Finite Group Databasebeta

← #14664922

Subgroups — #14664922

Order 2816.

568 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 107 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#13068608C211yesmaximal, characteristic
2#13066934C211yesmaximal, 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—
15C2×C22⋊(C11⋊C8)—21no—
16#10622537—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—
41C22×C11⋊C8—41no—
42C11×#95—22no—
43C11×#95—22no—
44C11×#95C2×C412yes—
45#66897—42no—
46C22⋊(C11⋊C8)—22no—
47C22⋊(C11⋊C8)—41no—
48C4⋊(C11⋊C8)—41no—
49C4⋊(C11⋊C8)—41no—
50#11904—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—41no—
63C2×D4×C11—41no—
64C2×D4×C11SD1612yes—
65C2×D4×C11Q1612yes—
66C22×C4×C11—22no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—22no—
72C22×C4×C11—44no—
73C22×C4×C11—42no—
74C22×C4×C11—42no—
75C22×C4×C11—42no—
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C11×C4⋊C4—41no—
82C11×C4⋊C4—42no—
83C11×C4⋊C4—44no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—44no—
87C11×C22⋊C4—42no—
88C42×C11—21no—
89C42×C11—21no—
90#4318—42no—
91#4318—42no—
92C2×C11⋊C8—42no—
93C2×C11⋊C8—42no—
94C2×C11⋊C8—82no—
95#2409D1111yescharacteristic
96#1800—111no—
97#1459—111no—
98#1354—114no—
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#10312yes—
108C23×C11#10312yes—
109C23×C11C2×C22⋊C411yescharacteristic
110Q8×C11—44no—
111Q8×C11—44no—
112Q8×C11—44no—
113Q8×C11—44no—
114D4×C11—42no—
115D4×C11—42no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—22no—
119C2×C4×C11—24no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—48no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—42no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—81no—
136C2×C4×C11#9911yescharacteristic
137C2×C4×C11#9911yescharacteristic
138C2×C4×C11C2×SD1611yescharacteristic
139C2×C4×C11C2×Q1611yescharacteristic
140C11⋊C8—82no—
141C11⋊C8—82no—
142C23×Q8Dic1111yescharacteristic
143C2×C22⋊Q8—21no—
144C2×C4×D4C2×D1111yescharacteristic
145#423—221no—
146C2×#100—221no—
147C2×C22⋊C8—221no—
148#395C2×D1112yes—
149#393Dic1112yes—
150#391—21no—
151#386—21no—
152#385—21no—
153#380Dic1111yescharacteristic
154#343—112no—
155#324—112no—
156#323—221no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—22no—
160C22×C11—22no—
161C22×C11—42no—
162C22×C11—42no—
163C22×C11—42no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11—81no—
169C22×C11C2×#9911yescharacteristic
170C22×C11C2×#10311yescharacteristic
171C22×C11#42111yescharacteristic
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—44no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—82no—
180C4×C11AΣL(1,𝔽16)12yes—
181C22×Q8—21no—
182C22×Q8—41no—
183C22×Q8—41no—
184C22×Q8—44no—
185C22×Q8C2×Dic1112yes—
186C22×D4C22⋊D1111yescharacteristic
187C23×C4—21no—
188C23×C4C2×Dic1111yescharacteristic
189C23×C4C22⋊D1111yescharacteristic
190C2×M16—222no—
191C22×C8—441no—
192C22⋊Q8—44no—
193C4×D4—41no—
194C4×D4—41no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4C22×D1111yescharacteristic
198C2×C22⋊C4—22no—
199C2×C22⋊C4—21no—
200C2×C22⋊C4C2×Dic1111yescharacteristic
201C2×C22⋊C4C22⋊D1111yescharacteristic
202C2×C42C22⋊D1111yescharacteristic
203C4⋊C8—441no—
204C4⋊C8—441no—
205#100—442no—
206C22⋊C8—222no—
207C22⋊C8—441no—
208#95—22no—
209#95—22no—
210#95C2×Dic1112yes—
211C2×C11—21no—
212C2×C11—21no—
213C2×C11—42no—
214C2×C11—42no—
215C2×C11#152011yescharacteristic
216C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
217C2×C11#213511yescharacteristic
218C24C22⋊Dic1111yescharacteristic
219C24C22⋊Dic1111yescharacteristic
220C2×Q8—24no—
221C2×Q8—44no—
222C2×Q8—42no—
223C2×Q8—42no—
224C2×Q8—44no—
225C2×Q8—48no—
226C2×Q8—44no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×D4—41no—
230C2×D4—41no—
231C2×D4#432512yes—
232C2×D4#432612yes—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—44no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4C22⋊Dic1111yescharacteristic
244C22×C4C22⋊Dic1111yescharacteristic
245C22×C4C22×Dic1111yescharacteristic
246C22×C4C2×C22⋊D1111yescharacteristic
247C22×C4C2×C22⋊D1111yescharacteristic
248M16—442no—
249M16—442no—
250C2×C8—442no—
251C2×C8—442no—
252C2×C8—882no—
253C4⋊C4—41no—
254C4⋊C4—42no—
255C4⋊C4—44no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C22⋊C4—44no—
259C22⋊C4—42no—
260C42—21no—
261C42—21no—
262C11#1190411yescharacteristic, complemented, Sylow
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23#6689912yes—
272C23#6689912yes—
273C23C2×C22⋊Dic1111yescharacteristic
274Q8—44no—
275Q8—44no—
276Q8—44no—
277Q8—44no—
278D4—42no—
279D4—42no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—48no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—81no—
300C2×C4#6689811yescharacteristic
301C2×C4#6689811yescharacteristic
302C2×C4C2×#432511yescharacteristic
303C2×C4C2×#432611yescharacteristic
304C8—882no—
305C8—882no—
306C22—21no—
307C22—21no—
308C22—22no—
309C22—22no—
310C22—42no—
311C22—42no—
312C22—42no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—81no—
318C22C2×#6689811yescharacteristic
319C22C2×#6689911yescharacteristic
320C22#1062284911yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—44no—
326C4—41no—
327C4—41no—
328C4—82no—
329C4#1062217412yes—
330C2—21no—
331C2—21no—
332C2—42no—
333C2—42no—
334C2#1306718811yescharacteristic
335C2C2×#1062217411yescharacteristic
336C2#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#11904
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
262. C11#11904semidirect

Maximal subgroups

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

subgroupindex
#130686082
#130669342
#130666462
C11×#24092
#1190411