Finite Group Databasebeta

← #15624524

Subgroups — #15624524

Order 2816.

2342 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66977C211yesmaximal, characteristic, complemented
2#13079442C214yesmaximal, complemented
3#13079437C212yesmaximal, complemented
4#13079422C212yesmaximal, complemented
5#13079393C214yesmaximal, complemented
6#13079388C212yesmaximal, complemented
7#13079373C212yesmaximal, complemented
8#13078564C212yesmaximal, complemented
9#13078536C212yesmaximal, complemented
10#13078248C214yesmaximal, complemented
11#13077876C212yesmaximal, complemented
12#13077849C212yesmaximal, complemented
13C2×#10622820C211yesmaximal, characteristic, complemented
14C2×C11×#525C211yesmaximal, characteristic
15C22×C11×#41C2211yescharacteristic
16C24×C4×C11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic, complemented
18C11×#525—21no—
19C11×#525—21no—
20C11×#525—21no—
21C11×#525—21no—
22C11×#525C2212yes—
23C11×#525C2212yes—
24C11×#525C2212yes—
25C11×#525C2212yes—
26C2×C11×#123—21no—
27C2×C11×C22⋊Q8C2211yescharacteristic
28C2×C11×C22⋊Q8C2211yescharacteristic
29C2×C11×#121C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic
31C2×C11×#120—21no—
32C2×C4×D4×C11—21no—
33C2×C4×D4×C11—21no—
34C2×C11×#117C2211yescharacteristic
35C22×C22⋊Dic11—21no—
36C2×#67004C2214yescomplemented
37C22×C4⋊Dic11C2211yescharacteristic, complemented
38C2×#66977—21no—
39C2×#66977—21no—
40C2×#66977—21no—
41C2×#66977—21no—
42C2×#66977—21no—
43C2×#66977—21no—
44C2×#66977C2212yes—
45C2×#66977C2212yes—
46C2×#66977C2212yes—
47C2×#66977C2212yescomplemented
48C2×#66977C2212yescomplemented
49C2×#66977C2212yescomplemented
50C22×Dic11⋊C4—21no—
51C22×#4318C2212yescomplemented
52#10622852C2218yescomplemented
53#10622845C2214yescomplemented
54#10622841C2214yescomplemented
55#10622831C2214yescomplemented
56#10622820C2212yes—
57#10622820C2212yes—
58#10622820C2212yescomplemented
59#10622820C2212yescomplemented
60C2×C22⋊(C11⋊C8)C2212yes—
61C2×C22⋊(C11⋊C8)C2212yescomplemented
62#10622665C2218yescomplemented
63#10622664C2218yescomplemented
64#10622663C2214yescomplemented
65#10622663C2214yescomplemented
66#10622657C2214yescomplemented
67#10622656C2214yescomplemented
68#10622655C2218yescomplemented
69#10622654C2218yescomplemented
70#10622653C2214yescomplemented
71#10622653C2214yescomplemented
72#10622647C2214yescomplemented
73#10622646C2214yescomplemented
74#10622617C2214yescomplemented
75#10622609C2218yescomplemented
76#10622608C2214yescomplemented
77#10622584C2214yescomplemented
78#10622583C2214yescomplemented
79C25×C11D411yescharacteristic
80C2×C11×#41—21no—
81C2×C11×#41—21no—
82C2×C11×#41—44no—
83C2×C11×#41C2312yes—
84C2×C11×#41C2312yes—
85C22×Q8×C11C2311yescharacteristic
86C22×D4×C11—21no—
