Finite Group Databasebeta

← #14655686

Subgroups — #14655686

Order 2816.

574 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 109 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
1#13079541C211yesmaximal, characteristic
2#13079073C211yesmaximal, characteristic
3#13069606C211yesmaximal, characteristic, complemented
4#13067288C211yesmaximal, characteristic, complemented
5#13067068C211yesmaximal, characteristic
6#13066453C211yesmaximal, characteristic, complemented
7C2×C11×#487C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#66995—22no—
11#10623008C2211yescharacteristic
12C11×#487—22no—
13C11×#487—22no—
14C2×C11×#103—22no—
15C2×C4×C8×C11C2211yescharacteristic
16#10622840—22no—
17#10622705—21no—
18#10622699—22no—
19#10622698—21no—
20#10622698—21no—
21#10622696—22no—
22#10622694—21no—
23#10622538C2211yescharacteristic
24#10622537C2211yescharacteristic
25C4×#4318C2211yescharacteristic
26#10622185—22no—
27#10622168—22no—
28#10622097—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11D412yes—
31C2×#4339—21no—
32C22×C8×C11—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8D412yes—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C42×C11C2311yescharacteristic
46C2×#4326—24no—
47#66995—44no—
48#66995—44no—
49C2×#4325—24no—
50C2×#4325—24no—
51#66983—21no—
52#66983—21no—
53C2×#4318—21no—
54C2×#4318D412yes—
55#66928—21no—
56#66927D411yescharacteristic
57C4×D44—21no—
58C4×D44—21no—
59#66922D411yescharacteristic
60C11×#103—28no—
61C4×C8×C11—21no—
62C4×C8×C11D412yes—
63#66899—24no—
64C22⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)D412yes—
68#66867—21no—
69C4×C11⋊C8—21no—
70C4×C11⋊C8—21no—
71#10170—111nomaximal, Sylow
72C2×Q8×C11—22no—
73C2×Q8×C11—22no—
74C2×Q8×C11—22no—
75C2×Q8×C11—44no—
76C2×Q8×C11—41no—
77C2×Q8×C11—42no—
78C2×Q8×C11—42no—
79C22×C4×C11—22no—
80C22×C4×C11—41no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C2×C22⋊D11—41no—
85#4339—42no—
86#4339—42no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—21no—
90C2×C4×D11—41no—
91C2×Dic22—21no—
92C2×C8×C11—22no—
93C2×C8×C11—42no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106#4326—48no—
107#4325—48no—
108#4325—84no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—41no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113#4318—22no—
114#4318—42no—
115#4318SD1614yescomplemented
116C2×C11⋊C8—22no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—41no—
119#3206—111no—
120#3152—111no—
121C2×#487D1111yescharacteristic, complemented
122#1997—111no—
123#1546—111no—
124#1492—111no—
125#1278—111no—
126C23×C11#12111yescharacteristic
127C22×D11—41no—
128Q8×C11—44no—
129Q8×C11—44no—
130Q8×C11—44no—
131Q8×C11—81no—
132Q8×C11—81no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—82no—
138C2×C4×C11—82no—
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12711yescharacteristic
145C2×C4×C11C2×SD1612yes—
146C2×C4×C11AGL(1,ℤ/8)12yes—
147C22⋊D11—82no—
148C2×Dic11—41no—
149D44—42no—
150D44—42no—
151D44—42no—
152C4×D11—81no—
153C4×D11—81no—
154Dic22—42no—
155C8×C11—42no—
156C11⋊C8—24no—
157C11⋊C8—42no—
158C11⋊C8—81no—
159C2×#137—222no—
160#532—111no—
161C2×C4⋊Q8C2×D1111yescharacteristic
162C2×C4⋊Q8C2×D1111yescharacteristic
163#497—222no—
164#494—221no—
165#492—221no—
166#492—221no—
167#487—22no—
168#487—22no—
169#487—221no—
170#461—222no—
171#448—222no—
172#431—111no—
173#423—111no—
174C2×#103—22no—
175C4×M16—111no—
176C2×C4×C8C2×D1111yescharacteristic
177#343—222no—
178#332—222no—
