Finite Group Databasebeta

← #11887405

Subgroups — #11887405

Order 1152.

959 conjugacy classes of subgroups.

The subgroup lattice has 851 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595985C211yesmaximal, characteristic, complemented
2#10594889C211yesmaximal, characteristic, complemented
3C3×#4970C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5#10591177C211yesmaximal, characteristic, complemented
6#10591162C211yesmaximal, characteristic, complemented
7#10591148C211yesmaximal, characteristic, complemented
8#10590617C211yesmaximal, characteristic, complemented
9#10590611C211yesmaximal, characteristic, complemented
10#10590540C211yesmaximal, characteristic, complemented
11#10590539C211yesmaximal, characteristic, complemented
12#10590512C211yesmaximal, characteristic, complemented
13#10590509C211yesmaximal, characteristic, complemented
14#10590473C211yesmaximal, characteristic, complemented
15#10590459C211yesmaximal, characteristic, complemented
16#81485—31nomaximal
17#78760—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21#64139—21no—
22#64139C2211yescharacteristic
23C4×#638—21no—
24C4×#638C2211yescharacteristic
25#64107—21no—
26#64104C2211yescharacteristic, complemented
27#64103—21no—
28#64102C2211yescharacteristic, complemented
29#64101C2211yescharacteristic, complemented
30#64099C2211yescharacteristic, complemented
31C3×#924C2211yescharacteristic
32C22×C3×C3⋊C8C2211yescharacteristic
33#63977—21no—
34D3×#217—21no—
35#63916C2211yescharacteristic
36#63898C2211yescharacteristic
37#63886—21no—
38#63884—21no—
39#63863C2211yescharacteristic
40C2×#3717C2211yescharacteristic, complemented
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C2×#3710C2211yescharacteristic, complemented
44C3×#830C2211yescharacteristic
45C3×#810C2211yescharacteristic, complemented
46C3×#810C2211yescharacteristic, complemented
47C3×#809C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#807C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63557C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61#5806—31no—
62#5630—31no—
63#5514—31no—
64#5514—31no—
65#5514—61no—
66C3×#484—31no—
67C2×C3×#102—31no—
68#5217—31no—
69#5114—31no—
70C8×#67—31no—
71#5048—31no—
72#4970D311yescharacteristic, complemented
73C2×#809D311yescharacteristic, complemented
74#4891—31no—
75#4885—31no—
76#4883—31no—
77#4872—31no—
78#4819—31no—
79#4810—31no—
80#4804—31no—
81#4800—31no—
82#4787—31no—
83#4781—31no—
84#4779—31no—
85#4775—31no—
86#4772—31no—
87#4768—31no—
88#4763—31no—
89#4756—31no—
90#4732—31no—
91#67⋊C8—31no—
92C23×C3×D3—21no—
93C22×C32×C4—21no—
94C22×C32×C4C2311yescharacteristic
95C2×#638—21no—
96C2×#638D411yescharacteristic
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×D12—22no—
102C2×C3×D12—21no—
103C2×C3×D12—41no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×#626—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111#3796—22no—
112#3796—41no—
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116#3757D411yescharacteristic
117#3752—21no—
118#3752—21no—
119#3752—21no—
120#3752—21no—
121#3752D411yescharacteristic
122C4⋊(C3⋊Dic3)—21no—
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124#3750—21no—
125#3750D411yescharacteristic
126C4×C3⋊Dic3—21no—
127C4×C3⋊Dic3C2311yescharacteristic
