Finite Group Databasebeta

← C11×#10068 #14587261

Subgroups — C11×#10068 #14587261

Order 2816.

670 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#498C211yesmaximal, characteristic, complemented
2C2×C11×#461C211yesmaximal, characteristic
3C11×#2542C211yesmaximal, characteristic
4C11×#1988C211yesmaximal, characteristic, complemented
5C2×C11×#332C211yesmaximal, characteristic, complemented
6C2×C11×D4⋊C8C211yesmaximal, characteristic
7C11×#1279C211yesmaximal, characteristic, complemented
8C22×C11×SD16—21no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C22⋊Q8—22no—
12C2×C4×D4×C11C2211yescharacteristic
13C11×#498—22no—
14C11×#498—22no—
15C11×#461—22no—
16C11×#461—22no—
17C2×C11×#106—22no—
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#103—21no—
21C2×C4×C8×C11C2211yescharacteristic
22C11×#399—22no—
23C11×#390—21no—
24C11×#384—21no—
25C4×C11×C4⋊C4C2211yescharacteristic
26C11×#340—22no—
27C11×#332—22no—
28C11×D4⋊C8—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11—21no—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11—21no—
33C2×C11×SD16—24no—
34C2×C11×SD16—42no—
35C2×C11×SD16—42no—
36C22×C8×C11—21no—
37C22×C8×C11—21no—
38C22×C8×C11—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8D412yes—
47C11×C22⋊Q8—44no—
48C11×C22⋊Q8—44no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—24no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4D412yes—
59C2×C11×C4⋊C4D412yes—
60C2×C11×C22⋊C4—24no—
61C2×C11×C22⋊C4—21no—
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64C11×#106—28no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8D412yes—
69C11×#103—24no—
70C4×C8×C11—21no—
71C4×C8×C11D412yes—
72C11×#95—21no—
73#10068C1111yesmaximal, characteristic, direct product factor, Sylow
74C24×C11—21no—
75C2×Q8×C11—22no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—42no—
80C2×Q8×C11—42no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11SD1612yes—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—21no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—42no—
98C22×C4×C11—42no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C11×SD16—48no—
103C2×C8×C11—24no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—41no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C2×C8×C11—42no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—48no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4SD1614yescomplemented
123C11×C22⋊C4—48no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—41no—
126C42×C11—41no—
127C42×C11—41no—
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11#4111yescharacteristic
132C2×#498C2×C1111yescharacteristic, complemented
133C2×#461C2×C1111yescharacteristic
134#2542C2×C1111yescharacteristic
135#1988C2×C1111yescharacteristic, complemented
136C2×#332C2×C1111yescharacteristic, complemented
137C2×D4⋊C8C2×C1111yescharacteristic
138#1279C2×C1111yescharacteristic, complemented
139C23×C11—22no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11—42no—
143C23×C11—42no—
144C23×C11#12011yescharacteristic
145Q8×C11—42no—
146Q8×C11—42no—
147Q8×C11—82no—
148Q8×C11—81no—
149Q8×C11—81no—
150Q8×C11—81no—
151Q8×C11—81no—
152D4×C11—22no—
153D4×C11—22no—
154D4×C11—41no—
155D4×C11—41no—
156C2×C4×C11—22no—
157C2×C4×C11—24no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—41no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—44no—
164C2×C4×C11—42no—
165C2×C4×C11—81no—
166C2×C4×C11—81no—
167C2×C4×C11—82no—
168C2×C4×C11—81no—
169C2×C4×C11—81no—
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12711yescharacteristic
176C2×C4×C11C2×SD1611yescharacteristic
177C2×C4×C11C2×SD1612yes—
178C2×C4×C11#13511yescharacteristic
179C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C11AGL(1,ℤ/8)12yes—
181C2×C4×C11#13711yescharacteristic
182C8×C11—24no—
183C8×C11—42no—
184C8×C11—81no—
185C22×SD16—21no—
186C2×C4⋊Q8C22×C1111yescharacteristic
187C2×C4⋊Q8C22×C1111yescharacteristic
188C2×C22⋊Q8—22no—
189C2×C4×D4C22×C1111yescharacteristic
190#498—22no—
191#498—22no—
192#461—22no—
193#461—22no—
194C2×#106—22no—
195C2×C4⋊C8C22×C1111yescharacteristic
196C2×C4⋊C8C22×C1111yescharacteristic
197C2×#103—21no—
198C2×C4×C8C22×C1111yescharacteristic
199#399—22no—
200#390—21no—
201#384—21no—
202C4×C4⋊C4C22×C1111yescharacteristic
203#340—22no—
204#332—22no—
205D4⋊C8—22no—
206C22×C11—44no—
207C22×C11—42no—
208C22×C11—82no—
209C22×C11—81no—
