Finite Group Databasebeta

← C11×#61322 #14638515

Subgroups — C11×#61322 #14638515

Order 2816.

1782 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C11×#41C211yesmaximal, characteristic
2C2×C11×#557C211yesmaximal, characteristic, complemented
3C11×#3374C216yesmaximal, complemented
4C11×#3372C216yesmaximal, complemented
5C11×#3363C212yesmaximal, complemented
6C11×#3359C212yesmaximal, complemented
7C11×#3139C213yesmaximal, complemented
8C11×#3078C213yesmaximal, complemented
9C11×#3039C213yesmaximal
10Q8×C11×M16C211yesmaximal, characteristic, complemented
11C4×C11×#137C213yesmaximal
12C2×C11×#137C2213yes—
13Q82×C11C2211yescharacteristic
14C11×#557—21no—
15C11×#557—23no—
16C11×#557C2212yes—
17C11×#557C2216yes—
18C11×#557C2213yes—
19C11×#554—23no—
20C11×#554C2213yes—
21D4×Q8×C11—21no—
22D4×Q8×C11C2211yescharacteristic
23C11×#533—23no—
24C11×#533C2213yes—
25C2×C11×C4⋊Q8C2213yes—
26C2×C11×#125—23no—
27C4×C11×#41C2213yes—
28C2×C4×Q8×C11—21no—
29C2×C4×Q8×C11—21no—
30C2×C4×Q8×C11C2213yes—
31C2×C4×Q8×C11C2211yescharacteristic
32C11×#491C22112yes—
33C11×#487C2216yes—
34C11×#487C2216yes—
35C11×#479C22112yes—
36C11×#477C2216yes—
37C11×#475C2216yes—
38C11×#462C2216yes—
39C11×#462C2216yes—
40C11×#461C2216yes—
41C11×#461C2216yes—
42C11×#446C2216yes—
43C8×Q8×C11C2212yes—
44C11×#441C2216yes—
45C11×#440C2216yes—
46C4×C11×Q16C2216yes—
47C4×C11×SD16C2216yes—
48C11×#428C2213yes—
49C11×#423C2213yes—
50C11×#419C2213yes—
51C11×#419C2216yes—
52C11×#417C2211yescharacteristic
53C4×C11×M16C2213yes—
54C2×C11×#41C2311yescharacteristic
55C22×Q8×C11—21no—
56C22×Q8×C11D411yescharacteristic
57C22×Q8×C11C2313yes—
58C11×#137—212no—
59C2×C11×Q16C2316yes—
60C2×C11×SD16C2316yes—
61C2×C11×M16C2311yescharacteristic
62C2×C11×M16C2313yes—
63C11×C4⋊Q8—23no—
64C11×C4⋊Q8—23no—
65C11×C4⋊Q8—23no—
66C11×C4⋊Q8—23no—
67C11×C4⋊Q8C2316yes—
68C11×C4⋊Q8C2316yes—
69C11×C4⋊Q8C2313yes—
70C11×C4⋊Q8C2313yes—
71C11×#125—26no—
72C11×#125—212no—
73C11×#125—26no—
74C11×#125—26no—
75C11×#125C2316yes—
76C11×C22⋊Q8—23no—
77C11×C22⋊Q8—23no—
78C11×C22⋊Q8—23no—
79C11×C22⋊Q8—23no—
80C11×C22⋊Q8—26no—
81C4×Q8×C11—21no—
82C4×Q8×C11—26no—
83C4×Q8×C11—22no—
84C4×Q8×C11—23no—
85C4×Q8×C11—23no—
86C4×Q8×C11—23no—
87C4×Q8×C11—23no—
88C4×Q8×C11—23no—
89C4×Q8×C11D411yescharacteristic
90C4×Q8×C11D413yes—
91C4×Q8×C11C2316yes—
92C4×Q8×C11C2316yes—
93C4×Q8×C11C2313yes—
94C4×Q8×C11C2313yes—
95C4×Q8×C11C2311yescharacteristic
96C4×Q8×C11C2313yes—
97C4×D4×C11—23no—
98C4×D4×C11—23no—
99C4×D4×C11C2313yes—
100C4×D4×C11C2313yes—
101C11×#117—23no—
102C11×#117C2313yes—
103C2×C11×C4⋊C4—23no—
104C2×C11×C4⋊C4—23no—
105C2×C11×C4⋊C4—23no—
106C2×C11×C4⋊C4—23no—
107C2×C11×C4⋊C4D413yes—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C42×C11—23no—
110C2×C42×C11—23no—
111C2×C42×C11C2313yes—
112C11×#107C2316yes—
113C11×#106C2316yes—
114C11×C4⋊C8C2316yes—
115C11×C4⋊C8C2316yes—
116C11×#103C2316yes—
117C11×#103C2316yes—
