Finite Group Databasebeta

← #14664643

Subgroups — #14664643

Order 2816.

390 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 69 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#13074194C211yesmaximal, characteristic
2#13068692C211yesmaximal, characteristic
3#13066927C211yesmaximal, characteristic
4#13066638C211yesmaximal, characteristic
5#13066636C211yesmaximal, characteristic
6#13066616C211yesmaximal, characteristic
7C11×#1344C211yesmaximal, characteristic
8C2×#66940C411yescharacteristic, complemented
9C2×#66930C2211yescharacteristic
10C11×#397C2211yescharacteristic
11#10622593C411yescharacteristic, complemented
12#10622564—21no—
13#10622560C2211yescharacteristic
14#10622559—21no—
15#10622556—21no—
16#10622331—21no—
17#10622269C411yescharacteristic, complemented
18#10622267—21no—
19#10622265—21no—
20#10622264C411yescharacteristic, complemented
21C11×#342C2211yescharacteristic
22C11×#323C2211yescharacteristic
23#10622165—21no—
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622107—21no—
27C23×Dic11D411yescharacteristic
28C22×Dic22C2×C411yescharacteristic
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C22⋊C4—21no—
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4C2311yescharacteristic
33C2×C22⋊Dic11—21no—
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11D411yescharacteristic
36C2×C4⋊Dic11—21no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4C2×C411yescharacteristic
40C2×Dic11⋊C4D411yescharacteristic
41C2×C4×Dic11—21no—
42C2×C4×Dic11C2×C411yescharacteristic
43C2×C4×Dic11D411yescharacteristic
44#66940—41no—
45#66940—41no—
46#66930—41no—
47#66930—41no—
48C11×C22⋊C8—21no—
49C11×#95—21no—
50C11×#95C2×C411yescharacteristic
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—41no—
57C11⋊#95—41no—
58C11⋊#95C2×C411yescharacteristic
59C22⋊(C11⋊C8)—21no—
60Dic11⋊C8—41no—
61C8×Dic11—41no—
62#11842—111nomaximal, Sylow
63C24×C11C2×D411yescharacteristic
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—41no—
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—41no—
76C22×Dic11—41no—
77C22×Dic11C22⋊C411yescharacteristic
78C22×Dic11C22⋊C411yescharacteristic
79C22×Dic11C22⋊C411yescharacteristic
80C22×Dic11C22⋊C411yescharacteristic
81C2×Dic22—41no—
82C2×Dic22—42no—
83C2×C8×C11—41no—
84C11×C4⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—41no—
90C22⋊Dic11—41no—
91C22⋊Dic11—41no—
92C22⋊Dic11—42no—
93C22⋊Dic11—41no—
94C4⋊Dic11—42no—
95Dic11⋊C4—41no—
96Dic11⋊C4—41no—
97Dic11⋊C4—42no—
98Dic11⋊C4—41no—
99Dic11⋊C4—41no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—42no—
105C2×C11⋊C8—41no—
106#2599—111no—
107#1820—111no—
108#1458—111no—
109#1351—111no—
110#1351—111no—
111#1344—111no—
112#1344D1111yescharacteristic
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11C2×C22⋊C411yescharacteristic
118C23×C11#13511yescharacteristic
119C23×C11#13511yescharacteristic
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—81no—
131C2×C4×C11—81no—
132C2×C4×C11—81no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—22no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—81no—
153C2×Dic11—81no—
154C2×Dic11—81no—
155C2×Dic11#9911yescharacteristic
156C2×Dic11#9911yescharacteristic
157Dic22—42no—
158Dic22—42no—
159C8×C11—81no—
160C11⋊C8—81no—
161C2×C4×Q8—111no—
162C2×#117—111no—
163#431—221no—
164#398—111no—
165#397C2×D1111yescharacteristic
166#395—111no—
167#393—111no—
168#388—221no—
169#387—221no—
170#387—221no—
171#385—221no—
172#383—111no—
173#381—221no—
174#342—111no—
175#342—221no—
