Finite Group Databasebeta

← #28389507

Subgroups — #28389507

Order 14464.

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

normal subgroups only

This group has 310 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#20299175C211yesmaximal, characteristic, complemented
2#20298732C211yesmaximal, characteristic, complemented
3#20298512C211yesmaximal, characteristic, complemented
4#20298333C211yesmaximal, characteristic, complemented
5#20298332C211yesmaximal, characteristic, complemented
6#20298323C211yesmaximal, characteristic, complemented
7#447×C113C211yesmaximal, characteristic, complemented
8C2×#14268646—21no—
9C2×#14268632—21no—
10#16813600—21no—
11#16813599—21no—
12#16813596C2211yescharacteristic
13#16813595—21no—
14#16813594—21no—
15#16813594—21no—
16C2×#14268626C2211yescharacteristic
17C2×C22⋊Dic113—21no—
18C2×C22⋊Dic113—21no—
19#16813543—21no—
20C22⋊#11744751C2211yescharacteristic
21#16813529C2211yescharacteristic
22C22×D4×C113C2211yescharacteristic
23C2×D8×C113—21no—
24#121×C113C2211yescharacteristic
25#102×C113—21no—
26C22⋊C8×C113C2211yescharacteristic
27#14268646—42no—
28#14268646—42no—
29C2×Dic226—21no—
30C2×D452D411yescharacteristic
31C2×C22⋊D113—21no—
32C2×C22⋊D113—21no—
33C2×C22⋊D113—21no—
34C22×Dic113—21no—
35C22×Dic113—21no—
36C22×Dic113D411yescharacteristic
37C22×Dic113D411yescharacteristic
38C2×C4×D113—21no—
39#14268632—42no—
40C2×#11744751—21no—
41C4⋊Dic113D411yescharacteristic
42#14268626—21no—
43#14268626—21no—
44#14268626—21no—
45C22⋊Dic113—21no—
46C22⋊Dic113—42no—
47C22⋊Dic113—42no—
48#14268624—21no—
49#14268624—21no—
50C24×C113—21no—
51C2×D4×C113—21no—
52C2×D4×C113—21no—
53C2×D4×C113—21no—
54C2×D4×C113—42no—
55C2×D4×C113D411yescharacteristic
56C22×C4×C113C2311yescharacteristic
57D8×C113—42no—
58C2×C8×C113—21no—
59C4⋊C4×C113D411yescharacteristic
60C22⋊C4×C113—21no—
61C23×C113—22no—
62C23×C113—21no—
63C23×C113—41no—
64C23×C113—41no—
65C23×C113—41no—
66C23×C113—41no—
67C23×C113—41no—
68C23×C113—41no—
69C23×C113C2×D411yescharacteristic
70C22×D113—21no—
71D4×C113—22no—
72D4×C113—22no—
73D4×C113—41no—
74D4×C113—41no—
75D4×C113—41no—
76D4×C113—41no—
77D4×C113—41no—
78C2×C4×C113—21no—
79C2×C4×C113—41no—
80C2×C4×C113C2×D411yescharacteristic
81C2×C4×C113C2×D411yescharacteristic
82C22⋊D113—42no—
83C22⋊D113—41no—
84C22⋊D113—41no—
85C22⋊D113—81no—
86C2×Dic113—21no—
87C2×Dic113—21no—
88C2×Dic113—21no—
89C2×Dic113—21no—
90C2×Dic113—42no—
91C2×Dic113—41no—
92C2×Dic113—41no—
93C2×Dic113—41no—
94C2×Dic113—41no—
95C2×Dic113D812yescomplemented
96D452—41no—
97C4×D113—42no—
98Dic226—42no—
99C8×C113—41no—
100#11744751—41no—
101C22×C113—21no—
102C22×C113—21no—
103C22×C113—42no—
104C22×C113—42no—
105C22×C113—41no—
106C22×C113—41no—
107C22×C113—41no—
108C22×C113—42no—
109C22×C113—81no—
110C22×C113—81no—
111C22×C113—81no—
112C22×C113—81no—
113C22×C113#12011yescharacteristic
114C22×C113C2×D811yescharacteristic
115C22×C113AGL(1,ℤ/8)11yescharacteristic
116C2×D113—41no—
117C2×D113—41no—
118C2×D113—41no—
119C4×C113—21no—
120C4×C113—21no—
121C4×C113—41no—
122Dic113—22no—
123Dic113—41no—
124Dic113—41no—
125Dic113—81no—
126C2×C113—21no—
127C2×C113—21no—
128C2×C113—81no—
