Finite Group Databasebeta

← #11887283

Subgroups — #11887283

Order 1152.

864 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595427C211yesmaximal, characteristic
2#10594456C211yesmaximal, characteristic, complemented
3#10592499C211yesmaximal, characteristic, complemented
4C3×#4813C211yesmaximal, characteristic, complemented
5C3×#4804C211yesmaximal, characteristic, complemented
6#10591597C211yesmaximal, characteristic, complemented
7#10591579C211yesmaximal, characteristic, complemented
8#10591549C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590847C211yesmaximal, characteristic, complemented
11#10590742C211yesmaximal, characteristic, complemented
12C8×#625C211yesmaximal, characteristic, complemented
13#10590596C211yesmaximal, characteristic, complemented
14#10590473C211yesmaximal, characteristic, complemented
15#10590424C211yesmaximal, characteristic, complemented
16#80775—31nomaximal
17#78845—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20#64156C2211yescharacteristic
21#64099C2211yescharacteristic, complemented
22C3×#946C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic, complemented
24C2×C3×D3×C8C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic, complemented
26C3×#897C2211yescharacteristic
27C3×#892C2211yescharacteristic, complemented
28#63922—21no—
29D3×(C2×D3)⋊C4—21no—
30#63909C2211yescharacteristic
31C4×#625C2211yescharacteristic
32#63898C2211yescharacteristic
33#63891—21no—
34D3×C4⋊Dic3C2211yescharacteristic
35#63886—21no—
36#63877—21no—
37#63869—21no—
38#63858—21no—
39#63856C2211yescharacteristic, complemented
40#63850—21no—
41#63843C2211yescharacteristic, complemented
42C2×#3717C2211yescharacteristic
43C2×#3715C2211yescharacteristic
44C32×#103C2211yescharacteristic, complemented
45#63662C2211yescharacteristic, complemented
46#63648C2211yescharacteristic
47C8×C3⋊Dic3C2211yescharacteristic, complemented
48#63636C2211yescharacteristic
49C3×#835C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic
51C3×#816C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#807C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63563C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61#5829—31no—
62#5642—31no—
63#5630—31no—
64#5529—31no—
65C3×#467—31no—
66C3×#416—31no—
67#5239—31no—
68#5187—31no—
69#5185—31no—
70#5114—31no—
71C2×#821—31no—
72C8×#67—31no—
73C8×#67—31no—
74#5046—31no—
75#5043—31no—
76#5003—31no—
77#4891—31no—
78#4885—31no—
79#4813D311yescharacteristic, complemented
80#4807—31no—
81#4805—31no—
82#4804D311yescharacteristic, complemented
83#4800—31no—
84#4800—31no—
85#4800—61no—
86#4798—31no—
87#4788—31no—
88#4776—31no—
89D3×#102—31no—
90#4763—31no—
91#4758—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C3×#239—22no—
96C3×#239—41no—
97C2×C3×D12—21no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×#626—21no—
104C2×#626—21no—
105C2×#625D411yescharacteristic
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108D3×D12—22no—
109D3×D12—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3752—21no—
113#3752—21no—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#216—41no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3—21no—
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×D3×C8—41no—
131C3×D3×C8—41no—
132#3724—21no—
133#3724D411yescharacteristic
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142#3717—41no—
143#3715—22no—
144#3296—91noSylow
145C2×C3×#41—31no—
146C2×#239C2×D311yescharacteristic
147C2×D3×D4—31no—
148C22×D12—31no—
149C2×C3×Q16—31no—
150C22×C3×C8—31no—
151C22×C3×C8—31no—
152C3×C22⋊Q8—31no—
153C3×C22⋊Q8—31no—
154C3×#117—31no—
155#947—31no—
156#947—31no—
157#947—61no—
158#946—31no—
159#946C2×D311yescharacteristic
