Finite Group Databasebeta

← #31019278

Subgroups — #31019278

Order 17152.

2766 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863960C211yesmaximal, characteristic
2#22563384C212yesmaximal, complemented
3#22563346C212yesmaximal, complemented
4#22563272C212yesmaximal, complemented
5#22563247C212yesmaximal, complemented
6#22563225C212yesmaximal, complemented
7#22563190C212yesmaximal, complemented
8#22563104C212yesmaximal, complemented
9#22563029C212yesmaximal, complemented
10#22563021C214yesmaximal, complemented
11#22562898C212yesmaximal, complemented
12#22562865C214yesmaximal, complemented
13#22562715C212yesmaximal, complemented
14#22562700C211yesmaximal, characteristic, complemented
15C67×#2311C211yesmaximal, characteristic, complemented
16C23×D268C2211yescharacteristic
17#16863960C4116yescomplemented
18C2×#14524039C2212yes—
19C2×#14524032C2212yes—
20C2×#14524017C2212yes—
21C2×#14524017C2212yes—
22C2×#14524011C2212yes—
23C2×#14524011C2212yes—
24C2×#14524005C2212yes—
25C2×#14524005C2212yes—
26C2×C4×C22⋊D67C2214yescomplemented
27C2×(C22⋊D67)⋊C4C2214yescomplemented
28C2×#14524002C2211yescharacteristic
29C2×#14524002C2211yescharacteristic, complemented
30C2×C22⋊C4×D67C2214yes—
31C22×C4×Dic67C2211yescharacteristic, complemented
32#16863303C2212yescomplemented
33#16863299C2212yes—
34#16863297C2212yes—
35#16863297C2212yes—
36#16863296C2214yescomplemented
37#16863296C2214yescomplemented
38#16863292C2212yescomplemented
39#16863292C2212yescomplemented
40#16863288C2214yescomplemented
41#16863287C2214yescomplemented
42#16863286C2214yescomplemented
43#16863285C2214yescomplemented
44#16863284C2214yes—
45#16863284C2214yes—
46#16863276C2211yescharacteristic
47#16863276C2211yescharacteristic
48#16863276C2211yescharacteristic, complemented
49#16863276C2211yescharacteristic, complemented
50#16863275C2214yescomplemented
51#16863274C2214yes—
52#16863274C2214yes—
53#16863273C2214yescomplemented
54#16863272C2214yescomplemented
55#16863272C2214yescomplemented
56#16863270C2214yescomplemented
57#16863267C2214yescomplemented
58#16863263C2214yescomplemented
59#16863251C2214yes—
60C4⋊C4×Dic67C2212yescomplemented
61C4⋊C4×Dic67C2212yescomplemented
62#16863247C2214yescomplemented
63C4×(C2×D67)⋊C4C2214yescomplemented
64C4×C22⋊Dic67C2212yes—
65C4×C22⋊Dic67C2212yescomplemented
66#16863243C2214yescomplemented
67C22×#41×C67C2211yescharacteristic
68C2×#117×C67C2211yescharacteristic, complemented
69C22×C4⋊C4×C67C2211yescharacteristic, complemented
70#391×C67C2212yescomplemented
71#390×C67C2212yes—
72#386×C67C2212yes—
73#386×C67C2212yescomplemented
74#380×C67C2212yes—
