Finite Group Databasebeta

← #14672139

Subgroups — #14672139

Order 2816.

464 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 103 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#13070308C212yesmaximal, complemented
2#13070266C212yesmaximal, complemented
3#13068666C211yesmaximal, characteristic, complemented
4#13068416C211yesmaximal, characteristic, complemented
5C11×#3058C211yesmaximal, characteristic
6C22×C11×D8C411yescharacteristic, complemented
7C2×C11×#131C2211yescharacteristic
8C11×#535C2212yes—
9C11×#469—21no—
10C11×#469—21no—
11C11×#466—21no—
12C11×#466—21no—
13C11×#427C411yescharacteristic, complemented
14C11×#418C412yescomplemented
15#10622853C2211yescharacteristic
16#10622850C2212yes—
17#10622850C2211yescharacteristic
18C2×#66883—21no—
19#10622714—21no—
20C11⋊#338—21no—
21#10622194—21no—
22#10622180—24no—
23#10622174—24no—
24C2×C11×#41C2311yescharacteristic
25C22×D4×C11C2×C412yes—
26C2×C11×D8—21no—
27C2×C11×D8—21no—
28C2×C11×D8—41no—
29C2×C11×D8—41no—
30C11×#131—41no—
31C11×#131—41no—
32C2×C11×M16C2×C411yescharacteristic
33C2×C11×M16D411yescharacteristic
34C2×C11×M16D411yescharacteristic
35C22×C8×C11C2×C411yescharacteristic
36C22×C8×C11D411yescharacteristic
37C22×C8×C11D411yescharacteristic
38C11×#127—22no—
39C11×#124—22no—
40C11×#121—22no—
41C11×#121—22no—
42C11×#120—22no—
43C11×#120—22no—
44C11×#117C2×C412yes—
45#66979—21no—
46C2×#4318—21no—
47C2×#4318—22no—
48C11×#107—21no—
49C11×#106—21no—
50C11×#102—22no—
51C11×#102—22no—
52#66900—22no—
53#66900D412yes—
54#66898—21no—
55#66898D412yes—
56#66897—21no—
57#66897—22no—
58#66883—41no—
59#66883—41no—
60#66879—41no—
61C8×Dic11—41no—
62#13234—111nomaximal, Sylow
63C24×C11—22no—
64C11×#41—41no—
65C11×#41—41no—
66C2×Q8×C11C2×D411yescharacteristic
67C2×D4×C11—22no—
68C2×D4×C11—22no—
69C2×D4×C11—42no—
70C2×D4×C11—42no—
71C2×D4×C11—42no—
72C2×D4×C11—42no—
73C2×D4×C11C2×D411yescharacteristic
74C2×D4×C11#4111yescharacteristic
75C2×D4×C11#4111yescharacteristic
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C11×D8—42no—
80C11×D8—41no—
81C11×D8—41no—
82C11×M16—41no—
83C11×M16—41no—
84C11×M16—41no—
85C2×C8×C11—21no—
86C2×C8×C11—21no—
87C2×C8×C11—21no—
88C2×C8×C11—21no—
89C2×C8×C11—21no—
90C2×C8×C11—21no—
91C2×C8×C11C22⋊C411yescharacteristic
92C2×C8×C11C22⋊C411yescharacteristic
93C2×C8×C11C22⋊C411yescharacteristic
94C2×C8×C11C22⋊C411yescharacteristic
95C11×C4⋊C4—22no—
96C11×C22⋊C4—22no—
97C11×C22⋊C4—42no—
98C11×C22⋊C4—42no—
99C42×C11—22no—
100C22⋊Dic11—22no—
101C4⋊Dic11—41no—
102C4×Dic11—41no—
103#4318—22no—
104#4318—41no—
105#4318—42no—
106#4318—42no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—42no—
109#3058D1111yescharacteristic
110#2134—112no—
111#2122—112no—
112#1813—111no—
113#1757—111no—
114C23×C11—42no—
115C23×C11—82no—
116C23×C11—162no—
117C23×C11C4×D411yescharacteristic
118C23×C11#12111yescharacteristic
119C23×C11#12411yescharacteristic
120Q8×C11—41no—
121D4×C11—41no—
122D4×C11—41no—
123D4×C11—41no—
124D4×C11—42no—
125D4×C11—42no—
126D4×C11—82no—
127D4×C11—162no—
128D4×C11—162no—
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—42no—
136C2×C4×C11C2×C22⋊C411yescharacteristic
137C2×C4×C11C4×D411yescharacteristic
138C2×C4×C11#12111yescharacteristic
139C2×C4×C11#12711yescharacteristic
140C2×Dic11—42no—
141C8×C11—21no—
142C8×C11—21no—
143C8×C11—21no—
144C8×C11#9911yescharacteristic
145C8×C11#9911yescharacteristic
146C11⋊C8—42no—
147C11⋊C8—82no—
148C22×D8Dic1111yescharacteristic, complemented
149C2×#131C2×D1111yescharacteristic
150#535C2×D1112yes—
151#469—21no—
152#469—21no—
153#466—21no—
154#466—21no—
155C2×#108—221no—
156#427Dic1111yescharacteristic, complemented
157#418Dic1112yescomplemented
158#413—111no—
159#413—112no—
160#410—111no—
161#405—221no—
162#355—224no—
163AΣL(1,𝔽16)—224no—
164#344—221no—
