Finite Group Databasebeta

← #32974254

Subgroups — #32974254

Order 18688.

468 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 127 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#22609680C211yesmaximal, characteristic
2#22609680C211yesmaximal, characteristic
3#22607754C214yesmaximal
4C4×C4⋊Q8×C73C211yesmaximal, characteristic
5C2×#14556502—21no—
6C2×#14556502—21no—
7#17988342—21no—
8#17988342—21no—
9#17988342C2212yes—
10#17988342C2212yes—
11C2×C4⋊Q8×C73C411yescharacteristic
12C2×C4×Q8×C73—21no—
13#391×C73—21no—
14#389×C73—21no—
15#389×C73C2212yes—
16#384×C73C411yescharacteristic
17C4×C4⋊C4×C73—21no—
18C4×C4⋊C4×C73C412yes—
19C43×C73C2211yescharacteristic
20C22×#10596831—22no—
21C22×#10596831—22no—
22#14556502—24no—
23#14556502—24no—
24C22×Q8×C73—21no—
25C4⋊Q8×C73—24no—
26C4×Q8×C73—44no—
27C2×C4⋊C4×C73—21no—
28C2×C4⋊C4×C73—21no—
29C2×C4⋊C4×C73—21no—
30C2×C4⋊C4×C73—22no—
31C2×C4⋊C4×C73C2×C412yes—
32C2×C4⋊C4×C73C2×C412yes—
33C2×C42×C73—22no—
34C2×C42×C73C2×C411yescharacteristic
35C2×C42×C73C2×C411yescharacteristic
36C2×C42×C73D411yescharacteristic
37C2×C42×C73D411yescharacteristic
38C2×C42×C73D411yescharacteristic
39C2×C42×C73D411yescharacteristic
40C2×C42×C73C2311yescharacteristic
41#95×C73—22no—
42#95×C73—22no—
43C2×#10596831—24no—
44C2×#10596831—24no—
45C2×#10596831—42no—
46C2×#10596831—42no—
47C2×#10596831—42no—
48C2×#10596831—42no—
49C2×Q8×C73—24no—
50C2×Q8×C73—42no—
51C2×Q8×C73—42no—
52C22×C4×C73—22no—
53C22×C4×C73—22no—
54C22×C4×C73C22⋊C411yescharacteristic
55C22×C4×C73C22⋊C411yescharacteristic
56C22×C4×C73C22⋊C411yescharacteristic
57C22×C4×C73C22⋊C411yescharacteristic
58C22×C4×C73C22×C411yescharacteristic
59C22×C4×C73C2×D411yescharacteristic
60C22×C4×C73C2×D411yescharacteristic
61C4⋊C4×C73—24no—
62C4⋊C4×C73—22no—
63C4⋊C4×C73—42no—
64C4⋊C4×C73—42no—
65C4⋊C4×C73—42no—
66C4⋊C4×C73—44no—
67C4⋊C4×C73M1614yes—
68C42×C73—22no—
69C42×C73—22no—
70C42×C73—22no—
71C42×C73—22no—
72C42×C73—22no—
73C42×C73—22no—
74C42×C73—41no—
75C42×C73—44no—
76C23×C73C2×C22⋊C411yescharacteristic
77Q8×C73—48no—
78C2×C4×C73—21no—
79C2×C4×C73—21no—
80C2×C4×C73—21no—
81C2×C4×C73—21no—
82C2×C4×C73—21no—
83C2×C4×C73—21no—
84C2×C4×C73—21no—
85C2×C4×C73—21no—
86C2×C4×C73—21no—
87C2×C4×C73—21no—
88C2×C4×C73—21no—
89C2×C4×C73—21no—
90C2×C4×C73—24no—
91C2×C4×C73—21no—
92C2×C4×C73—21no—
93C2×C4×C73—21no—
94C2×C4×C73—42no—
95C2×C4×C73—42no—
96C2×C4×C73—42no—
97C2×C4×C73—42no—
98C2×C4×C73—42no—
99C2×C4×C73#10112yes—
100C2×C4×C73#10412yes—
101C2×C4×C73#10412yes—
102C2×C4×C73C2×M1612yes—
103C2×C4×C73AGL(1,ℤ/8)12yes—
104C2×C4×C73#13712yes—
105#10596831—44no—
106#10596831—44no—
107C22×C73#40711yescharacteristic
108C22×C73#41011yescharacteristic
109C22×C73C2×#10111yescharacteristic
110C22×C73#41811yescharacteristic
111C22×C73#41911yescharacteristic
112C22×C73C2×#10411yescharacteristic
113C22×C73C2×#10411yescharacteristic
114C4×C73—22no—
115C4×C73—22no—
116C4×C73—22no—
117C4×C73—22no—
118C4×C73—22no—
119C4×C73—22no—
120C4×C73—44no—
121C4×C73—41no—
122C4×C73—82no—
123#7638—731nomaximal, Sylow
124C2×C73#146711yescharacteristic
125C2×C73#149011yescharacteristic
126C2×C73#149111yescharacteristic
127C2×C73#150511yescharacteristic
