Finite Group Databasebeta

← #14670054

Subgroups — #14670054

Order 2816.

334 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 87 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#13077267C211yesmaximal, characteristic
2#13068720C211yesmaximal, characteristic
3#13066746C211yesmaximal, characteristic
4#13066744C211yesmaximal, characteristic
5#13066738C211yesmaximal, characteristic
6#13066736C211yesmaximal, characteristic
7C11×#1827C211yesmaximal, characteristic
8C4×C11×#41C2211yescharacteristic
9C11×#413C2211yescharacteristic
10C11×#410C2211yescharacteristic
11#10622853C2211yescharacteristic
12#10622850C2211yescharacteristic
13#10622847C2211yescharacteristic
14#10622847C2211yescharacteristic
15#10622613—21no—
16#10622613—21no—
17#10622612C411yescharacteristic, complemented
18#10622612C411yescharacteristic, complemented
19#10622539—21no—
20#10622539—21no—
21C4×#4318C411yescharacteristic, complemented
22C2×#66867C411yescharacteristic, complemented
23C11×#339—21no—
24C11×H(3,ℤ/4)—21no—
25#10622169—21no—
26#10622161—21no—
27C2×C11×#41C2311yescharacteristic
28C2×C11×M16—21no—
29C4×Q8×C11—21no—
30C4×D4×C11—21no—
31C4×D4×C11—21no—
32C4×D4×C11—21no—
33C11×#117—21no—
34C11×#117C2×C411yescharacteristic
35C11×#117D411yescharacteristic
36C11×#117D411yescharacteristic
37C2×C42×C11C2×C411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C42×C11D411yescharacteristic
40#66979—21no—
41C2×#4318—21no—
42C2×#4318C2×C411yescharacteristic
43C2×#4318C2×C411yescharacteristic
44C22×C11⋊C8C2×C411yescharacteristic
45C22×C11⋊C8C2×C411yescharacteristic
46C11×#101—21no—
47C11×#100—21no—
48C11×#99—21no—
49C11×#99—21no—
50#66900—21no—
51#66898—21no—
52#66898—21no—
53#66897—21no—
54C22⋊(C11⋊C8)—21no—
55C22⋊(C11⋊C8)—21no—
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62#66867—21no—
63#66867—21no—
64#66867—21no—
65C4×C11⋊C8—21no—
66#12865—111nomaximal, Sylow
67C11×#41—41no—
68C11×#41—41no—
69C2×Q8×C11#4111yescharacteristic
70C2×D4×C11#4111yescharacteristic
71C2×D4×C11#4111yescharacteristic
72C2×D4×C11#4111yescharacteristic
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C11×M16—41no—
80C11×M16—41no—
81C2×C8×C11—41no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—41no—
86C11×C22⋊C4—21no—
87C11×C22⋊C4—21no—
88C11×C22⋊C4—21no—
89C11×C22⋊C4—41no—
90C42×C11—21no—
91C42×C11—21no—
92C42×C11—21no—
93C42×C11—41no—
94C42×C11C22⋊C411yescharacteristic
95C42×C11C22⋊C411yescharacteristic
96C42×C11C22⋊C411yescharacteristic
97C42×C11C22⋊C411yescharacteristic
98C22⋊Dic11—41no—
99C4⋊Dic11—41no—
100C4×Dic11—41no—
101#4318—41no—
102#4318—41no—
103#4318—41no—
104#4318—41no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—21no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112#2923—111no—
113#1827—111no—
114#1827D1111yescharacteristic
115#1395—111no—
116#1395—111no—
117#1392—111no—
118#1391—111no—
119C23×C11#11711yescharacteristic
120C23×C11#12311yescharacteristic
121C23×C11#12311yescharacteristic
122Q8×C11—41no—
123D4×C11—41no—
124D4×C11—41no—
125D4×C11—41no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—81no—
137C2×C4×C11—81no—
138C2×C4×C11—81no—
139C2×C4×C11—81no—
140C2×C4×C11C2×C22⋊C411yescharacteristic
141C2×C4×C11#11711yescharacteristic
142C2×C4×C11#12311yescharacteristic
143C2×C4×C11#12311yescharacteristic
144C2×Dic11—81no—
145C8×C11—81no—
146C11⋊C8—41no—
147C11⋊C8—41no—
148C11⋊C8—41no—
149C11⋊C8—41no—
150C11⋊C8—81no—
151C4×#41C2×D1111yescharacteristic
152#433—221no—
153#433—221no—
154#432—221no—
155#432—221no—
156#424—111no—
157#424—111no—
158#413—111no—
159#413C2×D1111yescharacteristic
