Finite Group Databasebeta

← #49157355

Subgroups — #49157355

Order 37504.

288 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C22⋊Q8×D293C211yesmaximal, characteristic
2C22⋊C8×D293C211yesmaximal, characteristic
3#34035988C211yesmaximal, characteristic
4#34035867C211yesmaximal, characteristic, complemented
5#34035866C211yesmaximal, characteristic, complemented
6#34035865C211yesmaximal, characteristic, complemented
7#328×C293C211yesmaximal, characteristic, complemented
8C2×Q8×D293C411yescharacteristic, complemented
9C22×C4×D293C2211yescharacteristic
10C2×C8×D293—21no—
11#22627604C411yescharacteristic, complemented
12#22627603C2211yescharacteristic
13#22627602—21no—
14#22627601—21no—
15#22627600C411yescharacteristic, complemented
16C2×#17989781—21no—
17C4⋊C4×D293—21no—
18C4⋊C4×D293C411yescharacteristic, complemented
19C2×#17989779—21no—
20C22⋊C4×D293—21no—
21C22⋊#14556873C2211yescharacteristic
22#22627536—21no—
23#22627531C2211yescharacteristic
24C22⋊Q8×C293C2211yescharacteristic
25C22⋊C8×C293C2211yescharacteristic
26#95×C293C2211yescharacteristic
27C23×D293D411yescharacteristic
28C2×Dic586—21no—
29C2×Dic586C2×C411yescharacteristic
30Q8×D293—42no—
31C22×Dic293—21no—
32C22×Dic293D411yescharacteristic
33C2×C4×D293—21no—
34C2×C4×D293—21no—
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—
45#17989781—21no—
46#17989781—21no—
47#17989781—42no—
48C22⋊Dic293—21no—
49#17989779—21no—
50#17989779—21no—
51#17989779—42no—
52C2×Q8×C293C2×C411yescharacteristic
53C22×C4×C293—21no—
54C22×C4×C293C2311yescharacteristic
55C2×C8×C293—21no—
56C4⋊C4×C293—21no—
57C4⋊C4×C293C2×C411yescharacteristic
58C22⋊C4×C293—21no—
59C22×D293—41no—
60C22×D293—41no—
61C22×D293C22⋊C411yescharacteristic
62C22×D293C22⋊C411yescharacteristic
63C22×D293SD1612yes—
64C22×D293Q1612yes—
65Dic586—42no—
66Dic586—41no—
67C2×Dic293—22no—
68C2×Dic293—21no—
69C2×Dic293—21no—
70C2×Dic293—41no—
71C2×Dic293—41no—
72C2×Dic293—41no—
73C2×Dic293C22⋊C411yescharacteristic
74C2×Dic293C22⋊C411yescharacteristic
75C4×D293—22no—
76C4×D293—22no—
77C4×D293—41no—
78C4×D293—41no—
79C4×D293—42no—
80C4×D293—42no—
81#14556873—41no—
82C23×C293C2×D411yescharacteristic
83Q8×C293—41no—
84C2×C4×C293—21no—
85C2×C4×C293—21no—
86C2×C4×C293—41no—
87C2×C4×C293—41no—
88C2×C4×C293—41no—
89C2×C4×C293—41no—
90C2×C4×C293C22×C411yescharacteristic
91C2×C4×C293C2×D411yescharacteristic
92C8×C293—41no—
93C22×C293—21no—
94C22×C293—21no—
95C22×C293C2×C22⋊C411yescharacteristic
96C22×C293C2×SD1611yescharacteristic
97C22×C293C2×Q1611yescharacteristic
98C2×D293—21no—
99C2×D293—21no—
100C2×D293—21no—
101C2×D293—21no—
102C2×D293—42no—
103C2×D293—42no—
104C2×D293#10312yes—
105C2×D293#10312yes—
106C4×C293—21no—
107C4×C293—21no—
108C4×C293—41no—
109C4×C293—41no—
110C4×C293—81no—
111Dic293—21no—
112Dic293—41no—
113Dic293—41no—
114Dic293—81no—
115Dic293#9912yes—
116C2×C293—21no—
117C2×C293—21no—
118C2×C293C2×#9911yescharacteristic
119C2×C293C2×#10311yescharacteristic
120C2×C293#42111yescharacteristic
121D293—22no—
122D293—22no—
