Finite Group Databasebeta

← #11878365

Subgroups — #11878365

Order 1152.

856 conjugacy classes of subgroups.

The subgroup lattice has 825 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595043C211yesmaximal, characteristic
2#10594884C211yesmaximal, characteristic, complemented
3#10592432C211yesmaximal, characteristic, complemented
4C3×#4727C211yesmaximal, characteristic, complemented
5C3×#4722C211yesmaximal, characteristic, complemented
6#10591184C211yesmaximal, characteristic, complemented
7#10591124C211yesmaximal, characteristic, complemented
8#10590952C211yesmaximal, characteristic, complemented
9#10590951C211yesmaximal, characteristic, complemented
10#10590852C211yesmaximal, characteristic, complemented
11#10590849C211yesmaximal, characteristic, complemented
12#10590847C211yesmaximal, characteristic, complemented
13#10590838C211yesmaximal, characteristic, complemented
14#10590708C211yesmaximal, characteristic, complemented
15#10590705C211yesmaximal, characteristic, complemented
16#81472—31nomaximal
17#78681—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21#64133C2211yescharacteristic
22C2×#3746C2211yescharacteristic
23C2×#3744C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C3×#924C2211yescharacteristic
26C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic
28#63978—21no—
29#63978—21no—
30#63969—21no—
31#63959—21no—
32#63916—21no—
33#63909C2211yescharacteristic
34#63909C2211yescharacteristic
35#63884—21no—
36#63871—21no—
37#63857C2211yescharacteristic
38#63857C2211yescharacteristic
39#63857C2211yescharacteristic
40#63856C2211yescharacteristic
41#63841C2211yescharacteristic
42#63839—21no—
43C2×#3719C2211yescharacteristic
44C2×#3717C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46#63648C2211yescharacteristic
47#63643C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#818C2211yescharacteristic
52C3×#818C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#816C2211yescharacteristic
55#63573C2211yescharacteristic
56#63573C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59#63567C2211yescharacteristic
60#63564C2211yescharacteristic
61#5833—31no—
62#5825—31no—
63#5628—31no—
64#5510—31no—
65C3×#484—31no—
66C3×#408—31no—
67#5137—31no—
68#5134—31no—
69#5116—31no—
70#5114—31no—
71#5047—31no—
72#4971—31no—
73#4888—31no—
74#4887—31no—
75#4886—31no—
76#4885—31no—
77#4816—31no—
78#4809—31no—
79#4807—31no—
80#4806—31no—
81#4739—31no—
82#4738—31no—
83#4737—31no—
84#4733—31no—
85#4733—31no—
86#4733—31no—
87#4733—61no—
88#4727D311yescharacteristic, complemented
89#4723—31no—
90#4722D311yescharacteristic, complemented
91#4721—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#638—21no—
94#3828—41no—
95#3828—41no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×#634C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67D411yescharacteristic
101C2×C3×#67D411yescharacteristic
102C22×C3×Dic3—21no—
103C3×#235—41no—
104C3×#235—41no—
105C2×C3×D12D411yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6D411yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×#627—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×D3×Dic3—21no—
