Finite Group Databasebeta

← #22620588

Subgroups — #22620588

Order 9344.

338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 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#17989195C212yesmaximal
2#17988987C211yesmaximal, characteristic, complemented
3#17988965C211yesmaximal, characteristic, complemented
4#17988954C212yesmaximal, complemented
5#17988846C211yesmaximal, characteristic
6#17988842C211yesmaximal, characteristic
7#17988827C212yesmaximal
8#17988695C211yesmaximal, characteristic, complemented
9C4×#11924018C212yesmaximal, complemented
10#17988544C211yesmaximal, characteristic
11#441×C73C211yesmaximal, characteristic, complemented
12C2×Dic292C2211yescharacteristic
13C2×#11924018C2212yes—
14C2×#11924011C2211yescharacteristic
15C2×C8×D73C2211yescharacteristic
16#14556589C2212yes—
17#14556586—22no—
18#14556585—22no—
19#14556583—22no—
20#14556582C2212yes—
21#14556581—22no—
22#14556571C2212yes—
23#14556567C2212yes—
24C4×Dic146C2212yes—
25#14556548C2211yescharacteristic
26#14556524C2212yes—
27#14556523C2211yescharacteristic
28#14556516C2212yes—
29#14556515C2212yes—
30#14556514C2212yes—
31#14556501C2211yescharacteristic
32C4×#10596831C2211yescharacteristic
33C8×Dic73C2211yescharacteristic
34C2×Q16×C73C2211yescharacteristic
35C4×Q8×C73C2212yes—
36#106×C73C2211yescharacteristic
37#103×C73C2212yes—
38#97×C73C2211yescharacteristic
39C2×Dic146C2312yes—
40C2×C4×D73C2311yescharacteristic
41Dic292—22no—
42#11924018—24no—
43#11924011—22no—
44C2×#10596831C2311yescharacteristic
45C2×#10596831C2311yescharacteristic
46C8×D73—22no—
47C4⋊Dic73—22no—
48C4⋊Dic73—22no—
49C4⋊Dic73C2312yes—
50#11924007—22no—
51#11924007—22no—
52#11924007—22no—
53#11924007—22no—
54#11924007—22no—
55#11924007D412yes—
56#11924005—22no—
57#11924005—22no—
58#11924005D412yes—
59C4×Dic73—22no—
60C4×Dic73C2311yescharacteristic
61C2×Q8×C73C2312yes—
62Q16×C73—22no—
63C2×C8×C73C2311yescharacteristic
64C2×C8×C73C2311yescharacteristic
65C4⋊C4×C73—22no—
66C4⋊C4×C73C2312yes—
67C42×C73—22no—
68C42×C73C2311yescharacteristic
69C22×D73C2×D411yescharacteristic
70Q8×C73—22no—
71Q8×C73—22no—
72C2×C4×C73—22no—
73C2×C4×C73—22no—
74C2×C4×C73C2×D412yes—
75C2×C4×C73C2411yescharacteristic
76C2×Dic73—22no—
77C2×Dic73—22no—
78C2×Dic73C2×D412yes—
79C2×Dic73C2×D411yescharacteristic
80C4×D73—21no—
81C4×D73—21no—
82Dic146—22no—
83Dic146—22no—
84C8×C73—21no—
85C8×C73#4112yes—
86#10596831—21no—
87#10596831#4112yes—
88C22×C73C22×D411yescharacteristic
89C2×D73—21no—
90C2×D73—22no—
91C4×C73—22no—
92C4×C73—42no—
93C4×C73—42no—
94C4×C73C2×#4111yescharacteristic
95C4×C73C2×#4111yescharacteristic
96Dic73—21no—
97Dic73—22no—
98Dic73—42no—
99Dic73—42no—
100C2×C73#53211yescharacteristic
101C2×C73#57812yes—
102D73—41no—
103#3177—731nomaximal, Sylow
104C73#317711yescharacteristic, complemented, Sylow
105#541—732no—
106#499—731no—
107#494—731no—
108#491—732no—
109#470—731no—
110#470—731no—
111#467—732no—
112#441—731no—
113#441D7311yescharacteristic, complemented
114C4×Q16—732no—
115#405—731no—
116C2×Q16—732no—
117C2×Q16—731no—
118C2×Q16C2×D7311yescharacteristic
119C2×M16—731no—
120C22×C8—731no—
121C4⋊Q8—732no—
122#126—1462no—
123#126—1462no—
124#125—732no—
125#125—1462no—
126#125—1462no—
127C22⋊Q8—732no—
128C22⋊Q8—732no—
129C4×Q8—732no—
130C4×Q8C2×D7312yes—
131#117—731no—
132#107—732no—
133#106—731no—
134#106C2×D7311yescharacteristic
135#103—732no—
136#103—732no—
137#103—732no—
138#103C2×D7312yes—
139#97—731no—
140#97C2×D7311yescharacteristic
141C4×C8—731no—
142C4×C8—731no—
143C2×Q8—732no—
144C2×Q8C22×D7312yes—
145C22×C4—731no—
146Q16—22no—
147Q16—1464no—
148Q16—1462no—
149M16—1462no—
150C2×C8—731no—
151C2×C8—731no—
152C2×C8—1462no—
153C2×C8C22×D7311yescharacteristic
154C2×C8C22×D7311yescharacteristic
155C4⋊C4—22no—
156C4⋊C4—732no—
157C4⋊C4—732no—
158C4⋊C4—1462no—
159C4⋊C4—1462no—
160C4⋊C4—1462no—
161C4⋊C4—1462no—
162C4⋊C4—1462no—
163C4⋊C4—1462no—
164C4⋊C4—1462no—
165C4⋊C4C22×D7312yes—
166C22⋊C4—732no—
167C22⋊C4—1462no—
168C22⋊C4—1462no—
169C42—22no—
170C42—731no—
171C42—1462no—
172C42C22×D7311yescharacteristic
173C23—731no—
174Q8—22no—
175Q8—22no—
176Q8—1462no—
177Q8—1462no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—732no—
181C2×C4—731no—
182C2×C4—1462no—
183C2×C4—1462no—
184C2×C4—1461no—
185C2×C4—1461no—
186C2×C4D4×D7312yes—
187C2×C4C23×D7311yescharacteristic
188C8—21no—
189C8—732no—
190C8—1461no—
191C8#1192402812yes—
192C22—1461no—
193C22—1462no—
194C22C2×D4×D7311yescharacteristic
195C4—22no—
196C4—42no—
197C4—42no—
198C4—2922no—
199C4—2922no—
200C4—1461no—
201C4—1462no—
202C4#41×D7311yescharacteristic
203C4C2×#1192402811yescharacteristic
204C2—2921no—
205C2#1798913411yescharacteristic
206C2#1798940312yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#441×C73C2
socleC22×C73C22×D4
hypercenter#441D73
hypocenterC73#3177
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
2. #17988987C2semidirect
3. #17988965C2semidirect
4. #17988954C2semidirect
8. #17988695C2semidirect
9. C4×#11924018C2semidirect
11. #441×C73C2semidirect
104. C73#3177semidirect
113. #441D73semidirect