Finite Group Databasebeta

← #14763579

Subgroups — #14763579

Order 2816.

1598 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13070999C211yesmaximal, characteristic, complemented
2C2×#10622825C211yesmaximal, characteristic, complemented
3#13069602C212yesmaximal, complemented
4#13069453C212yesmaximal, complemented
5#13069070C214yesmaximal, complemented
6#13068604C214yesmaximal, complemented
7C2×C11×#525C211yesmaximal, characteristic
8C22×C11×#41C411yescharacteristic, complemented
9C24×C4×C11C2211yescharacteristic
10C11×#525—21no—
11C11×#525—21no—
12C11×#525—21no—
13C11×#525—21no—
14C11×#525—21no—
15C11×#525—21no—
16C11×#525—21no—
17C11×#525—21no—
18C2×C11×#123C412yescomplemented
19C2×C11×C22⋊Q8C411yescharacteristic, complemented
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#121C411yescharacteristic, complemented
22C2×C11×#121C2211yescharacteristic
23C2×C11×#120C2212yes—
24C2×C4×D4×C11C412yescomplemented
25C2×C4×D4×C11C2212yes—
26C2×C11×#117C411yescharacteristic, complemented
27C22×C22⋊Dic11C2212yes—
28C2×#66979—21no—
29C22×C4⋊Dic11—21no—
30#10622860C2212yes—
31C2×#66898C2218yes—
32#10622825—21no—
33#10622825—21no—
34#10622825—21no—
35#10622825C2212yes—
36#10622825C2212yes—
37#10622825C2212yes—
38#10622824—21no—
39C4×C22⋊Dic11—21no—
40C4×C22⋊Dic11C2212yes—
41C2×C11⋊#95—21no—
42#10622164C2218yes—
43C25×C11C2311yescharacteristic
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41—44no—
49C22×Q8×C11C2×C411yescharacteristic, complemented
50C22×D4×C11C2×C412yes—
51C22×D4×C11C2×C412yes—
52C22×D4×C11C2×C411yescharacteristic, complemented
53C22×D4×C11C2312yes—
54C23×C4×C11—44no—
55C23×C4×C11C2×C411yescharacteristic
56C23×C4×C11C2×C411yescharacteristic
57C23×C4×C11C2×C411yescharacteristic
58C23×C4×C11C2×C411yescharacteristic
59C23×C4×C11C2×C412yescomplemented
60C23×C4×C11D411yescharacteristic
61C23×C4×C11D411yescharacteristic
62C23×C4×C11D411yescharacteristic
63C23×C4×C11D411yescharacteristic
64C23×C4×C11D411yescharacteristic
65C23×C4×C11D411yescharacteristic
66C23×C4×C11D411yescharacteristic
67C23×C4×C11D411yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×Dic11—22no—
71C11×#123—22no—
72C11×#123—22no—
73C11×#123—22no—
74C11×#123—22no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—21no—
82C11×C22⋊Q8—21no—
83C11×#121—21no—
84C11×#121—21no—
85C11×#121—21no—
86C11×#121—21no—
87C11×#121—21no—
88C11×#121—21no—
89C11×#121—21no—
90C11×#121—21no—
91C11×#120—22no—
92C11×#120—22no—
93C11×#120—22no—
94C11×#120—22no—
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C4×D4×C11—22no—
101C4×D4×C11—22no—
102C4×D4×C11—22no—
103C11×#117—21no—
104C11×#117—21no—
105C11×#117—21no—
106C11×#117—21no—
107C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
108C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
109C2×C11×C4⋊C4C2×C412yescomplemented
110C2×C11×C4⋊C4C2×C412yescomplemented
