Finite Group Databasebeta

← #10972872

Subgroups — #10972872

Order 768.

2378 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×Q8C211yesmaximal, characteristic, complemented
2C2×#5557C211yesmaximal, characteristic
3C3×#2538C211yesmaximal, characteristic, complemented
4#82751C212yesmaximal, complemented
5#82744C212yesmaximal, complemented
6#82482C211yesmaximal, characteristic, complemented
7#82376C211yesmaximal, characteristic, complemented
8#77415C214yesmaximal, complemented
9#77336C214yesmaximal, complemented
10#76475C212yesmaximal
11#76365C212yesmaximal, complemented
12#76287C212yesmaximal, complemented
13#76078C212yesmaximal, complemented
14#74343C211yesmaximal, characteristic, complemented
15#74318C211yesmaximal, characteristic, complemented
16#73911C212yesmaximal, complemented
17#73871C212yesmaximal, complemented
18#35247—31nomaximal, Sylow
19C22×D3×Q8C2211yescharacteristic
20C2×C3×C22⋊Q8C2212yes—
21C2×C3×C4×Q8C2211yescharacteristic
22C2×C3×C4×D4C2211yescharacteristic
23C2×Q8×Dic3C2211yescharacteristic
24C2×#938C2211yescharacteristic
25C2×#936C2211yescharacteristic
26C2×C4×#67C2212yes—
27C2×#926C2212yes—
28C2×#924C2212yes—
29C4×D3×Q8—28no—
30#5557—28no—
31C2×#897C2211yescharacteristic
32C2×#892C2212yes—
33C2×D3×C4⋊C4C2212yes—
34C2×D3×C4⋊C4C2211yescharacteristic
35C2×#890C2211yescharacteristic
36C2×#887C2212yes—
37C2×#887C2211yescharacteristic
38C2×#883C2212yes—
39C2×#883C2214yes—
40C2×#879C2212yes—
41C2×C42×D3C2212yes—
42C2×C42×D3C2211yescharacteristic
43C2×C4×Dic6C2211yescharacteristic
44C2×C4×Dic6C2212yes—
45C2×C4×Dic6C2211yescharacteristic
46C3×#396C2214yes—
47C3×#390C2212yes—
48C3×#389C2212yes—
49C3×#384C2211yescharacteristic
50C3×#380C2212yes—
51#5229C2212yes—
52#5221C2212yes—
53#5212C2212yes—
54#4989C2214yes—
55#4987C2212yes—
56#4987C2212yes—
57#4984C2214yes—
58#4984C2212yes—
59#4984C2212yes—
60#4982C2214yes—
61#4981C2214yes—
62#4980C2214yes—
63#4979C2214yes—
64#4977C2212yes—
65Dic3×C4⋊C4C2212yes—
66Dic3×C4⋊C4C2212yes—
67#4973C2212yes—
68#4973C2212yes—
69#4972C2212yes—
70#4972C2212yes—
71#4956C2214yes—
72#4952C2214yes—
73#4951C2214yes—
74#4951C2214yes—
75#4948C2214yes—
76#4947C2214yes—
77#4945C2214yes—
78#4944C2214yes—
79#4935C2211yescharacteristic
80#4929C2212yes—
81#4928C2212yes—
82#4664C2214yes—
83#4657C2214yes—
84#4655C2214yes—
85#4647C2214yes—
86C2×#529—31no—
87C22×C4×Q8—31no—
88#2855—32no—
89#2854—32no—
90#2637—34no—
91#2592—32no—
92#2584—32no—
93#2582—31no—
94#2582—31no—
95#2538—31no—
96#2538D311yescharacteristic, complemented
97#2486—32no—
98#2413—34no—
99#2409—32no—
100#2323—32no—
101#2323—32no—
