Finite Group Databasebeta

← #11887261

Subgroups — #11887261

Order 1152.

910 conjugacy classes of subgroups.

The subgroup lattice has 811 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5642C211yesmaximal, characteristic, complemented
2#10595018C211yesmaximal, characteristic
3#10592745C211yesmaximal, characteristic, complemented
4C3×#5051C211yesmaximal, characteristic, complemented
5#10591657C211yesmaximal, characteristic, complemented
6#10591607C211yesmaximal, characteristic, complemented
7#10591585C211yesmaximal, characteristic, complemented
8#10591536C211yesmaximal, characteristic, complemented
9C3⋊C8×#67C211yesmaximal, characteristic, complemented
10#10591101C211yesmaximal, characteristic, complemented
11C2×#63564C211yesmaximal, characteristic, complemented
12#10590610C211yesmaximal, characteristic, complemented
13#10590537C211yesmaximal, characteristic, complemented
14#10590468C211yesmaximal, characteristic, complemented
15#10590424C211yesmaximal, characteristic, complemented
16#83598—31nomaximal
17#80775—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21C2×#3755C2211yescharacteristic
22C2×#3755C2211yescharacteristic
23C3×#946C2211yescharacteristic, complemented
24C3×Q8×Dic3C2211yescharacteristic, complemented
25C2×C3×#216C2211yescharacteristic, complemented
26C3×C4×#67C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C22×C3×C3⋊C8C2211yescharacteristic
30C3×#898—21no—
31C3×#892C2211yescharacteristic, complemented
32C3×#890—21no—
33C3×#890C2211yescharacteristic, complemented
34C3×#886—21no—
35C3×#877—21no—
36#63981—21no—
37#63974—21no—
38#63910—21no—
39#63909C2211yescharacteristic
40#63897—21no—
41#63894C2211yescharacteristic
42#63864C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63657C2211yescharacteristic
45#63636C2211yescharacteristic
46#63636C2211yescharacteristic
47C3×#835C2211yescharacteristic, complemented
48C3×#810C2211yescharacteristic, complemented
49C3×#807C2211yescharacteristic, complemented
50#63574C2211yescharacteristic, complemented
51#63574C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63565C2211yescharacteristic, complemented
54#63565C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#552—31no—
62#5642D311yescharacteristic, complemented
63#5630—31no—
64#5550—31no—
65C3×#467—31no—
66#5187—31no—
67#5185—31no—
68C2×#821—31no—
69C8×#67—31no—
70#5068—31no—
71#5066—31no—
72#5051D311yescharacteristic, complemented
73#5048—31no—
74#5047—31no—
75#5046—31no—
76#5046—31no—
77#5046—61no—
78#5043—31no—
79#5028—31no—
80C4×#215—31no—
81D4×C3⋊C8—31no—
82#5003—31no—
83#5002—31no—
84#4971—31no—
85C2×#809—31no—
86#4891—31no—
87#4885—31no—
88#4807—31no—
89#4804—31no—
90#4800—31no—
91#4788—31no—
92C23×C3⋊D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×C4⋊(C3⋊D3)—22no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)—41no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C3×#67D411yescharacteristic
101C22×C3×Dic3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×#624—21no—
107C2×#624—21no—
108#3799—22no—
109#3799—41no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113#3755—22no—
114#3755—41no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#217D411yescharacteristic
119C3×#216—41no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8—41no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139#3722—21no—
140#3722—21no—
141#3722—21no—
142#3722—21no—
143D3×C3⋊C8—41no—
144#3296—91noSylow
145C2×#239—31no—
146C2×#235—31no—
147C22×D12—31no—
148C22×D12—31no—
149C22×D12—61no—
150C2×C3×Q16—31no—
151C22×C3×C8—31no—
152C3×#126—61no—
153C3×#125—31no—
154C3×#125—61no—
155C3×#123—61no—
156C3×C22⋊Q8—21no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—31no—
159C3×C22⋊Q8C2×D311yescharacteristic
160C3×C22⋊Q8C2×D311yescharacteristic
161C3×C4×Q8—31no—
162C3×C4×D4—31no—
