Finite Group Databasebeta

← #14649822

Subgroups — #14649822

Order 2816.

560 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 135 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#13071234C211yesmaximal, characteristic
2#13067188C212yesmaximal
3C2×#10622166C211yesmaximal, characteristic
4#13066483C212yesmaximal
5C11×#2627C211yesmaximal, characteristic
6C2×C11×C22⋊Q8C2211yescharacteristic
7C22×C11×C4⋊C4C2211yescharacteristic
8C2×#66979—21no—
9C11×#400C412yescomplemented
10C11×#398—22no—
11C11×#395C412yescomplemented
12C11×#385—21no—
13C11×#381—21no—
14C11×#380C2211yescharacteristic
15#10622825—21no—
16#10622825C2212yes—
17C2×C22⋊(C11⋊C8)C2212yes—
18#10622598—24no—
19#10622176—24no—
20#10622166—22no—
21C22×Q8×C11C2×C411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C23×C4×C11C2311yescharacteristic
25C11×C22⋊Q8—22no—
26C11×C22⋊Q8—22no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—22no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4C2×C412yes—
34C2×C11×C4⋊C4D412yes—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C22⋊Dic11—22no—
38#66979—42no—
39#66979—42no—
40C2×C4⋊Dic11—22no—
41C2×C4⋊Dic11—22no—
42C2×C4⋊Dic11—22no—
43C2×C4×Dic11—22no—
44C22×C11⋊C8—22no—
45C11×#95—22no—
46C11×#95—22no—
47C11×#95—22no—
48C11×#95C2×C412yes—
49C11⋊#95—22no—
50C11⋊#95D414yes—
51C22⋊(C11⋊C8)—22no—
52C22⋊(C11⋊C8)—22no—
53#9200—111nomaximal, Sylow
54C24×C11C2×D411yescharacteristic
55C2×Q8×C11—22no—
56C2×Q8×C11—81no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—22no—
65C22×C4×C11—21no—
66C22×C4×C11—81no—
67C22×C4×C11—81no—
68C22×C4×C11C22⋊C412yes—
69C22×C4×C11C22⋊C412yes—
70C22×C4×C11SD1612yes—
71C22×C4×C11Q1612yes—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D412yes—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11#4112yes—
76C22×Dic11—24no—
77C11×C4⋊C4—24no—
78C11×C4⋊C4—24no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—42no—
81C11×C4⋊C4—81no—
82C11×C4⋊C4—82no—
83C11×C22⋊C4—41no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—41no—
87C22⋊Dic11—42no—
88C22⋊Dic11—42no—
89C4⋊Dic11—44no—
90C4⋊Dic11—82no—
91C4⋊Dic11—82no—
92C4×Dic11—44no—
93C2×C11⋊C8—42no—
94C2×C11⋊C8—82no—
95#2627D1111yescharacteristic
96#2316—111no—
97#1520—112no—
98C2×#324—111no—
99#1289—112no—
100C23×C11—41no—
101C23×C11—41no—
102C23×C11C2×C22⋊C411yescharacteristic
103C23×C11#12011yescharacteristic
104C23×C11#12311yescharacteristic
105C23×C11C2×SD1611yescharacteristic
106C23×C11C2×Q1611yescharacteristic
107C23×C11AGL(1,ℤ/8)11yescharacteristic
108C23×C11#13711yescharacteristic
109Q8×C11—82no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—42no—
130C2×C4×C11—81no—
131C2×C4×C11#10314yes—
132C2×C4×C11C4×D412yes—
133C2×C4×C11#12112yes—
134C2×Dic11—44no—
135C2×Dic11—44no—
136C2×Dic11—44no—
137C11⋊C8—82no—
138C2×C22⋊Q8C2×D1111yescharacteristic
139C2×#117—221no—
140C22×C4⋊C4C2×D1111yescharacteristic
141C2×C22⋊C8—112no—
142#400Dic1112yescomplemented
143#398—22no—
144#395Dic1112yescomplemented
145#389—224no—
146#385—21no—
147#381—21no—
148#380—112no—
149#380—221no—
150#380C2×D1111yescharacteristic
151#328—224no—
152#324—222no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11#38611yescharacteristic
164C22×C11C2×#10311yescharacteristic
165C22×C11#41711yescharacteristic
166C22×C11#45011yescharacteristic
167C22×C11#45111yescharacteristic
