Finite Group Databasebeta

← C2×C11×#1672 #14596308

Subgroups — C2×C11×#1672 #14596308

Order 2816.

670 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#498C211yesmaximal, characteristic
2C2×C11×#477C211yesmaximal, characteristic
3C2×C11×#462C211yesmaximal, characteristic
4C2×C8×Q8×C11C211yesmaximal, characteristic
5C11×#1672C218yesmaximal, direct product factor
6C2×C11×#334C211yesmaximal, characteristic
7C2×C11×#333C211yesmaximal, characteristic
8C2×C11×#332C211yesmaximal, characteristic
9C22×C11×Q16—21no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C4×Q8×C11C2211yescharacteristic
13C11×#498—22no—
14C11×#498C2214yes—
15C11×#477—22no—
16C11×#477C2214yes—
17C11×#462—22no—
18C11×#462C2214yes—
19C8×Q8×C11—22no—
20C8×Q8×C11C2214yes—
21C2×C11×#107—21no—
22C2×C11×#106—21no—
23C2×C11×#106—21no—
24C2×C11×C4⋊C8—21no—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×#103—21no—
29C2×C11×#103—21no—
30C2×C4×C8×C11—21no—
31C2×C4×C8×C11C2211yescharacteristic
32C11×#334C2214yes—
33C11×#333C2214yes—
34C11×#332C2214yes—
35C22×Q8×C11—21no—
36C22×Q8×C11—21no—
37C22×Q8×C11D411yescharacteristic
38C2×C11×Q16—24no—
39C2×C11×Q16—44no—
40C22×C8×C11—21no—
41C22×C8×C11—21no—
42C22×C8×C11—21no—
43C22×C8×C11D411yescharacteristic
44C22×C8×C11D411yescharacteristic
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8C2312yes—
52C11×C4⋊Q8C2312yes—
53C4×Q8×C11—21no—
54C4×Q8×C11—21no—
55C4×Q8×C11D412yes—
56C4×Q8×C11C2312yes—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C42×C11—21no—
64C2×C42×C11C2311yescharacteristic
65C11×#107—24no—
66C11×#106—24no—
67C11×#106—24no—
68C11×C4⋊C8—24no—
69C11×C4⋊C8—21no—
70C11×C4⋊C8—21no—
71C11×C4⋊C8—21no—
72C11×C4⋊C8C2312yes—
73C11×C4⋊C8C2312yes—
74C11×C4⋊C8C2312yes—
75C11×#103—24no—
76C11×#103—24no—
77C4×C8×C11—24no—
78C4×C8×C11D412yes—
79C4×C8×C11C2312yes—
80C2×#1672C1111yesmaximal, characteristic, direct product factor, Sylow
81C2×Q8×C11—21no—
82C2×Q8×C11—22no—
83C2×Q8×C11—22no—
84C2×Q8×C11—22no—
85C2×Q8×C11—41no—
86C2×Q8×C11—41no—
87C2×Q8×C11—42no—
88C2×Q8×C11—42no—
89C2×Q8×C11—82no—
90C2×Q8×C11SD1614yes—
91C2×Q8×C11C2×D412yes—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11#4111yescharacteristic
99C11×Q16—48no—
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—42no—
105C2×C8×C11—42no—
106C2×C8×C11—42no—
107C2×C8×C11Q1614yescomplemented
108C2×C8×C11C2×D412yes—
109C2×C8×C11C2×D412yes—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4C2×D412yes—
122C42×C11—22no—
123C42×C11—22no—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11#4111yescharacteristic
127C42×C11C2411yescharacteristic
128C2×#498C2×C1111yescharacteristic
129C2×#477C2×C1111yescharacteristic
130C2×#462C2×C1111yescharacteristic
131C2×C8×Q8C2×C1111yescharacteristic
132#1672C2×C1118yesdirect product factor
133C2×#334C2×C1111yescharacteristic
134C2×#333C2×C1111yescharacteristic
135C2×#332C2×C1111yescharacteristic
136C23×C11#12111yescharacteristic
137Q8×C11—22no—
138Q8×C11—24no—
139Q8×C11—42no—
140Q8×C11—42no—
141Q8×C11—82no—
142Q8×C11—82no—
143Q8×C11—82no—
144Q8×C11C2×SD1614yes—
145C2×C4×C11—22no—
146C2×C4×C11—24no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—82no—
153C2×C4×C11—82no—
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11C2×SD1612yes—
158C2×C4×C11C2×Q1612yes—
159C2×C4×C11#13512yes—
160C2×C4×C11#13712yes—
161C2×C4×C11C22×D411yescharacteristic
162C2×C4×C11C22×D411yescharacteristic
163C2×C4×C11C2×#4111yescharacteristic
164C8×C11—22no—
165C8×C11—42no—
166C8×C11—42no—
167C8×C11—42no—
168C8×C11C2×Q1614yescomplemented
169C22×Q16—21no—
170C2×C4⋊Q8C22×C1111yescharacteristic
171C2×C4⋊Q8C22×C1111yescharacteristic
172C2×C4×Q8C22×C1111yescharacteristic
173#498—22no—
174#498C22×C1114yes—
175#477—22no—
176#477C22×C1114yes—
177#462—22no—
178#462C22×C1114yes—
179C8×Q8—22no—
180C8×Q8C22×C1114yes—
181C2×#107—21no—
182C2×#106—21no—
183C2×#106—21no—
184C2×C4⋊C8—21no—
185C2×C4⋊C8C22×C1111yescharacteristic
186C2×C4⋊C8C22×C1111yescharacteristic
187C2×C4⋊C8C22×C1111yescharacteristic
188C2×#103—21no—
189C2×#103—21no—
