Finite Group Databasebeta

← #11887434

Subgroups — #11887434

Order 1152.

902 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595427C211yesmaximal, characteristic, complemented
2#10594559C211yesmaximal, characteristic, complemented
3#10592518C211yesmaximal, characteristic, complemented
4C3×#4811C211yesmaximal, characteristic, complemented
5C3×#4804C211yesmaximal, characteristic, complemented
6#10591588C211yesmaximal, characteristic, complemented
7#10591585C211yesmaximal, characteristic, complemented
8#10591539C211yesmaximal, characteristic, complemented
9#10590947C211yesmaximal, characteristic, complemented
10#10590832C211yesmaximal, characteristic, complemented
11#10590780C211yesmaximal, characteristic, complemented
12#10590717C211yesmaximal, characteristic, complemented
13D3×#809C211yesmaximal, characteristic, complemented
14#10590459C211yesmaximal, characteristic, complemented
15#10590424C211yesmaximal, characteristic, complemented
16#81485—31nomaximal
17#78846—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20#64156C2211yescharacteristic
21C2×#3755C2211yescharacteristic, complemented
22C2×#3745C2211yescharacteristic
23#64102C2211yescharacteristic, complemented
24C3×#946C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic, complemented
26C3×#892C2211yescharacteristic, complemented
27C3×D3×C4⋊C4C2211yescharacteristic
28#63922—21no—
29D3×(C2×D3)⋊C4—21no—
30#63909C2211yescharacteristic
31#63909C2211yescharacteristic
32#63909C2211yescharacteristic, complemented
33#63906—21no—
34C4×#626—21no—
35C4×#625C2211yescharacteristic
36#63898C2211yescharacteristic
37#63886—21no—
38#63872C2211yescharacteristic, complemented
39#63868—21no—
40#63853—21no—
41#63850—21no—
42C2×#3714C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#103C2211yescharacteristic, complemented
45#63641C2211yescharacteristic, complemented
46#63636C2211yescharacteristic
47C3×#835C2211yescharacteristic, complemented
48C3×#835C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#818C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#807C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61#5829—31no—
62#5630—31no—
63#5530—31no—
64#5514—31no—
65C3×#484—31no—
66C3×#416—31no—
67#5238—31no—
68#5115—31no—
69C8×#67—31no—
70#5048—31no—
71#5003—31no—
72C2×#809—31no—
73#4891—31no—
74#4885—31no—
75#4883—31no—
76#4872—31no—
77#4819—31no—
78#4819—31no—
79#4819—61no—
80#4811D311yescharacteristic, complemented
81#4810—31no—
82#4807—31no—
83#4804D311yescharacteristic, complemented
84#4800—31no—
85#4800—31no—
86#4773—31no—
87D3×#102—31no—
88#4766—31no—
89#4756—31no—
90#4732—31no—
91#67⋊C8—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C3×#239—22no—
98C3×#239—41no—
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×#626—21no—
106C2×#626—21no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#625D411yescharacteristic
110C2×D3×Dic3—21no—
111D3×D12—22no—
112D3×D12—41no—
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3755—41no—
116#3752—21no—
117#3752—21no—
118#3752—21no—
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121#3745—41no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×D3×C8—41no—
133#3724D411yescharacteristic
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136#3722—21no—
137#3722—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141(C2×D3)⋊Dic3D411yescharacteristic
142#3714—22no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C2×C3×#41—31no—
146C2×#239C2×D311yescharacteristic
147C2×D3×D4—31no—
148C22×D12—31no—
149C22×C3×C8—31no—
150C3×C22⋊Q8—31no—
151C3×#117—31no—
152C2×C3×C4⋊C4—31no—
153#947—31no—
154#947—31no—
155#947—61no—
156#946C2×D311yescharacteristic
157C2×#215—31no—
158C2×#215—31no—
159C2×#215—61no—
160#939—61no—
161#937—61no—
162D4×Dic3—31no—
163C2×#213—31no—
164#930—31no—
165#930—31no—
166#930—31no—
167#930—61no—
168#929—61no—
169C4×#67—31no—
