Finite Group Databasebeta

← #14649819

Subgroups — #14649819

Order 2816.

560 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 127 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#13074429C211yesmaximal, characteristic
2#13071234C211yesmaximal, characteristic
3#13067189C212yesmaximal
4#13066484C212yesmaximal
5C2×C11×#324C211yesmaximal, characteristic
6C22×C11×C4⋊C4C2211yescharacteristic
7C2×#66979—21no—
8C2×#66977C2211yescharacteristic
9C2×C11×C22⋊C8C2212yes—
10#10622825—21no—
11#10622825C2211yescharacteristic
12#10622825C2212yes—
13#10622824—21no—
14#10622823—21no—
15#10622599C412yescomplemented
16#10622598—24no—
17#10622597—22no—
18#10622592C412yescomplemented
19C11×#324—22no—
20#10622105—24no—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C22×Dic22C2×C411yescharacteristic
25C22×C8×C11—22no—
26C2×C11×C4⋊C4—22no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4C2×C412yes—
29C2×C11×C4⋊C4D412yes—
30C2×C22⋊Dic11—21no—
31C2×C22⋊Dic11—22no—
32C2×C22⋊Dic11—21no—
33#66979—42no—
34#66979—42no—
35C2×C4⋊Dic11—22no—
36C2×C4⋊Dic11—22no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—22no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40#66977—22no—
41#66977—22no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—22no—
44C2×C4×Dic11—22no—
45C11×C22⋊C8—22no—
46C11×C22⋊C8—22no—
47C11⋊#95—22no—
48C11⋊#95—22no—
49C11⋊#95—22no—
50C11⋊#95—22no—
51C11⋊#95C2×C412yes—
52C11⋊#95D414yes—
53#9200—111nomaximal, Sylow
54C24×C11C2×D411yescharacteristic
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—81no—
62C22×C4×C11—81no—
63C22×C4×C11C22⋊C412yes—
64C22×C4×C11C22⋊C412yes—
65C22×C4×C11SD1612yes—
66C22×C4×C11Q1612yes—
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D412yes—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11#4112yes—
71C22×Dic11—21no—
72C22×Dic11—22no—
73C22×Dic11—21no—
74C22×Dic11—24no—
75C2×Dic22—22no—
76C2×Dic22—81no—
77C2×C8×C11—42no—
78C2×C8×C11—82no—
79C11×C4⋊C4—24no—
80C11×C4⋊C4—24no—
81C22⋊Dic11—41no—
82C22⋊Dic11—41no—
83C22⋊Dic11—42no—
84C22⋊Dic11—42no—
85C22⋊Dic11—41no—
86C22⋊Dic11—41no—
87C4⋊Dic11—22no—
88C4⋊Dic11—44no—
89C4⋊Dic11—81no—
90C4⋊Dic11—82no—
91C4⋊Dic11—82no—
92Dic11⋊C4—42no—
93Dic11⋊C4—82no—
94C4×Dic11—44no—
95#2627—111no—
96#2316—111no—
97#1520—112no—
98C2×#324D1111yescharacteristic
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
109C2×C4×C11—22no—
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—42no—
117C2×C4×C11—41no—
118C2×C4×C11—42no—
119C2×C4×C11—41no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—81no—
123C2×C4×C11#10314yes—
124C2×C4×C11C4×D412yes—
125C2×C4×C11#12112yes—
126C2×Dic11—42no—
127C2×Dic11—42no—
128C2×Dic11—44no—
129C2×Dic11—42no—
130C2×Dic11—44no—
131C2×Dic11—42no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—42no—
135C2×Dic11—44no—
136Dic22—82no—
137C8×C11—82no—
138C2×C22⋊Q8—111no—
139C2×#117—221no—
140C22×C4⋊C4C2×D1111yescharacteristic
141C2×C22⋊C8C2×D1112yes—
142#400—112no—
143#398—222no—
144#395—112no—
145#389—224no—
146#385—221no—
147#381—221no—
148#380—111no—
149#380—112no—
150#380—221no—
151#328—224no—
152#324—22no—
