Finite Group Databasebeta

← #34010089

Subgroups — #34010089

Order 18688.

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

normal subgroups only

This group has 446 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
2#22624873C212yesmaximal, complemented
3#22624871C212yesmaximal, complemented
4#22612338C211yesmaximal, characteristic
5#17989607—22no—
6#17989432C2214yes—
7#17989430—22no—
8C2×#14556550C411yescharacteristic
9C2×#14556550C2211yescharacteristic
10#17988457C411yescharacteristic
11#17988457C2211yescharacteristic
12#17988453C411yescharacteristic
13#17988453C2211yescharacteristic
14#17988447—22no—
15C4×C4⋊Dic73—22no—
16C22×C42×C73C411yescharacteristic
17#14556658—42no—
18C22⋊#10596833—24no—
19#14556646—42no—
20#14556550—41no—
21#14556550—41no—
22#14556550—41no—
23#14556550—41no—
24C2×C4⋊Dic73—22no—
25C2×C4⋊Dic73—22no—
26C2×C4⋊Dic73C2×C411yescharacteristic
27C2×C4⋊Dic73C2×C411yescharacteristic
28C2×C4⋊Dic73C2×C411yescharacteristic
29C2×C4⋊Dic73C2311yescharacteristic
30C2×C22⋊Dic73—21no—
31C2×C22⋊Dic73D412yes—
32C2×C4×Dic73—21no—
33C2×C4×Dic73D412yes—
34#14556498—22no—
35#14556498—22no—
36C23×C4×C73—21no—
37C23×C4×C73C2×C411yescharacteristic
38C2×C42×C73—21no—
39C2×C42×C73—22no—
40C2×C42×C73—22no—
41C2×C42×C73C2×C411yescharacteristic
42C2×C42×C73C2×C411yescharacteristic
43C2×#10596833—44no—
44C22×Dic73—21no—
45C22×Dic73—21no—
46C22×Dic73C22⋊C412yes—
47C22×Dic73C2×D412yes—
48C4⋊Dic73—41no—
49C4⋊Dic73—41no—
50C4⋊Dic73—44no—
51C4⋊Dic73—44no—
52C4⋊Dic73—41no—
53C4⋊Dic73—41no—
54C22⋊Dic73—42no—
55C22⋊Dic73—42no—
56C4×Dic73—22no—
57C4×Dic73—22no—
58C4×Dic73—41no—
59C4×Dic73—41no—
60C24×C73C22⋊C411yescharacteristic
61C22×C4×C73—22no—
62C22×C4×C73—21no—
63C22×C4×C73—21no—
64C22×C4×C73—21no—
65C22×C4×C73—21no—
66C22×C4×C73—21no—
67C22×C4×C73—24no—
68C22×C4×C73—21no—
69C22×C4×C73—42no—
70C22×C4×C73—42no—
71C22×C4×C73C22⋊C411yescharacteristic
72C22×C4×C73C22×C411yescharacteristic
73C42×C73—24no—
74C42×C73—21no—
75C42×C73—21no—
76C42×C73M1612yes—
77C42×C73M1612yes—
78C23×C73—21no—
79C23×C73—21no—
80C23×C73—41no—
81C23×C73—41no—
82C23×C73#10112yes—
83C23×C73C2×C22⋊C411yescharacteristic
84C2×C4×C73—22no—
85C2×C4×C73—22no—
86C2×C4×C73—22no—
87C2×C4×C73—22no—
88C2×C4×C73—22no—
89C2×C4×C73—22no—
90C2×C4×C73—21no—
91C2×C4×C73—22no—
92C2×C4×C73—21no—
93C2×C4×C73—21no—
94C2×C4×C73—21no—
95C2×C4×C73—22no—
96C2×C4×C73—48no—
97C2×C4×C73—41no—
98C2×C4×C73—41no—
99C2×C4×C73#9911yescharacteristic
100C2×C4×C73#9911yescharacteristic
101C2×C4×C73C2×M1611yescharacteristic
102C2×C4×C73C2×M1611yescharacteristic
103C2×Dic73—22no—
104C2×Dic73—22no—
105C2×Dic73—42no—
106C2×Dic73—42no—
107C2×Dic73—42no—
108C2×Dic73—42no—
109C2×Dic73—41no—
110C2×Dic73—41no—
111#10596833—84no—
112C22×C73—21no—
113C22×C73—21no—
114C22×C73—22no—
115C22×C73—42no—
116C22×C73—42no—
117C22×C73—41no—
118C22×C73—41no—
119C22×C73#40711yescharacteristic
120C22×C73C2×#9911yescharacteristic
121C22×C73C2×#10111yescharacteristic
122C4×C73—24no—
123C4×C73—21no—
124C4×C73—21no—
125C4×C73—21no—
126C4×C73—21no—
127C4×C73—42no—
128Dic73—42no—
129Dic73—42no—
130Dic73—81no—
131Dic73—81no—
