Finite Group Databasebeta

← #14909296

Subgroups — #14909296

Order 2816.

514 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#13079129C211yesmaximal, characteristic
2D11×#500C211yesmaximal, characteristic
3#13070903C211yesmaximal, characteristic, complemented
4#13070902C211yesmaximal, characteristic, complemented
5#13070899C211yesmaximal, characteristic, complemented
6#13070897C212yesmaximal, complemented
7#13070890C212yesmaximal, complemented
8#13070403C212yesmaximal
9#13070401C212yesmaximal
10#13070209C211yesmaximal, characteristic
11C11×#2255C211yesmaximal, characteristic, complemented
12D11×C4⋊Q8—21no—
13#10623219—21no—
14C11×#500C2211yescharacteristic
15C11×#499C2211yescharacteristic
16#10622691—21no—
17#10622677—21no—
18C2×#66862C2212yes—
19#10622493C2211yescharacteristic
20#10622493C2211yescharacteristic
21D11×#107—21no—
22D11×#107C2212yes—
23#10622487—21no—
24#10622487C2211yescharacteristic
25#10622487C2212yes—
26#10622487C2211yescharacteristic
27#10622473—21no—
28#10622468—21no—
29C4×C8×D11C2211yescharacteristic
30#10622296C2211yescharacteristic
31#10622295C2211yescharacteristic
32C11×#367C2212yes—
33C11×#366C2212yes—
34C11×#346C2211yescharacteristic
35#10622143C2212yes—
36#10622142C2212yes—
37C16×Dic11C2212yes—
38#10622128C2212yes—
39#10622128C2212yes—
40#10622127C2212yes—
41#10622127C2212yes—
42#10622099C2211yescharacteristic
43C2×Q8×D11—41no—
44C11×C4⋊Q8—21no—
45C11×#125—21no—
46#66997—41no—
47C2×C8×D11D411yescharacteristic
48C2×C8×D11C2311yescharacteristic
49#66949—41no—
50#66949—41no—
51#66945—21no—
52#66945—21no—
53C4⋊C4×D11—22no—
54C4⋊C4×D11—41no—
55#66941—21no—
56#66941—21no—
57#66941—22no—
58#66941—41no—
59#66940—41no—
60#66940—41no—
61C42×D11D411yescharacteristic
62#66923—21no—
63#66922—21no—
64C2×C11×C16C2312yes—
65C11×#107—21no—
66C11×#107C2311yescharacteristic
67C11×#107C2311yescharacteristic
68C11×#107C2312yes—
69C11×#106—21no—
70C4×C8×C11C2311yescharacteristic
71#66882—21no—
72#66882C2312yes—
73#66882C2311yescharacteristic
74#66882C2311yescharacteristic
75#66881—21no—
76C8×Dic11D411yescharacteristic
77C8×Dic11C2311yescharacteristic
78C2×C11⋊C16C2312yes—
79#66872—21no—
80#66872—21no—
81#66871—21no—
82#66871—21no—
83#66871—22no—
84#66871—22no—
85C4×C11⋊C8D411yescharacteristic
86#66862Q818yescomplemented
87#33731—111nomaximal, Sylow
88C2×Q8×C11—41no—
89Q8×D11—84no—
90C2×C4×D11—42no—
91C2×C4×D11D811yescharacteristic
92C2×C4×D11D811yescharacteristic
93C2×C4×D11C2×D411yescharacteristic
94C2×Dic22—41no—
95C2×Dic22—41no—
96C2×Dic22—42no—
97C2×Dic22—41no—
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2411yescharacteristic
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C42×C11C2×D411yescharacteristic
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—41no—
109C4⋊Dic11—22no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112C4⋊Dic11—41no—
113Dic11⋊C4—41no—
114Dic11⋊C4—41no—
115Dic11⋊C4—42no—
116Dic11⋊C4—42no—
117Dic11⋊C4—41no—
118Dic11⋊C4—41no—
119C4×Dic11—41no—
120C4×Dic11—41no—
121C4×Dic11D811yescharacteristic
122C4×Dic11D811yescharacteristic
123C4×Dic11C2×D411yescharacteristic
124C2×C11⋊C8C2×D411yescharacteristic
125C2×C11⋊C8C2×D411yescharacteristic
126C8×D11Q1614yes—
127C8×D11C2×Q814yes—
128C11×C16C2×Q814yescomplemented
129C11⋊C16C2×Q814yescomplemented
130#3160—111no—
131C2×#500—111no—
132#2255—111no—
133#2255—111no—
134#2255—111no—
135#2255D1111yescharacteristic, complemented
136#2254—112no—
137#2252—112no—
138#2159—112no—
139#2159—112no—
140C4×M32—111no—
141C22×D11C2×D811yescharacteristic
142Q8×C11—82no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11C2×D811yescharacteristic
147C2×C4×C11C2×D811yescharacteristic
148C2×C4×C11C22×D411yescharacteristic
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—42no—
152C2×Dic11C2×D811yescharacteristic
153C2×Dic11C2×D811yescharacteristic
154C2×Dic11C2×D811yescharacteristic
155C4×D11—22no—
156C4×D11—22no—
157C4×D11—84no—
158C4×D11C4⋊Q812yes—
159C4×D11C2×Q1612yes—
160Dic22—82no—
161Dic22—82no—
162Dic22—84no—
163Dic22—82no—
164C8×C11C2×Q1612yes—
165C8×C11C22×Q812yes—
166C11⋊C8C4⋊Q812yes—
167C11⋊C8C2×Q1612yes—
168#533—221no—
169C2×C4⋊Q8—221no—
170C2×M32—112no—
171#500—112no—
172#500—111no—
