Finite Group Databasebeta

← #11870624

Subgroups — #11870624

Order 1152.

909 conjugacy classes of subgroups.

The subgroup lattice has 779 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596051C211yesmaximal, characteristic, complemented
2C4×#3796C211yesmaximal, characteristic, complemented
3C3×C4×#216C211yesmaximal, characteristic, complemented
4C3×C4×#215C211yesmaximal, characteristic, complemented
5#10591656C211yesmaximal, characteristic, complemented
6#10591579C211yesmaximal, characteristic, complemented
7#10591570C211yesmaximal, characteristic, complemented
8#10591561C211yesmaximal, characteristic, complemented
9#10590617C211yesmaximal, characteristic
10#10590495C211yesmaximal, characteristic, complemented
11#10590473C211yesmaximal, characteristic, complemented
12#10590451C211yesmaximal, characteristic, complemented
13C4×#3717C211yesmaximal, characteristic, complemented
14C4×#3714C211yesmaximal, characteristic, complemented
15#10590297C211yesmaximal, characteristic, complemented
16#79746—31nomaximal
17#79652—31nomaximal
18C2×#3796C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20#64156C2211yescharacteristic
21#64155C2211yescharacteristic
22#64107—21no—
23#64104C2211yescharacteristic
24#64103—21no—
25#64099C2211yescharacteristic
26C4×C4⋊(C3⋊D3)—21no—
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28#64081—21no—
29C42×C3⋊D3C2211yescharacteristic
30C2×C3×#216C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34C4×#626—21no—
35#63898C2211yescharacteristic
36#63881—21no—
37#63878—21no—
38C4×D3×Dic3—21no—
39#63849C2211yescharacteristic
40#63843C2211yescharacteristic
41C2×#3717C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C3×#835C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#810C2211yescharacteristic
46C3×#809C2211yescharacteristic
47C3×#808C2211yescharacteristic
48C3×#807C2211yescharacteristic
49C3×C4×C3⋊C8C2211yescharacteristic
50C3×C4×C3⋊C8C2211yescharacteristic
51#63575C2211yescharacteristic
52#63573C2211yescharacteristic
53#63572C2211yescharacteristic
54#63572C2211yescharacteristic
55#63566C2211yescharacteristic
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63563C2211yescharacteristic
59#63557C2211yescharacteristic
60#63557C2211yescharacteristic
61#5580—31no—
62#5580—31no—
63#5580—61no—
64C4×#239—31no—
65C4×#237—31no—
66C3×C4×Q16—31no—
67C3×C4×SD16—31no—
68#5187—31no—
69#5185—31no—
70#5173—31no—
71#5165—31no—
72C4×#216D311yescharacteristic, complemented
73C4×#215—31no—
74C4×#215D311yescharacteristic, complemented
75C4×#213—31no—
76#4891—31no—
77#4885—31no—
78#4866—31no—
79#4857—31no—
80#4819—31no—
81#4815—31no—
82#4814—31no—
83#4810—31no—
84#4798—31no—
85#4796—31no—
86#4781—31no—
87#4763—31no—
88C4×D24—31no—
89C4×#204—31no—
90#4685—31no—
91#4685—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4⋊(C3⋊D3)—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3D411yescharacteristic
97C2×C4×C3⋊D3D411yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×Dic6C2311yescharacteristic
102C2×#626—21no—
103C2×D3×Dic3—21no—
104C2×D3×Dic3—21no—
105#3796—22no—
106#3796—22no—
107C32×C4⋊C4—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C42—21no—
110C32×C42C2311yescharacteristic
111#3752—21no—
112#3752—21no—
113#3752—21no—
114#3752—21no—
115#3752—21no—
116C4⋊(C3⋊Dic3)—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119#3750—21no—
120C4×C3⋊Dic3D411yescharacteristic
121C4×C3⋊Dic3D411yescharacteristic
122C4×C3⋊Dic3C2311yescharacteristic
123C3×#216—22no—
124C3×#215—22no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134Dic3⋊Dic3—21no—
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137Dic32—21no—
138Dic32—21no—
