Finite Group Databasebeta

← #22609019

Subgroups — #22609019

Order 9344.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 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#17989242C211yesmaximal, characteristic, complemented
2#17988933C211yesmaximal, characteristic, complemented
3#17988779C211yesmaximal, characteristic, complemented
4#17988332C211yesmaximal, characteristic, complemented
5D4⋊#10596831C211yesmaximal, characteristic, complemented
6#17988314C211yesmaximal, characteristic, complemented
7#459×C73C211yesmaximal, characteristic, complemented
8C2×#11924028—21no—
9C2×#11924013—21no—
10#14556591C2211yescharacteristic
11#14556573—22no—
12#14556570—21no—
13#14556562—21no—
14C4×D292C2211yescharacteristic
15C4⋊C4×D73—21no—
16C4⋊#10596831C2211yescharacteristic
17#14556512—22no—
18#14556512—21no—
19C4×#10596831C2211yescharacteristic
20C2×D8×C73—21no—
21#127×C73C2211yescharacteristic
22C4×D4×C73C2211yescharacteristic
23C4⋊C8×C73C2211yescharacteristic
24#102×C73—21no—
25#11924028—42no—
26#11924028—42no—
27C2×Dic146—21no—
28C2×D292D411yescharacteristic
29C2×C22⋊D73—22no—
30C2×C4×D73—22no—
31C2×C4×D73—21no—
32#11924013—42no—
33C2×#10596831—21no—
34C2×#10596831—21no—
35C4⋊Dic73—21no—
36C4⋊Dic73D411yescharacteristic
37C4⋊Dic73D412yes—
38#11924007—22no—
39C22⋊Dic73—22no—
40#11924005—21no—
41C2×D4×C73—21no—
42C2×D4×C73—21no—
43C2×D4×C73—21no—
44C2×D4×C73D411yescharacteristic
45C22×C4×C73—21no—
46D8×C73—42no—
47C2×C8×C73—21no—
48C4⋊C4×C73D411yescharacteristic
49C22⋊C4×C73—21no—
50C42×C73C2311yescharacteristic
51C23×C73—21no—
52C23×C73—41no—
53C22×D73—21no—
54D4×C73—21no—
55D4×C73—21no—
56D4×C73—42no—
57D4×C73—41no—
58D4×C73—41no—
59D4×C73—41no—
60D4×C73—41no—
61C2×C4×C73—21no—
62C2×C4×C73—41no—
63C2×C4×C73—41no—
64C2×C4×C73C2×D411yescharacteristic
65C2×C4×C73C2×D411yescharacteristic
66C2×C4×C73C2×D411yescharacteristic
67C22⋊D73—44no—
68C2×Dic73—21no—
69C2×Dic73—22no—
70D292—21no—
71D292D812yescomplemented
72C4×D73—44no—
73C4×D73—41no—
74C4×D73—41no—
75Dic146—41no—
76Dic146—41no—
77C8×C73—41no—
78#10596831—41no—
79#10596831—41no—
80C22×C73—41no—
81C22×C73—41no—
82C22×C73—41no—
83C22×C73—81no—
84C22×C73—81no—
85C22×C73—81no—
86C22×C73#12011yescharacteristic
87C2×D73—22no—
88C2×D73—41no—
89C2×D73—41no—
90C4×C73—21no—
91C4×C73—41no—
92C4×C73C2×D811yescharacteristic
93C4×C73#13511yescharacteristic
94C4×C73AGL(1,ℤ/8)11yescharacteristic
95C4×C73AGL(1,ℤ/8)11yescharacteristic
96Dic73—42no—
97Dic73—41no—
98C2×C73—81no—
99C2×C73—161no—
100C2×C73#44711yescharacteristic
101C2×C73#44911yescharacteristic
102C2×C73#45411yescharacteristic
103D73—42no—
104#1625—731nomaximal, Sylow
105C73#162511yescharacteristic, complemented, Sylow
106#547—731no—
107#486—731no—
108#459—731no—
109#459D7311yescharacteristic, complemented
110#332—731no—
111D4⋊C8—731no—
112D4⋊C8—731no—
113C2×#41—1461no—
114C2×D8—21no—
115C2×D8—1461no—
116C4⋊Q8—731no—
117#127C2×D7311yescharacteristic
118#123—1462no—
119C22⋊Q8—1461no—
120#121—1461no—
121C4×D4—731no—
122C4×D4C2×D7311yescharacteristic
123C2×C4⋊C4—1461no—
124C4⋊C8—731no—
125C4⋊C8C2×D7311yescharacteristic
126#102—21no—
127#102—1461no—
128#102—1462no—
129C4×C8—731no—
130#41—2922no—
131#41—2922no—
132C2×Q8—1461no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—731no—
137C2×D4—1462no—
138C2×D4C22⋊D7311yescharacteristic
139C22×C4—21no—
140C22×C4—1462no—
141C22×C4—1461no—
142D8—42no—
143D8—2922no—
144C2×C8—21no—
145C2×C8—1461no—
146C2×C8—1461no—
147C4⋊C4—731no—
148C4⋊C4—732no—
149C4⋊C4—1462no—
150C4⋊C4—1461no—
151C4⋊C4C22⋊D7311yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—1462no—
154C22⋊C4—1461no—
155C42C22×D7311yescharacteristic
156C23—21no—
157C23—41no—
158C23—1461no—
159Q8—2921no—
160Q8—2921no—
161D4—21no—
162D4—21no—
163D4—42no—
164D4—41no—
165D4—41no—
166D4—41no—
167D4—41no—
168D4—2924no—
169D4—732no—
170D4—1461no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—2924no—
175C2×C4—2921no—
176C2×C4—2921no—
177C2×C4—1461no—
178C2×C4—1462no—
179C2×C4D4×D7311yescharacteristic
180C2×C4D4×D7311yescharacteristic
181C2×C4C2×C22⋊D7311yescharacteristic
182C8—41no—
183C8—2921no—
184C8—2921no—
185C22—41no—
186C22—41no—
187C22—41no—
188C22—81no—
189C22—81no—
190C22—81no—
191C22—2921no—
192C22—2921no—
193C22—1462no—
194C22#1455655911yescharacteristic
195C4—21no—
196C4—41no—
197C4—2922no—
198C4—2921no—
199C4D8×D7311yescharacteristic
200C4#1455661111yescharacteristic
201C4#1455661511yescharacteristic
202C4#1455661711yescharacteristic
203C2—81no—
204C2—161no—
205C2—2922no—
206C2#1798871911yescharacteristic
207C2#1798873011yescharacteristic
208C2#1798875811yescharacteristic
subgroupG/H
centerC22#14556559
commutatorC42×C73C23
FrattiniC42C22×D73
Fitting#459×C73C2
socleC22×C73#120
hypercenter#459D73
hypocenterC73#1625
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #17989242C2semidirect
2. #17988933C2semidirect
3. #17988779C2semidirect
4. #17988332C2semidirect
5. D4⋊#10596831C2semidirect
6. #17988314C2semidirect
7. #459×C73C2semidirect
71. D292D8semidirect
105. C73#1625semidirect
109. #459D73semidirect