111C2×C11×C22⋊C4C2×C412yes—
112C2×C11×C22⋊C4C2×C412yes—
113C2×C11×C22⋊C4C2×C412yescomplemented
114C2×C11×C22⋊C4C2×C412yescomplemented
115C2×C11×C22⋊C4C2312yes—
116C2×C42×C11C2×C412yescomplemented
117C2×C22⋊Dic11—22no—
118C2×C22⋊Dic11—22no—
119C2×C22⋊Dic11—22no—
120C2×C22⋊Dic11—44no—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2314yes—
123#66979—44no—
124C2×C4⋊Dic11—22no—
125C2×C4⋊Dic11—22no—
126C2×C4⋊Dic11—22no—
127C2×C4⋊Dic11—44no—
128C2×C4×Dic11—22no—
129#66898—48no—
130C11⋊#95—22no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—22no—
134#21874—111nomaximal, Sylow
135C24×C11—22no—
136C24×C11—22no—
137C24×C11—42no—
138C24×C11—42no—
139C24×C11C22×C411yescharacteristic
140C24×C11C22×C411yescharacteristic
141C24×C11C22×C412yes—
142C24×C11C2×D411yescharacteristic
143C24×C11C2×D411yescharacteristic
144C24×C11C2×D411yescharacteristic
145C24×C11C2×D411yescharacteristic
146C24×C11C2411yescharacteristic
147C11×#41—44no—
148C11×#41—44no—
149C11×#41—44no—
150C11×#41—44no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—42no—
154C2×D4×C11—22no—
155C2×D4×C11—22no—
156C2×D4×C11—22no—
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—24no—
161C2×D4×C11—24no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—42no—
165C2×D4×C11—44no—
166C2×D4×C11—44no—
167C22×C4×C11—24no—
168C22×C4×C11—24no—
169C22×C4×C11—24no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—42no—
173C22×C4×C11—42no—
174C22×C4×C11—42no—
175C22×C4×C11—42no—
176C22×C4×C11—42no—
177C22×C4×C11—42no—
178C22×C4×C11—42no—
179C22×C4×C11—42no—
180C22×C4×C11—42no—
181C22×C4×C11—42no—
182C22×C4×C11—42no—
183C22×C4×C11—44no—
184C22×C4×C11C22⋊C411yescharacteristic
185C22×C4×C11C22⋊C411yescharacteristic
186C22×C4×C11C22⋊C411yescharacteristic
187C22×C4×C11C22⋊C411yescharacteristic
188C22×C4×C11C22⋊C411yescharacteristic
189C22×C4×C11C22⋊C411yescharacteristic
190C22×C4×C11C22⋊C411yescharacteristic
191C22×C4×C11C22⋊C411yescharacteristic
192C22×C4×C11C22⋊C411yescharacteristic
193C22×C4×C11C22⋊C411yescharacteristic
194C22×C4×C11C22⋊C411yescharacteristic
195C22×C4×C11C22⋊C411yescharacteristic
196C22×C4×C11C22⋊C411yescharacteristic
197C22×C4×C11C22⋊C411yescharacteristic
198C22×C4×C11C22⋊C411yescharacteristic
199C22×C4×C11C22⋊C411yescharacteristic
200C22×C4×C11C22×C412yes—
201C22×C4×C11C22×C411yescharacteristic
202C22×C4×C11C22×C411yescharacteristic
203C22×C4×C11C22×C412yes—
204C22×C4×C11C22×C412yes—
205C22×C4×C11C22×C411yescharacteristic
206C22×C4×C11C22×C411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D411yescharacteristic
215C22×Dic11—24no—
216C22×Dic11—24no—
217C22×Dic11—44no—
218C22×Dic11—44no—
219C22×Dic11—44no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—22no—
225C11×C4⋊C4—22no—
226C11×C4⋊C4—22no—
227C11×C4⋊C4—22no—
228C11×C22⋊C4—22no—
229C11×C22⋊C4—22no—
230C11×C22⋊C4—22no—
231C11×C22⋊C4—22no—
232C11×C22⋊C4—22no—
233C11×C22⋊C4—22no—
