Finite Group Databasebeta

← #34009876

Subgroups — #34009876

Order 18688.

462 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 104 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#22625162C212yesmaximal
2#22624876C214yesmaximal
3#22612414C211yesmaximal, characteristic
4#17989603—22no—
5#17989432—22no—
6#17989430C2214yes—
7C2×#14556550C411yescharacteristic
8C2×#14556550C2211yescharacteristic
9#17988485—22no—
10#17988460C412yes—
11#17988460C2212yes—
12C4×#11924007—22no—
13C22×C42×C73C411yescharacteristic
14C4⋊#10596833—42no—
15C22⋊#10596833—24no—
16C4×#10596833—42no—
17#14556550—22no—
18#14556550—41no—
19#14556550—41no—
20#14556550C814yescomplemented
21C2×C4⋊Dic73—21no—
22C2×C4⋊Dic73D412yes—
23C2×#11924007—22no—
24C2×#11924007—22no—
25C2×C22⋊Dic73C2×C412yes—
26C2×C22⋊Dic73C2×C411yescharacteristic
27C2×C22⋊Dic73C2311yescharacteristic
28C2×C4×Dic73—21no—
29C2×C4×Dic73D412yes—
30#14556498—22no—
31#14556498—22no—
32C23×C4×C73C2×C411yescharacteristic
33C23×C4×C73C2×C412yes—
34C2×C42×C73—21no—
35C2×C42×C73—21no—
36C2×C42×C73—41no—
37C2×C42×C73—41no—
38C2×#10596833—44no—
39C22×Dic73—22no—
40C22×Dic73C22⋊C412yes—
41C22×Dic73C2×D412yes—
42C4⋊Dic73—24no—
43C4⋊Dic73—42no—
44#11924007—44no—
45#11924007—44no—
46C22⋊Dic73—22no—
47C22⋊Dic73—41no—
48C22⋊Dic73—41no—
49C22⋊Dic73C2×C814yes—
50C4×Dic73—24no—
51C4×Dic73—22no—
52C4×Dic73—22no—
53C24×C73C22×C411yescharacteristic
54C22×C4×C73—21no—
55C22×C4×C73—21no—
56C22×C4×C73—22no—
57C22×C4×C73—22no—
58C22×C4×C73—44no—
59C22×C4×C73—42no—
60C22×C4×C73C22⋊C411yescharacteristic
61C22×C4×C73C22⋊C411yescharacteristic
62C22×C4×C73C2×C812yes—
63C22×C4×C73M1612yes—
64C42×C73—42no—
65C42×C73—41no—
66C42×C73—41no—
67C23×C73—21no—
68C23×C73—21no—
69C23×C73—42no—
70C23×C73C2×C22⋊C411yescharacteristic
71C23×C73C22×C811yescharacteristic
72C23×C73C2×M1611yescharacteristic
73C2×C4×C73—21no—
74C2×C4×C73—21no—
75C2×C4×C73—22no—
76C2×C4×C73—22no—
77C2×C4×C73—22no—
78C2×C4×C73—22no—
79C2×C4×C73—24no—
80C2×C4×C73—42no—
81C2×C4×C73—44no—
82C2×C4×C73—42no—
83C2×C4×C73—44no—
84C2×C4×C73C22⋊C812yes—
85C2×C4×C73C22⋊C812yes—
86C2×C4×C73#9911yescharacteristic
87C2×C4×C73#9911yescharacteristic
88C2×C4×C73#10112yes—
89C2×Dic73—24no—
90C2×Dic73—22no—
91C2×Dic73—22no—
92C2×Dic73—42no—
93C2×Dic73—42no—
94C2×Dic73—42no—
95C2×Dic73—42no—
96#10596833—84no—
97C22×C73—22no—
98C22×C73—21no—
99C22×C73—21no—
100C22×C73—41no—
101C22×C73—41no—
102C22×C73—42no—
103C22×C73—42no—
104C22×C73C2×C22⋊C811yescharacteristic
105C22×C73C2×#9911yescharacteristic
106C22×C73C2×#10111yescharacteristic
107C4×C73—22no—
108C4×C73—44no—
109C4×C73#32412yes—
110C4×C73#32412yes—
111Dic73—44no—
112Dic73—42no—
113Dic73—42no—
114#11452—731nomaximal, Sylow
115C2×C73—21no—
116C2×C73—21no—
117C2×C73—41no—
118C2×C73—41no—
