Finite Group Databasebeta

← #11882213

Subgroups — #11882213

Order 1152.

926 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594369C211yesmaximal, characteristic, complemented
2#10594367C211yesmaximal, characteristic, complemented
3#10592589C211yesmaximal, characteristic, complemented
4C3×#4890C211yesmaximal, characteristic, complemented
5C3×#4883C211yesmaximal, characteristic, complemented
6#10590826C211yesmaximal, characteristic, complemented
7#10590753C211yesmaximal, characteristic, complemented
8#10590749C211yesmaximal, characteristic, complemented
9D3×Dic3⋊C8C211yesmaximal, characteristic, complemented
10#10590576C211yesmaximal, characteristic, complemented
11#10590551C211yesmaximal, characteristic, complemented
12#10590547C211yesmaximal, characteristic, complemented
13#10590499C211yesmaximal, characteristic, complemented
14#10590471C211yesmaximal, characteristic, complemented
15#10590463C211yesmaximal, characteristic, complemented
16#80975—31nomaximal
17#80702—31nomaximal
18C2×#3796—21no—
19C2×#3795—21no—
20#64102C2211yescharacteristic
21#64097C2211yescharacteristic
22C2×C3×D24C2211yescharacteristic
23C2×C3×D3×C8C2211yescharacteristic
24C3×#895C2211yescharacteristic
25C3×#895C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#888C2211yescharacteristic
28#63914C2211yescharacteristic
29#63913—21no—
30#63911C2211yescharacteristic
31#63909C2211yescharacteristic
32#63908C2211yescharacteristic
33#63907—21no—
34#63898C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36#63886—21no—
37#63885—21no—
38#63881—21no—
39#63879—21no—
40C4×D3×Dic3C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C2×#3713C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45C32×#107C2211yescharacteristic
46#63648C2211yescharacteristic
47#63641C2211yescharacteristic
48#63636C2211yescharacteristic
49#63634C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×#809C2211yescharacteristic
53C3×#809C2211yescharacteristic
54C3×#809C2211yescharacteristic
55C3×#807C2211yescharacteristic
56#63575C2211yescharacteristic
57#63572C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic
59#63563C2211yescharacteristic
60#63562C2211yescharacteristic
61#5725—31no—
62#5596—31no—
63#5596—31no—
64#5548—31no—
65C3×#474—31no—
66C3×#466—31no—
67#5150—31no—
68#5150—31no—
69#5115—31no—
70C2×Dic3⋊C8—31no—
71#5087—31no—
72#5038—31no—
73#5038—31no—
74#5015—31no—
75#4890—31no—
76#4890—31no—
77#4890—31no—
78#4890—61no—
79#4890D311yescharacteristic, complemented
80#4883—31no—
81#4883D311yescharacteristic, complemented
82#4843—31no—
83D3×C4⋊C8—31no—
84#4786—31no—
85#4786—31no—
86#4786—31no—
87#4786—31no—
88#4775—31no—
89#4775—31no—
90#4759—31no—
91#4759—31no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×#634—21no—
95C2×C3×D12—21no—
96C2×C3×D12—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6—21no—
103C2×#626—21no—
104C2×#626—21no—
105C2×#626—21no—
106C2×#625—21no—
107C2×#625—21no—
108C2×#625—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3D411yescharacteristic
112C2×D3×Dic3D411yescharacteristic
113#3796—44no—
114#3795—44no—
115C2×C32×C8C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118#3752—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121C4×C3⋊Dic3C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D24—41no—
132C3×D3×C8—41no—
133#3722—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137Dic32D411yescharacteristic
138Dic32D411yescharacteristic
139#3714—41no—
140#3714—41no—
141#3713—41no—
142D3×C3⋊C8—41no—
143#3245—91noSylow
144C2×#239—61no—
145C2×#237—61no—
146C2×#237—61no—
147C2×#235—61no—
148C2×C3×D8—31no—
149C22×C3×C8—31no—
150C3×C4⋊Q8—31no—
151C3×#121—31no—
152C3×#121—31no—
153C3×C4×D4—31no—
154#947—61no—
