Finite Group Databasebeta

← #10967752

Subgroups — #10967752

Order 768.

3038 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
1C2×#5804C211yesmaximal, characteristic
2C22×#67⋊C4C211yesmaximal, characteristic, complemented
3C3×#2308C211yesmaximal, characteristic, complemented
4C2×#5220C211yesmaximal, characteristic, complemented
5#82121C211yesmaximal, characteristic, complemented
6#82095C211yesmaximal, characteristic, complemented
7C2×#4950C211yesmaximal, characteristic, complemented
8#74936C212yesmaximal, complemented
9#74906C212yesmaximal, complemented
10#74871C212yesmaximal, complemented
11#74782C212yesmaximal, complemented
12#74707C214yesmaximal, complemented
13#74704C214yesmaximal, complemented
14#74065C214yesmaximal, complemented
15#73826C214yesmaximal, complemented
16#34983—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C24×Dic3C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic, complemented
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C2×#953C2212yes—
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2212yescomplemented
27#5804—28no—
28C2×#939C2212yes—
29C2×#939C2212yes—
30C2×#937C2212yes—
31C2×#935C2212yes—
32C2×#929C2212yes—
33C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
34C22×C4⋊Dic3C2212yescomplemented
35C22×Dic3⋊C4C2211yescharacteristic, complemented
36C22×C4×Dic3C2211yescharacteristic, complemented
37C2×#883C2214yescomplemented
38C2×#67⋊C4—28no—
39C2×#67⋊C4C2214yes—
40C2×#67⋊C4C2214yescomplemented
41C3×#386C2212yes—
42C3×#386C2212yes—
43C3×#386C2214yescomplemented
44C3×#381C2212yescomplemented
45C3×#379C2212yescomplemented
46#5220C2212yes—
47#5220C2212yes—
48#5220C2214yescomplemented
49#5213C2214yescomplemented
50#5210C2212yescomplemented
51#5210C2212yescomplemented
52C2×C3⋊#95C2212yescomplemented
53C2×C3⋊#95C2212yescomplemented
54#4961C2214yescomplemented
55#4959C2214yescomplemented
56#4958C2214yes—
57#4956C2214yescomplemented
58#4955C2212yescomplemented
59#4952C2214yescomplemented
60#4951C2214yescomplemented
61#4950C2212yescomplemented
62#4950C2214yescomplemented
63#4950C2212yescomplemented
64#4949C2214yescomplemented
65#4946C2212yescomplemented
66#4946C2212yescomplemented
67#4945C2214yescomplemented
68#4943C2212yescomplemented
69#4942C2214yescomplemented
70#4675C2214yescomplemented
71#4674C2214yescomplemented
72#4668C2214yescomplemented
73#4664C2214yescomplemented
74#4658C2214yescomplemented
75#4657C2214yescomplemented
76#4654C2214yescomplemented
77#4652C2214yescomplemented
78C2×#534—31no—
79C22×C4×D4—31no—
80#2853—32no—
81#2849—32no—
82#2623—32no—
83#2622—32no—
84#2444—34no—
85#2443—34no—
86#2419—34no—
87#2418—34no—
88#2315—31no—
89#2308—31no—
90#2308D311yescharacteristic, complemented
91C2×#386—31no—
92C2×#385—31no—
93C25×C3C2311yescharacteristic
94C25×C3C2311yescharacteristic
95C24×D3C2311yescharacteristic
96C22×C3×D4—24no—
