Finite Group Databasebeta

← #14910735

Subgroups — #14910735

Order 2816.

568 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081040C211yesmaximal, characteristic, complemented
2#13080375C211yesmaximal, characteristic, complemented
3#13070840C211yesmaximal, characteristic, complemented
4#13070809C212yesmaximal, complemented
5#13070768C211yesmaximal, characteristic, complemented
6#13070701C212yesmaximal, complemented
7#13070651C211yesmaximal, characteristic, complemented
8#13070538C212yesmaximal, complemented
9C16×D44C211yesmaximal, characteristic, complemented
10#13070322C212yesmaximal, complemented
11C4×C11×SD32C211yesmaximal, characteristic, complemented
12C2×#66972C2212yes—
13#10623108—21no—
14#10623094—21no—
15C2×C11×SD32C2211yescharacteristic
16C4×C11×Q16C2211yescharacteristic
17C4×C11×D8C2211yescharacteristic
18#10622770C2212yes—
19C2×#66890C2212yes—
20#10622640—21no—
21#10622621—21no—
22C2×C16×D11C2212yes—
23#10622496C2212yes—
24#10622493C2212yes—
25#10622424—22no—
26#10622397—22no—
27#10622308C2211yescharacteristic
28C8×D44C2211yescharacteristic
29#10622295C2211yescharacteristic
30C11×#367C2211yescharacteristic
31C11×#358C2211yescharacteristic
32C11×#357C2211yescharacteristic
33C4×C11×C16C2211yescharacteristic
34#10622202C2212yes—
35#10622147C2212yes—
36#10622147C2212yes—
37(C2×D11)⋊C16C2212yes—
38#10622129C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C2×#4343—22no—
42C2×C11×Q16C2311yescharacteristic
43C2×C11×D8C2311yescharacteristic
44C4×Q8×C11—21no—
45C4×D4×C11—21no—
46C2×#4325—22no—
47#66991—22no—
48#66983—41no—
49#66979—41no—
50#66972—24no—
51#66972—42no—
52C2×D88—21no—
53C2×D88C2312yes—
54C2×C8×D11C2312yes—
55#66948—22no—
56#66948—42no—
57#66945—22no—
58#66938—42no—
59#66927—21no—
60#66927—41no—
61C4×D44—41no—
62C4×D44D411yescharacteristic
63#66922—21no—
64C11×SD32—22no—
65C2×C11×C16C2311yescharacteristic
66C2×C11×C16C2311yescharacteristic
67C11×#107C2311yescharacteristic
68C11×#107C2311yescharacteristic
69C11×#103—21no—
70C11×#102—21no—
71C4×C8×C11C2311yescharacteristic
72#66896—22no—
73#66890—42no—
74(C2×D11)⋊C8D412yes—
75#66882—21no—
76#66882C2312yes—
77C2×C11⋊C16C2312yes—
78#66873—22no—
79#66872—22no—
80C4⋊(C11⋊C8)D411yescharacteristic
81C16×D11—42no—
82#33872—111nomaximal, Sylow
83C2×Q8×C11—21no—
84C2×D4×C11—21no—
85C22×C4×C11—41no—
86C2×C22⋊D11—42no—
87#4343—44no—
88#4343—82no—
89C2×D44—22no—
90C2×D44—42no—
91C2×D44—42no—
92C2×D44—41no—
93C2×D44—41no—
94C2×D44D811yescharacteristic
95C2×C4×D11—42no—
96C2×C4×D11C2×D412yes—
97C2×Dic22—41no—
98C11×Q16—21no—
99C11×Q16#4112yes—
100C11×D8—21no—
101C11×D8—21no—
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11C2411yescharacteristic
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—41no—
107C11×C22⋊C4—41no—
108C42×C11—41no—
