Finite Group Databasebeta

← #14664910

Subgroups — #14664910

Order 2816.

508 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 99 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#13073569C211yesmaximal, characteristic
2#13068604C211yesmaximal, characteristic
3#13066641C214yesmaximal, complemented
4C11×#1459C211yesmaximal, characteristic
5C2×C4×D4×C11C2211yescharacteristic
6C2×#66977—21no—
7C2×#66977—21no—
8C2×#66922C411yescharacteristic, complemented
9C2×C11×C22⋊C8—21no—
10#10622834—21no—
11C2×#66898—21no—
12#10622825—21no—
13#10622589—21no—
14#10622562C412yescomplemented
15#10622562C2212yes—
16C4×C4⋊Dic11C411yescharacteristic, complemented
17C11×#324—21no—
18C11×#323C2212yes—
19#10622164C2212yes—
20C22×D4×C11D411yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C22×Dic22—21no—
24C22×C8×C11—41no—
25C4×D4×C11—41no—
26C4×D4×C11—41no—
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C11×C22⋊C4C2×C411yescharacteristic
29C2×C11×C22⋊C4C2311yescharacteristic
30C2×C42×C11C2×C411yescharacteristic
31C2×C22⋊Dic11—22no—
32C2×C22⋊Dic11—22no—
33C2×C22⋊Dic11—22no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—41no—
37C2×C4⋊Dic11C2×C412yes—
38#66977—44no—
39#66977—44no—
40C2×Dic11⋊C4—22no—
41C2×Dic11⋊C4—22no—
42C2×C4×Dic11—21no—
43#66922—41no—
44#66922—41no—
45C11×C22⋊C8—22no—
46C11×C22⋊C8—41no—
47#66898—42no—
48C11⋊#95—41no—
49C11⋊#95C2×C412yes—
50#11901—111nomaximal, Sylow
51C24×C11C22⋊C411yescharacteristic
52C24×C11C2×D411yescharacteristic
53C2×D4×C11—41no—
54C2×D4×C11—41no—
55C2×D4×C11SD1612yes—
56C2×D4×C11Q1612yes—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—42no—
62C22×C4×C11—42no—
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—22no—
69C22×Dic11—22no—
70C22×Dic11—42no—
71C2×Dic22—42no—
72C2×Dic22—42no—
73C2×Dic22—41no—
74C2×Dic22—41no—
75C2×C8×C11—42no—
76C2×C8×C11—82no—
77C11×C4⋊C4—41no—
78C11×C22⋊C4—41no—
79C11×C22⋊C4—41no—
80C42×C11—21no—
81C42×C11—21no—
82C22⋊Dic11—42no—
83C22⋊Dic11—44no—
84C22⋊Dic11—44no—
85C22⋊Dic11—42no—
86C4⋊Dic11—24no—
87C4⋊Dic11—42no—
88C4⋊Dic11—42no—
89C4⋊Dic11—82no—
90Dic11⋊C4—44no—
91Dic11⋊C4—44no—
92C4×Dic11—42no—
93#2542—111no—
94#1799—111no—
95#1459D1111yescharacteristic
96#1352—114no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—41no—
102C23×C11—41no—
103C23×C11—41no—
104C23×C11—41no—
105C23×C11#10312yes—
106C23×C11C2×C22⋊C411yescharacteristic
107C23×C11C2×SD1611yescharacteristic
108C23×C11C2×Q1611yescharacteristic
109D4×C11—42no—
110D4×C11—42no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—22no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—81no—
123C2×C4×C11—81no—
124C2×C4×C11#9911yescharacteristic
125C2×C4×C11#9911yescharacteristic
126C2×C4×C11#10312yes—
127C2×Dic11—24no—
128C2×Dic11—42no—
129C2×Dic11—42no—
130C2×Dic11—42no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133C2×Dic11—82no—
134C2×Dic11—82no—
135C2×Dic11—82no—
136Dic22—82no—
137Dic22—82no—
138C8×C11—82no—
139C2×C4⋊Q8—111no—
140C2×C22⋊Q8—221no—
141C2×C22⋊Q8—221no—
142C2×C4×D4C2×D1111yescharacteristic
143C2×#99—221no—
144C2×C22⋊C8—21no—
145#399—112no—
146#399—112no—
147#390—221no—
148#384—221no—
149#380—221no—
150C4×C4⋊C4—111no—
151#342—112no—
152#324—21no—
153#323C2×D1112yes—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—22no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—42no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—81no—
167C22×C11—81no—
168C22×C11C2×#9911yescharacteristic
