Finite Group Databasebeta

← #11872311

Subgroups — #11872311

Order 1152.

912 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596006C211yesmaximal, characteristic, complemented
2C3×#5523C211yesmaximal, characteristic, complemented
3C3×#5000C211yesmaximal, characteristic, complemented
4#10591163C211yesmaximal, characteristic, complemented
5#10591163C211yesmaximal, characteristic, complemented
6#10591133C211yesmaximal, characteristic, complemented
7#10591125C211yesmaximal, characteristic, complemented
8#10590367C211yesmaximal, characteristic, complemented
9#10590362C211yesmaximal, characteristic, complemented
10C4×#3717C211yesmaximal, characteristic, complemented
11#10590349C211yesmaximal, characteristic, complemented
12#10590346C211yesmaximal, characteristic, complemented
13C4×#3714C211yesmaximal, characteristic, complemented
14#10590302C211yesmaximal, characteristic, complemented
15#10590271C211yesmaximal, characteristic, complemented
16#82568—31nomaximal
17#79384—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C32×#117C2211yescharacteristic
20#64139C2211yescharacteristic
21#64139C2211yescharacteristic
22#64103—21no—
23#64103—21no—
24#64093—21no—
25#64093—21no—
26#64083C2211yescharacteristic
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29#64079C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C3×#892—21no—
32C3×D3×C4⋊C4—21no—
33C3×#67⋊C4—21no—
34C3×#67⋊C4—21no—
35C3×C4×D12C2211yescharacteristic
36C3×C4×D12C2211yescharacteristic
37C3×C4×Dic6C2211yescharacteristic
38C3×C4×Dic6C2211yescharacteristic
39C2×#3717C2211yescharacteristic
40C2×#3717C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C3×#830C2211yescharacteristic
44C3×#830C2211yescharacteristic
45C3×C4⋊(C3⋊C8)C2211yescharacteristic
46C3×C4⋊(C3⋊C8)C2211yescharacteristic
47C3×#803C2211yescharacteristic
48C3×C4×C3⋊C8C2211yescharacteristic
49#63575C2211yescharacteristic
50#63575C2211yescharacteristic
51#63573C2211yescharacteristic
52#63573C2211yescharacteristic
53#63566C2211yescharacteristic
54#63566C2211yescharacteristic
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61C3×#520—31no—
62#5535—31no—
63#5535—31no—
64#5535—61no—
65#5523D311yescharacteristic, complemented
66C3×#433—31no—
67#5238—31no—
68#5238—31no—
69#5027—31no—
70#5026—31no—
71C4×#215—31no—
72#5022—31no—
73#5015—31no—
74#5014—31no—
75C4×#213—31no—
76#5009—31no—
77#5000D311yescharacteristic, complemented
78#4968—31no—
79#4967—31no—
80#4848—31no—
81#4847—31no—
82#4843—31no—
83#4829—31no—
84#4736—31no—
85#4735—31no—
86#4734—31no—
87#4734—31no—
88#4711—31no—
89#4710—31no—
90C4×D24—31no—
91C4×#204—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#638—21no—
94C2×#638—21no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3—21no—
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C3×#235—22no—
104C3×#235—22no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×Dic6C2311yescharacteristic
110C32×C4⋊C4D411yescharacteristic
111C32×C4⋊C4D411yescharacteristic
112C32×C22⋊C4D411yescharacteristic
113C32×C22⋊C4D411yescharacteristic
114C32×C42C2311yescharacteristic
115C32×C42C2311yescharacteristic
116#3752—21no—
117#3752—21no—
118#3752—21no—
119#3752—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122#3750—21no—
123#3750—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3717—22no—
138#3717—22no—
139#3714—22no—
140#3714—22no—
141#3119—91noSylow
142C2×C3×#41—31no—
143C2×#235C2×D311yescharacteristic
144C3×C4×Q8—31no—
145C3×C4×Q8—31no—
146C3×C4×D4—31no—
147C3×C4×D4—31no—
148C3×C4×D4—61no—
149C3×C4×D4—61no—
150C3×#117—21no—
151C3×#117—61no—
152C3×#117C2×D311yescharacteristic
153C3×#117C2×D311yescharacteristic
154C2×C3×C4⋊C4—31no—
155C2×C3×C4⋊C4—61no—
156C2×#215—31no—
157C2×#215—31no—
158C2×#213—31no—
159C2×#213—31no—
160#930—31no—
