Finite Group Databasebeta

← C11×#61693 #14638886

Subgroups — C11×#61693 #14638886

Order 2816.

2014 conjugacy classes of subgroups.

The subgroup lattice has 1192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3547C211yesmaximal, characteristic, complemented
2C11×#3499C211yesmaximal, characteristic, complemented
3C11×#3331C211yesmaximal, characteristic, complemented
4C11×#3329C211yesmaximal, characteristic, complemented
5C11×#3315C212yesmaximal, complemented
6C11×#3312C212yesmaximal, complemented
7C11×#3303C211yesmaximal, characteristic, complemented
8C11×#3299C211yesmaximal, characteristic, complemented
9D4×C11×Q16C211yesmaximal, characteristic, complemented
10C11×#3283C211yesmaximal, characteristic, complemented
11C11×#3276C211yesmaximal, characteristic, complemented
12C11×#3276C211yesmaximal, characteristic, complemented
13C11×#3270C212yesmaximal, complemented
14C11×#3269C212yesmaximal, complemented
15C11×#3218C211yesmaximal, characteristic, complemented
16C11×#3209C211yesmaximal, characteristic, complemented
17C11×#3202C212yesmaximal, complemented
18C11×#3201C212yesmaximal, complemented
19C11×#3116C211yesmaximal, characteristic, complemented
20C11×#3102C211yesmaximal, characteristic, complemented
21C11×#3013C212yesmaximal, complemented
22C11×#3011C212yesmaximal, complemented
23C11×#2981C211yesmaximal, characteristic, complemented
24C2×C11×2−1+4C2212yes—
25C2×C11×#137C2212yes—
26C2×C11×#137C2212yes—
27C2×C11×#135C2212yes—
28C22×C11×Q16C2212yes—
29C11×#562—22no—
30C11×#555—21no—
31C11×#555C2211yescharacteristic
32C11×#554C2211yescharacteristic
33C11×#553—21no—
34C11×#552C2212yes—
35D4×Q8×C11C2212yes—
36D4×Q8×C11C2211yescharacteristic
37D4×Q8×C11C2211yescharacteristic
38D4×Q8×C11C2211yescharacteristic
39C11×#548C2212yes—
40C11×#547—21no—
41C11×#547—21no—
42C11×#547—22no—
43C11×#547C2212yes—
44C11×#547C2211yescharacteristic
45C11×#547C2211yescharacteristic
46C11×#547C2211yescharacteristic
47C11×#544—21no—
48C11×#542—22no—
49C11×#540—21no—
50C11×#537C2212yes—
51C11×#536—22no—
52C11×#536C2212yes—
53C11×#536C2212yes—
54C11×#533C2211yescharacteristic
55C11×#532—21no—
56C11×#532C2211yescharacteristic
57C2×C11×C4⋊Q8—21no—
58C2×C11×C4⋊Q8C2211yescharacteristic
59C11×#529C2211yescharacteristic
60C4×C11×#41C2211yescharacteristic
61C11×#497C2212yes—
62C11×#494C2211yescharacteristic
63C11×#494C2211yescharacteristic
64C11×#491C2212yes—
65C11×#487C2211yescharacteristic
66C11×#487C2211yescharacteristic
67C11×#485C2212yes—
68C11×#485C2211yescharacteristic
69C11×#485C2212yes—
70C11×#485C2212yes—
71C11×#484C2212yes—
72C11×#483C2212yes—
73C11×#482C2211yescharacteristic
74C11×#479C2211yescharacteristic
75C11×#478C2211yescharacteristic
76C11×#477C2211yescharacteristic
77C11×#476C2211yescharacteristic
78C11×#470C2212yes—
79C11×#470C2212yes—
80C11×#470C2212yes—
81C11×#468C2212yes—
82C11×#467C2212yes—
83C11×#467C2212yes—
84C11×#467C2212yes—
85C11×#465C2212yes—
86C11×#464C2211yescharacteristic
87C11×#463C2211yescharacteristic
88C11×#462C2212yes—
89C11×#462C2212yes—
90C11×#462C2211yescharacteristic
91C11×#462C2211yescharacteristic
92C11×#462C2211yescharacteristic
93C11×#461C2211yescharacteristic
94C11×#461C2211yescharacteristic
95C11×#461C2211yescharacteristic
96C11×#452C2212yes—
97C11×#452C2212yes—
98C11×#452C2211yescharacteristic
99C11×#452C2212yes—
100C11×#452C2212yes—
101C11×#452C2212yes—
102C11×#452C2212yes—
103C11×#451C2212yes—
104C11×#451C2212yes—
105C11×#451C2212yes—
106C11×#451C2212yes—
107C11×#451C2212yes—
108C11×#451C2212yes—
109C11×#451C2212yes—
110C11×#451C2212yes—
111C11×#449C2211yescharacteristic
112C11×#449C2212yes—
113C11×#448C2212yes—
114C11×#448C2212yes—
