Finite Group Databasebeta

← #49174929

Subgroups — #49174929

Order 37504.

312 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 70 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#34037132C211yesmaximal, characteristic, complemented
2C2×#22627685C212yesmaximal, complemented
3C2×#22627684C212yesmaximal
4C4×#17989811C211yesmaximal, characteristic, complemented
5C2×#22627610C211yesmaximal, characteristic
6C2×#17989811C2212yes—
7C2×#17989811C2212yes—
8#22627691—21no—
9C4⋊#14556880—21no—
10#22627685—24no—
11#22627684—24no—
12#22627679—21no—
13C4×#14556880—21no—
14C22×Dic586C2211yescharacteristic
15C22×C22⋊D293C2211yescharacteristic
16#22627610—21no—
17#22627610—21no—
18#22627610—21no—
19#22627610—21no—
20C2×C22⋊Dic293C411yescharacteristic
21C2×#17989779C411yescharacteristic
22C2×#17989779C411yescharacteristic
23C2×C4×Dic293C2211yescharacteristic
24C2×C22⋊C4×C293C411yescharacteristic
25#17989811—22no—
26#17989811—22no—
27#17989811—22no—
28#17989811D414yes—
29C2×#14556880—22no—
30C2×#14556880—22no—
31C23×D293C2×C411yescharacteristic
32C2×Dic586—21no—
33C2×Dic586—21no—
34C2×Dic586—22no—
35C2×Dic586—22no—
36C2×C22⋊D293—21no—
37C2×C22⋊D293—21no—
38C2×C22⋊D293—22no—
39C2×C22⋊D293—22no—
40C22×Dic293C2×C411yescharacteristic
41C22×Dic293C2×C411yescharacteristic
42C22×Dic293C2311yescharacteristic
43C22⋊Dic293—21no—
44C22⋊Dic293—21no—
45#17989779—21no—
46#17989779—21no—
47#17989779—21no—
48#17989779—21no—
49C4×Dic293D411yescharacteristic
50C4×Dic293D411yescharacteristic
51C4×Dic293D411yescharacteristic
52C4×Dic293D411yescharacteristic
53C24×C293C2×C411yescharacteristic
54C22×C4×C293C2×C411yescharacteristic
55C22×C4×C293C2×C411yescharacteristic
56C22⋊C4×C293—21no—
57C22⋊C4×C293—21no—
58#14556880—24no—
59#14556880—42no—
60C22×D293—21no—
61C22×D293—22no—
62C22×D293—41no—
63C22×D293—41no—
64Dic586—42no—
65Dic586—41no—
66Dic586—41no—
67C22⋊D293—42no—
68C22⋊D293—41no—
69C22⋊D293—41no—
70C2×Dic293—21no—
71C2×Dic293—22no—
72C2×Dic293—41no—
73C2×Dic293C22⋊C411yescharacteristic
74C2×Dic293C22⋊C411yescharacteristic
75C2×Dic293C2×D411yescharacteristic
76C2×Dic293C2×D412yes—
77C2×Dic293C2×D411yescharacteristic
78C2×Dic293#4112yes—
79C23×C293—21no—
80C23×C293—22no—
81C23×C293—41no—
82C23×C293—41no—
83C23×C293C22×C411yescharacteristic
84C2×C4×C293—21no—
85C2×C4×C293—22no—
86C2×C4×C293—41no—
87C2×C4×C293C22⋊C411yescharacteristic
88C2×C4×C293C22⋊C411yescharacteristic
89C22×C293—21no—
90C22×C293—21no—
91C22×C293—41no—
92C22×C293—41no—
93C22×C293—41no—
94C22×C293—82no—
95C22×C293C2×C22⋊C411yescharacteristic
96C22×C293C4×D412yes—
97C2×D293—41no—
98C2×D293—41no—
99C2×D293—41no—
100C2×D293—82no—
101C4×C293—21no—
102C4×C293—21no—
103C4×C293—41no—
104Dic293—21no—
105Dic293—21no—
106Dic293—41no—
107Dic293#12112yes—
108Dic293#12411yescharacteristic
109Dic293#12711yescharacteristic
110C2×C293—22no—
111C2×C293—81no—
