Finite Group Databasebeta

← #14720937

Subgroups — #14720937

Order 2816.

1574 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622820C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
3#13067136C212yesmaximal, complemented
4#13067132C212yesmaximal, complemented
5#13067120C214yesmaximal, complemented
6#13067107C214yesmaximal, 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×#525C412yescomplemented
15C11×#525C412yescomplemented
16C11×#525C2212yes—
17C11×#525C2212yes—
18C2×C11×#123—21no—
19C2×C11×C22⋊Q8C411yescharacteristic, complemented
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#121C411yescharacteristic, complemented
22C2×C11×#121C2211yescharacteristic
23C2×C11×#120—21no—
24C2×C4×D4×C11—21no—
25C2×C4×D4×C11—21no—
26C2×C11×#117C411yescharacteristic, complemented
27C22×C22⋊Dic11—21no—
28C22×C4×Dic11—21no—
29C22×#4318—21no—
30C4×C22⋊Dic11—21no—
31C4×C22⋊Dic11—21no—
32C4×C22⋊Dic11C2212yes—
33C4×C22⋊Dic11C2212yescomplemented
34C2×C11⋊#95C2212yescomplemented
35#10622820—21no—
36#10622820—21no—
37#10622820C2212yes—
38#10622820C2212yescomplemented
39C2×C22⋊(C11⋊C8)—21no—
40C2×C22⋊(C11⋊C8)C2212yescomplemented
41#10622176C2218yescomplemented
42#10622175C2218yescomplemented
43C25×C11D411yescharacteristic
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—44no—
47C2×C11×#41C2×C412yes—
48C2×C11×#41C2×C412yescomplemented
49C22×Q8×C11C2×C411yescharacteristic, complemented
50C22×D4×C11—21no—
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C22×D4×C11C2×C411yescharacteristic, complemented
54C23×C4×C11—21no—
55C23×C4×C11—44no—
56C23×C4×C11C2×C411yescharacteristic
57C23×C4×C11C2×C411yescharacteristic
58C23×C4×C11C2×C411yescharacteristic
59C23×C4×C11C2×C411yescharacteristic
60C23×C4×C11D411yescharacteristic
61C23×C4×C11D411yescharacteristic
62C23×C4×C11D411yescharacteristic
63C23×C4×C11D411yescharacteristic
64C23×C4×C11D411yescharacteristic
65C23×C4×C11D411yescharacteristic
66C23×C4×C11D411yescharacteristic
67C23×C4×C11C2311yescharacteristic
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⋊Q8C2×C412yes—
80C11×C22⋊Q8C2×C412yescomplemented
81C11×C22⋊Q8C2×C412yescomplemented
82C11×C22⋊Q8C2312yes—
83C11×#121—21no—
84C11×#121—21no—
85C11×#121—21no—
86C11×#121—21no—
87C11×#121C2×C412yes—
88C11×#121C2×C412yescomplemented
89C11×#121C2×C412yescomplemented
90C11×#121C2312yes—
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×#117C2×C412yes—
106C11×#117C2×C412yescomplemented
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
110C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C42×C11—21no—
117C2×C22⋊Dic11—28no—
118C2×C22⋊Dic11—22no—
119C2×C22⋊Dic11—22no—
120C2×C4×Dic11—22no—
121C2×C4×Dic11—22no—
122C2×C4×Dic11—44no—
123C2×#4318—22no—
124C2×#4318—22no—
125C2×#4318—44no—
126C22×C11⋊C8—22no—
127C11⋊#95—22no—
128C11⋊#95C2314yes—
129C22⋊(C11⋊C8)—22no—
130C22⋊(C11⋊C8)—22no—
131C22⋊(C11⋊C8)—22no—
132C22⋊(C11⋊C8)C2314yes—
133#17542—111nomaximal, Sylow
134C24×C11—24no—
135C24×C11—21no—
136C24×C11—42no—
137C24×C11—42no—
138C24×C11C22⋊C411yescharacteristic
