Finite Group Databasebeta

← C11×#10182 #14587375

Subgroups — C11×#10182 #14587375

Order 2816.

508 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3209C211yesmaximal, characteristic, complemented
2C11×#3077C211yesmaximal, characteristic
3C2×C11×#476C211yesmaximal, characteristic
4C11×#1549C211yesmaximal, characteristic, complemented
5C11×#1481C211yesmaximal, characteristic, complemented
6C11×#1460C211yesmaximal, characteristic
7C11×#1301C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C11×#494—21no—
12C11×#487—21no—
13C11×#478—22no—
14C11×#476—22no—
15C11×#476—21no—
16C11×#476—22no—
17C11×#474—21no—
18C11×#462—22no—
19C11×#451—22no—
20C11×#431C2211yescharacteristic
21C11×#431C2211yescharacteristic
22C11×#428—21no—
23C2×C11×#106—21no—
24C11×#423C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C11×#418—21no—
27C2×C11×#102—21no—
28C11×#332—22no—
29C11×Q8⋊C8—22no—
30C11×#323—22no—
31C22×Q8×C11—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C2×C11×Q16—24no—
35C2×C11×M16—21no—
36C22×C8×C11—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8D411yescharacteristic
41C11×C4⋊Q8D412yes—
42C11×C4⋊Q8D411yescharacteristic
43C11×#125—21no—
44C11×C22⋊Q8—21no—
45C11×C22⋊Q8—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C11×#117—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C22⋊C4—21no—
57C2×C42×C11C2311yescharacteristic
58C11×#107—22no—
59C11×#106—24no—
60C11×#106—22no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8D412yes—
66C11×C4⋊C8D412yes—
67C11×#103—24no—
68C11×#102—24no—
69C11×#102—22no—
70C11×#102—22no—
71C11×C22⋊C8—21no—
72C11×C22⋊C8D412yes—
73C4×C8×C11—21no—
74C4×C8×C11—21no—
75#10182C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11—21no—
77C2×Q8×C11—22no—
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—41no—
81C2×Q8×C11—82no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11Q1612yescomplemented
88C22×C4×C11—21no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—82no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C11×Q16—84no—
97C11×M16—41no—
98C11×M16—41no—
99C2×C8×C11—22no—
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11—41no—
103C2×C8×C11—41no—
104C2×C8×C11—41no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C42×C11—41no—
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125#3209C2×C1111yescharacteristic, complemented
126#3077C2×C1111yescharacteristic
127C2×#476C2×C1111yescharacteristic
128#1549C2×C1111yescharacteristic, complemented
129#1481C2×C1111yescharacteristic, complemented
130#1460C2×C1111yescharacteristic
131#1301C2×C1111yescharacteristic, complemented
132C23×C11—22no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—81no—
136C23×C11—81no—
137C23×C11#12111yescharacteristic
138Q8×C11—42no—
139Q8×C11—44no—
140Q8×C11—42no—
141Q8×C11—82no—
142D4×C11—22no—
143D4×C11—22no—
144D4×C11—41no—
145D4×C11—41no—
146C2×C4×C11—22no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—82no—
153C2×C4×C11—82no—
154C2×C4×C11—82no—
155C2×C4×C11—81no—
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12711yescharacteristic
162C2×C4×C11C2×Q1611yescharacteristic
163C2×C4×C11#13511yescharacteristic
164C2×C4×C11#13711yescharacteristic
165C2×C4×C11#13711yescharacteristic
166C8×C11—42no—
167C8×C11—42no—
168C8×C11—42no—
169C8×C11—81no—
170#533C22×C1111yescharacteristic
171C2×C4⋊Q8C22×C1111yescharacteristic
172C2×C4×D4C22×C1111yescharacteristic
173#494—21no—
174#487—21no—
175#478—22no—
176#476—21no—
177#476—22no—
178#476—22no—
179#474—21no—
180#462—22no—
181#451—22no—
182#431C22×C1111yescharacteristic
183#431C22×C1111yescharacteristic
184#428—21no—
185C2×#106—21no—
186#423C22×C1111yescharacteristic
187C2×C4⋊C8C22×C1111yescharacteristic
188#418—21no—
189C2×#102—21no—
190#332—22no—
191Q8⋊C8—22no—
192#323—22no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—42no—