155#940—31no—
156#940—31no—
157#940—31no—
158#939—61no—
159#939—61no—
160#938—31no—
161D4×Dic3—31no—
162D4×Dic3—31no—
163C2×#213—31no—
164C2×#213—31no—
165C2×#213—31no—
166C2×#213—31no—
167#930—31no—
168#930—31no—
169C4×#67—61no—
170C2×C4×Dic3—31no—
171C22×C3⋊C8—31no—
172C2×D24—31no—
173C2×D24—31no—
174C2×D24C2×D311yescharacteristic
175C2×D3×C8—31no—
176C2×D3×C8C2×D311yescharacteristic
177#895—31no—
178#895—61no—
179#895C2×D311yescharacteristic
180#895C2×D311yescharacteristic
181#893—31no—
182#893—31no—
183#893—31no—
184#893—61no—
185#893—61no—
186#893C2×D311yescharacteristic
187#888—31no—
188#888—31no—
189#888—61no—
190#888C2×D311yescharacteristic
191#885—61no—
192#885—61no—
193#885—61no—
194#884—61no—
195#67⋊C4—61no—
196#67⋊C4—61no—
197#874—31no—
198C4×D12—31no—
199C42×D3—31no—
200C3×#107—21no—
201C3×#107—31no—
202C3×#107C2×D311yescharacteristic
203C3×#107C2×D311yescharacteristic
204C3×C4⋊C8—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209#832—31no—
210#832—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—61no—
215#821C2×D311yescharacteristic
216#818—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—31no—
221Dic3⋊C8—31no—
222Dic3⋊C8—61no—
223Dic3⋊C8C2×D311yescharacteristic
224#809—31no—
225#809—31no—
226#809—31no—
227#809—61no—
228#809C2×D311yescharacteristic
229#809C2×D311yescharacteristic
230#809C2×D311yescharacteristic
231#807—31no—
232#807—31no—
233#807—31no—
234#807—61no—
235#807C2×D311yescharacteristic
236C4⋊(C3⋊C8)—31no—
237C22×C3⋊D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3C2×D411yescharacteristic
247C2×C3⋊Dic3C2×D411yescharacteristic
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)—21no—
250C4×C3⋊D3—42no—
251#634—42no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—21no—
262C3×D12—42no—
263C3×D12—42no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—42no—
267C3×Dic6—42no—
268#626—42no—
269#626—42no—
270#626—42no—
271#625—42no—
272#625—42no—
273#625—42no—
274D3×Dic3—41no—
275D3×Dic3—42no—
276D3×Dic3—42no—
277D3×Dic3D814yescomplemented
278C32×C8—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#532—91no—
283#532—91no—
284#474—31no—
285#474—91no—
286#474—91no—
287#474—91no—
288#466—31no—
289#466—91no—
290#466—91no—
291#466—91no—
292#459—91no—
293#459—91no—
294#459—91no—
295#459—91no—
296C2×C4⋊C8—91no—
297C2×C3×Q8—61no—
298C2×C3×D4—31no—
299C2×C3×D4—31no—
300C2×C3×D4—31no—
301C2×C3×D4—61no—
302C2×C3×D4—61no—
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C22×Dic3—31no—
315C22×Dic3—31no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318#239—124no—
319#237—124no—
320#237—124no—
321#235—124no—
322C2×D12—21no—
323C2×D12—21no—
324C2×D12—31no—
325C2×D12—31no—
326C2×D12—61no—
327C2×D12—61no—
328C2×D12—61no—
329C2×D12—61no—
330C2×D12C22×D311yescharacteristic
331C2×D12C22×D311yescharacteristic
332C2×D12C22×D311yescharacteristic
333C2×C4×D3—21no—
334C2×C4×D3—31no—
335C2×C4×D3—31no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—121no—
341C2×C4×D3C22×D311yescharacteristic
342C2×Dic6—21no—
343C2×Dic6—61no—
344C2×Dic6—61no—
345C2×Dic6—121no—
346C3×D8—121no—
347C2×C3×C8—21no—
348C2×C3×C8—31no—
349C2×C3×C8—31no—
350C2×C3×C8—121no—
351C2×C3×C8C22×D311yescharacteristic
352C2×C3×C8C22×D311yescharacteristic
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C42—31no—
365#217—61no—
366#217—61no—
367#217—61no—
368#213—121no—
369#213—121no—
370#213—121no—
371#213—121no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—61no—
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—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—61no—
386C4⋊Dic3C22×D311yescharacteristic
387Dic3⋊C4—21no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—121no—
