Finite Group Databasebeta

← #11878378

Subgroups — #11878378

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
1C3×#5628C211yesmaximal, characteristic, complemented
2#10595043C211yesmaximal, characteristic
3#10592746C211yesmaximal, characteristic, complemented
4C3×#5043C211yesmaximal, characteristic, complemented
5#10591596C211yesmaximal, characteristic, complemented
6#10591595C211yesmaximal, characteristic, complemented
7#10591589C211yesmaximal, characteristic, complemented
8#10591584C211yesmaximal, characteristic, complemented
9#10591184C211yesmaximal, characteristic, complemented
10#10591145C211yesmaximal, characteristic, complemented
11#10591132C211yesmaximal, characteristic, complemented
12#10590587C211yesmaximal, characteristic, complemented
13#10590577C211yesmaximal, characteristic, complemented
14#10590428C211yesmaximal, characteristic, complemented
15#10590425C211yesmaximal, characteristic, complemented
16#83408—31nomaximal
17#81431—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22C2×#3756C2211yescharacteristic
23C2×#3755C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C3×#897C2211yescharacteristic
28C3×#894—21no—
29C3×#892C2211yescharacteristic
30C3×#888—21no—
31C3×#885—21no—
32C3×#883—21no—
33#63978—21no—
34#63978—21no—
35#63916—21no—
36#63909C2211yescharacteristic
37#63909C2211yescharacteristic
38#63871—21no—
39#63857C2211yescharacteristic
40#63857C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45#63657C2211yescharacteristic
46#63637C2211yescharacteristic
47#63636C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×#808C2211yescharacteristic
52C3×#808C2211yescharacteristic
53#63576C2211yescharacteristic
54#63576C2211yescharacteristic
55#63567C2211yescharacteristic
56#63565C2211yescharacteristic
57#63565C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#536—31no—
62#5833—31no—
63#5628D311yescharacteristic, complemented
64#5510—31no—
65C3×#483—31no—
66#5234—31no—
67#5228—31no—
68#5227—31no—
69#5052—31no—
70#5051—31no—
71#5049—31no—
72#5048—31no—
73#5047—31no—
74#5047—31no—
75#5047—31no—
76#5047—61no—
77#5044—31no—
78#5043D311yescharacteristic, complemented
79#5003—31no—
80#4996—31no—
81#4970—31no—
82#4868—31no—
83#4867—31no—
84#4866—31no—
85#4864—31no—
86#4813—31no—
87#4812—31no—
88#4809—31no—
89#4806—31no—
90#4733—31no—
91#4727—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95#3828—41no—
96#3828—41no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×#634C2311yescharacteristic
100C2×C3×#67D411yescharacteristic
101C2×C3×#67D411yescharacteristic
102C22×C3×Dic3—21no—
103C3×D3×Q8—41no—
104C3×D3×Q8—41no—
105C3×#235—41no—
106C3×#235—41no—
107C2×C3×D12D411yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6—21no—
112C2×C3×Dic6D411yescharacteristic
113C2×C3×Dic6C2311yescharacteristic
114C2×#626—21no—
115C2×#626—21no—
116C32×C4⋊C4—21no—
117C32×C4⋊C4C2311yescharacteristic
118C32×C22⋊C4—21no—
119#3756—41no—
120#3755—41no—
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×#217—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×C4×Dic3—21no—
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139#3722—21no—
140#3722—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143#3719—41no—
144#3717—41no—
145#3711—41no—
146D3×C3⋊C8—41no—
147#3201—91noSylow
148C2×C3×#41—31no—
149C22×C3×Q8—31no—
150C2×D3×Q8C2×D311yescharacteristic
151C2×#235—31no—
152C2×#235—31no—
153C2×#235—61no—
154C2×#235C2×D311yescharacteristic