118C11×#103C23112yes—
119C11×#103C23112yes—
120C11×#103C2312yes—
121C11×#102C2312yes—
122C11×#97C2316yes—
123C4×C8×C11C2316yes—
124#61322C1111yesmaximal, characteristic, direct product factor, Sylow
125C11×#41—22no—
126C11×#41#4114yes—
127C2×Q8×C11—24no—
128C2×Q8×C11—23no—
129C2×Q8×C11—23no—
130C2×Q8×C11—23no—
131C2×Q8×C11—26no—
132C2×Q8×C11—26no—
133C2×Q8×C11—44no—
134C2×Q8×C11C2×D413yes—
135C2×Q8×C11C2×D411yescharacteristic
136C2×Q8×C11C2416yes—
137C2×Q8×C11C2411yescharacteristic
138C2×D4×C11—21no—
139C2×D4×C11C2411yescharacteristic
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—23no—
143C22×C4×C11—23no—
144C22×C4×C11—23no—
145C22×C4×C11C2×D413yes—
146C22×C4×C11C2×D413yes—
147C22×C4×C11C2411yescharacteristic
148C11×Q16—212no—
149C11×SD16—212no—
150C11×M16—26no—
151C11×M16—22no—
152C2×C8×C11C2412yes—
153C2×C8×C11C2416yes—
154C11×C4⋊C4—26no—
155C11×C4⋊C4—23no—
156C11×C4⋊C4—26no—
157C11×C4⋊C4—26no—
158C11×C4⋊C4—26no—
159C11×C4⋊C4—26no—
160C11×C4⋊C4—26no—
161C11×C4⋊C4—26no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—23no—
164C11×C4⋊C4—23no—
165C11×C4⋊C4—23no—
166C11×C4⋊C4—26no—
167C11×C4⋊C4C2×D413yes—
168C11×C4⋊C4C2×D416yes—
169C11×C4⋊C4C2×D413yes—
170C11×C4⋊C4C2412yes—
171C11×C4⋊C4C2413yes—
172C11×C4⋊C4C2413yes—
173C11×C22⋊C4—23no—
174C11×C22⋊C4—23no—
175C11×C22⋊C4—23no—
176C42×C11—23no—
177C42×C11—23no—
178C42×C11—23no—
179C42×C11—26no—
180C42×C11—26no—
181C42×C11C2×D413yes—
182C42×C11C2×D413yes—
183C42×C11C2413yes—
184C42×C11C2413yes—
185Q8×#41C2×C1111yescharacteristic
186C2×#557C2×C1111yescharacteristic, complemented
187#3374C2×C1116yescomplemented
188#3372C2×C1116yescomplemented
189#3363C2×C1112yescomplemented
190#3359C2×C1112yescomplemented
191#3139C2×C1113yescomplemented
192#3078C2×C1113yescomplemented
193#3039C2×C1113yes—
194Q8×M16C2×C1111yescharacteristic, complemented
195C4×#137C2×C1113yes—
196C23×C11—21no—
197C23×C11C22×D411yescharacteristic
198Q8×C11—26no—
199Q8×C11—21no—
200Q8×C11—26no—
201Q8×C11—26no—
202Q8×C11—46no—
203Q8×C11—46no—
204Q8×C11—83no—
205Q8×C11#13714yescomplemented
206Q8×C11C2×#4112yes—
207D4×C11—24no—
208D4×C11—21no—
209D4×C11C2×#4112yes—
210C2×C4×C11—21no—
211C2×C4×C11—24no—
212C2×C4×C11—26no—
213C2×C4×C11—22no—
214C2×C4×C11—23no—
215C2×C4×C11—23no—
216C2×C4×C11—26no—
217C2×C4×C11—43no—
218C2×C4×C11—42no—
219C2×C4×C11—46no—
220C2×C4×C11—46no—
221C2×C4×C11—83no—
222C2×C4×C11C22×D413yes—
223C2×C4×C11C22×D413yes—
224C2×C4×C11C22×D413yes—
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D413yes—
227C2×C4×C11C2×#4112yes—
228C2×C4×C112−1+412yes—
229C2×C4×C11C2511yescharacteristic
230C8×C11—26no—
231C8×C11—22no—
232C2×#137C22×C1113yes—
233Q82C22×C1111yescharacteristic
234#557—21no—
235#557—23no—
236#557C22×C1112yes—
237#557C22×C1116yes—
238#557C22×C1113yes—
239#554—23no—
240#554C22×C1113yes—
241D4×Q8—21no—
242D4×Q8C22×C1111yescharacteristic
243#533—23no—
244#533C22×C1113yes—
