Finite Group Databasebeta

← C11×#10132 #14587325

Subgroups — C11×#10132 #14587325

Order 2816.

558 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3227C211yesmaximal, characteristic, complemented
2C11×#3213C211yesmaximal, characteristic
3C2×C11×#497C211yesmaximal, characteristic, complemented
4C11×#1556C211yesmaximal, characteristic, complemented
5C11×#1530C211yesmaximal, characteristic, complemented
6C11×#1469C211yesmaximal, characteristic, complemented
7C11×#1302C211yesmaximal, characteristic, complemented
8C22×C11×Q16—21no—
9C22×C11×SD16—21no—
10C11×#532C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×#124C2211yescharacteristic
13C11×#498—21no—
14C11×#497—22no—
15C11×#497—22no—
16C11×#496—21no—
17C11×#489—21no—
18C11×#486—21no—
19C11×#481—22no—
20C11×#476—22no—
21C11×#463—22no—
22C11×#448—21no—
23C11×#447—21no—
24C11×#432C2211yescharacteristic
25C11×#432C2211yescharacteristic
26C11×#431C2211yescharacteristic
27C2×C11×#97C2211yescharacteristic
28C11×#332—22no—
29C11×#329—22no—
30C11×#323—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C22×Q8×C11D411yescharacteristic
34C22×D4×C11D411yescharacteristic
35C2×C11×Q16—24no—
36C2×C11×Q16—44no—
37C2×C11×SD16—24no—
38C2×C11×SD16—22no—
39C2×C11×SD16—44no—
40C2×C11×D8—22no—
41C22×C8×C11—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8D411yescharacteristic
46C11×C4⋊Q8D412yes—
47C11×#127D411yescharacteristic
48C11×#124—21no—
49C11×#124—21no—
50C11×#124—21no—
51C11×#124—21no—
52C11×#124—21no—
53C11×#121—21no—
54C11×#121—21no—
55C4×D4×C11—21no—
56C4×D4×C11—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—21no—
61C2×C42×C11C2311yescharacteristic
62C11×#106—24no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8D412yes—
66C11×#103—22no—
67C11×#102—22no—
68C11×#102—24no—
69C11×C22⋊C8—21no—
70C11×C22⋊C8—21no—
71C11×C22⋊C8D412yes—
72C11×#97—21no—
73C11×#97—21no—
74C11×#97—21no—
75C11×#97D412yes—
76C4×C8×C11—21no—
77#10132C1111yesmaximal, characteristic, direct product factor, Sylow
78C24×C11—21no—
79C11×#41—82no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—22no—
83C2×Q8×C11—21no—
84C2×Q8×C11—42no—
85C2×Q8×C11—42no—
86C2×Q8×C11—42no—
87C2×Q8×C11—41no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—42no—
94C2×D4×C11—41no—
95C22×C4×C11—21no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11#4111yescharacteristic
101C11×Q16—48no—
102C11×SD16—48no—
103C11×SD16—82no—
104C11×D8—82no—
105C2×C8×C11—24no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—41no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126#3227C2×C1111yescharacteristic, complemented
127#3213C2×C1111yescharacteristic
128C2×#497C2×C1111yescharacteristic, complemented
129#1556C2×C1111yescharacteristic, complemented
130#1530C2×C1111yescharacteristic, complemented
131#1469C2×C1111yescharacteristic, complemented
132#1302C2×C1111yescharacteristic, complemented
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—42no—
136C23×C11—81no—
137C23×C11—81no—
138C23×C11#12111yescharacteristic
139Q8×C11—42no—
140Q8×C11—42no—
141Q8×C11—42no—
142Q8×C11—42no—
143Q8×C11—81no—
144Q8×C11—82no—
145D4×C11—42no—
146D4×C11—42no—
147D4×C11—42no—
148D4×C11—42no—
149D4×C11—81no—
150D4×C11—82no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—82no—
158C2×C4×C11—82no—
159C2×C4×C11—81no—
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12711yescharacteristic
166C8×C11—24no—
167C8×C11—42no—
168C8×C11—42no—
169C8×C11—81no—
170C22×Q16—21no—
171C22×SD16—21no—
172#532C22×C1111yescharacteristic
173C2×C4⋊Q8C22×C1111yescharacteristic
174C2×#124C22×C1111yescharacteristic
175#498—21no—
176#497—22no—
177#497—22no—
178#496—21no—
179#489—21no—
180#486—21no—
181#481—22no—
182#476—22no—
183#463—22no—
184#448—21no—
185#447—21no—
