Finite Group Databasebeta

← #25259527

Subgroups — #25259527

Order 11008.

2630 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137743C214yesmaximal, complemented
2#19137591C214yesmaximal, complemented
3#19137472C212yesmaximal, complemented
4#19137444C212yesmaximal, complemented
5#19137444C212yesmaximal, complemented
6D4×C22⋊Dic43C212yesmaximal
7#19137389C214yesmaximal, complemented
8#19137267C214yesmaximal, complemented
9#19137213C211yesmaximal, characteristic, complemented
10#19137209C211yesmaximal, characteristic, complemented
11#19137198C211yesmaximal, characteristic, complemented
12#19137193C211yesmaximal, characteristic, complemented
13#19136978C211yesmaximal, characteristic, complemented
14C2×#14582759C211yesmaximal, characteristic, complemented
15C22×#123×C43C211yesmaximal, characteristic
16C2×D4×Dic43C2214yes—
17C2×#13063284C2212yes—
18C2×#13063284C2212yescomplemented
19C22×C4⋊Dic43C2212yescomplemented
20C22×C22⋊Dic43C2212yes—
21C22×C22⋊Dic43C2212yes—
22#14582802C2214yes—
23#14582798C2214yescomplemented
24#14582798C2214yescomplemented
25#14582798C2214yescomplemented
26#14582792C2214yescomplemented
27#14582792C2214yescomplemented
28#14582792C2214yescomplemented
29#14582792C2214yescomplemented
30#14582792C2214yescomplemented
31#14582792C2214yescomplemented
32#14582785C2214yescomplemented
33#14582785C2214yescomplemented
34#14582785C2214yescomplemented
35#14582785C2214yescomplemented
36#14582779C2214yes—
37#14582779C2214yes—
38#14582774C2214yescomplemented
39#14582774C2214yescomplemented
40#14582774C2214yescomplemented
41#14582774C2214yescomplemented
42#14582762C2212yes—
43#14582762C2212yescomplemented
44#14582759C2212yes—
45#14582759C2212yes—
46#14582759C2212yes—
47#14582759C2211yescharacteristic
48#14582759C2211yescharacteristic
49#14582759C2211yescharacteristic
50#14582759C2211yescharacteristic
51#14582759C2212yescomplemented
52#14582759C2212yescomplemented
53#14582759C2212yescomplemented
54#14582755C2212yes—
55#14582755C2212yes—
56C4⋊C4×Dic43C2214yescomplemented
57C22⋊C4×Dic43C2214yescomplemented
58C22⋊C4×Dic43C2214yescomplemented
59C4×C22⋊Dic43C2212yes—
60C4×C22⋊Dic43C2212yes—
61C4×C22⋊Dic43C2212yes—
62C4×C22⋊Dic43C2212yescomplemented
63C2×C43⋊#95C2212yescomplemented
64C23×D4×C43C2211yescharacteristic
65C24×C4×C43C2211yescharacteristic
66C2×#123×C43C4116yescomplemented
67C2×#123×C43C2212yes—
68C2×#123×C43C2212yes—
69C2×#123×C43C2212yes—
70C2×#123×C43C2212yes—
71C22×C4⋊C4×C43C2211yescharacteristic
72C22×C4⋊C4×C43C2211yescharacteristic
73C22×C22⋊C4×C43C2211yescharacteristic
