Finite Group Databasebeta

← #14651542

Subgroups — #14651542

Order 2816.

578 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 135 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#13072933C211yesmaximal, characteristic
2#13068707C212yesmaximal, complemented
3#13068604C211yesmaximal, characteristic
4#13066484C212yesmaximal, complemented
5C11×#2972C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C22×C4⋊Dic11C2211yescharacteristic
8C8×D4×C11—24no—
9C11×#431—21no—
10C2×C11×C22⋊C8—21no—
11C2×C11×C22⋊C8C2212yes—
12#10622833—21no—
13C2×#66898—21no—
14#10622825—21no—
15#10622825C2212yes—
16#10622825C2211yescharacteristic
17#10622599C412yescomplemented
18#10622562C412yescomplemented
19#10622559—21no—
20#10622541—21no—
21#10622189—24no—
22#10622164—21no—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11C2311yescharacteristic
26C23×Dic11—21no—
27C22×C8×C11—22no—
28C22×C8×C11D414yes—
29C4×D4×C11—22no—
30C4×D4×C11—22no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C22⋊C4C2×C411yescharacteristic
33C2×C11×C22⋊C4D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—22no—
37C2×C22⋊Dic11—22no—
38C2×C4⋊Dic11—22no—
39C2×C4⋊Dic11—22no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—22no—
43C2×C4⋊Dic11C2×C412yes—
44C2×Dic11⋊C4—22no—
45C11×C4⋊C8—22no—
46C11×C22⋊C8—22no—
47C11×C22⋊C8—22no—
48C11×C22⋊C8—22no—
49C4×C8×C11—22no—
50#66898—42no—
51C11⋊#95—22no—
52C11⋊#95—22no—
53C11⋊#95—22no—
54C11⋊#95C2×C412yes—
55#9469—111nomaximal, Sylow
56C24×C11C22⋊C411yescharacteristic
57C24×C11C2×D411yescharacteristic
58C2×D4×C11—22no—
59C2×D4×C11—22no—
60C2×D4×C11SD1612yes—
61C2×D4×C11Q1612yes—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—42no—
65C22×C4×C11—42no—
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D412yes—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4112yes—
73C22×Dic11—22no—
74C22×Dic11—22no—
75C22×Dic11—42no—
76C22×Dic11—42no—
77C22×Dic11—82no—
78C2×C8×C11—24no—
79C2×C8×C11—44no—
80C2×C8×C11—82no—
81C11×C4⋊C4—22no—
82C11×C22⋊C4—22no—
83C11×C22⋊C4—22no—
84C42×C11—21no—
85C42×C11—21no—
86C22⋊Dic11—42no—
87C22⋊Dic11—42no—
88C22⋊Dic11—42no—
89C22⋊Dic11—82no—
90C4⋊Dic11—24no—
91C4⋊Dic11—42no—
92C4⋊Dic11—44no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95Dic11⋊C4—82no—
96#2972D1111yescharacteristic
97#2487—111no—
98#1824—112no—
99#1799—111no—
100#1289—112no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—41no—
104C23×C11—41no—
105C23×C11—41no—
106C23×C11—41no—
107C23×C11#10312yes—
108C23×C11C2×C22⋊C411yescharacteristic
109C23×C11#12112yes—
110C23×C11C2×SD1611yescharacteristic
111C23×C11C2×Q1611yescharacteristic
112C23×C11#13512yes—
113D4×C11—24no—
114D4×C11—24no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—24no—
118C2×C4×C11—22no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—41no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—81no—
127C2×C4×C11#10312yes—
128C2×C4×C11C4×D412yes—
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12311yescharacteristic
131C2×Dic11—42no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11—42no—
135C2×Dic11—42no—
136C2×Dic11—42no—
137C2×Dic11—84no—
138C2×Dic11—82no—
139C2×Dic11—82no—
140C2×Dic11—82no—
141C8×C11—44no—
142C2×C4×D4C2×D1111yescharacteristic
143C22×C4⋊C4—111no—
144C8×D4—24no—
145#431—21no—
146C2×#99—221no—
147C2×C22⋊C8—21no—
148C2×C22⋊C8C2×D1112yes—
149#400—112no—
150#399—112no—
151#389—221no—
152#386—221no—
153#385—221no—
154#380—111no—
155#380—112no—
156#380—221no—
157#342—221no—
158#340—224no—
159C22×C11—21no—
160C22×C11—22no—
161C22×C11—21no—
162C22×C11—22no—
163C22×C11—22no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—42no—
167C22×C11—42no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—81no—
171C22×C11#38611yescharacteristic
172C22×C11C2×#10311yescharacteristic
