Finite Group Databasebeta

← #14910700

Subgroups — #14910700

Order 2816.

546 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081047C211yesmaximal, characteristic, complemented
2#13070843C211yesmaximal, characteristic, complemented
3#13070821C212yesmaximal, complemented
4#13070753C211yesmaximal, characteristic, complemented
5#13070705C212yesmaximal, complemented
6#13070663C211yesmaximal, characteristic, complemented
7#13070556C212yesmaximal, complemented
8C4×#66891C211yesmaximal, characteristic, complemented
9D4×C11⋊C16C211yesmaximal, characteristic, complemented
10#13070323C212yesmaximal, complemented
11C11×#3283C211yesmaximal, characteristic
12C2×C11×#135C2212yes—
13C11×#547—21no—
14#10623073—21no—
15C11×#494C2211yescharacteristic
16C11×#467C2212yes—
17C11×#461—21no—
18C11×#452—22no—
19C4×C11×D8C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21C2×#66893C2212yes—
22C2×#66891C2211yescharacteristic
23#10622729C2212yes—
24#10622719C2212yes—
25C22×C11⋊C16C2212yes—
26#10622464—21no—
27#10622336—22no—
28C4×Dic44C2211yescharacteristic
29#10622295C2211yescharacteristic
30#10622202C2212yes—
31#10622202C2212yes—
32#10622202C2212yes—
33#10622200C2211yescharacteristic
34#10622200C2212yes—
35C22⋊(C11⋊C16)C2212yes—
36#10622130C2211yescharacteristic
37#10622128C2211yescharacteristic
38#10622127C2212yes—
39C4⋊(C11⋊C16)C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×#41—22no—
42C11×#135—24no—
43C11×#135—42no—
44C2×C11×Q16—21no—
45C2×C11×Q16C2312yes—
46C2×C11×SD16—22no—
47C2×C11×D8C2311yescharacteristic
48C22×C8×C11C2312yes—
49C11×C4⋊Q8—21no—
50C11×#123—42no—
51C11×C22⋊Q8—22no—
52C11×#121—41no—
53C4×D4×C11—21no—
54C4×D4×C11D411yescharacteristic
55C2×C11×C4⋊C4—41no—
56#66989—41no—
57#66979—22no—
58#66977—22no—
59C2×Dic44C2311yescharacteristic
60#66940—41no—
61#66932—42no—
62#66922—21no—
63C4×Dic22—21no—
64C11×#107C2311yescharacteristic
65C11×C4⋊C8D411yescharacteristic
66C11×#103—22no—
67C11×#102—21no—
68C11×C22⋊C8D412yes—
69C4×C8×C11C2311yescharacteristic
70#66893—42no—
71#66891—22no—
72#66882—21no—
73#66882C2312yes—
74#66882C2311yescharacteristic
75#66881—22no—
76#66880—22no—
77#66880—21no—
78C2×C11⋊C16—42no—
79C2×C11⋊C16C2311yescharacteristic
80C2×C11⋊C16C2312yes—
81C2×C11⋊C16C2311yescharacteristic
82#33869—111nomaximal, Sylow
83C11×#41—44no—
84C11×#41—82no—
85C2×Q8×C11—22no—
86C2×D4×C11—21no—
87C2×D4×C11—42no—
88C2×D4×C11D811yescharacteristic
89C22×C4×C11—41no—
90C22×C4×C11—42no—
91C22×C4×C11C2×D412yes—
92C2×Dic22—21no—
93C2×Dic22—41no—
94C11×Q16—22no—
95C11×Q16—22no—
96C11×Q16—81no—
97C11×SD16—44no—
98C11×D8—21no—
99C11×D8#4112yes—
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11C2×D412yes—
103C2×C8×C11C2×D411yescharacteristic
104C2×C8×C11C2411yescharacteristic
105C11×C4⋊C4—21no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—42no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4D811yescharacteristic
110C11×C22⋊C4—42no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4D812yes—
113C42×C11C2×D411yescharacteristic
114C22⋊Dic11—42no—
115C22⋊Dic11—42no—
116C4⋊Dic11—21no—
117C4⋊Dic11—22no—
118C4⋊Dic11—41no—
119Dic11⋊C4—41no—
120Dic11⋊C4—42no—
121C4×Dic11—41no—
122C4×Dic11—42no—
123Dic44—21no—
124Dic44—21no—
125C11⋊C16—21no—
126C11⋊C16—21no—
127C11⋊C16—22no—
128#3342—111no—
129#3283D1111yescharacteristic
130#2241—111no—
131#2237—112no—
132#2224—111no—
133#2216—112no—
134#2209—111no—
135#2189—112no—
136C4×SD32—111no—
137D4×C16—111no—
138#2138—112no—
139C23×C11—41no—
140C23×C11C2×D812yes—
141Q8×C11—42no—
142Q8×C11—42no—
143D4×C11—22no—
144D4×C11—22no—
145D4×C11—41no—
146D4×C11—84no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—84no—
152C2×C4×C11—82no—
153C2×C4×C11C2×D812yes—
154C2×C4×C11C2×D811yescharacteristic
155C2×C4×C11C2×D811yescharacteristic
156C2×C4×C11C22×D411yescharacteristic
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—42no—
160Dic22—41no—
161Dic22—41no—
162Dic22—82no—
163C8×C11—22no—
164C8×C11—21no—
165C8×C11C2×#4111yescharacteristic
166C8×C11H(5,𝔽2)11yescharacteristic
167C2×#135C2×D1112yes—
168#556—221no—
169#547—21no—
170C2×Q32—112no—
171C2×SD32—111no—
172C22×C16—112no—
173#500—111no—
