Finite Group Databasebeta

← #25260044

Subgroups — #25260044

Order 11008.

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×#14583463C211yesmaximal, characteristic
2#19137770C212yesmaximal, complemented
3#19137732C212yesmaximal, complemented
4#19137658C212yesmaximal, complemented
5#19137633C212yesmaximal, complemented
6#19137611C212yesmaximal, complemented
7#19137576C212yesmaximal, complemented
8#19137490C212yesmaximal, complemented
9#19137415C212yesmaximal, complemented
10#19137407C214yesmaximal, complemented
11#19137284C212yesmaximal, complemented
12#19137251C214yesmaximal, complemented
13#19137101C212yesmaximal, complemented
14#19137086C211yesmaximal, characteristic, complemented
15C43×#2311C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17#14583463C4116yescomplemented
18C2×#13063321C2212yes—
19C2×#13063314C2212yes—
20C2×#13063299C2212yes—
21C2×#13063299C2212yes—
22C2×#13063293C2212yes—
23C2×#13063293C2212yes—
24C2×#13063287C2212yes—
25C2×#13063287C2212yes—
26C2×C4×C22⋊D43C2214yescomplemented
27C2×(C22⋊D43)⋊C4C2214yescomplemented
28C2×#13063284C2211yescharacteristic
29C2×#13063284C2211yescharacteristic, complemented
30C2×C22⋊C4×D43C2214yes—
31C22×C4×Dic43C2211yescharacteristic, complemented
32#14582806C2212yescomplemented
33#14582802C2212yes—
34#14582800C2212yes—
35#14582800C2212yes—
36#14582799C2214yescomplemented
37#14582799C2214yescomplemented
38#14582795C2212yescomplemented
39#14582795C2212yescomplemented
40#14582791C2214yescomplemented
41#14582790C2214yescomplemented
42#14582789C2214yescomplemented
43#14582788C2214yescomplemented
44#14582787C2214yes—
45#14582787C2214yes—
46#14582779C2211yescharacteristic
47#14582779C2211yescharacteristic
48#14582779C2211yescharacteristic, complemented
49#14582779C2211yescharacteristic, complemented
50#14582778C2214yescomplemented
51#14582777C2214yes—
52#14582777C2214yes—
53#14582776C2214yescomplemented
54#14582775C2214yescomplemented
55#14582775C2214yescomplemented
56#14582773C2214yescomplemented
57#14582770C2214yescomplemented
58#14582766C2214yescomplemented
59#14582754C2214yes—
60C4⋊C4×Dic43C2212yescomplemented
61C4⋊C4×Dic43C2212yescomplemented
62#14582750C2214yescomplemented
63C4×(C2×D43)⋊C4C2214yescomplemented
64C4×C22⋊Dic43C2212yes—
65C4×C22⋊Dic43C2212yescomplemented
66#14582746C2214yescomplemented
67C22×#41×C43C2211yescharacteristic
68C2×#117×C43C2211yescharacteristic, complemented
69C22×C4⋊C4×C43C2211yescharacteristic, complemented
70C43×#391C2212yescomplemented
71C43×#390C2212yes—
72C43×#386C2212yes—
73C43×#386C2212yescomplemented
74C43×#380C2212yes—
75C43×#380C2212yescomplemented
76C24×D43C2312yes—
77C22×D172—42no—
78C22×D172—42no—
79C22×D172C2×C418yescomplemented
80C22×D172C2312yes—
81C22×D172C2312yes—
82C22×C22⋊D43C2314yes—
83C22×C22⋊D43C2314yes—
84C23×Dic43C2311yescharacteristic
85C23×Dic43C2311yescharacteristic
86C22×C4×D43C2314yes—
87C22×C4×D43C2314yes—
