Finite Group Databasebeta

← #14655946

Subgroups — #14655946

Order 2816.

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

normal subgroups only

This group has 474 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#13079958C211yesmaximal, characteristic
2#13079760C211yesmaximal, characteristic
3#13069569C211yesmaximal, characteristic
4#13069560C211yesmaximal, characteristic
5#13067115C211yesmaximal, characteristic
6#13066467C211yesmaximal, characteristic
7C11×#3139C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#491—22no—
12C11×#487—21no—
13C11×#487—21no—
14C11×#419—22no—
15C4×C11×M16C2211yescharacteristic
16#10622707—22no—
17#10622706—21no—
18#10622704—21no—
19#10622703—21no—
20#10622692—21no—
21#10622664—22no—
22#10622644—21no—
23#10622634—21no—
24#10622584—22no—
25C4×C4⋊Dic11C2211yescharacteristic
26#10622538C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28#10622193—22no—
29#10622176—22no—
30#10622167—22no—
31C22×Q8×C11—21no—
32C2×C11×M16D412yes—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8D412yes—
37C11×C4⋊Q8D411yescharacteristic
38C11×C4⋊Q8D411yescharacteristic
39C11×#125—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C11×#117—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C42×C11C2311yescharacteristic
48C2×#4326—22no—
49#66979—21no—
50C2×C4⋊Dic11—21no—
51#66977—21no—
52#66977—21no—
53C2×C4×Dic11—21no—
54C22×C11⋊C8D412yes—
55#66923—21no—
56#66922D411yescharacteristic
57#66922D411yescharacteristic
58C4×Dic22—21no—
59C4×Dic22—21no—
60C11×#103—24no—
61C11×#103—24no—
62C11×#97—21no—
63C4×C8×C11—21no—
64#66899—22no—
65C11⋊#95—21no—
66C22⋊(C11⋊C8)D412yes—
67#66874—24no—
68#66874—22no—
69#66872—24no—
70#66871—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4×C11⋊C8—21no—
75#10207—111nomaximal, Sylow
76C2×Q8×C11—21no—
77C2×Q8×C11—22no—
78C2×Q8×C11—21no—
79C2×Q8×C11—41no—
80C2×Q8×C11—42no—
81C2×Q8×C11—42no—
82C22×C4×C11—41no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×Dic11—41no—
87C2×Dic22—21no—
88C2×Dic22—21no—
89C11×M16—22no—
90C11×M16—22no—
91C2×C8×C11—22no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C22⋊C4—41no—
103C42×C11—41no—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11#4111yescharacteristic
108C22⋊Dic11—41no—
109#4326—82no—
110C4⋊Dic11—22no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—41no—
116Dic11⋊C4—41no—
117Dic11⋊C4—41no—
118C4×Dic11—41no—
119C4×Dic11—42no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—42no—
123#3249—111no—
124#3229—111no—
125#3139D1111yescharacteristic
126#1988—111no—
127#1986—111no—
128#1503—111no—
129#1283—111no—
130C23×C11#12711yescharacteristic
131Q8×C11—44no—
132Q8×C11—41no—
133Q8×C11—41no—
134Q8×C11—81no—
135Q8×C11—82no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—81no—
143C2×C4×C11—81no—
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#13512yes—
151C2×C4×C11#13712yes—
152C2×Dic11—42no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—81no—
156C2×Dic11—81no—
157Dic22—42no—
158Dic22—41no—
159Dic22—41no—
160C8×C11—42no—
161C11⋊C8—42no—
162C11⋊C8—42no—
163#533—111no—
164#533C2×D1111yescharacteristic
165C2×C4⋊Q8C2×D1111yescharacteristic
166#498—221no—
167#491—22no—
168#487—21no—
169#487—21no—
170#487—221no—
171#483—222no—
172#477—221no—
173#477—221no—
174#475—222no—
175#467—222no—
176#462—221no—
177#462—221no—
178#431—111no—
179C2×C4⋊C8—111no—
180#419—22no—
181C4×M16C2×D1111yescharacteristic
182C4×C4⋊C4—111no—
183#340—222no—
184#339—222no—
185#328—222no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11#39211yescharacteristic
189C22×C11#49511yescharacteristic
