Finite Group Databasebeta

← #25256764

Subgroups — #25256764

Order 11008.

2914 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063287C211yesmaximal, characteristic
2#19137564C212yesmaximal, complemented
3#19137534C214yesmaximal, complemented
4#19137504C212yesmaximal, complemented
5#19137464C211yesmaximal, characteristic, complemented
6#19137445C212yesmaximal, complemented
7#19137437C212yesmaximal, complemented
8C22⋊C4×D172C211yesmaximal, characteristic
9#19137415C211yesmaximal, characteristic
10#19137234C212yesmaximal, complemented
11#19137227C214yesmaximal, complemented
12#19136990C211yesmaximal, characteristic, complemented
13#19136989C211yesmaximal, characteristic, complemented
14#19136974C212yesmaximal, complemented
15#381×D43C212yesmaximal, complemented
16#19136955C212yesmaximal, complemented
17C43×#2344C211yesmaximal, characteristic, complemented
18C23×D172C2211yescharacteristic
19C23×C4×D43C2212yes—
20C2×C4×D172C2212yes—
21C2×#13063287C4116yescomplemented
22C2×#13063287C2212yes—
23C2×#13063287C2211yescharacteristic
24C2×#13063287C2211yescharacteristic
25C2×#13063287C2211yescharacteristic
26C2×#13063287C2212yes—
27C2×#13063287C2211yescharacteristic
28C2×#13063287C2212yes—
29C2×#13063284C2212yes—
30C22×(C2×D43)⋊C4C2212yes—
31C2×C22⋊C4×D43C2212yes—
32C2×C22⋊C4×D43C2212yes—
33C22×C4×Dic43C2211yescharacteristic
34#14582801C2212yes—
35#14582800C2212yes—
36#14582798C2212yescomplemented
37#14582791C2214yescomplemented
38#14582790C2214yescomplemented
39#14582789C2214yescomplemented
40#14582788C2214yescomplemented
41#14582785C2214yescomplemented
42#14582777C2214yes—
43#14582777C2214yes—
44#14582773C2214yescomplemented
45#14582770C2214yescomplemented
46#14582766C2212yescomplemented
47#14582766C2212yescomplemented
48#14582764C2212yescomplemented
49#14582763C2212yescomplemented
50#14582762C2212yes—
51#14582761C2214yescomplemented
52#14582761C2214yescomplemented
53#14582760C2211yescharacteristic
54#14582760C2212yes—
55#14582760C2211yescharacteristic
56#14582759C2211yescharacteristic
57#14582757C2211yescharacteristic
58#14582757C2211yescharacteristic
59#14582756C2214yescomplemented
60#14582756C2214yescomplemented
61#14582754C2212yes—
62#14582754C2212yes—
63C4⋊C4×Dic43C2212yescomplemented
64C4⋊C4×Dic43C2212yescomplemented
65C4×Dic43⋊C4C2212yescomplemented
66C22⋊C4×Dic43C2212yes—
67C4×(C2×D43)⋊C4C2214yescomplemented
68C4×(C2×D43)⋊C4C2214yescomplemented
69C4×(C2×D43)⋊C4C2214yescomplemented
70C4×C22⋊Dic43C2211yescharacteristic
71#14582746C2214yescomplemented
72#14582745C2212yescomplemented
73#14582744C2212yescomplemented
74#95×D43C2214yescomplemented
