Finite Group Databasebeta

← #11872838

Subgroups — #11872838

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 793 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596016C211yesmaximal, characteristic
2#10593883C211yesmaximal, characteristic, complemented
3C3×#5018C211yesmaximal, characteristic, complemented
4C3×C4×#214C211yesmaximal, characteristic, complemented
5#10591497C211yesmaximal, characteristic, complemented
6#10591479C211yesmaximal, characteristic, complemented
7#10591467C211yesmaximal, characteristic
8#10591467C211yesmaximal, characteristic
9#10590565C211yesmaximal, characteristic, complemented
10#10590527C211yesmaximal, characteristic, complemented
11#10590526C211yesmaximal, characteristic, complemented
12#10590435C211yesmaximal, characteristic, complemented
13#10590362C211yesmaximal, characteristic, complemented
14C4×#3717C211yesmaximal, characteristic, complemented
15#10590298C211yesmaximal, characteristic, complemented
16#79787—31nomaximal
17#79659—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic
21C4×#638—21no—
22C2×#3752—21no—
23#64102C2211yescharacteristic
24#64101C2211yescharacteristic
25#64090—21no—
26C22⋊C4×C3⋊D3—21no—
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28#64081C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic, complemented
32C3×C4×Dic6C2211yescharacteristic, complemented
33#63873C2211yescharacteristic, complemented
34#63872C2211yescharacteristic, complemented
35#63871C2211yescharacteristic
36#63871C2211yescharacteristic
37#63868—21no—
38#63868—21no—
39#63867—21no—
40#63867—21no—
41C2×#3717C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43C3×#832C2211yescharacteristic
44C3×#832C2211yescharacteristic
45C3×#810C2211yescharacteristic, complemented
46C3×#810C2211yescharacteristic, complemented
47C3×#808C2211yescharacteristic, complemented
48C3×#807C2211yescharacteristic, complemented
49C3×#803C2211yescharacteristic, complemented
50C3×C4×C3⋊C8C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63572C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63557C2211yescharacteristic
60#63557C2211yescharacteristic
61#5583—31no—
62#5583—31no—
63#5545—31no—
64#5545—31no—
65#5545—61no—
66C3×#440—31no—
67C3×C4×SD16—31no—
68#5169—31no—
69#5169—31no—
70#5162—31no—
71#5162—31no—
72#5026—31no—
73C4×#215—31no—
74#5018D311yescharacteristic, complemented
75C4×#214D311yescharacteristic, complemented
76#4891—31no—
77#4888—31no—
78#4871—31no—
79#4868—31no—
80#4818—31no—
81#4818—31no—
82#4815—31no—
83#4814—31no—
84#4776—31no—
85#4776—31no—
86#4766—31no—
87#4763—31no—
88#4710—31no—
89#4709—31no—
90C4×#204—31no—
91#4690—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×#638—21no—
96C22×C3⋊Dic3—21no—
97D4×C3⋊D3—22no—
98D4×C3⋊D3—22no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C32×C4⋊C4C2311yescharacteristic
106C32×C22⋊C4—21no—
107C32×C42C2311yescharacteristic
108#3757—21no—
109#3752—21no—
110#3752—21no—
111#3752—21no—
112#3752D411yescharacteristic
113#3752D411yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750D411yescharacteristic
116#3750D411yescharacteristic
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3C2311yescharacteristic
119C3×#214—22no—
120C3×#214—22no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3—21no—
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138#3722—21no—
139#3717—22no—
140#3717—22no—
141#3123—91noSylow
142C2×D3×D4—31no—
143C2×D3×D4—31no—
144C2×D3×D4—61no—
145C2×C3×SD16—31no—
146C2×C3×SD16—31no—
147C3×C4×Q8—31no—
148C3×C4×Q8—31no—
149C3×C4×D4—21no—
150C3×C4×D4C2×D311yescharacteristic
151C3×C4×D4C2×D311yescharacteristic
152#946—31no—
153#946—31no—
154#944—31no—
155#944—31no—
156C2×#215—31no—
157C2×#215—31no—
158D4×Dic3—31no—
159D4×Dic3—31no—
160D4×Dic3—61no—
161C2×#214C2×D311yescharacteristic
162C2×#214C2×D311yescharacteristic