160Q8×Dic3—31no—
161C2×#216C2×D311yescharacteristic, complemented
162C2×#215—31no—
163C2×#215—31no—
164#939—61no—
165#937—61no—
166D4×Dic3—31no—
167C2×#214—31no—
168#930—31no—
169#929—61no—
170C4×#67—31no—
171C4×#67—31no—
172C2×(C2×D3)⋊C4—61no—
173C2×C4⋊Dic3—31no—
174#924—31no—
175C2×#204—31no—
176C2×D3×C8C2×D311yescharacteristic
177C2×D3×C8C2×D311yescharacteristic, complemented
178#898—61no—
179#897C2×D311yescharacteristic
180#895—31no—
181#895—61no—
182#894—61no—
183#893—31no—
184#892C2×D311yescharacteristic, complemented
185D3×C4⋊C4—31no—
186#890—31no—
187#890—31no—
188#890—61no—
189#890—61no—
190#887—31no—
191#886—61no—
192#883—61no—
193#882—61no—
194D3×C22⋊C4—61no—
195#879—61no—
196#877—61no—
197#872—61no—
198#870—61no—
199C3×#107—31no—
200C3×#103—21no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#103C2×D311yescharacteristic, complemented
204C3×#103C2×D311yescharacteristic, complemented
205C3×#102—31no—
206C3×#102—31no—
207#835—31no—
208#835—31no—
209#835—61no—
210#835C2×D311yescharacteristic, complemented
211#832—31no—
212#830—31no—
213#830—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—61no—
219#821C2×D311yescharacteristic
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222#817—31no—
223#816C2×D311yescharacteristic, complemented
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226C8×Dic3—31no—
227C8×Dic3—31no—
228C8×Dic3—61no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—61no—
233#809C2×D311yescharacteristic
234#808—31no—
235#808—31no—
236#808—31no—
237#807C2×D311yescharacteristic, complemented
238C22×C3⋊D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C32×Q8—21no—
246C32×Q8—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12—42no—
262C3×D12#4112yes—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—42no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270#626—42no—
271#626—81no—
272#625—22no—
273D3×Dic3—42no—
274D3×Dic3—81no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—91no—
280#546—91no—
281#488—91no—
282#483—91no—
283#482—91no—
284#478—91no—
285#467—31no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290C4×SD16—91no—
291C8×D4—91no—
292#416—31no—
293C2×#102—91no—
294C23×D3—61no—
295C23×D3—61no—
296C3×#41—62no—
297C3×#41—121no—
298C2×C3×Q8—21no—
299C2×C3×Q8—31no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—61no—
307C2×#67—31no—
308C2×#67—31no—
309C2×#67—61no—
310C2×#67—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313#239—22no—
314#239—41no—
315D3×D4—62no—
316D3×D4—121no—
317C2×D12—21no—
318C2×D12—31no—
319C2×D12—31no—
320C2×D12—61no—
321C2×D12—62no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12—121no—
325C2×D12C22×D311yescharacteristic
326C2×C4×D3—21no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3C22×D311yescharacteristic
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6C22×D311yescharacteristic
332C3×Q16—121no—
333C2×C3×C8—21no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C2×C3×C8—121no—
337C2×C3×C8—121no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C3×C4⋊C4—21no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C42—61no—
351#217—31no—
352#217—31no—
353#217—61no—
354#217—61no—
355#216—41no—
356#215—62no—
357#215—121no—
358#214—62no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—31no—
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—121no—
373(C2×D3)⋊C4—121no—
374C4⋊Dic3—21no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—121no—
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—21no—
386Dic3⋊C4—31no—
387Dic3⋊C4—31no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—121no—
395C4×Dic3—21no—
396C4×Dic3—31no—
