Finite Group Databasebeta

← #14908624

Subgroups — #14908624

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#13078267C211yesmaximal, characteristic
2#13077212C211yesmaximal, characteristic
3#13070823C212yesmaximal, complemented
4#13070822C212yesmaximal, complemented
5#13070817C212yesmaximal, complemented
6#13070812C212yesmaximal, complemented
7#13070402C211yesmaximal, characteristic, complemented
8#13070400C211yesmaximal, characteristic, complemented
9#13070336C211yesmaximal, characteristic, complemented
10#13070229C211yesmaximal, characteristic
11C2×C11×#358C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13#10623347—21no—
14C2×#66954C2211yescharacteristic
15#10623035—21no—
16C22×C11×C16C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18#10622838—21no—
19#10622802—22no—
20#10622801C2212yes—
21#10622801C2212yes—
22#10622719C2211yescharacteristic
23#10622719C2211yescharacteristic
24C2×#66876C2211yescharacteristic
25#10622577—21no—
26#10622494—22no—
27#10622493C2212yes—
28D11×#107C2212yes—
29C11×#358C2212yes—
30C11×#358C2212yes—
31#10622202C2212yes—
32#10622202C2212yes—
33(C2×D11)⋊C16C2212yes—
34(C2×D11)⋊C16C2212yes—
35#10622143C2211yescharacteristic
36#10622143C2211yescharacteristic
37#10622142C2211yescharacteristic
38#10622142C2211yescharacteristic
39#10622128C2212yes—
40#10622127C2212yes—
41C22×Q8×C11—21no—
42C2×#4339D411yescharacteristic
43C2×C11×Q16—21no—
44C2×C11×Q16—22no—
45C2×C11×Q16—22no—
46C2×C11×Q16C2312yes—
47C22×C8×C11C2311yescharacteristic
48C2×C11×C4⋊C4—21no—
49#67000—41no—
50#66999—22no—
51#66999—22no—
52#66997—41no—
53#66982—42no—
54C4×C22⋊D11—42no—
55#66979—21no—
56#66979—21no—
57C2×#4318D411yescharacteristic
58#66954—22no—
59#66954—22no—
60C2×#4313D412yes—
61C2×C8×D11C2312yes—
62#66946—41no—
63#66945—22no—
64C4⋊C4×D11—22no—
65#66940—41no—
66C2×C11×C16—22no—
67C2×C11×C16C2311yescharacteristic
68C2×C11×C16C2311yescharacteristic
69C11×#107—21no—
70C11×#107C2312yes—
71#66899—22no—
72#66899—22no—
73#66882C2311yescharacteristic
74#66882C2311yescharacteristic
75#66882C2311yescharacteristic
76#66882C2311yescharacteristic
77#66881—21no—
78#66881—21no—
79#66876—22no—
80C2×C11⋊C16C2312yes—
81#66872—22no—
82#66871—22no—
83#33651—111nomaximal, Sylow
84C2×Q8×C11—22no—
85C2×Q8×C11—41no—
86C2×Q8×C11—42no—
87C2×Q8×C11—42no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11C2×D411yescharacteristic
91C2×C22⋊D11D812yes—
92#4339—22no—
93#4339—22no—
94C2×D44D811yescharacteristic
95C2×C4×D11—42no—
96C2×C4×D11C2×D412yes—
97C2×Dic22D811yescharacteristic
98C11×Q16—22no—
99C11×Q16—22no—
100C11×Q16—42no—
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11#4112yes—
103C2×C8×C11#4112yes—
104C2×C8×C11C2411yescharacteristic
105C11×C4⋊C4—22no—
106C11×C4⋊C4—41no—
107C22⋊Dic11—41no—
108C22⋊Dic11—41no—
109(C2×D11)⋊C4—42no—
110(C2×D11)⋊C4—42no—
111(C2×D11)⋊C4—42no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116Dic11⋊C4—42no—
117Dic11⋊C4—42no—
118Dic11⋊C4—42no—
119C4×Dic11—42no—
120C4×Dic11—41no—
121C4×Dic11—41no—
122#4318—22no—
123C2×C11⋊C8C2×D412yes—
124#4313—24no—
125C8×D11—22no—
126C8×D11—22no—
127C11×C16—21no—
128C11×C16—21no—
129C11⋊C16—22no—
130#3059—111no—
131#2913—111no—
132#2237—112no—
133#2237—112no—
134#2236—112no—
135#2235—112no—
136#2159—111no—
137#2158—111no—
138#2141—111no—
139C2×#358D1111yescharacteristic, complemented
140#2113—111no—
141C23×C11C2×D811yescharacteristic
142C22×D11C2×D812yes—
143Q8×C11—42no—
144Q8×C11—42no—
145Q8×C11—82no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—82no—
149C2×C4×C11—161no—
150C2×C4×C11#12312yes—
151C2×C4×C11C2×D811yescharacteristic
152C2×C4×C11#13712yes—
153C2×C4×C11C22×D411yescharacteristic
154C22⋊D11—24no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11C2×D812yes—
160D44—22no—
161C4×D11—22no—
162C4×D11—22no—
163C4×D11—162no—
164Dic22—22no—
165C8×C11#12312yes—
166C8×C11C2×#4111yescharacteristic
167C8×C11C2×#4111yescharacteristic
168C11⋊C8—22no—
169C22×Q16C2×D1111yescharacteristic
170C2×#131—111no—
171#536—221no—
172#520—221no—
173C2×M32—111no—
174C22×C16C2×D1111yescharacteristic
175#470—222no—
