Finite Group Databasebeta

← #14655273

Subgroups — #14655273

Order 2816.

476 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 89 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#13080003C211yesmaximal, characteristic
2#13079760C211yesmaximal, characteristic, complemented
3#13069606C211yesmaximal, characteristic, complemented
4#13067210C211yesmaximal, characteristic, complemented
5#13067033C211yesmaximal, characteristic
6#13066506C211yesmaximal, characteristic, complemented
7C11×#3141C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#489—22no—
12C11×#487—21no—
13C11×#486—21no—
14C11×#417—22no—
15C4×C11×M16C2211yescharacteristic
16#10622707—22no—
17#10622706—21no—
18#10622704—21no—
19#10622692—21no—
20#10622688—21no—
21#10622655—22no—
22#10622632—21no—
23#10622620—21no—
24#10622584—22no—
25#10622538C2211yescharacteristic
26#10622537C2211yescharacteristic
27C4×#4318C2211yescharacteristic
28D4⋊(C11⋊C8)—22no—
29#10622168—22no—
30#10622103—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C2×C11×M16—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8D411yescharacteristic
39C11×#127D411yescharacteristic
40C11×#124—21no—
41C11×#121—21no—
42C11×#121—21no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D412yes—
47C2×C42×C11C2311yescharacteristic
48C2×#4324—22no—
49#66979—21no—
50#66977—21no—
51#66977—21no—
52C2×#4318—21no—
53C2×#4318D412yes—
54#66923—21no—
55#66922D411yescharacteristic
56#66922D411yescharacteristic
57C4×Dic22—21no—
58C4×Dic22—21no—
59C11×#103—24no—
60C11×#102—24no—
61C11×#97D412yes—
62C4×C8×C11—21no—
63#66896—22no—
64C22⋊(C11⋊C8)—21no—
65#66874—24no—
66#66874—22no—
67#66872—24no—
68#66871—22no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)D412yes—
72#66867—21no—
73C4×C11⋊C8—21no—
74C4×C11⋊C8—21no—
75#10111—111nomaximal, Sylow
76C11×#41—44no—
77C2×Q8×C11—21no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—82no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—41no—
85C22×C4×C11—22no—
86C22×C4×C11—41no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C2×Dic22—21no—
91C2×Dic22—21no—
92C11×M16—42no—
93C2×C8×C11—22no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C22⋊Dic11—41no—
107#4324—82no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112Dic11⋊C4—41no—
113Dic11⋊C4—41no—
114C4×Dic11—41no—
115#4318—22no—
116#4318—42no—
117#4318—41no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—41no—
121#3254—111no—
122#3229—111no—
123#3141D1111yescharacteristic
124#1997—111no—
125#1526—111no—
126#1484—111no—
127#1299—111no—
128C23×C11—41no—
129C23×C11#12111yescharacteristic
130Q8×C11—42no—
131Q8×C11—82no—
132Q8×C11—82no—
133D4×C11—42no—
134D4×C11—41no—
135D4×C11—41no—
136D4×C11—42no—
137D4×C11—82no—
138C2×C4×C11—22no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—82no—
145C2×C4×C11—82no—
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12711yescharacteristic
152C2×Dic11—41no—
153C2×Dic11—41no—
154Dic22—42no—
155Dic22—41no—
156Dic22—41no—
157C8×C11—42no—
158C11⋊C8—42no—
159C11⋊C8—42no—
160C11⋊C8—42no—
161#533—111no—
162#532C2×D1111yescharacteristic
163C2×C4⋊Q8C2×D1111yescharacteristic
164#498—221no—
165#489—22no—
166#487—21no—
167#487—221no—
168#486—21no—
169#483—222no—
170#477—221no—
171#475—222no—
172#474—221no—
173#468—222no—
174#461—221no—
175#460—221no—
176#431—111no—
177#423—111no—
178#417—22no—
179C4×M16—111no—
180C4×M16C2×D1111yescharacteristic
181#343—222no—
182#330—222no—
183D4⋊C8—222no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—81no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11#39211yescharacteristic
