Finite Group Databasebeta

← #44487716

Subgroups — #44487716

Order 30592.

464 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C2×#21439939C211yesmaximal, characteristic
2#29504676C212yesmaximal, complemented
3#29504669C212yesmaximal, complemented
4#29504666C212yesmaximal
5#29504660C212yesmaximal
6#29504659C212yesmaximal, complemented
7#29504657C212yesmaximal, complemented
8#29504632C211yesmaximal, characteristic
9#381×C239C211yesmaximal, characteristic
10C22×Dic478C2211yescharacteristic
11#21439939C418yescomplemented
12C2×C4⋊Dic239C2212yes—
13C2×C4⋊Dic239C2211yescharacteristic
14C2×Dic239⋊C4C2212yes—
15C2×Dic239⋊C4C2212yes—
16C2×Dic239⋊C4C2212yes—
17C2×C22⋊Dic239C2211yescharacteristic
18C2×C22⋊Dic239C2211yescharacteristic
19C2×C22⋊Dic239C2212yes—
20C2×C4×Dic239C2212yes—
21C2×C4×Dic239C2212yes—
22C239⋊#95C2212yes—
23C239⋊#95C2212yes—
24C239⋊#95C2212yes—
25C239⋊#95C2212yes—
26C239⋊#95C2212yes—
27C23×C4×C239C2211yescharacteristic
28C2×C22⋊C4×C239C2212yes—
29#95×C239C2212yes—
30#95×C239C2211yescharacteristic
31#95×C239C2211yescharacteristic
32C2×Dic478—42no—
33C2×Dic478C2×C414yes—
34C22×Dic239C2312yes—
35C22×Dic239C2312yes—
36C22×Dic239C2312yes—
37C22×Dic239C2312yes—
38C4⋊Dic239—42no—
39C4⋊Dic239C2×C414yes—
40Dic239⋊C4—42no—
41Dic239⋊C4—42no—
42Dic239⋊C4C2×C418yes—
43C22⋊Dic239—41no—
44C22⋊Dic239—41no—
45C22⋊Dic239C2×C418yes—
46C4×Dic239—42no—
47C4×Dic239—42no—
48C24×C239C2311yescharacteristic
49C22×C4×C239—42no—
50C22×C4×C239C2×C414yes—
51C22×C4×C239C2312yes—
52C22×C4×C239C2312yes—
53C22×C4×C239C2311yescharacteristic
54C22×C4×C239C2311yescharacteristic
55C22⋊C4×C239—42no—
56Dic478—44no—
57C2×Dic239—22no—
58C2×Dic239—22no—
59C2×Dic239—22no—
60C2×Dic239—22no—
61C2×Dic239—22no—
62C2×Dic239—22no—
63C2×Dic239—22no—
64C2×Dic239—22no—
65C2×Dic239—22no—
66C2×Dic239—22no—
67C2×Dic239C22×C414yes—
68C2×Dic239C22×C414yes—
69C23×C239—22no—
70C23×C239—21no—
71C23×C239—22no—
72C23×C239—21no—
73C23×C239C22×C412yes—
74C23×C239C2411yescharacteristic
75C2×C4×C239—22no—
76C2×C4×C239—22no—
77C2×C4×C239—22no—
78C2×C4×C239—22no—
79C2×C4×C239—22no—
80C2×C4×C239—22no—
81C2×C4×C239—22no—
82C2×C4×C239—22no—
83C2×C4×C239—44no—
84C2×C4×C239C22×C412yes—
85C2×C4×C239C22×C412yes—
86C22×C239—22no—
87C22×C239—22no—
88C22×C239—22no—
89C22×C239—42no—
90C22×C239—42no—
91C22×C239C23×C411yescharacteristic
92C22×C239H(5,𝔽2)12yes—
93C22×C239H(5,𝔽2)11yescharacteristic
94C22×C2392−1+412yes—
95C22×C2392−1+411yescharacteristic
96C4×C239—22no—
97C4×C239—22no—
98C4×C239—42no—
99C4×C239—42no—
100Dic239—24no—
101Dic239—24no—
102Dic239—42no—
103Dic239—42no—
104C2×C239—42no—
105C2×C239#51811yescharacteristic
106C2×C239#51911yescharacteristic
107C2×C239#52011yescharacteristic
108C2×C239#56212yes—
109C2×C239#56312yes—
