Finite Group Databasebeta

← #33095440

Subgroups — #33095440

Order 18688.

990 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989215C211yesmaximal, characteristic
2#22612532C212yesmaximal
3#22610914C218yesmaximal
4#22610008C211yesmaximal, characteristic
5#22610006C212yesmaximal
6C73×#1820C211yesmaximal, characteristic
7#17989215—24no—
8#17989215—24no—
9C2×#14556591C412yescomplemented
10C2×#14556590C412yescomplemented
11C2×#14556583C412yescomplemented
12C2×#14556582C412yescomplemented
13C2×#14556568C2214yes—
14C2×#14556550C2211yescharacteristic
15C22×C4⋊Dic73C2211yescharacteristic
16#17988472—24no—
17#17988470—24no—
18#17988450C2212yes—
19#17988445C2214yes—
20C22⋊C4×Dic73C2214yes—
21#17988354C2214yes—
22#17988353C2218yes—
23C2×#117×C73C2211yescharacteristic
24#381×C73C2212yes—
25#342×C73C2214yes—
26C22×Dic146C2×C414yes—
27C23×Dic73C2312yes—
28#14556591—24no—
29#14556591—24no—
30#14556590—28no—
31#14556583—24no—
32#14556583—24no—
33#14556582—28no—
34#14556568—28no—
35#14556568—28no—
36#14556550—22no—
37#14556550—22no—
38C2×C4⋊Dic73C2×C411yescharacteristic
39C2×C4⋊Dic73C2×C414yes—
40C2×C4⋊Dic73C2×C411yescharacteristic
41C2×C4⋊Dic73C2×C412yes—
42C2×C4⋊Dic73C2×C412yes—
43C2×C4⋊Dic73D414yes—
44C2×C4⋊Dic73D414yes—
45C2×#11924007—24no—
46C2×#11924007C2×C414yes—
47C2×#11924007C2×C414yes—
48C2×C22⋊Dic73C2314yes—
49C2×C22⋊Dic73C2312yes—
50C2×C4×Dic73—24no—
51C2×C4×Dic73C2×C412yes—
52#14556498—24no—
53#14556498—24no—
54#14556498—22no—
55#14556498—22no—
56C23×C4×C73C2311yescharacteristic
57#117×C73—22no—
58#117×C73—22no—
59C2×C4⋊C4×C73C2×C411yescharacteristic
60C2×C4⋊C4×C73C2×C411yescharacteristic
61C2×C22⋊C4×C73C2314yes—
62C2×C22⋊C4×C73C2312yes—
63C2×C42×C73C2×C412yes—
64#95×C73—22no—
65#95×C73—22no—
66C2×Dic146—28no—
67C2×Dic146—84no—
68C22×Dic73—24no—
69C22×Dic73—82no—
70C22×Dic73C22×C412yes—
71C22×Dic73C22×C412yes—
72C22×Dic73C22×C414yes—
73C22×Dic73C2×D414yes—
74C22×Dic73C2×D414yes—
75C4⋊Dic73—21no—
76C4⋊Dic73—21no—
77C4⋊Dic73—21no—
78C4⋊Dic73—21no—
79C4⋊Dic73—28no—
80C4⋊Dic73C22⋊C418yes—
81C4⋊Dic73C22⋊C414yes—
82C4⋊Dic73C22⋊C414yes—
83#11924007—28no—
84#11924007—28no—
85#11924007—84no—
86C22⋊Dic73—24no—
87C22⋊Dic73—28no—
88C4×Dic73—24no—
89C4×Dic73—84no—
90C24×C73C2411yescharacteristic
91C22×C4×C73—24no—
92C22×C4×C73—24no—
93C22×C4×C73C22×C411yescharacteristic
94C22×C4×C73C22×C411yescharacteristic
95C22×C4×C73C22×C412yes—
96C22×C4×C73C22×C412yes—
97C22×C4×C73C2×D412yes—
98C22×C4×C73C2×D412yes—
99C4⋊C4×C73—22no—
100C4⋊C4×C73—22no—
101C22⋊C4×C73—24no—
102C22⋊C4×C73—28no—
103C42×C73—22no—
104C42×C73—22no—
105C23×C73—41no—
106C23×C73—41no—
107C23×C73C23×C411yescharacteristic
108C23×C73C22×D412yes—
109C23×C732−1+414yes—
110C2×C4×C73—22no—
111C2×C4×C73—22no—
112C2×C4×C73—24no—
113C2×C4×C73—24no—
114C2×C4×C73—22no—
115C2×C4×C73—22no—
116C2×C4×C73—42no—
117C2×C4×C73—42no—
118C2×C4×C73—44no—
119C2×C4×C73—44no—
120C2×C4×C73—44no—
121C2×C4×C73C2×C22⋊C411yescharacteristic
122C2×C4×C73C2×C22⋊C411yescharacteristic
123C2×C4×C73C2×C22⋊C412yes—
124C2×Dic73—22no—
125C2×Dic73—22no—
126C2×Dic73—44no—
127C2×Dic73—44no—
128C2×Dic73—44no—
129C2×Dic73—42no—
130C2×Dic73—42no—
131C2×Dic73—44no—
132C2×Dic73—44no—
133C2×Dic73—44no—
134C2×Dic73C2×C22⋊C418yes—
135Dic146—88no—
136C22×C73—21no—
137C22×C73—22no—
138C22×C73—21no—
139C22×C73—22no—
140C22×C73—44no—
141C22×C73C22×C22⋊C411yescharacteristic
142C22×C73#51912yes—
143C22×C73#53614yes—
144C4×C73—21no—
145C4×C73—21no—
146C4×C73—22no—
147C4×C73—42no—
148C4×C73—42no—
149C4×C73—84no—
150Dic73—28no—
151Dic73—42no—
152Dic73—42no—
153Dic73—84no—
154#21828—731nomaximal, Sylow
155C2×C73—24no—
156C2×C73—22no—
157C2×C73#231011yescharacteristic
158C2×C73#288311yescharacteristic