88#13063321C2×C4116yescomplemented
89#13063314C2×C4116yescomplemented
90#13063299C2×C4116yescomplemented
91#13063299C2×C4116yescomplemented
92#13063293C2×C4116yescomplemented
93#13063293C2×C4116yescomplemented
94#13063287—44no—
95#13063287—44no—
96C4×C22⋊D43—48no—
97(C22⋊D43)⋊C4—48no—
98#13063284—42no—
99#13063284C2×C418yescomplemented
100C2×C4⋊Dic43C2312yes—
101C2×C4⋊Dic43C2312yes—
102C2×Dic43⋊C4C2314yes—
103C2×Dic43⋊C4C2314yes—
104C2×C22⋊Dic43C2312yes—
105C2×C22⋊Dic43C2312yes—
106C2×C22⋊Dic43C2312yes—
107C2×C22⋊Dic43C2311yescharacteristic
108C2×C22⋊Dic43C2312yes—
109C2×C22⋊Dic43C2311yescharacteristic
110C2×C22⋊Dic43C2312yes—
111C2×(C2×D43)⋊C4C2314yes—
112C2×(C2×D43)⋊C4C2314yes—
113C2×(C2×D43)⋊C4C2314yes—
114C2×(C2×D43)⋊C4C2314yes—
115C2×(C2×D43)⋊C4C2314yes—
116C2×(C2×D43)⋊C4C2314yes—
117C2×(C2×D43)⋊C4C2314yes—
118C2×(C2×D43)⋊C4C2314yes—
119C22⋊C4×D43—48no—
120C2×C4×Dic43—42no—
121C2×C4×Dic43C2312yes—
122C2×C4×Dic43C2312yes—
123C2×C4×Dic43C2314yes—
124C2×C4×Dic43C2314yes—
125C2×C4×Dic43C2312yes—
126C2×C4×Dic43C2312yes—
127C43⋊#95C2314yes—
128C43⋊#95C2314yes—
129C43⋊#95C2314yes—
130C43⋊#95C2314yes—
131C43⋊#95C2312yes—
132C43⋊#95C2312yes—
133C43⋊#95C2312yes—
134C43⋊#95C2312yes—
135C2×#41×C43—42no—
136C2×#41×C43—42no—
137C2×#41×C43C2×C418yescomplemented
138C22×Q8×C43C2311yescharacteristic
139C22×D4×C43C2311yescharacteristic
140C22×D4×C43C2311yescharacteristic
141C22×D4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2312yes—
146#117×C43—42no—
147C2×C4⋊C4×C43—42no—
148C2×C4⋊C4×C43C2312yes—
149C2×C4⋊C4×C43C2312yes—
150C2×C4⋊C4×C43C2312yes—
151C2×C22⋊C4×C43C2314yes—
152C2×C22⋊C4×C43C2312yes—
153C2×C22⋊C4×C43C2314yes—
154C2×C42×C43C2312yes—
155#95×C43C2314yes—
156#95×C43C2314yes—
157C24×C43C2411yescharacteristic
158C24×C43C2411yescharacteristic
159C24×C43C2411yescharacteristic
160C23×D43—44no—
161C23×D43—42no—
162C23×D43—42no—
163C23×D43—44no—
164C23×D43C22×C418yes—
165C23×D43C2414yes—
166#41×C43—416no—
167C2×Q8×C43—41no—
168C2×Q8×C43—41no—
169C2×Q8×C43C22×C414yes—
170C2×D4×C43—41no—
171C2×D4×C43—41no—
172C2×D4×C43—41no—
173C2×D4×C43—41no—
174C2×D4×C43—41no—
175C2×D4×C43—41no—
176C2×D4×C43C22×C414yes—
177C2×D4×C43C22×C414yes—
178C2×D4×C43C22×C414yes—
179C22×C4×C43—22no—
180C22×C4×C43—22no—
181C22×C4×C43—22no—
182C22×C4×C43—22no—
183C22×C4×C43—22no—
184C22×C4×C43—22no—
185C22×C4×C43—42no—
186C22×C4×C43—44no—
187C22×C4×C43C22×C414yes—
188C22×C4×C43C22×C414yes—
189C22×C4×C43C22×C414yes—
190C22×C4×C43C2414yes—
191C22×C4×C43C2414yes—
192C22×C4×C43C2411yescharacteristic
193C22×C4×C43C2411yescharacteristic
194C22×C4×C43C2411yescharacteristic
195C22×C4×C43C2411yescharacteristic
196C2×C22⋊D43—44no—
197C2×C22⋊D43—44no—
198C2×C22⋊D43—44no—
199C2×C22⋊D43—44no—
200C2×C22⋊D43C22×C4116yes—
201C2×C22⋊D43C22×C4116yes—
202C22×Dic43—24no—
203C22×Dic43—41no—
204C22×Dic43—41no—
205C22×Dic43—42no—
206C22×Dic43C2412yes—
207C22×Dic43C2412yes—
208C22×Dic43C2412yes—