234C11×C22⋊C4—22no—
235C11×C22⋊C4—22no—
236C11×C22⋊C4—22no—
237C11×C22⋊C4—22no—
238C42×C11—22no—
239C42×C11—22no—
240C22⋊Dic11—24no—
241C22⋊Dic11—28no—
242C22⋊Dic11—24no—
243C22⋊Dic11—44no—
244C22⋊Dic11—44no—
245C22⋊Dic11—44no—
246C4⋊Dic11—44no—
247C4⋊Dic11—44no—
248C4⋊Dic11—44no—
249C4×Dic11—44no—
250C2×#525D1111yescharacteristic
251#2280—111no—
252C2×#380—111no—
253#1996—112no—
254#1964—112no—
255#1898—114no—
256#1799—114no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—22no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—22no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—22no—
268C23×C11—22no—
269C23×C11—22no—
270C23×C11—22no—
271C23×C11—22no—
272C23×C11—24no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—48no—
282C23×C11—48no—
283C23×C11—42no—
284C23×C11—42no—
285C23×C11C2×C22⋊C411yescharacteristic
286C23×C11C2×C22⋊C411yescharacteristic
287C23×C11C2×C22⋊C411yescharacteristic
288C23×C11C2×C22⋊C411yescharacteristic
289C23×C11C23×C411yescharacteristic
290C23×C11C22×D411yescharacteristic
291C23×C11C22×D411yescharacteristic
292C23×C11H(5,𝔽2)12yes—
293C23×C112−1+412yes—
294Q8×C11—42no—
295Q8×C11—42no—
296D4×C11—42no—
297D4×C11—44no—
298D4×C11—44no—
299D4×C11—42no—
300D4×C11—42no—
301D4×C11—44no—
302D4×C11—44no—
303D4×C11—44no—
304D4×C11—42no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—24no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—44no—
337C2×C4×C11—44no—
338C2×C4×C11—42no—
339C2×C4×C11—42no—
340C2×C4×C11#9914yescomplemented
341C2×C4×C11C2×C22⋊C411yescharacteristic
342C2×C4×C11C2×C22⋊C411yescharacteristic
343C2×C4×C11C2×C22⋊C411yescharacteristic
344C2×C4×C11C2×C22⋊C411yescharacteristic
345C2×C4×C11C2×C22⋊C411yescharacteristic
346C2×C4×C11C2×C22⋊C411yescharacteristic
347C2×C4×C11C2×C22⋊C411yescharacteristic
348C2×C4×C11C2×C22⋊C411yescharacteristic
349C2×Dic11—44no—
350C2×Dic11—44no—
351C2×Dic11—44no—
352C2×Dic11—44no—
353C2×Dic11—44no—
354C2×Dic11—44no—
355C2×Dic11—88no—
356C22×#41Dic1111yescharacteristic, complemented
357C24×C4C2×D1111yescharacteristic
358#525—21no—
359#525—21no—
360#525—21no—
361#525—21no—
362#525—21no—
363#525—21no—
364#525—21no—
365#525—21no—
366C2×#123Dic1112yescomplemented
367C2×C22⋊Q8Dic1111yescharacteristic, complemented
368C2×C22⋊Q8C2×D1111yescharacteristic
369C2×#121Dic1111yescharacteristic, complemented
370C2×#121C2×D1111yescharacteristic
371C2×#120C2×D1112yes—
372C2×C4×D4Dic1112yescomplemented
373C2×C4×D4C2×D1112yes—
374C2×#117—221no—
375C2×#117Dic1111yescharacteristic, complemented
376C22×C4⋊C4—221no—
377C22×C22⋊C4—112no—
378C2×#99—118no—
379#381—221no—
380#380—112no—
381#380—112no—
382#380—112no—
383#380—221no—
384#380—221no—
385#380—221no—
386#379—112no—
387C4×C22⋊C4—112no—
388C4×C22⋊C4—221no—
389C2×#95—221no—
390#342—118no—
391C22×C11—24no—
392C22×C11—24no—
393C22×C11—21no—
394C22×C11—21no—
395C22×C11—21no—
396C22×C11—21no—