139#3717—22no—
140#3714—22no—
141#3102—91noSylow
142C2×#239—31no—
143C2×#237—31no—
144C2×C3×Q16—31no—
145C2×C3×SD16—31no—
146C3×C4×Q8—21no—
147C3×C4×Q8—31no—
148C3×C4×Q8C2×D311yescharacteristic
149C3×C4×Q8C2×D311yescharacteristic
150C3×C4×D4—31no—
151#947—31no—
152#947—31no—
153#947—61no—
154#946—31no—
155#946—31no—
156#946—61no—
157Q8×Dic3—31no—
158C2×#216C2×D311yescharacteristic
159C2×#215—31no—
160C2×#215C2×D311yescharacteristic
161D4×Dic3—31no—
162C2×#213—31no—
163C4×#67—61no—
164C2×C4×Dic3—61no—
165C2×D24—31no—
166C2×#204—31no—
167#898—61no—
168#898—61no—
169#898—62no—
170#895—31no—
171#895—31no—
172#895—61no—
173#894—61no—
174#894—61no—
175#894—62no—
176#893—31no—
177#893—61no—
178#892—31no—
179#892—31no—
180#892—61no—
181#890—31no—
182#890—31no—
183#890—61no—
184#887—31no—
185#67⋊C4—61no—
186#877—61no—
187C4×D12—31no—
188C4×D12—31no—
189C4×D12—61no—
190C4×D12—61no—
191C4×D12—61no—
192C4×D12—62no—
193C4×D12—61no—
194C4×D12C2×D311yescharacteristic
195#872—61no—
196#872—61no—
197#872—62no—
198C42×D3—31no—
199C42×D3—31no—
200C42×D3—61no—
201C42×D3—61no—
202C4×Dic6C2×D311yescharacteristic
203C3×#107—31no—
204C3×#106—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#102—31no—
209C3×C4×C8—31no—
210C3×C4×C8—31no—
211#835—31no—
212#835C2×D311yescharacteristic
213#835C2×D311yescharacteristic
214#832—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222#818—31no—
223#817—31no—
224#816—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—31no—
227Dic3⋊C8—31no—
228Dic3⋊C8—31no—
229#810C2×D311yescharacteristic
230#809—31no—
231#809—31no—
232#809C2×D311yescharacteristic
233#808—31no—
234#808C2×D311yescharacteristic
235#807—31no—
236#807C2×D311yescharacteristic
237C4×C3⋊C8C2×D311yescharacteristic
238C4×C3⋊C8C2×D311yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C32×Q8—21no—
243C32×Q8—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3C2×D411yescharacteristic
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—42no—
256C4×C3⋊D3—22no—
257C4×C3⋊D3—21no—
258C4×C3⋊D3—21no—
259C4×C3⋊D3—41no—
260C4×C3⋊D3—42no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C3×D12—21no—
265C3×D12#4112yes—
266C3×C4×D3—42no—
267C3×Dic6—21no—
268C3×Dic6#4112yes—
269#626—24no—
270D3×Dic3—24no—
271D3×Dic3—42no—
272C3×C3⋊C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#529—91no—
277C4×#41—91no—
278#485—91no—
279#482—91no—
280#479—91no—
281#478—91no—
282#464—91no—
283#463—91no—
284#452—91no—
285#449—91no—
286C4×Q16—31no—
287C4×SD16—31no—
288C4×SD16—91no—
289C4×D8—91no—
290#431—91no—
291C2×C3×Q8—21no—
292C2×C3×Q8—31no—
293C2×C3×Q8C22×D311yescharacteristic
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×D4—31no—
296C22×C3×C4—61no—
297C2×#67—61no—
298C22×Dic3—61no—
299C22×Dic3—61no—
300#239—62no—
301#239—62no—
302#237—62no—
303#237—62no—
304C2×D12—31no—
305C2×D12—31no—
306C2×D12—61no—
307C2×D12—61no—
308C2×D12—61no—
309C2×D12—61no—
310C2×D12—62no—
311C2×D12C22×D311yescharacteristic
312C2×C4×D3—21no—
313C2×C4×D3—31no—
314C2×C4×D3—31no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—62no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×Dic6C22×D311yescharacteristic
328C3×Q16—62no—
329C3×SD16—62no—
330C2×C3×C8—31no—
331C2×C3×C8—31no—
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C3×C4⋊C4—22no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C22⋊C4—61no—
344C3×C42—22no—
345C3×C42—21no—
346C3×C42—21no—
347C3×C42—21no—
348C3×C42—61no—
349C3×C42C22×D311yescharacteristic
350C3×C42C22×D311yescharacteristic
351#217—61no—
352#216—22no—
353#215—22no—
354#215—62no—
355#213—62no—
356(C2×D3)⋊C4—21no—
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—62no—