163C3×#117—31no—
164C3×#117—61no—
165C2×C3×C4⋊C4—31no—
166#947—31no—
167#946C2×D311yescharacteristic, complemented
168Q8×Dic3C2×D311yescharacteristic, complemented
169C2×#216C2×D311yescharacteristic, complemented
170C2×#215—31no—
171C2×#215—31no—
172C2×#215—31no—
173C2×#215—31no—
174C2×#215—61no—
175C2×#215—61no—
176#937—61no—
177#930—31no—
178C4×#67C2×D311yescharacteristic
179C2×C4⋊Dic3C2×D311yescharacteristic
180#924C2×D311yescharacteristic
181C22×C3⋊C8—31no—
182C22×C3⋊C8C2×D311yescharacteristic
183C2×D3×C8—31no—
184#898—21no—
185#895—31no—
186#895—61no—
187#894—61no—
188#894—61no—
189#893—31no—
190#892C2×D311yescharacteristic, complemented
191#890—21no—
192#890C2×D311yescharacteristic, complemented
193#886—21no—
194#884—61no—
195#882—61no—
196D3×C22⋊C4—61no—
197D3×C22⋊C4—61no—
198#877—21no—
199#875—31no—
200C4×D12—31no—
201C3×#107—31no—
202C3×#103—31no—
203C3×#103—31no—
204#835—31no—
205#835—31no—
206#835C2×D311yescharacteristic, complemented
207#830—31no—
208#830—31no—
209#830—31no—
210#830—61no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215(C2×D3)⋊C8—31no—
216Dic3⋊C8—31no—
217C8×Dic3—31no—
218#810—31no—
219#810—31no—
220#810C2×D311yescharacteristic, complemented
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—31no—
229#809—61no—
230#809—61no—
231#808—31no—
232#808—31no—
233#808—31no—
234#808—31no—
235#807C2×D311yescharacteristic, complemented
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—42no—
242C22×C3⋊D3—42no—
243C22×C3⋊D3—81no—
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
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—42no—
257C4⋊(C3⋊D3)#4112yes—
258C3×#67—22no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—42no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#626—42no—
272#626—81no—
273#624—42no—
274#624—81no—
275C3⋊(C3⋊C8)—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—31no—
280#546—91no—
281#488—91no—
282#483—91no—
283#482—91no—
284#478—91no—
285#467—31no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290C4×SD16—91no—
291C8×D4—91no—
292#416—91no—
293C2×#102—91no—
294C23×D3—61no—
295C23×D3—61no—
296C23×D3—121no—
297C2×C3×Q8—21no—
298C2×C3×Q8—31no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×D4—31no—
302C22×C3×C4—21no—
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C2×#67—61no—
308C2×#67—61no—
309C2×#67#6711yescharacteristic
310C22×Dic3—21no—
311#239—62no—
312#239—121no—
313#235—62no—
314#235—121no—
315C2×D12—31no—
316C2×D12—31no—
317C2×D12—31no—
318C2×D12—31no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12—62no—
322C2×D12—62no—
323C2×D12—61no—
324C2×D12—61no—
325C2×D12—61no—
326C2×D12—61no—
327C2×D12—122no—
328C2×D12—121no—
329C2×D12—121no—
330C2×D12—121no—
331C2×D12—122no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3C22×D311yescharacteristic
337C2×Dic6C22×D311yescharacteristic
338C3×Q16—121no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8—121no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—41no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C22⋊C4—21no—
359C3×C22⋊C4—21no—
360C3×C22⋊C4—31no—
361C3×C22⋊C4—31no—
362C3×C22⋊C4—41no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C42—31no—
367C3×C42—61no—
368C3×C42—61no—
369#217—21no—
370#217#6711yescharacteristic
371#216—41no—
372#215—62no—
373#215—62no—
374#215—122no—
375#215—121no—
376#215—121no—
377#215—122no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
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#6711yescharacteristic
389C4⋊Dic3—21no—
390C4⋊Dic3—21no—
391C4⋊Dic3—21no—
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4#6711yescharacteristic
399C4×Dic3—21no—
400C4×Dic3—21no—
401C4×Dic3C22×D311yescharacteristic
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—41no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8—121no—