160#410—111no—
161#410C2×D1111yescharacteristic
162#408—111no—
163#408—111no—
164C4×M16—111no—
165C2×#97—111no—
166#339—21no—
167#339—221no—
168H(3,ℤ/4)—21no—
169H(3,ℤ/4)—221no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11#38111yescharacteristic
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—161no—
185C4×C11#41011yescharacteristic
186C4×C11#41011yescharacteristic
187Dic11—161no—
188C2×#41C22×D1111yescharacteristic
189C2×M16—21no—
190C2×M16—111no—
191C2×M16—111no—
192C2×M16—221no—
193C22×C8—111no—
194C22×C8—111no—
195C4×Q8—21no—
196C4×D4—21no—
197C4×D4—21no—
198C4×D4—21no—
199#117—21no—
200#117—221no—
201#117C4×D1111yescharacteristic
202#117D4411yescharacteristic
203#117C22⋊D1111yescharacteristic
204C2×C42C4×D1111yescharacteristic
205C2×C42D4411yescharacteristic
206C2×C42C22⋊D1111yescharacteristic
207C4⋊C8—221no—
208C4⋊C8—221no—
209C4⋊C8—221no—
210C4⋊C8—221no—
211#101—21no—
212#101—221no—
213#100—21no—
214#100—221no—
215#99—21no—
216#99—21no—
217#99—221no—
218#99—221no—
219C22⋊C8—221no—
220C22⋊C8—221no—
221C22⋊C8—221no—
222C22⋊C8—221no—
223#97—221no—
224#97—221no—
225#97—221no—
226C4×C8—221no—
227C2×C11—21no—
228C2×C11—41no—
229C2×C11—41no—
230C2×C11—41no—
231C2×C11#182011yescharacteristic
232#41—41no—
233#41—41no—
234C2×Q8#434111yescharacteristic
235C2×D4#434111yescharacteristic
236C2×D4#434111yescharacteristic
237C2×D4#434111yescharacteristic
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4C2×C4×D1111yescharacteristic
242C22×C4C2×D4411yescharacteristic
243C22×C4C2×C22⋊D1111yescharacteristic
244M16—41no—
245M16—41no—
246M16—441no—
247M16—441no—
248M16—441no—
249M16—441no—
250C2×C8—41no—
251C2×C8—221no—
252C2×C8—221no—
253C2×C8—221no—
254C2×C8—221no—
255C2×C8—441no—
256C2×C8—441no—
257C2×C8—441no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—41no—
262C4⋊C4—441no—
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—41no—
267C22⋊C4—441no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—41no—
272C42—441no—
273C42(C2×D11)⋊C411yescharacteristic
274C42(C2×D11)⋊C411yescharacteristic
275C42(C2×D11)⋊C411yescharacteristic
276C42(C2×D11)⋊C411yescharacteristic
277C11#1286511yescharacteristic, complemented, Sylow
278C23#6693011yescharacteristic
279C23#6693911yescharacteristic
280C23#6698811yescharacteristic
281Q8—41no—
282D4—41no—
283D4—41no—
284D4—41no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—881no—
300C2×C4#6693011yescharacteristic
301C2×C4#6693911yescharacteristic
302C2×C4C2×(C2×D11)⋊C411yescharacteristic
303C2×C4#6698811yescharacteristic
304C8—81no—
305C8—441no—
306C8—441no—
307C8—441no—
308C8—441no—
309C8—881no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22#1062255611yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—161no—
325C4—1761no—
326C4#1062261911yescharacteristic
327C4#1062261911yescharacteristic
328C2—21no—
329C2—41no—
330C2—41no—
331C2—41no—
332C2#1306869111yescharacteristic
subgroupG/H
centerC4#10622619
commutatorC22×C4×C11C22×C4
FrattiniC2×#41C22×D11
FittingC11×#1827C2
socleC2×C11#1820
prime radical, cosocleC2×C11×#41C23
hypercenter#1827D11
hypocenterC11#12865
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C42 ◁ C4×#41 ◁ #1827

Complements

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

NH ≅ G/Ntype
17. #10622612C4semidirect
18. #10622612C4semidirect
21. C4×#4318C4semidirect
22. C2×#66867C4semidirect
277. C11#12865semidirect

Maximal subgroups

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

subgroupindex
#130772672
#130687202
#130667462
#130667442
#130667382
#130667362
C11×#18272
#1286511