97C22×C3×D4—24no—
98C22×C3×D4—24no—
99C22×C3×D4C2312yes—
100C22×C3×D4C2312yes—
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2311yescharacteristic
103C23×C3×C4C2312yes—
104C23×C3×C4C2311yescharacteristic
105C22×#67—24no—
106C22×#67—24no—
107C22×#67D418yes—
108C22×#67C2312yes—
109C22×#67C2312yes—
110C22×#67C2312yes—
111C22×#67C2312yes—
112C23×Dic3—24no—
113C23×Dic3—44no—
114C23×Dic3C2311yescharacteristic
115C23×Dic3C2312yes—
116C23×Dic3C2312yes—
117C23×Dic3C2311yescharacteristic
118C23×Dic3C2312yes—
119C23×Dic3C2311yescharacteristic
120C23×Dic3C2311yescharacteristic
121C23×Dic3C2311yescharacteristic
122C22×C4×D3—24no—
123C22×C4×D3—44no—
124C22×C4×D3C2314yes—
125C2×C3×C22⋊C4—24no—
126C2×C3×C22⋊C4—24no—
127C2×C3×C22⋊C4C2312yes—
128C2×C3×C22⋊C4C2312yes—
129C2×C3×C22⋊C4C2312yes—
130C2×C3×C22⋊C4C2312yes—
131C2×C3×C22⋊C4C2314yes—
132C2×C3×C22⋊C4C2314yes—
133#953—28no—
134C2×#217—24no—
135C2×#217—24no—
136C2×#217—44no—
137C2×#217C2312yes—
138C2×#217C2312yes—
139C2×#217C2312yes—
140C2×#217C2314yes—
141C2×#217C2312yes—
142C2×#217C2312yes—
143C2×#217C2312yes—
144C2×#217C2314yes—
145#939—28no—
146#939—28no—
147#937—28no—
148#935—28no—
149#929—28no—
150C2×(C2×D3)⋊C4—24no—
151C2×(C2×D3)⋊C4C2312yes—
152C2×(C2×D3)⋊C4C2312yes—
153C2×(C2×D3)⋊C4C2314yes—
154C2×(C2×D3)⋊C4C2314yes—
155C2×(C2×D3)⋊C4C2314yes—
156C2×C4⋊Dic3—44no—
157C2×C4⋊Dic3C2314yes—
158C2×C4⋊Dic3C2314yes—
159C2×Dic3⋊C4—24no—
160C2×Dic3⋊C4C2312yes—
161C2×Dic3⋊C4C2312yes—
162C2×Dic3⋊C4C2314yes—
163C2×Dic3⋊C4C2314yes—
164C2×Dic3⋊C4C2314yes—
165C2×C4×Dic3—24no—
166C2×C4×Dic3C2314yes—
167#883—48no—
168#67⋊C4—216no—
169#67⋊C4—216no—
170C3×#95C2314yes—
171C3×#95C2314yes—
172C3⋊#95C2314yes—
173C3⋊#95C2314yes—
174C3⋊#95C2314yes—
175C3⋊#95C2314yes—
176C3⋊#95C2314yes—
177C3⋊#95C2314yes—
178C3⋊#95C2314yes—
179C3⋊#95C2314yes—
180C23×D4—31no—
181C23×D4C2×D311yescharacteristic
182C24×C4—31no—
183C24×C4—31no—
184#534—68no—
185C2×#123—32no—
186C2×#123—32no—
187C2×#123—34no—
188C2×#121—32no—
189C2×#121—32no—
190C2×#120—32no—
191C2×#120—32no—
192C2×C4×D4—34no—
193C2×C4×D4—34no—
194C2×C4×D4—68no—
195C22×C4⋊C4—31no—
196C22×C4⋊C4—32no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4—32no—
201C22×C22⋊C4C2×D311yescharacteristic
202C22×C22⋊C4C2×D311yescharacteristic
203C22×C42—31no—
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—32no—
218#386—34no—
219#386—34no—
220#386—34no—
221#386—34no—
222#386C2×D312yes—
223#386C2×D312yes—
224#386C2×D314yescomplemented
225#385—32no—
226#385—32no—
227#385—32no—
228#385—32no—
229#385—32no—
230#385—32no—
231#385—34no—
232#385—34no—
233#381—32no—
234#381—34no—
235#381C2×D312yescomplemented
236#380—34no—
237#379—32no—
238#379C2×D312yescomplemented
239C2×#95—32no—
240C2×#95—32no—
241C24×C3—22no—
242C24×C3—22no—
243C24×C3—22no—
244C24×C3—42no—
245C24×C3—42no—
246C24×C3—42no—
247C24×C3—42no—
248C24×C3C2×D414yes—