132#11513—731nomaximal, Sylow
133C2×C73—21no—
134C2×C73—21no—
135C2×C73—42no—
136C2×C73#146311yescharacteristic
137C2×C73#212611yescharacteristic
138C2×C73#213211yescharacteristic
139#2285—731no—
140#1464—732no—
141#1325—732no—
142#1324—732no—
143C73#1151311yescharacteristic, complemented, Sylow
144C2×#117—731no—
145C2×#117—731no—
146C22×C42#6440811yescharacteristic
147#432—1462no—
148#384—731no—
149#384—731no—
150#382—731no—
151#382—731no—
152#380—1462no—
153C4×C4⋊C4—1462no—
154#324—734no—
155#323—1462no—
156C23×C4—21no—
157C23×C4C2×#6440811yescharacteristic
158#117—2921no—
159#117—2921no—
160#117—2921no—
161#117—2921no—
162C2×C4⋊C4—731no—
163C2×C4⋊C4—731no—
164C2×C4⋊C4—731no—
165C2×C4⋊C4—731no—
166C2×C4⋊C4—1462no—
167C2×C4⋊C4—1462no—
168C2×C22⋊C4—732no—
169C2×C22⋊C4—1461no—
170C2×C42—21no—
171C2×C42—22no—
172C2×C42—22no—
173C2×C42—732no—
174C2×C42—1461no—
175C2×C42C2×#6440811yescharacteristic
176C2×C42C2×#6440811yescharacteristic
177C4⋊C8—2922no—
178C22⋊C8—1464no—
179#97—2922no—
180#95—1462no—
181#95—1462no—
182C24C22⋊#6440811yescharacteristic
183C22×C4—22no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—24no—
190C22×C4—21no—
191C22×C4—42no—
192C22×C4—42no—
193C22×C4—732no—
194C22×C4—732no—
195C22×C4—1461no—
196C22×C4—1461no—
197C22×C4C22⋊#6440811yescharacteristic
198C22×C4C22×#6440811yescharacteristic
199C2×C8—2924no—
200C4⋊C4—2921no—
201C4⋊C4—2921no—
202C4⋊C4—2924no—
203C4⋊C4—2924no—
204C4⋊C4—2921no—
205C4⋊C4—2921no—
206C22⋊C4—2922no—
207C22⋊C4—2922no—
208C42—24no—
209C42—21no—
210C42—21no—
211C42—2921no—
212C42—2921no—
213C42—1462no—
214C42—1462no—
215C42#1192403712yes—
216C42#1192403712yes—
217C23—21no—
218C23—21no—
219C23—41no—
220C23—41no—
221C23#1455665212yes—
222C23C2×C22⋊#6440811yescharacteristic
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—48no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—2922no—
239C2×C4—2922no—
240C2×C4—2922no—
241C2×C4—2922no—
242C2×C4—2921no—
243C2×C4—2921no—
244C2×C4—1462no—
245C2×C4—1462no—
246C2×C4#1455665011yescharacteristic
247C2×C4#1455665011yescharacteristic
248C2×C4C2×#1192403711yescharacteristic
249C2×C4C2×#1192403711yescharacteristic
250C8—5844no—
251C22—21no—
252C22—21no—
253C22—22no—
254C22—42no—
255C22—42no—
256C22—41no—
257C22—41no—
258C22#1798955711yescharacteristic
259C22C2×#1455665011yescharacteristic
260C22C2×#1455665211yescharacteristic
261C4—24no—
262C4—21no—
263C4—21no—
264C4—21no—
265C4—21no—
266C4—42no—
267C4—2922no—
268C4—2922no—
269C4—5841no—
270C4—5841no—
271C2—21no—
272C2—21no—
273C2—42no—
274C2#2262517911yescharacteristic
275C2#2262620411yescharacteristic
276C2#2262622411yescharacteristic
subgroupG/H
centerC22C2×#14556650
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
FittingC22×C42×C73C4
socleC22×C73C2×#99
prime radicalC24×C73C22⋊C4
cosocleC2×C4⋊Dic73C23
hypercenterC22×C42#64408
hypocenterC73#11513
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. #22624873C2semidirect
3. #22624871C2semidirect
143. C73#11513semidirect

Maximal subgroups

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

subgroupindex
#226251822
#226248732
#226248712
#226123382
#1151373