Finite Group Databasebeta

← #32996633

Subgroups — #32996633

Order 18688.

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

normal subgroups only

This group has 378 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#22615143C211yesmaximal, characteristic
2C4×#14556510C211yesmaximal, characteristic
3#22607959C214yesmaximal
4C73×#1467C211yesmaximal, characteristic
5C2×#14556591C411yescharacteristic
6C2×#14556510—21no—
7C4×#11924012—21no—
8#17988526C412yes—
9#17988526C2212yes—
10#17988494—21no—
11#17988493—21no—
12#17988493—21no—
13#17988452—21no—
14C4×C4⋊Dic73C411yescharacteristic
15#17988356C2212yes—
16C2×C4×Q8×C73C2211yescharacteristic
17#432×C73—21no—
18#324×C73—21no—
19#324×C73C2212yes—
20C22×Dic146—21no—
21C2×#11924012—22no—
22#14556591—41no—
23#14556591—41no—
24C2×C4⋊Dic73—21no—
25C2×C4⋊Dic73—21no—
26C2×C4⋊Dic73C2×C412yes—
27C2×C4×Dic73—21no—
28#14556510—24no—
29#14556502—41no—
30C4×#10596831—41no—
31#14556498—22no—
32#14556498—22no—
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—44no—
49C2×Dic146—41no—
50C2×Dic146—41no—
51C22×Dic73—22no—
52C22×Dic73—22no—
53#11924012—24no—
54#11924012—42no—
55C2×#10596831—42no—
56C4⋊Dic73—42no—
57C4⋊Dic73—42no—
58C4⋊Dic73—42no—
59C4×Dic73—42no—
60C2×Q8×C73—22no—
61C2×Q8×C73—22no—
62C2×Q8×C73—41no—
63C22×C4×C73C22⋊C411yescharacteristic
64C22×C4×C73C22⋊C411yescharacteristic
65C22×C4×C73C22⋊C411yescharacteristic
66C22×C4×C73C22⋊C411yescharacteristic
67C22×C4×C73C22×C411yescharacteristic
68C22×C4×C73C2×D411yescharacteristic
69C22×C4×C73C2×D411yescharacteristic
70C2×C8×C73—42no—
71C4⋊C4×C73—41no—
72C4⋊C4×C73—41no—
73C4⋊C4×C73—41no—
74C42×C73—21no—
75C42×C73—21no—
76C42×C73—21no—
77C42×C73—21no—
78C42×C73—21no—
79C42×C73—21no—
80C23×C73C2×C22⋊C411yescharacteristic
81Q8×C73—44no—
82C2×C4×C73—21no—
83C2×C4×C73—21no—
84C2×C4×C73—21no—
85C2×C4×C73—21no—
86C2×C4×C73—22no—
87C2×C4×C73—21no—
88C2×C4×C73—21no—
89C2×C4×C73—21no—
90C2×C4×C73—21no—
91C2×C4×C73—21no—
92C2×C4×C73—21no—
93C2×C4×C73—41no—
94C2×C4×C73—41no—
95C2×C4×C73—41no—
96C2×C4×C73#9911yescharacteristic
97C2×C4×C73#9911yescharacteristic
98C2×C4×C73#10412yes—
99C2×C4×C73#13712yes—
100C2×Dic73—42no—
101C2×Dic73—42no—
102C2×Dic73—44no—
103C2×Dic73—42no—
104C2×Dic73—42no—
105Dic146—82no—
106Dic146—82no—
107C8×C73—82no—
108#10596831—44no—
109C22×C73—21no—
110C22×C73—21no—
111C22×C73C2×#9911yescharacteristic
112C22×C73#41911yescharacteristic
113C22×C73C2×#10411yescharacteristic
114C4×C73—21no—
115C4×C73—22no—
116C4×C73—22no—
117C4×C73—41no—
118C4×C73—41no—
119C4×C73—41no—
120C4×C73—41no—
121C4×C73#35512yes—
122Dic73—82no—
123Dic73—82no—
124#11794—731nomaximal, Sylow
125C2×C73—21no—
126C2×C73—21no—
127C2×C73#150811yescharacteristic
128C2×C73#212311yescharacteristic
