Finite Group Databasebeta

← #14672152

Subgroups — #14672152

Order 2816.

474 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66892C211yesmaximal, characteristic
2C2×#10622128C211yesmaximal, characteristic, complemented
3C2×#10622202C211yesmaximal, characteristic, complemented
4C2×#10622129C211yesmaximal, characteristic
5C2×C4×C11⋊C16C211yesmaximal, characteristic, complemented
6#13069482C211yesmaximal, characteristic
7C11×#1969C211yesmaximal, characteristic, complemented
8C22×C11×Q16C2211yescharacteristic
9C22×D88C2211yescharacteristic
10C2×C11×#107C2211yescharacteristic
11C2×C11×#103—21no—
12C2×C4×C8×C11C2211yescharacteristic
13C11×#391—21no—
14C2×#66892—22no—
15C2×#66892—22no—
16C2×#66892C414yescomplemented
17C2×#66885—21no—
18C2×#66882C2211yescharacteristic
19C22×C11⋊C16C2211yescharacteristic
20C22×C11⋊C16C2211yescharacteristic
21#10622552—21no—
22#10622202—22no—
23#10622129—22no—
24#10622128—22no—
25C4×C11⋊C16—22no—
26C22×Q8×C11—21no—
27C22×D44—21no—
28C2×C11×Q16—21no—
29C2×C11×Q16—21no—
30C2×C11×Q16—21no—
31C2×C11×Q16—21no—
32C2×C11×Q16—21no—
33C2×C11×Q16C2×C412yes—
34C22×C8×C11D411yescharacteristic
35C22×C8×C11C2311yescharacteristic
36C2×C11×C4⋊C4—21no—
37C2×C42×C11D411yescharacteristic
38C2×(C2×D11)⋊C4—42no—
39C2×C4⋊Dic11—21no—
40C2×D88—21no—
41C2×D88—21no—
42C2×D88—21no—
43C2×D88—21no—
44C2×D88—21no—
45C2×D88C2×C412yes—
46C11×#107—21no—
47C11×#107—21no—
48C11×#103—42no—
49C4×C8×C11—21no—
50C4×C8×C11—21no—
51C11×#95—42no—
52#66892—28no—
53#66885—42no—
54#66882—21no—
55#66882—21no—
56C2×C11⋊C16—21no—
57C2×C11⋊C16—21no—
58C2×C11⋊C16C2×C412yes—
59C2×C11⋊C16D412yes—
60C2×C11⋊C16D412yes—
61C2×C11⋊C16D412yes—
62#13237—111nomaximal, Sylow
63C23×D11—41no—
64C2×Q8×C11—22no—
65C2×Q8×C11—41no—
66C2×Q8×C11—41no—
67C2×Q8×C11—41no—
68C2×Q8×C11—41no—
69C2×Q8×C11—41no—
70C22×C4×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11D812yes—
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—41no—
75C2×D44—22no—
76C2×D44—41no—
77C2×D44—41no—
78C2×D44—41no—
79C2×D44—41no—
80C2×D44—41no—
81C11×Q16—22no—
82C11×Q16—22no—
83C11×Q16—41no—
84C11×Q16—41no—
85C2×C8×C11—21no—
86C2×C8×C11—21no—
87C2×C8×C11D812yes—
88C2×C8×C11C22×C411yescharacteristic
89C2×C8×C11C2×D411yescharacteristic
90C2×C8×C11C2×D411yescharacteristic
91C2×C8×C11C2×D411yescharacteristic
92C2×C8×C11#4111yescharacteristic
93C2×C8×C11#4111yescharacteristic
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C42×C11—21no—
97C42×C11—21no—
98(C2×D11)⋊C4—84no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101D88—22no—
102D88—22no—
103D88—41no—
104D88—41no—
105C11⋊C16—22no—
106C11⋊C16C22⋊C414yescomplemented
107C22×SD32—111no—
108C2×#367—111no—
109C2×#358—111no—
110C2×#357—111no—
111C2×C4×C16—111no—
112#1970—111no—
113#1969D1111yescharacteristic, complemented
114C23×C11C2×D811yescharacteristic
115C22×D11—42no—
116C22×D11—81no—
117C22×D11—81no—
118C22×D11—82no—
119C22×D11—82no—
120Q8×C11—42no—
121Q8×C11—42no—
122Q8×C11—81no—
123Q8×C11—81no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—42no—
127C2×C4×C11—81no—
128C2×C4×C11—81no—
129C2×C4×C11—81no—
130C2×C4×C11—82no—
131C2×C4×C11SD3214yescomplemented
132C2×C4×C11C4×D411yescharacteristic
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11#12711yescharacteristic
135C2×C4×C11C2×D811yescharacteristic
136C2×C4×C11#13511yescharacteristic
137C2×C4×C11#13511yescharacteristic
138C2×Dic11—81no—
139C2×Dic11—82no—
140D44—42no—
141D44—42no—
142D44—81no—
143D44—81no—
144C8×C11—22no—
145C8×C11C2×C22⋊C411yescharacteristic
146C8×C11C4×D411yescharacteristic
147C8×C11#12111yescharacteristic
148C8×C11#12411yescharacteristic
149C22×Q16C2×D1111yescharacteristic
150C22×D8—111no—
151C2×SD32—114no—
152C2×SD32—222no—
153C2×SD32—222no—
154C22×C16—111no—
155C22×C16—111no—
156C2×#107—111no—
157C2×#107C2×D1111yescharacteristic
158C2×#103—21no—
159C2×#102—221no—
160C2×C4×C8C2×D1111yescharacteristic
161#391—21no—
162#390—221no—
163#367—222no—
164#358—222no—
165#357—222no—
166C4×C16—222no—
167C22×C11C4×D811yescharacteristic
168C22×C11#46611yescharacteristic
169C22×C11#49311yescharacteristic
170C22×C11C2×SD3212yes—