391C4×Dic3—31no—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—31no—
396C4×Dic3—31no—
397C4×Dic3—61no—
398C4×Dic3C22×D311yescharacteristic
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8—121no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405D24—41no—
406D24—121no—
407D24—121no—
408D3×C8—41no—
409D3×C8—121no—
410C22×C32C22×D411yescharacteristic
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C2×C3⋊D3—41no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3C2×D812yes—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4H(5,𝔽2)11yescharacteristic
429C32×C42−1+411yescharacteristic
430C3⋊Dic3—21no—
431C3⋊Dic3—41no—
432C3⋊Dic3C2×D812yes—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3C2×D812yes—
437C2×#41—181no—
438C2×#41—181no—
439C2×D8—31no—
440C2×D8—91no—
441C2×D8—91no—
442C2×D8—91no—
443C22×C8—31no—
444C22×C8—91no—
445C4⋊Q8—31no—
446C4⋊Q8—91no—
447#127—91no—
448#127—91no—
449#124—181no—
450#124—181no—
451#121—31no—
452#121—31no—
453#121—91no—
454#121—91no—
455#121—181no—
456#121—181no—
457C4×D4—31no—
458C4×D4—91no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—181no—
462C4×D4—181no—
463C2×C42—91no—
464#107—31no—
465#107—91no—
466#107—91no—
467#107D3211yescharacteristic
468C4⋊C8—31no—
469C4⋊C8—91no—
470C4⋊C8—91no—
471C4⋊C8—91no—
472#102—31no—
473#102—31no—
474#102—31no—
475#102—31no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480C23×C3—31no—
481C23×C3—61no—
482C23×C3—61no—
483C23×C3—61no—
484C22×D3—21no—
485C22×D3—21no—
486C22×D3—21no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—121no—
490C22×D3D3×D411yescharacteristic
491C3×Q8—122no—
492C3×D4—61no—
493C3×D4—61no—
494C3×D4—61no—
495C3×D4—61no—
496C3×D4—61no—
497C3×D4—61no—
498C3×D4—122no—
499C3×D4—122no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—122no—
514C2×C3×C4C23×D311yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516#67—122no—
517#67—122no—
518#67—122no—
519#67—122no—
520#67—122no—
521#67—122no—
522#67—122no—
523#67—122no—
524#67—122no—
525C2×Dic3—21no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—34no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—121no—
536C2×Dic3—121no—
537C2×Dic3—122no—
538C2×Dic3—122no—
539C2×Dic3D3×D411yescharacteristic
540C2×Dic3D3×D411yescharacteristic
541C2×Dic3D3×D411yescharacteristic
542D12—21no—
543D12—21no—
544D12—21no—
545D12—21no—
546D12—21no—
547D12—21no—
548D12—42no—
549D12—42no—
550D12—62no—
551D12—61no—
552D12—61no—
553D12—61no—
554D12—61no—
555D12—121no—
556D12—122no—
557D12—122no—
558D12—122no—
559C4×D3—21no—
560C4×D3—21no—
561C4×D3—34no—
562C4×D3—42no—
563C4×D3—122no—
564C4×D3—122no—
565C4×D3—122no—
566C4×D3—121no—
567C4×D3—122no—
568C4×D3—242no—
569Dic6—42no—
570Dic6—122no—
571Dic6—122no—
572Dic6—242no—
573C3×C8—21no—
574C3×C8—21no—
575C3×C8—41no—
576C3×C8—61no—
577C3×C8—61no—
578C3⋊C8—21no—
579C3⋊C8—21no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—121no—
583C2×C32#53711yescharacteristic
584C2×C32C22×D811yescharacteristic
585C2×C32#57511yescharacteristic
586C3⋊D3—81no—
587C3×D3—22no—
588C3×D3—81no—
589C3×D3—81no—
590C3×D3—81no—
591#41—364no—
592#41—364no—
593C2×Q8—61no—
594C2×Q8—181no—
595C2×D4—31no—
596C2×D4—31no—
597C2×D4—31no—
598C2×D4—61no—
599C2×D4—61no—
600C2×D4—91no—
601C2×D4—181no—
602C2×D4—181no—
603C2×D4—181no—
604C2×D4—181no—
605C2×D4—181no—
606C2×D4—181no—
607C22×C4—31no—
608C22×C4—61no—
609C22×C4—91no—
610C22×C4—91no—
611C22×C4—181no—
612C22×C4—181no—
613C22×C4—181no—
614D8—121no—
615D8—361no—
616D8—361no—
617D8—361no—
618C2×C8—31no—
619C2×C8—31no—
620C2×C8—91no—
621C2×C8—121no—
622C2×C8—361no—
623C2×C8C2×D3211yescharacteristic
624C4⋊C4—31no—
625C4⋊C4—61no—
626C4⋊C4—91no—
627C4⋊C4—181no—
628C4⋊C4C2×D3211yescharacteristic