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—
174Dic11—84no—
175Dic11—82no—
176Dic11—81no—
177Dic11—81no—
178C22×Q8—111no—
179C23×C4D4411yescharacteristic
180C23×C4D4411yescharacteristic
181C23×C4C22×D1111yescharacteristic
182C22×C8—22no—
183C22⋊Q8—222no—
184C22⋊Q8—222no—
185#117—442no—
186#117—442no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—111no—
190C2×C4⋊C4—222no—
191C2×C4⋊C4—221no—
192C2×C4⋊C4—222no—
193C2×C4⋊C4—222no—
194C2×C4⋊C4—222no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4C4×D1112yes—
197C2×C4⋊C4C22⋊D1112yes—
198C2×C22⋊C4—222no—
199C2×C22⋊C4—221no—
200C2×C22⋊C4—221no—
201C2×C42—222no—
202C22⋊C8—22no—
203C22⋊C8—22no—
204#95—112no—
205#95—114no—
206#95—222no—
207#95—222no—
208#95—222no—
209#95—222no—
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×D4411yescharacteristic
220C2×Q8—222no—
221C2×Q8—881no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—81no—
229C22×C4—81no—
230C22×C4—224no—
231C22×C4—222no—
232C22×C4—221no—
233C22×C4—221no—
234C22×C4#431412yes—
235C22×C4Dic4412yes—
236C22×C4(C2×D11)⋊C412yes—
237C22×C4(C2×D11)⋊C412yes—
238C22×C4C2×C4×D1111yescharacteristic
239C22×C4D4×D1112yes—
240C22×C4#434112yes—
241C22×C4C2×C22⋊D1111yescharacteristic
242C2×C8—42no—
243C2×C8—82no—
244C4⋊C4—24no—
245C4⋊C4—24no—
246C4⋊C4—222no—
247C4⋊C4—444no—
248C4⋊C4—442no—
249C4⋊C4—882no—
250C4⋊C4—882no—
251C4⋊C4—881no—
252C4⋊C4—882no—
253C22⋊C4—441no—
254C22⋊C4—441no—
255C22⋊C4—442no—
256C22⋊C4—442no—
257C22⋊C4—441no—
258C22⋊C4—441no—
259C42—444no—
260C11#920011yescharacteristic, complemented, Sylow
261C23—41no—
262C23—41no—
263C23#6693511yescharacteristic
264C23#6693911yescharacteristic
265C23C2×#431411yescharacteristic
266C23C2×Dic4411yescharacteristic
267C23#6696111yescharacteristic
268C23#6696211yescharacteristic
269C23C2×(C2×D11)⋊C411yescharacteristic
270Q8—882no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—81no—
285C2×C4—444no—
286C2×C4—442no—
287C2×C4—442no—
288C2×C4—444no—
289C2×C4—442no—
290C2×C4—442no—
291C2×C4—442no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—444no—
295C2×C4#6688014yes—
296C2×C4(C22⋊D11)⋊C412yes—
297C2×C4#6699212yes—
298C8—82no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22#1062233411yescharacteristic
310C22#1062233511yescharacteristic
311C22#1062234411yescharacteristic
312C22#1062235211yescharacteristic
313C22#1062257111yescharacteristic
314C22C2×#6688011yescharacteristic
315C22#1062274611yescharacteristic
316C4—22no—
317C4—22no—
318C4—24no—
319C4—42no—
320C4—884no—
321C4—882no—
322C4—881no—
323C4—881no—
324C2—21no—
325C2—21no—
326C2—21no—
327C2—21no—
328C2—21no—
329C2—21no—
330C2#1306892111yescharacteristic
331C2#1306915111yescharacteristic
332C2#1306915611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#324C2
socleC22×C11#386
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC2×#324D11
hypocenterC11#9200
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
15. #10622599C4semidirect
18. #10622592C4semidirect
260. C11#9200semidirect

Maximal subgroups

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

subgroupindex
#130744292
#130712342
#130671892
#130664842
C2×C11×#3242
#920011