Finite Group Databasebeta

← #22610607

Subgroups — #22610607

Order 9344.

256 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 101 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×#14556516C211yesmaximal, characteristic
2C2×#14556516C211yesmaximal, characteristic
3#17988493C211yesmaximal, characteristic
4#17988485C211yesmaximal, characteristic
5#17988350C211yesmaximal, characteristic
6#17988350C211yesmaximal, characteristic
7C2×C4×C8×C73C211yesmaximal, characteristic
8C22×Dic146C2211yescharacteristic
9C2×C4⋊Dic73C2211yescharacteristic
10C2×C4⋊Dic73C2211yescharacteristic
11C2×C4⋊Dic73C2211yescharacteristic
12C2×#11924007—21no—
13#14556516—22no—
14#14556516C414yescomplemented
15#14556498—21no—
16#14556498—21no—
17#14556498—21no—
18C22×C8×C73C2211yescharacteristic
19C22×C8×C73C2211yescharacteristic
20C2×C42×C73C2211yescharacteristic
21C4×C8×C73—22no—
22C2×Dic146—21no—
23C2×Dic146—21no—
24C2×Dic146—21no—
25C2×Dic146—21no—
26C2×Dic146—21no—
27C2×Dic146C2×C412yes—
28C22×Dic73—21no—
29C22×Dic73—21no—
30C22×Dic73—21no—
31C22×Dic73—21no—
32C4⋊Dic73—21no—
33C4⋊Dic73—21no—
34C4⋊Dic73—21no—
35C4⋊Dic73—21no—
36C4⋊Dic73—21no—
37C4⋊Dic73C2×C412yes—
38#11924007—42no—
39C22×C4×C73D411yescharacteristic
40C22×C4×C73D411yescharacteristic
41C22×C4×C73C2311yescharacteristic
42C2×C8×C73—21no—
43C2×C8×C73—21no—
44C2×C8×C73—21no—
45C2×C8×C73—21no—
46C2×C8×C73C2×C412yes—
47C2×C8×C73D412yes—
48C42×C73—21no—
49C42×C73—21no—
50C23×C73C2×D411yescharacteristic
51C2×C4×C73—21no—
52C2×C4×C73—21no—
53C2×C4×C73—21no—
54C2×C4×C73—21no—
55C2×C4×C73SD1612yes—
56C2×C4×C73Q1612yes—
57C2×C4×C73C22×C411yescharacteristic
58C2×C4×C73C2×D411yescharacteristic
59C2×C4×C73#4111yescharacteristic
60C2×C4×C73#4111yescharacteristic
61C2×C4×C73#4111yescharacteristic
62C2×C4×C73#4111yescharacteristic
63C2×Dic73—22no—
64C2×Dic73—22no—
65C2×Dic73—41no—
66C2×Dic73—41no—
67C2×Dic73—41no—
68C2×Dic73—41no—
69C2×Dic73—41no—
70C2×Dic73—41no—
71C2×Dic73—41no—
72C2×Dic73—41no—
73C2×Dic73—41no—
74C2×Dic73—41no—
75Dic146—22no—
76Dic146—22no—
77Dic146—41no—
78Dic146—41no—
79C8×C73—22no—
80C8×C73—22no—
81C22×C73C4×D411yescharacteristic
82C22×C73#12111yescharacteristic
83C22×C73#12411yescharacteristic
84C22×C73C2×SD1611yescharacteristic
85C22×C73C2×Q1611yescharacteristic
86C22×C73#13511yescharacteristic
87C22×C73#13511yescharacteristic
88C4×C73—22no—
89C4×C73—22no—
90C4×C73#11711yescharacteristic
91C4×C73C4×D411yescharacteristic
92C4×C73#12311yescharacteristic
93C4×C73#12611yescharacteristic
94Dic73—42no—
95Dic73—42no—
96Dic73—81no—
97Dic73—81no—
98C2×C73#38811yescharacteristic
99C2×C73C4×SD1611yescharacteristic
100C2×C73C4×Q1611yescharacteristic
101C2×C73#46511yescharacteristic
102C2×C73#46711yescharacteristic
