Finite Group Databasebeta

← #14915023

Subgroups — #14915023

Order 2816.

2194 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071716C212yesmaximal, complemented
2#13071716C212yesmaximal, complemented
3#13071706C212yesmaximal, complemented
4#13071701C214yesmaximal
5#13071676C212yesmaximal, complemented
6#13071625C214yesmaximal
7#13071365C212yesmaximal, complemented
8#13071358C212yesmaximal, complemented
9#13071239C211yesmaximal, characteristic
10C4⋊Q8×Dic11C212yesmaximal, complemented
11#125×Dic11C212yesmaximal, complemented
12#13071100C211yesmaximal, characteristic
13C2×#10622598C211yesmaximal, characteristic
14#13070973C211yesmaximal, characteristic
15#13070972C211yesmaximal, characteristic
16#117×Dic11C211yesmaximal, characteristic
17C2×C11×#544C211yesmaximal, characteristic
18C11×#544C4116yescomplemented
19C2×C11×C4⋊Q8C2212yes—
20C2×C11×C4⋊Q8C2212yes—
21C2×C11×#125C2212yes—
22C2×C11×#125C2212yes—
23C2×C11×C22⋊Q8C2214yes—
24C2×C11×#117C2211yescharacteristic
25C2×C11×#117C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C2×Q8×Dic11C2214yes—
28C2×#66979C2211yescharacteristic
29C2×#66979C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33#10622843C2214yes—
34#10622843C2214yes—
35#10622843C2214yes—
36C4×C22⋊Dic11C2214yes—
37C2×C11⋊#95C2212yes—
38#10622598C2211yescharacteristic
39#10622598C2212yes—
40#10622598C2214yes—
41#10622598C2214yes—
42#10622598C2214yes—
43#10622598C2212yes—
44#10622598C2212yes—
45#10622598C2211yescharacteristic
46#10622598C2212yes—
47#10622598C2211yescharacteristic
48#10622598C2212yes—
49#10622598C2212yes—
50#10622598C2211yescharacteristic
51#10622594C2214yes—
52#10622594C2214yes—
53#10622594C2214yes—
54#10622594C2214yes—
55#10622594C2214yes—
56#10622594C2214yes—
57C4⋊C4×Dic11C2212yes—
58C4⋊C4×Dic11C2212yes—
59C4⋊C4×Dic11C2214yes—
60C4⋊C4×Dic11C2211yescharacteristic
61C4⋊C4×Dic11C2212yes—
62C4⋊C4×Dic11C2214yes—
63C4⋊C4×Dic11C2212yes—
64C4⋊C4×Dic11C2214yes—
65C4⋊C4×Dic11C2212yes—
66C4⋊C4×Dic11C2211yescharacteristic
67C4⋊C4×Dic11C2212yes—
68C4⋊C4×Dic11C2211yescharacteristic
69C4⋊C4×Dic11C2211yescharacteristic
70#10622563C2212yes—
71#10622563C2214yes—
72#10622563C2212yes—
73C22⋊C4×Dic11C2212yes—
74C22⋊C4×Dic11C2214yes—
75C22⋊C4×Dic11C2212yes—
76#10622549C2212yes—
77#10622548C2212yes—
78C4×C4⋊Dic11C2212yes—
79C4×C4⋊Dic11C2212yes—
80C4×C4⋊Dic11C2212yes—
81C4×C4⋊Dic11C2212yes—
82#10622545C2212yes—
83C42×Dic11C2212yes—
84C22×Q8×C11C2314yes—
85C23×C4×C11C2312yes—
86C23×C4×C11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2312yes—
90C11×C4⋊Q8C2×C4116yescomplemented
91C11×C4⋊Q8C2×C4116yescomplemented