209C22×Dic43C2414yes—
210C22×Dic43C2412yes—
211C2×D172—24no—
212C2×D172—24no—
213C2×D172—42no—
214C2×D172—42no—
215C2×D172—416no—
216C2×D172C22×C418yes—
217C2×D172C22×C418yes—
218C2×C4×D43—28no—
219C2×C4×D43—44no—
220C2×C4×D43—44no—
221C2×C4×D43—44no—
222C2×C4×D43—44no—
223C2×C4×D43—44no—
224C4⋊C4×C43—24no—
225C4⋊C4×C43—24no—
226C4⋊C4×C43—42no—
227C22⋊C4×C43—42no—
228C22⋊C4×C43—44no—
229C22⋊C4×C43—44no—
230C42×C43—42no—
231C22⋊Dic43—24no—
232C22⋊Dic43—24no—
233C22⋊Dic43—42no—
234C22⋊Dic43—42no—
235C22⋊Dic43—41no—
236C22⋊Dic43—41no—
237C22⋊Dic43C22×C418yes—
238(C2×D43)⋊C4—28no—
239(C2×D43)⋊C4—44no—
240(C2×D43)⋊C4—44no—
241(C2×D43)⋊C4—44no—
242(C2×D43)⋊C4—44no—
243(C2×D43)⋊C4—44no—
244(C2×D43)⋊C4C22×C4116yes—
245(C2×D43)⋊C4C22×C4116yes—
246C4⋊Dic43—42no—
247C4⋊Dic43C22×C418yes—
248Dic43⋊C4—28no—
249Dic43⋊C4—44no—
250C4×Dic43—24no—
251C4×Dic43—24no—
252C4×Dic43—42no—
253C4×Dic43—44no—
254C4×Dic43—44no—
255C4×Dic43C22×C418yes—
256C23×C43—22no—
257C23×C43—22no—
258C23×C43—21no—
259C23×C43—22no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—22no—
266C23×C43—22no—
267C23×C43—22no—
268C23×C43C23×C412yes—
269C23×C43C23×C412yes—
270C23×C43C23×C412yes—
271C23×C43C2511yescharacteristic
272C22×D43—24no—
273C22×D43—24no—
274C22×D43—24no—
275C22×D43—24no—
276C22×D43—24no—
277C22×D43—24no—
278C22×D43—48no—
279C22×D43—416no—
280C22×D43—84no—
281C22×D43—84no—
282C22×D43—88no—
283C22×D43C23×C418yes—
284Q8×C43—44no—
285D4×C43—44no—
286D4×C43—44no—
287D4×C43—44no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—28no—
295C2×C4×C43—28no—
296C2×C4×C43—28no—
297C2×C4×C43—24no—
298C2×C4×C43—24no—
299C2×C4×C43—24no—
300C2×C4×C43—24no—
301C2×C4×C43—24no—
302C2×C4×C43—24no—
303C2×C4×C43—84no—
304C2×C4×C43C23×C412yes—
305C2×C4×C43C23×C412yes—
306C2×C4×C43C23×C412yes—
307C2×C4×C43C23×C412yes—
308C2×C4×C43H(5,𝔽2)12yes—
309C2×C4×C43H(5,𝔽2)12yes—
310C22⋊D43—416no—
311C22⋊D43—416no—
312C2×Dic43—22no—
313C2×Dic43—24no—
314C2×Dic43—22no—
315C2×Dic43—24no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—44no—
326C2×Dic43—44no—
327C2×Dic43C23×C418yes—
328C2×Dic43H(5,𝔽2)14yes—
329D172—216no—
330D172—48no—
331C4×D43—88no—
332C4×D43—88no—
333#34411—431nomaximal, Sylow
334C22×C43—22no—
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—24no—
338C22×C43—24no—
339C22×C43—24no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43C24×C411yescharacteristic
350C22×C43C2×H(5,𝔽2)12yes—
351C22×C43C2×H(5,𝔽2)11yescharacteristic
352C22×C43C2×H(5,𝔽2)11yescharacteristic
353C22×C43#58512yes—
354C2×D43—28no—
355C2×D43—28no—
356C2×D43—28no—
357C2×D43—44no—
358C2×D43—44no—
359C2×D43—44no—
360C2×D43—44no—
361C2×D43—816no—
362C4×C43—22no—
363C4×C43—22no—
364C4×C43—22no—
365C4×C43—44no—
366C4×C43—44no—
367C4×C43#51814yes—
368Dic43—28no—
369Dic43—24no—
370Dic43—42no—
371Dic43—42no—
372Dic43—42no—
373C2×#535—431no—
374#2380—432no—
375#2375—432no—
376#2366—432no—
377#2363—432no—
378#2361—432no—
