Finite Group Databasebeta

← #11872167

Subgroups — #11872167

Order 1152.

879 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593994C211yesmaximal, characteristic, complemented
2#10593878C211yesmaximal, characteristic, complemented
3C4×#3745C211yesmaximal, characteristic, complemented
4C3×C4×#204C211yesmaximal, characteristic, complemented
5C3×#4690C211yesmaximal, characteristic, complemented
6#10590947C211yesmaximal, characteristic
7#10590942C211yesmaximal, characteristic, complemented
8#10590770C211yesmaximal, characteristic, complemented
9#10590762C211yesmaximal, characteristic, complemented
10#10590759C211yesmaximal, characteristic, complemented
11#10590754C211yesmaximal, characteristic, complemented
12#10590710C211yesmaximal, characteristic, complemented
13#10590704C211yesmaximal, characteristic, complemented
14#10590362C211yesmaximal, characteristic, complemented
15#10590346C211yesmaximal, characteristic, complemented
16#79696—31nomaximal
17#79383—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3745C2211yescharacteristic
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
22C2×C3×#204C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×#872C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic, complemented
26#63921—21no—
27D3×(C2×D3)⋊C4—21no—
28#63918C2211yescharacteristic, complemented
29#63909C2211yescharacteristic
30#63904—21no—
31#63894C2211yescharacteristic
32Dic3×D12C2211yescharacteristic
33#63881—21no—
34#63868—21no—
35#63865—21no—
36#63864C2211yescharacteristic, complemented
37#63856C2211yescharacteristic
38#63853—21no—
39#63852—21no—
40#63841C2211yescharacteristic
41C2×#3717C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C32×C4×C8C2211yescharacteristic, complemented
44#63648C2211yescharacteristic
45#63648C2211yescharacteristic, complemented
46#63645C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#817C2211yescharacteristic, complemented
51C3×#816C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×#803C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic, complemented
60#63563C2211yescharacteristic
61#5582—31no—
62#5545—31no—
63#5534—31no—
64#5521—31no—
65C3×C4×SD16—31no—
66C3×#433—31no—
67#5169—31no—
68#5165—31no—
69#5026—31no—
70#5014—31no—
71#4870—31no—
72#4866—31no—
73#4846—31no—
74#4844—31no—
75#4844—31no—
76#4842—31no—
77#4819—31no—
78#4814—31no—
79#4773—31no—
80#4759—31no—
81#4737—31no—
82#4732—31no—
83#4731—31no—
84#4723—31no—
85#4711—31no—
86#4710—31no—
87C4×D24—31no—
88C4×D24—31no—
89C4×D24—61no—
90C4×#204D311yescharacteristic, complemented
91#4690D311yescharacteristic, complemented
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×#627—21no—
102C2×#626—21no—
103C2×#626—21no—
104C2×#624—21no—
105C2×D3×Dic3—21no—
106D3×D12—22no—
107D3×D12—22no—
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C42C2311yescharacteristic
111#3752—21no—
112#3752—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3745—22no—
116C3×(C2×D3)⋊C4—21no—
117C3×(C2×D3)⋊C4D411yescharacteristic
118C3×(C2×D3)⋊C4D411yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4D411yescharacteristic