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412D3×C8—121no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32#13512yes—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—22no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—84no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C32×C4—21no—
428C32×C4—41no—
429C32×C4—41no—
430C32×C4C2×#4111yescharacteristic
431C32×C4H(5,𝔽2)11yescharacteristic
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—91no—
440C22×D4—91no—
441C2×Q16—31no—
442C2×SD16—91no—
443C2×SD16—91no—
444C22×C8—31no—
445C22×C8—91no—
446#126—61no—
447#125—31no—
448#125—61no—
449#124—91no—
450#123—61no—
451#123—181no—
452C22⋊Q8—31no—
453C22⋊Q8—31no—
454C22⋊Q8D3211yescharacteristic
455#121—91no—
456#121—181no—
457#120—181no—
458C4×Q8—31no—
459C4×D4—31no—
460C4×D4—91no—
461#117—31no—
462#117—61no—
463C2×C4⋊C4—31no—
464C2×C22⋊C4—181no—
465#107—31no—
466#106—91no—
467#106—91no—
468C4⋊C8—91no—
469#103—31no—
470#103—31no—
471#103—91no—
472#103—91no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479C22⋊C8—91no—
480C22⋊C8—91no—
481C4×C8—91no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3D3×D411yescharacteristic
485C23×C3C2×#6711yescharacteristic
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—121no—
491C22×D3—121no—
492C22×D3—122no—
493C22×D3—122no—
494C22×D3—124no—
495C22×D3—122no—
496C22×D3—122no—
497C22×D3—242no—
498C22×D3—241no—
499C22×D3—241no—
500C22×D3—242no—
501C22×D3C2×#6711yescharacteristic
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—21no—
506C3×Q8—41no—
507C3×Q8—41no—
508C3×Q8—61no—
509C3×Q8—61no—
510C3×D4—62no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—122no—
535C2×C3×C4D3×D411yescharacteristic
536C2×C3×C4C2×#6711yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538C2×C3×C4C23×D311yescharacteristic
539#67—22no—
540#67—122no—
541#67—241no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—42no—
547C2×Dic3C2×#6711yescharacteristic
548C2×Dic3C2×#6711yescharacteristic
549C2×Dic3C2×#6711yescharacteristic
550D12—32no—
551D12—32no—
552D12—62no—
553D12—62no—
554D12—61no—
555D12—61no—
556D12—61no—
557D12—61no—
558D12—61no—
559D12—61no—
560D12—121no—
561D12—121no—
562D12—122no—
563D12—122no—
564D12—124no—
565D12—122no—
566D12—241no—
567C4×D3—21no—
568C4×D3—21no—
569C4×D3—122no—
570C4×D3—122no—
571C4×D3—241no—
572C4×D3—241no—
573Dic6—21no—
574Dic6—21no—
575C3×C8—61no—
576C3×C8—61no—
577C3⋊C8—21no—
578C3⋊C8—21no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—61no—
583C3⋊C8—121no—
584C3⋊C8—121no—
585C2×C32—22no—
586C2×C32#54611yescharacteristic
587C2×C32C2×#13511yescharacteristic
588C2×C32#57711yescharacteristic
589C3⋊D3—42no—
590C3⋊D3—81no—
591C3×D3—41no—
592C24—181no—
593#41—182no—
594#41—361no—
595C2×Q8—31no—
596C2×Q8C2×D3211yescharacteristic
597C2×D4—31no—
598C2×D4—91no—
599C2×D4—91no—
600C2×D4—182no—
601C2×D4—181no—
602C2×D4—181no—
603C2×D4—181no—
604C2×D4—361no—
605C22×C4—31no—
606C22×C4—61no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4C2×D3211yescharacteristic
610Q16—121no—
611SD16—182no—
612SD16—361no—
613C2×C8—31no—
614C2×C8—31no—
615C2×C8—91no—
616C2×C8—91no—
617C2×C8—121no—
618C2×C8—361no—
619C4⋊C4—21no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—31no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4—61no—
628C4⋊C4—61no—
629C4⋊C4—61no—
630C4⋊C4C2×D3211yescharacteristic
631C22⋊C4—21no—
632C22⋊C4—31no—
633C22⋊C4—31no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C42—31no—
642C42—61no—
643C42—61no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—22no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3#91912yes—
656C22×C3#95012yes—
657C22×C3C2×D3×D411yescharacteristic
658C22×C3C22×#6711yescharacteristic
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—62no—
663C2×D3—62no—
