Finite Group Databasebeta

← #22625812

Subgroups — #22625812

Order 9344.

272 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 76 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×#14556662C211yesmaximal, characteristic, complemented
2C2×#14556661C211yesmaximal, characteristic, complemented
3#17989558C212yesmaximal
4#17989463C212yesmaximal, complemented
5C2×M16×D73C211yesmaximal, characteristic
6C2×#11924038C2212yes—
7C2×#11924038C2212yes—
8#14556662—22no—
9#14556661—22no—
10#14556648—22no—
11C22⋊#10596833—22no—
12C22×C4×D73C2211yescharacteristic
13C2×#11924012C411yescharacteristic
14C2×#11924011C411yescharacteristic
15C2×#11924011C411yescharacteristic
16M16×D73—22no—
17M16×D73—22no—
18C2×C8×D73C2211yescharacteristic
19C2×C8×D73C2211yescharacteristic
20C2×M16×C73C411yescharacteristic
21#11924038—22no—
22#11924038—22no—
23#11924038—22no—
24#11924038—22no—
25C2×#10596833—22no—
26C2×#10596833—22no—
27C23×D73Q811yescharacteristic
28C22×Dic73D411yescharacteristic
29C2×C4×D73—21no—
30C2×C4×D73—21no—
31C2×C4×D73—21no—
32C2×C4×D73—21no—
33C2×C4×D73C2×C411yescharacteristic
34C2×C4×D73D411yescharacteristic
35C2×C4×D73Q811yescharacteristic
36C2×C4×D73C2311yescharacteristic
37#11924012—22no—
38#11924011—22no—
39#11924011—22no—
40C2×#10596831C2×C411yescharacteristic
41C2×#10596831C2×C411yescharacteristic
42C8×D73—21no—
43C8×D73—21no—
44C8×D73D412yes—
45C8×D73D412yes—
46C22×C4×C73C2×C411yescharacteristic
47M16×C73—22no—
48C2×C8×C73C2×C411yescharacteristic
49C2×C8×C73C2×C411yescharacteristic
50C23×C73C4⋊C411yescharacteristic
51C22×D73—21no—
52C22×D73—21no—
53C22×D73—42no—
54C22×D73C4⋊C411yescharacteristic
55C22×D73C2×Q811yescharacteristic
56C2×C4×C73—21no—
57C2×C4×C73—21no—
58C2×C4×C73C4⋊C411yescharacteristic
59C2×C4×C73C22×C411yescharacteristic
60C2×Dic73—21no—
61C2×Dic73—21no—
62C2×Dic73C4⋊C411yescharacteristic
63C2×Dic73C2×D411yescharacteristic
64C4×D73—21no—
65C4×D73—21no—
66C4×D73—21no—
67C4×D73—21no—
68C4×D73—21no—
69C4×D73—21no—
70C4×D73C2×D411yescharacteristic
71C4×D73C2×D411yescharacteristic
72C4×D73#4111yescharacteristic
73C4×D73#4111yescharacteristic
74#10596833—42no—
75#10596833—42no—
76C8×C73—21no—
77C8×C73C22⋊C412yes—
78#10596831—21no—
79#10596831C22⋊C412yes—
80C22×C73—21no—
81C22×C73—22no—
82C22×C73C2×C4⋊C411yescharacteristic
83C2×D73—22no—
84C2×D73—21no—
85C2×D73—22no—
86C2×D73—42no—
87C2×D73—42no—
88C2×D73C22⋊Q811yescharacteristic
89C2×D73C22⋊Q811yescharacteristic
90C4×C73—21no—
91C4×C73C2×C22⋊C411yescharacteristic
92C4×C73#11711yescharacteristic
93Dic73—21no—
94Dic73#12111yescharacteristic
95Dic73#12111yescharacteristic
96C2×C73—41no—
97C2×C73#38011yescharacteristic
98C2×C73#43012yes—
99D73—21no—
100D73—21no—
101D73—41no—
102#1811—731nomaximal, Sylow
103C73#181111yescharacteristic, complemented, Sylow
104C22×M16—731no—
105C2×#108—731no—
106C2×#108—731no—
107#407—732no—
108#341—732no—
109C23×C4—731no—
110C2×M16—731no—
111C2×M16—731no—
112C2×M16—731no—
113C2×M16—732no—
114C2×M16—732no—
115C2×M16—1462no—
116C2×M16—1462no—
117C2×M16#6440811yescharacteristic
118C22×C8—731no—
119C22×C8—731no—
120#108—1462no—
121#108—1462no—
122C22⋊C8—1462no—
123C22⋊C8—1462no—
124C24—731no—
125C22×C4—731no—
126C22×C4—731no—
127C22×C4—731no—
128C22×C4—731no—
129C22×C4—731no—
130C22×C4—1461no—
131C22×C4—1461no—
132C22×C4—1461no—
133C22×C4—1461no—
134C22×C4C2×#6440811yescharacteristic
135M16—22no—
136M16—1462no—
137M16—1462no—
138M16—1462no—
139M16—1462no—
140M16—1462no—
141M16—1462no—
142M16—1462no—
143C2×C8—731no—
144C2×C8—732no—
145C2×C8—732no—
146C2×C8—731no—
147C2×C8—1461no—
148C2×C8—1461no—
149C2×C8—1462no—
150C2×C8—1462no—
151C2×C8C2×#6440811yescharacteristic
152C2×C8C2×#6440811yescharacteristic
153C23—2922no—
154C23—731no—
155C23—731no—
156C23—1461no—
157C23—1461no—
158C23C4⋊#6440811yescharacteristic
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—731no—
162C2×C4—731no—
163C2×C4—731no—
164C2×C4—731no—
165C2×C4—731no—
166C2×C4—731no—
167C2×C4—1461no—
168C2×C4—1461no—
169C2×C4—1461no—
170C2×C4—1461no—
171C2×C4—1461no—
172C2×C4—1461no—
173C2×C4—1461no—
174C2×C4—1461no—
175C2×C4C4⋊#6440811yescharacteristic
176C2×C4C22×#6440811yescharacteristic
177C8—21no—
178C8—2922no—
179C8—2922no—
180C8—732no—
181C8—1461no—
182C8C22⋊#6440812yes—
183C22—21no—
184C22—22no—
185C22—2922no—
186C22—2922no—
187C22—731no—
188C22—731no—
189C22—1461no—
190C22—1462no—
191C22—1462no—
192C22C2×C4⋊#6440811yescharacteristic
193C4—21no—
194C4—731no—
195C4—731no—
196C4—1461no—
197C4C2×C22⋊#6440811yescharacteristic
198C4#1455667011yescharacteristic
199C2—41no—
200C2—2921no—
201C2—1461no—
202C2—1461no—
203C2#1798952911yescharacteristic
204C2#1798960212yes—
subgroupG/H
centerC22C2×C4⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC2×M16×C73C4
socleC22×C73C2×C4⋊C4
hypercenterC2×M16#64408
hypocenterC73#1811
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#14556662C2semidirect
2. C2×#14556661C2semidirect
4. #17989463C2semidirect
103. C73#1811semidirect