Finite Group Databasebeta

← #10974301

Subgroups — #10974301

Order 768.

3006 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#930C211yesmaximal, characteristic
2C2×#5486C211yesmaximal, characteristic, complemented
3C2×C3×#385C211yesmaximal, characteristic, complemented
4C2×#5210C211yesmaximal, characteristic, complemented
5#82195C214yesmaximal, complemented
6#82121C211yesmaximal, characteristic, complemented
7#82121C211yesmaximal, characteristic, complemented
8#82121C211yesmaximal, characteristic, complemented
9#74614C212yesmaximal, complemented
10#74599C212yesmaximal, complemented
11#74456C212yesmaximal, complemented
12#74455C212yesmaximal, complemented
13#74419C214yesmaximal, complemented
14#74418C214yesmaximal, complemented
15#73377C214yesmaximal, complemented
16#35351—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×D12C2211yescharacteristic
21C22×C3×C4⋊C4C2212yescomplemented
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C2×#930—28no—
27C2×#930C2214yes—
28C2×#930C2214yes—
29C2×C4×#67C2212yescomplemented
30C2×C4×#67C2212yescomplemented
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×C4⋊Dic3C2211yescharacteristic
34C22×Dic3⋊C4C2212yescomplemented
35C2×#894C2214yescomplemented
36#5486—28no—
37C2×#67⋊C4C2212yescomplemented
38C2×#67⋊C4C2212yescomplemented
39C2×D3×C22⋊C4C2212yes—
40C2×#877C2212yes—
41C3×#385C2212yes—
42C3×#385C2212yes—
43C3×#385C2214yescomplemented
44C2×C3×#95C2212yescomplemented
45#5213C2212yescomplemented
46#5213C2214yescomplemented
47#5213C2214yescomplemented
48#5213C2212yescomplemented
49#5210C2212yes—
50#5210C2212yes—
51#5210C2214yescomplemented
52C2×C3⋊#95C2212yescomplemented
53#4993C2214yescomplemented
54#4992C2214yescomplemented
55#4991C2214yescomplemented
56#4990C2214yescomplemented
57#4989C2214yescomplemented
58#4982C2214yescomplemented
59#4980C2214yescomplemented
60#4958C2212yescomplemented
61#4958C2214yescomplemented
62#4958C2214yescomplemented
63#4958C2212yescomplemented
64#4955C2212yes—
65#4955C2212yes—
66#4955C2212yes—
67#4943C2212yes—
68#4943C2212yes—
69#4943C2212yes—
70#4675C2214yescomplemented
71#4675C2214yescomplemented
72#4672C2214yescomplemented
73#4669C2214yescomplemented
74#4665C2214yescomplemented
75#4664C2214yescomplemented
76#4660C2214yescomplemented
77#4655C2214yescomplemented
78C22×#121—31no—
79C2×#518—31no—
80#2484—32no—
81#2483—32no—
82#2482—32no—
83#2444—34no—
84#2444—34no—
85#2443—34no—
86#2443—34no—
87#2405—32no—
88#2308—31no—
89#2308—31no—
90#2308—31no—
91C2×#385—31no—
92C2×#385D311yescharacteristic, complemented
93C25×C3C2311yescharacteristic
94C24×D3C2311yescharacteristic
95C24×D3C2311yescharacteristic
96C23×C3×C4—24no—
97C23×C3×C4—44no—
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2312yes—
100C23×C3×C4C2312yes—
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2312yes—