75#95×D43C2214yescomplemented
76C2×#117×C43C2212yes—
77C22×C4⋊C4×C43C2211yescharacteristic
78C43×#389C2212yescomplemented
79C43×#387C2214yescomplemented
80C43×#381C2212yes—
81C43×#380C2211yescharacteristic
82C4×C4⋊C4×C43C2212yescomplemented
83C4×C22⋊C4×C43C2211yescharacteristic
84C24×D43C2312yes—
85C22×D172—28no—
86C22×D172C2×C418yes—
87C22×D172C2311yescharacteristic
88C22×D172C2312yes—
89C22×D172C2311yescharacteristic
90C23×Dic43C2311yescharacteristic
91C23×Dic43C2311yescharacteristic
92C22×C4×D43—44no—
93C22×C4×D43—44no—
94C22×C4×D43C2×C4116yescomplemented
95C22×C4×D43C2314yes—
96C22×C4×D43C2314yes—
97C22×C4×D43C2312yes—
98C22×C4×D43C2312yes—
99C22×C4×D43C2312yes—
100C22×C4×D43C2312yes—
101C4×D172—28no—
102#13063287—28no—
103#13063287C2×C418yes—
104#13063287C2×C418yes—
105#13063287C2×C418yescomplemented
106#13063287C2×C418yescomplemented
107#13063287C2×C4116yescomplemented
108#13063287C2×C4116yescomplemented
109#13063284—44no—
110C2×C4⋊Dic43C2312yes—
111C2×C4⋊Dic43C2314yes—
112C2×Dic43⋊C4C2312yes—
113C2×Dic43⋊C4C2312yes—
114C2×C22⋊Dic43C2311yescharacteristic
115C2×C22⋊Dic43C2312yes—
116C2×C22⋊Dic43C2311yescharacteristic
117C2×(C2×D43)⋊C4C2×C4116yescomplemented
118C2×(C2×D43)⋊C4C2314yes—
119C2×(C2×D43)⋊C4C2314yes—
120C2×(C2×D43)⋊C4C2314yes—
121C2×(C2×D43)⋊C4C2314yes—
122C2×(C2×D43)⋊C4C2314yes—
123C2×(C2×D43)⋊C4C2314yes—
124C2×(C2×D43)⋊C4C2312yes—
125C2×(C2×D43)⋊C4C2312yes—
126C2×(C2×D43)⋊C4C2312yes—
127C2×(C2×D43)⋊C4C2312yes—
128C22⋊C4×D43—44no—
129C22⋊C4×D43—44no—
130C2×C4×Dic43C2×C418yescomplemented
131C2×C4×Dic43C2312yes—
132C2×C4×Dic43C2314yes—
133C2×C4×Dic43C2314yes—
134C2×C4×Dic43C2311yescharacteristic
135C2×C4×Dic43C2311yescharacteristic
136C2×C4×Dic43C2311yescharacteristic
137C2×C4×Dic43C2311yescharacteristic
138C43⋊#95C2312yes—
139C43⋊#95C2312yes—
140C43⋊#95C2314yes—
141C43⋊#95C2314yes—
142C43⋊#95C2314yes—
143C43⋊#95C2312yes—
144C43⋊#95C2312yes—
145C43⋊#95C2312yes—
146C43⋊#95C2312yes—
147C43⋊#95C2314yes—
148C43⋊#95C2314yes—
149C43⋊#95C2312yes—
150C43⋊#95C2312yes—
151C23×C4×C43C2312yes—
152C23×C4×C43C2311yescharacteristic
153#117×C43—44no—
154C2×C4⋊C4×C43C2×C418yescomplemented
155C2×C4⋊C4×C43C2312yes—
156C2×C4⋊C4×C43C2314yes—
157C2×C4⋊C4×C43C2312yes—
158C2×C4⋊C4×C43C2311yescharacteristic
159C2×C4⋊C4×C43C2311yescharacteristic
160C2×C22⋊C4×C43C2311yescharacteristic
161C2×C22⋊C4×C43C2312yes—
162C2×C22⋊C4×C43C2311yescharacteristic
163C2×C42×C43C2312yes—
164C2×C42×C43C2314yes—
165#95×C43C2314yes—
166#95×C43C2314yes—
167#95×C43C2312yes—
168#95×C43C2312yes—
169C24×C43C2411yescharacteristic
170C23×D43—24no—
171C23×D43—24no—
172C23×D43—28no—