115C11×#441C2212yes—
116C11×#440C2212yes—
117C4×C11×Q16C2211yescharacteristic
118C4×C11×SD16C2211yescharacteristic
119C4×C11×SD16C2211yescharacteristic
120C4×C11×D8C2211yescharacteristic
121C11×#436C2211yescharacteristic
122C11×#436C2211yescharacteristic
123C11×#435C2212yes—
124C11×#435C2212yes—
125C8×D4×C11C2211yescharacteristic
126C8×D4×C11C2211yescharacteristic
127C11×#432C2211yescharacteristic
128C11×#431C2211yescharacteristic
129C11×#419C2212yes—
130C11×#417C2212yes—
131C11×#416C2212yes—
132C2×C11×#103C2212yes—
133C11×#408C2212yes—
134C11×#408C2212yes—
135C11×2−1+4—44no—
136C11×2−1+4—44no—
137C2×C11×#41—22no—
138C2×C11×#41—22no—
139C2×C11×#41—22no—
140C2×C11×#41C2311yescharacteristic
141C2×C11×#41C2312yes—
142C2×C11×#41C2312yes—
143C2×C11×#41C2312yes—
144C2×C11×#41C2312yes—
145C22×Q8×C11—22no—
146C22×Q8×C11C2312yes—
147C22×Q8×C11C2312yes—
148C22×Q8×C11C2312yes—
149C22×Q8×C11C2312yes—
150C11×#137—44no—
151C11×#137—44no—
152C11×#135—44no—
153C2×C11×Q16—44no—
154C2×C11×Q16C2311yescharacteristic
155C2×C11×Q16C2312yes—
156C2×C11×Q16C2312yes—
157C2×C11×Q16C2312yes—
158C2×C11×Q16C2312yes—
159C2×C11×Q16C2312yes—
160C2×C11×Q16C2312yes—
161C2×C11×Q16C2312yes—
162C2×C11×SD16C2312yes—
163C2×C11×SD16C2311yescharacteristic
164C2×C11×SD16C2311yescharacteristic
165C2×C11×SD16C2312yes—
166C2×C11×SD16C2312yes—
167C2×C11×D8C2311yescharacteristic
168C2×C11×M16C2312yes—
169C2×C11×M16C2312yes—
170C22×C8×C11C2312yes—
171C22×C8×C11C2312yes—
172C11×C4⋊Q8—22no—
173C11×C4⋊Q8—22no—
174C11×C4⋊Q8—21no—
175C11×C4⋊Q8—21no—
176C11×C4⋊Q8—22no—
177C11×C4⋊Q8—21no—
178C11×C4⋊Q8—21no—
179C11×C4⋊Q8—21no—
180C11×C4⋊Q8D411yescharacteristic
181C11×C4⋊Q8C2312yes—
182C11×C4⋊Q8C2311yescharacteristic
183C11×C4⋊Q8C2311yescharacteristic
184C11×C4⋊Q8C2311yescharacteristic
185C11×C4⋊Q8C2311yescharacteristic
186C11×#127D411yescharacteristic
187C11×#126—22no—
188C11×#126—21no—
189C11×#125—22no—
190C11×#125—21no—
191C11×#125—21no—
192C11×#125C2311yescharacteristic
193C11×#124—22no—
194C11×#124—22no—
195C11×#124—22no—
196C11×#124—22no—
197C11×#124D412yes—
198C11×#124C2311yescharacteristic
199C11×#123—22no—
200C11×#123—22no—
201C11×#123—22no—
202C11×#123—22no—
203C11×#123—22no—
204C11×#123—21no—
205C11×#123—22no—
206C11×#123—22no—
207C11×#123—22no—
208C11×#123—22no—
209C11×#123—22no—
210C11×C22⋊Q8—22no—
211C11×C22⋊Q8—21no—
212C11×C22⋊Q8—22no—
213C11×C22⋊Q8—22no—
214C11×C22⋊Q8—22no—
215C11×C22⋊Q8—22no—
216C11×C22⋊Q8—22no—
217C11×C22⋊Q8—22no—
218C11×C22⋊Q8—22no—
219C11×C22⋊Q8C2311yescharacteristic
220C11×C22⋊Q8C2312yes—
221C11×C22⋊Q8C2312yes—
222C11×C22⋊Q8C2312yes—
223C11×C22⋊Q8C2312yes—
224C11×C22⋊Q8C2312yes—
225C11×C22⋊Q8C2312yes—
226C11×C22⋊Q8C2312yes—
227C11×C22⋊Q8C2312yes—
228C11×#121—21no—
229C11×#121—21no—
230C11×#121—22no—
231C11×#121—22no—
232C11×#121—22no—
233C11×#121—22no—
234C11×#121—21no—
235C11×#121—22no—
236C11×#121—21no—
237C11×#121D411yescharacteristic
238C11×#121D411yescharacteristic
239C11×#121D412yes—
240C11×#121C2311yescharacteristic
241C11×#121C2312yes—
242C4×Q8×C11—21no—
243C4×Q8×C11C2311yescharacteristic
244C4×Q8×C11C2311yescharacteristic
245C4×Q8×C11C2311yescharacteristic
246C4×Q8×C11C2312yes—
247C4×D4×C11—21no—
248C4×D4×C11—21no—
249C4×D4×C11—22no—
250C4×D4×C11—21no—
251C4×D4×C11—21no—
252C4×D4×C11—21no—
253C4×D4×C11—21no—
254C4×D4×C11—21no—
255C4×D4×C11—22no—
256C4×D4×C11C2311yescharacteristic
257C4×D4×C11C2311yescharacteristic
258C4×D4×C11C2311yescharacteristic
259C4×D4×C11C2311yescharacteristic
260C4×D4×C11C2312yes—
261C4×D4×C11C2311yescharacteristic
262C11×#117—21no—
263C11×#117—21no—
264C11×#117—22no—
265C11×#117—21no—
266C11×#117—21no—
267C11×#117C2311yescharacteristic