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C22×#67—24no—
106C22×#67—24no—
107C22×#67—24no—
108C22×#67—24no—
109C22×#67—24no—
110C22×#67D418yes—
111C22×#67C2312yes—
112C22×#67C2312yes—
113C22×#67C2312yes—
114C22×#67C2312yes—
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C23×Dic3C2311yescharacteristic
118C23×Dic3C2312yes—
119C23×Dic3C2311yescharacteristic
120C22×D12—24no—
121C22×D12—44no—
122C22×D12C2314yes—
123C22×C4×D3C2312yes—
124C22×C4×D3C2312yes—
125C2×C3×C4⋊C4—44no—
126C2×C3×C4⋊C4C2314yes—
127C2×C3×C4⋊C4C2314yes—
128C2×C3×C22⋊C4—24no—
129C2×C3×C22⋊C4—24no—
130C2×C3×C22⋊C4C2312yes—
131C2×C3×C22⋊C4C2312yes—
132C2×C3×C22⋊C4C2312yes—
133C2×C3×C22⋊C4C2312yes—
134C2×#217—24no—
135C2×#217—24no—
136C2×#217C2312yes—
137C2×#217C2312yes—
138C2×#217C2312yes—
139C2×#217C2312yes—
140#930—216no—
141#930—216no—
142C4×#67—28no—
143C4×#67—28no—
144C2×(C2×D3)⋊C4—24no—
145C2×(C2×D3)⋊C4—24no—
146C2×(C2×D3)⋊C4C2314yes—
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×(C2×D3)⋊C4C2314yes—
154C2×(C2×D3)⋊C4C2314yes—
155C2×(C2×D3)⋊C4C2314yes—
156C2×C4⋊Dic3—24no—
157C2×C4⋊Dic3C2314yes—
158C2×Dic3⋊C4—44no—
159C2×Dic3⋊C4C2314yes—
160C2×Dic3⋊C4C2312yes—
161C2×Dic3⋊C4C2312yes—
162C2×Dic3⋊C4C2314yes—
163C2×C4×Dic3C2312yes—
164C2×C4×Dic3C2312yes—
165#894—48no—
166#67⋊C4—28no—
167#67⋊C4—28no—
168D3×C22⋊C4—28no—
169#877—28no—
170C3×#95C2314yes—
171C3×#95C2314yes—
172C3⋊#95C2314yes—
173C3⋊#95C2314yes—
174C3⋊#95C2314yes—
175C3⋊#95C2314yes—
176C3⋊#95C2314yes—
177C3⋊#95C2314yes—
178C3⋊#95C2314yes—
179C3⋊#95C2314yes—
180C23×D4—31no—
181C23×D4—31no—
182C23×D4—31no—
183C24×C4C2×D311yescharacteristic
184C2×#123—34no—
185C2×#121—34no—
186C2×#121—34no—
187C2×#121—68no—
188#518—68no—
189C2×C4×D4—32no—
190C2×C4×D4—32no—
191C2×C4×D4—32no—
192C2×C4×D4—32no—
193C2×#117—32no—
194C22×C4⋊C4—31no—
195C22×C4⋊C4—32no—
196C22×C4⋊C4C2×D312yescomplemented
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4—31no—
201C22×C22⋊C4—32no—
202C22×C22⋊C4C2×D311yescharacteristic
203C22×C22⋊C4C2×D311yescharacteristic
204#400—34no—
205#399—34no—
206#398—34no—
207#397—34no—
208#397—34no—
209#397—34no—
210#394—34no—
211#394—34no—
212#388—34no—
213#388—34no—
214#387—34no—
215#387—34no—
216#386—32no—
217#386—34no—
218#386—34no—
219#386—32no—
220#386—32no—
221#386—34no—
222#386—34no—
223#386—32no—
224#386—34no—
225#385—32no—
226#385—32no—
227#385—34no—
228#385—34no—
229#385C2×D312yes—
230#385C2×D312yes—
231#385C2×D314yescomplemented
232#381—32no—
233#381—32no—
234#381—32no—
235#381—34no—
236#379—32no—
237#379—32no—
238#379—32no—
239C2×#95—32no—
240C2×#95C2×D312yescomplemented
241C24×C3—42no—
242C24×C3—42no—
243C24×C3C2×D414yes—
244C24×C3#4114yes—
245C24×C3#4114yes—
246C24×C3C2411yescharacteristic
247C24×C3C2411yescharacteristic
248C24×C3C2411yescharacteristic
249C23×D3—22no—
250C23×D3—22no—