173C23×D43—44no—
174C23×D43C22×C418yes—
175C23×D43C2412yes—
176C23×D43C2412yes—
177C22×C4×C43—24no—
178C22×C4×C43—24no—
179C22×C4×C43—24no—
180C22×C4×C43C22×C414yes—
181C22×C4×C43C22×C418yes—
182C22×C4×C43C2412yes—
183C22×C4×C43C2414yes—
184C22×C4×C43C2412yes—
185C22×C4×C43C2411yescharacteristic
186C22×C4×C43C2412yes—
187C22×C4×C43C2412yes—
188C22×C4×C43C2411yescharacteristic
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—42no—
192C22×Dic43C22×C414yes—
193C22×Dic43C22×C414yes—
194C22×Dic43C2412yes—
195C22×Dic43C2414yes—
196C22×Dic43C2412yes—
197C22×Dic43C2411yescharacteristic
198C22×Dic43C2411yescharacteristic
199C22×Dic43C2411yescharacteristic
200C22×Dic43C2411yescharacteristic
201C2×D172—24no—
202C2×D172—232no—
203C2×D172—28no—
204C2×D172C22×C414yes—
205C2×D172C22×C418yes—
206C2×D172C22×C414yes—
207C2×D172#4118yes—
208C2×C4×D43—28no—
209C2×C4×D43—28no—
210C2×C4×D43—432no—
211C2×C4×D43—42no—
212C2×C4×D43—42no—
213C2×C4×D43—42no—
214C2×C4×D43—42no—
215C2×C4×D43—42no—
216C2×C4×D43—42no—
217C2×C4×D43—42no—
218C2×C4×D43—42no—
219C2×C4×D43—44no—
220C2×C4×D43—44no—
221C2×C4×D43—44no—
222C2×C4×D43—44no—
223C2×C4×D43C22×C418yes—
224C2×C4×D43C22×C418yes—
225C2×C4×D43C22×C418yes—
226C2×C4×D43C22×C418yes—
227C4⋊C4×C43—24no—
228C4⋊C4×C43—44no—
229C4⋊C4×C43C22×C414yes—
230C4⋊C4×C43C22×C414yes—
231C4⋊C4×C43C22×C418yes—
232C22⋊C4×C43—22no—
233C22⋊C4×C43—24no—
234C22⋊C4×C43—22no—
235C42×C43—24no—
236C42×C43—44no—
237C22⋊Dic43—22no—
238C22⋊Dic43—24no—
239C22⋊Dic43—22no—
240(C2×D43)⋊C4—28no—
241(C2×D43)⋊C4—28no—
242(C2×D43)⋊C4—44no—
243(C2×D43)⋊C4—44no—
244(C2×D43)⋊C4—44no—
245(C2×D43)⋊C4—44no—
246(C2×D43)⋊C4C22×C418yes—
247(C2×D43)⋊C4C22×C418yes—
248(C2×D43)⋊C4C22×C418yes—
249(C2×D43)⋊C4C22×C418yes—
250C4⋊Dic43—24no—
251C4⋊Dic43—44no—
252Dic43⋊C4—42no—
253Dic43⋊C4—42no—
254C4×Dic43—24no—
255C4×Dic43—44no—
256C4×Dic43—44no—
257C4×Dic43C22×C414yes—
258C4×Dic43C22×C414yes—
259C4×Dic43C22×C414yes—
260C4×Dic43C22×C414yes—
261C23×C43—22no—
262C23×C43—22no—
263C23×C43C23×C412yes—
264C23×C43H(5,𝔽2)12yes—
265C23×C43H(5,𝔽2)12yes—
266C23×C43C2511yescharacteristic
267C22×D43—22no—
268C22×D43—22no—
269C22×D43—24no—
270C22×D43—216no—
271C22×D43—24no—
272C22×D43—22no—
273C22×D43—22no—
274C22×D43—24no—
275C22×D43—216no—
276C22×D43—48no—
277C22×D43—416no—
278C22×D43—416no—
279C22×D43C23×C414yes—
280C22×D43C23×C414yes—
281C22×D43C2×#4118yes—
282C2×C4×C43—216no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—28no—
289C2×C4×C43—22no—
290C2×C4×C43—24no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—24no—
294C2×C4×C43—22no—