102#2285—31no—
103C22×C3×Q8C2311yescharacteristic
104C22×C3×D4C2311yescharacteristic
105C23×C3×C4C2312yes—
106C22×#67C2312yes—
107C2×D3×Q8—24no—
108C2×D3×Q8—24no—
109C2×D3×Q8—24no—
110C22×C4×D3C2312yes—
111C22×C4×D3C2312yes—
112C22×C4×D3C2311yescharacteristic
113C22×C4×D3C2311yescharacteristic
114C22×C4×D3C2311yescharacteristic
115C22×Dic6C2311yescharacteristic
116C22×Dic6C2312yes—
117C22×Dic6C2311yescharacteristic
118C3×C22⋊Q8—28no—
119C3×C4×Q8—24no—
120C3×C4×D4—24no—
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C4⋊C4C2312yes—
124C2×C3×C4⋊C4C2312yes—
125C2×C3×C4⋊C4C2314yes—
126C2×C3×C4⋊C4C2312yes—
127C2×C3×C4⋊C4C2312yes—
128C2×C3×C22⋊C4C2314yes—
129C2×C3×C22⋊C4C2312yes—
130C2×C3×C22⋊C4C2314yes—
131C2×C3×C42C2312yes—
132C2×C3×C42C2311yescharacteristic
133C2×#217C2312yes—
134C2×#217C2314yes—
135C2×#217C2312yes—
136C2×#217C2312yes—
137C2×#217C2314yes—
138Q8×Dic3—24no—
139#938—24no—
140#936—24no—
141C4×#67—28no—
142C2×(C2×D3)⋊C4C2312yes—
143C2×(C2×D3)⋊C4C2314yes—
144#926—28no—
145C2×C4⋊Dic3C2312yes—
146C2×C4⋊Dic3C2312yes—
147C2×C4⋊Dic3C2311yescharacteristic
148C2×C4⋊Dic3C2312yes—
149C2×C4⋊Dic3C2312yes—
150C2×C4⋊Dic3C2312yes—
151C2×C4⋊Dic3C2311yescharacteristic
152C2×C4⋊Dic3C2314yes—
153C2×C4⋊Dic3C2312yes—
154#924—28no—
155C2×Dic3⋊C4C2312yes—
156C2×Dic3⋊C4C2314yes—
157C2×Dic3⋊C4C2312yes—
158C2×Dic3⋊C4C2312yes—
159C2×Dic3⋊C4C2312yes—
160C2×Dic3⋊C4C2312yes—
161C2×Dic3⋊C4C2314yes—
162C2×C4×Dic3C2312yes—
163C2×C4×Dic3C2312yes—
164C2×C4×Dic3C2312yes—
165C2×C4×Dic3C2312yes—
166C2×C4×Dic3C2314yes—
167C2×C4×Dic3C2311yescharacteristic
168C2×C4×Dic3C2311yescharacteristic
169C2×C4×Dic3C2311yescharacteristic
170#897—24no—
171#892—44no—
172D3×C4⋊C4—28no—
173D3×C4⋊C4—24no—
174#890—24no—
175#887—24no—
176#887—28no—
177#883—28no—
178#883—48no—
179#879—28no—
180C42×D3—28no—
181C42×D3D418yes—
182C4×Dic6—24no—
183C4×Dic6—24no—
184C4×Dic6—28no—
185C3×#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191C3⋊#95C2314yes—
192C3⋊#95C2314yes—
193C3⋊#95C2314yes—
194C3⋊#95C2314yes—
195C23×Q8—31no—
196#529—68no—
197C2×#126—32no—
198C2×#125—31no—
199C2×#124—31no—
200C2×#123—32no—
201C2×#123—34no—
202C2×C22⋊Q8—32no—
203C2×C22⋊Q8—31no—
204C2×C22⋊Q8C2×D312yes—
205C2×#121—31no—
206C2×C4×Q8—31no—
207C2×C4×Q8—31no—
208C2×C4×Q8—32no—
209C2×C4×Q8—31no—
210C2×C4×Q8—31no—
211C2×C4×Q8—32no—
212C2×C4×Q8—68no—
213C2×C4×Q8C2×D311yescharacteristic
214C2×C4×D4—32no—
215C2×C4×D4C2×D311yescharacteristic
216C2×#117—32no—
217C2×#117—32no—
218C22×C4⋊C4—32no—
219C22×C4⋊C4—31no—
220C22×C42—31no—
221C22×C42—32no—
222#398—34no—
223#398—34no—
224#398—34no—
