Finite Group Databasebeta

← #11887221

Subgroups — #11887221

Order 1152.

892 conjugacy classes of subgroups.

The subgroup lattice has 805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5639C211yesmaximal, characteristic, complemented
2#10595078C211yesmaximal, characteristic
3#10592746C211yesmaximal, characteristic, complemented
4C3×#5048C211yesmaximal, characteristic, complemented
5#10591651C211yesmaximal, characteristic, complemented
6#10591604C211yesmaximal, characteristic, complemented
7#10591596C211yesmaximal, characteristic, complemented
8#10591536C211yesmaximal, characteristic, complemented
9C3⋊C8×#67C211yesmaximal, characteristic, complemented
10#10591105C211yesmaximal, characteristic, complemented
11#10591090C211yesmaximal, characteristic, complemented
12D3×#809C211yesmaximal, characteristic, complemented
13#10590533C211yesmaximal, characteristic, complemented
14#10590470C211yesmaximal, characteristic, complemented
15#10590426C211yesmaximal, characteristic, complemented
16#83598—31nomaximal
17#80671—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic, complemented
21C2×#3756C2211yescharacteristic, complemented
22C2×#3755C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic, complemented
25C2×C3×#215C2211yescharacteristic
26C3×#930C2211yescharacteristic
27C3×C4×#67C2211yescharacteristic
28C3×#926C2211yescharacteristic, complemented
29C22×C3×C3⋊C8C2211yescharacteristic, complemented
30C3×#892—21no—
31C3×D3×C4⋊C4C2211yescharacteristic
32C3×#890C2211yescharacteristic, complemented
33C3×#889—21no—
34C3×#883—21no—
35C3×#879—21no—
36#63983—21no—
37#63958—21no—
38#63921—21no—
39#63894C2211yescharacteristic
40#63860C2211yescharacteristic
41#63857C2211yescharacteristic
42#63853—21no—
43C2×D3×C3⋊C8C2211yescharacteristic
44#63657C2211yescharacteristic, complemented
45#63637C2211yescharacteristic, complemented
46#63636C2211yescharacteristic
47C3×#835C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic
49C3×#808C2211yescharacteristic, complemented
50#63576C2211yescharacteristic, complemented
51#63574C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63567C2211yescharacteristic, complemented
54#63567C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#552—31no—
62#5639D311yescharacteristic, complemented
63#5612—31no—
64#5550—31no—
65C3×#465—31no—
66#5169—31no—
67#5166—31no—
68#5113—31no—
69C8×#67—31no—
70#5068—31no—
71#5066—31no—
72#5051—31no—
73#5048D311yescharacteristic, complemented
74#5047—31no—
75#5047—31no—
76#5047—61no—
77#5046—31no—
78#5035—31no—
79#5028—31no—
80C4×#215—31no—
81D4×C3⋊C8—31no—
82#5003—31no—
83#5002—31no—
84#4971—31no—
85C2×#809—31no—
86#4871—31no—
87#4862—31no—
88#4813—31no—
89#4788—31no—
90D3×#102—31no—
91#4768—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#638—21no—
96#3828—22no—
97#3828—41no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C2×#634C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×#626—21no—
107C2×#624—21no—
108D3×D12—22no—
109D3×D12—41no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113#3756—41no—
114#3755—22no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#217D411yescharacteristic
119C3×#215—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⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8—41no—
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138Dic3⋊Dic3—21no—
139#3722—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143D3×C3⋊C8—41no—
144#3296—91noSylow
145C2×D3×D4—31no—
146C2×#235—31no—
147C2×#235—31no—
148C2×#235—61no—
149C22×D12—31no—
