Finite Group Databasebeta

← C11×#61952 #14639145

Subgroups — C11×#61952 #14639145

Order 2816.

1824 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3503C211yesmaximal, characteristic
2Q8×C11×#41C211yesmaximal, characteristic
3C11×#3395C212yesmaximal, complemented
4C11×#3363C212yesmaximal, complemented
5C11×#3299C216yesmaximal, complemented
6D4×C11×Q16C216yesmaximal, complemented
7C11×#3249C213yesmaximal, complemented
8C11×#3209C213yesmaximal, complemented
9C11×#3104C213yesmaximal, complemented
10C2×C11×#462C213yesmaximal, complemented
11C11×#2988C211yesmaximal, characteristic
12C22×C11×Q16C2216yes—
13Q82×C11—21no—
14Q82×C11C2211yescharacteristic
15C11×#557—21no—
16C11×#557C2211yescharacteristic
17C11×#557C2212yes—
18C11×#554—23no—
19C11×#554—23no—
20C11×#554C2213yes—
21D4×Q8×C11C2213yes—
22D4×Q8×C11C2216yes—
23C11×#544—23no—
24C11×#533—23no—
25C11×#533C2213yes—
26C11×#533C2213yes—
27C2×C11×C4⋊Q8C2213yes—
28C11×#520—21no—
29C4×C11×#41—21no—
30C4×C11×#41C2211yescharacteristic
31C2×C4×Q8×C11C2213yes—
32C11×#494C2216yes—
33C11×#487C2216yes—
34C11×#484C2216yes—
35C11×#477C2213yes—
36C11×#477C2216yes—
37C11×#477C2211yescharacteristic
38C11×#467C22112yes—
39C11×#462C2213yes—
40C11×#462C2216yes—
41C11×#462C2216yes—
42C11×#462C2216yes—
43C11×#462C2213yes—
44C11×#462C2216yes—
45C11×#451C22112yes—
46C11×#451C2216yes—
47C8×Q8×C11C2212yes—
48C4×C11×Q16C2216yes—
49C4×C11×Q16C2216yes—
50C8×D4×C11C2216yes—
51C11×#431C2213yes—
52C2×C11×C4⋊C8C2213yes—
53C2×C11×#103C2216yes—
54C2×C11×#41D411yescharacteristic
55C22×Q8×C11C2313yes—
56C22×Q8×C11C2316yes—
57C2×C11×Q16—412no—
58C2×C11×Q16C2316yes—
59C2×C11×Q16C2316yes—
60C2×C11×Q16C23112yes—
61C22×C8×C11C2316yes—
62C11×C4⋊Q8—23no—
63C11×C4⋊Q8—23no—
64C11×C4⋊Q8—26no—
65C11×C4⋊Q8—23no—
66C11×C4⋊Q8—23no—
67C11×C4⋊Q8C2313yes—
68C11×C4⋊Q8C2316yes—
69C11×C4⋊Q8C2313yes—
70C11×C4⋊Q8C2311yescharacteristic
71C11×C4⋊Q8C2313yes—
72C11×#125—23no—
73C11×#125—23no—
74C11×#125—26no—
75C11×#125—23no—
76C11×#125—23no—
77C11×C22⋊Q8—23no—
78C11×C22⋊Q8—23no—
79C11×C22⋊Q8—26no—
80C11×C22⋊Q8—26no—
81C11×C22⋊Q8—212no—
82C11×C22⋊Q8C2316yes—
83C11×C22⋊Q8C2316yes—
84C4×Q8×C11—21no—
85C4×Q8×C11—21no—
86C4×Q8×C11—22no—
87C4×Q8×C11—23no—
88C4×Q8×C11—23no—
89C4×Q8×C11—23no—
90C4×Q8×C11—23no—
91C4×Q8×C11D411yescharacteristic
92C4×Q8×C11C2311yescharacteristic
93C4×Q8×C11C2313yes—
94C4×Q8×C11C2313yes—
95C4×Q8×C11C2313yes—
96C4×Q8×C11C2316yes—
97C4×Q8×C11C2311yescharacteristic
98C4×D4×C11—23no—
99C4×D4×C11—23no—
100C4×D4×C11—26no—
101C4×D4×C11D413yes—
102C4×D4×C11C2313yes—
103C11×#117—23no—
104C11×#117—23no—
105C11×#117D413yes—
106C2×C11×C4⋊C4—23no—
107C2×C11×C4⋊C4—23no—
108C2×C11×C4⋊C4—23no—
109C2×C11×C4⋊C4C2313yes—
110C2×C42×C11—23no—
111C2×C42×C11C2313yes—
112C11×#107C2312yes—
113C11×#107C2316yes—
114C11×C4⋊C8C2313yes—
115C11×C4⋊C8C2316yes—
116C11×C4⋊C8C2311yescharacteristic
117C11×#103C2316yes—
118C11×#103C23112yes—
