Finite Group Databasebeta

← #22611191

Subgroups — #22611191

Order 9344.

276 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 69 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
1C22×#11924015C211yesmaximal, characteristic
2#17988614C211yesmaximal, characteristic, complemented
3#17988591C211yesmaximal, characteristic
4C2×#14556510C211yesmaximal, characteristic, complemented
5C2×#14556507C211yesmaximal, characteristic
6#17988351C211yesmaximal, characteristic, complemented
7#419×C73C211yesmaximal, characteristic, complemented
8C22×D292C2211yescharacteristic
9C2×#11924015—22no—
10C2×#11924015—22no—
11C2×#11924015—22no—
12C2×#11924012C2211yescharacteristic
13C2×#11924012C2211yescharacteristic
14C22×#10596831C2211yescharacteristic
15C4⋊#10596831—22no—
16#14556511—22no—
17#14556510—22no—
18#14556507—22no—
19C22×Q8×C73C2211yescharacteristic
20C2×M16×C73C2211yescharacteristic
21#117×C73C2211yescharacteristic
22#103×C73—22no—
23C23×D73—21no—
24C2×D292—21no—
25C2×D292—21no—
26C2×D292—21no—
27C2×D292—21no—
28C2×D292—21no—
29C2×D292D412yes—
30#11924015—28no—
31#11924012—21no—
32#11924012—21no—
33#11924012—21no—
34#11924012—21no—
35C2×#10596831—21no—
36C2×#10596831—21no—
37C2×#10596831—21no—
38C2×#10596831—21no—
39C2×#10596831D412yes—
40C2×Q8×C73—21no—
41C2×Q8×C73—21no—
42C2×Q8×C73—21no—
43C2×Q8×C73—21no—
44C2×Q8×C73—21no—
45C2×Q8×C73D412yes—
46C22×C4×C73—21no—
47C22×C4×C73C2311yescharacteristic
48M16×C73—21no—
49M16×C73—21no—
50C2×C8×C73—21no—
51C4⋊C4×C73D412yes—
52C22⋊C4×C73—21no—
53C42×C73—21no—
54C23×C73#4111yescharacteristic
55C22×D73—22no—
56C22×D73—41no—
57C22×D73—41no—
58C22×D73—82no—
59Q8×C73—22no—
60Q8×C73—22no—
61Q8×C73—41no—
62Q8×C73—41no—
63C2×C4×C73—22no—
64C2×C4×C73—22no—
65C2×C4×C73—41no—
66C2×C4×C73—41no—
67C2×C4×C73C2×D411yescharacteristic
68C2×C4×C73C2×D411yescharacteristic
69C2×C4×C73C2×D411yescharacteristic
70C2×C4×C73C2×D411yescharacteristic
71C2×C4×C73#4111yescharacteristic
72C2×C4×C73#4111yescharacteristic
73D292—22no—
74D292—22no—
75D292—41no—
76D292—41no—
77C8×C73—41no—
78#10596831—22no—
79#10596831—41no—
80#10596831—41no—
81C22×C73—22no—
82C22×C73#12111yescharacteristic
83C22×C73#12311yescharacteristic
84C22×C73#12311yescharacteristic
85C2×D73—42no—
86C2×D73—82no—
87C2×D73—82no—
88C2×D73—82no—
89C4×C73—42no—
90C4×C73—42no—
91C4×C73#12011yescharacteristic
92C4×C73#12111yescharacteristic
93C4×C73#12111yescharacteristic
94C4×C73#12411yescharacteristic
95C2×C73—21no—
96C2×C73—21no—
97C2×C73#39411yescharacteristic
98C2×C73#47112yes—
99D73—82no—
100#2046—731nomaximal, Sylow
101C73#204611yescharacteristic, complemented, Sylow
102C22×SD16—731no—
103#424—731no—
104#419D7311yescharacteristic, complemented
105#418—731no—
106C2×#101—731no—
107C2×#100—731no—
108#341—731no—
109C22×Q8C2×D7311yescharacteristic
110C22×D4—731no—
111C2×SD16—1462no—
112C2×SD16—1462no—
113C2×SD16—1462no—
114C2×M16—731no—
115C2×M16—731no—
116C2×M16C2×D7311yescharacteristic
117C22×C8—731no—
118#117C2×D7311yescharacteristic
119C4⋊C8—1462no—
120#103—22no—
121#102—1462no—
122#101—1462no—
123#100—1462no—
124C24—1461no—
125C2×Q8—21no—
126C2×Q8—21no—
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8D29212yes—
131C2×D4—732no—
132C2×D4—1461no—
133C2×D4—1461no—
134C2×D4—1461no—
135C2×D4—1461no—
136C2×D4—1461no—
137C22×C4—21no—
138C22×C4C22×D7311yescharacteristic
139SD16—1468no—
140M16—21no—
141M16—21no—
142M16—1461no—
143M16—1461no—
144M16—1461no—
145M16—1461no—
146C2×C8—21no—
147C2×C8—732no—
148C2×C8—1461no—
149C2×C8—1461no—
150C2×C8—1461no—
151C2×C8—1461no—
152C4⋊C4C22⋊D7312yes—
153C22⋊C4—21no—
154C42—21no—
155C23—2921no—
156C23—2921no—
157C23—5842no—
158C23—1462no—
159C23#1192402711yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—41no—
163Q8—41no—
164D4—2921no—
165D4—2921no—
166D4—1462no—
167D4—1462no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4D4×D7311yescharacteristic
173C2×C4D4×D7311yescharacteristic
174C2×C4C2×C22⋊D7311yescharacteristic
175C2×C4C2×D29211yescharacteristic
176C2×C4#1192402711yescharacteristic
177C2×C4#1192402811yescharacteristic
178C8—41no—
179C8—2921no—
180C8—2921no—
181C8—1462no—
182C22—22no—
183C22—2922no—
184C22—5842no—
185C22—5842no—
186C22—5842no—
187C22#1455656311yescharacteristic
188C22#1455657311yescharacteristic
189C22#1455657511yescharacteristic
190C4—42no—
191C4—42no—
192C4#1455656111yescharacteristic
193C4#1455656211yescharacteristic
194C4#1455656511yescharacteristic
195C4#1455657711yescharacteristic
196C2—21no—
197C2—21no—
198C2—5842no—
199C2#1798850311yescharacteristic
200C2#1798885212yes—
subgroupG/H
centerC22#14556563
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#419×C73C2
socleC22×C73#121
hypercenter#419D73
hypocenterC73#2046
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
2. #17988614C2semidirect
4. C2×#14556510C2semidirect
6. #17988351C2semidirect
7. #419×C73C2semidirect
101. C73#2046semidirect
104. #419D73semidirect