Finite Group Databasebeta

← #32981512

Subgroups — #32981512

Order 18688.

522 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 115 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#22619016C211yesmaximal, characteristic, complemented
2#22612638C211yesmaximal, characteristic
3#22608321C212yesmaximal
4#22607759C212yesmaximal, complemented
5C73×#1461C211yesmaximal, characteristic, complemented
6C2×#14556580C411yescharacteristic
7C2×C4×D292C2211yescharacteristic
8#17988718—24no—
9#17988644—22no—
10#17988640C2212yes—
11#17988494C411yescharacteristic
12#17988488C411yescharacteristic
13#17988478—22no—
14#17988458—22no—
15#17988456C411yescharacteristic
16#17988433C2211yescharacteristic
17#17988314—24no—
18C2×C4×Q8×C73C2211yescharacteristic
19#431×C73C2212yes—
20#324×C73—22no—
21C22×D292C2×C411yescharacteristic
22C22×C4×D73—21no—
23#14556580—22no—
24#14556580—22no—
25C4×D292—22no—
26C4×D292—22no—
27C2×C4⋊Dic73C2×C411yescharacteristic
28C2×#11924007—22no—
29C2×#11924005—22no—
30C2×#11924005—22no—
31C2×#11924005—21no—
32C2×C4×Dic73C2×C411yescharacteristic
33C2×C4×Dic73C2×C411yescharacteristic
34C4⋊#10596831—24no—
35C4⋊#10596831—22no—
36C22⋊#10596831—22no—
37#14556502—24no—
38C4×#10596831D414yes—
39#14556498—22no—
40#14556498—21no—
41#14556498—21no—
42C22×Q8×C73C2×C411yescharacteristic
43C4×Q8×C73—22no—
44C4×Q8×C73—22no—
45C2×C4⋊C4×C73C2×C411yescharacteristic
46C2×C4⋊C4×C73D412yes—
47C2×C42×C73D412yes—
48C2×C42×C73C2311yescharacteristic
49C4⋊C8×C73—22no—
50C22⋊C8×C73—22no—
51C4×C8×C73—22no—
52C23×D73—21no—
53C2×D292—22no—
54C2×D292—22no—
55C2×D292—21no—
56C2×D292M1612yes—
57C22×Dic73—21no—
58C22×Dic73—21no—
59C22×Dic73—21no—
60C2×C4×D73—42no—
61C2×C4×D73—82no—
62C2×#10596831—24no—
63C4⋊Dic73—22no—
64#11924007—82no—
65#11924005—28no—
66#11924005—41no—
67#11924005—41no—
68#11924005—82no—
69C4×Dic73—21no—
70C4×Dic73—22no—
71C4×Dic73M1612yes—
72C2×Q8×C73—22no—
73C2×Q8×C73—21no—
74C2×Q8×C73—21no—
75C2×Q8×C73—22no—
76C22×C4×C73C22⋊C412yes—
77C22×C4×C73C22⋊C412yes—
78C22×C4×C73C22×C411yescharacteristic
79C22×C4×C73C2×D411yescharacteristic
80C22×C4×C73C2×D411yescharacteristic
81C2×C8×C73—42no—
82C4⋊C4×C73—22no—
83C4⋊C4×C73—24no—
84C42×C73—22no—
85C42×C73—22no—
86C42×C73C2×D412yes—
87C42×C73#4112yes—
88C23×C73C2×C22⋊C411yescharacteristic
89C22×D73—22no—
90C22×D73—42no—
91C22×D73—42no—
92C22×D73—41no—
93C22×D73—41no—
94Q8×C73—42no—
95Q8×C73—42no—
96C2×C4×C73—22no—
97C2×C4×C73—22no—
98C2×C4×C73—22no—
99C2×C4×C73—22no—
100C2×C4×C73—41no—
101C2×C4×C73—41no—
102C2×C4×C73—42no—
103C2×C4×C73C4×D412yes—
104C2×C4×C73#12011yescharacteristic
105C2×C4×C73#12112yes—
106C2×C4×C73#12311yescharacteristic
107C2×C4×C73C2×M1611yescharacteristic
108C2×C4×C73C2×M1611yescharacteristic
109C2×C4×C73#13112yes—
110C2×Dic73—22no—
111C2×Dic73—41no—
112C2×Dic73—41no—
113C2×Dic73—41no—
114C2×Dic73—42no—
115C2×Dic73—41no—
116C2×Dic73—41no—
117C2×Dic73—41no—
118D292—24no—
119D292—42no—
120C4×D73—84no—
121C8×C73—82no—
122#10596831—44no—
123C22×C73—21no—
124C22×C73—21no—
125C22×C73#38611yescharacteristic
126C22×C73#40711yescharacteristic
127C22×C73#40811yescharacteristic
128C2×D73—44no—
129C2×D73—42no—
130C2×D73—82no—
131C2×D73—81no—
132C2×D73—81no—
133C4×C73—22no—
134C4×C73—21no—
135C4×C73—21no—
136C4×C73—42no—
137C4×C73—42no—
138C4×C73#43512yes—
139C4×C73#43612yes—
140Dic73—42no—
141Dic73—81no—
142Dic73—81no—
143#9106—731nomaximal, Sylow
144C2×C73—21no—
145C2×C73—21no—
