Finite Group Databasebeta

← #14910724

Subgroups — #14910724

Order 2816.

556 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081048C211yesmaximal, characteristic, complemented
2#13080375C211yesmaximal, characteristic
3#13070840C211yesmaximal, characteristic, complemented
4#13070810C212yesmaximal, complemented
5#13070758C211yesmaximal, characteristic, complemented
6#13070715C212yesmaximal, complemented
7#13070656C211yesmaximal, characteristic, complemented
8#13070555C212yesmaximal, complemented
9C16×D44C211yesmaximal, characteristic, complemented
10#13070322C212yesmaximal, complemented
11C4×C11×Q32C211yesmaximal, characteristic, complemented
12C2×#66972C2212yes—
13#10623115—21no—
14#10623108—21no—
15C2×C11×Q32C2211yescharacteristic
16C4×C11×Q16C2211yescharacteristic
17C4×C11×Q16C2211yescharacteristic
18#10622801C2212yes—
19C2×#66892C2212yes—
20#10622640—21no—
21#10622633—21no—
22C2×C16×D11C2212yes—
23#10622496C2212yes—
24#10622493C2212yes—
25#10622427—22no—
26#10622424—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#10622128C2212yes—
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#66951—42no—
54#66948—22no—
55#66948—42no—
56#66945—22no—
57#66928—41no—
58#66927—21no—
59#66927—41no—
60C4×D44—41no—
61C4×D44D411yescharacteristic
62#66922—21no—
63C4×Dic22—41no—
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#66872—22no—
80C4⋊(C11⋊C8)D411yescharacteristic
81C16×D11—42no—
82#33871—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×D11C2×D412yes—
95C2×Dic22—41no—
96C11×Q16—21no—
97C11×Q16—21no—
98C11×Q16—21no—
99C11×Q16#4112yes—
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2411yescharacteristic
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C42×C11—41no—
107C42×C11—41no—
108C42×C11C2×D411yescharacteristic
109#4325—44no—
110(C2×D11)⋊C4—42no—
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—
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#3342—111no—
129#3287—111no—
130#2240—111no—
131#2234—112no—
132#2225—111no—
133#2217—112no—
134#2207—111no—
135#2189—112no—
136C4×Q32D1111yescharacteristic, complemented
137D4×C16—111no—
138#2138—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—
164Dic22—82no—
165C8×C11—21no—
166C8×C11C2×#4111yescharacteristic
167C8×C11H(5,𝔽2)11yescharacteristic
168C11⋊C8—22no—
169C2×#135—112no—
170#556—221no—
171#550—221no—
172C2×Q32C2×D1111yescharacteristic
173C2×SD32—112no—
174C22×C16—112no—
175#500—111no—
176#493—111no—
177#485—222no—
178#475—221no—
179#467—112no—
180#466—112no—
181#460—221no—
182#449—222no—
183C4×Q16C2×D1111yescharacteristic
184C4×Q16C2×D1111yescharacteristic
185C8×D4—111no—
186#427—112no—
187#367—112no—
188#366C2×D1111yescharacteristic
189C4⋊C16—111no—
190#358—112no—
191#358C2×D1111yescharacteristic
192#358C2×D1111yescharacteristic
193#357—112no—
194#357—112no—
195#357—112no—
196C22⋊C16—112no—
197C4×C16C2×D1111yescharacteristic
198C22×C11C22×D811yescharacteristic
199C2×D11—22no—
200C2×D11—22no—
201C2×D11—22no—
202C2×D11—82no—
203C2×D11—82no—
204C2×D11—82no—
205C4×C11—21no—
206C4×C11—42no—
207C4×C11—81no—
208C4×C11—81no—
209C4×C11—81no—
210C4×C11#50812yes—
211C4×C11#54611yescharacteristic
212C4×C11#57711yescharacteristic
213Dic11—22no—
214Dic11—82no—
215C2×#41—222no—
216#135—224no—
