Finite Group Databasebeta

← #14655161

Subgroups — #14655161

Order 2816.

480 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 85 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#13079802C211yesmaximal, characteristic
2#13074566C211yesmaximal, characteristic, complemented
3#13067333C211yesmaximal, characteristic, complemented
4#13067217C211yesmaximal, characteristic, complemented
5#13067124C211yesmaximal, characteristic
6#13066510C211yesmaximal, characteristic, complemented
7C11×#3141C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#66923C2211yescharacteristic
11C11×#489—22no—
12C11×#487—21no—
13C11×#486—21no—
14C11×#417—22no—
15C4×C11×M16C2211yescharacteristic
16#10622843—21no—
17#10622843—21no—
18#10622693—21no—
19#10622684—21no—
20#10622647—21no—
21#10622646—21no—
22#10622622—22no—
23#10622595—22no—
24#10622595—22no—
25#10622545C2211yescharacteristic
26#10622539C2211yescharacteristic
27#10622539C2211yescharacteristic
28#10622185—22no—
29#10622175—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×C4⋊Dic11D411yescharacteristic
49C2×C4⋊Dic11D411yescharacteristic
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4—21no—
52C2×C4×Dic11—21no—
53#66923—21no—
54#66923—21no—
55#66923—21no—
56#66923—21no—
57C11×#103—24no—
58C11×#102—24no—
59C11×#97D412yes—
60C4×C8×C11—21no—
61#66896—22no—
62#66896—22no—
63C11⋊#95—24no—
64C11⋊#95—24no—
65C11⋊#95—21no—
66C11⋊#95D412yes—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69#66872—22no—
70#66871—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)D412yes—
73#66867—21no—
74#66867—21no—
75#10095—111nomaximal, Sylow
76C11×#41—44no—
77C2×Q8×C11—21no—
78C2×Q8×C11—44no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
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×C11C2×D411yescharacteristic
90C22×Dic11—22no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C11×M16—42no—
94C2×C8×C11—22no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11#4111yescharacteristic
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111Dic11⋊C4—41no—
112Dic11⋊C4—41no—
113Dic11⋊C4—41no—
114Dic11⋊C4—41no—
115C4×Dic11—42no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—41no—
118#3234—111no—
119#3141D1111yescharacteristic
120#2642—111no—
121#1556—111no—
122#1528—111no—
123#1505—111no—
124#1300—111no—
125C23×C11—41no—
126C23×C11#12011yescharacteristic
127Q8×C11—42no—
128Q8×C11—82no—
129Q8×C11—82no—
130D4×C11—42no—
131D4×C11—42no—
132D4×C11—81no—
133D4×C11—82no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—41no—
137C2×C4×C11—44no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11—82no—
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12711yescharacteristic
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—42no—
153C2×Dic11—42no—
154C8×C11—42no—
155C11⋊C8—42no—
156C11⋊C8—81no—
157#532C2×D1111yescharacteristic
158C2×C4⋊Q8C2×D1111yescharacteristic
159C2×#125—111no—
160#501—221no—
161#490—221no—
162#489—22no—
163#487—21no—
164#486—21no—
165#481—221no—
166#480—221no—
167#478—222no—
168#432—111no—
169#432—111no—
170#417—22no—
171C4×M16C2×D1111yescharacteristic
172#400—222no—
173#400—222no—
174#391—221no—
175#391—221no—
176#376—111no—
177#332—222no—
178#330—222no—
179#327—222no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11—81no—
185C22×C11#39211yescharacteristic
186C22×C11#45412yes—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—82no—
193C4×C11—81no—
194C4×C11#45412yes—
195Dic11—82no—
196Dic11—81no—
197Dic11—81no—
198C2×#41—21no—
199C22×Q8—21no—
200C2×M16—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8C22⋊D1111yescharacteristic
206#127C22⋊D1111yescharacteristic
207#125—221no—
208#125—221no—
209#125—221no—
210#125—221no—
211#124—21no—
212#121—21no—
213#121—21no—
214C4×D4—21no—
215C4×D4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—111no—
218C2×C4⋊C4—111no—
219C2×C4⋊C4—221no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4C22⋊D1112yes—
222C2×C42—221no—
223C2×C42C22×D1111yescharacteristic
224#107—222no—
225#106—222no—
226C4⋊C8—112no—
227C4⋊C8—221no—
228#103—24no—
229#102—24no—
230#102—222no—
231#102—222no—
232C22⋊C8—221no—
233C22⋊C8—221no—
234#97—221no—
235#97—221no—
236#97C22⋊D1112yes—
237C4×C8—21no—
238#95—112no—
239#95—224no—
240#95—224no—
241#95—221no—
242C2×C11—22no—
243C2×C11—161no—
244C2×C11#200311yescharacteristic
245C2×C11#200311yescharacteristic
246C2×C11#200911yescharacteristic
247#41—44no—
248C2×Q8—21no—
249C2×Q8—44no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—41no—
256C22×C4—22no—
257C22×C4—41no—
258C22×C4—222no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4D4×D1111yescharacteristic
262C22×C4D4×D1111yescharacteristic
263C22×C4C2×C22⋊D1111yescharacteristic
264M16—42no—
265C2×C8—22no—
266C2×C8—222no—
267C2×C8—441no—
268C4⋊C4—21no—
269C4⋊C4—22no—
270C4⋊C4—21no—
271C4⋊C4—22no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C4⋊C4—441no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C42—442no—
285C42D4×D1111yescharacteristic
286C42#434111yescharacteristic
287C42C2×C22⋊D1111yescharacteristic
288C42C2×C22⋊D1111yescharacteristic
289C11#1009511yescharacteristic, complemented, Sylow
290C23—41no—
291C23#6699011yescharacteristic
292Q8—42no—
293Q8—82no—
294Q8—82no—
295D4—42no—
296D4—42no—
297D4—81no—
298D4—82no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—44no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—82no—
306C2×C4—442no—
307C2×C4—442no—
308C2×C4—442no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—442no—
312C2×C4—442no—
313C2×C4#6699011yescharacteristic
314C2×C4#6699111yescharacteristic
315C2×C4#6699211yescharacteristic
316C2×C4#6699211yescharacteristic
317C2×C4#6699311yescharacteristic
318C2×C4#6700611yescharacteristic
319C8—42no—
320C8—442no—
321C8—881no—
322C22—21no—
323C22—21no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22#1062267512yes—
328C22#1062283611yescharacteristic
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—82no—
335C4—81no—
336C4—882no—
337C4—881no—
338C4—881no—
339C4#1062281412yes—
340C2—22no—
341C2—161no—
342C2#1306963511yescharacteristic
343C2#1306963811yescharacteristic
344C2#1306967411yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3141C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3141D11
hypocenterC11#10095
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. #13074566C2semidirect
3. #13067333C2semidirect
4. #13067217C2semidirect
6. #13066510C2semidirect
289. C11#10095semidirect

Maximal subgroups

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

subgroupindex
#130798022
#130745662
#130673332
#130672172
#130671242
#130665102
C11×#31412
#1009511