123C3×Dic3⋊C4D411yescharacteristic
124C3×C4×Dic3—21no—
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×#204—22no—
129#3724—21no—
130Dic3⋊Dic3—21no—
131#3722—21no—
132#3722—21no—
133#3722—21no—
134#3722—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139#3717—22no—
140#3714—22no—
141#3118—91noSylow
142C2×D3×D4—31no—
143C22×D12—31no—
144C2×C3×SD16—31no—
145C3×C4×Q8—31no—
146C3×C4×D4—31no—
147C3×#117—31no—
148#947—31no—
149#946—31no—
150C2×#215—31no—
151D4×Dic3—31no—
152C2×#213—31no—
153#930—31no—
154C4×#67—61no—
155C2×(C2×D3)⋊C4—61no—
156#926—31no—
157#924—31no—
158C2×D24—31no—
159C2×D24—31no—
160C2×D24—31no—
161C2×D24—61no—
162C2×#204—31no—
163C2×#204C2×D311yescharacteristic
164#898—61no—
165#896—61no—
166#896—61no—
167#895—31no—
168#894—61no—
169#893—31no—
170#893—61no—
171#893—61no—
172#892—31no—
173#888—31no—
174#885—61no—
175#883—61no—
176#67⋊C4—61no—
177D3×C22⋊C4—61no—
178D3×C22⋊C4—61no—
179D3×C22⋊C4—61no—
180#876—61no—
181#875—31no—
182#875—61no—
183C4×D12—31no—
184C4×D12—31no—
185C4×D12—31no—
186C4×D12—31no—
187C4×D12—31no—
188C4×D12—31no—
189C4×D12—61no—
190C4×D12—61no—
191C4×D12C2×D311yescharacteristic
192#872C2×D311yescharacteristic
193#869—31no—
194C4×Dic6C2×D311yescharacteristic, complemented
195C3×#106—31no—
196C3×C4⋊C8—31no—
197C3×C4⋊C8—31no—
198C3×#103—31no—
199C3×#102—31no—
200C3×C22⋊C8—31no—
201C3×C22⋊C8—31no—
202C3×#97—31no—
203C3×C4×C8—21no—
204C3×C4×C8C2×D311yescharacteristic, complemented
205C3×C4×C8C2×D311yescharacteristic, complemented
206#835—31no—
207#832—31no—
208#821—31no—
209#821—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—61no—
216#821—61no—
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8C2×D311yescharacteristic
219(C2×D3)⋊C8C2×D311yescharacteristic
220#818—31no—
221#818—31no—
222#818—31no—
223#818—61no—
224#817—31no—
225#817C2×D311yescharacteristic, complemented
226#816—31no—
227#816C2×D311yescharacteristic, complemented
228Dic3⋊C8C2×D311yescharacteristic, complemented
229Dic3⋊C8C2×D311yescharacteristic, complemented
230#809—31no—
231#809—31no—
232#808—31no—
233#807—31no—
234#803C2×D311yescharacteristic, complemented
235C22×C3⋊D3—21no—
236C22×C3⋊D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C2×D32—24no—
240C2×D32—81no—
241C2×D32—81no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C4⋊(C3⋊D3)—21no—
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)—21no—
250C4⋊(C3⋊D3)#4112yes—
251C4×C3⋊D3—81no—
252C4×C3⋊D3—81no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—21no—
260C3×D12#4112yes—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—81no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266#627—81no—
267#626—24no—
268#626—81no—
269#624—81no—
270D3×Dic3—81no—
271C32×C8—21no—
272C32×C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#542—91no—
276#518—91no—
277#485—91no—
278#482—91no—
279#476—91no—
280#474—91no—
281#463—91no—
282#463—91no—
283#450—91no—
284#447—91no—
285#442—91no—
286#440—91no—
287C4×SD16—31no—
288C4×D8—91no—
289#433—31no—
290C23×D3—61no—
291C23×D3—61no—
292C2×C3×Q8—31no—
293C2×C3×D4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—61no—