159C2×C73#288411yescharacteristic
160C2×#544—731no—
161#2313—732no—
162#1996—738no—
163#1820—732no—
164#1820—731no—
165#1820D7311yescharacteristic
166C73#2182811yescharacteristic, complemented, Sylow
167#544—1464no—
168#544—1464no—
169C2×C4⋊Q8—732no—
170C2×C4⋊Q8—732no—
171C2×#125—732no—
172C2×#125—732no—
173C2×C22⋊Q8—734no—
174C2×#117—731no—
175C2×#117C2×D7311yescharacteristic
176C22×C4⋊C4—731no—
177#387—1464no—
178#387—1464no—
179#381—732no—
180#381C2×D7312yes—
181#380—734no—
182C4×C22⋊C4—734no—
183#342—738no—
184#342—734no—
185#342C2×D7314yes—
186C22×Q8—734no—
187C23×C4—732no—
188C23×C4C22×D7311yescharacteristic
189C4⋊Q8—1464no—
190C4⋊Q8—1464no—
191C4⋊Q8—1468no—
192#125—1464no—
193#125—1464no—
194#125—1468no—
195C22⋊Q8—1468no—
196C22⋊Q8—1468no—
197#117—22no—
198#117—22no—
199#117—1462no—
200#117—1462no—
201C2×C4⋊C4—732no—
202C2×C4⋊C4—732no—
203C2×C4⋊C4—734no—
204C2×C4⋊C4—734no—
205C2×C4⋊C4—731no—
206C2×C4⋊C4—731no—
207C2×C4⋊C4—734no—
208C2×C4⋊C4—734no—
209C2×C4⋊C4—734no—
210C2×C4⋊C4—1464no—
211C2×C4⋊C4C4×D7311yescharacteristic
212C2×C4⋊C4C4×D7311yescharacteristic
213C2×C22⋊C4—732no—
214C2×C22⋊C4—734no—
215C2×C22⋊C4C22×D7314yes—
216C2×C22⋊C4C22×D7312yes—
217C2×C42—732no—
218C2×C42—1464no—
219C2×C42C4×D7312yes—
220#95—22no—
221#95—22no—
222#95—1464no—
223#95—1464no—
224#95—1462no—
225#95—1462no—
226C24C23×D7311yescharacteristic
227C2×Q8—5844no—
228C2×Q8—1468no—
229C22×C4—24no—
230C22×C4—24no—
231C22×C4—5842no—
232C22×C4—734no—
233C22×C4—734no—
234C22×C4—734no—
235C22×C4—732no—
236C22×C4—732no—
237C22×C4—1464no—
238C22×C4C2×C4×D7311yescharacteristic
239C22×C4C2×C4×D7311yescharacteristic
240C22×C4C2×C4×D7312yes—
241C22×C4C2×C4×D7312yes—
242C22×C4D4×D7312yes—
243C22×C4D4×D7312yes—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—5844no—
247C4⋊C4—734no—
248C4⋊C4—734no—
249C4⋊C4—738no—
250C4⋊C4—1468no—
251C4⋊C4—1468no—
252C4⋊C4—1468no—
253C4⋊C4—1461no—
254C4⋊C4—1461no—
255C4⋊C4—1461no—
256C4⋊C4—1461no—
257C22⋊C4—24no—
258C22⋊C4—28no—
259C22⋊C4—1468no—
260C22⋊C4—1464no—
261C42—22no—
262C42—22no—
263C42—5844no—
264C42—1464no—
265C23—41no—
266C23—41no—
267C23C22×C4×D7311yescharacteristic
268C23C2×D4×D7312yes—
269C23#1455663814yes—
270Q8—5848no—
271C2×C4—24no—
272C2×C4—24no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—44no—
280C2×C4—44no—
281C2×C4—44no—
282C2×C4—2922no—
283C2×C4—2922no—
284C2×C4—2924no—
285C2×C4—2924no—
286C2×C4—2924no—
287C2×C4—2924no—
288C2×C4—2924no—
289C2×C4—2924no—
290C2×C4—738no—
291C2×C4—1462no—
292C2×C4—1462no—
293C2×C4C22⋊C4×D7311yescharacteristic
294C2×C4C22⋊C4×D7311yescharacteristic
295C2×C4C22⋊C4×D7312yes—
296C22—21no—
297C22—22no—
298C22—21no—
299C22—22no—
300C22—44no—
301C22C2×C22⋊C4×D7311yescharacteristic
302C22#1798906412yes—
303C22#1798915914yes—
304C4—21no—
305C4—21no—
306C4—22no—
307C4—42no—
308C4—42no—
309C4—84no—
310C4—2922no—
311C4—2922no—
312C4—5844no—
313C4—1468no—
314C2—24no—
315C2—22no—
316C2#2261251611yescharacteristic
317C2#2261839011yescharacteristic
318C2#2261839311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D73
commutatorC23×C73C23×C4
FrattiniC24C23×D73
FittingC73×#1820C2
socleC22×C73C22×C22⋊C4
prime radical, cosocleC24×C73C24
hypercenter#1820D73
hypocenterC73#21828
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1820

Complements

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

NH ≅ G/Ntype
9. C2×#14556591C4semidirect
10. C2×#14556590C4semidirect
11. C2×#14556583C4semidirect
12. C2×#14556582C4semidirect
166. C73#21828semidirect

Maximal subgroups

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

subgroupindex
C2×#179892152
#226125322
#226109142
#226100082
#226100062
C73×#18202
#2182873