92C11×#125C2×C4116yescomplemented
93C11×#125C2×C4116yescomplemented
94C11×C22⋊Q8C2×C4132yes—
95C11×#117C2×C418yes—
96C11×#117C2×C418yes—
97C2×C11×C4⋊C4C2×C418yes—
98C2×C11×C4⋊C4C2312yes—
99C2×C11×C4⋊C4C2312yes—
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2314yes—
105C2×C11×C4⋊C4C2314yes—
106C2×C11×C4⋊C4C2314yes—
107C2×C11×C22⋊C4C2312yes—
108C2×C11×C22⋊C4C2312yes—
109C2×C42×C11C2312yes—
110C2×C42×C11C2312yes—
111C2×C22⋊Dic11C2312yes—
112C2×C22⋊Dic11C2312yes—
113Q8×Dic11—48no—
114#66979—24no—
115#66979Q818yescomplemented
116C2×C4⋊Dic11—24no—
117C2×C4⋊Dic11—44no—
118C2×C4⋊Dic11C2312yes—
119C2×C4⋊Dic11C2312yes—
120C2×C4⋊Dic11C2312yes—
121C2×C4⋊Dic11C2311yescharacteristic
122C2×C4⋊Dic11C2312yes—
123C2×C4⋊Dic11C2314yes—
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2312yes—
126C2×C4⋊Dic11C2312yes—
127C2×C4⋊Dic11C2314yes—
128C2×C4⋊Dic11C2314yes—
129C2×C4⋊Dic11C2314yes—
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4×Dic11—24no—
133C2×C4×Dic11C2311yescharacteristic
134C2×C4×Dic11C2312yes—
135C2×C4×Dic11C2312yes—
136C2×C4×Dic11C2311yescharacteristic
137C2×C4×Dic11C2311yescharacteristic
138C2×C4×Dic11C2311yescharacteristic
139C2×C4×Dic11C2312yes—
140C2×C4×Dic11C2312yes—
141C2×C4×Dic11C2312yes—
142C2×C4×Dic11C2314yes—
143C2×C4×Dic11C2314yes—
144C2×C4×Dic11C2314yes—
145C2×C4×Dic11C2314yes—
146C2×C4×Dic11C2312yes—
147C11⋊#95C2312yes—
148C11⋊#95C2312yes—
149C11⋊#95C2312yes—
150C11⋊#95C2312yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2312yes—
154C11⋊#95C2312yes—
155C11⋊#95C2312yes—
156C11⋊#95C2312yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163#34272—111nomaximal, Sylow
164C24×C11C2411yescharacteristic
165C2×Q8×C11—44no—
166C2×Q8×C11—44no—
167C2×Q8×C11C22×C4116yes—
168C22×C4×C11—42no—
169C22×C4×C11—42no—
170C22×C4×C11C22×C418yes—
171C22×C4×C11C22×C414yes—
172C22×C4×C11C2×Q814yes—
173C22×C4×C11#4114yes—
174C22×C4×C11C2412yes—
175C22×C4×C11C2412yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2412yes—
178C22×C4×C11C2414yes—
179C22×C4×C11C2411yescharacteristic
180C22×C4×C11C2411yescharacteristic
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—24no—
186C22×Dic11—41no—
187C22×Dic11—41no—
188C22×Dic11—42no—
189C22×Dic11—42no—
190C22×Dic11C2411yescharacteristic
191C22×Dic11C2412yes—
192C22×Dic11C2411yescharacteristic
193C22×Dic11C2414yes—
194C22×Dic11C2412yes—
195C22×Dic11C2412yes—
196C22×Dic11C2412yes—
197C22×Dic11C2411yescharacteristic
198C22×Dic11C2411yescharacteristic
199C11×C4⋊C4C22×C418yes—
200C11×C4⋊C4C22×C418yes—
201C11×C4⋊C4C22×C414yes—
202C11×C4⋊C4C22×C414yes—
203C11×C4⋊C4C22×C414yes—