296C2×#67—61no—
297C2×#67—61no—
298C22×Dic3—61no—
299D3×D4—62no—
300D3×D4—62no—
301C2×D12—31no—
302C2×D12—31no—
303C2×D12—31no—
304C2×D12—31no—
305C2×D12—61no—
306C2×D12—61no—
307C2×D12—62no—
308C2×D12—61no—
309C2×D12—62no—
310C2×D12—61no—
311C2×D12C22×D311yescharacteristic
312C2×C4×D3—21no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—121no—
321C2×C4×D3—121no—
322C2×C4×D3C22×D311yescharacteristic
323C2×Dic6—61no—
324C2×Dic6—61no—
325C2×Dic6C22×D311yescharacteristic
326C3×SD16—62no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8—31no—
330C2×C3×C8—31no—
331C2×C3×C8C22×D311yescharacteristic
332C2×C3×C8C22×D311yescharacteristic
333C2×C3×C8C22×D311yescharacteristic
334C2×C3×C8C22×D311yescharacteristic
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—61no—
340C3×C22⋊C4—31no—
341C3×C22⋊C4—31no—
342C3×C22⋊C4—61no—
343C3×C42—21no—
344C3×C42—31no—
345C3×C42—61no—
346C3×C42C22×D311yescharacteristic
347C3×C42C22×D311yescharacteristic
348#217—61no—
349#217—61no—
350#217—61no—
351#215—62no—
352#213—62no—
353(C2×D3)⋊C4—21no—
354(C2×D3)⋊C4—61no—
355(C2×D3)⋊C4—61no—
356(C2×D3)⋊C4—61no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—121no—
370(C2×D3)⋊C4—121no—
371(C2×D3)⋊C4D1211yescharacteristic
372(C2×D3)⋊C4D1211yescharacteristic
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4D1211yescharacteristic
387Dic3⋊C4D1211yescharacteristic
388C4×Dic3—21no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3C22×D311yescharacteristic
392C2×C3⋊C8C22×D311yescharacteristic
393C2×C3⋊C8C22×D311yescharacteristic
394D24—62no—
395D24—62no—
396D24—64no—
397D24—62no—
398#204—22no—
399#204—62no—
400C22×C32C22×D411yescharacteristic
401C2×C3⋊D3—22no—
402C2×C3⋊D3—41no—
403C2×C3⋊D3—41no—
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3×D3—22no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413D32—84no—
414C32×C4—21no—
415C32×C4—21no—
416C32×C4C2×#4111yescharacteristic
417C32×C4C2×#4111yescharacteristic
418C3⋊Dic3—41no—
419C3⋊Dic3—41no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C22×D4—91no—
427C2×SD16—31no—
428C2×SD16—91no—
429C2×D8—91no—
430C2×D8—91no—
431C4⋊Q8—91no—
432#126—181no—
433#124—91no—
434#124—181no—
435#123—181no—
436C22⋊Q8—91no—
437C22⋊Q8—181no—
438#121—91no—
439C4×Q8—31no—
440C4×D4—31no—
441C4×D4—91no—
442C4×D4—91no—
443C4×D4—91no—
444C4×D4—91no—
445C4×D4—181no—
446C4×D4—181no—
447#117—31no—
448#117—91no—
449C2×C22⋊C4—181no—
450C2×C22⋊C4—181no—
451#107—91no—
452#107—91no—
453#106—31no—
454#106—91no—
455C4⋊C8—31no—
456C4⋊C8—31no—
457#103—31no—
458#103—91no—
459#102—31no—
460#102—91no—
461#102—91no—
462#102—91no—
463#102—91no—
464#102—91no—
465C22⋊C8—31no—
466C22⋊C8—31no—
467#97—31no—
468C4×C8D3211yescharacteristic, complemented
469C23×C3—31no—
470C23×C3—61no—
471C22×D3—21no—
472C22×D3—64no—
473C22×D3—64no—
474C22×D3—61no—
475C22×D3—61no—
476C22×D3—61no—
477C22×D3—61no—
478C22×D3—121no—
479C22×D3—121no—
480C22×D3—241no—
481C22×D3—241no—
482C22×D3—241no—
483C22×D3—241no—
484C22×D3C2×D1211yescharacteristic
485C3×Q8—61no—
486C3×Q8—61no—
487C3×D4—32no—
488C3×D4—61no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—241no—