114D3×Dic6—41no—
115D3×Dic6—41no—
116C2×C32×C8C2311yescharacteristic
117C2×C32×C8C2311yescharacteristic
118#3757—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121#3746—41no—
122#3744—41no—
123C3×#217—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×ΓL(1,𝔽25)—41no—
132C3×D3×C8—41no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144Dic32—21no—
145#3719—41no—
146#3717—41no—
147#3201—91noSylow
148C2×C3×#41—31no—
149C2×D3×Q8—31no—
150C2×#235—31no—
151C2×#235—31no—
152C2×#235—61no—
153C2×#235C2×D311yescharacteristic
154C22×Dic6—31no—
155C2×C3×M16—31no—
156C22×C3×C8—31no—
157C3×C22⋊Q8—31no—
158C2×C3×C4⋊C4—31no—
159#946—31no—
160#946—61no—
161#944—61no—
162C2×#216—31no—
163C2×#215—31no—
164#939—61no—
165#939—61no—
166#938—61no—
167#936—61no—
168#935—61no—
169#935—61no—
170#930—31no—
171#930—31no—
172#930—61no—
173#930—61no—
174#926—31no—
175C2×C4⋊Dic3C2×D311yescharacteristic
176#924—31no—
177#924—31no—
178#924—31no—
179#924—31no—
180#924—31no—
181#924—31no—
182#924—61no—
183#924C2×D311yescharacteristic
184C2×Dic12—31no—
185C2×Dic12—31no—
186C2×Dic12—31no—
187C2×Dic12—61no—
188C2×#204—31no—
189C2×#204—31no—
190C2×#204—31no—
191C2×#204—61no—
192C2×ΓL(1,𝔽25)C2×D311yescharacteristic
193C2×D3×C8C2×D311yescharacteristic
194#897—31no—
195#897—31no—
196#897—31no—
197#897—61no—
198#895—31no—
199#895—31no—
200#895—61no—
201#894—61no—
202#892—31no—
203#888—61no—
204#885—61no—
205#883—61no—
206C3×#107—31no—
207C3×#107—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×C22⋊C8—21no—
211C3×C22⋊C8—31no—
212C3×C22⋊C8—31no—
213C3×C22⋊C8—31no—
214C3×C22⋊C8C2×D311yescharacteristic
215C3×C22⋊C8C2×D311yescharacteristic
216#830C2×D311yescharacteristic
217#821—31no—
218#821—31no—
219#821—31no—
220#821—61no—
221(C2×D3)⋊C8C2×D311yescharacteristic
222(C2×D3)⋊C8C2×D311yescharacteristic
223#818C2×D311yescharacteristic
224#818C2×D311yescharacteristic
225#817—31no—
226#817—31no—
227#816—31no—
228#816—31no—
229#816—31no—
230#816—31no—
231#816—31no—
232#816—61no—
233#816C2×D311yescharacteristic
234#816C2×D311yescharacteristic
235#810—31no—
236#810—31no—
237#810—31no—
238#809—31no—
239#808—31no—
240#808—31no—
241C23×C32C2×D411yescharacteristic
242C22×C3⋊D3—21no—
243C22×C3×D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249#638—42no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255C4×C3⋊D3—42no—
256#634—21no—
257#634—21no—
258#634—21no—
259#634—21no—
260C3×#67—41no—
261C3×#67—41no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—81no—
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C3×D12—41no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×Dic6—21no—
275C3×Dic6—21no—
276C3×Dic6—41no—
277#627—42no—
278#626—81no—
279#626—81no—
280D3×Dic3—42no—
281C32×C8—21no—
282C32×C8—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#537—91no—
286#536—91no—
287#485—91no—
288#484—31no—
289#483—91no—
290#482—91no—
291#470—91no—
292#468—91no—
293#467—91no—
294#465—91no—
295#452—91no—
296#452—91no—
297#451—91no—
298#448—91no—
299#408—31no—
300C3×#41—121no—
301C3×#41—121no—
302C2×C3×Q8—31no—
303C2×C3×Q8—31no—