75#380×C67C2212yescomplemented
76C24×D67C2312yes—
77C22×D268—42no—
78C22×D268—42no—
79C22×D268C2×C418yescomplemented
80C22×D268C2312yes—
81C22×D268C2312yes—
82C22×C22⋊D67C2314yes—
83C22×C22⋊D67C2314yes—
84C23×Dic67C2311yescharacteristic
85C23×Dic67C2311yescharacteristic
86C22×C4×D67C2314yes—
87C22×C4×D67C2314yes—
88#14524039C2×C4116yescomplemented
89#14524032C2×C4116yescomplemented
90#14524017C2×C4116yescomplemented
91#14524017C2×C4116yescomplemented
92#14524011C2×C4116yescomplemented
93#14524011C2×C4116yescomplemented
94#14524005—44no—
95#14524005—44no—
96C4×C22⋊D67—48no—
97(C22⋊D67)⋊C4—48no—
98#14524002—42no—
99#14524002C2×C418yescomplemented
100C2×C4⋊Dic67C2312yes—
101C2×C4⋊Dic67C2312yes—
102C2×Dic67⋊C4C2314yes—
103C2×Dic67⋊C4C2314yes—
104C2×C22⋊Dic67C2312yes—
105C2×C22⋊Dic67C2312yes—
106C2×C22⋊Dic67C2312yes—
107C2×C22⋊Dic67C2312yes—
108C2×C22⋊Dic67C2311yescharacteristic
109C2×C22⋊Dic67C2311yescharacteristic
110C2×C22⋊Dic67C2312yes—
111C2×(C2×D67)⋊C4C2314yes—
112C2×(C2×D67)⋊C4C2314yes—
113C2×(C2×D67)⋊C4C2314yes—
114C2×(C2×D67)⋊C4C2314yes—
115C2×(C2×D67)⋊C4C2314yes—
116C2×(C2×D67)⋊C4C2314yes—
117C2×(C2×D67)⋊C4C2314yes—
118C2×(C2×D67)⋊C4C2314yes—
119C22⋊C4×D67—48no—
120C2×C4×Dic67—42no—
121C2×C4×Dic67C2312yes—
122C2×C4×Dic67C2312yes—
123C2×C4×Dic67C2312yes—
124C2×C4×Dic67C2314yes—
125C2×C4×Dic67C2314yes—
126C2×C4×Dic67C2312yes—
127C67⋊#95C2314yes—
128C67⋊#95C2312yes—
129C67⋊#95C2312yes—
130C67⋊#95C2312yes—
131C67⋊#95C2312yes—
132C67⋊#95C2314yes—
133C67⋊#95C2314yes—
134C67⋊#95C2314yes—
135C2×#41×C67—42no—
136C2×#41×C67—42no—
137C2×#41×C67C2×C418yescomplemented
138C22×Q8×C67C2311yescharacteristic
139C22×D4×C67C2311yescharacteristic
140C22×D4×C67C2311yescharacteristic
141C22×D4×C67C2311yescharacteristic
142C23×C4×C67C2311yescharacteristic
143C23×C4×C67C2311yescharacteristic
144C23×C4×C67C2311yescharacteristic
145C23×C4×C67C2312yes—
146#117×C67—42no—
147C2×C4⋊C4×C67—42no—
148C2×C4⋊C4×C67C2312yes—
149C2×C4⋊C4×C67C2312yes—
150C2×C4⋊C4×C67C2312yes—
151C2×C22⋊C4×C67C2314yes—
152C2×C22⋊C4×C67C2312yes—
153C2×C22⋊C4×C67C2314yes—
154C2×C42×C67C2312yes—
155#95×C67C2314yes—
156#95×C67C2314yes—
157C23×D67—44no—
158C23×D67—42no—
159C23×D67—42no—
160C23×D67—44no—
161C23×D67C22×C418yes—
162C23×D67C2414yes—
163C2×D268—24no—
164C2×D268—24no—
165C2×D268—416no—
166C2×D268—42no—
167C2×D268—42no—
168C2×D268C22×C418yes—
169C2×D268C22×C418yes—
170C2×C22⋊D67—44no—
171C2×C22⋊D67—44no—
172C2×C22⋊D67—44no—
173C2×C22⋊D67—44no—
174C2×C22⋊D67C22×C4116yes—
175C2×C22⋊D67C22×C4116yes—
176C22×Dic67—24no—
177C22×Dic67—41no—
178C22×Dic67—41no—
179C22×Dic67—42no—
180C22×Dic67C2412yes—
181C22×Dic67C2412yes—
