Finite Group Databasebeta

← #14655626

Subgroups — #14655626

Order 2816.

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

normal subgroups only

This group has 556 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#13079163C211yesmaximal, characteristic, complemented
2C2×#10622683C211yesmaximal, characteristic
3#13069457C211yesmaximal, characteristic
4#13067296C211yesmaximal, characteristic, complemented
5#13067071C211yesmaximal, characteristic, complemented
6#13066452C211yesmaximal, characteristic, complemented
7C11×#3208C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#492—21no—
12C11×#486—21no—
13C11×#460—22no—
14C11×#450—22no—
15C11×#431C2211yescharacteristic
16C2×#66897—22no—
17C2×#66896—22no—
18#10622692—21no—
19#10622691—21no—
20#10622683—22no—
21#10622683—22no—
22#10622678—22no—
23#10622608—22no—
24#10622537C2211yescharacteristic
25C4×#4318C2211yescharacteristic
26C2×C4×C11⋊C8C2211yescharacteristic
27Q8⋊(C11⋊C8)—22no—
28#10622119—22no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11D412yes—
32C22×Dic22—21no—
33C2×C11×SD16—24no—
34C11×C4⋊Q8D411yescharacteristic
35C11×C4⋊Q8D411yescharacteristic
36C11×#127—21no—
37C11×#127—21no—
38C11×#127—21no—
39C11×#127—21no—
40C11×#125—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C11×#117—21no—
46C2×C42×C11C2311yescharacteristic
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49C2×#4318—21no—
50C2×#4318D412yes—
51C22×C11⋊C8—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55#66922D412yes—
56C11×C4⋊C8D412yes—
57C11×#102—24no—
58C11×C22⋊C8—21no—
59C4×C8×C11—21no—
60#66897—44no—
61#66896—28no—
62#66872—24no—
63#66871—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66#66867—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8D412yes—
70#10161—111nomaximal, Sylow
71C24×C11—22no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×D4×C11—22no—
75C2×D4×C11—22no—
76C2×D4×C11—44no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—42no—
82C2×D4×C11—42no—
83C2×D4×C11—82no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C22×Dic11—41no—
88C2×Dic22—22no—
89C2×Dic22—41no—
90C2×Dic22—82no—
91C11×SD16—84no—
92C2×C8×C11—22no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C22⋊C4—41no—
100C42×C11—41no—
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C4⋊Dic11—22no—
106C4⋊Dic11—22no—
107C4⋊Dic11—41no—
108C4⋊Dic11—41no—
109#4318—22no—
110#4318—42no—
111#4318SD1614yescomplemented
112C2×C11⋊C8—22no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—42no—
115C2×C11⋊C8—41no—
116#3208D1111yescharacteristic
117#3165—111no—
118C2×#486—111no—
119#1965—111no—
120#1548—111no—
121#1493—111no—
122#1278—111no—
123C23×C11—42no—
124C23×C11—44no—
125C23×C11—82no—
126C23×C11—82no—
127C23×C11#12111yescharacteristic
128Q8×C11—42no—
129Q8×C11—42no—
130D4×C11—44no—
131D4×C11—44no—
132D4×C11—82no—
133D4×C11—82no—
134D4×C11—82no—
135D4×C11—81no—
136D4×C11—81no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12711yescharacteristic
147C2×C4×C11C2×SD1612yes—
148C2×C4×C11#13712yes—
149C2×Dic11—42no—
150C2×Dic11—82no—
151Dic22—82no—
152Dic22—82no—
153C8×C11—42no—
154C11⋊C8—24no—
155C11⋊C8—42no—
156C11⋊C8—81no—
157#533C2×D1111yescharacteristic
158C2×C4⋊Q8—111no—
159C2×#127C2×D1111yescharacteristic
160#501—222no—
161#500—221no—
162#498—221no—
163#492—21no—
164#486—21no—
165#486—222no—
166#486—222no—
167#460—22no—
168#450—22no—
169#431C2×D1111yescharacteristic
170#428—222no—
171#423—111no—
172C2×#102—222no—
173C2×#100—222no—
174C4×M16—111no—
175C2×C4×C8—111no—
176#333—222no—
177Q8⋊C8—222no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—82no—
181C22×C11—82no—
182C22×C11—82no—
183C22×C11—164no—
