Finite Group Databasebeta

← C11×#34950 #14612143

Subgroups — C11×#34950 #14612143

Order 2816.

1796 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2586C214yesmaximal
2C11×#2582C211yesmaximal, characteristic
3C11×#2567C212yesmaximal
4C11×#2551C211yesmaximal, characteristic
5C11×#2507C214yesmaximal
6C11×#2451C214yesmaximal
7C11×#2399C214yesmaximal
8C4×C11×C4⋊Q8C211yesmaximal, characteristic
9C4×C11×C4⋊Q8C214yesmaximal
10C11×#2295C214yesmaximal
11C42×Q8×C11C212yesmaximal
12C2×C11×C4⋊Q8C2214yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2212yes—
15C2×C4×Q8×C11C2212yes—
16C2×C4×Q8×C11C2212yes—
17C2×C4×Q8×C11C2214yes—
18C2×C4×Q8×C11C2212yes—
19C11×#398C2218yes—
20C11×#398C2214yes—
21C11×#398C2214yes—
22C11×#395C2214yes—
23C11×#395C2214yes—
24C11×#395C2218yes—
25C11×#391C2214yes—
26C11×#391C2214yes—
27C11×#391C2218yes—
28C11×#391C2212yes—
29C11×#389C2214yes—
30C11×#389C2214yes—
31C11×#389C2214yes—
32C11×#389C2214yes—
33C11×#389C2214yes—
34C11×#389C2218yes—
35C11×#387C2218yes—
36C11×#387C2218yes—
37C11×#384C2214yes—
38C11×#384C2211yescharacteristic
39C4×C11×C4⋊C4C2214yes—
40C4×C11×C4⋊C4C2218yes—
41C4×C11×C4⋊C4C2214yes—
42C4×C11×C4⋊C4C2212yes—
43C4×C11×C4⋊C4C2212yes—
44C4×C11×C4⋊C4C2212yes—
45C4×C11×C4⋊C4C2214yes—
46C4×C11×C4⋊C4C2214yes—
47C11×#376C2214yes—
48C43×C11C2211yescharacteristic
49C43×C11C2214yes—
50C22×Q8×C11C2314yes—
51C22×Q8×C11C2312yes—
52C22×Q8×C11C2312yes—
53C11×C4⋊Q8—216no—
54C11×C4⋊Q8—24no—
55C4×Q8×C11—28no—
56C4×Q8×C11—28no—
57C4×Q8×C11—44no—
58C4×Q8×C11—48no—
59C4×Q8×C11Q8116yescomplemented
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2314yes—
62C2×C11×C4⋊C4C2314yes—
63C2×C11×C4⋊C4C2314yes—
64C2×C11×C4⋊C4C2314yes—
65C2×C11×C4⋊C4C2318yes—
66C2×C11×C4⋊C4C2318yes—
67C2×C11×C4⋊C4C2318yes—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2314yes—
70C2×C11×C4⋊C4C2314yes—
71C2×C11×C4⋊C4C2314yes—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C42×C11C2312yes—
75C2×C42×C11C2314yes—
76C2×C42×C11C2314yes—
77C2×C42×C11C2314yes—
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2314yes—
80C2×C42×C11C2314yes—
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2314yes—
83C2×C42×C11C2312yes—
84C2×C42×C11C2314yes—
85C2×C42×C11C2311yescharacteristic
86C11×#95C2314yes—
87C11×#95C2318yes—
88C11×#95C2314yes—
89C11×#95C2314yes—
90C11×#95C2314yes—
91C11×#95C2314yes—
92C11×#95C2318yes—
93C11×#95C2318yes—
94C11×#95C2318yes—
95#34950C1111yesmaximal, characteristic, direct product factor, Sylow
96C2×Q8×C11—24no—
97C2×Q8×C11—24no—
98C2×Q8×C11—216no—
99C2×Q8×C11—24no—
100C2×Q8×C11—44no—
101C2×Q8×C11—42no—
102C2×Q8×C11—42no—
103C2×Q8×C11C2×Q818yes—
104C22×C4×C11C2414yes—
105C22×C4×C11C2414yes—
106C22×C4×C11C2411yescharacteristic
107C22×C4×C11C2414yes—
108C22×C4×C11C2414yes—
109C22×C4×C11C2412yes—
110C22×C4×C11C2414yes—
111C22×C4×C11C2414yes—
112C22×C4×C11C2411yescharacteristic
113C22×C4×C11C2412yes—
114C22×C4×C11C2411yescharacteristic
115C11×C4⋊C4—28no—
116C11×C4⋊C4—28no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—216no—
119C11×C4⋊C4—28no—
120C11×C4⋊C4—28no—
121C11×C4⋊C4—48no—
122C11×C4⋊C4—48no—