251C23×D3—22no—
252C23×D3—22no—
253C23×D3—22no—
254C23×D3—42no—
255C23×D3—42no—
256C23×D3—42no—
257C23×D3—42no—
258C23×D3C2×D414yes—
259C23×D3C2412yes—
260C23×D3C2412yes—
261C22×C3×C4—22no—
262C22×C3×C4—24no—
263C22×C3×C4—22no—
264C22×C3×C4—24no—
265C22×C3×C4—24no—
266C22×C3×C4—24no—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—24no—
270C22×C3×C4—24no—
271C22×C3×C4—42no—
272C22×C3×C4—42no—
273C22×C3×C4—42no—
274C22×C3×C4—42no—
275C22×C3×C4—42no—
276C22×C3×C4—42no—
277C22×C3×C4—42no—
278C22×C3×C4—416no—
279C22×C3×C4C2414yes—
280C22×C3×C4C2412yes—
281C22×C3×C4C2412yes—
282C22×C3×C4C2412yes—
283C22×C3×C4C2412yes—
284C2×#67—232no—
285C2×#67—24no—
286C2×#67—24no—
287C2×#67—24no—
288C2×#67—24no—
289C2×#67—24no—
290C2×#67—24no—
291C2×#67—24no—
292C2×#67—24no—
293C2×#67—24no—
294C2×#67—24no—
295C2×#67—416no—
296C2×#67C2×D418yes—
297C2×#67C2×D418yes—
298C22×Dic3—22no—
299C22×Dic3—22no—
300C22×Dic3—22no—
301C22×Dic3—24no—
302C22×Dic3—22no—
303C22×Dic3—22no—
304C22×Dic3—22no—
305C22×Dic3—22no—
306C22×Dic3—42no—
307C22×Dic3—42no—
308C22×Dic3—42no—
309C22×Dic3—42no—
310C22×Dic3C2×D414yes—
311C22×Dic3C2412yes—
312C22×Dic3C2412yes—
313C22×Dic3C2414yes—
314C22×Dic3C2412yes—
315C22×Dic3C2412yes—
316C2×D12—28no—
317C2×D12—28no—
318C2×D12—44no—
319C2×D12—416no—
320C2×C4×D3—24no—
321C2×C4×D3—24no—
322C2×C4×D3—44no—
323C2×C4×D3—44no—
324C3×C4⋊C4—28no—
325C3×C4⋊C4—44no—
326C3×C22⋊C4—24no—
327C3×C22⋊C4—24no—
328C3×C22⋊C4—24no—
329C3×C22⋊C4—24no—
330#217—24no—
331#217—24no—
332#217—24no—
333#217—24no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—24no—
336(C2×D3)⋊C4—28no—
337(C2×D3)⋊C4—28no—
338(C2×D3)⋊C4—44no—
339(C2×D3)⋊C4—44no—
340(C2×D3)⋊C4—44no—
341(C2×D3)⋊C4—44no—
342(C2×D3)⋊C4—44no—
343(C2×D3)⋊C4—44no—
344C4⋊Dic3—28no—
345Dic3⋊C4—28no—
346Dic3⋊C4—24no—
347Dic3⋊C4—24no—
348Dic3⋊C4—44no—
349C4×Dic3—24no—
350C4×Dic3—24no—
351C25—31no—
352C25—31no—
353C25C22×D311yescharacteristic
354C22×D4—38no—
355C22×D4—32no—
356C22×D4—32no—
357C22×D4—32no—
358C22×D4—32no—
359C22×D4—34no—
360C22×D4—64no—
361C22×D4—64no—
362C22×D4—64no—
363C22×D4—64no—
364C22×D4—64no—
365C22×D4—64no—
366C22×D4—124no—
367C23×C4—24no—
368C23×C4—31no—
369C23×C4—31no—
370C23×C4—31no—
371C23×C4—32no—
372C23×C4—31no—
373C23×C4—32no—
374C23×C4—32no—
375C23×C4—44no—
376C23×C4C22×D311yescharacteristic
377C23×C4C22×D312yes—
378C23×C4C22×D312yes—
379C23×C4C22×D311yescharacteristic
380C23×C4C22×D311yescharacteristic
381C23×C4C22×D312yes—
382C23×C4C22×D311yescharacteristic
383#123—128no—
384#121—616no—
385#121—616no—
386C4×D4—68no—
387C4×D4—68no—
388C4×D4—68no—
389C4×D4—68no—
390#117—68no—
391C2×C4⋊C4—34no—
392C2×C4⋊C4—34no—
393C2×C4⋊C4—32no—
394C2×C4⋊C4—32no—
395C2×C4⋊C4—34no—
396C2×C4⋊C4—44no—
397C2×C4⋊C4—64no—
398C2×C4⋊C4—124no—
399C2×C4⋊C4C22×D314yes—