155C3×C4⋊Q8—61no—
156C3×#124—61no—
157C3×#123—61no—
158C3×#123—61no—
159C3×C22⋊Q8—21no—
160C3×C22⋊Q8—31no—
161C3×C22⋊Q8—31no—
162C3×C22⋊Q8—31no—
163C3×C22⋊Q8C2×D311yescharacteristic
164C3×C22⋊Q8C2×D311yescharacteristic
165C3×#117—31no—
166C2×C3×C4⋊C4—31no—
167#946—61no—
168#946C2×D311yescharacteristic
169C2×#216—31no—
170C2×#216—31no—
171C2×#216—31no—
172C2×#216—61no—
173C2×#215—31no—
174C2×#215—31no—
175C2×#215—31no—
176C2×#215—61no—
177#939—61no—
178#939—61no—
179#938—61no—
180#930—31no—
181#930—31no—
182#930—61no—
183#930—61no—
184C2×C4⋊Dic3C2×D311yescharacteristic
185#924—31no—
186#924—31no—
187#924C2×D311yescharacteristic
188C2×#208—31no—
189C22×C3⋊C8—31no—
190C2×Dic12—31no—
191C2×#204—31no—
192C2×ΓL(1,𝔽25)—31no—
193C2×D3×C8—31no—
194#897—31no—
195#897—31no—
196#897—61no—
197#897C2×D311yescharacteristic
198#895—31no—
199#895—31no—
200#895—61no—
201#894—21no—
202#892C2×D311yescharacteristic
203#888—21no—
204#885—21no—
205#883—21no—
206C3×#106—31no—
207C3×#106—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×C22⋊C8—31no—
211#835—31no—
212#835—31no—
213#835C2×D311yescharacteristic
214#835C2×D311yescharacteristic
215#830—31no—
216#830—31no—
217#830—31no—
218#830—31no—
219#830—61no—
220#830C2×D311yescharacteristic
221#821—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224#816—31no—
225#810—31no—
226#810—31no—
227#810—31no—
228#810—31no—
229#810—31no—
230#810—61no—
231#809—31no—
232#809—31no—
233#809—31no—
234#809—61no—
235#808C2×D311yescharacteristic
236#808C2×D311yescharacteristic
237#807—31no—
238#807—31no—
239#807—31no—
240#807—31no—
241C23×C32C2×D411yescharacteristic
242C22×C3⋊D3—21no—
243C22×C3×D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253#638—42no—
254C2×C3⋊Dic3—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—21no—
257C4×C3⋊D3—42no—
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×C4×D3—42no—
275C3×Dic6—21no—
276C3×Dic6—21no—
277C3×Dic6—41no—
278C3×Dic6—42no—
279#626—81no—
280#626—81no—
281C3⋊(C3⋊C8)—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#537—91no—
286#536—31no—
287#485—91no—
288#484—91no—
289#483—31no—
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—91no—
300C3×#41—121no—
301C3×#41—121no—
302C2×C3×Q8—21no—
303C2×C3×Q8—31no—
304C2×C3×Q8—31no—
305C2×C3×Q8—61no—
306C2×C3×Q8—121no—
307C2×C3×Q8—121no—
308C2×C3×Q8C22×D311yescharacteristic
309C2×C3×Q8C22×D311yescharacteristic
310C2×C3×D4—31no—
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C22×C3×C4—21no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—121no—
325C2×#67#6711yescharacteristic
326C2×#67#6711yescharacteristic
327C22×Dic3—21no—
328D3×Q8—41no—
329D3×Q8—41no—
330#235—41no—
331#235—41no—
332#235—121no—
333#235—121no—
334#235—121no—
335#235—121no—
336#235—122no—
337#235—122no—
338C2×D12—31no—
339C2×D12—31no—
340C2×D12—61no—
341C2×D12—61no—
342C2×D12—61no—
343C2×D12#6711yescharacteristic
344C2×C4×D3—21no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—121no—
348C2×C4×D3C22×D311yescharacteristic
349C2×C4×D3C22×D311yescharacteristic
350C2×Dic6—21no—
351C2×Dic6—31no—
352C2×Dic6—31no—
353C2×Dic6—61no—
354C2×Dic6#6711yescharacteristic
355C2×Dic6C22×D311yescharacteristic
356C2×C3×C8—31no—
357C2×C3×C8—31no—
358C3×C4⋊C4—21no—
359C3×C4⋊C4—21no—
360C3×C4⋊C4—21no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—41no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4C22×D311yescharacteristic
370C3×C4⋊C4C22×D311yescharacteristic
371C3×C22⋊C4—21no—