146C2×C73#187011yescharacteristic
147C2×C73#191011yescharacteristic
148C2×C73#191211yescharacteristic
149D73—82no—
150#2983—731no—
151#2326—731no—
152#1478—732no—
153#1461D7311yescharacteristic, complemented
154#1274—732no—
155C73#910611yescharacteristic, complemented, Sylow
156C2×#124—731no—
157C2×C4×Q8C2×D7311yescharacteristic
158C2×C4×D4—731no—
159#446—1464no—
160#432—1462no—
161#431—732no—
162#431C2×D7312yes—
163#391—731no—
164#390—731no—
165#388—1462no—
166#385—1462no—
167#384—731no—
168#376—731no—
169D4⋊C8—1464no—
170#324—22no—
171C22×Q8C4×D7311yescharacteristic
172C22×D4—731no—
173C23×C4—1461no—
174#124—1462no—
175#124—1462no—
176C4×Q8—22no—
177C4×Q8—22no—
178C4×D4—1462no—
179C4×D4—1462no—
180C2×C4⋊C4—731no—
181C2×C4⋊C4—1462no—
182C2×C4⋊C4C4×D7311yescharacteristic
183C2×C4⋊C4C22⋊D7312yes—
184C2×C22⋊C4—1461no—
185C2×C22⋊C4—1462no—
186C2×C22⋊C4—1462no—
187C2×C42—731no—
188C2×C42—731no—
189C2×C42D29212yes—
190C2×C42C22×D7311yescharacteristic
191C4⋊C8—22no—
192C4⋊C8—1464no—
193C4⋊C8—1462no—
194C22⋊C8—22no—
195C22⋊C8—1462no—
196#97—1464no—
197C4×C8—22no—
198C4×C8—734no—
199#95—1462no—
200#95—1461no—
201#95—1461no—
202C24—1461no—
203C2×Q8—22no—
204C2×Q8—21no—
205C2×Q8—21no—
206C2×Q8—22no—
207C2×D4—732no—
208C2×D4—1462no—
209C2×D4—1461no—
210C2×D4—1462no—
211C22×C4—2922no—
212C22×C4—5842no—
213C22×C4—1461no—
214C22×C4—1461no—
215C22×C4—1461no—
216C22×C4#1192400512yes—
217C22×C4#1192400512yes—
218C22×C4C2×C4×D7311yescharacteristic
219C22×C4C2×C22⋊D7311yescharacteristic
220C22×C4C2×D29211yescharacteristic
221C2×C8—42no—
222C2×C8—1464no—
223C4⋊C4—22no—
224C4⋊C4—24no—
225C4⋊C4—5842no—
226C4⋊C4—1462no—
227C22⋊C4—2921no—
228C22⋊C4—2921no—
229C22⋊C4—5842no—
230C22⋊C4—1468no—
231C42—22no—
232C42—22no—
233C42—732no—
234C42—1462no—
235C42—1461no—
236C42D4×D7312yes—
237C42#1192402712yes—
238C23—2922no—
239C23—2922no—
240C23—2921no—
241C23—2921no—
242C23—1462no—
243C23C2×#1192400511yescharacteristic
244Q8—42no—
245Q8—42no—
246D4—2922no—
247D4—1464no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—2921no—
256C2×C4—2921no—
257C2×C4—2921no—
258C2×C4—2922no—
259C2×C4—2921no—
260C2×C4—2921no—
261C2×C4—2921no—
262C2×C4—5844no—
263C2×C4—1462no—
264C2×C4#1455655112yes—
265C2×C4#1455656111yescharacteristic
266C2×C4#1455656312yes—
267C2×C4#1455657511yescharacteristic
268C2×C4M16×D7311yescharacteristic
269C2×C4M16×D7311yescharacteristic
270C2×C4#1455659712yes—
271C8—82no—
272C8—2924no—
273C22—21no—
274C22—21no—
275C22—2924no—
276C22—2922no—
277C22—5842no—
278C22—5841no—
279C22—5841no—
280C22#1798846411yescharacteristic
281C22#1798855011yescharacteristic
282C22#1798855311yescharacteristic
283C4—22no—
284C4—21no—
285C4—21no—
286C4—42no—
287C4—42no—
288C4—2922no—
289C4—5841no—
290C4—5841no—
291C4#1798866112yes—
292C4#1798866212yes—
293C2—21no—
294C2—21no—
295C2—5842no—
296C2#2261022611yescharacteristic
297C2#2261045611yescharacteristic
298C2#2261046611yescharacteristic
subgroupG/H
centerC22#17988464
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1461C2
socleC22×C73#386
prime radicalC22×D292C2×C4
cosocleC2×C42×C73C23
hypercenter#1461D73
hypocenterC73#9106
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
1. #22619016C2semidirect
4. #22607759C2semidirect
5. C73×#1461C2semidirect
153. #1461D73semidirect
155. C73#9106semidirect

Maximal subgroups

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

subgroupindex
#226190162
#226126382
#226083212
#226077592
C73×#14612
#910673