379#2358—432no—
380#2347—432no—
381D4×C22⋊C4—432no—
382#2337—434no—
383#2324—432no—
384#2321—434no—
385#2311D4311yescharacteristic, complemented
386C4×#121—432no—
387#2297—431no—
388C2×C43—42no—
389C2×C43—42no—
390C2×C43—42no—
391C2×C43C2×#51811yescharacteristic
392C2×C43C4×H(5,𝔽2)12yes—
393C2×C43#353711yescharacteristic
394C2×C43#354011yescharacteristic
395C2×C43#354612yes—
396D43—48no—
397C22×#41C2×D4311yescharacteristic
398C23×D4—431no—
399#535—4316no—
400C2×#127—432no—
401C2×#124—432no—
402C2×#121—432no—
403C2×#121—432no—
404C2×#120—432no—
405C2×#120—432no—
406C2×C4×D4—434no—
407C2×C4×D4—432no—
408C2×C4×D4—432no—
409C2×C4×D4—434no—
410C2×#117—431no—
411C2×#117—431no—
412C2×#117C2×D4311yescharacteristic, complemented
413C22×C4⋊C4C2×D4311yescharacteristic, complemented
414C22×C22⋊C4—434no—
415C22×C42—431no—
416#391—432no—
417#391C2×D4312yescomplemented
418#390—432no—
419#390—432no—
420#390—432no—
421#390—434no—
422#390—434no—
423#390C2×D4312yes—
424#389—432no—
425#389—432no—
426#388—434no—
427#388—434no—
428#388—434no—
429#388—434no—
430#388—434no—
431#388—434no—
432#386—431no—
433#386—431no—
434#386—431no—
435#386—431no—
436#386—434no—
437#386—434no—
438#386—434no—
439#386—434no—
440#386—434no—
441#386—434no—
442#386C2×D4312yes—
443#386C2×D4312yescomplemented
444#385—434no—
445#385—434no—
446#383—434no—
447#380C2×D4312yes—
448#380C2×D4312yescomplemented
449#379—434no—
450C4×C4⋊C4—432no—
451C4×C4⋊C4—432no—
452C4×C4⋊C4—434no—
453C4×C22⋊C4—432no—
454C4×C22⋊C4—432no—
455C4×C22⋊C4—434no—
456C4×C22⋊C4—434no—
457C43#3441111yescharacteristic, complemented, Sylow
458C25—432no—
459C2×#41—42no—
460C2×#41—42no—
461C2×#41C4×D4318yescomplemented
462C22×Q8C22×D4311yescharacteristic
463C22×D4—434no—
464C22×D4—434no—
465C22×D4—438no—
466C22×D4—432no—
467C22×D4—432no—
468C22×D4—1722no—
469C22×D4—1722no—
470C22×D4C22×D4311yescharacteristic
471C22×D4C22×D4311yescharacteristic
472C22×D4C22×D4311yescharacteristic
473C23×C4—431no—
474C23×C4—431no—
475C23×C4—434no—
476C23×C4—434no—
477C23×C4C22×D4311yescharacteristic
478C23×C4C22×D4311yescharacteristic
479C23×C4C22×D4311yescharacteristic
480C23×C4C22×D4312yes—
481#127—4316no—
482#124—4316no—
483#121—4316no—
484#121—4316no—
485#120—4316no—
486#120—4316no—
487C4×D4—1724no—
488C4×D4—1724no—
489C4×D4—1728no—
490C4×D4—1728no—
491#117—42no—
492#117—438no—
493#117—1722no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—432no—
496C2×C4⋊C4—434no—
497C2×C4⋊C4—432no—
498C2×C4⋊C4—434no—
499C2×C4⋊C4C22×D4312yes—
500C2×C4⋊C4C22×D4312yes—
501C2×C4⋊C4C22×D4312yes—
502C2×C22⋊C4—432no—
503C2×C22⋊C4—434no—
504C2×C22⋊C4—434no—
505C2×C22⋊C4—432no—
506C2×C22⋊C4—432no—
507C2×C22⋊C4—434no—
508C2×C22⋊C4—431no—
509C2×C22⋊C4—431no—
510C2×C22⋊C4—432no—
511C2×C22⋊C4—432no—
512C2×C22⋊C4—434no—
513C2×C22⋊C4—434no—
514C2×C22⋊C4—434no—
515C2×C22⋊C4—434no—
516C2×C22⋊C4—434no—
517C2×C22⋊C4—1728no—
518C2×C22⋊C4C22×D4314yes—
