Finite Group Databasebeta

← #14664086

Subgroups — #14664086

Order 2816.

432 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 83 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#13074444C211yesmaximal, characteristic
2#13068353C211yesmaximal, characteristic
3#13066929C211yesmaximal, characteristic
4#13066644C211yesmaximal, characteristic, complemented
5#13066643C211yesmaximal, characteristic, complemented
6#13066642C211yesmaximal, characteristic, complemented
7C11×#1353C211yesmaximal, characteristic, complemented
8C2×M16×D11—21no—
9C2×#66945C2211yescharacteristic
10C2×#66941C411yescharacteristic
11C11×#400C2211yescharacteristic
12#10622605C411yescharacteristic
13#10622599C2211yescharacteristic
14#10622331—21no—
15#10622290C411yescharacteristic
16#10622286—21no—
17#10622280—21no—
18#10622269—21no—
19#10622263C411yescharacteristic
20#10622260—21no—
21C11×#343C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622192—21no—
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622106—21no—
27C22×C4×D11D411yescharacteristic
28C22×Dic22—21no—
29C2×C11×M16—21no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C4⋊C4C2311yescharacteristic
32C2×(C2×D11)⋊C4—21no—
33C2×(C2×D11)⋊C4—21no—
34C2×(C2×D11)⋊C4C2×C411yescharacteristic
35C2×(C2×D11)⋊C4D411yescharacteristic
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×C4×Dic11C2×C411yescharacteristic
43C2×C4×Dic11D411yescharacteristic
44C2×#4318—21no—
45M16×D11—24no—
46M16×D11—42no—
47C2×#4313—41no—
48C2×C8×D11—41no—
49#66945—41no—
50#66945—41no—
51#66941—41no—
52#66941—41no—
53C11×C22⋊C8—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95C2×C411yescharacteristic
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95C2×C411yescharacteristic
61C22⋊(C11⋊C8)—21no—
62Dic11⋊C8—41no—
63C8×Dic11—41no—
64#11723—111nomaximal, Sylow
65C23×D11C22⋊C411yescharacteristic
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11C22⋊C411yescharacteristic
74C22×Dic11C22⋊C411yescharacteristic
75C22×Dic11C22⋊C411yescharacteristic
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11—22no—
79C2×C4×D11SD1612yes—
80C2×C4×D11Q1612yes—
81C2×Dic22—42no—
82C2×Dic22—81no—
83C2×Dic22—81no—
84C11×M16—22no—
85C11×M16—41no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90(C2×D11)⋊C4—41no—
91(C2×D11)⋊C4—41no—
92(C2×D11)⋊C4—81no—
93(C2×D11)⋊C4—81no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96C4⋊Dic11—81no—
97Dic11⋊C4—41no—
98Dic11⋊C4—41no—
99Dic11⋊C4—42no—
100Dic11⋊C4—81no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105#4318—22no—
106#4318—41no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109#4313—44no—
110C8×D11—44no—
111#2628—111no—
112#1742—111no—
113#1458—111no—
114#1353—111no—
115#1353—111no—
116#1353—111no—
117#1353D1111yescharacteristic, complemented
118C23×C11C2×C22⋊C411yescharacteristic
119C22×D11—21no—
120C22×D11—21no—
121C22×D11—41no—
122C22×D11—41no—
123C22×D11#10312yes—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11C2×SD1611yescharacteristic
137C2×C4×C11C2×Q1611yescharacteristic
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11#9911yescharacteristic
149C2×Dic11#9911yescharacteristic
150C2×Dic11#10312yes—
151C2×Dic11#10412yes—
152C4×D11—22no—
153C4×D11—22no—
154C4×D11—22no—
155C4×D11—22no—
156Dic22—84no—
157C8×C11—42no—
158C8×C11—81no—
159C11⋊C8—42no—
160C11⋊C8—81no—
161C22×M16—221no—
162C2×C4⋊Q8—111no—
163C2×#117—111no—
164#431—221no—
165#400—111no—
166#400C2×D1111yescharacteristic
167#399—111no—
168#399—111no—
169#395—221no—
170#393—221no—
171#389—221no—
172#382—111no—
173#380—221no—
174#343—111no—
175#343—221no—
176#343C2×D1111yescharacteristic
177#324—111no—
178#324C2×D1111yescharacteristic
