Finite Group Databasebeta

← #14754069

Subgroups — #14754069

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068761C212yesmaximal, complemented
2#13068736C212yesmaximal, complemented
3#13068684C212yesmaximal
4#13068596C212yesmaximal
5#13068473C212yesmaximal, complemented
6#13068378C211yesmaximal, characteristic
7C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic
8#13068368C212yesmaximal, complemented
9C2×C11×#376C211yesmaximal, characteristic
10C22×C42×C11C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C11×#376C412yes—
14C11×#376C412yes—
15C11×#376C2211yescharacteristic
16C11×#376C2211yescharacteristic
17C11×#376C2211yescharacteristic
18C11×#376C2211yescharacteristic
19C2×C11×#95C412yes—
20C2×C11×#95C412yes—
21C2×C22⋊(C11⋊C8)C2212yes—
22C2×C22⋊(C11⋊C8)C2212yes—
23C2×C4⋊(C11⋊C8)C2214yes—
24C2×#66867C2212yes—
25C2×C4×C11⋊C8C2212yes—
26#10622162C2214yes—
27#10622162C2214yes—
28#10622162C2212yes—
29#10622162C2212yes—
30#10622162C2214yes—
31C23×C4×C11C2×C411yescharacteristic
32C23×C4×C11C2×C412yes—
33C23×C4×C11C2×C412yes—
34C23×C4×C11C2×C411yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C2×C42×C11—24no—
37C2×C42×C11—24no—
38C2×C42×C11—24no—
39C2×C42×C11C2×C411yescharacteristic
40C2×C42×C11C2×C411yescharacteristic
41C2×C42×C11C2×C412yes—
42C2×C42×C11C2×C412yes—
43C2×C42×C11C2311yescharacteristic
44C2×C42×C11C2311yescharacteristic
45C2×C42×C11C2311yescharacteristic
46C2×C42×C11C2311yescharacteristic
47C2×C42×C11C2311yescharacteristic
48C2×C42×C11C2311yescharacteristic
49C22×C11⋊C8C2314yes—
50C22×C11⋊C8C2314yes—
51C11×#95C2×C412yes—
52C11×#95C2×C412yes—
53C11×#95C2×C412yes—
54C11×#95C2×C412yes—
55C11×#95C2×C412yes—
56C11×#95C2×C412yes—
57C11×#95C2×C412yes—
58C11×#95C2×C412yes—
59C22⋊(C11⋊C8)—24no—
60C22⋊(C11⋊C8)—24no—
61C4⋊(C11⋊C8)—28no—
62#66867—24no—
63C4×C11⋊C8—24no—
64#20779—111nomaximal, Sylow
65C24×C11C22×C411yescharacteristic
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—24no—
71C22×C4×C11—24no—
72C22×C4×C11—24no—
73C22×C4×C11—24no—
74C22×C4×C11—24no—
75C22×C4×C11—42no—
76C22×C4×C11—42no—
77C22×C4×C11—42no—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C22×C412yes—
81C22×C4×C11C22×C412yes—
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C22×C412yes—
85C22×C4×C11C22×C412yes—
86C22×C4×C11C22×C411yescharacteristic
87C22×C4×C11#4114yes—
88C22×C4×C11C2411yescharacteristic
89C42×C11—24no—
90C42×C11—24no—
91C42×C11—22no—
92C42×C11—22no—
93C42×C11—22no—
94C42×C11—22no—
95C42×C11—22no—
96C42×C11—22no—
97C42×C11#4114yes—
98C42×C11#4114yes—
99C2×C11⋊C8—24no—
100C2×C11⋊C8—24no—
101C2×C11⋊C8—24no—
102C2×C11⋊C8—24no—
103C2×C11⋊C8—24no—
104C2×C11⋊C8—24no—
105C2×#376D1111yescharacteristic
106#1840—112no—
107#1832—112no—
108#1817—112no—
109#1797—112no—
110#1768—112no—
111#1749—111no—
112C4×C22⋊C8—111no—
113#1746—112no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—22no—
117C23×C11#11712yes—
118C23×C11#13114yes—
119C23×C11C23×C411yescharacteristic
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—28no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—48no—
142C2×C4×C11—48no—
143C2×C4×C11—44no—
144C2×C4×C11—44no—
145C2×C4×C11#11712yes—
146C2×C4×C11#11714yes—
147C2×C4×C11#11714yes—
148C2×C4×C11C2×#4112yes—
149C2×C4×C11C2×#4112yes—
150C2×C4×C11C2×#4112yes—
151C11⋊C8—44no—
152C11⋊C8—44no—
153C22×C42C2×D1111yescharacteristic
154C22×C42C2×D1111yescharacteristic
155C22×C42C2×D1111yescharacteristic
156C2×C4⋊C8—114no—
157C2×C22⋊C8—112no—
158C2×C22⋊C8—112no—
159C2×#97—112no—
160C2×C4×C8—112no—
161#376Dic1112yes—
162#376Dic1112yes—
163#376C2×D1111yescharacteristic
164#376C2×D1111yescharacteristic
165#376C2×D1111yescharacteristic
166#376C2×D1111yescharacteristic
167C2×#95Dic1112yes—
168C2×#95Dic1112yes—
169#336—114no—
170#336—114no—
171#336—114no—
172#336—112no—
173#336—112no—