129C2×C73C2×#35511yescharacteristic
130#2568—731no—
131C4×#101—731no—
132#1467D7311yescharacteristic
133#1353—734no—
134C73#1179411yescharacteristic, complemented, Sylow
135C2×C4⋊Q8—731no—
136C2×C4×Q8C2×D7311yescharacteristic
137#432—21no—
138C2×#101—1461no—
139C4×M16—1461no—
140#400—732no—
141#400—732no—
142#391—1461no—
143#391—1461no—
144#391—1461no—
145#382—1461no—
146C4×C4⋊C4—731no—
147#343—732no—
148#324—21no—
149#324C2×D7312yes—
150C22×Q8—1461no—
151C22×Q8D29211yescharacteristic
152C2×M16—1462no—
153C4⋊Q8—2921no—
154C4⋊Q8—2921no—
155C4×Q8—41no—
156C4×Q8—41no—
157C2×C4⋊C4—732no—
158C2×C4⋊C4—1461no—
159C2×C4⋊C4—1461no—
160C2×C4⋊C4C4×D7311yescharacteristic
161C2×C4⋊C4C22⋊D7311yescharacteristic
162C2×C4⋊C4C22×D7311yescharacteristic
163C2×C42—1461no—
164C2×C42C4×D7311yescharacteristic
165C2×C42D29211yescharacteristic
166C2×C42C22⋊D7311yescharacteristic
167C4⋊C8—41no—
168#101—1464no—
169C22⋊C8—22no—
170#97—41no—
171#97—2921no—
172C4×C8—2921no—
173#95—732no—
174#95—1462no—
175#95—1462no—
176#95—1462no—
177#95—1462no—
178C2×Q8—22no—
179C2×Q8—22no—
180C2×Q8—41no—
181C2×Q8—2924no—
182C2×Q8—2921no—
183C2×Q8—2921no—
184C22×C4—1462no—
185C22×C4—1462no—
186C22×C4#1192400511yescharacteristic
187C22×C4#1192400511yescharacteristic
188C22×C4#1192400511yescharacteristic
189C22×C4#1192400511yescharacteristic
190C22×C4C2×C4×D7311yescharacteristic
191C22×C4C2×C22⋊D7311yescharacteristic
192C22×C4C2×D29211yescharacteristic
193M16—2922no—
194M16—1464no—
195C2×C8—42no—
196C2×C8—2922no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—2922no—
201C4⋊C4—2922no—
202C4⋊C4—2922no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—2922no—
210C23C2×#1192400511yescharacteristic
211Q8—44no—
212Q8—5842no—
213Q8—5842no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—2922no—
229C2×C4—2924no—
230C2×C4—2922no—
231C2×C4—2922no—
232C2×C4—2922no—
233C2×C4#1455650511yescharacteristic
234C2×C4#1455650511yescharacteristic
235C2×C4#1455651712yes—
236C2×C4#1455662412yes—
237C8—82no—
238C8—2924no—
239C22—21no—
240C22—21no—
241C22C2×#1455650511yescharacteristic
242C22#1798859711yescharacteristic
243C22C2×#1455651711yescharacteristic
244C4—22no—
245C4—22no—
246C4—21no—
247C4—41no—
248C4—41no—
249C4—41no—
250C4—41no—
251C4—5842no—
252C4—5842no—
253C4#1798838312yes—
254C2—21no—
255C2—21no—
256C2#2260845211yescharacteristic
257C2#2261158411yescharacteristic
258C2C2×#1798838311yescharacteristic
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#11794
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
134. C73#11794semidirect

Maximal subgroups

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

subgroupindex
#226151432
C4×#145565102
#226079592
C73×#14672
#1179473