Finite Group Databasebeta

← #10972903

Subgroups — #10972903

Order 768.

2654 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5596C211yesmaximal, characteristic
2C22×C4×Dic6C211yesmaximal, characteristic, complemented
3C3×#2854C211yesmaximal, characteristic, complemented
4#82859C212yesmaximal, complemented
5#82841C212yesmaximal, complemented
6#82699C211yesmaximal, characteristic, complemented
7#82080C211yesmaximal, characteristic, complemented
8#76364C212yesmaximal, complemented
9#76353C212yesmaximal, complemented
10#76075C212yesmaximal, complemented
11#76071C212yesmaximal, complemented
12#75652C214yesmaximal, complemented
13#75462C214yesmaximal, complemented
14#74701C212yesmaximal, complemented
15#74687C212yesmaximal, complemented
16#73999C211yesmaximal, characteristic, complemented
17#73863C211yesmaximal, characteristic, complemented
18#35249—31nomaximal, Sylow
19C22×#237C2212yes—
20C23×Dic6C2211yescharacteristic
21C2×C3×#123C2212yes—
22C2×C3×#121C2211yescharacteristic
23C22×C3×C42C2211yescharacteristic
24C2×#940C2211yescharacteristic
25C2×#939C2212yes—
26C2×#935C2212yes—
27C2×D4×Dic3C2211yescharacteristic
28C2×#930C2211yescharacteristic
29C2×#929C2212yes—
30C22×C4⋊Dic3C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C22×C4×Dic3C2211yescharacteristic
35#5596—28no—
36C2×#893C2211yescharacteristic
37C2×#888C2211yescharacteristic
38C2×#886C2212yes—
39C2×#885C2214yes—
40C2×#885C2212yes—
41C2×#67⋊C4C2212yes—
42C2×C4×Dic6—28no—
43C2×C4×Dic6C2212yes—
44C2×C4×Dic6C2212yes—
45C2×C4×Dic6C2212yes—
46C2×C4×Dic6C2212yes—
47C3×#390C2212yes—
48C3×#389C2212yes—
49C3×#388C2214yes—
50C3×#386C2212yes—
51C3×#380C2211yescharacteristic
52#5221C2212yes—
53#5220C2212yes—
54#5213C2212yes—
55#5212C2211yescharacteristic
56#4993C2214yes—
57#4989C2214yes—
58#4988C2212yes—
59#4984C2212yes—
60#4979C2214yes—
61#4977C2212yes—
62#4975C2214yes—
63Dic3×C4⋊C4C2212yes—
64#4972C2212yes—
65#4961C2214yes—
66#4959C2214yes—
67#4958C2212yes—
68#4957C2214yes—
69#4950C2214yes—
70#4949C2214yes—
71#4947C2214yes—
72#4946C2214yes—
73#4944C2214yes—
74#4943C2212yes—
75Dic3×C22⋊C4C2212yes—
76#4940C2214yes—
77#4939C2212yes—
78#4928C2212yes—
79#4673C2214yes—
80#4670C2214yes—
81#4668C2214yes—
82#4656C2214yes—
83#4651C2212yes—
84#4648C2212yes—
85#4646C2214yes—
86C2×#532—31no—
87C22×C4×Q8—31no—
88#2854—31no—
89#2854—31no—
90#2854—31no—
91#2854D311yescharacteristic, complemented
92#2632—34no—
93#2580—32no—
94#2580—32no—
95#2567—32no—
96#2548—32no—
97#2501—32no—
98#2436—32no—
99#2406—32no—
100#2406—32no—
101#2326—34no—
102#2283—31no—
103C22×C3×D4C2312yes—
104C22×C3×D4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C22×#67C2312yes—