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C22×C3×C4—21no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—61no—
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C22×D311yescharacteristic
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—121no—
318C2×#67D1211yescharacteristic
319C2×#67D1211yescharacteristic
320C22×Dic3—21no—
321C22×Dic3—61no—
322D3×Q8—121no—
323D3×Q8—121no—
324#235—41no—
325#235—41no—
326#235—121no—
327#235—121no—
328#235—121no—
329#235—121no—
330#235—122no—
331#235—122no—
332C2×D12—31no—
333C2×D12—31no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12—61no—
337C2×D12D1211yescharacteristic
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—121no—
342C2×C4×D3C22×D311yescharacteristic
343C2×C4×D3C22×D311yescharacteristic
344C2×Dic6—31no—
345C2×Dic6—31no—
346C2×Dic6—31no—
347C2×Dic6—31no—
348C2×Dic6—61no—
349C2×Dic6—61no—
350C2×Dic6—61no—
351C2×Dic6—61no—
352C2×Dic6—121no—
353C2×Dic6—121no—
354C2×Dic6D1211yescharacteristic
355C2×Dic6C22×D311yescharacteristic
356C3×M16—121no—
357C2×C3×C8—21no—
358C2×C3×C8—21no—
359C2×C3×C8—31no—
360C2×C3×C8—31no—
361C2×C3×C8—121no—
362C2×C3×C8C22×D311yescharacteristic
363C2×C3×C8C22×D311yescharacteristic
364C2×C3×C8C22×D311yescharacteristic
365C2×C3×C8C22×D311yescharacteristic
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4—61no—
371C3×C22⋊C4—61no—
372#217—21no—
373#217—61no—
374#217—61no—
375#217—61no—
376#217—61no—
377#217—61no—
378#217—61no—
379#217—61no—
380#217—121no—
381#216—121no—
382#215—121no—
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—
392C4⋊Dic3—21no—
393C4⋊Dic3—31no—
394C4⋊Dic3—31no—
395C4⋊Dic3—61no—
396C4⋊Dic3—61no—
397C4⋊Dic3—61no—
398C4⋊Dic3—61no—
399C4⋊Dic3C22×D311yescharacteristic
400C4⋊Dic3C22×D311yescharacteristic
401C4⋊Dic3C22×D311yescharacteristic
402Dic3⋊C4—21no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—121no—
411C4×Dic3—61no—
412C4×Dic3—61no—
413C2×C3⋊C8C22×D311yescharacteristic
414C2×C3⋊C8C22×D311yescharacteristic
415Dic12—121no—
416Dic12—121no—
417Dic12—122no—
418Dic12—121no—
419#204—121no—
420#204—121no—
421#204—122no—
422#204—121no—
423ΓL(1,𝔽25)—41no—
424D3×C8—41no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32C22×D411yescharacteristic
429C2×C3⋊D3—41no—
430C2×C3⋊D3—41no—
431C2×C3⋊D3—41no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—21no—
437C2×C3×D3—21no—
438C32×C4—21no—
439C32×C4H(5,𝔽2)11yescharacteristic
440C32×C4H(5,𝔽2)11yescharacteristic
441C3⋊Dic3—41no—
442C3⋊Dic3—41no—
443C3⋊Dic3—41no—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C2×#41—31no—
451C2×#41—91no—
452C22×Q8—91no—
453C2×Q16—91no—
454C2×Q16—91no—
455C2×SD16—91no—
456C2×SD16—91no—
457C2×M16—31no—
458C22×C8—31no—
459C4⋊Q8—181no—
460#124—181no—
461#123—181no—
462#123—181no—
463C22⋊Q8—31no—
464C22⋊Q8—91no—
465C22⋊Q8—91no—
466C22⋊Q8—91no—
467C22⋊Q8—91no—
468C22⋊Q8—91no—
469C22⋊Q8—181no—
470#121—91no—
471#121—91no—
472#121—181no—
473#121—181no—
474#121—181no—
475#117—91no—
476C2×C4⋊C4—31no—
477#107—31no—
478#107—31no—
479#106—91no—
480#106—91no—
481#103—31no—
482#103—31no—
483#103—91no—
484#103—91no—
485#103—91no—
486#103—91no—
487#102—91no—