295C2×C4×C43—24no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43C23×C412yes—
299C2×C4×C43C23×C414yes—
300C2×C4×C43C23×C414yes—
301C2×C4×C43C23×C412yes—
302C2×C4×C43C2×#4114yes—
303C2×Dic43—28no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—24no—
313C2×Dic43—22no—
314C2×Dic43—24no—
315C2×Dic43—22no—
316C2×Dic43—24no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—44no—
320C2×Dic43C23×C412yes—
321C2×Dic43C23×C412yes—
322C2×Dic43C23×C412yes—
323C2×Dic43C23×C412yes—
324D172—216no—
325D172—28no—
326D172#117116yescomplemented
327C4×D43—48no—
328C4×D43—48no—
329C4×D43—48no—
330C4×D43—48no—
331C4×D43—88no—
332C4×D43—88no—
333#34190—431nomaximal, Sylow
334C22×C43—22no—
335C22×C43—22no—
336C22×C43—24no—
337C22×C43—24no—
338C22×C43#51814yes—
339C22×C43C24×C411yescharacteristic
340C22×C43C22×#4112yes—
341C22×C43C2×H(5,𝔽2)11yescharacteristic
342C22×C43C2×H(5,𝔽2)11yescharacteristic
343C22×C43#58512yes—
344C2×D43—24no—
345C2×D43—24no—
346C2×D43—28no—
347C2×D43—28no—
348C2×D43—24no—
349C2×D43—24no—
350C2×D43—24no—
351C2×D43—432no—
352C2×D43—44no—
353C2×D43—44no—
354C2×D43C2×#11718yes—
355C4×C43—22no—
356C4×C43—24no—
357C4×C43—24no—
358C4×C43—42no—
359C4×C43—44no—
360C4×C43—42no—
361C4×C43C2×#11714yes—
362Dic43—22no—
363Dic43—22no—
364Dic43—22no—
365Dic43—22no—
366Dic43—42no—
367Dic43—44no—
368Dic43—42no—
369C22×C4×D4—431no—
370#2357—432no—
371#2353—434no—
372#2349—432no—
373#2344—431no—
374#2344D4311yescharacteristic, complemented
375#2342—432no—
376#2342—432no—
377D4×C22⋊C4—431no—
378D4×C22⋊C4—431no—
379#2319—432no—
380#2318—434no—
381#2283—431no—
382#2283—431no—
383#2280—432no—
384C2×#381—432no—
385#2275—432no—
386C2×C43—24no—
387C2×C43C22×#11711yescharacteristic
388C2×C43C2×#51811yescharacteristic
389C2×C43#342811yescharacteristic
390C2×C43#351312yes—
391C2×C43#351312yes—
392D43—28no—
393D43—44no—
394C23×D4—431no—
395C24×C4—432no—
396C2×C4×D4—432no—
397C2×C4×D4—431no—
398C2×C4×D4—431no—
399C2×C4×D4—432no—
400C2×C4×D4—431no—
401C2×C4×D4—431no—
402C2×C4×D4—432no—
403C2×C4×D4—4316no—
404C2×C4×D4—432no—
405C2×#117—432no—
406C2×#117C2×D4312yes—
407C22×C4⋊C4C2×D4311yescharacteristic
408C22×C22⋊C4—432no—
409C22×C22⋊C4—432no—
410C22×C22⋊C4—432no—
411C22×C42—431no—
412#390—432no—
413#390—432no—
414#389—432no—
415#389C2×D4312yescomplemented
416#388—434no—
417#388—434no—
418#388—434no—
419#388—434no—
420#387—434no—
421#387C2×D4314yescomplemented
422#386—434no—
423#386—434no—
424#385—434no—
425#385—434no—
426#383—432no—
427#383—432no—
428#382—432no—
429#382—432no—
430#381—432no—
431#381—431no—
432#381—432no—
433#381—431no—
434#381—434no—
435#381—434no—
436#381C2×D4312yes—
