Finite Group Databasebeta

← #11887402

Subgroups — #11887402

Order 1152.

919 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595246C211yesmaximal, characteristic, complemented
2#10594437C211yesmaximal, characteristic, complemented
3#10592471C211yesmaximal, characteristic, complemented
4C3×#4773C211yesmaximal, characteristic, complemented
5C3×#4766C211yesmaximal, characteristic, complemented
6#10591457C211yesmaximal, characteristic, complemented
7Dic3×#213C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10590906C211yesmaximal, characteristic, complemented
10#10590844C211yesmaximal, characteristic, complemented
11#10590755C211yesmaximal, characteristic, complemented
12#10590684C211yesmaximal, characteristic, complemented
13#10590578C211yesmaximal, characteristic, complemented
14#10590533C211yesmaximal, characteristic, complemented
15#10590513C211yesmaximal, characteristic, complemented
16#81187—31nomaximal
17#80015—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×C8×C3⋊D3C2211yescharacteristic, complemented
21#64101C2211yescharacteristic, complemented
22C3×D4×Dic3C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
24C2×C3×D24C2211yescharacteristic
25C3×#895C2211yescharacteristic
26C3×#890C2211yescharacteristic, complemented
27#63978—21no—
28#63977—21no—
29#63962—21no—
30C2×(C2×D3)⋊Dic3—21no—
31#63916C2211yescharacteristic
32#63916C2211yescharacteristic, complemented
33C4×#626C2211yescharacteristic
34#63898—21no—
35Dic3×D12C2211yescharacteristic, complemented
36#63890—21no—
37D3×C4⋊Dic3C2211yescharacteristic
38#63886—21no—
39#63862—21no—
40#63860C2211yescharacteristic
41#63857C2211yescharacteristic
42C2×#3716C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63643C2211yescharacteristic, complemented
47#63637C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#818C2211yescharacteristic, complemented
51C3×Dic3⋊C8C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#808C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5806—31no—
62#5695—31no—
63#5618—31no—
64#5554—31no—
65C3×#478—31no—
66C3×#447—31no—
67C2×#832—31no—
68#5158—31no—
69#5157—31no—
70#5153—31no—
71Dic3×D8—31no—
72#5068—31no—
73#5041—31no—
74C4×#213—31no—
75#4884—31no—
76#4883—31no—
77#4866—31no—
78#4864—31no—
79#4844—31no—
80#4834—31no—
81#4784—31no—
82#4781—31no—
83#4773D311yescharacteristic, complemented
84#4772—31no—
85#4772—31no—
86#4772—61no—
87D3×#102—31no—
88#4768—31no—
89#4766D311yescharacteristic, complemented
90#67⋊C8—31no—
91#4722—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C22×C3⋊Dic3—21no—
96#3830—22no—
97#3830—41no—
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C3×D3×D4—22no—
103C3×D3×D4—41no—
104C2×C3×D12—21no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×#626—21no—
109C2×#626—21no—
110C2×#626D411yescharacteristic
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4×C3⋊Dic3—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C8×C3⋊D3—41no—
120C3×#217—21no—
121C3×#213—22no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×D24—41no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3D411yescharacteristic
134#3722D411yescharacteristic
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142#3716—41no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C22×C3×D4—31no—
146C2×#237—31no—
147C2×#237—31no—
148C2×#237—61no—
149C2×D3×D4C2×D311yescharacteristic
150C2×C3×D8—31no—
151C2×C3×D8—31no—
152C3×#125—31no—
153C3×#121—31no—
154C3×C4×D4—31no—
155#953—61no—
156C2×#217—61no—
157#939—61no—
158#939—61no—
159#938—31no—
160#938—31no—
161#936—31no—
162#935—61no—
163D4×Dic3—31no—
164D4×Dic3—61no—
165D4×Dic3C2×D311yescharacteristic
166C2×#214—31no—
167C2×#213C2×D311yescharacteristic
168#930—61no—
169C4×#67—31no—
170C2×(C2×D3)⋊C4—61no—
171C2×C4⋊Dic3—31no—
172#924—31no—
173C22×C3⋊C8—31no—