372C3×C22⋊C4—21no—
373C3×C22⋊C4—41no—
374C3×C22⋊C4—61no—
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C42—61no—
379#217—21no—
380#217—61no—
381#217—61no—
382#216—121no—
383#216—121no—
384#216—121no—
385#216—122no—
386#215—121no—
387#215—121no—
388#215—121no—
389#215—122no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399C4⋊Dic3—21no—
400C4⋊Dic3—21no—
401C4⋊Dic3—61no—
402C4⋊Dic3—61no—
403C4⋊Dic3C22×D311yescharacteristic
404C4⋊Dic3C22×D311yescharacteristic
405C4⋊Dic3C22×D311yescharacteristic
406Dic3⋊C4—21no—
407Dic3⋊C4—21no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410C4×Dic3—21no—
411#208—121no—
412C2×C3⋊C8—31no—
413C2×C3⋊C8—31no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—31no—
416C2×C3⋊C8—61no—
417C2×C3⋊C8—61no—
418C2×C3⋊C8—121no—
419C2×C3⋊C8C22×D311yescharacteristic
420C2×C3⋊C8C22×D311yescharacteristic
421Dic12—121no—
422#204—121no—
423ΓL(1,𝔽25)—121no—
424D3×C8—121no—
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×C4—41no—
440C32×C4—41no—
441C32×C4H(5,𝔽2)11yescharacteristic
442C32×C4H(5,𝔽2)11yescharacteristic
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—31no—
453C2×Q16—91no—
454C2×Q16—91no—
455C2×SD16—91no—
456C2×SD16—91no—
457C2×M16—91no—
458C22×C8—91no—
459C4⋊Q8—61no—
460#124—61no—
461#123—61no—
462#123—61no—
463C22⋊Q8—31no—
464C22⋊Q8—31no—
465C22⋊Q8—31no—
466C22⋊Q8—91no—
467C22⋊Q8—91no—
468C22⋊Q8—181no—
469C22⋊Q8D3211yescharacteristic
470#121—91no—
471#121—91no—
472#121—181no—
473#121—181no—
474#121—181no—
475#117—31no—
476C2×C4⋊C4—31no—
477#107—91no—
478#107—91no—
479#106—31no—
480#106—31no—
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—91no—
491C22⋊C8—91no—
492C22⋊C8—91no—
493C23×C3—21no—
494C23×C3—31no—
495C23×C3—31no—
496C23×C3D3×D411yescharacteristic
497C23×C3C2×#6711yescharacteristic
498C22×D3—61no—
499C22×D3—61no—
500C22×D3—121no—
501C22×D3C2×#6711yescharacteristic
502C22×D3C2×#6711yescharacteristic
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—21no—
506C3×Q8—21no—
507C3×Q8—41no—
508C3×Q8—41no—
509C3×Q8—61no—
510C3×Q8—61no—
511C3×Q8—121no—
512C3×Q8—122no—
513C3×D4—121no—
514C3×D4—121no—
515C3×D4—121no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—31no—
527C2×C3×C4—31no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—122no—
541C2×C3×C4—241no—
542C2×C3×C4D3×D411yescharacteristic
543C2×C3×C4C2×#6711yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545C2×C3×C4C23×D311yescharacteristic
546#67—41no—
547#67—41no—
548#67—122no—
549#67—122no—
550#67—124no—
551#67—241no—
552#67—241no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—81no—
560C2×Dic3—121no—
561C2×Dic3C2×#6711yescharacteristic
562C2×Dic3C2×#6711yescharacteristic
563D12—41no—
564D12—62no—
565D12—61no—
566D12—61no—
567D12—61no—
568D12—61no—
569D12—121no—
570D12—241no—
571D12—241no—
572C4×D3—21no—
573C4×D3—21no—
574C4×D3—21no—
575C4×D3—21no—
576C4×D3—42no—
577C4×D3—122no—
578C4×D3—122no—
579C4×D3—124no—
580Dic6—21no—
581Dic6—21no—
582Dic6—41no—
583Dic6—42no—
584Dic6—62no—
585Dic6—61no—
586Dic6—61no—
587Dic6—61no—
588Dic6—61no—
589Dic6—121no—
590C3×C8—61no—
591C3×C8—61no—
592C3⋊C8—21no—
593C3⋊C8—21no—
594C3⋊C8—61no—
595C3⋊C8—61no—
596C3⋊C8—61no—
597C3⋊C8—61no—
598C3⋊C8—121no—
599C3⋊C8—121no—
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—61no—
614C2×Q8—91no—
615C2×Q8—121no—
616C2×Q8—121no—
617C2×Q8C2×D3211yescharacteristic
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—61no—
629C22×C4—181no—
