Finite Group Databasebeta

← #22611336

Subgroups — #22611336

Order 9344.

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

normal subgroups only

This group has 274 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
1C2×#14556513C212yesmaximal
2#17988489C211yesmaximal, characteristic
3#17988457C211yesmaximal, characteristic, complemented
4#17988350C212yesmaximal, complemented
5#336×C73C211yesmaximal, characteristic, complemented
6C22×D292C2211yescharacteristic
7C2×C4⋊Dic73—21no—
8C2×C4⋊Dic73—21no—
9C2×C4⋊Dic73C2212yes—
10C2×C4⋊Dic73C2211yescharacteristic
11C2×#11924005—21no—
12C2×#11924005—21no—
13#14556513—24no—
14C22×C8×C73C2212yes—
15C2×C42×C73C2211yescharacteristic
16C23×D73—21no—
17C2×D292—22no—
18C2×D292—22no—
19C2×D292—21no—
20C2×D292D412yes—
21C22×Dic73—21no—
22C22×Dic73—22no—
23C4⋊Dic73—22no—
24C4⋊Dic73—22no—
25C4⋊Dic73—22no—
26C4⋊Dic73—42no—
27C4⋊Dic73—42no—
28#11924005—42no—
29#11924005—42no—
30C22×C4×C73D411yescharacteristic
31C22×C4×C73D411yescharacteristic
32C22×C4×C73C2311yescharacteristic
33C2×C8×C73—22no—
34C2×C8×C73—22no—
35C2×C8×C73—22no—
36C42×C73—22no—
37C23×C73C2×D411yescharacteristic
38C22×D73—22no—
39C22×D73—41no—
40C22×D73—41no—
41C22×D73—41no—
42C22×D73—41no—
43C22×D73—41no—
44C22×D73—41no—
45C2×C4×C73—21no—
46C2×C4×C73—21no—
47C2×C4×C73—21no—
48C2×C4×C73—21no—
49C2×C4×C73D812yes—
50C2×C4×C73SD1612yes—
51C2×C4×C73C2×D411yescharacteristic
52C2×C4×C73#4112yes—
53C2×C4×C73#4112yes—
54C2×C4×C73#4111yescharacteristic
55C2×Dic73—42no—
56C2×Dic73—41no—
57C2×Dic73—41no—
58C2×Dic73—42no—
59C2×Dic73—41no—
60C2×Dic73—42no—
61D292—24no—
62D292—42no—
63C8×C73—42no—
64C22×C73#12111yescharacteristic
65C22×C73#12311yescharacteristic
66C22×C73#12411yescharacteristic
67C22×C73C2×D811yescharacteristic
68C22×C73C2×SD1611yescharacteristic
69C22×C73AGL(1,ℤ/8)11yescharacteristic
70C22×C73#13711yescharacteristic
71C2×D73—42no—
72C2×D73—42no—
73C2×D73—42no—
74C2×D73—81no—
75C2×D73—81no—
76C2×D73—81no—
77C2×D73—81no—
78C4×C73—22no—
79C4×C73—22no—
80C4×C73#12312yes—
81C4×C73#12612yes—
82Dic73—82no—
83Dic73—81no—
84C2×C73#39711yescharacteristic
85C2×C73#45911yescharacteristic
86C2×C73#46111yescharacteristic
87C2×C73#48011yescharacteristic
88C2×C73#48111yescharacteristic
89C2×C73#48611yescharacteristic
90C2×C73#48911yescharacteristic
91D73—82no—
92#2071—731nomaximal, Sylow
93C73#207111yescharacteristic, complemented, Sylow
94C2×#102—732no—
95#390—731no—
96#384—731no—
97#340—732no—
98#336D7311yescharacteristic, complemented
99C22×D4—731no—
100C22×C8C2×D7312yes—
101C2×C4⋊C4—731no—
102C2×C4⋊C4—732no—
103C2×C4⋊C4—1461no—
104C2×C4⋊C4—1461no—
105C2×C22⋊C4—1461no—
106C2×C22⋊C4—1461no—
107C2×C42C2×D7311yescharacteristic
108#102—1464no—
109C24—1461no—
110C2×D4—732no—
111C2×D4—1462no—
112C2×D4—1462no—
113C2×D4—1461no—
114C22×C4—1461no—
115C22×C4—1462no—
116C22×C4D29211yescharacteristic
117C22×C4D29211yescharacteristic
118C22×C4C22×D7311yescharacteristic
119C2×C8—22no—
120C2×C8—22no—
121C2×C8—22no—
122C4⋊C4—2922no—
123C4⋊C4—2922no—
124C4⋊C4—1462no—
125C4⋊C4—1462no—
126C4⋊C4—1462no—
127C22⋊C4—2922no—
128C22⋊C4—2922no—
129C42—22no—
130C23—2921no—
131C23—2921no—
132C23—2921no—
133C23—2921no—
134C23—2921no—
135C23—2921no—
136C23—1462no—
137C23C2×D29211yescharacteristic
138D4—2922no—
139D4—1464no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—2922no—
145C2×C4—2921no—
146C2×C4—2921no—
147C2×C4—2922no—
148C2×C4—2921no—
149C2×C4—2922no—
150C2×C4D58412yes—
151C2×C4#1192401712yes—
152C2×C4D4×D7311yescharacteristic
153C2×C4#1192402712yes—
154C2×C4#1192402812yes—
155C2×C4#1192402911yescharacteristic
156C8—42no—
157C22—2922no—
158C22—2922no—
159C22—2922no—
160C22—5841no—
161C22—5841no—
162C22—5841no—
163C22—5841no—
164C22#1455656611yescharacteristic
165C22#1455657511yescharacteristic
166C22#1455657911yescharacteristic
167C22C2×D58411yescharacteristic
168C22C2×#1192401711yescharacteristic
169C22#1455661911yescharacteristic
170C22#1455662411yescharacteristic
171C4—22no—
172C4—22no—
173C4—5841no—
174C4—5842no—
175C4#1455657312yes—
176C4#1455658612yes—
177C2—5842no—
178C2#1798851411yescharacteristic
179C2#1798878311yescharacteristic
180C2#1798879311yescharacteristic
181C2#1798890111yescharacteristic
182C2#1798890611yescharacteristic
183C2#1798893411yescharacteristic
184C2#1798894711yescharacteristic
subgroupG/H
centerC23C2×D292
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#336×C73C2
socleC23×C73C2×D4
hypercenter#336D73
hypocenterC73#2071
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
3. #17988457C2semidirect
4. #17988350C2semidirect
5. #336×C73C2semidirect
93. C73#2071semidirect
98. #336D73semidirect