Finite Group Databasebeta

← #32997152

Subgroups — #32997152

Order 18688.

388 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 99 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#22615136C211yesmaximal, characteristic
2#22609927C211yesmaximal, characteristic
3#22607962C214yesmaximal
4C73×#1461C211yesmaximal, characteristic
5C2×#14556591C411yescharacteristic
6#17988611—21no—
7C2×#14556510—21no—
8#17988507C412yes—
9#17988507C2212yes—
10#17988494—21no—
11#17988485—21no—
12#17988485—21no—
13#17988456—21no—
14C4×C4⋊Dic73C411yescharacteristic
15#17988356C2212yes—
16C2×C4×Q8×C73C2211yescharacteristic
17#431×C73—21no—
18#324×C73—21no—
19#324×C73C2212yes—
20C22×Dic146C2×C412yes—
21C2×#11924012—22no—
22#14556591—41no—
23#14556591—41no—
24C2×C4⋊Dic73—21no—
25C2×C4⋊Dic73—21no—
26C2×C4⋊Dic73—21no—
27C2×#11924007—22no—
28C2×#11924007—22no—
29C2×C4×Dic73—21no—
30C4⋊#10596831—41no—
31C4⋊#10596831—41no—
32#14556510—42no—
33#14556498—22no—
34#14556498—22no—
35#14556498C2×C412yes—
36C22×Q8×C73D411yescharacteristic
37C4×Q8×C73—41no—
38C4×Q8×C73—41no—
39C2×C4⋊C4×C73C2×C411yescharacteristic
40C2×C4⋊C4×C73D411yescharacteristic
41C2×C4⋊C4×C73C2311yescharacteristic
42C2×C42×C73C2×C411yescharacteristic
43C2×C42×C73D411yescharacteristic
44C2×C42×C73D411yescharacteristic
45C4⋊C8×C73—41no—
46C22⋊C8×C73—22no—
47C4×C8×C73—41no—
48C2×Dic146—42no—
49C2×Dic146—82no—
50C22×Dic73—22no—
51C22×Dic73—22no—
52#11924012—42no—
53#11924012—42no—
54C2×#10596831—42no—
55C4⋊Dic73—24no—
56C4⋊Dic73—42no—
57C4⋊Dic73—41no—
58C4⋊Dic73—41no—
59#11924007—82no—
60#11924007—82no—
61C4×Dic73—42no—
62C2×Q8×C73—41no—
63C2×Q8×C73—41no—
64C2×Q8×C73SD1612yes—
65C2×Q8×C73Q1612yes—
66C22×C4×C73C22⋊C411yescharacteristic
67C22×C4×C73C22⋊C411yescharacteristic
68C22×C4×C73C22⋊C411yescharacteristic
69C22×C4×C73C22⋊C411yescharacteristic
70C22×C4×C73C22×C411yescharacteristic
71C22×C4×C73C2×D411yescharacteristic
72C22×C4×C73C2×D411yescharacteristic
73C2×C8×C73—42no—
74C4⋊C4×C73—41no—
75C4⋊C4×C73—41no—
76C4⋊C4×C73—41no—
77C42×C73—21no—
78C42×C73—21no—
79C42×C73—21no—
80C42×C73—21no—
81C42×C73—21no—
82C42×C73—21no—
83C23×C73C2×C22⋊C411yescharacteristic
84Q8×C73—42no—
85Q8×C73—42no—
86C2×C4×C73—21no—
87C2×C4×C73—21no—
88C2×C4×C73—21no—
89C2×C4×C73—21no—
90C2×C4×C73—21no—
91C2×C4×C73—21no—
92C2×C4×C73—22no—
93C2×C4×C73—21no—
94C2×C4×C73—21no—
95C2×C4×C73—21no—
96C2×C4×C73—41no—
97C2×C4×C73—41no—
98C2×C4×C73—41no—
99C2×C4×C73#9911yescharacteristic
100C2×C4×C73#9911yescharacteristic
101C2×C4×C73#10312yes—
102C2×C4×C73#10312yes—
103C2×C4×C73C2×SD1611yescharacteristic
104C2×C4×C73C2×Q1611yescharacteristic
105C2×Dic73—24no—
106C2×Dic73—42no—
107C2×Dic73—42no—
108C2×Dic73—42no—
109C2×Dic73—42no—
110C2×Dic73—42no—
111Dic146—84no—
112C8×C73—82no—
113#10596831—82no—
114C22×C73—21no—
115C22×C73—21no—
116C22×C73C2×#9911yescharacteristic
117C22×C73C2×#10311yescharacteristic
118C22×C73#42111yescharacteristic
119C4×C73—21no—
120C4×C73—21no—
121C4×C73—22no—
122C4×C73—22no—
123C4×C73—21no—
124C4×C73—41no—
125C4×C73—41no—
126C4×C73—41no—
127C4×C73#35612yes—
128Dic73—44no—
129Dic73—82no—
130#11908—731nomaximal, Sylow
131C2×C73—21no—