87C22×D4×C11—21no—
88C22×D4×C11—21no—
89C22×D4×C11C2311yescharacteristic
90C23×C4×C11—21no—
91C23×C4×C11—44no—
92C23×C4×C11D411yescharacteristic
93C23×C4×C11D411yescharacteristic
94C23×C4×C11D411yescharacteristic
95C23×C4×C11D411yescharacteristic
96C23×C4×C11D411yescharacteristic
97C23×C4×C11D411yescharacteristic
98C23×C4×C11D411yescharacteristic
99C23×C4×C11C2311yescharacteristic
100C23×C4×C11C2311yescharacteristic
101C23×C4×C11C2311yescharacteristic
102C23×C4×C11C2311yescharacteristic
103C23×C4×C11C2311yescharacteristic
104C23×C4×C11C2311yescharacteristic
105C23×C4×C11C2311yescharacteristic
106C23×Dic11—21no—
107C23×Dic11—21no—
108C22×Dic22—21no—
109C22×Dic22—21no—
110C22×Dic22—21no—
111C22×Dic22—44no—
112C22×Dic22C2312yes—
113C22×Dic22C2312yes—
114C22×Dic22C2312yes—
115C11×#123—22no—
116C11×#123—22no—
117C11×#123—22no—
118C11×#123—22no—
119C11×C22⋊Q8—21no—
120C11×C22⋊Q8—21no—
121C11×C22⋊Q8—21no—
122C11×C22⋊Q8—21no—
123C11×C22⋊Q8C2312yes—
124C11×C22⋊Q8C2312yes—
125C11×C22⋊Q8C2312yes—
126C11×C22⋊Q8C2312yes—
127C11×#121—21no—
128C11×#121—21no—
129C11×#121—21no—
130C11×#121—21no—
131C11×#121C2312yes—
132C11×#121C2312yes—
133C11×#121C2312yes—
134C11×#121C2312yes—
135C11×#120—22no—
136C11×#120—22no—
137C11×#120—22no—
138C11×#120—22no—
139C4×D4×C11—22no—
140C4×D4×C11—22no—
141C4×D4×C11—22no—
142C4×D4×C11—22no—
143C4×D4×C11—22no—
144C4×D4×C11—22no—
145C4×D4×C11—22no—
146C4×D4×C11—22no—
147C11×#117—21no—
148C11×#117—21no—
149C11×#117C2312yes—
150C11×#117C2312yes—
151C2×C11×C4⋊C4—21no—
152C2×C11×C4⋊C4—21no—
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C22⋊C4—21no—
156C2×C11×C22⋊C4—21no—
157C2×C11×C22⋊C4—21no—
158C2×C11×C22⋊C4—21no—
159C2×C11×C22⋊C4—21no—
160C2×C42×C11—21no—
161C2×C22⋊Dic11—22no—
162C2×C22⋊Dic11—22no—
163C2×C22⋊Dic11—22no—
164C2×C22⋊Dic11—22no—
165C2×C22⋊Dic11—22no—
166C2×C22⋊Dic11—22no—
167#67004—48no—
168C2×#4326C2318yescomplemented
169C2×#4324C2318yescomplemented
170C2×C4⋊Dic11—21no—
171C2×C4⋊Dic11—21no—
172C2×C4⋊Dic11—21no—
173C2×C4⋊Dic11C2312yes—
174C2×C4⋊Dic11C2312yes—
175C2×C4⋊Dic11C2312yes—
176#66977—22no—
177#66977—22no—
178#66977—22no—
179#66977—22no—
180#66977—22no—
181#66977—22no—
182#66977—22no—
183#66977—22no—
184#66977—22no—
185#66977—22no—
186#66977—22no—
187#66977—22no—
188#66977C2314yes—
189#66977C2314yes—
190#66977C2314yes—
191#66977C2314yes—
192C2×Dic11⋊C4—22no—
193C2×Dic11⋊C4—22no—
194C2×Dic11⋊C4—22no—
195C2×Dic11⋊C4—22no—
196C2×Dic11⋊C4—22no—
197C2×Dic11⋊C4—22no—
198C2×#4318—44no—
199C2×#4318C2314yes—
200C2×#4318C2314yes—
201C22×C11⋊C8C2314yes—
202#66899C2318yescomplemented
203#66896C2318yescomplemented
204C22⋊(C11⋊C8)C2314yes—
205C22⋊(C11⋊C8)C2314yes—
206C22⋊(C11⋊C8)C2314yes—
207C22⋊(C11⋊C8)C2314yes—
208#66874C2318yescomplemented
