Finite Group Databasebeta

← C11×#19435 #14596628

Subgroups — C11×#19435 #14596628

Order 2816.

582 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3209C211yesmaximal, characteristic
2C11×#3078C211yesmaximal, characteristic
3C2×C11×#475C211yesmaximal, characteristic
4C11×#2983C211yesmaximal, characteristic
5C11×#1704C214yesmaximal, complemented
6C11×#1690C214yesmaximal, complemented
7C11×#1570C211yesmaximal, characteristic
8C11×#1549C211yesmaximal, characteristic
9C11×#1542C211yesmaximal, characteristic
10C11×#533C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C4×Q8×C11C2211yescharacteristic
13C11×#494C2212yes—
14C11×#487C2212yes—
15C11×#479—22no—
16C11×#477C2212yes—
17C11×#475—22no—
18C11×#475C2212yes—
19C11×#475C2214yes—
20C11×#462—22no—
21C11×#451—22no—
22C11×#446—22no—
23C11×#446C2214yes—
24C11×#432—22no—
25C11×#431C2211yescharacteristic
26C11×#431C2211yescharacteristic
27C11×#428—21no—
28C2×C11×#106—21no—
29C11×#423C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C11×#419—21no—
32C2×C11×#103—21no—
33C11×#334C2214yes—
34C11×#333C2212yes—
35C11×#332C2212yes—
36C11×#332C2214yes—
37C22×Q8×C11—21no—
38C22×Q8×C11D411yescharacteristic
39C2×C11×Q16—24no—
40C2×C11×M16—21no—
41C22×C8×C11—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8C2311yescharacteristic
46C11×C4⋊Q8C2312yes—
47C11×C4⋊Q8C2311yescharacteristic
48C11×#125—21no—
49C11×C22⋊Q8—21no—
50C11×C22⋊Q8—21no—
51C4×Q8×C11—21no—
52C4×Q8×C11—21no—
53C4×Q8×C11—21no—
54C4×Q8×C11—21no—
55C4×Q8×C11D412yes—
56C4×Q8×C11C2312yes—
57C11×#117—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64C11×#107—22no—
65C11×#106—24no—
66C11×#106—22no—
67C11×C4⋊C8—24no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8—21no—
70C11×C4⋊C8D412yes—
71C11×C4⋊C8C2312yes—
72C11×C4⋊C8C2312yes—
73C11×C4⋊C8C2312yes—
74C11×#103—24no—
75C11×#103—22no—
76C11×#103—22no—
77C11×#103—24no—
78C11×C22⋊C8—21no—
79C11×C22⋊C8D412yes—
80C11×#97—24no—
81C4×C8×C11—21no—
82C4×C8×C11C2312yes—
83#19435C1111yesmaximal, characteristic, direct product factor, Sylow
84C2×Q8×C11—21no—
85C2×Q8×C11—22no—
86C2×Q8×C11—22no—
87C2×Q8×C11—22no—
88C2×Q8×C11—21no—
89C2×Q8×C11—21no—
90C2×Q8×C11—41no—
91C2×Q8×C11—82no—
92C2×Q8×C11C2×D412yes—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—41no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11#4111yescharacteristic
99C11×Q16—84no—
100C11×M16—42no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—42no—
105C2×C8×C11C2×D414yes—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4C2×D412yes—
120C11×C22⋊C4—41no—
121C42×C11—22no—
122C42×C11—22no—
123C42×C11—41no—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11#4111yescharacteristic
127C42×C11C2411yescharacteristic
128#3209C2×C1111yescharacteristic
129#3078C2×C1111yescharacteristic
130C2×#475C2×C1111yescharacteristic
131#2983C2×C1111yescharacteristic
132#1704C2×C1114yescomplemented
133#1690C2×C1114yescomplemented
134#1570C2×C1111yescharacteristic
135#1549C2×C1111yescharacteristic
136#1542C2×C1111yescharacteristic
137C23×C11#12111yescharacteristic
138Q8×C11—22no—
139Q8×C11—22no—
140Q8×C11—42no—
141Q8×C11—42no—
142Q8×C11—44no—
143Q8×C11—81no—
144Q8×C11—82no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—81no—
154C2×C4×C11—82no—
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#13712yes—
159C2×C4×C11#13712yes—
160C2×C4×C11C22×D411yescharacteristic
161C2×C4×C11C22×D411yescharacteristic
162C2×C4×C11C2×#4111yescharacteristic
163C8×C11—24no—
164C8×C11—42no—
165C8×C11—42no—
166C8×C11—42no—
167#533C22×C1111yescharacteristic
168C2×C4⋊Q8C22×C1111yescharacteristic
169C2×C4×Q8C22×C1111yescharacteristic
170#494C22×C1112yes—
171#487C22×C1112yes—
172#479—22no—
173#477C22×C1112yes—
174#475—22no—
175#475C22×C1114yes—
176#475C22×C1112yes—
177#462—22no—
178#451—22no—
179#446—22no—