268C11×#117C2312yes—
269C2×C11×C4⋊C4—21no—
270C2×C11×C4⋊C4—21no—
271C2×C11×C4⋊C4—21no—
272C2×C11×C4⋊C4—21no—
273C2×C11×C4⋊C4—22no—
274C2×C11×C4⋊C4—21no—
275C2×C11×C4⋊C4C2312yes—
276C2×C42×C11—21no—
277C2×C42×C11C2311yescharacteristic
278C11×#107C2311yescharacteristic
279C11×#107C2311yescharacteristic
280C11×#107C2312yes—
281C11×#106C2311yescharacteristic
282C11×#106C2311yescharacteristic
283C11×#106C2312yes—
284C11×C4⋊C8C2311yescharacteristic
285C11×C4⋊C8C2311yescharacteristic
286C11×C4⋊C8C2311yescharacteristic
287C11×C4⋊C8C2311yescharacteristic
288C11×#103C2312yes—
289C11×#103C2312yes—
290C11×#103C2312yes—
291C11×#103C2312yes—
292C11×#103C2311yescharacteristic
293C11×#103C2312yes—
294C11×#103C2312yes—
295C11×#103C2312yes—
296C11×#103C2312yes—
297C11×#103C2311yescharacteristic
298C11×#103C2312yes—
299C11×#103C2311yescharacteristic
300C11×#103C2311yescharacteristic
301C11×#103C2312yes—
302C11×#103C2312yes—
303C11×#102C2311yescharacteristic
304C11×#102C2312yes—
305C11×#102C2311yescharacteristic
306C11×#102C2311yescharacteristic
307C11×#102C2311yescharacteristic
308C11×C22⋊C8C2311yescharacteristic
309C11×C22⋊C8C2311yescharacteristic
310C11×C22⋊C8C2312yes—
311C11×C22⋊C8C2312yes—
312C11×C22⋊C8C2312yes—
313C11×C22⋊C8C2312yes—
314C11×C22⋊C8C2312yes—
315C11×#97C2312yes—
316C4×C8×C11C2311yescharacteristic
317C4×C8×C11C2311yescharacteristic
318#61693C1111yesmaximal, characteristic, direct product factor, Sylow
319C11×#41—22no—
320C11×#41—22no—
321C11×#41—24no—
322C11×#41—24no—
323C11×#41—42no—
324C11×#41—42no—
325C11×#41—42no—
326C11×#41—42no—
327C11×#41—48no—
328C11×#41—42no—
329C11×#41—42no—
330C11×#41—48no—
331C11×#41—48no—
332C2×Q8×C11—22no—
333C2×Q8×C11—22no—
334C2×Q8×C11—22no—
335C2×Q8×C11—21no—
336C2×Q8×C11—22no—
337C2×Q8×C11—24no—
338C2×Q8×C11—24no—
339C2×Q8×C11—42no—
340C2×Q8×C11—42no—
341C2×Q8×C11—42no—
342C2×Q8×C11—42no—
343C2×Q8×C11—48no—
344C2×Q8×C11—42no—
345C2×Q8×C11—42no—
346C2×Q8×C11C2×D412yes—
347C2×Q8×C11C2412yes—
348C2×Q8×C11C2412yes—
349C2×Q8×C11C2411yescharacteristic
350C2×Q8×C11C2412yes—
351C2×Q8×C11C2411yescharacteristic
352C2×D4×C11—21no—
353C2×D4×C11—22no—
354C2×D4×C11—22no—
355C2×D4×C11—21no—
356C2×D4×C11—22no—
357C2×D4×C11—22no—
358C2×D4×C11C2×D411yescharacteristic
359C2×D4×C11C2×D411yescharacteristic
360C2×D4×C11C2×D412yes—
361C2×D4×C11C2×D412yes—
362C2×D4×C11C2×D412yes—
363C2×D4×C11C2×D412yes—
364C2×D4×C11C2411yescharacteristic
365C2×D4×C11C2411yescharacteristic
366C22×C4×C11—21no—
367C22×C4×C11—22no—
368C22×C4×C11—22no—
369C22×C4×C11—22no—
370C22×C4×C11—22no—
371C22×C4×C11—22no—
372C22×C4×C11—21no—
373C22×C4×C11—21no—
374C22×C4×C11—22no—
375C22×C4×C11—22no—
376C22×C4×C11—21no—
377C22×C4×C11—22no—
378C22×C4×C11C2×D411yescharacteristic
379C22×C4×C11C2×D411yescharacteristic
380C22×C4×C11C2411yescharacteristic
381C22×C4×C11C2412yes—
382C22×C4×C11C2412yes—
383C11×Q16—22no—
384C11×Q16—24no—
385C11×Q16—42no—
386C11×Q16—42no—
387C11×Q16—42no—
388C11×Q16—42no—
389C11×Q16—42no—
390C11×Q16—42no—
391C11×SD16—22no—
392C11×SD16—24no—
393C11×SD16—22no—
394C11×SD16—42no—
395C11×SD16—42no—
396C11×D8—22no—
397C11×M16—42no—
398C11×M16—42no—
399C2×C8×C11—42no—
400C2×C8×C11—42no—
401C2×C8×C11C2411yescharacteristic
402C2×C8×C11C2411yescharacteristic
403C2×C8×C11C2411yescharacteristic
404C2×C8×C11C2411yescharacteristic
405C2×C8×C11C2412yes—
406C2×C8×C11C2412yes—
407C11×C4⋊C4—22no—
408C11×C4⋊C4—21no—
409C11×C4⋊C4—21no—
410C11×C4⋊C4—21no—
411C11×C4⋊C4—22no—
412C11×C4⋊C4—21no—
413C11×C4⋊C4—21no—
414C11×C4⋊C4—22no—
415C11×C4⋊C4—22no—
416C11×C4⋊C4—22no—
417C11×C4⋊C4—22no—
418C11×C4⋊C4—22no—
419C11×C4⋊C4—22no—
420C11×C4⋊C4—21no—
421C11×C4⋊C4—21no—
422C11×C4⋊C4—21no—