161#930—31no—
162#930—31no—
163#930—31no—
164#930—61no—
165#930—61no—
166C2×C4⋊Dic3C2×D311yescharacteristic
167C2×D24—31no—
168C2×D24—31no—
169C2×#204—31no—
170C2×#204—31no—
171#894—62no—
172#894—62no—
173#894—61no—
174#894—61no—
175#894—61no—
176#894—61no—
177#892—21no—
178D3×C4⋊C4—21no—
179#884—62no—
180#884—62no—
181#884—61no—
182#884—61no—
183#884—61no—
184#884—61no—
185#67⋊C4—21no—
186#67⋊C4—21no—
187#874—31no—
188#874—31no—
189#874—61no—
190C4×D12—31no—
191C4×D12—31no—
192C4×D12—31no—
193C4×D12—31no—
194C4×D12—61no—
195C4×D12—61no—
196C4×D12C2×D311yescharacteristic
197C4×D12C2×D311yescharacteristic
198#870—31no—
199#870—31no—
200#870—61no—
201C4×Dic6C2×D311yescharacteristic
202C4×Dic6C2×D311yescharacteristic
203C3×C4⋊C8—31no—
204C3×C4⋊C8—31no—
205C3×C22⋊C8—31no—
206C3×C22⋊C8—31no—
207C3×#97—31no—
208C3×C4×C8—31no—
209#835—31no—
210#835—31no—
211#832—31no—
212#832—31no—
213#830C2×D311yescharacteristic
214#830C2×D311yescharacteristic
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#818—31no—
222#818—31no—
223#817—31no—
224#817—31no—
225#816—31no—
226#816—31no—
227#809—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#808—31no—
232#808—31no—
233#807—31no—
234#807—31no—
235C4⋊(C3⋊C8)C2×D311yescharacteristic
236C4⋊(C3⋊C8)C2×D311yescharacteristic
237#803C2×D311yescharacteristic
238C4×C3⋊C8C2×D311yescharacteristic
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3⋊D3—21no—
242C22×C3×D3—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2411yescharacteristic
251#638—81no—
252#638—81no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)—21no—
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)—81no—
260C4⋊(C3⋊D3)—81no—
261C4×C3⋊D3—81no—
262C4×C3⋊D3—81no—
263C3×#67—24no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—81no—
268C3×D12—21no—
269C3×D12#4112yes—
270C3×C4×D3—24no—
271C3×C4×D3—81no—
272C3×C4×D3—81no—
273C3×Dic6—21no—
274C3×Dic6#4112yes—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#540—91no—
280#520—31no—
281#481—91no—
282#480—91no—
283#479—91no—
284#478—91no—
285#460—91no—
286#459—91no—
287#449—91no—
288#449—91no—
289#442—91no—
290#440—91no—
291C4×SD16—91no—
292C4×D8—91no—
293#433—31no—
294C3×#41—62no—
295C3×#41—62no—
296C2×C3×Q8—31no—
297C2×C3×D4—31no—
298C2×C3×D4—61no—
299C22×C3×C4—21no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C2×#67—21no—
307C2×#67—62no—
308C2×#67—62no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C22×Dic3—21no—
314#235—22no—
315#235—22no—
316C2×D12—31no—
317C2×D12—31no—
318C2×D12—31no—
319C2×D12—31no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12—62no—
323C2×D12—62no—
324C2×D12—61no—
325C2×D12—61no—
326C2×D12—61no—
327C2×D12—61no—
328C2×D12C22×D311yescharacteristic
329C2×C4×D3—21no—
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×C4×D3—62no—
333C2×C4×D3—62no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×Dic6C22×D311yescharacteristic
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4D1211yescharacteristic
351C3×C4⋊C4D1211yescharacteristic
352C3×C4⋊C4#6711yescharacteristic
353C3×C4⋊C4#6711yescharacteristic
354C3×C22⋊C4—21no—
355C3×C22⋊C4—21no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4D1211yescharacteristic
359C3×C22⋊C4D1211yescharacteristic
360C3×C22⋊C4#6711yescharacteristic
361C3×C22⋊C4#6711yescharacteristic
362C3×C42—21no—
363C3×C42—21no—
364C3×C42—61no—
365C3×C42—61no—
366C3×C42C22×D311yescharacteristic
367C3×C42C22×D311yescharacteristic
368C3×C42C22×D311yescharacteristic
369C3×C42C22×D311yescharacteristic
370#215—62no—
371#215—62no—
372#213—62no—
373#213—62no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—62no—
377(C2×D3)⋊C4—62no—
378(C2×D3)⋊C4—62no—
379(C2×D3)⋊C4—62no—
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—