225#397—34no—
226#396—34no—
227#396C2×D314yes—
228#395—34no—
229#393—34no—
230#391—32no—
231#391—32no—
232#391—32no—
233#391—32no—
234#390—32no—
235#390C2×D312yes—
236#389—32no—
237#389—32no—
238#389—34no—
239#389—32no—
240#389—32no—
241#389—32no—
242#389—34no—
243#389C2×D312yes—
244#388—34no—
245#388—34no—
246#388—34no—
247#388—34no—
248#387—34no—
249#387—34no—
250#386—34no—
251#385—34no—
252#384—31no—
253#384C2×D311yescharacteristic
254#382—32no—
255#381—34no—
256#380—32no—
257#380—32no—
258#380—32no—
259#380C2×D312yes—
260C4×C4⋊C4—32no—
261C4×C4⋊C4—32no—
262C24×C3C2412yes—
263C23×D3C2411yescharacteristic
264C2×C3×Q8—22no—
265C2×C3×Q8—22no—
266C2×C3×Q8#4114yes—
267C2×C3×D4—22no—
268C2×C3×D4—22no—
269C2×C3×D4—22no—
270C22×C3×C4—24no—
271C22×C3×C4—24no—
272C22×C3×C4—24no—
273C22×C3×C4C2414yes—
274C22×C3×C4C2412yes—
275C22×C3×C4C2412yes—
276C22×C3×C4C2411yescharacteristic
277C22×C3×C4C2412yes—
278C22×C3×C4C2411yescharacteristic
279C22×C3×C4C2411yescharacteristic
280C2×#67—24no—
281C2×#67—24no—
282C2×#67—24no—
283C22×Dic3C2412yes—
284C22×Dic3C2414yes—
285C22×Dic3C2412yes—
286C22×Dic3C2412yes—
287C22×Dic3C2411yescharacteristic
288C22×Dic3C2411yescharacteristic
289C22×Dic3C2411yescharacteristic
290C22×Dic3C2412yes—
291D3×Q8—232no—
292C2×C4×D3—24no—
293C2×C4×D3—22no—
294C2×C4×D3—22no—
295C2×C4×D3—24no—
296C2×C4×D3—22no—
297C2×C4×D3—22no—
298C2×C4×D3—22no—
299C2×C4×D3—22no—
300C2×C4×D3—24no—
301C2×C4×D3—24no—
302C2×C4×D3—24no—
303C2×C4×D3—24no—
304C2×C4×D3C2×D414yes—
305C2×C4×D3C2×D414yes—
306C2×C4×D3C2×D414yes—
307C2×Dic6—22no—
308C2×Dic6—24no—
309C2×Dic6—22no—
310C2×Dic6—24no—
311C2×Dic6—24no—
312C2×Dic6—22no—
313C2×Dic6—22no—
314C2×Dic6—22no—
315C2×Dic6#4114yes—
316C3×C4⋊C4—24no—
317C3×C4⋊C4—22no—
318C3×C4⋊C4—22no—
319C3×C4⋊C4—24no—
320C3×C4⋊C4—28no—
321C3×C4⋊C4—24no—
322C3×C4⋊C4—42no—
323C3×C22⋊C4—24no—
324C3×C22⋊C4—28no—
325C3×C22⋊C4—44no—
326C3×C42—24no—
327C3×C42C2×D414yes—
328#217—24no—
329#217—24no—
330#217—24no—
331#217—28no—
332#217—44no—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—28no—
335C4⋊Dic3—22no—
336C4⋊Dic3—22no—
337C4⋊Dic3—24no—
338C4⋊Dic3—24no—
339C4⋊Dic3—24no—
340C4⋊Dic3—24no—
341C4⋊Dic3—24no—
342C4⋊Dic3—44no—
343C4⋊Dic3—42no—
344Dic3⋊C4—24no—
345Dic3⋊C4—24no—
346Dic3⋊C4—24no—
347Dic3⋊C4—24no—
348Dic3⋊C4—24no—
349Dic3⋊C4—28no—
350Dic3⋊C4—44no—
351C4×Dic3—24no—
352C4×Dic3—24no—
353C4×Dic3—24no—
354C4×Dic3—24no—
355C4×Dic3—44no—
356C4×Dic3C2×D414yes—
357C4×Dic3C2×D414yes—
358C4×Dic3C2×D414yes—
359C22×Q8—31no—
360C22×Q8—32no—
361C22×Q8—31no—
362C22×Q8—64no—
363C22×Q8—64no—
364C22×Q8—64no—
