Finite Group Databasebeta

← #14911123

Subgroups — #14911123

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081010C211yesmaximal, characteristic, complemented
2#13080375C211yesmaximal, characteristic
3#13070840C211yesmaximal, characteristic, complemented
4#13070798C212yesmaximal, complemented
5#13070768C211yesmaximal, characteristic, complemented
6#13070732C212yesmaximal, complemented
7#13070656C211yesmaximal, characteristic, complemented
8#13070555C212yesmaximal, complemented
9#13070449C211yesmaximal, characteristic, complemented
10#13070327C212yesmaximal, complemented
11C4×C11×Q32C211yesmaximal, characteristic, complemented
12C2×#66972C2212yes—
13#10623110—21no—
14#10623108—21no—
15C2×C11×Q32C2211yescharacteristic
16C4×C11×Q16C2211yescharacteristic
17C4×C11×Q16C2211yescharacteristic
18#10622801C2212yes—
19C2×#66892C2212yes—
20#10622640—21no—
21#10622634—21no—
22C2×#66862C2212yes—
23#10622496C2212yes—
24D11×#107C2212yes—
25#10622424—22no—
26#10622422—22no—
27#10622308C2211yescharacteristic
28C8×D44C2211yescharacteristic
29#10622295C2211yescharacteristic
30C11×#366C2211yescharacteristic
31C11×#358C2211yescharacteristic
32C11×#358C2211yescharacteristic
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×Q16C2311yescharacteristic
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46#66999—22no—
47C2×#4325—22no—
48#66972—24no—
49#66972—42no—
50C2×D88—21no—
51C2×D88C2312yes—
52C2×C8×D11C2312yes—
53#66949—42no—
54#66948—22no—
55#66948—42no—
56C4⋊C4×D11—22no—
57#66927—21no—
58#66927—41no—
59C4×D44—41no—
60C4×D44—41no—
61C4×D44D411yescharacteristic
62#66923—41no—
63#66922—21no—
64C11×Q32—22no—
65C2×C11×C16C2311yescharacteristic
66C2×C11×C16C2311yescharacteristic
67C11×#107C2311yescharacteristic
68C11×#107C2311yescharacteristic
69C11×#103—21no—
70C11×#103—21no—
71C4×C8×C11C2311yescharacteristic
72#66899—22no—
73#66892—42no—
74(C2×D11)⋊C8D412yes—
75#66882—21no—
76#66882C2312yes—
77C2×C11⋊C16C2312yes—
78#66873—22no—
79#66871—22no—
80C4⋊(C11⋊C8)D411yescharacteristic
81#66862—42no—
82#33900—111nomaximal, Sylow
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85#4343—44no—
86#4343—82no—
87C2×D44—22no—
88C2×D44—42no—
89C2×D44—42no—
90C2×D44—41no—
91C2×D44—41no—
92C2×D44D811yescharacteristic
93C2×C4×D11—42no—
94C2×C4×D11—42no—
95C2×C4×D11C2×D412yes—
96C2×Dic22—41no—
97C11×Q16—21no—
98C11×Q16—21no—
99C11×Q16—21no—
100C11×Q16#4112yes—
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2411yescharacteristic
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C42×C11—41no—
108C42×C11—41no—
109C42×C11C2×D411yescharacteristic
110#4325—44no—
111(C2×D11)⋊C4—42no—
112(C2×D11)⋊C4—42no—
113(C2×D11)⋊C4D812yes—
114C4⋊Dic11—22no—
115C4⋊Dic11—41no—
116C4⋊Dic11D811yescharacteristic
117Dic11⋊C4—42no—
118Dic11⋊C4—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#3338—111no—
129#3287—111no—
130#2240—111no—
131#2232—112no—
132#2227—111no—
133#2220—112no—
134#2207—111no—
135#2189—112no—
136C4×Q32D1111yescharacteristic, complemented
137#2169—111no—
138#2139—112no—
139C22×D11—42no—
140C22×D11C2×D812yes—
141Q8×C11—22no—
142Q8×C11—41no—
143Q8×C11—41no—
144Q8×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11C2×D811yescharacteristic
150C2×C4×C11C2×D811yescharacteristic
151C2×C4×C11C22×D411yescharacteristic
152C2×Dic11—42no—
153C2×Dic11C2×D812yes—
154D44—22no—
155D44—42no—
156D44—42no—
157D44—84no—
158D44—82no—
159D44—161no—
160D44—162no—
161C4×D11—22no—
162C4×D11—22no—
163C4×D11—84no—
164C4×D11—162no—
165Dic22—161no—
166C8×C11—21no—
167C8×C11C2×#4111yescharacteristic
168C8×C11H(5,𝔽2)11yescharacteristic
169C11⋊C8—22no—
170C2×#135—112no—
171#554—221no—
172#550—221no—
173C2×Q32C2×D1111yescharacteristic
174C2×SD32—112no—
175C2×M32—112no—
176#500—111no—
177#493—111no—
178#484—222no—
179#477—221no—
180#467—112no—
181#466—112no—
182#460—221no—
183#449—222no—
184C4×Q16C2×D1111yescharacteristic
185C4×Q16C2×D1111yescharacteristic
186C8×D4—111no—
187C2×#107—112no—
188#366—112no—
