Finite Group Databasebeta

← #25257152

Subgroups — #25257152

Order 11008.

2698 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583411C211yesmaximal, characteristic
2#19137725C214yesmaximal, complemented
3#19137635C212yesmaximal, complemented
4#19137621C212yesmaximal, complemented
5#19137566C212yesmaximal, complemented
6#19137528C212yesmaximal, complemented
7#19137480C211yesmaximal, characteristic, complemented
8#19137435C211yesmaximal, characteristic, complemented
9#19137423C211yesmaximal, characteristic, complemented
10#19137248C214yesmaximal, complemented
11#19137226C212yesmaximal, complemented
12C4×#13063305C212yesmaximal, complemented
13#19137103C212yesmaximal, complemented
14#19136977C211yesmaximal, characteristic, complemented
15#19136955C212yesmaximal, complemented
16C4×C22⋊C4×D43C211yesmaximal, characteristic, complemented
17C43×#2347C211yesmaximal, characteristic, complemented
18C22×#10621898C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20#14583411C4116yescomplemented
21C2×#13063309C2212yes—
22C2×#13063305C2211yescharacteristic
23C2×#13063305C2211yescharacteristic
24C2×#13063300C2211yescharacteristic
25C2×#13063300C2211yescharacteristic
26C2×#13063295C2212yes—
27C2×C4×Dic86C2212yescomplemented
28C2×C4×D172C2212yes—
29C2×C4×D172C2212yes—
30C2×#13063287C2214yes—
31C2×#13063287C2212yescomplemented
32C2×#13063283C2212yes—
33C2×C22⋊C4×D43C2212yes—
34C2×C42×D43C2212yes—
35#14582804C2212yescomplemented
36#14582801C2214yes—
37#14582801C2212yescomplemented
38#14582799C2214yes—
39#14582798C2212yescomplemented
40#14582792C2214yes—
41#14582791C2214yescomplemented
42#14582789C2214yes—
43#14582789C2214yescomplemented
44#14582788C2214yes—
45#14582784C2214yescomplemented
46#14582782C2214yescomplemented
47#14582777C2214yes—
48#14582777C2214yes—
49#14582775C2214yes—
50#14582773C2214yes—
51#14582765C2212yescomplemented
52#14582761C2212yes—
53#14582761C2212yescomplemented
54#14582759C2211yescharacteristic
55#14582758C2212yescomplemented
56#14582756C2212yes—
57#14582754C2212yes—
58C4⋊C4×Dic43C2212yescomplemented
59C4⋊C4×Dic43C2214yescomplemented
60C4×C4⋊Dic43C2214yescomplemented
61C22⋊C4×Dic43C2212yes—
62C22⋊C4×Dic43C2212yes—
63C4×(C2×D43)⋊C4C2212yes—
64C4×(C2×D43)⋊C4C2214yes—
65C4×(C2×D43)⋊C4C2214yescomplemented
66C4×C22⋊Dic43C2211yescharacteristic
67#14582746C2211yescharacteristic
68#14582746C2211yescharacteristic
69#14582746C2212yes—
70#14582746C2212yescomplemented
71#14582746C2214yescomplemented
72#14582745C2212yescomplemented
73#95×D43C2211yescharacteristic
74#95×D43C2211yescharacteristic
75#95×D43C2212yescomplemented
76C2×#117×C43C2211yescharacteristic