119C11×#103C2312yes—
120C11×#103C2316yes—
121C11×#103C2316yes—
122C11×C22⋊C8C2316yes—
123C4×C8×C11C2316yes—
124#61952C1111yesmaximal, characteristic, direct product factor, Sylow
125C11×#41Q1618yescomplemented
126C2×Q8×C11—21no—
127C2×Q8×C11—23no—
128C2×Q8×C11—23no—
129C2×Q8×C11—26no—
130C2×Q8×C11—26no—
131C2×Q8×C11—43no—
132C2×Q8×C11—46no—
133C2×Q8×C11—46no—
134C2×Q8×C11C2×D411yescharacteristic
135C2×Q8×C11C2416yes—
136C2×Q8×C11C2413yes—
137C2×Q8×C11C2411yescharacteristic
138C2×D4×C11C2×D413yes—
139C22×C4×C11—23no—
140C22×C4×C11—23no—
141C22×C4×C11—26no—
142C22×C4×C11C2×D413yes—
143C22×C4×C11C2×D413yes—
144C22×C4×C11C2413yes—
145C11×Q16—212no—
146C11×Q16—412no—
147C11×Q16—46no—
148C2×C8×C11—46no—
149C2×C8×C11C2412yes—
150C2×C8×C11C2416yes—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—23no—
153C11×C4⋊C4—23no—
154C11×C4⋊C4—26no—
155C11×C4⋊C4—23no—
156C11×C4⋊C4—23no—
157C11×C4⋊C4—23no—
158C11×C4⋊C4—26no—
159C11×C4⋊C4—23no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—23no—
162C11×C4⋊C4—23no—
163C11×C4⋊C4—23no—
164C11×C4⋊C4—26no—
165C11×C4⋊C4—26no—
166C11×C4⋊C4—26no—
167C11×C4⋊C4C2×D413yes—
168C11×C4⋊C4C2×D413yes—
169C11×C4⋊C4C2411yescharacteristic
170C11×C4⋊C4C2413yes—
171C11×C4⋊C4C2412yes—
172C11×C22⋊C4—26no—
173C11×C22⋊C4—26no—
174C11×C22⋊C4C2×D416yes—
175C42×C11—21no—
176C42×C11—23no—
177C42×C11—23no—
178C42×C11—23no—
179C42×C11—26no—
180C42×C11C2×D413yes—
181C42×C11C2×D413yes—
182C42×C11C2413yes—
183C42×C11C2411yescharacteristic
184#3503C2×C1111yescharacteristic
185Q8×#41C2×C1111yescharacteristic
186#3395C2×C1112yescomplemented
187#3363C2×C1112yescomplemented
188#3299C2×C1116yescomplemented
189D4×Q16C2×C1116yescomplemented
190#3249C2×C1113yescomplemented
191#3209C2×C1113yescomplemented
192#3104C2×C1113yescomplemented
193C2×#462C2×C1113yescomplemented
194#2988C2×C1111yescharacteristic
195C23×C11C22×D413yes—
196Q8×C11—21no—
197Q8×C11—26no—
198Q8×C11—23no—
199Q8×C11—23no—
200Q8×C11—26no—
201Q8×C11—46no—
202Q8×C11—42no—
203Q8×C11—83no—
204Q8×C11—86no—
205Q8×C11C2×Q1614yescomplemented
206Q8×C11H(5,𝔽2)12yes—
207D4×C11C2×Q16112yescomplemented
208C2×C4×C11—21no—
209C2×C4×C11—23no—
210C2×C4×C11—23no—
211C2×C4×C11—21no—
212C2×C4×C11—22no—
213C2×C4×C11—23no—
214C2×C4×C11—23no—
215C2×C4×C11—26no—
216C2×C4×C11—43no—
217C2×C4×C11—46no—
218C2×C4×C11—83no—
219C2×C4×C11—86no—
220C2×C4×C11C2×Q16112yescomplemented
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C22×D413yes—
223C2×C4×C11C22×D413yes—
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D413yes—
226C2×C4×C11C2511yescharacteristic
227C8×C11—26no—
228C8×C11—22no—
229C22×Q16C22×C1116yes—
230Q82—21no—
231Q82C22×C1111yescharacteristic
232#557—21no—
233#557C22×C1112yes—
234#557C22×C1111yescharacteristic
235#554—23no—
236#554—23no—
237#554C22×C1113yes—
238D4×Q8C22×C1113yes—
239D4×Q8C22×C1116yes—
240#544—23no—
241#533—23no—
242#533C22×C1113yes—
243#533C22×C1113yes—
