

subgroupindex
C3×#56122
#105949462
#105927372
C3×#50352
#105914782
#105914482
#105914322
D3×#8322
#105911632
#67⋊(C3⋊C8)2
#105910832
#105905772
#105905452
#105904562
#105904402
#834953
#813823