109C22×#67C2312yes—
110C22×#67C2312yes—
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2311yescharacteristic
115C23×Dic3C2312yes—
116C2×#237—28no—
117C2×#237—44no—
118C2×#237—44no—
119C22×D12C2311yescharacteristic
120C22×C4×D3C2312yes—
121C22×Dic6—24no—
122C22×Dic6—28no—
123C22×Dic6C2312yes—
124C22×Dic6C2312yes—
125C22×Dic6C2312yes—
126C3×#123—44no—
127C3×#121—24no—
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2312yes—
130C2×C3×C4⋊C4C2314yes—
131C2×C3×C22⋊C4C2312yes—
132C2×C3×C22⋊C4C2312yes—
133C2×C3×C22⋊C4C2314yes—
134C2×C3×C22⋊C4C2314yes—
135C2×C3×C42—24no—
136C2×C3×C42C2312yes—
137C2×C3×C42C2312yes—
138C2×#217C2312yes—
139C2×#217C2314yes—
140C2×#217C2312yes—
141C2×#217C2314yes—
142#940—24no—
143#939—28no—
144#935—44no—
145D4×Dic3—24no—
146#930—24no—
147#929—44no—
148C2×(C2×D3)⋊C4C2314yes—
149C2×(C2×D3)⋊C4C2312yes—
150C2×(C2×D3)⋊C4C2314yes—
151C2×(C2×D3)⋊C4C2312yes—
152C2×(C2×D3)⋊C4C2314yes—
153C2×(C2×D3)⋊C4C2314yes—
154C2×C4⋊Dic3—24no—
155C2×C4⋊Dic3C2312yes—
156C2×C4⋊Dic3C2312yes—
157C2×C4⋊Dic3C2311yescharacteristic
158C2×C4⋊Dic3C2312yes—
159C2×C4⋊Dic3C2314yes—
160C2×Dic3⋊C4—24no—
161C2×Dic3⋊C4—24no—
162C2×Dic3⋊C4C2312yes—
163C2×Dic3⋊C4C2312yes—
164C2×Dic3⋊C4C2312yes—
165C2×Dic3⋊C4C2312yes—
166C2×Dic3⋊C4C2312yes—
167C2×Dic3⋊C4C2314yes—
168C2×Dic3⋊C4C2314yes—
169C2×C4×Dic3—24no—
170C2×C4×Dic3D418yes—
171C2×C4×Dic3C2314yes—
172C2×C4×Dic3C2312yes—
173C2×C4×Dic3C2312yes—
174C2×C4×Dic3C2311yescharacteristic
175C2×C4×Dic3C2311yescharacteristic
176C2×C4×Dic3C2311yescharacteristic
177C2×C4×Dic3C2311yescharacteristic
178#893—24no—
179#888—24no—
180#886—44no—
181#885—216no—
182#885—28no—
183#67⋊C4—28no—
184C4×Dic6—28no—
185C4×Dic6—28no—
186C4×Dic6—28no—
187C4×Dic6—28no—
188C3×#95C2314yes—
189C3×#95C2312yes—
190C3⋊#95C2314yes—
191C3⋊#95C2314yes—
192C3⋊#95C2314yes—
193C3⋊#95C2312yes—
194C3⋊#95C2314yes—
195C3⋊#95C2314yes—
196C3⋊#95C2314yes—
197C22×#41—32no—
198C23×Q8—31no—
199#532—68no—
200C2×C4⋊Q8—31no—
201C2×#127—31no—
202C2×#124—34no—
203C2×#124—32no—
204C2×#123—32no—
205C2×#123—32no—
206C2×#123—32no—
207C2×#123C2×D312yes—
208C2×#121—32no—
209C2×#121—31no—
210C2×#121C2×D311yescharacteristic
211C2×C4×Q8—32no—
212C2×C4×Q8—32no—
213C2×C4×Q8—32no—
214C2×C4×Q8—32no—
215C2×C4×Q8—68no—
216C2×C4×D4—31no—
217C2×C4×D4—31no—
218C2×C4×D4—32no—
219C22×C4⋊C4—31no—
220C22×C4⋊C4—31no—
221C22×C4⋊C4—31no—
222C22×C42—31no—
223C22×C42—31no—
224C22×C42C2×D311yescharacteristic
225#399—34no—
226#399—34no—
227#395—34no—
228#395—34no—
229#394—34no—
230#394—34no—
231#393—34no—
232#393—34no—
233#391—34no—
234#390—32no—
235#390—32no—
236#390—34no—
237#390—32no—