170C4×#67—31no—
171C4×#67—61no—
172C2×(C2×D3)⋊C4—61no—
173C22×C3⋊C8—31no—
174C2×D24—31no—
175C2×D24—31no—
176C2×D24—31no—
177C2×D24—61no—
178C2×D3×C8—31no—
179C2×D3×C8C2×D311yescharacteristic, complemented
180#898—61no—
181#895—31no—
182#895—31no—
183#895—31no—
184#895—61no—
185#894—61no—
186#894—61no—
187#893—31no—
188#893—31no—
189#893—31no—
190#893—61no—
191#892C2×D311yescharacteristic, complemented
192D3×C4⋊C4C2×D311yescharacteristic
193#890—31no—
194#890—31no—
195#884—61no—
196#883—61no—
197#882—61no—
198D3×C22⋊C4—61no—
199#876—61no—
200C4×D12—61no—
201C3×#107—31no—
202C3×#107—31no—
203C3×#103—21no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103C2×D311yescharacteristic, complemented
207C3×#103C2×D311yescharacteristic, complemented
208C3×#102—31no—
209C3×#102—31no—
210C3×C22⋊C8—31no—
211#835C2×D311yescharacteristic, complemented
212#835C2×D311yescharacteristic, complemented
213#832—31no—
214#830—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821C2×D311yescharacteristic
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8C2×D311yescharacteristic
221#818C2×D311yescharacteristic, complemented
222Dic3⋊C8—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8—61no—
225C8×Dic3—31no—
226C8×Dic3—31no—
227#809—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—61no—
234#809C2×D311yescharacteristic
235#808—31no—
236#808—31no—
237#807C2×D311yescharacteristic, complemented
238C22×C3⋊D3—21no—
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C22×C3×D3C2×D411yescharacteristic
243C2×D32—42no—
244C2×D32—42no—
245C2×D32—81no—
246C32×Q8—21no—
247C32×Q8—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2411yescharacteristic
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—21no—
257C4×C3⋊D3—81no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—21no—
264C3×D12—42no—
265C3×D12#4112yes—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—42no—
271C3×C4×D3—81no—
272#626—42no—
273#626—42no—
274#626—81no—
275#626—81no—
276#625—22no—
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—31no—
286#482—91no—
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—31no—
296C2×#102—91no—
297C23×D3—61no—
298C23×D3—61no—
299C3×#41—62no—
300C3×#41—121no—
301C2×C3×Q8—21no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×D4—31no—
305C2×C3×D4—61no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C2×#67—31no—
311C2×#67—31no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C22×Dic3—61no—
317#239—22no—
318#239—41no—
319D3×D4—62no—
320D3×D4—121no—
321C2×D12—21no—
322C2×D12—31no—
323C2×D12—31no—
324C2×D12—31no—
325C2×D12—31no—
326C2×D12—61no—
327C2×D12—61no—
328C2×D12—62no—
329C2×D12—61no—
330C2×D12—61no—
331C2×D12—61no—
332C2×D12—61no—
333C2×D12—121no—
334C2×D12C22×D311yescharacteristic
335C2×C4×D3—21no—
336C2×C4×D3—21no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—121no—
341C2×C4×D3C22×D311yescharacteristic
342C2×C4×D3C22×D311yescharacteristic
343C2×C3×C8—21no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C2×C3×C8—121no—
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C42—61no—
360#217—31no—
361#217—31no—
362#217—61no—
363#215—121no—
364#215—121no—
365#215—122no—
366#213—62no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
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—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—121no—
385(C2×D3)⋊C4—121no—
386(C2×D3)⋊C4—121no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391C4⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4—31no—
395Dic3⋊C4—31no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398C4×Dic3—21no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—61no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—121no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408D24—62no—
409D24—121no—
410D24—121no—
411D24—122no—
412D3×C8—41no—
413D3×C8—121no—
