Finite Group Databasebeta

← #32995380

Subgroups — #32995380

Order 18688.

490 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#17988452C211yesmaximal, characteristic
2#22608261C211yesmaximal, characteristic
3#22607874C214yesmaximal, complemented
4C73×#1463C211yesmaximal, characteristic
5C22×C4⋊Dic73C411yescharacteristic
6C22×C4×Dic73C411yescharacteristic
7#17988551—21no—
8#17988452—21no—
9#17988452—21no—
10#17988452C412yes—
11#17988452C2212yes—
12C2×#14556498—21no—
13C2×#14556498—21no—
14#17988313—21no—
15#17988313C2212yes—
16C22×C4⋊C4×C73C2211yescharacteristic
17#407×C73—21no—
18#324×C73—21no—
19#324×C73C2212yes—
20C23×Dic73—21no—
21C23×Dic73—21no—
22C2×#11924012—41no—
23C2×C4⋊Dic73—21no—
24C2×C4⋊Dic73—41no—
25C2×C4⋊Dic73—41no—
26C2×C4⋊Dic73C2×C412yes—
27C2×C4×Dic73—24no—
28C2×C4×Dic73—21no—
29C2×C4×Dic73C2×C412yes—
30C22⋊#10596831—22no—
31C22⋊#10596831—41no—
32#14556498—22no—
33#14556498—22no—
34#14556498—22no—
35#14556498—22no—
36C23×C4×C73C2×C411yescharacteristic
37C23×C4×C73D411yescharacteristic
38C23×C4×C73D411yescharacteristic
39C2×M16×C73—41no—
40C2×C4⋊C4×C73—41no—
41C2×C4⋊C4×C73—41no—
42C2×C4⋊C4×C73C2×C411yescharacteristic
43C2×C4⋊C4×C73D411yescharacteristic
44C2×C4⋊C4×C73D411yescharacteristic
45C2×C4⋊C4×C73C2311yescharacteristic
46C22⋊C8×C73—22no—
47C22⋊C8×C73—41no—
48C22×Dic73—24no—
49C22×Dic73—22no—
50C22×Dic73—22no—
51C22×Dic73—42no—
52C22×Dic73—42no—
53C22×Dic73—44no—
54C22×Dic73—41no—
55C22×Dic73—41no—
56#11924012—82no—
57C2×#10596831—42no—
58C4⋊Dic73—42no—
59C4⋊Dic73—42no—
60C4×Dic73—24no—
61C4×Dic73—22no—
62C4×Dic73M1614yescomplemented
63C24×C73C22⋊C411yescharacteristic
64C22×C4×C73—21no—
65C22×C4×C73—21no—
66C22×C4×C73—22no—
67C22×C4×C73—22no—
68C22×C4×C73—21no—
69C22×C4×C73—21no—
70C22×C4×C73—21no—
71C22×C4×C73—21no—
72C22×C4×C73—42no—
73C22×C4×C73—42no—
74C22×C4×C73C22⋊C411yescharacteristic
75C22×C4×C73C22⋊C411yescharacteristic
76C22×C4×C73C22⋊C411yescharacteristic
77C22×C4×C73C22×C411yescharacteristic
78C22×C4×C73C2×D411yescharacteristic
79C22×C4×C73C2×D411yescharacteristic
80M16×C73—82no—
81C2×C8×C73—42no—
82C4⋊C4×C73—41no—
83C4⋊C4×C73—41no—
84C4⋊C4×C73—41no—
85C4⋊C4×C73—41no—
86C23×C73—22no—
87C23×C73—22no—
88C23×C73—21no—
89C23×C73—21no—
90C23×C73#9911yescharacteristic
91C23×C73#9911yescharacteristic
92C23×C73C2×C22⋊C411yescharacteristic
93C2×C4×C73—24no—
94C2×C4×C73—24no—
95C2×C4×C73—21no—
96C2×C4×C73—21no—
97C2×C4×C73—21no—
98C2×C4×C73—21no—
99C2×C4×C73—21no—
100C2×C4×C73—21no—
101C2×C4×C73—21no—
102C2×C4×C73—21no—
103C2×C4×C73—42no—
104C2×C4×C73—42no—
105C2×C4×C73—41no—
106C2×C4×C73—41no—
107C2×C4×C73—41no—
108C2×C4×C73—41no—
109C2×C4×C73—81no—
110C2×C4×C73—81no—
111C2×C4×C73#10112yes—
112C2×C4×C73C2×M1612yes—
113C2×Dic73—24no—
114C2×Dic73—48no—
115C2×Dic73—42no—
116C2×Dic73—42no—
117C2×Dic73—44no—
118C2×Dic73—42no—
119C2×Dic73—82no—
120C2×Dic73—82no—
121C8×C73—82no—
122#10596831—82no—
123C22×C73—24no—
124C22×C73—24no—
125C22×C73—21no—
126C22×C73—21no—
127C22×C73—21no—
128C22×C73—21no—
129C22×C73—21no—
130C22×C73—21no—
131C22×C73#35412yes—
132C22×C73#35512yes—
133C22×C73#40711yescharacteristic
134C22×C73C2×#9911yescharacteristic
135C22×C73C2×#10111yescharacteristic
136C4×C73—22no—
137C4×C73—22no—
138C4×C73—41no—
139C4×C73—41no—
140C4×C73—41no—
141C4×C73—41no—
142Dic73—44no—
143Dic73—82no—
