Finite Group Databasebeta

← C11×#11884 #14589077

Subgroups — C11×#11884 #14589077

Order 2816.

510 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 114 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×#2543C211yesmaximal, characteristic
2C11×#1800C211yesmaximal, characteristic, complemented
3C11×#1459C211yesmaximal, characteristic, complemented
4C11×#1346C212yesmaximal, complemented
5C11×#1345C212yesmaximal, complemented
6C2×C11×#121—21no—
7C2×C11×#121C411yescharacteristic
8C2×C4×D4×C11C2211yescharacteristic
9C11×#423—21no—
10C2×C11×#100—21no—
11C2×C11×C22⋊C8—21no—
12C11×#398C2211yescharacteristic
13C11×#397C411yescharacteristic
14C11×#394C2211yescharacteristic
15C11×#392C411yescharacteristic
16C11×#388—21no—
17C11×#386—21no—
18C11×#386—21no—
19C2×C11×#95C411yescharacteristic
20C11×#343C2212yes—
21C11×#324C2212yes—
22C11×#323—21no—
23C22×D4×C11—21no—
24C22×D4×C11—21no—
25C22×D4×C11C2×C411yescharacteristic
26C22×D4×C11D411yescharacteristic
27C23×C4×C11—21no—
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C2×C11×M16—22no—
31C22×C8×C11—41no—
32C11×#121—42no—
33C11×#121—42no—
34C11×#121—41no—
35C11×#121—41no—
36C4×D4×C11—41no—
37C4×D4×C11—41no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C4⋊C4C2311yescharacteristic
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4C2×C411yescharacteristic
47C2×C11×C22⋊C4D411yescharacteristic
48C2×C42×C11D411yescharacteristic
49C11×C4⋊C8—41no—
50C11×C4⋊C8—41no—
51C11×#100—42no—
52C11×C22⋊C8—22no—
53C11×C22⋊C8—41no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95C2×C411yescharacteristic
58C11×#95C2×C411yescharacteristic
59#11884C1111yesmaximal, characteristic, direct product factor, Sylow
60C24×C11—21no—
61C24×C11C22⋊C411yescharacteristic
62C24×C11C22⋊C411yescharacteristic
63C2×D4×C11—41no—
64C2×D4×C11—41no—
65C2×D4×C11—42no—
66C2×D4×C11—41no—
67C2×D4×C11—42no—
68C2×D4×C11—42no—
69C2×D4×C11—42no—
70C2×D4×C11—42no—
71C2×D4×C11—81no—
72C2×D4×C11—81no—
73C2×D4×C11D812yes—
74C2×D4×C11SD1612yes—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—42no—
83C22×C4×C11—42no—
84C22×C4×C11—81no—
85C22×C4×C11—81no—
86C22×C4×C11—81no—
87C22×C4×C11C22⋊C411yescharacteristic
88C22×C4×C11C22⋊C411yescharacteristic
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C11×M16—42no—
93C11×M16—42no—
94C2×C8×C11—42no—
95C2×C8×C11—42no—
96C2×C8×C11—82no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—42no—
104C11×C22⋊C4—42no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—81no—
110C42×C11—21no—
111C42×C11—21no—
112#2543C2×C1111yescharacteristic
113#1800C2×C1111yescharacteristic, complemented
114#1459C2×C1111yescharacteristic, complemented
115#1346C2×C1112yescomplemented
116#1345C2×C1112yescomplemented
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11#10212yes—
133C23×C11#10212yes—
134C23×C11C2×C22⋊C411yescharacteristic
135D4×C11—42no—
136D4×C11—42no—
137D4×C11—84no—
138D4×C11—82no—
139D4×C11—84no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—22no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—81no—
160C2×C4×C11—81no—
161C2×C4×C11—81no—
162C2×C4×C11—84no—
163C2×C4×C11#9911yescharacteristic
164C2×C4×C11#9911yescharacteristic
165C2×C4×C11C2×D811yescharacteristic
166C2×C4×C11C2×SD1611yescharacteristic
167C8×C11—82no—
168C8×C11—82no—
169C2×#121—21no—
170C2×#121C4×C1111yescharacteristic
171C2×C4×D4C22×C1111yescharacteristic
172#423—21no—
173C2×#100—21no—
174C2×C22⋊C8—21no—
175#398C22×C1111yescharacteristic
176#397C4×C1111yescharacteristic
177#394C22×C1111yescharacteristic
178#392C4×C1111yescharacteristic
179#388—21no—
180#386—21no—
181#386—21no—
182C2×#95C4×C1111yescharacteristic
183#343C22×C1112yes—
