Finite Group Databasebeta

← #34010049

Subgroups — #34010049

Order 18688.

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

normal subgroups only

This group has 662 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#22624857C212yesmaximal, complemented
3#22624855C212yesmaximal
4#22612314C211yesmaximal, characteristic
5#17989607—22no—
6#17989432—22no—
7#17989430C2214yes—
8C2×#14556550C411yescharacteristic
9C2×#14556550C2211yescharacteristic
10#17988450C411yescharacteristic
11#17988450C2211yescharacteristic
12#17988447—22no—
13#17988443C411yescharacteristic
14#17988443C2211yescharacteristic
15C4×C22⋊Dic73—22no—
16C24×C4×C73C411yescharacteristic
17#14556658—42no—
18C22⋊#10596833—24no—
19#14556646—42no—
20#14556550—42no—
21#14556550—42no—
22C2×C4⋊Dic73—21no—
23C2×C4⋊Dic73D412yes—
24C2×C22⋊Dic73—22no—
25C2×C22⋊Dic73—22no—
26C2×C22⋊Dic73C2×C411yescharacteristic
27C2×C22⋊Dic73C2×C411yescharacteristic
28C2×C22⋊Dic73C2×C411yescharacteristic
29C2×C22⋊Dic73C2311yescharacteristic
30C2×C4×Dic73—21no—
31C2×C4×Dic73D412yes—
32#14556498—22no—
33#14556498—22no—
34C25×C73C2×C411yescharacteristic
35C23×C4×C73—22no—
36C23×C4×C73—21no—
37C23×C4×C73—21no—
38C23×C4×C73—22no—
39C23×C4×C73—42no—
40C23×C4×C73—42no—
41C23×C4×C73C2×C411yescharacteristic
42C23×C4×C73C2×C411yescharacteristic
43C2×#10596833—44no—
44C22×Dic73—21no—
45C22×Dic73—21no—
46C22×Dic73C22⋊C412yes—
47C22×Dic73C2×D412yes—
48C4⋊Dic73—42no—
49C4⋊Dic73—42no—
50C22⋊Dic73—41no—
51C22⋊Dic73—41no—
52C22⋊Dic73—44no—
53C22⋊Dic73—44no—
54C22⋊Dic73—41no—
55C22⋊Dic73—41no—
56C4×Dic73—22no—
57C4×Dic73—22no—
58C4×Dic73—42no—
59C24×C73—21no—
60C24×C73—21no—
61C24×C73—41no—
62C24×C73—41no—
63C24×C73—44no—
64C24×C73M1612yes—
65C24×C73C22×C411yescharacteristic
66C22×C4×C73—21no—
67C22×C4×C73—21no—
68C22×C4×C73—22no—
69C22×C4×C73—22no—
70C22×C4×C73—24no—
71C22×C4×C73—24no—
72C22×C4×C73—21no—
73C22×C4×C73—21no—
74C22×C4×C73—48no—
75C22×C4×C73—48no—
76C22×C4×C73—42no—
77C22×C4×C73—42no—
78C22×C4×C73—42no—
79C22×C4×C73—42no—
80C22×C4×C73—41no—
81C22×C4×C73—41no—
82C22×C4×C73C22⋊C411yescharacteristic
83C22×C4×C73C22⋊C411yescharacteristic
84C22×C4×C73M1612yes—
85C23×C73—24no—
86C23×C73—22no—
87C23×C73—21no—
88C23×C73—21no—
89C23×C73—42no—
90C23×C73—44no—
91C23×C73—42no—
92C23×C73—42no—
93C23×C73—42no—
94C23×C73—44no—
95C23×C73—44no—
96C23×C73—48no—
97C23×C73—44no—
98C23×C73—41no—
99C23×C73—41no—
100C23×C73C2×C22⋊C411yescharacteristic
101C23×C73C2×M1611yescharacteristic
102C23×C73C2×M1611yescharacteristic
103C2×C4×C73—24no—
104C2×C4×C73—24no—
105C2×C4×C73—21no—
106C2×C4×C73—21no—
107C2×C4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73—22no—
110C2×C4×C73—48no—
111C2×C4×C73—48no—
112C2×C4×C73—42no—
113C2×C4×C73—41no—
114C2×C4×C73—41no—
115C2×C4×C73—42no—
116C2×C4×C73#9912yes—
117C2×C4×C73#10012yes—
118C2×Dic73—22no—
119C2×Dic73—22no—
120C2×Dic73—42no—
121C2×Dic73—42no—
122C2×Dic73—42no—
123C2×Dic73—42no—
124C2×Dic73—41no—
125C2×Dic73—41no—
126#10596833—84no—
127C22×C73—22no—
128C22×C73—24no—
129C22×C73—21no—
130C22×C73—21no—
131C22×C73—41no—
132C22×C73—41no—
133C22×C73—44no—
134C22×C73—42no—
135C22×C73—42no—
136C22×C73—44no—
137C22×C73—44no—
138C22×C73—48no—
139C22×C73—44no—
140C22×C73—42no—
141C22×C73—42no—
142C22×C73#40711yescharacteristic
143C22×C73C2×#9911yescharacteristic
144C22×C73C2×#10011yescharacteristic
145C4×C73—22no—
146C4×C73—22no—
147C4×C73—42no—
148Dic73—42no—
149Dic73—42no—
150Dic73—81no—
