Finite Group Databasebeta

← #49157338

Subgroups — #49157338

Order 37504.

284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 63 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#34035991C211yesmaximal, 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—
20C22⋊#14556873C2211yescharacteristic
21#22627536—21no—
22#22627531—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—21no—
48#17989779—21no—
49#17989779—42no—
50C4×Dic293—21no—
51C2×D4×C293—21no—
52C2×D4×C293C2×C411yescharacteristic
53C22×C4×C293—21no—
54C22×C4×C293C2311yescharacteristic
55C2×C8×C293—21no—
56C4⋊C4×C293C2×C411yescharacteristic
57C22⋊C4×C293—21no—
58C22×D293—21no—
59C22×D293—21no—
60C22×D293—22no—
61C22×D293—41no—
62C22×D293C22⋊C411yescharacteristic
63C22×D293C22⋊C411yescharacteristic
64Dic586—41no—
65C22⋊D293—42no—
66C22⋊D293—42no—
67C2×Dic293—21no—
68C2×Dic293—21no—
69C2×Dic293—41no—
70C2×Dic293—42no—
71C2×Dic293—41no—
72C2×Dic293—41no—
73C2×Dic293—41no—
74C2×Dic293C22⋊C411yescharacteristic
75C2×Dic293C22⋊C411yescharacteristic
76C4×D293—22no—
77C4×D293—22no—
78C4×D293—41no—
79C4×D293—41no—
80#14556873—41no—
81C23×C293—21no—
82C23×C293C2×D411yescharacteristic
83D4×C293—41no—
84D4×C293—41no—
85D4×C293—41no—
86C2×C4×C293—21no—
87C2×C4×C293—41no—
88C2×C4×C293—41no—
89C2×C4×C293—41no—
90C2×C4×C293—41no—
91C2×C4×C293C22×C411yescharacteristic
92C2×C4×C293C2×D411yescharacteristic
93C8×C293—41no—
94C22×C293—21no—
95C22×C293—21no—
96C22×C293—41no—
97C22×C293—41no—
98C22×C293—41no—
99C22×C293C2×C22⋊C411yescharacteristic
100C22×C293#13511yescharacteristic
101C22×C293#13511yescharacteristic
102C2×D293—21no—
103C2×D293—21no—
104C2×D293—21no—
105C2×D293—21no—
106C2×D293—21no—
107C2×D293—42no—
108C2×D293—42no—
109C2×D293#9912yes—
110C4×C293—21no—
111C4×C293—21no—
112C4×C293—41no—
113C4×C293—81no—
114Dic293—21no—
115Dic293—21no—
116Dic293—41no—
117Dic293—41no—
118Dic293—81no—
119C2×C293—21no—
120C2×C293—21no—
121C2×C293—81no—
122C2×C293C2×#9911yescharacteristic
123C2×C293#41611yescharacteristic
124C2×C293#42111yescharacteristic
125D293—22no—
126D293—41no—
127C293#151611yescharacteristic, complemented, Sylow
128#1516—2931nomaximal, Sylow
129#525—2931no—
130C2×C22⋊C8—2931no—
131#381—2931no—
132#328—2931no—
133#328—2931no—
134#327—2931no—
135#327D29311yescharacteristic, complemented
136C2×#41—2931no—
137C23×C4—2931no—
138C22×C8—5861no—
139#123—5861no—
140C22⋊Q8—2931no—
141C22⋊Q8—2931no—
142#121—2931no—
143#121C2×D29311yescharacteristic
144#120—5861no—
145C4×D4—5861no—
146C4×D4—5861no—
147#117—2931no—
148C2×C22⋊C4—5861no—
149C22⋊C8—2931no—
150C22⋊C8—5861no—
151C22⋊C8C2×D29311yescharacteristic
152#95—2931no—
153#95—5861no—
154#95C2×D29311yescharacteristic
155C24—2931no—
156#41—11722no—
157C2×Q8—2931no—
158C2×D4—21no—
159C2×D4—5861no—
160C2×D4—5861no—
161C2×D4C4×D29311yescharacteristic
162C22×C4—21no—
163C22×C4—2931no—
164C22×C4—2931no—
165C22×C4—2931no—
166C22×C4—2931no—
167C22×C4—2931no—
168C22×C4—5861no—
169C22×C4—5861no—
170C22×C4—11722no—
171C22×C4C22×D29311yescharacteristic
172C2×C8—21no—
173C2×C8—5861no—
174C2×C8—11722no—
175C4⋊C4—2931no—
176C4⋊C4—5861no—
177C4⋊C4—5861no—
178C4⋊C4C4×D29311yescharacteristic
179C22⋊C4—21no—
180C22⋊C4—5861no—
181C22⋊C4—5861no—
182C22⋊C4—5861no—
183C22⋊C4—5861no—
184C22⋊C4—11722no—
185C42—5861no—
186C23—21no—
187C23—2931no—
188C23—2931no—
189C23—5862no—
190C23—5861no—
191C23—5861no—
192C23—11721no—
193C23D4×D29311yescharacteristic
194Q8—11721no—
195D4—41no—
196D4—41no—
197D4—41no—
198D4—11722no—
199D4—11722no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—2931no—
206C2×C4—2931no—
207C2×C4—5862no—
208C2×C4—5862no—
209C2×C4—5861no—
210C2×C4—5861no—
211C2×C4—11721no—
212C2×C4—11721no—
213C2×C4—11721no—
214C2×C4—11721no—
215C2×C4—11721no—
216C2×C4—11721no—
217C2×C4—11722no—
218C2×C4C2×C4×D29311yescharacteristic
219C2×C4D4×D29311yescharacteristic
220C8—41no—
221C8—11721no—
222C22—21no—
223C22—21no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—2932no—
228C22—5861no—
229C22—5861no—
230C22—5861no—
231C22—5861no—
232C22—5861no—
233C22—11722no—
234C22—11722no—
235C22C22⋊C4×D29311yescharacteristic
236C22#2262764311yescharacteristic
237C22#2262764511yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—81no—
242C4—23441no—
243C4—5861no—
244C4—5861no—
245C4—11721no—
246C4—11721no—
247C2—21no—
248C2—21no—
249C2—81no—
250C2—5862no—
251C2—11721no—
252C2#99×D29311yescharacteristic
253C2#3403612211yescharacteristic
254C2#3403614411yescharacteristic
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#1516
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. #34035991C2semidirect
4. #34035867C2semidirect
5. #34035865C2semidirect
6. #34035863C2semidirect
7. #327×C293C2semidirect
8. C2×#17989801C4semidirect
12. #22627604C4semidirect
14. #22627595C4semidirect
18. #22627582C4semidirect
127. C293#1516semidirect
135. #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
#340359912
#340358672
#340358652
#340358632
#327×C2932
#1516293