Finite Group Databasebeta

← #14911417

Subgroups — #14911417

Order 2816.

562 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#13081590C211yesmaximal, characteristic, complemented
2#13081468C211yesmaximal, characteristic, complemented
3#13070841C211yesmaximal, characteristic, complemented
4#13070838C212yesmaximal, complemented
5#13070752C212yesmaximal, complemented
6#13070652C211yesmaximal, characteristic, complemented
7#13070650C212yesmaximal, complemented
8#13070518C211yesmaximal, characteristic, complemented
9#13070462C212yesmaximal, complemented
10C4×#66890C211yesmaximal, characteristic, complemented
11C11×#2224C211yesmaximal, characteristic, complemented
12#10623258—21no—
13#10623084—21no—
14C11×#500C2211yescharacteristic
15C4×C11×D8C2211yescharacteristic
16#10622764C2212yes—
17C2×#66890C2211yescharacteristic
18#10622700—21no—
19#10622628—21no—
20C2×D176C2212yes—
21#10622503—22no—
22#10622487C2212yes—
23#10622485C2212yes—
24#10622485C2212yes—
25#10622399—22no—
26#10622308C2211yescharacteristic
27C4×D88C2211yescharacteristic
28C8×Dic22C2211yescharacteristic
29C11×#366C2212yes—
30C11×C4⋊C16C2211yescharacteristic
31C11×#357C2212yes—
32#10622200C2211yescharacteristic
33#10622147C2212yes—
34Dic11⋊C16C2212yes—
35C16×Dic11C2212yes—
36#10622129C2212yes—
37#10622129C2211yescharacteristic
38#10622129C2212yes—
39#10622127C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×Q8×D11—41no—
42C2×#4339—41no—
43C2×C11×D8C2311yescharacteristic
44C11×C4⋊Q8—21no—
45C4×D4×C11—21no—
46#66999—41no—
47#66993—22no—
48C2×#4323—22no—
49#66983—41no—
50C2×D88—21no—
51C2×D88C2312yes—
52C2×D88C2311yescharacteristic
53#66949—42no—
54#66946—22no—
55#66946—22no—
56#66941—22no—
57#66937—42no—
58#66927—21no—
59C4×D44—21no—
60C4×Dic22D411yescharacteristic
61C2×C11×C16C2312yes—
62C11×#107—21no—
63C11×#107C2312yes—
64C11×#107C2311yescharacteristic
65C11×#102—21no—
66C4×C8×C11C2311yescharacteristic
67#66890—22no—
68#66885—21no—
69#66882C2311yescharacteristic
70Dic11⋊C8D412yes—
71C8×Dic11C2312yes—
72C2×C11⋊C16C2311yescharacteristic
73C2×C11⋊C16C2311yescharacteristic
74#66873—22no—
75#66873—22no—
76#66871—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78D176—24no—
79#33925—111nomaximal, Sylow
80C2×Q8×C11—41no—
81C2×D4×C11—21no—
82C22×C4×C11—41no—
83C2×C22⋊D11—42no—
84C2×C22⋊D11—42no—
85Q8×D11—84no—
86#4339—84no—
87C2×D44—21no—
88C2×D44—22no—
89C2×D44—41no—
90C2×D44—41no—
91C2×C4×D11—42no—
92C2×C4×D11—42no—
93C2×C4×D11—41no—
94C2×Dic22—42no—
95C2×Dic22D811yescharacteristic
96C11×D8—21no—
97C11×D8—21no—
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2411yescharacteristic
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—41no—
103C11×C22⋊C4—41no—
104C42×C11C2×D411yescharacteristic
105#4323—82no—
106(C2×D11)⋊C4—42no—
107(C2×D11)⋊C4—42no—
108(C2×D11)⋊C4—41no—
109C4⋊Dic11—21no—
110C4⋊Dic11D811yescharacteristic
111Dic11⋊C4—42no—
112Dic11⋊C4D812yes—
113C4×Dic11C2×D412yes—
114C2×C11⋊C8C2×D412yes—
115D88—22no—
116D88—21no—
117D88—22no—
118D88—81no—
119D88#4112yescomplemented
120C11×C16—22no—
121C11⋊C16—21no—
122C11⋊C16—21no—
123#3391—111no—
124Q8×D8—111no—
125#2240—111no—
126#2240—112no—
127#2224—112no—
128#2224D1111yescharacteristic, complemented
129#2206—111no—
130#2206—112no—
131Q8×C16—111no—
132C4×D16—111no—
133C4×D16—112no—
134C23×C11—41no—
135C22×D11—41no—
136C22×D11—42no—
137Q8×C11—82no—
138D4×C11—41no—
139D4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—41no—
142C2×C4×C11—82no—
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11C2×D811yescharacteristic
145C2×C4×C11C22×D411yescharacteristic
146C22⋊D11—84no—
147C22⋊D11—162no—
148C2×Dic11—41no—
149C2×Dic11C2×D812yes—
150C2×Dic11C2×D812yes—
151D44—22no—
152D44—42no—
153D44—41no—
154D44—42no—
155D44—82no—
156D44—161no—
157C4×D11—82no—
158C4×D11—84no—
159C4×D11—84no—
160Dic22—84no—
161Dic22D1614yescomplemented
162C8×C11—21no—
163C8×C11C2×#4111yescharacteristic
164C8×C112−1+411yescharacteristic
165C11⋊C8—22no—
166#550—221no—
167D4×Q8—221no—
168C2×D16—111no—
169C2×D16—112no—
170#500—112no—
171#500C2×D1111yescharacteristic
172#493—112no—
173#493—111no—
174#474—222no—
175#474—221no—
176#459—222no—