169C22×C11C2×#10311yescharacteristic
170C22×C11#42111yescharacteristic
171C4×C11—21no—
172C4×C11—22no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11#35312yes—
177Dic11—44no—
178Dic11—82no—
179Dic11—162no—
180C22×Q8—221no—
181C22×D4D4411yescharacteristic
182C23×C4D4411yescharacteristic
183C23×C4C22⋊D1111yescharacteristic
184C22×C8—41no—
185C4⋊Q8—441no—
186C4⋊Q8—441no—
187C22⋊Q8—444no—
188C22⋊Q8—444no—
189C4×D4—41no—
190C4×D4—41no—
191C2×C4⋊C4—112no—
192C2×C4⋊C4—221no—
193C2×C4⋊C4—222no—
194C2×C4⋊C4—221no—
195C2×C4⋊C4—222no—
196C2×C4⋊C4—441no—
197C2×C4⋊C4C22⋊D1111yescharacteristic
198C2×C22⋊C4—222no—
199C2×C22⋊C4—222no—
200C2×C22⋊C4—222no—
201C2×C22⋊C4C4×D1111yescharacteristic
202C2×C22⋊C4C22×D1111yescharacteristic
203C2×C42—221no—
204C2×C42C4×D1111yescharacteristic
205#99—442no—
206C22⋊C8—22no—
207C22⋊C8—41no—
208#95—112no—
209#95—441no—
210C2×C11—21no—
211C2×C11—21no—
212C2×C11—41no—
213C2×C11—42no—
214C2×C11—41no—
215C2×C11#152011yescharacteristic
216C2×C11#212311yescharacteristic
217C2×C11C2×#35311yescharacteristic
218C24(C2×D11)⋊C411yescharacteristic
219C24C2×D4411yescharacteristic
220C2×Q8—442no—
221C2×Q8—442no—
222C2×Q8—441no—
223C2×Q8—441no—
224C2×D4—41no—
225C2×D4—41no—
226C2×D4#431412yes—
227C2×D4Dic4412yes—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—222no—
235C22×C4—222no—
236C22×C4—442no—
237C22×C4(C2×D11)⋊C411yescharacteristic
238C22×C4(C2×D11)⋊C411yescharacteristic
239C22×C4(C2×D11)⋊C411yescharacteristic
240C22×C4C2×C4×D1111yescharacteristic
241C22×C4C2×C22⋊D1111yescharacteristic
242C2×C8—42no—
243C2×C8—82no—
244C4⋊C4—41no—
245C4⋊C4—224no—
246C4⋊C4—442no—
247C4⋊C4—442no—
248C4⋊C4—444no—
249C4⋊C4—444no—
250C4⋊C4—882no—
251C22⋊C4—41no—
252C22⋊C4—41no—
253C22⋊C4—444no—
254C22⋊C4—444no—
255C22⋊C4—442no—
256C22⋊C4—442no—
257C42—21no—
258C42—21no—
259C42—442no—
260C11#1190111yescharacteristic, complemented, Sylow
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23#6688012yes—
270C23C2×#431411yescharacteristic
271C23C2×Dic4411yescharacteristic
272C23C2×(C2×D11)⋊C411yescharacteristic
273Q8—882no—
274Q8—882no—
275D4—42no—
276D4—42no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—224no—
291C2×C4—442no—
292C2×C4—442no—
293C2×C4—442no—
294C2×C4—442no—
295C2×C4—442no—
296C2×C4—882no—
297C2×C4—882no—
298C2×C4—882no—
299C2×C4#6687011yescharacteristic
300C2×C4#6687011yescharacteristic
301C2×C4#6688012yes—
302C8—82no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—22no—
307C22—21no—
308C22—42no—
309C22—41no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—81no—
316C22—81no—
317C22C2×#6687011yescharacteristic
318C22C2×#6688011yescharacteristic
319C22#1062275211yescharacteristic
320C4—22no—
321C4—21no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—444no—
326C4—882no—
327C4—1762no—
328C4#1062211212yes—
329C2—21no—
330C2—21no—
331C2—41no—
332C2—42no—
333C2—41no—
334C2#1306718911yescharacteristic
335C2#1307027111yescharacteristic
336C2C2×#1062211211yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1459C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1459D11
hypocenterC11#11901
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #13066641C2semidirect
8. C2×#66922C4semidirect
14. #10622562C4semidirect
16. C4×C4⋊Dic11C4semidirect
260. C11#11901semidirect

Maximal subgroups

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

subgroupindex
#130735692
#130686042
#130666412
C11×#14592
#1190111