209#66874C2318yescomplemented
210#66872C2318yescomplemented
211#66871C2318yescomplemented
212#60751—111nomaximal, Sylow
213C24×C11—24no—
214C24×C11—21no—
215C24×C11—42no—
216C24×C11—42no—
217C24×C11C2×D411yescharacteristic
218C24×C11C2×D411yescharacteristic
219C24×C11C2×D411yescharacteristic
220C24×C11C2×D411yescharacteristic
221C24×C11C2×D411yescharacteristic
222C24×C11C2×D411yescharacteristic
223C24×C11C2×D411yescharacteristic
224C11×#41—28no—
225C11×#41—44no—
226C11×#41—44no—
227C11×#41—44no—
228C2×Q8×C11—21no—
229C2×Q8×C11—42no—
230C2×Q8×C11C2412yes—
231C2×D4×C11—22no—
232C2×D4×C11—22no—
233C2×D4×C11—22no—
234C2×D4×C11—22no—
235C2×D4×C11—22no—
236C2×D4×C11—22no—
237C2×D4×C11—21no—
238C2×D4×C11—42no—
239C2×D4×C11—44no—
240C2×D4×C11—44no—
241C2×D4×C11—44no—
242C2×D4×C11C2412yes—
243C22×C4×C11—24no—
244C22×C4×C11—24no—
245C22×C4×C11—24no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—22no—
250C22×C4×C11—22no—
251C22×C4×C11—42no—
252C22×C4×C11—42no—
253C22×C4×C11—42no—
254C22×C4×C11—42no—
255C22×C4×C11—42no—
256C22×C4×C11—42no—
257C22×C4×C11—42no—
258C22×C4×C11—42no—
259C22×C4×C11—42no—
260C22×C4×C11—42no—
261C22×C4×C11—42no—
262C22×C4×C11—44no—
263C22×C4×C11C2×D411yescharacteristic
264C22×C4×C11C2×D411yescharacteristic
265C22×C4×C11C2×D411yescharacteristic
266C22×C4×C11C2×D411yescharacteristic
267C22×C4×C11C2×D411yescharacteristic
268C22×C4×C11C2×D411yescharacteristic
269C22×C4×C11C2×D411yescharacteristic
270C22×C4×C11C2×D411yescharacteristic
271C22×C4×C11C2×D411yescharacteristic
272C22×C4×C11C2×D411yescharacteristic
273C22×C4×C11C2×D411yescharacteristic
274C22×C4×C11C2×D411yescharacteristic
275C22×C4×C11C2×D411yescharacteristic
276C22×C4×C11C2×D411yescharacteristic
277C22×C4×C11C2×D411yescharacteristic
278C22×C4×C11C2×D411yescharacteristic
279C22×C4×C11C2×D411yescharacteristic
280C22×C4×C11C2×D411yescharacteristic
281C22×C4×C11C2×D411yescharacteristic
282C22×C4×C11C2×D411yescharacteristic
283C22×C4×C11C2×D411yescharacteristic
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C22×Dic11—22no—
292C22×Dic11—22no—
293C22×Dic11—22no—
294C22×Dic11—22no—
295C22×Dic11—22no—
296C22×Dic11—22no—
297C22×Dic11—44no—
298C22×Dic11—44no—
299C2×Dic22—22no—
300C2×Dic22—22no—
301C2×Dic22—22no—
302C2×Dic22—28no—
303C2×Dic22—44no—
304C2×Dic22—44no—
305C2×Dic22—44no—
306C2×Dic22—44no—
307C2×Dic22—44no—
308C2×Dic22C2414yes—
309C11×C4⋊C4—22no—
310C11×C4⋊C4—22no—
311C11×C4⋊C4—22no—
312C11×C4⋊C4—22no—
313C11×C4⋊C4—21no—
314C11×C4⋊C4—21no—
315C11×C4⋊C4C2412yes—
316C11×C4⋊C4C2412yes—
317C11×C22⋊C4—22no—
318C11×C22⋊C4—22no—
319C11×C22⋊C4—22no—
320C11×C22⋊C4—22no—
321C11×C22⋊C4—22no—
322C11×C22⋊C4—22no—
323C11×C22⋊C4—22no—
324C11×C22⋊C4—22no—
325C11×C22⋊C4—22no—