74C22×C22⋊C4×C43C2211yescharacteristic
75C22×C22⋊C4×C43C2211yescharacteristic
76C23×Dic43C2314yes—
77C23×Dic43C2314yes—
78D4×Dic43—48no—
79#13063284—44no—
80#13063284—44no—
81C2×C4⋊Dic43—44no—
82C2×C4⋊Dic43C2312yes—
83C2×C4⋊Dic43C2312yes—
84C2×C4⋊Dic43C2314yes—
85C2×C4⋊Dic43C2314yes—
86C2×C4⋊Dic43C2312yes—
87C2×C4⋊Dic43C2314yes—
88C2×C4⋊Dic43C2314yes—
89C2×C4⋊Dic43C2312yes—
90C2×C22⋊Dic43—44no—
91C2×C22⋊Dic43—44no—
92C2×C22⋊Dic43C2312yes—
93C2×C22⋊Dic43C2312yes—
94C2×C22⋊Dic43C2312yes—
95C2×C22⋊Dic43C2314yes—
96C2×C22⋊Dic43C2312yes—
97C2×C22⋊Dic43C2314yes—
98C2×C22⋊Dic43C2314yes—
99C2×C22⋊Dic43C2314yes—
100C2×C22⋊Dic43C2314yes—
101C2×C22⋊Dic43C2314yes—
102C2×C4×Dic43C2314yes—
103C2×C4×Dic43C2314yes—
104C2×C4×Dic43C2314yes—
105C2×C4×Dic43C2314yes—
106C43⋊#95C2314yes—
107C43⋊#95C2314yes—
108C43⋊#95C2312yes—
109C43⋊#95C2314yes—
110C43⋊#95C2314yes—
111C43⋊#95C2314yes—
112C43⋊#95C2312yes—
113C43⋊#95C2314yes—
114C43⋊#95C2314yes—
115C43⋊#95C2314yes—
116C43⋊#95C2312yes—
117C43⋊#95C2312yes—
118C25×C43C2311yescharacteristic
119C25×C43C2311yescharacteristic
120C22×D4×C43—44no—
121C22×D4×C43C2×C418yes—
122C22×D4×C43C2312yes—
123C22×D4×C43C2312yes—
124C23×C4×C43—44no—
125C23×C4×C43C2×C418yescomplemented
126C23×C4×C43C2311yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135#123×C43C2×C4116yescomplemented
136#123×C43C2×C4116yescomplemented
137#123×C43C2×C4116yescomplemented
138#123×C43C2×C4116yescomplemented
139C2×C4⋊C4×C43C2×C418yescomplemented
140C2×C4⋊C4×C43C2×C418yescomplemented
141C2×C4⋊C4×C43C2312yes—
142C2×C4⋊C4×C43C2312yes—
143C2×C4⋊C4×C43C2312yes—
144C2×C4⋊C4×C43C2312yes—
145C2×C22⋊C4×C43C2×C418yescomplemented
146C2×C22⋊C4×C43C2×C418yescomplemented
147C2×C22⋊C4×C43C2×C418yescomplemented
148C2×C22⋊C4×C43C2312yes—
149C2×C22⋊C4×C43C2312yes—
150C2×C22⋊C4×C43C2312yes—
151C2×C22⋊C4×C43C2312yes—
152C2×C22⋊C4×C43C2312yes—
153C2×C22⋊C4×C43C2312yes—
154C24×C43—24no—
155C24×C43—22no—
156C24×C43—22no—
157C24×C43—22no—
158C24×C43—22no—
159C24×C43—42no—
160C24×C43—42no—
161C24×C43—42no—
162C24×C43C22×C414yes—
163C24×C43C22×C414yes—
164C24×C43C2412yes—
165C24×C43C2411yescharacteristic
166C24×C43C2411yescharacteristic
167C24×C43C2411yescharacteristic
168C2×D4×C43—28no—
169C2×D4×C43—44no—
170C2×D4×C43—416no—
171C2×D4×C43C22×C418yes—
172C2×D4×C43C22×C418yes—
173C22×C4×C43—24no—
174C22×C4×C43—24no—
175C22×C4×C43—22no—
176C22×C4×C43—22no—
177C22×C4×C43—416no—
178C22×C4×C43—42no—
179C22×C4×C43—42no—
180C22×C4×C43—42no—
181C22×C4×C43—42no—
182C22×C4×C43—42no—
183C22×C4×C43—42no—
184C22×C4×C43C22×C414yes—
185C22×C4×C43C22×C414yes—
