Finite Group Databasebeta

← C11×#11872 #14589065

Subgroups — C11×#11872 #14589065

Order 2816.

372 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×#3060C211yesmaximal, characteristic
2C11×#2115C211yesmaximal, characteristic, complemented
3C11×#1813C211yesmaximal, characteristic, complemented
4C11×#1342C212yesmaximal, complemented
5C11×#1341C212yesmaximal, complemented
6C2×C11×#135C411yescharacteristic
7C2×C11×#131C2211yescharacteristic
8C11×#537—21no—
9C2×C11×M32—21no—
10C11×#470C411yescharacteristic
11C11×#470C2211yescharacteristic
12C11×#469C411yescharacteristic
13C11×#469C2211yescharacteristic
14C11×#465—21no—
15C11×#465—21no—
16C2×C11×#108—21no—
17C2×C11×#106C411yescharacteristic
18C11×#417—21no—
19C11×#413—21no—
20C11×#349—21no—
21C11×#349C2212yes—
22C11×#338C2212yes—
23C2×C11×#41—21no—
24C2×C11×#41D411yescharacteristic
25C11×#135—41no—
26C11×#135—41no—
27C2×C11×Q16C2×C411yescharacteristic
28C2×C11×SD16—21no—
29C2×C11×D8C2×C411yescharacteristic
30C11×#131—41no—
31C11×#131—41no—
32C2×C11×M16—22no—
33C2×C11×M16C2×C411yescharacteristic
34C2×C11×M16D411yescharacteristic
35C2×C11×M16C2311yescharacteristic
36C22×C8×C11C2×C411yescharacteristic
37C22×C8×C11D411yescharacteristic
38C22×C8×C11D411yescharacteristic
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—41no—
42C11×#121—21no—
43C11×#121—21no—
44C11×#121—41no—
45C11×#121—41no—
46C11×#121—41no—
47C2×C11×C4⋊C4—21no—
48C11×M32—22no—
49C11×M32—41no—
50C2×C11×C16—41no—
51C11×#108—41no—
52C11×#108—41no—
53C11×#106—21no—
54C11×#106C2×C411yescharacteristic
55C11×#106C2×C411yescharacteristic
56C11×#103—21no—
57C11×#103—21no—
58C11×#102—21no—
59C11×#102—21no—
60C11×#101—41no—
61C11×#100—41no—
62#11872C1111yesmaximal, characteristic, direct product factor, Sylow
63C11×#41—41no—
64C11×#41—41no—
65C11×#41—42no—
66C11×#41—42no—
67C2×Q8×C11—21no—
68C2×Q8×C11D811yescharacteristic
69C2×D4×C11—21no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11D811yescharacteristic
74C2×D4×C11SD1611yescharacteristic
75C2×D4×C11SD1611yescharacteristic
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C11×Q16—41no—
82C11×SD16—41no—
83C11×SD16—41no—
84C11×D8—41no—
85C11×M16—41no—
86C11×M16—41no—
87C11×M16—41no—
88C11×M16—42no—
89C11×M16—42no—
90C2×C8×C11—21no—
91C2×C8×C11—21no—
92C2×C8×C11—21no—
93C2×C8×C11—21no—
94C2×C8×C11—21no—
95C2×C8×C11—21no—
96C2×C8×C11—42no—
97C2×C8×C11C22⋊C411yescharacteristic
98C2×C8×C11C22⋊C411yescharacteristic
99C2×C8×C11C22×C411yescharacteristic
100C2×C8×C11C2×D411yescharacteristic
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C11×C16—42no—
111#3060C2×C1111yescharacteristic
112#2115C2×C1111yescharacteristic, complemented
113#1813C2×C1111yescharacteristic, complemented
114#1342C2×C1112yescomplemented
115#1341C2×C1112yescomplemented
116C23×C11—41no—
117C23×C11#10211yescharacteristic
118C23×C11#10211yescharacteristic
119C23×C11C2×SD1611yescharacteristic
120Q8×C11—41no—
121Q8×C11—41no—
122Q8×C11—41no—
123D4×C11—41no—
124D4×C11—41no—
125D4×C11—41no—
126D4×C11—41no—
127D4×C11—41no—
128D4×C11—82no—
129D4×C11—161no—
130D4×C11—161no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—82no—
141C2×C4×C11—161no—
142C2×C4×C11#10211yescharacteristic
143C2×C4×C11#10211yescharacteristic
144C2×C4×C11C2×C22⋊C411yescharacteristic
145C2×C4×C11C2×D811yescharacteristic
146C8×C11—21no—
147C8×C11—21no—
148C8×C11—21no—
149C8×C11—82no—
150C8×C11#9911yescharacteristic
151C8×C11#9911yescharacteristic
152C2×#135C4×C1111yescharacteristic
153C2×#131C22×C1111yescharacteristic
154#537—21no—
155C2×M32—21no—
156#470C4×C1111yescharacteristic
157#470C22×C1111yescharacteristic
158#469C4×C1111yescharacteristic
159#469C22×C1111yescharacteristic
160#465—21no—
161#465—21no—
162C2×#108—21no—
163C2×#106C4×C1111yescharacteristic