238#390C2×D312yes—
239#389—32no—
240#389—32no—
241#389—32no—
242#389C2×D312yes—
243#388—34no—
244#388—34no—
245#388—34no—
246#388C2×D314yes—
247#386—32no—
248#386—32no—
249#386—32no—
250#386C2×D312yes—
251#385—34no—
252#385—34no—
253#385—34no—
254#385—34no—
255#384—34no—
256#383—32no—
257#382—32no—
258#381—32no—
259#380—31no—
260#380C2×D311yescharacteristic
261C4×C4⋊C4—32no—
262C4×C22⋊C4—32no—
263#376—32no—
264C24×C3C2412yes—
265C24×C3C2411yescharacteristic
266C23×D3C2412yes—
267C2×C3×D4—24no—
268C2×C3×D4—24no—
269C2×C3×D4—24no—
270C2×C3×D4—22no—
271C2×C3×D4—24no—
272C22×C3×C4—22no—
273C22×C3×C4—24no—
274C22×C3×C4—24no—
275C22×C3×C4—22no—
276C22×C3×C4—22no—
277C22×C3×C4—22no—
278C22×C3×C4C2×D414yes—
279C22×C3×C4C2414yes—
280C22×C3×C4C2412yes—
281C22×C3×C4C2412yes—
282C22×C3×C4C2411yescharacteristic
283C22×C3×C4C2412yes—
284C22×C3×C4C2411yescharacteristic
285C2×#67—24no—
286C2×#67—24no—
287C2×#67—24no—
288C2×#67—24no—
289C2×#67—24no—
290C2×#67—28no—
291C2×#67—42no—
292C2×#67—42no—
293C22×Dic3—22no—
294C22×Dic3—22no—
295C22×Dic3—22no—
296C22×Dic3—24no—
297C22×Dic3—24no—
298C22×Dic3—22no—
299C22×Dic3—22no—
300C22×Dic3—22no—
301C22×Dic3—24no—
302C22×Dic3—42no—
303C22×Dic3—42no—
304C22×Dic3C2×D414yes—
305C22×Dic3C2×D414yes—
306C22×Dic3C2414yes—
307C22×Dic3C2412yes—
308C22×Dic3C2412yes—
309C22×Dic3C2411yescharacteristic
310C22×Dic3C2411yescharacteristic
311C22×Dic3C2411yescharacteristic
312C22×Dic3C2412yes—
313C22×Dic3C2411yescharacteristic
314#237—432no—
315C2×D12—22no—
316C2×D12—24no—
317C2×C4×D3—24no—
318C2×C4×D3—42no—
319C2×C4×D3—42no—
320C2×Dic6—232no—
321C2×Dic6—24no—
322C2×Dic6—24no—
323C2×Dic6—24no—
324C2×Dic6—24no—
325C2×Dic6—24no—
326C2×Dic6—24no—
327C2×Dic6—42no—
328C2×Dic6—42no—
329C2×Dic6#4118yescomplemented
330C3×C4⋊C4—22no—
331C3×C4⋊C4—24no—
332C3×C4⋊C4—44no—
333C3×C22⋊C4—24no—
334C3×C22⋊C4—24no—
335C3×C22⋊C4—28no—
336C3×C22⋊C4—44no—
337C3×C42—24no—
338C3×C42—24no—
339#217—24no—
340#217—24no—
341#217—28no—
342#217—44no—
343(C2×D3)⋊C4—24no—
344(C2×D3)⋊C4—28no—
345(C2×D3)⋊C4—24no—
346(C2×D3)⋊C4—28no—
347(C2×D3)⋊C4—44no—
348(C2×D3)⋊C4—44no—
349C4⋊Dic3—22no—
350C4⋊Dic3—24no—
351C4⋊Dic3—24no—
352C4⋊Dic3—24no—
353C4⋊Dic3—44no—
354Dic3⋊C4—24no—
355Dic3⋊C4—24no—
356Dic3⋊C4—24no—
357Dic3⋊C4—24no—
358Dic3⋊C4—24no—
359Dic3⋊C4—44no—
360Dic3⋊C4—44no—
361C4×Dic3—24no—
362C4×Dic3—24no—
363C4×Dic3—28no—
364C4×Dic3C2×D414yes—
365C4×Dic3C2×D414yes—
366C4×Dic3C2×D414yes—
367C4×Dic3C2×D414yes—
368C2×#41—68no—
369C2×#41—124no—
370C2×#41—124no—
371C22×Q8—32no—
372C22×Q8—32no—
373C22×Q8—32no—
374C22×Q8—64no—
375C22×Q8—68no—
376C22×D4—32no—
377C22×D4—32no—
378C22×D4—32no—
379C22×D4—31no—