174#494C2×D1111yescharacteristic
175#485—222no—
176#475—221no—
177#467—112no—
178#467C2×D1112yes—
179#461—21no—
180#452—22no—
181C4×Q16—111no—
182C4×D8C2×D1111yescharacteristic
183C8×D4C2×D1111yescharacteristic
184#427—112no—
185#367—111no—
186#366—112no—
187C4⋊C16—111no—
188#358—112no—
189#358—112no—
190#358—112no—
191#358—111no—
192#357—111no—
193#357—112no—
194C22⋊C16—112no—
195C4×C16—111no—
196C22×C11—22no—
197C22×C11—22no—
198C22×C11—22no—
199C22×C11—42no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11C22×D811yescharacteristic
203C4×C11—21no—
204C4×C11—22no—
205C4×C11—81no—
206C4×C11—82no—
207C4×C11#50812yes—
208C4×C11#54611yescharacteristic
209C4×C11#57711yescharacteristic
210Dic11—82no—
211Dic11—81no—
212Dic11—81no—
213C2×#41—22no—
214#135—24no—
215#135—42no—
216C2×Q16—21no—
217C2×Q16—111no—
218C2×Q16C22×D1112yes—
219C2×SD16—22no—
220C2×D8C22×D1111yescharacteristic
221C22×C8C22×D1112yes—
222C4⋊Q8—21no—
223C4⋊Q8—221no—
224#126—442no—
225#124—441no—
226#123—42no—
227C22⋊Q8—22no—
228C22⋊Q8—222no—
229#121—41no—
230C4×Q8—221no—
231C4×Q8—441no—
232C4×D4—21no—
233C4×D4C22⋊D1111yescharacteristic
234#117—222no—
235C2×C4⋊C4—41no—
236Q32—442no—
237SD32—222no—
238C2×C16—111no—
239C2×C16—111no—
240C2×C16—112no—
241C2×C16—442no—
242#107—112no—
243#107—111no—
244#107—221no—
245#107C22×D1111yescharacteristic
246#106—222no—
247C4⋊C8C22⋊D1111yescharacteristic
248#103—22no—
249#103—221no—
250#103—222no—
251#102—21no—
252C22⋊C8C22⋊D1112yes—
253C4×C8C22×D1111yescharacteristic
254C2×C11—42no—
255C2×C11—82no—
256C2×C11#329411yescharacteristic
257C2×C11C2×#50811yescharacteristic
258C2×C11#341711yescharacteristic
259#41—44no—
260#41—82no—
261C2×Q8—22no—
262C2×Q8—221no—
263C2×Q8—441no—
264C2×D4—21no—
265C2×D4—42no—
266C2×D4#432311yescharacteristic
267C22×C4—41no—
268C22×C4—42no—
269C22×C4C2×C22⋊D1112yes—
270Q16—22no—
271Q16—22no—
272Q16—81no—
273Q16—221no—
274Q16—221no—
275SD16—44no—
276D8—21no—
277D8#434112yes—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8C2×C22⋊D1111yescharacteristic
281C2×C8C2×C22⋊D1112yes—
282C2×C8C23×D1111yescharacteristic
283C4⋊C4—21no—
284C4⋊C4—41no—
285C4⋊C4—42no—
286C4⋊C4—41no—
287C4⋊C4—221no—
288C4⋊C4—222no—
289C4⋊C4—441no—
290C4⋊C4—442no—
291C4⋊C4—441no—
292C4⋊C4#432311yescharacteristic
293C22⋊C4—42no—
294C22⋊C4—41no—
295C22⋊C4—442no—
296C22⋊C4—442no—
297C22⋊C4#432312yes—
298C42—442no—
299C42—441no—
300C42C2×C22⋊D1111yescharacteristic
301C16—221no—
302C16—221no—
303C16—222no—
304C11#3386911yescharacteristic, complemented, Sylow
305C23—41no—
306C23C2×#432312yes—
307Q8—42no—
308Q8—42no—
309Q8—441no—
310Q8—441no—
311Q8—882no—
312D4—22no—
313D4—22no—
314D4—41no—
315D4—84no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—84no—
321C2×C4—82no—
322C2×C4—441no—
323C2×C4—442no—
324C2×C4—441no—
325C2×C4C2×#432312yes—
326C2×C4C2×#432311yescharacteristic
327C2×C4C2×#432311yescharacteristic
328C2×C4C22×C22⋊D1111yescharacteristic
329C8—22no—
330C8—21no—
331C8C2×#434111yescharacteristic
332C8#6703711yescharacteristic
333C22—22no—
334C22—22no—
335C22—22no—
336C22—42no—
337C22—81no—
338C22—81no—
339C22C22×#432311yescharacteristic
340C4—22no—
341C4—21no—
342C4—82no—
343C4—81no—
344C4—881no—
345C4—882no—
346C4—881no—
347C4#1062280712yes—
348C4#1062333711yescharacteristic
349C4#1062336711yescharacteristic
350C2—42no—
351C2—82no—
352C2#1308042911yescharacteristic
353C2C2×#1062280711yescharacteristic
354C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC11×#3283C2
socleC22×C11C22×D8
hypercenter#3283D11
hypocenterC11#33869
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3283

Complements

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

NH ≅ G/Ntype
1. #13081047C2semidirect
2. #13070843C2semidirect
3. #13070821C2semidirect
4. #13070753C2semidirect
5. #13070705C2semidirect
6. #13070663C2semidirect
7. #13070556C2semidirect
8. C4×#66891C2semidirect
9. D4×C11⋊C16C2semidirect
10. #13070323C2semidirect
304. C11#33869semidirect

Maximal subgroups

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

subgroupindex
#130810472
#130708432
#130708212
#130707532
#130707052
#130706632
#130705562
C4×#668912
D4×C11⋊C162
#130703232
C11×#32832
#3386911