519C2×C22⋊C4C22×D4312yes—
520C2×C22⋊C4C22×D4314yes—
521C2×C42—432no—
522C2×C42—432no—
523C2×C42—432no—
524C2×C42—434no—
525C2×C42—434no—
526C2×C42—432no—
527C2×C42—1722no—
528C2×C42C22×D4312yes—
529#95—432no—
530#95—432no—
531#95—432no—
532#95—434no—
533#95—434no—
534#95—432no—
535#95—434no—
536#95—434no—
537#95C22×D4314yes—
538#95C22×D4314yes—
539C24—434no—
540C24—438no—
541C24—1724no—
542C24—1722no—
543C24—1722no—
544C24—1724no—
545C24C23×D4311yescharacteristic
546C24C23×D4311yescharacteristic
547C24C23×D4311yescharacteristic
548#41—416no—
549C2×Q8—41no—
550C2×Q8—41no—
551C2×Q8C2×C4×D4314yes—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—4316no—
559C2×D4—4316no—
560C2×D4—438no—
561C2×D4—438no—
562C2×D4—864no—
563C2×D4—864no—
564C2×D4—17216no—
565C2×D4—1722no—
566C2×D4—1722no—
567C2×D4—1724no—
568C2×D4—1724no—
569C2×D4—1724no—
570C2×D4—1724no—
571C2×D4C2×C4×D4314yes—
572C2×D4C2×C4×D4314yes—
573C2×D4C2×C4×D4314yes—
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—434no—
583C22×C4—432no—
584C22×C4—432no—
585C22×C4—432no—
586C22×C4—432no—
587C22×C4—868no—
588C22×C4—864no—
589C22×C4—1724no—
590C22×C4—1724no—
591C22×C4—1724no—
592C22×C4—1724no—
593C22×C4—1724no—
594C22×C4—1721no—
595C22×C4—1721no—
596C22×C4—1722no—
597C22×C4C2×C4×D4314yes—
598C22×C4C2×C4×D4314yes—
599C22×C4C2×C4×D4314yes—
600C22×C4C23×D4314yes—
601C22×C4C23×D4314yes—
602C22×C4C23×D4311yescharacteristic
603C22×C4C23×D4311yescharacteristic
604C22×C4C23×D4311yescharacteristic
605C22×C4C23×D4311yescharacteristic
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—42no—
609C4⋊C4—438no—
610C4⋊C4—868no—
611C4⋊C4—1722no—
612C4⋊C4—1724no—
613C22⋊C4—44no—
614C22⋊C4—42no—
615C22⋊C4—44no—
616C22⋊C4—438no—
617C22⋊C4—4316no—
618C22⋊C4—4316no—
619C22⋊C4—868no—
620C22⋊C4—864no—
621C22⋊C4—864no—
622C22⋊C4—1724no—
623C22⋊C4—1724no—
624C22⋊C4—1724no—
625C22⋊C4—1724no—
626C22⋊C4—1724no—
627C22⋊C4—1721no—
628C22⋊C4—1721no—
629C22⋊C4—1722no—
630C22⋊C4—1722no—
631C42—42no—
632C42—438no—
633C42—864no—
634C42—864no—
635C42—1722no—
636C42—1724no—
637C42—1724no—
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—438no—
651C23—864no—
652C23—864no—
653C23—864no—
654C23—864no—
655C23—864no—
656C23—864no—
657C23—3444no—
658C23—3444no—
659C23—3448no—
660C23—1728no—
661C23—17216no—
662C23C22×C4×D4312yes—
663C23C22×C4×D4312yes—
664C23C22×C4×D4312yes—
665C23C24×D4311yescharacteristic
666Q8—44no—
667D4—44no—
668D4—44no—
669D4—44no—
670D4—8616no—
671D4—1728no—
672D4—17216no—
673D4—17216no—
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—438no—
691C2×C4—434no—
692C2×C4—864no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—864no—
696C2×C4—862no—
697C2×C4—862no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—3448no—
706C2×C4—3448no—
707C2×C4—1724no—
708C2×C4—1724no—
709C2×C4C22×C4×D4312yes—
710C2×C4C22×C4×D4312yes—
711C2×C4C22×C4×D4312yes—
712C2×C4C22×C4×D4312yes—
713C2×C4#1306337012yes—