204C11×C4⋊C4C22×C414yes—
205C11×C4⋊C4C22×C4116yes—
206C11×C4⋊C4C22×C4116yes—
207C11×C4⋊C4C22×C4116yes—
208C11×C22⋊C4C22×C418yes—
209C11×C22⋊C4C22×C418yes—
210C42×C11C22×C418yes—
211C42×C11C22×C418yes—
212C22⋊Dic11—24no—
213C22⋊Dic11C2×Q818yes—
214C4⋊Dic11—28no—
215C4⋊Dic11—24no—
216C4⋊Dic11—24no—
217C4⋊Dic11—24no—
218C4⋊Dic11—24no—
219C4⋊Dic11—22no—
220C4⋊Dic11—22no—
221C4⋊Dic11—44no—
222C4⋊Dic11—42no—
223C4⋊Dic11—44no—
224C4⋊Dic11—42no—
225C4⋊Dic11—44no—
226C4⋊Dic11C2×Q814yes—
227C4⋊Dic11C2×Q814yes—
228C4×Dic11—24no—
229C4×Dic11—24no—
230C4×Dic11—22no—
231C4×Dic11—22no—
232C4×Dic11—22no—
233C4×Dic11—22no—
234C4×Dic11—24no—
235C4×Dic11—44no—
236C4×Dic11—42no—
237C4×Dic11—44no—
238C4×Dic11—42no—
239C4×Dic11—44no—
240C4×Dic11—44no—
241C4×Dic11C2×Q818yes—
242C2×#544D1111yescharacteristic
243#2370—112no—
244#2370—112no—
245#2369—112no—
246#2368—114no—
247#2365—112no—
248#2360—114no—
249#2331—112no—
250#2330—112no—
251#2317—111no—
252C4×C4⋊Q8—112no—
253C4×#125—112no—
254#2296—111no—
255C2×#389—111no—
256#2274—111no—
257#2274—111no—
258C4×#117—111no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11C23×C412yes—
264C23×C11C22×Q812yes—
265C23×C11C2×#4112yes—
266C23×C11C2511yescharacteristic
267Q8×C11—416no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—24no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—24no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—48no—
279C2×C4×C11C4×Q8116yescomplemented
280C2×C4×C11C23×C414yes—
281C2×C4×C11C23×C414yes—
282C2×C4×C11C23×C414yes—
283C2×C4×C11C23×C414yes—
284C2×C4×C11C23×C418yes—
285C2×C4×C11C23×C412yes—
286C2×C4×C11C23×C412yes—
287C2×C4×C11C22×Q812yes—
288C2×C4×C11C22×Q812yes—
289C2×C4×C11C2×#4112yes—
290C2×C4×C11C2×#4112yes—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—22no—
294C2×Dic11—22no—
295C2×Dic11—22no—
296C2×Dic11—22no—
297C2×Dic11—21no—
298C2×Dic11—21no—
299C2×Dic11—21no—
300C2×Dic11—21no—
301C2×Dic11—22no—
302C2×Dic11—22no—
303C2×Dic11—24no—
304C2×Dic11—22no—
305C2×Dic11—24no—
306C2×Dic11—21no—
307C2×Dic11—22no—
308C2×Dic11—21no—
309C2×Dic11—22no—
310C2×Dic11—24no—
311C2×Dic11—22no—
312C2×Dic11—21no—
313C2×Dic11—21no—
314C2×Dic11—44no—
315C2×Dic11—44no—
316C2×Dic11—84no—
317C2×Dic11C22×Q814yes—
318C2×Dic11C22×Q814yes—
319C2×Dic11H(5,𝔽2)12yes—
320C2×Dic112−1+412yes—
321#544Dic11116yescomplemented
322C2×C4⋊Q8C2×D1112yes—
323C2×C4⋊Q8C2×D1112yes—
324C2×#125C2×D1112yes—
325C2×#125C2×D1112yes—
326C2×C22⋊Q8C2×D1114yes—
327C2×C4×Q8—114no—
328C2×#117—111no—
329C2×#117—111no—
330C2×#117C2×D1111yescharacteristic
331C2×#117C2×D1111yescharacteristic
332C22×C4⋊C4—111no—