173C22×C11#41611yescharacteristic
174C22×C11#46512yes—
175C22×C11#46712yes—
176C4×C11—21no—
177C4×C11—22no—
178C4×C11—22no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11#45812yes—
182Dic11—82no—
183Dic11—82no—
184Dic11—162no—
185C22×D4D4411yescharacteristic
186C23×C4—221no—
187C23×C4C22⋊D1111yescharacteristic
188C23×C4C22×D1111yescharacteristic
189C22×C8—22no—
190C22×C8C22⋊D1114yes—
191C4×D4—22no—
192C4×D4—22no—
193C2×C4⋊C4—112no—
194C2×C4⋊C4—222no—
195C2×C4⋊C4—222no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—222no—
199C2×C4⋊C4—222no—
200C2×C4⋊C4C4×D1111yescharacteristic
201C2×C22⋊C4—221no—
202C2×C22⋊C4—222no—
203C2×C22⋊C4—222no—
204C2×C22⋊C4C4×D1111yescharacteristic
205C2×C22⋊C4D4411yescharacteristic
206C2×C42C22⋊D1111yescharacteristic
207C4⋊C8—22no—
208#99—442no—
209C22⋊C8—22no—
210C22⋊C8—22no—
211C22⋊C8—22no—
212C4×C8—22no—
213#95—112no—
214#95—222no—
215#95—222no—
216#95—222no—
217C2×C11—21no—
218C2×C11—22no—
219C2×C11—21no—
220C2×C11—22no—
221C2×C11—42no—
222C2×C11#189011yescharacteristic
223C2×C11#189211yescharacteristic
224C2×C11#191011yescharacteristic
225C24(C2×D11)⋊C411yescharacteristic
226C24C2×D4411yescharacteristic
227C2×D4—22no—
228C2×D4—22no—
229C2×D4#431412yes—
230C2×D4Dic4412yes—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—222no—
236C22×C4—222no—
237C22×C4—442no—
238C22×C4—442no—
239C22×C4—882no—
240C22×C4(C2×D11)⋊C411yescharacteristic
241C22×C4(C2×D11)⋊C411yescharacteristic
242C22×C4(C2×D11)⋊C411yescharacteristic
243C22×C4C2×C4×D1111yescharacteristic
244C22×C4#433912yes—
245C22×C4C2×C22⋊D1112yes—
246C22×C4C2×C22⋊D1111yescharacteristic
247C2×C8—24no—
248C2×C8—44no—
249C2×C8—82no—
250C4⋊C4—22no—
251C4⋊C4—224no—
252C4⋊C4—442no—
253C4⋊C4—444no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C4⋊C4—882no—
257C22⋊C4—22no—
258C22⋊C4—22no—
259C22⋊C4—442no—
260C22⋊C4—442no—
261C22⋊C4—442no—
262C22⋊C4—882no—
263C42—21no—
264C42—21no—
265C11#946911yescharacteristic, complemented, Sylow
266C23—21no—
267C23—21no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23—41no—
272C23#6688012yes—
273C23C2×#431411yescharacteristic
274C23#6695712yes—
275C23C2×Dic4411yescharacteristic
276C23C2×(C2×D11)⋊C411yescharacteristic
277C23#6698312yes—
278D4—24no—
279D4—24no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—24no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—81no—
292C2×C4—442no—
293C2×C4—442no—
294C2×C4—442no—
295C2×C4—442no—
296C2×C4—442no—
297C2×C4—442no—
298C2×C4—884no—
299C2×C4—882no—
300C2×C4—882no—
301C2×C4—882no—
302C2×C4#6688012yes—
303C2×C4C4×C22⋊D1112yes—
304C2×C4#6698211yescharacteristic
305C2×C4#6700611yescharacteristic
306C8—44no—
307C22—21no—
308C22—22no—
309C22—21no—
310C22—22no—
311C22—22no—
312C22—41no—
313C22—42no—
314C22—41no—
315C22—42no—
316C22—41no—
317C22—41no—
318C22—81no—
319C22C2×#6688011yescharacteristic
320C22#1062272611yescharacteristic
321C22#1062272712yes—
322C22#1062272912yes—
323C22#1062282611yescharacteristic
324C4—21no—
325C4—22no—
326C4—22no—
327C4—41no—
328C4—41no—
329C4—882no—
330C4—882no—
331C4—1762no—
332C4#1062285612yes—
333C2—21no—
334C2—22no—
335C2—21no—
336C2—22no—
337C2—42no—
338C2#1306902911yescharacteristic
339C2#1306903911yescharacteristic
340C2#1306914311yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2972C2
socleC22×C11#386
prime radicalC22×D4×C11D4
cosocleC23×C4×C11C23
hypercenter#2972D11
hypocenterC11#9469
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2972

Complements

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

NH ≅ G/Ntype
2. #13068707C2semidirect
4. #13066484C2semidirect
17. #10622599C4semidirect
18. #10622562C4semidirect
265. C11#9469semidirect

Maximal subgroups

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

subgroupindex
#130729332
#130687072
#130686042
#130664842
C11×#29722
#946911