163C4×#67—61no—
164C4×#67—61no—
165C4×#67—62no—
166C2×(C2×D3)⋊C4—61no—
167C2×(C2×D3)⋊C4—61no—
168C2×(C2×D3)⋊C4—62no—
169C2×#204—31no—
170C2×#204—31no—
171#898—61no—
172#898—61no—
173#897—31no—
174#897—31no—
175#893—31no—
176#893—31no—
177#893—61no—
178#892—31no—
179#892—31no—
180#892—61no—
181#890—31no—
182#890—31no—
183#889—61no—
184#889—61no—
185#67⋊C4—61no—
186#67⋊C4—61no—
187#67⋊C4—62no—
188D3×C22⋊C4—61no—
189D3×C22⋊C4—61no—
190D3×C22⋊C4—62no—
191#876—61no—
192#876—61no—
193C4×D12—31no—
194C4×D12—31no—
195C4×D12—61no—
196#872—31no—
197#872—31no—
198#872—61no—
199#870—61no—
200#870—61no—
201C4×Dic6C2×D311yescharacteristic, complemented
202C4×Dic6C2×D311yescharacteristic, complemented
203C3×#107—31no—
204C3×#106—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#97—31no—
210C3×C4×C8—31no—
211#835—31no—
212#835—31no—
213#832C2×D311yescharacteristic
214#832C2×D311yescharacteristic
215#821—31no—
216#821—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221#818—31no—
222#817—31no—
223#816—31no—
224#816—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—31no—
227Dic3⋊C8—31no—
228Dic3⋊C8—31no—
229#810C2×D311yescharacteristic, complemented
230#810C2×D311yescharacteristic, complemented
231#809—31no—
232#809—31no—
233#808—31no—
234#808C2×D311yescharacteristic, complemented
235#807—31no—
236#807C2×D311yescharacteristic, complemented
237#803C2×D311yescharacteristic, complemented
238C4×C3⋊C8C2×D311yescharacteristic, complemented
239C23×C32—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—24no—
242C22×C3⋊D3—81no—
243C22×C3⋊D3—81no—
244C22×C3⋊D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4#4112yes—
247C2×C32×C4—21no—
248C2×C32×C4—81no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252#638—24no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—81no—
255C2×C3⋊Dic3C2×D411yescharacteristic
256C2×C3⋊Dic3C2×D411yescharacteristic
257C2×C3⋊Dic3C2×D411yescharacteristic
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)#4112yes—
260C4×C3⋊D3—21no—
261C4×C3⋊D3—21no—
262C4×C3⋊D3—81no—
263C4×C3⋊D3—81no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×C3⋊C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#541—91no—
277#518—91no—
278#485—91no—
279#485—91no—
280#478—91no—
281#478—91no—
282#461—91no—
283#461—91no—
284#450—91no—
285#450—91no—
286#440—31no—
287#440—91no—
288C4×SD16—31no—
289C4×SD16—91no—
290#433—91no—
291C23×D3—61no—
292C23×D3—61no—
293C23×D3—62no—
294C2×C3×Q8—31no—
295C2×C3×Q8—31no—
296C2×C3×D4—21no—
297C2×C3×D4C22×D311yescharacteristic
298C2×C3×D4C22×D311yescharacteristic
299C22×C3×C4—22no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C2×#67—61no—
303C2×#67—61no—
304C2×#67—62no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307C22×Dic3—62no—
308D3×D4—62no—
309D3×D4—62no—
310D3×D4—64no—
311D3×D4—64no—
312D3×D4—62no—
313D3×D4—62no—
314C2×D12—31no—
315C2×D12—31no—
316C2×D12—61no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—62no—
323C2×C4×D3—62no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×Dic6C22×D311yescharacteristic
327C2×Dic6C22×D311yescharacteristic
328C3×SD16—62no—
329C3×SD16—62no—
330C2×C3×C8—31no—
331C2×C3×C8—31no—
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4C22×D311yescharacteristic
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C22⋊C4—22no—
342C3×C22⋊C4—21no—
343C3×C22⋊C4—21no—
344C3×C42—21no—
345C3×C42—61no—
346C3×C42—61no—
347C3×C42C22×D311yescharacteristic
348C3×C42C22×D311yescharacteristic
349#217—61no—
350#217—61no—
351#217—62no—
352#215—62no—
353#215—62no—
354#214—22no—
355#214—22no—
356(C2×D3)⋊C4—31no—
357(C2×D3)⋊C4—31no—
358(C2×D3)⋊C4—31no—
359(C2×D3)⋊C4—31no—
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—61no—
370(C2×D3)⋊C4—62no—
371(C2×D3)⋊C4—62no—
372(C2×D3)⋊C4—62no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—31no—
