Finite Group Databasebeta

← #10974277

Subgroups — #10974277

Order 768.

2834 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#5486C211yesmaximal, characteristic
3#84068C212yesmaximal, complemented
4C2×#5213C211yesmaximal, characteristic
5C2×#5210C211yesmaximal, characteristic, complemented
6#82816C214yesmaximal, complemented
7#82765C214yesmaximal, complemented
8#82764C214yesmaximal, complemented
9#82762C214yesmaximal, complemented
10#82198C212yesmaximal, complemented
11#82198C212yesmaximal, complemented
12#82197C212yesmaximal, complemented
13#82121C211yesmaximal, characteristic
14#82095C211yesmaximal, characteristic, complemented
15#82094C211yesmaximal, characteristic, complemented
16#35349—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic, complemented
18C24×C3×C4C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C2×C3×C22⋊Q8—28no—
21C2×C3×C22⋊Q8C2214yes—
22C2×C3×C22⋊Q8C2214yescomplemented
23C22×C3×C4⋊C4C2211yescharacteristic, complemented
24C22×C3×C4⋊C4C2211yescharacteristic, complemented
25C22×C3×C4⋊C4C2211yescharacteristic, complemented
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C2×#946C2214yescomplemented
32C2×C4×#67C2212yes—
33C2×C4×#67C2212yes—
34C22×(C2×D3)⋊C4C2212yes—
35C22×Dic3⋊C4C2212yescomplemented
36#5486—28no—
37C2×#67⋊C4C2212yes—
38C2×#67⋊C4C2212yes—
39C2×D3×C22⋊C4C2212yes—
40C2×#877C2212yes—
41#5231C2214yescomplemented
42#5230C2214yescomplemented
43#5229C2214yescomplemented
44#5213C2212yes—
45#5213C2212yes—
46#5213C2212yes—
47#5213C2212yes—
48#5213C2214yes—
49#5212C2212yescomplemented
50#5212C2212yescomplemented
51#5210C2214yes—
52#5210C2212yescomplemented
53#5210C2212yescomplemented
54#5210C2212yescomplemented
55#5210C2212yescomplemented
56C2×C3⋊#95C2212yes—
57C2×C3⋊#95C2212yescomplemented
58#4994C2214yescomplemented
59#4994C2214yescomplemented
60#4993C2214yescomplemented
61#4989C2214yescomplemented
62#4989C2214yescomplemented
63#4987C2214yescomplemented
64#4985C2214yescomplemented
65#4982C2214yescomplemented
66#4982C2214yescomplemented
67#4978C2214yescomplemented
68#4978C2214yescomplemented
69#4972C2214yescomplemented
70#4958C2214yes—
71#4955C2212yes—
72#4950C2214yes—
73#4950C2214yescomplemented
74#4946C2212yescomplemented
75#4946C2212yescomplemented
76#4943C2212yes—
77#4942C2214yes—
78C22×C22⋊Q8D311yescharacteristic, complemented
79C2×#518—31no—
80#2579—32no—
81#2579—32no—
82#2487—32no—
83#2450—34no—
84#2449—34no—
85#2438—34no—
86#2437—34no—
87#2409—32no—
88#2315—31no—
89#2315—31no—
90#2308—31no—
91C2×#386—31no—
92C2×#385—31no—
93C25×C3C2311yescharacteristic
94C24×D3C2311yescharacteristic
95C22×C3×Q8—24no—
96C22×C3×Q8—44no—
97C22×C3×Q8C2314yes—
98C23×C3×C4—24no—
99C23×C3×C4—44no—
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2312yes—