180#446C22×C1114yes—
181#432—22no—
182#431C22×C1111yescharacteristic
183#431C22×C1111yescharacteristic
184#428—21no—
185C2×#106—21no—
186#423C22×C1111yescharacteristic
187C2×C4⋊C8C22×C1111yescharacteristic
188#419—21no—
189C2×#103—21no—
190#334C22×C1114yes—
191#333C22×C1112yes—
192#332C22×C1112yes—
193#332C22×C1114yes—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11#47012yes—
197C22×C11C2×#12111yescharacteristic
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—42no—
202C4×C11—42no—
203C4×C11—82no—
204C4×C11—81no—
205C4×C11—81no—
206C4×C11#47012yes—
207C4×C11C2×#13711yescharacteristic
208C4×C11C2×#13711yescharacteristic
209C4×C11#57712yes—
210C22×Q8—21no—
211C22×Q8D4×C1111yescharacteristic
212C2×Q16—24no—
213C2×M16—21no—
214C22×C8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8C23×C1112yes—
219C4⋊Q8C23×C1111yescharacteristic
220C4⋊Q8C23×C1111yescharacteristic
221#125—21no—
222C22⋊Q8—21no—
223C22⋊Q8—21no—
224C4×Q8—21no—
225C4×Q8—21no—
226C4×Q8—21no—
227C4×Q8—21no—
228C4×Q8D4×C1112yes—
229C4×Q8C23×C1112yes—
230#117—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4D4×C1111yescharacteristic
235C2×C42—21no—
236C2×C42C23×C1111yescharacteristic
237#107—22no—
238#106—24no—
239#106—22no—
240C4⋊C8—24no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8D4×C1112yes—
244C4⋊C8C23×C1112yes—
245C4⋊C8C23×C1112yes—
246C4⋊C8C23×C1112yes—
247#103—24no—
248#103—22no—
249#103—22no—
250#103—24no—
251C22⋊C8—21no—
252C22⋊C8D4×C1112yes—
253#97—24no—
254C4×C8—21no—
255C4×C8C23×C1112yes—
256C2×C11—22no—
257C2×C11#304311yescharacteristic
258C2×C11C2×#47011yescharacteristic
259C2×C11#306911yescharacteristic
260C2×Q8—21no—
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—41no—
267C2×Q8—82no—
268C2×Q8C2×D4×C1112yes—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—41no—
272C22×C4C2×D4×C1111yescharacteristic
273C22×C4C2×D4×C1111yescharacteristic
274C22×C4C11×#4111yescharacteristic
275Q16—84no—
276M16—42no—
277C2×C8—22no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—42no—
281C2×C8C2×D4×C1114yes—
282C4⋊C4—22no—
283C4⋊C4—21no—
284C4⋊C4—22no—
285C4⋊C4—21no—
286C4⋊C4—22no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—22no—
290C4⋊C4—21no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4C2×D4×C1112yes—
296C22⋊C4—41no—
297C42—22no—
298C42—22no—
299C42—41no—
300C42C2×D4×C1111yescharacteristic
301C42C2×D4×C1111yescharacteristic
302C42C11×#4111yescharacteristic
303C42C24×C1111yescharacteristic
304C11#1943511yescharacteristic, direct product factor, Sylow
305C23C11×#12111yescharacteristic
306Q8—22no—
307Q8—22no—
308Q8—42no—
309Q8—42no—
310Q8—44no—
311Q8—81no—
312Q8—82no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—82no—
323C2×C4C11×#12111yescharacteristic
324C2×C4C11×#12111yescharacteristic
325C2×C4C11×#12111yescharacteristic
326C2×C4C11×#13712yes—
327C2×C4C11×#13712yes—
328C2×C4C22×D4×C1111yescharacteristic
329C2×C4C22×D4×C1111yescharacteristic
330C2×C4C2×C11×#4111yescharacteristic
331C8—24no—
332C8—42no—
333C8—42no—
334C8—42no—
335C22—21no—
336C22—21no—
337C22C11×#47012yes—
338C22C2×C11×#12111yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—42no—
343C4—42no—
344C4—82no—
345C4—81no—
346C4—81no—
347C4C11×#47012yes—
348C4C2×C11×#13711yescharacteristic
349C4C2×C11×#13711yescharacteristic
350C4C11×#57712yes—
351C2—22no—
352C2C11×#304311yescharacteristic
353C2C2×C11×#47011yescharacteristic
354C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC23×C11#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
5. C11×#1704C2semidirect
6. C11×#1690C2semidirect
83. #19435C11direct (N × H)
132. #1704C2×C11semidirect
133. #1690C2×C11semidirect
304. C11#19435direct (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×#30782
C2×C11×#4752
C11×#29832
C11×#17042
C11×#16902
C11×#15702
C11×#15492
C11×#15422
#1943511