437#380—431no—
438#380—434no—
439#380—434no—
440#380—431no—
441#380—431no—
442#380C2×D4311yescharacteristic
443#379—432no—
444#379—432no—
445C4×C4⋊C4—432no—
446C4×C4⋊C4—432no—
447C4×C4⋊C4—432no—
448C4×C4⋊C4C2×D4312yescomplemented
449C4×C22⋊C4—431no—
450C4×C22⋊C4—432no—
451C4×C22⋊C4—434no—
452C4×C22⋊C4—434no—
453C4×C22⋊C4—434no—
454C4×C22⋊C4—434no—
455C4×C22⋊C4C2×D4311yescharacteristic
456#376—432no—
457#376—432no—
458C2×#95—434no—
459C2×#95—434no—
460C43#3419011yescharacteristic, complemented, Sylow
461C25—432no—
462C22×D4—438no—
463C22×D4—431no—
464C22×D4—432no—
465C22×D4—431no—
466C22×D4—868no—
467C23×C4—431no—
468C23×C4—431no—
469C23×C4—4316no—
470C23×C4—432no—
471C23×C4—432no—
472C23×C4—432no—
473C23×C4—432no—
474C23×C4—434no—
475C23×C4—434no—
476C23×C4—1724no—
477C23×C4—1724no—
478C23×C4C22×D4312yes—
479C23×C4C22×D4311yescharacteristic
480C4×D4—438no—
481C4×D4—438no—
482C4×D4—4316no—
483C4×D4—438no—
484C4×D4—4316no—
485C4×D4—438no—
486C4×D4—868no—
487C4×D4—868no—
488#117—44no—
489#117—1724no—
490C2×C4⋊C4—432no—
491C2×C4⋊C4—434no—
492C2×C4⋊C4—432no—
493C2×C4⋊C4—432no—
494C2×C4⋊C4C4×D4318yescomplemented
495C2×C4⋊C4C22×D4312yes—
496C2×C4⋊C4C22×D4314yes—
497C2×C4⋊C4C22×D4311yescharacteristic
498C2×C4⋊C4C22×D4312yes—
499C2×C4⋊C4C22×D4311yescharacteristic
500C2×C22⋊C4—4316no—
501C2×C22⋊C4—432no—
502C2×C22⋊C4—432no—
503C2×C22⋊C4—432no—
504C2×C22⋊C4—432no—
505C2×C22⋊C4—431no—
506C2×C22⋊C4—432no—
507C2×C22⋊C4—431no—
508C2×C22⋊C4—434no—
509C2×C22⋊C4—434no—
510C2×C22⋊C4—434no—
511C2×C22⋊C4—434no—
512C2×C22⋊C4—434no—
513C2×C22⋊C4—434no—
514C2×C22⋊C4—1724no—
515C2×C22⋊C4—1724no—
516C2×C22⋊C4C22×D4311yescharacteristic
517C2×C22⋊C4C22×D4312yes—
518C2×C22⋊C4C22×D4311yescharacteristic
519C2×C42—438no—
520C2×C42—431no—
521C2×C42—431no—
522C2×C42—431no—
523C2×C42—431no—
524C2×C42—432no—
525C2×C42—434no—
526C2×C42—434no—
527C2×C42C22×D4312yes—
528C2×C42C22×D4314yes—
529#95—432no—
530#95—432no—
531#95—434no—
532#95—434no—
533#95—434no—
534#95—434no—
535#95—432no—
536#95—432no—
537#95—432no—
538#95—432no—
539#95—432no—
540#95—434no—
541#95—432no—
542#95C22×D4314yes—
543#95C22×D4314yes—
544#95C22×D4312yes—
545#95C22×D4312yes—
546C24—432no—
547C24—432no—
548C24—438no—
549C24—868no—
550C24—864no—
551C24—864no—
552C24—1724no—
553C24C23×D4311yescharacteristic
554C2×D4—434no—
555C2×D4—438no—
556C2×D4—434no—
557C2×D4—438no—
558C2×D4—8632no—
559C2×D4—868no—
560C2×D4—864no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—434no—
565C22×C4—431no—
566C22×C4—431no—
567C22×C4—431no—
568C22×C4—431no—
569C22×C4—434no—
570C22×C4—438no—
571C22×C4—438no—
572C22×C4—438no—
