Finite Group Databasebeta

← C11×#10172 #14587365

Subgroups — C11×#10172 #14587365

Order 2816.

562 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3227C211yesmaximal, characteristic
2C2×C11×#498C211yesmaximal, characteristic, complemented
3C11×#3152C211yesmaximal, characteristic
4C11×#1997C211yesmaximal, characteristic, complemented
5C11×#1546C211yesmaximal, characteristic, complemented
6C11×#1492C211yesmaximal, characteristic
7C11×#1278C211yesmaximal, characteristic, complemented
8C2×C11×#137—22no—
9C11×#532C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C11×#498—22no—
13C11×#498—21no—
14C11×#498—22no—
15C11×#497—22no—
16C11×#494—21no—
17C11×#492—21no—
18C11×#486—21no—
19C11×#481—22no—
20C11×#476—22no—
21C11×#431C2211yescharacteristic
22C2×C11×#106—22no—
23C11×#423C2211yescharacteristic
24C4×C11×M16C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C11×#343—22no—
27C11×#332—22no—
28C11×D4⋊C8—22no—
29C2×C11×#41—21no—
30C22×Q8×C11—21no—
31C22×Q8×C11—21no—
32C11×#137—44no—
33C11×#137—44no—
34C2×C11×Q16—24no—
35C2×C11×SD16—24no—
36C2×C11×M16—21no—
37C2×C11×M16D412yes—
38C22×C8×C11—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8D411yescharacteristic
47C11×C4⋊Q8D412yes—
48C11×#127D411yescharacteristic
49C11×#124—21no—
50C11×#121—21no—
51C11×#121—21no—
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4D412yes—
58C2×C42×C11C2311yescharacteristic
59C11×#106—28no—
60C11×#106—24no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8D412yes—
64C11×#102—24no—
65C11×C22⋊C8—21no—
66C11×#97—21no—
67C4×C8×C11—21no—
68C4×C8×C11—21no—
69C4×C8×C11—21no—
70C4×C8×C11D412yes—
71#10172C1111yesmaximal, characteristic, direct product factor, Sylow
72C11×#41—42no—
73C11×#41—42no—
74C2×Q8×C11—21no—
75C2×Q8×C11—22no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—42no—
80C2×Q8×C11—42no—
81C2×Q8×C11—82no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—41no—
86C22×C4×C11—22no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C11×Q16—48no—
93C11×SD16—48no—
94C11×M16—22no—
95C11×M16—42no—
96C11×M16SD1614yes—
97C2×C8×C11—24no—
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11—22no—
101C2×C8×C11—41no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118#3227C2×C1111yescharacteristic
119C2×#498C2×C1111yescharacteristic, complemented
120#3152C2×C1111yescharacteristic
121#1997C2×C1111yescharacteristic, complemented
122#1546C2×C1111yescharacteristic, complemented
123#1492C2×C1111yescharacteristic
124#1278C2×C1111yescharacteristic, complemented
125C23×C11—41no—
126C23×C11#12111yescharacteristic
127Q8×C11—44no—
128Q8×C11—42no—
129Q8×C11—82no—
130Q8×C11—82no—
131Q8×C11—81no—
132Q8×C11—81no—
133D4×C11—42no—
134D4×C11—42no—
135D4×C11—42no—
136D4×C11—82no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11—82no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11—82no—
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12711yescharacteristic
152C2×C4×C11C2×SD1612yes—
153C2×C4×C11AGL(1,ℤ/8)12yes—
154C8×C11—24no—
155C8×C11—24no—
156C8×C11—42no—
157C8×C11—81no—
158C2×#137—22no—
159#532C22×C1111yescharacteristic
160C2×C4⋊Q8C22×C1111yescharacteristic
161C2×C4⋊Q8C22×C1111yescharacteristic
162#498—22no—
163#498—21no—
164#498—22no—
165#497—22no—
166#494—21no—
167#492—21no—
168#486—21no—
169#481—22no—
170#476—22no—
171#431C22×C1111yescharacteristic
172C2×#106—22no—
173#423C22×C1111yescharacteristic
174C4×M16C22×C1111yescharacteristic
175C2×C4×C8C22×C1111yescharacteristic
176#343—22no—
177#332—22no—