182C22×Dic67C2412yes—
183C22×Dic67C2414yes—
184C22×Dic67C2412yes—
185C2×C4×D67—28no—
186C2×C4×D67—44no—
187C2×C4×D67—44no—
188C2×C4×D67—44no—
189C2×C4×D67—44no—
190C2×C4×D67—44no—
191C4⋊Dic67—42no—
192C4⋊Dic67C22×C418yes—
193Dic67⋊C4—28no—
194Dic67⋊C4—44no—
195C22⋊Dic67—24no—
196C22⋊Dic67—24no—
197C22⋊Dic67—42no—
198C22⋊Dic67—42no—
199C22⋊Dic67—41no—
200C22⋊Dic67—41no—
201C22⋊Dic67C22×C418yes—
202(C2×D67)⋊C4—28no—
203(C2×D67)⋊C4—44no—
204(C2×D67)⋊C4—44no—
205(C2×D67)⋊C4—44no—
206(C2×D67)⋊C4—44no—
207(C2×D67)⋊C4—44no—
208(C2×D67)⋊C4C22×C4116yes—
209(C2×D67)⋊C4C22×C4116yes—
210C4×Dic67—24no—
211C4×Dic67—24no—
212C4×Dic67—42no—
213C4×Dic67—44no—
214C4×Dic67—44no—
215C4×Dic67C22×C418yes—
216C24×C67C2411yescharacteristic
217C24×C67C2411yescharacteristic
218C24×C67C2411yescharacteristic
219#41×C67—416no—
220C2×Q8×C67—41no—
221C2×Q8×C67—41no—
222C2×Q8×C67C22×C414yes—
223C2×D4×C67—41no—
224C2×D4×C67—41no—
225C2×D4×C67—41no—
226C2×D4×C67—41no—
227C2×D4×C67—41no—
228C2×D4×C67—41no—
229C2×D4×C67C22×C414yes—
230C2×D4×C67C22×C414yes—
231C2×D4×C67C22×C414yes—
232C22×C4×C67—22no—
233C22×C4×C67—22no—
234C22×C4×C67—22no—
235C22×C4×C67—22no—
236C22×C4×C67—22no—
237C22×C4×C67—22no—
238C22×C4×C67—42no—
239C22×C4×C67—44no—
240C22×C4×C67C22×C414yes—
241C22×C4×C67C22×C414yes—
242C22×C4×C67C22×C414yes—
243C22×C4×C67C2414yes—
244C22×C4×C67C2414yes—
245C22×C4×C67C2411yescharacteristic
246C22×C4×C67C2411yescharacteristic
247C22×C4×C67C2411yescharacteristic
248C22×C4×C67C2411yescharacteristic
249C4⋊C4×C67—24no—
250C4⋊C4×C67—24no—
251C4⋊C4×C67—42no—
252C22⋊C4×C67—42no—
253C22⋊C4×C67—44no—
254C22⋊C4×C67—44no—
255C42×C67—42no—
256C23×C67—21no—
257C23×C67—22no—
258C23×C67—22no—
259C23×C67—21no—
260C23×C67—21no—
261C23×C67—21no—
262C23×C67—21no—
263C23×C67—21no—
264C23×C67—22no—
265C23×C67—22no—
266C23×C67—22no—
267C23×C67—22no—
268C23×C67C23×C412yes—
269C23×C67C23×C412yes—
270C23×C67C23×C412yes—
271C23×C67C2511yescharacteristic
272C22×D67—24no—
273C22×D67—24no—
274C22×D67—24no—
275C22×D67—24no—
276C22×D67—24no—
277C22×D67—24no—
278C22×D67—48no—
279C22×D67—416no—
280C22×D67—84no—
281C22×D67—84no—
282C22×D67—88no—
283C22×D67C23×C418yes—
284Q8×C67—44no—
285D4×C67—44no—
286D4×C67—44no—
287D4×C67—44no—
288C2×C4×C67—21no—
289C2×C4×C67—21no—
290C2×C4×C67—21no—
291C2×C4×C67—21no—
292C2×C4×C67—21no—
293C2×C4×C67—21no—
294C2×C4×C67—28no—
295C2×C4×C67—28no—
296C2×C4×C67—28no—
297C2×C4×C67—24no—
298C2×C4×C67—24no—
299C2×C4×C67—24no—
300C2×C4×C67—24no—
301C2×C4×C67—24no—
302C2×C4×C67—24no—
303C2×C4×C67—84no—
304C2×C4×C67C23×C412yes—
305C2×C4×C67C23×C412yes—
306C2×C4×C67C23×C412yes—