629C4⋊C4C2×D3211yescharacteristic
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C42—31no—
639C42—91no—
640C42—91no—
641C42—91no—
642C22×C3—21no—
643C22×C3—32no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—121no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3C2×D3×D411yescharacteristic
656C22×C3C2×D3×D411yescharacteristic
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—122no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—241no—
676C2×D3—241no—
677C2×D3D3×D812yes—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—32no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—61no—
686C3×C4—61no—
687C3×C4—81no—
688C3×C4—81no—
689C3×C4—121no—
690C3×C4#100411yescharacteristic
691C3×C4#100711yescharacteristic
692C3×C4#100911yescharacteristic
693C3×C4#101011yescharacteristic
694Dic3—21no—
695Dic3—21no—
696Dic3—32no—
697Dic3—32no—
698Dic3—41no—
699Dic3—62no—
700Dic3—61no—
701Dic3—61no—
702Dic3—121no—
703Dic3—121no—
704Dic3—121no—
705Dic3—241no—
706Dic3D3×D812yes—
707C32#324511yescharacteristic, complemented, Sylow
708C23—31no—
709C23—61no—
710C23—61no—
711C23—61no—
712C23—181no—
713Q8—122no—
714Q8—362no—
715D4—61no—
716D4—61no—
717D4—61no—
718D4—61no—
719D4—61no—
720D4—61no—
721D4—122no—
722D4—122no—
723D4—181no—
724D4—181no—
725D4—362no—
726D4—362no—
727D4—362no—
728D4—362no—
729D4—362no—
730D4—362no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—31no—
734C2×C4—31no—
735C2×C4—31no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—94no—
740C2×C4—91no—
741C2×C4—91no—
742C2×C4—122no—
743C2×C4—181no—
744C2×C4—362no—
745C2×C4—362no—
746C2×C4—361no—
747C2×C4—362no—
748C2×C4C22×D3211yescharacteristic
749C8—21no—
750C8—61no—
751C8—61no—
752C8—181no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—62no—
757C2×C3—241no—
758C2×C3—241no—
759C2×C3—241no—
760C2×C3#559711yescharacteristic
761C2×C3#562911yescharacteristic
762C2×C3C2×D3×D811yescharacteristic
763C2×C3C2×D3×D811yescharacteristic
764C2×C3#576811yescharacteristic
765C2×C3#577711yescharacteristic
766D3—22no—
767D3—81no—
768D3—81no—
769D3—81no—
770D3—242no—
771D3—241no—
772D3—241no—
773C22—32no—
774C22—61no—
775C22—61no—
776C22—121no—
777C22—121no—
778C22—121no—
779C22—121no—
780C22—121no—
781C22—121no—
782C22—121no—
783C22—121no—
784C22—121no—
785C22—361no—
786C22—361no—
787C22—361no—
788C22D32×D411yescharacteristic
789C4—32no—
790C4—41no—
791C4—41no—
792C4—61no—
793C4—61no—
794C4—92no—
795C4—121no—
796C4—181no—
797C4—361no—
798C4#6430711yescharacteristic
799C4#6431511yescharacteristic
800C3—21no—
801C3#8070211yescharacteristic, complemented
802C3#8097511yescharacteristic, complemented
803C2—62no—
804C2—241no—
805C2—241no—
806C2—241no—
807C2—721no—
808C2#1059436811yescharacteristic
809C2D32×D811yescharacteristic
810C2#1059476311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
hypercenter#107D32
hypocenterC32#3245
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
1. #10594369C2semidirect
2. #10594367C2semidirect
3. #10592589C2semidirect
4. C3×#4890C2semidirect
5. C3×#4883C2semidirect
6. #10590826C2semidirect
7. #10590753C2semidirect
8. #10590749C2semidirect
9. D3×Dic3⋊C8C2semidirect
10. #10590576C2semidirect
11. #10590551C2semidirect
12. #10590547C2semidirect
13. #10590499C2semidirect
14. #10590471C2semidirect
15. #10590463C2semidirect
79. #4890D3semidirect
81. #4883D3semidirect
277. D3×Dic3D8semidirect
707. C32#3245semidirect
801. C3#80702semidirect
802. C3#80975semidirect

Maximal subgroups

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

subgroupindex
#105943692
#105943672
#105925892
C3×#48902
C3×#48832
#105908262
#105907532
#105907492
D3×Dic3⋊C82
#105905762
#105905512
#105905472
#105904992
#105904712
#105904632
#809753
#807023