Finite Group Databasebeta

← #28393788

Subgroups — #28393788

Order 14464.

944 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 944 conjugacy classes of subgroups — too many to draw. Only its 163 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
1C22×#14268646C211yesmaximal, characteristic, complemented
2C2×#16813584C211yesmaximal, characteristic, complemented
3C2×#16813582C212yesmaximal, complemented
4#20298518C211yesmaximal, characteristic, complemented
5#20298513C212yesmaximal, complemented
6#20298511C211yesmaximal, characteristic, complemented
7#20298507C212yesmaximal, complemented
8#20298506C211yesmaximal, characteristic, complemented
9C22⋊C4×Dic113C212yesmaximal, complemented
10#20298445C211yesmaximal, characteristic, complemented
11#394×C113C211yesmaximal, characteristic, complemented
12C2×#14268646—28no—
13C2×#14268646—24no—
14C22×Dic226C2211yescharacteristic
15C22×D452C2211yescharacteristic
16C22×C22⋊D113C2212yes—
17C22×C22⋊D113C2212yes—
18C23×Dic113C2212yes—
19C22×C4×D113C2211yescharacteristic
20C22×C4×D113C2211yescharacteristic
21#16813584—24no—
22#16813582—28no—
23C2×#14268626C2212yes—
24C2×C22⋊Dic113C2212yes—
25C2×#14268624C2211yescharacteristic
26C2×#14268624C2212yes—
27C2×#14268624C2212yes—
28C2×#14268624C2211yescharacteristic
29C2×C4×Dic113C2212yes—
30C2×C4×Dic113C2211yescharacteristic
31#16813529C2211yescharacteristic
32#16813529C2212yes—
33#16813529C2212yes—
34C22×D4×C113C2211yescharacteristic
35C2×C4⋊C4×C113C2211yescharacteristic
36C2×C22⋊C4×C113C2212yes—
37C2×C22⋊C4×C113C2212yes—
38#95×C113C2211yescharacteristic
39C23×D113C2311yescharacteristic
40C23×D113C2311yescharacteristic
41#14268646—232no—
42C2×Dic226—22no—
43C2×Dic226—24no—
44C2×D452—22no—
45C2×D452—22no—
46C2×D452—22no—
47C2×C22⋊D113—24no—
48C2×C22⋊D113—24no—
49C2×C22⋊D113—24no—
50C2×C22⋊D113—24no—
51C2×C22⋊D113—24no—
52C2×C22⋊D113—24no—
53C22×Dic113—24no—
54C22×Dic113—24no—
55C22×Dic113D418yescomplemented
56C22×Dic113C2311yescharacteristic
57C22×Dic113C2312yes—
58C22×Dic113C2312yes—
59C22×Dic113C2311yescharacteristic
60C2×C4×D113—24no—
61C2×C4×D113—24no—
62C2×C4×D113—22no—
63C2×C4×D113D414yescomplemented
64#14268626—24no—
65C22⋊Dic113—24no—
66#14268624—22no—
67#14268624—22no—
68#14268624—24no—
69#14268624—24no—
70C4×Dic113—24no—
71C4×Dic113—22no—
72C24×C113C2312yes—
73C2×D4×C113—24no—
74C2×D4×C113—22no—
75C22×C4×C113C2312yes—
76C22×C4×C113C2311yescharacteristic
77C22×C4×C113C2311yescharacteristic
78C22×C4×C113C2311yescharacteristic
79C4⋊C4×C113—22no—
80C22⋊C4×C113—24no—
81C22⋊C4×C113—24no—
82C23×C113—22no—
83C23×C113—22no—
84C23×C113—22no—
85C23×C113—22no—
86C23×C113—22no—
87C23×C113—22no—
88C23×C113C2×D414yes—
89C23×C113C2411yescharacteristic
90C22×D113—22no—
91C22×D113—21no—
92C22×D113—22no—