109C42×C11C2×D411yescharacteristic
110C22⋊Dic11—42no—
111#4325—44no—
112(C2×D11)⋊C4—42no—
113(C2×D11)⋊C4—42no—
114(C2×D11)⋊C4D812yes—
115C4⋊Dic11—22no—
116C4⋊Dic11—41no—
117C4⋊Dic11D811yescharacteristic
118C4×Dic11—42no—
119C2×C11⋊C8C2×D412yes—
120D88—22no—
121D88—22no—
122D88—81no—
123C8×D11—22no—
124C8×D11—22no—
125C11×C16—21no—
126C11×C16—21no—
127C11⋊C16—22no—
128#3341—111no—
129#3287—111no—
130#2240—111no—
131#2234—112no—
132#2227—111no—
133#2215—112no—
134#2206—111no—
135#2186—112no—
136C4×SD32D1111yescharacteristic, complemented
137D4×C16—111no—
138#2138—112no—
139C23×C11—41no—
140C22×D11—42no—
141C22×D11C2×D812yes—
142Q8×C11—22no—
143Q8×C11—41no—
144D4×C11—41no—
145D4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—82no—
150C2×C4×C11C2×D811yescharacteristic
151C2×C4×C11C2×D811yescharacteristic
152C2×C4×C11C22×D411yescharacteristic
153C22⋊D11—162no—
154C2×Dic11—42no—
155C2×Dic11C2×D812yes—
156D44—22no—
157D44—42no—
158D44—42no—
159D44—84no—
160D44—82no—
161D44—161no—
162D44—162no—
163C4×D11—22no—
164C4×D11—22no—
165C4×D11—84no—
166Dic22—161no—
167C8×C11—21no—
168C8×C11C2×#4111yescharacteristic
169C8×C11H(5,𝔽2)11yescharacteristic
170C11⋊C8—22no—
171C2×#135—112no—
172#555—221no—
173#550—221no—
174C2×SD32C2×D1111yescharacteristic
175C2×D16—112no—
176C22×C16—112no—
177#500—111no—
178#493—111no—
179#482—222no—
180#476—221no—
181#466—112no—
182#466—112no—
183#460—221no—
184#449—222no—
185C4×Q16C2×D1111yescharacteristic
186C4×D8C2×D1111yescharacteristic
187C8×D4—111no—
188#427—112no—
189#367C2×D1111yescharacteristic
190#366—112no—
191C4⋊C16—111no—
192#358—112no—
193#358C2×D1111yescharacteristic
194#357—112no—
195#357—112no—
196#357—112no—
197#357C2×D1111yescharacteristic
198C22⋊C16—112no—
199C4×C16C2×D1111yescharacteristic
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11C22×D811yescharacteristic
204C2×D11—22no—
205C2×D11—22no—
206C2×D11—22no—
207C2×D11—82no—
208C2×D11—82no—
209C2×D11—82no—
210C4×C11—21no—
211C4×C11—42no—
212C4×C11—81no—
213C4×C11—81no—
214C4×C11#50812yes—
215C4×C11#54611yescharacteristic
216C4×C11#57711yescharacteristic
217Dic11—22no—
218Dic11—82no—
219C2×#41—222no—
220#135—224no—
221#135—442no—
222C2×Q16C22×D1111yescharacteristic
223C2×SD16—222no—
224C2×D8—112no—
225C2×D8—221no—
226C2×D8C22×D1111yescharacteristic
227C22×C8—112no—
228C4⋊Q8—221no—
229#127—221no—
230#127—441no—
231#124—442no—
232#121—222no—
233#121—222no—
234#121—442no—
235#121—441no—
236C4×Q8—21no—
237C4×D4—21no—
238C4×D4—111no—
239C4×D4—441no—
240#117—222no—
241#117—441no—
242SD32—22no—
243D16—442no—
244C2×C16—112no—
245C2×C16—442no—
246C2×C16C22×D1111yescharacteristic
247C2×C16C22×D1111yescharacteristic
248#107—112no—
249#107—221no—
250#107C22×D1111yescharacteristic
251#107C22×D1111yescharacteristic
252#106—222no—
253C4⋊C8—111no—