365C22×Q8C22×D311yescharacteristic
366C22×D4—32no—
367C22×D4C22×D311yescharacteristic
368C23×C4—31no—
369C23×C4—31no—
370C23×C4—31no—
371C23×C4—32no—
372C23×C4—32no—
373C23×C4C22×D312yes—
374#126—68no—
375#125—64no—
376#124—64no—
377#123—68no—
378#123—128no—
379C22⋊Q8—28no—
380C22⋊Q8—64no—
381C22⋊Q8—68no—
382#121—64no—
383C4×Q8—24no—
384C4×Q8—68no—
385C4×Q8—64no—
386C4×Q8—68no—
387C4×Q8—64no—
388C4×Q8—64no—
389C4×Q8—64no—
390C4×D4—24no—
391C4×D4—68no—
392#117—68no—
393#117—124no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—32no—
396C2×C4⋊C4—32no—
397C2×C4⋊C4—32no—
398C2×C4⋊C4—32no—
399C2×C4⋊C4—32no—
400C2×C4⋊C4—32no—
401C2×C4⋊C4—32no—
402C2×C4⋊C4—31no—
403C2×C4⋊C4—32no—
404C2×C4⋊C4—32no—
405C2×C4⋊C4—34no—
406C2×C4⋊C4—32no—
407C2×C4⋊C4—32no—
408C2×C4⋊C4—34no—
409C2×C4⋊C4—34no—
410C2×C4⋊C4—64no—
411C2×C4⋊C4—68no—
412C2×C4⋊C4C22×D311yescharacteristic
413C2×C4⋊C4C22×D312yes—
414C2×C4⋊C4C22×D311yescharacteristic
415C2×C4⋊C4C22×D312yes—
416C2×C4⋊C4C22×D314yes—
417C2×C4⋊C4C22×D312yes—
418C2×C4⋊C4C22×D312yes—
419C2×C22⋊C4—32no—
420C2×C22⋊C4—32no—
421C2×C22⋊C4—32no—
422C2×C22⋊C4—34no—
423C2×C22⋊C4—34no—
424C2×C22⋊C4—32no—
425C2×C22⋊C4—34no—
426C2×C22⋊C4C22×D312yes—
427C2×C22⋊C4C22×D314yes—
428C2×C22⋊C4C22×D314yes—
429C2×C42—31no—
430C2×C42—31no—
431C2×C42—31no—
432C2×C42—38no—
433C2×C42—32no—
434C2×C42—32no—
435C2×C42—32no—
436C2×C42—32no—
437C2×C42—34no—
438C2×C42—68no—
439C2×C42C22×D312yes—
440C2×C42C22×D311yescharacteristic
441#95—34no—
442#95—34no—
443#95—34no—
444#95—34no—
445#95—34no—
446#95—34no—
447#95—34no—
448#95—34no—
449#95—34no—
450#95C22×D314yes—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3C2511yescharacteristic
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—21no—
463C22×D3C22×D412yes—
464C22×D3H(5,𝔽2)12yes—
465C22×D32−1+412yes—
466C3×Q8—28no—
467C3×D4—44no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—24no—
476C2×C3×C4—22no—
477C2×C3×C4—24no—
478C2×C3×C4—22no—
479C2×C3×C4—24no—
480C2×C3×C4—22no—
481C2×C3×C4—48no—
482C2×C3×C4C22×D412yes—
483C2×C3×C4C22×D412yes—
484C2×C3×C4C22×D412yes—
485C2×C3×C4C2×#4114yes—
486C2×C3×C4C2×#4112yes—
487C2×C3×C4C2×#4112yes—
488C2×C3×C42−1+412yes—
489C2×C3×C42−1+412yes—
490#67—48no—
491C2×Dic3—22no—
492C2×Dic3—21no—
493C2×Dic3—22no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—24no—
503C2×Dic3—24no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—24no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3C22×D412yes—
512C2×Dic3C22×D412yes—
513C2×Dic3C22×D412yes—
514C2×Dic3C2×#4114yes—
515C4×D3—216no—
516C4×D3—28no—
517C4×D3—28no—
518C4×D3—28no—