244C2×C4⋊Q8C22×C1113yes—
245#520—21no—
246C4×#41—21no—
247C4×#41C22×C1111yescharacteristic
248C2×C4×Q8C22×C1113yes—
249#494C22×C1116yes—
250#487C22×C1116yes—
251#484C22×C1116yes—
252#477C22×C1111yescharacteristic
253#477C22×C1113yes—
254#477C22×C1116yes—
255#467C22×C11112yes—
256#462C22×C1113yes—
257#462C22×C1113yes—
258#462C22×C1116yes—
259#462C22×C1116yes—
260#462C22×C1116yes—
261#462C22×C1116yes—
262#451C22×C1116yes—
263#451C22×C11112yes—
264C8×Q8C22×C1112yes—
265C4×Q16C22×C1116yes—
266C4×Q16C22×C1116yes—
267C8×D4C22×C1116yes—
268#431C22×C1113yes—
269C2×C4⋊C8C22×C1113yes—
270C2×#103C22×C1116yes—
271C22×C11—23no—
272C22×C11—23no—
273C22×C11C22×Q1616yes—
274C22×C11C23×D411yescharacteristic
275C4×C11—21no—
276C4×C11—23no—
277C4×C11—23no—
278C4×C11—22no—
279C4×C11—41no—
280C4×C11—43no—
281C4×C11—42no—
282C4×C11—43no—
283C4×C11—46no—
284C4×C11C22×Q1612yes—
285C4×C11C22×Q1616yes—
286C4×C11C2×H(5,𝔽2)11yescharacteristic
287C4×C11#58511yescharacteristic
288C2×#41D4×C1111yescharacteristic
289C22×Q8C23×C1113yes—
290C22×Q8C23×C1116yes—
291C2×Q16—412no—
292C2×Q16C23×C1116yes—
293C2×Q16C23×C11112yes—
294C2×Q16C23×C1116yes—
295C22×C8C23×C1116yes—
296C4⋊Q8—23no—
297C4⋊Q8—23no—
298C4⋊Q8—26no—
299C4⋊Q8—23no—
300C4⋊Q8—23no—
301C4⋊Q8C23×C1113yes—
302C4⋊Q8C23×C1116yes—
303C4⋊Q8C23×C1113yes—
304C4⋊Q8C23×C1111yescharacteristic
305C4⋊Q8C23×C1113yes—
306#125—23no—
307#125—23no—
308#125—26no—
309#125—23no—
310#125—23no—
311C22⋊Q8—23no—
312C22⋊Q8—23no—
313C22⋊Q8—26no—
314C22⋊Q8—26no—
315C22⋊Q8—212no—
316C22⋊Q8C23×C1116yes—
317C22⋊Q8C23×C1116yes—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×Q8—22no—
321C4×Q8—23no—
322C4×Q8—23no—
323C4×Q8—23no—
324C4×Q8—23no—
325C4×Q8D4×C1111yescharacteristic
326C4×Q8C23×C1111yescharacteristic
327C4×Q8C23×C1113yes—
328C4×Q8C23×C1113yes—
329C4×Q8C23×C1113yes—
330C4×Q8C23×C1116yes—
331C4×Q8C23×C1111yescharacteristic
332C4×D4—23no—
333C4×D4—23no—
334C4×D4—26no—
335C4×D4D4×C1113yes—
336C4×D4C23×C1113yes—
337#117—23no—
338#117—23no—
339#117D4×C1113yes—
340C2×C4⋊C4—23no—
341C2×C4⋊C4—23no—
342C2×C4⋊C4—23no—
343C2×C4⋊C4C23×C1113yes—
344C2×C42—23no—
345C2×C42C23×C1113yes—
346#107C23×C1112yes—
347#107C23×C1116yes—
348C4⋊C8C23×C1113yes—
349C4⋊C8C23×C1116yes—
350C4⋊C8C23×C1111yescharacteristic
351#103C23×C1116yes—
352#103C23×C11112yes—
353#103C23×C1112yes—
354#103C23×C1116yes—
355#103C23×C1116yes—
356C22⋊C8C23×C1116yes—
357C4×C8C23×C1116yes—
358C2×C11—26no—
359C2×C11#348811yescharacteristic
360C2×C11C23×Q1611yescharacteristic
361C2×C11#358611yescharacteristic
362#41C11×Q1618yescomplemented
363C2×Q8—21no—
364C2×Q8—23no—
365C2×Q8—23no—
366C2×Q8—26no—
367C2×Q8—26no—
368C2×Q8—43no—
369C2×Q8—46no—
370C2×Q8—46no—
371C2×Q8C2×D4×C1111yescharacteristic
372C2×Q8C24×C1116yes—
373C2×Q8C24×C1113yes—
374C2×Q8C24×C1111yescharacteristic
375C2×D4C2×D4×C1113yes—
376C22×C4—23no—
377C22×C4—23no—
378C22×C4—26no—
379C22×C4C2×D4×C1113yes—
380C22×C4C2×D4×C1113yes—