307C2×C4×C67C23×C412yes—
308C2×C4×C67H(5,𝔽2)12yes—
309C2×C4×C67H(5,𝔽2)12yes—
310C22⋊D67—416no—
311C22⋊D67—416no—
312C2×Dic67—22no—
313C2×Dic67—24no—
314C2×Dic67—22no—
315C2×Dic67—24no—
316C2×Dic67—22no—
317C2×Dic67—22no—
318C2×Dic67—22no—
319C2×Dic67—22no—
320C2×Dic67—22no—
321C2×Dic67—22no—
322C2×Dic67—22no—
323C2×Dic67—22no—
324C2×Dic67—22no—
325C2×Dic67—44no—
326C2×Dic67—44no—
327C2×Dic67C23×C418yes—
328C2×Dic67H(5,𝔽2)14yes—
329D268—216no—
330D268—48no—
331C4×D67—88no—
332C4×D67—88no—
333C22×C67—22no—
334C22×C67—22no—
335C22×C67—22no—
336C22×C67—24no—
337C22×C67—24no—
338C22×C67—24no—
339C22×C67—41no—
340C22×C67—41no—
341C22×C67—41no—
342C22×C67—41no—
343C22×C67—41no—
344C22×C67—41no—
345C22×C67—42no—
346C22×C67—42no—
347C22×C67—42no—
348C22×C67C24×C411yescharacteristic
349C22×C67C2×H(5,𝔽2)12yes—
350C22×C67C2×H(5,𝔽2)11yescharacteristic
351C22×C67C2×H(5,𝔽2)11yescharacteristic
352C22×C67#58512yes—
353C2×D67—28no—
354C2×D67—28no—
355C2×D67—28no—
356C2×D67—44no—
357C2×D67—44no—
358C2×D67—44no—
359C2×D67—44no—
360C2×D67—816no—
361C4×C67—22no—
362C4×C67—22no—
363C4×C67—22no—
364C4×C67—44no—
365C4×C67—44no—
366C4×C67#51814yes—
367Dic67—28no—
368Dic67—24no—
369Dic67—42no—
370Dic67—42no—
371Dic67—42no—
372#34411—671nomaximal, Sylow
373C2×C67—42no—
374C2×C67—42no—
375C2×C67—42no—
376C2×C67C2×#51811yescharacteristic
377C2×C67C4×H(5,𝔽2)12yes—
378C2×C67#353711yescharacteristic
379C2×C67#354011yescharacteristic
380C2×C67#354612yes—
381D67—48no—
382C2×#535—671no—
383#2380—672no—
384#2375—672no—
385#2366—672no—
386#2363—672no—
387#2361—672no—
388#2358—672no—
389#2347—672no—
390D4×C22⋊C4—672no—
391#2337—674no—
392#2324—672no—
393#2321—674no—
394#2311D6711yescharacteristic, complemented
395C4×#121—672no—
396#2297—671no—
397C67#3441111yescharacteristic, complemented, Sylow
398C22×#41C2×D6711yescharacteristic
399C23×D4—671no—
400#535—6716no—
401C2×#127—672no—
402C2×#124—672no—
403C2×#121—672no—
404C2×#121—672no—
405C2×#120—672no—
406C2×#120—672no—
407C2×C4×D4—674no—
408C2×C4×D4—672no—
409C2×C4×D4—672no—
410C2×C4×D4—674no—
411C2×#117—671no—
412C2×#117—671no—
413C2×#117C2×D6711yescharacteristic, complemented
414C22×C4⋊C4C2×D6711yescharacteristic, complemented
415C22×C22⋊C4—674no—
416C22×C42—671no—
417#391—672no—
418#391C2×D6712yescomplemented
419#390—672no—
420#390—672no—
421#390—672no—
422#390—674no—
423#390—674no—
424#390C2×D6712yes—
425#389—672no—
426#389—672no—
427#388—674no—
428#388—674no—
429#388—674no—
430#388—674no—
431#388—674no—
432#388—674no—
433#386—671no—
434#386—671no—
435#386—671no—
436#386—671no—
437#386—674no—
438#386—674no—
439#386—674no—
440#386—674no—