102C23×C3×C4C2312yes—
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C22×#67—24no—
109C22×#67—24no—
110C22×#67Q818yescomplemented
111C22×#67C2312yes—
112C22×#67C2312yes—
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2312yes—
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C23×Dic3C2312yes—
118C22×C4×D3C2312yes—
119C22×C4×D3C2312yes—
120C3×C22⋊Q8—216no—
121C3×C22⋊Q8—216no—
122C2×C3×C4⋊C4—24no—
123C2×C3×C4⋊C4—24no—
124C2×C3×C4⋊C4—24no—
125C2×C3×C4⋊C4C2314yes—
126C2×C3×C4⋊C4C2314yes—
127C2×C3×C4⋊C4C2314yes—
128C2×C3×C22⋊C4—24no—
129C2×C3×C22⋊C4D418yes—
130C2×C3×C22⋊C4C2312yes—
131C2×C3×C22⋊C4C2312yes—
132C2×C3×C22⋊C4C2312yes—
133C2×C3×C22⋊C4C2312yes—
134C2×#217—24no—
135C2×#217—24no—
136C2×#217—24no—
137C2×#217C2312yes—
138C2×#217C2312yes—
139C2×#217C2312yes—
140C2×#217C2312yes—
141C2×#217C2312yes—
142C2×#217C2312yes—
143#946—48no—
144C4×#67—28no—
145C4×#67—28no—
146C2×(C2×D3)⋊C4—44no—
147C2×(C2×D3)⋊C4C2314yes—
148C2×(C2×D3)⋊C4C2312yes—
149C2×(C2×D3)⋊C4C2312yes—
150C2×(C2×D3)⋊C4C2314yes—
151C2×(C2×D3)⋊C4C2314yes—
152C2×(C2×D3)⋊C4C2314yes—
153C2×C4⋊Dic3C2314yes—
154C2×C4⋊Dic3C2314yes—
155C2×Dic3⋊C4—44no—
156C2×Dic3⋊C4C2314yes—
157C2×Dic3⋊C4C2312yes—
158C2×Dic3⋊C4C2312yes—
159C2×Dic3⋊C4C2314yes—
160C2×Dic3⋊C4C2314yes—
161C2×Dic3⋊C4C2314yes—
162C2×C4×Dic3C2312yes—
163C2×C4×Dic3C2312yes—
164#67⋊C4—28no—
165#67⋊C4—28no—
166D3×C22⋊C4—28no—
167#877—28no—
168C3⋊#95C2314yes—
169C3⋊#95C2314yes—
170C3⋊#95C2314yes—
171C3⋊#95C2314yes—
172C3⋊#95C2314yes—
173C3⋊#95C2314yes—
174C3⋊#95C2314yes—
175C3⋊#95C2314yes—
176C3⋊#95C2314yes—
177C3⋊#95C2314yes—
178C23×Q8C2×D311yescharacteristic, complemented
179C23×D4—31no—
180C24×C4C2×D311yescharacteristic
181C2×C22⋊Q8—28no—
182C2×C22⋊Q8—34no—
183C2×C22⋊Q8C2×D314yes—
184C2×C22⋊Q8C2×D314yescomplemented
185#518—68no—
186C2×C4×D4—32no—
187C2×C4×D4—32no—
188C2×C4×D4—32no—
189C2×C4×D4—32no—
190C2×#117—32no—
191C22×C4⋊C4—32no—
192C22×C4⋊C4C2×D311yescharacteristic, complemented
193C22×C4⋊C4C2×D311yescharacteristic, complemented
194C22×C4⋊C4C2×D311yescharacteristic, complemented
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—32no—
199C22×C22⋊C4—32no—
200C22×C22⋊C4C2×D311yescharacteristic
201C22×C22⋊C4C2×D311yescharacteristic
202#400—34no—
203#399—34no—
204#398—34no—
205#398—34no—
206#396—34no—
207#396—34no—
208#395—34no—
209#393—34no—
210#391—34no—
211#389—34no—
212#387—34no—
213#387—34no—
214#386—32no—
215#386—32no—
216#386—32no—
217#386—32no—
218#386—34no—
219#386—34no—
220#385—32no—
221#385—32no—
222#385—32no—
223#385—32no—
224#385—34no—
225#385—34no—
226#385—34no—
227#385—32no—
228#385—32no—
229#385—34no—
230#385—34no—
231#381—32no—
232#380—32no—
233#380—32no—
234#380—34no—
235#380—34no—
236#379—32no—
237C2×#95—32no—
238C2×#95—32no—
