Finite Group Databasebeta

← #22608964

Subgroups — #22608964

Order 9344.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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
1#17989184C211yesmaximal, characteristic
2#17988923C211yesmaximal, characteristic, complemented
3#17988906C211yesmaximal, characteristic
4#17988526C211yesmaximal, characteristic, complemented
5#17988325C211yesmaximal, characteristic, complemented
6#17988322C211yesmaximal, characteristic
7#324×C73C211yesmaximal, characteristic, complemented
8#14556586—21no—
9#14556581—21no—
10#14556576—21no—
11#14556574—21no—
12#14556570C2211yescharacteristic
13#14556569—21no—
14#14556565C2211yescharacteristic
15C4×C22⋊D73—21no—
16C2×C4⋊Dic73C2211yescharacteristic
17#14556525—21no—
18#14556523—21no—
19#14556516—21no—
20#14556513—21no—
21#14556498—21no—
22#14556498—21no—
23#14556498C2211yescharacteristic
24C2×C4⋊C4×C73C2211yescharacteristic
25C22⋊C8×C73C2211yescharacteristic
26C22⋊C8×C73C2211yescharacteristic
27C2×Dic146D411yescharacteristic
28C2×D292D411yescharacteristic
29C2×C22⋊D73—21no—
30C22×Dic73—21no—
31C22×Dic73—21no—
32C2×C4×D73—21no—
33C4⋊Dic73—21no—
34C4⋊Dic73—21no—
35C4⋊Dic73D411yescharacteristic
36C4⋊Dic73D411yescharacteristic
37#11924007—21no—
38#11924007—21no—
39#11924007—21no—
40#11924007—21no—
41C22⋊Dic73—21no—
42#11924005—21no—
43#11924005—21no—
44#11924005—21no—
45#11924005—21no—
46C4×Dic73—21no—
47C22×C4×C73D411yescharacteristic
48C22×C4×C73D411yescharacteristic
49C22×C4×C73C2311yescharacteristic
50C2×C8×C73—21no—
51C2×C8×C73—21no—
52C4⋊C4×C73—21no—
53C4⋊C4×C73—21no—
54C23×C73C2×D411yescharacteristic
55C22×D73—21no—
56C2×C4×C73—21no—
57C2×C4×C73—21no—
58C2×C4×C73—21no—
59C2×C4×C73—21no—
60C2×C4×C73—41no—
61C2×C4×C73—41no—
62C2×C4×C73C2×D411yescharacteristic
63C2×C4×C73C2×D411yescharacteristic
64C22⋊D73—41no—
65C22⋊D73—41no—
66C2×Dic73—21no—
67C2×Dic73—21no—
68C2×Dic73—21no—
69C2×Dic73—41no—
70C2×Dic73—41no—
71C2×Dic73—42no—
72C2×Dic73—41no—
73C2×Dic73—41no—
74D292—41no—
75C4×D73—81no—
76Dic146—41no—
77C8×C73—41no—
78C8×C73—41no—
79C22×C73—21no—
80C22×C73—21no—
81C22×C73#12011yescharacteristic
82C22×C73#13511yescharacteristic
83C22×C73#13711yescharacteristic
84C2×D73—41no—
85C2×D73—41no—
86C2×D73—41no—
87C4×C73—21no—
88C4×C73—21no—
89C4×C73—41no—
90C4×C73—41no—
91Dic73—41no—
92Dic73—41no—
93Dic73—41no—
94Dic73—81no—
95Dic73—81no—
96C2×C73—21no—
97C2×C73—21no—
98C2×C73#45211yescharacteristic
99C2×C73#45411yescharacteristic
100C2×C73#45811yescharacteristic
101D73—81no—
102#1615—731nomaximal, Sylow
103C73#161511yescharacteristic, complemented, Sylow
104#539—731no—
105#484—731no—
106#481—731no—
107#400—731no—
108#328—731no—
109#327—731no—
110#324D7311yescharacteristic, complemented
111#126—1461no—
112#125—1461no—
113#123—1461no—
114#123—1461no—
115C22⋊Q8—731no—
116C22⋊Q8—1461no—
117#121—731no—
118C4×D4—1461no—
119C2×C4⋊C4—731no—
120C2×C4⋊C4C2×D7311yescharacteristic
121#107—1461no—
122#106—1461no—
123#103—1461no—
124#102—1461no—
125C22⋊C8C2×D7311yescharacteristic
126C22⋊C8C2×D7311yescharacteristic
127#95—731no—
128#95—1461no—
129#95—1461no—
130C2×Q8—731no—
131C2×D4—731no—
132C2×D4—1461no—
133C22×C4—1461no—
134C22×C4—1461no—
135C22×C4—1461no—
136C22×C4D29211yescharacteristic
137C22×C4D29211yescharacteristic
138C22×C4C22×D7311yescharacteristic
139C2×C8—21no—
140C2×C8—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—731no—
144C4⋊C4—731no—
145C4⋊C4—1461no—
146C4⋊C4—1461no—
147C4⋊C4—1461no—
148C4⋊C4—1461no—
149C4⋊C4—1461no—
150C4⋊C4—1461no—
151C22⋊C4—1461no—
152C22⋊C4—1461no—
153C22⋊C4—1461no—
154C22⋊C4—1461no—
155C22⋊C4—1461no—
156C42—1461no—
157C23—1461no—
158C23C2×D29211yescharacteristic
159Q8—2921no—
160D4—2921no—
161D4—2921no—
162D4—2921no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—2921no—
170C2×C4—2921no—
171C2×C4—2922no—
172C2×C4—2921no—
173C2×C4—2921no—
174C2×C4—5841no—
175C2×C4—1461no—
176C2×C4—1461no—
177C2×C4—1461no—
178C2×C4D4×D7311yescharacteristic
179C2×C4D4×D7311yescharacteristic
180C8—41no—
181C8—41no—
182C22—21no—
183C22—21no—
184C22—2921no—
185C22—2921no—
186C22—2921no—
187C22#1455656111yescharacteristic
188C22#1455661311yescharacteristic
189C22#1455662411yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—2921no—
195C4—2921no—
196C4—2921no—
197C4—5841no—
198C4—5841no—
199C2—21no—
200C2—21no—
201C2—5841no—
202C2#1798875111yescharacteristic
203C2#1798876211yescharacteristic
204C2#1798877811yescharacteristic
subgroupG/H
centerC22#14556561
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#324×C73C2
socleC22×C73#120
hypercenter#324D73
hypocenterC73#1615
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #17988923C2semidirect
4. #17988526C2semidirect
5. #17988325C2semidirect
7. #324×C73C2semidirect
103. C73#1615semidirect
110. #324D73semidirect