184C22×C11#39211yescharacteristic
185C22×C11#46112yes—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—81no—
189C4×C11—81no—
190C4×C11#44812yes—
191C4×C11#45512yes—
192C4×C11#47212yes—
193C4×C11#49211yescharacteristic
194C4×C11#49711yescharacteristic
195Dic11—82no—
196C22×Q8—221no—
197C22×D4—21no—
198C22×D4—21no—
199C22×D4C22⋊D1112yes—
200C2×SD16—24no—
201C2×M16—112no—
202C2×M16—221no—
203C22×C8—221no—
204C4⋊Q8—112no—
205C4⋊Q8—221no—
206C4⋊Q8—221no—
207C4⋊Q8—221no—
208C4⋊Q8C22⋊D1111yescharacteristic
209C4⋊Q8C22⋊D1111yescharacteristic
210#127—21no—
211#127—21no—
212#127—21no—
213#127—21no—
214#125—21no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C4×Q8—21no—
218C4×Q8—21no—
219#117—21no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—221no—
222C2×C42C22×D1111yescharacteristic
223#107—224no—
224#106—224no—
225C4⋊C8—221no—
226C4⋊C8—221no—
227C4⋊C8C22⋊D1112yes—
228#102—24no—
229#102—228no—
230#100—444no—
231C22⋊C8—21no—
232#97—221no—
233C4×C8—21no—
234C4×C8—112no—
235C4×C8—221no—
236C4×C8—221no—
237C2×C11—22no—
238C2×C11—162no—
239C2×C11#200411yescharacteristic
240C2×C11#201311yescharacteristic
241C2×C11#201811yescharacteristic
242C24—22no—
243C2×Q8—21no—
244C2×Q8—21no—
245C2×Q8—222no—
246C2×Q8—441no—
247C2×Q8—882no—
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—44no—
251C2×D4—42no—
252C2×D4—42no—
253C2×D4—41no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—82no—
258C22×C4—441no—
259C22×C4D4×D1111yescharacteristic
260C22×C4#434111yescharacteristic
261C22×C4C2×C22⋊D1111yescharacteristic
262SD16—84no—
263M16—114no—
264M16—222no—
265M16—442no—
266C2×C8—22no—
267C2×C8—222no—
268C2×C8—222no—
269C2×C8—442no—
270C2×C8—441no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—222no—
278C4⋊C4—222no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C22⋊C4—41no—
282C42—41no—
283C42D4×D1111yescharacteristic
284C42D4×D1111yescharacteristic
285C42C2×C22⋊D1111yescharacteristic
286C42C2×C22⋊D1111yescharacteristic
287C11#1016111yescharacteristic, complemented, Sylow
288C23—42no—
289C23—44no—
290C23—82no—
291C23—82no—
292C23#6699211yescharacteristic
293Q8—42no—
294Q8—42no—
295Q8—882no—
296Q8—882no—
297D4—44no—
298D4—44no—
299D4—82no—
300D4—81no—
301D4—82no—
302D4—81no—
303D4—82no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—442no—
309C2×C4—882no—
310C2×C4SD16×D1112yes—
311C2×C4#6696812yes—
312C2×C4#6699011yescharacteristic
313C2×C4#6699011yescharacteristic
314C2×C4#6699111yescharacteristic
315C2×C4#6699211yescharacteristic
316C2×C4#6699311yescharacteristic
317C2×C4#6700611yescharacteristic
318C8—42no—
319C8—224no—
320C8—442no—
321C8—881no—
322C22—21no—
323C22—21no—
324C22—82no—
325C22—82no—
326C22—82no—
327C22—164no—
328C22#1062277512yes—
329C22#1062283611yescharacteristic
330C4—21no—
331C4—21no—
332C4—81no—
333C4—81no—
334C4—882no—
335C4#1062278011yescharacteristic
336C4#1062278312yes—
337C4#1062278811yescharacteristic
338C4#1062281212yes—
339C4#1062285512yes—
340C2—22no—
341C2—162no—
342C2#1306964311yescharacteristic
343C2#1306969711yescharacteristic
344C2#1306972211yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3208C2
socleC22×C11#392
prime radicalC2×C11×#127C22
hypercenter#3208D11
hypocenterC11#10161
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3208

Complements

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

NH ≅ G/Ntype
1. #13079163C2semidirect
4. #13067296C2semidirect
5. #13067071C2semidirect
6. #13066452C2semidirect
111. #4318SD16semidirect
287. C11#10161semidirect

Maximal subgroups

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

subgroupindex
#130791632
C2×#106226832
#130694572
#130672962
#130670712
#130664522
C11×#32082
#1016111