249C24×C3#4114yes—
250C24×C3#4114yes—
251C24×C3C2412yes—
252C24×C3C2411yescharacteristic
253C24×C3C2411yescharacteristic
254C24×C3C2411yescharacteristic
255C23×D3—22no—
256C23×D3—22no—
257C23×D3—42no—
258C23×D3—42no—
259C23×D3C2×D414yes—
260C23×D3C2412yes—
261C2×C3×D4—24no—
262C2×C3×D4—24no—
263C2×C3×D4—24no—
264C2×C3×D4—24no—
265C2×C3×D4—24no—
266C2×C3×D4—24no—
267C2×C3×D4—416no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4—24no—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—42no—
275C22×C3×C4—42no—
276C22×C3×C4—42no—
277C22×C3×C4—42no—
278C22×C3×C4C2412yes—
279C22×C3×C4C2414yes—
280C22×C3×C4C2412yes—
281C22×C3×C4C2412yes—
282C2×#67—232no—
283C2×#67—24no—
284C2×#67—24no—
285C2×#67—24no—
286C2×#67—24no—
287C2×#67—24no—
288C2×#67—24no—
289C2×#67—44no—
290C2×#67—44no—
291C2×#67C2×D418yes—
292C2×#67C2×D418yes—
293C22×Dic3—22no—
294C22×Dic3—22no—
295C22×Dic3—22no—
296C22×Dic3—24no—
297C22×Dic3—24no—
298C22×Dic3—24no—
299C22×Dic3—22no—
300C22×Dic3—22no—
301C22×Dic3—22no—
302C22×Dic3—24no—
303C22×Dic3—24no—
304C22×Dic3—24no—
305C22×Dic3—42no—
306C22×Dic3—42no—
307C22×Dic3—42no—
308C22×Dic3—42no—
309C22×Dic3—42no—
310C22×Dic3—42no—
311C22×Dic3—42no—
312C22×Dic3—416no—
313C22×Dic3C2×D414yes—
314C22×Dic3C2412yes—
315C22×Dic3C2414yes—
316C22×Dic3C2412yes—
317C22×Dic3C2412yes—
318C22×Dic3C2412yes—
319C22×Dic3C2412yes—
320C2×C4×D3—28no—
321C2×C4×D3—28no—
322C2×C4×D3—44no—
323C2×C4×D3—416no—
324C3×C22⋊C4—24no—
325C3×C22⋊C4—24no—
326C3×C22⋊C4—24no—
327C3×C22⋊C4—24no—
328C3×C22⋊C4—44no—
329C3×C22⋊C4—44no—
330#217—24no—
331#217—24no—
332#217—24no—
333#217—24no—
334#217—24no—
335#217—24no—
336#217—28no—
337#217—44no—
338(C2×D3)⋊C4—28no—
339(C2×D3)⋊C4—24no—
340(C2×D3)⋊C4—24no—
341(C2×D3)⋊C4—44no—
342(C2×D3)⋊C4—44no—
343C4⋊Dic3—28no—
344C4⋊Dic3—44no—
345Dic3⋊C4—28no—
346Dic3⋊C4—24no—
347Dic3⋊C4—24no—
348Dic3⋊C4—44no—
349Dic3⋊C4—44no—
350C4×Dic3—28no—
351C25—31no—
352C25C22×D311yescharacteristic
353C25C22×D311yescharacteristic
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—38no—
358C22×D4—32no—
359C22×D4—32no—
360C22×D4—32no—
361C22×D4—32no—
362C22×D4—64no—
363C22×D4—64no—
364C22×D4C22×D312yes—
365C22×D4C22×D312yes—
366C23×C4—31no—
367C23×C4—31no—
368C23×C4—32no—
369C23×C4—32no—
370C23×C4—32no—
371C23×C4—31no—
372C23×C4—31no—
373C23×C4—31no—
374C23×C4—34no—
375C23×C4—64no—
376C23×C4—64no—
377C23×C4—124no—
378C23×C4—124no—
379C23×C4C22×D311yescharacteristic
380C23×C4C22×D311yescharacteristic
381C23×C4C22×D311yescharacteristic
382C23×C4C22×D312yes—
383#123—68no—
384#123—68no—
385#123—128no—
386#121—68no—
387#121—68no—
388#120—68no—
389#120—68no—
390C4×D4—616no—
391C4×D4—616no—
392C2×C4⋊C4—34no—
393C2×C4⋊C4—34no—
394C2×C4⋊C4—32no—
395C2×C4⋊C4—32no—
396C2×C4⋊C4—34no—
397C2×C4⋊C4—34no—
398C2×C4⋊C4—34no—
399C2×C4⋊C4—64no—
400C2×C4⋊C4—124no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—32no—