369(C2×D3)⋊C4—62no—
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—62no—
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—62no—
391Dic3⋊C4—62no—
392C4×Dic3—21no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—31no—
396C4×Dic3—31no—
397C4×Dic3—31no—
398C4×Dic3—31no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410D24—62no—
411#204—62no—
412C22×C32C22×D411yescharacteristic
413C2×C3⋊D3—21no—
414C2×C3⋊D3—21no—
415C2×C3⋊D3—21no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3×D3—22no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C32×C4—21no—
423C32×C4—41no—
424C32×C4—41no—
425C32×C4#13512yes—
426C32×C4C2×#4111yescharacteristic
427C32×C4C2×#4111yescharacteristic
428C3⋊Dic3—21no—
429C3⋊Dic3—21no—
430C3⋊Dic3—21no—
431C3⋊Dic3—41no—
432C3×Dic3—22no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—91no—
436C2×Q16—31no—
437C2×SD16—31no—
438C2×SD16—91no—
439C2×D8—91no—
440#126—181no—
441#125—91no—
442#124—91no—
443#123—181no—
444C22⋊Q8—91no—
445#121—91no—
446C4×Q8—31no—
447C4×Q8—91no—
448C4×Q8D3211yescharacteristic
449C4×D4—31no—
450C4×D4—91no—
451C4×D4—91no—
452C4×D4—181no—
453C4×D4—181no—
454C4×D4—181no—
455#117—91no—
456#117—181no—
457#117—181no—
458C2×C42—91no—
459C2×C42—181no—
460#107—31no—
461#107—91no—
462#106—31no—
463#106—91no—
464C4⋊C8—91no—
465C4⋊C8—91no—
466#103—31no—
467#103—31no—
468#103—31no—
469#103—91no—
470#102—31no—
471#102—91no—
472#102—91no—
473#102—91no—
474C22⋊C8—91no—
475C22⋊C8—91no—
476C4×C8—31no—
477C4×C8—31no—
478C23×C3—61no—
479C22×D3—21no—
480C22×D3—31no—
481C22×D3—31no—
482C22×D3—61no—
483C22×D3—62no—
484C22×D3—61no—
485C22×D3—61no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—32no—
491C3×Q8—41no—
492C3×Q8—41no—
493C3×Q8—61no—
494C3×D4—32no—
495C3×D4—61no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—21no—
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—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—122no—
509C2×C3×C4D3×D411yescharacteristic
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4D3×D411yescharacteristic
512C2×C3×C4D3×D411yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515#67—64no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—64no—
529C2×Dic3—62no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—122no—
533D12—21no—
534D12—64no—
535D12—61no—
536D12—61no—
537D12—61no—
538D12—61no—
539D12—121no—
540D12—121no—
541D12—124no—
542D12—122no—
543D12—122no—
544D12#23512yes—
545C4×D3—42no—
546C4×D3—64no—
547C4×D3—62no—
548C4×D3—62no—
549C4×D3—61no—
550C4×D3—61no—
551C4×D3—61no—
552C4×D3—61no—
553C4×D3—121no—
554C4×D3—121no—
555C4×D3—122no—
556C4×D3—121no—
557C4×D3—121no—
558C4×D3—122no—
559C4×D3—124no—
560C4×D3—122no—
561C4×D3—122no—
562C4×D3—122no—
563Dic6—21no—
564Dic6#23512yes—
565C3×C8—61no—
566C3×C8—61no—
567C3×C8—61no—
568C3×C8—61no—
569C3⋊C8—21no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C3⋊C8—21no—
573C2×C32#52511yescharacteristic
574C2×C32C2×#13511yescharacteristic
575C2×C32#57511yescharacteristic
576C3⋊D3—41no—
577C3⋊D3—81no—
578C3×D3—42no—
579#41—182no—
580#41—182no—
581C2×Q8—31no—
582C2×Q8C2×D3211yescharacteristic
583C2×D4—31no—
584C2×D4—91no—
585C2×D4—181no—
586C2×D4—181no—
587C22×C4—61no—
588C22×C4—91no—
589C22×C4—91no—
590C22×C4—91no—
591C22×C4—181no—
592C22×C4—181no—
593C22×C4—181no—
594Q16—62no—
595SD16—62no—
596SD16—182no—
597D8—182no—
598C2×C8—31no—
599C2×C8—31no—
600C2×C8—31no—
601C2×C8—31no—
602C4⋊C4—21no—
603C4⋊C4—31no—
604C4⋊C4—31no—
605C4⋊C4—61no—
606C4⋊C4—91no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4C2×D3211yescharacteristic
612C22⋊C4—61no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C42—21no—
621C42—61no—
622C42—91no—