174C2×D24C2×D311yescharacteristic
175C2×#204—31no—
176C2×D3×C8—31no—
177C2×D3×C8—31no—
178C2×D3×C8—31no—
179C2×D3×C8—61no—
180#898—61no—
181#897—31no—
182#895—31no—
183#895—31no—
184#895—61no—
185#895C2×D311yescharacteristic
186#894—61no—
187#893—61no—
188#892—31no—
189#892—31no—
190#892—61no—
191D3×C4⋊C4—31no—
192#890C2×D311yescharacteristic, complemented
193#886—61no—
194#886—61no—
195#882—61no—
196#879—61no—
197#875—31no—
198C4×D12—31no—
199C4×D12—31no—
200C3×#107—31no—
201C3×#106—31no—
202C3×C4⋊C8—31no—
203C3×#102—21no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102C2×D311yescharacteristic
207C3×#102C2×D311yescharacteristic
208C3×C22⋊C8—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—61no—
215#832C2×D311yescharacteristic
216#821—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8C2×D311yescharacteristic
220#818—31no—
221#818C2×D311yescharacteristic, complemented
222#816—31no—
223#816—31no—
224#816—31no—
225#816—61no—
226Dic3⋊C8C2×D311yescharacteristic, complemented
227C8×Dic3—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#810—61no—
232#809—31no—
233#809—31no—
234#809C2×D311yescharacteristic
235#808C2×D311yescharacteristic, complemented
236#807—31no—
237C4×C3⋊C8—31no—
238C23×C32—21no—
239C22×C3⋊D3C2×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#4112yes—
248C2×C32×C4—21no—
249C2×C32×C4C2411yescharacteristic
250#638—42no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—42no—
254C2×C3⋊Dic3C2×D411yescharacteristic
255C4×C3⋊D3—21no—
256C4×C3⋊D3—21no—
257#634—21no—
258#634—21no—
259C3×#67—42no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—81no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—42no—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273#626—22no—
274#626—81no—
275#626—81no—
276D3×Dic3—81no—
277D3×Dic3—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—31no—
288#466—91no—
289#465—91no—
290#463—91no—
291#449—91no—
292#447—31no—
293C4×D8—91no—
294C8×D4—91no—
295#416—91no—
296C2×#102—91no—
297C24×C3—61no—
298C23×D3—21no—
299C2×C3×D4—21no—
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C2×C3×D4—62no—
305C2×C3×D4—121no—
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C22×D311yescharacteristic
308C22×C3×C4—31no—
309C22×C3×C4—61no—
310C2×#67—21no—
311C2×#67—31no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—121no—
317C22×Dic3—21no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—121no—
323#237—64no—
324#237—62no—
325#237—62no—
326#237—121no—
327#237—121no—
328#237—122no—
329D3×D4—22no—
330D3×D4—41no—
331C2×D12—21no—
332C2×D12—31no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12C22×D311yescharacteristic
336C2×D12C22×D311yescharacteristic
337C2×C4×D3—31no—
338C2×C4×D3—31no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3C22×D311yescharacteristic
343C2×Dic6—31no—
344C2×Dic6—31no—
345C2×Dic6—61no—
346C3×D8—62no—
347C3×D8—121no—
348C2×C3×C8—21no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C2×C3×C8C22×D311yescharacteristic
352C2×C3×C8C22×D311yescharacteristic
353C3×C4⋊C4—21no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C42—31no—
363#217—21no—
364#217—31no—
365#217—61no—
366#217—61no—
367#217—61no—
368#217—61no—
369#217—61no—
370#217—61no—
371#214—121no—
372#213—22no—
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—121no—
386C4⋊Dic3—21no—
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—21no—
396Dic3⋊C4—31no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—121no—
402C4×Dic3C22×D311yescharacteristic
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—121no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409D24—41no—
410#204—121no—
411D3×C8—121no—
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—21no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—84no—
431C2×C3×D3#13512yes—
432C32×C4—41no—
