Finite Group Databasebeta

← #14641965

Subgroups — #14641965

Order 2816.

410 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 101 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#13071175C211yesmaximal, characteristic
2#13068731C211yesmaximal, characteristic
3#13068363C211yesmaximal, characteristic
4#13066440C211yesmaximal, characteristic
5#13066439C211yesmaximal, characteristic
6#13066438C211yesmaximal, characteristic
7C11×#1271C211yesmaximal, characteristic
8C2×#66943C411yescharacteristic
9C11×#389C2211yescharacteristic
10C2×#66879—21no—
11C2×Dic11⋊C8—21no—
12#10622591—21no—
13#10622590C411yescharacteristic
14C4⋊C4×Dic11—21no—
15C4⋊C4×Dic11C411yescharacteristic
16C4⋊C4×Dic11C411yescharacteristic
17C42×Dic11C2211yescharacteristic
18#10622541C2211yescharacteristic
19#10622266—21no—
20#10622262—21no—
21C11×#336C2211yescharacteristic
22C11×#336C2211yescharacteristic
23#10622188—21no—
24#10622188—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×C8×C11—21no—
28C22×C8×C11—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11C2×C411yescharacteristic
35C2×C4⋊Dic11C2×C411yescharacteristic
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C2×C4×Dic11—21no—
39C2×C4×Dic11—21no—
40C2×C4×Dic11C2×C411yescharacteristic
41C2×C4×Dic11C2×C411yescharacteristic
42C2×C4×Dic11D411yescharacteristic
43C2×C4×Dic11D411yescharacteristic
44C2×C4×Dic11D411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46C22×C11⋊C8—21no—
47C22×C11⋊C8—21no—
48#66943—22no—
49#66943—22no—
50C11×#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56#66879—24no—
57Dic11⋊C8—42no—
58#7619—111nomaximal, Sylow
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11C22×C411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×Dic11—21no—
65C22×Dic11—21no—
66C22×Dic11C22⋊C411yescharacteristic
67C22×Dic11C22⋊C411yescharacteristic
68C22×Dic11C22⋊C411yescharacteristic
69C22×Dic11C22⋊C411yescharacteristic
70C2×C8×C11—22no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C2×C8×C11—41no—
74C2×C8×C11—41no—
75C2×C8×C11—41no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4M1612yes—
81C42×C11—41no—
82C4⋊Dic11—24no—
83C4⋊Dic11—21no—
84C4⋊Dic11—41no—
85C4⋊Dic11M1612yes—
86Dic11⋊C4—24no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89C4×Dic11—22no—
90C4×Dic11—22no—
91C4×Dic11—21no—
92C4×Dic11—21no—
93C4×Dic11—21no—
94C4×Dic11—21no—
95C4×Dic11—21no—
96C4×Dic11—21no—
97C4×Dic11—41no—
98C4×Dic11—42no—
99C4×Dic11—42no—
100C2×C11⋊C8—22no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106C4×#125—111no—
107#1831—111no—
108#1745—111no—
109#1271—111no—
110#1271—111no—
111#1271—111no—
112#1271D1111yescharacteristic
113C23×C11C2×C22⋊C411yescharacteristic
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—22no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11C2×M1611yescharacteristic
127C2×C4×C11C2×M1611yescharacteristic
128C2×C4×C11#13511yescharacteristic
129C2×C4×C11#13511yescharacteristic
130C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C11#13711yescharacteristic
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—22no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11#10112yes—
149C2×Dic11#10412yes—
150C8×C11—42no—
151C8×C11—81no—
152C11⋊C8—42no—
153C11⋊C8—81no—
154C2×#125—111no—
155C2×C4⋊C8—221no—
156C2×#97—221no—
157#389—111no—
158#389C2×D1111yescharacteristic
159#387—221no—
160#387—221no—
161#382—111no—
162C4×C4⋊C4—111no—
163C4×C4⋊C4—111no—
164C4×C4⋊C4—221no—
165C4×C4⋊C4—221no—
166C43—111no—
167#336—111no—
168#336—111no—
169#336—221no—
170#336—221no—