333C22×C4⋊C4—112no—
334C22×C4⋊C4C2×D1111yescharacteristic
335C22×C42—111no—
336#391—114no—
337#391—114no—
338#391—114no—
339#389—111no—
340#389—112no—
341#389—111no—
342#389—114no—
343#389—112no—
344#389—112no—
345#389—111no—
346#389—112no—
347#389—114no—
348#389—114no—
349#389—111no—
350#389—112no—
351#389—112no—
352#387—114no—
353#387—114no—
354#387—114no—
355#387—114no—
356#387—114no—
357#387—114no—
358#385—114no—
359#385—112no—
360#385—112no—
361#384—112no—
362#382—112no—
363C4×C4⋊C4—112no—
364C4×C4⋊C4—112no—
365C4×C4⋊C4—114no—
366C4×C4⋊C4—114no—
367C4×C4⋊C4—112no—
368C4×C4⋊C4—112no—
369C4×C4⋊C4—114no—
370C4×C4⋊C4—111no—
371C4×C4⋊C4—112no—
372C4×C4⋊C4—111no—
373C4×C4⋊C4—112no—
374C4×C4⋊C4—111no—
375C4×C4⋊C4—111no—
376C4×C4⋊C4—112no—
377C4×C4⋊C4—112no—
378C4×C4⋊C4—112no—
379C4×C4⋊C4—112no—
380C4×C22⋊C4—114no—
381C4×C22⋊C4—112no—
382C4×C22⋊C4—114no—
383C4×C22⋊C4—112no—
384#376—112no—
385C2×#95—112no—
386C43—112no—
387C22×C11—22no—
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11C2×C4×Q814yes—
394C22×C11C24×C411yescharacteristic
395C22×C11C23×Q811yescharacteristic
396C22×C11C22×#4111yescharacteristic
397C22×C11C2×H(5,𝔽2)11yescharacteristic
398C22×C11C2×2−1+411yescharacteristic
399C22×C11#58511yescharacteristic
400C22×C11#58511yescharacteristic
401C4×C11—28no—
402C4×C11—24no—
403C4×C11—24no—
404C4×C11—24no—
405C4×C11—24no—
406C4×C11C2×C4×Q814yes—
407C4×C11C2×C4×Q814yes—
408Dic11—22no—
409Dic11—22no—
410Dic11—24no—
411Dic11—24no—
412Dic11—42no—
413Dic11—41no—
414Dic11—44no—
415Dic11—42no—
416Dic11—41no—
417C22×Q8C22×D1114yes—
418C23×C4—111no—
419C23×C4—111no—
420C23×C4—112no—
421C23×C4C22×D1112yes—
422C23×C4C22×D1111yescharacteristic
423C4⋊Q8C2×Dic11116yescomplemented
424C4⋊Q8C2×Dic11116yescomplemented
425#125C2×Dic11116yescomplemented
426#125C2×Dic11116yescomplemented
427C22⋊Q8C2×Dic11132yes—
428C4×Q8—448no—
429#117—118no—
430#117—224no—
431#117C2×Dic1118yes—
432#117C2×Dic1118yes—
433C2×C4⋊C4—111no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—114no—
436C2×C4⋊C4—112no—
437C2×C4⋊C4—112no—
438C2×C4⋊C4—111no—
439C2×C4⋊C4—111no—
440C2×C4⋊C4—112no—
441C2×C4⋊C4—112no—
442C2×C4⋊C4—114no—
443C2×C4⋊C4—114no—
444C2×C4⋊C4—114no—
445C2×C4⋊C4—112no—
446C2×C4⋊C4—112no—
447C2×C4⋊C4—224no—
448C2×C4⋊C4—444no—
449C2×C4⋊C4C2×Dic1118yes—
450C2×C4⋊C4C22×D1112yes—
451C2×C4⋊C4C22×D1112yes—
452C2×C4⋊C4C22×D1111yescharacteristic
453C2×C4⋊C4C22×D1111yescharacteristic
454C2×C4⋊C4C22×D1111yescharacteristic
455C2×C4⋊C4C22×D1111yescharacteristic
456C2×C4⋊C4C22×D1114yes—
457C2×C4⋊C4C22×D1114yes—
458C2×C4⋊C4C22×D1114yes—
459C2×C22⋊C4—112no—
460C2×C22⋊C4—112no—