190C2×C4×C8—21no—
191C2×C4×C8C22×C1111yescharacteristic
192#334C22×C1114yes—
193#333C22×C1114yes—
194#332C22×C1114yes—
195C22×C11#46212yes—
196C22×C11#46512yes—
197C22×C11#47112yes—
198C22×C11C2×#12111yescharacteristic
199C4×C11—24no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—42no—
203C4×C11—82no—
204C4×C11—82no—
205C4×C11#46212yes—
206C4×C11#46512yes—
207C4×C11C22×SD1611yescharacteristic
208C4×C11C22×Q1611yescharacteristic
209C4×C11C2×#13511yescharacteristic
210C4×C11C2×#13711yescharacteristic
211C22×Q8—21no—
212C22×Q8—21no—
213C22×Q8D4×C1111yescharacteristic
214C2×Q16—24no—
215C2×Q16—44no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8D4×C1111yescharacteristic
220C22×C8D4×C1111yescharacteristic
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8C23×C1112yes—
228C4⋊Q8C23×C1112yes—
229C4×Q8—21no—
230C4×Q8—21no—
231C4×Q8D4×C1112yes—
232C4×Q8C23×C1112yes—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4D4×C1111yescharacteristic
239C2×C42—21no—
240C2×C42C23×C1111yescharacteristic
241#107—24no—
242#106—24no—
243#106—24no—
244C4⋊C8—24no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8C23×C1112yes—
249C4⋊C8C23×C1112yes—
250C4⋊C8C23×C1112yes—
251#103—24no—
252#103—24no—
253C4×C8—24no—
254C4×C8D4×C1112yes—
255C4×C8C23×C1112yes—
256C2×C11#167214yesdirect product factor
257C2×C11C2×#46211yescharacteristic
258C2×C11C2×#46511yescharacteristic
259C2×C11C2×#47111yescharacteristic
260C2×Q8—21no—
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—42no—
267C2×Q8—42no—
268C2×Q8—82no—
269C2×Q8C11×SD1614yes—
270C2×Q8C2×D4×C1112yes—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4C2×D4×C1111yescharacteristic
276C22×C4C2×D4×C1111yescharacteristic
277C22×C4C11×#4111yescharacteristic
278Q16—48no—
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—22no—
282C2×C8—22no—
283C2×C8—42no—
284C2×C8—42no—
285C2×C8—42no—
286C2×C8C11×Q1614yescomplemented
287C2×C8C2×D4×C1112yes—
288C2×C8C2×D4×C1112yes—
289C4⋊C4—22no—
290C4⋊C4—21no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4C2×D4×C1112yes—
301C42—22no—
302C42—22no—
303C42C2×D4×C1111yescharacteristic
304C42C2×D4×C1111yescharacteristic
305C42C11×#4111yescharacteristic
306C42C24×C1111yescharacteristic
307C11C2×#167211yescharacteristic, direct product factor, Sylow
308C23C11×#12111yescharacteristic
309Q8—22no—
310Q8—24no—
311Q8—42no—
312Q8—42no—
313Q8—82no—
314Q8—82no—
315Q8—82no—
316Q8C2×C11×SD1614yes—
317C2×C4—22no—
318C2×C4—24no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—82no—
325C2×C4—82no—
326C2×C4C11×#12111yescharacteristic
327C2×C4C11×#12111yescharacteristic
328C2×C4C11×#12111yescharacteristic
329C2×C4C2×C11×SD1612yes—
330C2×C4C2×C11×Q1612yes—
331C2×C4C11×#13512yes—
332C2×C4C11×#13712yes—
333C2×C4C22×D4×C1111yescharacteristic
334C2×C4C22×D4×C1111yescharacteristic
335C2×C4C2×C11×#4111yescharacteristic
336C8—22no—
337C8—42no—
338C8—42no—
339C8—42no—
340C8C2×C11×Q1614yescomplemented
341C22C11×#46212yes—
342C22C11×#46512yes—
343C22C11×#47112yes—
344C22C2×C11×#12111yescharacteristic
345C4—24no—
346C4—21no—
347C4—21no—
348C4—42no—
349C4—82no—
350C4—82no—
351C4C11×#46212yes—
352C4C11×#46512yes—
353C4C22×C11×SD1611yescharacteristic
354C4C22×C11×Q1611yescharacteristic
355C4C2×C11×#13511yescharacteristic
356C4C2×C11×#13711yescharacteristic
357C2C11×#167214yesdirect product factor
358C2C2×C11×#46211yescharacteristic
359C2C2×C11×#46511yescharacteristic
360C2C2×C11×#47111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11#121
commutator, Frattini, cosocleC42C24×C11
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
5. C11×#1672C2direct (N × H)
80. C2×#1672C11direct (N × H)
107. C2×C8×C11Q16semidirect
132. #1672C2×C11direct (N × H)
168. C8×C11C2×Q16semidirect
256. C2×C11#1672direct (N × H)
286. C2×C8C11×Q16semidirect
307. C11C2×#1672direct (N × H)
340. C8C2×C11×Q16semidirect
357. C2C11×#1672direct (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×#4772
C2×C11×#4622
C2×C8×Q8×C112
C11×#16722
C2×C11×#3342
C2×C11×#3332
C2×C11×#3322
C2×#167211