Finite Group Databasebeta

← #22626174

Subgroups — #22626174

Order 9344.

220 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 72 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×#14556666C211yesmaximal, characteristic, complemented
2#17989643C211yesmaximal, characteristic, complemented
3#17989486C212yesmaximal, complemented
4#17989485C212yesmaximal, complemented
5#131×D73C211yesmaximal, characteristic
6#14556666—21no—
7#14556666—21no—
8#14556666—21no—
9#14556665C2212yescomplemented
10#14556664—21no—
11C2×#11924031C2212yescomplemented
12#41×D73C411yescharacteristic
13#14556599—21no—
14#14556599C2211yescharacteristic
15#14556598C2211yescharacteristic
16#14556597—21no—
17#14556597C411yescharacteristic
18M16×D73—21no—
19M16×D73C411yescharacteristic
20C2×C8×D73—21no—
21C2×C8×D73C2211yescharacteristic
22#131×C73C411yescharacteristic
23#11924031—22no—
24#11924031—22no—
25#11924029C811yescharacteristic
26#11924028—21no—
27#11924028C2×C411yescharacteristic
28#11924027—21no—
29#11924027C811yescharacteristic
30Q8×D73C811yescharacteristic
31D4×D73—21no—
32D4×D73C811yescharacteristic
33C2×C4×D73—21no—
34C2×C4×D73C2×C411yescharacteristic
35#11924012—21no—
36#11924012C2×C411yescharacteristic
37#11924011—21no—
38#11924011—21no—
39#11924011—21no—
40C2×#10596831—21no—
41C2×#10596831C2311yescharacteristic
42C8×D73—21no—
43C8×D73—21no—
44C8×D73—21no—
45C8×D73D411yescharacteristic
46C8×D73D411yescharacteristic
47C8×D73D411yescharacteristic
48C8×D73D411yescharacteristic
49#41×C73C2×C411yescharacteristic
50M16×C73—21no—
51M16×C73C2×C411yescharacteristic
52C2×C8×C73—21no—
53C2×C8×C73C2×C411yescharacteristic
54C22×D73—21no—
55C22×D73M1611yescharacteristic
56Q8×C73C2×C811yescharacteristic
57D4×C73—21no—
58D4×C73C2×C811yescharacteristic
59C2×C4×C73—21no—
60C2×C4×C73C22×C411yescharacteristic
61C22⋊D73—21no—
62C22⋊D73—21no—
63C22⋊D73—21no—
64C2×Dic73—21no—
65C2×Dic73M1611yescharacteristic
66D292—21no—
67D292C2×C811yescharacteristic
68C4×D73—21no—
69C4×D73—21no—
70C4×D73—21no—
71C4×D73C22⋊C411yescharacteristic
72C4×D73C22⋊C411yescharacteristic
73C4×D73C2×C811yescharacteristic
74C4×D73C2×C811yescharacteristic
75Dic146—21no—
76Dic146C2×C811yescharacteristic
77C8×C73—21no—
78C8×C73C22⋊C411yescharacteristic
79C8×C73C22⋊C411yescharacteristic
80#10596831—21no—
81#10596831C2×D411yescharacteristic
82#10596831C2×D411yescharacteristic
83C22×C73—21no—
84C22×C73C2×M1611yescharacteristic
85C2×D73—21no—
86C2×D73—41no—
87C2×D73—42no—
88C2×D73C22⋊C811yescharacteristic
89C2×D73C22⋊C811yescharacteristic
90C4×C73—21no—
91C4×C73C2×C22⋊C411yescharacteristic
92C4×C73C22×C811yescharacteristic
93Dic73—21no—
94Dic73C22⋊C811yescharacteristic
95Dic73C22⋊C811yescharacteristic
96C2×C73—21no—
97C2×C73—41no—
98C2×C73C2×C22⋊C811yescharacteristic
99D73—21no—
100D73—21no—
101D73—41no—
102#2117—731nomaximal, Sylow
103C73#211711yescharacteristic, complemented, Sylow
104C2×#131—731no—
105C2×M32—731no—
106C2×M32—731no—
107#350—732no—
108#350—732no—
109C2×#41—731no—
110#131—731no—
111#131—731no—
112#131—731no—
113#131—1461no—
114#131—1461no—
115#131#6440811yescharacteristic
116C2×M16—731no—
117C2×M16—1461no—
118C22×C8—731no—
119C22×C8—1461no—
120M32—732no—
121M32—1461no—
122M32—1461no—
123M32—1461no—
124C2×C16—732no—
125C2×C16—1461no—
126#41—731no—
127#41—731no—
128#41—731no—
129#41—1461no—
130#41—1461no—
131#41C2×#6440811yescharacteristic
132C2×Q8—731no—
133C2×D4—731no—
134C2×D4—1461no—
135C22×C4—731no—
136C22×C4—1461no—
137M16—21no—
138M16—731no—
139M16—1461no—
140M16—1461no—
141M16—1461no—
142M16—1461no—
143M16C2×#6440811yescharacteristic
144C2×C8—21no—
145C2×C8—731no—
146C2×C8—731no—
147C2×C8—731no—
148C2×C8—731no—
149C2×C8—731no—
150C2×C8—1461no—
151C2×C8—1461no—
152C2×C8—1461no—
153C2×C8—1461no—
154C2×C8C2×#6440811yescharacteristic
155C16—1462no—
156C16—1462no—
157C23—731no—
158C23—1461no—
159Q8—731no—
160Q8—1461no—
161Q8#1192403611yescharacteristic
162D4—21no—
163D4—731no—
164D4—1461no—
165D4—1461no—
166D4—1461no—
167D4—1461no—
168D4#1192403611yescharacteristic
169C2×C4—21no—
170C2×C4—731no—
171C2×C4—731no—
172C2×C4—731no—
173C2×C4—731no—
174C2×C4—731no—
175C2×C4—1461no—
176C2×C4—1461no—
177C2×C4—1461no—
178C2×C4—1461no—
179C2×C4C22×#6440811yescharacteristic
180C8—21no—
181C8—731no—
182C8—731no—
183C8—1461no—
184C8C22⋊#6440811yescharacteristic
185C8C22⋊#6440811yescharacteristic
186C22—21no—
187C22—2921no—
188C22—2922no—
189C22—731no—
190C22—731no—
191C22—1461no—
192C22D73⋊M1611yescharacteristic
193C4—21no—
194C4—731no—
195C4—731no—
196C4—1461no—
197C4C2×C22⋊#6440811yescharacteristic
198C4C2×#1192403611yescharacteristic
199C2—21no—
200C2—41no—
201C2—2921no—
202C2—1461no—
203C2—1461no—
204C2#1798955511yescharacteristic
subgroupG/H
centerC4C2×C22⋊#64408
commutatorC4×C73C22×C8
FrattiniC2×C4C22×#64408
Fitting#131×C73C4
socleC2×C73C2×C22⋊C8
hypercenter#131#64408
hypocenterC73#2117
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C8 ◁ #131

Complements

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

NH ≅ G/Ntype
1. C2×#14556666C2semidirect
2. #17989643C2semidirect
3. #17989486C2semidirect
4. #17989485C2semidirect
9. #14556665C22semidirect
11. C2×#11924031C22semidirect
103. C73#2117semidirect