397C22×C11—21no—
398C22×C11—21no—
399C22×C11—21no—
400C22×C11—21no—
401C22×C11—21no—
402C22×C11—21no—
403C22×C11—21no—
404C22×C11—21no—
405C22×C11—21no—
406C22×C11—21no—
407C22×C11—21no—
408C22×C11—21no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—44no—
412C22×C11—44no—
413C22×C11—44no—
414C22×C11—44no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—84no—
421C22×C11C2×#9912yes—
422C22×C11#41012yes—
423C22×C11C22×C22⋊C411yescharacteristic
424C22×C11#52012yes—
425C22×C11#53511yescharacteristic
426C22×C11#53611yescharacteristic
427C22×C11#53712yes—
428C4×C11—21no—
429C4×C11—21no—
430C4×C11—21no—
431C4×C11—21no—
432C4×C11—21no—
433C4×C11—21no—
434C4×C11—42no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11C2×#9912yes—
438C4×C11C2×#9912yes—
439Dic11—84no—
440Dic11—84no—
441C25C22×D1111yescharacteristic
442C2×#41—21no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—44no—
447C22×Q8C2×Dic1111yescharacteristic, complemented
448C22×D4C2×Dic1112yes—
449C22×D4C2×Dic1112yes—
450C22×D4C2×Dic1111yescharacteristic, complemented
451C22×D4C22×D1112yes—
452C23×C4—44no—
453C23×C4—222no—
454C23×C4C2×Dic1111yescharacteristic
455C23×C4C2×Dic1111yescharacteristic
456C23×C4C2×Dic1111yescharacteristic
457C23×C4C2×Dic1111yescharacteristic
458C23×C4C2×Dic1112yescomplemented
459C23×C4C22⋊D1111yescharacteristic
460C23×C4C22⋊D1111yescharacteristic
461C23×C4C22⋊D1111yescharacteristic
462C23×C4C22⋊D1111yescharacteristic
463C23×C4C22⋊D1111yescharacteristic
464C23×C4C22⋊D1111yescharacteristic
465C23×C4C22⋊D1111yescharacteristic
466C23×C4C22⋊D1111yescharacteristic
467C23×C4C22×D1111yescharacteristic
468C23×C4C22×D1111yescharacteristic
469#123—22no—
470#123—22no—
471#123—22no—
472#123—22no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481#121—21no—
482#121—21no—
483#121—21no—
484#121—21no—
485#121—21no—
486#121—21no—
487#121—21no—
488#121—21no—
489#120—22no—
490#120—22no—
491#120—22no—
492#120—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501#117—21no—
502#117—21no—
503#117—21no—
504#117—21no—
505#117—444no—
506C2×C4⋊C4—222no—
507C2×C4⋊C4—222no—
508C2×C4⋊C4—222no—
509C2×C4⋊C4—444no—
510C2×C4⋊C4C2×Dic1111yescharacteristic, complemented
511C2×C4⋊C4C2×Dic1111yescharacteristic, complemented
512C2×C4⋊C4C2×Dic1112yescomplemented
513C2×C4⋊C4C2×Dic1112yescomplemented
514C2×C22⋊C4—114no—
515C2×C22⋊C4—114no—
516C2×C22⋊C4—222no—
517C2×C22⋊C4—222no—
518C2×C22⋊C4—222no—
519C2×C22⋊C4—444no—
520C2×C22⋊C4C2×Dic1112yes—
521C2×C22⋊C4C2×Dic1112yes—
522C2×C22⋊C4C2×Dic1112yescomplemented
523C2×C22⋊C4C2×Dic1112yescomplemented
524C2×C22⋊C4C22×D1112yes—
525C2×C42—222no—
526C2×C42C2×Dic1112yescomplemented
527#99—448no—
528#95—222no—
529#95—222no—
530#95—222no—
531#95—222no—
532C2×C11—21no—
533C2×C11—22no—
534C2×C11—21no—
535C2×C11—22no—
536C2×C11—22no—
537C2×C11—22no—
538C2×C11—41no—
539C2×C11—41no—
540C2×C11—82no—
