Finite Group Databasebeta

← #22615837

Subgroups — #22615837

Order 9344.

450 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14556585C211yesmaximal, characteristic
2#17988520C212yesmaximal, complemented
3#17988518C211yesmaximal, characteristic, complemented
4#17988513C211yesmaximal, characteristic
5#17988509C212yesmaximal
6#17988506C211yesmaximal, characteristic, complemented
7#17988498C211yesmaximal, characteristic
8#17988478C212yesmaximal
9#17988471C212yesmaximal, complemented
10#17988453C211yesmaximal, characteristic, complemented
11C2×C4×Q8×C73C211yesmaximal, characteristic, complemented
12#14556585—24no—
13C2×C4⋊Dic73C2212yes—
14C2×#11924007C2211yescharacteristic
15C2×#11924007C2212yes—
16C2×#11924007C2211yescharacteristic
17C2×#11924007C2211yescharacteristic
18C2×#11924007C2212yes—
19C2×#11924005C2211yescharacteristic
20C2×#11924005C2212yes—
21C2×#11924005C2211yescharacteristic
22C2×#11924005C2211yescharacteristic
23C2×#11924005C2212yes—
24#14556498C2212yes—
25#14556498C2211yescharacteristic
26#14556498C2211yescharacteristic
27#14556498C2212yes—
28#14556498C2212yes—
29#14556498C2212yes—
30#14556498C2212yes—
31C22×Q8×C73C2211yescharacteristic
32C4×Q8×C73—24no—
33C2×C4⋊C4×C73C2212yes—
34C2×C4⋊C4×C73C2211yescharacteristic
35C2×C42×C73C2212yes—
36C2×C42×C73C2211yescharacteristic
37C23×D73C2311yescharacteristic
38C22×Dic73C2311yescharacteristic
39C22×Dic73C2312yes—
40C22×Dic73C2312yes—
41C22×Dic73C2311yescharacteristic
42C22×Dic73C2311yescharacteristic
43C4⋊Dic73—42no—
44#11924007—22no—
45#11924007—22no—
46#11924007—22no—
47#11924007—24no—
48#11924007—42no—
49#11924005—22no—
50#11924005—22no—
51#11924005—22no—
52#11924005—24no—
53#11924005—42no—
54C2×Q8×C73—22no—
55C2×Q8×C73—24no—
56C22×C4×C73C2312yes—
57C22×C4×C73C2311yescharacteristic
58C22×C4×C73C2311yescharacteristic
59C22×C4×C73C2311yescharacteristic
60C22×C4×C73C2312yes—
61C4⋊C4×C73—24no—
62C4⋊C4×C73—22no—
63C42×C73—24no—
64C42×C73D414yes—
65C23×C73C2411yescharacteristic
66C22×D73—21no—
67C22×D73—22no—
68C22×D73—21no—
69C22×D73—21no—
70C22×D73—22no—
71Q8×C73—28no—
72C2×C4×C73—22no—
73C2×C4×C73—22no—
74C2×C4×C73—22no—
75C2×C4×C73—21no—
76C2×C4×C73—21no—
77C2×C4×C73—22no—
78C2×C4×C73—22no—
79C2×C4×C73—22no—
80C2×C4×C73—22no—
81C2×C4×C73C2×D412yes—
82C2×C4×C73C2×D412yes—
83C2×C4×C73C2×D412yes—
84C2×C4×C73#4114yes—
85C2×Dic73—21no—
86C2×Dic73—21no—
87C2×Dic73—21no—
88C2×Dic73—22no—
89C2×Dic73—22no—
90C2×Dic73—22no—
91C2×Dic73—22no—
92C2×Dic73—21no—
93C2×Dic73—22no—
94C2×Dic73—21no—
95C2×Dic73—22no—
96C2×Dic73—22no—
97C2×Dic73—22no—
98C22×C73C22×D411yescharacteristic
99C22×C73C2×#4112yes—
100C22×C73H(5,𝔽2)11yescharacteristic
101C22×C732−1+411yescharacteristic
102C22×C732−1+412yes—
103C2×D73—41no—
104C2×D73—41no—
105C2×D73—41no—
106C2×D73—42no—
107C2×D73—42no—
108C4×C73—22no—
109C4×C73—24no—
110C4×C73—22no—
111C4×C73—22no—
112C4×C73—42no—
113Dic73—41no—
114Dic73—41no—