186C22×C4×C43C22×C414yes—
187C22×C4×C43C22×C414yes—
188C22×C4×C43C22×C414yes—
189C22×C4×C43C22×C414yes—
190C22×C4×C43C22×C414yes—
191C22×C4×C43C22×C414yes—
192C22×C4×C43C22×C414yes—
193C22×C4×C43C2412yes—
194C22×C4×C43C2412yes—
195C22×C4×C43C2411yescharacteristic
196C22×C4×C43C2411yescharacteristic
197C22×C4×C43C2411yescharacteristic
198C22×C4×C43C2411yescharacteristic
199C22×C4×C43C2412yes—
200C22×Dic43—28no—
201C22×Dic43—44no—
202C22×Dic43—44no—
203C22×Dic43—44no—
204C22×Dic43—44no—
205C22×Dic43—44no—
206C22×Dic43C2414yes—
207C22×Dic43C2414yes—
208C22×Dic43C2414yes—
209C22×Dic43C2414yes—
210C4⋊C4×C43C22×C418yes—
211C4⋊C4×C43C22×C418yes—
212C4⋊C4×C43C22×C418yes—
213C4⋊C4×C43C22×C418yes—
214C22⋊C4×C43C22×C418yes—
215C22⋊C4×C43C22×C418yes—
216C22⋊C4×C43C22×C418yes—
217C22⋊C4×C43C22×C418yes—
218C22⋊C4×C43C22×C418yes—
219C22⋊C4×C43C22×C418yes—
220C22⋊Dic43—24no—
221C22⋊Dic43—24no—
222C22⋊Dic43—24no—
223C22⋊Dic43—28no—
224C22⋊Dic43—24no—
225C22⋊Dic43—44no—
226C22⋊Dic43—44no—
227C22⋊Dic43—44no—
228C22⋊Dic43—44no—
229C22⋊Dic43—44no—
230C4⋊Dic43—42no—
231C4⋊Dic43—44no—
232C4⋊Dic43—42no—
233C4⋊Dic43—44no—
234C4⋊Dic43—42no—
235C4⋊Dic43—42no—
236C4⋊Dic43—44no—
237C4⋊Dic43—44no—
238C4×Dic43—44no—
239C4×Dic43—44no—
240C4×Dic43—44no—
241C4×Dic43—44no—
242C23×C43—21no—
243C23×C43—22no—
244C23×C43—21no—
245C23×C43—22no—
246C23×C43—22no—
247C23×C43—28no—
248C23×C43—28no—
249C23×C43—21no—
250C23×C43—22no—
251C23×C43—24no—
252C23×C43—22no—
253C23×C43—21no—
254C23×C43—22no—
255C23×C43—22no—
256C23×C43—24no—
257C23×C43—28no—
258C23×C43—44no—
259C23×C43—44no—
260C23×C43—44no—
261C23×C43—48no—
262C23×C43—48no—
263C23×C43—84no—
264C23×C43—84no—
265C23×C43C23×C414yes—
266C23×C43C23×C412yes—
267C23×C43C23×C412yes—
268C23×C43C23×C412yes—
269C23×C43H(5,𝔽2)14yes—
270C23×C43H(5,𝔽2)12yes—
271C23×C432−1+412yes—
272C23×C43C2511yescharacteristic
273D4×C43—216no—
274D4×C43—48no—
275C2×C4×C43—28no—
276C2×C4×C43—28no—
277C2×C4×C43—28no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—24no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—24no—
286C2×C4×C43—44no—
287C2×C4×C43—44no—
288C2×C4×C43—44no—
289C2×C4×C43—44no—
290C2×C4×C43—44no—
291C2×C4×C43—44no—
292C2×C4×C43C23×C414yes—
293C2×C4×C43C23×C414yes—
294C2×C4×C43C23×C412yes—
295C2×C4×C43C23×C412yes—
296C2×C4×C43C23×C412yes—
297C2×C4×C43C23×C412yes—
298C2×C4×C43C23×C414yes—
299C2×Dic43—24no—
300C2×Dic43—24no—
301C2×Dic43—24no—
302C2×Dic43—24no—
303C2×Dic43—24no—
304C2×Dic43—24no—
305C2×Dic43—24no—
306C2×Dic43—24no—
307C2×Dic43—24no—
308C2×Dic43—24no—
309C2×Dic43—24no—