501C2×C3×C4C2×D1211yescharacteristic
502C2×C3×C4C2×D1211yescharacteristic
503C2×C3×C4D3×D411yescharacteristic
504C2×C3×C4D3×D411yescharacteristic
505C2×C3×C4C23×D311yescharacteristic
506C2×C3×C4C23×D311yescharacteristic
507#67—64no—
508#67—241no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—121no—
517C2×Dic3—121no—
518C2×Dic3—241no—
519C2×Dic3C2×D1211yescharacteristic
520C2×Dic3C2×D1211yescharacteristic
521C2×Dic3C2×D1211yescharacteristic
522D12—21no—
523D12—32no—
524D12—32no—
525D12—62no—
526D12—62no—
527D12—64no—
528D12—61no—
529D12—61no—
530D12—61no—
531D12—61no—
532D12—61no—
533D12—61no—
534D12—121no—
535D12—121no—
536D12—241no—
537D12#23512yes—
538C4×D3—21no—
539C4×D3—21no—
540C4×D3—81no—
541C4×D3—241no—
542C4×D3—241no—
543C4×D3—241no—
544C4×D3—241no—
545C4×D3—241no—
546C4×D3—241no—
547C4×D3—241no—
548C4×D3—242no—
549C4×D3—242no—
550Dic6—21no—
551Dic6—21no—
552Dic6—241no—
553Dic6—241no—
554C3×C8—22no—
555C3×C8—21no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—41no—
560C3×C8—61no—
561C3×C8—61no—
562C3⋊C8—21no—
563C3⋊C8—21no—
564C2×C32#52511yescharacteristic
565C2×C32#57611yescharacteristic
566C2×C32#57711yescharacteristic
567C3⋊D3—42no—
568C3⋊D3—81no—
569C3×D3—41no—
570C3×D3—42no—
571C24—181no—
572C2×Q8—31no—
573C2×Q8—181no—
574C2×D4—31no—
575C2×D4—91no—
576C2×D4—91no—
577C2×D4—181no—
578C2×D4—182no—
579C2×D4—182no—
580C2×D4—181no—
581C22×C4—31no—
582C22×C4—61no—
583C22×C4—181no—
584C22×C4—181no—
585C22×C4—181no—
586C22×C4—181no—
587SD16—62no—
588SD16—182no—
589D8—182no—
590D8—182no—
591C2×C8—31no—
592C2×C8—31no—
593C2×C8C2×D3211yescharacteristic
594C2×C8C2×D3211yescharacteristic
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—61no—
600C4⋊C4—91no—
601C4⋊C4—91no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C22⋊C4—31no—
605C22⋊C4—31no—
606C22⋊C4—61no—
607C22⋊C4—181no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C42—31no—
617C42—61no—
618C42—181no—
619C42C2×D3211yescharacteristic
620C22×C3—21no—
621C22×C3—61no—
622C22×C3—61no—
623C22×C3—62no—
624C22×C3—61no—
625C22×C3—121no—
626C22×C3—121no—
627C22×C3C22×D1211yescharacteristic
628C22×C3C2×D3×D411yescharacteristic
629C2×D3—21no—
630C2×D3—21no—
631C2×D3—21no—
632C2×D3—22no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—62no—
636C2×D3—62no—
637C2×D3—122no—
638C2×D3—121no—
639C2×D3—121no—
640C2×D3—121no—
641C2×D3—121no—
642C2×D3—122no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—121no—
649C2×D3—241no—
650C2×D3—241no—
651C2×D3—241no—
652C2×D3—241no—
653C2×D3—244no—
654C2×D3—244no—
655C3×C4—22no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—41no—
663C3×C4—61no—
664C3×C4—61no—
665C3×C4—61no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4C2×#23511yescharacteristic
670C3×C4D3×#4111yescharacteristic
671C3×C4D3×#4111yescharacteristic
672C3×C4D3×#4111yescharacteristic
673Dic3—21no—
674Dic3—21no—
675Dic3—21no—
676Dic3—41no—
677Dic3—41no—
678Dic3—41no—
679Dic3—121no—
680Dic3—121no—
681Dic3—121no—
682Dic3—121no—
683Dic3—241no—
684Dic3—241no—
685C32#311811yescharacteristic, complemented, Sylow
686C23—31no—
