Finite Group Databasebeta

← #22611185

Subgroups — #22611185

Order 9344.

296 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 67 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
1C22×#11924013C211yesmaximal, characteristic
2#17988615C211yesmaximal, characteristic, complemented
3#17988593C211yesmaximal, characteristic, complemented
4#17988592C211yesmaximal, characteristic, complemented
5C2×#14556507C211yesmaximal, characteristic, complemented
6#17988351C211yesmaximal, characteristic, complemented
7C2×#100×C73C211yesmaximal, characteristic, complemented
8C22×D292C2211yescharacteristic
9C2×#11924013—22no—
10C2×#11924013—22no—
11C2×#11924013—22no—
12C2×#11924012C2211yescharacteristic
13C22×#10596831C2211yescharacteristic
14#14556550C2211yescharacteristic
15#14556520—22no—
16#14556513—22no—
17#14556512—22no—
18#14556507—22no—
19C22×D4×C73C2211yescharacteristic
20C2×M16×C73C2211yescharacteristic
21C2×M16×C73C2211yescharacteristic
22#100×C73—22no—
23C23×D73—21no—
24C2×D292—21no—
25C2×D292—21no—
26C2×D292—21no—
27C2×D292—21no—
28C2×D292—21no—
29C2×D292D412yes—
30#11924013—28no—
31#11924012—21no—
32#11924012—21no—
33C2×#10596831—21no—
34C2×#10596831—21no—
35C2×#10596831—21no—
36C2×#10596831D412yes—
37C4⋊Dic73D412yes—
38C22⋊Dic73—21no—
39C4×Dic73—21no—
40C24×C73—21no—
41C2×D4×C73—21no—
42C2×D4×C73—21no—
43C2×D4×C73—21no—
44C2×D4×C73—21no—
45C2×D4×C73—21no—
46C2×D4×C73D412yes—
47C22×C4×C73C2311yescharacteristic
48M16×C73—21no—
49M16×C73—21no—
50M16×C73—21no—
51M16×C73—21no—
52C2×C8×C73—21no—
53C2×C8×C73—21no—
54C23×C73—22no—
55C23×C73—41no—
56C23×C73—41no—
57C23×C73—82no—
58C23×C73#4111yescharacteristic
59C22×D73—22no—
60C22×D73—41no—
61C22×D73—41no—
62C22×D73—82no—
63D4×C73—22no—
64D4×C73—22no—
65D4×C73—41no—
66D4×C73—41no—
67C2×C4×C73C2×D411yescharacteristic
68C2×C4×C73C2×D411yescharacteristic
69C2×C4×C73C2×D411yescharacteristic
70C2×C4×C73C2×D411yescharacteristic
71C2×C4×C73#4111yescharacteristic
72C2×C4×C73#4111yescharacteristic
73C2×Dic73—22no—
74D292—22no—
75D292—22no—
76D292—41no—
77D292—41no—
78C8×C73—41no—
79C8×C73—41no—
80#10596831—22no—
81#10596831—41no—
82C22×C73—22no—
83C22×C73—42no—
84C22×C73—82no—
85C22×C73—82no—
86C22×C73—82no—
87C22×C73#12111yescharacteristic
88C22×C73#12311yescharacteristic
89C22×C73#12311yescharacteristic
90C2×D73—42no—
91C2×D73—82no—
92C2×D73—82no—
93C2×D73—82no—
94C4×C73#12011yescharacteristic
95C4×C73#12111yescharacteristic
96C4×C73#12111yescharacteristic
97C4×C73#12411yescharacteristic
98Dic73—42no—
99C2×C73—21no—
100C2×C73—21no—
101C2×C73—82no—
102C2×C73#39411yescharacteristic
103C2×C73#47212yes—
104D73—82no—
105#2045—731nomaximal, Sylow
106C73#204511yescharacteristic, complemented, Sylow
107C22×D8—731no—
108#424—731no—
109#418—731no—
110#418—731no—
111C2×#100—731no—
112C2×#100D7311yescharacteristic, complemented
113#341—731no—
114C22×D4—731no—
115C22×D4C2×D7311yescharacteristic
116C2×D8—1462no—
117C2×D8—1462no—
118C2×D8—1462no—
119C2×M16—731no—
120C2×M16C2×D7311yescharacteristic
121C2×M16C2×D7311yescharacteristic
122C22×C8—731no—
123#117—731no—
124C4⋊C8—1462no—
125#102—1462no—
126#102—1462no—
127#100—22no—
128#100—1462no—
129C24—21no—
130C24—1461no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—732no—
137C2×D4—1461no—
138C2×D4—1461no—
139C2×D4—1461no—
140C2×D4—1461no—
141C2×D4—1461no—
142C2×D4C22⋊D7312yes—
143C22×C4C22×D7311yescharacteristic
144D8—1468no—
145M16—21no—
146M16—21no—
147M16—21no—
148M16—21no—
149M16—1461no—
150M16—1461no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—732no—
154C2×C8—1461no—
155C2×C8—1461no—
156C2×C8—1461no—
157C4⋊C4—732no—
158C22⋊C4—1461no—
159C42—1461no—
160C23—22no—
161C23—41no—
162C23—41no—
163C23—82no—
164C23—2921no—
165C23—2921no—
166C23—5842no—
167C23—1462no—
168C23#1192402811yescharacteristic
169D4—22no—
170D4—22no—
171D4—41no—
172D4—41no—
173D4—2921no—
174D4—2921no—
175D4—1462no—
176D4—1462no—
177C2×C4—1462no—
178C2×C4D4×D7311yescharacteristic
179C2×C4D4×D7311yescharacteristic
180C2×C4D4×D7311yescharacteristic
181C2×C4C2×C22⋊D7311yescharacteristic
182C2×C4#1192402711yescharacteristic
183C2×C4#1192402811yescharacteristic
184C8—41no—
185C8—41no—
186C8—2921no—
187C8—1462no—
188C22—22no—
189C22—42no—
190C22—82no—
191C22—82no—
192C22—82no—
193C22—2922no—
194C22—5842no—
195C22—5842no—
196C22—5842no—
197C22#1455656411yescharacteristic
198C22#1455657311yescharacteristic
199C22#1455657411yescharacteristic
200C4—2922no—
201C4#1455655911yescharacteristic
202C4#1455656311yescharacteristic
203C4#1455656411yescharacteristic
204C4#1455657711yescharacteristic
205C2—21no—
206C2—21no—
207C2—82no—
208C2—5842no—
209C2#1798850211yescharacteristic
210C2#1798885612yes—
subgroupG/H
centerC22#14556564
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
FittingC2×#100×C73C2
socleC22×C73#121
hypercenterC2×#100D73
hypocenterC73#2045
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. #17988615C2semidirect
3. #17988593C2semidirect
4. #17988592C2semidirect
5. C2×#14556507C2semidirect
6. #17988351C2semidirect
7. C2×#100×C73C2semidirect
106. C73#2045semidirect
112. C2×#100D73semidirect