397C4×Dic3—31no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406#204—121no—
407D3×C8—41no—
408D3×C8—41no—
409C22×C32C22×D411yescharacteristic
410C2×C3⋊D3—41no—
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—22no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3#13512yes—
422D32—84no—
423C32×C4—41no—
424C32×C4—41no—
425C32×C4C2×#4111yescharacteristic
426C32×C4H(5,𝔽2)11yescharacteristic
427C3⋊Dic3—21no—
428C3⋊Dic3—21no—
429C3⋊Dic3—41no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—31no—
436C22×D4—91no—
437C2×Q16—31no—
438C2×SD16—91no—
439C2×SD16—91no—
440C22×C8—31no—
441C22×C8—31no—
442#126—181no—
443#125—91no—
444#125—181no—
445#124—91no—
446#123—181no—
447#123—181no—
448C22⋊Q8—31no—
449C22⋊Q8—31no—
450C22⋊Q8—91no—
451#121—91no—
452#121—181no—
453#120—181no—
454C4×Q8—91no—
455C4×D4—91no—
456C4×D4—91no—
457#117—31no—
458#117—181no—
459C2×C4⋊C4—91no—
460C2×C22⋊C4—181no—
461#107—31no—
462#106—91no—
463#106—91no—
464C4⋊C8—91no—
465#103—31no—
466#103—31no—
467#103—91no—
468#103D3211yescharacteristic, complemented
469#102—31no—
470#102—31no—
471#102—91no—
472#102—91no—
473#102—91no—
474#102—91no—
475C22⋊C8—91no—
476C22⋊C8—91no—
477C4×C8—91no—
478C23×C3—31no—
479C23×C3—31no—
480C23×C3—61no—
481C22×D3—21no—
482C22×D3—61no—
483C22×D3—61no—
484C22×D3—121no—
485C22×D3—122no—
486C22×D3—122no—
487C22×D3—122no—
488C22×D3—122no—
489C22×D3—241no—
490C22×D3—241no—
491C22×D3D3×D411yescharacteristic
492C22×D3D3×D411yescharacteristic
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—41no—
498C3×Q8—41no—
499C3×Q8—61no—
500C3×Q8—61no—
501C3×D4—32no—
502C3×D4—61no—
503C3×D4—122no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—122no—
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523#67—62no—
524#67—62no—
525#67—122no—
526#67—241no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—121no—
539C2×Dic3—122no—
540C2×Dic3—241no—
541C2×Dic3D3×D411yescharacteristic
542C2×Dic3D3×D411yescharacteristic
543D12—21no—
544D12—42no—
545D12—61no—
546D12—61no—
547D12—61no—
548D12—61no—
549D12—121no—
550D12—121no—
551D12—122no—
552D12—241no—
553D12#23512yes—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—21no—
558C4×D3—42no—
559C4×D3—122no—
560C4×D3—241no—
561Dic6—21no—
562Dic6—21no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—41no—
566C3×C8—61no—
567C3×C8—61no—
568C3⋊C8—21no—
569C3⋊C8—21no—
570C3⋊C8—61no—
571C3⋊C8—61no—
572C3⋊C8—121no—
573C2×C32#54611yescharacteristic
574C2×C32C2×#13511yescharacteristic
575C2×C32#57711yescharacteristic
576C3⋊D3—81no—
577C3×D3—22no—
578C3×D3—42no—
579C3×D3—41no—
580C24—181no—
581#41—62no—
582#41—121no—
583C2×Q8—31no—
584C2×Q8C2×D3211yescharacteristic
585C2×D4—31no—
586C2×D4—61no—
587C2×D4—91no—
588C2×D4—91no—
589C2×D4—181no—
590C2×D4—182no—
591C2×D4—181no—
592C2×D4—361no—
593C22×C4—31no—
594C22×C4—31no—
595C22×C4—61no—
596C22×C4—181no—
597C22×C4—181no—
598Q16—121no—
599SD16—182no—
600SD16—361no—
601C2×C8—31no—
602C2×C8—31no—
603C2×C8—91no—
604C2×C8—121no—
605C2×C8—121no—
606C2×C8C2×D3211yescharacteristic
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4C2×D3211yescharacteristic
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—91no—
623C22⋊C4—91no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C42—61no—
630C42—91no—
631C42—181no—
632C22×C3—21no—
633C22×C3—32no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—62no—
639C22×C3—61no—
640C22×C3—121no—
641C22×C3—121no—
642C22×C3C2×D3×D411yescharacteristic
643C22×C3C2×D3×D411yescharacteristic
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—22no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—121no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—241no—
659C2×D3—241no—
660C2×D3—241no—