190C22×C11#49711yescharacteristic
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11—82no—
197C4×C11#45212yes—
198C4×C11#45511yescharacteristic
199C4×C11#45611yescharacteristic
200C4×C11#46412yes—
201Dic11—82no—
202Dic11—81no—
203Dic11—81no—
204C22×Q8—21no—
205C2×Q16—222no—
206C2×M16C22⋊D1112yes—
207C22×C8—112no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—111no—
212C4⋊Q8—111no—
213C4⋊Q8C22⋊D1112yes—
214C4⋊Q8C22⋊D1111yescharacteristic
215C4⋊Q8C22⋊D1111yescharacteristic
216#125—21no—
217#125—221no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220C22⋊Q8—221no—
221C22⋊Q8—221no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8—221no—
225C4×Q8—221no—
226#117—21no—
227#117—221no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—221no—
231C2×C42—221no—
232C2×C42C22×D1111yescharacteristic
233#107—222no—
234#106—224no—
235C4⋊C8—221no—
236C4⋊C8—221no—
237C4⋊C8—221no—
238#103—24no—
239#103—24no—
240#103—222no—
241#103—224no—
242#103—222no—
243C22⋊C8—112no—
244#97—21no—
245C4×C8—21no—
246C4×C8—221no—
247#95—221no—
248C2×C11—21no—
249C2×C11—21no—
250C2×C11#200711yescharacteristic
251C2×C11#200911yescharacteristic
252C2×C11#201511yescharacteristic
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—22no—
256C2×Q8—41no—
257C2×Q8—42no—
258C2×Q8—42no—
259C2×Q8—221no—
260C2×Q8—221no—
261C22×C4—41no—
262C22×C4—441no—
263C22×C4D4×D1111yescharacteristic
264C22×C4D4×D1111yescharacteristic
265C22×C4C2×C22⋊D1111yescharacteristic
266Q16—882no—
267M16—22no—
268M16—22no—
269C2×C8—22no—
270C2×C8—222no—
271C2×C8—222no—
272C2×C8—442no—
273C4⋊C4—22no—
274C4⋊C4—21no—
275C4⋊C4—22no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—222no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4—221no—
287C4⋊C4—221no—
288C4⋊C4—441no—
289C4⋊C4—441no—
290C4⋊C4—441no—
291C22⋊C4—41no—
292C22⋊C4—441no—
293C42—41no—
294C42—441no—
295C42—442no—
296C42D4×D1111yescharacteristic
297C42#434111yescharacteristic
298C42C2×C22⋊D1111yescharacteristic
299C42C2×C22⋊D1111yescharacteristic
300C11#1020711yescharacteristic, complemented, Sylow
301C23#6699311yescharacteristic
302Q8—41no—
303Q8—41no—
304Q8—44no—
305Q8—81no—
306Q8—82no—
307Q8—442no—
308Q8—441no—
309Q8—441no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—442no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—881no—
322C2×C4—881no—
323C2×C4#6699011yescharacteristic
324C2×C4#6699011yescharacteristic
325C2×C4#6699111yescharacteristic
326C2×C4#6699211yescharacteristic
327C2×C4#6699211yescharacteristic
328C2×C4#6700312yes—
329C2×C4#6700412yes—
330C2×C4#6700611yescharacteristic
331C8—42no—
332C8—442no—
333C8—442no—
334C22—21no—
335C22—21no—
336C22#1062267211yescharacteristic
337C22#1062267311yescharacteristic
338C22#1062283611yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—81no—
343C4—81no—
344C4—82no—
345C4—882no—
346C4—881no—
347C4—881no—
348C4#1062266712yes—
349C4#1062281511yescharacteristic
350C4#1062281811yescharacteristic
351C4#1062285212yes—
352C2—21no—
353C2—21no—
354C2#1306966111yescharacteristic
355C2#1306967411yescharacteristic
356C2#1306971011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3139C2
socleC22×C11#392
prime radicalC23×C11#127
hypercenter#3139D11
hypocenterC11#10207
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3139

Complements

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

NH ≅ G/Ntype
300. C11#10207semidirect

Maximal subgroups

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

subgroupindex
#130799582
#130797602
#130695692
#130695602
#130671152
#130664672
C11×#31392
#1020711