Finite Group Databasebeta

← #49161953

Subgroups — #49161953

Order 37504.

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×#22627603C211yesmaximal, characteristic
2#34036033C212yesmaximal, complemented
3#34036026C212yesmaximal, complemented
4#34036023C212yesmaximal
5#34036017C212yesmaximal
6#34036016C212yesmaximal, complemented
7#34036014C212yesmaximal, complemented
8#34035989C211yesmaximal, characteristic
9#381×C293C211yesmaximal, characteristic
10C22×Dic586C2211yescharacteristic
11#22627603C418yescomplemented
12C2×C4⋊Dic293C2212yes—
13C2×C4⋊Dic293C2211yescharacteristic
14C2×#17989781C2212yes—
15C2×#17989781C2212yes—
16C2×#17989781C2212yes—
17C2×C22⋊Dic293C2211yescharacteristic
18C2×C22⋊Dic293C2211yescharacteristic
19C2×C22⋊Dic293C2212yes—
20C2×C4×Dic293C2212yes—
21C2×C4×Dic293C2212yes—
22#22627531C2212yes—
23#22627531C2212yes—
24#22627531C2212yes—
25#22627531C2212yes—
26#22627531C2212yes—
27C23×C4×C293C2211yescharacteristic
28C2×C22⋊C4×C293C2212yes—
29#95×C293C2212yes—
30#95×C293C2211yescharacteristic
31#95×C293C2211yescharacteristic
32C2×Dic586—42no—
33C2×Dic586C2×C414yes—
34C22×Dic293C2312yes—
35C22×Dic293C2312yes—
36C22×Dic293C2312yes—
37C22×Dic293C2312yes—
38C4⋊Dic293—42no—
39C4⋊Dic293C2×C414yes—
40#17989781—42no—
41#17989781—42no—
42#17989781C2×C418yes—
43C22⋊Dic293—41no—
44C22⋊Dic293—41no—
45C22⋊Dic293C2×C418yes—
46C4×Dic293—42no—
47C4×Dic293—42no—
48C24×C293C2311yescharacteristic
49C22×C4×C293—42no—
50C22×C4×C293C2×C414yes—
51C22×C4×C293C2312yes—
52C22×C4×C293C2312yes—
53C22×C4×C293C2311yescharacteristic
54C22×C4×C293C2311yescharacteristic
55C22⋊C4×C293—42no—
56Dic586—44no—
57C2×Dic293—22no—
58C2×Dic293—22no—
59C2×Dic293—22no—
60C2×Dic293—22no—
61C2×Dic293—22no—
62C2×Dic293—22no—
63C2×Dic293—22no—
64C2×Dic293—22no—
65C2×Dic293—22no—
66C2×Dic293—22no—
67C2×Dic293C22×C414yes—
68C2×Dic293C22×C414yes—
69C23×C293—22no—
70C23×C293—21no—
71C23×C293—22no—
72C23×C293—21no—
73C23×C293C22×C412yes—
74C23×C293C2411yescharacteristic
75C2×C4×C293—22no—
76C2×C4×C293—22no—
77C2×C4×C293—22no—
78C2×C4×C293—22no—
79C2×C4×C293—22no—
80C2×C4×C293—22no—
81C2×C4×C293—22no—
82C2×C4×C293—22no—
83C2×C4×C293—44no—
84C2×C4×C293C22×C412yes—
85C2×C4×C293C22×C412yes—
86C22×C293—22no—
87C22×C293—22no—
88C22×C293—22no—
89C22×C293—42no—
90C22×C293—42no—
91C22×C293C23×C411yescharacteristic
92C22×C293H(5,𝔽2)12yes—
93C22×C293H(5,𝔽2)11yescharacteristic
94C22×C2932−1+412yes—
95C22×C2932−1+411yescharacteristic
96C4×C293—22no—
97C4×C293—22no—
98C4×C293—42no—
99C4×C293—42no—
100Dic293—24no—
101Dic293—24no—
102Dic293—42no—
103Dic293—42no—
104C2×C293—42no—
105C2×C293#51811yescharacteristic
106C2×C293#51911yescharacteristic
107C2×C293#52011yescharacteristic
108C2×C293#56212yes—
