Finite Group Databasebeta

← #14672430

Subgroups — #14672430

Order 2816.

488 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 107 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#13072933C211yesmaximal, characteristic
2#13068608C211yesmaximal, characteristic
3#13066733C214yesmaximal
4C4×C11×#99C211yesmaximal, characteristic
5C2×C4×D4×C11C2211yescharacteristic
6C22×C4⋊Dic11C411yescharacteristic, complemented
7C2×C11×#99C2212yes—
8C4×C11×C22⋊C4—21no—
9#10622833C2212yes—
10C2×#66897C2212yes—
11#10622825—21no—
12#10622825C411yescharacteristic, complemented
13#10622599—21no—
14#10622562—21no—
15#10622559C412yescomplemented
16#10622541—21no—
17#10622537—21no—
18C11×#342—21no—
19#10622168—21no—
20C22×D4×C11C2311yescharacteristic
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×Dic11C2×C412yes—
24C4×D4×C11—41no—
25C4×D4×C11—41no—
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C22⋊C4—22no—
28C2×C11×C22⋊C4C2×C411yescharacteristic
29C2×C11×C22⋊C4D411yescharacteristic
30C2×C42×C11—41no—
31C2×C42×C11D411yescharacteristic
32C2×C22⋊Dic11—22no—
33C2×C22⋊Dic11C2×C412yes—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—41no—
38C2×C4⋊Dic11—41no—
39C2×Dic11⋊C4—22no—
40C2×#4318—22no—
41C11×#99—22no—
42C11×#99Q814yes—
43C11×#95—41no—
44#66897—24no—
45C11⋊#95—22no—
46C11⋊#95—21no—
47C11⋊#95—22no—
48C4⋊(C11⋊C8)—41no—
49C4⋊(C11⋊C8)—41no—
50#13295—111nomaximal, Sylow
51C24×C11C22×C411yescharacteristic
52C24×C11C2×D411yescharacteristic
53C2×D4×C11—41no—
54C2×D4×C11—41no—
55C2×D4×C11C2×Q812yes—
56C2×D4×C11#4112yes—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—42no—
62C22×C4×C11—42no—
63C22×C4×C11—42no—
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—22no—
70C22×Dic11—22no—
71C22×Dic11—42no—
72C22×Dic11—82no—
73C11×C4⋊C4—41no—
74C11×C22⋊C4—24no—
75C11×C22⋊C4—41no—
76C11×C22⋊C4—41no—
77C11×C22⋊C4—42no—
78C42×C11—21no—
79C42×C11—21no—
80C42×C11—82no—
81C22⋊Dic11—42no—
82C22⋊Dic11—82no—
83C4⋊Dic11—42no—
84C4⋊Dic11—42no—
85C4⋊Dic11—41no—
86C4⋊Dic11—41no—
87Dic11⋊C4—82no—
88#4318—42no—
89#4318—42no—
90C2×C11⋊C8—42no—
91#2487—111no—
92#1800—111no—
93C4×#99D1111yescharacteristic
94#1390—114no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—41no—
100C23×C11—41no—
101C23×C11—41no—
102C23×C11—41no—
103C23×C11C2×C22⋊C411yescharacteristic
104C23×C11C4×Q812yes—
105C23×C11C22⋊Q812yes—
106D4×C11—42no—
107D4×C11—42no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—22no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—44no—
121C2×C4×C11—81no—
122C2×C4×C11—82no—
123C2×C4×C11—82no—
124C2×C4×C11#9911yescharacteristic
125C2×C4×C11#9911yescharacteristic
126C2×C4×C11#12411yescharacteristic
127C2×C4×C11C4⋊Q811yescharacteristic
128C2×Dic11—42no—
129C2×Dic11—42no—
130C2×Dic11—42no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11—84no—
135C11⋊C8—82no—
136C2×C4×D4C2×D1111yescharacteristic
137C22×C4⋊C4—111no—
138#423—221no—
139C2×#100—112no—
140C2×#99C2×D1112yes—
141#400—221no—
142#399—221no—
143#389—221no—
144#386—112no—
145#385—112no—
146#380—111no—
147#380—221no—
148C4×C22⋊C4—21no—
149#343—221no—
150#342—21no—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11—22no—
154C22×C11—22no—
155C22×C11—42no—
156C22×C11—42no—
157C22×C11—42no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—81no—
163C22×C11#39111yescharacteristic
