Finite Group Databasebeta

← #49174194

Subgroups — #49174194

Order 37504.

274 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 58 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#34037100C211yesmaximal, characteristic
2#34037072C211yesmaximal, characteristic
3#34036983C212yesmaximal, complemented
4#34036982C212yesmaximal, complemented
5C22⋊Q8×D293C211yesmaximal, characteristic
6C2×#17989812—21no—
7C2×C22⋊#11924078—21no—
8#22627681C2212yes—
9C22⋊#14556880—21no—
10(C2×#11924078)⋊C4—21no—
11(C2×#11924078)⋊C4C2212yes—
12C2×Q8×D293C411yescharacteristic, complemented
13C22×C4×D293C2211yescharacteristic
14#22627604C2211yescharacteristic
15#22627603C411yescharacteristic, complemented
16#22627602—21no—
17#22627601—21no—
18#22627600C2211yescharacteristic
19C4⋊C4×D293—21no—
20C4⋊C4×D293C411yescharacteristic, complemented
21C22⋊C4×D293—21no—
22C22⋊Q8×C293C411yescharacteristic, complemented
23C22×#11924078—22no—
24#17989812—42no—
25C2×#14556880—22no—
26C22⋊#11924078—42no—
27C23×D293D411yescharacteristic
28C2×Dic586—21no—
29C2×Dic586C2×C411yescharacteristic
30Q8×D293—42no—
31C22×Dic293D411yescharacteristic
32C2×C4×D293—21no—
33C2×C4×D293—21no—
34C2×C4×D293—42no—
35C2×C4×D293C2×C411yescharacteristic
36C2×C4×D293D411yescharacteristic
37C2×C4×D293D411yescharacteristic
38C2×C4×D293C2311yescharacteristic
39C4⋊Dic293—21no—
40C4⋊Dic293C2×C411yescharacteristic
41#17989781—21no—
42#17989781—21no—
43#17989781—21no—
44C22⋊Dic293—21no—
45#17989779—21no—
46#17989779—21no—
47C2×Q8×C293C2×C411yescharacteristic
48C22×C4×C293C2×C411yescharacteristic
49C4⋊C4×C293—21no—
50C4⋊C4×C293C2×C411yescharacteristic
51C22⋊C4×C293—21no—
52C2×#11924078—42no—
53C2×#11924078—42no—
54C2×#11924078—42no—
55#14556880—42no—
56C22×D293—22no—
57C22×D293—22no—
58C22×D293—41no—
59C22×D293C22⋊C411yescharacteristic
60C22×D293C2×D411yescharacteristic
61Dic586—42no—
62Dic586—41no—
63C2×Dic293—21no—
64C2×Dic293—21no—
65C2×Dic293—41no—
66C2×Dic293C22⋊C411yescharacteristic
67C2×Dic293C2×D411yescharacteristic
68C4×D293—22no—
69C4×D293—22no—
70C4×D293—41no—
71C4×D293—41no—
72C4×D293—42no—
73C4×D293—42no—
74C23×C293C22⋊C411yescharacteristic
75Q8×C293—41no—
76C2×C4×C293—21no—
77C2×C4×C293—21no—
78C2×C4×C293—41no—
79C2×C4×C293C22⋊C411yescharacteristic
80C2×C4×C293C22×C411yescharacteristic
81C22×C293—21no—
82C22×C293—21no—
83C22×C293—21no—
84C22×C293C2×C22⋊C411yescharacteristic
85C2×D293—21no—
86C2×D293—21no—
87C2×D293—21no—
88C2×D293—21no—
89C2×D293—44no—
90C2×D293#9912yes—
91C2×D293#13712yes—
92#11924078—82no—
93C4×C293—21no—
94C4×C293—21no—
95C4×C293—41no—
96C4×C293—41no—
97Dic293—21no—
98Dic293—21no—
99Dic293—41no—
100Dic293—41no—
101C2×C293—41no—
102C2×C293C2×#9911yescharacteristic
103C2×C293#41911yescharacteristic