630C22×C4C2×D3211yescharacteristic
631Q16—361no—
632Q16—361no—
633SD16—361no—
634SD16—361no—
635M16—361no—
636C2×C8—31no—
637C2×C8—31no—
638C2×C8—91no—
639C2×C8—91no—
640C2×C8—361no—
641C4⋊C4—21no—
642C4⋊C4—31no—
643C4⋊C4—31no—
644C4⋊C4—31no—
645C4⋊C4—61no—
646C4⋊C4—61no—
647C4⋊C4—61no—
648C4⋊C4—61no—
649C4⋊C4—181no—
650C4⋊C4—181no—
651C4⋊C4C2×D3211yescharacteristic
652C22⋊C4—21no—
653C22⋊C4—61no—
654C22⋊C4—61no—
655C22⋊C4—61no—
656C22⋊C4—61no—
657C22⋊C4—181no—
658C22⋊C4—181no—
659C22⋊C4—181no—
660C22⋊C4—181no—
661C42—61no—
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×C3C2×D3×D411yescharacteristic
679C22×C3C22×#6711yescharacteristic
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—41no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—41no—
704C3×C4—61no—
705C3×C4—61no—
706C3×C4—81no—
707C3×C4—81no—
708C3×C4—121no—
709C3×C4—121no—
710C3×C4—121no—
711C3×C4—121no—
712C3×C4#100411yescharacteristic
713C3×C4#100411yescharacteristic
714C3×C4#100911yescharacteristic
715C3×C4#100911yescharacteristic
716Dic3—21no—
717Dic3—21no—
718Dic3—41no—
719Dic3—41no—
720Dic3—41no—
721Dic3—41no—
722Dic3—122no—
723Dic3—121no—
724Dic3—121no—
725C32#320111yescharacteristic, complemented, Sylow
726C23—31no—
727C23—31no—
728C23—181no—
729C23D3×#6711yescharacteristic
730Q8—21no—
731Q8—21no—
732Q8—61no—
733Q8—61no—
734Q8—121no—
735Q8—122no—
736Q8—181no—
737Q8—181no—
738D4—121no—
739D4—121no—
740D4—121no—
741D4—181no—
742D4—181no—
743D4—362no—
744D4—721no—
745D4—721no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—31no—
751C2×C4—31no—
752C2×C4—61no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—122no—
761C2×C4—181no—
762C2×C4—241no—
763C2×C4—362no—
764C2×C4D3×#6711yescharacteristic
765C2×C4C22×D3211yescharacteristic
766C8—61no—
767C8—61no—
768C8—181no—
769C8—181no—
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#565311yescharacteristic
779C2×C3#576211yescharacteristic
780C2×C3#577911yescharacteristic
781C2×C3#580411yescharacteristic
782C2×C3#583711yescharacteristic
783C2×C3#583811yescharacteristic
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×#6711yescharacteristic
802C4—21no—
803C4—41no—
804C4—41no—
805C4—61no—
806C4—61no—
807C4—121no—
808C4—121no—
809C4—121no—
810C4—121no—
811C4—361no—
812C4#6431411yescharacteristic
813C4#6431411yescharacteristic
814C3—21no—
815C3#8143111yescharacteristic, complemented
816C3#8340811yescharacteristic, complemented
817C2—41no—
818C2—121no—
819C2—121no—
820C2—721no—
821C2#1059523411yescharacteristic
822C2#1059531811yescharacteristic
823C2#1059546511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10595043C2
hypercenterC22⋊Q8D32
hypocenterC32#3201
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5628C2semidirect
3. #10592746C2semidirect
4. C3×#5043C2semidirect
5. #10591596C2semidirect
6. #10591595C2semidirect
7. #10591589C2semidirect
8. #10591584C2semidirect
9. #10591184C2semidirect
10. #10591145C2semidirect
11. #10591132C2semidirect
12. #10590587C2semidirect
13. #10590577C2semidirect
14. #10590428C2semidirect
15. #10590425C2semidirect
63. #5628D3semidirect
78. #5043D3semidirect
725. C32#3201semidirect
815. C3#81431semidirect
816. C3#83408semidirect

Maximal subgroups

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

subgroupindex
C3×#56282
#105950432
#105927462
C3×#50432
#105915962
#105915952
#105915892
#105915842
#105911842
#105911452
#105911322
#105905872
#105905772
#105904282
#105904252
#834083
#814313