Finite Group Databasebeta

← #34010077

Subgroups — #34010077

Order 18688.

670 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 80 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#22625182C212yesmaximal, complemented
2#22624859C214yesmaximal, complemented
3#22612513C211yesmaximal, characteristic
4#17989607—22no—
5#17989432C2214yescomplemented
6#17989430—22no—
7C2×#14556550C411yescharacteristic
8C2×#14556550C2211yescharacteristic
9#17988490—22no—
10#17988490C412yes—
11#17988490C2212yes—
12#17988443—22no—
13C23×D4×C73C411yescharacteristic
14#14556658—42no—
15C22⋊#10596833—24no—
16#14556646—42no—
17#14556550—42no—
18#14556550—42no—
19C2×C4⋊Dic73—21no—
20C2×C4⋊Dic73C2×C411yescharacteristic
21C2×C4⋊Dic73C2311yescharacteristic
22C2×C22⋊Dic73—24no—
23C2×C22⋊Dic73—24no—
24C2×C22⋊Dic73—21no—
25C2×C22⋊Dic73D412yes—
26C2×C4×Dic73C2×C412yes—
27C2×C4×Dic73D412yes—
28C25×C73—21no—
29C22×D4×C73—24no—
30C22×D4×C73—21no—
31C22×D4×C73—42no—
32C22×D4×C73—42no—
33C22×D4×C73C2×C412yes—
34C23×C4×C73C2×C411yescharacteristic
35C2×#10596833—44no—
36C22×Dic73—22no—
37C22×Dic73C22⋊C412yes—
38C22×Dic73C2×D412yes—
39C4⋊Dic73—41no—
40C4⋊Dic73—41no—
41C4⋊Dic73—42no—
42C22⋊Dic73—42no—
43C22⋊Dic73—42no—
44C22⋊Dic73—84no—
45C22⋊Dic73—84no—
46C4×Dic73—22no—
47C4×Dic73—22no—
48C4×Dic73—42no—
49C24×C73—24no—
50C24×C73—22no—
51C24×C73—42no—
52C24×C73—42no—
53C24×C73—82no—
54C24×C73—82no—
55C24×C73C22⋊C411yescharacteristic
56C2×D4×C73—24no—
57C2×D4×C73—22no—
58C2×D4×C73—42no—
59C2×D4×C73—42no—
60C2×D4×C73—416no—
61C2×D4×C73—42no—
62C2×D4×C73—42no—
63C2×D4×C73M1614yes—
64C22×C4×C73—22no—
65C22×C4×C73—22no—
66C22×C4×C73—22no—
67C22×C4×C73C22⋊C411yescharacteristic
68C22×C4×C73C22×C411yescharacteristic
69C23×C73—21no—
70C23×C73—21no—
71C23×C73—24no—
72C23×C73—41no—
73C23×C73—41no—
74C23×C73—48no—
75C23×C73—44no—
76C23×C73—44no—
77C23×C73—42no—
78C23×C73—42no—
79C23×C73—88no—
80C23×C73—88no—
81C23×C73—84no—
82C23×C73—84no—
83C23×C73#10012yes—
84C23×C73C2×C22⋊C411yescharacteristic
85D4×C73—44no—
86D4×C73—48no—
87D4×C73—44no—
88C2×C4×C73—28no—
89C2×C4×C73—21no—
90C2×C4×C73—21no—
91C2×C4×C73—21no—
92C2×C4×C73—21no—
93C2×C4×C73#9912yes—
94C2×C4×C73C2×M1612yes—
95C2×Dic73—22no—
96C2×Dic73—22no—
97C2×Dic73—42no—
98C2×Dic73—42no—
99C2×Dic73—42no—
100C2×Dic73—42no—
101C2×Dic73—42no—
102#10596833—84no—
103C22×C73—21no—
104C22×C73—21no—
105C22×C73—22no—
106C22×C73—42no—
107C22×C73—42no—
108C22×C73—48no—
109C22×C73—41no—
110C22×C73—41no—
111C22×C73—44no—
112C22×C73—84no—
113C22×C73—816no—
114C22×C73—82no—
115C22×C73—82no—
116C22×C73#40711yescharacteristic
117C22×C73C2×#9911yescharacteristic
118C22×C73C2×#10011yescharacteristic
119C4×C73—22no—
120C4×C73—22no—
121Dic73—42no—
122Dic73—42no—
123Dic73—82no—
124#11509—731nomaximal, Sylow
125C2×C73—21no—
126C2×C73—21no—
127C2×C73—42no—
128C2×C73—84no—
129C2×C73#146211yescharacteristic
