Finite Group Databasebeta

← #11870879

Subgroups — #11870879

Order 1152.

975 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595173C211yesmaximal, characteristic, complemented
2D3×D4×Dic3C211yesmaximal, characteristic, complemented
3D8×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#5156C211yesmaximal, characteristic
5C3×#5153C211yesmaximal, characteristic, complemented
6#10591458C211yesmaximal, characteristic, complemented
7#10591445C211yesmaximal, characteristic, complemented
8#10591435C211yesmaximal, characteristic, complemented
9#10591431C211yesmaximal, characteristic, complemented
10#10591415C211yesmaximal, characteristic, complemented
11#10591411C211yesmaximal, characteristic, complemented
12#10590767C211yesmaximal, characteristic, complemented
13#10590742C211yesmaximal, characteristic, complemented
14#10590682C211yesmaximal, characteristic, complemented
15#10590656C211yesmaximal, characteristic, complemented
16#80505—31nomaximal
17#79989—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C22×D3×Dic3—21no—
20C2×C32×D8C2211yescharacteristic
21D4×C3⋊Dic3C2211yescharacteristic
22D4×C3⋊Dic3C2211yescharacteristic, complemented
23C3×#938C2211yescharacteristic
24C3×#936C2211yescharacteristic, complemented
25C3×D4×Dic3C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27C2×C3×#213C2211yescharacteristic
28#67⋊Dic3—21no—
29#67⋊Dic3—21no—
30Dic3×#67—21no—
31#63969—21no—
32D3×#217—21no—
33#63957—21no—
34#63956—21no—
35#63898C2211yescharacteristic
36Dic3×D12C2211yescharacteristic
37D3×C4⋊Dic3C2211yescharacteristic
38C4×D3×Dic3C2211yescharacteristic
39#63869C2211yescharacteristic, complemented
40#63856C2211yescharacteristic
41#63843C2211yescharacteristic, complemented
42C2×#3715C2211yescharacteristic
43#63659C2211yescharacteristic
44#63659C2211yescharacteristic, complemented
45#63645C2211yescharacteristic, complemented
46C8×C3⋊Dic3C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic, complemented
61C2×D4×Dic3—31no—
62#5680—31no—
63#5600—31no—
64C4×D3×D4—31no—
65C3×#463—31no—
66C3×#447—31no—
67#5218—31no—
68#5169—31no—
69Dic3×SD16—31no—
70#5156D311yescharacteristic
71#5153—31no—
72#5153D311yescharacteristic, complemented
73Dic3×D8—31no—
74Dic3×D8—31no—
75Dic3×D8—31no—
76Dic3×D8—61no—
77#5057—31no—
78#5034—31no—
79#5009—31no—
80#4847—31no—
81#4833—31no—
82#4811—31no—
83#4788—31no—
84#4777—31no—
85#4766—31no—
86#4766—31no—
87#4758—31no—
88#4758—31no—
89#4756—31no—
90#4722—31no—
91#4718—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C22×C3⋊Dic3—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C3×D3×D4—22no—
101C3×D3×D4—22no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—44no—
109C2×D3×Dic3D411yescharacteristic
110C2×D3×Dic3D411yescharacteristic
111C32×D8—22no—
112C2×C32×C8C2311yescharacteristic
113#3757—21no—
114#3757—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#217—21no—
123C3×#214—22no—
124C3×#213—22no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130#3724—21no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139Dic32D411yescharacteristic
140Dic32D411yescharacteristic
141#3715—22no—
142#3105—91noSylow
143C22×C3×D4—31no—
144C23×Dic3—61no—
145C2×D3×D4C2×D311yescharacteristic
146C22×C4×D3—61no—
147C2×C3×SD16—31no—
148C2×C3×D8—21no—
149C2×C3×D8—31no—
150C2×C3×D8C2×D311yescharacteristic
151C2×C3×D8C2×D311yescharacteristic
152C3×#124—31no—
153C3×#121—31no—
154C3×C4×D4—31no—
155C2×#217—61no—
156#946—31no—
157Q8×Dic3—31no—
158C2×#215—31no—
159#938C2×D311yescharacteristic
160#936C2×D311yescharacteristic, complemented
161#935—61no—
162D4×Dic3—31no—
163D4×Dic3—31no—
164D4×Dic3—31no—
165D4×Dic3—31no—
166D4×Dic3—31no—
167D4×Dic3—31no—
168D4×Dic3—61no—
169D4×Dic3—61no—
170D4×Dic3—61no—