661C2×D3—244no—
662C2×D3—244no—
663C2×D3#91912yes—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—61no—
671C3×C4—61no—
672C3×C4—81no—
673C3×C4—81no—
674C3×C4—121no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4C2×#23511yescharacteristic
678C3×C4#100411yescharacteristic
679C3×C4#100411yescharacteristic
680C3×C4D3×#4111yescharacteristic
681Dic3—21no—
682Dic3—21no—
683Dic3—41no—
684Dic3—41no—
685Dic3—41no—
686Dic3—61no—
687Dic3—61no—
688Dic3—61no—
689Dic3—61no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—241no—
695C32#329611yescharacteristic, complemented, Sylow
696C23—31no—
697C23—31no—
698C23—61no—
699C23—181no—
700C23—362no—
701C23—362no—
702C23—721no—
703Q8—21no—
704Q8—21no—
705Q8—61no—
706Q8—61no—
707D4—32no—
708D4—61no—
709D4—122no—
710D4—182no—
711D4—181no—
712D4—181no—
713D4—362no—
714D4—721no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—31no—
718C2×C4—31no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—91no—
727C2×C4—91no—
728C2×C4—122no—
729C2×C4—181no—
730C2×C4—362no—
731C2×C4—721no—
732C2×C4C22×D3211yescharacteristic
733C8—21no—
734C8—61no—
735C8—61no—
736C8—181no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—62no—
741C2×C3—122no—
742C2×C3—121no—
743C2×C3#549011yescharacteristic
744C2×C3#561011yescharacteristic
745C2×C3C2×#91911yescharacteristic
746C2×C3D3×#13511yescharacteristic
747C2×C3#577011yescharacteristic
748C2×C3#577011yescharacteristic
749D3—22no—
750D3—41no—
751D3—42no—
752D3—241no—
753D3—241no—
754D3—481no—
755C22—32no—
756C22—61no—
757C22—61no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—62no—
762C22—121no—
763C22—121no—
764C22—361no—
765C22—361no—
766C22—361no—
767C22—724no—
768C22D32×D411yescharacteristic
769C4—41no—
770C4—41no—
771C4—61no—
772C4—61no—
773C4—121no—
774C4—121no—
775C4—121no—
776C4—181no—
777C4—181no—
778C4—361no—
779C4D3×#23511yescharacteristic
780C4#6431311yescharacteristic
781C3—21no—
782C3#7884511yescharacteristic, complemented
783C3#8077511yescharacteristic, complemented
784C2—62no—
785C2—121no—
786C2—122no—
787C2—721no—
788C2#1059427311yescharacteristic
789C2#1059475711yescharacteristic
790C2D3×#91911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10595427C2
hypercenter#103D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. #10594456C2semidirect
3. #10592499C2semidirect
4. C3×#4813C2semidirect
5. C3×#4804C2semidirect
6. #10591597C2semidirect
7. #10591579C2semidirect
8. #10591549C2semidirect
9. D3×#821C2semidirect
10. #10590847C2semidirect
11. #10590742C2semidirect
12. C8×#625C2semidirect
13. #10590596C2semidirect
14. #10590473C2semidirect
15. #10590424C2semidirect
21. #64099C22semidirect
23. C2×C3×#216C22semidirect
25. C2×C3×D3×C8C22semidirect
27. C3×#892C22semidirect
39. #63856C22semidirect
41. #63843C22semidirect
44. C32×#103C22semidirect
45. #63662C22semidirect
47. C8×C3⋊Dic3C22semidirect
49. C3×#835C22semidirect
51. C3×#816C22semidirect
53. C3×#807C22semidirect
54. #63574C22semidirect
55. #63573C22semidirect
56. #63572C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
79. #4813D3semidirect
82. #4804D3semidirect
161. C2×#216C2×D3semidirect
177. C2×D3×C8C2×D3semidirect
184. #892C2×D3semidirect
203. C3×#103C2×D3semidirect
204. C3×#103C2×D3semidirect
210. #835C2×D3semidirect
223. #816C2×D3semidirect
237. #807C2×D3semidirect
468. #103D32semidirect
695. C32#3296semidirect
782. C3#78845semidirect
783. C3#80775semidirect

Maximal subgroups

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

subgroupindex
#105954272
#105944562
#105924992
C3×#48132
C3×#48042
#105915972
#105915792
#105915492
D3×#8212
#105908472
#105907422
C8×#6252
#105905962
#105904732
#105904242
#807753
#788453