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—81no—
195C4×C11—82no—
196C4×C11#45412yes—
197C4×C11#45511yescharacteristic
198C4×C11#45611yescharacteristic
199C4×C11#47112yes—
200Dic11—81no—
201Dic11—81no—
202C2×#41—21no—
203C22×Q8—21no—
204C2×SD16—222no—
205C2×M16—21no—
206C2×M16—112no—
207C2×M16—221no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—111no—
213C4⋊Q8—111no—
214C4⋊Q8C22⋊D1111yescharacteristic
215#127C22⋊D1111yescharacteristic
216#125—221no—
217#124—21no—
218C22⋊Q8—221no—
219C22⋊Q8—221no—
220#121—21no—
221#121—21no—
222C4×Q8—221no—
223C4×Q8—221no—
224C4×D4—21no—
225C4×D4—21no—
226#117—221no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4C22⋊D1112yes—
229C2×C42C22×D1111yescharacteristic
230#107—222no—
231#106—224no—
232C4⋊C8—112no—
233C4⋊C8—221no—
234C4⋊C8—221no—
235#103—24no—
236#103—222no—
237#103—224no—
238#102—24no—
239#102—222no—
240C22⋊C8—221no—
241#97—221no—
242#97C22⋊D1112yes—
243C4×C8—21no—
244C4×C8—221no—
245C4×C8—221no—
246C2×C11—41no—
247C2×C11—161no—
248C2×C11#200311yescharacteristic
249C2×C11#200711yescharacteristic
250C2×C11#201911yescharacteristic
251#41—44no—
252C2×Q8—21no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—82no—
256C2×Q8—221no—
257C2×Q8—221no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—41no—
262C22×C4—22no—
263C22×C4—41no—
264C22×C4D4×D1111yescharacteristic
265C22×C4#434111yescharacteristic
266C22×C4C2×C22⋊D1111yescharacteristic
267SD16—882no—
268M16—42no—
269M16—222no—
270M16—441no—
271M16—442no—
272C2×C8—22no—
273C2×C8—222no—
274C2×C8—222no—
275C2×C8—441no—
276C4⋊C4—22no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—22no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—221no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—441no—
291C42—441no—
292C42D4×D1111yescharacteristic
293C42D4×D1111yescharacteristic
294C42C2×C22⋊D1111yescharacteristic
295C42C2×C22⋊D1111yescharacteristic
296C11#1011111yescharacteristic, complemented, Sylow
297C23—41no—
298C23#6699211yescharacteristic
299Q8—42no—
300Q8—82no—
301Q8—82no—
302Q8—441no—
303Q8—441no—
304Q8—442no—
305D4—42no—
306D4—42no—
307D4—41no—
308D4—41no—
309D4—82no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—82no—
317C2×C4—82no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4#6699011yescharacteristic
321C2×C4#6699011yescharacteristic
322C2×C4#6699111yescharacteristic
323C2×C4#6699211yescharacteristic
324C2×C4#6699311yescharacteristic
325C2×C4#6700611yescharacteristic
326C8—42no—
327C8—442no—
328C8—442no—
329C8—442no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—81no—
334C22—81no—
335C22—81no—
336C22#1062283611yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—81no—
341C4—82no—
342C4—881no—
343C4—881no—
344C4#1062267512yes—
345C4#1062281312yes—
346C4#1062281511yescharacteristic
347C4#1062281811yescharacteristic
348C2—41no—
349C2—161no—
350C2#1306963811yescharacteristic
351C2#1306966111yescharacteristic
352C2#1306973011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3141C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3141D11
hypocenterC11#10111
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

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

NH ≅ G/Ntype
2. #13079760C2semidirect
3. #13069606C2semidirect
4. #13067210C2semidirect
6. #13066506C2semidirect
296. C11#10111semidirect

Maximal subgroups

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

subgroupindex
#130800032
#130797602
#130696062
#130672102
#130670332
#130665062
C11×#31412
#1011111