Finite Group Databasebeta

← #11888043

Subgroups — #11888043

Order 1152.

848 conjugacy classes of subgroups.

The subgroup lattice has 777 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5824C211yesmaximal, characteristic
2#10594840C211yesmaximal, characteristic, complemented
3#10592938C211yesmaximal, characteristic, complemented
4C3×#5233C211yesmaximal, characteristic, complemented
5#10591623C211yesmaximal, characteristic, complemented
6#10591596C211yesmaximal, characteristic, complemented
7#10591575C211yesmaximal, characteristic, complemented
8#10591558C211yesmaximal, characteristic, complemented
9#10591463C211yesmaximal, characteristic, complemented
10#10591420C211yesmaximal, characteristic, complemented
11#10591410C211yesmaximal, characteristic, complemented
12#10591401C211yesmaximal, characteristic, complemented
13#10591187C211yesmaximal, characteristic, complemented
14C3⋊C8×#67C211yesmaximal, characteristic, complemented
15#10591102C211yesmaximal, characteristic, complemented
16#83510—31nomaximal
17#78849—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×#3756C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22#64133C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×#944C2211yescharacteristic
25C3×#939—21no—
26C3×#935—21no—
27C3×D4×Dic3C2211yescharacteristic
28C3×#929—21no—
29C3×C4×#67C2211yescharacteristic
30C3×#926C2211yescharacteristic
31C3×#924C2211yescharacteristic
32C2×C3×Dic3⋊C4—21no—
33C22×C3×C3⋊C8C2211yescharacteristic
34#63959—21no—
35#63956—21no—
36#63918C2211yescharacteristic
37#63859—21no—
38#63857C2211yescharacteristic
39#63844C2211yescharacteristic
40#63841C2211yescharacteristic
41#63837—21no—
42C2×#3719C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63659C2211yescharacteristic
46#63657C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#832C2211yescharacteristic
51#63576C2211yescharacteristic
52#63575C2211yescharacteristic
53#63574C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#547—31no—
62#5824D311yescharacteristic
63#5542—31no—
64#5533—31no—
65C3×#416—31no—
66#5239—31no—
67#5239—31no—
68#5239—31no—
69#5239—61no—
70#5233—31no—
71#5233D311yescharacteristic, complemented
72#5116—31no—
73C8×#67—31no—
74#5090—31no—
75#5079—31no—
76#5051—31no—
77#5051—31no—
78#5045—31no—
79#5045—31no—
80C4×#214—31no—
81D4×C3⋊C8—31no—
82#5007—31no—
83#4996—31no—
84#4814—31no—
85#4813—31no—
86#4795—31no—
87#4792—31no—
88#4783—31no—
89#4772—31no—
90#4759—31no—
91#4758—31no—
92C32×#41—22no—
93C32×#41—41no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67D411yescharacteristic
102C22×C3×Dic3—21no—
103C22×C3×Dic3—21no—
104C3×#237—22no—
105C3×#237—41no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#627—21no—
109#3757—21no—
110#3756—41no—
111#3754—22no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113#3750—21no—
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C3×#217—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#217D411yescharacteristic
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8—41no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142#3719—41no—
143D3×C3⋊C8—41no—
144#3302—91noSylow
145C2×C3×#41—21no—
146C2×C3×#41—31no—
147C2×C3×#41C2×D311yescharacteristic
148C2×C3×#41C2×D311yescharacteristic
149C2×#237C2×D311yescharacteristic
150C22×C3×C8—31no—
151C3×C4⋊Q8—31no—
152C3×#123—61no—
153C3×#123—61no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×#121—61no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C3×#117—31no—