128C3×#217—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C2×C3×C3⋊C8—41no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140#3717—41no—
141#3714—22no—
142#3714—41no—
143#3710—41no—
144#3297—91noSylow
145C22×C3×D4—31no—
146C2×#239—31no—
147C2×#237—31no—
148C22×D12C2×D311yescharacteristic
149C22×C3×C8—31no—
150C3×C22⋊Q8—31no—
151C2×C3×C4⋊C4—21no—
152C2×C3×C4⋊C4C2×D311yescharacteristic
153C2×C3×C4⋊C4C2×D311yescharacteristic
154#953—61no—
155C2×#217—61no—
156#947—31no—
157C2×#215—31no—
158#939—61no—
159#938—31no—
160#936—31no—
161#935—61no—
162D4×Dic3—31no—
163C2×#213—31no—
164C2×#213—31no—
165#930—31no—
166#930—31no—
167#930—61no—
168#930—61no—
169#930—61no—
170#930—62no—
171C4×#67—31no—
172C4×#67—31no—
173C4×#67—61no—
174C4×#67—61no—
175C4×#67—61no—
176C4×#67—62no—
177#924C2×D311yescharacteristic
178C22×C3⋊C8C2×D311yescharacteristic
179C2×D24—31no—
180C2×D24—31no—
181C2×#204—31no—
182C2×D3×C8—31no—
183C2×D3×C8—31no—
184#898—61no—
185#898—61no—
186#898—62no—
187#895—31no—
188#895—31no—
189#895—31no—
190#895—61no—
191#895—61no—
192#894—61no—
193#894—61no—
194#894—61no—
195#894—62no—
196#893—31no—
197#893—31no—
198#893—31no—
199#893—61no—
200#892—31no—
201#892—31no—
202#892—61no—
203#890—31no—
204#890—31no—
205#890—61no—
206#882—61no—
207D3×C22⋊C4—61no—
208C3×#107—31no—
209C3×#107—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×C22⋊C8—31no—
217#835—31no—
218#832—31no—
219#832—31no—
220#830C2×D311yescharacteristic
221#821—31no—
222#821—31no—
223#821—31no—
224(C2×D3)⋊C8—31no—
225(C2×D3)⋊C8—31no—
226#817—31no—
227#816—31no—
228Dic3⋊C8—31no—
229Dic3⋊C8—31no—
230C8×Dic3—31no—
231C8×Dic3—31no—
232#810C2×D311yescharacteristic, complemented
233#810C2×D311yescharacteristic, complemented
234#809—31no—
235#809C2×D311yescharacteristic
236#809C2×D311yescharacteristic
237#809C2×D311yescharacteristic
238#809C2×D311yescharacteristic
239#808—31no—
240#807C2×D311yescharacteristic, complemented
241#807C2×D311yescharacteristic, complemented
242C23×C32C2×D411yescharacteristic
243C22×C3⋊D3—21no—
244C22×C3⋊D3C2×D411yescharacteristic
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—42no—
248C22×C3×D3—42no—
249C22×C3×D3—81no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—81no—
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257#638—22no—
258#638—42no—
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3C2×D411yescharacteristic
261C2×C3⋊Dic3C2×D411yescharacteristic
262C2×C3⋊Dic3C2×D411yescharacteristic
263C4⋊(C3⋊D3)—21no—
264C4⋊(C3⋊D3)—21no—
265C4⋊(C3⋊D3)—81no—
266C4×C3⋊D3—21no—
267C4×C3⋊D3—21no—
268C4×C3⋊D3—81no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C3×D12—21no—
272C3×D12—21no—
273C3×D12—21no—
274C3×D12—42no—
275C3×D12#4112yes—
276C3×Dic6—21no—
277C3×Dic6—21no—
278#626—42no—
279#626—81no—
280D3×Dic3—42no—
281D3×Dic3—81no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285C3×C3⋊C8—21no—
286#553—91no—
287#546—91no—
288#488—91no—
289#484—31no—
290#482—91no—
291#478—91no—
292#466—91no—
293#465—91no—
294#463—91no—
295#449—91no—
296#447—91no—
297C4×D8—91no—
298C8×D4—91no—
299#416—91no—
300C2×#102—31no—
301C24×C3—61no—
302C23×D3—21no—
303C2×C3×Q8—31no—
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C2×C3×D4—62no—
307C2×C3×D4—61no—
308C2×C3×D4—121no—
309C22×C3×C4—22no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C2×#67—31no—
316C2×#67—31no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—62no—