414C22×C32C22×D411yescharacteristic
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—22no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3#13512yes—
430D32—84no—
431C32×C4—41no—
432C32×C4—41no—
433C32×C4C2×#4111yescharacteristic
434C32×C4H(5,𝔽2)11yescharacteristic
435C3⋊Dic3—21no—
436C3⋊Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C2×#41—31no—
443C22×D4—91no—
444C2×SD16—91no—
445C2×D8—91no—
446C2×D8—91no—
447C22×C8—31no—
448C22×C8—91no—
449#126—181no—
450#125—91no—
451#124—91no—
452#123—181no—
453#123—181no—
454C22⋊Q8—31no—
455#121—91no—
456#121—91no—
457#121—91no—
458#121—181no—
459#121—181no—
460#120—181no—
461C4×D4—91no—
462C4×D4—91no—
463C4×D4—91no—
464C4×D4—181no—
465#117—31no—
466C2×C4⋊C4—31no—
467C2×C22⋊C4—181no—
468#107—31no—
469#107—31no—
470#106—91no—
471C4⋊C8—91no—
472#103—31no—
473#103—31no—
474#103D3211yescharacteristic, complemented
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—31no—
486C23×C3—31no—
487C23×C3—61no—
488C22×D3—21no—
489C22×D3—61no—
490C22×D3—61no—
491C22×D3—61no—
492C22×D3—61no—
493C22×D3—121no—
494C22×D3—121no—
495C22×D3—122no—
496C22×D3—122no—
497C22×D3—122no—
498C22×D3—122no—
499C22×D3—241no—
500C22×D3—241no—
501C22×D3D3×D411yescharacteristic
502C22×D3D3×D411yescharacteristic
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—21no—
506C3×Q8—21no—
507C3×Q8—41no—
508C3×Q8—41no—
509C3×D4—32no—
510C3×D4—61no—
511C3×D4—122no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—122no—
529C2×C3×C4—241no—
530C2×C3×C4C23×D311yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532#67—62no—
533#67—62no—
534#67—122no—
535#67—122no—
536#67—241no—
537#67—241no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—31no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—241no—
548C2×Dic3D3×D411yescharacteristic
549C2×Dic3D3×D411yescharacteristic
550D12—21no—
551D12—42no—
552D12—62no—
553D12—61no—
554D12—61no—
555D12—61no—
556D12—61no—
557D12—61no—
558D12—61no—
559D12—61no—
560D12—61no—
561D12—121no—
562D12—121no—
563D12—121no—
564D12—122no—
565D12—122no—
566D12—241no—
567D12—241no—
568D12#23512yes—
569C4×D3—21no—
570C4×D3—21no—
571C4×D3—21no—
572C4×D3—21no—
573C4×D3—42no—
574C4×D3—81no—
575C4×D3—241no—
576C4×D3—241no—
577C4×D3—241no—
578C4×D3—242no—
579C3×C8—21no—
580C3×C8—21no—
581C3×C8—41no—
582C3×C8—61no—
583C3×C8—61no—
584C3⋊C8—21no—
585C3⋊C8—21no—
586C3⋊C8—61no—
587C3⋊C8—61no—
588C3⋊C8—121no—
589C2×C32#54611yescharacteristic
590C2×C32C2×#13511yescharacteristic
591C2×C32#57611yescharacteristic
592C3⋊D3—81no—
593C3⋊D3—81no—
594C3×D3—22no—
595C3×D3—42no—
596C3×D3—41no—
597C24—181no—
598#41—62no—
599#41—121no—
600C2×Q8C2×D3211yescharacteristic
601C2×D4—31no—
602C2×D4—61no—
603C2×D4—91no—
604C2×D4—91no—
605C2×D4—91no—
606C2×D4—181no—
607C2×D4—182no—
608C2×D4—181no—
609C2×D4—181no—
610C2×D4—181no—
611C2×D4—361no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—181no—
617C22×C4—181no—
618SD16—361no—
619D8—182no—
620D8—361no—
621C2×C8—31no—
622C2×C8—31no—
623C2×C8—91no—
624C2×C8—121no—
625C2×C8—361no—
626C2×C8C2×D3211yescharacteristic
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—61no—
631C4⋊C4—61no—
632C4⋊C4—91no—
633C4⋊C4—181no—
634C4⋊C4—181no—
635C4⋊C4C2×D3211yescharacteristic
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—91no—
639C22⋊C4—91no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C42—61no—
648C42—91no—
649C22×C3—21no—
650C22×C3—32no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—62no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3—61no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3C2×D3×D411yescharacteristic
660C22×C3C2×D3×D411yescharacteristic
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—22no—
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—122no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3—121no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—241no—