239C24×C3—42no—
240C24×C3—42no—
241C24×C3C2×D414yes—
242C24×C3C2×Q814yes—
243C24×C3#4114yes—
244C24×C3C2411yescharacteristic
245C24×C3C2411yescharacteristic
246C24×C3C2411yescharacteristic
247C23×D3—22no—
248C23×D3—22no—
249C23×D3—42no—
250C23×D3—42no—
251C23×D3C2×Q814yescomplemented
252C23×D3C2412yes—
253C2×C3×Q8—28no—
254C2×C3×Q8—28no—
255C2×C3×Q8—44no—
256C2×C3×Q8—416no—
257C22×C3×C4—22no—
258C22×C3×C4—24no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—24no—
263C22×C3×C4—24no—
264C22×C3×C4—24no—
265C22×C3×C4—24no—
266C22×C3×C4—42no—
267C22×C3×C4—42no—
268C22×C3×C4—42no—
269C22×C3×C4—42no—
270C22×C3×C4—42no—
271C22×C3×C4—42no—
272C22×C3×C4—42no—
273C22×C3×C4—416no—
274C22×C3×C4C2×D414yes—
275C22×C3×C4C2×D414yes—
276C22×C3×C4C2412yes—
277C22×C3×C4C2412yes—
278C22×C3×C4C2412yes—
279C22×C3×C4C2412yes—
280C22×C3×C4C2412yes—
281C22×C3×C4C2412yes—
282C2×#67—232no—
283C2×#67—24no—
284C2×#67—24no—
285C2×#67—24no—
286C2×#67—24no—
287C2×#67C2×Q818yes—
288C2×#67C2×Q818yescomplemented
289C22×Dic3—22no—
290C22×Dic3—22no—
291C22×Dic3—24no—
292C22×Dic3—22no—
293C22×Dic3—22no—
294C22×Dic3—24no—
295C22×Dic3—42no—
296C22×Dic3—42no—
297C22×Dic3—42no—
298C22×Dic3—42no—
299C22×Dic3—42no—
300C22×Dic3—42no—
301C22×Dic3C2×Q814yescomplemented
302C22×Dic3C2412yes—
303C22×Dic3C2414yes—
304C22×Dic3C2414yes—
305C22×Dic3C2412yes—
306C22×Dic3C2412yes—
307C2×C4×D3—24no—
308C2×C4×D3—24no—
309C2×C4×D3—44no—
310C2×C4×D3—44no—
311C3×C4⋊C4—28no—
312C3×C4⋊C4—28no—
313C3×C4⋊C4—28no—
314C3×C22⋊C4—24no—
315C3×C22⋊C4—24no—
316C3×C22⋊C4C2×D418yes—
317C3×C22⋊C4C2×D418yes—
318#217—24no—
319#217—24no—
320#217—24no—
321#217—24no—
322#217—24no—
323#217—24no—
324(C2×D3)⋊C4—24no—
325(C2×D3)⋊C4—24no—
326(C2×D3)⋊C4—28no—
327(C2×D3)⋊C4—44no—
328(C2×D3)⋊C4—44no—
329(C2×D3)⋊C4—44no—
330C4⋊Dic3—44no—
331C4⋊Dic3—44no—
332Dic3⋊C4—24no—
333Dic3⋊C4—24no—
334Dic3⋊C4—28no—
335Dic3⋊C4—44no—
336Dic3⋊C4—44no—
337Dic3⋊C4—44no—
338C4×Dic3—24no—
339C4×Dic3—24no—
340C25—31no—
341C25C22×D311yescharacteristic
342C22×Q8—24no—
343C22×Q8—44no—
344C22×Q8C22×D314yes—
345C22×D4—38no—
346C22×D4—32no—
347C22×D4—32no—
348C22×D4—64no—
349C22×D4—64no—
350C23×C4—24no—
351C23×C4—31no—
352C23×C4—32no—
353C23×C4—31no—
354C23×C4—32no—
355C23×C4—31no—
356C23×C4—32no—
357C23×C4—32no—
358C23×C4—44no—
359C23×C4C22×D311yescharacteristic
360C23×C4C22×D312yes—
361C23×C4C22×D312yes—
362C23×C4C22×D311yescharacteristic
363C23×C4C22×D311yescharacteristic
364C23×C4C22×D311yescharacteristic
365C23×C4C22×D311yescharacteristic
366C23×C4C22×D311yescharacteristic
367C22⋊Q8—216no—
368C22⋊Q8—216no—
369C22⋊Q8—128no—
370C4×D4—68no—
371C4×D4—68no—
372C4×D4—68no—
373C4×D4—68no—
374#117—68no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—34no—
379C2×C4⋊C4—32no—
380C2×C4⋊C4—32no—