381C22×C4C24×C1113yes—
382Q16—212no—
383Q16—412no—
384Q16—46no—
385C2×C8—46no—
386C2×C8C24×C1112yes—
387C2×C8C24×C1116yes—
388C4⋊C4—21no—
389C4⋊C4—23no—
390C4⋊C4—23no—
391C4⋊C4—26no—
392C4⋊C4—23no—
393C4⋊C4—23no—
394C4⋊C4—23no—
395C4⋊C4—26no—
396C4⋊C4—23no—
397C4⋊C4—21no—
398C4⋊C4—23no—
399C4⋊C4—23no—
400C4⋊C4—23no—
401C4⋊C4—26no—
402C4⋊C4—26no—
403C4⋊C4—26no—
404C4⋊C4C2×D4×C1113yes—
405C4⋊C4C2×D4×C1113yes—
406C4⋊C4C24×C1111yescharacteristic
407C4⋊C4C24×C1113yes—
408C4⋊C4C24×C1112yes—
409C22⋊C4—26no—
410C22⋊C4—26no—
411C22⋊C4C2×D4×C1116yes—
412C42—21no—
413C42—23no—
414C42—23no—
415C42—23no—
416C42—26no—
417C42C2×D4×C1113yes—
418C42C2×D4×C1113yes—
419C42C24×C1113yes—
420C42C24×C1111yescharacteristic
421C11#6195211yescharacteristic, direct product factor, Sylow
422C23C22×D4×C1113yes—
423Q8—21no—
424Q8—26no—
425Q8—23no—
426Q8—23no—
427Q8—26no—
428Q8—46no—
429Q8—42no—
430Q8—83no—
431Q8—86no—
432Q8C2×C11×Q1614yescomplemented
433Q8C11×H(5,𝔽2)12yes—
434D4C2×C11×Q16112yescomplemented
435C2×C4—21no—
436C2×C4—23no—
437C2×C4—23no—
438C2×C4—21no—
439C2×C4—22no—
440C2×C4—23no—
441C2×C4—23no—
442C2×C4—26no—
443C2×C4—43no—
444C2×C4—46no—
445C2×C4—83no—
446C2×C4—86no—
447C2×C4C2×C11×Q16112yescomplemented
448C2×C4C22×D4×C1111yescharacteristic
449C2×C4C22×D4×C1113yes—
450C2×C4C22×D4×C1113yes—
451C2×C4C22×D4×C1111yescharacteristic
452C2×C4C22×D4×C1113yes—
453C2×C4C25×C1111yescharacteristic
454C8—26no—
455C8—22no—
456C22—23no—
457C22—23no—
458C22C22×C11×Q1616yes—
459C22C23×D4×C1111yescharacteristic
460C4—23no—
461C4—22no—
462C4—21no—
463C4—23no—
464C4—43no—
465C4—46no—
466C4—41no—
467C4—43no—
468C4—42no—
469C4C22×C11×Q1612yes—
470C4C22×C11×Q1616yes—
471C4C2×C11×H(5,𝔽2)11yescharacteristic
472C4C11×#58511yescharacteristic
473C2—26no—
474C2C11×#348811yescharacteristic
475C2C23×C11×Q1611yescharacteristic
476C2C11×#358611yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC2×C11×#41D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#3395C2semidirect
4. C11×#3363C2semidirect
5. C11×#3299C2semidirect
6. D4×C11×Q16C2semidirect
7. C11×#3249C2semidirect
8. C11×#3209C2semidirect
9. C11×#3104C2semidirect
10. C2×C11×#462C2semidirect
124. #61952C11direct (N × H)
125. C11×#41Q16semidirect
186. #3395C2×C11semidirect
187. #3363C2×C11semidirect
188. #3299C2×C11semidirect
189. D4×Q16C2×C11semidirect
190. #3249C2×C11semidirect
191. #3209C2×C11semidirect
192. #3104C2×C11semidirect
193. C2×#462C2×C11semidirect
205. Q8×C11C2×Q16semidirect
207. D4×C11C2×Q16semidirect
220. C2×C4×C11C2×Q16semidirect
362. #41C11×Q16semidirect
421. C11#61952direct (N × H)
432. Q8C2×C11×Q16semidirect
434. D4C2×C11×Q16semidirect
447. C2×C4C2×C11×Q16semidirect

Maximal subgroups

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

subgroupindex
C11×#35032
Q8×C11×#412
C11×#33952
C11×#33632
C11×#32992
D4×C11×Q162
C11×#32492
C11×#32092
C11×#31042
C2×C11×#4622
C11×#29882
#6195211