Finite Group Databasebeta

← #14664407

Subgroups — #14664407

Order 2816.

572 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C4×#66897C211yesmaximal, characteristic
2#13066954C211yesmaximal, characteristic
3#13066646C214yesmaximal, complemented
4C11×#2409C211yesmaximal, characteristic
5C23×Q8×C11C411yescharacteristic
6C2×C11×C22⋊Q8—21no—
7C2×C4×D4×C11C2211yescharacteristic
8C11×#395C2212yes—
9C11×#393C412yes—
10C11×#391—21no—
11C11×#386—21no—
12C11×#385—21no—
13C11×#380C411yescharacteristic
14C2×#66897—21no—
15#10622820—21no—
16C4×#4318—21no—
17#10622168C2212yes—
18#10622166C2212yes—
19#10622163—21no—
20C22×Q8×C11—21no—
21C22×Q8×C11—41no—
22C22×Q8×C11—41no—
23C22×Q8×C11—44no—
24C22×Q8×C11C2×C412yes—
25C22×D4×C11D411yescharacteristic
26C23×C4×C11—21no—
27C23×C4×C11C2×C411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C11×C22⋊Q8—44no—
30C4×D4×C11—41no—
31C4×D4×C11—41no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—22no—
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4C2×C411yescharacteristic
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C42×C11D411yescharacteristic
40C2×#4318—22no—
41C2×#4318—41no—
42C11×#95—22no—
43C11×#95—22no—
44C11×#95C2×C412yes—
45#66897—24no—
46C22⋊(C11⋊C8)—22no—
47C22⋊(C11⋊C8)—41no—
48#66867—41no—
49C4×C11⋊C8—41no—
50#11791—111nomaximal, Sylow
51C24×C11C22⋊C411yescharacteristic
52C24×C11C22⋊C411yescharacteristic
53C2×Q8×C11—24no—
54C2×Q8×C11—42no—
55C2×Q8×C11—44no—
56C2×Q8×C11—42no—
57C2×Q8×C11—48no—
58C2×Q8×C11—44no—
59C2×Q8×C11—44no—
60C2×Q8×C11—41no—
61C2×Q8×C11—41no—
62C2×D4×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—41no—
65C22×C4×C11—22no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—22no—
71C22×C4×C11—44no—
72C22×C4×C11—42no—
73C22×C4×C11—42no—
74C22×C4×C11—42no—
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—42no—
82C11×C4⋊C4—44no—
83C11×C22⋊C4—41no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—44no—
86C11×C22⋊C4—42no—
87C42×C11—21no—
88C42×C11—21no—
89#4318—24no—
90#4318—42no—
91#4318—82no—
92C2×C11⋊C8—42no—
93C2×C11⋊C8—42no—
94#2409D1111yescharacteristic
95C4×#100—111no—
96#1465—111no—
97#1354—114no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—41no—
104C23×C11—41no—
105C23×C11—41no—
106C23×C11—41no—
107C23×C11#10412yes—
108C23×C11C2×C22⋊C411yescharacteristic
109Q8×C11—44no—
110Q8×C11—44no—
111Q8×C11—44no—
112Q8×C11—44no—
113D4×C11—44no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—22no—
117C2×C4×C11—24no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—48no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—81no—
134C2×C4×C11#9911yescharacteristic
135C2×C4×C11#9911yescharacteristic
136C2×C4×C11#13712yes—
137C11⋊C8—44no—
138C11⋊C8—82no—
139C23×Q8Dic1111yescharacteristic
140C2×C22⋊Q8—21no—
141C2×C4×D4C2×D1111yescharacteristic
142C2×#100—221no—
143#407—221no—
144C4×M16—221no—
145#395C2×D1112yes—
146#393Dic1112yes—
147#391—21no—
148#386—21no—
149#385—21no—
150#380Dic1111yescharacteristic
151#343—112no—
152#324—112no—
153#323—221no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—22no—
157C22×C11—42no—
158C22×C11—42no—
159C22×C11—42no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—81no—
166C22×C11C2×#9911yescharacteristic
167C22×C11#41911yescharacteristic
168C22×C11C2×#10411yescharacteristic