93C22×D113—22no—
94C22×D113—22no—
95C22×D113—21no—
96C22×D113—21no—
97C22×D113—21no—
98C22×D113C2×D412yes—
99C22×D113#4112yescomplemented
100D4×C113—28no—
101C2×C4×C113—21no—
102C2×C4×C113—22no—
103C2×C4×C113—21no—
104C2×C4×C113—22no—
105C2×C4×C113—22no—
106C2×C4×C113—21no—
107C2×C4×C113—22no—
108C2×C4×C113—22no—
109C2×C4×C113C2×D412yes—
110C2×C4×C113#4112yescomplemented
111C22⋊D113—216no—
112C22⋊D113—216no—
113C2×Dic113—22no—
114C2×Dic113—22no—
115C2×Dic113—22no—
116C2×Dic113—22no—
117C2×Dic113—216no—
118C2×Dic113—21no—
119C2×Dic113—22no—
120C2×Dic113C2×D414yes—
121C2×Dic113C2×D414yes—
122C2×Dic113C2×D412yes—
123C2×Dic113#4114yescomplemented
124D452—28no—
125C4×D113—28no—
126C4×D113—44no—
127Dic226—28no—
128C22×C113—24no—
129C22×C113—24no—
130C22×C113—24no—
131C22×C113—42no—
132C22×C113—42no—
133C22×C113—42no—
134C22×C113—42no—
135C22×C113C22×D411yescharacteristic
136C22×C113C22×D412yes—
137C22×C113C2×#4111yescharacteristic
138C22×C113C2×#4112yes—
139C22×C113C2×#4111yescharacteristic
140C2×D113—22no—
141C2×D113—22no—
142C2×D113—22no—
143C2×D113—24no—
144C2×D113—22no—
145C2×D113—41no—
146C2×D113—42no—
147C2×D113—42no—
148C2×D113—42no—
149C2×D113—41no—
150C4×C113—22no—
151C4×C113—22no—
152C4×C113—41no—
153C4×C113—42no—
154Dic113—24no—
155Dic113—24no—
156Dic113—41no—
157Dic113#12014yes—
158C2×C113—44no—
159C2×C113C2×#12011yescharacteristic
160C2×C113#52512yes—
161C2×C113#52511yescharacteristic
162C2×C113#53212yes—
163C2×C113#53211yescharacteristic
164D113—42no—
165D113—42no—
166#2388—1131nomaximal, Sylow
167C113#238811yescharacteristic, complemented, Sylow
168C22×#41—1131no—
169C2×C4×D4—1131no—
170C2×C4×D4—1132no—
171#395—1131no—
172#394—1132no—
173#394D11311yescharacteristic, complemented
174#393—1131no—
175#392—1131no—
176#392—1132no—
177C4×C22⋊C4—1132no—
178C4×C22⋊C4—1131no—
179C2×#41—2268no—
180C2×#41—2264no—
181C22×Q8—1131no—
182C22×D4—1132no—
183C22×D4—1132no—
184C22×D4—1131no—
185C22×D4C2×D11311yescharacteristic
186C23×C4—1132no—
187C23×C4—1131no—
188C23×C4—1131no—
189C4×D4—2268no—
190C4×D4—2264no—
191C2×C4⋊C4—1132no—
192C2×C4⋊C4C2×D11311yescharacteristic
193C2×C22⋊C4—1132no—
194C2×C22⋊C4—1132no—
195C2×C22⋊C4—1131no—
196C2×C22⋊C4—1131no—
197C2×C22⋊C4—1132no—
198C2×C22⋊C4C2×D11312yes—
199C2×C22⋊C4C2×D11312yes—
200C2×C42—1132no—
201C2×C42—1131no—
202#95—1131no—
203#95—1132no—
204#95—1132no—
205#95C2×D11311yescharacteristic
206C24—1131no—
207C24—1131no—
208C24C22×D11312yes—
209#41—22632no—
210C2×Q8—2264no—
211C2×Q8—2262no—
212C2×D4—24no—
213C2×D4—22no—
214C2×D4—2262no—
215C2×D4—2262no—
216C2×D4—2264no—
217C2×D4—2264no—
218C2×D4—2264no—
219C2×D4—2264no—
220C2×D4—2264no—
221C2×D4—2264no—
222C2×D4—2262no—
223C22×C4—1131no—
224C22×C4—1138no—
225C22×C4—1132no—
226C22×C4—1132no—