151Dic73—81no—
152#11501—731nomaximal, Sylow
153C2×C73—21no—
154C2×C73—21no—
155C2×C73—44no—
156C2×C73—41no—
157C2×C73—41no—
158C2×C73#146211yescharacteristic
159C2×C73#212012yes—
160#2280—731no—
161#1464—732no—
162#1317—732no—
163#1316—732no—
164C73#1150111yescharacteristic, complemented, Sylow
165C24×C4#6440811yescharacteristic
166C2×#117—731no—
167C2×#117—731no—
168#432—1462no—
169#381—731no—
170#381—731no—
171#380—1462no—
172#379—731no—
173#379—731no—
174C4×C22⋊C4—1462no—
175#324—1462no—
176#323—734no—
177C25C2×#6440811yescharacteristic
178C23×C4—22no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—22no—
182C23×C4—42no—
183C23×C4—42no—
184C23×C4C2×#6440811yescharacteristic
185C23×C4C2×#6440811yescharacteristic
186#117—2922no—
187#117—2922no—
188C2×C4⋊C4—732no—
189C2×C4⋊C4—1461no—
190C2×C22⋊C4—731no—
191C2×C22⋊C4—731no—
192C2×C22⋊C4—731no—
193C2×C22⋊C4—731no—
194C2×C22⋊C4—1462no—
195C2×C22⋊C4—1462no—
196C2×C42—732no—
197C2×C42—1461no—
198C4⋊C8—2922no—
199C22⋊C8—1464no—
200#97—2922no—
201#95—1462no—
202#95—1462no—
203C24—21no—
204C24—21no—
205C24—41no—
206C24—41no—
207C24—44no—
208C24#1192403712yes—
209C24C22×#6440811yescharacteristic
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—24no—
215C22×C4—24no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—48no—
219C22×C4—48no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—732no—
227C22×C4—732no—
228C22×C4—1461no—
229C22×C4—1461no—
230C22×C4C22⋊#6440811yescharacteristic
231C22×C4C22⋊#6440811yescharacteristic
232C22×C4#1192403712yes—
233C2×C8—2924no—
234C4⋊C4—2922no—
235C4⋊C4—2922no—
236C22⋊C4—2924no—
237C22⋊C4—2924no—
238C22⋊C4—2921no—
239C22⋊C4—2921no—
240C22⋊C4—2921no—
241C22⋊C4—2921no—
242C42—2922no—
243C42—1462no—
244C42—1462no—
245C23—24no—
246C23—22no—
247C23—21no—
248C23—21no—
249C23—42no—
250C23—44no—
251C23—42no—
252C23—42no—
253C23—42no—
254C23—44no—
255C23—44no—
256C23—48no—
257C23—44no—
258C23—41no—
259C23—41no—
260C23C2×C22⋊#6440811yescharacteristic
261C23C2×#1192403711yescharacteristic
262C23C2×#1192403711yescharacteristic
263C2×C4—24no—
264C2×C4—24no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—48no—
271C2×C4—48no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—2922no—
277C2×C4—2922no—
278C2×C4—2922no—
279C2×C4—2922no—
280C2×C4—2921no—
281C2×C4—2921no—
282C2×C4—1462no—
283C2×C4—1462no—
284C2×C4#1455664912yes—
285C2×C4#1455665112yes—
286C8—5844no—
287C22—22no—
288C22—24no—
289C22—21no—
290C22—21no—
291C22—41no—
292C22—41no—
293C22—44no—
294C22—42no—
295C22—42no—
296C22—44no—
297C22—44no—
298C22—48no—
299C22—44no—
300C22—42no—
301C22—42no—
302C22#1798955711yescharacteristic
303C22C2×#1455664911yescharacteristic
304C22C2×#1455665111yescharacteristic
305C4—22no—
306C4—22no—
307C4—42no—
308C4—2922no—
309C4—2922no—
310C4—5841no—
311C4—5841no—
312C2—21no—
313C2—21no—
314C2—44no—
315C2—41no—
316C2—41no—
317C2#2262517611yescharacteristic
318C2#2262618212yes—
subgroupG/H
centerC22C2×#14556649
commutatorC24×C73C22×C4
FrattiniC24C22×#64408
FittingC24×C4×C73C4
socleC22×C73C2×#99
prime radicalC25×C73C2×C4
cosocleC2×C22⋊Dic73C23
hypercenterC24×C4#64408
hypocenterC73#11501
LCSG ▷ C24×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
1. #22625182C2semidirect
2. #22624857C2semidirect
164. C73#11501semidirect

Maximal subgroups

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

subgroupindex
#226251822
#226248572
#226248552
#226123142
#1150173