Finite Group Databasebeta

← #11887522

Subgroups — #11887522

Order 1152.

892 conjugacy classes of subgroups.

The subgroup lattice has 785 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594907C211yesmaximal, characteristic
2Dic6×#67C211yesmaximal, characteristic, complemented
3#10592420C211yesmaximal, characteristic, complemented
4C3×#4738C211yesmaximal, characteristic, complemented
5C3×#67⋊C8C211yesmaximal, characteristic, complemented
6#10591175C211yesmaximal, characteristic, complemented
7C2×#63566C211yesmaximal, characteristic, complemented
8#10590890C211yesmaximal, characteristic, complemented
9#10590829C211yesmaximal, characteristic, complemented
10#10590822C211yesmaximal, characteristic, complemented
11#10590803C211yesmaximal, characteristic, complemented
12Dic3×#204C211yesmaximal, characteristic, complemented
13#10590752C211yesmaximal, characteristic, complemented
14#10590675C211yesmaximal, characteristic, complemented
15D3×#816C211yesmaximal, characteristic, complemented
16#80049—31nomaximal
17#79447—31nomaximal
18C22×C3×Dic6C2211yescharacteristic
19C2×#3805—21no—
20C2×D3×Dic6C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22#64133C2211yescharacteristic
23C3×#930C2211yescharacteristic
24C3×C4×#67C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29Dic3×#67—21no—
30#63964—21no—
31#63962—21no—
32#63918C2211yescharacteristic
33#63908C2211yescharacteristic
34#63893—21no—
35Dic3×D12C2211yescharacteristic
36#63891—21no—
37D3×C4⋊Dic3C2211yescharacteristic
38#63887—21no—
39#63866C2211yescharacteristic
40#63856C2211yescharacteristic
41Dic3×Dic6C2211yescharacteristic
42#63839—21no—
43C2×#3716C2211yescharacteristic
44C32×C22⋊C8C2211yescharacteristic
45#63644C2211yescharacteristic
46#63644C2211yescharacteristic
47#63643C2211yescharacteristic
48#63643C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54#63573C2211yescharacteristic
55#63567C2211yescharacteristic
56#63566C2211yescharacteristic
57#63566C2211yescharacteristic
58#63566C2211yescharacteristic
59#63566C2211yescharacteristic
60#63563C2211yescharacteristic
61Q8×#67—31no—
62#5611—31no—
63#5555—31no—
64D4×Dic6—31no—
65C3×#448—31no—
66C3×C8×D4—31no—
67C2×#835—31no—
68#5171—31no—
69#5170—31no—
70#5162—31no—
71Dic3×SD16—31no—
72#5114—31no—
73#5114—31no—
74C2×#816—31no—
75C2×#816—31no—
76#5041—31no—
77#4851—31no—
78#4841—31no—
79#4805—31no—
80D3×#103—31no—
81#4792—31no—
82#4791—31no—
83#4738—31no—
84#4738D311yescharacteristic, complemented
85#67⋊C8D311yescharacteristic, complemented
86#4721—31no—
87#4721—31no—
88#4721—31no—
89#4721—61no—
90C4×#204—31no—
91#4681—31no—
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3—21no—
94C2×#634C2311yescharacteristic
95C2×C3×#67—21no—
96C2×C3×#67D411yescharacteristic
97C22×C3×Dic3—21no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6—22no—
101C2×C3×Dic6—21no—
102C2×C3×Dic6—41no—
103C2×C3×Dic6C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×#627—21no—
107C2×#625—21no—
108#3805—44no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112D3×Dic6—22no—
113D3×Dic6—41no—
114C2×C32×C8C2311yescharacteristic
115C2×C32×C8C2311yescharacteristic
116#3757—21no—
117C4⋊(C3⋊Dic3)—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121#3750—21no—
122C3×#217D411yescharacteristic
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4D411yescharacteristic
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8—41no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×#204—22no—
132C3×#204—41no—
133C3×D3×C8—41no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143Dic32—21no—
144#3716—41no—
145#3298—91noSylow
146C22×C3×Q8—31no—
147C2×D3×Q8—31no—
148C2×#237—61no—
149C2×#237—61no—
150C22×Dic6—31no—
151C22×Dic6C2×D311yescharacteristic