423C11×C4⋊C4—21no—
424C11×C4⋊C4—22no—
425C11×C4⋊C4—21no—
426C11×C4⋊C4—21no—
427C11×C4⋊C4—22no—
428C11×C4⋊C4—22no—
429C11×C4⋊C4—21no—
430C11×C4⋊C4—22no—
431C11×C4⋊C4—21no—
432C11×C4⋊C4C2×D411yescharacteristic
433C11×C4⋊C4C2×D411yescharacteristic
434C11×C4⋊C4C2×D412yes—
435C11×C4⋊C4C2411yescharacteristic
436C11×C4⋊C4C2412yes—
437C11×C4⋊C4C2411yescharacteristic
438C11×C4⋊C4C2411yescharacteristic
439C11×C4⋊C4C2411yescharacteristic
440C11×C22⋊C4—22no—
441C11×C22⋊C4—22no—
442C11×C22⋊C4—21no—
443C11×C22⋊C4—22no—
444C11×C22⋊C4—22no—
445C11×C22⋊C4—22no—
446C11×C22⋊C4—22no—
447C11×C22⋊C4—22no—
448C11×C22⋊C4—22no—
449C11×C22⋊C4—22no—
450C11×C22⋊C4—21no—
451C11×C22⋊C4—21no—
452C11×C22⋊C4—21no—
453C11×C22⋊C4—21no—
454C11×C22⋊C4—21no—
455C11×C22⋊C4—22no—
456C11×C22⋊C4—21no—
457C11×C22⋊C4—21no—
458C11×C22⋊C4C2×D412yes—
459C11×C22⋊C4C2×D412yes—
460C11×C22⋊C4C2×D412yes—
461C11×C22⋊C4C2×D412yes—
462C42×C11—21no—
463C42×C11—21no—
464C42×C11—21no—
465C42×C11—22no—
466C42×C11—22no—
467C42×C11—21no—
468C42×C11C2×D411yescharacteristic
469C42×C11C2×D411yescharacteristic
470C42×C11C2411yescharacteristic
471C42×C11C2411yescharacteristic
472#3547C2×C1111yescharacteristic, complemented
473#3499C2×C1111yescharacteristic, complemented
474#3331C2×C1111yescharacteristic, complemented
475#3329C2×C1111yescharacteristic, complemented
476#3315C2×C1112yescomplemented
477#3312C2×C1112yescomplemented
478#3303C2×C1111yescharacteristic, complemented
479#3299C2×C1111yescharacteristic, complemented
480D4×Q16C2×C1111yescharacteristic, complemented
481#3283C2×C1111yescharacteristic, complemented
482#3276C2×C1111yescharacteristic, complemented
483#3276C2×C1111yescharacteristic, complemented
484#3270C2×C1112yescomplemented
485#3269C2×C1112yescomplemented
486#3218C2×C1111yescharacteristic, complemented
487#3209C2×C1111yescharacteristic, complemented
488#3202C2×C1112yescomplemented
489#3201C2×C1112yescomplemented
490#3116C2×C1111yescharacteristic, complemented
491#3102C2×C1111yescharacteristic, complemented
492#3013C2×C1112yescomplemented
493#3011C2×C1112yescomplemented
494#2981C2×C1111yescharacteristic, complemented
495C23×C11—21no—
496C23×C11—21no—
497C23×C11C22×D412yes—
498C23×C11C22×D412yes—
499C23×C11C22×D411yescharacteristic
500Q8×C11—21no—
501Q8×C11—21no—
502Q8×C11—22no—
503Q8×C11—22no—
504Q8×C11—22no—
505Q8×C11—21no—
506Q8×C11—22no—
507Q8×C11—22no—
508Q8×C11—22no—
509Q8×C11—42no—
510Q8×C11—44no—
511Q8×C11—44no—
512Q8×C11—44no—
513Q8×C11—81no—
514Q8×C11—82no—
515Q8×C11H(5,𝔽2)12yes—
516D4×C11—24no—
517D4×C11—22no—
518D4×C11—22no—
519D4×C11—21no—
520D4×C11—21no—
521D4×C11—21no—
522D4×C11—42no—
523D4×C11—42no—
524D4×C11—42no—
525D4×C11—42no—
526D4×C11—44no—
527D4×C11—44no—
528D4×C11—81no—
529D4×C11—82no—
530D4×C11—82no—
531D4×C11H(5,𝔽2)12yes—
532C2×C4×C11—24no—
533C2×C4×C11—21no—
534C2×C4×C11—22no—
535C2×C4×C11—22no—
536C2×C4×C11—22no—
537C2×C4×C11—22no—
538C2×C4×C11—22no—
539C2×C4×C11—21no—
540C2×C4×C11—21no—
541C2×C4×C11—21no—
542C2×C4×C11—21no—
543C2×C4×C11—21no—
544C2×C4×C11—22no—
545C2×C4×C11—21no—
546C2×C4×C11—21no—
547C2×C4×C11—22no—
548C2×C4×C11—22no—
549C2×C4×C11—22no—
550C2×C4×C11—41no—
551C2×C4×C11—44no—
552C2×C4×C11—44no—
553C2×C4×C11—44no—
554C2×C4×C11—44no—
555C2×C4×C11—42no—
556C2×C4×C11—44no—
557C2×C4×C11—42no—
558C2×C4×C11—42no—
559C2×C4×C11—82no—
560C2×C4×C11—82no—
561C2×C4×C11—82no—
562C2×C4×C11C22×D411yescharacteristic
563C2×C4×C11C22×D411yescharacteristic
564C2×C4×C11C22×D411yescharacteristic
565C2×C4×C11C22×D412yes—
566C2×C4×C11C22×D411yescharacteristic
567C2×C4×C11C22×D412yes—
568C2×C4×C11C22×D411yescharacteristic
569C2×C4×C11C2511yescharacteristic
570C8×C11—21no—
