Finite Group Databasebeta

← #14664698

Subgroups — #14664698

Order 2816.

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

normal subgroups only

This group has 368 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#13074309C211yesmaximal, characteristic
2#13068698C211yesmaximal, characteristic
3#13066929C211yesmaximal, characteristic
4#13066644C211yesmaximal, characteristic, complemented
5#13066642C211yesmaximal, characteristic, complemented
6#13066622C211yesmaximal, characteristic, complemented
7C11×#1346C211yesmaximal, characteristic, complemented
8C2×#66945C2211yescharacteristic
9C2×#66943C411yescharacteristic
10C11×#398C2211yescharacteristic
11#10622739—21no—
12#10622606C411yescharacteristic
13#10622602—21no—
14#10622599C2211yescharacteristic
15#10622598—21no—
16#10622331—21no—
17#10622290C411yescharacteristic
18#10622283—21no—
19#10622267—21no—
20#10622261C411yescharacteristic
21C11×#343C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622192—21no—
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622106—21no—
27C22×C4×D11D411yescharacteristic
28C2×C11×M16—21no—
29C2×C11×C4⋊C4—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⋊Dic11—21no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4⋊Dic11D411yescharacteristic
40C2×Dic11⋊C4—21no—
41C2×C4×Dic11—21no—
42C2×C4×Dic11C2×C411yescharacteristic
43C2×C4×Dic11D411yescharacteristic
44C2×#4318—21no—
45#66945—41no—
46#66945—41no—
47#66943—41no—
48#66943—41no—
49C11×C22⋊C8—21no—
50C11×#95—21no—
51C11×#95C2×C411yescharacteristic
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95C2×C411yescharacteristic
57C22⋊(C11⋊C8)—21no—
58(C2×D11)⋊C8—41no—
59(C2×D11)⋊C8—41no—
60Dic11⋊C8—41no—
61C8×Dic11—41no—
62#11853—111nomaximal, Sylow
63C23×D11C22⋊C411yescharacteristic
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11C22⋊C411yescharacteristic
72C22×Dic11C22⋊C411yescharacteristic
73C22×Dic11C22⋊C411yescharacteristic
74C2×C4×D11—21no—
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11—41no—
79C11×M16—41no—
80C11×M16—41no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87(C2×D11)⋊C4—41no—
88(C2×D11)⋊C4—41no—
89(C2×D11)⋊C4—42no—
90(C2×D11)⋊C4—42no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93C4⋊Dic11—42no—
94C4⋊Dic11—42no—
95Dic11⋊C4—41no—
96Dic11⋊C4—41no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—42no—
102#4318—41no—
103#4318—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106#2611—111no—
107#1822—111no—
108#1458—111no—
109#1353—111no—
110#1353—111no—
111#1346—111no—
112#1346D1111yescharacteristic, complemented
113C23×C11C2×C22⋊C411yescharacteristic
114C22×D11—21no—
115C22×D11—21no—
116C22×D11—21no—
117C22×D11—41no—
118C22×D11—41no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—22no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
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—41no—
131C2×C4×C11#13511yescharacteristic
132C2×C4×C11#13511yescharacteristic
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
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#9911yescharacteristic
146C2×Dic11#9911yescharacteristic
147C4×D11—41no—
148C4×D11—41no—
149C4×D11—41no—
150C4×D11—41no—
151C8×C11—81no—
152C8×C11—81no—
153C11⋊C8—81no—
154C11⋊C8—81no—
155C2×#125—111no—
156C2×#117—111no—
157#431—221no—
158#407—221no—
159#400—111no—
160#399—111no—
161#398C2×D1111yescharacteristic
162#397—111no—
163#389—221no—
164#388—221no—
165#387—221no—
166#385—221no—
167#376—111no—
168#343—111no—
169#343—221no—
