Finite Group Databasebeta

← #22611292

Subgroups — #22611292

Order 9344.

228 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 65 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×#14556526C211yesmaximal, characteristic, complemented
2#17988627C211yesmaximal, characteristic, complemented
3#17988615C211yesmaximal, characteristic, complemented
4#17988593C211yesmaximal, characteristic
5C2×#14556511C211yesmaximal, characteristic
6C2×#14556507C211yesmaximal, characteristic
7#343×C73C211yesmaximal, characteristic, complemented
8C22×D292C2211yescharacteristic
9C2×#11924012C2211yescharacteristic
10C22×#10596831C2211yescharacteristic
11#14556550C2211yescharacteristic
12#14556526—22no—
13#14556524—21no—
14#14556522—21no—
15#14556520—22no—
16#14556513—21no—
17#14556513—21no—
18#14556511—22no—
19#14556507—22no—
20C2×M16×C73C2211yescharacteristic
21C2×M16×C73C2211yescharacteristic
22C2×C4⋊C4×C73C2211yescharacteristic
23C23×D73—21no—
24C2×D292—21no—
25C2×D292—21no—
26C2×D292—21no—
27C2×D292—21no—
28C2×D292—21no—
29C2×D292Q812yes—
30#11924012—21no—
31#11924012D412yes—
32C2×#10596831—21no—
33C2×#10596831—21no—
34C2×#10596831—21no—
35C2×#10596831D412yes—
36C4⋊Dic73D411yescharacteristic
37C4⋊Dic73D411yescharacteristic
38C22⋊Dic73—21no—
39C4×Dic73—21no—
40C22×C4×C73—21no—
41C22×C4×C73C2311yescharacteristic
42M16×C73—21no—
43M16×C73—21no—
44M16×C73—21no—
45M16×C73—21no—
46C2×C8×C73—21no—
47C2×C8×C73—21no—
48C4⋊C4×C73—21no—
49C4⋊C4×C73—21no—
50C23×C73#4111yescharacteristic
51C22×D73—22no—
52C22×D73—41no—
53C22×D73—41no—
54C22×D73—81no—
55C22×D73—81no—
56C2×C4×C73—41no—
57C2×C4×C73—81no—
58C2×C4×C73C2×D411yescharacteristic
59C2×C4×C73C2×D411yescharacteristic
60C2×C4×C73C2×D411yescharacteristic
61C2×C4×C73C2×Q811yescharacteristic
62C2×C4×C73#4111yescharacteristic
63C2×C4×C73#4111yescharacteristic
64C2×Dic73—21no—
65C2×Dic73—21no—
66D292—22no—
67D292—22no—
68D292—41no—
69D292—41no—
70C8×C73—41no—
71C8×C73—41no—
72#10596831—22no—
73#10596831—22no—
74C22×C73—21no—
75C22×C73—21no—
76C22×C73#12111yescharacteristic
77C22×C73C22⋊Q811yescharacteristic
78C22×C73#12611yescharacteristic
79C2×D73—42no—
80C2×D73—82no—
81C2×D73—81no—
82C2×D73—81no—
83C2×D73—82no—
84C4×C73—81no—
85C4×C73#12111yescharacteristic
86C4×C73#12111yescharacteristic
87C4×C73C22⋊Q811yescharacteristic
88C4×C73C22⋊Q811yescharacteristic
89Dic73—41no—
90Dic73—41no—
91C2×C73—21no—
92C2×C73—21no—
93C2×C73#39611yescharacteristic
94C2×C73#47111yescharacteristic
95C2×C73#47211yescharacteristic
96D73—82no—
97#2063—731nomaximal, Sylow
98C73#206311yescharacteristic, complemented, Sylow
99C2×#108—731no—
100#428—731no—
101#424—731no—
102#418—731no—
103C2×#102—731no—
104C2×#100—731no—
105#343D7311yescharacteristic, complemented
106C22×D4—731no—
107C2×M16—731no—
108C2×M16C2×D7311yescharacteristic
109C2×M16C2×D7311yescharacteristic
110C22×C8—731no—
111#117—731no—
112C2×C4⋊C4C2×D7311yescharacteristic
113#108—1462no—
114#107—1461no—
115#106—1461no—
116C4⋊C8—1462no—
117#102—1462no—
118#102—1461no—
119#102—1461no—
120#100—1462no—
121C24—1461no—
122C2×D4—732no—
123C2×D4—1461no—
124C2×D4—1461no—
125C2×D4—1461no—
126C2×D4—1461no—
127C2×D4—1461no—
128C22×C4—21no—
129C22×C4C22×D7311yescharacteristic
130M16—21no—
131M16—21no—
132M16—21no—
133M16—21no—
134M16—732no—
135M16—1461no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—732no—
139C2×C8—1461no—
140C2×C8—1461no—
141C2×C8—1461no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—731no—
145C4⋊C4—731no—
146C22⋊C4—1461no—
147C42—1461no—
148C23—2921no—
149C23—2921no—
150C23—5841no—
151C23—5841no—
152C23—1462no—
153C23#1192402811yescharacteristic
154D4—2921no—
155D4—2921no—
156D4—1462no—
157D4—1462no—
158C2×C4—41no—
159C2×C4—81no—
160C2×C4—1461no—
161C2×C4—1461no—
162C2×C4D4×D7311yescharacteristic
163C2×C4D4×D7311yescharacteristic
164C2×C4D4×D7311yescharacteristic
165C2×C4Q8×D7311yescharacteristic
166C2×C4#1192402811yescharacteristic
167C2×C4#1192402811yescharacteristic
168C8—41no—
169C8—41no—
170C8—1462no—
171C8—1462no—
172C22—21no—
173C22—21no—
174C22—2922no—
175C22—5842no—
176C22—5842no—
177C22—5841no—
178C22—5841no—
179C22#1455656411yescharacteristic
180C22#1455656911yescharacteristic
181C22#1455658511yescharacteristic
182C4—81no—
183C4—2921no—
184C4—2921no—
185C4#1455656411yescharacteristic
186C4#1455656411yescharacteristic
187C4#1455656911yescharacteristic
188C4#1455656911yescharacteristic
189C2—21no—
190C2—21no—
191C2—5842no—
192C2#1798851111yescharacteristic
193C2#1798885311yescharacteristic
194C2#1798885611yescharacteristic
subgroupG/H
centerC22#14556564
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#343×C73C2
socleC22×C73#121
hypercenter#343D73
hypocenterC73#2063
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. C2×#14556526C2semidirect
2. #17988627C2semidirect
3. #17988615C2semidirect
7. #343×C73C2semidirect
98. C73#2063semidirect
105. #343D73semidirect