150C2×C3×SD16—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⋊Q8C2×D311yescharacteristic, complemented
159C3×C22⋊Q8C2×D311yescharacteristic, complemented
160C3×#121—31no—
161C3×C4×Q8—31no—
162C3×C4×D4—31no—
163C3×#117—31no—
164C3×#117—61no—
165C2×C3×C4⋊C4—31no—
166#946C2×D311yescharacteristic
167Q8×Dic3C2×D311yescharacteristic, complemented
168C2×#216—31no—
169C2×#216—31no—
170C2×#216—61no—
171C2×#215—31no—
172C2×#215—31no—
173C2×#215—61no—
174C2×#215C2×D311yescharacteristic
175#938—61no—
176#937—61no—
177#937—61no—
178#936—31no—
179#930C2×D311yescharacteristic
180C4×#67C2×D311yescharacteristic
181#926C2×D311yescharacteristic, complemented
182#924—31no—
183C22×C3⋊C8—31no—
184C22×C3⋊C8C2×D311yescharacteristic, complemented
185C2×D3×C8—31no—
186#897—31no—
187#894—61no—
188#893—31no—
189#892—21no—
190D3×C4⋊C4C2×D311yescharacteristic
191#890C2×D311yescharacteristic, complemented
192#889—21no—
193#884—61no—
194#883—21no—
195#883—61no—
196D3×C22⋊C4—61no—
197D3×C22⋊C4—61no—
198#879—21no—
199#875—31no—
200C4×D12—31no—
201C3×#106—31no—
202C3×#103—31no—
203C3×#102—31no—
204#835C2×D311yescharacteristic, complemented
205#832—31no—
206#832—31no—
207#830—31no—
208#830—31no—
209#830—31no—
210#830—61no—
211#821—31no—
212#821—31no—
213(C2×D3)⋊C8—31no—
214#816—31no—
215#816—31no—
216Dic3⋊C8—31no—
217C8×Dic3—31no—
218#810—31no—
219#810—31no—
220#810—31no—
221#810—31no—
222#810—61no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—31no—
229#809—61no—
230#809C2×D311yescharacteristic
231#808—31no—
232#808—31no—
233#808C2×D311yescharacteristic, complemented
234#807—31no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
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)#4112yes—
257C4×C3⋊D3—42no—
258#634—21no—
259#634—21no—
260C3×#67—22no—
261C3×#67—81no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—21no—
269C3×D12—21no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—42no—
273#626—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—91no—
286#465—31no—
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—
296C2×C3×Q8—21no—
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×D4—31no—
300C2×C3×D4—31no—
301C2×C3×D4—61no—
302C22×C3×C4—21no—
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C2×#67—21no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—121no—
312C2×#67#6711yescharacteristic
313D3×D4—62no—
314D3×D4—121no—
315#235—62no—
316#235—62no—
317#235—122no—
318#235—121no—
319#235—121no—
320#235—122no—
321C2×D12—31no—
322C2×D12—31no—
323C2×D12—61no—
324C2×D12—62no—
325C2×D12—61no—
326C2×D12—121no—
327C2×D12C22×D311yescharacteristic
328C2×C4×D3—21no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—121no—
334C2×C4×D3C22×D311yescharacteristic
335C2×Dic6—31no—
336C2×Dic6—31no—
337C2×Dic6—61no—
338C3×SD16—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⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C22⋊C4—21no—
358C3×C22⋊C4—21no—
359C3×C22⋊C4—31no—
360C3×C22⋊C4—31no—
361C3×C22⋊C4—41no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C42—31no—
366C3×C42—61no—
367C3×C42—61no—
368#217—21no—
369#217—61no—
370#217—61no—
371#217—61no—
372#217#6711yescharacteristic
373#216—121no—
374#216—121no—
375#216—122no—
376#215—41no—
377#215—62no—
378#215—62no—
379#215—122no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—21no—
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#6711yescharacteristic
388C4⋊Dic3—21no—
389C4⋊Dic3—21no—
390C4⋊Dic3—61no—
391C4⋊Dic3C22×D311yescharacteristic
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—61no—