169C4×C11—21no—
170C4×C11—22no—
171C4×C11—44no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11—82no—
176C4×C11AΣL(1,𝔽16)12yes—
177C22×Q8—21no—
178C22×Q8—41no—
179C22×Q8—41no—
180C22×Q8—44no—
181C22×Q8C2×Dic1112yes—
182C22×D4C22⋊D1111yescharacteristic
183C23×C4—21no—
184C23×C4C2×Dic1111yescharacteristic
185C23×C4C22⋊D1111yescharacteristic
186C2×M16—222no—
187C2×M16—441no—
188C22⋊Q8—44no—
189C4×D4—41no—
190C4×D4—41no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4C22×D1111yescharacteristic
194C2×C22⋊C4—22no—
195C2×C22⋊C4—21no—
196C2×C22⋊C4C2×Dic1111yescharacteristic
197C2×C22⋊C4C22⋊D1111yescharacteristic
198C2×C42C22⋊D1111yescharacteristic
199#100—224no—
200C22⋊C8—222no—
201C22⋊C8—441no—
202#97—441no—
203C4×C8—441no—
204#95—22no—
205#95—22no—
206#95C2×Dic1112yes—
207C2×C11—21no—
208C2×C11—21no—
209C2×C11—42no—
210C2×C11—81no—
211C2×C11#150811yescharacteristic
212C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
213C2×C11#213511yescharacteristic
214C24C22⋊Dic1111yescharacteristic
215C24C22⋊Dic1111yescharacteristic
216C2×Q8—24no—
217C2×Q8—44no—
218C2×Q8—42no—
219C2×Q8—42no—
220C2×Q8—44no—
221C2×Q8—48no—
222C2×Q8—44no—
223C2×Q8—41no—
224C2×Q8—41no—
225C2×D4—22no—
226C2×D4—22no—
227C2×D4—41no—
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—44no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4C22⋊Dic1111yescharacteristic
239C22×C4C22⋊Dic1111yescharacteristic
240C22×C4C22×Dic1111yescharacteristic
241C22×C4C2×C22⋊D1111yescharacteristic
242C22×C4C2×C22⋊D1111yescharacteristic
243M16—224no—
244M16—442no—
245M16—882no—
246C2×C8—442no—
247C2×C8—442no—
248C4⋊C4—41no—
249C4⋊C4—42no—
250C4⋊C4—44no—
251C22⋊C4—41no—
252C22⋊C4—41no—
253C22⋊C4—44no—
254C22⋊C4—42no—
255C42—21no—
256C42—21no—
257C11#1179111yescharacteristic, complemented, Sylow
258C23—21no—
259C23—21no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23#6690112yes—
268C23C2×C22⋊Dic1111yescharacteristic
269Q8—44no—
270Q8—44no—
271Q8—44no—
272Q8—44no—
273D4—44no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—22no—
277C2×C4—24no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—48no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—81no—
294C2×C4#6689811yescharacteristic
295C2×C4#6689811yescharacteristic
296C2×C4#6699512yes—
297C8—444no—
298C8—882no—
299C22—21no—
300C22—21no—
301C22—22no—
302C22—42no—
303C22—42no—
304C22—42no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—81no—
311C22C2×#6689811yescharacteristic
312C22#1062283811yescharacteristic
313C22C2×#6690111yescharacteristic
314C4—22no—
315C4—21no—
316C4—41no—
317C4—44no—
318C4—41no—
319C4—41no—
320C4—82no—
321C4#1062217412yes—
322C2—21no—
323C2—21no—
324C2—42no—
325C2—81no—
326C2#1306713611yescharacteristic
327C2C2×#1062217411yescharacteristic
328C2#1307031111yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2409C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C4⋊C4C23
hypercenter#2409D11
hypocenterC11#11791
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2409

Complements

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

NH ≅ G/Ntype
3. #13066646C2semidirect
257. C11#11791semidirect

Maximal subgroups

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

subgroupindex
C4×#668972
#130669542
#130666462
C11×#24092
#1179111