245C2×C4⋊Q8C22×C1113yes—
246C2×#125—23no—
247C4×#41C22×C1113yes—
248C2×C4×Q8—21no—
249C2×C4×Q8—21no—
250C2×C4×Q8C22×C1113yes—
251C2×C4×Q8C22×C1111yescharacteristic
252#491C22×C11112yes—
253#487C22×C1116yes—
254#487C22×C1116yes—
255#479C22×C11112yes—
256#477C22×C1116yes—
257#475C22×C1116yes—
258#462C22×C1116yes—
259#462C22×C1116yes—
260#461C22×C1116yes—
261#461C22×C1116yes—
262#446C22×C1116yes—
263C8×Q8C22×C1112yes—
264#441C22×C1116yes—
265#440C22×C1116yes—
266C4×Q16C22×C1116yes—
267C4×SD16C22×C1116yes—
268#428C22×C1113yes—
269#423C22×C1113yes—
270#419C22×C1116yes—
271#419C22×C1113yes—
272#417C22×C1111yescharacteristic
273C4×M16C22×C1113yes—
274C22×C11—21no—
275C22×C11—21no—
276C22×C11—22no—
277C22×C11—41no—
278C22×C11—41no—
279C22×C11#54812yes—
280C22×C11C23×D411yescharacteristic
281C4×C11—23no—
282C4×C11—23no—
283C4×C11—22no—
284C4×C11—23no—
285C4×C11—42no—
286C4×C11—43no—
287C4×C11—46no—
288C4×C11—43no—
289C4×C11#54812yes—
290C4×C11C2×#13716yes—
291C4×C11C22×#4111yescharacteristic
292C4×C11C2×2−1+411yescharacteristic
293C2×#41C23×C1111yescharacteristic
294C22×Q8—21no—
295C22×Q8D4×C1111yescharacteristic
296C22×Q8C23×C1113yes—
297#137—212no—
298C2×Q16C23×C1116yes—
299C2×SD16C23×C1116yes—
300C2×M16C23×C1113yes—
301C2×M16C23×C1111yescharacteristic
302C4⋊Q8—23no—
303C4⋊Q8—23no—
304C4⋊Q8—23no—
305C4⋊Q8—23no—
306C4⋊Q8C23×C1116yes—
307C4⋊Q8C23×C1116yes—
308C4⋊Q8C23×C1113yes—
309C4⋊Q8C23×C1113yes—
310#125—26no—
311#125—212no—
312#125—26no—
313#125—26no—
314#125C23×C1116yes—
315C22⋊Q8—23no—
316C22⋊Q8—23no—
317C22⋊Q8—23no—
318C22⋊Q8—23no—
319C22⋊Q8—26no—
320C4×Q8—21no—
321C4×Q8—26no—
322C4×Q8—22no—
323C4×Q8—23no—
324C4×Q8—23no—
325C4×Q8—23no—
326C4×Q8—23no—
327C4×Q8—23no—
328C4×Q8D4×C1111yescharacteristic
329C4×Q8D4×C1113yes—
330C4×Q8C23×C1116yes—
331C4×Q8C23×C1116yes—
332C4×Q8C23×C1113yes—
333C4×Q8C23×C1113yes—
334C4×Q8C23×C1111yescharacteristic
335C4×Q8C23×C1113yes—
336C4×D4—23no—
337C4×D4—23no—
338C4×D4C23×C1113yes—
339C4×D4C23×C1113yes—
340#117—23no—
341#117C23×C1113yes—
342C2×C4⋊C4—23no—
343C2×C4⋊C4—23no—
344C2×C4⋊C4—23no—
345C2×C4⋊C4—23no—
346C2×C4⋊C4D4×C1113yes—
347C2×C4⋊C4C23×C1111yescharacteristic
348C2×C42—23no—
349C2×C42—23no—
350C2×C42C23×C1113yes—
351#107C23×C1116yes—
352#106C23×C1116yes—
353C4⋊C8C23×C1116yes—
354C4⋊C8C23×C1116yes—
355#103C23×C1112yes—
356#103C23×C1116yes—
357#103C23×C1116yes—
358#103C23×C11112yes—
359#103C23×C11112yes—
360#102C23×C1112yes—
361#97C23×C1116yes—
362C4×C8C23×C1116yes—
363C2×C11—22no—
364C2×C11—42no—
365C2×C11C2×#54811yescharacteristic
366C2×C11C22×#13711yescharacteristic
367C2×C11#358611yescharacteristic
368#41—22no—
369#41C11×#4114yes—
370C2×Q8—24no—
371C2×Q8—23no—
372C2×Q8—23no—
373C2×Q8—23no—
374C2×Q8—26no—
375C2×Q8—26no—
376C2×Q8—44no—
377C2×Q8C2×D4×C1113yes—
378C2×Q8C2×D4×C1111yescharacteristic
379C2×Q8C24×C1116yes—
380C2×Q8C24×C1111yescharacteristic
381C2×D4—21no—
