Finite Group Databasebeta

← #14664706

Subgroups — #14664706

Order 2816.

412 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068696C211yesmaximal, characteristic
2C2×#10622166C211yesmaximal, characteristic
3#13066646C212yesmaximal, complemented
4#13066622C212yesmaximal, complemented
5C11×#2583C211yesmaximal, characteristic
6C2×C11×C22⋊Q8C411yescharacteristic
7C22×C11×C4⋊C4C2211yescharacteristic
8C11×#398C411yescharacteristic
9C11×#398C2211yescharacteristic
10C11×#395C411yescharacteristic
11C11×#395C2211yescharacteristic
12C11×#389—21no—
13C11×#389—21no—
14C11×#385—21no—
15C11×#385—21no—
16C4×C11×C22⋊C4C411yescharacteristic
17#10622820—21no—
18C2×C22⋊(C11⋊C8)—21no—
19#10622168—21no—
20#10622168C2212yes—
21#10622166—21no—
22#10622166C2212yes—
23C22×Q8×C11C2×C411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C11×C22⋊Q8—41no—
28C11×C22⋊Q8—41no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—41no—
35C2×C11×C4⋊C4—41no—
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C4⋊C4C2311yescharacteristic
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C42×C11—21no—
44C2×#4318—22no—
45C22×C11⋊C8—41no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95C2×C411yescharacteristic
51C11×#95C2×C411yescharacteristic
52C22⋊(C11⋊C8)—22no—
53C22⋊(C11⋊C8)—41no—
54C22⋊(C11⋊C8)—41no—
55C22⋊(C11⋊C8)—41no—
56#11854—111nomaximal, Sylow
57C24×C11C22⋊C411yescharacteristic
58C2×Q8×C11—41no—
59C2×Q8×C11—81no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—22no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—41no—
72C22×C4×C11—81no—
73C22×C4×C11—81no—
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—42no—
85C11×C4⋊C4—42no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—42no—
88C11×C4⋊C4—81no—
89C11×C4⋊C4—81no—
90C11×C22⋊C4—24no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C42×C11—81no—
94#4318—42no—
95#4318—42no—
96C2×C11⋊C8—42no—
97C2×C11⋊C8—42no—
98C2×C11⋊C8—82no—
99#2583D1111yescharacteristic
100#1821—111no—
101C2×#324—111no—
102#1354—112no—
103#1346—112no—
104C23×C11—22no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—41no—
108C23×C11#9911yescharacteristic
109C23×C11#9911yescharacteristic
110C23×C11C2×C22⋊C411yescharacteristic
111Q8×C11—82no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
142C2×C4×C11—81no—
143C2×C4×C11#13512yes—
144C11⋊C8—82no—
145C11⋊C8—82no—
146C2×C22⋊Q8Dic1111yescharacteristic
147C22×C4⋊C4C2×D1111yescharacteristic
148#407—221no—
149C2×C22⋊C8—221no—
150#398Dic1111yescharacteristic
151#398C2×D1111yescharacteristic
152#395Dic1111yescharacteristic
153#395C2×D1111yescharacteristic
154#389—21no—
155#389—21no—
156#385—21no—
157#385—21no—
158C4×C22⋊C4Dic1111yescharacteristic
159#343—112no—
160#343—221no—
161#324—112no—
162#324—221no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—42no—
171C22×C11—42no—
172C22×C11#35612yes—
173C22×C11C2×#9911yescharacteristic
174C22×C11#41611yescharacteristic
175C22×C11#42111yescharacteristic
176C4×C11—22no—
177C4×C11—42no—
178C4×C11—42no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—81no—
185C4×C11—81no—
186C22×Q8C2×Dic1111yescharacteristic
187C23×C4C2×Dic1111yescharacteristic
188C23×C4C22⋊D1111yescharacteristic
189C23×C4C22⋊D1111yescharacteristic
190C2×M16—222no—
191C22×C8—441no—
192C22⋊Q8—41no—
193C22⋊Q8—41no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—41no—
200C2×C4⋊C4—41no—
201C2×C4⋊C4C2×Dic1111yescharacteristic
202C2×C4⋊C4C2×Dic1111yescharacteristic
203C2×C4⋊C4C22⋊D1111yescharacteristic
204C2×C4⋊C4C22⋊D1111yescharacteristic
205C2×C4⋊C4C22×D1111yescharacteristic
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C42—21no—
209C22⋊C8—222no—
210C22⋊C8—441no—
211C22⋊C8—441no—
212C22⋊C8—441no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95C2×Dic1111yescharacteristic
218#95C2×Dic1111yescharacteristic
219C2×C11—21no—
220C2×C11—21no—
221C2×C11—22no—
222C2×C11—41no—
223C2×C11#151611yescharacteristic
224C2×C11#212111yescharacteristic
225C2×C11C2×#35611yescharacteristic
226C24C22⋊Dic1111yescharacteristic
227C2×Q8—41no—
228C2×Q8—81no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—41no—
241C22×C4—81no—
242C22×C4—81no—
243C22×C4C22⋊Dic1111yescharacteristic
244C22×C4C22⋊Dic1111yescharacteristic
245C22×C4C22⋊Dic1111yescharacteristic
246C22×C4C22×Dic1111yescharacteristic
247C22×C4C2×C22⋊D1111yescharacteristic
248C22×C4C2×C22⋊D1111yescharacteristic
249M16—442no—
250M16—442no—
251C2×C8—442no—
252C2×C8—442no—
253C2×C8—882no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—81no—
263C4⋊C4—81no—
264C22⋊C4—24no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C42—81no—
268C11#1185411yescharacteristic, complemented, Sylow
269C23—21no—
270C23—21no—
271C23—22no—
272C23—41no—
273C23#6689811yescharacteristic
274C23#6689811yescharacteristic
275C23C2×C22⋊Dic1111yescharacteristic
276Q8—82no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4#6700312yes—
309C8—882no—
310C8—882no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—42no—
319C22—42no—
320C22#1062218612yes—
321C22C2×#6689811yescharacteristic
322C22#1062284611yescharacteristic
323C22#1062284911yescharacteristic
324C4—22no—
325C4—42no—
326C4—42no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—81no—
333C4—81no—
334C2—21no—
335C2—21no—
336C2—22no—
337C2—41no—
338C2#1306717211yescharacteristic
339C2#1307026211yescharacteristic
340C2C2×#1062218611yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2583C2
socleC22×C11C2×#99
prime radicalC24×C11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#2583D11
hypocenterC11#11854
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2583

Complements

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

NH ≅ G/Ntype
3. #13066646C2semidirect
4. #13066622C2semidirect
268. C11#11854semidirect

Maximal subgroups

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

subgroupindex
#130686962
C2×#106221662
#130666462
#130666222
C11×#25832
#1185411