326C11×C22⋊C4—22no—
327C42×C11—22no—
328C42×C11—22no—
329C22⋊Dic11—24no—
330C22⋊Dic11—24no—
331C22⋊Dic11—24no—
332C22⋊Dic11—24no—
333#4326—48no—
334#4324—48no—
335C4⋊Dic11—22no—
336C4⋊Dic11—22no—
337C4⋊Dic11—22no—
338C4⋊Dic11C2414yes—
339Dic11⋊C4—24no—
340Dic11⋊C4—24no—
341Dic11⋊C4—24no—
342Dic11⋊C4—24no—
343#4318—28no—
344#4318—44no—
345C2×C11⋊C8—44no—
346C2×C11⋊C8C2418yes—
347C2×#525D1111yescharacteristic
348C22×C22⋊Q8—111no—
349#3196—114no—
350#3195—112no—
351#3193—112no—
352#3190—114no—
353#3189—112no—
354#3187—112no—
355#3095—112no—
356#3092—112no—
357#3056—114no—
358#3007—112no—
359#3004—112no—
360C2×#407—111no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—41no—
375C23×C11—41no—
376C23×C11—41no—
377C23×C11—41no—
378C23×C11—41no—
379C23×C11—41no—
380C23×C11—41no—
381C23×C11—41no—
382C23×C11—416no—
383C23×C11—42no—
384C23×C11—42no—
385C23×C11—42no—
386C23×C11#13714yescomplemented
387C23×C11C22×D411yescharacteristic
388C23×C11C22×D411yescharacteristic
389C23×C11C22×D411yescharacteristic
390C23×C11C22×D411yescharacteristic
391C23×C11C22×D411yescharacteristic
392C23×C11C22×D411yescharacteristic
393C23×C11C22×D411yescharacteristic
394Q8×C11—24no—
395Q8×C11—42no—
396D4×C11—24no—
397D4×C11—42no—
398D4×C11—44no—
399D4×C11—44no—
400D4×C11—44no—
401D4×C11—44no—
402D4×C11—44no—
403D4×C11—44no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—41no—
423C2×C4×C11—41no—
424C2×C4×C11—41no—
425C2×C4×C11—41no—
426C2×C4×C11—41no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11—41no—
430C2×C4×C11—41no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—44no—
435C2×C4×C11—42no—
436C2×C4×C11—42no—
437C2×C4×C11—42no—
438C2×C4×C11—44no—
439C2×C4×C11C22×D411yescharacteristic
440C2×C4×C11C22×D411yescharacteristic
441C2×C4×C11C22×D411yescharacteristic
442C2×C4×C11C22×D411yescharacteristic
443C2×C4×C11C22×D411yescharacteristic
444C2×C4×C11C22×D411yescharacteristic
445C2×C4×C11C22×D411yescharacteristic
446C2×C4×C11H(5,𝔽2)14yes—
447C2×C4×C11C2511yescharacteristic
448C2×Dic11—24no—
449C2×Dic11—24no—
450C2×Dic11—44no—
451C2×Dic11—44no—
452C2×Dic11—44no—
453C2×Dic11—44no—
454C2×Dic11—44no—
455C2×Dic11—44no—
456Dic22—28no—
457Dic22—44no—
458Dic22—44no—
459Dic22—44no—
460C11⋊C8—28no—
461C22×#41C2×D1111yescharacteristic
462C23×Q8—111no—
463C24×C4C2×D1111yescharacteristic
464C2×#137—114no—
465C22×M16—112no—
466#525—21no—
467#525—21no—
468#525—21no—
469#525—21no—
470#525C2×D1112yes—
471#525C2×D1112yes—
472#525C2×D1112yes—
473#525C2×D1112yes—
474C2×#123—21no—
475C2×C22⋊Q8—112no—
476C2×C22⋊Q8—112no—
477C2×C22⋊Q8—112no—
478C2×C22⋊Q8—112no—
479C2×C22⋊Q8—112no—
480C2×C22⋊Q8—112no—
481C2×C22⋊Q8—221no—
482C2×C22⋊Q8—221no—
483C2×C22⋊Q8—221no—
484C2×C22⋊Q8—221no—
485C2×C22⋊Q8—221no—