321C2×#67—61no—
322C2×#67—61no—
323C22×Dic3—61no—
324C22×Dic3—61no—
325#239—62no—
326#239—121no—
327#237—62no—
328#237—121no—
329C2×D12—22no—
330C2×D12—21no—
331C2×D12—31no—
332C2×D12—31no—
333C2×D12—41no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12—61no—
337C2×D12—61no—
338C2×D12—62no—
339C2×D12—61no—
340C2×D12C22×D311yescharacteristic
341C2×D12C22×D311yescharacteristic
342C2×C4×D3—31no—
343C2×C4×D3—31no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—62no—
350C2×Dic6C22×D311yescharacteristic
351C2×C3×C8—31no—
352C2×C3×C8—31no—
353C2×C3×C8—31no—
354C2×C3×C8—31no—
355C2×C3×C8—121no—
356C3×C4⋊C4—22no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—21no—
359C3×C4⋊C4—21no—
360C3×C4⋊C4—21no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C22⋊C4—61no—
368#217—21no—
369#217—31no—
370#217—31no—
371#217—61no—
372#217—61no—
373#217—61no—
374#217—61no—
375#217—61no—
376#215—121no—
377#213—62no—
378#213—121no—
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—31no—
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—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—62no—
393(C2×D3)⋊C4—62no—
394(C2×D3)⋊C4—62no—
395(C2×D3)⋊C4—62no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398C4⋊Dic3—31no—
399C4⋊Dic3—31no—
400C4⋊Dic3—61no—
401C4⋊Dic3—61no—
402C4⋊Dic3—61no—
403C4⋊Dic3—62no—
404C4⋊Dic3C22×D311yescharacteristic
405Dic3⋊C4—21no—
406Dic3⋊C4—31no—
407Dic3⋊C4—31no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—62no—
412C4×Dic3—31no—
413C4×Dic3—31no—
414C4×Dic3—61no—
415C4×Dic3—61no—
416C4×Dic3—61no—
417C4×Dic3—62no—
418C2×C3⋊C8—41no—
419C2×C3⋊C8C22×D311yescharacteristic
420C2×C3⋊C8C22×D311yescharacteristic
421C2×C3⋊C8C22×D311yescharacteristic
422C2×C3⋊C8C22×D311yescharacteristic
423D24—62no—
424D24—121no—
425#204—121no—
426D3×C8—121no—
427D3×C8—121no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32#13512yes—
431C22×C32C22×D411yescharacteristic
432C2×C3⋊D3—21no—
433C2×C3⋊D3—21no—
434C2×C3⋊D3—21no—
435C2×C3⋊D3—41no—
436C2×C3⋊D3—41no—
437C2×C3⋊D3—41no—
438C2×C3×D3—22no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C2×C3×D3—84no—
445C32×C4—21no—
446C32×C4—41no—
447C32×C4—41no—
448C32×C4C2×#4111yescharacteristic
449C32×C4H(5,𝔽2)11yescharacteristic
450C3⋊Dic3—21no—
451C3⋊Dic3—21no—
452C3⋊Dic3—21no—
453C3⋊Dic3—41no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C2×#41—91no—
457C22×D4—31no—
458C2×SD16—91no—
459C2×D8—91no—
460C2×D8—91no—
461C22×C8—31no—
462C22×C8—91no—
463#126—181no—
464#125—91no—
465#124—91no—
466#123—181no—
467#123—181no—
468C22⋊Q8—31no—
469#121—91no—
470#121—91no—
471#121—91no—
472#121—181no—
473#121—181no—
474#120—181no—
475C4×D4—91no—
476C4×D4—91no—
477C4×D4—91no—
478C4×D4—181no—
479#117—91no—
480C2×C4⋊C4D3211yescharacteristic
481C2×C22⋊C4—181no—
482#107—31no—
483#107—31no—
484#106—91no—
485C4⋊C8—91no—
486#103—31no—
487#103—31no—
488#103—91no—
489#102—31no—
490#102—31no—
491#102—31no—
492#102—31no—
493#102—91no—
494#102—91no—
495#102—91no—
496C22⋊C8—31no—
497C22⋊C8—91no—
498C4×C8—91no—
499C23×C3—21no—
500C23×C3—61no—
501C23×C3—61no—
502C23×C3—122no—
503C23×C3—122no—
504C23×C3—241no—
505C23×C3D3×D411yescharacteristic
506C23×C3D3×D411yescharacteristic
507C22×D3—21no—
508C22×D3—21no—
509C22×D3—31no—
510C22×D3—31no—
511C22×D3—42no—
512C22×D3—42no—
513C22×D3—61no—