488#102—91no—
489C22⋊C8—31no—
490C22⋊C8—31no—
491C22⋊C8—31no—
492C22⋊C8D3211yescharacteristic
493C23×C3—21no—
494C23×C3—31no—
495C23×C3—31no—
496C23×C3C2×D1211yescharacteristic
497C23×C3D3×D411yescharacteristic
498C22×D3—61no—
499C22×D3—61no—
500C22×D3—121no—
501C22×D3C2×D1211yescharacteristic
502C22×D3C2×D1211yescharacteristic
503C3×Q8—61no—
504C3×Q8—61no—
505C3×Q8—121no—
506C3×D4—121no—
507C3×D4—121no—
508C3×D4—121no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
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—241no—
528C2×C3×C4C2×D1211yescharacteristic
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532#67—41no—
533#67—41no—
534#67—122no—
535#67—122no—
536#67—124no—
537#67—241no—
538#67—241no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—81no—
550C2×Dic3—121no—
551C2×Dic3—121no—
552C2×Dic3—121no—
553C2×Dic3—122no—
554C2×Dic3C2×D1211yescharacteristic
555C2×Dic3C2×D1211yescharacteristic
556D12—41no—
557D12—62no—
558D12—61no—
559D12—61no—
560D12—61no—
561D12—61no—
562D12—121no—
563D12—241no—
564D12—241no—
565C4×D3—21no—
566C4×D3—21no—
567C4×D3—21no—
568C4×D3—21no—
569C4×D3—122no—
570C4×D3—122no—
571C4×D3—124no—
572C4×D3—122no—
573Dic6—21no—
574Dic6—21no—
575Dic6—41no—
576Dic6—62no—
577Dic6—61no—
578Dic6—61no—
579Dic6—61no—
580Dic6—61no—
581Dic6—61no—
582Dic6—61no—
583Dic6—61no—
584Dic6—61no—
585Dic6—121no—
586Dic6—121no—
587Dic6—121no—
588Dic6—122no—
589Dic6—122no—
590C3×C8—21no—
591C3×C8—21no—
592C3×C8—21no—
593C3×C8—21no—
594C3×C8—41no—
595C3×C8—41no—
596C3×C8—61no—
597C3×C8—61no—
598C3⋊C8—21no—
599C3⋊C8—21no—
600C2×C32—41no—
601C2×C32#53411yescharacteristic
602C2×C32#57711yescharacteristic
603C2×C32#57811yescharacteristic
604C3⋊D3—81no—
605C3×D3—41no—
606C3×D3—41no—
607#41—121no—
608#41—121no—
609#41—361no—
610#41—361no—
611C2×Q8—31no—
612C2×Q8—31no—
613C2×Q8—91no—
614C2×Q8—91no—
615C2×Q8—181no—
616C2×Q8—361no—
617C2×Q8—361no—
618C2×D4—31no—
619C2×D4—31no—
620C2×D4—31no—
621C2×D4—91no—
622C2×D4—181no—
623C2×D4—181no—
624C2×D4—181no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—61no—
628C22×C4—181no—
629C22×C4—181no—
630C22×C4C2×D3211yescharacteristic
631Q16—361no—
632Q16—361no—
633SD16—361no—
634SD16—361no—
635M16—121no—
636C2×C8—31no—
637C2×C8—31no—
638C2×C8—121no—
639C2×C8C2×D3211yescharacteristic
640C2×C8C2×D3211yescharacteristic
641C4⋊C4—31no—
642C4⋊C4—31no—
643C4⋊C4—31no—
644C4⋊C4—61no—
645C4⋊C4—61no—
646C4⋊C4—91no—
647C4⋊C4—181no—
648C4⋊C4—181no—
649C4⋊C4—181no—
650C4⋊C4—181no—
651C4⋊C4—181no—
652C22⋊C4—61no—
653C22⋊C4—181no—
654C22⋊C4—181no—
655C22⋊C4—181no—
656C22⋊C4—181no—
657C22⋊C4—181no—
658C22⋊C4—181no—
659C22⋊C4—181no—
660C22⋊C4—181no—
661C42—181no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—61no—
673C22×C3—61no—
674C22×C3—61no—
675C22×C3—61no—
676C22×C3—61no—
677C22×C3—61no—
678C22×C3C22×D1211yescharacteristic
679C22×C3C2×D3×D411yescharacteristic
680C2×D3—21no—
681C2×D3—21no—
682C2×D3—21no—
683C2×D3—21no—
684C2×D3—21no—
685C2×D3—21no—
686C2×D3—122no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—121no—
691C2×D3—121no—
692C2×D3—121no—
693C2×D3—241no—