109C2×C293#56312yes—
110C293#237811yescharacteristic, complemented, Sylow
111#2378—2931nomaximal, Sylow
112C2×C22⋊Q8—2931no—
113#391—2932no—
114#389—2932no—
115#388—2932no—
116#388—2932no—
117#387—2932no—
118#387—2932no—
119#381D29311yescharacteristic
120#380—2931no—
121C22×Q8—2931no—
122C23×C4C2×D29311yescharacteristic
123C22⋊Q8—2938no—
124C2×C4⋊C4—2931no—
125C2×C4⋊C4—2932no—
126C2×C4⋊C4—2932no—
127C2×C4⋊C4—2932no—
128C2×C4⋊C4—2932no—
129C2×C22⋊C4—2932no—
130C2×C22⋊C4—2931no—
131C2×C22⋊C4—2931no—
132C2×C22⋊C4C2×D29312yes—
133C2×C42—2932no—
134C2×C42—2932no—
135#95—2932no—
136#95—2932no—
137#95—2932no—
138#95—2932no—
139#95—2932no—
140#95C2×D29311yescharacteristic
141#95C2×D29312yes—
142#95C2×D29311yescharacteristic
143C24C22×D29311yescharacteristic
144C2×Q8—2934no—
145C2×Q8—11722no—
146C22×C4—42no—
147C22×C4—2932no—
148C22×C4—2932no—
149C22×C4—2932no—
150C22×C4—2932no—
151C22×C4C4×D29314yes—
152C22×C4C22×D29312yes—
153C22×C4C22×D29312yes—
154C22×C4C22×D29311yescharacteristic
155C22×C4C22×D29311yescharacteristic
156C4⋊C4—2938no—
157C4⋊C4—2934no—
158C4⋊C4—11722no—
159C4⋊C4—11722no—
160C4⋊C4—11722no—
161C22⋊C4—42no—
162C22⋊C4—2938no—
163C22⋊C4—11721no—
164C22⋊C4—11721no—
165C42—11722no—
166C42—11722no—
167C23—22no—
168C23—21no—
169C23—22no—
170C23—21no—
171C23C2×C4×D29312yes—
172C23C23×D29311yescharacteristic
173Q8—11724no—
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—2934no—
184C2×C4—2934no—
185C2×C4—5862no—
186C2×C4—5862no—
187C2×C4—5862no—
188C2×C4—5862no—
189C2×C4—5862no—
190C2×C4—5862no—
191C2×C4—5862no—
192C2×C4—5862no—
193C2×C4—5862no—
194C2×C4—5862no—
195C2×C4C2×C4×D29312yes—
196C2×C4C2×C4×D29312yes—
197C22—22no—
198C22—22no—
199C22—22no—
200C22—42no—
201C22—42no—
202C22C22×C4×D29311yescharacteristic
203C22#2262766912yes—
204C22#2262767011yescharacteristic
205C22#2262767112yes—
206C22#2262767111yescharacteristic
207C4—22no—
208C4—22no—
209C4—42no—
210C4—42no—
211C4—5864no—
212C4—5864no—
213C4—11722no—
214C4—11722no—
215C2—42no—
216C2#3403660211yescharacteristic
217C2#3403660611yescharacteristic
218C2#3403660911yescharacteristic
219C2#3403687612yes—
220C2#3403688212yes—
subgroupG/H
center, FrattiniC23C23×D293
commutatorC22×C293C23×C4
Fitting#381×C293C2
socle, cosocleC23×C293C24
prime radicalC24×C293C23
hypercenter#381D293
hypocenterC293#2378
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. #34036033C2semidirect
3. #34036026C2semidirect
6. #34036016C2semidirect
7. #34036014C2semidirect
11. #22627603C4semidirect
110. C293#2378semidirect

Maximal subgroups

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

subgroupindex
C2×#226276032
#340360332
#340360262
#340360232
#340360172
#340360162
#340360142
#340359892
#381×C2932
#2378293