164C22×C11C2×#9911yescharacteristic
165C22×C11#41011yescharacteristic
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—84no—
173C4×C11#35212yes—
174Dic11—82no—
175Dic11—82no—
176C22×D4C22×D1111yescharacteristic
177C23×C4—112no—
178C23×C4C4×D1111yescharacteristic
179C23×C4C22⋊D1111yescharacteristic
180C2×M16—222no—
181C4×D4—41no—
182C4×D4—41no—
183C2×C4⋊C4—221no—
184C2×C4⋊C4—221no—
185C2×C4⋊C4—221no—
186C2×C4⋊C4—222no—
187C2×C4⋊C4—441no—
188C2×C4⋊C4—441no—
189C2×C4⋊C4D4411yescharacteristic
190C2×C22⋊C4—22no—
191C2×C22⋊C4—112no—
192C2×C22⋊C4—222no—
193C2×C22⋊C4C4×D1111yescharacteristic
194C2×C22⋊C4C22⋊D1111yescharacteristic
195C2×C42—41no—
196C2×C42D4411yescharacteristic
197C4⋊C8—441no—
198C4⋊C8—441no—
199#100—224no—
200#99—22no—
201#99Dic2214yes—
202#95—41no—
203#95—221no—
204#95—222no—
205#95—222no—
206C2×C11—21no—
207C2×C11—21no—
208C2×C11—42no—
209C2×C11—42no—
210C2×C11#199611yescharacteristic
211C2×C11C2×#35211yescharacteristic
212C2×C11#212211yescharacteristic
213C24C2×C4×D1111yescharacteristic
214C24C2×C22⋊D1111yescharacteristic
215C2×D4—41no—
216C2×D4—41no—
217C2×D4C2×Dic2212yes—
218C2×D4#433912yes—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—222no—
227C22×C4—222no—
228C22×C4—442no—
229C22×C4—882no—
230C22×C4(C2×D11)⋊C411yescharacteristic
231C22×C4(C2×D11)⋊C411yescharacteristic
232C22×C4(C2×D11)⋊C411yescharacteristic
233C22×C4(C2×D11)⋊C411yescharacteristic
234C22×C4C2×D4411yescharacteristic
235M16—442no—
236M16—442no—
237C2×C8—442no—
238C4⋊C4—41no—
239C4⋊C4—442no—
240C4⋊C4—442no—
241C4⋊C4—441no—
242C4⋊C4—441no—
243C4⋊C4—882no—
244C22⋊C4—24no—
245C22⋊C4—41no—
246C22⋊C4—41no—
247C22⋊C4—42no—
248C22⋊C4—442no—
249C22⋊C4—882no—
250C42—21no—
251C42—21no—
252C42—82no—
253C11#1329511yescharacteristic, complemented, Sylow
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23—41no—
259C23—41no—
260C23—41no—
261C23—41no—
262C23C4×Dic2212yes—
263C23#6697712yes—
264C23C2×(C2×D11)⋊C411yescharacteristic
265D4—42no—
266D4—42no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—44no—
280C2×C4—81no—
281C2×C4—82no—
282C2×C4—82no—
283C2×C4—442no—
284C2×C4—442no—
285C2×C4—442no—
286C2×C4—442no—
287C2×C4—442no—
288C2×C4—442no—
289C2×C4—884no—
290C2×C4#6687011yescharacteristic
291C2×C4#6687011yescharacteristic
292C2×C4#6692211yescharacteristic
293C2×C4#6692811yescharacteristic
294C8—882no—
295C22—21no—
296C22—21no—
297C22—22no—
298C22—22no—
299C22—42no—
300C22—42no—
301C22—42no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—81no—
307C22#1062254211yescharacteristic
308C22C2×#6687011yescharacteristic
309C22#1062261911yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—84no—
317C4—882no—
318C4—882no—
319C4#1062211012yes—
320C2—21no—
321C2—21no—
322C2—42no—
323C2—42no—
324C2#1306960111yescharacteristic
325C2C2×#1062211011yescharacteristic
326C2#1307026511yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC24×C11C22×C4
FrattiniC22×D4C22×D11
FittingC4×C11×#99C2
socleC22×C11C2×#99
prime radical, cosocleC22×D4×C11C23
hypercenterC4×#99D11
hypocenterC11#13295
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
6. C22×C4⋊Dic11C4semidirect
12. #10622825C4semidirect
15. #10622559C4semidirect
253. C11#13295semidirect

Maximal subgroups

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

subgroupindex
#130729332
#130686082
#130667332
C4×C11×#992
#1329511