380C22×D4C22×D311yescharacteristic
381C22×D4C22×D312yes—
382C23×C4—31no—
383C23×C4—31no—
384C23×C4—31no—
385C23×C4—31no—
386C23×C4—32no—
387C23×C4—32no—
388C23×C4C22×D311yescharacteristic
389C23×C4C22×D311yescharacteristic
390C23×C4C22×D311yescharacteristic
391C4⋊Q8—64no—
392#127—64no—
393#124—68no—
394#124—616no—
395#123—44no—
396#123—124no—
397#123—124no—
398#123—124no—
399#121—24no—
400#121—68no—
401#121—64no—
402C4×Q8—68no—
403C4×Q8—68no—
404C4×Q8—68no—
405C4×Q8—68no—
406C4×D4—68no—
407C4×D4—64no—
408C4×D4—64no—
409C2×C4⋊C4—32no—
410C2×C4⋊C4—32no—
411C2×C4⋊C4—32no—
412C2×C4⋊C4—32no—
413C2×C4⋊C4—32no—
414C2×C4⋊C4—32no—
415C2×C4⋊C4—32no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—32no—
418C2×C4⋊C4—34no—
419C2×C4⋊C4—34no—
420C2×C4⋊C4—34no—
421C2×C4⋊C4—64no—
422C2×C4⋊C4—64no—
423C2×C4⋊C4—64no—
424C2×C4⋊C4C22×D311yescharacteristic
425C2×C4⋊C4C22×D312yes—
426C2×C4⋊C4C22×D314yes—
427C2×C22⋊C4—32no—
428C2×C22⋊C4—32no—
429C2×C22⋊C4—34no—
430C2×C22⋊C4—32no—
431C2×C22⋊C4—32no—
432C2×C22⋊C4—34no—
433C2×C22⋊C4—34no—
434C2×C22⋊C4—34no—
435C2×C22⋊C4—34no—
436C2×C22⋊C4—34no—
437C2×C22⋊C4C22×D312yes—
438C2×C22⋊C4C22×D312yes—
439C2×C22⋊C4C22×D314yes—
440C2×C22⋊C4C22×D314yes—
441C2×C42—24no—
442C2×C42—38no—
443C2×C42—31no—
444C2×C42—31no—
445C2×C42—31no—
446C2×C42—31no—
447C2×C42—32no—
448C2×C42—32no—
449C2×C42—34no—
450C2×C42—64no—
451C2×C42C22×D312yes—
452C2×C42C22×D312yes—
453#95—32no—
454#95—34no—
455#95—34no—
456#95—34no—
457#95—34no—
458#95—34no—
459#95—34no—
460#95C22×D312yes—
461#95C22×D314yes—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—24no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—24no—
469C23×C3C22×D412yes—
470C23×C3H(5,𝔽2)12yes—
471C23×C3H(5,𝔽2)12yes—
472C23×C3C2511yescharacteristic
473C22×D3—22no—
474C22×D3—24no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—24no—
478C3×D4—48no—
479C3×D4—44no—
480C2×C3×C4—28no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—28no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—24no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—24no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—24no—
494C2×C3×C4—44no—
495C2×C3×C4C22×D412yes—
496C2×C3×C4C22×D412yes—
497C2×C3×C4C2×#4114yes—
498C2×C3×C42−1+414yes—
499#67—48no—
500#67—48no—
501#67—48no—
502C2×Dic3—28no—
503C2×Dic3—28no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—28no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514C2×Dic3—24no—
515C2×Dic3—24no—
516C2×Dic3—22no—
517C2×Dic3—22no—
518C2×Dic3—22no—
519C2×Dic3—22no—
520C2×Dic3—24no—
521C2×Dic3—48no—
522C2×Dic3—44no—
523C2×Dic3C22×D412yes—
524C2×Dic3C22×D412yes—