387Dic3⋊C4—31no—
388Dic3⋊C4—31no—
389Dic3⋊C4—31no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400C4×Dic3—21no—
401C4×Dic3—21no—
402C4×Dic3—31no—
403C4×Dic3—31no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—62no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412#204—62no—
413#204—62no—
414C22×C32—22no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—21no—
419C2×C3⋊D3—22no—
420C2×C3⋊D3—21no—
421C2×C3⋊D3—21no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—84no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4C2×#4111yescharacteristic
430C3⋊Dic3—21no—
431C3⋊Dic3—21no—
432C3⋊Dic3—21no—
433C3⋊Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C22×D4—91no—
439C2×SD16—31no—
440C2×SD16—31no—
441C2×SD16—91no—
442C2×SD16—91no—
443C4⋊Q8—91no—
444#126—181no—
445#126—181no—
446#125—91no—
447#125—181no—
448#125—181no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451C4×Q8—31no—
452C4×Q8—31no—
453C4×D4—91no—
454C4×D4—91no—
455C4×D4—91no—
456C4×D4—181no—
457C4×D4—181no—
458C4×D4D3211yescharacteristic
459#117—91no—
460#117—91no—
461C2×C22⋊C4—181no—
462C2×C22⋊C4—181no—
463#107—31no—
464#107—91no—
465#106—31no—
466#106—91no—
467C4⋊C8—91no—
468C4⋊C8—91no—
469#103—31no—
470#103—31no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477C22⋊C8—91no—
478C22⋊C8—91no—
479#97—31no—
480C4×C8—31no—
481C23×C3—22no—
482C23×C3—21no—
483C23×C3—21no—
484C22×D3—31no—
485C22×D3—31no—
486C22×D3—61no—
487C22×D3—62no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—68no—
491C22×D3—64no—
492C22×D3—64no—
493C22×D3—241no—
494C22×D3—241no—
495C22×D3—241no—
496C22×D3—241no—
497C22×D3—242no—
498C22×D3—242no—
499C3×Q8—61no—
500C3×Q8—61no—
501C3×Q8—61no—
502C3×Q8—61no—
503C3×D4—22no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—22no—
507C3×D4#23512yes—
508C3×D4#23512yes—
509C2×C3×C4—22no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—81no—
520C2×C3×C4—81no—
521C2×C3×C4—82no—
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4D3×D411yescharacteristic
524C2×C3×C4D3×D411yescharacteristic
525C2×C3×C4D3×D411yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528#67—68no—
529#67—64no—
530#67—64no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—62no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—241no—
548C2×Dic3—241no—
549C2×Dic3—242no—
550D12—32no—
551D12—32no—
552D12—62no—
553D12—62no—
554D12—61no—
555D12—61no—
556C4×D3—62no—
557C4×D3—62no—
558C4×D3—61no—
559C4×D3—61no—
560C4×D3—61no—
561C4×D3—61no—
562C4×D3—241no—
563C4×D3—241no—
564C4×D3—241no—
565C4×D3—241no—
566C4×D3—242no—
567C4×D3—242no—
568Dic6—21no—
569Dic6—21no—
570Dic6—21no—
571Dic6—21no—
572C3×C8—61no—
573C3×C8—61no—
574C3×C8—61no—
575C3×C8—61no—
576C3⋊C8—21no—
577C3⋊C8—21no—
578C3⋊C8—21no—
579C3⋊C8—21no—
580C2×C32—42no—
581C2×C32#52511yescharacteristic
582C2×C32#57711yescharacteristic
583C2×C32#57711yescharacteristic
584C3⋊D3—41no—
585C3⋊D3—42no—
586C24—181no—
587C2×Q8—31no—
588C2×Q8—31no—
589C2×D4—91no—
590C2×D4—181no—
591C2×D4—182no—
592C2×D4—182no—
593C2×D4C2×D3211yescharacteristic
594C22×C4—21no—
595C22×C4—91no—
596C22×C4—181no—
597C22×C4—181no—
598C22×C4—181no—
599SD16—62no—
600SD16—62no—
601SD16—182no—
602SD16—182no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—31no—
606C2×C8—31no—
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—91no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4C2×D3211yescharacteristic
621C22⋊C4—21no—
622C22⋊C4—91no—
623C22⋊C4—91no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C42—61no—
631C42—61no—
632C42—91no—
633C42—181no—
634C42C2×D3211yescharacteristic
635C22×C3—24no—
636C22×C3—22no—
637C22×C3—22no—
638C22×C3—21no—
639C22×C3—42no—
640C22×C3—42no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3C2×D3×D411yescharacteristic
646C22×C3C2×D3×D411yescharacteristic
647C2×D3—62no—