139C24×C11C22⋊C411yescharacteristic
140C24×C11C22⋊C411yescharacteristic
141C24×C11C22⋊C411yescharacteristic
142C24×C11C2×D411yescharacteristic
143C24×C11C2×D411yescharacteristic
144C24×C11C2×D411yescharacteristic
145C11×#41—44no—
146C11×#41—44no—
147C11×#41—44no—
148C11×#41—44no—
149C2×Q8×C11—21no—
150C2×Q8×C11—42no—
151C2×Q8×C11C22×C412yes—
152C2×D4×C11—22no—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—22no—
156C2×D4×C11—22no—
157C2×D4×C11—22no—
158C2×D4×C11—21no—
159C2×D4×C11—42no—
160C2×D4×C11—44no—
161C2×D4×C11—44no—
162C2×D4×C11—44no—
163C2×D4×C11C22×C412yes—
164C22×C4×C11—24no—
165C22×C4×C11—24no—
166C22×C4×C11—24no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
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×C411yescharacteristic
201C22×C4×C11C22×C411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2411yescharacteristic
212C22×Dic11—28no—
213C22×Dic11—24no—
214C22×Dic11—44no—
215C22×Dic11—44no—
216C11×C4⋊C4—22no—
217C11×C4⋊C4—22no—
218C11×C4⋊C4—22no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—22no—
222C11×C4⋊C4C22×C412yes—
223C11×C4⋊C4C22×C412yes—
224C11×C22⋊C4—22no—
225C11×C22⋊C4—22no—
226C11×C22⋊C4—22no—
227C11×C22⋊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—
234C42×C11—22no—
235C42×C11—22no—
236C22⋊Dic11—28no—
237C22⋊Dic11—28no—
238C4×Dic11—44no—
239C4×Dic11—44no—
240#4318—44no—
241#4318—44no—
242C2×C11⋊C8—24no—
243C2×C11⋊C8—44no—
244C2×#525D1111yescharacteristic
245C2×#407—111no—
246C2×C4×C22⋊C4—111no—
247#1508—112no—
248#1507—112no—
249#1504—114no—
250#1501—114no—
251C23×C11—22no—
252C23×C11—22no—
253C23×C11—22no—
254C23×C11—22no—
255C23×C11—22no—
256C23×C11—22no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—22no—
263C23×C11—22no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—416no—
273C23×C11—42no—
274C23×C11—42no—
275C23×C11—42no—
276C23×C11#10414yes—
277C23×C11C2×C22⋊C411yescharacteristic
278C23×C11C2×C22⋊C411yescharacteristic
279C23×C11C2×C22⋊C411yescharacteristic
280C23×C11C2×C22⋊C411yescharacteristic
281C23×C11C2×C22⋊C411yescharacteristic
282C23×C11C2×C22⋊C411yescharacteristic
283C23×C11C22×D411yescharacteristic
284Q8×C11—42no—
285Q8×C11—42no—
286D4×C11—42no—
287D4×C11—44no—
288D4×C11—44no—
289D4×C11—44no—
290D4×C11—44no—
291D4×C11—44no—
292D4×C11—44no—
293D4×C11—42no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
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—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—44no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11—44no—
329C2×C4×C11#9914yes—
330C2×C4×C11C2×C22⋊C411yescharacteristic
331C2×C4×C11C2×C22⋊C411yescharacteristic
332C2×C4×C11C2×C22⋊C411yescharacteristic
333C2×C4×C11C2×C22⋊C411yescharacteristic
334C2×C4×C11C2×C22⋊C411yescharacteristic
335C2×C4×C11C2×C22⋊C411yescharacteristic
336C2×C4×C11C23×C411yescharacteristic
337C2×C4×C11C22×D411yescharacteristic
338C2×Dic11—28no—
339C2×Dic11—44no—
340C2×Dic11—416no—
341C2×Dic11—44no—
342C11⋊C8—44no—
343C22×#41Dic1111yescharacteristic, complemented
344C24×C4C2×D1111yescharacteristic
345C22×M16—221no—
