Finite Group Databasebeta

← #49157273

Subgroups — #49157273

Order 37504.

304 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 65 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#34036639C211yesmaximal, characteristic
2C22⋊C8×D293C211yesmaximal, characteristic, complemented
3#34035976C211yesmaximal, characteristic, complemented
4#34035867C211yesmaximal, characteristic, complemented
5#34035865C211yesmaximal, characteristic, complemented
6#34035863C211yesmaximal, characteristic, complemented
7#327×C293C211yesmaximal, characteristic, complemented
8C2×#17989801C411yescharacteristic, complemented
9C22×C4×D293C2211yescharacteristic
10C2×C8×D293—21no—
11#22627606—21no—
12#22627604C411yescharacteristic, complemented
13#22627603C2211yescharacteristic
14#22627595C411yescharacteristic, complemented
15#22627592—21no—
16D4×Dic293—21no—
17#22627584—21no—
18#22627582C411yescharacteristic, complemented
19C2×#17989779—21no—
20C2×C4×Dic293—21no—
21C22⋊#14556873C2211yescharacteristic
22#22627536—21no—
23#22627531C2211yescharacteristic
24#121×C293C2211yescharacteristic
25C22⋊C8×C293C2211yescharacteristic
26#95×C293C2211yescharacteristic
27C23×D293D411yescharacteristic
28#17989801—42no—
29C2×Dic586C2×C411yescharacteristic
30C2×C22⋊D293—21no—
31C2×C22⋊D293—21no—
32C22×Dic293—21no—
33C22×Dic293—21no—
34C22×Dic293D411yescharacteristic
35C2×C4×D293—42no—
36C2×C4×D293C2×C411yescharacteristic
37C2×C4×D293C2×C411yescharacteristic
38C2×C4×D293D411yescharacteristic
39C2×C4×D293D411yescharacteristic
40C2×#14556873—21no—
41C8×D293—42no—
42C4⋊Dic293—21no—
43C4⋊Dic293C2×C411yescharacteristic
44#17989781—21no—
45C22⋊Dic293—21no—
46C22⋊Dic293—21no—
47#17989779—24no—
48#17989779—21no—
49#17989779—21no—
50C4×Dic293—21no—
51C4×Dic293—42no—
52C2×D4×C293—21no—
53C2×D4×C293C2×C411yescharacteristic
54C22×C4×C293—21no—
55C22×C4×C293C2311yescharacteristic
56C2×C8×C293—21no—
57C4⋊C4×C293C2×C411yescharacteristic
58C22⋊C4×C293—21no—
59C22×D293—21no—
60C22×D293—21no—
61C22×D293—22no—
62C22×D293—41no—
63C22×D293C22⋊C411yescharacteristic
64C22×D293C22⋊C411yescharacteristic
65Dic586—41no—
66C22⋊D293—42no—
67C22⋊D293—42no—
68C2×Dic293—22no—
69C2×Dic293—22no—
70C2×Dic293—21no—
71C2×Dic293—21no—
72C2×Dic293—41no—
73C2×Dic293—41no—
74C2×Dic293—42no—
75C2×Dic293C22⋊C411yescharacteristic
76C2×Dic293C22⋊C411yescharacteristic
77C4×D293—22no—
78C4×D293—22no—
79C4×D293—41no—
80C4×D293—41no—
81#14556873—41no—
82C23×C293—21no—
83C23×C293C2×D411yescharacteristic
84D4×C293—41no—
85D4×C293—41no—
86D4×C293—41no—
87C2×C4×C293—22no—
88C2×C4×C293—21no—
89C2×C4×C293—41no—
90C2×C4×C293—41no—
91C2×C4×C293—41no—
92C2×C4×C293C22×C411yescharacteristic
93C2×C4×C293C2×D411yescharacteristic
94C8×C293—41no—
95C22×C293—21no—
96C22×C293—21no—
97C22×C293—41no—
98C22×C293—41no—
99C22×C293—41no—
100C22×C293C2×C22⋊C411yescharacteristic
101C22×C293#13511yescharacteristic
102C22×C293#13511yescharacteristic
103C2×D293—21no—
104C2×D293—21no—
105C2×D293—21no—
106C2×D293—21no—
107C2×D293—21no—
108C2×D293—42no—
109C2×D293—42no—
110C2×D293#10412yes—
111C4×C293—21no—
112C4×C293—21no—
113C4×C293—42no—
114C4×C293—41no—
115Dic293—21no—
116Dic293—42no—
117Dic293—41no—
118Dic293—41no—
119Dic293#9912yes—
120C2×C293—21no—
121C2×C293—21no—
122C2×C293—81no—