486C2×C22⋊Q8—221no—
487C2×C22⋊Q8C2×D1111yescharacteristic
488C2×C22⋊Q8C2×D1111yescharacteristic
489C2×#121C2×D1111yescharacteristic
490C2×#121C2×D1111yescharacteristic
491C2×#120—21no—
492C2×C4×D4—21no—
493C2×C4×D4—21no—
494C2×#117C2×D1111yescharacteristic
495C22×C4⋊C4—111no—
496C22×C4⋊C4—221no—
497C22×C22⋊C4—221no—
498#485—118no—
499#484—114no—
500#484—114no—
501#483—114no—
502#483—114no—
503#481—114no—
504#480—114no—
505#470—118no—
506#468—118no—
507#467—118no—
508#465—118no—
509#452—118no—
510#451—114no—
511#451—114no—
512#451—114no—
513#450—114no—
514#448—114no—
515#448—114no—
516#428—114no—
517#419—114no—
518#417—114no—
519#407—112no—
520#407—112no—
521#407—112no—
522#407—112no—
523C2×C22⋊C8—112no—
524C2×C22⋊C8—112no—
525C22×C11—28no—
526C22×C11—21no—
527C22×C11—21no—
528C22×C11—21no—
529C22×C11—21no—
530C22×C11—21no—
531C22×C11—21no—
532C22×C11—21no—
533C22×C11—21no—
534C22×C11—21no—
535C22×C11—21no—
536C22×C11—21no—
537C22×C11—21no—
538C22×C11—21no—
539C22×C11—21no—
540C22×C11—21no—
541C22×C11—21no—
542C22×C11—44no—
543C22×C11—44no—
544C22×C11—44no—
545C22×C11—44no—
546C22×C11—44no—
547C22×C11—44no—
548C22×C11—42no—
549C22×C11—42no—
550C22×C11—42no—
551C22×C11—84no—
552C22×C11#53412yes—
553C22×C11C2×#13712yes—
554C22×C11C2×#13712yes—
555C22×C11C2×#13712yes—
556C22×C11#57512yes—
557C22×C11C23×D411yescharacteristic
558C4×C11—21no—
559C4×C11—21no—
560C4×C11—21no—
561C4×C11—21no—
562C4×C11—21no—
563C4×C11—21no—
564C4×C11—42no—
565C4×C11—42no—
566C4×C11—42no—
567C4×C11#53412yes—
568C4×C11C2×H(5,𝔽2)12yes—
569Dic11—44no—
570Dic11—44no—
571C25C22⋊D1111yescharacteristic
572C2×#41—21no—
573C2×#41—21no—
574C2×#41—44no—
575C2×#41C22×D1112yes—
576C2×#41C22×D1112yes—
577C22×Q8—112no—
578C22×Q8—112no—
579C22×Q8—112no—
580C22×Q8—221no—
581C22×Q8—221no—
582C22×Q8—221no—
583C22×Q8—444no—
584C22×Q8C22×D1111yescharacteristic
585C22×D4—21no—
586C22×D4—21no—
587C22×D4—21no—
588C22×D4C22×D1111yescharacteristic
589C23×C4—21no—
590C23×C4—44no—
591C23×C4—221no—
592C23×C4—221no—
593C23×C4C22⋊D1111yescharacteristic
594C23×C4C22⋊D1111yescharacteristic
595C23×C4C22⋊D1111yescharacteristic
596C23×C4C22⋊D1111yescharacteristic
597C23×C4C22⋊D1111yescharacteristic
598C23×C4C22⋊D1111yescharacteristic
599C23×C4C22⋊D1111yescharacteristic
600C23×C4C22×D1111yescharacteristic
601C23×C4C22×D1111yescharacteristic
602C23×C4C22×D1111yescharacteristic
603C23×C4C22×D1111yescharacteristic
604C23×C4C22×D1111yescharacteristic
605C23×C4C22×D1111yescharacteristic
606C23×C4C22×D1111yescharacteristic
607#137—448no—
608C2×Q16—118no—
609C2×SD16—118no—
610C2×M16—114no—
611C2×M16—114no—
612C2×M16—444no—
613C22×C8—114no—
614#123—22no—
615#123—22no—
616#123—22no—
617#123—22no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8—21no—