519C4×D3—48no—
520Dic6—216no—
521Dic6—28no—
522Dic6—44no—
523C24—31no—
524C24C23×D312yes—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—34no—
528C2×Q8—64no—
529C2×Q8—64no—
530C2×Q8—632no—
531C2×Q8—62no—
532C2×Q8—62no—
533C2×Q8—64no—
534C2×Q8—62no—
535C2×Q8—62no—
536C2×Q8—62no—
537C2×Q8#23714yes—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—64no—
542C2×D4—64no—
543C2×D4—64no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—32no—
550C22×C4—31no—
551C22×C4—34no—
552C22×C4—34no—
553C22×C4—34no—
554C22×C4—32no—
555C22×C4—34no—
556C22×C4—32no—
557C22×C4—32no—
558C22×C4—64no—
559C22×C4—64no—
560C22×C4—62no—
561C22×C4—62no—
562C22×C4—64no—
563C22×C4—64no—
564C22×C4—64no—
565C22×C4—64no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4C23×D314yes—
571C22×C4C23×D312yes—
572C22×C4C23×D312yes—
573C22×C4C23×D311yescharacteristic
574C22×C4C23×D312yes—
575C22×C4C23×D311yescharacteristic
576C22×C4C23×D311yescharacteristic
577C4⋊C4—24no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—24no—
581C4⋊C4—28no—
582C4⋊C4—24no—
583C4⋊C4—42no—
584C4⋊C4—64no—
585C4⋊C4—64no—
586C4⋊C4—64no—
587C4⋊C4—64no—
588C4⋊C4—64no—
589C4⋊C4—64no—
590C4⋊C4—68no—
591C4⋊C4—64no—
592C4⋊C4—62no—
593C4⋊C4—62no—
594C4⋊C4—64no—
595C4⋊C4—64no—
596C4⋊C4—64no—
597C4⋊C4—122no—
598C4⋊C4—124no—
599C4⋊C4—124no—
600C22⋊C4—24no—
601C22⋊C4—28no—
602C22⋊C4—44no—
603C22⋊C4—68no—
604C22⋊C4—64no—
605C22⋊C4—64no—
606C22⋊C4—64no—
607C22⋊C4—64no—
608C22⋊C4—68no—
609C22⋊C4—124no—
610C42—24no—
611C42—34no—
612C42—34no—
613C42—34no—
614C42—64no—
615C42—64no—
616C42—64no—
617C42—64no—
618C42—124no—
619C42D3×D414yes—
620C22×C3—42no—
621C22×C3—42no—
622C22×C3—42no—
623C22×C3—42no—
624C22×C3—42no—
625C22×C3—42no—
626C22×C3—42no—
627C22×C3C23×D411yescharacteristic
628C22×C3C22×#4111yescharacteristic
629C22×C3C22×#4111yescharacteristic
630C22×C3C2×H(5,𝔽2)11yescharacteristic
631C22×C3C2×2−1+411yescharacteristic
632C22×C3C2×2−1+411yescharacteristic
633C22×C3C2×2−1+411yescharacteristic
634C2×D3—22no—
635C2×D3—22no—
636C2×D3—22no—
637C2×D3—22no—
638C2×D3—22no—
639C2×D3—22no—
640C2×D3#53714yes—
641C3×C4—24no—
642C3×C4—22no—
643C3×C4—42no—
644C3×C4—42no—
645C3×C4—44no—
646C3×C4#52514yes—
647C3×C4#53614yes—
648Dic3—22no—
649Dic3—24no—
650Dic3—22no—
651Dic3—22no—
652Dic3—42no—
653Dic3—42no—
654Dic3—42no—
655Dic3—44no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—32no—
664C23—32no—
665C23—32no—
666C23—61no—
667C23—61no—
668C23—61no—
669C23—61no—
670C23C24×D311yescharacteristic
671Q8—28no—
672Q8—616no—
673Q8—68no—
674Q8—124no—
675D4—44no—