160C2×C3×C4⋊C4—61no—
161#946C2×D311yescharacteristic
162#944C2×D311yescharacteristic
163C2×#216—31no—
164C2×#216—31no—
165C2×#216—31no—
166C2×#216—61no—
167#939—21no—
168#936—61no—
169#935—21no—
170D4×Dic3C2×D311yescharacteristic
171C2×#214—31no—
172C2×#214—31no—
173C2×#214—61no—
174#929—21no—
175C4×#67C2×D311yescharacteristic
176#926—31no—
177#926C2×D311yescharacteristic
178#924—31no—
179#924—31no—
180#924—31no—
181#924—61no—
182#924C2×D311yescharacteristic
183C2×Dic3⋊C4—21no—
184C22×C3⋊C8—31no—
185C22×C3⋊C8C2×D311yescharacteristic
186C2×Dic12—31no—
187C2×D3×C8—31no—
188#897—31no—
189#892—31no—
190#888—31no—
191#887—31no—
192#887—61no—
193#885—61no—
194#879—61no—
195#879—61no—
196#879—61no—
197#876—61no—
198#869—31no—
199C4×Dic6—31no—
200C4×Dic6—61no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#102—31no—
204C3×#102—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—61no—
211#835C2×D311yescharacteristic
212#835C2×D311yescharacteristic
213#832—31no—
214#832—31no—
215#832—61no—
216#832C2×D311yescharacteristic
217#832C2×D311yescharacteristic
218#830—31no—
219#830—31no—
220#830—31no—
221#830—61no—
222(C2×D3)⋊C8—31no—
223#818—31no—
224#816—31no—
225#816—31no—
226Dic3⋊C8—31no—
227C8×Dic3—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#808—31no—
232#808—31no—
233#807—31no—
234#807—31no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32—21no—
239C23×C32C2×D411yescharacteristic
240C22×C3×D3C2×D411yescharacteristic
241C32×Q8—21no—
242C32×Q8—21no—
243C32×D4—21no—
244C32×D4—42no—
245C32×D4#4112yes—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—42no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254#634—21no—
255#634—21no—
256C3×#67—22no—
257C3×#67—42no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—42no—
263C2×C3×Dic3—42no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#627—42no—
272C3⋊(C3⋊C8)—21no—
273C3⋊(C3⋊C8)—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#556—91no—
277#547—31no—
278#487—91no—
279#485—91no—
280#485—91no—
281#474—91no—
282#467—91no—
283#467—91no—
284#462—91no—
285#452—91no—
286#452—91no—
287C4×SD16—91no—
288C8×D4—91no—
289#416—31no—
290#416—91no—
291C3×#41—22no—
292C3×#41—22no—
293C3×#41—42no—
294C3×#41—41no—
295C3×#41—41no—
296C3×#41—42no—
297C3×#41—62no—
298C3×#41—121no—
299C2×C3×Q8—21no—
300C2×C3×Q8—31no—
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×D4—21no—
304C2×C3×D4—21no—
305C2×C3×D4—21no—
306C2×C3×D4—31no—
307C2×C3×D4—41no—
308C2×C3×D4—61no—
309C2×C3×D4C22×D311yescharacteristic
310C2×C3×D4C22×D311yescharacteristic
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—31no—
315C22×C3×C4—41no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C2×#67—21no—
321C2×#67#6711yescharacteristic
322C22×Dic3—21no—
323C22×Dic3—21no—
324#237—22no—
325#237—41no—
326C2×C4×D3C22×D311yescharacteristic
327C2×Dic6—31no—
328C2×Dic6—31no—
329C2×Dic6—61no—
330C2×Dic6—61no—
331C2×Dic6—61no—
332C2×Dic6C22×D311yescharacteristic
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C2×C3×C8—121no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C22⋊C4—31no—
345C3×C22⋊C4—31no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C42—31no—
351C3×C42—61no—
352#217—21no—
353#217—21no—
354#217—21no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—121no—
360#217#6711yescharacteristic
361#216—121no—
362#216—121no—
363#216—121no—
364#216—122no—
365#214—62no—
366#214—62no—
367#214—122no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4#6711yescharacteristic