112C2×C293#39011yescharacteristic
113C2×C293#41311yescharacteristic
114C2×C293#41311yescharacteristic
115D293—81no—
116C293#196711yescharacteristic, complemented, Sylow
117#1967—2931nomaximal, Sylow
118C2×#124—2931no—
119#423—2931no—
120C2×#101—2932no—
121C2×#100—2932no—
122C4×M16—2931no—
123C22×Q8—2931no—
124C22×D4—2931no—
125C2×M16—2932no—
126C2×M16—2932no—
127#124—5861no—
128#124—5861no—
129#124—5861no—
130#124—5861no—
131C2×C22⋊C4—2931no—
132C2×C22⋊C4—2931no—
133C2×C22⋊C4—2931no—
134C2×C22⋊C4#1192407811yescharacteristic
135C2×C42—2931no—
136C4⋊C8—5861no—
137C4⋊C8—5861no—
138#101—5864no—
139#100—5864no—
140#97—5861no—
141C4×C8—5861no—
142C24—2931no—
143C24C2×#1192407811yescharacteristic
144C2×Q8—5862no—
145C2×Q8—5861no—
146C2×Q8—5861no—
147C2×Q8—5862no—
148C2×D4—5862no—
149C2×D4—5861no—
150C2×D4—5861no—
151C2×D4—5862no—
152C22×C4—2931no—
153C22×C4—2931no—
154C22×C4—2931no—
155C22×C4C2×#1192407811yescharacteristic
156C22×C4C2×#1192407811yescharacteristic
157M16—2934no—
158M16—5862no—
159M16—5862no—
160M16—5862no—
161C2×C8—5862no—
162C2×C8—5862no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—5861no—
166C22⋊C4—5861no—
167C22⋊C4—5861no—
168C22⋊C4—5861no—
169C22⋊C4—5861no—
170C22⋊C4—5861no—
171C42—2931no—
172C42—2931no—
173C42—2931no—
174C42—2931no—
175C23—21no—
176C23—22no—
177C23—41no—
178C23—41no—
179C23—5862no—
180C23—5861no—
181C23—11721no—
182C23—11721no—
183C23C22×#1192407811yescharacteristic
184Q8—11722no—
185Q8—11721no—
186Q8—11721no—
187D4—11722no—
188D4—11721no—
189D4—11721no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—41no—
193C2×C4—2931no—
194C2×C4—2931no—
195C2×C4—2932no—
196C2×C4—2932no—
197C2×C4—2931no—
198C2×C4—2931no—
199C2×C4—5861no—
200C2×C4—5862no—
201C2×C4—11721no—
202C2×C4C22⋊#1192407811yescharacteristic
203C2×C4C22⋊#1192407811yescharacteristic
204C8—5864no—
205C8—11722no—
206C22—21no—
207C22—21no—
208C22—41no—
209C22—41no—
210C22—41no—
211C22—82no—
212C22—23442no—
213C22—11721no—
214C22—11721no—
215C22—11721no—
216C22C2×C22⋊#1192407811yescharacteristic
217C22D4×#1192407812yes—
218C4—21no—
219C4—21no—
220C4—41no—
221C4—2932no—
222C4—2931no—
223C4—2931no—
224C4—5861no—
225C4—5861no—
226C4—11721no—
227C2—22no—
228C2—81no—
229C2—23441no—
230C2#3403708111yescharacteristic
231C2#3403711511yescharacteristic
232C2#3403711611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC23×C293C22×C4
FrattiniC23C22×#11924078
FittingC2×C22⋊C4×C293C4
socleC22×C293C2×C22⋊C4
prime radicalC22×C22⋊D293C22
cosocleC22×Dic293C23
hypercenterC2×C22⋊C4#11924078
hypocenterC293#1967
LCSG ▷ C23×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #34037132C2semidirect
2. C2×#22627685C2semidirect
4. C4×#17989811C2semidirect
116. C293#1967semidirect

Maximal subgroups

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

subgroupindex
#340371322
C2×#226276852
C2×#226276842
C4×#179898112
C2×#226276102
#1967293