Finite Group Databasebeta

← #14910407

Subgroups — #14910407

Order 2816.

668 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 147 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
1C2×#10622531C212yesmaximal, complemented
2#13080358C212yesmaximal, complemented
3#13070877C211yesmaximal, characteristic, complemented
4#13070730C212yesmaximal, complemented
5#13070678C212yesmaximal, complemented
6#13070551C212yesmaximal, complemented
7#13070542C212yesmaximal, complemented
8#13070449C211yesmaximal, characteristic, complemented
9C4×C11×Q32C211yesmaximal, characteristic, complemented
10C2×#66972C2212yes—
11C2×Q16×D11C2212yes—
12#10623107—22no—
13C2×C11×Q32C2211yescharacteristic
14C4×C11×Q16C2212yes—
15C2×#66893C2212yes—
16C2×#66892C2212yes—
17#10622641—22no—
18#10622531—28no—
19C2×Dic88C2211yescharacteristic
20C2×#66864C2212yes—
21C2×D176C2211yescharacteristic
22C2×#66862C2212yes—
23#10622500C2212yes—
24#10622496C2212yes—
25#10622423—22no—
26#10622419—22no—
27#10622309C2212yes—
28C8×D44C2211yescharacteristic
29C11×#366C2211yescharacteristic
30C11×#358C2212yes—
31C4×C11×C16C2211yescharacteristic
32(C2×D11)⋊C16C2212yes—
33#10622130C2212yes—
34#10622129C2212yes—
35C4⋊(C11⋊C16)C2211yescharacteristic
36C2×#4343—22no—
37C2×Q8×D11—22no—
38C2×C11×Q16C2312yes—
39C4×Q8×C11—22no—
40C2×#4326—22no—
41C2×#4325—22no—
42#66972—24no—
43#66972—42no—
44Q16×D11—24no—
45Q16×D11—42no—
46C2×Dic44C2312yes—
47C2×D88C2312yes—
48C2×#4314—22no—
49C2×C8×D11C2312yes—
50#66950—22no—
51#66950—42no—
52#66948—22no—
53#66948—42no—
54#66928—22no—
55#66928—42no—
56C4×D44—42no—
57C4×D44D411yescharacteristic
58C11×Q32D414yescomplemented
59C2×C11×C16C2311yescharacteristic
60C2×C11×C16C2311yescharacteristic
61C11×#107C2312yes—
62C11×#103—22no—
63C4×C8×C11C2311yescharacteristic
64#66893—24no—
65#66892—24no—
66(C2×D11)⋊C8D412yes—
67C2×C11⋊C16C2312yes—
68#66874—22no—
69#66873—22no—
70C4⋊(C11⋊C8)D411yescharacteristic
71Dic88—41no—
72#66864—24no—
73D176—41no—
74#66862—24no—
75#33843—111nomaximal, Sylow
76C2×Q8×C11—22no—
77#4343—44no—
78#4343—82no—
79Q8×D11—44no—
80Q8×D11—82no—
81C2×D44—22no—
82C2×D44—42no—
83C2×D44—42no—
84C2×D44D811yescharacteristic
85C2×C4×D11—42no—
86C2×C4×D11—42no—
87C2×C4×D11C2×D412yes—
88C2×Dic22—22no—
89C2×Dic22—42no—
90C11×Q16—22no—
91C11×Q16C2×D414yes—
92C2×C8×C11C2×D411yescharacteristic
93C2×C8×C11C2411yescharacteristic
94C11×C4⋊C4—22no—
95C11×C4⋊C4—42no—
96C42×C11—42no—
97C42×C11C2×D411yescharacteristic
98#4326—44no—
99#4325—44no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—42no—
104(C2×D11)⋊C4D812yes—
105C4⋊Dic11—42no—
106C4⋊Dic11D811yescharacteristic
107C2×C11⋊C8C2×D412yes—
108Dic44—22no—
109Dic44—22no—
110D88—22no—
111D88—22no—
112#4314—82no—
113C8×D11—22no—
114C8×D11—22no—
115C11×C16—21no—
116C11×C16C2×D412yes—
117C11⋊C16—22no—
118C2×#510—112no—
119#3285—112no—
120#2249—111no—
121#2220—112no—
122#2211—112no—
123#2188—112no—
124#2186—112no—
125C4×Q32D1111yescharacteristic, complemented
126#2169—111no—
127C22×D11—42no—
128C22×D11C2×D812yes—
129Q8×C11—24no—
130Q8×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11C2×D811yescharacteristic
134C2×C4×C11C2×D811yescharacteristic
135C2×C4×C11C22×D411yescharacteristic
136C2×Dic11—42no—
137C2×Dic11C2×D812yes—
138D44—41no—
139D44—42no—
140D44—42no—
141D44—84no—
142D44—84no—
143C4×D11—22no—
144C4×D11—22no—
145C4×D11—84no—
146C4×D11—84no—
147Dic22—42no—
148Dic22—42no—
149Dic22—84no—
150C8×C11—21no—
151C8×C11C22×D411yescharacteristic
152C8×C11H(5,𝔽2)11yescharacteristic
153C11⋊C8—22no—
154C2×#135—112no—
155C22×Q16—112no—
156#548—222no—
157#510—228no—
158C2×Q32—112no—
159C2×Q32—111no—
160C2×Q32C2×D1111yescharacteristic
161C2×SD32—112no—
162C2×SD32—112no—
163C2×D16—111no—
164C2×M32—112no—
165#495—112no—
166#467—112no—
167#466—112no—
168#464—222no—
