Finite Group Databasebeta

← #14672142

Subgroups — #14672142

Order 2816.

510 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66890C211yesmaximal, characteristic
2C2×#10622127C211yesmaximal, characteristic, complemented
3C2×#10622200C211yesmaximal, characteristic, complemented
4C2×#10622129C211yesmaximal, characteristic, complemented
5C2×C4×C11⋊C16C211yesmaximal, characteristic, complemented
6#13069482C211yesmaximal, characteristic, complemented
7C11×#1970C211yesmaximal, characteristic, complemented
8C22×C11×D8C2211yescharacteristic
9C22×D88C2211yescharacteristic
10C2×C11×#107C2211yescharacteristic
11C2×C11×#102—21no—
12C2×C4×C8×C11C2211yescharacteristic
13C11×#390—21no—
14C2×#66890—22no—
15C2×#66890—22no—
16C2×#66890C414yescomplemented
17C2×#66885—21no—
18C2×#66882C2211yescharacteristic
19C22×C11⋊C16C2211yescharacteristic
20C22×C11⋊C16C2211yescharacteristic
21#10622552—21no—
22#10622200—22no—
23#10622129—22no—
24#10622127—22no—
25C4×C11⋊C16—22no—
26C22×D4×C11—21no—
27C22×D44—21no—
28C2×C11×D8—21no—
29C2×C11×D8—21no—
30C2×C11×D8—21no—
31C2×C11×D8—21no—
32C2×C11×D8—21no—
33C2×C11×D8C2×C412yes—
34C22×C8×C11D411yescharacteristic
35C22×C8×C11C2311yescharacteristic
36C2×C11×C4⋊C4—21no—
37C2×C11×C22⋊C4—42no—
38C2×C42×C11D411yescharacteristic
39C2×(C2×D11)⋊C4—42no—
40C2×C4⋊Dic11—21no—
41C2×D88—21no—
42C2×D88—21no—
43C2×D88—21no—
44C2×D88—21no—
45C2×D88—21no—
46C2×D88C2×C412yes—
47C11×#107—21no—
48C11×#107—21no—
49C11×#102—42no—
50C4×C8×C11—21no—
51C4×C8×C11—21no—
52#66890—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#13235—111nomaximal, Sylow
63C24×C11—41no—
64C23×D11—41no—
65C2×D4×C11—22no—
66C2×D4×C11—41no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×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×D8—22no—
82C11×D8—22no—
83C11×D8—41no—
84C11×D8—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—
96C11×C22⋊C4—84no—
97C42×C11—21no—
98C42×C11—21no—
99(C2×D11)⋊C4—84no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102D88—22no—
103D88—22no—
104D88—41no—
105D88—41no—
106C11⋊C16—22no—
107C11⋊C16C22⋊C414yescomplemented
108C22×D16—111no—
109C2×#366—111no—
110C2×#357—111no—
111C2×#357—111no—
112C2×C4×C16—111no—
113#1970—111no—
114#1970D1111yescharacteristic, complemented
115C23×C11—42no—
116C23×C11—81no—
117C23×C11—81no—
118C23×C11—82no—
119C23×C11—82no—
120C23×C11C2×D811yescharacteristic
121C22×D11—42no—
122C22×D11—81no—
123C22×D11—81no—
124C22×D11—82no—
125C22×D11—82no—
126D4×C11—42no—
127D4×C11—42no—
128D4×C11—81no—
129D4×C11—81no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—81no—
133C2×C4×C11—82no—
134C2×C4×C11D1614yescomplemented
135C2×C4×C11C4×D411yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12711yescharacteristic
138C2×C4×C11C2×D811yescharacteristic
139C2×C4×C11#13511yescharacteristic
140C2×C4×C11#13511yescharacteristic
141C2×Dic11—81no—
142C2×Dic11—82no—
143D44—42no—
144D44—42no—
145D44—81no—
146D44—81no—
147C8×C11—22no—
148C8×C11C2×C22⋊C411yescharacteristic
149C8×C11C4×D411yescharacteristic
150C8×C11#12111yescharacteristic
151C8×C11#12411yescharacteristic
152C22×D8—111no—
153C22×D8C2×D1111yescharacteristic
154C2×D16—114no—
155C2×D16—222no—
156C2×D16—222no—
157C22×C16—111no—
158C22×C16—111no—
159C2×#107—111no—
160C2×#107C2×D1111yescharacteristic
161C2×#102—21no—
162C2×#102—221no—
163C2×C4×C8C2×D1111yescharacteristic
164#390—21no—
165#390—221no—
166#366—222no—
167#357—222no—
168#357—222no—
169C4×C16—222no—
170C22×C11—84no—
171C22×C11—82no—
172C22×C11—162no—
173C22×C11—161no—
174C22×C11—161no—
175C22×C11C4×D811yescharacteristic
176C22×C11#46611yescharacteristic
177C22×C11#49311yescharacteristic
178C22×C11C2×D1612yes—
179C22×C11#50812yes—
180C2×D11—84no—
181C2×D11—82no—
182C2×D11—162no—
183C2×D11—161no—
184C2×D11—161no—
185C4×C11—24no—
186C4×C11—161no—
187C4×C11#39011yescharacteristic
188C4×C11C4×D811yescharacteristic
189C4×C11#46611yescharacteristic
190C4×C11#49511yescharacteristic
191Dic11—161no—
192C22×D4—21no—
193C22×D4—221no—
