Finite Group Databasebeta

← #14647368

Subgroups — #14647368

Order 2816.

426 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 99 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#13071587C211yesmaximal, characteristic
2#13068605C211yesmaximal, characteristic
3#13066936C211yesmaximal, characteristic
4#13066519C211yesmaximal, characteristic, complemented
5#13066476C211yesmaximal, characteristic, complemented
6#13066475C211yesmaximal, characteristic, complemented
7C11×#1303C211yesmaximal, characteristic, complemented
8C2×C4×D44C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C4×C11×C4⋊C4C2211yescharacteristic
12C2×#66887—21no—
13#10622603—22no—
14#10622552—21no—
15#10622549C2211yescharacteristic
16C4×C4⋊Dic11—21no—
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19#10622279C412yes—
20#10622277C412yes—
21#10622192—21no—
22#10622106—22no—
23C22×D44D411yescharacteristic
24C22×C4×D11C2×C412yes—
25C2×C11×M16—21no—
26C2×C11×C4⋊C4—21no—
27C2×C42×C11—21no—
28C2×C42×C11C2311yescharacteristic
29C2×(C2×D11)⋊C4—22no—
30C2×(C2×D11)⋊C4—22no—
31C2×(C2×D11)⋊C4D412yes—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11D411yescharacteristic
34C2×C4×Dic11—22no—
35C2×#4318—21no—
36C4×D44—21no—
37C4×D44—21no—
38C4×D44—21no—
39C4×D44—21no—
40C11×C4⋊C8—21no—
41C11×C4⋊C8—21no—
42C11×C4⋊C8—21no—
43C11×C22⋊C8—21no—
44C4×C8×C11—21no—
45C11×#95C2×C411yescharacteristic
46C11×#95C2×C411yescharacteristic
47C11⋊#95—21no—
48C11⋊#95—22no—
49C11⋊#95C2×C412yes—
50C22⋊(C11⋊C8)—21no—
51#66887—42no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4×C11⋊C8—21no—
56#8770—111nomaximal, Sylow
57C23×D11C22⋊C412yes—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11C22×C411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×Dic11—22no—
64C22×Dic11C22⋊C412yes—
65C2×D44—21no—
66C2×D44—21no—
67C2×D44—21no—
68C2×D44—21no—
69C2×D44—21no—
70C2×D44—21no—
71C2×C4×D11—22no—
72C2×C4×D11—22no—
73C2×C4×D11—82no—
74C11×M16—41no—
75C11×M16—41no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C11×C4⋊C4—42no—
79C42×C11—41no—
80C42×C11—41no—
81C42×C11#4111yescharacteristic
82C42×C11#4111yescharacteristic
83C42×C11#4111yescharacteristic
84C42×C11#4111yescharacteristic
85(C2×D11)⋊C4—22no—
86(C2×D11)⋊C4—22no—
87(C2×D11)⋊C4—44no—
88(C2×D11)⋊C4—82no—
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93C4×Dic11—82no—
94#4318—41no—
95#4318—41no—
96C2×C11⋊C8—41no—
97C2×C11⋊C8—41no—
98#2357—111no—
99#1800—111no—
100#1460—111no—
101#1303—111no—
102#1303D1111yescharacteristic, complemented
103#1286—111no—
104#1286—111no—
105C23×C11C2×C22⋊C411yescharacteristic
106C22×D11—22no—
107C22×D11—22no—
108C22×D11—22no—
109C22×D11—42no—
110C22×D11—42no—
111C2×C4×C11—22no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11#11711yescharacteristic
120C2×C4×C11#11711yescharacteristic
121C2×C4×C11#12311yescharacteristic
122C2×C4×C11#12311yescharacteristic
123C2×C4×C11#12311yescharacteristic
124C2×C4×C11#12311yescharacteristic
125C2×C4×C11#13511yescharacteristic
126C2×C4×C11#13511yescharacteristic
127C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C11#13711yescharacteristic
129C2×Dic11—22no—
130C2×Dic11—42no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134D44—41no—
135D44—41no—
136D44—41no—
137D44—41no—
138C4×D11—82no—
139C4×D11—82no—
140C8×C11—81no—
141C8×C11—81no—
142C11⋊C8—81no—
143C11⋊C8—81no—
144C2×C4×D4—111no—
145#431—111no—
146#431C2×D1111yescharacteristic
147#423—111no—
148#423C2×D1111yescharacteristic
149C2×#100—221no—
150#390—221no—
151#388—222no—
152#382—111no—
153#381—112no—
154C4×C4⋊C4—221no—
155C4×C4⋊C4C2×D1111yescharacteristic
156C4×C22⋊C4—112no—
157#343—221no—
158#323—222no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11#38111yescharacteristic
162C22×C11#41611yescharacteristic
163C22×C11#41711yescharacteristic