77C43×#389C2212yescomplemented
78C43×#388C2214yes—
79C43×#383C2212yescomplemented
80C43×#380C2211yescharacteristic
81C4×C4⋊C4×C43C2212yescomplemented
82C4×C4⋊C4×C43C2212yescomplemented
83C4×C22⋊C4×C43C2211yescharacteristic
84C24×D43C2311yescharacteristic
85C2×#10621898—44no—
86C2×#10621898C2×C418yescomplemented
87C22×Dic86C2311yescharacteristic
88C22×D172C2311yescharacteristic
89C22×D172C2312yes—
90C22×D172C2312yes—
91C22×C22⋊D43C2312yes—
92C23×Dic43C2311yescharacteristic
93C22×C4×D43—44no—
94C22×C4×D43C2×C418yescomplemented
95C22×C4×D43C2311yescharacteristic
96C22×C4×D43C2311yescharacteristic
97C22×C4×D43C2312yes—
98C22×C4×D43C2314yes—
99C22×C4×D43C2311yescharacteristic
100C22×C4×D43C2311yescharacteristic
101C22×C4×D43C2312yes—
102C22×C4×D43C2312yes—
103#13063309C2×C4116yescomplemented
104#13063305C2×C418yescomplemented
105#13063305C2×C418yescomplemented
106#13063300C2×C418yes—
107#13063300C2×C418yescomplemented
108#13063295C2×C4116yescomplemented
109C4×Dic86—44no—
110C4×D172C2×C4116yescomplemented
111C4×D172C2×C4116yescomplemented
112#13063287—216no—
113#13063287—44no—
114#13063283—44no—
115C2×C4⋊Dic43C2312yes—
116C2×C4⋊Dic43C2314yes—
117C2×C4⋊Dic43C2312yes—
118C2×C4⋊Dic43C2312yes—
119C2×Dic43⋊C4C2314yes—
120C2×C22⋊Dic43C2312yes—
121C2×C22⋊Dic43C2312yes—
122C2×(C2×D43)⋊C4C2312yes—
123C2×(C2×D43)⋊C4C2312yes—
124C2×(C2×D43)⋊C4C2314yes—
125C2×(C2×D43)⋊C4C2314yes—
126C2×(C2×D43)⋊C4C2314yes—
127C2×(C2×D43)⋊C4C2314yes—
128C2×(C2×D43)⋊C4C2314yes—
129C2×(C2×D43)⋊C4C2312yes—
130C2×(C2×D43)⋊C4C2312yes—
131C2×(C2×D43)⋊C4C2312yes—
132C2×(C2×D43)⋊C4C2312yes—
133C22⋊C4×D43—28no—
134C2×C4×Dic43C2314yes—
135C2×C4×Dic43C2312yes—
136C2×C4×Dic43C2312yes—
137C2×C4×Dic43C2314yes—
138C2×C4×Dic43C2312yes—
139C2×C4×Dic43C2314yes—
140C42×D43—44no—
141C43⋊#95C2314yes—
142C43⋊#95C2314yes—
143C43⋊#95C2314yes—
144C43⋊#95C2314yes—
145C43⋊#95C2314yes—
146C43⋊#95C2312yes—
147C43⋊#95C2311yescharacteristic
148C43⋊#95C2311yescharacteristic
149C43⋊#95C2312yes—
150C43⋊#95C2312yes—
151C23×C4×C43C2311yescharacteristic
152#117×C43C2×C418yescomplemented
153C2×C4⋊C4×C43C2314yes—
154C2×C4⋊C4×C43C2312yes—
155C2×C4⋊C4×C43C2311yescharacteristic
156C2×C4⋊C4×C43C2311yescharacteristic
157C2×C22⋊C4×C43C2312yes—
158C2×C22⋊C4×C43C2312yes—
159C2×C22⋊C4×C43C2312yes—
160C2×C42×C43C2312yes—
161C2×C42×C43C2314yes—
162C2×C42×C43C2312yes—
163#95×C43C2314yes—
164#95×C43C2314yes—
165#95×C43C2311yescharacteristic
166#95×C43C2311yescharacteristic
167#95×C43C2312yes—
168C24×C43C2411yescharacteristic
169C23×D43—24no—
170C23×D43—42no—
171C23×D43—41no—
172C23×D43—41no—
173C23×D43C22×C414yes—
174C23×D43C2411yescharacteristic
175C23×D43C2412yes—