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—121no—
391Dic3⋊C4#6711yescharacteristic
392C4×Dic3—21no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3C22×D311yescharacteristic
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—41no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—121no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408Dic12—121no—
409D3×C8—121no—
410C22×C32—22no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32C22×D411yescharacteristic
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C32×C4—21no—
421C32×C4—41no—
422C32×C4C2×#4111yescharacteristic
423C32×C4H(5,𝔽2)11yescharacteristic
424C3⋊Dic3—41no—
425C3⋊Dic3—41no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3—41no—
432C3×Dic3#13512yes—
433C2×#41—31no—
434C2×#41D3211yescharacteristic
435C2×Q16—91no—
436C2×Q16—91no—
437C2×SD16—91no—
438C22×C8—31no—
439C22×C8—91no—
440C4⋊Q8—31no—
441C4⋊Q8—91no—
442#126—181no—
443#126—181no—
444#124—181no—
445#123—61no—
446#123—61no—
447C22⋊Q8—31no—
448C22⋊Q8—31no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451#121—61no—
452C4×Q8—91no—
453C4×Q8—181no—
454C4×D4—31no—
455C4×D4—31no—
456#117—31no—
457#117—91no—
458C2×C4⋊C4—61no—
459#107—91no—
460#107—91no—
461#106—91no—
462C4⋊C8—91no—
463#103—31no—
464#103—31no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#102—31no—
471#102—31no—
472#102—91no—
473C22⋊C8—91no—
474C22⋊C8—91no—
475C4×C8—91no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—31no—
480C23×C3—41no—
481C23×C3D3×D411yescharacteristic
482C23×C3C2×#6711yescharacteristic
483C22×D3C2×#6711yescharacteristic
484C3×Q8—22no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—41no—
490C3×Q8—61no—
491C3×Q8—61no—
492C3×D4—21no—
493C3×D4—21no—
494C3×D4—22no—
495C3×D4—41no—
496C3×D4—42no—
497C3×D4—42no—
498C3×D4—44no—
499C3×D4—62no—
500C3×D4—122no—
501C3×D4#23512yes—
502C3×D4#23712yes—
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—21no—
510C2×C3×C4—21no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—42no—
518C2×C3×C4—42no—
519C2×C3×C4—44no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—122no—
527C2×C3×C4—122no—
528C2×C3×C4D3×D411yescharacteristic
529C2×C3×C4C2×#6711yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532#67—22no—
533#67—42no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—42no—
539C2×Dic3—42no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—121no—
545C2×Dic3—121no—
546C2×Dic3C2×#6711yescharacteristic
547C2×Dic3C2×#6711yescharacteristic
548C2×Dic3C2×#6711yescharacteristic
549C4×D3—21no—
550C4×D3—21no—
551Dic6—21no—
552Dic6—21no—
553Dic6—61no—
554Dic6—61no—
555Dic6—61no—
556Dic6—61no—
557Dic6—121no—
558Dic6—121no—
559Dic6—122no—
560Dic6—122no—
561C3×C8—61no—
562C3×C8—61no—
563C3⋊C8—21no—
564C3⋊C8—21no—
565C3⋊C8—61no—
566C3⋊C8—61no—
567C3⋊C8—61no—
568C3⋊C8—61no—
569C3⋊C8—121no—
570C3⋊C8—121no—
571C2×C32—41no—
572C2×C32—42no—
573C2×C32#54611yescharacteristic
574C2×C32C2×#13511yescharacteristic
575C2×C32#57811yescharacteristic
576C3×D3—41no—
577#41—22no—
578#41—41no—
579#41—62no—
580#41—121no—
581C2×Q8—31no—
582C2×Q8—91no—
583C2×Q8—181no—
584C2×Q8C2×D3211yescharacteristic
585C2×D4—21no—
586C2×D4—31no—
587C2×D4—61no—
588C2×D4C2×D3211yescharacteristic
589C22×C4—21no—
590C22×C4—31no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4C2×D3211yescharacteristic
594Q16—361no—
595Q16—361no—
596SD16—182no—
597C2×C8—31no—
598C2×C8—31no—
599C2×C8—91no—
600C2×C8—91no—
601C2×C8—121no—
602C2×C8—361no—
603C4⋊C4—31no—
