Finite Group Databasebeta

← C11×#10149 #14587342

Subgroups — C11×#10149 #14587342

Order 2816.

528 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3230C211yesmaximal, characteristic, complemented
2C11×#3138C211yesmaximal, characteristic
3C2×C11×#486C211yesmaximal, characteristic
4C11×#1997C211yesmaximal, characteristic, complemented
5C11×#1545C211yesmaximal, characteristic
6C11×#1493C211yesmaximal, characteristic, complemented
7C11×#1278C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C11×#500—21no—
12C11×#490—22no—
13C11×#487—21no—
14C11×#486—21no—
15C11×#486—21no—
16C11×#486—22no—
17C11×#486—22no—
18C11×#484—22no—
19C11×#477—22no—
20C11×#431C2211yescharacteristic
21C11×#423C2211yescharacteristic
22C11×#418—22no—
23C2×C11×#102—22no—
24C4×C11×M16C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C11×#343—22no—
27C11×#331—22no—
28C11×Q8⋊C8—22no—
29C22×Q8×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C2×C11×M16—21no—
34C2×C11×M16D412yes—
35C22×C8×C11—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8D411yescharacteristic
41C11×C4⋊Q8D411yescharacteristic
42C11×#127—21no—
43C11×#127—21no—
44C11×#127—21no—
45C11×#127D412yes—
46C11×#125—21no—
47C11×C22⋊Q8—21no—
48C11×C22⋊Q8—21no—
49C4×Q8×C11—21no—
50C4×Q8×C11—21no—
51C11×#117—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4D412yes—
54C2×C42×C11C2311yescharacteristic
55C11×#107—24no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8D412yes—
59C11×#103—24no—
60C11×#102—24no—
61C11×#102—24no—
62C11×#102—28no—
63C11×C22⋊C8—21no—
64C11×#97—21no—
65C4×C8×C11—21no—
66C4×C8×C11—21no—
67C4×C8×C11—21no—
68C4×C8×C11D412yes—
69#10149C1111yesmaximal, characteristic, direct product factor, Sylow
70C24×C11—41no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—41no—
74C2×Q8×C11—41no—
75C2×Q8×C11—82no—
76C2×D4×C11—22no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—44no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—42no—
84C2×D4×C11—42no—
85C2×D4×C11—82no—
86C22×C4×C11—22no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C11×M16—22no—
91C11×M16—22no—
92C11×M16—42no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11—42no—
97C2×C8×C11—41no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C22⋊C4—41no—
109C42×C11—41no—
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114#3230C2×C1111yescharacteristic, complemented
115#3138C2×C1111yescharacteristic
116C2×#486C2×C1111yescharacteristic
117#1997C2×C1111yescharacteristic, complemented
118#1545C2×C1111yescharacteristic
119#1493C2×C1111yescharacteristic, complemented
120#1278C2×C1111yescharacteristic, complemented
121C23×C11—42no—
122C23×C11—82no—
123C23×C11—82no—
124C23×C11—82no—
125C23×C11#12111yescharacteristic
126Q8×C11—42no—
127Q8×C11—42no—
128Q8×C11—82no—
129Q8×C11—82no—
130D4×C11—44no—
131D4×C11—44no—
132D4×C11—82no—
133D4×C11—82no—
134D4×C11—82no—
135D4×C11—81no—
136D4×C11—81no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—82no—
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12711yescharacteristic
149C2×C4×C11#13512yes—
150C2×C4×C11#13712yes—
151C8×C11—42no—
152C8×C11—42no—
153C8×C11—42no—
154C8×C11—81no—
155#533C22×C1111yescharacteristic
156C2×C4⋊Q8C22×C1111yescharacteristic
157C2×#127C22×C1111yescharacteristic
158#500—21no—
159#490—22no—
160#487—21no—
161#486—21no—
162#486—21no—
163#486—22no—
164#486—22no—
165#484—22no—
166#477—22no—
167#431C22×C1111yescharacteristic
168#423C22×C1111yescharacteristic
169#418—22no—
170C2×#102—22no—
171C4×M16C22×C1111yescharacteristic
172C2×C4×C8C22×C1111yescharacteristic