346#525—21no—
347#525—21no—
348#525—21no—
349#525—21no—
350#525Dic1112yescomplemented
351#525Dic1112yescomplemented
352#525C2×D1112yes—
353#525C2×D1112yes—
354C2×#123—21no—
355C2×C22⋊Q8Dic1111yescharacteristic, complemented
356C2×C22⋊Q8C2×D1111yescharacteristic
357C2×#121Dic1111yescharacteristic, complemented
358C2×#121C2×D1111yescharacteristic
359C2×#120—21no—
360C2×C4×D4—21no—
361C2×C4×D4—21no—
362C2×#117Dic1111yescharacteristic, complemented
363C22×C22⋊C4—221no—
364C22×C42—221no—
365#407—112no—
366#407—112no—
367#407—221no—
368#407—221no—
369C2×C22⋊C8—112no—
370C2×C22⋊C8—221no—
371C4×C22⋊C4—112no—
372C4×C22⋊C4—112no—
373C4×C22⋊C4—221no—
374C4×C22⋊C4—221no—
375C2×#95—112no—
376#328—118no—
377#327—118no—
378C22×C11—28no—
379C22×C11—21no—
380C22×C11—21no—
381C22×C11—21no—
382C22×C11—21no—
383C22×C11—21no—
384C22×C11—21no—
385C22×C11—21no—
386C22×C11—21no—
387C22×C11—21no—
388C22×C11—21no—
389C22×C11—21no—
390C22×C11—21no—
391C22×C11—21no—
392C22×C11—21no—
393C22×C11—21no—
394C22×C11—21no—
395C22×C11—44no—
396C22×C11—44no—
397C22×C11—44no—
398C22×C11—44no—
399C22×C11—44no—
400C22×C11—44no—
401C22×C11—42no—
402C22×C11—42no—
403C22×C11—42no—
404C22×C11—84no—
405C22×C11C2×#9912yes—
406C22×C11C2×#10412yes—
407C22×C11C2×#10412yes—
408C22×C11C2×#10412yes—
409C22×C11C22×C22⋊C411yescharacteristic
410C22×C11#57512yes—
411C4×C11—21no—
412C4×C11—21no—
413C4×C11—21no—
414C4×C11—21no—
415C4×C11—21no—
416C4×C11—21no—
417C4×C11—42no—
418C4×C11—42no—
419C4×C11—42no—
420C4×C11C2×#9912yes—
421C4×C11C2×#9912yes—
422Dic11—48no—
423C25C22⋊D1111yescharacteristic
424C2×#41—21no—
425C2×#41—21no—
426C2×#41—44no—
427C2×#41C2×Dic1112yes—
428C2×#41C2×Dic1112yescomplemented
429C22×Q8C2×Dic1111yescharacteristic, complemented
430C22×D4—21no—
431C22×D4—21no—
432C22×D4—21no—
433C22×D4C2×Dic1111yescharacteristic, complemented
434C23×C4—21no—
435C23×C4—44no—
436C23×C4—222no—
437C23×C4C2×Dic1111yescharacteristic
438C23×C4C2×Dic1111yescharacteristic
439C23×C4C2×Dic1111yescharacteristic
440C23×C4C2×Dic1111yescharacteristic
441C23×C4C22⋊D1111yescharacteristic
442C23×C4C22⋊D1111yescharacteristic
443C23×C4C22⋊D1111yescharacteristic
444C23×C4C22⋊D1111yescharacteristic
445C23×C4C22⋊D1111yescharacteristic
446C23×C4C22⋊D1111yescharacteristic
447C23×C4C22⋊D1111yescharacteristic
448C23×C4C22×D1111yescharacteristic
449C23×C4C22×D1111yescharacteristic
450C23×C4C22×D1111yescharacteristic
451C2×M16—222no—
452C2×M16—222no—
453C2×M16—444no—
454C22×C8—222no—
455#123—22no—
456#123—22no—
457#123—22no—
458#123—22no—
459C22⋊Q8—21no—
460C22⋊Q8—21no—
461C22⋊Q8—21no—
462C22⋊Q8—21no—
463C22⋊Q8C2×Dic1112yes—
464C22⋊Q8C2×Dic1112yescomplemented
465C22⋊Q8C2×Dic1112yescomplemented
466C22⋊Q8C22×D1112yes—
467#121—21no—
468#121—21no—
469#121—21no—
470#121—21no—
471#121C2×Dic1112yes—
472#121C2×Dic1112yescomplemented
473#121C2×Dic1112yescomplemented
474#121C22×D1112yes—
475#120—22no—
476#120—22no—
477#120—22no—
478#120—22no—
479C4×D4—22no—
480C4×D4—22no—
481C4×D4—22no—
482C4×D4—22no—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—22no—