404C2×C22⋊C4—32no—
405C2×C22⋊C4—34no—
406C2×C22⋊C4—32no—
407C2×C22⋊C4—32no—
408C2×C22⋊C4—32no—
409C2×C22⋊C4—32no—
410C2×C22⋊C4—34no—
411C2×C22⋊C4—32no—
412C2×C22⋊C4—32no—
413C2×C22⋊C4—34no—
414C2×C22⋊C4—34no—
415C2×C22⋊C4—34no—
416C2×C22⋊C4—64no—
417C2×C22⋊C4—64no—
418C2×C22⋊C4—64no—
419C2×C22⋊C4—124no—
420C2×C22⋊C4C22×D312yes—
421C2×C22⋊C4C22×D312yes—
422C2×C22⋊C4C22×D312yes—
423C2×C22⋊C4C22×D312yes—
424C2×C22⋊C4C22×D314yes—
425C2×C22⋊C4C22×D314yes—
426C2×C42—34no—
427C2×C42—64no—
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—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—24no—
448C23×C3—24no—
449C23×C3—44no—
450C23×C3—44no—
451C23×C3—48no—
452C23×C3—48no—
453C23×C3—48no—
454C23×C3—44no—
455C23×C3—82no—
456C23×C3—82no—
457C23×C3—84no—
458C23×C3#123116yescomplemented
459C23×C3C22×D412yes—
460C23×C3C22×D412yes—
461C23×C3C22×D412yes—
462C23×C3C2×#4112yes—
463C23×C3C2×#4112yes—
464C23×C3C2×#4112yes—
465C23×C3C2×#4112yes—
466C23×C3C2×#4112yes—
467C23×C3C2×#4112yes—
468C23×C3C2511yescharacteristic
469C22×D3—28no—
470C22×D3—22no—
471C22×D3—22no—
472C22×D3—24no—
473C22×D3—24no—
474C22×D3—44no—
475C22×D3—44no—
476C22×D3—48no—
477C22×D3—48no—
478C22×D3C22×D414yes—
479C3×D4—48no—
480C3×D4—48no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—24no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—24no—
488C2×C3×C4—24no—
489C2×C3×C4—24no—
490C2×C3×C4—24no—
491C2×C3×C4—44no—
492C2×C3×C4—48no—
493C2×C3×C4—44no—
494C2×C3×C4—44no—
495#67—216no—
496#67—216no—
497#67—84no—
498#67—84no—
499C2×Dic3—28no—
500C2×Dic3—28no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—24no—
509C2×Dic3—24no—
510C2×Dic3—24no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—24no—
514C2×Dic3—24no—
515C2×Dic3—48no—
516C2×Dic3—48no—
517C2×Dic3—44no—
518C2×Dic3—82no—
519C2×Dic3—82no—
520C2×Dic3—84no—
521C2×Dic3C22×D414yes—
522C2×Dic3H(5,𝔽2)14yes—
523C4×D3—416no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—32no—
528C24—34no—
529C24—42no—
530C24—42no—
531C24—42no—
532C24—42no—
533C24—62no—
534C24—62no—
535C24—122no—
536C24—122no—
537C24#23514yes—
538C24D3×D414yes—
539C24#23714yes—
540C24C23×D312yes—
541C24C23×D311yescharacteristic
542C24C23×D311yescharacteristic
543C24C23×D311yescharacteristic
544C2×D4—24no—
545C2×D4—24no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—24no—
550C2×D4—38no—
551C2×D4—38no—
552C2×D4—416no—
553C2×D4—632no—
554C2×D4—64no—
555C2×D4—64no—
556C2×D4—64no—
557C2×D4—64no—
558C2×D4—64no—
559C2×D4—64no—
560C2×D4—124no—
561C2×D4—124no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—34no—
569C22×C4—32no—
570C22×C4—32no—
571C22×C4—34no—
572C22×C4—32no—
573C22×C4—32no—
574C22×C4—32no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—68no—
580C22×C4—68no—
581C22×C4—64no—
582C22×C4—64no—
583C22×C4—64no—
584C22×C4—62no—
585C22×C4—62no—
586C22×C4—62no—