104C2×C293#42111yescharacteristic
105D293—22no—
106D293—22no—
107C293#151111yescharacteristic, complemented, Sylow
108#1511—2931nomaximal, Sylow
109C2×C22⋊Q8—2931no—
110#407—2931no—
111#381—2931no—
112#328—2932no—
113#328—2932no—
114C22×Q8—2931no—
115C23×C4—2931no—
116C2×M16—5861no—
117C22⋊Q8—2931no—
118C22⋊Q8—2931no—
119C22⋊Q8—2931no—
120C22⋊Q8—5861no—
121C22⋊Q8—5861no—
122C22⋊Q8#1192407811yescharacteristic, complemented
123C2×C4⋊C4—2931no—
124C2×C4⋊C4—5861no—
125C2×C22⋊C4—5861no—
126C2×C22⋊C4—5861no—
127C22⋊C8—2932no—
128C22⋊C8—5861no—
129#95—2932no—
130#95—5861no—
131C24—2931no—
132C2×Q8—2931no—
133C2×Q8—5861no—
134C2×Q8—11722no—
135C2×Q8C2×#1192407811yescharacteristic
136C22×C4—2931no—
137C22×C4—2931no—
138C22×C4—2931no—
139C22×C4—2931no—
140C22×C4—2931no—
141C22×C4—5861no—
142C22×C4—5861no—
143C22×C4—5862no—
144C22×C4—11722no—
145C22×C4C2×#1192407811yescharacteristic
146M16—11722no—
147C2×C8—5862no—
148C4⋊C4—21no—
149C4⋊C4—2931no—
150C4⋊C4—5861no—
151C4⋊C4—5861no—
152C4⋊C4—5861no—
153C4⋊C4—5861no—
154C4⋊C4C2×#1192407811yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—5861no—
157C22⋊C4—5861no—
158C22⋊C4—5861no—
159C22⋊C4—11722no—
160C23—2931no—
161C23—2931no—
162C23—5862no—
163C23—5862no—
164C23—11721no—
165C23C22⋊#1192407811yescharacteristic
166Q8—41no—
167Q8—11721no—
168Q8—11722no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—2931no—
173C2×C4—2931no—
174C2×C4—5862no—
175C2×C4—5862no—
176C2×C4—5861no—
177C2×C4—5861no—
178C2×C4—11721no—
179C2×C4—11721no—
180C2×C4—11722no—
181C2×C4—11722no—
182C2×C4—11722no—
183C2×C4—11722no—
184C2×C4—11722no—
185C2×C4—11721no—
186C2×C4C22⋊#1192407811yescharacteristic
187C2×C4C22×#1192407811yescharacteristic
188C8—11722no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—2932no—
193C22—2932no—
194C22—5861no—
195C22—5861no—
196C22—5861no—
197C22—5861no—
198C22—11724no—
199C22C2×C22⋊#1192407811yescharacteristic
200C4—21no—
201C4—21no—
202C4—41no—
203C4—41no—
204C4—23442no—
205C4—5861no—
206C4—5861no—
207C4—11721no—
208C4—11721no—
209C2—41no—
210C2—5862no—
211C2—5862no—
212C2D293⋊#9911yescharacteristic
213C2#3403712211yescharacteristic
214C2#3403712611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
FittingC22⋊Q8×C293C4
socleC22×C293C2×C22⋊C4
prime radicalC23×D293D4
cosocleC2×C4×D293C23
hypercenterC22⋊Q8#11924078
hypocenterC293#1511
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #34036983C2semidirect
4. #34036982C2semidirect
12. C2×Q8×D293C4semidirect
15. #22627603C4semidirect
20. C4⋊C4×D293C4semidirect
22. C22⋊Q8×C293C4semidirect
107. C293#1511semidirect
122. C22⋊Q8#11924078semidirect

Maximal subgroups

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

subgroupindex
#340371002
#340370722
#340369832
#340369822
C22⋊Q8×D2932
#1511293