388C4⋊Dic3—21no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—31no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3C22×D311yescharacteristic
396C4⋊Dic3C22×D311yescharacteristic
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—62no—
400Dic3⋊C4—62no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405C4×Dic3—21no—
406C4×Dic3—21no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411D24—62no—
412D24—62no—
413#204—62no—
414#204—62no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32C22×D411yescharacteristic
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3×D3—22no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C32×C4—21no—
429C32×C4—21no—
430C32×C4—21no—
431C32×C4—21no—
432C32×C4—21no—
433C32×C4C2×#4111yescharacteristic
434C32×C4C2×#4111yescharacteristic
435C3⋊Dic3—41no—
436C3⋊Dic3—41no—
437C3×Dic3—22no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C2×#41—31no—
441C2×SD16—91no—
442C2×SD16—91no—
443C2×D8—91no—
444C2×D8—91no—
445#127—91no—
446#125—91no—
447#123—181no—
448#123—181no—
449#121—91no—
450#121—91no—
451#121—181no—
452#121—181no—
453C4×Q8—31no—
454C4×Q8—31no—
455C4×D4—31no—
456C4×D4—31no—
457C4×D4—61no—
458C4×D4—61no—
459C4×D4—91no—
460C4×D4—91no—
461#117—61no—
462#117D3211yescharacteristic
463C2×C4⋊C4—31no—
464C2×C4⋊C4—61no—
465#107—91no—
466#107—91no—
467#106—91no—
468#106—91no—
469C4⋊C8—31no—
470C4⋊C8—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—31no—
480C22⋊C8—31no—
481#97—31no—
482C4×C8—31no—
483C23×C3—21no—
484C23×C3—61no—
485C23×C3C2×D1211yescharacteristic
486C23×C3C2×#6711yescharacteristic
487C22×D3—21no—
488C22×D3—62no—
489C22×D3—62no—
490C22×D3—61no—
491C22×D3—61no—
492C22×D3—61no—
493C22×D3—61no—
494C3×Q8—32no—
495C3×Q8—61no—
496C3×D4—32no—
497C3×D4—64no—
498C3×D4—61no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—64no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—241no—
516C2×C3×C4—241no—
517C2×C3×C4—241no—
518C2×C3×C4C2×D1211yescharacteristic
519C2×C3×C4C2×D1211yescharacteristic
520C2×C3×C4C2×D1211yescharacteristic
521C2×C3×C4C2×D1211yescharacteristic
522C2×C3×C4C2×D1211yescharacteristic
523C2×C3×C4C2×#6711yescharacteristic
524C2×C3×C4C2×#6711yescharacteristic
525C2×C3×C4C2×#6711yescharacteristic
526C2×C3×C4C2×#6711yescharacteristic
527C2×C3×C4C2×#6711yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530#67—24no—
531#67—241no—
532#67—241no—
533#67—241no—
534#67—241no—
535#67—242no—
536#67—242no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—62no—
541C2×Dic3—62no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—81no—
547D12—21no—
548D12—61no—
549D12—61no—
550D12—61no—
551D12—61no—
552D12—61no—
553D12—61no—
554D12—61no—
555D12—61no—
556D12—121no—
557D12—121no—
558D12—121no—
559D12—121no—
560D12—241no—
561D12—241no—
562D12—241no—
563D12—241no—
564D12—242no—
565D12—242no—
566D12#23512yes—
567C4×D3—24no—
568C4×D3—81no—
569C4×D3—81no—
570C4×D3—241no—
571C4×D3—241no—
572C4×D3—241no—
573C4×D3—241no—
574C4×D3—242no—
575C4×D3—242no—
576Dic6—21no—
577Dic6#23512yes—
578C3×C8—61no—
579C3×C8—61no—
580C3×C8—61no—
581C3×C8—61no—
582C3⋊C8—21no—
583C3⋊C8—21no—
584C3⋊C8—21no—
585C3⋊C8—21no—
586C2×C32—41no—
587C2×C32#52511yescharacteristic
588C2×C32#57611yescharacteristic
589C2×C32#57711yescharacteristic
590C3⋊D3—81no—
591C3⋊D3—81no—
592C3×D3—42no—
593#41—62no—
594#41—62no—
595C2×Q8—31no—
596C2×D4—31no—
597C2×D4—61no—
598C2×D4—91no—
599C2×D4—91no—
600C2×D4—181no—
601C2×D4—181no—
602C2×D4—181no—
603C2×D4—181no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—181no—
609C22×C4—181no—
610C22×C4C2×D3211yescharacteristic
611SD16—182no—
612SD16—182no—
613D8—182no—
614D8—182no—
615C2×C8—31no—
616C2×C8—31no—
617C2×C8—31no—
618C2×C8—31no—
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—91no—