176#467—112no—
177#467—112no—
178#428—222no—
179#428—221no—
180#427—111no—
181#427—111no—
182#427—112no—
183C2×#107—112no—
184C2×#107C2×D1111yescharacteristic
185#419—221no—
186#367—111no—
187#367—111no—
188#367—112no—
189#366—111no—
190#366—111no—
191#366—112no—
192#358—112no—
193#358—112no—
194#358C2×D1112yes—
195#358C2×D1112yes—
196C22⋊C16—112no—
197C22⋊C16—112no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11#48012yes—
201C22×C11C22×D811yescharacteristic
202C2×D11—22no—
203C2×D11—22no—
204C2×D11—22no—
205C4×C11—82no—
206C4×C11—82no—
207C4×C11#48012yes—
208C4×C11C2×#12311yescharacteristic
209C4×C11C2×#13711yescharacteristic
210Dic11—22no—
211Dic11—81no—
212Dic11—81no—
213Dic11—81no—
214Dic11—81no—
215C2×#41—111no—
216C22×Q8—21no—
217C2×Q16—22no—
218C2×Q16—21no—
219C2×Q16—22no—
220C2×Q16C22×D1112yes—
221#131—222no—
222#131—222no—
223C2×M16—111no—
224C2×M16—112no—
225C22×C8—112no—
226C22×C8C22×D1111yescharacteristic
227C4⋊Q8—441no—
228#124—441no—
229#123—442no—
230C22⋊Q8—222no—
231C22⋊Q8—222no—
232C4×Q8—441no—
233C4×D4—441no—
234C4×D4—442no—
235#117—222no—
236#117—221no—
237#117—221no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—222no—
240M32—222no—
241C2×C16—22no—
242C2×C16—112no—
243C2×C16C22×D1111yescharacteristic
244C2×C16C22×D1111yescharacteristic
245#107—21no—
246#107—111no—
247#107—111no—
248#107—111no—
249#107—111no—
250#107—222no—
251#107C22×D1112yes—
252#106—222no—
253#106—221no—
254#106—221no—
255#103—222no—
256#103—222no—
257C2×C11—22no—
258C2×C11C2×#48011yescharacteristic
259C2×C11#341611yescharacteristic
260C2×C11#341711yescharacteristic
261D11—42no—
262#41—222no—
263#41—222no—
264C2×Q8—22no—
265C2×Q8—41no—
266C2×Q8—42no—
267C2×Q8—42no—
268C2×Q8—111no—
269C2×D4—112no—
270C2×D4—111no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—112no—
274C22×C4—442no—
275C22×C4D4×D1111yescharacteristic
276Q16—22no—
277Q16—22no—
278Q16—42no—
279M16—222no—
280M16—224no—
281C2×C8—112no—
282C2×C8—222no—
283C2×C8—222no—
284C2×C8#433912yes—
285C2×C8D4×D1111yescharacteristic
286C2×C8#434112yes—
287C2×C8C23×D1111yescharacteristic
288C4⋊C4—22no—
289C4⋊C4—41no—
290C4⋊C4—221no—
291C4⋊C4—221no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4—442no—
295C4⋊C4—442no—
296C4⋊C4—442no—
297C22⋊C4—442no—
298C22⋊C4—442no—
299C22⋊C4—442no—
300C22⋊C4—441no—
301C22⋊C4—441no—
302C42—442no—
303C42—441no—
304C42—441no—
305C16—21no—
306C16—21no—
307C16—222no—
308C11#3365111yescharacteristic, complemented, Sylow
309C23—112no—
310C23D8×D1111yescharacteristic
311Q8—42no—
312Q8—42no—
313Q8—82no—
314Q8—222no—
315D4—224no—
316D4—222no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—82no—
320C2×C4—112no—
321C2×C4—161no—
322C2×C4—222no—
323C2×C4—222no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—1762no—
329C2×C4#6693612yes—
330C2×C4D8×D1111yescharacteristic
331C2×C4#6696812yes—
332C2×C4C2×D4×D1111yescharacteristic
333C8—222no—
334C8#6693612yes—
335C8C2×#433911yescharacteristic
336C8C2×#434111yescharacteristic
337C22—21no—
338C22—21no—
339C22—222no—
340C22—222no—
341C22—222no—
342C22#1062238712yes—
343C22C2×D8×D1111yescharacteristic
344C4—82no—
345C4—82no—
346C4—222no—
347C4—881no—
348C4—881no—
349C4—881no—
350C4—881no—
351C4#1062238712yes—
352C4C2×#6693611yescharacteristic
353C4C2×#6696811yescharacteristic
354C2—22no—
355C2—442no—
356C2C2×#1062238711yescharacteristic
357C2#1308175811yescharacteristic
358C2#1308176511yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#358C2
socleC22×C11C22×D8
prime radicalC2×#4339D4
hypercenterC2×#358D11
hypocenterC11#33651
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
3. #13070823C2semidirect
4. #13070822C2semidirect
5. #13070817C2semidirect
6. #13070812C2semidirect
7. #13070402C2semidirect
8. #13070400C2semidirect
9. #13070336C2semidirect
11. C2×C11×#358C2semidirect
139. C2×#358D11semidirect
308. C11#33651semidirect

Maximal subgroups

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

subgroupindex
#130782672
#130772122
#130708232
#130708222
#130708172
#130708122
#130704022
#130704002
#130703362
#130702292
C2×C11×#3582
#3365111