Finite Group Databasebeta

← #28389595

Subgroups — #28389595

Order 14464.

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

normal subgroups only

This group has 288 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
2#20298917C211yesmaximal, characteristic, complemented
3#20298914C211yesmaximal, characteristic, complemented
4#20298535C211yesmaximal, characteristic, complemented
5#20298331C211yesmaximal, characteristic, complemented
6#20298321C211yesmaximal, characteristic, complemented
7#327×C113C211yesmaximal, characteristic, complemented
8C2×D4×D113—21no—
9#16813607—21no—
10#16813604—21no—
11#16813596C2211yescharacteristic
12#16813594—21no—
13#16813592—21no—
14#16813590—21no—
15C2×C4⋊Dic113—21no—
16C2×C4⋊Dic113C2211yescharacteristic, complemented
17C2×#14268624—21no—
18C2×#14268624C2211yescharacteristic
19#16813554—21no—
20#16813553—21no—
21#16813544—21no—
22#16813543—21no—
23C22⋊#11744751C2211yescharacteristic, complemented
24#121×C113C2211yescharacteristic
25C22⋊C8×C113C2211yescharacteristic, complemented
26#95×C113C2211yescharacteristic, complemented
27C23×D113—21no—
28C23×D113D411yescharacteristic
29C2×D452—21no—
30C2×D452D411yescharacteristic
31C2×C22⋊D113—21no—
32C2×C22⋊D113—21no—
33C2×C22⋊D113—21no—
34D4×D113—42no—
35D4×D113—42no—
36C22×Dic113—21no—
37C22×Dic113D411yescharacteristic
38C2×C4×D113—21no—
39C2×#11744751—21no—
40C4⋊Dic113—21no—
41C4⋊Dic113—21no—
42C4⋊Dic113—42no—
43C4⋊Dic113D411yescharacteristic
44#14268626—21no—
45C22⋊Dic113—21no—
46#14268624—21no—
47#14268624—21no—
48#14268624—21no—
49#14268624—21no—
50#14268624—42no—
51C2×D4×C113—21no—
52C2×D4×C113D411yescharacteristic
53C22×C4×C113—21no—
54C22×C4×C113C2311yescharacteristic
55C2×C8×C113—21no—
56C4⋊C4×C113D411yescharacteristic
57C22⋊C4×C113—21no—
58C23×C113—21no—
59C23×C113C2×D411yescharacteristic
60C22×D113—21no—
61C22×D113—21no—
62C22×D113—21no—
63C22×D113—42no—
64C22×D113—41no—
65C22×D113—41no—
66C22×D113—81no—
67C22×D113—81no—
68C22×D113SD1612yes—
69D4×C113—41no—
70D4×C113—41no—
71D4×C113—41no—
72C2×C4×C113—22no—
73C2×C4×C113—21no—
74C2×C4×C113—41no—
75C2×C4×C113—41no—
76C2×C4×C113—41no—
77C2×C4×C113C2×D411yescharacteristic
78C2×C4×C113C2×D411yescharacteristic
79C22⋊D113—42no—
80C22⋊D113—41no—
81C22⋊D113—41no—
82C22⋊D113—81no—
83C2×Dic113—21no—
84C2×Dic113—21no—
85C2×Dic113—41no—
86C2×Dic113—41no—
87C2×Dic113—41no—
88C2×Dic113—41no—
89D452—41no—
90D452—42no—
91C4×D113—42no—
92C8×C113—41no—
93#11744751—41no—
94C22×C113—21no—
95C22×C113—21no—
96C22×C113—41no—
97C22×C113—41no—
98C22×C113—41no—
99C22×C113#12011yescharacteristic
100C22×C113C2×SD1611yescharacteristic
101C22×C113AGL(1,ℤ/8)11yescharacteristic
102C2×D113—22no—
103C2×D113—41no—
104C2×D113—41no—
105C2×D113—42no—
106C2×D113—41no—
107C2×D113—41no—
108C2×D113—41no—
109C2×D113—81no—
110C2×D113—84no—
111C4×C113—21no—
112C4×C113—21no—
113C4×C113—42no—
114C4×C113—41no—
115Dic113—41no—
116Dic113—41no—
117Dic113—81no—
118C2×C113—21no—
119C2×C113—21no—
120C2×C113—81no—
121C2×C113#45011yescharacteristic
122C2×C113#45311yescharacteristic
123C2×C113#45811yescharacteristic