179#323—221no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11C2×#9911yescharacteristic
183C22×C11C2×#10311yescharacteristic
184C22×C11C2×#10411yescharacteristic
185C2×D11—22no—
186C2×D11—41no—
187C2×D11—41no—
188C2×D11—42no—
189C2×D11—81no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11—81no—
195C4×C11—81no—
196Dic11—41no—
197Dic11—41no—
198Dic11—81no—
199Dic11—81no—
200Dic11#32812yes—
201Dic11#32812yes—
202C22×Q8—221no—
203C23×C4—111no—
204C2×M16—21no—
205C2×M16—224no—
206C2×M16—221no—
207C2×M16—441no—
208C2×M16—442no—
209C22×C8—441no—
210C4⋊Q8—441no—
211C4⋊Q8—441no—
212#117—441no—
213#117—441no—
214C2×C4⋊C4—111no—
215C2×C4⋊C4—111no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4—221no—
219C2×C4⋊C4—221no—
220C2×C4⋊C4C4×D1111yescharacteristic
221C2×C4⋊C4C22×D1111yescharacteristic
222C2×C22⋊C4—111no—
223C2×C22⋊C4—111no—
224C2×C22⋊C4—221no—
225C2×C22⋊C4—221no—
226C2×C42—111no—
227C2×C42—111no—
228C4⋊C8—441no—
229C22⋊C8—21no—
230C22⋊C8—221no—
231C4×C8—441no—
232#95—21no—
233#95—21no—
234#95—111no—
235#95—221no—
236#95—221no—
237#95—221no—
238#95C4×D1111yescharacteristic
239C2×C11—21no—
240C2×C11—21no—
241C2×C11C2×#32811yescharacteristic
242C2×C11#212311yescharacteristic
243C2×C11#213411yescharacteristic
244D11—42no—
245C24—111no—
246C2×Q8—442no—
247C2×Q8—881no—
248C2×Q8—881no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—111no—
252C22×C4—112no—
253C22×C4—112no—
254C22×C4—111no—
255C22×C4—111no—
256C22×C4—221no—
257C22×C4—221no—
258C22×C4—222no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4C2×C4×D1111yescharacteristic
262C22×C4D4×D1111yescharacteristic
263C22×C4D4×D1111yescharacteristic
264M16—22no—
265M16—41no—
266M16—222no—
267M16—444no—
268M16—441no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—444no—
272C2×C8—441no—
273C2×C8—441no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C4⋊C4—442no—
281C4⋊C4—881no—
282C4⋊C4—881no—
283C22⋊C4—441no—
284C22⋊C4—441no—
285C22⋊C4—881no—
286C22⋊C4—881no—
287C42—221no—
288C42—221no—
289C42—221no—
290C42—221no—
291C11#1172311yescharacteristic, complemented, Sylow
292C23—112no—
293C23—221no—
294C23—221no—
295C23—441no—
296C23—441no—
297C23C22⋊C4×D1111yescharacteristic
298Q8—884no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—111no—
312C2×C4—111no—
313C2×C4—112no—
314C2×C4—112no—
315C2×C4—222no—
316C2×C4—222no—
317C2×C4—222no—
318C2×C4—222no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4SD16×D1111yescharacteristic
330C2×C4Q16×D1111yescharacteristic
331C8—42no—
332C8—81no—
333C8—442no—
334C8—881no—
335C22—21no—
336C22—21no—
337C22—222no—
338C22—442no—
339C22—441no—
340C22—441no—
341C22—881no—
342C22D11×#9911yescharacteristic
343C22D11×#10311yescharacteristic
344C22D11×#10411yescharacteristic
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—81no—
350C4—81no—
351C4—112no—
352C4—112no—
353C4—441no—
354C4—441no—
355C4—881no—
356C4—881no—
357C2—21no—
358C2—21no—
359C2—442no—
360C2D11×#32811yescharacteristic
361C2#1307026811yescharacteristic
362C2#1307030611yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1353C2
socleC22×C11C2×#99
prime radicalC23×D11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1353D11
hypocenterC11#11723
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1353

Complements

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

NH ≅ G/Ntype
4. #13066644C2semidirect
5. #13066643C2semidirect
6. #13066642C2semidirect
7. C11×#1353C2semidirect
117. #1353D11semidirect
291. C11#11723semidirect

Maximal subgroups

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

subgroupindex
#130744442
#130683532
#130669292
#130666442
#130666432
#130666422
C11×#13532
#1172311