177#459—221no—
178C8×Q8—111no—
179C4×D8—112no—
180C4×D8—112no—
181C4×D8—111no—
182C4×D8C2×D1111yescharacteristic
183#366—111no—
184#366C2×D1112yes—
185C4⋊C16—112no—
186C4⋊C16C2×D1111yescharacteristic
187#357—111no—
188#357—112no—
189#357—111no—
190#357—112no—
191#357—112no—
192#357C2×D1112yes—
193C4×C16—112no—
194C4×C16—111no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11C22×D811yescharacteristic
199C2×D11—42no—
200C2×D11—81no—
201C2×D11—81no—
202C2×D11—82no—
203C2×D11—82no—
204C2×D11—82no—
205C4×C11—21no—
206C4×C11—81no—
207C4×C11—82no—
208C4×C11C2×D1612yes—
209C4×C11#54811yescharacteristic
210C4×C11#57711yescharacteristic
211Dic11—22no—
212Dic11—81no—
213Dic11C2×D1614yes—
214C2×#41—441no—
215C22×Q8—441no—
216C2×D8—111no—
217C2×D8—112no—
218C2×D8—222no—
219C2×D8—221no—
220C2×D8C22×D1111yescharacteristic
221C4⋊Q8—21no—
222C4⋊Q8—222no—
223#127—222no—
224#127—221no—
225C22⋊Q8—442no—
226C22⋊Q8—441no—
227#121—442no—
228#121—441no—
229C4×Q8—111no—
230C4×D4—21no—
231C4×D4—222no—
232C4×D4—222no—
233C4×D4—221no—
234D16—224no—
235D16—222no—
236C2×C16—111no—
237C2×C16—111no—
238C2×C16C22×D1112yes—
239#107—21no—
240#107—111no—
241#107—222no—
242#107C22×D1112yes—
243#107C22×D1111yescharacteristic
244C4⋊C8—112no—
245C4⋊C8—111no—
246#102—21no—
247#102—222no—
248#102—222no—
249#102—221no—
250C4×C8—112no—
251C4×C8C22×D1111yescharacteristic
252C2×C11—161no—
253C2×C11#335811yescharacteristic
254C2×C11C22×D1611yescharacteristic
255C2×C11#341611yescharacteristic
256D11—82no—
257D11—162no—
258#41—884no—
259C2×Q8—41no—
260C2×Q8—111no—
261C2×Q8—442no—
262C2×Q8—884no—
263C2×D4—21no—
264C2×D4—221no—
265C2×D4—222no—
266C2×D4—442no—
267C2×D4—442no—
268C2×D4—441no—
269C2×D4—441no—
270C22×C4—41no—
271C22×C4—442no—
272C22×C4—442no—
273C22×C4—441no—
274D8—21no—
275D8—21no—
276D8—112no—
277D8—221no—
278D8—222no—
279D8—222no—
280D8—881no—
281D8—882no—
282C2×C8—112no—
283C2×C8D4×D1111yescharacteristic
284C2×C8C23×D1111yescharacteristic
285C4⋊C4—21no—
286C4⋊C4—22no—
287C4⋊C4—41no—
288C4⋊C4—112no—
289C4⋊C4—111no—
290C4⋊C4—221no—
291C4⋊C4—442no—
292C22⋊C4—41no—
293C22⋊C4—442no—
294C22⋊C4—442no—
295C22⋊C4—441no—
296C42—112no—
297C42D4×D1111yescharacteristic
298C16—22no—
299C16—221no—
300C16—221no—
301C11#3392511yescharacteristic, complemented, Sylow
302C23—41no—
303C23—441no—
304C23—442no—
305Q8—82no—
306Q8—114no—
307Q8—884no—
308D4—41no—
309D4—41no—
310D4—222no—
311D4—441no—
312D4—442no—
313D4—442no—
314D4—884no—
315D4—882no—
316D4—1761no—
317D4—1762no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—82no—
321C2×C4—112no—
322C2×C4—112no—
323C2×C4—441no—
324C2×C4—884no—
325C2×C4—884no—
326C2×C4—882no—
327C2×C4D8×D1111yescharacteristic
328C2×C4D8×D1111yescharacteristic
329C2×C4C2×D4×D1111yescharacteristic
330C8—21no—
331C8—222no—
332C8#6704011yescharacteristic
333C8#41×D1111yescharacteristic
334C22—81no—
335C22—81no—
336C22—81no—
337C22—442no—
338C22—881no—
339C22—881no—
340C22—882no—
341C22—882no—
342C22—882no—
343C22C2×D8×D1111yescharacteristic
344C4—21no—
345C4—81no—
346C4—82no—
347C4—114no—
348C4—222no—
349C4—881no—
350C4D11×D1612yes—
351C4#1062316411yescharacteristic
352C4#1062330911yescharacteristic
353C2—161no—
354C2—882no—
355C2—1762no—
356C2#1308125011yescharacteristic
357C2C2×D11×D1611yescharacteristic
358C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2224C2
socleC22×C11C22×D8
hypercenter#2224D11
hypocenterC11#33925
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2224

Complements

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

NH ≅ G/Ntype
1. #13081590C2semidirect
2. #13081468C2semidirect
3. #13070841C2semidirect
4. #13070838C2semidirect
5. #13070752C2semidirect
6. #13070652C2semidirect
7. #13070650C2semidirect
8. #13070518C2semidirect
9. #13070462C2semidirect
10. C4×#66890C2semidirect
11. C11×#2224C2semidirect
119. D88#41semidirect
128. #2224D11semidirect
161. Dic22D16semidirect
301. C11#33925semidirect

Maximal subgroups

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

subgroupindex
#130815902
#130814682
#130708412
#130708382
#130707522
#130706522
#130706502
#130705182
#130704622
C4×#668902
C11×#22242
#3392511