103C2×C73#48711yescharacteristic
104C2×C73#48811yescharacteristic
105#1933—731nomaximal, Sylow
106C73#193311yescharacteristic, complemented, Sylow
107C2×#103—731no—
108C2×#103—731no—
109C2×C4×C8D7311yescharacteristic
110#391—731no—
111#389—731no—
112#340—731no—
113#340—731no—
114C22×Q8—731no—
115C22×C8C2×D7311yescharacteristic
116C22×C8C2×D7311yescharacteristic
117C2×C4⋊C4—731no—
118C2×C4⋊C4—731no—
119C2×C4⋊C4—731no—
120C2×C4⋊C4—1461no—
121C2×C42C2×D7311yescharacteristic
122#103—734no—
123#103—1462no—
124C4×C8—22no—
125#95—1461no—
126#95—1461no—
127#95—1461no—
128C2×Q8—732no—
129C2×Q8—1461no—
130C2×Q8—1461no—
131C2×Q8—1461no—
132C2×Q8—1461no—
133C2×Q8—1461no—
134C22×C4—1461no—
135C22×C4—1461no—
136C22×C4—1461no—
137C22×C4—1461no—
138C22×C4D29211yescharacteristic
139C22×C4D29211yescharacteristic
140C22×C4C22×D7311yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—21no—
144C2×C8—21no—
145C2×C8C4×D7312yes—
146C2×C8C22⋊D7312yes—
147C4⋊C4—2922no—
148C4⋊C4—732no—
149C4⋊C4—1461no—
150C4⋊C4—1461no—
151C4⋊C4—1461no—
152C4⋊C4—1461no—
153C4⋊C4—1461no—
154C42—21no—
155C42—21no—
156C23C2×D29211yescharacteristic
157Q8—2921no—
158Q8—2921no—
159Q8—1462no—
160Q8—1462no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—2921no—
166C2×C4—2921no—
167C2×C4—2921no—
168C2×C4—2921no—
169C2×C4—2921no—
170C2×C4—2921no—
171C2×C4—2921no—
172C2×C4—2921no—
173C2×C4—2921no—
174C2×C4—2921no—
175C2×C4—1462no—
176C2×C4—1462no—
177C2×C4#1192401712yes—
178C2×C4Dic29212yes—
179C2×C4C2×C4×D7311yescharacteristic
180C2×C4C2×C22⋊D7311yescharacteristic
181C2×C4#1192402811yescharacteristic
182C2×C4#1192402811yescharacteristic
183C2×C4#1192402811yescharacteristic
184C2×C4#1192402811yescharacteristic
185C8—22no—
186C8—22no—
187C22C4×D29211yescharacteristic
188C22#1455656511yescharacteristic
189C22#1455657911yescharacteristic
190C22C2×#1192401711yescharacteristic
191C22C2×Dic29211yescharacteristic
192C22#1455661311yescharacteristic
193C22#1455661311yescharacteristic
194C4—22no—
195C4—22no—
196C4—2922no—
197C4—2922no—
198C4—5841no—
199C4—5841no—
200C4#1455654811yescharacteristic
201C4C4×C22⋊D7311yescharacteristic
202C4#1455657411yescharacteristic
203C4#1455658511yescharacteristic
204C2#1798847811yescharacteristic
205C2C4×#1192401711yescharacteristic
206C2C4×Dic29211yescharacteristic
207C2#1798881611yescharacteristic
208C2#1798882811yescharacteristic
209C2#1798893811yescharacteristic
210C2#1798894211yescharacteristic
subgroupG/H
centerC23C2×D292
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
FittingC2×C4×C8×C73C2
socleC23×C73C2×D4
hypercenterC2×C4×C8D73
hypocenterC73#1933
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
14. #14556516C4semidirect
106. C73#1933semidirect