400C2×C4⋊C4C22×D314yes—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—32no—
404C2×C22⋊C4—32no—
405C2×C22⋊C4—32no—
406C2×C22⋊C4—32no—
407C2×C22⋊C4—32no—
408C2×C22⋊C4—32no—
409C2×C22⋊C4—34no—
410C2×C22⋊C4—34no—
411C2×C22⋊C4—34no—
412C2×C22⋊C4—34no—
413C2×C22⋊C4—34no—
414C2×C22⋊C4—34no—
415C2×C22⋊C4—34no—
416C2×C22⋊C4—34no—
417C2×C22⋊C4—68no—
418C2×C22⋊C4—64no—
419C2×C22⋊C4—64no—
420C2×C22⋊C4—64no—
421C2×C22⋊C4—64no—
422C2×C22⋊C4C22×D312yes—
423C2×C22⋊C4C22×D312yes—
424C2×C22⋊C4C22×D312yes—
425C2×C22⋊C4C22×D312yes—
426C2×C42—32no—
427C2×C42—32no—
428#95—34no—
429#95—34no—
430#95—34no—
431#95—34no—
432#95—34no—
433#95—34no—
434#95—34no—
435#95—34no—
436#95C22×D314yes—
437#95C22×D314yes—
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—44no—
445C23×C3—44no—
446C23×C3—48no—
447C23×C3—48no—
448C23×C3#123116yescomplemented
449C23×C3C22×D412yes—
450C23×C3C22×D412yes—
451C23×C3C22×D412yes—
452C23×C3C2×#4112yes—
453C23×C3C2×#4112yes—
454C23×C3C2×#4112yes—
455C23×C3C2×#4112yes—
456C23×C3C2×#4112yes—
457C23×C3C2×#4112yes—
458C23×C3C2511yescharacteristic
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—24no—
462C22×D3—24no—
463C22×D3—28no—
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—24no—
468C22×D3—24no—
469C22×D3—44no—
470C22×D3—44no—
471C22×D3—44no—
472C22×D3—44no—
473C22×D3—44no—
474C22×D3—84no—
475C22×D3—84no—
476C22×D3—84no—
477C22×D3—84no—
478C22×D3C22×D414yes—
479C2×C3×C4—28no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—24no—
486C2×C3×C4—22no—
487C2×C3×C4—24no—
488C2×C3×C4—24no—
489C2×C3×C4—22no—
490C2×C3×C4—24no—
491C2×C3×C4—24no—
492C2×C3×C4—48no—
493C2×C3×C4—48no—
494C2×C3×C4—48no—
495C2×C3×C4—44no—
496C2×C3×C4—82no—
497C2×C3×C4—82no—
498C2×C3×C4H(5,𝔽2)14yes—
499#67—216no—
500#67—216no—
501#67—48no—
502#67—48no—
503C2×Dic3—28no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—24no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—24no—
513C2×Dic3—24no—
514C2×Dic3—24no—
515C2×Dic3—24no—
516C2×Dic3—48no—
517C2×Dic3—44no—
518C2×Dic3—82no—
519C2×Dic3—82no—
520C2×Dic3C22×D414yes—
521D12—416no—
522C4×D3—84no—
523C4×D3—84no—
524C24—32no—
525C24—34no—
526C24—32no—
527C24—42no—
528C24—42no—
529C24—62no—
530C24—62no—
531C24—62no—
532C24—62no—
533C24—62no—
534C24—122no—
535C24—122no—
536C24—122no—
537C24—122no—
538C24#23514yes—
539C24D3×D414yes—
540C24#23914yes—
541C24C23×D311yescharacteristic
542C24C23×D311yescharacteristic
543C24C23×D311yescharacteristic
544C2×D4—38no—
545C2×D4—38no—
546C2×D4—68no—
547C2×D4—632no—
548C2×D4—64no—
549C2×D4—64no—
550C2×D4—64no—
551C2×D4—64no—
552C2×D4—64no—
553C2×D4—64no—
554C2×D4—64no—
555C2×D4—64no—
556C2×D4—64no—
557C2×D4—64no—
558C2×D4—68no—
559C2×D4—124no—
560C2×D4—1216no—
561C2×D4—1216no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—34no—
573C22×C4—32no—
574C22×C4—32no—
575C22×C4—32no—
576C22×C4—34no—