573C22×C4—438no—
574C22×C4—432no—
575C22×C4—434no—
576C22×C4—432no—
577C22×C4—868no—
578C22×C4—868no—
579C22×C4—862no—
580C22×C4—862no—
581C22×C4—1724no—
582C22×C4—1724no—
583C22×C4—1724no—
584C22×C4—1724no—
585C22×C4—17232no—
586C22×C4—1722no—
587C22×C4—1722no—
588C22×C4—1722no—
589C22×C4—1722no—
590C22×C4—1722no—
591C22×C4—1722no—
592C22×C4—1722no—
593C22×C4—1722no—
594C22×C4—1722no—
595C22×C4C2×C4×D4314yes—
596C22×C4C2×C4×D4318yes—
597C22×C4C23×D4312yes—
598C22×C4C23×D4314yes—
599C22×C4C23×D4312yes—
600C22×C4C23×D4311yescharacteristic
601C22×C4C23×D4312yes—
602C22×C4C23×D4312yes—
603C22×C4C23×D4311yescharacteristic
604C4⋊C4—24no—
605C4⋊C4—44no—
606C4⋊C4—864no—
607C4⋊C4—1724no—
608C4⋊C4—1722no—
609C4⋊C4—1722no—
610C4⋊C4C2×C4×D4318yes—
611C4⋊C4C2×C4×D4314yes—
612C4⋊C4C2×C4×D4314yes—
613C22⋊C4—24no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—438no—
617C22⋊C4—438no—
618C22⋊C4—438no—
619C22⋊C4—438no—
620C22⋊C4—868no—
621C22⋊C4—868no—
622C22⋊C4—862no—
623C22⋊C4—864no—
624C22⋊C4—862no—
625C22⋊C4—1724no—
626C22⋊C4—1724no—
627C22⋊C4—1724no—
628C22⋊C4—1724no—
629C42—24no—
630C42—44no—
631C42—434no—
632C42—434no—
633C42—434no—
634C42—434no—
635C42—864no—
636C42—1724no—
637C42—1724no—
638C23—22no—
639C23—22no—
640C23—434no—
641C23—438no—
642C23—434no—
643C23—8616no—
644C23—862no—
645C23—862no—
646C23—864no—
647C23—8616no—
648C23—864no—
649C23—862no—
650C23—862no—
651C23—864no—
652C23—1728no—
653C23—17216no—
654C23—17216no—
655C23C22×C4×D4312yes—
656C23#1306337012yes—
657C23#1306337112yes—
658C23C24×D4311yescharacteristic
659D4—4316no—
660D4—8616no—
661D4—868no—
662C2×C4—216no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—28no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—432no—
679C2×C4—432no—
680C2×C4—432no—
681C2×C4—432no—
682C2×C4—868no—
683C2×C4—861no—
684C2×C4—861no—
685C2×C4—861no—
686C2×C4—861no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—864no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—864no—
695C2×C4—864no—
696C2×C4—862no—
697C2×C4—862no—
698C2×C4—3448no—
699C2×C4—3448no—
700C2×C4—1728no—
701C2×C4—1728no—
702C2×C4—1728no—
703C2×C4—1728no—
704C2×C4—1724no—
705C2×C4C22×C4×D4312yes—
706C2×C4C22×C4×D4314yes—
707C2×C4C22×C4×D4314yes—
708C2×C4C22×C4×D4312yes—
709C2×C4#41×D4314yes—
710C22—22no—
711C22—22no—
712C22—24no—
713C22—24no—
714C22—438no—
715C22—864no—
716C22—864no—
717C22—868no—
718C22—868no—
719C22—864no—
720C22—864no—
721C22—864no—
722C22—17232no—
723C22—1724no—
724C22—1724no—
725C22#1458337114yes—
726C22C23×C4×D4311yescharacteristic
727C22C2×#41×D4312yes—
728C22C2×#1306337011yescharacteristic
