Finite Group Databasebeta

← #32980652

Subgroups — #32980652

Order 18688.

510 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 119 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
2C4×#14556589C211yesmaximal, characteristic
3#22608327C212yesmaximal
4#22607763C212yesmaximal
5C73×#1461C211yesmaximal, characteristic
6C2×#14556589C411yescharacteristic
7C2×C4×Dic146C2211yescharacteristic
8#17988718—24no—
9#17988644—22no—
10#17988640C2212yes—
11#17988494C411yescharacteristic
12#17988492C411yescharacteristic
13#17988482—22no—
14#17988456C411yescharacteristic
15C4×#11924007—22no—
16C42×Dic73C2211yescharacteristic
17#17988319—24no—
18C2×C4×Q8×C73C2211yescharacteristic
19#431×C73C2212yes—
20#324×C73—22no—
21C22×Dic146C2×C411yescharacteristic
22#14556589—22no—
23#14556589—22no—
24C4×Dic146—22no—
25C4×Dic146—22no—
26C2×C4⋊Dic73C2×C411yescharacteristic
27C2×#11924007—22no—
28C2×#11924007—22no—
29C2×#11924007—21no—
30C2×C4×Dic73—21no—
31C2×C4×Dic73—21no—
32C2×C4×Dic73—21no—
33C2×C4×Dic73C2×C411yescharacteristic
34C2×C4×Dic73C2×C411yescharacteristic
35C4⋊#10596831—24no—
36C4⋊#10596831D414yes—
37C22⋊#10596831—22no—
38#14556502—24no—
39C4×#10596831—22no—
40#14556498—22no—
41#14556498—22no—
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—
52C2×Dic146—22no—
53C2×Dic146—22no—
54C2×Dic146—21no—
55C2×Dic146M1612yes—
56C22×Dic73—21no—
57C22×Dic73—21no—
58C22×Dic73—21no—
59C22×Dic73—21no—
60C2×#10596831—24no—
61C4⋊Dic73—22no—
62#11924007—28no—
63#11924007—44no—
64#11924007—42no—
65C4×Dic73—24no—
66C4×Dic73—21no—
67C4×Dic73—22no—
68C4×Dic73—42no—
69C4×Dic73—41no—
70C4×Dic73—41no—
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
89Q8×C73—42no—
90Q8×C73—42no—
91C2×C4×C73—22no—
92C2×C4×C73—22no—
93C2×C4×C73—22no—
94C2×C4×C73—22no—
95C2×C4×C73—22no—
96C2×C4×C73—41no—
97C2×C4×C73—42no—
98C2×C4×C73C4×D412yes—
99C2×C4×C73#12011yescharacteristic
100C2×C4×C73#12112yes—
101C2×C4×C73#12311yescharacteristic
102C2×C4×C73C2×M1611yescharacteristic
103C2×C4×C73C2×M1611yescharacteristic
104C2×C4×C73#13112yes—
105C2×Dic73—22no—
106C2×Dic73—22no—
107C2×Dic73—22no—
108C2×Dic73—22no—
109C2×Dic73—22no—
110C2×Dic73—41no—
111C2×Dic73—41no—
112C2×Dic73—41no—
113C2×Dic73—41no—
114C2×Dic73—42no—
115C2×Dic73—41no—
116Dic146—24no—
117Dic146—42no—
118C8×C73—82no—
119#10596831—44no—
120C22×C73—21no—
121C22×C73—21no—
122C22×C73#38611yescharacteristic
123C22×C73#40711yescharacteristic
124C22×C73#40811yescharacteristic
125C4×C73—22no—
126C4×C73—21no—
127C4×C73—42no—
128C4×C73—42no—
129C4×C73#43512yes—
130C4×C73#43612yes—
131C4×C73#45612yes—
132Dic73—24no—
133Dic73—42no—
134Dic73—42no—
135Dic73—81no—
136#8962—731nomaximal, Sylow
137C2×C73—21no—
138C2×C73—21no—
139C2×C73#187011yescharacteristic
140C2×C73#188411yescharacteristic
141C2×C73#188611yescharacteristic
142#2983—731no—
143C4×C4⋊Q8—731no—
144#1479—732no—
145#1461D7311yescharacteristic
146#1276—732no—
147C73#896211yescharacteristic, complemented, Sylow
