Finite Group Databasebeta

← #32996637

Subgroups — #32996637

Order 18688.

394 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 87 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
2C4×#14556510C211yesmaximal, characteristic
3#22607962C214yesmaximal
4C73×#1467C211yesmaximal, characteristic
5C2×#14556591C411yescharacteristic
6C2×#14556510—21no—
7C4×#11924012—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#432×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—
30#14556510—24no—
31#14556502—41no—
32C4×#10596831—41no—
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—
47#97×C73—41no—
48C2×Dic146—42no—
49C2×Dic146—82no—
50C22×Dic73—22no—
51C22×Dic73—22no—
52#11924012—24no—
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—22no—
63C2×Q8×C73—22no—
64C2×Q8×C73—41no—
65C22×C4×C73C22⋊C411yescharacteristic
66C22×C4×C73C22⋊C411yescharacteristic
67C22×C4×C73C22⋊C411yescharacteristic
68C22×C4×C73C22⋊C411yescharacteristic
69C22×C4×C73C22×C411yescharacteristic
70C22×C4×C73C2×D411yescharacteristic
71C22×C4×C73C2×D411yescharacteristic
72C2×C8×C73—42no—
73C4⋊C4×C73—41no—
74C4⋊C4×C73—41no—
75C4⋊C4×C73—41no—
76C42×C73—21no—
77C42×C73—21no—
78C42×C73—21no—
79C42×C73—21no—
80C42×C73—21no—
81C42×C73—21no—
82C23×C73C2×C22⋊C411yescharacteristic
83Q8×C73—44no—
84C2×C4×C73—21no—
85C2×C4×C73—21no—
86C2×C4×C73—21no—
87C2×C4×C73—21no—
88C2×C4×C73—22no—
89C2×C4×C73—21no—
90C2×C4×C73—21no—
91C2×C4×C73—21no—
92C2×C4×C73—21no—
93C2×C4×C73—21no—
94C2×C4×C73—21no—
95C2×C4×C73—41no—
96C2×C4×C73—41no—
97C2×C4×C73—41no—
98C2×C4×C73#9911yescharacteristic
99C2×C4×C73#9911yescharacteristic
100C2×C4×C73#10412yes—
101C2×C4×C73#13712yes—
102C2×Dic73—24no—
103C2×Dic73—42no—
104C2×Dic73—42no—
105C2×Dic73—42no—
106C2×Dic73—42no—
107C2×Dic73—42no—
108Dic146—84no—
109C8×C73—82no—
110#10596831—44no—
111C22×C73—21no—
112C22×C73—21no—
113C22×C73C2×#9911yescharacteristic
114C22×C73#41911yescharacteristic
115C22×C73C2×#10411yescharacteristic
116C4×C73—21no—
117C4×C73—22no—
118C4×C73—22no—
119C4×C73—41no—
120C4×C73—41no—
121C4×C73—41no—
122C4×C73—41no—
123C4×C73#35612yes—
124Dic73—44no—
125Dic73—82no—
126#11795—731nomaximal, Sylow
127C2×C73—21no—
128C2×C73—21no—
129C2×C73#150811yescharacteristic
130C2×C73#212211yescharacteristic
131C2×C73C2×#35611yescharacteristic
132#2567—731no—
133C4×#101—731no—
134#1467D7311yescharacteristic
135#1354—734no—
136C73#1179511yescharacteristic, complemented, Sylow
137C2×C4⋊Q8—731no—
138C2×C4×Q8C2×D7311yescharacteristic
139#432—21no—
140C2×#101—1461no—
141C4×M16—1461no—
142#395—732no—
143#395—732no—
144#391—1461no—
145#389—1461no—
146#389—1461no—
147#384—1461no—
148C4×C4⋊C4—731no—
149#343—732no—
150#324—21no—
151#324C2×D7312yes—
152C22×Q8—732no—
153C22×Q8D29211yescharacteristic
154C2×M16—1462no—
155C4⋊Q8—2921no—
156C4⋊Q8—2921no—
157C4×Q8—41no—
158C4×Q8—41no—
159C2×C4⋊C4—1461no—
160C2×C4⋊C4—1461no—
161C2×C4⋊C4—1462no—
162C2×C4⋊C4—1462no—
163C2×C4⋊C4—1461no—
164C2×C4⋊C4C4×D7311yescharacteristic
165C2×C4⋊C4C22⋊D7311yescharacteristic
166C2×C4⋊C4C22×D7311yescharacteristic
167C2×C42—1461no—
168C2×C42C4×D7311yescharacteristic
169C2×C42D29211yescharacteristic
170C2×C42C22⋊D7311yescharacteristic
171C4⋊C8—41no—
172#101—1464no—
173C22⋊C8—22no—
174#97—41no—
175#97—2921no—
176C4×C8—2921no—
177#95—732no—
178#95—1462no—
179#95—1462no—
180C2×Q8—22no—
181C2×Q8—22no—
182C2×Q8—41no—
183C2×Q8—2922no—
184C2×Q8—5842no—
185C22×C4—1462no—
186C22×C4—1462no—
187C22×C4#1192400511yescharacteristic
188C22×C4#1192400511yescharacteristic
189C22×C4#1192400511yescharacteristic
190C22×C4#1192400511yescharacteristic
191C22×C4C2×C4×D7311yescharacteristic
192C22×C4C2×C22⋊D7311yescharacteristic
193C22×C4C2×D29211yescharacteristic
194M16—2922no—
195M16—1464no—
196C2×C8—42no—
197C2×C8—2922no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—2922no—
202C4⋊C4—2921no—
203C4⋊C4—2921no—
204C4⋊C4—5842no—
205C4⋊C4—5842no—
206C4⋊C4—1464no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—2922no—
214C23C2×#1192400511yescharacteristic
215Q8—44no—
216Q8—5844no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—2922no—
232C2×C4—2922no—
233C2×C4—2922no—
234C2×C4—2922no—
235C2×C4—2922no—
236C2×C4—1464no—
237C2×C4#1455650511yescharacteristic
238C2×C4#1455650511yescharacteristic
239C2×C4#1455651712yes—
240C2×C4#1455662412yes—
241C8—82no—
242C8—2924no—
243C22—21no—
244C22—21no—
245C22C2×#1455650511yescharacteristic
246C22#1798859711yescharacteristic
247C22C2×#1455651711yescharacteristic
248C4—22no—
249C4—22no—
250C4—21no—
251C4—41no—
252C4—41no—
253C4—41no—
254C4—41no—
255C4—2924no—
256C4—5842no—
257C4#1798838512yes—
258C2—21no—
259C2—21no—
260C2#2260845211yescharacteristic
261C2#2261158011yescharacteristic
262C2C2×#1798838511yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC22×C4×C73C22×C4
FrattiniC2×C4⋊C4C22×D73
FittingC73×#1467C2
socleC22×C73C2×#99
prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4⋊C4×C73C23
hypercenter#1467D73
hypocenterC73#11795
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
136. C73#11795semidirect

Maximal subgroups

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

subgroupindex
#226151362
C4×#145565102
#226079622
C73×#14672
#1179573