Finite Group Databasebeta

← #14655891

Subgroups — #14655891

Order 2816.

486 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079961C211yesmaximal, characteristic
2#13079564C211yesmaximal, characteristic
3#13079158C211yesmaximal, characteristic
4#13069559C211yesmaximal, characteristic
5#13067114C211yesmaximal, characteristic
6#13066466C211yesmaximal, characteristic
7C11×#1987C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9#10623001C2211yescharacteristic
10#10623001C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13#10622841—22no—
14#10622729—22no—
15#10622705—21no—
16#10622703—22no—
17#10622694—21no—
18#10622693—22no—
19#10622692—21no—
20#10622691—21no—
21#10622577—22no—
22#10622538C2211yescharacteristic
23C4×#4318C2211yescharacteristic
24#10622463—21no—
25#10622463—21no—
26#10622462—21no—
27#10622462—21no—
28C11×#340—22no—
29#10622161—22no—
30#10622090—22no—
31C22×Q8×C11—21no—
32C22×C8×C11D412yes—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8D412yes—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C42×C11—21no—
41C2×C42×C11C2311yescharacteristic
42C2×#4326—24no—
43#66979—21no—
44#66979—21no—
45#66977—21no—
46#66977—21no—
47#66977—21no—
48#66977—21no—
49C2×#4318D412yes—
50C2×Dic44—22no—
51#66923—21no—
52#66923—21no—
53#66922D411yescharacteristic
54#66922D411yescharacteristic
55#66922D411yescharacteristic
56#66922D411yescharacteristic
57C4×Dic22—21no—
58C4×Dic22—21no—
59C4×Dic22—21no—
60C4×Dic22—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×#95—21no—
64#66899—24no—
65C22⋊(C11⋊C8)D412yes—
66#66882—22no—
67#66880—22no—
68#66880—22no—
69#66872—24no—
70#66871—24no—
71C4⋊(C11⋊C8)—21no—
72#66867—21no—
73C4×C11⋊C8—21no—
74C4×C11⋊C8—21no—
75#10199—111nomaximal, Sylow
76C2×Q8×C11—22no—
77C2×Q8×C11—41no—
78C2×Q8×C11—82no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C2×Dic22—21no—
85C2×Dic22—21no—
86C2×Dic22—21no—
87C2×Dic22—21no—
88C2×C8×C11—22no—
89C2×C8×C11—42no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C42×C11—42no—
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11#4111yescharacteristic
101C22⋊Dic11—41no—
102C22⋊Dic11—41no—
103#4326—84no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112Dic11⋊C4—41no—
113Dic11⋊C4—41no—
114Dic11⋊C4—41no—
115Dic11⋊C4—41no—
116C4×Dic11—41no—
117C4×Dic11—41no—
118#4318—22no—
119#4318Q1614yescomplemented
120C2×C11⋊C8—22no—
121C2×C11⋊C8—22no—
122Dic44—82no—
123#3249—111no—
124#3209—111no—
125#3165—111no—
126#1987D1111yescharacteristic
127#1986—111no—
128#1503—111no—
129#1283—111no—
130C23×C11#12711yescharacteristic
131Q8×C11—44no—
132Q8×C11—82no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—41no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—81no—
139C2×C4×C11—82no—
140C2×C4×C11—81no—
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11C2×Q1612yes—
148C2×C4×C11#13712yes—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153Dic22—42no—
154Dic22—41no—
155Dic22—41no—
156Dic22—41no—
157Dic22—41no—
158Dic22—81no—
159C8×C11—42no—
160C11⋊C8—24no—
161C11⋊C8—42no—
162#533—111no—
163#533—111no—
164C2×C4⋊Q8C2×D1111yescharacteristic
165#501—222no—
166#500—221no—
167#498—221no—
168#494—221no—
169#487—221no—
170#477—221no—
171#477—221no—
172#467—222no—
173#462—221no—
174#462—221no—
175#462—222no—
176#451—222no—
177#431—111no—
178#428—222no—
179C2×C4⋊C8C2×D1111yescharacteristic
180C4×M16—111no—
181C4×C4⋊C4C2×D1111yescharacteristic
182#340—22no—
183#339—222no—