176C23×D43C2411yescharacteristic
177C22×C4×C43—24no—
178C22×C4×C43C22×C414yes—
179C22×C4×C43C2412yes—
180C22×C4×C43C2414yes—
181C22×C4×C43C2411yescharacteristic
182C22×C4×C43C2412yes—
183C22×C4×C43C2412yes—
184C22×C4×C43C2412yes—
185C22×C4×C43C2411yescharacteristic
186C2×C22⋊D43—44no—
187C2×C22⋊D43C22×C418yes—
188C22×Dic43—42no—
189C22×Dic43C22×C414yes—
190C22×Dic43C2412yes—
191C22×Dic43C2414yes—
192C22×Dic43C2411yescharacteristic
193C22×Dic43C2411yescharacteristic
194C22×Dic43C2412yes—
195C22×Dic43C2412yes—
196#10621898—416no—
197C2×D172—24no—
198C2×D172—28no—
199C2×D172—42no—
200C2×D172—42no—
201C2×D172C22×C418yes—
202C2×D172C22×C414yes—
203C2×D172C22×C418yes—
204C2×C4×D43—24no—
205C2×C4×D43—24no—
206C2×C4×D43—28no—
207C2×C4×D43—24no—
208C2×C4×D43—42no—
209C2×C4×D43—42no—
210C2×C4×D43—42no—
211C2×C4×D43—42no—
212C2×C4×D43—42no—
213C2×C4×D43—42no—
214C2×C4×D43—44no—
215C2×C4×D43—44no—
216C2×C4×D43—44no—
217C2×C4×D43—416no—
218C2×C4×D43C22×C414yes—
219C2×C4×D43C22×C414yes—
220C2×C4×D43C22×C414yes—
221C2×C4×D43C22×C414yes—
222C2×C4×D43C22×C418yes—
223C2×C4×D43#4118yescomplemented
224C2×Dic86—24no—
225C2×Dic86C22×C414yes—
226C4⋊C4×C43—28no—
227C4⋊C4×C43—24no—
228C4⋊C4×C43C22×C414yes—
229C4⋊C4×C43C22×C414yes—
230C22⋊C4×C43—24no—
231C22⋊C4×C43—42no—
232C22⋊C4×C43C22×C418yes—
233C42×C43—24no—
234C42×C43—44no—
235C42×C43C22×C418yes—
236C22⋊Dic43—24no—
237C22⋊Dic43—42no—
238(C2×D43)⋊C4—24no—
239(C2×D43)⋊C4—28no—
240(C2×D43)⋊C4—24no—
241(C2×D43)⋊C4—28no—
242(C2×D43)⋊C4—44no—
243(C2×D43)⋊C4—44no—
244(C2×D43)⋊C4—44no—
245(C2×D43)⋊C4C22×C418yes—
246(C2×D43)⋊C4C22×C418yes—
247(C2×D43)⋊C4C22×C418yes—
248(C2×D43)⋊C4C22×C418yes—
249C4⋊Dic43—24no—
250C4⋊Dic43—44no—
251C4⋊Dic43C22×C418yes—
252C4⋊Dic43C22×C418yes—
253Dic43⋊C4—44no—
254C4×Dic43—24no—
255C4×Dic43—28no—
256C4×Dic43—42no—
257C4×Dic43—42no—
258C4×Dic43—44no—
259C4×Dic43—44no—
260C23×C43—22no—
261C23×C43—22no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43C23×C412yes—
265C23×C43C2511yescharacteristic
266C22×D43—22no—
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—22no—
270C22×D43—24no—
271C22×D43—22no—
272C22×D43—24no—
273C22×D43—22no—
274C22×D43—22no—
275C22×D43—21no—
276C22×D43—21no—
277C22×D43—28no—
278C22×D43—44no—
279C22×D43—44no—
280C22×D43—48no—
281C22×D43—48no—
282C22×D43C23×C412yes—
283C22×D43C23×C414yes—
284C22×D43C23×C412yes—
285C22×D43C2×#4114yes—
286C2×C4×C43—24no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—28no—
293C2×C4×C43—22no—
294C2×C4×C43—24no—
295C2×C4×C43—22no—
296C2×C4×C43—24no—
297C2×C4×C43—22no—
298C2×C4×C43—24no—
299C2×C4×C43C23×C414yes—
300C2×C4×C43C23×C414yes—
301C2×C4×C43C23×C412yes—