729C22C2×#1306337111yescharacteristic
730C22#1458373612yes—
731C4—24no—
732C4—24no—
733C4—22no—
734C4—44no—
735C4—42no—
736C4—42no—
737C4—862no—
738C4—862no—
739C4—862no—
740C4—862no—
741C4—1722no—
742C4—1724no—
743C4—1722no—
744C4#117×D4314yes—
745C2—24no—
746C2—868no—
747C2—1724no—
748C2C2×#117×D4311yescharacteristic
749C2C2×#1458337111yescharacteristic
750C2#1914779711yescharacteristic
751C2#1914853012yes—
752C2#1914854012yes—
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2344C2
socle, cosocleC23×C43C25
prime radicalC23×D172C22
hypercenter#2344D43
hypocenterC43#34190
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2344

Complements

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

NH ≅ G/Ntype
2. #19137564C2semidirect
3. #19137534C2semidirect
4. #19137504C2semidirect
5. #19137464C2semidirect
6. #19137445C2semidirect
7. #19137437C2semidirect
10. #19137234C2semidirect
11. #19137227C2semidirect
12. #19136990C2semidirect
13. #19136989C2semidirect
14. #19136974C2semidirect
15. #381×D43C2semidirect
16. #19136955C2semidirect
17. C43×#2344C2semidirect
21. C2×#13063287C4semidirect
36. #14582798C22semidirect
37. #14582791C22semidirect
38. #14582790C22semidirect
39. #14582789C22semidirect
40. #14582788C22semidirect
41. #14582785C22semidirect
44. #14582773C22semidirect
45. #14582770C22semidirect
46. #14582766C22semidirect
47. #14582766C22semidirect
48. #14582764C22semidirect
49. #14582763C22semidirect
51. #14582761C22semidirect
52. #14582761C22semidirect
59. #14582756C22semidirect
60. #14582756C22semidirect
63. C4⋊C4×Dic43C22semidirect
64. C4⋊C4×Dic43C22semidirect
65. C4×Dic43⋊C4C22semidirect
67. C4×(C2×D43)⋊C4C22semidirect
68. C4×(C2×D43)⋊C4C22semidirect
69. C4×(C2×D43)⋊C4C22semidirect
71. #14582746C22semidirect
72. #14582745C22semidirect
73. #14582744C22semidirect
74. #95×D43C22semidirect
75. #95×D43C22semidirect
78. C43×#389C22semidirect
79. C43×#387C22semidirect
82. C4×C4⋊C4×C43C22semidirect
94. C22×C4×D43C2×C4semidirect
105. #13063287C2×C4semidirect
106. #13063287C2×C4semidirect
107. #13063287C2×C4semidirect
108. #13063287C2×C4semidirect
117. C2×(C2×D43)⋊C4C2×C4semidirect
130. C2×C4×Dic43C2×C4semidirect
154. C2×C4⋊C4×C43C2×C4semidirect
326. D172#117semidirect
374. #2344D43semidirect
415. #389C2×D43semidirect
421. #387C2×D43semidirect
448. C4×C4⋊C4C2×D43semidirect
460. C43#34190semidirect
494. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130632872
#191375642
#191375342
#191375042
#191374642
#191374452
#191374372
C22⋊C4×D1722
#191374152
#191372342
#191372272
#191369902
#191369892
#191369742
#381×D432
#191369552
C43×#23442
#3419043