687C23—61no—
688C23—184no—
689C23—181no—
690C23—181no—
691C23—721no—
692C23—721no—
693Q8—61no—
694Q8—61no—
695Q8—721no—
696D4—32no—
697D4—61no—
698D4—92no—
699D4—184no—
700D4—181no—
701D4—181no—
702D4—181no—
703D4—721no—
704C2×C4—31no—
705C2×C4—31no—
706C2×C4—31no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—181no—
713C2×C4—181no—
714C2×C4—241no—
715C2×C4—721no—
716C2×C4—721no—
717C2×C4—721no—
718C2×C4—721no—
719C2×C4D3×D1211yescharacteristic
720C2×C4D3×D1211yescharacteristic
721C2×C4C22×D3211yescharacteristic
722C8—21no—
723C8—21no—
724C8—61no—
725C8—61no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—122no—
730C2×C3—121no—
731C2×C3#552411yescharacteristic
732C2×C3#554711yescharacteristic
733C2×C3#575111yescharacteristic
734C2×C3#575211yescharacteristic
735C2×C3#576211yescharacteristic
736C2×C3#576911yescharacteristic
737D3—41no—
738D3—42no—
739D3—122no—
740D3—122no—
741D3—242no—
742D3—242no—
743D3—241no—
744D3—241no—
745C22—61no—
746C22—61no—
747C22—61no—
748C22—62no—
749C22—121no—
750C22—121no—
751C22—182no—
752C22—361no—
753C22—361no—
754C22—361no—
755C22—361no—
756C22—361no—
757C22—724no—
758C22C2×D3×D1211yescharacteristic
759C4—21no—
760C4—21no—
761C4—61no—
762C4—61no—
763C4—61no—
764C4—121no—
765C4—121no—
766C4—121no—
767C4—361no—
768C4—361no—
769C4D3×#23511yescharacteristic
770C4#6430611yescharacteristic
771C3—21no—
772C3#7938311yescharacteristic, complemented
773C3#7969611yescharacteristic, complemented
774C2—121no—
775C2—122no—
776C2—362no—
777C2—721no—
778C2#1059399711yescharacteristic
779C2#1059467711yescharacteristic
780C2#1059468011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10590947C2
hypercenterC4×C8D32
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #10593994C2semidirect
2. #10593878C2semidirect
3. C4×#3745C2semidirect
4. C3×C4×#204C2semidirect
5. C3×#4690C2semidirect
7. #10590942C2semidirect
8. #10590770C2semidirect
9. #10590762C2semidirect
10. #10590759C2semidirect
11. #10590754C2semidirect
12. #10590710C2semidirect
13. #10590704C2semidirect
14. #10590362C2semidirect
15. #10590346C2semidirect
21. C4×C4⋊(C3⋊D3)C22semidirect
25. C3×C4×Dic6C22semidirect
28. #63918C22semidirect
36. #63864C22semidirect
43. C32×C4×C8C22semidirect
45. #63648C22semidirect
46. #63645C22semidirect
50. C3×#817C22semidirect
51. C3×#816C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×#803C22semidirect
55. #63575C22semidirect
56. #63573C22semidirect
57. #63566C22semidirect
59. #63564C22semidirect
90. C4×#204D3semidirect
91. #4690D3semidirect
194. C4×Dic6C2×D3semidirect
204. C3×C4×C8C2×D3semidirect
205. C3×C4×C8C2×D3semidirect
225. #817C2×D3semidirect
227. #816C2×D3semidirect
228. Dic3⋊C8C2×D3semidirect
229. Dic3⋊C8C2×D3semidirect
234. #803C2×D3semidirect
468. C4×C8D32semidirect
685. C32#3118semidirect
772. C3#79383semidirect
773. C3#79696semidirect

Maximal subgroups

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

subgroupindex
#105939942
#105938782
C4×#37452
C3×C4×#2042
C3×#46902
#105909472
#105909422
#105907702
#105907622
#105907592
#105907542
#105907102
#105907042
#105903622
#105903462
#796963
#793833