Finite Group Databasebeta

← #22614414

Subgroups — #22614414

Order 9344.

512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#14556568C211yesmaximal, characteristic
2C22×#11924007C211yesmaximal, characteristic
3#17988529C212yesmaximal, complemented
4#17988528C212yesmaximal, complemented
5#17988491C212yesmaximal, complemented
6#17988451C212yesmaximal, complemented
7#17988450C211yesmaximal, characteristic
8#17988448C211yesmaximal, characteristic
9#17988448C211yesmaximal, characteristic
10C22⋊C4×Dic73C211yesmaximal, characteristic
11#381×C73C211yesmaximal, characteristic
12C22×Dic146C2211yescharacteristic
13C23×Dic73C2211yescharacteristic
14C23×Dic73C2211yescharacteristic
15#14556568—24no—
16C2×C4⋊Dic73C2211yescharacteristic
17C2×#11924007—24no—
18C2×#11924007C2211yescharacteristic
19C2×#11924007C2212yes—
20C2×#11924007C2212yes—
21C2×#11924007C2211yescharacteristic
22C2×C22⋊Dic73C2211yescharacteristic
23C2×C22⋊Dic73C2211yescharacteristic
24C2×C4×Dic73C2212yes—
25#14556498C2212yes—
26#14556498C2212yes—
27#14556498C2212yes—
28#14556498C2212yes—
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C23×C4×C73C2211yescharacteristic
33C2×C22⋊C4×C73C2211yescharacteristic
34C2×C22⋊C4×C73C2211yescharacteristic
35#95×C73C2212yes—
36#95×C73C2212yes—
37C2×Dic146—22no—
38C2×Dic146—24no—
39C22×Dic73—24no—
40C22×Dic73—22no—
41C22×Dic73—22no—
42C22×Dic73—22no—
43C22×Dic73D414yes—
44C22×Dic73C2312yes—
45C22×Dic73C2311yescharacteristic
46C22×Dic73C2311yescharacteristic
47C22×Dic73C2312yes—
48C22×Dic73C2311yescharacteristic
49C22×Dic73C2311yescharacteristic
50C4⋊Dic73—22no—
51#11924007—24no—
52#11924007—24no—
53#11924007—22no—
54#11924007—22no—
55C22⋊Dic73—22no—
56C22⋊Dic73—22no—
57C4×Dic73—24no—
58C24×C73C2311yescharacteristic
59C22×C4×C73—22no—
60C22×C4×C73—22no—
61C22×C4×C73—22no—
62C22×C4×C73C2312yes—
63C22×C4×C73C2311yescharacteristic
64C22×C4×C73C2311yescharacteristic
65C22×C4×C73C2312yes—
66C22⋊C4×C73—22no—
67C22⋊C4×C73—22no—
68C23×C73—22no—
69C23×C73—22no—
70C23×C73C2×D412yes—
71C23×C73#4112yes—
72C23×C73#4112yes—
73C23×C73C2411yescharacteristic
74C2×C4×C73—21no—
75C2×C4×C73—21no—
76C2×C4×C73—22no—
77C2×C4×C73—22no—
78C2×C4×C73—22no—
79C2×C4×C73—22no—
80C2×C4×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73—22no—
83C2×C4×C73—22no—
84C2×C4×C73—44no—
85C2×Dic73—22no—
86C2×Dic73—28no—
87C2×Dic73—21no—
88C2×Dic73—21no—
89C2×Dic73—22no—
90C2×Dic73—22no—
91C2×Dic73—22no—
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73—22no—
95C2×Dic73—22no—
96C2×Dic73—22no—
97C2×Dic73—44no—
98C2×Dic73C2×D412yes—
99C2×Dic73C2×D412yes—
100C2×Dic73#4114yes—
101Dic146—44no—
102C22×C73—22no—
103C22×C73—22no—
104C22×C73—24no—
105C22×C73—24no—
106C22×C73#12414yes—
107C22×C73C22×D411yescharacteristic
108C22×C73C2×#4112yes—
109C22×C73C2×#4111yescharacteristic
110C22×C73C2×#4111yescharacteristic
111C22×C732−1+412yes—
112C4×C73—41no—
113C4×C73—42no—
