Finite Group Databasebeta

← #14664921

Subgroups — #14664921

Order 2816.

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

normal subgroups only

This group has 568 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#13071981C211yesmaximal, characteristic
2#13066934C211yesmaximal, characteristic
3#13066645C214yesmaximal, complemented
4C11×#1800C211yesmaximal, characteristic
5C23×Dic22C411yescharacteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66977—21no—
8C11×#423—21no—
9C2×C11×#100—21no—
10#10622833—21no—
11#10622825C411yescharacteristic
12C2×C22⋊(C11⋊C8)—21no—
13#10622592C2212yes—
14#10622560C412yes—
15#10622559—21no—
16#10622542—21no—
17C11×#343C2212yes—
18#10622166C2212yes—
19#10622163—21no—
20C22×D4×C11D411yescharacteristic
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×Dic11—21no—
24C22×Dic22—21no—
25C22×Dic22—44no—
26C22×Dic22—41no—
27C22×Dic22—41no—
28C22×Dic22C2×C412yes—
29C2×C11×M16—22no—
30C4×D4×C11—41no—
31C4×D4×C11—41no—
32C2×C11×C4⋊C4C2311yescharacteristic
33C2×C11×C22⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C22⋊Dic11—22no—
37C2×C22⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39#66977—44no—
40C2×Dic11⋊C4—22no—
41C22×C11⋊C8—41no—
42C11×C4⋊C8—41no—
43C11×C4⋊C8—41no—
44C11×#100—42no—
45C11⋊#95—22no—
46C11⋊#95—22no—
47C11⋊#95C2×C412yes—
48C22⋊(C11⋊C8)—22no—
49C22⋊(C11⋊C8)—41no—
50#11904—111nomaximal, Sylow
51C24×C11C22⋊C411yescharacteristic
52C24×C11C22⋊C411yescharacteristic
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×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—22no—
69C22×Dic11—22no—
70C22×Dic11—42no—
71C22×Dic11—44no—
72C2×Dic22—24no—
73C2×Dic22—42no—
74C2×Dic22—42no—
75C2×Dic22—48no—
76C2×Dic22—44no—
77C2×Dic22—44no—
78C2×Dic22—44no—
79C2×Dic22—41no—
80C2×Dic22—41no—
81C11×M16—42no—
82C11×M16—42no—
83C2×C8×C11—42no—
84C11×C4⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—41no—
87C42×C11—21no—
88C42×C11—21no—
89C22⋊Dic11—42no—
90C22⋊Dic11—44no—
91C4⋊Dic11—42no—
92Dic11⋊C4—44no—
93C2×C11⋊C8—42no—
94C2×C11⋊C8—82no—
95#2409—111no—
96#1800D1111yescharacteristic
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
110D4×C11—42no—
111D4×C11—42no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—22no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—81no—
125C2×C4×C11#9911yescharacteristic
126C2×C4×C11#9911yescharacteristic
127C2×C4×C11C2×SD1611yescharacteristic
128C2×C4×C11C2×Q1611yescharacteristic
129C2×Dic11—24no—
130C2×Dic11—42no—
131C2×Dic11—48no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11—42no—
135C2×Dic11—42no—
136Dic22—44no—
137Dic22—44no—
138Dic22—44no—
139Dic22—44no—
140C8×C11—82no—
141C11⋊C8—82no—
142C23×Q8—111no—
143C2×C22⋊Q8—221no—
144C2×C4×D4C2×D1111yescharacteristic
145#423—21no—
146C2×#100—21no—
147C2×C22⋊C8—221no—
148#395—112no—
149#393—112no—
150#391—221no—
151#386—221no—
152#385—221no—
153#380—111no—
154#343C2×D1112yes—
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—41no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11AΣL(1,𝔽16)12yes—
179Dic11—44no—
180Dic11—82no—
181C22×Q8—112no—
182C22×Q8—221no—
183C22×Q8—441no—
184C22×Q8—441no—
185C22×Q8—444no—
186C22×D4C22⋊D1111yescharacteristic
187C23×C4—221no—
188C23×C4C4×D1111yescharacteristic
189C23×C4D4411yescharacteristic
190C2×M16—22no—
191C22×C8—441no—
192C22⋊Q8—444no—
193C4×D4—41no—
194C4×D4—41no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4—222no—
197C2×C4⋊C4C22×D1111yescharacteristic
198C2×C22⋊C4—222no—
199C2×C22⋊C4—221no—
200C2×C22⋊C4C4×D1111yescharacteristic
201C2×C22⋊C4D4411yescharacteristic
202C2×C42C22⋊D1111yescharacteristic
203C4⋊C8—41no—
204C4⋊C8—41no—
205#100—42no—
206C22⋊C8—222no—
207C22⋊C8—441no—
208#95—112no—
209#95—222no—
210#95—222no—
211C2×C11—21no—
212C2×C11—21no—
213C2×C11—42no—
214C2×C11—42no—
215C2×C11#152011yescharacteristic
216C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
217C2×C11#213511yescharacteristic
218C24(C2×D11)⋊C411yescharacteristic
219C24(C2×D11)⋊C411yescharacteristic
220C2×Q8—224no—
221C2×Q8—442no—
222C2×Q8—442no—
223C2×Q8—444no—
224C2×Q8—444no—
225C2×Q8—448no—
226C2×Q8—444no—
227C2×Q8—441no—
228C2×Q8—441no—
229C2×D4—41no—
230C2×D4—41no—
231C2×D4#432412yes—
232C2×D4#432612yes—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—222no—
240C22×C4—222no—
241C22×C4—444no—
242C22×C4—442no—
243C22×C4(C2×D11)⋊C411yescharacteristic
244C22×C4(C2×D11)⋊C411yescharacteristic
245C22×C4C2×C4×D1111yescharacteristic
246C22×C4C2×D4411yescharacteristic
247C22×C4C2×C22⋊D1111yescharacteristic
248M16—42no—
249M16—42no—
250C2×C8—42no—
251C2×C8—442no—
252C2×C8—882no—
253C4⋊C4—41no—
254C4⋊C4—442no—
255C4⋊C4—444no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C22⋊C4—444no—
259C22⋊C4—442no—
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#6687412yes—
272C23#6687412yes—
273C23C2×(C2×D11)⋊C411yescharacteristic
274Q8—444no—
275Q8—444no—
276Q8—444no—
277Q8—444no—
278D4—42no—
279D4—42no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—81no—
293C2×C4—224no—
294C2×C4—442no—
295C2×C4—448no—
296C2×C4—442no—
297C2×C4—442no—
298C2×C4—442no—
299C2×C4—442no—
300C2×C4#6687011yescharacteristic
301C2×C4#6687011yescharacteristic
302C2×C4C2×#432411yescharacteristic
303C2×C4C2×#432611yescharacteristic
304C8—82no—
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×#6687011yescharacteristic
319C22C2×#6687411yescharacteristic
320C22#1062261811yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—444no—
328C4—882no—
329C4#1062211312yes—
330C2—21no—
331C2—21no—
332C2—42no—
333C2—42no—
334C2#1306718711yescharacteristic
335C2C2×#1062211311yescharacteristic
336C2#1307031011yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1800C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C4⋊C4C23
hypercenter#1800D11
hypocenterC11#11904
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1800

Complements

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

NH ≅ G/Ntype
3. #13066645C2semidirect
262. C11#11904semidirect

Maximal subgroups

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

subgroupindex
#130719812
#130669342
#130666452
C11×#18002
#1190411