Finite Group Databasebeta

← #22620309

Subgroups — #22620309

Order 9344.

380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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#17989140C211yesmaximal, characteristic
2C2×#14556589C211yesmaximal, characteristic
3#17988954C214yesmaximal, complemented
4#17988936C214yesmaximal, complemented
5#17988597C211yesmaximal, characteristic
6#17988596C211yesmaximal, characteristic
7#17988595C211yesmaximal, characteristic
8M16×Dic73C211yesmaximal, characteristic
9#419×C73C211yesmaximal, characteristic
10C22×Dic146C2211yescharacteristic
11C2×#11924012C2211yescharacteristic
12#14556590C2212yes—
13#14556589—22no—
14#14556589C2212yes—
15#14556589C2212yes—
16#14556582C2212yes—
17#14556568—22no—
18C4×Dic146—22no—
19#14556550C2211yescharacteristic
20C2×#11924007—22no—
21C2×C4×Dic73C2211yescharacteristic
22#14556516C2214yes—
23#14556515C2214yes—
24#14556514C2214yes—
25#14556501C2212yes—
26C8×Dic73C2212yes—
27C22×Q8×C73C2211yescharacteristic
28C2×M16×C73C2211yescharacteristic
29#117×C73C2211yescharacteristic
30#103×C73C2214yes—
31C2×Dic146—22no—
32C2×Dic146—22no—
33C2×Dic146—21no—
34C2×Dic146—22no—
35C2×Dic146C2312yes—
36C22×Dic73—21no—
37C22×Dic73D412yes—
38#11924012—22no—
39C2×#10596831C2312yes—
40C4⋊Dic73—22no—
41C4⋊Dic73C2312yes—
42#11924007—24no—
43#11924007—24no—
44#11924007—22no—
45#11924007—22no—
46C22⋊Dic73—21no—
47C4×Dic73—21no—
48C4×Dic73D412yes—
49C4×Dic73C2311yescharacteristic
50C4×Dic73C2311yescharacteristic
51C2×Q8×C73—21no—
52C2×Q8×C73—22no—
53C2×Q8×C73—22no—
54C2×Q8×C73C2312yes—
55C22×C4×C73—21no—
56C22×C4×C73C2311yescharacteristic
57M16×C73—22no—
58C2×C8×C73C2312yes—
59C4⋊C4×C73C2312yes—
60C22⋊C4×C73—21no—
61C42×C73—21no—
62C23×C73C2×D411yescharacteristic
63Q8×C73—22no—
64Q8×C73—22no—
65Q8×C73—42no—
66C2×C4×C73—22no—
67C2×C4×C73—22no—
68C2×C4×C73—42no—
69C2×C4×C73C2×D411yescharacteristic
70C2×C4×C73#4112yes—
71C2×C4×C73#4112yes—
72C2×C4×C73C2411yescharacteristic
73C2×Dic73—24no—
74C2×Dic73—22no—
75C2×Dic73—22no—
76C2×Dic73—42no—
77C2×Dic73C2×D412yes—
78C2×Dic73C2×D412yes—
79Dic146—22no—
80Dic146—22no—
81Dic146—42no—
82Dic146—44no—
83C8×C73—22no—
84#10596831—22no—
85C22×C73—22no—
86C22×C73#12412yes—
87C22×C73C22×D411yescharacteristic
88C4×C73—42no—
89C4×C73—42no—
90C4×C73#12412yes—
91C4×C73C2×#4111yescharacteristic
92C4×C73C2×#4111yescharacteristic
93Dic73—22no—
94Dic73—42no—
95Dic73—42no—
96Dic73#13714yes—
97C2×C73—22no—
98C2×C73C2×#12411yescharacteristic
99C2×C73C2×#13712yes—
100#3139—731nomaximal, Sylow
101C73#313911yescharacteristic, complemented, Sylow
102#533—731no—
103C2×C4⋊Q8—731no—
104#491—734no—
105#487—734no—
106#419—731no—
107#419—731no—
108#419—731no—
109#419D7311yescharacteristic
110C4×M16—731no—
111C22×Q8—731no—
112C22×Q8C2×D7311yescharacteristic
113C2×M16—731no—
114C2×M16C2×D7311yescharacteristic
115C4⋊Q8—732no—
116C4⋊Q8—732no—
117C4⋊Q8—732no—
118C4⋊Q8—1462no—
119#125—732no—
120C22⋊Q8—1462no—
121C4×Q8—1462no—
122#117—731no—
123#117C2×D7311yescharacteristic
124C2×C4⋊C4—1462no—
125C2×C42—731no—
126#103—734no—
127#103—734no—
128#103—734no—
129#103C2×D7314yes—
130#97—732no—
131C4×C8—732no—
132C2×Q8—21no—
133C2×Q8—22no—
134C2×Q8—22no—
135C2×Q8—732no—
136C2×Q8—1462no—
137C2×Q8—1462no—
138C2×Q8—1462no—
139C2×Q8—1461no—
140C2×Q8C22×D7312yes—
141C22×C4—21no—
142C22×C4—732no—
143C22×C4—1461no—
144C22×C4C22×D7311yescharacteristic
145M16—22no—
146M16—1462no—
147C2×C8—732no—
148C2×C8C22×D7312yes—
149C4⋊C4—732no—
150C4⋊C4—1464no—
151C4⋊C4—1464no—
152C4⋊C4—1462no—
153C4⋊C4—1462no—
154C4⋊C4—1462no—
155C4⋊C4C22×D7312yes—
156C22⋊C4—21no—
157C22⋊C4—1461no—
158C42—21no—
159C42—732no—
160C42—731no—
161C42—731no—
162C42—1461no—
163C23D4×D7311yescharacteristic
164Q8—22no—
165Q8—22no—
166Q8—42no—
167Q8—2924no—
168Q8—2922no—
169Q8—1462no—
170Q8—1462no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—42no—
174C2×C4—2922no—
175C2×C4—732no—
176C2×C4—732no—
177C2×C4—1462no—
178C2×C4—1462no—
179C2×C4—1464no—
180C2×C4D4×D7311yescharacteristic
181C2×C4#1192402712yes—
182C2×C4#1192402812yes—
183C2×C4C23×D7311yescharacteristic
184C8—22no—
185C8—1462no—
186C22—22no—
187C22#1455657712yes—
188C22C2×D4×D7311yescharacteristic
189C4—42no—
190C4—42no—
191C4—2922no—
192C4—2922no—
193C4—734no—
194C4—1462no—
195C4#1455657712yes—
196C4C2×#1192402711yescharacteristic
197C4C2×#1192402811yescharacteristic
198C2—22no—
199C2C2×#1455657711yescharacteristic
200C2#137×D7312yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#419×C73C2
socleC22×C73C22×D4
hypercenter#419D73
hypocenterC73#3139
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #17988954C2semidirect
4. #17988936C2semidirect
101. C73#3139semidirect