441#386—674no—
442#386—674no—
443#386C2×D6712yes—
444#386C2×D6712yescomplemented
445#385—674no—
446#385—674no—
447#383—674no—
448#380C2×D6712yes—
449#380C2×D6712yescomplemented
450#379—674no—
451C4×C4⋊C4—672no—
452C4×C4⋊C4—672no—
453C4×C4⋊C4—674no—
454C4×C22⋊C4—672no—
455C4×C22⋊C4—672no—
456C4×C22⋊C4—674no—
457C4×C22⋊C4—674no—
458C25—672no—
459C2×#41—42no—
460C2×#41—42no—
461C2×#41C4×D6718yescomplemented
462C22×Q8C22×D6711yescharacteristic
463C22×D4—2682no—
464C22×D4—2682no—
465C22×D4—674no—
466C22×D4—674no—
467C22×D4—678no—
468C22×D4—672no—
469C22×D4—672no—
470C22×D4C22×D6711yescharacteristic
471C22×D4C22×D6711yescharacteristic
472C22×D4C22×D6711yescharacteristic
473C23×C4—671no—
474C23×C4—674no—
475C23×C4—674no—
476C23×C4—671no—
477C23×C4C22×D6711yescharacteristic
478C23×C4C22×D6711yescharacteristic
479C23×C4C22×D6711yescharacteristic
480C23×C4C22×D6712yes—
481#127—6716no—
482#124—6716no—
483#121—6716no—
484#121—6716no—
485#120—6716no—
486#120—6716no—
487C4×D4—2688no—
488C4×D4—2688no—
489C4×D4—2684no—
490C4×D4—2684no—
491#117—42no—
492#117—2682no—
493#117—678no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—672no—
496C2×C4⋊C4—674no—
497C2×C4⋊C4—672no—
498C2×C4⋊C4—674no—
499C2×C4⋊C4C22×D6712yes—
500C2×C4⋊C4C22×D6712yes—
501C2×C4⋊C4C22×D6712yes—
502C2×C22⋊C4—2688no—
503C2×C22⋊C4—671no—
504C2×C22⋊C4—671no—
505C2×C22⋊C4—672no—
506C2×C22⋊C4—672no—
507C2×C22⋊C4—674no—
508C2×C22⋊C4—674no—
509C2×C22⋊C4—674no—
510C2×C22⋊C4—674no—
511C2×C22⋊C4—674no—
512C2×C22⋊C4—672no—
513C2×C22⋊C4—674no—
514C2×C22⋊C4—674no—
515C2×C22⋊C4—672no—
516C2×C22⋊C4—672no—
517C2×C22⋊C4—674no—
518C2×C22⋊C4C22×D6714yes—
519C2×C22⋊C4C22×D6712yes—
520C2×C22⋊C4C22×D6714yes—
521C2×C42—2682no—
522C2×C42—674no—
523C2×C42—674no—
524C2×C42—672no—
525C2×C42—672no—
526C2×C42—672no—
527C2×C42—672no—
528C2×C42C22×D6712yes—
529#95—672no—
530#95—672no—
531#95—672no—
532#95—674no—
533#95—674no—
534#95—672no—
535#95—674no—
536#95—674no—
537#95C22×D6714yes—
538#95C22×D6714yes—
539C24—2684no—
540C24—2682no—
541C24—2682no—
542C24—2684no—
543C24—678no—
544C24—674no—
545C24C23×D6711yescharacteristic
546C24C23×D6711yescharacteristic
547C24C23×D6711yescharacteristic
548#41—416no—
549C2×Q8—41no—
550C2×Q8—41no—
551C2×Q8C2×C4×D6714yes—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—2682no—
559C2×D4—2682no—
560C2×D4—26816no—
561C2×D4—2684no—
562C2×D4—2684no—
563C2×D4—2684no—
564C2×D4—2684no—
565C2×D4—6716no—
566C2×D4—6716no—
567C2×D4—678no—
568C2×D4—678no—
569C2×D4—1344no—
570C2×D4—1344no—
571C2×D4C2×C4×D6714yes—
572C2×D4C2×C4×D6714yes—
573C2×D4C2×C4×D6714yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—42no—
