Finite Group Databasebeta

← C11×#10174 #14587367

Subgroups — C11×#10174 #14587367

Order 2816.

578 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3226C211yesmaximal, characteristic
2C2×C11×#500C211yesmaximal, characteristic, complemented
3C11×#3152C211yesmaximal, characteristic
4C11×#1966C211yesmaximal, characteristic, complemented
5C11×#1546C211yesmaximal, characteristic, complemented
6C11×#1492C211yesmaximal, characteristic
7C11×#1278C211yesmaximal, characteristic, complemented
8C2×C11×#137—22no—
9C11×#532C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C11×#500—22no—
13C11×#500—21no—
14C11×#500—22no—
15C11×#497—22no—
16C11×#494—21no—
17C11×#492—21no—
18C11×#486—21no—
19C11×#480—22no—
20C11×#474—22no—
21C11×#431C2211yescharacteristic
22C2×C11×#107—22no—
23C11×#423C2211yescharacteristic
24C2×C11×#101—22no—
25C4×C11×M16C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C11×#332—22no—
28C11×D4⋊C8—22no—
29C2×C11×#41—21no—
30C22×Q8×C11—21no—
31C22×Q8×C11—21no—
32C11×#137—44no—
33C11×#137—44no—
34C2×C11×Q16—24no—
35C2×C11×SD16—24no—
36C2×C11×M16—21no—
37C2×C11×M16D412yes—
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⋊Q8D411yescharacteristic
47C11×C4⋊Q8D412yes—
48C11×#127D411yescharacteristic
49C11×#124—21no—
50C11×#121—21no—
51C11×#121—21no—
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4D412yes—
58C2×C42×C11C2311yescharacteristic
59C11×#107—28no—
60C11×#107—24no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8D412yes—
64C11×#102—24no—
65C11×#101—44no—
66C11×C22⋊C8—21no—
67C11×#97—21no—
68C4×C8×C11—21no—
69C4×C8×C11—21no—
70C4×C8×C11—21no—
71C4×C8×C11D412yes—
72#10174C1111yesmaximal, characteristic, direct product factor, Sylow
73C11×#41—42no—
74C11×#41—42no—
75C2×Q8×C11—21no—
76C2×Q8×C11—22no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—42no—
81C2×Q8×C11—42no—
82C2×Q8×C11—42no—
83C2×Q8×C11—42no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—41no—
88C22×C4×C11—22no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C11×Q16—48no—
95C11×SD16—48no—
96C11×M16—22no—
97C11×M16—42no—
98C11×M16D814yes—
99C2×C8×C11—24no—
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—41no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120#3226C2×C1111yescharacteristic
121C2×#500C2×C1111yescharacteristic, complemented
122#3152C2×C1111yescharacteristic
123#1966C2×C1111yescharacteristic, complemented
124#1546C2×C1111yescharacteristic, complemented
125#1492C2×C1111yescharacteristic
126#1278C2×C1111yescharacteristic, complemented
127C23×C11—41no—
128C23×C11#12111yescharacteristic
129Q8×C11—44no—
130Q8×C11—42no—
131Q8×C11—82no—
132Q8×C11—81no—
133Q8×C11—81no—
134Q8×C11—81no—
135Q8×C11—81no—
136D4×C11—42no—
137D4×C11—42no—
138D4×C11—42no—
139D4×C11—82no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—44no—
146C2×C4×C11—82no—
147C2×C4×C11—81no—
148C2×C4×C11—81no—
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12711yescharacteristic
155C2×C4×C11C2×D812yes—
156C2×C4×C11AGL(1,ℤ/8)12yes—
157C8×C11—24no—
158C8×C11—24no—
159C8×C11—42no—
160C8×C11—81no—
161C2×#137—22no—
162#532C22×C1111yescharacteristic
163C2×C4⋊Q8C22×C1111yescharacteristic
164C2×C4⋊Q8C22×C1111yescharacteristic
165#500—22no—
166#500—21no—
167#500—22no—
168#497—22no—
169#494—21no—
170#492—21no—
171#486—21no—
172#480—22no—
173#474—22no—
174#431C22×C1111yescharacteristic
175C2×#107—22no—
176#423C22×C1111yescharacteristic
177C2×#101—22no—
178C4×M16C22×C1111yescharacteristic
179C2×C4×C8C22×C1111yescharacteristic
180#332—22no—