169#452—222no—
170#448—222no—
171C4×Q16C2×D1112yes—
172C8×D4—111no—
173#366C2×D1111yescharacteristic
174C4⋊C16—111no—
175#358—112no—
176#358C2×D1112yes—
177#357—112no—
178C22⋊C16—112no—
179C4×C16C2×D1111yescharacteristic
180C22×C11C22×D811yescharacteristic
181C2×D11—22no—
182C2×D11—22no—
183C2×D11—22no—
184C2×D11—82no—
185C2×D11—82no—
186C2×D11—82no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—44no—
190C4×C11—82no—
191C4×C11D4211yescharacteristic
192C4×C11#57611yescharacteristic
193Dic11—22no—
194Dic11—82no—
195C2×#41—222no—
196C22×Q8—222no—
197#135—224no—
198#135—442no—
199C2×Q16—112no—
200C2×Q16—222no—
201C2×Q16—224no—
202C2×Q16—442no—
203C2×Q16C22×D1112yes—
204C2×SD16—222no—
205C2×SD16—222no—
206C2×D8—112no—
207C22×C8—112no—
208#124—222no—
209#124—442no—
210C22⋊Q8—222no—
211C22⋊Q8—442no—
212#121—222no—
213#121—442no—
214C4×Q8—22no—
215C4×D4—111no—
216C4×D4—442no—
217Q32—224no—
218Q32—441no—
219Q32D4414yescomplemented
220SD32—224no—
221SD32—224no—
222D16—441no—
223M32—224no—
224C2×C16—112no—
225C2×C16C22×D1111yescharacteristic
226C2×C16C22×D1111yescharacteristic
227#107C22×D1112yes—
228C4⋊C8—111no—
229#103—22no—
230#103—222no—
231#102—222no—
232C22⋊C8—112no—
233C4×C8C22×D1111yescharacteristic
234C2×C11D4×D811yescharacteristic
235C2×C11#341411yescharacteristic
236C2×C11#341711yescharacteristic
237D11—42no—
238D11—162no—
239#41—444no—
240#41—882no—
241C2×Q8—22no—
242C2×Q8—222no—
243C2×Q8—442no—
244C2×Q8—444no—
245C2×Q8—882no—
246C2×D4—111no—
247C2×D4—222no—
248C2×D4—442no—
249C2×D4—442no—
250C22×C4—112no—
251C22×C4—442no—
252C22×C4—442no—
253Q16—22no—
254Q16—222no—
255Q16—222no—
256Q16—444no—
257Q16C2×D4414yes—
258SD16—444no—
259SD16—882no—
260D8—222no—
261D8—222no—
262C2×C8—112no—
263C2×C8—222no—
264C2×C8—222no—
265C2×C8D4×D1111yescharacteristic
266C2×C8C23×D1111yescharacteristic
267C4⋊C4—22no—
268C4⋊C4—42no—
269C4⋊C4—111no—
270C4⋊C4—442no—
271C22⋊C4—112no—
272C22⋊C4—442no—
273C22⋊C4—442no—
274C22⋊C4—442no—
275C22⋊C4—442no—
276C42—42no—
277C42D4×D1111yescharacteristic
278C16—21no—
279C16—222no—
280C16C2×D4412yes—
281C11#3384311yescharacteristic, complemented, Sylow
282C23—112no—
283C23—442no—
284Q8—24no—
285Q8—42no—
286Q8—442no—
287Q8—442no—
288Q8—884no—
289D4—441no—
290D4—442no—
291D4—442no—
292D4—884no—
293D4—884no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—112no—
297C2×C4—222no—
298C2×C4—222no—
299C2×C4—442no—
300C2×C4—884no—
301C2×C4—884no—
302C2×C4D8×D1111yescharacteristic
303C2×C4D8×D1111yescharacteristic
304C2×C4C2×D4×D1111yescharacteristic
305C8—21no—
306C8—222no—
307C8C22×D4411yescharacteristic
308C8#6704211yescharacteristic
309C22—222no—
310C22—222no—
311C22—222no—
312C22—882no—
313C22—882no—
314C22—882no—
315C22C2×D8×D1111yescharacteristic
316C4—21no—
317C4—21no—
318C4—44no—
319C4—82no—
320C4—222no—
321C4—882no—
322C4D4×D4411yescharacteristic
323C4#1062330011yescharacteristic
324C2—442no—
325C2—1762no—
326C2D8×D4411yescharacteristic
327C2#1308174911yescharacteristic
328C2#1308176511yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×Q32C2
socleC22×C11C22×D8
hypercenterC4×Q32D11
hypocenterC11#33843
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×Q32

Complements

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

NH ≅ G/Ntype
1. C2×#10622531C2semidirect
2. #13080358C2semidirect
3. #13070877C2semidirect
4. #13070730C2semidirect
5. #13070678C2semidirect
6. #13070551C2semidirect
7. #13070542C2semidirect
8. #13070449C2semidirect
9. C4×C11×Q32C2semidirect
58. C11×Q32D4semidirect
125. C4×Q32D11semidirect
219. Q32D44semidirect
281. C11#33843semidirect

Maximal subgroups

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

subgroupindex
C2×#106225312
#130803582
#130708772
#130707302
#130706782
#130705512
#130705422
#130704492
C4×C11×Q322
#3384311