525C2×Dic3C22×D412yes—
526C2×Dic3C22×D412yes—
527C2×Dic3C2×#4114yes—
528C2×Dic3C2×#4114yes—
529D12—44no—
530C4×D3—48no—
531Dic6—216no—
532Dic6—216no—
533Dic6—48no—
534C24—32no—
535C24C23×D312yes—
536C24C23×D311yescharacteristic
537#41—1232no—
538C2×Q8—38no—
539C2×Q8—64no—
540C2×Q8—64no—
541C2×Q8—64no—
542C2×Q8—64no—
543C2×Q8—64no—
544C2×Q8—632no—
545C2×Q8—64no—
546C2×Q8—122no—
547C2×Q8—122no—
548C2×D4—24no—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—22no—
552C2×D4—24no—
553C2×D4—64no—
554C2×D4—64no—
555C2×D4—68no—
556C2×D4—64no—
557C2×D4—64no—
558C2×D4—64no—
559C2×D4—62no—
560C2×D4—64no—
561C2×D4—122no—
562C2×D4—122no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—31no—
570C22×C4—34no—
571C22×C4—34no—
572C22×C4—31no—
573C22×C4—32no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—34no—
577C22×C4—32no—
578C22×C4—32no—
579C22×C4—64no—
580C22×C4—64no—
581C22×C4—64no—
582C22×C4—64no—
583C22×C4—62no—
584C22×C4—62no—
585C22×C4—62no—
586C22×C4—62no—
587C22×C4—62no—
588C22×C4—62no—
589C22×C4—122no—
590C22×C4—122no—
591C22×C4—122no—
592C22×C4—122no—
593C22×C4D3×D414yes—
594C22×C4C23×D314yes—
595C22×C4C23×D312yes—
596C22×C4C23×D312yes—
597C22×C4C23×D311yescharacteristic
598C22×C4C23×D312yes—
599C22×C4C23×D311yescharacteristic
600C4⋊C4—22no—
601C4⋊C4—24no—
602C4⋊C4—44no—
603C4⋊C4—64no—
604C4⋊C4—64no—
605C4⋊C4—64no—
606C4⋊C4—64no—
607C4⋊C4—64no—
608C4⋊C4—64no—
609C4⋊C4—64no—
610C4⋊C4—62no—
611C4⋊C4—64no—
612C4⋊C4—124no—
613C4⋊C4—124no—
614C4⋊C4—124no—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—28no—
618C22⋊C4—44no—
619C22⋊C4—64no—
620C22⋊C4—68no—
621C22⋊C4—64no—
622C22⋊C4—68no—
623C22⋊C4—64no—
624C22⋊C4—64no—
625C22⋊C4—68no—
626C22⋊C4—124no—
627C22⋊C4—124no—
628C22⋊C4—124no—
629C42—24no—
630C42—24no—
631C42—34no—
632C42—34no—
633C42—34no—
634C42—34no—
635C42—68no—
636C42—64no—
637C42—64no—
638C22×C3—22no—
639C22×C3—22no—
640C22×C3—24no—
641C22×C3—24no—
642C22×C3—42no—
643C22×C3—42no—
644C22×C3—42no—
645C22×C3—44no—
646C22×C3—44no—
647C22×C3#53514yes—
648C22×C3C23×D411yescharacteristic
649C22×C3C22×#4112yes—
650C22×C3C2×H(5,𝔽2)11yescharacteristic
651C22×C3C2×H(5,𝔽2)11yescharacteristic
652C22×C3C2×2−1+412yes—
653C2×D3—42no—
654C2×D3—42no—
655C2×D3—42no—
656C2×D3—44no—
657C2×D3—44no—
658C3×C4—24no—
659C3×C4—22no—
660C3×C4—42no—
661C3×C4—42no—
662C3×C4—44no—
663C3×C4#53614yes—
664Dic3—22no—
665Dic3—24no—
666Dic3—22no—
667Dic3—22no—
668Dic3—42no—
669Dic3—42no—
670Dic3—44no—
671Dic3#52514yes—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—24no—
677C23—22no—
678C23—24no—
679C23—62no—
680C23—62no—
681C23—64no—
682C23—62no—
683C23—64no—
684C23C2×D3×D412yes—