164#417—21no—
165#413—21no—
166#349—21no—
167#349C22×C1112yes—
168#338C22×C1112yes—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—81no—
176C22×C11—81no—
177C22×C11—81no—
178C22×C11C2×#10211yescharacteristic
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—81no—
183C4×C11—81no—
184C4×C11—81no—
185C4×C11C2×#9911yescharacteristic
186C4×C11#42111yescharacteristic
187C2×#41—21no—
188C2×#41D4×C1111yescharacteristic
189#135—41no—
190#135—41no—
191C2×Q16C2×C4×C1111yescharacteristic
192C2×SD16—21no—
193C2×D8C2×C4×C1111yescharacteristic
194#131—41no—
195#131—41no—
196C2×M16—22no—
197C2×M16C2×C4×C1111yescharacteristic
198C2×M16D4×C1111yescharacteristic
199C2×M16C23×C1111yescharacteristic
200C22×C8C2×C4×C1111yescharacteristic
201C22×C8D4×C1111yescharacteristic
202C22×C8D4×C1111yescharacteristic
203C22⋊Q8—21no—
204C22⋊Q8—21no—
205C22⋊Q8—41no—
206#121—21no—
207#121—21no—
208#121—41no—
209#121—41no—
210#121—41no—
211C2×C4⋊C4—21no—
212M32—22no—
213M32—41no—
214C2×C16—41no—
215#108—41no—
216#108—41no—
217#106—21no—
218#106C2×C4×C1111yescharacteristic
219#106C2×C4×C1111yescharacteristic
220#103—21no—
221#103—21no—
222#102—21no—
223#102—21no—
224#101—41no—
225#100—41no—
226C2×C11—21no—
227C2×C11—41no—
228C2×C11—41no—
229C2×C11—41no—
230C2×C11—161no—
231C2×C11#151911yescharacteristic
232#41—41no—
233#41—41no—
234#41—42no—
235#41—42no—
236C2×Q8—21no—
237C2×Q8C11×D811yescharacteristic
238C2×D4—21no—
239C2×D4—41no—
240C2×D4—41no—
241C2×D4—41no—
242C2×D4C11×D811yescharacteristic
243C2×D4C11×SD1611yescharacteristic
244C2×D4C11×SD1611yescharacteristic
245C22×C4—41no—
246C22×C4—41no—
247C22×C4C11×C22⋊C411yescharacteristic
248C22×C4C11×C22⋊C411yescharacteristic
249C22×C4C2×D4×C1111yescharacteristic
250Q16—41no—
251SD16—41no—
252SD16—41no—
253D8—41no—
254M16—41no—
255M16—41no—
256M16—41no—
257M16—42no—
258M16—42no—
259C2×C8—21no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—42no—
266C2×C8C11×C22⋊C411yescharacteristic
267C2×C8C11×C22⋊C411yescharacteristic
268C2×C8C22×C4×C1111yescharacteristic
269C2×C8C2×D4×C1111yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C16—42no—
280C11#1187211yescharacteristic, direct product factor, Sylow
281C23—41no—
282C23C11×#10211yescharacteristic
283C23C11×#10211yescharacteristic
284C23C2×C11×SD1611yescharacteristic
285Q8—41no—
286Q8—41no—
287Q8—41no—
288D4—41no—
289D4—41no—
290D4—41no—
291D4—41no—
292D4—41no—
293D4—82no—
294D4—161no—
295D4—161no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—82no—
306C2×C4—161no—
307C2×C4C11×#10211yescharacteristic
308C2×C4C11×#10211yescharacteristic
309C2×C4C2×C11×C22⋊C411yescharacteristic
310C2×C4C2×C11×D811yescharacteristic
311C8—21no—
312C8—21no—
313C8—21no—
314C8—82no—
315C8C11×#9911yescharacteristic
316C8C11×#9911yescharacteristic
317C22—21no—
318C22—21no—
319C22—21no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—81no—
324C22—81no—
325C22—81no—
326C22C2×C11×#10211yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—81no—
331C4—81no—
332C4—81no—
333C4C2×C11×#9911yescharacteristic
334C4C11×#42111yescharacteristic
335C2—21no—
336C2—41no—
337C2—41no—
338C2—41no—
339C2—161no—
340C2C11×#151911yescharacteristic
subgroupG/H
center, socleC2×C11#1519
commutatorC2×C8C22×C4×C11
Frattini, cosocleC2×M16C23×C11
prime radicalC11×#3060C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C2×C11×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2115C2semidirect
3. C11×#1813C2semidirect
4. C11×#1342C2semidirect
5. C11×#1341C2semidirect
62. #11872C11direct (N × H)
112. #2115C2×C11semidirect
113. #1813C2×C11semidirect
114. #1342C2×C11semidirect
115. #1341C2×C11semidirect
280. C11#11872direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30602
C11×#21152
C11×#18132
C11×#13422
C11×#13412
#1187211