Finite Group Databasebeta

← #28389490

Subgroups — #28389490

Order 14464.

368 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 51 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#20299156C211yesmaximal, characteristic, complemented
2#20298732C211yesmaximal, characteristic, complemented
3#20298506C211yesmaximal, characteristic, complemented
4#20298333C211yesmaximal, characteristic, complemented
5#20298332C211yesmaximal, characteristic, complemented
6#20298321C211yesmaximal, characteristic, complemented
7#447×C113C211yesmaximal, characteristic, complemented
8C22×C22⋊D113—21no—
9C2×D4×D113—21no—
10C2×#14268632—21no—
11#16813607—21no—
12#16813604—21no—
13#16813596C2211yescharacteristic
14#16813594—21no—
15#16813592—21no—
16#16813590—21no—
17C2×C22⋊Dic113—21no—
18C2×#14268624C2211yescharacteristic
19#16813543—21no—
20C22⋊#11744751C2211yescharacteristic, complemented
21#16813529C2211yescharacteristic, complemented
22C22×D4×C113C2211yescharacteristic, complemented
23C2×D8×C113—21no—
24#121×C113C2211yescharacteristic
25#102×C113—21no—
26C22⋊C8×C113C2211yescharacteristic, complemented
27C23×D113—21no—
28C23×D113D411yescharacteristic
29C2×D452—21no—
30C2×D452D411yescharacteristic, complemented
31C2×C22⋊D113—21no—
32C2×C22⋊D113—21no—
33C2×C22⋊D113—21no—
34C2×C22⋊D113—42no—
35C2×C22⋊D113—42no—
36C2×C22⋊D113—42no—
37D4×D113—42no—
38D4×D113—42no—
39C22×Dic113—21no—
40C22×Dic113D411yescharacteristic
41C2×C4×D113—21no—
42#14268632—42no—
43C2×#11744751—21no—
44C4⋊Dic113D411yescharacteristic, complemented
45#14268626—21no—
46C22⋊Dic113—21no—
47C22⋊Dic113—42no—
48#14268624—21no—
49#14268624—21no—
50#14268624—21no—
51#14268624—21no—
52C24×C113—21no—
53C2×D4×C113—21no—
54C2×D4×C113—21no—
55C2×D4×C113—21no—
56C2×D4×C113—42no—
57C2×D4×C113D411yescharacteristic, complemented
58C22×C4×C113C2311yescharacteristic
59D8×C113—42no—
60C2×C8×C113—21no—
61C4⋊C4×C113D411yescharacteristic, complemented
62C22⋊C4×C113—21no—
63C23×C113—22no—
64C23×C113—21no—
65C23×C113—41no—
66C23×C113—41no—
67C23×C113—41no—
68C23×C113—41no—
69C23×C113—41no—
70C23×C113—41no—
71C23×C113C2×D411yescharacteristic
72C22×D113—21no—
73C22×D113—21no—
74C22×D113—21no—
75C22×D113—42no—
76C22×D113—41no—
77C22×D113—41no—
78C22×D113—81no—
79C22×D113—81no—
80C22×D113D812yescomplemented
81D4×C113—22no—
82D4×C113—22no—
83D4×C113—41no—
84D4×C113—41no—
85D4×C113—41no—
86D4×C113—41no—
87D4×C113—41no—
88C2×C4×C113—21no—
89C2×C4×C113—41no—
90C2×C4×C113C2×D411yescharacteristic
91C2×C4×C113C2×D411yescharacteristic
92C22⋊D113—42no—
93C22⋊D113—48no—
94C22⋊D113—41no—
95C22⋊D113—41no—
96C22⋊D113—81no—
97C2×Dic113—22no—
98C2×Dic113—21no—
99C2×Dic113—21no—
100C2×Dic113—41no—
101C2×Dic113—41no—
102C2×Dic113—41no—
103D452—41no—
104D452—42no—
105C4×D113—42no—
106C8×C113—41no—
107#11744751—41no—
108C22×C113—21no—
109C22×C113—21no—
110C22×C113—42no—
111C22×C113—42no—
112C22×C113—41no—
113C22×C113—41no—
114C22×C113—42no—
115C22×C113—41no—
116C22×C113—81no—
117C22×C113—81no—
118C22×C113—81no—
119C22×C113—81no—
120C22×C113#12011yescharacteristic
121C22×C113C2×D811yescharacteristic
122C22×C113AGL(1,ℤ/8)11yescharacteristic
123C2×D113—22no—
124C2×D113—41no—
125C2×D113—41no—
126C2×D113—42no—
127C2×D113—41no—
128C2×D113—41no—
129C2×D113—41no—
130C2×D113—81no—
131C2×D113—84no—
132C4×C113—21no—
133C4×C113—21no—
134C4×C113—41no—
135Dic113—42no—
136Dic113—41no—
137Dic113—41no—
138C2×C113—21no—
139C2×C113—21no—
140C2×C113—81no—
141C2×C113—82no—
142C2×C113#44711yescharacteristic
143C2×C113#45311yescharacteristic
144C2×C113B(4,𝔽2)11yescharacteristic
145D113—42no—