196C22×C11—82no—
197C22×C11—82no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11#39211yescharacteristic
201C22×C11#46711yescharacteristic
202C22×C11#47011yescharacteristic
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—82no—
207C4×C11—81no—
208C4×C11—81no—
209C4×C11—81no—
210C4×C11#45111yescharacteristic
211C4×C11#45111yescharacteristic
212C4×C11#45211yescharacteristic
213C4×C11#45211yescharacteristic
214C4×C11#47112yes—
215C22×Q8—21no—
216C22×D4D4×C1111yescharacteristic
217C23×C4—21no—
218C2×Q16—24no—
219C2×M16—21no—
220C22×C8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8D4×C1112yes—
225C4⋊Q8D4×C1111yescharacteristic
226C4⋊Q8D4×C1111yescharacteristic
227#125—21no—
228C22⋊Q8—21no—
229C22⋊Q8—21no—
230C4×Q8—21no—
231C4×Q8—21no—
232C4×D4—21no—
233C4×D4—21no—
234C4×D4—21no—
235C4×D4—21no—
236#117—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4D4×C1111yescharacteristic
240C2×C22⋊C4—21no—
241C2×C42C23×C1111yescharacteristic
242#107—22no—
243#106—24no—
244#106—22no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8D4×C1112yes—
250C4⋊C8D4×C1112yes—
251#103—24no—
252#102—24no—
253#102—22no—
254#102—22no—
255C22⋊C8—21no—
256C22⋊C8D4×C1112yes—
257C4×C8—21no—
258C4×C8—21no—
259C2×C11—21no—
260C2×C11—21no—
261C2×C11—82no—
262C2×C11#200111yescharacteristic
263C2×C11#200811yescharacteristic
264C2×C11#201911yescharacteristic
265C24—21no—
266C2×Q8—22no—
267C2×Q8—21no—
268C2×Q8—21no—
269C2×Q8—41no—
270C2×Q8—82no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4C11×Q1612yescomplemented
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—82no—
282C22×C4C2×D4×C1111yescharacteristic
283C22×C4C2×D4×C1111yescharacteristic
284C22×C4C11×#4111yescharacteristic
285Q16—84no—
286M16—41no—
287M16—41no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C42—41no—
310C42C2×D4×C1111yescharacteristic
311C42C2×D4×C1111yescharacteristic
312C42C2×D4×C1111yescharacteristic
313C42C2×D4×C1111yescharacteristic
314C11#1018211yescharacteristic, direct product factor, Sylow
315C23—22no—
316C23—41no—
317C23—41no—
318C23—81no—
319C23—81no—
320C23C11×#12111yescharacteristic
321Q8—42no—
322Q8—44no—
323Q8—42no—
324Q8—82no—
325D4—22no—
326D4—22no—
327D4—41no—
328D4—41no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4—81no—
339C2×C4C11×#12011yescharacteristic
340C2×C4C11×#12011yescharacteristic
341C2×C4C11×#12011yescharacteristic
342C2×C4C11×#12111yescharacteristic
343C2×C4C11×#12111yescharacteristic
344C2×C4C11×#12711yescharacteristic
345C2×C4C2×C11×Q1611yescharacteristic
346C2×C4C11×#13511yescharacteristic
347C2×C4C11×#13711yescharacteristic
348C2×C4C11×#13711yescharacteristic
349C8—42no—
350C8—42no—
351C8—42no—
352C8—81no—
353C22—21no—
354C22—21no—
355C22—42no—
356C22—82no—
357C22—82no—
358C22—81no—
359C22—81no—
360C22C11×#39211yescharacteristic
361C22C11×#46711yescharacteristic
362C22C11×#47011yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—81no—
368C4—81no—
369C4—81no—
370C4C11×#45111yescharacteristic
371C4C11×#45111yescharacteristic
372C4C11×#45211yescharacteristic
373C4C11×#45211yescharacteristic
374C4C11×#47112yes—
375C2—21no—
376C2—21no—
377C2—82no—
378C2C11×#200111yescharacteristic
379C2C11×#200811yescharacteristic
380C2C11×#201911yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC22×D4×C11D4
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×#3209C2semidirect
4. C11×#1549C2semidirect
5. C11×#1481C2semidirect
7. C11×#1301C2semidirect
75. #10182C11direct (N × H)
87. C2×D4×C11Q16semidirect
125. #3209C2×C11semidirect
128. #1549C2×C11semidirect
129. #1481C2×C11semidirect
131. #1301C2×C11semidirect
276. C2×D4C11×Q16semidirect
314. C11#10182direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32092
C11×#30772
C2×C11×#4762
C11×#15492
C11×#14812
C11×#14602
C11×#13012
#1018211