Finite Group Databasebeta

← #44450372

Subgroups — #44450372

Order 29824.

220 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 69 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#28416987C211yesmaximal, characteristic
2#28416485C211yesmaximal, characteristic
3#28416299C211yesmaximal, characteristic
4#28416173C211yesmaximal, characteristic
5#28416172C211yesmaximal, characteristic
6#28416171C211yesmaximal, characteristic
7#328×C233C211yesmaximal, characteristic
8#21418534C411yescharacteristic, complemented
9#21418533C411yescharacteristic, complemented
10#21418525—21no—
11#21418514C2211yescharacteristic
12#21418512—21no—
13Q8×Dic233C411yescharacteristic, complemented
14#21418500—21no—
15#21418500C411yescharacteristic, complemented
16#21418491—21no—
17C2×#16836573—21no—
18C2×C4×Dic233C2211yescharacteristic
19#21418464—21no—
20C22⋊#14272338C2211yescharacteristic
21C8×Dic233—21no—
22#21418442—21no—
23#21418442C2211yescharacteristic
24C22⋊Q8×C233C2211yescharacteristic
25C22⋊C8×C233C2211yescharacteristic
26#95×C233C2211yescharacteristic
27C2×Dic466—21no—
28C2×Dic466C2×C411yescharacteristic
29C22×Dic233—21no—
30C22×Dic233D411yescharacteristic
31C22×Dic233D411yescharacteristic
32C2×#14272338—21no—
33C4⋊Dic233—21no—
34C4⋊Dic233C2×C411yescharacteristic
35#16836573—21no—
36#16836573—21no—
37#16836573—21no—
38#16836573—21no—
39#16836573—21no—
40#16836573—42no—
41C22⋊Dic233—21no—
42C4×Dic233—21no—
43C4×Dic233—21no—
44C4×Dic233C2×C411yescharacteristic
45C4×Dic233C2×C411yescharacteristic
46C4×Dic233D411yescharacteristic
47C4×Dic233D411yescharacteristic
48C2×Q8×C233C2×C411yescharacteristic
49C22×C4×C233—21no—
50C22×C4×C233C2311yescharacteristic
51C2×C8×C233—21no—
52C4⋊C4×C233—21no—
53C4⋊C4×C233C2×C411yescharacteristic
54C22⋊C4×C233—21no—
55Dic466—42no—
56Dic466—41no—
57C2×Dic233—21no—
58C2×Dic233—21no—
59C2×Dic233—41no—
60C2×Dic233—41no—
61C2×Dic233—41no—
62C2×Dic233—41no—
63C2×Dic233C22⋊C411yescharacteristic
64C2×Dic233C22⋊C411yescharacteristic
65C2×Dic233C22⋊C411yescharacteristic
66C2×Dic233C22⋊C411yescharacteristic
67C2×Dic233SD1612yes—
68C2×Dic233Q1612yes—
69#14272338—41no—
70C23×C233C2×D411yescharacteristic
71Q8×C233—41no—
72C2×C4×C233—21no—
73C2×C4×C233—21no—
74C2×C4×C233—41no—
75C2×C4×C233—41no—
76C2×C4×C233—41no—
77C2×C4×C233—41no—
78C2×C4×C233C22×C411yescharacteristic
79C2×C4×C233C2×D411yescharacteristic
80C8×C233—41no—
81C22×C233—21no—
82C22×C233—21no—
83C22×C233C2×C22⋊C411yescharacteristic
84C22×C233C2×SD1611yescharacteristic
85C22×C233C2×Q1611yescharacteristic
86C4×C233—21no—
87C4×C233—21no—
88C4×C233—41no—
89C4×C233—41no—
90C4×C233—81no—
91Dic233—21no—
92Dic233—21no—
93Dic233—41no—
94Dic233—41no—
95Dic233—81no—
96Dic233#10312yes—
97Dic233#10312yes—
98C2×C233—21no—
99C2×C233—21no—
100C2×C233#41011yescharacteristic
101C2×C233C2×#10311yescharacteristic
102C2×C233#42111yescharacteristic
103C233#151811yescharacteristic, complemented, Sylow
104#1518—2331nomaximal, Sylow
105#533—2331no—
106#431—2331no—
107#382—2331no—
108#328—2331no—
109#328—2331no—
110#328—2331no—
111#328D23311yescharacteristic
112C4⋊Q8—2331no—
113C4⋊Q8—2331no—
114#125—4661no—
115C22⋊Q8—4661no—
116C22⋊Q8—2331no—
117C22⋊Q8C2×D23311yescharacteristic
118C4×Q8—4661no—
119C4×Q8—2331no—
120C4×Q8—2331no—
121#117—4661no—
122C2×C4⋊C4—4661no—
123C2×C42—2331no—
124C4⋊C8—4661no—
125C22⋊C8—2331no—
126C22⋊C8C2×D23311yescharacteristic
127C4×C8—4661no—
128#95—4661no—
129#95—2331no—
130#95C2×D23311yescharacteristic
131C2×Q8—4661no—
132C2×Q8—2331no—
133C2×Q8C4×D23311yescharacteristic
134C22×C4—21no—
135C22×C4—4661no—
136C22×C4—2331no—
137C22×C4—2331no—
138C22×C4C22×D23311yescharacteristic
139C2×C8—21no—
140C2×C8—4661no—
141C4⋊C4—21no—
142C4⋊C4—9322no—
143C4⋊C4—4661no—
144C4⋊C4—4661no—
145C4⋊C4—4661no—
146C4⋊C4—4661no—
147C4⋊C4—4661no—
148C4⋊C4—4661no—
149C4⋊C4—2331no—
150C4⋊C4C4×D23311yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—4661no—
153C42—4661no—
154C42—4661no—
155C42—2331no—
156C42—2331no—
157C42—2331no—
158C42—2331no—
159C23D4×D23311yescharacteristic
160Q8—41no—
161Q8—9321no—
162Q8—9322no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—9321no—
170C2×C4—9321no—
171C2×C4—9321no—
172C2×C4—9321no—
173C2×C4—4661no—
174C2×C4—4661no—
175C2×C4—2331no—
176C2×C4—2331no—
177C2×C4—2332no—
178C2×C4—2332no—
179C2×C4—2331no—
180C2×C4—2331no—
181C2×C4C2×C4×D23311yescharacteristic
182C2×C4D4×D23311yescharacteristic
183C8—41no—
184C8—9321no—
185C22—21no—
186C22—21no—
187C22C22⋊C4×D23311yescharacteristic
188C22SD16×D23311yescharacteristic
189C22Q16×D23311yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—18641no—
196C4—9321no—
197C4—9321no—
198C4—4661no—
199C4—4661no—
200C4—2332no—
201C4—2332no—
202C2—21no—
203C2—21no—
204C2#2841640711yescharacteristic
205C2#103×D23311yescharacteristic
206C2#2841645011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D233
commutatorC2×C4×C233C22×C4
FrattiniC22×C4C22×D233
Fitting#328×C233C2
socleC22×C233C2×C22⋊C4
prime radicalC23×C233C2×D4
cosocleC22×C4×C233C23
hypercenter#328D233
hypocenterC233#1518
LCSG ▷ C2×C4×C233 ▷ C22×C233 ▷ C233
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. #21418534C4semidirect
9. #21418533C4semidirect
13. Q8×Dic233C4semidirect
15. #21418500C4semidirect
103. C233#1518semidirect

Maximal subgroups

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

subgroupindex
#284169872
#284164852
#284162992
#284161732
#284161722
#284161712
#328×C2332
#1518233