571C8×C11—21no—
572C8×C11—22no—
573C8×C11—22no—
574C8×C11—21no—
575C8×C11—21no—
576C2×2−1+4C22×C1112yes—
577C2×#137C22×C1112yes—
578C2×#137C22×C1112yes—
579C2×#135C22×C1112yes—
580C22×Q16C22×C1112yes—
581#562—22no—
582#555—21no—
583#555C22×C1111yescharacteristic
584#554C22×C1111yescharacteristic
585#553—21no—
586#552C22×C1112yes—
587D4×Q8C22×C1111yescharacteristic
588D4×Q8C22×C1112yes—
589D4×Q8C22×C1111yescharacteristic
590D4×Q8C22×C1111yescharacteristic
591#548C22×C1112yes—
592#547—21no—
593#547—21no—
594#547—22no—
595#547C22×C1111yescharacteristic
596#547C22×C1112yes—
597#547C22×C1111yescharacteristic
598#547C22×C1111yescharacteristic
599#544—21no—
600#542—22no—
601#540—21no—
602#537C22×C1112yes—
603#536—22no—
604#536C22×C1112yes—
605#536C22×C1112yes—
606#533C22×C1111yescharacteristic
607#532—21no—
608#532C22×C1111yescharacteristic
609C2×C4⋊Q8—21no—
610C2×C4⋊Q8C22×C1111yescharacteristic
611#529C22×C1111yescharacteristic
612C4×#41C22×C1111yescharacteristic
613#497C22×C1112yes—
614#494C22×C1111yescharacteristic
615#494C22×C1111yescharacteristic
616#491C22×C1112yes—
617#487C22×C1111yescharacteristic
618#487C22×C1111yescharacteristic
619#485C22×C1112yes—
620#485C22×C1111yescharacteristic
621#485C22×C1112yes—
622#485C22×C1112yes—
623#484C22×C1112yes—
624#483C22×C1112yes—
625#482C22×C1111yescharacteristic
626#479C22×C1111yescharacteristic
627#478C22×C1111yescharacteristic
628#477C22×C1111yescharacteristic
629#476C22×C1111yescharacteristic
630#470C22×C1112yes—
631#470C22×C1112yes—
632#470C22×C1112yes—
633#468C22×C1112yes—
634#467C22×C1112yes—
635#467C22×C1112yes—
636#467C22×C1112yes—
637#465C22×C1112yes—
638#464C22×C1111yescharacteristic
639#463C22×C1111yescharacteristic
640#462C22×C1111yescharacteristic
641#462C22×C1111yescharacteristic
642#462C22×C1112yes—
643#462C22×C1112yes—
644#462C22×C1111yescharacteristic
645#461C22×C1111yescharacteristic
646#461C22×C1111yescharacteristic
647#461C22×C1111yescharacteristic
648#452C22×C1112yes—
649#452C22×C1111yescharacteristic
650#452C22×C1112yes—
651#452C22×C1112yes—
652#452C22×C1112yes—
653#452C22×C1112yes—
654#452C22×C1112yes—
655#451C22×C1112yes—
656#451C22×C1112yes—
657#451C22×C1112yes—
658#451C22×C1112yes—
659#451C22×C1112yes—
660#451C22×C1112yes—
661#451C22×C1112yes—
662#451C22×C1112yes—
663#449C22×C1111yescharacteristic
664#449C22×C1112yes—
665#448C22×C1112yes—
666#448C22×C1112yes—
667#441C22×C1112yes—
668#440C22×C1112yes—
669C4×Q16C22×C1111yescharacteristic
670C4×SD16C22×C1111yescharacteristic
671C4×SD16C22×C1111yescharacteristic
672C4×D8C22×C1111yescharacteristic
673#436C22×C1111yescharacteristic
674#436C22×C1111yescharacteristic
675#435C22×C1112yes—
676#435C22×C1112yes—
677C8×D4C22×C1111yescharacteristic
678C8×D4C22×C1111yescharacteristic
679#432C22×C1111yescharacteristic
680#431C22×C1111yescharacteristic
681#419C22×C1112yes—
682#417C22×C1112yes—
683#416C22×C1112yes—
684C2×#103C22×C1112yes—
685#408C22×C1112yes—
686#408C22×C1112yes—
687C22×C11—21no—
688C22×C11—22no—
689C22×C11—22no—
690C22×C11—21no—
691C22×C11—22no—
692C22×C11—22no—
693C22×C11—22no—
694C22×C11—21no—
695C22×C11—22no—
696C22×C11—22no—
697C22×C11—41no—
698C22×C11—41no—
699C22×C11—41no—
700C22×C11—41no—
701C22×C11—41no—
702C22×C11C23×D411yescharacteristic
703C4×C11—21no—
704C4×C11—21no—
705C4×C11—21no—
706C4×C11—22no—
707C4×C11—22no—
708C4×C11—22no—
709C4×C11—21no—
710C4×C11—41no—
711C4×C11—41no—
712C4×C11—42no—
713C4×C11—42no—
714C4×C11—42no—
715C4×C11—42no—
716C4×C11—41no—
717C4×C11—41no—
718C4×C11—41no—
719C4×C11#57812yes—
720C4×C11C2×H(5,𝔽2)11yescharacteristic
721C4×C11C2×H(5,𝔽2)11yescharacteristic
7222−1+4—44no—
7232−1+4—44no—
724C2×#41—22no—