461C2×C22⋊C4C22×D1112yes—
462C2×C22⋊C4C22×D1112yes—
463C2×C42—112no—
464C2×C42—112no—
465C2×C42—112no—
466C2×C42—111no—
467C2×C42—112no—
468C2×C42—111no—
469C2×C42—111no—
470C2×C42—111no—
471C2×C42—114no—
472C2×C42—114no—
473C2×C42—112no—
474C2×C42—112no—
475C2×C42—114no—
476C2×C42—114no—
477C2×C42—224no—
478C2×C42C22×D1112yes—
479C2×C42C22×D1112yes—
480#95—114no—
481#95—114no—
482#95—112no—
483#95—112no—
484#95—112no—
485#95—112no—
486#95—114no—
487#95—114no—
488#95—114no—
489#95—114no—
490#95—112no—
491#95—112no—
492#95—114no—
493#95—114no—
494#95—112no—
495#95—112no—
496C2×C11—24no—
497C2×C11C22×C4×Q811yescharacteristic
498C2×C11C4×H(5,𝔽2)11yescharacteristic
499C2×C11C4×2−1+411yescharacteristic
500C2×C11#349411yescharacteristic
501C2×C11#349511yescharacteristic
502C2×C11#350311yescharacteristic
503C2×C11#350411yescharacteristic
504C24C23×D1111yescharacteristic
505C2×Q8—44no—
506C2×Q8—44no—
507C2×Q8C22×Dic11116yes—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—112no—
511C22×C4—112no—
512C22×C4—111no—
513C22×C4—111no—
514C22×C4—111no—
515C22×C4—112no—
516C22×C4—111no—
517C22×C4—114no—
518C22×C4—112no—
519C22×C4—222no—
520C22×C4—222no—
521C22×C4—222no—
522C22×C4—222no—
523C22×C4—224no—
524C22×C4—441no—
525C22×C4—441no—
526C22×C4—442no—
527C22×C4—442no—
528C22×C4Q8×D1114yes—
529C22×C4#434314yes—
530C22×C4C22×Dic1118yes—
531C22×C4C22×Dic1114yes—
532C22×C4C23×D1112yes—
533C22×C4C23×D1112yes—
534C22×C4C23×D1112yes—
535C22×C4C23×D1112yes—
536C22×C4C23×D1114yes—
537C22×C4C23×D1111yescharacteristic
538C22×C4C23×D1111yescharacteristic
539C4⋊C4—114no—
540C4⋊C4—114no—
541C4⋊C4—228no—
542C4⋊C4—224no—
543C4⋊C4—224no—
544C4⋊C4—224no—
545C4⋊C4—224no—
546C4⋊C4—222no—
547C4⋊C4—222no—
548C4⋊C4—444no—
549C4⋊C4—444no—
550C4⋊C4—442no—
551C4⋊C4—442no—
552C4⋊C4—444no—
553C4⋊C4C22×Dic1118yes—
554C4⋊C4C22×Dic1118yes—
555C4⋊C4C22×Dic1114yes—
556C4⋊C4C22×Dic1114yes—
557C4⋊C4C22×Dic1114yes—
558C4⋊C4C22×Dic1114yes—
559C4⋊C4C22×Dic11116yes—
560C4⋊C4C22×Dic11116yes—
561C4⋊C4C22×Dic11116yes—
562C22⋊C4—118no—
563C22⋊C4—224no—
564C22⋊C4C22×Dic1118yes—
565C22⋊C4C22×Dic1118yes—
566C42—118no—
567C42—224no—
568C42—224no—
569C42—222no—
570C42—222no—
571C42—222no—
572C42—222no—
573C42—224no—
574C42—444no—
575C42—444no—
576C42—444no—
577C42—442no—
578C42—444no—
579C42—442no—
580C42C22×Dic1118yes—
581C42C22×Dic1118yes—
582C11#3427211yescharacteristic, complemented, Sylow
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23C2×Q8×D1112yes—
588C23C2×#434312yes—
589C23C23×Dic1112yes—
590C23C24×D1111yescharacteristic
591Q8—416no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—48no—