114C4×C73—41no—
115C4×C73—42no—
116Dic73—22no—
117Dic73—41no—
118Dic73—42no—
119Dic73—41no—
120Dic73—42no—
121Dic73#12314yes—
122C2×C73—24no—
123C2×C73C2×#12311yescharacteristic
124C2×C73C2×#12411yescharacteristic
125C2×C73#53611yescharacteristic
126C2×C73#55212yes—
127C2×C73#55212yes—
128#2503—731nomaximal, Sylow
129C73#250311yescharacteristic, complemented, Sylow
130C2×C22⋊Q8—731no—
131C22×C4⋊C4—731no—
132#400—732no—
133#400—732no—
134#391—732no—
135#382—732no—
136#381—731no—
137#381—731no—
138#381—731no—
139#381D7311yescharacteristic
140C4×C22⋊C4—731no—
141C22×Q8—731no—
142C23×C4—731no—
143C23×C4—731no—
144C23×C4C2×D7311yescharacteristic
145C22⋊Q8—1464no—
146C2×C4⋊C4—732no—
147C2×C4⋊C4—732no—
148C2×C4⋊C4—731no—
149C2×C4⋊C4—731no—
150C2×C4⋊C4—731no—
151C2×C4⋊C4—1464no—
152C2×C22⋊C4—731no—
153C2×C22⋊C4—731no—
154C2×C22⋊C4C2×D7311yescharacteristic
155C2×C22⋊C4C2×D7311yescharacteristic
156C2×C42—732no—
157#95—732no—
158#95—732no—
159#95—732no—
160#95—732no—
161#95—732no—
162#95—732no—
163#95—732no—
164#95C2×D7312yes—
165#95C2×D7312yes—
166C24C22×D7311yescharacteristic
167C2×Q8—1462no—
168C2×Q8—1464no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—731no—
173C22×C4—734no—
174C22×C4—731no—
175C22×C4—732no—
176C22×C4—731no—
177C22×C4—731no—
178C22×C4—732no—
179C22×C4—1462no—
180C22×C4—1462no—
181C22×C4—1462no—
182C22×C4—1464no—
183C22×C4C22×D7312yes—
184C22×C4C22×D7311yescharacteristic
185C22×C4C22×D7311yescharacteristic
186C22×C4C22×D7312yes—
187C4⋊C4—1464no—
188C4⋊C4—1464no—
189C4⋊C4—1462no—
190C4⋊C4—1462no—
191C4⋊C4—1462no—
192C22⋊C4—22no—
193C22⋊C4—22no—
194C22⋊C4—1462no—
195C22⋊C4—1462no—
196C42—1464no—
197C23—22no—
198C23—22no—
199C23D4×D7312yes—
200C23#1192402712yes—
201C23#1192402812yes—
202C23C23×D7311yescharacteristic
203Q8—2924no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—44no—
215C2×C4—2924no—
216C2×C4—732no—
217C2×C4—734no—
218C2×C4—732no—
219C2×C4—1461no—
220C2×C4—1461no—
221C2×C4—1462no—
222C2×C4—1462no—
223C2×C4—1462no—
224C2×C4—1462no—
225C2×C4—1462no—
226C2×C4—1462no—
227C2×C4—1462no—
228C2×C4—1462no—
229C2×C4—1468no—
230C2×C4—1462no—
231C22—22no—
232C22—24no—
233C22—24no—
234C22—22no—
235C22#1455657714yes—
236C22C2×D4×D7311yescharacteristic
237C22#41×D7312yes—
238C22C2×#1192402711yescharacteristic
239C22C2×#1192402811yescharacteristic
240C22#1455663812yes—
241C4—41no—
242C4—42no—
243C4—41no—
244C4—42no—
245C4—2921no—
246C4—2922no—
247C4—2921no—
248C4—2922no—
249C4—734no—
250C4—1462no—
251C2—24no—
252C2#123×D7311yescharacteristic
253C2C2×#1455657711yescharacteristic
254C2#1798915911yescharacteristic
255C2#1798927012yes—
256C2#1798927412yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#381×C73C2
hypercenter#381D73
hypocenterC73#2503
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
3. #17988529C2semidirect
4. #17988528C2semidirect
5. #17988491C2semidirect
6. #17988451C2semidirect
129. C73#2503semidirect