Finite Group Databasebeta

← #22626015

Subgroups — #22626015

Order 9344.

224 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 60 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×#14556656C211yesmaximal, characteristic
3#17989562C211yesmaximal, characteristic
4#17989552C211yesmaximal, characteristic, complemented
5#17989457C211yesmaximal, characteristic, complemented
6#17989452C211yesmaximal, characteristic, complemented
7#17988582C211yesmaximal, characteristic
8C2×#11924038C2211yescharacteristic
9C2×#11924038C2211yescharacteristic
10C2×#11924036C2211yescharacteristic
11C2×C4×#64408C2211yescharacteristic
12#14556662—22no—
13#14556656—22no—
14#14556648—21no—
15#14556648—21no—
16#14556646—21no—
17C4×#10596833—21no—
18C2×#11924029C2211yescharacteristic
19C2×C8×D73C2211yescharacteristic
20#14556549C2211yescharacteristic
21#14556515C411yescharacteristic, complemented
22#14556513C411yescharacteristic, complemented
23#14556511C411yescharacteristic, complemented
24#103×C73C411yescharacteristic, complemented
25C22×#64408—21no—
26#11924038—21no—
27#11924038—21no—
28#11924038—21no—
29#11924038D412yes—
30#11924036—21no—
31#11924036—21no—
32C2×#10596833—21no—
33C2×#10596833—21no—
34C2×#10596833D411yescharacteristic
35C2×#10596833D411yescharacteristic
36C4×#64408—21no—
37C4×#64408—21no—
38#11924029—21no—
39#11924029—21no—
40#11924029—21no—
41#11924029—21no—
42C2×D292—21no—
43C2×D292C2×C411yescharacteristic
44C2×C4×D73—21no—
45C2×C4×D73C2311yescharacteristic
46C2×#10596831C2×C411yescharacteristic
47C8×D73—21no—
48C8×D73—21no—
49C4⋊Dic73C2×C411yescharacteristic
50#11924005—21no—
51C4×Dic73—21no—
52C2×Q8×C73C2×C411yescharacteristic
53C2×C8×C73C2×C411yescharacteristic
54C4⋊C4×C73C2×C411yescharacteristic
55C22×D73—21no—
56C22×D73#4111yescharacteristic
57C2×#64408—22no—
58C2×#64408—41no—
59C2×#64408—41no—
60Q8×C73—21no—
61Q8×C73—21no—
62C2×C4×C73—21no—
63C2×C4×C73—21no—
64C2×C4×C73C22×C411yescharacteristic
65C2×Dic73—21no—
66C2×Dic73C2×D411yescharacteristic
67D292—21no—
68D292—21no—
69D292—41no—
70D292—41no—
71C4×D73—41no—
72C4×D73—41no—
73C4×D73C2×D411yescharacteristic
74C4×D73#4111yescharacteristic
75C4×D73#4111yescharacteristic
76C4×D73#4111yescharacteristic
77#10596833—22no—
78#10596833—21no—
79#10596833—21no—
80#10596833—41no—
81C8×C73—21no—
82#10596831—21no—
83C22×C73C4×D411yescharacteristic
84C2×D73—21no—
85C2×D73—21no—
86C2×D73—41no—
87C2×D73—41no—
88C2×D73—41no—
89C2×D73#12411yescharacteristic
90C2×D73#12611yescharacteristic
91#64408—42no—
92C4×C73—41no—
93C4×C73—41no—
94C4×C73#11711yescharacteristic
95C4×C73C4×D411yescharacteristic
96Dic73—41no—
97Dic73#12111yescharacteristic
98Dic73#12311yescharacteristic
99C2×C73#38811yescharacteristic
100C2×C73#44311yescharacteristic
101C2×C73#44411yescharacteristic
102D73—21no—
103D73—21no—
104D73—81no—
105#1929—731nomaximal, Sylow
106C73#192911yescharacteristic, complemented, Sylow
107C2×#108—731no—
108C2×#104—731no—
109#416—731no—
110#408—731no—
111#405—731no—
112#339—731no—
113#336—731no—
114C2×#41—731no—
115C2×M16—731no—
116C2×M16—731no—
117C22×C8—731no—
118C22×C8—731no—
119#117—731no—
120C2×C42—731no—
121#108—1462no—
122#104—1462no—
123#103—731no—
124#103#6440811yescharacteristic, complemented
125#102—731no—
126#102—731no—
127C22⋊C8—1461no—
128C22⋊C8—1461no—
129#97—1461no—
130C4×C8—1461no—
131#41—1461no—
132#41—1461no—
133#41—1461no—
134#41—1461no—
135C2×Q8C2×#6440811yescharacteristic
136C2×D4—731no—
137C2×D4—1461no—
138C22×C4—731no—
139C22×C4—1461no—
140C22×C4—1461no—
141M16—732no—
142M16—1461no—
143M16—1461no—
144M16—1461no—
145C2×C8—731no—
146C2×C8—731no—
147C2×C8—731no—
148C2×C8—1461no—
149C2×C8—1461no—
150C2×C8—1461no—
151C2×C8—1461no—
152C2×C8—1461no—
153C2×C8—1461no—
154C2×C8C2×#6440811yescharacteristic
155C4⋊C4—731no—
156C4⋊C4C2×#6440811yescharacteristic
157C22⋊C4—1461no—
158C42—1461no—
159C42—1461no—
160C42—1461no—
161C23—731no—
162C23—1461no—
163Q8—21no—
164Q8—21no—
165D4—2921no—
166D4—2921no—
167D4—1461no—
168D4—1461no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—2921no—
172C2×C4—2921no—
173C2×C4—2921no—
174C2×C4—2921no—
175C2×C4—731no—
176C2×C4—731no—
177C2×C4—731no—
178C2×C4—731no—
179C2×C4—731no—
180C2×C4—1462no—
181C2×C4—1461no—
182C2×C4C22×#6440811yescharacteristic
183C8—21no—
184C8—2921no—
185C8—1461no—
186C8—1461no—
187C8—1462no—
188C8—1461no—
189C22—2921no—
190C22—2921no—
191C22—2921no—
192C22—731no—
193C22—731no—
194C22—1461no—
195C22—1461no—
196C22D4×#6440811yescharacteristic
197C4—41no—
198C4—41no—
199C4—2922no—
200C4—2921no—
201C4—731no—
202C4—731no—
203C4#1455667011yescharacteristic
204C4D4×#6440811yescharacteristic
205C2—5841no—
206C2—1461no—
207C2—1461no—
208C2#1798953711yescharacteristic
209C2#1798963111yescharacteristic
210C2#1798963211yescharacteristic
subgroupG/H
centerC22D4×#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#103×C73C4
socleC22×C73C4×D4
hypercenter#103#64408
hypocenterC73#1929
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. C2×#14556662C2semidirect
4. #17989552C2semidirect
5. #17989457C2semidirect
6. #17989452C2semidirect
21. #14556515C4semidirect
22. #14556513C4semidirect
23. #14556511C4semidirect
24. #103×C73C4semidirect
106. C73#1929semidirect
124. #103#64408semidirect