310C2×Dic43—24no—
311C2×Dic43—88no—
312C2×Dic43—88no—
313#34376—431nomaximal, Sylow
314C22×C43—22no—
315C22×C43—22no—
316C22×C43—22no—
317C22×C43—22no—
318C22×C43—24no—
319C22×C43—24no—
320C22×C43—24no—
321C22×C43—24no—
322C22×C43—22no—
323C22×C43—24no—
324C22×C43—22no—
325C22×C43—24no—
326C22×C43—22no—
327C22×C43—24no—
328C22×C43—416no—
329C22×C43—42no—
330C22×C43—44no—
331C22×C43—42no—
332C22×C43—44no—
333C22×C43—88no—
334C22×C43#51814yes—
335C22×C43#52014yes—
336C22×C43C24×C411yescharacteristic
337C22×C43C2×H(5,𝔽2)12yes—
338C22×C43C2×H(5,𝔽2)11yescharacteristic
339C22×C43C2×2−1+411yescharacteristic
340C22×C43#58512yes—
341C4×C43—22no—
342C4×C43—22no—
343C4×C43—22no—
344C4×C43—22no—
345C4×C43—24no—
346C4×C43—24no—
347C4×C43—24no—
348Dic43—44no—
349Dic43—44no—
350Dic43—44no—
351Dic43—44no—
352C22×#123D4311yescharacteristic
353#2376—434no—
354#2359—434no—
355#2345—432no—
356#2342—432no—
357#2342—432no—
358D4×C22⋊C4—432no—
359#2335—434no—
360#2322—434no—
361#2316—431no—
362#2315—431no—
363#2313—431no—
364#2312—431no—
365#2280—431no—
366C2×#380—431no—
367C2×C43—24no—
368C2×C43—24no—
369C2×C43—42no—
370C2×C43—44no—
371C2×C43C2×#51811yescharacteristic
372C2×C43C2×#52011yescharacteristic
373C2×C43#342811yescharacteristic
374C2×C43#353412yes—
375C2×C43#353512yes—
376C23×D4C2×D4311yescharacteristic
377C24×C4C2×D4311yescharacteristic
378C2×#123Dic43116yescomplemented
379C2×#123C2×D4312yes—
380C2×#123C2×D4312yes—
381C2×#123C2×D4312yes—
382C2×#123C2×D4312yes—
383C2×C4×D4—434no—
384C2×#117—432no—
385C2×#117—432no—
386C22×C4⋊C4—432no—
387C22×C4⋊C4C2×D4311yescharacteristic
388C22×C4⋊C4C2×D4311yescharacteristic
389C22×C22⋊C4—432no—
390C22×C22⋊C4—432no—
391C22×C22⋊C4C2×D4311yescharacteristic
392C22×C22⋊C4C2×D4311yescharacteristic
393C22×C22⋊C4C2×D4311yescharacteristic
394#390—434no—
395#389—434no—
396#389—434no—
397#389—434no—
398#388—434no—
399#388—434no—
400#388—434no—
401#388—434no—
402#388—434no—
403#388—434no—
404#387—434no—
405#387—434no—
406#387—434no—
407#387—434no—
408#386—434no—
409#386—434no—
410#385—434no—
411#385—434no—
412#385—434no—
413#385—434no—
414#381—432no—
415#381—432no—
416#380—431no—
417#380—431no—
418#380—431no—
419#380—431no—
420#380—432no—
421#380—432no—
422#380—432no—
423#380—432no—
424#380—432no—
425#380—432no—
426#379—432no—
427#379—432no—
428C4×C4⋊C4—434no—
429C4×C22⋊C4—432no—
430C4×C22⋊C4—432no—
431C4×C22⋊C4—432no—
432C4×C22⋊C4—432no—
433C4×C22⋊C4—434no—
434C4×C22⋊C4—434no—
435C2×#95—432no—
436C43#3437611yescharacteristic, complemented, Sylow
437C25C22×D4311yescharacteristic