164C2×D11—42no—
165C2×D11—42no—
166C2×D11—42no—
167C2×D11—82no—
168C2×D11—82no—
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—42no—
174C4×C11—81no—
175C4×C11#48211yescharacteristic
176C4×C11#48211yescharacteristic
177C4×C11#48511yescharacteristic
178C4×C11#48511yescharacteristic
179Dic11—42no—
180Dic11—82no—
181C22×D4—111no—
182C23×C4—112no—
183C2×M16—21no—
184C2×M16—221no—
185C4×D4—221no—
186C4×D4—221no—
187C4×D4—221no—
188C4×D4—221no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—111no—
191C2×C4⋊C4—221no—
192C2×C22⋊C4—112no—
193C2×C22⋊C4—222no—
194C2×C22⋊C4—222no—
195C2×C42—21no—
196C2×C42—222no—
197C2×C42C22×D1111yescharacteristic
198C4⋊C8—21no—
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—221no—
202C4⋊C8—221no—
203C4⋊C8—221no—
204#100—442no—
205C22⋊C8—21no—
206C22⋊C8—221no—
207C4×C8—21no—
208C4×C8—221no—
209#95—112no—
210#95—222no—
211#95—221no—
212#95C4×D1111yescharacteristic
213#95C4×D1111yescharacteristic
214C2×C11—21no—
215C2×C11—21no—
216C2×C11#182511yescharacteristic
217C2×C11#182711yescharacteristic
218C2×C11#182911yescharacteristic
219D11—82no—
220C24—112no—
221C2×D4—221no—
222C2×D4—221no—
223C2×D4—221no—
224C2×D4—221no—
225C2×D4—221no—
226C2×D4—221no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—112no—
230C22×C4—222no—
231C22×C4—222no—
232C22×C4—222no—
233C22×C4—882no—
234C22×C4C2×C4×D1111yescharacteristic
235C22×C4D4×D1111yescharacteristic
236C22×C4D4×D1111yescharacteristic
237M16—41no—
238M16—41no—
239M16—441no—
240M16—441no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—441no—
244C2×C8—441no—
245C4⋊C4—42no—
246C4⋊C4—221no—
247C4⋊C4—221no—
248C4⋊C4—441no—
249C4⋊C4—441no—
250C22⋊C4—222no—
251C22⋊C4—222no—
252C22⋊C4—444no—
253C22⋊C4—882no—
254C42—41no—
255C42—41no—
256C42—882no—
257C42#433911yescharacteristic
258C42#433911yescharacteristic
259C42#434111yescharacteristic
260C42#434311yescharacteristic
261C11#877011yescharacteristic, complemented, Sylow
262C23—222no—
263C23—222no—
264C23—222no—
265C23—442no—
266C23—442no—
267C23C22⋊C4×D1111yescharacteristic
268D4—441no—
269D4—441no—
270D4—441no—
271D4—441no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—222no—
281C2×C4—442no—
282C2×C4—442no—
283C2×C4—442no—
284C2×C4—442no—
285C2×C4—882no—
286C2×C4—882no—
287C2×C4#6692511yescharacteristic
288C2×C4#6693611yescharacteristic
289C2×C4#6693611yescharacteristic
290C2×C4#6694511yescharacteristic
291C2×C4#6694711yescharacteristic
292C2×C4#6694711yescharacteristic
293C2×C4#6696411yescharacteristic
294C2×C4#6696811yescharacteristic
295C2×C4#6696911yescharacteristic
296C2×C4#6697211yescharacteristic
297C8—81no—
298C8—81no—
299C8—881no—
300C8—881no—
301C22—21no—
302C22—21no—
303C22—442no—
304C22—442no—
305C22—442no—
306C22—882no—
307C22—882no—
308C22#1062227711yescharacteristic
309C22#1062238411yescharacteristic
310C22#1062241711yescharacteristic
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—42no—
316C4—81no—
317C4—442no—
318C4—882no—
319C4#1062239211yescharacteristic
320C4#1062242711yescharacteristic
321C4#1062248011yescharacteristic
322C4#1062249811yescharacteristic
323C2—21no—
324C2—21no—
325C2—882no—
326C2#1306871011yescharacteristic
327C2#1306871911yescharacteristic
328C2#1306872611yescharacteristic
subgroupG/H
centerC22#10622277
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1303C2
socleC22×C11#381
prime radicalC22×D44D4
cosocleC2×C42×C11C23
hypercenter#1303D11
hypocenterC11#8770
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
4. #13066519C2semidirect
5. #13066476C2semidirect
6. #13066475C2semidirect
7. C11×#1303C2semidirect
102. #1303D11semidirect
261. C11#8770semidirect

Maximal subgroups

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

subgroupindex
#130715872
#130686052
#130669362
#130665192
#130664762
#130664752
C11×#13032
#877011