Finite Group Databasebeta

← #14655627

Subgroups — #14655627

Order 2816.

556 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 111 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#13079557C211yesmaximal, characteristic
2#13079162C211yesmaximal, characteristic, complemented
3C2×#10622683C211yesmaximal, characteristic
4#13067298C211yesmaximal, characteristic, complemented
5#13067070C211yesmaximal, characteristic, complemented
6#13066454C211yesmaximal, characteristic, complemented
7C11×#1965C211yesmaximal, characteristic
8C2×C11×#127C2211yescharacteristic
9#10623001C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C11×#100—22no—
13C4×C11×M16C2211yescharacteristic
14#10622831—22no—
15C2×#66896—22no—
16#10622734—22no—
17#10622689—21no—
18#10622688—22no—
19#10622683—21no—
20#10622683—22no—
21#10622683—22no—
22#10622538C2211yescharacteristic
23C2×C4×C11⋊C8C2211yescharacteristic
24#10622315—22no—
25#10622295—21no—
26#10622293—21no—
27#10622122—22no—
28#10622119—22no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11D412yes—
32C22×Dic22—21no—
33C2×C11×M16—21no—
34C2×C11×M16D412yes—
35C11×#127—21no—
36C11×#127—21no—
37C11×#127—21no—
38C11×#127—21no—
39C2×C42×C11C2311yescharacteristic
40C2×#4324—24no—
41#66979—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44#66977—21no—
45#66977—21no—
46C22×C11⋊C8—21no—
47#66923—21no—
48#66922—21no—
49#66922—21no—
50#66922—21no—
51#66922D412yes—
52#66922D411yescharacteristic
53#66922D411yescharacteristic
54C4×Dic22—21no—
55C4×Dic22—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×#100—44no—
59C11×#97—21no—
60C4×C8×C11—21no—
61#66896—28no—
62#66896—24no—
63C22⋊(C11⋊C8)—21no—
64#66882—24no—
65#66881—24no—
66C4⋊(C11⋊C8)D412yes—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8D412yes—
70#10161—111nomaximal, Sylow
71C24×C11—22no—
72C2×D4×C11—22no—
73C2×D4×C11—22no—
74C2×D4×C11—44no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—42no—
80C2×D4×C11—42no—
81C2×D4×C11—82no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×Dic11—41no—
86C2×Dic22—21no—
87C2×Dic22—21no—
88C2×Dic22—22no—
89C2×Dic22—41no—
90C2×Dic22—82no—
91C11×M16—22no—
92C11×M16—42no—
93C11×M16SD1614yescomplemented
94C2×C8×C11—22no—
95C2×C8×C11—41no—
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C22⋊Dic11—41no—
101#4324—84no—
102C4⋊Dic11—21no—
103C4⋊Dic11—22no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11—22no—
107C4⋊Dic11—21no—
108C4⋊Dic11—41no—
109C4⋊Dic11—41no—
110Dic11⋊C4—41no—
111Dic11⋊C4—41no—
112C4×Dic11—41no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—42no—
116#3208—111no—
117#3165—111no—
118C2×#486—111no—
119#1965D1111yescharacteristic
120#1548—111no—
121#1493—111no—
122#1278—111no—
123C23×C11—42no—
124C23×C11—44no—
125C23×C11—82no—
126C23×C11—82no—
127C23×C11#12111yescharacteristic
128D4×C11—44no—
129D4×C11—44no—
130D4×C11—82no—
131D4×C11—82no—
132D4×C11—82no—
133D4×C11—81no—
134D4×C11—81no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12711yescharacteristic
143C2×C4×C11C2×SD1612yes—
144C2×C4×C11#13712yes—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—42no—
148C2×Dic11—82no—
149Dic22—42no—
150Dic22—42no—
151Dic22—82no—
152Dic22—82no—
153C8×C11—24no—
154C8×C11—81no—
155C11⋊C8—42no—
156C11⋊C8—42no—
157#533—111no—
158C2×C4⋊Q8—111no—
159C2×#127C2×D1111yescharacteristic
160#501—222no—
161#500—221no—
162#498—221no—
163#492—221no—
164#486—222no—
165#486—222no—
166#486—221no—
167#460—222no—
168#450—222no—
169#431—111no—
170#428—222no—
171#423C2×D1111yescharacteristic
172C2×#102—222no—