487#117—21no—
488#117—21no—
489#117C2×Dic1112yes—
490#117C2×Dic1112yescomplemented
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4C2×Dic1111yescharacteristic, complemented
494C2×C4⋊C4C2×Dic1111yescharacteristic, complemented
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—228no—
501C2×C22⋊C4—222no—
502C2×C22⋊C4—222no—
503C2×C42—21no—
504C2×C42—222no—
505C2×C42—222no—
506C2×C42—444no—
507C22⋊C8—114no—
508C22⋊C8—222no—
509C22⋊C8—222no—
510C22⋊C8—222no—
511#95—114no—
512#95—222no—
513C2×C11—22no—
514C2×C11—22no—
515C2×C11—22no—
516C2×C11—22no—
517C2×C11—22no—
518C2×C11—41no—
519C2×C11—41no—
520C2×C11—82no—
521C2×C11C22×#9911yescharacteristic
522C2×C11#289611yescharacteristic
523C2×C11C22×#10411yescharacteristic
524C24—24no—
525C24—21no—
526C24—42no—
527C24—42no—
528C24C22⋊Dic1111yescharacteristic
529C24C22⋊Dic1111yescharacteristic
530C24C22⋊Dic1111yescharacteristic
531C24C22⋊Dic1111yescharacteristic
532C24C2×C22⋊D1111yescharacteristic
533C24C2×C22⋊D1111yescharacteristic
534C24C2×C22⋊D1111yescharacteristic
535#41—44no—
536#41—44no—
537#41—44no—
538#41—44no—
539C2×Q8—21no—
540C2×Q8—42no—
541C2×Q8C22×Dic1112yes—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—42no—
550C2×D4—44no—
551C2×D4—44no—
552C2×D4—44no—
553C2×D4C22×Dic1112yes—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—44no—
574C22×C4—228no—
575C22×C4—224no—
576C22×C4—444no—
577C22×C4—444no—
578C22×C4C22⋊Dic1111yescharacteristic
579C22×C4C22⋊Dic1111yescharacteristic
580C22×C4C22⋊Dic1111yescharacteristic
581C22×C4C22⋊Dic1111yescharacteristic
582C22×C4C22⋊Dic1111yescharacteristic
583C22×C4C22⋊Dic1111yescharacteristic
584C22×C4C22⋊Dic1111yescharacteristic
585C22×C4C22⋊Dic1111yescharacteristic
586C22×C4C22⋊Dic1111yescharacteristic
587C22×C4C22⋊Dic1111yescharacteristic
588C22×C4C22⋊Dic1111yescharacteristic
589C22×C4C22⋊Dic1111yescharacteristic
590C22×C4C22×Dic1111yescharacteristic
591C22×C4C22×Dic1111yescharacteristic
592C22×C4C22×Dic1111yescharacteristic
593C22×C4C22×Dic1111yescharacteristic
594C22×C4C22×Dic1111yescharacteristic
595C22×C4C22×Dic1111yescharacteristic
596C22×C4C2×C22⋊D1111yescharacteristic
597C22×C4C2×C22⋊D1111yescharacteristic
598C22×C4C2×C22⋊D1111yescharacteristic
599C22×C4C2×C22⋊D1111yescharacteristic
600C22×C4C2×C22⋊D1111yescharacteristic
601C22×C4C2×C22⋊D1111yescharacteristic
602C22×C4C2×C22⋊D1111yescharacteristic
603C22×C4C2×C22⋊D1111yescharacteristic
604C22×C4C2×C22⋊D1111yescharacteristic
605C22×C4C23×D1111yescharacteristic
606M16—444no—
607M16—444no—
608C2×C8—224no—
609C2×C8—444no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—22no—
616C4⋊C4C22×Dic1112yes—
617C4⋊C4C22×Dic1112yes—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—228no—
629C22⋊C4—228no—
630C42—22no—
631C42—22no—
632C42—444no—
633C42—444no—
634C11#1754211yescharacteristic, complemented, Sylow
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—416no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23#6690114yes—
661C23C2×C22⋊Dic1111yescharacteristic
662C23C2×C22⋊Dic1111yescharacteristic
663C23C2×C22⋊Dic1111yescharacteristic