129C2×C113—82no—
130C2×C113#44711yescharacteristic
131C2×C113#45411yescharacteristic
132C2×C113B(4,𝔽2)11yescharacteristic
133D113—81no—
134#1598—1131nomaximal, Sylow
135C113#159811yescharacteristic, complemented, Sylow
136#537—1131no—
137#447—1131no—
138#447D11311yescharacteristic, complemented
139#394—1131no—
140#327—1131no—
141#327—1131no—
142#324—1131no—
143C2×#41—2261no—
144C22×D4C2×D11311yescharacteristic
145C2×D8—21no—
146C2×D8—2261no—
147C22⋊Q8—2261no—
148C22⋊Q8—2261no—
149#121—1131no—
150#121—2261no—
151#121—2261no—
152#121—2261no—
153#121C2×D11311yescharacteristic
154C2×C4⋊C4—1131no—
155C2×C22⋊C4—2261no—
156C2×C22⋊C4—2261no—
157#102—21no—
158#102—2261no—
159C22⋊C8—1131no—
160C22⋊C8C2×D11311yescharacteristic
161#95—1131no—
162C24—21no—
163#41—4522no—
164#41—4522no—
165C2×Q8—2261no—
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—42no—
170C2×D4—1131no—
171C2×D4—2261no—
172C2×D4—2261no—
173C2×D4—2261no—
174C2×D4C22⋊D11311yescharacteristic
175C22×C4—1131no—
176C22×C4—1131no—
177C22×C4—2261no—
178C22×C4—2261no—
179C22×C4—2261no—
180C22×C4C22×D11311yescharacteristic
181D8—42no—
182D8—4522no—
183C2×C8—21no—
184C2×C8—2261no—
185C4⋊C4—1131no—
186C4⋊C4—2261no—
187C4⋊C4—2261no—
188C4⋊C4—2261no—
189C4⋊C4C22⋊D11311yescharacteristic
190C22⋊C4—21no—
191C22⋊C4—4522no—
192C22⋊C4—4522no—
193C22⋊C4—2261no—
194C22⋊C4—2261no—
195C22⋊C4—2261no—
196C23—22no—
197C23—21no—
198C23—41no—
199C23—41no—
200C23—41no—
201C23—41no—
202C23—41no—
203C23—41no—
204C23—2261no—
205C23D4×D11311yescharacteristic
206Q8—4522no—
207D4—22no—
208D4—22no—
209D4—41no—
210D4—41no—
211D4—41no—
212D4—41no—
213D4—41no—
214D4—9041no—
215D4—4521no—
216D4—4521no—
217D4—4521no—
218D4—4522no—
219C2×C4—21no—
220C2×C4—41no—
221C2×C4—1132no—
222C2×C4—4522no—
223C2×C4—4521no—
224C2×C4—4521no—
225C2×C4—4521no—
226C2×C4—4522no—
227C2×C4—4521no—
228C2×C4—2261no—
229C2×C4—2261no—
230C2×C4—2261no—
231C2×C4—2261no—
232C2×C4D4×D11311yescharacteristic
233C2×C4C2×C22⋊D11311yescharacteristic
234C8—41no—
235C8—4521no—
236C22—21no—
237C22—21no—
238C22—42no—
239C22—42no—
240C22—41no—
241C22—42no—
242C22—41no—
243C22—41no—
244C22—81no—
245C22—81no—
246C22—81no—
247C22—81no—
248C22—4521no—
249C22—4521no—
250C22—4521no—
251C22#1681359011yescharacteristic
252C22D8×D11311yescharacteristic
253C22#1681364611yescharacteristic
254C4—21no—
255C4—21no—
256C4—41no—
257C4—9041no—
258C4—4521no—
259C4—4521no—
260C4—2262no—
261C2—21no—
262C2—21no—
263C2—82no—
264C2—81no—
265C2—9041no—
266C2#2029873011yescharacteristic
267C2#2029876911yescharacteristic
268C2#2029878411yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#447×C113C2
socleC22×C113#120
hypercenter#447D113
hypocenterC113#1598
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. #20299175C2semidirect
2. #20298732C2semidirect
3. #20298512C2semidirect
4. #20298333C2semidirect
5. #20298332C2semidirect
6. #20298323C2semidirect
7. #447×C113C2semidirect
95. C2×Dic113D8semidirect
135. C113#1598semidirect
138. #447D113semidirect

Maximal subgroups

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

subgroupindex
#202991752
#202987322
#202985122
#202983332
#202983322
#202983232
#447×C1132
#1598113