110C239#237811yescharacteristic, complemented, Sylow
111#2378—2391nomaximal, Sylow
112C2×C22⋊Q8—2391no—
113#391—2392no—
114#389—2392no—
115#388—2392no—
116#388—2392no—
117#387—2392no—
118#387—2392no—
119#381D23911yescharacteristic
120#380—2391no—
121C22×Q8—2391no—
122C23×C4C2×D23911yescharacteristic
123C22⋊Q8—2398no—
124C2×C4⋊C4—2392no—
125C2×C4⋊C4—2392no—
126C2×C4⋊C4—2392no—
127C2×C4⋊C4—2391no—
128C2×C4⋊C4—2392no—
129C2×C22⋊C4—2391no—
130C2×C22⋊C4—2391no—
131C2×C22⋊C4—2392no—
132C2×C22⋊C4C2×D23912yes—
133C2×C42—2392no—
134C2×C42—2392no—
135#95—2392no—
136#95—2392no—
137#95—2392no—
138#95—2392no—
139#95—2392no—
140#95C2×D23911yescharacteristic
141#95C2×D23912yes—
142#95C2×D23911yescharacteristic
143C24C22×D23911yescharacteristic
144C2×Q8—9562no—
145C2×Q8—2394no—
146C22×C4—42no—
147C22×C4—2392no—
148C22×C4—2392no—
149C22×C4—2392no—
150C22×C4—2392no—
151C22×C4C4×D23914yes—
152C22×C4C22×D23912yes—
153C22×C4C22×D23912yes—
154C22×C4C22×D23911yescharacteristic
155C22×C4C22×D23911yescharacteristic
156C4⋊C4—9562no—
157C4⋊C4—9562no—
158C4⋊C4—9562no—
159C4⋊C4—2398no—
160C4⋊C4—2394no—
161C22⋊C4—42no—
162C22⋊C4—9561no—
163C22⋊C4—9561no—
164C22⋊C4—2398no—
165C42—9562no—
166C42—9562no—
167C23—22no—
168C23—21no—
169C23—22no—
170C23—21no—
171C23C2×C4×D23912yes—
172C23C23×D23911yescharacteristic
173Q8—9564no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—44no—
183C2×C4—4782no—
184C2×C4—4782no—
185C2×C4—4782no—
186C2×C4—4782no—
187C2×C4—4782no—
188C2×C4—4782no—
189C2×C4—4782no—
190C2×C4—4782no—
191C2×C4—4782no—
192C2×C4—4782no—
193C2×C4—2394no—
194C2×C4—2394no—
195C2×C4C2×C4×D23912yes—
196C2×C4C2×C4×D23912yes—
197C22—22no—
198C22—22no—
199C22—22no—
200C22—42no—
201C22—42no—
202C22C22×C4×D23911yescharacteristic
203C22#2144000512yes—
204C22#2144000611yescharacteristic
205C22#2144000712yes—
206C22#2144000711yescharacteristic
207C4—22no—
208C4—22no—
209C4—42no—
210C4—42no—
211C4—9562no—
212C4—9562no—
213C4—4784no—
214C4—4784no—
215C2—42no—
216C2#2950524511yescharacteristic
217C2#2950524911yescharacteristic
218C2#2950525211yescharacteristic
219C2#2950551912yes—
220C2#2950552512yes—
subgroupG/H
center, FrattiniC23C23×D239
commutatorC22×C239C23×C4
Fitting#381×C239C2
socle, cosocleC23×C239C24
prime radicalC24×C239C23
hypercenter#381D239
hypocenterC239#2378
LCSG ▷ C22×C239 ▷ C239
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. #29504676C2semidirect
3. #29504669C2semidirect
6. #29504659C2semidirect
7. #29504657C2semidirect
11. #21439939C4semidirect
110. C239#2378semidirect

Maximal subgroups

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

subgroupindex
C2×#214399392
#295046762
#295046692
#295046662
#295046602
#295046592
#295046572
#295046322
#381×C2392
#2378239