168C22×C11#48311yescharacteristic
169C22×C11#48411yescharacteristic
170C4×C11—24no—
171C4×C11—22no—
172C4×C11—22no—
173C4×C11—42no—
174C4×C11—82no—
175C4×C11—81no—
176C4×C11—81no—
177Dic11—84no—
178C22×Q8C2×Dic1111yescharacteristic
179C23×C4C22⋊D1111yescharacteristic
180C23×C4C22⋊D1111yescharacteristic
181C23×C4C22×D1111yescharacteristic
182C22×C8—222no—
183C22⋊Q8—22no—
184C22⋊Q8—22no—
185#117—442no—
186#117—442no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—222no—
193C2×C4⋊C4—222no—
194C2×C4⋊C4—222no—
195C2×C4⋊C4C2×Dic1111yescharacteristic
196C2×C4⋊C4C2×Dic1112yes—
197C2×C4⋊C4C22⋊D1112yes—
198C2×C22⋊C4—21no—
199C2×C22⋊C4—21no—
200C2×C22⋊C4—222no—
201C2×C42—222no—
202C22⋊C8—222no—
203C22⋊C8—222no—
204#95—22no—
205#95—22no—
206#95—22no—
207#95—114no—
208#95—222no—
209#95C2×Dic1112yes—
210C2×C11—21no—
211C2×C11—21no—
212C2×C11—21no—
213C2×C11—21no—
214C2×C11—21no—
215C2×C11—21no—
216C2×C11#187211yescharacteristic
217C2×C11#191211yescharacteristic
218C2×C11#191311yescharacteristic
219C24C2×C22⋊D1111yescharacteristic
220C2×Q8—22no—
221C2×Q8—81no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—22no—
230C22×C4—21no—
231C22×C4—81no—
232C22×C4—81no—
233C22×C4—224no—
234C22×C4#432512yes—
235C22×C4#432612yes—
236C22×C4C22⋊Dic1112yes—
237C22×C4C22⋊Dic1112yes—
238C22×C4D4×D1112yes—
239C22×C4#434112yes—
240C22×C4C22×Dic1111yescharacteristic
241C22×C4C2×C22⋊D1111yescharacteristic
242C2×C8—442no—
243C2×C8—882no—
244C4⋊C4—24no—
245C4⋊C4—24no—
246C4⋊C4—22no—
247C4⋊C4—42no—
248C4⋊C4—81no—
249C4⋊C4—82no—
250C4⋊C4—444no—
251C4⋊C4—882no—
252C4⋊C4—882no—
253C22⋊C4—41no—
254C22⋊C4—41no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C22⋊C4—442no—
258C22⋊C4—442no—
259C42—444no—
260C11#920011yescharacteristic, complemented, Sylow
261C23—41no—
262C23—41no—
263C23#6698811yescharacteristic
264C23#6699011yescharacteristic
265C23C2×#432511yescharacteristic
266C23C2×#432611yescharacteristic
267C23#6700211yescharacteristic
268C23#6700411yescharacteristic
269C23C2×C22⋊Dic1111yescharacteristic
270Q8—82no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—81no—
292C2×C4—444no—
293C2×C4—444no—
294C2×C4—444no—
295C2×C4#6689914yes—
296C2×C4D4×Dic1112yes—
297C2×C4#6699212yes—
298C8—882no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22#1062265611yescharacteristic
310C22#1062265711yescharacteristic
311C22#1062265911yescharacteristic
312C22#1062266311yescharacteristic
313C22#1062283311yescharacteristic
314C22C2×#6689911yescharacteristic
315C22#1062284511yescharacteristic
316C4—22no—
317C4—22no—
318C4—24no—
319C4—42no—
320C4—82no—
321C4—81no—
322C4—81no—
323C4—884no—
324C2—21no—
325C2—21no—
326C2—21no—
327C2—21no—
328C2—21no—
329C2—21no—
330C2#1306892411yescharacteristic
331C2#1306915411yescharacteristic
332C2#1306915911yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2627C2
socleC22×C11#386
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#2627D11
hypocenterC11#9200
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2627

Complements

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

NH ≅ G/Ntype
9. C11×#400C4semidirect
11. C11×#395C4semidirect
142. #400Dic11semidirect
144. #395Dic11semidirect
260. C11#9200semidirect

Maximal subgroups

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

subgroupindex
#130712342
#130671882
C2×#106221662
#130664832
C11×#26272
#920011