587C22×C4—62no—
588C22×C4—64no—
589C22×C4—64no—
590C22×C4—64no—
591C22×C4—62no—
592C22×C4—62no—
593C22×C4—124no—
594C22×C4—1216no—
595C22×C4—122no—
596C22×C4—122no—
597C22×C4—122no—
598C22×C4—122no—
599C22×C4—122no—
600C22×C4—122no—
601C22×C4—122no—
602C22×C4—1216no—
603C22×C4C23×D312yes—
604C22×C4C23×D314yes—
605C22×C4C23×D312yes—
606C22×C4C23×D312yes—
607C4⋊C4—68no—
608C4⋊C4—68no—
609C4⋊C4—64no—
610C4⋊C4—64no—
611C4⋊C4—124no—
612C4⋊C4—124no—
613C4⋊C4—124no—
614C22⋊C4—24no—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—68no—
621C22⋊C4—64no—
622C22⋊C4—64no—
623C22⋊C4—68no—
624C22⋊C4—64no—
625C22⋊C4—64no—
626C22⋊C4—64no—
627C22⋊C4—64no—
628C22⋊C4—64no—
629C22⋊C4—64no—
630C22⋊C4—124no—
631C22⋊C4—124no—
632C22⋊C4—124no—
633C42—68no—
634C22×C3—24no—
635C22×C3—24no—
636C22×C3—24no—
637C22×C3—22no—
638C22×C3—22no—
639C22×C3—22no—
640C22×C3—22no—
641C22×C3—22no—
642C22×C3—22no—
643C22×C3—24no—
644C22×C3—24no—
645C22×C3—24no—
646C22×C3—416no—
647C22×C3—42no—
648C22×C3—44no—
649C22×C3—42no—
650C22×C3—42no—
651C22×C3—44no—
652C22×C3—88no—
653C22×C3C2×#12314yes—
654C22×C3C2×#12314yes—
655C22×C3C2×#12314yes—
656C22×C3C23×D411yescharacteristic
657C22×C3C22×#4111yescharacteristic
658C22×C3C22×#4111yescharacteristic
659C22×C3C2×H(5,𝔽2)12yes—
660C22×C3#58512yes—
661C2×D3—24no—
662C2×D3—24no—
663C2×D3—24no—
664C2×D3—416no—
665C2×D3—44no—
666C2×D3—44no—
667C3×C4—42no—
668C3×C4—44no—
669C3×C4—42no—
670C3×C4—42no—
671Dic3—24no—
672Dic3—24no—
673Dic3—42no—
674Dic3—42no—
675Dic3—42no—
676Dic3—44no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—24no—
687C23—24no—
688C23—34no—
689C23—44no—
690C23—48no—
691C23—44no—
692C23—48no—
693C23—48no—
694C23—44no—
695C23—62no—
696C23—62no—
697C23—64no—
698C23—64no—
699C23—68no—
700C23—82no—
701C23—82no—
702C23—84no—
703C23—124no—
704C23—124no—
705C23—128no—
706C23—128no—
707C23#883116yescomplemented
708C23C2×#23512yes—
709C23C2×#23512yes—
710C23C2×#23512yes—
711C23C2×D3×D412yes—
712C23C2×D3×D412yes—
713C23C2×D3×D412yes—
714C23C2×#23712yes—
715C23C2×#23712yes—
716C23C2×#23712yes—
717C23C24×D311yescharacteristic
718D4—48no—
719D4—48no—
720D4—616no—
721D4—616no—
722D4—244no—
723D4—244no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—34no—
735C2×C4—34no—
736C2×C4—44no—
737C2×C4—48no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—68no—
741C2×C4—62no—
742C2×C4—62no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—68no—
746C2×C4—64no—
747C2×C4—62no—
748C2×C4—62no—
749C2×C4—62no—
750C2×C4—64no—
751C2×C4—62no—
752C2×C4—64no—
753C2×C4—62no—
754C2×C4—64no—
755C2×C4—64no—
756C2×C4—1216no—
757C2×C4—128no—
758C2×C4—128no—
759C2×C4—124no—
760C2×C4—242no—
761C2×C4—242no—
762C2×C4—244no—
763C2×C3—24no—
764C2×C3—24no—
765C2×C3—24no—
766C2×C3—82no—
767C2×C3C22×#12311yescharacteristic
768C2×C3#345912yes—
769C2×C3#348411yescharacteristic