381C2×C4⋊C4—34no—
382C2×C4⋊C4—34no—
383C2×C4⋊C4—34no—
384C2×C4⋊C4—34no—
385C2×C4⋊C4—34no—
386C2×C4⋊C4—124no—
387C2×C4⋊C4C22×D314yes—
388C2×C4⋊C4C22×D314yes—
389C2×C4⋊C4C22×D314yes—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—32no—
392C2×C22⋊C4—32no—
393C2×C22⋊C4—32no—
394C2×C22⋊C4—32no—
395C2×C22⋊C4—32no—
396C2×C22⋊C4—32no—
397C2×C22⋊C4—32no—
398C2×C22⋊C4—32no—
399C2×C22⋊C4—34no—
400C2×C22⋊C4—34no—
401C2×C22⋊C4—34no—
402C2×C22⋊C4—34no—
403C2×C22⋊C4—64no—
404C2×C22⋊C4—64no—
405C2×C22⋊C4—64no—
406C2×C22⋊C4—68no—
407C2×C22⋊C4—124no—
408C2×C22⋊C4#6718yes—
409C2×C22⋊C4C22×D312yes—
410C2×C22⋊C4C22×D312yes—
411C2×C22⋊C4C22×D312yes—
412C2×C22⋊C4C22×D312yes—
413C2×C42—32no—
414C2×C42—32no—
415#95—34no—
416#95—34no—
417#95—34no—
418#95—34no—
419#95—34no—
420#95—34no—
421#95—34no—
422#95—34no—
423#95—34no—
424#95—34no—
425C23×C3—22no—
426C23×C3—22no—
427C23×C3—22no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—44no—
432C23×C3—44no—
433C23×C3—48no—
434C23×C3—48no—
435C23×C3C22⋊Q8116yescomplemented
436C23×C3C22×D412yes—
437C23×C3C22×D412yes—
438C23×C3C22×D412yes—
439C23×C3C22×Q812yes—
440C23×C3C22×Q812yes—
441C23×C3C22×Q812yes—
442C23×C3C2×#4112yes—
443C23×C3C2×#4112yes—
444C23×C3C2×#4112yes—
445C23×C3C2511yescharacteristic
446C22×D3—22no—
447C22×D3—22no—
448C22×D3—24no—
449C22×D3—24no—
450C22×D3—28no—
451C22×D3—48no—
452C22×D3—82no—
453C22×D3—82no—
454C22×D3—84no—
455C22×D3C22×Q814yes—
456C3×Q8—416no—
457C2×C3×C4—28no—
458C2×C3×C4—22no—
459C2×C3×C4—24no—
460C2×C3×C4—22no—
461C2×C3×C4—24no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—24no—
467C2×C3×C4—22no—
468C2×C3×C4—24no—
469C2×C3×C4—44no—
470C2×C3×C4—44no—
471C2×C3×C4—48no—
472C2×C3×C4—48no—
473C2×C3×C4—44no—
474C2×C3×C4—44no—
475C2×C3×C4—44no—
476C2×C3×C4C22×D414yes—
477C2×C3×C4C22×D414yes—
478C2×C3×C4H(5,𝔽2)14yes—
479#67—216no—
480#67—216no—
481C2×Dic3—28no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—24no—
487C2×Dic3—24no—
488C2×Dic3—24no—
489C2×Dic3—24no—
490C2×Dic3—24no—
491C2×Dic3—24no—
492C2×Dic3—24no—
493C2×Dic3—24no—
494C2×Dic3—48no—
495C2×Dic3—82no—
496C2×Dic3—82no—
497C2×Dic3—84no—
498C2×Dic3C22×Q814yes—
499C4×D3—84no—
500C4×D3—84no—
501C24—32no—
502C24—34no—
503C24—42no—
504C24—42no—
505C24—62no—
506C24—62no—
507C24—122no—
508C24—122no—
509C24D3×Q814yes—
510C24#23914yes—
511C24C2×#6714yes—
512C24C23×D311yescharacteristic
513C24C23×D311yescharacteristic
514C24C23×D311yescharacteristic
515C2×Q8—28no—
516C2×Q8—28no—
517C2×Q8—44no—
518C2×Q8—416no—
519C2×D4—38no—
520C2×D4—38no—
521C2×D4—632no—
522C2×D4—64no—
523C2×D4—64no—
524C2×D4—64no—
525C2×D4—64no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—34no—
536C22×C4—32no—
537C22×C4—32no—
538C22×C4—34no—
539C22×C4—34no—