438C25C22×D4311yescharacteristic
439C22×D4—44no—
440C22×D4C2×Dic4318yes—
441C22×D4C22×D4312yes—
442C22×D4C22×D4312yes—
443C23×C4—44no—
444C23×C4—434no—
445C23×C4—434no—
446C23×C4C2×Dic4318yescomplemented
447C23×C4C22×D4311yescharacteristic
448C23×C4C22×D4311yescharacteristic
449C23×C4C22×D4311yescharacteristic
450C23×C4C22×D4311yescharacteristic
451C23×C4C22×D4311yescharacteristic
452C23×C4C22×D4311yescharacteristic
453C23×C4C22×D4311yescharacteristic
454C23×C4C22×D4311yescharacteristic
455C23×C4C22×D4311yescharacteristic
456#123C2×Dic43116yescomplemented
457#123C2×Dic43116yescomplemented
458#123C2×Dic43116yescomplemented
459#123C2×Dic43116yescomplemented
460C4×D4—1728no—
461#117—1724no—
462#117—1724no—
463C2×C4⋊C4—432no—
464C2×C4⋊C4—434no—
465C2×C4⋊C4—432no—
466C2×C4⋊C4—432no—
467C2×C4⋊C4—432no—
468C2×C4⋊C4—434no—
469C2×C4⋊C4—434no—
470C2×C4⋊C4—434no—
471C2×C4⋊C4—1724no—
472C2×C4⋊C4C2×Dic4318yescomplemented
473C2×C4⋊C4C2×Dic4318yescomplemented
474C2×C4⋊C4C22×D4312yes—
475C2×C4⋊C4C22×D4312yes—
476C2×C4⋊C4C22×D4312yes—
477C2×C4⋊C4C22×D4312yes—
478C2×C22⋊C4—432no—
479C2×C22⋊C4—432no—
480C2×C22⋊C4—432no—
481C2×C22⋊C4—434no—
482C2×C22⋊C4—432no—
483C2×C22⋊C4—434no—
484C2×C22⋊C4—434no—
485C2×C22⋊C4—434no—
486C2×C22⋊C4—434no—
487C2×C22⋊C4—434no—
488C2×C22⋊C4—1724no—
489C2×C22⋊C4—1724no—
490C2×C22⋊C4C2×Dic4318yescomplemented
491C2×C22⋊C4C2×Dic4318yescomplemented
492C2×C22⋊C4C2×Dic4318yescomplemented
493C2×C22⋊C4C22×D4312yes—
494C2×C22⋊C4C22×D4312yes—
495C2×C22⋊C4C22×D4312yes—
496C2×C22⋊C4C22×D4312yes—
497C2×C22⋊C4C22×D4312yes—
498C2×C22⋊C4C22×D4312yes—
499C2×C42—434no—
500C2×C42—434no—
501C2×C42—434no—
502C2×C42—434no—
503#95—434no—
504#95—432no—
505#95—432no—
506#95—432no—
507#95—434no—
508#95—432no—
509#95—434no—
510#95—434no—
511#95—434no—
512#95—434no—
513#95—434no—
514#95—434no—
515C24—24no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—42no—
521C24—42no—
522C24—42no—
523C24C22×Dic4314yes—
524C24C22×Dic4314yes—
525C24C23×D4311yescharacteristic
526C24C23×D4312yes—
527C24C23×D4311yescharacteristic
528C24C23×D4311yescharacteristic
529C2×D4—28no—
530C2×D4—44no—
531C2×D4—416no—
532C2×D4C22×Dic4318yes—
533C2×D4C22×Dic4318yes—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—416no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—434no—
546C22×C4—434no—
547C22×C4—434no—
548C22×C4—434no—
549C22×C4—868no—
550C22×C4—1724no—
551C22×C4—1724no—
552C22×C4—1724no—
553C22×C4—1724no—
554C22×C4—1724no—
555C22×C4C22×Dic4314yes—
556C22×C4C22×Dic4314yes—
557C22×C4C22×Dic4314yes—
558C22×C4C22×Dic4314yes—
559C22×C4C22×Dic4314yes—
