Finite Group Databasebeta

← C11×#10092 #14587285

Subgroups — C11×#10092 #14587285

Order 2816.

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

normal subgroups only

This group has 534 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×#3213C211yesmaximal, characteristic
2C11×#3141C211yesmaximal, characteristic, complemented
3C11×#2640C211yesmaximal, characteristic, complemented
4C11×#1556C211yesmaximal, characteristic, complemented
5C11×#1527C211yesmaximal, characteristic, complemented
6C11×#1505C211yesmaximal, characteristic, complemented
7C11×#1300C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#124C2211yescharacteristic
11C11×#496—21no—
12C11×#489—21no—
13C11×#489—22no—
14C11×#487—21no—
15C11×#486—21no—
16C11×#463—22no—
17C11×#448—21no—
18C11×#447—21no—
19C11×#432C2211yescharacteristic
20C11×#432C2211yescharacteristic
21C11×#417—22no—
22C4×C11×M16C2211yescharacteristic
23C11×#397—22no—
24C11×#393—22no—
25C11×#391—21no—
26C11×#390—21no—
27C11×#376C2211yescharacteristic
28C11×#332—22no—
29C11×#329—22no—
30C11×#327—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C22×Q8×C11D411yescharacteristic
34C22×D4×C11D411yescharacteristic
35C2×C11×SD16—22no—
36C2×C11×D8—22no—
37C2×C11×M16—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8D411yescharacteristic
43C11×#127D411yescharacteristic
44C11×#124—21no—
45C11×#124—21no—
46C11×#124—21no—
47C11×#124—21no—
48C11×#124—21no—
49C11×#121—21no—
50C11×#121—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D412yes—
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—24no—
58C2×C42×C11—21no—
59C2×C42×C11C2311yescharacteristic
60C11×C4⋊C8—21no—
61C11×C4⋊C8D412yes—
62C11×#103—24no—
63C11×#103—22no—
64C11×#102—24no—
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#10092C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11—21no—
77C11×#41—44no—
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—42no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C2×Q8×C11—82no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—42no—
91C2×D4×C11—41no—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—41no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C11×SD16—82no—
100C11×D8—82no—
101C11×M16—42no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—41no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—84no—
118C42×C11—42no—
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11#4111yescharacteristic
123#3213C2×C1111yescharacteristic
124#3141C2×C1111yescharacteristic, complemented
125#2640C2×C1111yescharacteristic, complemented
126#1556C2×C1111yescharacteristic, complemented
127#1527C2×C1111yescharacteristic, complemented
128#1505C2×C1111yescharacteristic, complemented
129#1300C2×C1111yescharacteristic, complemented
130C23×C11—42no—
131C23×C11—42no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—42no—
135C23×C11#12011yescharacteristic
136Q8×C11—42no—
137Q8×C11—42no—
138Q8×C11—81no—
139Q8×C11—82no—
140Q8×C11—82no—
141D4×C11—42no—
142D4×C11—42no—
143D4×C11—42no—
144D4×C11—81no—
145D4×C11—81no—
146D4×C11—82no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—44no—
153C2×C4×C11—42no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—82no—
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12711yescharacteristic
165C8×C11—42no—
166C8×C11—42no—
167C8×C11—81no—
168#532C22×C1111yescharacteristic
169C2×C4⋊Q8C22×C1111yescharacteristic
170C2×#124C22×C1111yescharacteristic
171#496—21no—
172#489—21no—
173#489—22no—
174#487—21no—
175#486—21no—
176#463—22no—
177#448—21no—
178#447—21no—
179#432C22×C1111yescharacteristic
180#432C22×C1111yescharacteristic
181#417—22no—
182C4×M16C22×C1111yescharacteristic
183#397—22no—
184#393—22no—
185#391—21no—