623C42—91no—
624C42—91no—
625C42—181no—
626C42—181no—
627C42C2×D3211yescharacteristic
628C22×C3—21no—
629C22×C3—62no—
630C22×C3—121no—
631C22×C3—121no—
632C22×C3C2×D3×D411yescharacteristic
633C22×C3C2×D3×D411yescharacteristic
634C2×D3—22no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—62no—
638C2×D3—61no—
639C2×D3—61no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—61no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—122no—
647C2×D3—122no—
648C2×D3—122no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—121no—
654C2×D3—121no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—22no—
660C3×C4—41no—
661C3×C4—42no—
662C3×C4—42no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—62no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4#91612yes—
671C3×C4#91912yes—
672C3×C4C2×#23511yescharacteristic
673C3×C4C2×#23511yescharacteristic
674C3×C4D3×#4111yescharacteristic
675C3×C4D3×#4111yescharacteristic
676Dic3—22no—
677Dic3—41no—
678Dic3—41no—
679Dic3—61no—
680Dic3—61no—
681Dic3—61no—
682Dic3—61no—
683Dic3—61no—
684Dic3—61no—
685Dic3—121no—
686Dic3—121no—
687Dic3—121no—
688Dic3—122no—
689Dic3—121no—
690Dic3—121no—
691C32#310211yescharacteristic, complemented, Sylow
692C23—61no—
693C23—91no—
694C23—181no—
695Q8—21no—
696Q8—21no—
697Q8—32no—
698Q8—61no—
699D4—32no—
700D4—61no—
701D4—184no—
702D4—181no—
703D4—181no—
704D4—362no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—91no—
711C2×C4—91no—
712C2×C4—91no—
713C2×C4—122no—
714C2×C4—184no—
715C2×C4—181no—
716C2×C4—181no—
717C2×C4—182no—
718C2×C4—181no—
719C2×C4—361no—
720C2×C4—362no—
721C2×C4—362no—
722C2×C4#381111yescharacteristic
723C2×C4#381111yescharacteristic
724C2×C4C22×D3211yescharacteristic
725C8—61no—
726C8—61no—
727C8—61no—
728C8—61no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—122no—
733C2×C3#554711yescharacteristic
734C2×C3#554711yescharacteristic
735C2×C3C2×#91611yescharacteristic
736C2×C3C2×#91911yescharacteristic
737C2×C3#576811yescharacteristic
738C2×C3#576811yescharacteristic
739D3—42no—
740D3—122no—
741D3—121no—
742D3—121no—
743D3—242no—
744D3—241no—
745D3—241no—
746C22—62no—
747C22—121no—
748C22—121no—
749C22—181no—
750C22—181no—
751C22—181no—
752C22—361no—
753C22—361no—
754C22—361no—
755C22C2×#381111yescharacteristic
756C4—21no—
757C4—41no—
758C4—41no—
759C4—62no—
760C4—121no—
761C4—121no—
762C4—181no—
763C4—181no—
764C4—181no—
765C4—361no—
766C4#6395012yes—
767C4D3×#23511yescharacteristic
768C4D3×#23511yescharacteristic
769C3—21no—
770C3#7965211yescharacteristic, complemented
771C3#7974611yescharacteristic, complemented
772C2—122no—
773C2—361no—
774C2—721no—
775C2#1059507611yescharacteristic
776C2C2×#6395011yescharacteristic
777C2#1059546011yescharacteristic
subgroupG/H
centerC2×C4#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10590617C2
hypercenterC4×Q8D32
hypocenterC32#3102
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596051C2semidirect
2. C4×#3796C2semidirect
3. C3×C4×#216C2semidirect
4. C3×C4×#215C2semidirect
5. #10591656C2semidirect
6. #10591579C2semidirect
7. #10591570C2semidirect
8. #10591561C2semidirect
10. #10590495C2semidirect
11. #10590473C2semidirect
12. #10590451C2semidirect
13. C4×#3717C2semidirect
14. C4×#3714C2semidirect
15. #10590297C2semidirect
72. C4×#216D3semidirect
74. C4×#215D3semidirect
691. C32#3102semidirect
770. C3#79652semidirect
771. C3#79746semidirect

Maximal subgroups

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

subgroupindex
#105960512
C4×#37962
C3×C4×#2162
C3×C4×#2152
#105916562
#105915792
#105915702
#105915612
#105906172
#105904952
#105904732
#105904512
C4×#37172
C4×#37142
#105902972
#797463
#796523