146D113—81no—
147#1595—1131nomaximal, Sylow
148C113#159511yescharacteristic, complemented, Sylow
149#534—1131no—
150#447—1131no—
151#447D11311yescharacteristic, complemented
152#392—1131no—
153#327—1131no—
154#327—1131no—
155#323—1131no—
156C22×D4—2261no—
157C22×D4—2261no—
158C22×D4C2×D11311yescharacteristic, complemented
159C2×D8—21no—
160C2×D8—2261no—
161#123—2261no—
162#123—2261no—
163#121—1131no—
164#121—2261no—
165#121C2×D11311yescharacteristic
166#120—2261no—
167#120—2261no—
168C2×C22⋊C4—1131no—
169C2×C22⋊C4—2261no—
170#102—21no—
171#102—2261no—
172C22⋊C8—1131no—
173C22⋊C8C2×D11311yescharacteristic, complemented
174#95—1131no—
175C24—21no—
176C24—1131no—
177C24—2261no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—42no—
182C2×D4—1131no—
183C2×D4—4522no—
184C2×D4—4522no—
185C2×D4—4522no—
186C2×D4—4522no—
187C2×D4—4522no—
188C2×D4—2261no—
189C2×D4—2261no—
190C2×D4—2261no—
191C2×D4—2261no—
192C2×D4C22⋊D11311yescharacteristic, complemented
193C22×C4—1131no—
194C22×C4—2261no—
195C22×C4—2261no—
196C22×C4C22×D11311yescharacteristic
197D8—42no—
198D8—4522no—
199C2×C8—21no—
200C2×C8—2261no—
201C4⋊C4—1131no—
202C4⋊C4—2261no—
203C4⋊C4C22⋊D11311yescharacteristic, complemented
204C22⋊C4—21no—
205C22⋊C4—4522no—
206C22⋊C4—2261no—
207C22⋊C4—2261no—
208C22⋊C4—2261no—
209C22⋊C4—2261no—
210C22⋊C4—2261no—
211C23—22no—
212C23—21no—
213C23—41no—
214C23—41no—
215C23—41no—
216C23—41no—
217C23—41no—
218C23—41no—
219C23—1132no—
220C23—9041no—
221C23—9041no—
222C23—4521no—
223C23—4521no—
224C23—4522no—
225C23—2261no—
226C23—2261no—
227C23—2261no—
228C23D4×D11311yescharacteristic
229D4—22no—
230D4—22no—
231D4—41no—
232D4—41no—
233D4—41no—
234D4—41no—
235D4—41no—
236D4—9041no—
237D4—4521no—
238D4—4522no—
239D4—4528no—
240D4—4522no—
241D4—4521no—
242D4—4521no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—4522no—
246C2×C4—4521no—
247C2×C4—4521no—
248C2×C4—4521no—
249C2×C4—2262no—
250C2×C4—2261no—
251C2×C4—2261no—
252C2×C4D4×D11311yescharacteristic
253C2×C4C2×C22⋊D11311yescharacteristic
254C8—41no—
255C8—4521no—
256C22—21no—
257C22—21no—
258C22—42no—
259C22—42no—
260C22—41no—
261C22—42no—
262C22—41no—
263C22—41no—
264C22—81no—
265C22—81no—
266C22—81no—
267C22—81no—
268C22—9041no—
269C22—9044no—
270C22—4522no—
271C22—4521no—
272C22—4521no—
273C22—4521no—
274C22—4521no—
275C22—4521no—
276C22—2262no—
277C22#1681359011yescharacteristic
278C22D8×D11311yescharacteristic
279C22#1681364611yescharacteristic
280C4—21no—
281C4—21no—
282C4—41no—
283C4—4522no—
284C4—4521no—
285C4—4521no—
286C2—21no—
287C2—21no—
288C2—82no—
289C2—81no—
290C2—9041no—
291C2—4522no—
292C2#2029873011yescharacteristic
293C2#2029876411yescharacteristic
294C2#2029878411yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#447×C113C2
socleC22×C113#120
hypercenter#447D113
hypocenterC113#1595
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #20299156C2semidirect
2. #20298732C2semidirect
3. #20298506C2semidirect
4. #20298333C2semidirect
5. #20298332C2semidirect
6. #20298321C2semidirect
7. #447×C113C2semidirect
20. C22⋊#11744751C22semidirect
21. #16813529C22semidirect
22. C22×D4×C113C22semidirect
26. C22⋊C8×C113C22semidirect
30. C2×D452D4semidirect
44. C4⋊Dic113D4semidirect
57. C2×D4×C113D4semidirect
61. C4⋊C4×C113D4semidirect
80. C22×D113D8semidirect
148. C113#1595semidirect
151. #447D113semidirect
158. C22×D4C2×D113semidirect
173. C22⋊C8C2×D113semidirect
192. C2×D4C22⋊D113semidirect
203. C4⋊C4C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
#202991562
#202987322
#202985062
#202983332
#202983322
#202983212
#447×C1132
#1595113