683C2×D3—241no—
684C2×D3—241no—
685C2×D3—241no—
686C2×D3—241no—
687C2×D3—244no—
688C2×D3—244no—
689C2×D3#91912yes—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—41no—
693C3×C4—41no—
694C3×C4—41no—
695C3×C4—41no—
696C3×C4—61no—
697C3×C4—61no—
698C3×C4—81no—
699C3×C4—81no—
700C3×C4—121no—
701C3×C4—121no—
702C3×C4—121no—
703C3×C4C2×#23511yescharacteristic
704C3×C4#100411yescharacteristic
705C3×C4D3×#4111yescharacteristic
706C3×C4#100911yescharacteristic
707Dic3—21no—
708Dic3—21no—
709Dic3—41no—
710Dic3—41no—
711Dic3—41no—
712Dic3—61no—
713Dic3—61no—
714Dic3—61no—
715Dic3—61no—
716Dic3—121no—
717Dic3—121no—
718C32#329711yescharacteristic, complemented, Sylow
719C23—31no—
720C23—31no—
721C23—61no—
722C23—181no—
723C23—181no—
724C23—362no—
725C23—362no—
726C23—721no—
727Q8—21no—
728Q8—21no—
729D4—32no—
730D4—61no—
731D4—122no—
732D4—182no—
733D4—181no—
734D4—181no—
735D4—181no—
736D4—181no—
737D4—362no—
738D4—362no—
739D4—721no—
740D4—721no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—31no—
744C2×C4—31no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—91no—
753C2×C4—91no—
754C2×C4—122no—
755C2×C4—241no—
756C2×C4—721no—
757C2×C4—721no—
758C2×C4C22×D3211yescharacteristic
759C8—21no—
760C8—61no—
761C8—61no—
762C8—181no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—62no—
767C2×C3—122no—
768C2×C3—121no—
769C2×C3#549011yescharacteristic
770C2×C3#565411yescharacteristic
771C2×C3C2×#91911yescharacteristic
772C2×C3D3×#13511yescharacteristic
773C2×C3#576911yescharacteristic
774C2×C3#577411yescharacteristic
775D3—22no—
776D3—41no—
777D3—42no—
778D3—242no—
779D3—241no—
780D3—241no—
781D3—241no—
782D3—241no—
783D3—481no—
784C22—32no—
785C22—61no—
786C22—61no—
787C22—61no—
788C22—61no—
789C22—61no—
790C22—62no—
791C22—121no—
792C22—121no—
793C22—361no—
794C22—361no—
795C22—361no—
796C22—361no—
797C22—361no—
798C22—361no—
799C22—724no—
800C22D32×D411yescharacteristic
801C4—41no—
802C4—41no—
803C4—61no—
804C4—61no—
805C4—121no—
806C4—121no—
807C4—121no—
808C4—181no—
809C4—181no—
810C4D3×#23511yescharacteristic
811C4#6431411yescharacteristic
812C3—21no—
813C3#7884611yescharacteristic, complemented
814C3#8148511yescharacteristic, complemented
815C2—62no—
816C2—121no—
817C2—122no—
818C2—721no—
819C2—721no—
820C2#1059427211yescharacteristic
821C2#1059475511yescharacteristic
822C2D3×#91911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3297
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
1. #10595427C2semidirect
2. #10594559C2semidirect
3. #10592518C2semidirect
4. C3×#4811C2semidirect
5. C3×#4804C2semidirect
6. #10591588C2semidirect
7. #10591585C2semidirect
8. #10591539C2semidirect
9. #10590947C2semidirect
10. #10590832C2semidirect
11. #10590780C2semidirect
12. #10590717C2semidirect
13. D3×#809C2semidirect
14. #10590459C2semidirect
15. #10590424C2semidirect
21. C2×#3755C22semidirect
23. #64102C22semidirect
25. C2×C3×D3×C8C22semidirect
26. C3×#892C22semidirect
32. #63909C22semidirect
38. #63872C22semidirect
44. C32×#103C22semidirect
45. #63641C22semidirect
47. C3×#835C22semidirect
48. C3×#835C22semidirect
51. C3×#818C22semidirect
53. C3×#807C22semidirect
54. #63574C22semidirect
57. #63564C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63553C22semidirect
80. #4811D3semidirect
83. #4804D3semidirect
179. C2×D3×C8C2×D3semidirect
191. #892C2×D3semidirect
206. C3×#103C2×D3semidirect
207. C3×#103C2×D3semidirect
211. #835C2×D3semidirect
212. #835C2×D3semidirect
221. #818C2×D3semidirect
237. #807C2×D3semidirect
474. #103D32semidirect
718. C32#3297semidirect
813. C3#78846semidirect
814. C3#81485semidirect

Maximal subgroups

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

subgroupindex
#105954272
#105945592
#105925182
C3×#48112
C3×#48042
#105915882
#105915852
#105915392
#105909472
#105908322
#105907802
#105907172
D3×#8092
#105904592
#105904242
#814853
#788463