132C2×C73—21no—
133C2×C73#152011yescharacteristic
134C2×C73#212211yescharacteristic
135C2×C73C2×#35611yescharacteristic
136#2567—731no—
137#1801—731no—
138#1461D7311yescharacteristic
139#1354—734no—
140C73#1190811yescharacteristic, complemented, Sylow
141C2×C4⋊Q8—731no—
142C2×C4×Q8C2×D7311yescharacteristic
143#431—21no—
144#423—1461no—
145C2×#101—1461no—
146#395—732no—
147#395—732no—
148#391—1461no—
149#389—1461no—
150#389—1461no—
151#384—1461no—
152C4×C4⋊C4—731no—
153#343—732no—
154#324—21no—
155#324C2×D7312yes—
156C22×Q8—732no—
157C22×Q8D29211yescharacteristic
158C2×M16—1462no—
159C4⋊Q8—2921no—
160C4⋊Q8—2921no—
161C4×Q8—41no—
162C4×Q8—41no—
163C2×C4⋊C4—1461no—
164C2×C4⋊C4—1461no—
165C2×C4⋊C4—1462no—
166C2×C4⋊C4—1462no—
167C2×C4⋊C4—1461no—
168C2×C4⋊C4C4×D7311yescharacteristic
169C2×C4⋊C4C22⋊D7311yescharacteristic
170C2×C4⋊C4C22×D7311yescharacteristic
171C2×C42—1461no—
172C2×C42C4×D7311yescharacteristic
173C2×C42D29211yescharacteristic
174C2×C42C22⋊D7311yescharacteristic
175C4⋊C8—41no—
176C4⋊C8—2921no—
177C4⋊C8—2921no—
178#101—2922no—
179C22⋊C8—22no—
180C4×C8—41no—
181#95—732no—
182#95—1462no—
183#95—1462no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8—2922no—
187C2×Q8—5842no—
188C2×Q8#1192401712yes—
189C2×Q8Dic29212yes—
190C22×C4—1462no—
191C22×C4—1462no—
192C22×C4#1192400511yescharacteristic
193C22×C4#1192400511yescharacteristic
194C22×C4#1192400511yescharacteristic
195C22×C4#1192400511yescharacteristic
196C22×C4C2×C4×D7311yescharacteristic
197C22×C4C2×C22⋊D7311yescharacteristic
198C22×C4C2×D29211yescharacteristic
199M16—2922no—
200M16—2922no—
201C2×C8—42no—
202C2×C8—2922no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—2922no—
207C4⋊C4—2921no—
208C4⋊C4—2921no—
209C4⋊C4—5842no—
210C4⋊C4—5842no—
211C4⋊C4—1464no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—2922no—
219C23C2×#1192400511yescharacteristic
220Q8—42no—
221Q8—42no—
222Q8—5844no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—2922no—
237C2×C4—2922no—
238C2×C4—2922no—
239C2×C4—2922no—
240C2×C4—2922no—
241C2×C4—1464no—
242C2×C4#1455650511yescharacteristic
243C2×C4#1455650511yescharacteristic
244C2×C4#1455651612yes—
245C2×C4#1455651612yes—
246C2×C4C2×#1192401711yescharacteristic
247C2×C4C2×Dic29211yescharacteristic
248C8—82no—
249C8—5842no—
250C22—21no—
251C22—21no—
252C22C2×#1455650511yescharacteristic
253C22C2×#1455651611yescharacteristic
254C22#1798860311yescharacteristic
255C4—21no—
256C4—22no—
257C4—22no—
258C4—21no—
259C4—21no—
260C4—41no—
261C4—41no—
262C4—41no—
263C4—2924no—
264C4—5842no—
265C4#1798838512yes—
266C2—21no—
267C2—21no—
268C2#2260850411yescharacteristic
269C2#2261158011yescharacteristic
270C2C2×#1798838511yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC22×C4×C73C22×C4
FrattiniC2×C4⋊C4C22×D73
FittingC73×#1461C2
socleC22×C73C2×#99
prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4⋊C4×C73C23
hypercenter#1461D73
hypocenterC73#11908
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
140. C73#11908semidirect

Maximal subgroups

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

subgroupindex
#226151362
#226099272
#226079622
C73×#14612
#1190873