181D4⋊C8—22no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11#39211yescharacteristic
188C22×C11#45912yes—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—82no—
192C4×C11—81no—
193C4×C11—82no—
194C4×C11#44712yes—
195C4×C11#45612yes—
196C4×C11#47312yes—
197C4×C11#49311yescharacteristic
198C4×C11#49611yescharacteristic
199C2×#41—21no—
200C22×Q8—21no—
201C22×Q8—21no—
202#137—44no—
203#137—44no—
204C2×Q16—24no—
205C2×SD16—24no—
206C2×M16—21no—
207C2×M16D4×C1112yes—
208C22×C8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8D4×C1112yes—
217C4⋊Q8D4×C1111yescharacteristic
218#127D4×C1111yescharacteristic
219#124—21no—
220#121—21no—
221#121—21no—
222C4×D4—21no—
223C4×D4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4D4×C1112yes—
228C2×C42C23×C1111yescharacteristic
229#107—28no—
230#107—24no—
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8D4×C1112yes—
234#102—24no—
235#101—44no—
236C22⋊C8—21no—
237#97—21no—
238C4×C8—21no—
239C4×C8—21no—
240C4×C8—21no—
241C4×C8D4×C1112yes—
242C2×C11—22no—
243C2×C11—161no—
244C2×C11#200511yescharacteristic
245C2×C11#201111yescharacteristic
246C2×C11#202011yescharacteristic
247#41—42no—
248#41—42no—
249C2×Q8—21no—
250C2×Q8—22no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8—42no—
255C2×Q8—42no—
256C2×Q8—42no—
257C2×Q8—42no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—41no—
262C22×C4—22no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4C2×D4×C1111yescharacteristic
266C22×C4C2×D4×C1111yescharacteristic
267C22×C4C11×#4111yescharacteristic
268Q16—48no—
269SD16—48no—
270M16—22no—
271M16—42no—
272M16C11×D814yes—
273C2×C8—24no—
274C2×C8—22no—
275C2×C8—22no—
276C2×C8—22no—
277C2×C8—41no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—21no—
282C4⋊C4—22no—
283C4⋊C4—21no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C42C2×D4×C1111yescharacteristic
291C42C2×D4×C1111yescharacteristic
292C42C2×D4×C1111yescharacteristic
293C42C2×D4×C1111yescharacteristic
294C11#1017411yescharacteristic, direct product factor, Sylow
295C23—41no—
296C23C11×#12111yescharacteristic
297Q8—44no—
298Q8—42no—
299Q8—81no—
300Q8—81no—
301Q8—81no—
302Q8—81no—
303Q8—82no—
304D4—42no—
305D4—42no—
306D4—42no—
307D4—82no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—44no—
314C2×C4—82no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4C11×#12011yescharacteristic
318C2×C4C11×#12011yescharacteristic
319C2×C4C11×#12011yescharacteristic
320C2×C4C11×#12111yescharacteristic
321C2×C4C11×#12111yescharacteristic
322C2×C4C11×#12711yescharacteristic
323C2×C4C2×C11×D812yes—
324C2×C4C11×AGL(1,ℤ/8)12yes—
325C8—24no—
326C8—24no—
327C8—42no—
328C8—81no—
329C22—21no—
330C22—21no—
331C22—81no—
332C22—81no—
333C22—81no—
334C22C11×#39211yescharacteristic
335C22C11×#45912yes—
336C4—21no—
337C4—21no—
338C4—82no—
339C4—81no—
340C4—82no—
341C4C11×#44712yes—
342C4C11×#45612yes—
343C4C11×#47312yes—
344C4C11×#49311yescharacteristic
345C4C11×#49611yescharacteristic
346C2—22no—
347C2—161no—
348C2C11×#200511yescharacteristic
349C2C11×#201111yescharacteristic
350C2C11×#202011yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#532C22
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
2. C2×C11×#500C2semidirect
4. C11×#1966C2semidirect
5. C11×#1546C2semidirect
7. C11×#1278C2semidirect
72. #10174C11direct (N × H)
121. C2×#500C2×C11semidirect
123. #1966C2×C11semidirect
124. #1546C2×C11semidirect
126. #1278C2×C11semidirect
294. C11#10174direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32262
C2×C11×#5002
C11×#31522
C11×#19662
C11×#15462
C11×#14922
C11×#12782
#1017411