560C22×C4C22×Dic4314yes—
561C22×C4C22×Dic4314yes—
562C22×C4C22×Dic4314yes—
563C22×C4C22×Dic4314yes—
564C22×C4C23×D4311yescharacteristic
565C22×C4C23×D4312yes—
566C22×C4C23×D4312yes—
567C22×C4C23×D4312yes—
568C22×C4C23×D4311yescharacteristic
569C22×C4C23×D4311yescharacteristic
570C22×C4C23×D4311yescharacteristic
571C4⋊C4—1722no—
572C4⋊C4—1724no—
573C4⋊C4—1722no—
574C4⋊C4—1722no—
575C4⋊C4—1722no—
576C4⋊C4—1724no—
577C4⋊C4—1724no—
578C4⋊C4—1724no—
579C4⋊C4C22×Dic4318yes—
580C4⋊C4C22×Dic4318yes—
581C4⋊C4C22×Dic4318yes—
582C4⋊C4C22×Dic4318yes—
583C22⋊C4—868no—
584C22⋊C4—864no—
585C22⋊C4—864no—
586C22⋊C4—864no—
587C22⋊C4—864no—
588C22⋊C4—1724no—
589C22⋊C4—1724no—
590C22⋊C4—1724no—
591C22⋊C4—1724no—
592C22⋊C4—1724no—
593C22⋊C4C22×Dic4318yes—
594C22⋊C4C22×Dic4318yes—
595C22⋊C4C22×Dic4318yes—
596C22⋊C4C22×Dic4318yes—
597C22⋊C4C22×Dic4318yes—
598C22⋊C4C22×Dic4318yes—
599C42—1724no—
600C42—1724no—
601C42—1724no—
602C42—1724no—
603C23—22no—
604C23—21no—
605C23—21no—
606C23—22no—
607C23—22no—
608C23—28no—
609C23—28no—
610C23—24no—
611C23—22no—
612C23—21no—
613C23—22no—
614C23—21no—
615C23—22no—
616C23—22no—
617C23—24no—
618C23—28no—
619C23—44no—
620C23—44no—
621C23—44no—
622C23—48no—
623C23—48no—
624C23—84no—
625C23—84no—
626C23C23×Dic4314yes—
627C23C23×Dic4312yes—
628C23C23×Dic4312yes—
629C23C23×Dic4312yes—
630C23#1306337014yes—
631C23#1306337112yes—
632C23#1306337212yes—
633C23C24×D4311yescharacteristic
634D4—216no—
635D4—48no—
636C2×C4—28no—
637C2×C4—28no—
638C2×C4—28no—
639C2×C4—22no—
640C2×C4—24no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—44no—
648C2×C4—44no—
649C2×C4—44no—
650C2×C4—44no—
651C2×C4—44no—
652C2×C4—44no—
653C2×C4—864no—
654C2×C4—864no—
655C2×C4—864no—
656C2×C4—864no—
657C2×C4—864no—
658C2×C4—864no—
659C2×C4—864no—
660C2×C4—864no—
661C2×C4—864no—
662C2×C4—864no—
663C2×C4—864no—
664C2×C4—864no—
665C2×C4—3448no—
666C2×C4—3448no—
667C2×C4C23×Dic4314yes—
668C2×C4C23×Dic4314yes—
669C2×C4C23×Dic4312yes—
670C2×C4C23×Dic4312yes—
671C2×C4C23×Dic4312yes—
672C2×C4C23×Dic4312yes—
673C2×C4C23×Dic4314yes—
674C22—22no—
675C22—24no—
676C22—24no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—24no—
681C22—24no—
682C22—22no—
683C22—24no—
684C22—22no—
685C22—24no—
686C22—22no—
687C22—24no—
688C22—416no—
689C22—42no—
690C22—44no—
691C22—44no—
692C22—42no—
693C22—88no—
694C22#1458337414yes—
695C22#1458338214yes—
696C22C24×Dic4311yescharacteristic
697C22C2×#1306337012yes—
698C22C2×#1306337111yescharacteristic
699C22C2×#1306337211yescharacteristic
700C22#1458373512yes—
701C4—22no—
702C4—22no—
