Finite Group Databasebeta

← #49174930

Subgroups — #49174930

Order 37504.

348 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 82 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×#22627692C211yesmaximal, characteristic, complemented
2C2×#22627687C211yesmaximal, characteristic, complemented
3C2×#22627686C211yesmaximal, characteristic
4C2×C8×#11924078C211yesmaximal, characteristic, complemented
5(C2×#11924078)⋊Q8C211yesmaximal, characteristic, complemented
6#34037081C211yesmaximal, characteristic
7C2×SD16×D293C211yesmaximal, characteristic
8C2×D293⋊C8C2211yescharacteristic
9C2×C4⋊#11924078C2211yescharacteristic
10C2×C4⋊#11924078C2211yescharacteristic
11C2×C22⋊#11924078—22no—
12C2×C4×#11924078C2211yescharacteristic
13#22627692—22no—
14#22627687—22no—
15#22627686—22no—
16C8×#11924078—22no—
17(C2×#11924078)⋊C4—22no—
18C2×Q8×D293C2211yescharacteristic
19C2×D4×D293C2211yescharacteristic
20C2×#17989791C411yescharacteristic, complemented
21C2×#17989790C411yescharacteristic, complemented
22C2×#17989789C411yescharacteristic, complemented
23SD16×D293—22no—
24SD16×D293—22no—
25C2×C8×D293C2211yescharacteristic
26C2×SD16×C293C411yescharacteristic, complemented
27C22×#11924078—21no—
28C22×#11924078—21no—
29C22×#11924078D412yes—
30D293⋊C8—21no—
31D293⋊C8D412yes—
32C2×#14556880—21no—
33C4⋊#11924078—21no—
34C4⋊#11924078—21no—
35C4⋊#11924078—21no—
36C4⋊#11924078—21no—
37C22⋊#11924078—44no—
38C4×#11924078—21no—
39C4×#11924078—21no—
40C23×D293—21no—
41C2×Dic586—21no—
42C2×Dic586C2×C411yescharacteristic
43Q8×D293—21no—
44Q8×D293—21no—
45Q8×D293—21no—
46Q8×D293—21no—
47C2×D1172C2×C411yescharacteristic
48C2×C22⋊D293—21no—
49D4×D293—21no—
50D4×D293—21no—
51D4×D293—21no—
52D4×D293—21no—
53C2×C4×D293—21no—
54C2×C4×D293C2311yescharacteristic
55#17989791—22no—
56#17989790—22no—
57#17989789—22no—
58C2×#14556873C2×C411yescharacteristic
59C8×D293D412yes—
60C8×D293D412yes—
61C2×Q8×C293C2×C411yescharacteristic
62C2×D4×C293C2×C411yescharacteristic
63SD16×C293—22no—
64C2×C8×C293C2×C411yescharacteristic
65C2×#11924078—22no—
66C2×#11924078—22no—
67C2×#11924078—41no—
68C2×#11924078—41no—
69C2×#11924078—42no—
70C2×#11924078—42no—
71C2×#11924078SD1614yescomplemented
72#14556880—22no—
73C22×D293—21no—
74C22×D293—41no—
75C22×D293—41no—
76C22×D293—42no—
77C22×D293—42no—
78C22×D293C2×D411yescharacteristic
79Dic586—21no—
80Dic586—21no—
81Dic586—41no—
82Dic586—41no—
83D1172—21no—
84D1172—21no—
85C22⋊D293—41no—
86C22⋊D293—41no—
87C2×Dic293—21no—
88C2×Dic293#4111yescharacteristic
89C4×D293—41no—
90C4×D293—41no—
91C4×D293C2×D411yescharacteristic
92C4×D293C2×D411yescharacteristic
93C4×D293C2×D411yescharacteristic
94C4×D293#4111yescharacteristic
95#14556873C22⋊C412yescomplemented
96C23×C293—21no—
97Q8×C293—21no—
98Q8×C293—21no—
99D4×C293—21no—
100D4×C293—21no—
101C2×C4×C293—21no—
102C2×C4×C293C22×C411yescharacteristic
103C8×C293C22⋊C412yescomplemented
104C22×C293—41no—
105C22×C293—42no—
106C22×C293C4×D411yescharacteristic
107C2×D293—41no—
108C2×D293—42no—
109C2×D293—82no—
110C2×D293—81no—
111C2×D293—81no—
112C2×D293#12111yescharacteristic
113C2×D293#12711yescharacteristic
114C2×D293C2×SD1612yes—
115C2×D293#13512yes—
116#11924078—24no—
117#11924078—81no—
118#11924078—81no—
119C4×C293—41no—
120C4×C293C2×C22⋊C411yescharacteristic
121C4×C293C4×D411yescharacteristic
122Dic293—41no—
123Dic293#12111yescharacteristic
124Dic293#12411yescharacteristic
125C2×C293—81no—
126C2×C293#39011yescharacteristic
127C2×C293C4×SD1612yes—
