Finite Group Databasebeta

← #49174212

Subgroups — #49174212

Order 37504.

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

normal subgroups only

This group has 284 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
1D293⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
2#34037072C211yesmaximal, characteristic, complemented
3#34036983C212yesmaximal, complemented
4#34036981C212yesmaximal, complemented
5#34036642C211yesmaximal, characteristic
6C2×D293⋊C8—21no—
7C2×C22⋊#11924078—21no—
8#22627681C2212yes—
9C22⋊#14556880—21no—
10(C2×#11924078)⋊C4—21no—
11(C2×#11924078)⋊C4C2212yes—
12C2×#17989803C411yescharacteristic, complemented
13C22×C4×D293C2211yescharacteristic
14#22627609—21no—
15#22627600C2211yescharacteristic
16#22627599C2211yescharacteristic
17#22627598C411yescharacteristic, complemented
18#22627594—21no—
19#22627586—21no—
20#22627584—21no—
21#22627582C411yescharacteristic, complemented
22C22⋊Q8×C293C411yescharacteristic, complemented
23C22×#11924078—22no—
24D293⋊C8—42no—
25C2×#14556880—22no—
26C22⋊#11924078—42no—
27C23×D293D411yescharacteristic
28#17989803—42no—
29C2×D1172—21no—
30C2×D1172—21no—
31C2×D1172C2×C411yescharacteristic
32C2×C22⋊D293—21no—
33C22×Dic293D411yescharacteristic
34C2×C4×D293—21no—
35C2×C4×D293—42no—
36C2×C4×D293C2×C411yescharacteristic
37C2×C4×D293D411yescharacteristic
38C2×C4×D293D411yescharacteristic
39C2×C4×D293C2311yescharacteristic
40C4⋊Dic293C2×C411yescharacteristic
41#17989781—21no—
42#17989779—21no—
43#17989779—21no—
44#17989779—21no—
45#17989779—21no—
46C4×Dic293—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—21no—
59C22×D293—41no—
60C22×D293C22⋊C411yescharacteristic
61C22×D293C2×D411yescharacteristic
62D1172—41no—
63D1172—42no—
64D1172—42no—
65C22⋊D293—42no—
66C2×Dic293—21no—
67C2×Dic293—41no—
68C2×Dic293C22⋊C411yescharacteristic
69C2×Dic293C2×D411yescharacteristic
70C4×D293—22no—
71C4×D293—22no—
72C4×D293—41no—
73C4×D293—41no—
74C4×D293—42no—
75C23×C293C22⋊C411yescharacteristic
76Q8×C293—41no—
77C2×C4×C293—21no—
78C2×C4×C293—21no—
79C2×C4×C293—41no—
80C2×C4×C293C22⋊C411yescharacteristic
81C2×C4×C293C22×C411yescharacteristic
82C22×C293—21no—
83C22×C293—21no—
84C22×C293—21no—
85C22×C293C2×C22⋊C411yescharacteristic
86C2×D293—21no—
87C2×D293—21no—
88C2×D293—21no—
89C2×D293—21no—
90C2×D293—44no—
91C2×D293—41no—
92C2×D293—41no—
93C2×D293—41no—
94C2×D293#9912yes—
95C2×D293#13512yes—
96#11924078—82no—
97C4×C293—21no—
98C4×C293—21no—
99C4×C293—41no—
100C4×C293—41no—
101Dic293—21no—
102Dic293—21no—
103Dic293—41no—
104C2×C293—41no—
105C2×C293C2×#9911yescharacteristic
106C2×C293#41611yescharacteristic
107C2×C293#42111yescharacteristic
108D293—22no—
109D293—22no—
110D293—81no—
111C293#151611yescharacteristic, complemented, Sylow
112#1516—2931nomaximal, Sylow
113#525—2931no—
114C2×C22⋊C8—2931no—
115#381—2931no—
116#328—2932no—
117#327—2932no—
118C2×#41—2931no—
119C23×C4—2931no—
120C22×C8—5861no—
121#123—5861no—
122C22⋊Q8—2931no—
123C22⋊Q8#1192407811yescharacteristic, complemented
124#121—2931no—
125#121—2931no—
126#120—5861no—
127C4×D4—5861no—
128C4×D4—5861no—
129#117—2931no—
130C2×C22⋊C4—5861no—
131C22⋊C8—2932no—
132C22⋊C8—5861no—
133#95—2932no—
134#95—5861no—
135C24—2931no—
136#41—11722no—
137C2×Q8C2×#1192407811yescharacteristic
138C2×D4—2931no—
139C2×D4—5861no—
140C2×D4—5861no—
141C2×D4—5861no—
142C22×C4—2931no—
143C22×C4—2931no—
144C22×C4—2931no—
145C22×C4—2931no—
146C22×C4—2931no—
147C22×C4—5861no—
148C22×C4—5862no—
149C22×C4—11722no—
150C22×C4C2×#1192407811yescharacteristic
151C2×C8—5862no—
152C2×C8—11722no—
153C4⋊C4—21no—
154C4⋊C4—2931no—
155C4⋊C4—5861no—
156C4⋊C4C2×#1192407811yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—5861no—
159C22⋊C4—5861no—
160C22⋊C4—5861no—
161C22⋊C4—5861no—
162C22⋊C4—11722no—
163C42—5861no—
164C23—2931no—
165C23—2931no—
166C23—5862no—
167C23—5862no—
168C23—5861no—
169C23—11721no—
170C23C22⋊#1192407811yescharacteristic
171Q8—41no—
172D4—11721no—
173D4—11722no—
174D4—11722no—
175D4—11722no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—2931no—
180C2×C4—2931no—
181C2×C4—5862no—
182C2×C4—5862no—
183C2×C4—5861no—
184C2×C4—11721no—
185C2×C4—11721no—
186C2×C4—11722no—
187C2×C4—11722no—
188C2×C4—11722no—
189C2×C4—11722no—
190C2×C4—11721no—
191C2×C4C22⋊#1192407811yescharacteristic
192C2×C4C22×#1192407811yescharacteristic
193C8—11722no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—2932no—
198C22—2932no—
199C22—5861no—
200C22—5861no—
201C22—5861no—
202C22—5861no—
203C22—11724no—
204C22—11721no—
205C22—11721no—
206C22—11721no—
207C22C2×C22⋊#1192407811yescharacteristic
208C4—21no—
209C4—21no—
210C4—41no—
211C4—41no—
212C4—23442no—
213C4—5861no—
214C4—5861no—
215C4—11721no—
216C2—41no—
217C2—23441no—
218C2—5862no—
219C2—5862no—
220C2D293⋊#9911yescharacteristic
221C2#3403711911yescharacteristic
222C2#3403712811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
FittingC22⋊Q8×C293C4
socleC22×C293C2×C22⋊C4
prime radical#34036642C2
cosocleC2×C4×D293C23
hypercenterC22⋊Q8#11924078
hypocenterC293#1516
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
1. D293⋊(C22⋊C8)C2semidirect
2. #34037072C2semidirect
3. #34036983C2semidirect
4. #34036981C2semidirect
12. C2×#17989803C4semidirect
17. #22627598C4semidirect
21. #22627582C4semidirect
22. C22⋊Q8×C293C4semidirect
111. C293#1516semidirect
123. C22⋊Q8#11924078semidirect

Maximal subgroups

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

subgroupindex
D293⋊(C22⋊C8)2
#340370722
#340369832
#340369812
#340366422
#1516293