123C293#152011yescharacteristic, complemented, Sylow
124#1520—2931nomaximal, Sylow
125C2×C22⋊Q8—2931no—
126C2×C22⋊C8—2931no—
127#380—2931no—
128#328—2931no—
129#328—2931no—
130#328—2931no—
131#328D29311yescharacteristic, complemented
132C22×Q8—2931no—
133C23×C4—2931no—
134C22×C8—5861no—
135C22⋊Q8—2931no—
136C22⋊Q8—2931no—
137C22⋊Q8—2931no—
138C22⋊Q8—5861no—
139C22⋊Q8—5861no—
140C22⋊Q8C2×D29311yescharacteristic
141C2×C4⋊C4—2931no—
142C2×C4⋊C4—5861no—
143C2×C4⋊C4—5861no—
144C2×C22⋊C4—5861no—
145C2×C22⋊C4—5861no—
146C22⋊C8—2931no—
147C22⋊C8—5861no—
148C22⋊C8C2×D29311yescharacteristic
149#95—2931no—
150#95C2×D29311yescharacteristic
151C24—2931no—
152C2×Q8—2931no—
153C2×Q8—5861no—
154C2×Q8—11722no—
155C2×Q8C4×D29311yescharacteristic
156C22×C4—21no—
157C22×C4—2931no—
158C22×C4—2931no—
159C22×C4—2931no—
160C22×C4—2931no—
161C22×C4—2931no—
162C22×C4—5861no—
163C22×C4—5861no—
164C22×C4—5861no—
165C22×C4—11722no—
166C22×C4C22×D29311yescharacteristic
167C2×C8—21no—
168C2×C8—5861no—
169C2×C8—11722no—
170C4⋊C4—21no—
171C4⋊C4—2931no—
172C4⋊C4—5861no—
173C4⋊C4—5861no—
174C4⋊C4—5861no—
175C4⋊C4—5861no—
176C4⋊C4—11722no—
177C4⋊C4C4×D29311yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—5861no—
180C22⋊C4—5861no—
181C22⋊C4—5861no—
182C22⋊C4—11722no—
183C23—2931no—
184C23—2931no—
185C23—2932no—
186C23—2932no—
187C23—11721no—
188C23—11721no—
189C23D4×D29311yescharacteristic
190Q8—41no—
191Q8—11721no—
192Q8—11722no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—2931no—
200C2×C4—2931no—
201C2×C4—5862no—
202C2×C4—5862no—
203C2×C4—5862no—
204C2×C4—5861no—
205C2×C4—5861no—
206C2×C4—11721no—
207C2×C4—11721no—
208C2×C4—11722no—
209C2×C4—11722no—
210C2×C4—11721no—
211C2×C4—11721no—
212C2×C4—11721no—
213C2×C4C2×C4×D29311yescharacteristic
214C2×C4D4×D29311yescharacteristic
215C8—41no—
216C8—11721no—
217C22—21no—
218C22—21no—
219C22—2932no—
220C22—2932no—
221C22—5861no—
222C22—5861no—
223C22—5861no—
224C22—5861no—
225C22—11722no—
226C22—11722no—
227C22C22⋊C4×D29311yescharacteristic
228C22SD16×D29311yescharacteristic
229C22Q16×D29311yescharacteristic
230C4—21no—
231C4—21no—
232C4—41no—
233C4—41no—
234C4—81no—
235C4—2932no—
236C4—23441no—
237C4—5861no—
238C4—11721no—
239C4—11721no—
240C2—21no—
241C2—21no—
242C2—5862no—
243C2—5862no—
244C2#99×D29311yescharacteristic
245C2#103×D29311yescharacteristic
246C2#3403614411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D293
commutatorC2×C4×C293C22×C4
FrattiniC22×C4C22×D293
Fitting#328×C293C2
socleC22×C293C2×C22⋊C4
prime radicalC23×D293D4
cosocleC22×C4×C293C23
hypercenter#328D293
hypocenterC293#1520
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
4. #34035867C2semidirect
5. #34035866C2semidirect
6. #34035865C2semidirect
7. #328×C293C2semidirect
8. C2×Q8×D293C4semidirect
11. #22627604C4semidirect
15. #22627600C4semidirect
18. C4⋊C4×D293C4semidirect
123. C293#1520semidirect
131. #328D293semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D2932
C22⋊C8×D2932
#340359882
#340358672
#340358662
#340358652
#328×C2932
#1520293