Finite Group Databasebeta

← #14910713

Subgroups — #14910713

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081040C211yesmaximal, characteristic, complemented
2#13080337C211yesmaximal, characteristic, complemented
3#13070844C211yesmaximal, characteristic, complemented
4#13070826C212yesmaximal, complemented
5#13070763C211yesmaximal, characteristic, complemented
6#13070711C212yesmaximal, complemented
7#13070661C211yesmaximal, characteristic, complemented
8#13070536C212yesmaximal, complemented
9C16×D44C211yesmaximal, characteristic, complemented
10#13070320C212yesmaximal, complemented
11C4×C11×D16C211yesmaximal, characteristic, complemented
12C2×#66965C2212yes—
13#10623094—21no—
14#10623086—21no—
15C2×C11×D16C2211yescharacteristic
16C4×C11×D8C2211yescharacteristic
17C4×C11×D8C2211yescharacteristic
18#10622770C2212yes—
19C2×#66891C2212yes—
20#10622632—21no—
21#10622621—21no—
22C2×C16×D11C2212yes—
23#10622500C2212yes—
24#10622493C2212yes—
25#10622397—22no—
26#10622396—22no—
27#10622312C2211yescharacteristic
28C8×D44C2211yescharacteristic
29#10622295C2211yescharacteristic
30C11×#366C2211yescharacteristic
31C11×#357C2211yescharacteristic
32C11×#357C2211yescharacteristic
33C4×C11×C16C2211yescharacteristic
34#10622200C2212yes—
35(C2×D11)⋊C16C2212yes—
36#10622141C2212yes—
37#10622141C2212yes—
38#10622130C2212yes—
39#10622128C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C2×#4341—22no—
42C2×C11×D8C2311yescharacteristic
43C2×C11×D8C2311yescharacteristic
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46#66991—22no—
47C2×#4324—22no—
48#66983—41no—
49#66983—41no—
50#66979—41no—
51C2×C4⋊Dic11—41no—
52#66965—24no—
53#66965—42no—
54C2×Dic44—21no—
55C2×Dic44C2312yes—
56C2×C8×D11C2312yes—
57#66950—22no—
58#66945—22no—
59#66939—42no—
60#66938—42no—
61C4×D44D411yescharacteristic
62#66922—21no—
63#66922—21no—
64C11×D16—22no—
65C2×C11×C16C2311yescharacteristic
66C2×C11×C16C2311yescharacteristic
67C11×#107C2311yescharacteristic
68C11×#107C2311yescharacteristic
69C11×#102—21no—
70C11×#102—21no—
71C4×C8×C11C2311yescharacteristic
72#66896—22no—
73#66891—42no—
74(C2×D11)⋊C8D412yes—
75#66882—21no—
76#66882C2312yes—
77C2×C11⋊C16C2312yes—
78#66874—22no—
79#66872—22no—
80C4⋊(C11⋊C8)D411yescharacteristic
81C16×D11—42no—
82#33870—111nomaximal, Sylow
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C2×C22⋊D11—42no—
88C2×C22⋊D11—42no—
89C22×Dic11—42no—
90#4341—44no—
91#4341—82no—
92C2×D44D811yescharacteristic
93C2×C4×D11C2×D412yes—
94C2×Dic22—22no—
95C2×Dic22—41no—
96C11×D8—21no—
97C11×D8—21no—
98C11×D8—21no—
99C11×D8#4112yes—
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2411yescharacteristic
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C42×C11C2×D411yescharacteristic
107C22⋊Dic11—42no—
108#4324—44no—
109(C2×D11)⋊C4—42no—
110(C2×D11)⋊C4—42no—
111(C2×D11)⋊C4D812yes—
112C4⋊Dic11—22no—
113C4⋊Dic11—42no—
114C4⋊Dic11—41no—
115C4⋊Dic11—41no—
116C4⋊Dic11—41no—
117C4⋊Dic11D811yescharacteristic
118C4×Dic11—42no—
119C2×C11⋊C8C2×D412yes—
120Dic44—22no—
121Dic44—22no—
122Dic44—81no—
123C8×D11—22no—
124C8×D11—22no—
125C11×C16—21no—
126C11×C16—21no—
127C11⋊C16—22no—
128#3341—111no—
129#3283—111no—
130#2241—111no—
131#2237—112no—
132#2226—111no—
133#2217—112no—
134#2208—111no—
135#2186—112no—
136C4×D16D1111yescharacteristic, complemented
137D4×C16—111no—
138#2138—112no—
139C23×C11—41no—
140C23×C11—41no—
141C22×D11C2×D812yes—
142D4×C11—22no—
143D4×C11—41no—
144D4×C11—41no—
145D4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—82no—
149C2×C4×C11—82no—
150C2×C4×C11C2×D811yescharacteristic
151C2×C4×C11C2×D811yescharacteristic
152C2×C4×C11C22×D411yescharacteristic
153C22⋊D11—84no—
154C22⋊D11—162no—
155C2×Dic11—42no—
156C2×Dic11—42no—
157C2×Dic11—84no—
158C2×Dic11C2×D812yes—
159D44—22no—
160C4×D11—22no—
161C4×D11—22no—
162Dic22—42no—
163Dic22—42no—
164Dic22—161no—
165C8×C11—21no—
166C8×C11C2×#4111yescharacteristic
167C8×C11H(5,𝔽2)11yescharacteristic
168C11⋊C8—22no—
169C2×#135—112no—
170#555—221no—
171#547—221no—
172C2×SD32—112no—
173C2×D16C2×D1111yescharacteristic
174C22×C16—112no—
175#500—111no—
176#494—111no—
177#482—222no—
178#476—221no—
179#467—112no—
180#466—112no—
181#461—221no—
182#452—222no—