664C23C2×C22⋊Dic1111yescharacteristic
665C23C2×C22⋊Dic1111yescharacteristic
666C23C2×C22⋊Dic1111yescharacteristic
667C23C22×C22⋊D1111yescharacteristic
668Q8—42no—
669Q8—42no—
670D4—42no—
671D4—44no—
672D4—44no—
673D4—44no—
674D4—44no—
675D4—44no—
676D4—44no—
677D4—42no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—44no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—44no—
713C2×C4—228no—
714C2×C4—444no—
715C2×C4—4416no—
716C2×C4—444no—
717C2×C4#6689814yes—
718C2×C4C2×C22⋊Dic1111yescharacteristic
719C2×C4C2×C22⋊Dic1111yescharacteristic
720C2×C4C2×C22⋊Dic1111yescharacteristic
721C2×C4C2×C22⋊Dic1111yescharacteristic
722C2×C4C2×C22⋊Dic1111yescharacteristic
723C2×C4C2×C22⋊Dic1111yescharacteristic
724C2×C4C23×Dic1111yescharacteristic
725C2×C4C22×C22⋊D1111yescharacteristic
726C8—444no—
727C22—28no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—84no—
754C22C2×#6689812yes—
755C22C2×#6690112yes—
756C22C2×#6690112yes—
757C22C2×#6690112yes—
758C22#1062335312yes—
759C22C22×C22⋊Dic1111yescharacteristic
760C4—21no—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—42no—
767C4—42no—
768C4—42no—
769C4—448no—
770C4C2×#6689812yes—
771C4C2×#6689812yes—
772C2—22no—
773C2—22no—
774C2—22no—
775C2—22no—
776C2—22no—
777C2—41no—
778C2—41no—
779C2—82no—
780C2C22×#6689811yescharacteristic
781C2#1307713511yescharacteristic
782C2C22×#6690111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#525C2
socleC22×C11C22×C22⋊C4
cosocleC22×C4×C11C24
hypercenterC2×#525D11
hypocenterC11#17542
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#10622820C2semidirect
2. C2×C4×C22⋊Dic11C2semidirect
3. #13067136C2semidirect
4. #13067132C2semidirect
5. #13067120C2semidirect
6. #13067107C2semidirect
8. C22×C11×#41C4semidirect
14. C11×#525C4semidirect
15. C11×#525C4semidirect
19. C2×C11×C22⋊Q8C4semidirect
21. C2×C11×#121C4semidirect
26. C2×C11×#117C4semidirect
33. C4×C22⋊Dic11C22semidirect
34. C2×C11⋊#95C22semidirect
38. #10622820C22semidirect
40. C2×C22⋊(C11⋊C8)C22semidirect
41. #10622176C22semidirect
42. #10622175C22semidirect
48. C2×C11×#41C2×C4semidirect
49. C22×Q8×C11C2×C4semidirect
53. C22×D4×C11C2×C4semidirect
80. C11×C22⋊Q8C2×C4semidirect
81. C11×C22⋊Q8C2×C4semidirect
88. C11×#121C2×C4semidirect
89. C11×#121C2×C4semidirect
106. C11×#117C2×C4semidirect
109. C2×C11×C4⋊C4C2×C4semidirect
110. C2×C11×C4⋊C4C2×C4semidirect
343. C22×#41Dic11semidirect
350. #525Dic11semidirect
351. #525Dic11semidirect
355. C2×C22⋊Q8Dic11semidirect
357. C2×#121Dic11semidirect
362. C2×#117Dic11semidirect
428. C2×#41C2×Dic11semidirect
429. C22×Q8C2×Dic11semidirect
433. C22×D4C2×Dic11semidirect
464. C22⋊Q8C2×Dic11semidirect
465. C22⋊Q8C2×Dic11semidirect
472. #121C2×Dic11semidirect
473. #121C2×Dic11semidirect
490. #117C2×Dic11semidirect
493. C2×C4⋊C4C2×Dic11semidirect
494. C2×C4⋊C4C2×Dic11semidirect
634. C11#17542semidirect

Maximal subgroups

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

subgroupindex
C2×#106228202
C2×C4×C22⋊Dic112
#130671362
#130671322
#130671202
#130671072
C2×C11×#5252
#1754211