194C2×D8—21no—
195C2×D8—21no—
196C2×D8—21no—
197C2×D8—21no—
198C2×D8—21no—
199C2×D8—112no—
200C2×D8—221no—
201C2×D8—221no—
202C2×D8—221no—
203C2×D8—221no—
204C2×D8—221no—
205C2×D8C4×D1112yes—
206C22×C8C22⋊D1111yescharacteristic
207C22×C8C22×D1111yescharacteristic
208C2×C4⋊C4—21no—
209C2×C4⋊C4—221no—
210C2×C22⋊C4—42no—
211C2×C22⋊C4—442no—
212C2×C42C22⋊D1111yescharacteristic
213D16—228no—
214C2×C16—112no—
215C2×C16—112no—
216C2×C16—112no—
217C2×C16—112no—
218C2×C16—221no—
219C2×C16—221no—
220#107—21no—
221#107—21no—
222#107—221no—
223#107—221no—
224#102—42no—
225#102—442no—
226C4×C8—21no—
227C4×C8—21no—
228C2×C11—162no—
229C2×C11#197011yescharacteristic
230C2×C11C4×D1612yes—
231C2×C11#221512yes—
232C2×C11#224611yescharacteristic
233C2×C11#224911yescharacteristic
234D11—162no—
235C24—41no—
236C24—441no—
237C2×D4—22no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4—41no—
241C2×D4—41no—
242C2×D4—41no—
243C2×D4—222no—
244C2×D4—441no—
245C2×D4—441no—
246C2×D4—441no—
247C2×D4—441no—
248C2×D4—441no—
249C22×C4—41no—
250C22×C4—441no—
251C22×C4#432312yes—
252C22×C4C2×C22⋊D1111yescharacteristic
253D8—22no—
254D8—22no—
255D8—41no—
256D8—41no—
257D8—222no—
258D8—222no—
259D8—441no—
260D8—441no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8#432312yes—
264C2×C8C2×C4×D1111yescharacteristic
265C2×C8#433911yescharacteristic
266C2×C8D4×D1111yescharacteristic
267C2×C8D4×D1111yescharacteristic
268C2×C8D4×D1111yescharacteristic
269C2×C8#434111yescharacteristic
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—441no—
273C4⋊C4—441no—
274C22⋊C4—84no—
275C22⋊C4—884no—
276C42—21no—
277C42—21no—
278C16—114no—
279C16—222no—
280C11#1323511yescharacteristic, complemented, Sylow
281C23—42no—
282C23—82no—
283C23—82no—
284C23—81no—
285C23—81no—
286C23—442no—
287C23—882no—
288C23—882no—
289C23—881no—
290C23—881no—
291C23C2×#432311yescharacteristic
292D4—42no—
293D4—42no—
294D4—81no—
295D4—81no—
296D4—442no—
297D4—442no—
298D4—881no—
299D4—881no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—82no—
303C2×C4—81no—
304C2×C4—882no—
305C2×C4—881no—
306C2×C4#6689014yescomplemented
307C2×C4C4×C22⋊D1111yescharacteristic
308C2×C4C2×#432311yescharacteristic
309C2×C4#6699211yescharacteristic
310C2×C4#6699311yescharacteristic
311C2×C4#6700311yescharacteristic
312C2×C4#6700311yescharacteristic
313C8—22no—
314C8C22⋊C4×D1111yescharacteristic
315C8(C22⋊D11)⋊C411yescharacteristic
316C8#6693711yescharacteristic
317C8#6693811yescharacteristic
318C22—84no—
319C22—82no—
320C22—161no—
321C22—161no—
322C22—162no—
323C22—884no—
324C22—882no—
325C22—1761no—
326C22—1761no—
327C22—1762no—
328C22C4×#432311yescharacteristic
329C22#1062265111yescharacteristic
330C22#1062268611yescharacteristic
331C22C2×#6689012yes—
332C22#1062280712yes—
333C4—24no—
334C4—161no—
335C4—1761no—
336C4#1062257011yescharacteristic
337C4C4×#432311yescharacteristic
338C4#1062265111yescharacteristic
339C4#1062267211yescharacteristic
340C2—162no—
341C2—1762no—
342C2#1306948111yescharacteristic
343C2C4×#6689012yes—
344C2#1307070012yes—
345C2#1307086511yescharacteristic
346C2#1307087511yescharacteristic
subgroupG/H
centerC23C2×#4323
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1970C2
socleC23×C11C2×D8
prime radicalC22×#66890C2
cosocleC22×C8×C11C23
hypercenter#1970D11
hypocenterC11#13235
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1970

Complements

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

NH ≅ G/Ntype
2. C2×#10622127C2semidirect
3. C2×#10622200C2semidirect
4. C2×#10622129C2semidirect
5. C2×C4×C11⋊C16C2semidirect
6. #13069482C2semidirect
7. C11×#1970C2semidirect
16. C2×#66890C4semidirect
107. C11⋊C16C22⋊C4semidirect
114. #1970D11semidirect
134. C2×C4×C11D16semidirect
280. C11#13235semidirect
306. C2×C4#66890semidirect

Maximal subgroups

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

subgroupindex
C22×#668902
C2×#106221272
C2×#106222002
C2×#106221292
C2×C4×C11⋊C162
#130694822
C11×#19702
#1323511