703C4—22no—
704C4—22no—
705C4—24no—
706C4—24no—
707C4—24no—
708C4—1724no—
709C4—1724no—
710C4—1724no—
711C4—1724no—
712C2—24no—
713C2—24no—
714C2—42no—
715C2—44no—
716C2C2×#1458337411yescharacteristic
717C2C2×#1458338211yescharacteristic
718C2#1914779811yescharacteristic
719C2#1914878912yes—
720C2#1914880812yes—
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC22×#123×C43C2
socle, cosocleC23×C43C25
prime radicalC23×D4×C43C22
hypercenterC22×#123D43
hypocenterC43#34376
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. #19137743C2semidirect
2. #19137591C2semidirect
3. #19137472C2semidirect
4. #19137444C2semidirect
5. #19137444C2semidirect
7. #19137389C2semidirect
8. #19137267C2semidirect
9. #19137213C2semidirect
10. #19137209C2semidirect
11. #19137198C2semidirect
12. #19137193C2semidirect
13. #19136978C2semidirect
14. C2×#14582759C2semidirect
18. C2×#13063284C22semidirect
19. C22×C4⋊Dic43C22semidirect
23. #14582798C22semidirect
24. #14582798C22semidirect
25. #14582798C22semidirect
26. #14582792C22semidirect
27. #14582792C22semidirect
28. #14582792C22semidirect
29. #14582792C22semidirect
30. #14582792C22semidirect
31. #14582792C22semidirect
32. #14582785C22semidirect
33. #14582785C22semidirect
34. #14582785C22semidirect
35. #14582785C22semidirect
38. #14582774C22semidirect
39. #14582774C22semidirect
40. #14582774C22semidirect
41. #14582774C22semidirect
43. #14582762C22semidirect
51. #14582759C22semidirect
52. #14582759C22semidirect
53. #14582759C22semidirect
56. C4⋊C4×Dic43C22semidirect
57. C22⋊C4×Dic43C22semidirect
58. C22⋊C4×Dic43C22semidirect
62. C4×C22⋊Dic43C22semidirect
63. C2×C43⋊#95C22semidirect
66. C2×#123×C43C4semidirect
125. C23×C4×C43C2×C4semidirect
135. #123×C43C2×C4semidirect
136. #123×C43C2×C4semidirect
137. #123×C43C2×C4semidirect
138. #123×C43C2×C4semidirect
139. C2×C4⋊C4×C43C2×C4semidirect
140. C2×C4⋊C4×C43C2×C4semidirect
145. C2×C22⋊C4×C43C2×C4semidirect
146. C2×C22⋊C4×C43C2×C4semidirect
147. C2×C22⋊C4×C43C2×C4semidirect
378. C2×#123Dic43semidirect
436. C43#34376semidirect
446. C23×C4C2×Dic43semidirect
456. #123C2×Dic43semidirect
457. #123C2×Dic43semidirect
458. #123C2×Dic43semidirect
459. #123C2×Dic43semidirect
472. C2×C4⋊C4C2×Dic43semidirect
473. C2×C4⋊C4C2×Dic43semidirect
490. C2×C22⋊C4C2×Dic43semidirect
491. C2×C22⋊C4C2×Dic43semidirect
492. C2×C22⋊C4C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
#191377432
#191375912
#191374722
#191374442
D4×C22⋊Dic432
#191373892
#191372672
#191372132
#191372092
#191371982
#191371932
#191369782
C2×#145827592
C22×#123×C432
#3437643