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C22×C3×C8—31no—
155C22×C3×C8—31no—
156C3×#121—31no—
157C3×C4×D4—31no—
158#946—31no—
159#946—61no—
160Q8×Dic3—31no—
161#944—31no—
162#944—61no—
163#938—31no—
164#935—61no—
165D4×Dic3—31no—
166D4×Dic3—61no—
167C2×#214—31no—
168#930—31no—
169#930C2×D311yescharacteristic
170C4×#67—61no—
171C4×#67C2×D311yescharacteristic
172C2×C4⋊Dic3—31no—
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3—31no—
175C2×C4⋊Dic3—61no—
176#924—31no—
177#924—31no—
178#924—31no—
179#924—61no—
180#924—61no—
181C22×C3⋊C8C2×D311yescharacteristic
182C2×#204—31no—
183C2×#204C2×D311yescharacteristic
184C2×#204C2×D311yescharacteristic
185C2×D3×C8C2×D311yescharacteristic
186#897—61no—
187D3×C4⋊C4—31no—
188#888—31no—
189#888—61no—
190#886—61no—
191#886—61no—
192#883—61no—
193#878—61no—
194#878—61no—
195#878—61no—
196C4×D12—31no—
197#869—31no—
198#869—31no—
199C4×Dic6—31no—
200C3×C4⋊C8—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×C22⋊C8—21no—
204C3×C22⋊C8—31no—
205C3×C22⋊C8C2×D311yescharacteristic
206C3×C22⋊C8C2×D311yescharacteristic
207C3×C4×C8—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#832—31no—
213#821—31no—
214(C2×D3)⋊C8C2×D311yescharacteristic
215#817—31no—
216#817—31no—
217#817—31no—
218#817—31no—
219#817—31no—
220#817—61no—
221#817—61no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816—31no—
226#816—31no—
227#816—31no—
228#816—31no—
229#816—31no—
230#816—31no—
231#816—61no—
232#816—61no—
233#816C2×D311yescharacteristic
234#816C2×D311yescharacteristic
235Dic3⋊C8C2×D311yescharacteristic
236C8×Dic3C2×D311yescharacteristic
237#810—31no—
238#808—31no—
239C23×C32C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—42no—
251#634—21no—
252#634—21no—
253C3×#67—42no—
254C3×#67SD1614yescomplemented
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—42no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—21no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—42no—
270C3×Dic6#4112yescomplemented
271#627—42no—
272#627—42no—
273#625—42no—
274D3×Dic3—42no—
275D3×Dic3—42no—
276D3×Dic3—42no—
277C32×C8—21no—
278C32×C8—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281D4×Q8—91no—
282#547—91no—
283#487—91no—
284#483—91no—
285#483—91no—
286#475—91no—
287#465—91no—
288#465—91no—
289#461—91no—
290#448—31no—
291#448—91no—
292C4×SD16—91no—
293C8×D4—31no—
294C2×#103—91no—
295C2×#103—91no—
296C2×C3×Q8—31no—
297C2×C3×Q8—31no—
298C2×C3×Q8—62no—
299C2×C3×Q8—61no—
300C2×C3×Q8—121no—
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C22×C3×C4—21no—
305C22×C3×C4—31no—
306C22×C3×C4—61no—
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C2×#67—21no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67D1211yescharacteristic
313C22×Dic3—21no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—121no—
320D3×Q8—62no—
321D3×Q8—121no—
322#237—124no—
323#237—124no—
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3C22×D311yescharacteristic
329C2×Dic6—22no—
330C2×Dic6—21no—
331C2×Dic6—31no—
332C2×Dic6—31no—
333C2×Dic6—41no—
334C2×Dic6—61no—
335C2×Dic6—62no—
336C2×Dic6—61no—
337C2×Dic6—61no—
338C2×Dic6—61no—
339C2×Dic6—61no—
340C2×Dic6—121no—
341C2×Dic6C22×D311yescharacteristic
342C2×Dic6C22×D311yescharacteristic
343C3×SD16—62no—
344C3×SD16—121no—
345C2×C3×C8—21no—
346C2×C3×C8—21no—
347C2×C3×C8—31no—
348C2×C3×C8—31no—
349C2×C3×C8—121no—
350C2×C3×C8—121no—
351C2×C3×C8C22×D311yescharacteristic
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C22×D311yescharacteristic
354C2×C3×C8C22×D311yescharacteristic
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C22⋊C4—31no—
358C3×C22⋊C4—31no—
359C3×C22⋊C4—61no—
360C3×C42—31no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—121no—