176#342C2×D1111yescharacteristic
177#324—221no—
178#323—111no—
179#323C2×D1111yescharacteristic
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11—41no—
187C22×C11—41no—
188C22×C11—81no—
189C22×C11C2×#9911yescharacteristic
190C22×C11#41611yescharacteristic
191C22×C11#42111yescharacteristic
192C4×C11—41no—
193C4×C11—41no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11—161no—
197Dic11—21no—
198Dic11—21no—
199Dic11—42no—
200Dic11—41no—
201Dic11—41no—
202Dic11—41no—
203Dic11—81no—
204Dic11—161no—
205C22×Q8—111no—
206C23×C4—111no—
207C4×Q8—441no—
208C4×Q8—441no—
209#117—441no—
210#117—441no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4C4×D1111yescharacteristic
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—111no—
220C2×C22⋊C4—221no—
221C2×C22⋊C4—221no—
222C2×C22⋊C4C22×D1111yescharacteristic
223C2×C42—111no—
224C2×C42—111no—
225C2×C42—221no—
226C4⋊C8—441no—
227C22⋊C8—21no—
228C22⋊C8—221no—
229C4×C8—441no—
230#95—21no—
231#95—111no—
232#95—221no—
233#95—221no—
234#95—221no—
235#95—221no—
236#95—221no—
237#95—441no—
238#95—441no—
239#95C4×D1111yescharacteristic
240C2×C11—21no—
241C2×C11—21no—
242C2×C11—41no—
243C2×C11—41no—
244C2×C11#151611yescharacteristic
245C2×C11#212011yescharacteristic
246C2×C11#212911yescharacteristic
247C24D4×D1111yescharacteristic
248C2×Q8—441no—
249C2×Q8—442no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—111no—
254C22×C4—111no—
255C22×C4—111no—
256C22×C4—111no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4—221no—
263C22×C4—441no—
264C22×C4—441no—
265C22×C4C2×C4×D1111yescharacteristic
266C22×C4D4×D1111yescharacteristic
267C2×C8—41no—
268C2×C8—441no—
269C4⋊C4—41no—
270C4⋊C4—441no—
271C4⋊C4—441no—
272C4⋊C4—441no—
273C4⋊C4—441no—
274C4⋊C4—442no—
275C4⋊C4—442no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—441no—
282C22⋊C4—442no—
283C22⋊C4—441no—
284C22⋊C4—441no—
285C42—221no—
286C42—221no—
287C42—221no—
288C42—221no—
289C42—442no—
290C11#1184211yescharacteristic, complemented, Sylow
291C23—21no—
292C23—21no—
293C23—41no—
294C23—41no—
295C23C22⋊C4×D1111yescharacteristic
296C23#6696511yescharacteristic
297C23#6696911yescharacteristic
298Q8—442no—
299Q8—442no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—111no—
314C2×C4—111no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—222no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—881no—
335C2×C4—881no—
336C2×C4—881no—
337C8—81no—
338C8—881no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—81no—
348C22D11×#9911yescharacteristic
349C22#1062238511yescharacteristic
350C22#1062243411yescharacteristic
351C4—41no—
352C4—41no—
353C4—81no—
354C4—81no—
355C4—161no—
356C4—221no—
357C4—221no—
358C4—441no—
359C4—442no—
360C4—441no—
361C4—441no—
362C4—881no—
363C4—1761no—
364C2—21no—
365C2—21no—
366C2—41no—
367C2—41no—
368C2#1306716911yescharacteristic
369C2#1307025611yescharacteristic
370C2#1307028911yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1344C2
socleC22×C11C2×#99
prime radicalC24×C11C2×D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1344D11
hypocenterC11#11842
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1344

Complements

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

NH ≅ G/Ntype
8. C2×#66940C4semidirect
11. #10622593C4semidirect
17. #10622269C4semidirect
20. #10622264C4semidirect
290. C11#11842semidirect

Maximal subgroups

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

subgroupindex
#130741942
#130686922
#130669272
#130666382
#130666362
#130666162
C11×#13442
#1184211