770C2×C3#348511yescharacteristic
771C2×C3#350512yes—
772D3—44no—
773C22—24no—
774C22—24no—
775C22—24no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—416no—
786C22—44no—
787C22—42no—
788C22—42no—
789C22—44no—
790C22—42no—
791C22—64no—
792C22—64no—
793C22—64no—
794C22—88no—
795C22—1216no—
796C22—124no—
797C22—124no—
798C22C2×#88314yes—
799C22C2×#88314yes—
800C22C2×#88314yes—
801C22C22×#23511yescharacteristic
802C22C22×D3×D411yescharacteristic
803C22C22×#23711yescharacteristic
804C22D3×H(5,𝔽2)12yes—
805C22#596612yes—
806C4—44no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—64no—
811C4—64no—
812C4—122no—
813C4—122no—
814C4—122no—
815C4—124no—
816C3#3498311yescharacteristic, complemented, Sylow
817C2—24no—
818C2—24no—
819C2—24no—
820C2—82no—
821C2—124no—
822C2C22×#88311yescharacteristic
823C2#8586112yes—
824C2#8629512yes—
825C2#8629611yescharacteristic
826C2#8630811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2308C2
prime radicalC2×#5804C2
hypercenter#2308D3
hypocenterC3#34983
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2308

Complements

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

NH ≅ G/Ntype
2. C22×#67⋊C4C2semidirect
3. C3×#2308C2semidirect
4. C2×#5220C2semidirect
5. #82121C2semidirect
6. #82095C2semidirect
7. C2×#4950C2semidirect
8. #74936C2semidirect
9. #74906C2semidirect
10. #74871C2semidirect
11. #74782C2semidirect
12. #74707C2semidirect
13. #74704C2semidirect
14. #74065C2semidirect
15. #73826C2semidirect
20. C23×C4×D3C22semidirect
26. C22×#217C22semidirect
33. C22×(C2×D3)⋊C4C22semidirect
34. C22×C4⋊Dic3C22semidirect
35. C22×Dic3⋊C4C22semidirect
36. C22×C4×Dic3C22semidirect
37. C2×#883C22semidirect
40. C2×#67⋊C4C22semidirect
43. C3×#386C22semidirect
44. C3×#381C22semidirect
45. C3×#379C22semidirect
48. #5220C22semidirect
49. #5213C22semidirect
50. #5210C22semidirect
51. #5210C22semidirect
52. C2×C3⋊#95C22semidirect
53. C2×C3⋊#95C22semidirect
54. #4961C22semidirect
55. #4959C22semidirect
57. #4956C22semidirect
58. #4955C22semidirect
59. #4952C22semidirect
60. #4951C22semidirect
61. #4950C22semidirect
62. #4950C22semidirect
63. #4950C22semidirect
64. #4949C22semidirect
65. #4946C22semidirect
66. #4946C22semidirect
67. #4945C22semidirect
68. #4943C22semidirect
69. #4942C22semidirect
70. #4675C22semidirect
71. #4674C22semidirect
72. #4668C22semidirect
73. #4664C22semidirect
74. #4658C22semidirect
75. #4657C22semidirect
76. #4654C22semidirect
77. #4652C22semidirect
90. #2308D3semidirect
224. #386C2×D3semidirect
235. #381C2×D3semidirect
238. #379C2×D3semidirect
458. C23×C3#123semidirect
707. C23#883semidirect
816. C3#34983semidirect

Maximal subgroups

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

subgroupindex
C2×#58042
C22×#67⋊C42
C3×#23082
C2×#52202
#821212
#820952
C2×#49502
#749362
#749062
#748712
#747822
#747072
#747042
#740652
#738262
#349833