171#336C2×D1111yescharacteristic
172#336C2×D1111yescharacteristic
173C22×C11#40711yescharacteristic
174C22×C11#41011yescharacteristic
175C22×C11C2×#10111yescharacteristic
176C22×C11#41611yescharacteristic
177C22×C11#41711yescharacteristic
178C22×C11C2×#10411yescharacteristic
179C22×C11#42111yescharacteristic
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—42no—
187C4×C11—81no—
188Dic11—22no—
189Dic11—22no—
190Dic11—41no—
191Dic11—41no—
192Dic11—42no—
193Dic11—81no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—221no—
197C22×C8—221no—
198#125—222no—
199#125—222no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4C4×D1111yescharacteristic
207C2×C4⋊C4C4×D1111yescharacteristic
208C2×C42—111no—
209C2×C42—111no—
210C2×C42—111no—
211C2×C42—111no—
212C2×C42—111no—
213C2×C42—111no—
214C2×C42—221no—
215C2×C42—221no—
216C2×C42C22×D1111yescharacteristic
217C4⋊C8—442no—
218#97—224no—
219#95—21no—
220#95—221no—
221#95—221no—
222#95—221no—
223#95—221no—
224#95—221no—
225C2×C11#146711yescharacteristic
226C2×C11#148811yescharacteristic
227C2×C11#148911yescharacteristic
228C2×C11#150011yescharacteristic
229C2×C11#151211yescharacteristic
230C2×C11#152811yescharacteristic
231C2×C11#155211yescharacteristic
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—111no—
235C22×C4—111no—
236C22×C4—111no—
237C22×C4—111no—
238C22×C4—221no—
239C22×C4—221no—
240C22×C4C2×C4×D1111yescharacteristic
241C22×C4D4×D1111yescharacteristic
242C22×C4D4×D1111yescharacteristic
243C2×C8—22no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—222no—
250C2×C8—441no—
251C2×C8—441no—
252C2×C8—441no—
253C2×C8—441no—
254C2×C8—441no—
255C4⋊C4—21no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—112no—
260C4⋊C4—224no—
261C4⋊C4—224no—
262C4⋊C4—221no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C4⋊C4—441no—
266C4⋊C4#431312yes—
267C42—41no—
268C42—222no—
269C42—222no—
270C42—221no—
271C42—221no—
272C42—221no—
273C42—221no—
274C42—221no—
275C42—221no—
276C42—441no—
277C42—442no—
278C42—442no—
279C11#761911yescharacteristic, complemented, Sylow
280C23C22⋊C4×D1111yescharacteristic
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—112no—
294C2×C4—112no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—222no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4C2×#431311yescharacteristic
312C2×C4M16×D1111yescharacteristic
313C2×C4#6696511yescharacteristic
314C2×C4#6696711yescharacteristic
315C2×C4#6696911yescharacteristic
316C2×C4#6697111yescharacteristic
317C8—42no—
318C8—81no—
319C8—442no—
320C8—881no—
321C22#1062233911yescharacteristic
322C22#1062235311yescharacteristic
323C22D11×#10111yescharacteristic
324C22#1062238511yescharacteristic
325C22#1062241611yescharacteristic
326C22D11×#10411yescharacteristic
327C22#1062243411yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—42no—
335C4—81no—
336C4—222no—
337C4—222no—
338C4—441no—
339C4—441no—
340C4—442no—
341C4—881no—
342C2#1306695811yescharacteristic
343C2#1306704711yescharacteristic
344C2#1306705411yescharacteristic
345C2#1306709911yescharacteristic
346C2#1306715311yescharacteristic
347C2#1306721611yescharacteristic
348C2#1306731311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1271C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1271D11
hypocenterC11#7619
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
279. C11#7619semidirect

Maximal subgroups

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

subgroupindex
#130711752
#130687312
#130683632
#130664402
#130664392
#130664382
C11×#12712
#761911