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—21no—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—22no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3#13512yes—
426D32—84no—
427C32×C4—21no—
428C32×C4—41no—
429C32×C4—41no—
430C32×C4C2×#4111yescharacteristic
431C32×C4H(5,𝔽2)11yescharacteristic
432C3⋊Dic3—41no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—91no—
440C22×D4—91no—
441C2×Q16—91no—
442C2×SD16—31no—
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—91no—
454C22⋊Q8D3211yescharacteristic, complemented
455#121—31no—
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—91no—
466#106—31no—
467#106—91no—
468C4⋊C8—91no—
469#103—31no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
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×C3—61no—
485C23×C3D3×D411yescharacteristic
486C23×C3C2×#6711yescharacteristic
487C22×D3—21no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—121no—
491C22×D3—122no—
492C22×D3—122no—
493C22×D3—122no—
494C22×D3—122no—
495C22×D3—241no—
496C22×D3—241no—
497C22×D3C2×#6711yescharacteristic
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—41no—
503C3×Q8—41no—
504C3×D4—62no—
505C3×D4—61no—
506C3×D4—61no—
507C3×D4—241no—
508C2×C3×C4—21no—
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—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—122no—
531C2×C3×C4D3×D411yescharacteristic
532C2×C3×C4C2×#6711yescharacteristic
533C2×C3×C4C23×D311yescharacteristic
534C2×C3×C4C23×D311yescharacteristic
535#67—22no—
536#67—81no—
537#67—122no—
538#67—122no—
539#67—122no—
540#67—124no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—121no—
547C2×Dic3C2×#6711yescharacteristic
548C2×Dic3C2×#6711yescharacteristic
549C2×Dic3C2×#6711yescharacteristic
550D12—21no—
551D12—21no—
552D12—32no—
553D12—32no—
554D12—62no—
555D12—61no—
556D12—61no—
557D12—121no—
558D12—122no—
559C4×D3—21no—
560C4×D3—21no—
561C4×D3—42no—
562C4×D3—122no—
563C4×D3—122no—
564C4×D3—124no—
565C4×D3—241no—
566C4×D3—241no—
567Dic6—62no—
568Dic6—61no—
569Dic6—61no—
570Dic6—61no—
571Dic6—61no—
572Dic6—121no—
573C3×C8—61no—
574C3×C8—61no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C3⋊C8—61no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—121no—
582C3⋊C8—121no—
583C2×C32—41no—
584C2×C32#54611yescharacteristic
585C2×C32C2×#13511yescharacteristic
586C2×C32#57711yescharacteristic
587C3⋊D3—42no—
588C3×D3—22no—
589C3×D3—81no—
590C24—181no—
591#41—182no—
592#41—361no—
593C2×Q8—91no—
594C2×Q8C2×D3211yescharacteristic
595C2×D4—31no—
596C2×D4—31no—
597C2×D4—61no—
598C2×D4—91no—
599C2×D4—181no—
600C2×D4—182no—
601C2×D4—181no—
602C2×D4—361no—
603C22×C4—31no—
604C22×C4—61no—
605C22×C4—181no—
606C22×C4—181no—
607C22×C4C2×D3211yescharacteristic
608Q16—361no—
609SD16—121no—
610SD16—182no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—91no—
614C2×C8—91no—
615C2×C8—121no—
616C2×C8—361no—
617C4⋊C4—21no—
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4—181no—
628C4⋊C4C2×D3211yescharacteristic
629C22⋊C4—21no—
630C22⋊C4—31no—
631C22⋊C4—31no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C42—31no—
640C42—61no—
641C42—61no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—32no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3C2×D3×D411yescharacteristic
659C22×C3C22×#6711yescharacteristic
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—62no—
666C2×D3—62no—
667C2×D3—122no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—241no—
673C2×D3—241no—
674C2×D3—244no—
675C2×D3—244no—
676C2×D3#95012yes—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—41no—
686C3×C4—61no—