170#343C2×D1111yescharacteristic
171#324—111no—
172#324C2×D1111yescharacteristic
173#323—221no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11C2×#9911yescharacteristic
177C22×C11#41611yescharacteristic
178C22×C11#42111yescharacteristic
179C2×D11—42no—
180C2×D11—41no—
181C2×D11—41no—
182C2×D11—41no—
183C2×D11—81no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—42no—
187C4×C11—41no—
188C4×C11—41no—
189C4×C11—81no—
190Dic11—21no—
191Dic11—21no—
192Dic11—41no—
193Dic11—41no—
194Dic11—81no—
195Dic11—81no—
196C23×C4—111no—
197C2×M16—21no—
198C2×M16—221no—
199#125—441no—
200#125—441no—
201#117—441no—
202#117—441no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4C4×D1111yescharacteristic
210C2×C4⋊C4C22×D1111yescharacteristic
211C2×C22⋊C4—111no—
212C2×C22⋊C4—111no—
213C2×C22⋊C4—221no—
214C2×C22⋊C4—221no—
215C2×C42—111no—
216C2×C42—111no—
217C2×C42—221no—
218C4⋊C8—441no—
219C22⋊C8—21no—
220C22⋊C8—221no—
221C22⋊C8—441no—
222C22⋊C8—441no—
223C4×C8—441no—
224#95—21no—
225#95—111no—
226#95—221no—
227#95—221no—
228#95—221no—
229#95—221no—
230#95C4×D1111yescharacteristic
231C2×C11—21no—
232C2×C11—21no—
233C2×C11#151611yescharacteristic
234C2×C11#212311yescharacteristic
235C2×C11#213211yescharacteristic
236D11—81no—
237C24—111no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—111no—
241C22×C4—111no—
242C22×C4—111no—
243C22×C4—221no—
244C22×C4—221no—
245C22×C4—221no—
246C22×C4—221no—
247C22×C4—221no—
248C22×C4—221no—
249C22×C4—441no—
250C22×C4C2×C4×D1111yescharacteristic
251C22×C4D4×D1111yescharacteristic
252C22×C4D4×D1111yescharacteristic
253M16—41no—
254M16—41no—
255M16—441no—
256M16—441no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—441no—
260C2×C8—441no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—441no—
266C4⋊C4—441no—
267C4⋊C4—442no—
268C4⋊C4—441no—
269C4⋊C4—441no—
270C4⋊C4—442no—
271C22⋊C4—441no—
272C22⋊C4—441no—
273C22⋊C4—442no—
274C22⋊C4—442no—
275C42—221no—
276C42—221no—
277C42—221no—
278C42—221no—
279C42—442no—
280C11#1185311yescharacteristic, complemented, Sylow
281C23—221no—
282C23—221no—
283C23—221no—
284C23—441no—
285C23—441no—
286C23C22⋊C4×D1111yescharacteristic
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—111no—
300C2×C4—111no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—221no—
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—441no—
316C2×C4—441no—
317C2×C4#6696511yescharacteristic
318C2×C4#6696911yescharacteristic
319C8—81no—
320C8—81no—
321C8—881no—
322C8—881no—
323C22—21no—
324C22—21no—
325C22—442no—
326C22—441no—
327C22—441no—
328C22—441no—
329C22—881no—
330C22D11×#9911yescharacteristic
331C22#1062238511yescharacteristic
332C22#1062243411yescharacteristic
333C4—21no—
334C4—21no—
335C4—42no—
336C4—41no—
337C4—41no—
338C4—81no—
339C4—221no—
340C4—221no—
341C4—441no—
342C4—441no—
343C4—881no—
344C4—881no—
345C2—21no—
346C2—21no—
347C2—881no—
348C2#1306716911yescharacteristic
349C2#1307026811yescharacteristic
350C2#1307030011yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1346C2
socleC22×C11C2×#99
prime radicalC23×D11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1346D11
hypocenterC11#11853
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
4. #13066644C2semidirect
5. #13066642C2semidirect
6. #13066622C2semidirect
7. C11×#1346C2semidirect
112. #1346D11semidirect
280. C11#11853semidirect

Maximal subgroups

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

subgroupindex
#130743092
#130686982
#130669292
#130666442
#130666422
#130666222
C11×#13462
#1185311