Finite Group Databasebeta

← #14664418

Subgroups — #14664418

Order 2816.

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

normal subgroups only

This group has 444 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#13073792C211yesmaximal, characteristic
2C4×#66897C211yesmaximal, characteristic
3#13066647C212yesmaximal, complemented
4#13066644C212yesmaximal, complemented
5C11×#1465C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66977C411yescharacteristic
8C11×#407—21no—
9#10622833—21no—
10C2×#66897—21no—
11#10622823—21no—
12C2×C11⋊#95C411yescharacteristic
13#10622599C2211yescharacteristic
14#10622592C2211yescharacteristic
15#10622562C411yescharacteristic
16#10622560C411yescharacteristic
17#10622555—21no—
18#10622546—21no—
19C4×#4318—21no—
20C11×#324C2212yes—
21C11×#323—21no—
22#10622168C2212yes—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×Dic11—21no—
27C22×Dic22C2×C411yescharacteristic
28C2×C11×M16—41no—
29C4×D4×C11—41no—
30C4×D4×C11—41no—
31C2×C11×C4⋊C4C2311yescharacteristic
32C2×C11×C22⋊C4C2×C411yescharacteristic
33C2×C11×C22⋊C4D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39#66977—41no—
40#66977—41no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×#4318—22no—
45C11×C22⋊C8—22no—
46C11×C22⋊C8—41no—
47#66897—24no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95C2×C411yescharacteristic
54C11⋊#95C2×C411yescharacteristic
55#66867—41no—
56C4×C11⋊C8—41no—
57#11793—111nomaximal, Sylow
58C24×C11C22⋊C411yescharacteristic
59C24×C11C22⋊C411yescharacteristic
60C2×D4×C11—22no—
61C2×D4×C11—22no—
62C2×D4×C11—41no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—81no—
68C22×C4×C11—81no—
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—42no—
79C22×Dic11—42no—
80C22×Dic11—81no—
81C2×Dic22—41no—
82C2×Dic22—81no—
83C11×M16—82no—
84C2×C8×C11—42no—
85C11×C4⋊C4—41no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C42×C11—21no—
89C42×C11—21no—
90C22⋊Dic11—42no—
91C22⋊Dic11—42no—
92C22⋊Dic11—81no—
93C4⋊Dic11—41no—
94Dic11⋊C4—42no—
95Dic11⋊C4—41no—
96Dic11⋊C4—41no—
97Dic11⋊C4—81no—
98#4318—24no—
99#4318—42no—
100C2×C11⋊C8—42no—
101#2564—111no—
102C4×#100—111no—
103#1465D1111yescharacteristic
104#1354—112no—
105#1353—112no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11#10412yes—
116C23×C11C2×C22⋊C411yescharacteristic
117D4×C11—44no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—41no—
124C2×C4×C11—42no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—81no—
129C2×C4×C11—81no—
130C2×C4×C11—81no—
131C2×C4×C11#9911yescharacteristic
132C2×C4×C11#9911yescharacteristic
133C2×C4×C11#13712yes—
134C2×Dic11—22no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—84no—
147Dic22—82no—
148C8×C11—82no—
149C11⋊C8—44no—
150C2×C22⋊Q8—111no—
151C2×C4×D4C2×D1111yescharacteristic
152C2×#100—221no—
153#407—21no—
154C4×M16—221no—
155#400—111no—
156#399—111no—
157#395—111no—
158#393—111no—
159#387—221no—
160#386—221no—
161#385—221no—
162#380—221no—
163C2×#95—111no—
164#343—112no—
165#324C2×D1112yes—
166#323—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—22no—
170C22×C11—42no—
171C22×C11—42no—
172C22×C11—42no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—81no—
179C22×C11C2×#9911yescharacteristic
180C22×C11#41911yescharacteristic
181C22×C11C2×#10411yescharacteristic
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—22no—
185C4×C11—41no—
186C4×C11—41no—
187C4×C11—41no—
188Dic11—42no—
189Dic11—81no—
190Dic11—81no—
191Dic11—81no—
192C22×Q8—111no—
193C22×D4D4411yescharacteristic
194C23×C4—221no—
195C23×C4C4×D1111yescharacteristic
196C23×C4C22⋊D1111yescharacteristic
197C2×M16—41no—
198C2×M16—222no—
199C22⋊Q8—441no—
200C22⋊Q8—441no—
201C4×D4—41no—
202C4×D4—41no—
203C2×C4⋊C4—111no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4C22×D1111yescharacteristic
208C2×C22⋊C4—221no—
209C2×C22⋊C4—221no—
210C2×C22⋊C4—221no—
211C2×C22⋊C4C4×D1111yescharacteristic
212C2×C22⋊C4C22⋊D1111yescharacteristic
213C2×C42D4411yescharacteristic
214#100—224no—
215C22⋊C8—22no—
216C22⋊C8—41no—
217#97—441no—
218C4×C8—441no—
219#95—111no—
220#95—111no—
221#95—221no—
222#95—221no—
223#95—221no—
224#95—221no—
225#95—221no—
226C2×C11—21no—
227C2×C11—21no—
228C2×C11—42no—
229C2×C11—81no—
230C2×C11#150811yescharacteristic
231C2×C11#212111yescharacteristic
232C2×C11#213211yescharacteristic
233C24(C2×D11)⋊C411yescharacteristic
234C24(C2×D11)⋊C411yescharacteristic
235C2×Q8—441no—
236C2×Q8—881no—
237C2×D4—22no—
238C2×D4—22no—
239C2×D4—41no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—81no—
245C22×C4—81no—
246C22×C4—221no—
247C22×C4—221no—
248C22×C4—221no—
249C22×C4—221no—
250C22×C4—442no—
251C22×C4—442no—
252C22×C4—881no—
253C22×C4(C2×D11)⋊C411yescharacteristic
254C22×C4(C2×D11)⋊C411yescharacteristic
255C22×C4C2×C4×D1111yescharacteristic
256C22×C4C2×D4411yescharacteristic
257C22×C4C2×C22⋊D1111yescharacteristic
258M16—82no—
259M16—224no—
260M16—442no—
261C2×C8—42no—
262C2×C8—442no—
263C4⋊C4—41no—
264C4⋊C4—441no—
265C4⋊C4—442no—
266C4⋊C4—441no—
267C4⋊C4—441no—
268C4⋊C4—881no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—442no—
272C22⋊C4—442no—
273C22⋊C4—881no—
274C42—21no—
275C42—21no—
276C11#1179311yescharacteristic, complemented, Sylow
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23#6688912yes—
287C23C2×(C2×D11)⋊C411yescharacteristic
288Q8—882no—
289D4—44no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—222no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—884no—
316C2×C4#6687011yescharacteristic
317C2×C4#6687011yescharacteristic
318C2×C4#6696212yes—
319C8—82no—
320C8—444no—
321C22—21no—
322C22—21no—
323C22—22no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—81no—
333C22C2×#6687011yescharacteristic
334C22#1062273311yescharacteristic
335C22C2×#6688911yescharacteristic
336C4—22no—
337C4—21no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—442no—
343C4—881no—
344C4—881no—
345C4—881no—
346C2—21no—
347C2—21no—
348C2—42no—
349C2—81no—
350C2#1306713711yescharacteristic
351C2#1307026011yescharacteristic
352C2#1307029911yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1465C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C4⋊C4C23
hypercenter#1465D11
hypocenterC11#11793
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
3. #13066647C2semidirect
4. #13066644C2semidirect
276. C11#11793semidirect

Maximal subgroups

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

subgroupindex
#130737922
C4×#668972
#130666472
#130666442
C11×#14652
#1179311