119C2×C73C2×#32411yescharacteristic
120C2×C73#212012yes—
121#2296—731no—
122#1458—732no—
123#1326—734no—
124C73#1145211yescharacteristic, complemented, Sylow
125C2×#117—731no—
126C2×#117—731no—
127C22×C42#6440811yescharacteristic
128#431—1462no—
129#389—1462no—
130#385—732no—
131#385—732no—
132C4×C4⋊C4—1462no—
133#324—1462no—
134#323—734no—
135C23×C4C2×#6440812yes—
136C23×C4C2×#6440811yescharacteristic
137#117—2921no—
138#117—2921no—
139#117—734no—
140#117—1462no—
141C2×C4⋊C4—732no—
142C2×C4⋊C4—1462no—
143C2×C4⋊C4—1462no—
144C2×C4⋊C4—1461no—
145C2×C22⋊C4—731no—
146C2×C22⋊C4—731no—
147C2×C22⋊C4—732no—
148C2×C42—21no—
149C2×C42—21no—
150C2×C42—41no—
151C2×C42—41no—
152C2×C42—732no—
153C2×C42—1461no—
154C4⋊C8—2922no—
155C22⋊C8—1464no—
156C4×C8—2922no—
157#95—1462no—
158#95—1462no—
159C24C22×#6440811yescharacteristic
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—22no—
163C22×C4—22no—
164C22×C4—44no—
165C22×C4—42no—
166C22×C4—732no—
167C22×C4—732no—
168C22×C4—1462no—
169C22×C4C22⋊#6440811yescharacteristic
170C22×C4C22⋊#6440811yescharacteristic
171C22×C4#1192403612yes—
172C22×C4#1192403812yes—
173C2×C8—2924no—
174C4⋊C4—2924no—
175C4⋊C4—2924no—
176C4⋊C4—2922no—
177C4⋊C4—1464no—
178C22⋊C4—2921no—
179C22⋊C4—2921no—
180C22⋊C4—734no—
181C22⋊C4—1462no—
182C42—42no—
183C42—41no—
184C42—41no—
185C42—1464no—
186C42—1462no—
187C42—1462no—
188C23—21no—
189C23—21no—
190C23—42no—
191C23C2×C22⋊#6440811yescharacteristic
192C23C2×#1192403611yescharacteristic
193C23C2×#1192403811yescharacteristic
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—42no—
202C2×C4—44no—
203C2×C4—42no—
204C2×C4—44no—
205C2×C4—2922no—
206C2×C4—2922no—
207C2×C4—2922no—
208C2×C4—2922no—
209C2×C4—1464no—
210C2×C4—1462no—
211C2×C4—1462no—
212C2×C4#1455664812yes—
213C2×C4#1455664812yes—
214C2×C4#1455664911yescharacteristic
215C2×C4#1455664911yescharacteristic
216C2×C4#1455665212yes—
217C8—5844no—
218C22—22no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—42no—
224C22—42no—
225C22C2×#1455664811yescharacteristic
226C22C2×#1455664911yescharacteristic
227C22C2×#1455665211yescharacteristic
228C4—22no—
229C4—44no—
230C4—2924no—
231C4—2922no—
232C4—2922no—
233C4#1798943312yes—
234C4#1798943312yes—
235C2—21no—
236C2—21no—
237C2—41no—
238C2—41no—
239C2C2×#1798943311yescharacteristic
240C2#2262618212yes—
subgroupG/H
centerC2×C4#14556649
commutatorC23×C73C22×C8
FrattiniC24C22×#64408
FittingC22×C42×C73C4
socleC22×C73C2×#99
prime radicalC24×C73C22×C4
cosocleC2×C22⋊Dic73C23
hypercenterC22×C42#64408
hypocenterC73#11452
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
20. #14556550C8semidirect
124. C73#11452semidirect

Maximal subgroups

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

subgroupindex
#226251622
#226248762
#226124142
#1145273