179D4⋊C8—222no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11#39211yescharacteristic
183C22×C11#46012yes—
184C2×D11—81no—
185C2×D11—81no—
186C2×D11—81no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—82no—
190C4×C11—82no—
191C4×C11#45012yes—
192C4×C11#45512yes—
193C4×C11#47312yes—
194C4×C11#49211yescharacteristic
195C4×C11#49611yescharacteristic
196Dic11—81no—
197C2×#41—221no—
198C22×Q8—21no—
199C22×Q8C22⋊D1112yes—
200#137—444no—
201#137—444no—
202C2×Q16—224no—
203C2×SD16—224no—
204C2×SD16—224no—
205C2×M16—112no—
206C2×M16—221no—
207C22×C8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—111no—
216C4⋊Q8C22⋊D1112yes—
217#127—111no—
218#124—221no—
219#121—221no—
220#121—221no—
221C4×D4—221no—
222C4×D4—221no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C42C22×D1111yescharacteristic
228C4⋊C8—112no—
229C4⋊C8—221no—
230C4⋊C8—221no—
231#103—28no—
232#103—224no—
233C22⋊C8—221no—
234#97—221no—
235C4×C8—21no—
236C4×C8—221no—
237C4×C8—221no—
238C4×C8C22⋊D1112yes—
239C2×C11—22no—
240C2×C11#200411yescharacteristic
241C2×C11#201411yescharacteristic
242C2×C11#202011yescharacteristic
243D11—161no—
244#41—442no—
245#41—442no—
246C2×Q8—22no—
247C2×Q8—22no—
248C2×Q8—22no—
249C2×Q8—44no—
250C2×Q8—41no—
251C2×Q8—42no—
252C2×Q8—42no—
253C2×Q8—221no—
254C2×D4—221no—
255C2×D4—221no—
256C2×D4—221no—
257C2×D4—441no—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4—441no—
261C22×C4D4×D1111yescharacteristic
262C22×C4#434111yescharacteristic
263C22×C4C2×C22⋊D1111yescharacteristic
264Q16—448no—
265SD16—448no—
266SD16—884no—
267M16—114no—
268M16—222no—
269M16—442no—
270C2×C8—22no—
271C2×C8—42no—
272C2×C8—222no—
273C2×C8—222no—
274C2×C8—441no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C22⋊C4—441no—
286C22⋊C4—441no—
287C42D4×D1111yescharacteristic
288C42D4×D1111yescharacteristic
289C42C2×C22⋊D1111yescharacteristic
290C42C2×C22⋊D1111yescharacteristic
291C11#1017011yescharacteristic, complemented, Sylow
292C23—441no—
293C23#6699211yescharacteristic
294Q8—44no—
295Q8—44no—
296Q8—44no—
297Q8—81no—
298Q8—81no—
299Q8—442no—
300D4—442no—
301D4—442no—
302D4—442no—
303D4—882no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—441no—
311C2×C4—881no—
312C2×C4—881no—
313C2×C4SD16×D1112yes—
314C2×C4#6696712yes—
315C2×C4#6699011yescharacteristic
316C2×C4#6699011yescharacteristic
317C2×C4#6699111yescharacteristic
318C2×C4#6699211yescharacteristic
319C2×C4#6699311yescharacteristic
320C2×C4#6700611yescharacteristic
321C8—42no—
322C8—224no—
323C8—442no—
324C8—881no—
325C22—21no—
326C22—21no—
327C22—881no—
328C22—881no—
329C22—881no—
330C22#1062277612yes—
331C22#1062283611yescharacteristic
332C4—21no—
333C4—21no—
334C4—82no—
335C4—82no—
336C4—881no—
337C4#1062267412yes—
338C4#1062278212yes—
339C4#1062278811yescharacteristic
340C4#1062278911yescharacteristic
341C4#1062280512yes—
342C2—22no—
343C2—1761no—
344C2#1306964511yescharacteristic
345C2#1306970211yescharacteristic
346C2#1306973511yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#487C2
socleC22×C11#392
prime radical#10623008C22
hypercenterC2×#487D11
hypocenterC11#10170
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
3. #13069606C2semidirect
4. #13067288C2semidirect
6. #13066453C2semidirect
7. C2×C11×#487C2semidirect
115. #4318SD16semidirect
121. C2×#487D11semidirect
291. C11#10170semidirect

Maximal subgroups

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

subgroupindex
#130795412
#130790732
#130696062
#130672882
#130670682
#130664532
C2×C11×#4872
#1017011