173#500—111no—
174#500—111no—
175#500—221no—
176#500—221no—
177#500C2×D1111yescharacteristic
178#499—111no—
179#499—221no—
180#499C2×D1111yescharacteristic
181#498—221no—
182#427—111no—
183#427—111no—
184#427—221no—
185C2×#107—112no—
186C2×#107—221no—
187C2×C4×C8—111no—
188#367—112no—
189#367—112no—
190#367—112no—
191#367C2×D1112yes—
192#366—112no—
193#366—112no—
194#366—112no—
195#366C2×D1112yes—
196#346—111no—
197#346C2×D1111yescharacteristic
198C4×C16—112no—
199C22×C11C22×D811yescharacteristic
200C2×D11—21no—
201C2×D11—21no—
202C2×D11#50012yes—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—82no—
206C4×C11—81no—
207C4×C11—81no—
208C4×C11C2×C4⋊Q811yescharacteristic
209C4×C11C22×Q1611yescharacteristic
210Dic11—82no—
211Dic11—81no—
212Dic11—81no—
213Dic11#50012yes—
214Dic11#50912yes—
215Dic11#51012yes—
216C22×Q8—441no—
217C22×C8—111no—
218C22×C8—111no—
219C4⋊Q8—21no—
220C4⋊Q8—222no—
221C4⋊Q8—221no—
222C4⋊Q8—221no—
223C4⋊Q8—221no—
224C4⋊Q8—441no—
225C4⋊Q8—441no—
226#125—21no—
227#125—221no—
228C22⋊Q8—441no—
229C22⋊Q8—441no—
230C4×Q8—441no—
231C4×Q8—441no—
232#117—221no—
233#117—221no—
234C2×C4⋊C4—222no—
235C2×C4⋊C4—441no—
236C2×C42—111no—
237M32—118no—
238C2×C16—112no—
239C2×C16C22×D1112yes—
240#107—21no—
241#107—111no—
242#107—112no—
243#107—111no—
244#107—222no—
245#107—222no—
246#107—221no—
247#107—221no—
248#107—221no—
249#107C22×D1111yescharacteristic
250#107C22×D1112yes—
251#107C22×D1111yescharacteristic
252#106—21no—
253#106—221no—
254#106—221no—
255#106—221no—
256C4×C8—111no—
257C4×C8—111no—
258C4×C8—111no—
259C4×C8C22×D1111yescharacteristic
260C2×C11C2×#50011yescharacteristic
261C2×C11C2×#50911yescharacteristic
262C2×C11C2×#51011yescharacteristic
263D11—22no—
264C2×Q8—41no—
265C2×Q8—441no—
266C2×Q8—441no—
267C2×Q8—442no—
268C2×Q8—441no—
269C2×Q8—884no—
270C22×C4—111no—
271C22×C4—111no—
272C22×C4—111no—
273C22×C4—442no—
274C2×C8—111no—
275C2×C8—111no—
276C2×C8—114no—
277C2×C8—114no—
278C2×C8D4×D1111yescharacteristic
279C2×C8C23×D1111yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—22no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—221no—
287C4⋊C4—221no—
288C4⋊C4—222no—
289C4⋊C4—442no—
290C4⋊C4—442no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C4⋊C4—441no—
294C4⋊C4—441no—
295C4⋊C4—441no—
296C22⋊C4—441no—
297C22⋊C4—441no—
298C42—111no—
299C42—111no—
300C42—111no—
301C42—441no—
302C42—441no—
303C42D4×D1111yescharacteristic
304C16—114no—
305C16Q8×D1114yescomplemented
306C11#3373111yescharacteristic, complemented, Sylow
307C23—111no—
308Q8—82no—
309Q8—882no—
310Q8—884no—
311Q8—882no—
312Q8—882no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—111no—
317C2×C4—111no—
318C2×C4—111no—
319C2×C4—112no—
320C2×C4—112no—
321C2×C4—222no—
322C2×C4—222no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—442no—
326C2×C4—884no—
327C2×C4D8×D1111yescharacteristic
328C2×C4D8×D1111yescharacteristic
329C2×C4C2×D4×D1111yescharacteristic
330C8—112no—
331C8—112no—
332C8Q16×D1112yes—
333C8C2×Q8×D1112yes—
334C22—112no—
335C22—221no—
336C22—221no—
337C22C2×D8×D1111yescharacteristic
338C4—21no—
339C4—21no—
340C4—82no—
341C4—81no—
342C4—81no—
343C4—112no—
344C4—112no—
345C4—112no—
346C4—882no—
347C4—881no—
348C4—881no—
349C4D11×C4⋊Q811yescharacteristic
350C4C2×Q16×D1111yescharacteristic
351C2—222no—
352C2D11×#50011yescharacteristic
353C2D11×#50911yescharacteristic
354C2D11×#51011yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2255C2
socleC22×C11C22×D8
prime radicalC22×D11C2×D8
hypercenter#2255D11
hypocenterC11#33731
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2255

Complements

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

NH ≅ G/Ntype
3. #13070903C2semidirect
4. #13070902C2semidirect
5. #13070899C2semidirect
6. #13070897C2semidirect
7. #13070890C2semidirect
11. C11×#2255C2semidirect
86. #66862Q8semidirect
128. C11×C16C2×Q8semidirect
129. C11⋊C16C2×Q8semidirect
135. #2255D11semidirect
305. C16Q8×D11semidirect
306. C11#33731semidirect

Maximal subgroups

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

subgroupindex
#130791292
D11×#5002
#130709032
#130709022
#130708992
#130708972
#130708902
#130704032
#130704012
#130702092
C11×#22552
#3373111