514C22×D3—62no—
515C22×D3—61no—
516C22×D3—61no—
517C22×D3—81no—
518C3×Q8—61no—
519C3×Q8—61no—
520C3×D4—32no—
521C3×D4—61no—
522C3×D4—61no—
523C3×D4—61no—
524C3×D4—122no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—81no—
542C2×C3×C4—81no—
543C2×C3×C4—82no—
544C2×C3×C4D3×D411yescharacteristic
545C2×C3×C4D3×D411yescharacteristic
546C2×C3×C4C23×D311yescharacteristic
547C2×C3×C4C23×D311yescharacteristic
548#67—62no—
549#67—62no—
550#67—122no—
551#67—122no—
552#67—124no—
553#67—122no—
554#67—122no—
555#67—241no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—31no—
559C2×Dic3—31no—
560C2×Dic3—31no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—62no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—122no—
571C2×Dic3—241no—
572D12—21no—
573D12—21no—
574D12—21no—
575D12—42no—
576D12—61no—
577D12—61no—
578D12—61no—
579D12—61no—
580D12—121no—
581D12—121no—
582D12—122no—
583D12—241no—
584D12—241no—
585D12—242no—
586D12—241no—
587D12#23512yes—
588C4×D3—61no—
589C4×D3—61no—
590C4×D3—61no—
591C4×D3—61no—
592C4×D3—121no—
593C4×D3—121no—
594C4×D3—122no—
595C4×D3—241no—
596C4×D3—241no—
597C4×D3—241no—
598C4×D3—242no—
599Dic6—21no—
600Dic6—21no—
601C3×C8—61no—
602C3×C8—61no—
603C3×C8—61no—
604C3×C8—61no—
605C3⋊C8—21no—
606C3⋊C8—21no—
607C3⋊C8—21no—
608C3⋊C8—21no—
609C2×C32—22no—
610C2×C32#54611yescharacteristic
611C2×C32C2×#13511yescharacteristic
612C2×C32#57611yescharacteristic
613C3⋊D3—41no—
614C3⋊D3—81no—
615C3×D3—42no—
616C3×D3—81no—
617C24—61no—
618#41—182no—
619#41—361no—
620C2×Q8—31no—
621C2×D4—31no—
622C2×D4—31no—
623C2×D4—62no—
624C2×D4—61no—
625C2×D4—91no—
626C2×D4—91no—
627C2×D4—121no—
628C2×D4—181no—
629C2×D4—181no—
630C2×D4—181no—
631C2×D4—181no—
632C22×C4—21no—
633C22×C4—91no—
634C22×C4—181no—
635C22×C4—181no—
636C22×C4—181no—
637C22×C4C2×D3211yescharacteristic
638SD16—361no—
639D8—182no—
640D8—361no—
641C2×C8—31no—
642C2×C8—31no—
643C2×C8—31no—
644C2×C8—31no—
645C2×C8—121no—
646C2×C8—361no—
647C4⋊C4—21no—
648C4⋊C4—31no—
649C4⋊C4—61no—
650C4⋊C4—91no—
651C4⋊C4—91no—
652C4⋊C4—181no—
653C4⋊C4—181no—
654C4⋊C4C2×D3211yescharacteristic
655C4⋊C4C2×D3211yescharacteristic
656C22⋊C4—61no—
657C22⋊C4—91no—
658C22⋊C4—91no—
659C22⋊C4—181no—
660C22⋊C4—181no—
661C22⋊C4—181no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C22⋊C4—181no—
665C22⋊C4—181no—
666C22⋊C4—181no—
667C42—91no—
668C42—181no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—22no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—62no—
678C22×C3—121no—
679C22×C3—121no—
680C22×C3—121no—
681C22×C3—121no—
682C22×C3—121no—
683C22×C3—244no—
684C22×C3#91612yes—
685C22×C3#91912yes—
686C22×C3C2×D3×D411yescharacteristic
687C22×C3C2×D3×D411yescharacteristic
688C2×D3—22no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—41no—
694C2×D3—61no—
695C2×D3—61no—
696C2×D3—61no—
697C2×D3—61no—
698C2×D3—61no—
699C2×D3—61no—
700C2×D3—84no—
701C2×D3—121no—
702C2×D3—121no—
703C2×D3—121no—
704C2×D3—122no—
705C2×D3—122no—
706C2×D3—122no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—121no—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—41no—
718C3×C4—42no—
719C3×C4—42no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—121no—
725C3×C4—121no—
726C3×C4C2×#23511yescharacteristic
727C3×C4#100411yescharacteristic
728C3×C4D3×#4111yescharacteristic
729C3×C4#100911yescharacteristic
