Finite Group Databasebeta

← #22625840

Subgroups — #22625840

Order 9344.

262 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 62 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#17989573C211yesmaximal, characteristic
2#17989566C211yesmaximal, characteristic
3#17989458C212yesmaximal, complemented
4#17989454C212yesmaximal, complemented
5C4×#11924028C211yesmaximal, characteristic
6D73⋊M16C2212yes—
7#14556670C2212yes—
8#14556652—21no—
9#14556651—21no—
10#14556650—21no—
11#14556649—21no—
12C2×#11924028C2211yescharacteristic
13C4×Dic146—21no—
14C4×D292—21no—
15C4×C22⋊D73—21no—
16C4×C22⋊D73—21no—
17#14556550C411yescharacteristic, complemented
18#14556548C411yescharacteristic, complemented
19#14556548C2211yescharacteristic
20C42×D73C411yescharacteristic, complemented
21C42×D73C2211yescharacteristic
22C2×C42×C73C411yescharacteristic, complemented
23#11924038—22no—
24#11924037—22no—
25#11924036—22no—
26C4⋊#64408—22no—
27C22⋊#64408—22no—
28C4×#64408—22no—
29#11924028—22no—
30#11924028—22no—
31C2×Dic146D411yescharacteristic
32C2×D292D411yescharacteristic
33C2×C22⋊D73D411yescharacteristic
34C2×C22⋊D73D411yescharacteristic
35C2×C4×D73—21no—
36C2×C4×D73—21no—
37C2×C4×D73C2×C411yescharacteristic
38C2×C4×D73C2311yescharacteristic
39C4⋊Dic73—21no—
40#11924007—21no—
41#11924007—21no—
42C22⋊Dic73—21no—
43#11924005—21no—
44#11924005—21no—
45C4×Dic73—21no—
46C4×Dic73—21no—
47C4×Dic73C2×C411yescharacteristic
48C4×Dic73C2×C411yescharacteristic
49C22×C4×C73—21no—
50C22×C4×C73C2×C411yescharacteristic
51C42×C73—21no—
52C42×C73C2×C411yescharacteristic
53C42×C73C2×C411yescharacteristic
54C23×C73C22⋊C411yescharacteristic
55C22×D73C22⋊C411yescharacteristic
56C22×D73C2×D411yescharacteristic
57C2×#64408—42no—
58C2×C4×C73—21no—
59C2×C4×C73—21no—
60C2×C4×C73—21no—
61C2×C4×C73—21no—
62C2×C4×C73—42no—
63C2×C4×C73C22⋊C411yescharacteristic
64C2×C4×C73C22×C411yescharacteristic
65C22⋊D73—22no—
66C22⋊D73—22no—
67C2×Dic73—21no—
68C2×Dic73—21no—
69C2×Dic73C22⋊C411yescharacteristic
70C2×Dic73C2×D411yescharacteristic
71D292—22no—
72C4×D73—21no—
73C4×D73—21no—
74C4×D73—42no—
75C4×D73—42no—
76C4×D73#4112yes—
77C4×D73#4112yes—
78Dic146—22no—
79#10596833—42no—
80C22×C73—21no—
81C22×C73—41no—
82C22×C73C2×C22⋊C411yescharacteristic
83C2×D73—21no—
84C2×D73—41no—
85C2×D73—41no—
86C2×D73#12312yes—
87#64408—82no—
88C4×C73—22no—
89C4×C73—21no—
90C4×C73—41no—
91C4×C73#11711yescharacteristic
92C4×C73#11711yescharacteristic
93Dic73—21no—
94Dic73—41no—
95Dic73—41no—
96Dic73#12312yes—
97C2×C73—21no—
98C2×C73—41no—
99C2×C73#38111yescharacteristic
100D73—22no—
101D73—41no—
102#1827—731nomaximal, Sylow
103C73#182711yescharacteristic, complemented, Sylow
104C4×#41—731no—
105#413—731no—
106#410—731no—
107#339—732no—
108H(3,ℤ/4)—732no—
109C2×#41—731no—
110C2×M16—732no—
111C4×Q8—1461no—
112C4×D4—1461no—
113C4×D4—1461no—
114C4×D4—1461no—
115#117—731no—
116#117—731no—
117#117—731no—
118#117—732no—
119C2×C42—731no—
120C2×C42—731no—
121C2×C42#6440811yescharacteristic, complemented
122#101—1461no—
123#100—1461no—
124#99—1461no—
125#99—1461no—
126#41—1462no—
127#41—1462no—
128C2×Q8—731no—
129C2×D4—731no—
130C2×D4—731no—
131C2×D4—731no—
132C22×C4—21no—
133C22×C4—731no—
134C22×C4—731no—
135C22×C4—1461no—
136C22×C4—1461no—
137C22×C4C2×#6440811yescharacteristic
138M16—1462no—
139M16—1462no—
140C2×C8—1462no—
141C4⋊C4—1461no—
142C4⋊C4—1461no—
143C4⋊C4—1462no—
144C4⋊C4—1461no—
145C22⋊C4—1461no—
146C22⋊C4—1461no—
147C22⋊C4—1462no—
148C22⋊C4—1461no—
149C42—21no—
150C42—731no—
151C42—731no—
152C42—1461no—
153C42—1461no—
154C42—1462no—
155C42C2×#6440811yescharacteristic
156C42C2×#6440811yescharacteristic
157C23—731no—
158C23—731no—
159C23C22⋊#6440811yescharacteristic
160Q8—1462no—
161D4—1462no—
162D4—1462no—
163D4—1462no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—42no—
169C2×C4—2922no—
170C2×C4—2922no—
171C2×C4—2922no—
172C2×C4—731no—
173C2×C4—732no—
174C2×C4—732no—
175C2×C4—731no—
176C2×C4—1461no—
177C2×C4—1461no—
178C2×C4—1461no—
179C2×C4—1461no—
180C2×C4C22⋊#6440811yescharacteristic
181C2×C4C22×#6440811yescharacteristic
182C8—2922no—
183C22—21no—
184C22—41no—
185C22—2921no—
186C22—2921no—
187C22—732no—
188C22—1461no—
189C22C2×C22⋊#6440811yescharacteristic
190C4—22no—
191C4—21no—
192C4—41no—
193C4—2921no—
194C4—2921no—
195C4—5842no—
196C4—732no—
197C4—1461no—
198C4#1455667011yescharacteristic
199C4#1455667011yescharacteristic
200C2—21no—
201C2—41no—
202C2—2921no—
203C2—1462no—
204C2#1798953011yescharacteristic
subgroupG/H
centerC4#14556670
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC2×C42×C73C4
socleC2×C73#381
hypercenterC2×C42#64408
hypocenterC73#1827
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C42 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. #17989458C2semidirect
4. #17989454C2semidirect
17. #14556550C4semidirect
18. #14556548C4semidirect
20. C42×D73C4semidirect
22. C2×C42×C73C4semidirect
103. C73#1827semidirect
121. C2×C42#64408semidirect