217#135—442no—
218C2×Q16C22×D1111yescharacteristic
219C2×Q16C22×D1111yescharacteristic
220C2×SD16—222no—
221C2×D8—112no—
222C2×D8—221no—
223C22×C8—112no—
224C4⋊Q8—221no—
225#127—221no—
226#127—441no—
227#126—442no—
228#124—441no—
229C22⋊Q8—222no—
230#121—222no—
231#121—442no—
232C4×Q8—21no—
233C4×Q8—21no—
234C4×Q8—441no—
235C4×D4—111no—
236C4×D4—441no—
237#117—222no—
238Q32—22no—
239SD32—442no—
240C2×C16—112no—
241C2×C16—442no—
242C2×C16C22×D1111yescharacteristic
243C2×C16C22×D1111yescharacteristic
244#107—112no—
245#107—221no—
246#107C22×D1111yescharacteristic
247#107C22×D1111yescharacteristic
248#106—222no—
249C4⋊C8—111no—
250#103—21no—
251#103—21no—
252#103—222no—
253#102—222no—
254C22⋊C8—112no—
255C4×C8C22×D1111yescharacteristic
256C2×C11#329411yescharacteristic
257C2×C11C2×#50811yescharacteristic
258C2×C11#341611yescharacteristic
259D11—42no—
260D11—162no—
261#41—444no—
262#41—882no—
263C2×Q8—21no—
264C2×Q8—21no—
265C2×Q8—441no—
266C2×D4—111no—
267C2×D4—222no—
268C2×D4—442no—
269C2×D4—442no—
270C2×D4—441no—
271C2×D4—441no—
272C22×C4—112no—
273C22×C4—442no—
274Q16—21no—
275Q16—21no—
276Q16—21no—
277Q16#433912yes—
278SD16—444no—
279D8—222no—
280D8—222no—
281D8—881no—
282C2×C8—112no—
283C2×C8—222no—
284C2×C8—222no—
285C2×C8D4×D1111yescharacteristic
286C2×C8C23×D1111yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—111no—
292C4⋊C4—222no—
293C4⋊C4—442no—
294C4⋊C4—441no—
295C22⋊C4—112no—
296C22⋊C4—442no—
297C22⋊C4—442no—
298C22⋊C4—442no—
299C42—41no—
300C42—41no—
301C42—442no—
302C42D4×D1111yescharacteristic
303C16—21no—
304C16—21no—
305C16—222no—
306C11#3387111yescharacteristic, complemented, Sylow
307C23—112no—
308C23—442no—
309Q8—22no—
310Q8—41no—
311Q8—41no—
312Q8—41no—
313Q8—882no—
314D4—222no—
315D4—442no—
316D4—442no—
317D4—884no—
318D4—882no—
319D4—1761no—
320D4—1762no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—112no—
326C2×C4—222no—
327C2×C4—222no—
328C2×C4—442no—
329C2×C4—884no—
330C2×C4D8×D1111yescharacteristic
331C2×C4D8×D1111yescharacteristic
332C2×C4C2×D4×D1111yescharacteristic
333C8—21no—
334C8—222no—
335C8C2×#433911yescharacteristic
336C8#6704211yescharacteristic
337C22—222no—
338C22—222no—
339C22—222no—
340C22—882no—
341C22—882no—
342C22—882no—
343C22C2×D8×D1111yescharacteristic
344C4—21no—
345C4—42no—
346C4—81no—
347C4—81no—
348C4—81no—
349C4—222no—
350C4—882no—
351C4#1062253212yes—
352C4#1062308111yescharacteristic
353C4#1062330111yescharacteristic
354C2—442no—
355C2—1762no—
356C2#1308043111yescharacteristic
357C2C2×#1062253211yescharacteristic
358C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×Q32C2
socleC22×C11C22×D8
prime radical#13080375C2
hypercenterC4×Q32D11
hypocenterC11#33871
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. #13081048C2semidirect
3. #13070840C2semidirect
4. #13070810C2semidirect
5. #13070758C2semidirect
6. #13070715C2semidirect
7. #13070656C2semidirect
8. #13070555C2semidirect
9. C16×D44C2semidirect
10. #13070322C2semidirect
11. C4×C11×Q32C2semidirect
136. C4×Q32D11semidirect
306. C11#33871semidirect

Maximal subgroups

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

subgroupindex
#130810482
#130803752
#130708402
#130708102
#130707582
#130707152
#130706562
#130705552
C16×D442
#130703222
C4×C11×Q322
#3387111