123C11×C4⋊C4—42no—
124C11×C4⋊C4—44no—
125C11×C4⋊C4—44no—
126C11×C4⋊C4C2×Q8116yes—
127C11×C4⋊C4C2×Q818yes—
128C11×C4⋊C4#4118yes—
129C42×C11—28no—
130C42×C11—24no—
131C42×C11—28no—
132C42×C11—28no—
133C42×C11—22no—
134C42×C11—28no—
135C42×C11—28no—
136C42×C11—41no—
137C42×C11—44no—
138C42×C11C2×Q8116yes—
139C42×C11C2×Q818yes—
140C42×C11#4114yes—
141#2586C2×C1114yes—
142#2582C2×C1111yescharacteristic
143#2567C2×C1112yes—
144#2551C2×C1111yescharacteristic
145#2507C2×C1114yes—
146#2451C2×C1114yes—
147#2399C2×C1114yes—
148C4×C4⋊Q8C2×C1114yes—
149C4×C4⋊Q8C2×C1111yescharacteristic
150#2295C2×C1114yes—
151C42×Q8C2×C1112yes—
152C23×C11C2511yescharacteristic
153Q8×C11—216no—
154Q8×C11—416no—
155Q8×C11—48no—
156C2×C4×C11—22no—
157C2×C4×C11—24no—
158C2×C4×C11—24no—
159C2×C4×C11—24no—
160C2×C4×C11—24no—
161C2×C4×C11—21no—
162C2×C4×C11—24no—
163C2×C4×C11—22no—
164C2×C4×C11—24no—
165C2×C4×C11—21no—
166C2×C4×C11—24no—
167C2×C4×C11—22no—
168C2×C4×C11—24no—
169C2×C4×C11—28no—
170C2×C4×C11—24no—
171C2×C4×C11—21no—
172C2×C4×C11—24no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11C22×Q814yes—
177C2×C4×C11C22×Q818yes—
178C2×C4×C11C22×Q818yes—
179C2×C4×C11C22×Q814yes—
180C2×C4×C11C22×Q814yes—
181C2×C4×C11C2×#4118yes—
182C2×C4×C11C2×#4112yes—
183C2×C4×C11C2×#4114yes—
184C2×C4×C11C2×#4114yes—
185C2×C4×C11H(5,𝔽2)12yes—
186C2×C4⋊Q8C22×C1111yescharacteristic
187C2×C4⋊Q8C22×C1114yes—
188C2×C4×Q8C22×C1112yes—
189C2×C4×Q8C22×C1112yes—
190C2×C4×Q8C22×C1114yes—
191C2×C4×Q8C22×C1112yes—
192C2×C4×Q8C22×C1112yes—
193#398C22×C1114yes—
194#398C22×C1118yes—
195#398C22×C1114yes—
196#395C22×C1118yes—
197#395C22×C1114yes—
198#395C22×C1114yes—
199#391C22×C1112yes—
200#391C22×C1118yes—
201#391C22×C1114yes—
202#391C22×C1114yes—
203#389C22×C1114yes—
204#389C22×C1114yes—
205#389C22×C1118yes—
206#389C22×C1114yes—
207#389C22×C1114yes—
208#389C22×C1114yes—
209#387C22×C1118yes—
210#387C22×C1118yes—
211#384C22×C1114yes—
212#384C22×C1111yescharacteristic
213C4×C4⋊C4C22×C1112yes—
214C4×C4⋊C4C22×C1114yes—
215C4×C4⋊C4C22×C1118yes—
216C4×C4⋊C4C22×C1112yes—
217C4×C4⋊C4C22×C1114yes—
218C4×C4⋊C4C22×C1114yes—
219C4×C4⋊C4C22×C1114yes—
220C4×C4⋊C4C22×C1112yes—
221#376C22×C1114yes—
222C43C22×C1111yescharacteristic
223C43C22×C1114yes—
224C22×C11C23×Q812yes—
225C22×C11C22×#4111yescharacteristic
226C22×C11C22×#4112yes—
227C22×C11C2×H(5,𝔽2)11yescharacteristic
228C22×C11#58511yescharacteristic
229C4×C11—28no—
230C4×C11—22no—
231C4×C11—24no—
232C4×C11—28no—
233C4×C11—28no—
234C4×C11—44no—
235C4×C11—44no—
236C4×C11—41no—
237C4×C11—44no—
238C4×C11#53318yes—
239C4×C11Q8214yes—
240C22×Q8C23×C1114yes—
241C22×Q8C23×C1112yes—
242C22×Q8C23×C1112yes—
243C4⋊Q8—216no—
244C4⋊Q8—24no—
245C4×Q8—28no—
246C4×Q8—28no—
247C4×Q8—48no—
248C4×Q8—44no—
249C4×Q8Q8×C11116yescomplemented
250C2×C4⋊C4C23×C1112yes—
251C2×C4⋊C4C23×C1114yes—
252C2×C4⋊C4C23×C1114yes—
253C2×C4⋊C4C23×C1114yes—
254C2×C4⋊C4C23×C1114yes—
255C2×C4⋊C4C23×C1118yes—
256C2×C4⋊C4C23×C1118yes—
257C2×C4⋊C4C23×C1112yes—
258C2×C4⋊C4C23×C1114yes—
259C2×C4⋊C4C23×C1114yes—
260C2×C4⋊C4C23×C1118yes—
261C2×C4⋊C4C23×C1114yes—
262C2×C4⋊C4C23×C1112yes—