210C22×C11—81no—
211C22×C11#39211yescharacteristic
212C22×C11#44811yescharacteristic
213C22×C11#44911yescharacteristic
214C22×C11#45012yes—
215C22×C11#45612yes—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—44no—
219C4×C11—82no—
220C4×C11—81no—
221C4×C11—82no—
222C4×C11#45011yescharacteristic
223C4×C11#45211yescharacteristic
224C4×C11#46012yes—
225C4×C11#46511yescharacteristic
226C4×C11#46811yescharacteristic
227C4×C11#49211yescharacteristic
228C4×C11#49611yescharacteristic
229C22×Q8—21no—
230C22×Q8—21no—
231C22×D4D4×C1111yescharacteristic
232C23×C4—21no—
233C2×SD16—24no—
234C2×SD16—42no—
235C2×SD16—42no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—21no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8D4×C1112yes—
247C22⋊Q8—44no—
248C22⋊Q8—44no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4D4×C1111yescharacteristic
258C2×C4⋊C4D4×C1112yes—
259C2×C4⋊C4D4×C1112yes—
260C2×C22⋊C4—24no—
261C2×C22⋊C4—21no—
262C2×C42—21no—
263C2×C42C23×C1111yescharacteristic
264#106—28no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8D4×C1112yes—
269#103—24no—
270C4×C8—21no—
271C4×C8D4×C1112yes—
272#95—21no—
273C2×C11—82no—
274C2×C11#165112yes—
275C2×C11#165412yes—
276C2×C11#200011yescharacteristic
277C2×C11#200511yescharacteristic
278C2×C11#201411yescharacteristic
279C24—21no—
280C2×Q8—22no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8—41no—
284C2×Q8—42no—
285C2×Q8—42no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4C11×SD1612yes—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—21no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4C2×D4×C1111yescharacteristic
305C22×C4C2×D4×C1111yescharacteristic
306C22×C4C2×D4×C1111yescharacteristic
307SD16—48no—
308C2×C8—24no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—42no—
315C4⋊C4—22no—
316C4⋊C4—21no—
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—21no—
321C4⋊C4—22no—
322C4⋊C4—48no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4C11×SD1614yescomplemented
328C22⋊C4—48no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C42—41no—
332C42—41no—
333C42C2×D4×C1111yescharacteristic
334C42C2×D4×C1111yescharacteristic
335C42C2×D4×C1111yescharacteristic
336C42C11×#4111yescharacteristic
337C11#1006811yescharacteristic, direct product factor, Sylow
338C23—22no—
339C23—41no—
340C23—41no—
341C23—42no—
342C23—42no—
343C23C11×#12011yescharacteristic
344Q8—42no—
345Q8—42no—
346Q8—81no—
347Q8—81no—
348Q8—82no—
349Q8—81no—
350Q8—81no—
351D4—22no—
352D4—22no—
353D4—41no—
354D4—41no—
355C2×C4—22no—
356C2×C4—24no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—44no—
363C2×C4—42no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—82no—
369C2×C4C11×#12011yescharacteristic
370C2×C4C11×#12011yescharacteristic
371C2×C4C11×#12111yescharacteristic
372C2×C4C11×#12111yescharacteristic
373C2×C4C11×#12111yescharacteristic
374C2×C4C11×#12711yescharacteristic
375C2×C4C2×C11×SD1612yes—
376C2×C4C2×C11×SD1611yescharacteristic
377C2×C4C11×#13511yescharacteristic
378C2×C4C11×AGL(1,ℤ/8)12yes—
379C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
380C2×C4C11×#13711yescharacteristic
381C8—24no—
382C8—42no—
383C8—81no—
384C22—44no—
385C22—42no—
386C22—82no—
387C22—81no—
388C22—81no—
389C22C11×#39211yescharacteristic
390C22C11×#44811yescharacteristic
391C22C11×#44911yescharacteristic
392C22C11×#45012yes—
393C22C11×#45612yes—
394C4—21no—
395C4—21no—
396C4—44no—
397C4—82no—
398C4—81no—
399C4—82no—
400C4C11×#45011yescharacteristic
401C4C11×#45211yescharacteristic
402C4C11×#46012yes—
403C4C11×#46511yescharacteristic
404C4C11×#46811yescharacteristic
405C4C11×#49211yescharacteristic
406C4C11×#49611yescharacteristic
407C2—82no—
408C2C11×#165112yes—
409C2C11×#165412yes—
410C2C11×#200011yescharacteristic
411C2C11×#200511yescharacteristic
412C2C11×#201411yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC22×D4×C11D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#498C2semidirect
4. C11×#1988C2semidirect
5. C2×C11×#332C2semidirect
7. C11×#1279C2semidirect
73. #10068C11direct (N × H)
122. C11×C4⋊C4SD16semidirect
132. C2×#498C2×C11semidirect
135. #1988C2×C11semidirect
136. C2×#332C2×C11semidirect
138. #1279C2×C11semidirect
327. C4⋊C4C11×SD16semidirect
337. C11#10068direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4982
C2×C11×#4612
C11×#25422
C11×#19882
C2×C11×#3322
C2×C11×D4⋊C82
C11×#12792
#1006811