184#328—222no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11#39211yescharacteristic
188C22×C11#49411yescharacteristic
189C22×C11#49711yescharacteristic
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—82no—
194C4×C11—82no—
195C4×C11#45112yes—
196C4×C11#45511yescharacteristic
197C4×C11#45611yescharacteristic
198C4×C11#46212yes—
199Dic11—81no—
200Dic11—81no—
201Dic11—81no—
202Dic11—81no—
203C22×Q8—21no—
204C2×Q16—222no—
205C2×Q16—224no—
206C2×M16—112no—
207C22×C8C22⋊D1112yes—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—111no—
212C4⋊Q8—111no—
213C4⋊Q8—111no—
214C4⋊Q8—111no—
215C4⋊Q8D4412yes—
216#125—221no—
217#125—221no—
218C22⋊Q8—221no—
219C22⋊Q8—221no—
220C22⋊Q8—221no—
221C22⋊Q8—221no—
222C4×Q8—221no—
223C4×Q8—221no—
224C4×Q8—221no—
225C4×Q8—221no—
226#117—221no—
227#117—221no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C42—21no—
232C2×C42C22×D1111yescharacteristic
233#107—224no—
234#107—222no—
235#106—224no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—221no—
239#103—222no—
240#103—222no—
241#103—224no—
242C22⋊C8—112no—
243#97—221no—
244C4×C8—221no—
245C4×C8—221no—
246#95—21no—
247C2×C11—21no—
248C2×C11—21no—
249C2×C11#200711yescharacteristic
250C2×C11#200811yescharacteristic
251C2×C11#201611yescharacteristic
252C2×Q8—22no—
253C2×Q8—41no—
254C2×Q8—82no—
255C2×Q8—221no—
256C2×Q8—221no—
257C2×Q8—221no—
258C2×Q8—221no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4D4×D1111yescharacteristic
262C22×C4D4×D1111yescharacteristic
263C22×C4C2×C22⋊D1111yescharacteristic
264Q16—882no—
265Q16—884no—
266M16—114no—
267M16—222no—
268C2×C8—22no—
269C2×C8—42no—
270C2×C8—222no—
271C2×C8—222no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C4⋊C4—441no—
289C4⋊C4—441no—
290C22⋊C4—441no—
291C22⋊C4—441no—
292C42—42no—
293C42—441no—
294C42—441no—
295C42C2×D4411yescharacteristic
296C42#433911yescharacteristic
297C42D4×D1111yescharacteristic
298C42D4×D1111yescharacteristic
299C11#1019911yescharacteristic, complemented, Sylow
300C23#6699311yescharacteristic
301Q8—44no—
302Q8—82no—
303Q8—442no—
304Q8—441no—
305Q8—441no—
306Q8—441no—
307Q8—441no—
308Q8—881no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—81no—
315C2×C4—82no—
316C2×C4—81no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4#6693511yescharacteristic
322C2×C4#6693511yescharacteristic
323C2×C4#6693711yescharacteristic
324C2×C4#6693711yescharacteristic
325C2×C4#6696812yes—
326C2×C4Q16×D1112yes—
327C2×C4#6698311yescharacteristic
328C2×C4#6699011yescharacteristic
329C8—42no—
330C8—224no—
331C8—442no—
332C22—21no—
333C22—21no—
334C22#1062257311yescharacteristic
335C22#1062278011yescharacteristic
336C22#1062279411yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—82no—
341C4—82no—
342C4—881no—
343C4—881no—
344C4—881no—
345C4—881no—
346C4#1062240612yes—
347C4#1062242112yes—
348C4#1062267411yescharacteristic
349C4#1062270811yescharacteristic
350C2—21no—
351C2—21no—
352C2#1306966211yescharacteristic
353C2#1306967111yescharacteristic
354C2#1306971711yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1987C2
socleC22×C11#392
prime radicalC23×C11#127
hypercenter#1987D11
hypocenterC11#10199
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
119. #4318Q16semidirect
299. C11#10199semidirect

Maximal subgroups

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

subgroupindex
#130799612
#130795642
#130791582
#130695592
#130671142
#130664662
C11×#19872
#1019911