730Dic3—41no—
731Dic3—41no—
732Dic3—61no—
733Dic3—61no—
734Dic3—61no—
735Dic3—61no—
736Dic3—61no—
737Dic3—61no—
738Dic3—121no—
739Dic3—121no—
740Dic3—121no—
741Dic3—122no—
742Dic3—121no—
743Dic3—121no—
744C32#329711yescharacteristic, complemented, Sylow
745C23—61no—
746C23—61no—
747C23—91no—
748C23—122no—
749C23—122no—
750C23—181no—
751C23—241no—
752C23#381111yescharacteristic
753Q8—61no—
754Q8—61no—
755D4—32no—
756D4—61no—
757D4—61no—
758D4—61no—
759D4—122no—
760D4—182no—
761D4—181no—
762D4—181no—
763D4—362no—
764D4—362no—
765D4—721no—
766D4—721no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—81no—
774C2×C4—91no—
775C2×C4—91no—
776C2×C4—91no—
777C2×C4—181no—
778C2×C4—181no—
779C2×C4—181no—
780C2×C4—362no—
781C2×C4—721no—
782C2×C4—721no—
783C2×C4#381111yescharacteristic
784C2×C4C22×D3211yescharacteristic
785C8—61no—
786C8—61no—
787C8—61no—
788C8—61no—
789C2×C3—22no—
790C2×C3—22no—
791C2×C3—21no—
792C2×C3—21no—
793C2×C3—21no—
794C2×C3—42no—
795C2×C3—122no—
796C2×C3—241no—
797C2×C3#549011yescharacteristic
798C2×C3#565411yescharacteristic
799C2×C3#575711yescharacteristic
800C2×C3C2×#91611yescharacteristic
801C2×C3C2×#91911yescharacteristic
802C2×C3#577411yescharacteristic
803D3—42no—
804D3—81no—
805D3—121no—
806D3—121no—
807D3—241no—
808D3—242no—
809D3—241no—
810D3—241no—
811C22—21no—
812C22—21no—
813C22—62no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22—121no—
818C22—121no—
819C22—181no—
820C22—181no—
821C22—181no—
822C22—244no—
823C22—361no—
824C22—361no—
825C22—361no—
826C22#6395012yes—
827C22C2×#381111yescharacteristic
828C4—21no—
829C4—41no—
830C4—41no—
831C4—121no—
832C4—121no—
833C4—181no—
834C4—181no—
835C4—181no—
836C4—361no—
837C4D3×#23511yescharacteristic
838C4#6430711yescharacteristic
839C3—21no—
840C3#7876011yescharacteristic, complemented
841C3#8148511yescharacteristic, complemented
842C2—22no—
843C2—122no—
844C2—241no—
845C2—361no—
846C2—721no—
847C2#1059507711yescharacteristic
848C2#1059510211yescharacteristic
849C2C2×#6395011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #10595985C2semidirect
2. #10594889C2semidirect
3. C3×#4970C2semidirect
4. C2×C3×#809C2semidirect
5. #10591177C2semidirect
6. #10591162C2semidirect
7. #10591148C2semidirect
8. #10590617C2semidirect
9. #10590611C2semidirect
10. #10590540C2semidirect
11. #10590539C2semidirect
12. #10590512C2semidirect
13. #10590509C2semidirect
14. #10590473C2semidirect
15. #10590459C2semidirect
26. #64104C22semidirect
28. #64102C22semidirect
29. #64101C22semidirect
30. #64099C22semidirect
40. C2×#3717C22semidirect
43. C2×#3710C22semidirect
45. C3×#810C22semidirect
46. C3×#810C22semidirect
51. C3×#807C22semidirect
52. C3×#807C22semidirect
53. #63573C22semidirect
54. #63572C22semidirect
55. #63566C22semidirect
56. #63564C22semidirect
59. #63557C22semidirect
60. #63553C22semidirect
72. #4970D3semidirect
73. C2×#809D3semidirect
232. #810C2×D3semidirect
233. #810C2×D3semidirect
240. #807C2×D3semidirect
241. #807C2×D3semidirect
744. C32#3297semidirect
840. C3#78760semidirect
841. C3#81485semidirect

Maximal subgroups

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

subgroupindex
#105959852
#105948892
C3×#49702
C2×C3×#8092
#105911772
#105911622
#105911482
#105906172
#105906112
#105905402
#105905392
#105905122
#105905092
#105904732
#105904592
#814853
#787603