687C3×C4—61no—
688C3×C4—61no—
689C3×C4—81no—
690C3×C4—81no—
691C3×C4—121no—
692C3×C4—121no—
693C3×C4—121no—
694C3×C4#100411yescharacteristic
695C3×C4D3×#4111yescharacteristic
696C3×C4D3×#4111yescharacteristic
697C3×C4#100911yescharacteristic
698Dic3—21no—
699Dic3—21no—
700Dic3—21no—
701Dic3—41no—
702Dic3—41no—
703Dic3—41no—
704Dic3—122no—
705Dic3—121no—
706Dic3—121no—
707C32#329611yescharacteristic, complemented, Sylow
708C23—31no—
709C23—61no—
710C23—181no—
711C23—362no—
712C23—362no—
713C23—721no—
714C23D3×#6711yescharacteristic
715Q8—21no—
716Q8—21no—
717Q8—181no—
718Q8—181no—
719D4—62no—
720D4—61no—
721D4—61no—
722D4—92no—
723D4—181no—
724D4—241no—
725D4—362no—
726D4—362no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—31no—
732C2×C4—31no—
733C2×C4—31no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—122no—
740C2×C4—181no—
741C2×C4—362no—
742C2×C4—721no—
743C2×C4D3×#6711yescharacteristic
744C2×C4C22×D3211yescharacteristic
745C8—61no—
746C8—61no—
747C8—181no—
748C8—181no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—41no—
753C2×C3—41no—
754C2×C3—62no—
755C2×C3—81no—
756C2×C3—241no—
757C2×C3#561011yescharacteristic
758C2×C3#576211yescharacteristic
759C2×C3D3×#13511yescharacteristic
760C2×C3C2×#95011yescharacteristic
761C2×C3#582911yescharacteristic
762C2×C3#583711yescharacteristic
763D3—22no—
764D3—81no—
765D3—122no—
766D3—122no—
767D3—242no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—32no—
772C22—61no—
773C22—61no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—182no—
778C22—361no—
779C22—361no—
780C22—724no—
781C22C2×D3×#6711yescharacteristic
782C4—21no—
783C4—41no—
784C4—41no—
785C4—61no—
786C4—61no—
787C4—61no—
788C4—121no—
789C4—121no—
790C4—121no—
791C4—361no—
792C4#6431211yescharacteristic
793C4#6431411yescharacteristic
794C3—21no—
795C3#8067111yescharacteristic, complemented
796C3#8359811yescharacteristic, complemented
797C2—41no—
798C2—62no—
799C2—241no—
800C2—362no—
801C2#1059530511yescharacteristic
802C2#1059531811yescharacteristic
803C2D3×#95011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10595078C2
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×#5639C2semidirect
3. #10592746C2semidirect
4. C3×#5048C2semidirect
5. #10591651C2semidirect
6. #10591604C2semidirect
7. #10591596C2semidirect
8. #10591536C2semidirect
9. C3⋊C8×#67C2semidirect
10. #10591105C2semidirect
11. #10591090C2semidirect
12. D3×#809C2semidirect
13. #10590533C2semidirect
14. #10590470C2semidirect
15. #10590426C2semidirect
20. C32×C22⋊Q8C22semidirect
21. C2×#3756C22semidirect
24. C3×Q8×Dic3C22semidirect
28. C3×#926C22semidirect
29. C22×C3×C3⋊C8C22semidirect
32. C3×#890C22semidirect
44. #63657C22semidirect
45. #63637C22semidirect
47. C3×#835C22semidirect
49. C3×#808C22semidirect
50. #63576C22semidirect
51. #63574C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
53. #63567C22semidirect
54. #63567C22semidirect
60. Dic3×C3⋊C8C22semidirect
62. #5639D3semidirect
73. #5048D3semidirect
158. C3×C22⋊Q8C2×D3semidirect
159. C3×C22⋊Q8C2×D3semidirect
167. Q8×Dic3C2×D3semidirect
181. #926C2×D3semidirect
184. C22×C3⋊C8C2×D3semidirect
191. #890C2×D3semidirect
204. #835C2×D3semidirect
233. #808C2×D3semidirect
454. C22⋊Q8D32semidirect
707. C32#3296semidirect
795. C3#80671semidirect
796. C3#83598semidirect

Maximal subgroups

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

subgroupindex
C3×#56392
#105950782
#105927462
C3×#50482
#105916512
#105916042
#105915962
#105915362
C3⋊C8×#672
#105911052
#105910902
D3×#8092
#105905332
#105904702
#105904262
#835983
#806713