186#432C22×C1111yescharacteristic
187#432C22×C1111yescharacteristic
188#431C22×C1111yescharacteristic
189C2×#97C22×C1111yescharacteristic
190#332—22no—
191#329—22no—
192#323—22no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—162no—
202C22×C11#39211yescharacteristic
203C22×C11#47112yes—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—82no—
210C4×C11—81no—
211C4×C11—81no—
212C4×C11#45312yes—
213C2×#41—21no—
214C22×Q8—21no—
215C22×Q8D4×C1111yescharacteristic
216C22×D4D4×C1111yescharacteristic
217C2×Q16—24no—
218C2×Q16—44no—
219C2×SD16—24no—
220C2×SD16—22no—
221C2×SD16—44no—
222C2×D8—22no—
223C22×C8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8D4×C1112yes—
228C4⋊Q8D4×C1111yescharacteristic
229#127D4×C1111yescharacteristic
230#124—21no—
231#124—21no—
232#124—21no—
233#124—21no—
234#124—21no—
235#121—21no—
236#121—21no—
237C4×D4—21no—
238C4×D4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C42C23×C1111yescharacteristic
244#106—24no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8D4×C1112yes—
248#103—22no—
249#102—22no—
250#102—24no—
251C22⋊C8—21no—
252C22⋊C8—21no—
253C22⋊C8D4×C1112yes—
254#97—21no—
255#97—21no—
256#97—21no—
257#97D4×C1112yes—
258C4×C8—21no—
259C2×C11—22no—
260C2×C11—161no—
261C2×C11—161no—
262C2×C11#200211yescharacteristic
263C2×C11#200911yescharacteristic
264C2×C11#201911yescharacteristic
265C24—21no—
266#41—82no—
267C2×Q8—21no—
268C2×Q8—21no—
269C2×Q8—22no—
270C2×Q8—21no—
271C2×Q8—42no—
272C2×Q8—42no—
273C2×Q8—42no—
274C2×Q8—41no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—42no—
281C2×D4—41no—
282C22×C4—21no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4C2×D4×C1111yescharacteristic
286C22×C4C2×D4×C1111yescharacteristic
287C22×C4C11×#4111yescharacteristic
288Q16—48no—
289SD16—48no—
290SD16—82no—
291D8—82no—
292C2×C8—24no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—41no—
297C4⋊C4—21no—
298C4⋊C4—22no—
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C42C2×D4×C1111yescharacteristic
310C42C2×D4×C1111yescharacteristic
311C42C2×D4×C1111yescharacteristic
312C42C2×D4×C1111yescharacteristic
313C11#1013211yescharacteristic, direct product factor, Sylow
314C23—41no—
315C23—41no—
316C23—42no—
317C23—81no—
318C23—81no—
319C23C11×#12111yescharacteristic
320Q8—42no—
321Q8—42no—
322Q8—42no—
323Q8—42no—
324Q8—81no—
325Q8—82no—
326D4—42no—
327D4—42no—
328D4—42no—
329D4—42no—
330D4—81no—
331D4—82no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—82no—
339C2×C4—82no—
340C2×C4—81no—
341C2×C4C11×#12011yescharacteristic
342C2×C4C11×#12011yescharacteristic
343C2×C4C11×#12011yescharacteristic
344C2×C4C11×#12111yescharacteristic
345C2×C4C11×#12111yescharacteristic
346C2×C4C11×#12711yescharacteristic
347C8—24no—
348C8—42no—
349C8—42no—
350C8—81no—
351C22—21no—
352C22—21no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—162no—
360C22C11×#39211yescharacteristic
361C22C11×#47112yes—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—82no—
368C4—81no—
369C4—81no—
370C4C11×#45312yes—
371C2—22no—
372C2—161no—
373C2—161no—
374C2C11×#200211yescharacteristic
375C2C11×#200911yescharacteristic
376C2C11×#201911yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3213C2
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×#3227C2semidirect
3. C2×C11×#497C2semidirect
4. C11×#1556C2semidirect
5. C11×#1530C2semidirect
6. C11×#1469C2semidirect
7. C11×#1302C2semidirect
77. #10132C11direct (N × H)
126. #3227C2×C11semidirect
128. C2×#497C2×C11semidirect
129. #1556C2×C11semidirect
130. #1530C2×C11semidirect
131. #1469C2×C11semidirect
132. #1302C2×C11semidirect
313. C11#10132direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32272
C11×#32132
C2×C11×#4972
C11×#15562
C11×#15302
C11×#14692
C11×#13022
#1013211