178D4⋊C8—22no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—81no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11#39211yescharacteristic
185C22×C11#46012yes—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—81no—
189C4×C11—82no—
190C4×C11—82no—
191C4×C11#45012yes—
192C4×C11#45612yes—
193C4×C11#47112yes—
194C4×C11#49211yescharacteristic
195C4×C11#49611yescharacteristic
196C2×#41—21no—
197C22×Q8—21no—
198C22×Q8—21no—
199#137—44no—
200#137—44no—
201C2×Q16—24no—
202C2×SD16—24no—
203C2×M16—21no—
204C2×M16D4×C1112yes—
205C22×C8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8D4×C1112yes—
214C4⋊Q8D4×C1111yescharacteristic
215#127D4×C1111yescharacteristic
216#124—21no—
217#121—21no—
218#121—21no—
219C4×D4—21no—
220C4×D4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4D4×C1112yes—
225C2×C42C23×C1111yescharacteristic
226#106—28no—
227#106—24no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8D4×C1112yes—
231#102—24no—
232C22⋊C8—21no—
233#97—21no—
234C4×C8—21no—
235C4×C8—21no—
236C4×C8—21no—
237C4×C8D4×C1112yes—
238C2×C11—22no—
239C2×C11—161no—
240C2×C11#200511yescharacteristic
241C2×C11#201411yescharacteristic
242C2×C11#201911yescharacteristic
243#41—42no—
244#41—42no—
245C2×Q8—21no—
246C2×Q8—22no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—42no—
251C2×Q8—42no—
252C2×Q8—82no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—41no—
257C22×C4—22no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4C2×D4×C1111yescharacteristic
261C22×C4C2×D4×C1111yescharacteristic
262C22×C4C11×#4111yescharacteristic
263Q16—48no—
264SD16—48no—
265M16—22no—
266M16—42no—
267M16C11×SD1614yes—
268C2×C8—24no—
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—41no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—21no—
277C4⋊C4—22no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C42C2×D4×C1111yescharacteristic
286C42C2×D4×C1111yescharacteristic
287C42C2×D4×C1111yescharacteristic
288C42C2×D4×C1111yescharacteristic
289C11#1017211yescharacteristic, direct product factor, Sylow
290C23—41no—
291C23C11×#12111yescharacteristic
292Q8—44no—
293Q8—42no—
294Q8—82no—
295Q8—81no—
296Q8—81no—
297Q8—82no—
298D4—42no—
299D4—42no—
300D4—42no—
301D4—82no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—82no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—82no—
311C2×C4C11×#12011yescharacteristic
312C2×C4C11×#12011yescharacteristic
313C2×C4C11×#12011yescharacteristic
314C2×C4C11×#12111yescharacteristic
315C2×C4C11×#12111yescharacteristic
316C2×C4C11×#12711yescharacteristic
317C2×C4C2×C11×SD1612yes—
318C2×C4C11×AGL(1,ℤ/8)12yes—
319C8—24no—
320C8—24no—
321C8—42no—
322C8—81no—
323C22—21no—
324C22—21no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22C11×#39211yescharacteristic
329C22C11×#46012yes—
330C4—21no—
331C4—21no—
332C4—81no—
333C4—82no—
334C4—82no—
335C4C11×#45012yes—
336C4C11×#45612yes—
337C4C11×#47112yes—
338C4C11×#49211yescharacteristic
339C4C11×#49611yescharacteristic
340C2—22no—
341C2—161no—
342C2C11×#200511yescharacteristic
343C2C11×#201411yescharacteristic
344C2C11×#201911yescharacteristic
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
2. C2×C11×#498C2semidirect
4. C11×#1997C2semidirect
5. C11×#1546C2semidirect
7. C11×#1278C2semidirect
71. #10172C11direct (N × H)
119. C2×#498C2×C11semidirect
121. #1997C2×C11semidirect
122. #1546C2×C11semidirect
124. #1278C2×C11semidirect
289. C11#10172direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32272
C2×C11×#4982
C11×#31522
C11×#19972
C11×#15462
C11×#14922
C11×#12782
#1017211