648C2×D3—64no—
649C2×D3—61no—
650C2×D3—61no—
651C2×D3—61no—
652C2×D3—61no—
653C2×D3—61no—
654C2×D3—61no—
655C2×D3—62no—
656C2×D3—62no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—122no—
660C2×D3—122no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—248no—
666C2×D3—244no—
667C2×D3—244no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—42no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4C2×#23511yescharacteristic
684C3×C4C2×#23511yescharacteristic
685C3×C4D3×#4111yescharacteristic
686C3×C4D3×#4111yescharacteristic
687Dic3—41no—
688Dic3—41no—
689Dic3—41no—
690Dic3—41no—
691Dic3—62no—
692Dic3—61no—
693Dic3—61no—
694Dic3—61no—
695Dic3—61no—
696Dic3—61no—
697Dic3—61no—
698Dic3—121no—
699Dic3—121no—
700Dic3—122no—
701Dic3—121no—
702Dic3—121no—
703C32#312311yescharacteristic, complemented, Sylow
704C23—21no—
705C23—91no—
706C23—184no—
707C23—181no—
708C23—721no—
709C23—721no—
710Q8—61no—
711Q8—61no—
712Q8—61no—
713Q8—61no—
714D4—21no—
715D4—92no—
716D4—184no—
717D4—181no—
718D4#379812yes—
719C2×C4—21no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—81no—
725C2×C4—91no—
726C2×C4—91no—
727C2×C4—91no—
728C2×C4—181no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—721no—
732C2×C4—721no—
733C2×C4—721no—
734C2×C4#381111yescharacteristic
735C2×C4#381111yescharacteristic
736C2×C4C22×D3211yescharacteristic
737C8—61no—
738C8—61no—
739C8—61no—
740C8—61no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—44no—
745C2×C3—42no—
746C2×C3—42no—
747C2×C3#554711yescharacteristic
748C2×C3#554711yescharacteristic
749C2×C3#576211yescharacteristic
750C2×C3#577011yescharacteristic
751C2×C3#577511yescharacteristic
752C2×C3#577811yescharacteristic
753D3—122no—
754D3—124no—
755D3—121no—
756D3—122no—
757D3—121no—
758D3—122no—
759C22—22no—
760C22—41no—
761C22—41no—
762C22—181no—
763C22—181no—
764C22—181no—
765C22—182no—
766C22—361no—
767C22—361no—
768C22—724no—
769C22C2×#381111yescharacteristic
770C4—21no—
771C4—21no—
772C4—41no—
773C4—121no—
774C4—121no—
775C4—121no—
776C4—121no—
777C4—181no—
778C4—181no—
779C4—181no—
780C4—361no—
781C4C2×#379811yescharacteristic
782C4#6430611yescharacteristic
783C3—21no—
784C3#7965911yescharacteristic, complemented
785C3#7978711yescharacteristic, complemented
786C2—42no—
787C2—361no—
788C2—362no—
789C2#1059501611yescharacteristic
790C2#1059511511yescharacteristic
791C2#1059547311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
hypercenterC4×D4D32
hypocenterC32#3123
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593883C2semidirect
3. C3×#5018C2semidirect
4. C3×C4×#214C2semidirect
5. #10591497C2semidirect
6. #10591479C2semidirect
9. #10590565C2semidirect
10. #10590527C2semidirect
11. #10590526C2semidirect
12. #10590435C2semidirect
13. #10590362C2semidirect
14. C4×#3717C2semidirect
15. #10590298C2semidirect
31. C3×C4×Dic6C22semidirect
32. C3×C4×Dic6C22semidirect
33. #63873C22semidirect
34. #63872C22semidirect
45. C3×#810C22semidirect
46. C3×#810C22semidirect
47. C3×#808C22semidirect
48. C3×#807C22semidirect
49. C3×#803C22semidirect
50. C3×C4×C3⋊C8C22semidirect
51. #63575C22semidirect
52. #63573C22semidirect
53. #63572C22semidirect
54. #63572C22semidirect
55. #63566C22semidirect
56. #63566C22semidirect
74. #5018D3semidirect
75. C4×#214D3semidirect
201. C4×Dic6C2×D3semidirect
202. C4×Dic6C2×D3semidirect
229. #810C2×D3semidirect
230. #810C2×D3semidirect
234. #808C2×D3semidirect
236. #807C2×D3semidirect
237. #803C2×D3semidirect
238. C4×C3⋊C8C2×D3semidirect
703. C32#3123semidirect
784. C3#79659semidirect
785. C3#79787semidirect

Maximal subgroups

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

subgroupindex
#105960162
#105938832
C3×#50182
C3×C4×#2142
#105914972
#105914792
#105914672
#105905652
#105905272
#105905262
#105904352
#105903622
C4×#37172
#105902982
#797873
#796593