621C22⋊Q8—21no—
622C22⋊Q8—114no—
623C22⋊Q8—114no—
624C22⋊Q8—114no—
625C22⋊Q8—114no—
626C22⋊Q8—222no—
627C22⋊Q8—222no—
628C22⋊Q8—222no—
629C22⋊Q8—222no—
630C22⋊Q8—222no—
631C22⋊Q8—222no—
632C22⋊Q8—222no—
633C22⋊Q8—222no—
634C22⋊Q8—222no—
635C22⋊Q8—222no—
636C22⋊Q8—222no—
637C22⋊Q8—222no—
638C22⋊Q8C22×D1112yes—
639C22⋊Q8C22×D1112yes—
640C22⋊Q8C22×D1112yes—
641C22⋊Q8C22×D1112yes—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121C22×D1112yes—
647#121C22×D1112yes—
648#121C22×D1112yes—
649#121C22×D1112yes—
650#120—22no—
651#120—22no—
652#120—22no—
653#120—22no—
654C4×D4—22no—
655C4×D4—22no—
656C4×D4—22no—
657C4×D4—22no—
658C4×D4—22no—
659C4×D4—22no—
660C4×D4—22no—
661C4×D4—22no—
662#117—21no—
663#117—21no—
664#117C22×D1112yes—
665#117C22×D1112yes—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—112no—
669C2×C4⋊C4—112no—
670C2×C4⋊C4—112no—
671C2×C4⋊C4—221no—
672C2×C4⋊C4—221no—
673C2×C4⋊C4—221no—
674C2×C4⋊C4—222no—
675C2×C4⋊C4—222no—
676C2×C4⋊C4—222no—
677C2×C4⋊C4—222no—
678C2×C4⋊C4—222no—
679C2×C4⋊C4—222no—
680C2×C4⋊C4C22×D1111yescharacteristic
681C2×C4⋊C4C22×D1111yescharacteristic
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—222no—
688C2×C22⋊C4—222no—
689C2×C22⋊C4—222no—
690C2×C22⋊C4—222no—
691C2×C22⋊C4—222no—
692C2×C22⋊C4—222no—
693C2×C42—21no—
694#107—118no—
695#106—118no—
696#103—118no—
697#103—118no—
698#103—118no—
699#102—118no—
700C22⋊C8—114no—
701C22⋊C8—114no—
702C22⋊C8—114no—
703C22⋊C8—114no—
704C2×C11—22no—
705C2×C11—22no—
706C2×C11—22no—
707C2×C11—22no—
708C2×C11—22no—
709C2×C11—41no—
710C2×C11—41no—
711C2×C11—82no—
712C2×C11C2×#53411yescharacteristic
713C2×C11C22×#13711yescharacteristic
714C2×C11C2×#57511yescharacteristic
715C24—24no—
716C24—21no—
717C24—42no—
718C24—42no—
719C24C2×C22⋊D1111yescharacteristic
720C24C2×C22⋊D1111yescharacteristic
721C24C2×C22⋊D1111yescharacteristic
722C24C2×C22⋊D1111yescharacteristic
723C24C2×C22⋊D1111yescharacteristic
724C24C2×C22⋊D1111yescharacteristic
725C24C2×C22⋊D1111yescharacteristic
726#41—28no—
727#41—44no—
728#41—44no—
729#41—44no—
730C2×Q8—21no—
731C2×Q8—42no—
732C2×Q8—114no—
733C2×Q8—222no—
734C2×Q8—222no—
735C2×Q8—222no—
736C2×Q8—228no—
737C2×Q8—444no—
738C2×Q8—444no—
739C2×Q8—444no—
740C2×Q8—444no—
741C2×Q8—444no—
742C2×Q8C23×D1112yes—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—22no—
746C2×D4—22no—
747C2×D4—22no—
748C2×D4—22no—
749C2×D4—21no—
750C2×D4—42no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4C23×D1112yes—
755C22×C4—24no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—42no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—44no—
775C22×C4—222no—
776C22×C4—222no—
777C22×C4—222no—
778C22×C4—222no—
779C22×C4—222no—
780C22×C4—222no—