433C32×C4C2×#4111yescharacteristic
434C32×C4H(5,𝔽2)11yescharacteristic
435C3⋊Dic3—21no—
436C3⋊Dic3—41no—
437C3⋊Dic3—41no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—21no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C2×#41—91no—
444C22×D4—31no—
445C2×SD16—91no—
446C2×D8—31no—
447C2×D8—31no—
448C22×C8—91no—
449C22×C8—91no—
450#126—181no—
451#125—31no—
452#124—91no—
453#123—181no—
454#123—181no—
455C22⋊Q8—91no—
456#121—31no—
457#121—91no—
458#121—91no—
459#121—181no—
460#121—181no—
461#120—181no—
462C4×D4—31no—
463C4×D4—91no—
464C4×D4—91no—
465C4×D4—181no—
466#117—91no—
467C2×C4⋊C4—91no—
468C2×C22⋊C4—181no—
469#107—31no—
470#107—91no—
471#106—31no—
472C4⋊C8—31no—
473#103—91no—
474#103—91no—
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—31no—
484C22⋊C8—91no—
485C4×C8—91no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—31no—
489C23×C3—41no—
490C23×C3—61no—
491C23×C3—61no—
492C23×C3—122no—
493C23×C3—122no—
494C23×C3—241no—
495C22×D3—21no—
496C22×D3—21no—
497C22×D3—31no—
498C22×D3—31no—
499C22×D3—42no—
500C22×D3—42no—
501C22×D3—61no—
502C22×D3—81no—
503C22×D3D3×D411yescharacteristic
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—22no—
507C3×D4—41no—
508C3×D4—61no—
509C3×D4—61no—
510C3×D4—61no—
511C3×D4—61no—
512C3×D4—122no—
513C3×D4—122no—
514C3×D4#23712yes—
515C3×D4#23912yes—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—41no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—241no—
528C2×C3×C4C23×D311yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530#67—42no—
531#67—62no—
532#67—122no—
533#67—122no—
534#67—124no—
535#67—241no—
536#67—241no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—81no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3—122no—
550C2×Dic3—122no—
551C2×Dic3—124no—
552C2×Dic3—241no—
553C2×Dic3—241no—
554C2×Dic3D3×D411yescharacteristic
555C2×Dic3D3×D411yescharacteristic
556C2×Dic3D3×D411yescharacteristic
557D12—21no—
558D12—21no—
559D12—21no—
560D12—21no—
561D12—42no—
562D12—62no—
563D12—241no—
564D12—241no—
565C4×D3—21no—
566C4×D3—21no—
567C4×D3—62no—
568C4×D3—62no—
569C4×D3—61no—
570C4×D3—61no—
571C4×D3—61no—
572C4×D3—61no—
573C4×D3—241no—
574C4×D3—241no—
575Dic6—62no—
576Dic6—61no—
577Dic6—61no—
578Dic6—61no—
579Dic6—61no—
580Dic6—121no—
581C3×C8—21no—
582C3×C8—21no—
583C3×C8—41no—
584C3×C8—61no—
585C3×C8—61no—
586C3⋊C8—21no—
587C3⋊C8—21no—
588C3⋊C8—61no—
589C3⋊C8—61no—
590C3⋊C8—121no—
591C2×C32—42no—
592C2×C32#54611yescharacteristic
593C2×C32C2×#13511yescharacteristic
594C2×C32#57611yescharacteristic
595C3⋊D3—41no—
596C3×D3—22no—
597C3×D3—81no—
598C3×D3—81no—
599C24—61no—
600#41—182no—
601#41—361no—
602C2×Q8—91no—
603C2×D4—31no—
604C2×D4—31no—
605C2×D4—61no—
606C2×D4—61no—
607C2×D4—62no—
608C2×D4—91no—
609C2×D4—121no—
610C2×D4—181no—
611C2×D4—181no—
612C2×D4—181no—
613C2×D4C2×D3211yescharacteristic
614C22×C4—31no—
615C22×C4—61no—
616C22×C4—91no—
617C22×C4—181no—
618C22×C4—181no—
619C22×C4—181no—
620SD16—361no—
621D8—62no—
622D8—121no—
623C2×C8—31no—
624C2×C8—31no—
625C2×C8—91no—
626C2×C8—361no—
627C2×C8—361no—
628C2×C8C2×D3211yescharacteristic
629C4⋊C4—31no—
630C4⋊C4—31no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4—91no—
634C4⋊C4—91no—
635C4⋊C4—181no—
636C4⋊C4—181no—
637C4⋊C4C2×D3211yescharacteristic
638C22⋊C4—61no—
639C22⋊C4—61no—
640C22⋊C4—91no—
641C22⋊C4—91no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C42—31no—
650C42—181no—
651C22×C3—22no—
652C22×C3—22no—
653C22×C3—21no—
654C22×C3—32no—
655C22×C3—42no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—61no—
661C22×C3—61no—
662C22×C3—81no—
663C22×C3—81no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3—244no—
671C22×C3C2×D3×D411yescharacteristic
672C22×C3C2×D3×D411yescharacteristic
673C2×D3—21no—
674C2×D3—21no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—41no—