171D4×Dic3—61no—
172D4×Dic3—61no—
173D4×Dic3C2×D311yescharacteristic
174C2×#214—31no—
175C2×#214C2×D311yescharacteristic
176C2×#213C2×D311yescharacteristic
177C4×#67—61no—
178C2×C4⋊Dic3—31no—
179#924—31no—
180C2×C4×Dic3—31no—
181#893—31no—
182D3×C4⋊C4—31no—
183#890—31no—
184#887—31no—
185#883—61no—
186#67⋊C4—61no—
187#67⋊C4—61no—
188D3×C22⋊C4—61no—
189#879—61no—
190#879—61no—
191#877—61no—
192#877—61no—
193C4×D12—31no—
194C42×D3—31no—
195#870—31no—
196C3×C4⋊C8—31no—
197C3×#103—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×#102—31no—
201C3×C22⋊C8—31no—
202#835—31no—
203#832—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#832—61no—
209#832—61no—
210#832C2×D311yescharacteristic
211#832C2×D311yescharacteristic, complemented
212#830—31no—
213#821—31no—
214#821C2×D311yescharacteristic
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8C2×D311yescharacteristic
217#818—31no—
218#818—31no—
219#818—31no—
220#818—61no—
221#817—31no—
222#816—31no—
223#816C2×D311yescharacteristic, complemented
224Dic3⋊C8—31no—
225Dic3⋊C8C2×D311yescharacteristic, complemented
226C8×Dic3—31no—
227C8×Dic3—31no—
228C8×Dic3—31no—
229C8×Dic3—31no—
230C8×Dic3—61no—
231#808—31no—
232#808—31no—
233#808—31no—
234#807—31no—
235C4⋊(C3⋊C8)—31no—
236C23×C32—21no—
237C23×C32—21no—
238C22×C3×D3—24no—
239C22×C3×D3—21no—
240C22×C3×D3—42no—
241C22×C3×D3—42no—
242C22×C3×D3C2×D411yescharacteristic
243C32×D4—21no—
244C32×D4—21no—
245C32×D4—21no—
246C32×D4#4112yes—
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—42no—
251C2×C3⋊Dic3—42no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C2×C3⋊Dic3C2×D411yescharacteristic
254C3×#67—24no—
255C3×#67—42no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—21no—
264C3×D12#4112yes—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269D3×Dic3—22no—
270D3×Dic3—22no—
271D3×Dic3—42no—
272D3×Dic3—42no—
273D3×Dic3—42no—
274C32×C8—21no—
275C3⋊(C3⋊C8)—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278#529—91no—
279C2×C4×D4—91no—
280#484—91no—
281#481—91no—
282#478—91no—
283#478—91no—
284#463—31no—
285#463—91no—
286#450—91no—
287#447—31no—
288C4×SD16—91no—
289C4×SD16—91no—
290C4×D8—91no—
291C4×D8—91no—
292#431—91no—
293C24×C3—61no—
294C23×D3—21no—
295C2×C3×Q8—31no—
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—31no—
299C2×C3×D4—61no—
300C2×C3×D4—62no—
301C2×C3×D4—62no—
302C2×C3×D4—61no—
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C22×D311yescharacteristic
307C22×C3×C4—31no—
308C22×C3×C4—61no—
309C2×#67—21no—
310C2×#67—21no—
311C22×Dic3—21no—
312C22×Dic3—31no—
313C22×Dic3—31no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—121no—
322C22×Dic3—121no—
323C22×Dic3—124no—
324D3×D4—22no—
325D3×D4—22no—
326C2×D12C22×D311yescharacteristic
327C2×C4×D3—31no—
328C2×C4×D3—31no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—124no—
333C2×C4×D3C22×D311yescharacteristic
334C2×Dic6C22×D311yescharacteristic
335C3×SD16—62no—
336C3×D8—24no—
337C3×D8—22no—
338C3×D8—22no—
339C3×D8—62no—
340C2×C3×C8—21no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C42—31no—
352#217—21no—
353#217—21no—
354#217—21no—
355#217—21no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—121no—
364#217—121no—
365#215—62no—
366#214—22no—
367#214—62no—
368#213—22no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—31no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3C22×D311yescharacteristic
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405C22×C32—22no—
406C22×C32—41no—
407C22×C32—41no—
408C22×C32—41no—
409C22×C32—41no—
410C22×C32—41no—
411C22×C32C22×D411yescharacteristic
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—22no—
415C2×C3×D3—48no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C2×C3×D3#13512yes—