625C4⋊C4—91no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4#62611yescharacteristic
629C4⋊C4#62611yescharacteristic
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4#62611yescharacteristic
637C22⋊C4#62611yescharacteristic
638C42—61no—
639C42—61no—
640C42C2×D3211yescharacteristic
641C42C2×D3211yescharacteristic
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—62no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3C22×D1211yescharacteristic
656C22×C3C22×#6711yescharacteristic
657C2×D3—22no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—122no—
661C2×D3—122no—
662C2×D3—122no—
663C2×D3—122no—
664C2×D3—122no—
665C2×D3—122no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3—121no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—41no—
693C3×C4—41no—
694C3×C4—41no—
695C3×C4—62no—
696C3×C4—121no—
697C3×C4—121no—
698C3×C4C2×#23511yescharacteristic
699C3×C4C2×#23511yescharacteristic
700C3×C4D3×#4111yescharacteristic
701C3×C4D3×#4111yescharacteristic
702Dic3—22no—
703Dic3—41no—
704Dic3—41no—
705Dic3—122no—
706Dic3—122no—
707Dic3—121no—
708Dic3—121no—
709Dic3—121no—
710Dic3—121no—
711C32#311911yescharacteristic, complemented, Sylow
712C23—61no—
713C23—181no—
714C23—181no—
715C23C2×#62611yescharacteristic
716Q8—32no—
717Q8—61no—
718D4—32no—
719D4—64no—
720D4—61no—
721D4—181no—
722D4—181no—
723D4—181no—
724D4—181no—
725D4—721no—
726D4—721no—
727D4—721no—
728D4—721no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—64no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—181no—
736C2×C4—181no—
737C2×C4—241no—
738C2×C4—241no—
739C2×C4—241no—
740C2×C4—721no—
741C2×C4—721no—
742C2×C4C2×#62611yescharacteristic
743C2×C4C2×#62611yescharacteristic
744C2×C4C2×#62611yescharacteristic
745C2×C4C2×#62611yescharacteristic
746C2×C4C2×#62611yescharacteristic
747C2×C4C22×D3211yescharacteristic
748C8—61no—
749C8—61no—
750C8—61no—
751C8—61no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—41no—
756C2×C3—41no—
757C2×C3—81no—
758C2×C3—122no—
759C2×C3#552411yescharacteristic
760C2×C3#575111yescharacteristic
761C2×C3#575211yescharacteristic
762C2×C3#579111yescharacteristic
763C2×C3#583511yescharacteristic
764C2×C3#583711yescharacteristic
765D3—42no—
766D3—242no—
767D3—242no—
768D3—241no—
769D3—241no—
770D3—241no—
771D3—241no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—62no—
776C22—121no—
777C22—121no—
778C22—361no—
779C22—361no—
780C22—361no—
781C22—361no—
782C22—361no—
783C22—361no—
784C22C22×#62611yescharacteristic
785C4—21no—
786C4—21no—
787C4—21no—
788C4—21no—
789C4—21no—
790C4—62no—
791C4—121no—
792C4—121no—
793C4—361no—
794C4—361no—
795C4D3×#23511yescharacteristic
796C4D3×#23511yescharacteristic
797C3—21no—
798C3#7938411yescharacteristic, complemented
799C3#8256811yescharacteristic, complemented
800C2—41no—
801C2—122no—
802C2—721no—
803C2—721no—
804C2#1059502311yescharacteristic
805C2#1059544811yescharacteristic
806C2#1059544911yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
hypercenter#117D32
hypocenterC32#3119
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10596006C2semidirect
2. C3×#5523C2semidirect
3. C3×#5000C2semidirect
4. #10591163C2semidirect
5. #10591163C2semidirect
6. #10591133C2semidirect
7. #10591125C2semidirect
8. #10590367C2semidirect
9. #10590362C2semidirect
10. C4×#3717C2semidirect
11. #10590349C2semidirect
12. #10590346C2semidirect
13. C4×#3714C2semidirect
14. #10590302C2semidirect
15. #10590271C2semidirect
65. #5523D3semidirect
77. #5000D3semidirect
711. C32#3119semidirect
798. C3#79384semidirect
799. C3#82568semidirect

Maximal subgroups

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

subgroupindex
#105960062
C3×#55232
C3×#50002
#105911632
#105911332
#105911252
#105903672
#105903622
C4×#37172
#105903492
#105903462
C4×#37142
#105903022
#105902712
#825683
#793843