124D113—42no—
125D113—81no—
126#1613—1131nomaximal, Sylow
127C113#161311yescharacteristic, complemented, Sylow
128#534—1131no—
129#481—1131no—
130#481—1131no—
131#399—1131no—
132#327—1131no—
133#327D11311yescharacteristic, complemented
134#323—1131no—
135C22×D4—2261no—
136#123—2261no—
137#123—2261no—
138#121—1131no—
139#121—2261no—
140#121C2×D11311yescharacteristic
141#120—2261no—
142#120—2261no—
143C2×C4⋊C4—1131no—
144C2×C4⋊C4—2261no—
145C2×C22⋊C4—1131no—
146C2×C22⋊C4—2261no—
147#106—2261no—
148#106—2261no—
149#102—2261no—
150#102—2261no—
151C22⋊C8—1131no—
152C22⋊C8C2×D11311yescharacteristic, complemented
153#95C2×D11311yescharacteristic, complemented
154C24—1131no—
155C24—2261no—
156C2×D4—21no—
157C2×D4—1131no—
158C2×D4—4522no—
159C2×D4—4522no—
160C2×D4—2261no—
161C2×D4—2261no—
162C2×D4—2261no—
163C2×D4—2261no—
164C2×D4D45211yescharacteristic
165C22×C4—21no—
166C22×C4—1131no—
167C22×C4—2261no—
168C22×C4—2261no—
169C22×C4C22×D11311yescharacteristic
170C2×C8—21no—
171C2×C8—2261no—
172C4⋊C4—1131no—
173C4⋊C4—4522no—
174C4⋊C4—2261no—
175C4⋊C4—2261no—
176C4⋊C4—2261no—
177C4⋊C4D45211yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—4522no—
180C22⋊C4—2261no—
181C22⋊C4—2261no—
182C22⋊C4—2261no—
183C22⋊C4—2261no—
184C22⋊C4—2261no—
185C23—21no—
186C23—1132no—
187C23—9041no—
188C23—9041no—
189C23—4521no—
190C23—4521no—
191C23—4522no—
192C23—2261no—
193C23—2261no—
194C23—2261no—
195C23D4×D11311yescharacteristic
196D4—41no—
197D4—41no—
198D4—41no—
199D4—9041no—
200D4—4521no—
201D4—4522no—
202D4—4522no—
203D4—4521no—
204D4—4521no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—4522no—
211C2×C4—4521no—
212C2×C4—4521no—
213C2×C4—4521no—
214C2×C4—4521no—
215C2×C4—2261no—
216C2×C4—2261no—
217C2×C4D4×D11311yescharacteristic
218C2×C4C2×D45211yescharacteristic
219C8—41no—
220C8—4521no—
221C22—21no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—9041no—
227C22—9044no—
228C22—4522no—
229C22—4521no—
230C22—4521no—
231C22—4521no—
232C22—4521no—
233C22—4521no—
234C22—2262no—
235C22#1681359211yescharacteristic
236C22SD16×D11311yescharacteristic
237C22#1681364611yescharacteristic
238C4—21no—
239C4—21no—
240C4—42no—
241C4—41no—
242C4—9041no—
243C4—4521no—
244C4—4521no—
245C2—21no—
246C2—21no—
247C2—81no—
248C2—9041no—
249C2—4522no—
250C2#2029875011yescharacteristic
251C2#2029876711yescharacteristic
252C2#2029878911yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#327×C113C2
socleC22×C113#120
prime radical#20299156C2
hypercenter#327D113
hypocenterC113#1613
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #20298917C2semidirect
3. #20298914C2semidirect
4. #20298535C2semidirect
5. #20298331C2semidirect
6. #20298321C2semidirect
7. #327×C113C2semidirect
16. C2×C4⋊Dic113C22semidirect
23. C22⋊#11744751C22semidirect
25. C22⋊C8×C113C22semidirect
26. #95×C113C22semidirect
127. C113#1613semidirect
133. #327D113semidirect
152. C22⋊C8C2×D113semidirect
153. #95C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991562
#202989172
#202989142
#202985352
#202983312
#202983212
#327×C1132
#1613113