254#103—21no—
255#102—21no—
256#102—222no—
257#102—222no—
258C22⋊C8—112no—
259C4×C8C22×D1111yescharacteristic
260C2×C11—161no—
261C2×C11#329411yescharacteristic
262C2×C11C2×#50811yescharacteristic
263C2×C11#341511yescharacteristic
264D11—42no—
265D11—162no—
266#41—444no—
267#41—882no—
268C2×Q8—21no—
269C2×Q8—441no—
270C2×D4—21no—
271C2×D4—111no—
272C2×D4—222no—
273C2×D4—442no—
274C2×D4—442no—
275C2×D4—442no—
276C2×D4—441no—
277C2×D4—441no—
278C22×C4—41no—
279C22×C4—112no—
280C22×C4—442no—
281Q16—21no—
282Q16#433912yes—
283SD16—444no—
284D8—21no—
285D8—21no—
286D8—222no—
287D8—222no—
288D8—881no—
289C2×C8—112no—
290C2×C8—222no—
291C2×C8—222no—
292C2×C8D4×D1111yescharacteristic
293C2×C8C23×D1111yescharacteristic
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—111no—
298C4⋊C4—222no—
299C4⋊C4—441no—
300C22⋊C4—41no—
301C22⋊C4—112no—
302C22⋊C4—442no—
303C22⋊C4—442no—
304C22⋊C4—442no—
305C42—41no—
306C42—442no—
307C42D4×D1111yescharacteristic
308C16—21no—
309C16—21no—
310C16—222no—
311C11#3387211yescharacteristic, complemented, Sylow
312C23—41no—
313C23—112no—
314C23—442no—
315Q8—22no—
316Q8—41no—
317Q8—1761no—
318D4—41no—
319D4—41no—
320D4—222no—
321D4—442no—
322D4—442no—
323D4—884no—
324D4—882no—
325D4—1761no—
326D4—1762no—
327D4—1762no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—82no—
332C2×C4—112no—
333C2×C4—222no—
334C2×C4—222no—
335C2×C4—442no—
336C2×C4—884no—
337C2×C4D8×D1111yescharacteristic
338C2×C4D8×D1111yescharacteristic
339C2×C4C2×D4×D1111yescharacteristic
340C8—21no—
341C8—222no—
342C8C2×#433911yescharacteristic
343C8#6704211yescharacteristic
344C22—81no—
345C22—81no—
346C22—81no—
347C22—222no—
348C22—222no—
349C22—222no—
350C22—882no—
351C22—882no—
352C22—882no—
353C22C2×D8×D1111yescharacteristic
354C4—21no—
355C4—42no—
356C4—81no—
357C4—81no—
358C4—222no—
359C4—882no—
360C4#1062252912yes—
361C4#1062308111yescharacteristic
362C4#1062330111yescharacteristic
363C2—161no—
364C2—442no—
365C2—1762no—
366C2#1308043111yescharacteristic
367C2C2×#1062252911yescharacteristic
368C2#1308175411yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×SD32C2
socleC22×C11C22×D8
hypercenterC4×SD32D11
hypocenterC11#33872
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
1. #13081040C2semidirect
2. #13080375C2semidirect
3. #13070840C2semidirect
4. #13070809C2semidirect
5. #13070768C2semidirect
6. #13070701C2semidirect
7. #13070651C2semidirect
8. #13070538C2semidirect
9. C16×D44C2semidirect
10. #13070322C2semidirect
11. C4×C11×SD32C2semidirect
136. C4×SD32D11semidirect
311. C11#33872semidirect

Maximal subgroups

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

subgroupindex
#130810402
#130803752
#130708402
#130708092
#130707682
#130707012
#130706512
#130705382
C16×D442
#130703222
C4×C11×SD322
#3387211