189#366C2×D1111yescharacteristic
190C4⋊C16—111no—
191#358—112no—
192#358C2×D1111yescharacteristic
193#358C2×D1111yescharacteristic
194#357—112no—
195#357—112no—
196#357—112no—
197C22⋊C16—112no—
198C4×C16C2×D1111yescharacteristic
199C22×C11C22×D811yescharacteristic
200C2×D11—22no—
201C2×D11—22no—
202C2×D11—22no—
203C2×D11—82no—
204C2×D11—82no—
205C2×D11—82no—
206C4×C11—21no—
207C4×C11—42no—
208C4×C11—81no—
209C4×C11—81no—
210C4×C11—81no—
211C4×C11#51012yes—
212C4×C11#54611yescharacteristic
213C4×C11#57711yescharacteristic
214Dic11—22no—
215Dic11—82no—
216C2×#41—222no—
217#135—224no—
218#135—442no—
219C2×Q16C22×D1111yescharacteristic
220C2×Q16C22×D1111yescharacteristic
221C2×SD16—222no—
222C2×D8—112no—
223C2×D8—221no—
224C22×C8—112no—
225C4⋊Q8—221no—
226#127—221no—
227#127—441no—
228#125—441no—
229C22⋊Q8—222no—
230C22⋊Q8—442no—
231#121—222no—
232#121—442no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×D4—111no—
236C4×D4—441no—
237C4×D4—441no—
238C2×C4⋊C4—222no—
239Q32—22no—
240SD32—442no—
241M32—442no—
242C2×C16—112no—
243C2×C16C22×D1111yescharacteristic
244C2×C16C22×D1111yescharacteristic
245#107—112no—
246#107—222no—
247#107—221no—
248#107C22×D1111yescharacteristic
249#107C22×D1111yescharacteristic
250C4⋊C8—111no—
251#103—21no—
252#103—21no—
253#103—222no—
254#102—222no—
255C22⋊C8—112no—
256C4×C8C22×D1111yescharacteristic
257C2×C11#329411yescharacteristic
258C2×C11C2×#51011yescharacteristic
259C2×C11#341511yescharacteristic
260D11—42no—
261D11—162no—
262#41—444no—
263#41—882no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—441no—
267C2×D4—111no—
268C2×D4—222no—
269C2×D4—442no—
270C2×D4—442no—
271C2×D4—441no—
272C2×D4—441no—
273C22×C4—112no—
274C22×C4—442no—
275C22×C4—442no—
276Q16—21no—
277Q16—21no—
278Q16—21no—
279Q16#433912yes—
280SD16—444no—
281D8—222no—
282D8—222no—
283D8—881no—
284C2×C8—112no—
285C2×C8—222no—
286C2×C8—222no—
287C2×C8D4×D1111yescharacteristic
288C2×C8C23×D1111yescharacteristic
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—111no—
294C4⋊C4—222no—
295C4⋊C4—442no—
296C4⋊C4—442no—
297C4⋊C4—441no—
298C22⋊C4—112no—
299C22⋊C4—442no—
300C22⋊C4—442no—
301C42—41no—
302C42—41no—
303C42D4×D1111yescharacteristic
304C16—21no—
305C16—21no—
306C16—222no—
307C11#3390011yescharacteristic, complemented, Sylow
308C23—112no—
309C23—442no—
310Q8—22no—
311Q8—41no—
312Q8—41no—
313Q8—41no—
314Q8—1761no—
315D4—222no—
316D4—442no—
317D4—442no—
318D4—884no—
319D4—882no—
320D4—1761no—
321D4—1762no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—112no—
327C2×C4—222no—
328C2×C4—222no—
329C2×C4—442no—
330C2×C4—884no—
331C2×C4—1762no—
332C2×C4D8×D1111yescharacteristic
333C2×C4D8×D1111yescharacteristic
334C2×C4C2×D4×D1111yescharacteristic
335C8—21no—
336C8—222no—
337C8C2×#433911yescharacteristic
338C8#6704211yescharacteristic
339C22—222no—
340C22—222no—
341C22—222no—
342C22—882no—
343C22—882no—
344C22—882no—
345C22C2×D8×D1111yescharacteristic
346C4—21no—
347C4—42no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4—222no—
352C4—882no—
353C4#1062253112yes—
354C4#1062308111yescharacteristic
355C4#1062330111yescharacteristic
356C2—442no—
357C2—1762no—
358C2#1308043111yescharacteristic
359C2C2×#1062253111yescharacteristic
360C2#1308175411yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×Q32C2
socleC22×C11C22×D8
prime radical#13080375C2
hypercenterC4×Q32D11
hypocenterC11#33900
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. #13081010C2semidirect
3. #13070840C2semidirect
4. #13070798C2semidirect
5. #13070768C2semidirect
6. #13070732C2semidirect
7. #13070656C2semidirect
8. #13070555C2semidirect
9. #13070449C2semidirect
10. #13070327C2semidirect
11. C4×C11×Q32C2semidirect
136. C4×Q32D11semidirect
307. C11#33900semidirect

Maximal subgroups

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

subgroupindex
#130810102
#130803752
#130708402
#130707982
#130707682
#130707322
#130706562
#130705552
#130704492
#130703272
C4×C11×Q322
#3390011