676D4—128no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—32no—
691C2×C4—32no—
692C2×C4—32no—
693C2×C4—34no—
694C2×C4—48no—
695C2×C4—68no—
696C2×C4—616no—
697C2×C4—62no—
698C2×C4—61no—
699C2×C4—62no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—68no—
706C2×C4—68no—
707C2×C4—62no—
708C2×C4—62no—
709C2×C4—62no—
710C2×C4—64no—
711C2×C4—62no—
712C2×C4—64no—
713C2×C4—62no—
714C2×C4—64no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—128no—
720C2×C4C2×D3×D412yes—
721C2×C4C2×D3×D412yes—
722C2×C4C2×D3×D412yes—
723C2×C4C2×#23714yes—
724C2×C4C2×#23712yes—
725C2×C4#100712yes—
726C2×C4D3×#4112yes—
727C2×C4#101012yes—
728C2×C3—82no—
729C2×C3C2×#52511yescharacteristic
730C2×C3C2×#53611yescharacteristic
731C2×C3C2×#53711yescharacteristic
732C2×C3#352211yescharacteristic
733C2×C3#352211yescharacteristic
734C2×C3#352311yescharacteristic
735C2×C3#352311yescharacteristic
736D3—24no—
737C22—34no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—62no—
746C22—62no—
747C22—62no—
748C22—62no—
749C22—62no—
750C22—62no—
751C22C22×D3×D411yescharacteristic
752C22C22×#23711yescharacteristic
753C22C2×#100711yescharacteristic
754C22C2×D3×#4111yescharacteristic
755C22C2×#101011yescharacteristic
756C22D3×H(5,𝔽2)11yescharacteristic
757C22D3×2−1+411yescharacteristic
758C4—22no—
759C4—24no—
760C4—42no—
761C4—42no—
762C4—44no—
763C4—62no—
764C4—62no—
765C4—64no—
766C4—62no—
767C4—122no—
768C4—122no—
769C4—124no—
770C4—122no—
771C4#560614yes—
772C4#562814yes—
773C3#3524711yescharacteristic, complemented, Sylow
774C2—64no—
775C2—82no—
776C2C2×#560611yescharacteristic
777C2C2×#562811yescharacteristic
778C2D3×#53711yescharacteristic
779C2#8675311yescharacteristic
780C2#8677611yescharacteristic
781C2#8693611yescharacteristic
782C2#8699311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2538C2
prime radicalC2×#938C22
hypercenter#2538D3
hypocenterC3#35247
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2538

Complements

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

NH ≅ G/Ntype
1. C2×C4×D3×Q8C2semidirect
3. C3×#2538C2semidirect
4. #82751C2semidirect
5. #82744C2semidirect
6. #82482C2semidirect
7. #82376C2semidirect
8. #77415C2semidirect
9. #77336C2semidirect
11. #76365C2semidirect
12. #76287C2semidirect
13. #76078C2semidirect
14. #74343C2semidirect
15. #74318C2semidirect
16. #73911C2semidirect
17. #73871C2semidirect
96. #2538D3semidirect
773. C3#35247semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×Q82
C2×#55572
C3×#25382
#827512
#827442
#824822
#823762
#774152
#773362
#764752
#763652
#762872
#760782
#743432
#743182
#739112
#738712
#352473