367#217D1211yescharacteristic
368#214—121no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4D1211yescharacteristic
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—121no—
391C4⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—121no—
402Dic3⋊C4D1211yescharacteristic
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3C22×D311yescharacteristic
406C2×C3⋊C8—41no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409#204—22no—
410#204—41no—
411#204—121no—
412D3×C8—41no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32C2×SD1612yes—
416C22×C32C22×D411yescharacteristic
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3C2×SD1612yes—
423C32×C4—21no—
424C32×C4C2×#4111yescharacteristic
425C32×C4H(5,𝔽2)11yescharacteristic
426C3⋊Dic3—41no—
427C3⋊Dic3—41no—
428C3⋊Dic3—41no—
429C3⋊Dic3—41no—
430C3×Dic3—22no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3C2×SD1612yes—
436C2×#41—181no—
437C22×Q8—31no—
438C22×Q8—91no—
439C2×SD16—31no—
440C2×SD16—31no—
441C2×SD16—91no—
442C22×C8—31no—
443C22×C8—31no—
444C4⋊Q8—91no—
445C4⋊Q8—91no—
446C4⋊Q8—181no—
447#123—181no—
448#123—181no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451C22⋊Q8—181no—
452C22⋊Q8—181no—
453C22⋊Q8—181no—
454#121—31no—
455#121—91no—
456C4×Q8—91no—
457C4×D4—31no—
458C4×D4—91no—
459C4×D4—181no—
460C2×C4⋊C4—91no—
461C2×C4⋊C4—91no—
462#106—91no—
463#106—91no—
464#106—91no—
465C4⋊C8—31no—
466#103—31no—
467#103—31no—
468#103—91no—
469#103—91no—
470#103—91no—
471#103—91no—
472#103—91no—
473#103—91no—
474#103—91no—
475#102—91no—
476C22⋊C8—31no—
477C22⋊C8D3211yescharacteristic
478C4×C8—31no—
479C23×C3—21no—
480C23×C3—31no—
481C23×C3—61no—
482C23×C3C2×D1211yescharacteristic
483C23×C3D3×D411yescharacteristic
484C22×D3—21no—
485C22×D3C2×D1211yescharacteristic
486C3×Q8—32no—
487C3×Q8—61no—
488C3×Q8—61no—
489C3×Q8—61no—
490C3×Q8—122no—
491C3×D4—34no—
492C3×D4—61no—
493C3×D4—61no—
494C3×D4—122no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—122no—
512C2×C3×C4C2×D1211yescharacteristic
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516#67—42no—
517#67—122no—
518#67—122no—
519#67#20414yescomplemented
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—42no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—121no—
533C2×Dic3—121no—
534C2×Dic3—121no—
535C2×Dic3—121no—
536C2×Dic3—122no—
537C2×Dic3—122no—
538C2×Dic3—122no—
539C2×Dic3—122no—
540C2×Dic3—122no—
541C2×Dic3—242no—
542C2×Dic3C2×D1211yescharacteristic
543C2×Dic3C2×D1211yescharacteristic
544C2×Dic3C2×D1211yescharacteristic
545D12—21no—
546D12—21no—
547C4×D3—21no—
548C4×D3—21no—
549C4×D3—122no—
550C4×D3—122no—
551C4×D3—122no—
552Dic6—21no—
553Dic6—21no—
554Dic6—21no—
555Dic6—42no—
556Dic6—61no—
557Dic6—61no—
558Dic6—61no—
559Dic6—61no—
560Dic6—121no—
561Dic6—121no—
562Dic6—122no—
563Dic6—122no—
564Dic6—122no—
565Dic6—122no—
566Dic6#23712yescomplemented
567C3×C8—21no—
568C3×C8—21no—
569C3×C8—21no—
570C3×C8—21no—
571C3×C8—41no—
572C3×C8—41no—
573C3×C8—61no—
574C3×C8—61no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C2×C32—22no—
578C2×C32#54611yescharacteristic
579C2×C32C22×SD1611yescharacteristic
580C2×C32#57811yescharacteristic
581C3×D3—22no—
582C3×D3—81no—
583#41—364no—
584C2×Q8—31no—
585C2×Q8—31no—
586C2×Q8—62no—
587C2×Q8—61no—
588C2×Q8—91no—
589C2×Q8—121no—
590C2×Q8—181no—
591C2×Q8—181no—
592C2×Q8—182no—
593C2×Q8—361no—
594C2×D4—31no—
595C2×D4—31no—
596C2×D4—61no—
597C2×D4—181no—
598C22×C4—31no—
599C22×C4—61no—
600C22×C4—181no—
601C22×C4—181no—
602C22×C4—181no—
603C22×C4—181no—
604C22×C4C2×D3211yescharacteristic
605SD16—62no—
606SD16—121no—
607SD16—361no—
608C2×C8—31no—
609C2×C8—31no—
610C2×C8—121no—
611C2×C8—121no—
612C2×C8C2×D3211yescharacteristic
613C2×C8C2×D3211yescharacteristic