184#324C22×C1112yes—
185#323—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—22no—
189C22×C11—22no—
190C22×C11—42no—
191C22×C11—42no—
192C22×C11—42no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11C2×#9911yescharacteristic
206C22×C11C2×#10211yescharacteristic
207C22×C11#42111yescharacteristic
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—42no—
213C4×C11—41no—
214C4×C11—41no—
215C4×C11—41no—
216C4×C11—81no—
217C4×C11—81no—
218C22×D4—21no—
219C22×D4—21no—
220C22×D4C2×C4×C1111yescharacteristic
221C22×D4D4×C1111yescharacteristic
222C23×C4—21no—
223C23×C4C2×C4×C1111yescharacteristic
224C23×C4D4×C1111yescharacteristic
225C2×M16—22no—
226C22×C8—41no—
227#121—42no—
228#121—42no—
229#121—41no—
230#121—41no—
231C4×D4—41no—
232C4×D4—41no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4C2×C4×C1111yescharacteristic
235C2×C4⋊C4C23×C1111yescharacteristic
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4C2×C4×C1111yescharacteristic
242C2×C22⋊C4D4×C1111yescharacteristic
243C2×C42D4×C1111yescharacteristic
244C4⋊C8—41no—
245C4⋊C8—41no—
246#100—42no—
247C22⋊C8—22no—
248C22⋊C8—41no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95C2×C4×C1111yescharacteristic
253#95C2×C4×C1111yescharacteristic
254C2×C11—21no—
255C2×C11—21no—
256C2×C11—42no—
257C2×C11—42no—
258C2×C11—161no—
259C2×C11#151911yescharacteristic
260C2×C11#212111yescharacteristic
261C2×C11#213211yescharacteristic
262C24—21no—
263C24C11×C22⋊C411yescharacteristic
264C24C11×C22⋊C411yescharacteristic
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—42no—
269C2×D4—42no—
270C2×D4—42no—
271C2×D4—42no—
272C2×D4—42no—
273C2×D4—81no—
274C2×D4—81no—
275C2×D4C11×D812yes—
276C2×D4C11×SD1612yes—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—81no—
287C22×C4—81no—
288C22×C4—81no—
289C22×C4C11×C22⋊C411yescharacteristic
290C22×C4C11×C22⋊C411yescharacteristic
291C22×C4C22×C4×C1111yescharacteristic
292C22×C4C2×D4×C1111yescharacteristic
293C22×C4C2×D4×C1111yescharacteristic
294M16—42no—
295M16—42no—
296C2×C8—42no—
297C2×C8—42no—
298C2×C8—82no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—42no—
306C22⋊C4—42no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—81no—
312C42—21no—
313C42—21no—
314C11#1188411yescharacteristic, direct product factor, Sylow
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23C11×#10212yes—
331C23C11×#10212yes—
332C23C2×C11×C22⋊C411yescharacteristic
333D4—42no—
334D4—42no—
335D4—84no—
336D4—82no—
337D4—84no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—84no—
361C2×C4C11×#9911yescharacteristic
362C2×C4C11×#9911yescharacteristic
363C2×C4C2×C11×D811yescharacteristic
364C2×C4C2×C11×SD1611yescharacteristic
365C8—82no—
366C8—82no—
367C22—21no—
368C22—21no—
369C22—22no—
370C22—22no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22C2×C11×#9911yescharacteristic
387C22C2×C11×#10211yescharacteristic
388C22C11×#42111yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—42no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—81no—
398C4—81no—
399C2—21no—
400C2—21no—
401C2—42no—
402C2—42no—
403C2—161no—
404C2C11×#151911yescharacteristic
405C2C11×#212111yescharacteristic
406C2C11×#213211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC11×#2543C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1800C2semidirect
3. C11×#1459C2semidirect
4. C11×#1346C2semidirect
5. C11×#1345C2semidirect
59. #11884C11direct (N × H)
113. #1800C2×C11semidirect
114. #1459C2×C11semidirect
115. #1346C2×C11semidirect
116. #1345C2×C11semidirect
314. C11#11884direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25432
C11×#18002
C11×#14592
C11×#13462
C11×#13452
#1188411