173C2×#100—22no—
174C4×M16C2×D1111yescharacteristic
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#44812yes—
189C4×C11#45512yes—
190C4×C11#47212yes—
191C4×C11#49211yescharacteristic
192C4×C11#49711yescharacteristic
193Dic11—81no—
194Dic11—81no—
195Dic11—82no—
196C22×Q8—221no—
197C22×D4—21no—
198C22×D4—21no—
199C22×D4D4412yes—
200C2×SD16—224no—
201C2×M16—21no—
202C2×M16C22⋊D1112yes—
203C22×C8—221no—
204C4⋊Q8—112no—
205C4⋊Q8—111no—
206C4⋊Q8—111no—
207C4⋊Q8—221no—
208C4⋊Q8—221no—
209C4⋊Q8—221no—
210#127—21no—
211#127—21no—
212#127—21no—
213#127—21no—
214#125—221no—
215C22⋊Q8—221no—
216C22⋊Q8—221no—
217C4×Q8—221no—
218C4×Q8—221no—
219#117—221no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—221no—
222C2×C42C22×D1111yescharacteristic
223#107—224no—
224#106—224no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—112no—
228#102—228no—
229#102—224no—
230#100—44no—
231C22⋊C8—221no—
232#97—21no—
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—221no—
244C2×Q8—221no—
245C2×Q8—222no—
246C2×Q8—441no—
247C2×Q8—882no—
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—44no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—42no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—42no—
257C2×D4—82no—
258C22×C4—441no—
259C22×C4C2×D4411yescharacteristic
260C22×C4#433911yescharacteristic
261C22×C4C2×C22⋊D1111yescharacteristic
262SD16—884no—
263M16—22no—
264M16—42no—
265M16#432414yescomplemented
266C2×C8—22no—
267C2×C8—41no—
268C2×C8—222no—
269C2×C8—222no—
270C2×C8—442no—
271C4⋊C4—222no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4—222no—
276C4⋊C4—221no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C22⋊C4—441no—
282C42—441no—
283C42D4×D1111yescharacteristic
284C42D4×D1111yescharacteristic
285C42D4×D1111yescharacteristic
286C42D4×D1111yescharacteristic
287C11#1016111yescharacteristic, complemented, Sylow
288C23—42no—
289C23—44no—
290C23—82no—
291C23—82no—
292C23#6698311yescharacteristic
293Q8—442no—
294Q8—442no—
295Q8—882no—
296Q8—882no—
297D4—44no—
298D4—44no—
299D4—82no—
300D4—82no—
301D4—82no—
302D4—81no—
303D4—81no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—442no—
309C2×C4—882no—
310C2×C4#6693511yescharacteristic
311C2×C4#6693511yescharacteristic
312C2×C4#6693711yescharacteristic
313C2×C4#6693711yescharacteristic
314C2×C4C2×#432412yes—
315C2×C4#6699011yescharacteristic
316C2×C4#6699311yescharacteristic
317C2×C4#6700412yes—
318C8—24no—
319C8—81no—
320C8—442no—
321C8—442no—
322C22—21no—
323C22—21no—
324C22—82no—
325C22—82no—
326C22—82no—
327C22—164no—
328C22#1062257311yescharacteristic
329C22#1062263212yes—
330C4—21no—
331C4—21no—
332C4—881no—
333C4—882no—
334C4—881no—
335C4#1062235912yes—
336C4#1062236212yes—
337C4#1062265312yes—
338C4#1062267311yescharacteristic
339C4#1062268911yescharacteristic
340C2—22no—
341C2—162no—
342C2#1306964711yescharacteristic
343C2#1306969811yescharacteristic
344C2#1306972411yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1965C2
socleC22×C11#392
prime radicalC2×C11×#127C22
hypercenter#1965D11
hypocenterC11#10161
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1965

Complements

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

NH ≅ G/Ntype
2. #13079162C2semidirect
4. #13067298C2semidirect
5. #13067070C2semidirect
6. #13066454C2semidirect
93. C11×M16SD16semidirect
265. M16#4324semidirect
287. C11#10161semidirect

Maximal subgroups

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

subgroupindex
#130795572
#130791622
C2×#106226832
#130672982
#130670702
#130664542
C11×#19652
#1016111