128D293—81no—
129D293#46512yes—
130D293#49211yescharacteristic
131D293#49511yescharacteristic
132C293#196811yescharacteristic, complemented, Sylow
133#1968—2931nomaximal, Sylow
134C22×SD16—2931no—
135C2×#106—2931no—
136C2×#103—2931no—
137C2×#102—2931no—
138C2×C4×C8—2931no—
139#391—2931no—
140#390—2931no—
141C22×Q8—2931no—
142C22×D4—2931no—
143C2×SD16—2931no—
144C2×SD16—2931no—
145C2×SD16—2931no—
146C2×SD16—5862no—
147C2×SD16—5862no—
148C2×SD16#1192407811yescharacteristic, complemented
149C22×C8—2931no—
150C22×C8—2931no—
151C2×C4⋊C4—2931no—
152C2×C4⋊C4—2931no—
153C2×C22⋊C4—5862no—
154C2×C42—2931no—
155#106—5862no—
156#103—5862no—
157#102—5862no—
158C4×C8—5862no—
159#95—5862no—
160C24—5861no—
161C2×Q8—2931no—
162C2×Q8—5861no—
163C2×Q8—5861no—
164C2×Q8—5861no—
165C2×Q8—5861no—
166C2×Q8—5861no—
167C2×Q8C2×#1192407811yescharacteristic
168C2×D4—2931no—
169C2×D4—5861no—
170C2×D4—5861no—
171C2×D4—5861no—
172C2×D4—5861no—
173C2×D4—5861no—
174C2×D4C2×#1192407811yescharacteristic
175C22×C4—2931no—
176C22×C4—2932no—
177C22×C4—5861no—
178C22×C4—5861no—
179C22×C4—5861no—
180SD16—22no—
181SD16—5862no—
182SD16—5862no—
183SD16—5862no—
184C2×C8—2931no—
185C2×C8—2932no—
186C2×C8—2932no—
187C2×C8—2932no—
188C2×C8—5861no—
189C2×C8—5861no—
190C2×C8C2×#1192407811yescharacteristic
191C4⋊C4—5861no—
192C4⋊C4—5861no—
193C4⋊C4—5861no—
194C4⋊C4—5861no—
195C22⋊C4—11724no—
196C42—5861no—
197C42—5861no—
198C23—21no—
199C23—2931no—
200C23—5861no—
201C23—11722no—
202C23—11721no—
203C23—11721no—
204C23—11722no—
205Q8—21no—
206Q8—21no—
207Q8—5861no—
208Q8—5861no—
209Q8—11721no—
210Q8—11721no—
211D4—21no—
212D4—21no—
213D4—5861no—
214D4—5861no—
215D4—11721no—
216D4—11721no—
217C2×C4—21no—
218C2×C4—2931no—
219C2×C4—2931no—
220C2×C4—2931no—
221C2×C4—2931no—
222C2×C4—2931no—
223C2×C4—2934no—
224C2×C4—5862no—
225C2×C4—5862no—
226C2×C4—5861no—
227C2×C4—11721no—
228C2×C4—11721no—
229C2×C4—11722no—
230C2×C4—11721no—
231C2×C4—11721no—
232C2×C4—11722no—
233C2×C4C22×#1192407811yescharacteristic
234C8—2932no—
235C8—5862no—
236C8C22⋊#1192407812yescomplemented
237C22—41no—
238C22—42no—
239C22—2931no—
240C22—2931no—
241C22—2932no—
242C22—2932no—
243C22—23441no—
244C22—23441no—
245C22—23442no—
246C22—11721no—
247C22—11722no—
248C22D4×#1192407811yescharacteristic
249C4—41no—
250C4—2931no—
251C4—2931no—
252C4—23441no—
253C4—23441no—
254C4—5864no—
255C4—11721no—
256C4C2×C22⋊#1192407811yescharacteristic
257C4D4×#1192407811yescharacteristic
258C2—81no—
259C2—2931no—
260C2—2931no—
261C2—2932no—
262C2—23441no—
263C2#3403708111yescharacteristic
264C2SD16×#1192407812yes—
subgroupG/H
centerC22D4×#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
FittingC2×SD16×C293C4
socleC22×C293C4×D4
prime radicalC2×D4×D293C22
cosocleC2×C4×D293C23
hypercenterC2×SD16#11924078
hypocenterC293#1968
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#22627692C2semidirect
2. C2×#22627687C2semidirect
4. C2×C8×#11924078C2semidirect
5. (C2×#11924078)⋊Q8C2semidirect
20. C2×#17989791C4semidirect
21. C2×#17989790C4semidirect
22. C2×#17989789C4semidirect
26. C2×SD16×C293C4semidirect
71. C2×#11924078SD16semidirect
95. #14556873C22⋊C4semidirect
103. C8×C293C22⋊C4semidirect
132. C293#1968semidirect
148. C2×SD16#11924078semidirect
236. C8C22⋊#11924078semidirect

Maximal subgroups

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

subgroupindex
C2×#226276922
C2×#226276872
C2×#226276862
C2×C8×#119240782
(C2×#11924078)⋊Q82
#340370812
C2×SD16×D2932
#1968293