725C2×#41—22no—
726C2×#41—22no—
727C2×#41C23×C1111yescharacteristic
728C2×#41C23×C1112yes—
729C2×#41C23×C1112yes—
730C2×#41C23×C1112yes—
731C2×#41C23×C1112yes—
732C22×Q8—22no—
733C22×Q8C23×C1112yes—
734C22×Q8C23×C1112yes—
735C22×Q8C23×C1112yes—
736C22×Q8C23×C1112yes—
737#137—44no—
738#137—44no—
739#135—44no—
740C2×Q16—44no—
741C2×Q16C23×C1111yescharacteristic
742C2×Q16C23×C1112yes—
743C2×Q16C23×C1112yes—
744C2×Q16C23×C1112yes—
745C2×Q16C23×C1112yes—
746C2×Q16C23×C1112yes—
747C2×Q16C23×C1112yes—
748C2×Q16C23×C1112yes—
749C2×SD16C23×C1112yes—
750C2×SD16C23×C1111yescharacteristic
751C2×SD16C23×C1111yescharacteristic
752C2×SD16C23×C1112yes—
753C2×SD16C23×C1112yes—
754C2×D8C23×C1111yescharacteristic
755C2×M16C23×C1112yes—
756C2×M16C23×C1112yes—
757C22×C8C23×C1112yes—
758C22×C8C23×C1112yes—
759C4⋊Q8—22no—
760C4⋊Q8—22no—
761C4⋊Q8—21no—
762C4⋊Q8—21no—
763C4⋊Q8—22no—
764C4⋊Q8—21no—
765C4⋊Q8—21no—
766C4⋊Q8—21no—
767C4⋊Q8D4×C1111yescharacteristic
768C4⋊Q8C23×C1111yescharacteristic
769C4⋊Q8C23×C1111yescharacteristic
770C4⋊Q8C23×C1112yes—
771C4⋊Q8C23×C1111yescharacteristic
772C4⋊Q8C23×C1111yescharacteristic
773#127D4×C1111yescharacteristic
774#126—22no—
775#126—21no—
776#125—22no—
777#125—21no—
778#125—21no—
779#125C23×C1111yescharacteristic
780#124—22no—
781#124—22no—
782#124—22no—
783#124—22no—
784#124D4×C1112yes—
785#124C23×C1111yescharacteristic
786#123—22no—
787#123—22no—
788#123—22no—
789#123—22no—
790#123—22no—
791#123—21no—
792#123—22no—
793#123—22no—
794#123—22no—
795#123—22no—
796#123—22no—
797C22⋊Q8—22no—
798C22⋊Q8—21no—
799C22⋊Q8—22no—
800C22⋊Q8—22no—
801C22⋊Q8—22no—
802C22⋊Q8—22no—
803C22⋊Q8—22no—
804C22⋊Q8—22no—
805C22⋊Q8—22no—
806C22⋊Q8C23×C1111yescharacteristic
807C22⋊Q8C23×C1112yes—
808C22⋊Q8C23×C1112yes—
809C22⋊Q8C23×C1112yes—
810C22⋊Q8C23×C1112yes—
811C22⋊Q8C23×C1112yes—
812C22⋊Q8C23×C1112yes—
813C22⋊Q8C23×C1112yes—
814C22⋊Q8C23×C1112yes—
815#121—21no—
816#121—21no—
817#121—22no—
818#121—22no—
819#121—22no—
820#121—22no—
821#121—21no—
822#121—22no—
823#121—21no—
824#121D4×C1111yescharacteristic
825#121D4×C1111yescharacteristic
826#121D4×C1112yes—
827#121C23×C1111yescharacteristic
828#121C23×C1112yes—
829C4×Q8—21no—
830C4×Q8C23×C1111yescharacteristic
831C4×Q8C23×C1111yescharacteristic
832C4×Q8C23×C1111yescharacteristic
833C4×Q8C23×C1112yes—
834C4×D4—21no—
835C4×D4—21no—
836C4×D4—22no—
837C4×D4—21no—
838C4×D4—21no—
839C4×D4—21no—
840C4×D4—21no—
841C4×D4—21no—
842C4×D4—22no—
843C4×D4C23×C1111yescharacteristic
844C4×D4C23×C1111yescharacteristic
845C4×D4C23×C1111yescharacteristic
846C4×D4C23×C1111yescharacteristic
847C4×D4C23×C1112yes—
848C4×D4C23×C1111yescharacteristic
849#117—21no—
850#117—21no—
851#117—22no—
852#117—21no—
853#117—21no—
854#117C23×C1111yescharacteristic
855#117C23×C1112yes—
856C2×C4⋊C4—21no—
857C2×C4⋊C4—21no—
858C2×C4⋊C4—21no—
859C2×C4⋊C4—21no—
860C2×C4⋊C4—22no—
861C2×C4⋊C4—21no—
862C2×C4⋊C4C23×C1112yes—
863C2×C42—21no—
864C2×C42C23×C1111yescharacteristic
865#107C23×C1111yescharacteristic
866#107C23×C1111yescharacteristic
867#107C23×C1112yes—
868#106C23×C1111yescharacteristic
869#106C23×C1111yescharacteristic
870#106C23×C1112yes—
871C4⋊C8C23×C1111yescharacteristic
872C4⋊C8C23×C1111yescharacteristic
873C4⋊C8C23×C1111yescharacteristic
874C4⋊C8C23×C1111yescharacteristic
875#103C23×C1111yescharacteristic
876#103C23×C1112yes—
877#103C23×C1112yes—
878#103C23×C1112yes—
879#103C23×C1112yes—
880#103C23×C1112yes—
881#103C23×C1112yes—
882#103C23×C1112yes—
883#103C23×C1111yescharacteristic
884#103C23×C1112yes—
885#103C23×C1112yes—
886#103C23×C1111yescharacteristic
887#103C23×C1111yescharacteristic
888#103C23×C1112yes—
889#103C23×C1112yes—
