Finite Group Databasebeta

← #22611275

Subgroups — #22611275

Order 9344.

246 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 75 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#17989215C211yesmaximal, characteristic
2#17988630C211yesmaximal, characteristic
3#17988629C211yesmaximal, characteristic
4#17988457C211yesmaximal, characteristic
5#17988355C211yesmaximal, characteristic
6#17988347C211yesmaximal, characteristic
7#339×C73C211yesmaximal, characteristic
8C2×#11924012C2211yescharacteristic
9#14556591—21no—
10#14556590—21no—
11#14556583—21no—
12#14556582—21no—
13#14556568—22no—
14#14556550C2211yescharacteristic
15C2×C4⋊Dic73—22no—
16C2×C4⋊Dic73C2211yescharacteristic
17C2×C4⋊Dic73C2211yescharacteristic
18#14556525—21no—
19#14556524—21no—
20#14556523—21no—
21#14556522—21no—
22C2×M16×C73C2211yescharacteristic
23#117×C73C2211yescharacteristic
24C2×C42×C73C2211yescharacteristic
25C2×Dic146—22no—
26C22×Dic73—21no—
27C22×Dic73D412yes—
28#11924012—21no—
29#11924012Q812yescomplemented
30C2×#10596831—21no—
31C4⋊Dic73—22no—
32C4⋊Dic73—21no—
33C4⋊Dic73—21no—
34C4⋊Dic73—21no—
35C4⋊Dic73—21no—
36C4⋊Dic73—44no—
37C4⋊Dic73D411yescharacteristic
38C4⋊Dic73D411yescharacteristic
39#11924007—22no—
40#11924007—22no—
41C22⋊Dic73—21no—
42C4×Dic73—21no—
43C22×C4×C73—21no—
44C22×C4×C73C2311yescharacteristic
45M16×C73—21no—
46M16×C73Q812yescomplemented
47C2×C8×C73—21no—
48C4⋊C4×C73D411yescharacteristic
49C4⋊C4×C73D411yescharacteristic
50C22⋊C4×C73—21no—
51C42×C73—21no—
52C42×C73—21no—
53C42×C73Q812yescomplemented
54C23×C73C2×D411yescharacteristic
55C2×C4×C73—22no—
56C2×C4×C73—22no—
57C2×C4×C73—22no—
58C2×C4×C73—21no—
59C2×C4×C73—21no—
60C2×C4×C73C2×D411yescharacteristic
61C2×C4×C73C2×D411yescharacteristic
62C2×C4×C73C2×Q811yescharacteristic
63C2×C4×C73C2×Q811yescharacteristic
64C2×C4×C73C2×Q811yescharacteristic
65C2×C4×C73#4111yescharacteristic
66C2×Dic73—21no—
67C2×Dic73—21no—
68C2×Dic73—22no—
69C2×Dic73—42no—
70C2×Dic73—42no—
71C2×Dic73—41no—
72Dic146—82no—
73C8×C73—22no—
74#10596831—22no—
75C22×C73—21no—
76C22×C73—21no—
77C22×C73#12011yescharacteristic
78C22×C73C22⋊Q811yescharacteristic
79C22×C73C4⋊Q811yescharacteristic
80C4×C73—24no—
81C4×C73—41no—
82C4×C73—41no—
83C4×C73C22⋊Q811yescharacteristic
84C4×C73C22⋊Q811yescharacteristic
85C4×C73C4⋊Q811yescharacteristic
86C4×C73C4⋊Q811yescharacteristic
87Dic73—41no—
88Dic73—42no—
89Dic73—41no—
90Dic73—81no—
91C2×C73—21no—
92C2×C73—21no—
93C2×C73#39511yescharacteristic
94C2×C73#45311yescharacteristic
95C2×C73#45611yescharacteristic
96#2060—731nomaximal, Sylow
97C73#206011yescharacteristic, complemented, Sylow
98#544—731no—
99#428—731no—
100#428—731no—
101#384—731no—
102#343—731no—
103#339—731no—
104#339D7311yescharacteristic
105C2×M16—731no—
106C2×M16C2×D7311yescharacteristic
107C4⋊Q8—1461no—
108C4⋊Q8—1461no—
109#125—1461no—
110#125—1461no—
111C22⋊Q8—1462no—
112#117—731no—
113#117C2×D7311yescharacteristic
114C2×C4⋊C4—731no—
115C2×C4⋊C4—731no—
116C2×C4⋊C4—1462no—
117C2×C42C2×D7311yescharacteristic
118#107—1461no—
119#107—1461no—
120#106—1461no—
121#106—1461no—
122C2×Q8—1462no—
123C22×C4—21no—
124C22×C4—732no—
125C22×C4—1461no—
126C22×C4C22×D7311yescharacteristic
127M16—21no—
128M16—732no—
129M16—1461no—
130M16Dic14612yescomplemented
131C2×C8—21no—
132C2×C8—1461no—
133C4⋊C4—2924no—
134C4⋊C4—731no—
135C4⋊C4—731no—
136C4⋊C4—1462no—
137C4⋊C4—1462no—
138C4⋊C4—1462no—
139C4⋊C4—1461no—
140C4⋊C4—1461no—
141C4⋊C4—1461no—
142C4⋊C4—1461no—
143C4⋊C4D29211yescharacteristic
144C4⋊C4D29211yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—1461no—
147C42—21no—
148C42—21no—
149C42—1461no—
150C42Dic14612yescomplemented
151C23D4×D7311yescharacteristic
152Q8—5842no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—2922no—
159C2×C4—2922no—
160C2×C4—2921no—
161C2×C4—1461no—
162C2×C4—1461no—
163C2×C4—1462no—
164C2×C4D4×D7311yescharacteristic
165C2×C4C2×D29211yescharacteristic
166C2×C4Q8×D7311yescharacteristic
167C2×C4C2×Dic14611yescharacteristic
168C2×C4C2×Dic14611yescharacteristic
169C2×C4#1192402711yescharacteristic
170C8—22no—
171C8—1462no—
172C22—21no—
173C22—21no—
174C22#1455656111yescharacteristic
175C22#1455656811yescharacteristic
176C22#1455659011yescharacteristic
177C4—24no—
178C4—41no—
179C4—41no—
180C4—2922no—
181C4—2921no—
182C4—2921no—
183C4—5841no—
184C4#1455656811yescharacteristic
185C4#1455657111yescharacteristic
186C4#1455659011yescharacteristic
187C4#1455659111yescharacteristic
188C2—21no—
189C2—21no—
190C2#1798850811yescharacteristic
191C2#1798875611yescharacteristic
192C2#1798877111yescharacteristic
subgroupG/H
centerC22#14556561
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#339×C73C2
socleC22×C73#120
hypercenter#339D73
hypocenterC73#2060
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
29. #11924012Q8semidirect
46. M16×C73Q8semidirect
53. C42×C73Q8semidirect
97. C73#2060semidirect
130. M16Dic146semidirect
150. C42Dic146semidirect