130C2×C73#212811yescharacteristic
131C2×C73#213411yescharacteristic
132#2309—731no—
133#1464—732no—
134#1318—734no—
135C73#1150911yescharacteristic, complemented, Sylow
136C23×D4#6440811yescharacteristic
137C2×#117—731no—
138C2×#117—731no—
139#432—1462no—
140#390—732no—
141#390—732no—
142#390—1462no—
143#379—1462no—
144#324—734no—
145#323—1462no—
146C25—21no—
147C22×D4—24no—
148C22×D4—21no—
149C22×D4—42no—
150C22×D4—42no—
151C22×D4C2×#6440812yes—
152C23×C4C2×#6440811yescharacteristic
153#117—2922no—
154#117—2922no—
155C2×C4⋊C4—731no—
156C2×C4⋊C4—731no—
157C2×C4⋊C4—1461no—
158C2×C22⋊C4—732no—
159C2×C22⋊C4—1461no—
160C2×C22⋊C4—1464no—
161C2×C22⋊C4—1464no—
162C2×C42—732no—
163C2×C42—732no—
164C4⋊C8—2922no—
165C22⋊C8—1464no—
166#97—2922no—
167C24—24no—
168C24—22no—
169C24—42no—
170C24—42no—
171C24—82no—
172C24—82no—
173C24C22⋊#6440811yescharacteristic
174C2×D4—24no—
175C2×D4—22no—
176C2×D4—42no—
177C2×D4—42no—
178C2×D4—416no—
179C2×D4—42no—
180C2×D4—42no—
181C2×D4#1192403714yes—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—732no—
186C22×C4—732no—
187C22×C4—1462no—
188C22×C4C22⋊#6440811yescharacteristic
189C22×C4C22×#6440811yescharacteristic
190C2×C8—2924no—
191C4⋊C4—2922no—
192C4⋊C4—2921no—
193C4⋊C4—2921no—
194C22⋊C4—2922no—
195C22⋊C4—2922no—
196C22⋊C4—5844no—
197C22⋊C4—5844no—
198C42—2922no—
199C42—1462no—
200C42—1462no—
201C23—21no—
202C23—21no—
203C23—24no—
204C23—41no—
205C23—41no—
206C23—44no—
207C23—44no—
208C23—48no—
209C23—42no—
210C23—42no—
211C23—88no—
212C23—88no—
213C23—84no—
214C23—84no—
215C23#1455665112yes—
216C23C2×C22⋊#6440811yescharacteristic
217D4—44no—
218D4—44no—
219D4—48no—
220C2×C4—28no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—2922no—
226C2×C4—2922no—
227C2×C4—2922no—
228C2×C4—2922no—
229C2×C4—2922no—
230C2×C4—1462no—
231C2×C4—1462no—
232C2×C4#1455664912yes—
233C2×C4C2×#1192403712yes—
234C8—5844no—
235C22—21no—
236C22—21no—
237C22—22no—
238C22—42no—
239C22—42no—
240C22—48no—
241C22—41no—
242C22—41no—
243C22—44no—
244C22—84no—
245C22—816no—
246C22—82no—
247C22—82no—
248C22#1798955711yescharacteristic
249C22C2×#1455664911yescharacteristic
250C22C2×#1455665111yescharacteristic
251C4—22no—
252C4—22no—
253C4—2922no—
254C4—2922no—
255C4—5842no—
256C2—21no—
257C2—21no—
258C2—42no—
259C2—84no—
260C2#2262517611yescharacteristic
261C2#2262621011yescharacteristic
262C2#2262623011yescharacteristic
subgroupG/H
centerC22C2×#14556649
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
Fitting, prime radicalC23×D4×C73C4
socleC22×C73C2×#99
cosocleC2×C4⋊Dic73C23
hypercenterC23×D4#64408
hypocenterC73#11509
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. #22625182C2semidirect
2. #22624859C2semidirect
5. #17989432C22semidirect
135. C73#11509semidirect

Maximal subgroups

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

subgroupindex
#226251822
#226248592
#226125132
#1150973