603C2×C4—114no—
604C2×C4—114no—
605C2×C4—112no—
606C2×C4—112no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—221no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—224no—
620C2×C4—222no—
621C2×C4—224no—
622C2×C4—221no—
623C2×C4—222no—
624C2×C4—221no—
625C2×C4—222no—
626C2×C4—221no—
627C2×C4—224no—
628C2×C4—222no—
629C2×C4—221no—
630C2×C4—444no—
631C2×C4—444no—
632C2×C4—884no—
633C2×C4Q8×Dic11116yescomplemented
634C2×C4C2×Q8×D1112yes—
635C2×C4C2×Q8×D1112yes—
636C2×C4C2×#434312yes—
637C2×C4C2×#434312yes—
638C2×C4C23×Dic1114yes—
639C2×C4C23×Dic1114yes—
640C2×C4C23×Dic1114yes—
641C2×C4C23×Dic1114yes—
642C2×C4C23×Dic1118yes—
643C2×C4C23×Dic1112yes—
644C2×C4C23×Dic1112yes—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22C2×Q8×Dic1114yes—
652C22C22×Q8×D1111yescharacteristic
653C22C22×#434311yescharacteristic
654C22D11×H(5,𝔽2)11yescharacteristic
655C22#1062345511yescharacteristic
656C22D11×2−1+411yescharacteristic
657C22#1062345711yescharacteristic
658C22C24×Dic1111yescharacteristic
659C4—28no—
660C4—24no—
661C4—24no—
662C4—24no—
663C4—24no—
664C4—222no—
665C4—224no—
666C4—224no—
667C4—222no—
668C4—441no—
669C4—442no—
670C4—441no—
671C4—444no—
672C4—442no—
673C4C2×Q8×Dic1114yes—
674C4C2×Q8×Dic1114yes—
675C2—24no—
676C2C22×Q8×Dic1111yescharacteristic
677C2H(5,𝔽2)×Dic1111yescharacteristic
678C22−1+4×Dic1111yescharacteristic
679C2#1308235411yescharacteristic
680C2#1308237111yescharacteristic
681C2#1308243111yescharacteristic
682C2#1308243911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#544C2
socle, cosocleC23×C11C25
prime radicalC24×C11C24
hypercenterC2×#544D11
hypocenterC11#34272
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. #13071716C2semidirect
2. #13071716C2semidirect
3. #13071706C2semidirect
5. #13071676C2semidirect
7. #13071365C2semidirect
8. #13071358C2semidirect
10. C4⋊Q8×Dic11C2semidirect
11. #125×Dic11C2semidirect
18. C11×#544C4semidirect
90. C11×C4⋊Q8C2×C4semidirect
91. C11×C4⋊Q8C2×C4semidirect
92. C11×#125C2×C4semidirect
93. C11×#125C2×C4semidirect
115. #66979Q8semidirect
279. C2×C4×C11C4×Q8semidirect
321. #544Dic11semidirect
423. C4⋊Q8C2×Dic11semidirect
424. C4⋊Q8C2×Dic11semidirect
425. #125C2×Dic11semidirect
426. #125C2×Dic11semidirect
582. C11#34272semidirect
633. C2×C4Q8×Dic11semidirect

Maximal subgroups

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

subgroupindex
#130717162
#130717062
#130717012
#130716762
#130716252
#130713652
#130713582
#130712392
C4⋊Q8×Dic112
#125×Dic112
#130711002
C2×#106225982
#130709732
#130709722
#117×Dic112
C2×C11×#5442
#3427211