227C22×C4—1134no—
228C22×C4—1131no—
229C22×C4—2264no—
230C22×C4—2262no—
231C22×C4—2264no—
232C22×C4—2264no—
233C22×C4—2264no—
234C22×C4C22×D11312yes—
235C22×C4C22×D11311yescharacteristic
236C22×C4C22×D11311yescharacteristic
237C22×C4C22×D11311yescharacteristic
238C4⋊C4—22no—
239C4⋊C4—2264no—
240C22⋊C4—24no—
241C22⋊C4—24no—
242C22⋊C4—2264no—
243C22⋊C4—2264no—
244C22⋊C4—2262no—
245C22⋊C4—2264no—
246C22⋊C4—2262no—
247C42—2262no—
248C42—2264no—
249C23—22no—
250C23—22no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—1132no—
256C23—1132no—
257C23—2262no—
258C23—2261no—
259C23—2262no—
260C23—2262no—
261C23—2261no—
262C23—2262no—
263C23—2261no—
264C23—2261no—
265C23D4×D11314yes—
266C23C23×D11311yescharacteristic
267Q8—2268no—
268D4—28no—
269D4—2268no—
270D4—22616no—
271D4—22616no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—1134no—
281C2×C4—1132no—
282C2×C4—1134no—
283C2×C4—1134no—
284C2×C4—4524no—
285C2×C4—2268no—
286C2×C4—22616no—
287C2×C4—2261no—
288C2×C4—2262no—
289C2×C4—2262no—
290C2×C4—2262no—
291C2×C4—2262no—
292C2×C4—2262no—
293C2×C4D4×D11312yes—
294C2×C4#1426864612yescomplemented
295C22—24no—
296C22—24no—
297C22—24no—
298C22—42no—
299C22—42no—
300C22—42no—
301C22—42no—
302C22—4521no—
303C22—4522no—
304C22—4522no—
305C22—4522no—
306C22—4521no—
307C22—2262no—
308C22—2264no—
309C22—2262no—
310C22—2262no—
311C22—2262no—
312C22C2×D4×D11312yes—
313C22C2×D4×D11311yescharacteristic
314C22#41×D11311yescharacteristic
315C22#41×D11312yes—
316C22C2×#1426864611yescharacteristic
317C4—22no—
318C4—22no—
319C4—41no—
320C4—42no—
321C4—1134no—
322C4—4521no—
323C4—2264no—
324C4—2264no—
325C2—44no—
326C2—4522no—
327C2—4522no—
328C2#120×D11311yescharacteristic
329C2#2029910612yes—
330C2#2029910811yescharacteristic
331C2#2029914312yes—
332C2#2029914711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutator, socle, cosocleC23×C113C24
Fitting#394×C113C2
hypercenter#394D113
hypocenterC113#2388
LCSG ▷ C23×C113 ▷ C113
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C22×#14268646C2semidirect
2. C2×#16813584C2semidirect
3. C2×#16813582C2semidirect
4. #20298518C2semidirect
5. #20298513C2semidirect
6. #20298511C2semidirect
7. #20298507C2semidirect
8. #20298506C2semidirect
9. C22⋊C4×Dic113C2semidirect
10. #20298445C2semidirect
11. #394×C113C2semidirect
55. C22×Dic113D4semidirect
63. C2×C4×D113D4semidirect
99. C22×D113#41semidirect
110. C2×C4×C113#41semidirect
123. C2×Dic113#41semidirect
167. C113#2388semidirect
173. #394D113semidirect
294. C2×C4#14268646semidirect

Maximal subgroups

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

subgroupindex
C22×#142686462
C2×#168135842
C2×#168135822
#202985182
#202985132
#202985112
#202985072
#202985062
C22⋊C4×Dic1132
#202984452
#394×C1132
#2388113