Finite Group Databasebeta

← C11×#10093 #14587286

Subgroups — C11×#10093 #14587286

Order 2816.

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

normal subgroups only

This group has 496 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×#3234C211yesmaximal, characteristic
2C11×#3141C211yesmaximal, characteristic
3C11×#2660C211yesmaximal, characteristic, complemented
4C11×#1556C211yesmaximal, characteristic, complemented
5C11×#1528C211yesmaximal, characteristic, complemented
6C11×#1505C211yesmaximal, characteristic
7C11×#1300C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#125C2211yescharacteristic
11C11×#501—21no—
12C11×#490—21no—
13C11×#489—22no—
14C11×#487—21no—
15C11×#486—21no—
16C11×#481—21no—
17C11×#480—21no—
18C11×#478—22no—
19C11×#432C2211yescharacteristic
20C11×#432C2211yescharacteristic
21C11×#417—22no—
22C4×C11×M16C2211yescharacteristic
23C11×#398—22no—
24C11×#395—22no—
25C11×#384—21no—
26C11×#382—21no—
27C11×#376C2211yescharacteristic
28C11×#332—22no—
29C11×#330—22no—
30C11×#327—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C2×C11×M16—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8D411yescharacteristic
39C11×#127D411yescharacteristic
40C11×#125—21no—
41C11×#125—21no—
42C11×#125—21no—
43C11×#125—21no—
44C11×#124—21no—
45C11×#121—21no—
46C11×#121—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—24no—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C4⋊C4D412yes—
56C2×C42×C11—21no—
57C2×C42×C11C2311yescharacteristic
58C11×#107—22no—
59C11×#106—22no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8D412yes—
62C11×#103—24no—
63C11×#102—24no—
64C11×#102—22no—
65C11×#102—22no—
66C11×C22⋊C8—21no—
67C11×C22⋊C8—21no—
68C11×#97—21no—
69C11×#97—21no—
70C11×#97D412yes—
71C4×C8×C11—21no—
72C11×#95—24no—
73C11×#95—21no—
74C11×#95D412yes—
75#10093C1111yesmaximal, characteristic, direct product factor, Sylow
76C11×#41—44no—
77C2×Q8×C11—21no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—82no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—41no—
85C22×C4×C11—22no—
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11—21no—
89C22×C4×C11—41no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C11×M16—42no—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11—41no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—84no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C42×C11—24no—
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11#4111yescharacteristic
119#3234C2×C1111yescharacteristic
120#3141C2×C1111yescharacteristic
121#2660C2×C1111yescharacteristic, complemented
122#1556C2×C1111yescharacteristic, complemented
123#1528C2×C1111yescharacteristic, complemented
124#1505C2×C1111yescharacteristic
125#1300C2×C1111yescharacteristic, complemented
126C23×C11—41no—
127C23×C11#12011yescharacteristic
128Q8×C11—42no—
129Q8×C11—82no—
130Q8×C11—82no—
131D4×C11—42no—
132D4×C11—42no—
133D4×C11—81no—
134D4×C11—82no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—24no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11—44no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—82no—
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12711yescharacteristic
155C8×C11—42no—
156C8×C11—42no—
157C8×C11—81no—
158#532C22×C1111yescharacteristic
159C2×C4⋊Q8C22×C1111yescharacteristic
160C2×#125C22×C1111yescharacteristic
161#501—21no—
162#490—21no—
163#489—22no—
164#487—21no—
165#486—21no—
166#481—21no—
167#480—21no—
168#478—22no—
169#432C22×C1111yescharacteristic
170#432C22×C1111yescharacteristic
171#417—22no—
172C4×M16C22×C1111yescharacteristic
173#398—22no—
174#395—22no—
175#384—21no—
176#382—21no—
177#376C22×C1111yescharacteristic
178#332—22no—
179#330—22no—
180#327—22no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—81no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11#39211yescharacteristic
187C22×C11#45412yes—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—44no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11—82no—
198C4×C11#45612yes—
199C2×#41—21no—
200C22×Q8—21no—
201C2×M16—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8D4×C1111yescharacteristic
207#127D4×C1111yescharacteristic
208#125—21no—
209#125—21no—
210#125—21no—
211#125—21no—
212#124—21no—
213#121—21no—
214#121—21no—
215C4×D4—21no—
216C4×D4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—24no—
221C2×C4⋊C4D4×C1111yescharacteristic
222C2×C4⋊C4D4×C1111yescharacteristic
223C2×C4⋊C4D4×C1112yes—
224C2×C42—21no—
225C2×C42C23×C1111yescharacteristic
226#107—22no—
227#106—22no—
228C4⋊C8—21no—
229C4⋊C8D4×C1112yes—
230#103—24no—
231#102—24no—
232#102—22no—
233#102—22no—
234C22⋊C8—21no—
235C22⋊C8—21no—
236#97—21no—
237#97—21no—
238#97D4×C1112yes—
239C4×C8—21no—
240#95—24no—
241#95—21no—
242#95D4×C1112yes—
243C2×C11—22no—
244C2×C11—161no—
245C2×C11#200311yescharacteristic
246C2×C11#200511yescharacteristic
247C2×C11#200811yescharacteristic
248#41—44no—
249C2×Q8—21no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—82no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—41no—
257C22×C4—22no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—21no—
261C22×C4—41no—
262C22×C4C2×D4×C1111yescharacteristic
263C22×C4C2×D4×C1111yescharacteristic
264C22×C4C2×D4×C1111yescharacteristic
265M16—42no—
266C2×C8—22no—
267C2×C8—22no—
268C2×C8—41no—
269C4⋊C4—22no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—22no—
276C4⋊C4—21no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—84no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C42—24no—
287C42C2×D4×C1111yescharacteristic
288C42C2×D4×C1111yescharacteristic
289C42C2×D4×C1111yescharacteristic
290C42C11×#4111yescharacteristic
291C11#1009311yescharacteristic, direct product factor, Sylow
292C23—41no—
293C23C11×#12011yescharacteristic
294Q8—42no—
295Q8—82no—
296Q8—82no—
297D4—42no—
298D4—42no—
299D4—81no—
300D4—82no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—24no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—44no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—82no—
315C2×C4C11×#12011yescharacteristic
316C2×C4C11×#12011yescharacteristic
317C2×C4C11×#12111yescharacteristic
318C2×C4C11×#12111yescharacteristic
319C2×C4C11×#12111yescharacteristic
320C2×C4C11×#12711yescharacteristic
321C8—42no—
322C8—42no—
323C8—81no—
324C22—21no—
325C22—21no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22C11×#39211yescharacteristic
330C22C11×#45412yes—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—44no—
337C4—81no—
338C4—81no—
339C4—82no—
340C4—81no—
341C4C11×#45612yes—
342C2—22no—
343C2—161no—
344C2C11×#200311yescharacteristic
345C2C11×#200511yescharacteristic
346C2C11×#200811yescharacteristic
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
3. C11×#2660C2semidirect
4. C11×#1556C2semidirect
5. C11×#1528C2semidirect
7. C11×#1300C2semidirect
75. #10093C11direct (N × H)
121. #2660C2×C11semidirect
122. #1556C2×C11semidirect
123. #1528C2×C11semidirect
125. #1300C2×C11semidirect
291. C11#10093direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32342
C11×#31412
C11×#26602
C11×#15562
C11×#15282
C11×#15052
C11×#13002
#1009311