694C2×D3—241no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—21no—
698C3×C4—21no—
699C3×C4—41no—
700C3×C4—61no—
701C3×C4—61no—
702C3×C4—121no—
703C3×C4—121no—
704C3×C4—121no—
705C3×C4—121no—
706C3×C4#100411yescharacteristic
707C3×C4#100411yescharacteristic
708C3×C4#100911yescharacteristic
709C3×C4#100911yescharacteristic
710Dic3—21no—
711Dic3—21no—
712Dic3—41no—
713Dic3—41no—
714Dic3—41no—
715Dic3—41no—
716Dic3—122no—
717Dic3—121no—
718Dic3—121no—
719Dic3—121no—
720Dic3—121no—
721Dic3—121no—
722Dic3—121no—
723Dic3—241no—
724Dic3—241no—
725C32#320111yescharacteristic, complemented, Sylow
726C23—31no—
727C23—31no—
728C23—181no—
729C23D3×D1211yescharacteristic
730Q8—61no—
731Q8—61no—
732Q8—121no—
733Q8—181no—
734Q8—181no—
735Q8—181no—
736Q8—181no—
737Q8—362no—
738D4—121no—
739D4—121no—
740D4—121no—
741D4—181no—
742D4—181no—
743D4—362no—
744D4—721no—
745D4—721no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—31no—
749C2×C4—31no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—181no—
759C2×C4—181no—
760C2×C4—181no—
761C2×C4—241no—
762C2×C4—362no—
763C2×C4—362no—
764C2×C4D3×D1211yescharacteristic
765C2×C4C22×D3211yescharacteristic
766C8—21no—
767C8—21no—
768C8—61no—
769C8—61no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—41no—
774C2×C3—41no—
775C2×C3—81no—
776C2×C3—121no—
777C2×C3—121no—
778C2×C3#549311yescharacteristic
779C2×C3#565311yescharacteristic
780C2×C3#575111yescharacteristic
781C2×C3#575311yescharacteristic
782C2×C3#576611yescharacteristic
783C2×C3#577511yescharacteristic
784D3—41no—
785D3—41no—
786D3—242no—
787D3—241no—
788D3—241no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—61no—
793C22—61no—
794C22—61no—
795C22—61no—
796C22—61no—
797C22—61no—
798C22—361no—
799C22—361no—
800C22—361no—
801C22C2×D3×D1211yescharacteristic
802C4—21no—
803C4—61no—
804C4—61no—
805C4—121no—
806C4—121no—
807C4—121no—
808C4—121no—
809C4—361no—
810C4—361no—
811C4—361no—
812C4#6431411yescharacteristic
813C4#6431411yescharacteristic
814C3—21no—
815C3#7868111yescharacteristic, complemented
816C3#8147211yescharacteristic, complemented
817C2—41no—
818C2—121no—
819C2—121no—
820C2—721no—
821C2#1059429111yescharacteristic
822C2#1059469111yescharacteristic
823C2#1059471311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10595043C2
hypercenterC22⋊C8D32
hypocenterC32#3201
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10594884C2semidirect
3. #10592432C2semidirect
4. C3×#4727C2semidirect
5. C3×#4722C2semidirect
6. #10591184C2semidirect
7. #10591124C2semidirect
8. #10590952C2semidirect
9. #10590951C2semidirect
10. #10590852C2semidirect
11. #10590849C2semidirect
12. #10590847C2semidirect
13. #10590838C2semidirect
14. #10590708C2semidirect
15. #10590705C2semidirect
88. #4727D3semidirect
90. #4722D3semidirect
725. C32#3201semidirect
815. C3#78681semidirect
816. C3#81472semidirect

Maximal subgroups

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

subgroupindex
#105950432
#105948842
#105924322
C3×#47272
C3×#47222
#105911842
#105911242
#105909522
#105909512
#105908522
#105908492
#105908472
#105908382
#105907082
#105907052
#814723
#786813