173#343—22no—
174#331—22no—
175Q8⋊C8—22no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—82no—
179C22×C11—82no—
180C22×C11—82no—
181C22×C11—164no—
182C22×C11#39211yescharacteristic
183C22×C11#46412yes—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—81no—
187C4×C11—82no—
188C4×C11—81no—
189C4×C11#45212yes—
190C4×C11#45412yes—
191C4×C11#47212yes—
192C4×C11#49511yescharacteristic
193C4×C11#49711yescharacteristic
194C22×Q8—21no—
195C22×D4—21no—
196C22×D4—21no—
197C22×D4—21no—
198C2×M16—21no—
199C2×M16D4×C1112yes—
200C22×C8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8D4×C1111yescharacteristic
206C4⋊Q8D4×C1111yescharacteristic
207#127—21no—
208#127—21no—
209#127—21no—
210#127D4×C1112yes—
211#125—21no—
212C22⋊Q8—21no—
213C22⋊Q8—21no—
214C4×Q8—21no—
215C4×Q8—21no—
216#117—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4D4×C1112yes—
219C2×C42C23×C1111yescharacteristic
220#107—24no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8D4×C1112yes—
224#103—24no—
225#102—28no—
226#102—24no—
227#102—24no—
228C22⋊C8—21no—
229#97—21no—
230C4×C8—21no—
231C4×C8—21no—
232C4×C8—21no—
233C4×C8D4×C1112yes—
234C2×C11—22no—
235C2×C11—162no—
236C2×C11#200311yescharacteristic
237C2×C11#201511yescharacteristic
238C2×C11#201811yescharacteristic
239C24—41no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—82no—
245C2×D4—22no—
246C2×D4—22no—
247C2×D4—22no—
248C2×D4—44no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—42no—
253C2×D4—42no—
254C2×D4—82no—
255C22×C4—22no—
256C22×C4C2×D4×C1111yescharacteristic
257C22×C4C2×D4×C1111yescharacteristic
258C22×C4C11×#4111yescharacteristic
259M16—22no—
260M16—22no—
261M16—42no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—42no—
266C2×C8—41no—
267C4⋊C4—22no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C22⋊C4—41no—
278C42—41no—
279C42C2×D4×C1111yescharacteristic
280C42C2×D4×C1111yescharacteristic
281C42C2×D4×C1111yescharacteristic
282C42C2×D4×C1111yescharacteristic
283C11#1014911yescharacteristic, direct product factor, Sylow
284C23—42no—
285C23—82no—
286C23—82no—
287C23—82no—
288C23C11×#12111yescharacteristic
289Q8—42no—
290Q8—42no—
291Q8—82no—
292Q8—82no—
293D4—44no—
294D4—44no—
295D4—82no—
296D4—81no—
297D4—81no—
298D4—82no—
299D4—82no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—82no—
306C2×C4C11×#12011yescharacteristic
307C2×C4C11×#12011yescharacteristic
308C2×C4C11×#12011yescharacteristic
309C2×C4C11×#12111yescharacteristic
310C2×C4C11×#12111yescharacteristic
311C2×C4C11×#12711yescharacteristic
312C2×C4C11×#13512yes—
313C2×C4C11×#13712yes—
314C8—42no—
315C8—42no—
316C8—42no—
317C8—81no—
318C22—21no—
319C22—21no—
320C22—82no—
321C22—82no—
322C22—82no—
323C22—164no—
324C22C11×#39211yescharacteristic
325C22C11×#46412yes—
326C4—21no—
327C4—21no—
328C4—81no—
329C4—82no—
330C4—81no—
331C4C11×#45212yes—
332C4C11×#45412yes—
333C4C11×#47212yes—
334C4C11×#49511yescharacteristic
335C4C11×#49711yescharacteristic
336C2—22no—
337C2—162no—
338C2C11×#200311yescharacteristic
339C2C11×#201511yescharacteristic
340C2C11×#201811yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#127C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3230C2semidirect
4. C11×#1997C2semidirect
6. C11×#1493C2semidirect
7. C11×#1278C2semidirect
69. #10149C11direct (N × H)
114. #3230C2×C11semidirect
117. #1997C2×C11semidirect
119. #1493C2×C11semidirect
120. #1278C2×C11semidirect
283. C11#10149direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32302
C11×#31382
C2×C11×#4862
C11×#19972
C11×#15452
C11×#14932
C11×#12782
#1014911