382C2×D4C24×C1111yescharacteristic
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—23no—
386C22×C4—23no—
387C22×C4—23no—
388C22×C4C2×D4×C1113yes—
389C22×C4C2×D4×C1113yes—
390C22×C4C24×C1111yescharacteristic
391Q16—212no—
392SD16—212no—
393M16—26no—
394M16—22no—
395C2×C8C24×C1112yes—
396C2×C8C24×C1116yes—
397C4⋊C4—26no—
398C4⋊C4—23no—
399C4⋊C4—26no—
400C4⋊C4—26no—
401C4⋊C4—26no—
402C4⋊C4—26no—
403C4⋊C4—26no—
404C4⋊C4—26no—
405C4⋊C4—21no—
406C4⋊C4—23no—
407C4⋊C4—23no—
408C4⋊C4—23no—
409C4⋊C4—26no—
410C4⋊C4C2×D4×C1113yes—
411C4⋊C4C2×D4×C1116yes—
412C4⋊C4C2×D4×C1113yes—
413C4⋊C4C24×C1112yes—
414C4⋊C4C24×C1113yes—
415C4⋊C4C24×C1113yes—
416C22⋊C4—23no—
417C22⋊C4—23no—
418C22⋊C4—23no—
419C42—23no—
420C42—23no—
421C42—23no—
422C42—26no—
423C42—26no—
424C42C2×D4×C1113yes—
425C42C2×D4×C1113yes—
426C42C24×C1113yes—
427C42C24×C1113yes—
428C11#6132211yescharacteristic, direct product factor, Sylow
429C23—21no—
430C23C22×D4×C1111yescharacteristic
431Q8—26no—
432Q8—21no—
433Q8—26no—
434Q8—26no—
435Q8—46no—
436Q8—46no—
437Q8—83no—
438Q8C11×#13714yescomplemented
439Q8C2×C11×#4112yes—
440D4—24no—
441D4—21no—
442D4C2×C11×#4112yes—
443C2×C4—21no—
444C2×C4—24no—
445C2×C4—26no—
446C2×C4—22no—
447C2×C4—23no—
448C2×C4—23no—
449C2×C4—26no—
450C2×C4—43no—
451C2×C4—42no—
452C2×C4—46no—
453C2×C4—46no—
454C2×C4—83no—
455C2×C4C22×D4×C1113yes—
456C2×C4C22×D4×C1113yes—
457C2×C4C22×D4×C1113yes—
458C2×C4C22×D4×C1111yescharacteristic
459C2×C4C22×D4×C1113yes—
460C2×C4C2×C11×#4112yes—
461C2×C4C11×2−1+412yes—
462C2×C4C25×C1111yescharacteristic
463C8—26no—
464C8—22no—
465C22—21no—
466C22—21no—
467C22—22no—
468C22—41no—
469C22—41no—
470C22C11×#54812yes—
471C22C23×D4×C1111yescharacteristic
472C4—22no—
473C4—23no—
474C4—23no—
475C4—23no—
476C4—46no—
477C4—43no—
478C4—42no—
479C4—43no—
480C4C11×#54812yes—
481C4C2×C11×#13716yes—
482C4C22×C11×#4111yescharacteristic
483C4C2×C11×2−1+411yescharacteristic
484C2—22no—
485C2—42no—
486C2C2×C11×#54811yescharacteristic
487C2C22×C11×#13711yescharacteristic
488C2C11×#358611yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC2×C11×#41C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#557C2semidirect
3. C11×#3374C2semidirect
4. C11×#3372C2semidirect
5. C11×#3363C2semidirect
6. C11×#3359C2semidirect
7. C11×#3139C2semidirect
8. C11×#3078C2semidirect
10. Q8×C11×M16C2semidirect
124. #61322C11direct (N × H)
186. C2×#557C2×C11semidirect
187. #3374C2×C11semidirect
188. #3372C2×C11semidirect
189. #3363C2×C11semidirect
190. #3359C2×C11semidirect
191. #3139C2×C11semidirect
192. #3078C2×C11semidirect
194. Q8×M16C2×C11semidirect
205. Q8×C11#137semidirect
428. C11#61322direct (N × H)
438. Q8C11×#137semidirect

Maximal subgroups

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

subgroupindex
Q8×C11×#412
C2×C11×#5572
C11×#33742
C11×#33722
C11×#33632
C11×#33592
C11×#31392
C11×#30782
C11×#30392
Q8×C11×M162
C4×C11×#1372
#6132211