577C22×C4—32no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—416no—
586C22×C4—64no—
587C22×C4—64no—
588C22×C4—62no—
589C22×C4—62no—
590C22×C4—62no—
591C22×C4—62no—
592C22×C4—64no—
593C22×C4—62no—
594C22×C4—62no—
595C22×C4—62no—
596C22×C4—124no—
597C22×C4—124no—
598C22×C4—122no—
599C22×C4—122no—
600C22×C4—122no—
601C22×C4—122no—
602C22×C4C23×D314yes—
603C22×C4C23×D312yes—
604C22×C4C23×D312yes—
605C22×C4C23×D312yes—
606C22×C4C23×D312yes—
607C4⋊C4—28no—
608C4⋊C4—44no—
609C4⋊C4—68no—
610C4⋊C4—64no—
611C4⋊C4—64no—
612C4⋊C4—68no—
613C4⋊C4—124no—
614C22⋊C4—24no—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—68no—
619C22⋊C4—64no—
620C22⋊C4—64no—
621C22⋊C4—68no—
622C22⋊C4—64no—
623C22⋊C4—64no—
624C22⋊C4—64no—
625C22⋊C4—64no—
626C22⋊C4—124no—
627C22⋊C4—124no—
628C22⋊C4—124no—
629C22⋊C4—124no—
630C22⋊C4—124no—
631C22⋊C4—124no—
632C42—64no—
633C42—64no—
634C22×C3—22no—
635C22×C3—22no—
636C22×C3—22no—
637C22×C3—22no—
638C22×C3—22no—
639C22×C3—22no—
640C22×C3—24no—
641C22×C3—24no—
642C22×C3—24no—
643C22×C3—24no—
644C22×C3—24no—
645C22×C3—24no—
646C22×C3—416no—
647C22×C3C2×#12314yes—
648C22×C3C2×#12314yes—
649C22×C3C2×#12314yes—
650C22×C3C23×D411yescharacteristic
651C22×C3C22×#4111yescharacteristic
652C22×C3C22×#4111yescharacteristic
653C22×C3C2×H(5,𝔽2)12yes—
654C22×C3#58512yes—
655C2×D3—24no—
656C2×D3—24no—
657C2×D3—24no—
658C2×D3—44no—
659C2×D3—44no—
660C2×D3—42no—
661C2×D3—42no—
662C2×D3—42no—
663C2×D3—44no—
664C2×D3—44no—
665C2×D3—88no—
666C2×D3—88no—
667C3×C4—24no—
668C3×C4—42no—
669C3×C4—42no—
670C3×C4—42no—
671C3×C4—44no—
672Dic3—24no—
673Dic3—42no—
674Dic3—42no—
675Dic3—42no—
676Dic3—44no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—34no—
684C23—44no—
685C23—48no—
686C23—44no—
687C23—48no—
688C23—62no—
689C23—64no—
690C23—62no—
691C23—64no—
692C23—68no—
693C23—62no—
694C23—62no—
695C23—64no—
696C23—62no—
697C23—64no—
698C23—124no—
699C23—124no—
700C23—124no—
701C23—124no—
702C23—124no—
703C23—244no—
704C23—244no—
705C23—244no—
706C23—244no—
707C23#894116yescomplemented
708C23C2×#23512yes—
709C23C2×#23512yes—
710C23C2×#23512yes—
711C23C2×D3×D412yes—
712C23C2×D3×D412yes—
713C23C2×D3×D412yes—
714C23C2×#23912yes—
715C23C2×#23912yes—
716C23C2×#23912yes—
717C23C24×D311yescharacteristic
718D4—616no—
719D4—616no—
720D4—1216no—
721D4—128no—
722D4—128no—
723C2×C4—28no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—34no—
737C2×C4—48no—
738C2×C4—48no—
739C2×C4—44no—
740C2×C4—48no—
741C2×C4—62no—
742C2×C4—62no—
743C2×C4—68no—
744C2×C4—62no—
745C2×C4—62no—
746C2×C4—62no—
747C2×C4—62no—
748C2×C4—64no—
749C2×C4—64no—
750C2×C4—64no—
751C2×C4—62no—
752C2×C4—64no—
753C2×C4—64no—
754C2×C4—82no—
755C2×C4—82no—
756C2×C4—128no—
757C2×C4—124no—
758C2×C4—244no—
759C2×C4—244no—
760C2×C4—242no—
761C2×C4—242no—
762C2×C4#100414yes—
763C2×C3—24no—
764C2×C3—24no—
