Finite Group Databasebeta

← #22609253

Subgroups — #22609253

Order 9344.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#17989331C211yesmaximal, characteristic
2#17988955C211yesmaximal, characteristic, complemented
3#17988949C211yesmaximal, characteristic, complemented
4#17988328C211yesmaximal, characteristic, complemented
5#17988327C211yesmaximal, characteristic, complemented
6#17988326C211yesmaximal, characteristic, complemented
7#489×C73C211yesmaximal, characteristic, complemented
8#14556583C2211yescharacteristic
9#14556579C2211yescharacteristic
10#14556575—21no—
11#14556573—21no—
12#14556568—21no—
13#14556567—21no—
14#14556564—21no—
15#14556563—21no—
16#14556515—21no—
17#14556515—21no—
18#14556514—21no—
19#14556511—21no—
20#14556502C2211yescharacteristic
21#14556502C2211yescharacteristic
22C4⋊Q8×C73C2211yescharacteristic
23#124×C73C2211yescharacteristic
24#103×C73—21no—
25#102×C73—21no—
26#97×C73C2211yescharacteristic
27C2×Dic146D411yescharacteristic
28C2×D292D411yescharacteristic
29C2×C22⋊D73—21no—
30C2×C22⋊D73—21no—
31C22×Dic73—21no—
32C2×C4×D73—21no—
33C2×#10596831—21no—
34C2×#10596831—21no—
35C4⋊Dic73—21no—
36C4⋊Dic73D411yescharacteristic
37C4⋊Dic73D411yescharacteristic
38#11924007—21no—
39#11924007—21no—
40#11924007—21no—
41C22⋊Dic73—21no—
42#11924005—21no—
43#11924005—21no—
44#11924005—21no—
45C2×Q8×C73—21no—
46C2×Q8×C73D411yescharacteristic
47C2×D4×C73D411yescharacteristic
48C2×C8×C73—21no—
49C4⋊C4×C73—21no—
50C4⋊C4×C73—21no—
51C22⋊C4×C73—21no—
52C22⋊C4×C73—21no—
53C42×C73C2311yescharacteristic
54C23×C73—21no—
55C22×D73—21no—
56Q8×C73—41no—
57Q8×C73—42no—
58D4×C73—41no—
59C2×C4×C73—21no—
60C2×C4×C73—41no—
61C2×C4×C73C2×D411yescharacteristic
62C2×C4×C73C2×D411yescharacteristic
63C2×C4×C73C2×D411yescharacteristic
64C22⋊D73—81no—
65C22⋊D73—81no—
66C2×Dic73—21no—
67C2×Dic73—21no—
68C2×Dic73—21no—
69C2×Dic73—81no—
70D292—41no—
71C4×D73—81no—
72Dic146—41no—
73C8×C73—41no—
74#10596831—41no—
75#10596831—41no—
76C22×C73—41no—
77C22×C73—41no—
78C22×C73—41no—
79C22×C73#12011yescharacteristic
80C2×D73—41no—
81C2×D73—41no—
82C2×D73—41no—
83C4×C73—21no—
84C4×C73—21no—
85C4×C73—21no—
86C4×C73—41no—
87C4×C73—81no—
88Dic73—41no—
89Dic73—41no—
90Dic73—41no—
91C2×C73—81no—
92C2×C73#45411yescharacteristic
93C2×C73#45511yescharacteristic
94C2×C73#45511yescharacteristic
95D73—81no—
96#1662—731nomaximal, Sylow
97C73#166211yescharacteristic, complemented, Sylow
98#562—731no—
99#491—731no—
100#489—731no—
101#489D7311yescharacteristic, complemented
102#330—731no—
103#329—731no—
104#329—731no—
105C4⋊Q8C2×D7311yescharacteristic
106#125—731no—
107#124—731no—
108#124C2×D7311yescharacteristic
109#123—1461no—
110#123—1461no—
111C22⋊Q8—1461no—
112C22⋊Q8—1461no—
113#121—1461no—
114#121—1461no—
115#103—21no—
116#103—1461no—
117#103—1461no—
118#103—1461no—
119#102—21no—
120#102—1461no—
121#97—731no—
122#97—731no—
123#97C2×D7311yescharacteristic
124C2×Q8—21no—
125C2×Q8—731no—
126C2×Q8C22⋊D7311yescharacteristic
127C2×D4—731no—
128C2×D4—1461no—
129C2×D4—1461no—
130C2×D4C22⋊D7311yescharacteristic
131C22×C4—1461no—
132C22×C4—1461no—
133C2×C8—21no—
134C2×C8—1461no—
135C2×C8—1461no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—731no—
139C4⋊C4—731no—
140C4⋊C4—1461no—
141C4⋊C4—1461no—
142C4⋊C4—1461no—
143C4⋊C4—1461no—
144C22⋊C4—21no—
145C22⋊C4—21no—
146C22⋊C4—1461no—
147C22⋊C4—1461no—
148C22⋊C4—1461no—
149C22⋊C4—1461no—
150C42C22×D7311yescharacteristic
151C23—21no—
152C23—1461no—
153Q8—41no—
154Q8—42no—
155Q8—2921no—
156D4—41no—
157D4—2921no—
158D4—5841no—
159D4—5841no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—5841no—
163C2×C4—5841no—
164C2×C4—1461no—
165C2×C4—1461no—
166C2×C4—1461no—
167C2×C4D4×D7311yescharacteristic
168C2×C4D4×D7311yescharacteristic
169C2×C4C2×C22⋊D7311yescharacteristic
170C8—41no—
171C8—2921no—
172C8—2921no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—2921no—
177C22—2921no—
178C22—2921no—
179C22#1455655911yescharacteristic
180C4—21no—
181C4—21no—
182C4—21no—
183C4—41no—
184C4—81no—
185C4—2921no—
186C4—2921no—
187C4—2921no—
188C2—81no—
189C2—5841no—
190C2#1798875811yescharacteristic
191C2#1798876311yescharacteristic
192C2#1798876411yescharacteristic
subgroupG/H
centerC22#14556559
commutatorC42×C73C23
FrattiniC42C22×D73
Fitting#489×C73C2
socleC22×C73#120
hypercenter#489D73
hypocenterC73#1662
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. #17988955C2semidirect
3. #17988949C2semidirect
4. #17988328C2semidirect
5. #17988327C2semidirect
6. #17988326C2semidirect
7. #489×C73C2semidirect
97. C73#1662semidirect
101. #489D73semidirect