419C32×C4C2×#4111yescharacteristic
420C32×C4C2×#4111yescharacteristic
421C3⋊Dic3—21no—
422C3⋊Dic3—41no—
423C3⋊Dic3—41no—
424C3⋊Dic3AGL(1,ℤ/8)12yes—
425C3×Dic3—21no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C22×D4—31no—
432C23×C4—181no—
433C2×SD16—31no—
434C2×SD16—91no—
435C2×D8—31no—
436C2×D8D3211yescharacteristic
437#126—181no—
438#125—91no—
439#124—31no—
440#123—181no—
441C22⋊Q8—91no—
442#121—31no—
443C4×Q8—91no—
444C4×D4—31no—
445C4×D4—91no—
446C4×D4—91no—
447C4×D4—91no—
448C4×D4—91no—
449C4×D4—181no—
450C4×D4—181no—
451C4×D4—181no—
452#117—181no—
453C2×C4⋊C4—91no—
454C2×C22⋊C4—181no—
455C2×C42—91no—
456#107—91no—
457#107—91no—
458#106—91no—
459#106—91no—
460C4⋊C8—31no—
461C4⋊C8—91no—
462#103—31no—
463#103—91no—
464#102—31no—
465#102—31no—
466#102—31no—
467#102—91no—
468#102—91no—
469#102—91no—
470C22⋊C8—31no—
471C22⋊C8—91no—
472C4×C8—91no—
473C4×C8—91no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—31no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—64no—
482C23×C3—61no—
483C23×C3—122no—
484C23×C3—122no—
485C22×D3—24no—
486C22×D3—21no—
487C22×D3—42no—
488C22×D3—42no—
489C22×D3D3×D411yescharacteristic
490C3×Q8—61no—
491C3×Q8—61no—
492C3×D4—22no—
493C3×D4—21no—
494C3×D4—21no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—22no—
500C3×D4—32no—
501C3×D4—41no—
502C3×D4—41no—
503C3×D4—64no—
504C3×D4—61no—
505C3×D4—122no—
506C3×D4#23712yes—
507C3×D4#23712yes—
508C2×C3×C4—21no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—122no—
518C2×C3×C4C23×D311yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520#67—24no—
521#67—42no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—42no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—62no—
533C2×Dic3—62no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—121no—
539C2×Dic3—121no—
540C2×Dic3—122no—
541C2×Dic3—122no—
542C2×Dic3—122no—
543C2×Dic3—122no—
544C2×Dic3—122no—
545C2×Dic3—122no—
546C2×Dic3—122no—
547C2×Dic3—242no—
548C2×Dic3—242no—
549C2×Dic3D3×D411yescharacteristic
550C2×Dic3D3×D411yescharacteristic
551C2×Dic3D3×D411yescharacteristic
552D12—21no—
553D12#23712yes—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—62no—
557C4×D3—62no—
558C4×D3—122no—
559C4×D3—122no—
560C4×D3—122no—
561Dic6—21no—
562Dic6—21no—
563C3×C8—22no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—61no—
567C3×C8—61no—
568C3⋊C8—21no—
569C3⋊C8—21no—
570C3⋊C8—61no—
571C3⋊C8—61no—
572C3⋊C8—121no—
573C2×C32—42no—
574C2×C32—81no—
575C2×C32#52511yescharacteristic
576C2×C32C2×#13511yescharacteristic
577C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
578C3×D3—22no—
579C3×D3—42no—
580C24—61no—
581C2×Q8—31no—
582C2×D4—31no—
583C2×D4—61no—
584C2×D4—62no—
585C2×D4—62no—
586C2×D4—61no—
587C2×D4C2×D3211yescharacteristic
588C2×D4C2×D3211yescharacteristic
589C22×C4—31no—
590C22×C4—61no—
591C22×C4—91no—
592C22×C4—91no—
593C22×C4—181no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4—181no—
598C22×C4—364no—
599SD16—62no—
600SD16—182no—
601D8—22no—
602D8—62no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—91no—
606C2×C8C2×D3211yescharacteristic
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—91no—
610C4⋊C4—91no—
611C4⋊C4—181no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C42—31no—
626C42—91no—
627C42—91no—
628C42—91no—
629C42—181no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—21no—
633C22×C3—32no—
634C22×C3—42no—
635C22×C3—42no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—62no—
649C22×C3—81no—
650C22×C3—81no—
651C22×C3—81no—
652C22×C3—81no—
653C22×C3—128no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3C2×D3×D411yescharacteristic
657C22×C3C2×D3×D411yescharacteristic
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—22no—