685C23#100412yes—
686C23#100912yes—
687C23C24×D311yescharacteristic
688Q8—616no—
689Q8—616no—
690Q8—128no—
691D4—48no—
692D4—44no—
693D4—128no—
694D4—128no—
695D4—128no—
696D4—124no—
697C2×C4—28no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—28no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—32no—
712C2×C4—34no—
713C2×C4—32no—
714C2×C4—32no—
715C2×C4—32no—
716C2×C4—34no—
717C2×C4—44no—
718C2×C4—68no—
719C2×C4—68no—
720C2×C4—62no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—68no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—64no—
733C2×C4—64no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—64no—
737C2×C4—128no—
738C2×C4—128no—
739C2×C4—124no—
740C2×C4C2×D3×D412yes—
741C2×C4C2×D3×D412yes—
742C2×C4D3×#4114yes—
743C2×C4#101014yes—
744C2×C3—24no—
745C2×C3—82no—
746C2×C3C2×#52511yescharacteristic
747C2×C3C2×#53511yescharacteristic
748C2×C3C2×#53611yescharacteristic
749C2×C3#352212yes—
750C2×C3#352212yes—
751D3—82no—
752C22—22no—
753C22—24no—
754C22—24no—
755C22—22no—
756C22—42no—
757C22—44no—
758C22—42no—
759C22—44no—
760C22—42no—
761C22—122no—
762C22—124no—
763C22—122no—
764C22—124no—
765C22—122no—
766C22#560714yes—
767C22C22×D3×D411yescharacteristic
768C22C2×#100411yescharacteristic
769C22C2×D3×#4112yes—
770C22C2×#100911yescharacteristic
771C22C2×#101012yes—
772C4—24no—
773C4—22no—
774C4—34no—
775C4—42no—
776C4—42no—
777C4—44no—
778C4—62no—
779C4—64no—
780C4—62no—
781C4—62no—
782C4—124no—
783C4—122no—
784C4—122no—
785C4#564814yes—
786C3#3524911yescharacteristic, complemented, Sylow
787C2—24no—
788C2—82no—
789C2—242no—
790C2C2×#560711yescharacteristic
791C2C2×#564811yescharacteristic
792C2D3×#52511yescharacteristic
793C2#8612812yes—
794C2#8622912yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2854C2
prime radicalC2×#5596C2
hypercenter#2854D3
hypocenterC3#35249
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2854

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic6C2semidirect
3. C3×#2854C2semidirect
4. #82859C2semidirect
5. #82841C2semidirect
6. #82699C2semidirect
7. #82080C2semidirect
8. #76364C2semidirect
9. #76353C2semidirect
10. #76075C2semidirect
11. #76071C2semidirect
12. #75652C2semidirect
13. #75462C2semidirect
14. #74701C2semidirect
15. #74687C2semidirect
16. #73999C2semidirect
17. #73863C2semidirect
91. #2854D3semidirect
329. C2×Dic6#41semidirect
786. C3#35249semidirect

Maximal subgroups

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

subgroupindex
C2×#55962
C22×C4×Dic62
C3×#28542
#828592
#828412
#826992
#820802
#763642
#763532
#760752
#760712
#756522
#754622
#747012
#746872
#739992
#738632
#352493