540C22×C4—32no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—416no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—64no—
552C22×C4—64no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—64no—
556C22×C4—64no—
557C22×C4—124no—
558C22×C4—124no—
559C22×C4—122no—
560C22×C4—122no—
561C22×C4—122no—
562C22×C4—122no—
563C22×C4—122no—
564C22×C4—122no—
565C22×C4C2×#6714yes—
566C22×C4C2×#6714yes—
567C22×C4C23×D312yes—
568C22×C4C23×D312yes—
569C22×C4C23×D312yes—
570C22×C4C23×D312yes—
571C22×C4C23×D312yes—
572C22×C4C23×D312yes—
573C4⋊C4—28no—
574C4⋊C4—28no—
575C4⋊C4—28no—
576C4⋊C4—68no—
577C4⋊C4—64no—
578C4⋊C4—64no—
579C4⋊C4—124no—
580C4⋊C4—124no—
581C4⋊C4—124no—
582C4⋊C4—124no—
583C4⋊C4—124no—
584C22⋊C4—24no—
585C22⋊C4—24no—
586C22⋊C4—64no—
587C22⋊C4—64no—
588C22⋊C4—64no—
589C22⋊C4—64no—
590C22⋊C4—64no—
591C22⋊C4—64no—
592C22⋊C4—68no—
593C22⋊C4—64no—
594C22⋊C4—64no—
595C22⋊C4—124no—
596C22⋊C4—124no—
597C22⋊C4—124no—
598C22⋊C4C2×#6718yes—
599C22⋊C4C2×#6718yes—
600C42—64no—
601C42—64no—
602C22×C3—22no—
603C22×C3—22no—
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—22no—
608C22×C3—24no—
609C22×C3—24no—
610C22×C3—24no—
611C22×C3—24no—
612C22×C3—24no—
613C22×C3—24no—
614C22×C3—416no—
615C22×C3C2×C22⋊Q814yes—
616C22×C3C2×C22⋊Q814yes—
617C22×C3C2×C22⋊Q814yes—
618C22×C3C23×D411yescharacteristic
619C22×C3C23×Q811yescharacteristic
620C22×C3C22×#4111yescharacteristic
621C22×C3C2×H(5,𝔽2)12yes—
622C22×C3#58512yes—
623C2×D3—24no—
624C2×D3—28no—
625C2×D3—42no—
626C2×D3—42no—
627C2×D3—44no—
628C2×D3—88no—
629C3×C4—24no—
630C3×C4—24no—
631C3×C4—24no—
632C3×C4—42no—
633C3×C4—42no—
634C3×C4—42no—
635Dic3—24no—
636Dic3—42no—
637Dic3—42no—
638Dic3—44no—
639Dic3—44no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—34no—
647C23—44no—
648C23—48no—
649C23—48no—
650C23—44no—
651C23—64no—
652C23—62no—
653C23—64no—
654C23—62no—
655C23—68no—
656C23—128no—
657C23—242no—
658C23—244no—
659C23—242no—
660C23#946116yescomplemented
661C23C2×D3×Q812yes—
662C23C2×D3×Q812yes—
663C23C2×D3×Q812yes—
664C23C2×#23912yes—
665C23C2×#23912yes—
666C23C2×#23912yes—
667C23C22×#6712yes—
668C23C22×#6712yes—
669C23C22×#6712yes—
670C23C24×D311yescharacteristic
671Q8—416no—
672D4—616no—
673D4—616no—
674C2×C4—28no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—34no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—48no—
690C2×C4—48no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—68no—
697C2×C4—64no—
698C2×C4—64no—
699C2×C4—64no—
700C2×C4—64no—
701C2×C4—64no—
702C2×C4—64no—
703C2×C4—64no—
704C2×C4—64no—
705C2×C4—62no—
706C2×C4—62no—
707C2×C4—128no—
708C2×C4—244no—
709C2×C4—244no—
710C2×C4—242no—
711C2×C4—244no—
712C2×C4—242no—
713C2×C4#100414yes—
714C2×C4C22×#6714yes—
715C2×C4C22×#6714yes—
716C2×C3—24no—
717C2×C3—24no—
718C2×C3—24no—