302C2×C4×C43C23×C412yes—
303C2×C4×C43C2×#4114yes—
304C2×C4×C43H(5,𝔽2)14yes—
305C22⋊D43—48no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—24no—
310C2×Dic43—22no—
311C2×Dic43—24no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—24no—
315C2×Dic43—22no—
316C2×Dic43—24no—
317C2×Dic43—44no—
318C2×Dic43C23×C414yes—
319C2×Dic43C23×C412yes—
320C2×Dic43C23×C412yes—
321C2×Dic43C2×#4114yes—
322D172—216no—
323D172—28no—
324D172—48no—
325C4×D43—28no—
326C4×D43—28no—
327C4×D43—44no—
328C4×D43—44no—
329C4×D43—48no—
330C4×D43—48no—
331C4×D43—48no—
332C4×D43—88no—
333Dic86—28no—
334#34223—431nomaximal, Sylow
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—42no—
339C22×C43—42no—
340C22×C43C24×C411yescharacteristic
341C22×C43C22×#4112yes—
342C22×C43C2×H(5,𝔽2)12yes—
343C22×C43#58511yescharacteristic
344C22×C43#58511yescharacteristic
345C2×D43—22no—
346C2×D43—22no—
347C2×D43—24no—
348C2×D43—24no—
349C2×D43—22no—
350C2×D43—24no—
351C2×D43—22no—
352C2×D43—24no—
353C2×D43—22no—
354C2×D43—24no—
355C2×D43—416no—
356C2×D43—42no—
357C2×D43—44no—
358C2×D43—44no—
359C2×D43—42no—
360C2×D43C4×#4114yes—
361C4×C43—24no—
362C4×C43—22no—
363C4×C43—24no—
364C4×C43—24no—
365C4×C43—44no—
366C4×C43—42no—
367C4×C43#51814yes—
368Dic43—24no—
369Dic43—22no—
370Dic43—22no—
371Dic43—24no—
372Dic43—42no—
373Dic43—44no—
374C2×#525—431no—
375#2374—434no—
376#2363—432no—
377#2362—432no—
378#2357—432no—
379#2353—432no—
380#2347D4311yescharacteristic, complemented
381#2346—431no—
382#2341—431no—
383#2339—431no—
384#2321—434no—
385#2318—432no—
386C4×C22⋊Q8—432no—
387C4×#121—432no—
388#2280—431no—
389#2275—432no—
390C2×C4×C22⋊C4—431no—
391C2×C43—42no—
392C2×C43C2×C4×#4111yescharacteristic
393C2×C43C2×#51811yescharacteristic
394C2×C43#342811yescharacteristic
395C2×C43#350512yes—
396C2×C43#350612yes—
397D43—24no—
398D43—44no—
399D43—42no—
400C22×#41—431no—
401C24×C4—431no—
402#525—4316no—
403C2×#123—432no—
404C2×C22⋊Q8—431no—
405C2×C22⋊Q8—431no—
406C2×#121—431no—
407C2×#121—431no—
408C2×#120—432no—
409C2×C4×Q8—432no—
410C2×C4×D4—434no—
411C2×C4×D4—432no—
412C2×C4×D4—432no—
413C2×C4×D4—432no—
414C2×#117—432no—
415C2×#117C2×D4311yescharacteristic
416C22×C22⋊C4—432no—
417C22×C42—432no—
418#391—432no—
419#390—434no—
420#390—434no—
421#390—432no—
422#389—432no—
423#389C2×D4312yescomplemented
424#388—434no—
425#388—434no—
426#388—434no—
427#388—434no—
428#388—434no—
429#388C2×D4314yes—
430#387—434no—
431#387—434no—
432#386—434no—
433#386—434no—
434#386—434no—
435#385—434no—
436#383C2×D4312yescomplemented
437#382—432no—
438#381—432no—
439#381—432no—
440#380—431no—
441#380—432no—
442#380—432no—
443#380C2×D4311yescharacteristic