148C2×C4⋊Q8—731no—
149C2×C4×Q8—731no—
150C2×C4×Q8C2×D7311yescharacteristic
151#446—1464no—
152#432—1462no—
153#431—732no—
154#431C2×D7312yes—
155#391—731no—
156#391—731no—
157#389—1462no—
158#384—731no—
159C4×C4⋊C4—1462no—
160C43—731no—
161Q8⋊C8—1464no—
162#324—22no—
163C22×Q8—731no—
164C22×Q8C4×D7311yescharacteristic
165C4⋊Q8—1462no—
166C4⋊Q8—1462no—
167C4×Q8—22no—
168C4×Q8—22no—
169C4×Q8—1462no—
170C4×Q8—1462no—
171C2×C4⋊C4—731no—
172C2×C4⋊C4—1462no—
173C2×C4⋊C4—1461no—
174C2×C4⋊C4—1462no—
175C2×C4⋊C4C4×D7311yescharacteristic
176C2×C4⋊C4C22⋊D7312yes—
177C2×C42—731no—
178C2×C42—731no—
179C2×C42—1461no—
180C2×C42—1461no—
181C2×C42—1461no—
182C2×C42D29212yes—
183C2×C42C22×D7311yescharacteristic
184C4⋊C8—22no—
185C4⋊C8—734no—
186C4⋊C8—1464no—
187C22⋊C8—22no—
188C22⋊C8—1462no—
189#97—1464no—
190C4×C8—22no—
191C4×C8—1462no—
192#95—1462no—
193#95—1462no—
194C2×Q8—22no—
195C2×Q8—21no—
196C2×Q8—21no—
197C2×Q8—22no—
198C2×Q8—732no—
199C2×Q8—1462no—
200C2×Q8—1462no—
201C2×Q8—1461no—
202C22×C4—1461no—
203C22×C4—1461no—
204C22×C4—1461no—
205C22×C4—1461no—
206C22×C4#1192400512yes—
207C22×C4#1192400512yes—
208C22×C4C2×C4×D7311yescharacteristic
209C22×C4C2×C22⋊D7311yescharacteristic
210C22×C4C2×D29211yescharacteristic
211C2×C8—42no—
212C2×C8—1464no—
213C4⋊C4—22no—
214C4⋊C4—24no—
215C4⋊C4—2924no—
216C4⋊C4—2922no—
217C4⋊C4—1468no—
218C4⋊C4—1462no—
219C42—22no—
220C42—22no—
221C42—2922no—
222C42—2921no—
223C42—2921no—
224C42—732no—
225C42—1464no—
226C42—1462no—
227C42—1461no—
228C42D4×D7312yes—
229C42#1192402712yes—
230C23C2×#1192400511yescharacteristic
231Q8—42no—
232Q8—42no—
233Q8—2922no—
234Q8—1464no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—2921no—
243C2×C4—2921no—
244C2×C4—2921no—
245C2×C4—2921no—
246C2×C4—2922no—
247C2×C4—2921no—
248C2×C4—1462no—
249C2×C4—1462no—
250C2×C4—1462no—
251C2×C4—1462no—
252C2×C4—1462no—
253C2×C4#1455655112yes—
254C2×C4#1455656111yescharacteristic
255C2×C4#1455656312yes—
256C2×C4#1455657511yescharacteristic
257C2×C4M16×D7311yescharacteristic
258C2×C4M16×D7311yescharacteristic
259C2×C4#1455659712yes—
260C8—82no—
261C8—2924no—
262C22—21no—
263C22—21no—
264C22#1798846411yescharacteristic
265C22#1798855011yescharacteristic
266C22#1798855311yescharacteristic
267C4—22no—
268C4—21no—
269C4—42no—
270C4—42no—
271C4—2922no—
272C4—2922no—
273C4—5841no—
274C4—1464no—
275C4#1798866112yes—
276C4#1798866212yes—
277C4#1798877212yes—
278C2—21no—
279C2—21no—
280C2#2261022611yescharacteristic
281C2#2261031211yescharacteristic
282C2#2261032211yescharacteristic
subgroupG/H
centerC2×C4#14556561
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1461C2
socleC22×C73#386
prime radicalC23×C73C2×C22⋊C4
cosocleC2×C42×C73C23
hypercenter#1461D73
hypocenterC73#8962
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
147. C73#8962semidirect

Maximal subgroups

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

subgroupindex
#226190162
C4×#145565892
#226083272
#226077632
C73×#14612
#896273