541C2×C11#231111yescharacteristic
542C2×C11C22×#9911yescharacteristic
543C2×C11C2×#41011yescharacteristic
544C24—22no—
545C24—22no—
546C24—42no—
547C24—42no—
548C24C22×Dic1111yescharacteristic
549C24C22×Dic1111yescharacteristic
550C24C22×Dic1112yes—
551C24C2×C22⋊D1111yescharacteristic
552C24C2×C22⋊D1111yescharacteristic
553C24C2×C22⋊D1111yescharacteristic
554C24C2×C22⋊D1111yescharacteristic
555C24C23×D1111yescharacteristic
556#41—44no—
557#41—44no—
558#41—44no—
559#41—44no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—42no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—24no—
568C2×D4—24no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—42no—
574C2×D4—44no—
575C2×D4—44no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—44no—
593C22×C4—224no—
594C22×C4—224no—
595C22×C4—444no—
596C22×C4—444no—
597C22×C4—444no—
598C22×C4C22⋊Dic1111yescharacteristic
599C22×C4C22⋊Dic1111yescharacteristic
600C22×C4C22⋊Dic1111yescharacteristic
601C22×C4C22⋊Dic1111yescharacteristic
602C22×C4C22⋊Dic1111yescharacteristic
603C22×C4C22⋊Dic1111yescharacteristic
604C22×C4C22⋊Dic1111yescharacteristic
605C22×C4C22⋊Dic1111yescharacteristic
606C22×C4C22⋊Dic1111yescharacteristic
607C22×C4C22⋊Dic1111yescharacteristic
608C22×C4C22⋊Dic1111yescharacteristic
609C22×C4C22⋊Dic1111yescharacteristic
610C22×C4C22⋊Dic1111yescharacteristic
611C22×C4C22⋊Dic1111yescharacteristic
612C22×C4C22⋊Dic1111yescharacteristic
613C22×C4C22⋊Dic1111yescharacteristic
614C22×C4C22×Dic1112yes—
615C22×C4C22×Dic1111yescharacteristic
616C22×C4C22×Dic1111yescharacteristic
617C22×C4C22×Dic1112yes—
618C22×C4C22×Dic1112yes—
619C22×C4C22×Dic1111yescharacteristic
620C22×C4C22×Dic1111yescharacteristic
621C22×C4C2×C22⋊D1111yescharacteristic
622C22×C4C2×C22⋊D1111yescharacteristic
623C22×C4C2×C22⋊D1111yescharacteristic
624C22×C4C2×C22⋊D1111yescharacteristic
625C22×C4C2×C22⋊D1111yescharacteristic
626C22×C4C2×C22⋊D1111yescharacteristic
627C22×C4C2×C22⋊D1111yescharacteristic
628C22×C4C2×C22⋊D1111yescharacteristic
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—444no—
638C4⋊C4—444no—
639C4⋊C4—444no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—224no—
651C22⋊C4—228no—
652C22⋊C4—224no—
653C22⋊C4—444no—
654C22⋊C4—444no—
655C22⋊C4—444no—
656C42—22no—
657C42—22no—
658C42—444no—
659C11#2187411yescharacteristic, complemented, Sylow
660C23—22no—
661C23—21no—
662C23—21no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—21no—
667C23—22no—
668C23—22no—
669C23—21no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—48no—
685C23—48no—
686C23—42no—
687C23—42no—
688C23C2×C22⋊Dic1111yescharacteristic
689C23C2×C22⋊Dic1111yescharacteristic
690C23C2×C22⋊Dic1111yescharacteristic
691C23C2×C22⋊Dic1111yescharacteristic
692C23#6704212yes—
693C23#6704312yes—
694C23C23×Dic1111yescharacteristic
695C23C22×C22⋊D1111yescharacteristic
696C23C22×C22⋊D1111yescharacteristic