444#379—432no—
445C4×C4⋊C4—432no—
446C4×C4⋊C4—434no—
447C4×C4⋊C4—434no—
448C4×C4⋊C4C2×D4312yescomplemented
449C4×C4⋊C4C2×D4312yescomplemented
450C4×C22⋊C4—431no—
451C4×C22⋊C4—432no—
452C4×C22⋊C4—432no—
453C4×C22⋊C4—434no—
454C4×C22⋊C4—432no—
455C4×C22⋊C4—434no—
456C4×C22⋊C4—432no—
457C4×C22⋊C4—432no—
458C4×C22⋊C4—431no—
459C4×C22⋊C4—434no—
460C4×C22⋊C4—431no—
461C4×C22⋊C4C2×D4311yescharacteristic
462#376—432no—
463C2×#95—431no—
464C2×#95—432no—
465C2×#95—431no—
466C43#3422311yescharacteristic, complemented, Sylow
467C25—431no—
468C2×#41—438no—
469C2×#41—1724no—
470C22×Q8—431no—
471C22×D4—432no—
472C22×D4—432no—
473C22×D4—431no—
474C22×D4—432no—
475C23×C4—431no—
476C23×C4—431no—
477C23×C4—431no—
478C23×C4—438no—
479C23×C4—432no—
480C23×C4—431no—
481C23×C4—431no—
482C23×C4—432no—
483C23×C4—432no—
484C23×C4—434no—
485C23×C4—1724no—
486C23×C4C22×D4311yescharacteristic
487#123—4316no—
488C22⋊Q8—438no—
489C22⋊Q8—438no—
490#121—438no—
491#121—438no—
492#120—4316no—
493C4×Q8—1724no—
494C4×D4—4316no—
495C4×D4—4316no—
496C4×D4—8616no—
497C4×D4—1724no—
498#117—1724no—
499#117C4×D4318yescomplemented
500C2×C4⋊C4—432no—
501C2×C4⋊C4—432no—
502C2×C4⋊C4—432no—
503C2×C4⋊C4—434no—
504C2×C4⋊C4—434no—
505C2×C4⋊C4C22×D4312yes—
506C2×C4⋊C4C22×D4314yes—
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C4⋊C4C22×D4311yescharacteristic
509C2×C22⋊C4—432no—
510C2×C22⋊C4—432no—
511C2×C22⋊C4—432no—
512C2×C22⋊C4—432no—
513C2×C22⋊C4—432no—
514C2×C22⋊C4—432no—
515C2×C22⋊C4—432no—
516C2×C22⋊C4—434no—
517C2×C22⋊C4—434no—
518C2×C22⋊C4—432no—
519C2×C22⋊C4—434no—
520C2×C22⋊C4—434no—
521C2×C22⋊C4—434no—
522C2×C22⋊C4—868no—
523C2×C22⋊C4C22×D4312yes—
524C2×C22⋊C4C22×D4312yes—
525C2×C22⋊C4C22×D4312yes—
526C2×C42—434no—
527C2×C42—432no—
528C2×C42—434no—
529C2×C42—434no—
530C2×C42—432no—
531C2×C42—432no—
532C2×C42—1724no—
533C2×C42C22×D4312yes—
534C2×C42C22×D4314yes—
535C2×C42C22×D4312yes—
536#95—431no—
537#95—432no—
538#95—431no—
539#95—432no—
540#95—434no—
541#95—432no—
542#95—434no—
543#95—434no—
544#95—434no—
545#95—434no—
546#95C22×D4311yescharacteristic
547#95C22×D4311yescharacteristic
548#95C22×D4312yes—
549#95C22×D4314yes—
550#95C22×D4314yes—
551C24—431no—
552C24—431no—
553C24—432no—
554C24—434no—
555C24—864no—
556C24—1722no—
557C24—1721no—
558C24—1721no—
559C24C23×D4311yescharacteristic
560#41—17216no—
561C2×Q8—434no—
562C2×Q8—864no—
563C2×D4—438no—
564C2×D4—438no—
565C2×D4—434no—
566C2×D4—438no—
567C2×D4—868no—
568C2×D4—864no—
569C2×D4—1722no—
570C2×D4—1722no—
571C2×D4—1724no—
572C22×C4—24no—
573C22×C4—432no—
574C22×C4—431no—
575C22×C4—431no—
576C22×C4—432no—
577C22×C4—434no—
578C22×C4—434no—
579C22×C4—434no—