581C22×C4—44no—
582C22×C4—2684no—
583C22×C4—2684no—
584C22×C4—2684no—
585C22×C4—2684no—
586C22×C4—2684no—
587C22×C4—2681no—
588C22×C4—2681no—
589C22×C4—2682no—
590C22×C4—674no—
591C22×C4—672no—
592C22×C4—672no—
593C22×C4—672no—
594C22×C4—672no—
595C22×C4—1348no—
596C22×C4—1344no—
597C22×C4C2×C4×D6714yes—
598C22×C4C2×C4×D6714yes—
599C22×C4C2×C4×D6714yes—
600C22×C4C23×D6714yes—
601C22×C4C23×D6714yes—
602C22×C4C23×D6711yescharacteristic
603C22×C4C23×D6711yescharacteristic
604C22×C4C23×D6711yescharacteristic
605C22×C4C23×D6711yescharacteristic
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—42no—
609C4⋊C4—2682no—
610C4⋊C4—2684no—
611C4⋊C4—678no—
612C4⋊C4—1348no—
613C22⋊C4—44no—
614C22⋊C4—42no—
615C22⋊C4—44no—
616C22⋊C4—2684no—
617C22⋊C4—2684no—
618C22⋊C4—2684no—
619C22⋊C4—2684no—
620C22⋊C4—2684no—
621C22⋊C4—2681no—
622C22⋊C4—2681no—
623C22⋊C4—2682no—
624C22⋊C4—2682no—
625C22⋊C4—678no—
626C22⋊C4—6716no—
627C22⋊C4—6716no—
628C22⋊C4—1348no—
629C22⋊C4—1344no—
630C22⋊C4—1344no—
631C42—42no—
632C42—2682no—
633C42—2684no—
634C42—2684no—
635C42—678no—
636C42—1344no—
637C42—1344no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—2688no—
651C23—26816no—
652C23—5364no—
653C23—5364no—
654C23—5368no—
655C23—678no—
656C23—1344no—
657C23—1344no—
658C23—1344no—
659C23—1344no—
660C23—1344no—
661C23—1344no—
662C23C22×C4×D6712yes—
663C23C22×C4×D6712yes—
664C23C22×C4×D6712yes—
665C23C24×D6711yescharacteristic
666Q8—44no—
667D4—44no—
668D4—44no—
669D4—44no—
670D4—2688no—
671D4—26816no—
672D4—26816no—
673D4—13416no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—28no—
681C2×C4—28no—
682C2×C4—28no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—84no—
690C2×C4—2684no—
691C2×C4—2684no—
692C2×C4—5368no—
693C2×C4—5368no—
694C2×C4—678no—
695C2×C4—674no—
696C2×C4—1342no—
697C2×C4—1342no—
698C2×C4—1342no—
699C2×C4—1342no—
700C2×C4—1342no—
701C2×C4—1342no—
702C2×C4—1342no—
703C2×C4—1342no—
704C2×C4—1342no—
705C2×C4—1344no—
706C2×C4—1342no—
707C2×C4—1342no—
708C2×C4—1344no—
709C2×C4C22×C4×D6712yes—
710C2×C4C22×C4×D6712yes—
711C2×C4C22×C4×D6712yes—
712C2×C4C22×C4×D6712yes—
713C2×C4#1452408812yes—
714C2×C4#1452408812yes—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—24no—
719C22—24no—
720C22—24no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—2684no—
731C22—2684no—
732C22—2684no—
733C22—2684no—
734C22—53616no—
735C22—1348no—
736C22—1348no—
737C22—1348no—
738C22C23×C4×D6711yescharacteristic
739C22H(5,𝔽2)×D6712yes—
740C22C2×#1452408811yescharacteristic
741C22C2×#1452408811yescharacteristic
742C22#1686423312yes—
743C4—22no—
744C4—22no—