165#338—221no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—82no—
173C22×C11—82no—
174C22×C11—82no—
175C22×C11—164no—
176C22×C11#39011yescharacteristic
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—82no—
181C4×C11C2×#9911yescharacteristic
182C4×C11#41011yescharacteristic
183Dic11—82no—
184C2×#41C22×D1111yescharacteristic
185C22×D4C2×Dic1112yes—
186C2×D8—21no—
187C2×D8—21no—
188C2×D8—41no—
189C2×D8—41no—
190#131—41no—
191#131—41no—
192C2×M16—221no—
193C2×M16—222no—
194C2×M16C2×Dic1111yescharacteristic
195C2×M16C22⋊D1111yescharacteristic
196C2×M16C22⋊D1111yescharacteristic
197C22×C8C2×Dic1111yescharacteristic
198C22×C8C22⋊D1111yescharacteristic
199C22×C8C22⋊D1111yescharacteristic
200#127—22no—
201#124—22no—
202#121—22no—
203#121—22no—
204#120—22no—
205#120—22no—
206#117—221no—
207#117C2×Dic1112yes—
208#108—441no—
209#108—441no—
210#107—21no—
211#106—21no—
212#102—22no—
213#102—22no—
214#101—112no—
215#101—222no—
216#100—221no—
217#100—222no—
218#99—112no—
219#99—221no—
220#97—441no—
221C4×C8—441no—
222C2×C11—21no—
223C2×C11—41no—
224C2×C11—41no—
225C2×C11—41no—
226C2×C11—162no—
227C2×C11#196411yescharacteristic
228C24—22no—
229#41—41no—
230#41—41no—
231C2×Q8D4×D1111yescharacteristic
232C2×D4—22no—
233C2×D4—22no—
234C2×D4—42no—
235C2×D4—42no—
236C2×D4—42no—
237C2×D4—42no—
238C2×D4D4×D1111yescharacteristic
239C2×D4#434111yescharacteristic
240C2×D4#434111yescharacteristic
241C22×C4C22×Dic1111yescharacteristic
242C22×C4C2×C22⋊D1111yescharacteristic
243C22×C4C2×C22⋊D1111yescharacteristic
244D8—42no—
245D8—41no—
246D8—41no—
247M16—41no—
248M16—41no—
249M16—41no—
250M16—222no—
251M16—441no—
252M16—442no—
253M16—442no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—21no—
260C2×C8—441no—
261C2×C8—442no—
262C2×C8C22⋊Dic1111yescharacteristic
263C2×C8C22⋊Dic1111yescharacteristic
264C2×C8C22⋊Dic1111yescharacteristic
265C2×C8C22⋊Dic1111yescharacteristic
266C4⋊C4—22no—
267C4⋊C4—441no—
268C22⋊C4—22no—
269C22⋊C4—42no—
270C22⋊C4—42no—
271C22⋊C4—222no—
272C42—22no—
273C42—441no—
274C11#1323411yescharacteristic, complemented, Sylow
275C23—42no—
276C23—82no—
277C23—162no—
278C23D4×Dic1111yescharacteristic
279C23#6698911yescharacteristic
280C23#6699111yescharacteristic
281Q8—41no—
282D4—41no—
283D4—41no—
284D4—41no—
285D4—42no—
286D4—42no—
287D4—82no—
288D4—162no—
289D4—162no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—42no—
297C2×C4—442no—
298C2×C4D4×Dic1111yescharacteristic
299C2×C4#6699111yescharacteristic
300C2×C4#6699311yescharacteristic
301C2×C4C2×C22⋊Dic1111yescharacteristic
302C8—21no—
303C8—21no—
304C8—21no—
305C8—442no—
306C8—882no—
307C8#6689811yescharacteristic
308C8#6689811yescharacteristic
309C22—21no—
310C22—21no—
311C22—21no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—82no—
316C22—82no—
317C22—82no—
318C22—164no—
319C22#1062283411yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—82no—
324C4—882no—
325C4C2×#6689811yescharacteristic
326C4#1062285311yescharacteristic
327C2—21no—
328C2—41no—
329C2—41no—
330C2—41no—
331C2—162no—
332C2#1306945311yescharacteristic
subgroupG/H
centerC2#13069453
commutatorC22×C4×C11C22×C4
FrattiniC2×#41C22×D11
Fitting, prime radicalC11×#3058C2
socleC2×C11#1964
cosocleC2×C11×#41C23
hypercenter#3058D11
hypocenterC11#13234
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#131 ◁ #3058

Complements

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

NH ≅ G/Ntype
1. #13070308C2semidirect
2. #13070266C2semidirect
3. #13068666C2semidirect
4. #13068416C2semidirect
6. C22×C11×D8C4semidirect
13. C11×#427C4semidirect
14. C11×#418C4semidirect
148. C22×D8Dic11semidirect
156. #427Dic11semidirect
157. #418Dic11semidirect
274. C11#13234semidirect

Maximal subgroups

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

subgroupindex
#130703082
#130702662
#130686662
#130684162
C11×#30582
#1323411