183C4×D8C2×D1111yescharacteristic
184C4×D8C2×D1111yescharacteristic
185C8×D4—111no—
186#427—112no—
187#367—112no—
188#366C2×D1111yescharacteristic
189C4⋊C16—111no—
190#358—112no—
191#358—112no—
192#358—112no—
193#357—112no—
194#357C2×D1111yescharacteristic
195#357C2×D1111yescharacteristic
196C22⋊C16—112no—
197C4×C16C2×D1111yescharacteristic
198C22×C11—42no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11C22×D811yescharacteristic
205C2×D11—22no—
206C2×D11—22no—
207C2×D11—22no—
208C4×C11—21no—
209C4×C11—81no—
210C4×C11—81no—
211C4×C11#50812yes—
212C4×C11#54611yescharacteristic
213C4×C11#57711yescharacteristic
214Dic11—22no—
215Dic11—82no—
216Dic11—82no—
217C2×#41—222no—
218#135—224no—
219#135—442no—
220C2×Q16—112no—
221C2×Q16—221no—
222C2×SD16—222no—
223C2×D8C22×D1111yescharacteristic
224C2×D8C22×D1111yescharacteristic
225C22×C8—112no—
226C4⋊Q8—221no—
227C4⋊Q8—221no—
228#124—442no—
229#123—442no—
230C22⋊Q8—222no—
231#121—222no—
232#121—441no—
233#121—441no—
234C4×D4—21no—
235C4×D4—21no—
236C4×D4—111no—
237#117—222no—
238#117—441no—
239C2×C4⋊C4—441no—
240SD32—442no—
241D16—22no—
242C2×C16—112no—
243C2×C16—442no—
244C2×C16C22×D1111yescharacteristic
245C2×C16C22×D1111yescharacteristic
246#107—112no—
247#107—221no—
248#107C22×D1111yescharacteristic
249#107C22×D1111yescharacteristic
250#106—222no—
251C4⋊C8—111no—
252#103—222no—
253#102—21no—
254#102—21no—
255#102—222no—
256C22⋊C8—112no—
257C4×C8C22×D1111yescharacteristic
258C2×C11—82no—
259C2×C11—161no—
260C2×C11#329411yescharacteristic
261C2×C11C2×#50811yescharacteristic
262C2×C11#341611yescharacteristic
263D11—42no—
264#41—444no—
265#41—882no—
266C2×Q8—222no—
267C2×Q8—441no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—111no—
271C2×D4—442no—
272C2×D4—442no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—112no—
276C22×C4—442no—
277Q16—222no—
278Q16—222no—
279Q16—881no—
280SD16—444no—
281D8—21no—
282D8—21no—
283D8—21no—
284D8#433912yes—
285C2×C8—112no—
286C2×C8—222no—
287C2×C8—222no—
288C2×C8D4×D1111yescharacteristic
289C2×C8C23×D1111yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—111no—
293C4⋊C4—222no—
294C4⋊C4—442no—
295C4⋊C4—441no—
296C4⋊C4—441no—
297C4⋊C4—441no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—112no—
301C22⋊C4—442no—
302C22⋊C4—442no—
303C22⋊C4—442no—
304C42—442no—
305C42D4×D1111yescharacteristic
306C16—21no—
307C16—21no—
308C16—222no—
309C11#3387011yescharacteristic, complemented, Sylow
310C23—41no—
311C23—41no—
312C23—112no—
313Q8—442no—
314Q8—442no—
315Q8—1761no—
316D4—22no—
317D4—41no—
318D4—41no—
319D4—41no—
320D4—222no—
321D4—884no—
322D4—1762no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—112no—
328C2×C4—222no—
329C2×C4—222no—
330C2×C4—442no—
331C2×C4—442no—
332C2×C4—884no—
333C2×C4D8×D1111yescharacteristic
334C2×C4D8×D1111yescharacteristic
335C2×C4C2×D4×D1111yescharacteristic
336C8—21no—
337C8—222no—
338C8C2×#433911yescharacteristic
339C8#6704211yescharacteristic
340C22—42no—
341C22—81no—
342C22—81no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22—222no—
347C22—222no—
348C22—222no—
349C22C2×D8×D1111yescharacteristic
350C4—21no—
351C4—81no—
352C4—81no—
353C4—222no—
354C4—882no—
355C4—882no—
356C4#1062252512yes—
357C4#1062308111yescharacteristic
358C4#1062330111yescharacteristic
359C2—82no—
360C2—161no—
361C2—442no—
362C2#1308043111yescharacteristic
363C2C2×#1062252511yescharacteristic
364C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×D16C2
socleC22×C11C22×D8
hypercenterC4×D16D11
hypocenterC11#33870
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×D16

Complements

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

NH ≅ G/Ntype
1. #13081040C2semidirect
2. #13080337C2semidirect
3. #13070844C2semidirect
4. #13070826C2semidirect
5. #13070763C2semidirect
6. #13070711C2semidirect
7. #13070661C2semidirect
8. #13070536C2semidirect
9. C16×D44C2semidirect
10. #13070320C2semidirect
11. C4×C11×D16C2semidirect
136. C4×D16D11semidirect
309. C11#33870semidirect

Maximal subgroups

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

subgroupindex
#130810402
#130803372
#130708442
#130708262
#130707632
#130707112
#130706612
#130705362
C16×D442
#130703202
C4×C11×D162
#3387011