186#390—21no—
187#376C22×C1111yescharacteristic
188#332—22no—
189#329—22no—
190#327—22no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—84no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11#39211yescharacteristic
201C22×C11#45412yes—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—82no—
208C4×C11—81no—
209C4×C11—81no—
210C4×C11—82no—
211C4×C11#45512yes—
212C2×#41—21no—
213C22×Q8—21no—
214C22×Q8D4×C1111yescharacteristic
215C22×D4D4×C1111yescharacteristic
216C2×SD16—22no—
217C2×D8—22no—
218C2×M16—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8D4×C1111yescharacteristic
224#127D4×C1111yescharacteristic
225#124—21no—
226#124—21no—
227#124—21no—
228#124—21no—
229#124—21no—
230#121—21no—
231#121—21no—
232C4×D4—21no—
233C4×D4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4D4×C1112yes—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—24no—
239C2×C42—21no—
240C2×C42C23×C1111yescharacteristic
241C4⋊C8—21no—
242C4⋊C8D4×C1112yes—
243#103—24no—
244#103—22no—
245#102—24no—
246#102—22no—
247C22⋊C8—21no—
248C22⋊C8—21no—
249#97—21no—
250#97—21no—
251#97D4×C1112yes—
252C4×C8—21no—
253#95—24no—
254#95—21no—
255#95D4×C1112yes—
256C2×C11—22no—
257C2×C11—161no—
258C2×C11—161no—
259C2×C11#200311yescharacteristic
260C2×C11#200411yescharacteristic
261C2×C11#200811yescharacteristic
262C24—21no—
263#41—44no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—21no—
267C2×Q8—42no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—82no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—42no—
277C2×D4—41no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—41no—
282C22×C4C2×D4×C1111yescharacteristic
283C22×C4C2×D4×C1111yescharacteristic
284C22×C4C2×D4×C1111yescharacteristic
285SD16—82no—
286D8—82no—
287M16—42no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—41no—
291C4⋊C4—22no—
292C4⋊C4—21no—
293C4⋊C4—22no—
294C4⋊C4—21no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—84no—
304C42—42no—
305C42C2×D4×C1111yescharacteristic
306C42C2×D4×C1111yescharacteristic
307C42C2×D4×C1111yescharacteristic
308C42C11×#4111yescharacteristic
309C11#1009211yescharacteristic, direct product factor, Sylow
310C23—42no—
311C23—42no—
312C23—41no—
313C23—41no—
314C23—42no—
315C23C11×#12011yescharacteristic
316Q8—42no—
317Q8—42no—
318Q8—81no—
319Q8—82no—
320Q8—82no—
321D4—42no—
322D4—42no—
323D4—42no—
324D4—81no—
325D4—81no—
326D4—82no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—44no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—82no—
339C2×C4C11×#12011yescharacteristic
340C2×C4C11×#12011yescharacteristic
341C2×C4C11×#12111yescharacteristic
342C2×C4C11×#12111yescharacteristic
343C2×C4C11×#12111yescharacteristic
344C2×C4C11×#12711yescharacteristic
345C8—42no—
346C8—42no—
347C8—81no—
348C22—21no—
349C22—21no—
350C22—84no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22C11×#39211yescharacteristic
358C22C11×#45412yes—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—82no—
365C4—81no—
366C4—81no—
367C4—82no—
368C4C11×#45512yes—
369C2—22no—
370C2—161no—
371C2—161no—
372C2C11×#200311yescharacteristic
373C2C11×#200411yescharacteristic
374C2C11×#200811yescharacteristic
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
2. C11×#3141C2semidirect
3. C11×#2640C2semidirect
4. C11×#1556C2semidirect
5. C11×#1527C2semidirect
6. C11×#1505C2semidirect
7. C11×#1300C2semidirect
75. #10092C11direct (N × H)
124. #3141C2×C11semidirect
125. #2640C2×C11semidirect
126. #1556C2×C11semidirect
127. #1527C2×C11semidirect
128. #1505C2×C11semidirect
129. #1300C2×C11semidirect
309. C11#10092direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32132
C11×#31412
C11×#26402
C11×#15562
C11×#15272
C11×#15052
C11×#13002
#1009211