128C2×C73#150611yescharacteristic
129C2×C73#152611yescharacteristic
130C2×C73#155611yescharacteristic
131C4×C4⋊Q8D7311yescharacteristic
132#1745—731no—
133#1745—731no—
134#1271—734no—
135C73#763811yescharacteristic, complemented, Sylow
136C2×C4⋊Q8Dic7311yescharacteristic
137C2×C4×Q8—21no—
138C2×#97—1461no—
139C2×#97—1461no—
140#391—21no—
141#389—21no—
142#389C2×D7312yes—
143#384Dic7311yescharacteristic
144C4×C4⋊C4—21no—
145C4×C4⋊C4Dic7312yes—
146C43C2×D7311yescharacteristic
147#336—732no—
148#336—732no—
149#336—1461no—
150#336—1461no—
151C22×Q8—21no—
152C22×C8—1462no—
153C22×C8—1462no—
154C4⋊Q8—24no—
155C4×Q8—44no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4C2×Dic7312yes—
161C2×C4⋊C4C2×Dic7312yes—
162C2×C42—22no—
163C2×C42C2×Dic7311yescharacteristic
164C2×C42C2×Dic7311yescharacteristic
165C2×C42C22⋊D7311yescharacteristic
166C2×C42C22⋊D7311yescharacteristic
167C2×C42C22⋊D7311yescharacteristic
168C2×C42C22⋊D7311yescharacteristic
169C2×C42C22×D7311yescharacteristic
170#97—1464no—
171#97—1464no—
172#95—22no—
173#95—22no—
174C2×Q8—24no—
175C2×Q8—42no—
176C2×Q8—42no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4C22⋊Dic7311yescharacteristic
180C22×C4C22⋊Dic7311yescharacteristic
181C22×C4C22⋊Dic7311yescharacteristic
182C22×C4C22⋊Dic7311yescharacteristic
183C22×C4C22×Dic7311yescharacteristic
184C22×C4C2×C22⋊D7311yescharacteristic
185C22×C4C2×C22⋊D7311yescharacteristic
186C2×C8—2922no—
187C2×C8—2922no—
188C2×C8—2922no—
189C2×C8—2922no—
190C2×C8—1464no—
191C2×C8—1464no—
192C4⋊C4—24no—
193C4⋊C4—22no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C4⋊C4—44no—
198C4⋊C4#1192401214yes—
199C42—22no—
200C42—22no—
201C42—22no—
202C42—22no—
203C42—22no—
204C42—22no—
205C42—41no—
206C42—44no—
207C23C2×C22⋊Dic7311yescharacteristic
208Q8—48no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—24no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4#1455651012yes—
231C2×C4#1455651812yes—
232C2×C4#1455651812yes—
233C2×C4C2×#1192401212yes—
234C2×C4#1455661712yes—
235C2×C4#1455662212yes—
236C8—2924no—
237C8—2924no—
238C22#1798855111yescharacteristic
239C22#1798856111yescharacteristic
240C22C2×#1455651011yescharacteristic
241C22#1798859211yescharacteristic
242C22#1798859611yescharacteristic
243C22C2×#1455651811yescharacteristic
244C22C2×#1455651811yescharacteristic
245C4—22no—
246C4—22no—
247C4—22no—
248C4—22no—
249C4—22no—
250C4—22no—
251C4—41no—
252C4—44no—
253C4—82no—
254C2#2260827511yescharacteristic
255C2#2260837411yescharacteristic
256C2#2260837811yescharacteristic
257C2#2260843911yescharacteristic
258C2#2260844311yescharacteristic
259C2#2260852611yescharacteristic
260C2#2260864811yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic73
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC4×C4⋊Q8×C73C2
socle, prime radicalC23×C73C2×C22⋊C4
cosocleC2×C42×C73C23
hypercenterC4×C4⋊Q8D73
hypocenterC73#7638
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C43 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
135. C73#7638semidirect

Maximal subgroups

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

subgroupindex
#226096802
#226077542
C4×C4⋊Q8×C732
#763873