Finite Group Databasebeta

← #49174185

Subgroups — #49174185

Order 37504.

294 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 64 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
2C4×C22⋊#11924078C211yesmaximal, characteristic
3#34036983C214yesmaximal, complemented
4C2×#22627600C211yesmaximal, characteristic
5C2×#17989812—21no—
6C2×C22⋊#11924078—21no—
7C2×C4×#11924078—21no—
8#22627681C2212yes—
9C22⋊#14556880—21no—
10(C2×#11924078)⋊C4C2212yes—
11C22×C4×D293C2211yescharacteristic
12#22627600—21no—
13#22627600—21no—
14#22627600C412yescomplemented
15#22627600C2212yes—
16C2×C4⋊Dic293C411yescharacteristic, complemented
17C2×#17989781—21no—
18C2×#17989779—21no—
19C22×Q8×C293C411yescharacteristic, complemented
20C22×#11924078—22no—
21#17989812—42no—
22C2×#14556880—22no—
23C22⋊#11924078—24no—
24C4×#11924078—42no—
25C23×D293D411yescharacteristic
26C22×Dic293—21no—
27C22×Dic293D411yescharacteristic
28C2×C4×D293—42no—
29C2×C4×D293C2×C411yescharacteristic
30C2×C4×D293D411yescharacteristic
31C2×C4×D293D411yescharacteristic
32C2×C4×D293C2311yescharacteristic
33C4⋊Dic293—21no—
34C4⋊Dic293C2×C412yes—
35#17989781—22no—
36#17989781—22no—
37#17989779—22no—
38#17989779—22no—
39C2×Q8×C293—21no—
40C2×Q8×C293—42no—
41C2×Q8×C293C2×C412yes—
42C22×C4×C293—21no—
43C22×C4×C293C2×C411yescharacteristic
44C2×#11924078—24no—
45C2×#11924078—42no—
46C2×#11924078—42no—
47#14556880—42no—
48C22×D293—22no—
49C22×D293—22no—
50C22×D293—41no—
51C22×D293C22⋊C411yescharacteristic
52C22×D293C2×D411yescharacteristic
53C2×Dic293—22no—
54C2×Dic293—41no—
55C2×Dic293—42no—
56C2×Dic293C22⋊C411yescharacteristic
57C2×Dic293C2×D411yescharacteristic
58C4×D293—22no—
59C4×D293—22no—
60C4×D293—41no—
61C4×D293—41no—
62C23×C293C22⋊C411yescharacteristic
63Q8×C293—42no—
64Q8×C293—42no—
65C2×C4×C293—22no—
66C2×C4×C293—22no—
67C2×C4×C293—42no—
68C2×C4×C293C22⋊C411yescharacteristic
69C2×C4×C293C22×C411yescharacteristic
70C22×C293—21no—
71C22×C293—21no—
72C22×C293#10412yes—
73C22×C293C2×C22⋊C411yescharacteristic
74C2×D293—21no—
75C2×D293—21no—
76C2×D293—21no—
77C2×D293—21no—
78C2×D293—21no—
79C2×D293—44no—
80C2×D293#13712yes—
81#11924078—44no—
82C4×C293—21no—
83C4×C293—42no—
84C4×C293#9912yes—
85Dic293—21no—
86Dic293—21no—
87Dic293—42no—
88C2×C293—22no—
89C2×C293C2×#9911yescharacteristic
90C2×C293#41911yescharacteristic
91C2×C293C2×#10411yescharacteristic
92D293—22no—
93D293—41no—
94C293#150811yescharacteristic, complemented, Sylow
95#1508—2931nomaximal, Sylow
96C2×C22⋊Q8—2931no—
97#407—2931no—
98C4×C22⋊C4—2931no—
99#328—2934no—
100C22×Q8#1192407811yescharacteristic, complemented
101C23×C4—2931no—
102C2×M16—5861no—
103C22⋊Q8—2932no—
104C22⋊Q8—2932no—
105C22⋊Q8—5861no—
106C22⋊Q8—5861no—
107C2×C4⋊C4—2931no—
108C2×C4⋊C4—5861no—
109C2×C22⋊C4—5861no—
110C2×C22⋊C4—5861no—
111C2×C42—5861no—
112C22⋊C8—2932no—
113C22⋊C8—5861no—
114#95—2932no—
115C24—2931no—
116C2×Q8—21no—
117C2×Q8—42no—
118C2×Q8C2×#1192407812yes—
119C22×C4—21no—
120C22×C4—2931no—
121C22×C4—2931no—
122C22×C4—2931no—
123C22×C4—2931no—
124C22×C4—2931no—
125C22×C4—5862no—
126C22×C4—5861no—
127C22×C4—11722no—
128C22×C4C2×#1192407811yescharacteristic
129M16—11722no—
130C2×C8—5862no—
131C4⋊C4—2932no—
132C4⋊C4—5862no—
133C4⋊C4—5862no—
134C4⋊C4—5861no—
135C22⋊C4—5862no—
136C22⋊C4—5862no—
137C22⋊C4—5864no—
138C42—11722no—
139C23—2931no—
140C23—2931no—
141C23—5862no—
142C23—5862no—
143C23—11721no—
144C23C22⋊#1192407811yescharacteristic
145Q8—42no—
146Q8—42no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—42no—
150C2×C4—2931no—
151C2×C4—2931no—
152C2×C4—5862no—
153C2×C4—5862no—
154C2×C4—5864no—
155C2×C4—5862no—
156C2×C4—11721no—
157C2×C4—11721no—
158C2×C4—11721no—
159C2×C4—11722no—
160C2×C4—11722no—
161C2×C4—11722no—
162C2×C4C22⋊#1192407811yescharacteristic
163C2×C4C22×#1192407811yescharacteristic
164C8—11722no—
165C22—21no—
166C22—21no—
167C22—2932no—
168C22—5861no—
169C22—5861no—
170C22—5861no—
171C22—5861no—
172C22—5861no—
173C22—11724no—
174C22#2262768912yes—
175C22C2×C22⋊#1192407811yescharacteristic
176C4—21no—
177C4—42no—
178C4—5861no—
179C4—5861no—
180C4—11724no—
181C4—11722no—
182C4#2262768212yes—
183C2—22no—
184C2—5862no—
185C2—11721no—
186C2C2×#2262768211yescharacteristic
187C2#3403712211yescharacteristic
188C2C2×#2262768911yescharacteristic
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#1508
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
14. #22627600C4semidirect
16. C2×C4⋊Dic293C4semidirect
19. C22×Q8×C293C4semidirect
94. C293#1508semidirect
100. C22×Q8#11924078semidirect

Maximal subgroups

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

subgroupindex
#340371002
C4×C22⋊#119240782
#340369832
C2×#226276002
#1508293