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—91no—
617C4⋊C4—91no—
618C4⋊C4—91no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C22⋊C4—31no—
628C22⋊C4—31no—
629C22⋊C4—61no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C42—31no—
635C42—181no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—22no—
642C22×C3—32no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3C2×#20412yes—
651C22×C3D3×SD1612yes—
652C22×C3C22×D1211yescharacteristic
653C22×C3C2×D3×D411yescharacteristic
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3C2×#20412yes—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—32no—
665C3×C4—41no—
666C3×C4—61no—
667C3×C4—62no—
668C3×C4—61no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4C2×#23711yescharacteristic
672C3×C4#100411yescharacteristic
673C3×C4#100411yescharacteristic
674C3×C4D3×#4111yescharacteristic
675Dic3—21no—
676Dic3—21no—
677Dic3—22no—
678Dic3—41no—
679Dic3—41no—
680Dic3—121no—
681Dic3—121no—
682Dic3—121no—
683Dic3—121no—
684Dic3—121no—
685Dic3—121no—
686Dic3—121no—
687Dic3—121no—
688Dic3—241no—
689Dic3—241no—
690Dic3—241no—
691Dic3—241no—
692Dic3C2×#20412yes—
693C32#329811yescharacteristic, complemented, Sylow
694C23—31no—
695C23—61no—
696C23D3×D1211yescharacteristic
697Q8—32no—
698Q8—61no—
699Q8—61no—
700Q8—61no—
701Q8—122no—
702Q8—181no—
703Q8—181no—
704Q8—362no—
705Q8—362no—
706D4—34no—
707D4—61no—
708D4—61no—
709D4—122no—
710D4—362no—
711C2×C4—21no—
712C2×C4—21no—
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—122no—
722C2×C4—181no—
723C2×C4—181no—
724C2×C4—181no—
725C2×C4—181no—
726C2×C4—362no—
727C2×C4—362no—
728C2×C4—362no—
729C2×C4—362no—
730C2×C4D3×D1211yescharacteristic
731C2×C4C22×D3211yescharacteristic
732C8—21no—
733C8—21no—
734C8—61no—
735C8—61no—
736C2×C3—22no—
737C2×C3—22no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—42no—
742C2×C3—62no—
743C2×C3—241no—
744C2×C3#555411yescharacteristic
745C2×C3#559111yescharacteristic
746C2×C3C22×#20411yescharacteristic
747C2×C3#575311yescharacteristic
748C2×C3C2×D3×SD1611yescharacteristic
749C2×C3#577911yescharacteristic
750D3—22no—
751D3—81no—
752C22—21no—
753C22—21no—
754C22—32no—
755C22—61no—
756C22—61no—
757C22—121no—
758C22—121no—
759C22—121no—
760C22D3×#20412yes—
761C22C2×D3×D1211yescharacteristic
762C4—21no—
763C4—32no—
764C4—61no—
765C4—61no—
766C4—62no—
767C4—121no—
768C4—121no—
769C4—361no—
770C4—361no—
771C4—361no—
772C4—361no—
773C4D3×#23711yescharacteristic
774C4#6431311yescharacteristic
775C3—21no—
776C3#7944711yescharacteristic, complemented
777C3#8004911yescharacteristic, complemented
778C2—22no—
779C2—62no—
780C2—241no—
781C2#1059429211yescharacteristic
782C2C2×D3×#20411yescharacteristic
783C2#1059472111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10594907C2
hypercenterC22⋊C8D32
hypocenterC32#3298
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. Dic6×#67C2semidirect
3. #10592420C2semidirect
4. C3×#4738C2semidirect
5. C3×#67⋊C8C2semidirect
6. #10591175C2semidirect
7. C2×#63566C2semidirect
8. #10590890C2semidirect
9. #10590829C2semidirect
10. #10590822C2semidirect
11. #10590803C2semidirect
12. Dic3×#204C2semidirect
13. #10590752C2semidirect
14. #10590675C2semidirect
15. D3×#816C2semidirect
84. #4738D3semidirect
85. #67⋊C8D3semidirect
254. C3×#67SD16semidirect
270. C3×Dic6#41semidirect
519. #67#204semidirect
566. Dic6#237semidirect
693. C32#3298semidirect
776. C3#79447semidirect
777. C3#80049semidirect

Maximal subgroups

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

subgroupindex
#105949072
Dic6×#672
#105924202
C3×#47382
C3×#67⋊C82
#105911752
C2×#635662
#105908902
#105908292
#105908222
#105908032
Dic3×#2042
#105907522
#105906752
D3×#8162
#800493
#794473