890#102C23×C1111yescharacteristic
891#102C23×C1112yes—
892#102C23×C1111yescharacteristic
893#102C23×C1111yescharacteristic
894#102C23×C1111yescharacteristic
895C22⋊C8C23×C1111yescharacteristic
896C22⋊C8C23×C1111yescharacteristic
897C22⋊C8C23×C1112yes—
898C22⋊C8C23×C1112yes—
899C22⋊C8C23×C1112yes—
900C22⋊C8C23×C1112yes—
901C22⋊C8C23×C1112yes—
902#97C23×C1112yes—
903C4×C8C23×C1111yescharacteristic
904C4×C8C23×C1111yescharacteristic
905C2×C11—41no—
906C2×C11—42no—
907C2×C11—42no—
908C2×C11—42no—
909C2×C11—81no—
910C2×C11#348411yescharacteristic
911C2×C11C2×#57811yescharacteristic
912C2×C11#358611yescharacteristic
913#41—22no—
914#41—22no—
915#41—24no—
916#41—24no—
917#41—42no—
918#41—42no—
919#41—42no—
920#41—42no—
921#41—48no—
922#41—42no—
923#41—42no—
924#41—48no—
925#41—48no—
926C2×Q8—22no—
927C2×Q8—22no—
928C2×Q8—22no—
929C2×Q8—21no—
930C2×Q8—22no—
931C2×Q8—24no—
932C2×Q8—24no—
933C2×Q8—42no—
934C2×Q8—42no—
935C2×Q8—42no—
936C2×Q8—42no—
937C2×Q8—48no—
938C2×Q8—42no—
939C2×Q8—42no—
940C2×Q8C2×D4×C1112yes—
941C2×Q8C24×C1112yes—
942C2×Q8C24×C1112yes—
943C2×Q8C24×C1111yescharacteristic
944C2×Q8C24×C1112yes—
945C2×Q8C24×C1111yescharacteristic
946C2×D4—21no—
947C2×D4—22no—
948C2×D4—22no—
949C2×D4—21no—
950C2×D4—22no—
951C2×D4—22no—
952C2×D4C2×D4×C1111yescharacteristic
953C2×D4C2×D4×C1111yescharacteristic
954C2×D4C2×D4×C1112yes—
955C2×D4C2×D4×C1112yes—
956C2×D4C2×D4×C1112yes—
957C2×D4C2×D4×C1112yes—
958C2×D4C24×C1111yescharacteristic
959C2×D4C24×C1111yescharacteristic
960C22×C4—21no—
961C22×C4—22no—
962C22×C4—22no—
963C22×C4—22no—
964C22×C4—22no—
965C22×C4—22no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—22no—
969C22×C4—22no—
970C22×C4—21no—
971C22×C4—22no—
972C22×C4C2×D4×C1111yescharacteristic
973C22×C4C2×D4×C1111yescharacteristic
974C22×C4C24×C1111yescharacteristic
975C22×C4C24×C1112yes—
976C22×C4C24×C1112yes—
977Q16—22no—
978Q16—24no—
979Q16—42no—
980Q16—42no—
981Q16—42no—
982Q16—42no—
983Q16—42no—
984Q16—42no—
985SD16—22no—
986SD16—24no—
987SD16—22no—
988SD16—42no—
989SD16—42no—
990D8—22no—
991M16—42no—
992M16—42no—
993C2×C8—42no—
994C2×C8—42no—
995C2×C8C24×C1111yescharacteristic
996C2×C8C24×C1111yescharacteristic
997C2×C8C24×C1111yescharacteristic
998C2×C8C24×C1111yescharacteristic
999C2×C8C24×C1112yes—
1000C2×C8C24×C1112yes—
1001C4⋊C4—22no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—22no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—22no—
1009C4⋊C4—22no—
1010C4⋊C4—22no—
1011C4⋊C4—22no—
1012C4⋊C4—22no—
1013C4⋊C4—22no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—22no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—22no—
1022C4⋊C4—22no—
1023C4⋊C4—21no—
1024C4⋊C4—22no—
1025C4⋊C4—21no—
1026C4⋊C4C2×D4×C1111yescharacteristic
1027C4⋊C4C2×D4×C1111yescharacteristic
1028C4⋊C4C2×D4×C1112yes—
1029C4⋊C4C24×C1111yescharacteristic
1030C4⋊C4C24×C1112yes—
1031C4⋊C4C24×C1111yescharacteristic
1032C4⋊C4C24×C1111yescharacteristic
1033C4⋊C4C24×C1111yescharacteristic
1034C22⋊C4—22no—
1035C22⋊C4—22no—
1036C22⋊C4—21no—
1037C22⋊C4—22no—
1038C22⋊C4—22no—
1039C22⋊C4—22no—
1040C22⋊C4—22no—
1041C22⋊C4—22no—
1042C22⋊C4—22no—
1043C22⋊C4—22no—
1044C22⋊C4—21no—
1045C22⋊C4—21no—
1046C22⋊C4—21no—
1047C22⋊C4—21no—
1048C22⋊C4—21no—
1049C22⋊C4—22no—
1050C22⋊C4—21no—
1051C22⋊C4—21no—
1052C22⋊C4C2×D4×C1112yes—
1053C22⋊C4C2×D4×C1112yes—
1054C22⋊C4C2×D4×C1112yes—
1055C22⋊C4C2×D4×C1112yes—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—22no—
1060C42—22no—
1061C42—21no—
1062C42C2×D4×C1111yescharacteristic
1063C42C2×D4×C1111yescharacteristic
1064C42C24×C1111yescharacteristic
1065C42C24×C1111yescharacteristic
1066C11#6169311yescharacteristic, direct product factor, Sylow