171C22×C11#50812yes—
172C2×D11—84no—
173C2×D11—82no—
174C2×D11—162no—
175C2×D11—161no—
176C2×D11—161no—
177C4×C11—24no—
178C4×C11—82no—
179C4×C11—161no—
180C4×C11#39011yescharacteristic
181C4×C11C4×D811yescharacteristic
182C4×C11#46611yescharacteristic
183C4×C11#49511yescharacteristic
184Dic11—161no—
185C22×Q8—21no—
186C22×D4—221no—
187C2×Q16—21no—
188C2×Q16—21no—
189C2×Q16—21no—
190C2×Q16—21no—
191C2×Q16—21no—
192C2×Q16C4×D1112yes—
193C2×D8—112no—
194C2×D8—221no—
195C2×D8—221no—
196C2×D8—221no—
197C2×D8—221no—
198C2×D8—221no—
199C22×C8C22⋊D1111yescharacteristic
200C22×C8C22×D1111yescharacteristic
201C2×C4⋊C4—21no—
202C2×C4⋊C4—221no—
203C2×C22⋊C4—442no—
204C2×C42C22⋊D1111yescharacteristic
205SD32—228no—
206C2×C16—112no—
207C2×C16—112no—
208C2×C16—112no—
209C2×C16—112no—
210C2×C16—221no—
211C2×C16—221no—
212#107—21no—
213#107—21no—
214#107—221no—
215#107—221no—
216#103—42no—
217#102—442no—
218C4×C8—21no—
219C4×C8—21no—
220#95—42no—
221C2×C11#197011yescharacteristic
222C2×C11C4×SD3212yes—
223C2×C11#221712yes—
224C2×C11#224811yescharacteristic
225C2×C11#224911yescharacteristic
226D11—162no—
227C24—441no—
228C2×Q8—22no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×D4—222no—
235C2×D4—441no—
236C2×D4—441no—
237C2×D4—441no—
238C2×D4—441no—
239C2×D4—441no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—441no—
243C22×C4#432312yes—
244C22×C4C2×C22⋊D1111yescharacteristic
245Q16—22no—
246Q16—22no—
247Q16—41no—
248Q16—41no—
249D8—222no—
250D8—222no—
251D8—441no—
252D8—441no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8#432312yes—
256C2×C8C2×C4×D1111yescharacteristic
257C2×C8#433911yescharacteristic
258C2×C8D4×D1111yescharacteristic
259C2×C8D4×D1111yescharacteristic
260C2×C8D4×D1111yescharacteristic
261C2×C8#434111yescharacteristic
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—441no—
265C4⋊C4—441no—
266C22⋊C4—884no—
267C42—21no—
268C42—21no—
269C16—114no—
270C16—222no—
271C11#1323711yescharacteristic, complemented, Sylow
272C23—442no—
273C23—882no—
274C23—882no—
275C23—881no—
276C23—881no—
277C23C2×#432311yescharacteristic
278Q8—42no—
279Q8—42no—
280Q8—81no—
281Q8—81no—
282D4—442no—
283D4—442no—
284D4—881no—
285D4—881no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—42no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—82no—
292C2×C4—81no—
293C2×C4—882no—
294C2×C4—881no—
295C2×C4#6689214yescomplemented
296C2×C4C4×C22⋊D1111yescharacteristic
297C2×C4C2×#432311yescharacteristic
298C2×C4#6699211yescharacteristic
299C2×C4#6699311yescharacteristic
300C2×C4#6700311yescharacteristic
301C2×C4#6700311yescharacteristic
302C8—22no—
303C8C22⋊C4×D1111yescharacteristic
304C8(C22⋊D11)⋊C411yescharacteristic
305C8#6693711yescharacteristic
306C8#6693811yescharacteristic
307C22—884no—
308C22—882no—
309C22—1761no—
310C22—1761no—
311C22—1762no—
312C22C4×#432311yescharacteristic
313C22#1062265111yescharacteristic
314C22#1062268611yescharacteristic
315C22C2×#6689212yes—
316C22#1062280712yes—
317C4—24no—
318C4—82no—
319C4—161no—
320C4—1761no—
321C4#1062257011yescharacteristic
322C4C4×#432311yescharacteristic
323C4#1062265111yescharacteristic
324C4#1062267211yescharacteristic
325C2—1762no—
326C2#1306948111yescharacteristic
327C2C4×#6689212yes—
328C2#1307071412yes—
329C2#1307087311yescharacteristic
330C2#1307087511yescharacteristic
subgroupG/H
centerC23C2×#4323
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1969C2
socleC23×C11C2×D8
prime radicalC22×D88C22
cosocleC22×C8×C11C23
hypercenter#1969D11
hypocenterC11#13237
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1969

Complements

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

NH ≅ G/Ntype
2. C2×#10622128C2semidirect
3. C2×#10622202C2semidirect
5. C2×C4×C11⋊C16C2semidirect
7. C11×#1969C2semidirect
16. C2×#66892C4semidirect
106. C11⋊C16C22⋊C4semidirect
113. #1969D11semidirect
131. C2×C4×C11SD32semidirect
271. C11#13237semidirect
295. C2×C4#66892semidirect

Maximal subgroups

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

subgroupindex
C22×#668922
C2×#106221282
C2×#106222022
C2×#106221292
C2×C4×C11⋊C162
#130694822
C11×#19692
#1323711