123C2×C293C2×#9911yescharacteristic
124C2×C293#41611yescharacteristic
125C2×C293C2×#10411yescharacteristic
126D293—22no—
127D293—41no—
128C293#150111yescharacteristic, complemented, Sylow
129#1501—2931nomaximal, Sylow
130#525—2931no—
131C2×C22⋊C8—2931no—
132C4×C22⋊C4—2931no—
133#328—2931no—
134#328—2931no—
135#327—2931no—
136#327D29311yescharacteristic, complemented
137C2×#41—2931no—
138C23×C4—2931no—
139C22×C8—5861no—
140#123—5861no—
141C22⋊Q8—2931no—
142C22⋊Q8—2931no—
143#121—2931no—
144#121C2×D29311yescharacteristic
145#120—5861no—
146C4×D4—5861no—
147C4×D4—5861no—
148#117—2931no—
149C2×C22⋊C4—5861no—
150C2×C42—5861no—
151C22⋊C8—2931no—
152C22⋊C8—5861no—
153C22⋊C8C2×D29311yescharacteristic
154#95—2931no—
155#95C2×D29311yescharacteristic
156C24—2931no—
157#41—11722no—
158C2×Q8—2931no—
159C2×D4—21no—
160C2×D4—5861no—
161C2×D4—5861no—
162C2×D4C4×D29311yescharacteristic
163C22×C4—21no—
164C22×C4—2931no—
165C22×C4—2931no—
166C22×C4—2931no—
167C22×C4—2931no—
168C22×C4—2931no—
169C22×C4—5861no—
170C22×C4—5861no—
171C22×C4—11722no—
172C22×C4C22×D29311yescharacteristic
173C2×C8—21no—
174C2×C8—5861no—
175C2×C8—11722no—
176C4⋊C4—2931no—
177C4⋊C4—5861no—
178C4⋊C4—5861no—
179C4⋊C4C4×D29311yescharacteristic
180C22⋊C4—21no—
181C22⋊C4—5861no—
182C22⋊C4—5861no—
183C22⋊C4—5864no—
184C22⋊C4—5861no—
185C22⋊C4—5861no—
186C42—5861no—
187C42—11722no—
188C23—21no—
189C23—2931no—
190C23—2931no—
191C23—5862no—
192C23—5861no—
193C23—5861no—
194C23—11721no—
195C23D4×D29311yescharacteristic
196Q8—11721no—
197D4—41no—
198D4—41no—
199D4—41no—
200D4—11722no—
201D4—11722no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—2931no—
208C2×C4—2931no—
209C2×C4—5862no—
210C2×C4—5862no—
211C2×C4—5862no—
212C2×C4—5862no—
213C2×C4—5861no—
214C2×C4—5861no—
215C2×C4—11721no—
216C2×C4—11721no—
217C2×C4—11722no—
218C2×C4—11721no—
219C2×C4—11721no—
220C2×C4C2×C4×D29311yescharacteristic
221C2×C4D4×D29311yescharacteristic
222C8—41no—
223C8—11721no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—2932no—
230C22—5861no—
231C22—5861no—
232C22—5861no—
233C22—5861no—
234C22—5861no—
235C22—11722no—
236C22—11722no—
237C22C22⋊C4×D29311yescharacteristic
238C22#2262764311yescharacteristic
239C22#2262764511yescharacteristic
240C4—21no—
241C4—21no—
242C4—42no—
243C4—41no—
244C4—2932no—
245C4—5861no—
246C4—11722no—
247C4—11721no—
248C4—11721no—
249C2—21no—
250C2—21no—
251C2—81no—
252C2—5862no—
253C2—11721no—
254C2#99×D29311yescharacteristic
255C2#3403612211yescharacteristic
256C2#104×D29311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D293
commutatorC2×C4×C293C22×C4
FrattiniC22×C4C22×D293
Fitting#327×C293C2
socleC22×C293C2×C22⋊C4
prime radical#34036639C2
cosocleC22×C4×C293C23
hypercenter#327D293
hypocenterC293#1501
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D293C2semidirect
3. #34035976C2semidirect
4. #34035867C2semidirect
5. #34035865C2semidirect
6. #34035863C2semidirect
7. #327×C293C2semidirect
8. C2×#17989801C4semidirect
12. #22627604C4semidirect
14. #22627595C4semidirect
18. #22627582C4semidirect
128. C293#1501semidirect
136. #327D293semidirect

Maximal subgroups

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

subgroupindex
#340366392
C22⋊C8×D2932
#340359762
#340358672
#340358652
#340358632
#327×C2932
#1501293