745C4—22no—
746C4—44no—
747C4—44no—
748C4—2682no—
749C4—2682no—
750C4—2682no—
751C4—1348no—
752C4—1344no—
753C4#1686386914yes—
754C2—42no—
755C2—42no—
756C2—42no—
757C2—2688no—
758C2C2×#1686386911yescharacteristic
759C2#2257341512yes—
760C2#2257444211yescharacteristic
761C2#2257448611yescharacteristic
762C2#2257457112yes—
subgroupG/H
center, FrattiniC23C24×D67
commutatorC22×C67C24×C4
FittingC67×#2311C2
socle, cosocleC23×C67C25
prime radicalC2×#16863960C2
hypercenter#2311D67
hypocenterC67#34411
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. #22563384C2semidirect
3. #22563346C2semidirect
4. #22563272C2semidirect
5. #22563247C2semidirect
6. #22563225C2semidirect
7. #22563190C2semidirect
8. #22563104C2semidirect
9. #22563029C2semidirect
10. #22563021C2semidirect
11. #22562898C2semidirect
12. #22562865C2semidirect
13. #22562715C2semidirect
14. #22562700C2semidirect
15. C67×#2311C2semidirect
17. #16863960C4semidirect
26. C2×C4×C22⋊D67C22semidirect
27. C2×(C22⋊D67)⋊C4C22semidirect
29. C2×#14524002C22semidirect
31. C22×C4×Dic67C22semidirect
32. #16863303C22semidirect
36. #16863296C22semidirect
37. #16863296C22semidirect
38. #16863292C22semidirect
39. #16863292C22semidirect
40. #16863288C22semidirect
41. #16863287C22semidirect
42. #16863286C22semidirect
43. #16863285C22semidirect
48. #16863276C22semidirect
49. #16863276C22semidirect
50. #16863275C22semidirect
53. #16863273C22semidirect
54. #16863272C22semidirect
55. #16863272C22semidirect
56. #16863270C22semidirect
57. #16863267C22semidirect
58. #16863263C22semidirect
60. C4⋊C4×Dic67C22semidirect
61. C4⋊C4×Dic67C22semidirect
62. #16863247C22semidirect
63. C4×(C2×D67)⋊C4C22semidirect
65. C4×C22⋊Dic67C22semidirect
66. #16863243C22semidirect
68. C2×#117×C67C22semidirect
69. C22×C4⋊C4×C67C22semidirect
70. #391×C67C22semidirect
73. #386×C67C22semidirect
75. #380×C67C22semidirect
79. C22×D268C2×C4semidirect
88. #14524039C2×C4semidirect
89. #14524032C2×C4semidirect
90. #14524017C2×C4semidirect
91. #14524017C2×C4semidirect
92. #14524011C2×C4semidirect
93. #14524011C2×C4semidirect
99. #14524002C2×C4semidirect
137. C2×#41×C67C2×C4semidirect
394. #2311D67semidirect
397. C67#34411semidirect
413. C2×#117C2×D67semidirect
414. C22×C4⋊C4C2×D67semidirect
418. #391C2×D67semidirect
444. #386C2×D67semidirect
449. #380C2×D67semidirect
461. C2×#41C4×D67semidirect

Maximal subgroups

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

subgroupindex
C2×#168639602
#225633842
#225633462
#225632722
#225632472
#225632252
#225631902
#225631042
#225630292
#225630212
#225628982
#225628652
#225627152
#225627002
C67×#23112
#3441167