580C22×C4—434no—
581C22×C4—434no—
582C22×C4—438no—
583C22×C4—438no—
584C22×C4—432no—
585C22×C4—434no—
586C22×C4—868no—
587C22×C4—864no—
588C22×C4—864no—
589C22×C4—864no—
590C22×C4—17216no—
591C22×C4—1724no—
592C22×C4—1724no—
593C22×C4—1722no—
594C22×C4—1722no—
595C22×C4—1722no—
596C22×C4—1722no—
597C22×C4—1724no—
598C22×C4—1722no—
599C22×C4—1722no—
600C22×C4—1722no—
601C22×C4C2×C4×D4314yes—
602C22×C4C23×D4314yes—
603C22×C4C23×D4312yes—
604C22×C4C23×D4311yescharacteristic
605C22×C4C23×D4312yes—
606C22×C4C23×D4312yes—
607C22×C4C23×D4312yes—
608C22×C4C23×D4311yescharacteristic
609C4⋊C4—28no—
610C4⋊C4—24no—
611C4⋊C4—438no—
612C4⋊C4—438no—
613C4⋊C4—864no—
614C4⋊C4—1724no—
615C4⋊C4—1724no—
616C4⋊C4C2×C4×D4314yes—
617C4⋊C4C2×C4×D4314yes—
618C22⋊C4—24no—
619C22⋊C4—42no—
620C22⋊C4—438no—
621C22⋊C4—438no—
622C22⋊C4—438no—
623C22⋊C4—438no—
624C22⋊C4—864no—
625C22⋊C4—868no—
626C22⋊C4—864no—
627C22⋊C4—864no—
628C22⋊C4—868no—
629C22⋊C4—1724no—
630C22⋊C4—1724no—
631C22⋊C4—1724no—
632C22⋊C4—1722no—
633C22⋊C4C2×C4×D4318yes—
634C42—24no—
635C42—44no—
636C42—868no—
637C42—864no—
638C42—1722no—
639C42—1722no—
640C42—1724no—
641C42—1724no—
642C42C2×C4×D4318yes—
643C23—22no—
644C23—22no—
645C23—21no—
646C23—21no—
647C23—432no—
648C23—434no—
649C23—432no—
650C23—434no—
651C23—868no—
652C23—862no—
653C23—861no—
654C23—861no—
655C23—862no—
656C23—864no—
657C23—862no—
658C23—864no—
659C23—862no—
660C23—861no—
661C23—862no—
662C23—861no—
663C23—1724no—
664C23—1724no—
665C23—1728no—
666C23—1728no—
667C23C22×C4×D4312yes—
668C23C24×D4311yescharacteristic
669Q8—868no—
670D4—8616no—
671D4—868no—
672D4—1728no—
673D4—1728no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—28no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—432no—
688C2×C4—432no—
689C2×C4—434no—
690C2×C4—434no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—864no—
695C2×C4—862no—
696C2×C4—868no—
697C2×C4—868no—
698C2×C4—864no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—864no—
702C2×C4—864no—
703C2×C4—862no—
704C2×C4—3448no—
705C2×C4—1724no—
706C2×C4—1724no—
707C2×C4—1728no—
708C2×C4—1728no—
709C2×C4—1728no—
710C2×C4—1724no—
711C2×C4C22×C4×D4312yes—
712C2×C4C22×C4×D4314yes—
713C2×C4C22×C4×D4314yes—
714C2×C4C22×C4×D4312yes—
715C2×C4#41×D4314yes—
716C2×C4#1306337114yes—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—42no—
721C22—42no—
722C22—434no—
723C22—862no—
724C22—862no—
725C22—864no—
726C22—864no—
727C22—862no—
728C22—864no—
729C22—862no—
730C22—864no—
731C22—864no—
732C22—862no—
733C22—17216no—
734C22—1724no—
735C22—1722no—
736C22—1722no—
737C22—1724no—
738C22C23×C4×D4311yescharacteristic
739C22C2×#41×D4312yes—