263C2×C4⋊C4C23×C1112yes—
264C2×C42C23×C1114yes—
265C2×C42C23×C1111yescharacteristic
266C2×C42C23×C1114yes—
267C2×C42C23×C1112yes—
268C2×C42C23×C1114yes—
269C2×C42C23×C1114yes—
270C2×C42C23×C1114yes—
271C2×C42C23×C1111yescharacteristic
272C2×C42C23×C1114yes—
273C2×C42C23×C1112yes—
274C2×C42C23×C1114yes—
275C2×C42C23×C1111yescharacteristic
276#95C23×C1114yes—
277#95C23×C1118yes—
278#95C23×C1114yes—
279#95C23×C1114yes—
280#95C23×C1114yes—
281#95C23×C1114yes—
282#95C23×C1118yes—
283#95C23×C1118yes—
284#95C23×C1118yes—
285C2×C11C2×#53312yes—
286C2×C11#346011yescharacteristic
287C2×C11C2×Q8211yescharacteristic
288C2×C11Q8×#4112yes—
289C2×C11#348111yescharacteristic
290C2×Q8—24no—
291C2×Q8—24no—
292C2×Q8—216no—
293C2×Q8—24no—
294C2×Q8—44no—
295C2×Q8—42no—
296C2×Q8—42no—
297C2×Q8C2×Q8×C1118yes—
298C22×C4C24×C1114yes—
299C22×C4C24×C1114yes—
300C22×C4C24×C1111yescharacteristic
301C22×C4C24×C1114yes—
302C22×C4C24×C1114yes—
303C22×C4C24×C1112yes—
304C22×C4C24×C1114yes—
305C22×C4C24×C1114yes—
306C22×C4C24×C1111yescharacteristic
307C22×C4C24×C1111yescharacteristic
308C22×C4C24×C1112yes—
309C4⋊C4—28no—
310C4⋊C4—28no—
311C4⋊C4—24no—
312C4⋊C4—216no—
313C4⋊C4—28no—
314C4⋊C4—28no—
315C4⋊C4—48no—
316C4⋊C4—42no—
317C4⋊C4—44no—
318C4⋊C4—44no—
319C4⋊C4—48no—
320C4⋊C4C2×Q8×C11116yes—
321C4⋊C4C2×Q8×C1118yes—
322C4⋊C4C11×#4118yes—
323C42—28no—
324C42—24no—
325C42—28no—
326C42—28no—
327C42—22no—
328C42—28no—
329C42—28no—
330C42—41no—
331C42—44no—
332C42C2×Q8×C11116yes—
333C42C2×Q8×C1118yes—
334C42C11×#4114yes—
335C11#3495011yescharacteristic, direct product factor, Sylow
336C23C25×C1111yescharacteristic
337Q8—216no—
338Q8—416no—
339Q8—48no—
340C2×C4—22no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—21no—
346C2×C4—24no—
347C2×C4—22no—
348C2×C4—24no—
349C2×C4—21no—
350C2×C4—24no—
351C2×C4—22no—
352C2×C4—24no—
353C2×C4—28no—
354C2×C4—24no—
355C2×C4—21no—
356C2×C4—24no—
357C2×C4—24no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4C22×Q8×C1114yes—
361C2×C4C22×Q8×C1118yes—
362C2×C4C22×Q8×C1118yes—
363C2×C4C22×Q8×C1114yes—
364C2×C4C22×Q8×C1114yes—
365C2×C4C2×C11×#4118yes—
366C2×C4C2×C11×#4112yes—
367C2×C4C2×C11×#4114yes—
368C2×C4C2×C11×#4114yes—
369C2×C4C11×H(5,𝔽2)12yes—
370C22C23×Q8×C1112yes—
371C22C22×C11×#4111yescharacteristic
372C22C22×C11×#4112yes—
373C22C2×C11×H(5,𝔽2)11yescharacteristic
374C22C11×#58511yescharacteristic
375C4—28no—
376C4—22no—
377C4—24no—
378C4—28no—
379C4—28no—
380C4—44no—
381C4—44no—
382C4—44no—
383C4—41no—
384C4C11×#53318yes—
385C4Q82×C1114yes—
386C2C2×C11×#53312yes—
387C2C11×#346011yescharacteristic
388C2C2×Q82×C1111yescharacteristic
389C2Q8×C11×#4112yes—
390C2C11×#348111yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutator, Frattini, cosocleC23C25×C11
socle, prime radicalC23×C11C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
59. C4×Q8×C11Q8semidirect
95. #34950C11direct (N × H)
249. C4×Q8Q8×C11semidirect
335. C11#34950direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25862
C11×#25822
C11×#25672
C11×#25512
C11×#25072
C11×#24512
C11×#23992
C4×C11×C4⋊Q82
C11×#22952
C42×Q8×C112
#3495011