664C2×D3—122no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—122no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—241no—
677C2×D3—241no—
678C2×D3—241no—
679C2×D3—241no—
680C2×D3—244no—
681C2×D3—244no—
682C2×D3—248no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—61no—
693C3×C4—61no—
694C3×C4—61no—
695C3×C4—81no—
696C3×C4—81no—
697C3×C4—121no—
698C3×C4—121no—
699C3×C4—121no—
700C3×C4—121no—
701C3×C4#100411yescharacteristic
702C3×C4D3×#4111yescharacteristic
703C3×C4D3×#4111yescharacteristic
704C3×C4#100911yescharacteristic
705Dic3—21no—
706Dic3—21no—
707Dic3—21no—
708Dic3—41no—
709Dic3—41no—
710Dic3—41no—
711Dic3—41no—
712C32#329611yescharacteristic, complemented, Sylow
713C23—31no—
714C23—181no—
715C23—181no—
716C23—362no—
717C23—362no—
718C23—721no—
719C23D3×#6711yescharacteristic
720Q8—21no—
721Q8—21no—
722Q8—61no—
723Q8—61no—
724D4—62no—
725D4—92no—
726D4—181no—
727D4—181no—
728D4—181no—
729D4—362no—
730D4—362no—
731D4—721no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—31no—
737C2×C4—31no—
738C2×C4—31no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—122no—
746C2×C4—362no—
747C2×C4—721no—
748C2×C4D3×#6711yescharacteristic
749C2×C4C22×D3211yescharacteristic
750C8—61no—
751C8—61no—
752C8—181no—
753C8—181no—
754C2×C3—22no—
755C2×C3—22no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—42no—
760C2×C3—121no—
761C2×C3#561011yescharacteristic
762C2×C3C2×#91911yescharacteristic
763C2×C3#577011yescharacteristic
764C2×C3C2×#95011yescharacteristic
765C2×C3#582911yescharacteristic
766C2×C3#583711yescharacteristic
767D3—41no—
768D3—122no—
769D3—122no—
770D3—242no—
771D3—242no—
772D3—241no—
773D3—241no—
774C22—21no—
775C22—21no—
776C22—61no—
777C22—61no—
778C22—61no—
779C22—182no—
780C22—361no—
781C22—361no—
782C22—361no—
783C22—361no—
784C22—361no—
785C22—724no—
786C22#6394912yes—
787C22C2×D3×#6711yescharacteristic
788C4—21no—
789C4—41no—
790C4—41no—
791C4—61no—
792C4—61no—
793C4—61no—
794C4—121no—
795C4—121no—
796C4—121no—
797C4—121no—
798C4#6431211yescharacteristic
799C4#6431411yescharacteristic
800C3—21no—
801C3#8077511yescharacteristic, complemented
802C3#8359811yescharacteristic, complemented
803C2—22no—
804C2—121no—
805C2—362no—
806C2—721no—
807C2#1059530511yescharacteristic
808C2C2×#6394911yescharacteristic
809C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10595018C2
hypercenterC22⋊Q8D32
hypocenterC32#3296
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×#5642C2semidirect
3. #10592745C2semidirect
4. C3×#5051C2semidirect
5. #10591657C2semidirect
6. #10591607C2semidirect
7. #10591585C2semidirect
8. #10591536C2semidirect
9. C3⋊C8×#67C2semidirect
10. #10591101C2semidirect
11. C2×#63564C2semidirect
12. #10590610C2semidirect
13. #10590537C2semidirect
14. #10590468C2semidirect
15. #10590424C2semidirect
23. C3×#946C22semidirect
24. C3×Q8×Dic3C22semidirect
25. C2×C3×#216C22semidirect
31. C3×#892C22semidirect
33. C3×#890C22semidirect
43. C2×D3×C3⋊C8C22semidirect
47. C3×#835C22semidirect
48. C3×#810C22semidirect
49. C3×#807C22semidirect
50. #63574C22semidirect
51. #63574C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
53. #63565C22semidirect
54. #63565C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
62. #5642D3semidirect
72. #5051D3semidirect
167. #946C2×D3semidirect
168. Q8×Dic3C2×D3semidirect
169. C2×#216C2×D3semidirect
190. #892C2×D3semidirect
192. #890C2×D3semidirect
206. #835C2×D3semidirect
220. #810C2×D3semidirect
235. #807C2×D3semidirect
712. C32#3296semidirect
801. C3#80775semidirect
802. C3#83598semidirect

Maximal subgroups

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

subgroupindex
C3×#56422
#105950182
#105927452
C3×#50512
#105916572
#105916072
#105915852
#105915362
C3⋊C8×#672
#105911012
C2×#635642
#105906102
#105905372
#105904682
#105904242
#835983
#807753