781C22×C4—444no—
782C22×C4—444no—
783C22×C4C2×C22⋊D1111yescharacteristic
784C22×C4C2×C22⋊D1111yescharacteristic
785C22×C4C2×C22⋊D1111yescharacteristic
786C22×C4C2×C22⋊D1111yescharacteristic
787C22×C4C2×C22⋊D1111yescharacteristic
788C22×C4C2×C22⋊D1111yescharacteristic
789C22×C4C2×C22⋊D1111yescharacteristic
790C22×C4C2×C22⋊D1111yescharacteristic
791C22×C4C2×C22⋊D1111yescharacteristic
792C22×C4C2×C22⋊D1111yescharacteristic
793C22×C4C2×C22⋊D1111yescharacteristic
794C22×C4C2×C22⋊D1111yescharacteristic
795C22×C4C2×C22⋊D1111yescharacteristic
796C22×C4C2×C22⋊D1111yescharacteristic
797C22×C4C2×C22⋊D1111yescharacteristic
798C22×C4C2×C22⋊D1111yescharacteristic
799C22×C4C2×C22⋊D1111yescharacteristic
800C22×C4C2×C22⋊D1111yescharacteristic
801C22×C4C2×C22⋊D1111yescharacteristic
802C22×C4C2×C22⋊D1111yescharacteristic
803C22×C4C2×C22⋊D1111yescharacteristic
804C22×C4C23×D1111yescharacteristic
805C22×C4C23×D1111yescharacteristic
806C22×C4C23×D1111yescharacteristic
807C22×C4C23×D1111yescharacteristic
808C22×C4C23×D1111yescharacteristic
809C22×C4C23×D1111yescharacteristic
810C22×C4C23×D1111yescharacteristic
811Q16—448no—
812SD16—448no—
813M16—228no—
814M16—444no—
815C2×C8—118no—
816C2×C8—444no—
817C4⋊C4—22no—
818C4⋊C4—22no—
819C4⋊C4—22no—
820C4⋊C4—22no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—114no—
824C4⋊C4—222no—
825C4⋊C4—222no—
826C4⋊C4—222no—
827C4⋊C4—224no—
828C4⋊C4—224no—
829C4⋊C4—224no—
830C4⋊C4—224no—
831C4⋊C4C23×D1112yes—
832C4⋊C4C23×D1112yes—
833C22⋊C4—22no—
834C22⋊C4—22no—
835C22⋊C4—22no—
836C22⋊C4—22no—
837C22⋊C4—22no—
838C22⋊C4—22no—
839C22⋊C4—22no—
840C22⋊C4—22no—
841C22⋊C4—22no—
842C22⋊C4—22no—
843C22⋊C4—224no—
844C22⋊C4—224no—
845C22⋊C4—224no—
846C22⋊C4—224no—
847C42—22no—
848C42—22no—
849C11#6075111yescharacteristic, complemented, Sylow
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—416no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23#6700414yescomplemented
876C23C22×C22⋊D1111yescharacteristic
877C23C22×C22⋊D1111yescharacteristic
878C23C22×C22⋊D1111yescharacteristic
879C23C22×C22⋊D1111yescharacteristic
880C23C22×C22⋊D1111yescharacteristic
881C23C22×C22⋊D1111yescharacteristic
882C23C22×C22⋊D1111yescharacteristic
883Q8—24no—
884Q8—42no—
885Q8—228no—
886Q8—444no—
887Q8—444no—
888Q8—444no—
889D4—24no—
890D4—42no—
891D4—44no—
892D4—44no—
893D4—44no—
894D4—44no—
895D4—44no—
896D4—44no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—44no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—44no—
932C2×C4—224no—
933C2×C4—224no—
934C2×C4—444no—
935C2×C4—444no—
936C2×C4—444no—
937C2×C4—444no—
938C2×C4—444no—
939C2×C4—444no—
940C2×C4#6703714yes—
941C2×C4C22×C22⋊D1111yescharacteristic
942C2×C4C22×C22⋊D1111yescharacteristic