661C2×D3—48no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3#91212yes—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—61no—
668C3×C4—61no—
669C3×C4—61no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4C2×#23711yescharacteristic
674C3×C4C2×#23711yescharacteristic
675C3×C4C2×#23711yescharacteristic
676C3×C4D3×#4111yescharacteristic
677Dic3—21no—
678Dic3—21no—
679Dic3—21no—
680Dic3—32no—
681Dic3—32no—
682Dic3—41no—
683Dic3—41no—
684Dic3—41no—
685Dic3—62no—
686Dic3—61no—
687Dic3—61no—
688Dic3—121no—
689Dic3—121no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—241no—
694Dic3—241no—
695C32#310511yescharacteristic, complemented, Sylow
696C23—21no—
697C23—21no—
698C23—31no—
699C23—64no—
700C23—61no—
701C23—122no—
702C23—122no—
703Q8—61no—
704Q8—61no—
705D4—21no—
706D4—21no—
707D4—21no—
708D4—32no—
709D4—64no—
710D4—61no—
711D4—122no—
712D4#380512yes—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—91no—
722C2×C4—91no—
723C2×C4—122no—
724C2×C4—182no—
725C2×C4—182no—
726C2×C4—181no—
727C2×C4—181no—
728C2×C4—362no—
729C2×C4—362no—
730C2×C4—362no—
731C2×C4—362no—
732C2×C4—362no—
733C2×C4C22×D3211yescharacteristic
734C8—21no—
735C8—61no—
736C8—61no—
737C8—181no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—42no—
742C2×C3—42no—
743C2×C3—62no—
744C2×C3—82no—
745C2×C3—82no—
746C2×C3—81no—
747C2×C3—81no—
748C2×C3—122no—
749C2×C3#558611yescharacteristic
750C2×C3#560611yescharacteristic
751C2×C3C2×#91211yescharacteristic
752C2×C3D3×#13511yescharacteristic
753C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
754C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
755D3—22no—
756D3—42no—
757C22—22no—
758C22—32no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—61no—
765C22—61no—
766C22—62no—
767C22—128no—
768C22—121no—
769C22—121no—
770C22D32×D411yescharacteristic
771C4—61no—
772C4—61no—
773C4—61no—
774C4—92no—
775C4—121no—
776C4—121no—
777C4—121no—
778C4—181no—
779C4—361no—
780C4—361no—
781C4D3×#23711yescharacteristic
782C4C2×#380511yescharacteristic
783C3—21no—
784C3#7998911yescharacteristic, complemented
785C3#8050511yescharacteristic, complemented
786C2—42no—
787C2—62no—
788C2—81no—
789C2—122no—
790C2#1059472611yescharacteristic
791C2D3×#91211yescharacteristic
792C2#1059513011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
prime radicalC3×#5156C2
hypercenterC2×D8D32
hypocenterC32#3105
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #10595173C2semidirect
2. D3×D4×Dic3C2semidirect
3. D8×C3⋊Dic3C2semidirect
5. C3×#5153C2semidirect
6. #10591458C2semidirect
7. #10591445C2semidirect
8. #10591435C2semidirect
9. #10591431C2semidirect
10. #10591415C2semidirect
11. #10591411C2semidirect
12. #10590767C2semidirect
13. #10590742C2semidirect
14. #10590682C2semidirect
15. #10590656C2semidirect
22. D4×C3⋊Dic3C22semidirect
24. C3×#936C22semidirect
39. #63869C22semidirect
41. #63843C22semidirect
44. #63659C22semidirect
45. #63645C22semidirect
46. C8×C3⋊Dic3C22semidirect
48. C3×#832C22semidirect
51. C3×#816C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. #63575C22semidirect
54. #63574C22semidirect
55. #63573C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63566C22semidirect
60. #63553C22semidirect
72. #5153D3semidirect
160. #936C2×D3semidirect
211. #832C2×D3semidirect
223. #816C2×D3semidirect
225. Dic3⋊C8C2×D3semidirect
695. C32#3105semidirect
784. C3#79989semidirect
785. C3#80505semidirect

Maximal subgroups

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

subgroupindex
#105951732
D3×D4×Dic32
D8×C3⋊Dic32
C3×#51562
C3×#51532
#105914582
#105914452
#105914352
#105914312
#105914152
#105914112
#105907672
#105907422
#105906822
#105906562
#805053
#799893