115Dic73—41no—
116Dic73—42no—
117Dic73—42no—
118C2×C73#52511yescharacteristic
119C2×C73#53611yescharacteristic
120C2×C73#53711yescharacteristic
121C2×C73#54112yes—
122C2×C73#54212yes—
123D73—81no—
124#2637—731nomaximal, Sylow
125C73#263711yescharacteristic, complemented, Sylow
126C2×#126—731no—
127C2×C4×Q8D7311yescharacteristic, complemented
128#398—731no—
129#398—732no—
130#397—731no—
131#396—732no—
132#395—731no—
133#393—731no—
134#388—732no—
135#387—732no—
136#382—731no—
137C22×Q8C2×D7311yescharacteristic
138#126—1464no—
139C4×Q8—24no—
140C2×C4⋊C4—732no—
141C2×C4⋊C4—732no—
142C2×C4⋊C4—731no—
143C2×C4⋊C4—731no—
144C2×C4⋊C4—731no—
145C2×C4⋊C4—732no—
146C2×C4⋊C4C2×D7312yes—
147C2×C4⋊C4C2×D7311yescharacteristic
148C2×C22⋊C4—732no—
149C2×C22⋊C4—731no—
150C2×C22⋊C4—731no—
151C2×C22⋊C4—731no—
152C2×C22⋊C4—732no—
153C2×C42C2×D7312yes—
154C2×C42C2×D7311yescharacteristic
155#95—732no—
156#95—731no—
157#95—731no—
158#95—732no—
159#95—732no—
160#95—732no—
161#95—732no—
162C24—731no—
163C2×Q8—22no—
164C2×Q8—24no—
165C22×C4—731no—
166C22×C4—732no—
167C22×C4—732no—
168C22×C4—731no—
169C22×C4—731no—
170C22×C4C22×D7312yes—
171C22×C4C22×D7311yescharacteristic
172C22×C4C22×D7311yescharacteristic
173C22×C4C22×D7311yescharacteristic
174C22×C4C22×D7312yes—
175C4⋊C4—24no—
176C4⋊C4—22no—
177C4⋊C4—2922no—
178C4⋊C4—2922no—
179C4⋊C4—1462no—
180C4⋊C4—1462no—
181C4⋊C4—1462no—
182C4⋊C4—1464no—
183C22⋊C4—2922no—
184C22⋊C4—1462no—
185C22⋊C4—1462no—
186C22⋊C4—1462no—
187C22⋊C4—1464no—
188C42—24no—
189C42C22⋊D7314yes—
190C23—1461no—
191C23—1462no—
192C23—1461no—
193C23—1461no—
194C23—1462no—
195C23C23×D7311yescharacteristic
196Q8—28no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—1461no—
207C2×C4—1461no—
208C2×C4—1461no—
209C2×C4—1462no—
210C2×C4—1462no—
211C2×C4—1462no—
212C2×C4—1462no—
213C2×C4—1461no—
214C2×C4—1462no—
215C2×C4—1461no—
216C2×C4—1462no—
217C2×C4—1462no—
218C2×C4—1462no—
219C2×C4C2×C22⋊D7312yes—
220C2×C4C2×C22⋊D7312yes—
221C2×C4C2×C22⋊D7312yes—
222C2×C4#1192402814yes—
223C22—2921no—
224C22—2921no—
225C22—2922no—
226C22—2922no—
227C22—2921no—
228C22C22×C22⋊D7311yescharacteristic
229C22C2×#1192402812yes—
230C22#1455663711yescharacteristic
231C22#1455663811yescharacteristic
232C22#1455663912yes—
233C4—22no—
234C4—22no—
235C4—22no—
236C4—24no—
237C4—42no—
238C4—2921no—
239C4—2921no—
240C4—2922no—
241C4—2922no—
242C4—2921no—
243C2—5841no—
244C2#1798909811yescharacteristic
245C2#1798916111yescharacteristic
246C2#1798916511yescharacteristic
247C2#1798919512yes—
248C2#1798920912yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×C4×Q8×C73C2
hypercenterC2×C4×Q8D73
hypocenterC73#2637
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #17988520C2semidirect
3. #17988518C2semidirect
6. #17988506C2semidirect
9. #17988471C2semidirect
10. #17988453C2semidirect
11. C2×C4×Q8×C73C2semidirect
125. C73#2637semidirect
127. C2×C4×Q8D73semidirect