943C2×C4C22×C22⋊D1111yescharacteristic
944C2×C4C22×C22⋊D1111yescharacteristic
945C2×C4C22×C22⋊D1111yescharacteristic
946C2×C4C22×C22⋊D1111yescharacteristic
947C2×C4C22×C22⋊D1111yescharacteristic
948C2×C4C24×D1111yescharacteristic
949C8—228no—
950C22—28no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—84no—
977C22#1062333512yes—
978C22#1062335312yes—
979C22C2×#6700412yes—
980C22C2×#6700412yes—
981C22C2×#6700412yes—
982C22C23×C22⋊D1111yescharacteristic
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—42no—
990C4—42no—
991C4—42no—
992C4—444no—
993C4—444no—
994C4#1062333512yes—
995C4C2×#6703712yes—
996C2—22no—
997C2—22no—
998C2—22no—
999C2—22no—
1000C2—22no—
1001C2—41no—
1002C2—41no—
1003C2—82no—
1004C2C2×#1062333511yescharacteristic
1005C2C22×#6700411yescharacteristic
1006C2C2×#1062335311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#525C2
socleC22×C11C23×D4
hypercenterC2×#525D11
hypocenterC11#60751
LCSG ▷ C2×C4×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. C22×#66977C2semidirect
2. #13079442C2semidirect
3. #13079437C2semidirect
4. #13079422C2semidirect
5. #13079393C2semidirect
6. #13079388C2semidirect
7. #13079373C2semidirect
8. #13078564C2semidirect
9. #13078536C2semidirect
10. #13078248C2semidirect
11. #13077876C2semidirect
12. #13077849C2semidirect
13. C2×#10622820C2semidirect
17. C23×Dic22C22semidirect
36. C2×#67004C22semidirect
37. C22×C4⋊Dic11C22semidirect
47. C2×#66977C22semidirect
48. C2×#66977C22semidirect
49. C2×#66977C22semidirect
51. C22×#4318C22semidirect
52. #10622852C22semidirect
53. #10622845C22semidirect
54. #10622841C22semidirect
55. #10622831C22semidirect
58. #10622820C22semidirect
59. #10622820C22semidirect
61. C2×C22⋊(C11⋊C8)C22semidirect
62. #10622665C22semidirect
63. #10622664C22semidirect
64. #10622663C22semidirect
65. #10622663C22semidirect
66. #10622657C22semidirect
67. #10622656C22semidirect
68. #10622655C22semidirect
69. #10622654C22semidirect
70. #10622653C22semidirect
71. #10622653C22semidirect
72. #10622647C22semidirect
73. #10622646C22semidirect
74. #10622617C22semidirect
75. #10622609C22semidirect
76. #10622608C22semidirect
77. #10622584C22semidirect
78. #10622583C22semidirect
168. C2×#4326C23semidirect
169. C2×#4324C23semidirect
202. #66899C23semidirect
203. #66896C23semidirect
208. #66874C23semidirect
209. #66874C23semidirect
210. #66872C23semidirect
211. #66871C23semidirect
386. C23×C11#137semidirect
849. C11#60751semidirect
875. C23#67004semidirect

Maximal subgroups

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

subgroupindex
C22×#669772
#130794422
#130794372
#130794222
#130793932
#130793882
#130793732
#130785642
#130785362
#130782482
#130778762
#130778492
C2×#106228202
C2×C11×#5252
#6075111