604C4⋊C4—31no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—91no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C22⋊C4—31no—
617C22⋊C4—31no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C42—31no—
626C42—61no—
627C42—181no—
628C42—181no—
629C22×C3—21no—
630C22×C3—22no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—22no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—42no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—81no—
650C22×C3—81no—
651C22×C3C2×D3×D411yescharacteristic
652C22×C3C22×#6711yescharacteristic
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—32no—
661C3×C4—41no—
662C3×C4—42no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—61no—
666C3×C4—61no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4C2×#23511yescharacteristic
672C3×C4C2×#23711yescharacteristic
673C3×C4#100411yescharacteristic
674C3×C4#100411yescharacteristic
675Dic3—21no—
676Dic3—21no—
677Dic3—41no—
678Dic3—41no—
679Dic3—41no—
680Dic3—41no—
681Dic3—121no—
682Dic3—121no—
683Dic3—121no—
684Dic3—121no—
685Dic3—241no—
686Dic3—241no—
687Dic3#95012yes—
688C32#330211yescharacteristic, complemented, Sylow
689C23—21no—
690C23—31no—
691C23D3×#6711yescharacteristic
692Q8—21no—
693Q8—21no—
694Q8—61no—
695Q8—61no—
696Q8—181no—
697Q8—181no—
698Q8—362no—
699D4—21no—
700D4—42no—
701D4—62no—
702D4—122no—
703D4#380412yes—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—31no—
710C2×C4—42no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—122no—
718C2×C4—122no—
719C2×C4—181no—
720C2×C4—181no—
721C2×C4D3×#6711yescharacteristic
722C2×C4C22×D3211yescharacteristic
723C8—61no—
724C8—61no—
725C8—181no—
726C8—181no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—41no—
731C2×C3—42no—
732C2×C3—41no—
733C2×C3—42no—
734C2×C3—81no—
735C2×C3—82no—
736C2×C3—121no—
737C2×C3#549011yescharacteristic
738C2×C3D3×#13511yescharacteristic
739C2×C3#577111yescharacteristic
740C2×C3#580611yescharacteristic
741C2×C3C2×#95011yescharacteristic
742C2×C3#583811yescharacteristic
743D3—41no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—22no—
748C22—41no—
749C22—41no—
750C22—61no—
751C22—61no—
752C22—61no—
753C22C2×D3×#6711yescharacteristic
754C4—21no—
755C4—32no—
756C4—41no—
757C4—61no—
758C4—61no—
759C4—121no—
760C4—121no—
761C4—121no—
762C4—121no—
763C4—361no—
764C4—361no—
765C4C2×#380411yescharacteristic
766C4#6433011yescharacteristic
767C3—21no—
768C3#7884911yescharacteristic, complemented
769C3#8351011yescharacteristic, complemented
770C2—41no—
771C2—42no—
772C2—121no—
773C2D3×#95011yescharacteristic
774C2#1059546711yescharacteristic
775C2#1059549311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC3×#5824C2
hypercenterC2×#41D32
hypocenterC32#3302
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10594840C2semidirect
3. #10592938C2semidirect
4. C3×#5233C2semidirect
5. #10591623C2semidirect
6. #10591596C2semidirect
7. #10591575C2semidirect
8. #10591558C2semidirect
9. #10591463C2semidirect
10. #10591420C2semidirect
11. #10591410C2semidirect
12. #10591401C2semidirect
13. #10591187C2semidirect
14. C3⋊C8×#67C2semidirect
15. #10591102C2semidirect
71. #5233D3semidirect
688. C32#3302semidirect
768. C3#78849semidirect
769. C3#83510semidirect

Maximal subgroups

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

subgroupindex
C3×#58242
#105948402
#105929382
C3×#52332
#105916232
#105915962
#105915752
#105915582
#105914632
#105914202
#105914102
#105914012
#105911872
C3⋊C8×#672
#105911022
#835103
#788493