714C2×C4#1306337012yes—
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—868no—
731C22—868no—
732C22—868no—
733C22—34416no—
734C22—1724no—
735C22—1724no—
736C22—1724no—
737C22—1724no—
738C22C23×C4×D4311yescharacteristic
739C22H(5,𝔽2)×D4312yes—
740C22C2×#1306337011yescharacteristic
741C22C2×#1306337011yescharacteristic
742C22#1458373612yes—
743C4—22no—
744C4—22no—
745C4—22no—
746C4—44no—
747C4—44no—
748C4—868no—
749C4—864no—
750C4—1722no—
751C4—1722no—
752C4—1722no—
753C4#1458337214yes—
754C2—42no—
755C2—42no—
756C2—42no—
757C2—1728no—
758C2C2×#1458337211yescharacteristic
759C2#1914780112yes—
760C2#1914882811yescharacteristic
761C2#1914887211yescharacteristic
762C2#1914895712yes—
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2311C2
socle, cosocleC23×C43C25
prime radicalC2×#14583463C2
hypercenter#2311D43
hypocenterC43#34411
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. #19137770C2semidirect
3. #19137732C2semidirect
4. #19137658C2semidirect
5. #19137633C2semidirect
6. #19137611C2semidirect
7. #19137576C2semidirect
8. #19137490C2semidirect
9. #19137415C2semidirect
10. #19137407C2semidirect
11. #19137284C2semidirect
12. #19137251C2semidirect
13. #19137101C2semidirect
14. #19137086C2semidirect
15. C43×#2311C2semidirect
17. #14583463C4semidirect
26. C2×C4×C22⋊D43C22semidirect
27. C2×(C22⋊D43)⋊C4C22semidirect
29. C2×#13063284C22semidirect
31. C22×C4×Dic43C22semidirect
32. #14582806C22semidirect
36. #14582799C22semidirect
37. #14582799C22semidirect
38. #14582795C22semidirect
39. #14582795C22semidirect
40. #14582791C22semidirect
41. #14582790C22semidirect
42. #14582789C22semidirect
43. #14582788C22semidirect
48. #14582779C22semidirect
49. #14582779C22semidirect
50. #14582778C22semidirect
53. #14582776C22semidirect
54. #14582775C22semidirect
55. #14582775C22semidirect
56. #14582773C22semidirect
57. #14582770C22semidirect
58. #14582766C22semidirect
60. C4⋊C4×Dic43C22semidirect
61. C4⋊C4×Dic43C22semidirect
62. #14582750C22semidirect
63. C4×(C2×D43)⋊C4C22semidirect
65. C4×C22⋊Dic43C22semidirect
66. #14582746C22semidirect
68. C2×#117×C43C22semidirect
69. C22×C4⋊C4×C43C22semidirect
70. C43×#391C22semidirect
73. C43×#386C22semidirect
75. C43×#380C22semidirect
79. C22×D172C2×C4semidirect
88. #13063321C2×C4semidirect
89. #13063314C2×C4semidirect
90. #13063299C2×C4semidirect
91. #13063299C2×C4semidirect
92. #13063293C2×C4semidirect
93. #13063293C2×C4semidirect
99. #13063284C2×C4semidirect
137. C2×#41×C43C2×C4semidirect
385. #2311D43semidirect
412. C2×#117C2×D43semidirect
413. C22×C4⋊C4C2×D43semidirect
417. #391C2×D43semidirect
443. #386C2×D43semidirect
448. #380C2×D43semidirect
457. C43#34411semidirect
461. C2×#41C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834632
#191377702
#191377322
#191376582
#191376332
#191376112
#191375762
#191374902
#191374152
#191374072
#191372842
#191372512
#191371012
#191370862
C43×#23112
#3441143