1067C23—21no—
1068C23—21no—
1069C23C22×D4×C1112yes—
1070C23C22×D4×C1112yes—
1071C23C22×D4×C1111yescharacteristic
1072Q8—21no—
1073Q8—21no—
1074Q8—22no—
1075Q8—22no—
1076Q8—22no—
1077Q8—21no—
1078Q8—22no—
1079Q8—22no—
1080Q8—22no—
1081Q8—42no—
1082Q8—44no—
1083Q8—44no—
1084Q8—44no—
1085Q8—81no—
1086Q8—82no—
1087Q8C11×H(5,𝔽2)12yes—
1088D4—24no—
1089D4—22no—
1090D4—22no—
1091D4—21no—
1092D4—21no—
1093D4—21no—
1094D4—42no—
1095D4—42no—
1096D4—42no—
1097D4—42no—
1098D4—44no—
1099D4—44no—
1100D4—81no—
1101D4—82no—
1102D4—82no—
1103D4C11×H(5,𝔽2)12yes—
1104C2×C4—24no—
1105C2×C4—21no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—22no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—41no—
1123C2×C4—44no—
1124C2×C4—44no—
1125C2×C4—44no—
1126C2×C4—44no—
1127C2×C4—42no—
1128C2×C4—44no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—82no—
1132C2×C4—82no—
1133C2×C4—82no—
1134C2×C4C22×D4×C1111yescharacteristic
1135C2×C4C22×D4×C1111yescharacteristic
1136C2×C4C22×D4×C1111yescharacteristic
1137C2×C4C22×D4×C1112yes—
1138C2×C4C22×D4×C1111yescharacteristic
1139C2×C4C22×D4×C1112yes—
1140C2×C4C22×D4×C1111yescharacteristic
1141C2×C4C25×C1111yescharacteristic
1142C8—21no—
1143C8—21no—
1144C8—22no—
1145C8—22no—
1146C8—21no—
1147C8—21no—
1148C22—21no—
1149C22—22no—
1150C22—22no—
1151C22—22no—
1152C22—21no—
1153C22—22no—
1154C22—22no—
1155C22—21no—
1156C22—22no—
1157C22—22no—
1158C22—41no—
1159C22—41no—
1160C22—41no—
1161C22—41no—
1162C22—41no—
1163C22C23×D4×C1111yescharacteristic
1164C4—21no—
1165C4—22no—
1166C4—22no—
1167C4—22no—
1168C4—21no—
1169C4—21no—
1170C4—21no—
1171C4—42no—
1172C4—42no—
1173C4—42no—
1174C4—41no—
1175C4—41no—
1176C4—41no—
1177C4—41no—
1178C4—41no—
1179C4—42no—
1180C4C11×#57812yes—
1181C4C2×C11×H(5,𝔽2)11yescharacteristic
1182C4C2×C11×H(5,𝔽2)11yescharacteristic
1183C2—41no—
1184C2—42no—
1185C2—42no—
1186C2—42no—
1187C2—81no—
1188C2C11×#348411yescharacteristic
1189C2C2×C11×#57811yescharacteristic
1190C2C11×#358611yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#532 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3547C2semidirect
2. C11×#3499C2semidirect
3. C11×#3331C2semidirect
4. C11×#3329C2semidirect
5. C11×#3315C2semidirect
6. C11×#3312C2semidirect
7. C11×#3303C2semidirect
8. C11×#3299C2semidirect
9. D4×C11×Q16C2semidirect
10. C11×#3283C2semidirect
11. C11×#3276C2semidirect
12. C11×#3276C2semidirect
13. C11×#3270C2semidirect
14. C11×#3269C2semidirect
15. C11×#3218C2semidirect
16. C11×#3209C2semidirect
17. C11×#3202C2semidirect
18. C11×#3201C2semidirect
19. C11×#3116C2semidirect
20. C11×#3102C2semidirect
21. C11×#3013C2semidirect
22. C11×#3011C2semidirect
23. C11×#2981C2semidirect
318. #61693C11direct (N × H)
472. #3547C2×C11semidirect
473. #3499C2×C11semidirect
474. #3331C2×C11semidirect
475. #3329C2×C11semidirect
476. #3315C2×C11semidirect
477. #3312C2×C11semidirect
478. #3303C2×C11semidirect
479. #3299C2×C11semidirect
480. D4×Q16C2×C11semidirect
481. #3283C2×C11semidirect
482. #3276C2×C11semidirect
483. #3276C2×C11semidirect
484. #3270C2×C11semidirect
485. #3269C2×C11semidirect
486. #3218C2×C11semidirect
487. #3209C2×C11semidirect
488. #3202C2×C11semidirect
489. #3201C2×C11semidirect
490. #3116C2×C11semidirect
491. #3102C2×C11semidirect
492. #3013C2×C11semidirect
493. #3011C2×C11semidirect
494. #2981C2×C11semidirect
1066. C11#61693direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35472
C11×#34992
C11×#33312
C11×#33292
C11×#33152
C11×#33122
C11×#33032
C11×#32992
D4×C11×Q162
C11×#32832
C11×#32762
C11×#32702
C11×#32692
C11×#32182
C11×#32092
C11×#32022
C11×#32012
C11×#31162
C11×#31022
C11×#30132
C11×#30112
C11×#29812
#6169311