681C2×D3—62no—
682C2×D3—61no—
683C2×D3—61no—
684C2×D3—61no—
685C2×D3—61no—
686C2×D3—61no—
687C2×D3—61no—
688C2×D3—84no—
689C2×D3—121no—
690C2×D3—121no—
691C2×D3#91212yes—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—41no—
695C3×C4—41no—
696C3×C4—61no—
697C3×C4—61no—
698C3×C4—61no—
699C3×C4—81no—
700C3×C4—121no—
701C3×C4—121no—
702C3×C4C2×#23711yescharacteristic
703C3×C4#100411yescharacteristic
704C3×C4C2×#23911yescharacteristic
705C3×C4#100911yescharacteristic
706Dic3—21no—
707Dic3—21no—
708Dic3—21no—
709Dic3—41no—
710Dic3—41no—
711Dic3—62no—
712Dic3—61no—
713Dic3—61no—
714Dic3—122no—
715Dic3—121no—
716Dic3—121no—
717Dic3—121no—
718Dic3—121no—
719Dic3—241no—
720C32#329711yescharacteristic, complemented, Sylow
721C23—21no—
722C23—31no—
723C23—61no—
724C23—61no—
725C23—91no—
726C23—122no—
727C23—122no—
728C23—241no—
729Q8—181no—
730Q8—181no—
731D4—21no—
732D4—61no—
733D4—61no—
734D4—61no—
735D4—61no—
736D4—122no—
737D4—122no—
738D4—182no—
739D4—362no—
740D4—721no—
741D4—721no—
742D4#379612yes—
743C2×C4—21no—
744C2×C4—31no—
745C2×C4—31no—
746C2×C4—31no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—91no—
752C2×C4—181no—
753C2×C4—181no—
754C2×C4—181no—
755C2×C4—181no—
756C2×C4—241no—
757C2×C4—362no—
758C2×C4—721no—
759C2×C4—721no—
760C2×C4C22×D3211yescharacteristic
761C8—21no—
762C8—61no—
763C8—61no—
764C8—181no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—42no—
769C2×C3—42no—
770C2×C3—62no—
771C2×C3—82no—
772C2×C3—241no—
773C2×C3—241no—
774C2×C3#559111yescharacteristic
775C2×C3#563011yescharacteristic
776C2×C3C2×#91211yescharacteristic
777C2×C3D3×#13511yescharacteristic
778C2×C3#577411yescharacteristic
779C2×C3#577411yescharacteristic
780D3—22no—
781D3—81no—
782D3—81no—
783D3—122no—
784D3—121no—
785D3—121no—
786C22—22no—
787C22—32no—
788C22—41no—
789C22—41no—
790C22—61no—
791C22—61no—
792C22—121no—
793C22—121no—
794C22—121no—
795C22—121no—
796C22—121no—
797C22—121no—
798C22—181no—
799C22—181no—
800C22—181no—
801C22—244no—
802C22D32×D411yescharacteristic
803C4—41no—
804C4—61no—
805C4—61no—
806C4—61no—
807C4—121no—
808C4—121no—
809C4—181no—
810C4—361no—
811C4—361no—
812C4C2×#379611yescharacteristic
813C4#6431411yescharacteristic
814C3—21no—
815C3#8001511yescharacteristic, complemented
816C3#8118711yescharacteristic, complemented
817C2—42no—
818C2—62no—
819C2—241no—
820C2—241no—
821C2—361no—
822C2#1059406311yescharacteristic
823C2D3×#91211yescharacteristic
824C2#1059475011yescharacteristic
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. #10595246C2semidirect
2. #10594437C2semidirect
3. #10592471C2semidirect
4. C3×#4773C2semidirect
5. C3×#4766C2semidirect
6. #10591457C2semidirect
7. Dic3×#213C2semidirect
8. D3×#832C2semidirect
9. #10590906C2semidirect
10. #10590844C2semidirect
11. #10590755C2semidirect
12. #10590684C2semidirect
13. #10590578C2semidirect
14. #10590533C2semidirect
15. #10590513C2semidirect
20. C2×C8×C3⋊D3C22semidirect
21. #64101C22semidirect
26. C3×#890C22semidirect
32. #63916C22semidirect
35. Dic3×D12C22semidirect
42. C2×#3716C22semidirect
46. #63643C22semidirect
47. #63637C22semidirect
50. C3×#818C22semidirect
51. C3×Dic3⋊C8C22semidirect
53. C3×#808C22semidirect
54. #63575C22semidirect
55. #63567C22semidirect
58. #63562C22semidirect
59. #63557C22semidirect
60. Dic3×C3⋊C8C22semidirect
83. #4773D3semidirect
89. #4766D3semidirect
192. #890C2×D3semidirect
221. #818C2×D3semidirect
226. Dic3⋊C8C2×D3semidirect
235. #808C2×D3semidirect
720. C32#3297semidirect
815. C3#80015semidirect
816. C3#81187semidirect

Maximal subgroups

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

subgroupindex
#105952462
#105944372
#105924712
C3×#47732
C3×#47662
#105914572
Dic3×#2132
D3×#8322
#105909062
#105908442
#105907552
#105906842
#105905782
#105905332
#105905132
#811873
#800153