719C2×C3C22×C22⋊Q811yescharacteristic
720C2×C3#348411yescharacteristic
721C2×C3#348511yescharacteristic
722C2×C3#350112yes—
723C2×C3#350512yes—
724D3—44no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—24no—
729C22—24no—
730C22—24no—
731C22—24no—
732C22—24no—
733C22—24no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—416no—
738C22—64no—
739C22—68no—
740C22—122no—
741C22—124no—
742C22—122no—
743C22—248no—
744C22C2×#94614yes—
745C22C2×#94614yes—
746C22C2×#94614yes—
747C22C2×#100412yes—
748C22C22×D3×Q811yescharacteristic
749C22C22×#23911yescharacteristic
750C22#596412yes—
751C22C23×#6711yescharacteristic
752C4—24no—
753C4—24no—
754C4—24no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—64no—
759C4—122no—
760C4—124no—
761C4—124no—
762C4—122no—
763C3#3534911yescharacteristic, complemented, Sylow
764C2—24no—
765C2—24no—
766C2—24no—
767C2—124no—
768C2#8597112yes—
769C2#8598612yes—
770C2#8723911yescharacteristic
771C2C22×#94611yescharacteristic
772C2#8727311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC22×C3×C22⋊Q8C2
prime radicalC23×#67C22
hypercenterC22×C22⋊Q8D3
hypocenterC3#35349
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×C22⋊Q8C2semidirect
3. #84068C2semidirect
5. C2×#5210C2semidirect
6. #82816C2semidirect
7. #82765C2semidirect
8. #82764C2semidirect
9. #82762C2semidirect
10. #82198C2semidirect
11. #82198C2semidirect
12. #82197C2semidirect
14. #82095C2semidirect
15. #82094C2semidirect
17. C23×C3×Q8C22semidirect
22. C2×C3×C22⋊Q8C22semidirect
23. C22×C3×C4⋊C4C22semidirect
24. C22×C3×C4⋊C4C22semidirect
25. C22×C3×C4⋊C4C22semidirect
31. C2×#946C22semidirect
35. C22×Dic3⋊C4C22semidirect
41. #5231C22semidirect
42. #5230C22semidirect
43. #5229C22semidirect
49. #5212C22semidirect
50. #5212C22semidirect
52. #5210C22semidirect
53. #5210C22semidirect
54. #5210C22semidirect
55. #5210C22semidirect
57. C2×C3⋊#95C22semidirect
58. #4994C22semidirect
59. #4994C22semidirect
60. #4993C22semidirect
61. #4989C22semidirect
62. #4989C22semidirect
63. #4987C22semidirect
64. #4985C22semidirect
65. #4982C22semidirect
66. #4982C22semidirect
67. #4978C22semidirect
68. #4978C22semidirect
69. #4972C22semidirect
73. #4950C22semidirect
74. #4946C22semidirect
75. #4946C22semidirect
78. C22×C22⋊Q8D3semidirect
110. C22×#67Q8semidirect
178. C23×Q8C2×D3semidirect
184. C2×C22⋊Q8C2×D3semidirect
192. C22×C4⋊C4C2×D3semidirect
193. C22×C4⋊C4C2×D3semidirect
194. C22×C4⋊C4C2×D3semidirect
251. C23×D3C2×Q8semidirect
288. C2×#67C2×Q8semidirect
301. C22×Dic3C2×Q8semidirect
435. C23×C3C22⋊Q8semidirect
660. C23#946semidirect
763. C3#35349semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊Q82
C2×#54862
#840682
C2×#52132
C2×#52102
#828162
#827652
#827642
#827622
#821982
#821972
#821212
#820952
#820942
#353493