740C22C2×#1306337112yes—
741C22#1458373411yescharacteristic
742C22#1458373611yescharacteristic
743C4—22no—
744C4—24no—
745C4—24no—
746C4—24no—
747C4—44no—
748C4—42no—
749C4—862no—
750C4—862no—
751C4—864no—
752C4—864no—
753C4—1722no—
754C4—1724no—
755C4#1458337314yes—
756C2—42no—
757C2—864no—
758C2—1722no—
759C2—1724no—
760C2C4×#41×D4311yescharacteristic
761C2C2×#1458337311yescharacteristic
762C2#1914779511yescharacteristic
763C2#1914842412yes—
764C2#1914844812yes—
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2347C2
socle, cosocleC23×C43C25
prime radicalC2×#14583411C2
hypercenter#2347D43
hypocenterC43#34223
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2347

Complements

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

NH ≅ G/Ntype
2. #19137725C2semidirect
3. #19137635C2semidirect
4. #19137621C2semidirect
5. #19137566C2semidirect
6. #19137528C2semidirect
7. #19137480C2semidirect
8. #19137435C2semidirect
9. #19137423C2semidirect
10. #19137248C2semidirect
11. #19137226C2semidirect
12. C4×#13063305C2semidirect
13. #19137103C2semidirect
14. #19136977C2semidirect
15. #19136955C2semidirect
16. C4×C22⋊C4×D43C2semidirect
17. C43×#2347C2semidirect
20. #14583411C4semidirect
27. C2×C4×Dic86C22semidirect
31. C2×#13063287C22semidirect
35. #14582804C22semidirect
37. #14582801C22semidirect
39. #14582798C22semidirect
41. #14582791C22semidirect
43. #14582789C22semidirect
45. #14582784C22semidirect
46. #14582782C22semidirect
51. #14582765C22semidirect
53. #14582761C22semidirect
55. #14582758C22semidirect
58. C4⋊C4×Dic43C22semidirect
59. C4⋊C4×Dic43C22semidirect
60. C4×C4⋊Dic43C22semidirect
65. C4×(C2×D43)⋊C4C22semidirect
70. #14582746C22semidirect
71. #14582746C22semidirect
72. #14582745C22semidirect
75. #95×D43C22semidirect
77. C43×#389C22semidirect
79. C43×#383C22semidirect
81. C4×C4⋊C4×C43C22semidirect
82. C4×C4⋊C4×C43C22semidirect
86. C2×#10621898C2×C4semidirect
94. C22×C4×D43C2×C4semidirect
103. #13063309C2×C4semidirect
104. #13063305C2×C4semidirect
105. #13063305C2×C4semidirect
107. #13063300C2×C4semidirect
108. #13063295C2×C4semidirect
110. C4×D172C2×C4semidirect
111. C4×D172C2×C4semidirect
152. #117×C43C2×C4semidirect
223. C2×C4×D43#41semidirect
380. #2347D43semidirect
423. #389C2×D43semidirect
436. #383C2×D43semidirect
448. C4×C4⋊C4C2×D43semidirect
449. C4×C4⋊C4C2×D43semidirect
466. C43#34223semidirect
499. #117C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834112
#191377252
#191376352
#191376212
#191375662
#191375282
#191374802
#191374352
#191374232
#191372482
#191372262
C4×#130633052
#191371032
#191369772
#191369552
C4×C22⋊C4×D432
C43×#23472
#3422343