174C22×C11—22no—
175C22×C11—24no—
176C22×C11—24no—
177C22×C11—22no—
178C22×C11#43314yes—
179C22×C11C2×#11711yescharacteristic
180C22×C11C2×#11711yescharacteristic
181C22×C11C2×#11711yescharacteristic
182C22×C11C2×#13112yes—
183C22×C11#56812yes—
184C4×C11—24no—
185C4×C11—24no—
186C4×C11—22no—
187C4×C11—41no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11—42no—
192C4×C11—42no—
193C4×C11#52914yes—
194C23×C4C2×Dic1111yescharacteristic
195C23×C4C2×Dic1112yes—
196C23×C4C2×Dic1112yes—
197C23×C4C2×Dic1111yescharacteristic
198C23×C4C22×D1111yescharacteristic
199C22×C8—114no—
200C22×C8—114no—
201C2×C42—24no—
202C2×C42—24no—
203C2×C42—24no—
204C2×C42C2×Dic1111yescharacteristic
205C2×C42C2×Dic1111yescharacteristic
206C2×C42C2×Dic1112yes—
207C2×C42C2×Dic1112yes—
208C2×C42C22×D1111yescharacteristic
209C2×C42C22×D1111yescharacteristic
210C2×C42C22×D1111yescharacteristic
211C2×C42C22×D1111yescharacteristic
212C2×C42C22×D1111yescharacteristic
213C2×C42C22×D1111yescharacteristic
214C4⋊C8—228no—
215C22⋊C8—224no—
216C22⋊C8—224no—
217#97—224no—
218C4×C8—224no—
219#95C2×Dic1112yes—
220#95C2×Dic1112yes—
221#95C2×Dic1112yes—
222#95C2×Dic1112yes—
223#95C2×Dic1112yes—
224#95C2×Dic1112yes—
225#95C2×Dic1112yes—
226#95C2×Dic1112yes—
227C2×C11—24no—
228C2×C11#228311yescharacteristic
229C2×C11C2×#43311yescharacteristic
230C2×C11#292111yescharacteristic
231C2×C11#292412yes—
232C2×C11#292412yes—
233C24C22×Dic1111yescharacteristic
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—24no—
239C22×C4—24no—
240C22×C4—24no—
241C22×C4—24no—
242C22×C4—24no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4#433914yes—
247C22×C4C22×Dic1111yescharacteristic
248C22×C4C22×Dic1111yescharacteristic
249C22×C4C22×Dic1112yes—
250C22×C4C22×Dic1112yes—
251C22×C4C22×Dic1111yescharacteristic
252C22×C4C22×Dic1111yescharacteristic
253C22×C4C22×Dic1112yes—
254C22×C4C22×Dic1112yes—
255C22×C4C22×Dic1111yescharacteristic
256C22×C4C23×D1111yescharacteristic
257C2×C8—224no—
258C2×C8—224no—
259C2×C8—224no—
260C2×C8—224no—
261C2×C8—224no—
262C2×C8—224no—
263C42—24no—
264C42—24no—
265C42—22no—
266C42—22no—
267C42—22no—
268C42—22no—
269C42—22no—
270C42—22no—
271C42#433914yes—
272C42#433914yes—
273C11#2077911yescharacteristic, complemented, Sylow
274C23—21no—
275C23—21no—
276C23—22no—
277C23#6697912yes—
278C23#6700114yes—
279C23C23×Dic1111yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—28no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—48no—
302C2×C4—48no—
303C2×C4—44no—
304C2×C4—44no—
305C2×C4#6697912yes—
306C2×C4#6697914yes—
307C2×C4#6697914yes—
308C2×C4C2×#433912yes—
309C2×C4C2×#433912yes—
310C2×C4C2×#433912yes—
311C8—444no—
312C8—444no—
313C22—22no—
314C22—24no—
315C22—24no—
316C22—22no—
317C22#1062261314yes—
318C22C2×#6697911yescharacteristic
319C22C2×#6697911yescharacteristic
320C22C2×#6697911yescharacteristic
321C22C2×#6700112yes—
322C22#1062335012yes—
323C4—24no—
324C4—24no—
325C4—22no—
326C4—41no—
327C4—41no—
328C4—42no—
329C4—42no—
330C4—41no—
331C4—41no—
332C4#1062301014yes—
333C2—24no—
334C2#1307101411yescharacteristic
335C2C2×#1062261311yescharacteristic
336C2#1307725411yescharacteristic
337C2#1307727412yes—
338C2#1307727412yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC2×C11×#376C2
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenterC2×#376D11
hypocenterC11#20779
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#376

Complements

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

NH ≅ G/Ntype
1. #13068761C2semidirect
2. #13068736C2semidirect
5. #13068473C2semidirect
8. #13068368C2semidirect
273. C11#20779semidirect

Maximal subgroups

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

subgroupindex
#130687612
#130687362
#130686842
#130685962
#130684732
#130683782
C4×C22⋊(C11⋊C8)2
#130683682
C2×C11×#3762
#2077911