Finite Group Databasebeta

← #22609125

Subgroups — #22609125

Order 9344.

250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 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#17989257C211yesmaximal, characteristic
2#17988933C211yesmaximal, characteristic, complemented
3#17988868C211yesmaximal, characteristic, complemented
4#17988798C211yesmaximal, characteristic, complemented
5#17988317C211yesmaximal, characteristic, complemented
6#17988314C211yesmaximal, characteristic, complemented
7#331×C73C211yesmaximal, characteristic, complemented
8C2×#11924027—21no—
9C2×Dic292—21no—
10#14556591C2211yescharacteristic
11#14556587—21no—
12#14556563—22no—
13#14556562—21no—
14C4×Dic146C2211yescharacteristic
15C4×D292C2211yescharacteristic
16D4×Dic73—21no—
17#14556525—21no—
18#14556516—21no—
19#14556513—21no—
20#14556512—22no—
21C4×#10596831C2211yescharacteristic
22#127×C73C2211yescharacteristic
23C4⋊C8×C73C2211yescharacteristic
24C4⋊C8×C73C2211yescharacteristic
25#11924027—42no—
26#11924027—42no—
27C2×Dic146—21no—
28C2×Dic146D411yescharacteristic
29C2×D292D411yescharacteristic
30C2×C22⋊D73—22no—
31C2×C22⋊D73—22no—
32C22×Dic73—22no—
33C2×C4×D73—21no—
34Dic292—42no—
35C2×#10596831—21no—
36C4⋊Dic73—21no—
37C4⋊Dic73—21no—
38C4⋊Dic73D411yescharacteristic
39C4⋊Dic73D411yescharacteristic
40#11924007—21no—
41C22⋊Dic73—22no—
42#11924005—21no—
43C4×Dic73—21no—
44C2×D4×C73—21no—
45C2×D4×C73—21no—
46C2×D4×C73D412yes—
47C2×C8×C73—21no—
48C2×C8×C73—21no—
49C42×C73C2311yescharacteristic
50C23×C73—22no—
51C22×D73—21no—
52D4×C73—42no—
53D4×C73—41no—
54D4×C73—41no—
55D4×C73—41no—
56D4×C73—41no—
57C2×C4×C73C2×D411yescharacteristic
58C2×C4×C73C2×D411yescharacteristic
59C2×C4×C73C2×D411yescharacteristic
60C22⋊D73—44no—
61C22⋊D73—82no—
62C2×Dic73—21no—
63C2×Dic73—21no—
64C2×Dic73—21no—
65C2×Dic73—44no—
66C2×Dic73—41no—
67D292—21no—
68D292—21no—
69C4×D73—41no—
70C4×D73—41no—
71Dic146—21no—
72Dic146—41no—
73Dic146—41no—
74Dic146D812yes—
75C8×C73—41no—
76C8×C73—41no—
77#10596831—41no—
78C22×C73—42no—
79C22×C73—42no—
80C22×C73—42no—
81C22×C73#12011yescharacteristic
82C2×D73—41no—
83C2×D73—41no—
84C2×D73—41no—
85C4×C73—21no—
86C4×C73C2×D811yescharacteristic
87C4×C73#13511yescharacteristic
88C4×C73AGL(1,ℤ/8)11yescharacteristic
89C4×C73#13711yescharacteristic
90Dic73—22no—
91Dic73—41no—
92Dic73—41no—
93Dic73—81no—
94C2×C73—82no—
95C2×C73#44711yescharacteristic
96C2×C73#45211yescharacteristic
97C2×C73#45511yescharacteristic
98D73—81no—
99#1641—731nomaximal, Sylow
100C73#164111yescharacteristic, complemented, Sylow
101#550—731no—
102#486—731no—
103#474—731no—
104#462—731no—
105#331D7311yescharacteristic, complemented
106Q8⋊C8—731no—
107D4⋊C8—731no—
108C2×#41—1461no—
109C2×Q16—1461no—
110C4⋊Q8—731no—
111#127—1461no—
112#127C2×D7311yescharacteristic
113#121—1461no—
114#121—1462no—
115C4×Q8—731no—
116C4×D4—731no—
117C4×D4—1461no—
118#107—1461no—
119C4⋊C8C2×D7311yescharacteristic
120C4⋊C8C2×D7311yescharacteristic
121#103—1461no—
122#102—1461no—
123#102—1462no—
124C4×C8—731no—
125#41—2922no—
126#41—2922no—
127C2×Q8—731no—
128C2×Q8—1461no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—731no—
132C2×D4—1462no—
133C2×D4—1462no—
134C2×D4D29212yes—
135C22×C4—1462no—
136C22×C4—1461no—
137Q16—2922no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—1461no—
141C4⋊C4—731no—
142C4⋊C4—731no—
143C4⋊C4—1461no—
144C4⋊C4—1461no—
145C4⋊C4—1461no—
146C22⋊C4—1462no—
147C22⋊C4—1461no—
148C42—1461no—
149C42C22×D7311yescharacteristic
150C23—22no—
151C23—1461no—
152Q8—2921no—
153Q8—2921no—
154Q8—732no—
155Q8—1461no—
156D4—42no—
157D4—41no—
158D4—41no—
159D4—41no—
160D4—41no—
161D4—2924no—
162D4—5842no—
163D4—1461no—
164D4—1461no—
165C2×C4—2924no—
166C2×C4—2921no—
167C2×C4—2921no—
168C2×C4—2921no—
169C2×C4—1461no—
170C2×C4—1461no—
171C2×C4—1461no—
172C2×C4D4×D7311yescharacteristic
173C2×C4D4×D7311yescharacteristic
174C2×C4C2×D29211yescharacteristic
175C8—41no—
176C8—41no—
177C8—2921no—
178C22—42no—
179C22—42no—
180C22—42no—
181C22—2921no—
182C22—2921no—
183C22—2921no—
184C22#1455656111yescharacteristic
185C4—21no—
186C4—2921no—
187C4—2921no—
188C4—5841no—
189C4—1462no—
190C4D8×D7311yescharacteristic
191C4#1455661011yescharacteristic
192C4#1455661811yescharacteristic
193C4#1455662011yescharacteristic
194C2—82no—
195C2—5841no—
196C2#1798872211yescharacteristic
197C2#1798875011yescharacteristic
198C2#1798876711yescharacteristic
subgroupG/H
centerC22#14556561
commutatorC42×C73C23
FrattiniC42C22×D73
Fitting#331×C73C2
socleC22×C73#120
hypercenter#331D73
hypocenterC73#1641
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #17988933C2semidirect
3. #17988868C2semidirect
4. #17988798C2semidirect
5. #17988317C2semidirect
6. #17988314C2semidirect
7. #331×C73C2semidirect
100. C73#1641semidirect
105. #331D73semidirect