144#11511—731nomaximal, Sylow
145C2×C73—21no—
146C2×C73—22no—
147C2×C73—22no—
148C2×C73—21no—
149C2×C73#146311yescharacteristic
150C2×C73C2×#35411yescharacteristic
151C2×C73C2×#35511yescharacteristic
152C2×#382—731no—
153#1463—731no—
154#1463D7311yescharacteristic
155#1324—734no—
156C73#1151111yescharacteristic, complemented, Sylow
157C22×C4⋊C4—731no—
158C22×C4⋊C4C2×D7311yescharacteristic
159C22×C42—731no—
160#407—21no—
161#407—1461no—
162#382—732no—
163#382—732no—
164#382—1461no—
165#382—1461no—
166C2×#95—1461no—
167C2×#95—1461no—
168#324—21no—
169#324—732no—
170#324—1461no—
171#324C2×D7312yes—
172C23×C4—1461no—
173C23×C4—1461no—
174C23×C4C4×D7311yescharacteristic
175C23×C4D29211yescharacteristic
176C23×C4C22⋊D7311yescharacteristic
177C2×M16—41no—
178C2×M16—2921no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4—2921no—
182C2×C4⋊C4—2921no—
183C2×C4⋊C4—732no—
184C2×C4⋊C4—1461no—
185C2×C4⋊C4C4×D7311yescharacteristic
186C2×C4⋊C4D29211yescharacteristic
187C2×C4⋊C4C22⋊D7311yescharacteristic
188C2×C4⋊C4C22×D7311yescharacteristic
189C2×C42—732no—
190C2×C42—1464no—
191C2×C42—1461no—
192C22⋊C8—22no—
193C22⋊C8—41no—
194C22⋊C8—2921no—
195C22⋊C8—1462no—
196#95—1462no—
197#95—1462no—
198#95—1462no—
199#95—1462no—
200C24#1192400511yescharacteristic
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—2922no—
212C22×C4—2922no—
213C22×C4—2924no—
214C22×C4—2921no—
215C22×C4—2921no—
216C22×C4—1462no—
217C22×C4—1464no—
218C22×C4—1462no—
219C22×C4#1192400511yescharacteristic
220C22×C4#1192400511yescharacteristic
221C22×C4#1192400511yescharacteristic
222C22×C4C2×C4×D7311yescharacteristic
223C22×C4C2×C22⋊D7311yescharacteristic
224C22×C4C2×D29211yescharacteristic
225M16—82no—
226M16—5842no—
227C2×C8—42no—
228C2×C8—2922no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—2922no—
234C4⋊C4—2922no—
235C42—734no—
236C42—1464no—
237C42—1462no—
238C23—22no—
239C23—22no—
240C23—21no—
241C23—21no—
242C23#1455650511yescharacteristic
243C23#1455650511yescharacteristic
244C23C2×#1192400511yescharacteristic
245C2×C4—24no—
246C2×C4—24no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—2928no—
264C2×C4—2922no—
265C2×C4—2922no—
266C2×C4—2924no—
267C2×C4—2922no—
268C2×C4—5842no—
269C2×C4—5842no—
270C2×C4—1464no—
271C2×C4#1455650912yes—
272C2×C4M16×D7312yes—
273C8—82no—
274C8—5842no—
275C22—24no—
276C22—24no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22#1798838112yes—
284C22#1798838312yes—
285C22#1798855011yescharacteristic
286C22C2×#1455650511yescharacteristic
287C22C2×#1455650911yescharacteristic
288C4—22no—
289C4—22no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—41no—
294C4—2924no—
295C4—5842no—
296C2—21no—
297C2—22no—
298C2—22no—
299C2—21no—
300C2#2260826011yescharacteristic
301C2C2×#1798838111yescharacteristic
302C2C2×#1798838311yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC22×C4×C73C22×C4
FrattiniC2×C4⋊C4C22×D73
FittingC73×#1463C2
socleC22×C73C2×#99
prime radicalC24×C73C22⋊C4
cosocleC2×C4⋊C4×C73C23
hypercenter#1463D73
hypocenterC73#11511
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
3. #22607874C2semidirect
62. C4×Dic73M16semidirect
156. C73#11511semidirect

Maximal subgroups

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

subgroupindex
C2×#179884522
#226082612
#226078742
C73×#14632
#1151173