765C2×C3—24no—
766C2×C3C22×#12311yescharacteristic
767C2×C3#348411yescharacteristic
768C2×C3#348511yescharacteristic
769C2×C3#350512yes—
770C2×C3#350512yes—
771D3—44no—
772D3—82no—
773C22—24no—
774C22—24no—
775C22—24no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—24no—
780C22—24no—
781C22—24no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—416no—
786C22—64no—
787C22—64no—
788C22—64no—
789C22—124no—
790C22—124no—
791C22—124no—
792C22—122no—
793C22—122no—
794C22—124no—
795C22—122no—
796C22—248no—
797C22—248no—
798C22C2×#89414yes—
799C22C2×#89414yes—
800C22C2×#89414yes—
801C22C22×#23511yescharacteristic
802C22C22×D3×D411yescharacteristic
803C22C2×#100412yes—
804C22C22×#23911yescharacteristic
805C22#596412yes—
806C4—24no—
807C4—44no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—64no—
812C4—122no—
813C4—122no—
814C4—124no—
815C4—122no—
816C3#3535111yescharacteristic, complemented, Sylow
817C2—24no—
818C2—24no—
819C2—24no—
820C2—124no—
821C2—242no—
822C2C22×#89411yescharacteristic
823C2#8578712yes—
824C2#8591911yescharacteristic
825C2#8597112yes—
826C2#8601211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#385C2
prime radicalC22×#930C2
hypercenterC2×#385D3
hypocenterC3#35351
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×#5486C2semidirect
3. C2×C3×#385C2semidirect
4. C2×#5210C2semidirect
5. #82195C2semidirect
6. #82121C2semidirect
7. #82121C2semidirect
8. #82121C2semidirect
9. #74614C2semidirect
10. #74599C2semidirect
11. #74456C2semidirect
12. #74455C2semidirect
13. #74419C2semidirect
14. #74418C2semidirect
15. #73377C2semidirect
21. C22×C3×C4⋊C4C22semidirect
29. C2×C4×#67C22semidirect
30. C2×C4×#67C22semidirect
34. C22×Dic3⋊C4C22semidirect
35. C2×#894C22semidirect
37. C2×#67⋊C4C22semidirect
38. C2×#67⋊C4C22semidirect
43. C3×#385C22semidirect
44. C2×C3×#95C22semidirect
45. #5213C22semidirect
46. #5213C22semidirect
47. #5213C22semidirect
48. #5213C22semidirect
51. #5210C22semidirect
52. C2×C3⋊#95C22semidirect
53. #4993C22semidirect
54. #4992C22semidirect
55. #4991C22semidirect
56. #4990C22semidirect
57. #4989C22semidirect
58. #4982C22semidirect
59. #4980C22semidirect
60. #4958C22semidirect
61. #4958C22semidirect
62. #4958C22semidirect
63. #4958C22semidirect
70. #4675C22semidirect
71. #4675C22semidirect
72. #4672C22semidirect
73. #4669C22semidirect
74. #4665C22semidirect
75. #4664C22semidirect
76. #4660C22semidirect
77. #4655C22semidirect
92. C2×#385D3semidirect
196. C22×C4⋊C4C2×D3semidirect
231. #385C2×D3semidirect
240. C2×#95C2×D3semidirect
448. C23×C3#123semidirect
707. C23#894semidirect
816. C3#35351semidirect

Maximal subgroups

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

subgroupindex
C22×#9302
C2×#54862
C2×C3×#3852
C2×#52102
#821952
#821212
#746142
#745992
#744562
#744552
#744192
#744182
#733772
#353513