Finite Group Databasebeta

← #22611342

Subgroups — #22611342

Order 9344.

238 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14556515C211yesmaximal, characteristic
2#17988494C211yesmaximal, characteristic
3#17988456C211yesmaximal, characteristic
4#17988350C211yesmaximal, characteristic
5#17988349C211yesmaximal, characteristic
6#17988341C211yesmaximal, characteristic
7C2×#103×C73C211yesmaximal, characteristic
8C22×#10596831C2211yescharacteristic
9C2×C4⋊Dic73C2211yescharacteristic
10C2×C4⋊Dic73C2211yescharacteristic
11C2×#11924007—21no—
12C2×#11924007—21no—
13C2×C4×Dic73C2211yescharacteristic
14#14556515—22no—
15#14556498—21no—
16#14556498—21no—
17C22×Q8×C73C2211yescharacteristic
18C22×C8×C73C2211yescharacteristic
19C2×C4⋊C4×C73C2211yescharacteristic
20#103×C73—22no—
21C22×Dic73—21no—
22C22×Dic73—21no—
23C22×Dic73D411yescharacteristic
24C22×Dic73D411yescharacteristic
25C2×#10596831—21no—
26C2×#10596831—21no—
27C2×#10596831—21no—
28C4⋊Dic73—21no—
29C4⋊Dic73—21no—
30C4⋊Dic73—21no—
31C4⋊Dic73—21no—
32#11924007—42no—
33#11924007—42no—
34C4×Dic73—21no—
35C4×Dic73—21no—
36C2×Q8×C73—21no—
37C2×Q8×C73—21no—
38C2×Q8×C73—21no—
39C2×Q8×C73—21no—
40C2×Q8×C73—21no—
41C2×Q8×C73D412yes—
42C22×C4×C73—21no—
43C22×C4×C73—21no—
44C22×C4×C73C2311yescharacteristic
45C2×C8×C73—21no—
46C2×C8×C73—21no—
47C2×C8×C73—21no—
48C4⋊C4×C73—21no—
49C4⋊C4×C73—21no—
50C23×C73C2×D411yescharacteristic
51Q8×C73—22no—
52Q8×C73—22no—
53Q8×C73—41no—
54Q8×C73—41no—
55C2×C4×C73—22no—
56C2×C4×C73—41no—
57C2×C4×C73—41no—
58C2×C4×C73—41no—
59C2×C4×C73—41no—
60C2×C4×C73—41no—
61C2×C4×C73C2×D411yescharacteristic
62C2×C4×C73#4111yescharacteristic
63C2×C4×C73#4111yescharacteristic
64C2×C4×C73#4111yescharacteristic
65C2×C4×C73#4111yescharacteristic
66C2×C4×C73#4111yescharacteristic
67C2×Dic73—21no—
68C2×Dic73—21no—
69C2×Dic73—21no—
70C2×Dic73—21no—
71C2×Dic73—41no—
72C2×Dic73—41no—
73C2×Dic73—41no—
74C2×Dic73—41no—
75C2×Dic73—41no—
76C2×Dic73—41no—
77C2×Dic73SD1612yes—
78C2×Dic73Q1612yes—
79C8×C73—41no—
80#10596831—41no—
81C22×C73#12111yescharacteristic
82C22×C73#12311yescharacteristic
83C22×C73#12411yescharacteristic
84C22×C73C2×SD1611yescharacteristic
85C22×C73C2×Q1611yescharacteristic
86C22×C73AGL(1,ℤ/8)11yescharacteristic
87C22×C73#13711yescharacteristic
88C4×C73—42no—
89C4×C73—81no—
90C4×C73#12311yescharacteristic
91C4×C73#12311yescharacteristic
92C4×C73#12611yescharacteristic
93C4×C73#12611yescharacteristic
94Dic73—22no—
95Dic73—22no—
96Dic73—81no—
97Dic73—81no—
98C2×C73#39711yescharacteristic
99C2×C73#46011yescharacteristic
100C2×C73#46211yescharacteristic
101C2×C73#48311yescharacteristic
102C2×C73#48411yescharacteristic
103C2×C73#48711yescharacteristic
104C2×C73#48911yescharacteristic
105#2072—731nomaximal, Sylow
106C73#207211yescharacteristic, complemented, Sylow
107C2×#103—731no—
108C2×#103D7311yescharacteristic
109#391—731no—
110#384—731no—
111#340—731no—
112#340—731no—
113#336—731no—
114C22×Q8C2×D7311yescharacteristic
115C22×C8—731no—
116C22×C8C2×D7311yescharacteristic
117C2×C4⋊C4—731no—
118C2×C4⋊C4—731no—
119C2×C4⋊C4—1461no—
120C2×C4⋊C4—1461no—
121C2×C4⋊C4C2×D7311yescharacteristic
122C2×C42—731no—
123#103—22no—
124#103—1462no—
125#95—1461no—
126#95—1461no—
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8C22⋊D7312yes—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—731no—
136C22×C4—731no—
137C22×C4—1461no—
138C22×C4—1461no—
139C22×C4C22×D7311yescharacteristic
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—1461no—
144C2×C8—1461no—
145C2×C8—1461no—
146C4⋊C4—21no—
147C4⋊C4—21no—
148C4⋊C4—2922no—
149C4⋊C4—2922no—
150C4⋊C4—1461no—
151C4⋊C4—1461no—
152C4⋊C4—1461no—
153C4⋊C4—1461no—
154C42—1461no—
155C42—1461no—
156C23D4×D7311yescharacteristic
157Q8—22no—
158Q8—22no—
159Q8—41no—
160Q8—41no—
161C2×C4—22no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—2921no—
168C2×C4—2921no—
169C2×C4—2921no—
170C2×C4—2921no—
171C2×C4—2921no—
172C2×C4—2921no—
173C2×C4—732no—
174C2×C4—732no—
175C2×C4—1461no—
176C2×C4—1461no—
177C2×C4—1461no—
178C2×C4—1461no—
179C2×C4C2×C22⋊D7311yescharacteristic
180C2×C4#1192402711yescharacteristic
181C2×C4#1192402711yescharacteristic
182C2×C4#1192402711yescharacteristic
183C2×C4#1192402811yescharacteristic
184C2×C4#1192402811yescharacteristic
185C8—41no—
186C8—2921no—
187C22#1455656311yescharacteristic
188C22#1455657311yescharacteristic
189C22#1455657711yescharacteristic
190C22SD16×D7311yescharacteristic
191C22Q16×D7311yescharacteristic
192C22#1455661811yescharacteristic
193C22#1455662311yescharacteristic
194C4—42no—
195C4—81no—
196C4—5841no—
197C4—5841no—
198C4—1462no—
199C4—1462no—
200C4#1455657211yescharacteristic
201C4#1455657411yescharacteristic
202C4#1455658411yescharacteristic
203C4#1455658411yescharacteristic
204C2#1798851511yescharacteristic
205C2#1798878511yescharacteristic
206C2#1798879511yescharacteristic
207C2#1798891611yescharacteristic
208C2#1798892111yescharacteristic
209C2#1798893611yescharacteristic
210C2#1798894811yescharacteristic
subgroupG/H
centerC23D4×D73
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
FittingC2×#103×C73C2
socleC23×C73C2×D4
hypercenterC2×#103D73
hypocenterC73#2072
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
106. C73#2072semidirect