697Q8—42no—
698Q8—42no—
699D4—42no—
700D4—44no—
701D4—44no—
702D4—44no—
703D4—42no—
704D4—42no—
705D4—44no—
706D4—44no—
707D4—42no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—444no—
744C2×C4—444no—
745C2×C4—444no—
746C2×C4—444no—
747C2×C4—444no—
748C2×C4—444no—
749C2×C4—888no—
750C2×C4#6689814yescomplemented
751C2×C4C2×C22⋊Dic1111yescharacteristic
752C2×C4C2×C22⋊Dic1111yescharacteristic
753C2×C4C2×C22⋊Dic1111yescharacteristic
754C2×C4C2×C22⋊Dic1111yescharacteristic
755C2×C4C2×C22⋊Dic1111yescharacteristic
756C2×C4C2×C22⋊Dic1111yescharacteristic
757C2×C4C2×C22⋊Dic1111yescharacteristic
758C2×C4C2×C22⋊Dic1111yescharacteristic
759C22—24no—
760C22—24no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—84no—
789C22C2×#6689812yes—
790C22#1062285312yes—
791C22#1062335611yescharacteristic
792C22#1062335812yes—
793C22#1062336111yescharacteristic
794C22#1062336412yes—
795C22C22×C22⋊Dic1111yescharacteristic
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—884no—
806C4—884no—
807C4C2×#6689812yes—
808C4C2×#6689812yes—
809C2—21no—
810C2—22no—
811C2—22no—
812C2—21no—
813C2—22no—
814C2—22no—
815C2—41no—
816C2—41no—
817C2—82no—
818C2#1307120811yescharacteristic
819C2C22×#6689811yescharacteristic
820C2C2×#1062285311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
Fitting, prime radicalC2×C11×#525C2
socleC22×C11C22×C22⋊C4
cosocleC24×C11C24
hypercenterC2×#525D11
hypocenterC11#21874
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. #13070999C2semidirect
2. C2×#10622825C2semidirect
3. #13069602C2semidirect
4. #13069453C2semidirect
5. #13069070C2semidirect
6. #13068604C2semidirect
8. C22×C11×#41C4semidirect
18. C2×C11×#123C4semidirect
19. C2×C11×C22⋊Q8C4semidirect
21. C2×C11×#121C4semidirect
24. C2×C4×D4×C11C4semidirect
26. C2×C11×#117C4semidirect
49. C22×Q8×C11C2×C4semidirect
52. C22×D4×C11C2×C4semidirect
59. C23×C4×C11C2×C4semidirect
107. C2×C11×C4⋊C4C2×C4semidirect
108. C2×C11×C4⋊C4C2×C4semidirect
109. C2×C11×C4⋊C4C2×C4semidirect
110. C2×C11×C4⋊C4C2×C4semidirect
113. C2×C11×C22⋊C4C2×C4semidirect
114. C2×C11×C22⋊C4C2×C4semidirect
116. C2×C42×C11C2×C4semidirect
340. C2×C4×C11#99semidirect
356. C22×#41Dic11semidirect
366. C2×#123Dic11semidirect
367. C2×C22⋊Q8Dic11semidirect
369. C2×#121Dic11semidirect
372. C2×C4×D4Dic11semidirect
375. C2×#117Dic11semidirect
447. C22×Q8C2×Dic11semidirect
450. C22×D4C2×Dic11semidirect
458. C23×C4C2×Dic11semidirect
510. C2×C4⋊C4C2×Dic11semidirect
511. C2×C4⋊C4C2×Dic11semidirect
512. C2×C4⋊C4C2×Dic11semidirect
513. C2×C4⋊C4C2×Dic11semidirect
522. C2×C22⋊C4C2×Dic11semidirect
523. C2×C22⋊C4C2×Dic11semidirect
526. C2×C42C2×Dic11semidirect
659. C11#21874semidirect
750. C2×C4#66898semidirect

Maximal subgroups

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

subgroupindex
#130709992
C2×#106228252
#130696022
#130694532
#130690702
#130686042
C2×C11×#5252
#2187411