Finite Group Databasebeta

← #22611104

Subgroups — #22611104

Order 9344.

244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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#17989144C211yesmaximal, characteristic, complemented
2#17988603C211yesmaximal, characteristic
3C2×#14556519C211yesmaximal, characteristic
4#17988560C211yesmaximal, characteristic
5#17988358C211yesmaximal, characteristic, complemented
6#17988343C211yesmaximal, characteristic, complemented
7#339×C73C211yesmaximal, characteristic, complemented
8C2×#11924028C2211yescharacteristic
9C2×#11924012C2211yescharacteristic
10#14556591—21no—
11#14556583—21no—
12#14556570—22no—
13C4×Dic146—22no—
14#14556550C2211yescharacteristic
15#14556550C2211yescharacteristic
16#14556519—21no—
17#14556519—21no—
18#14556517—22no—
19#14556505—22no—
20C2×M16×C73C2211yescharacteristic
21#117×C73C2211yescharacteristic
22C2×C42×C73C2211yescharacteristic
23#11924028—21no—
24#11924028—21no—
25#11924028—21no—
26#11924028—21no—
27C2×Dic146—22no—
28C2×Dic146Q811yescharacteristic, complemented
29C2×D292Q811yescharacteristic, complemented
30C2×C22⋊D73—21no—
31C2×C4×D73—21no—
32#11924012—21no—
33#11924012—21no—
34C2×#10596831—21no—
35C4⋊Dic73—22no—
36C4⋊Dic73—21no—
37C4⋊Dic73—21no—
38#11924007—24no—
39C22⋊Dic73—21no—
40C22⋊Dic73D412yes—
41C4×Dic73—21no—
42C4×Dic73D412yes—
43C22×C4×C73—21no—
44C22×C4×C73C2311yescharacteristic
45M16×C73—21no—
46M16×C73—21no—
47C2×C8×C73—21no—
48C4⋊C4×C73—21no—
49C22⋊C4×C73—21no—
50C42×C73—21no—
51C42×C73—21no—
52C42×C73D411yescharacteristic
53C42×C73D411yescharacteristic
54C23×C73C2×D411yescharacteristic
55C22×D73—21no—
56C2×C4×C73—21no—
57C2×C4×C73—21no—
58C2×C4×C73—42no—
59C2×C4×C73—41no—
60C2×C4×C73C2×D411yescharacteristic
61C2×C4×C73C2×D411yescharacteristic
62C2×C4×C73C2×Q811yescharacteristic
63C2×C4×C73#4111yescharacteristic
64C2×C4×C73#4111yescharacteristic
65C2×C4×C73#4111yescharacteristic
66C22⋊D73—41no—
67C22⋊D73—41no—
68C2×Dic73—22no—
69C2×Dic73—22no—
70C2×Dic73—21no—
71D292—21no—
72D292—21no—
73C4×D73—41no—
74C4×D73—41no—
75Dic146—21no—
76Dic146—21no—
77Dic146—44no—
78C8×C73—41no—
79#10596831—41no—
80C22×C73—41no—
81C22×C73#12011yescharacteristic
82C22×C73C22⋊Q811yescharacteristic
83C22×C73#12411yescharacteristic
84C2×D73—41no—
85C2×D73—81no—
86C4×C73—22no—
87C4×C73—41no—
88C4×C73—81no—
89C4×C73C22⋊Q811yescharacteristic
90C4×C73C22⋊Q811yescharacteristic
91C4×C73#12411yescharacteristic
92C4×C73#12411yescharacteristic
93Dic73—42no—
94Dic73—42no—
95Dic73—41no—
96C2×C73—21no—
97C2×C73—21no—
98C2×C73—21no—
99C2×C73#39311yescharacteristic
100D73—81no—
101#2031—731nomaximal, Sylow
102C73#203111yescharacteristic, complemented, Sylow
103#533—731no—
104#421—731no—
105C2×#104—731no—
106#410—731no—
107#344—731no—
108#339D7311yescharacteristic, complemented
109H(3,ℤ/4)—731no—
110C2×#41—731no—
111C2×M16—731no—
112C2×M16C2×D7311yescharacteristic
113C4⋊Q8—1461no—
114#125—1461no—
115C22⋊Q8—1462no—
116C4×Q8—1462no—
117#117—731no—
118#117—731no—
119#117C2×D7311yescharacteristic
120C2×C42C2×D7311yescharacteristic
121#104—1462no—
122#104—1461no—
123#104—1461no—
124#99—1462no—
125#41—1461no—
126#41—1461no—
127#41—1461no—
128#41—1461no—
129C2×Q8—731no—
130C2×Q8—1462no—
131C2×D4—731no—
132C2×D4—1461no—
133C22×C4—21no—
134C22×C4—1461no—
135C22×C4C22×D7311yescharacteristic
136M16—21no—
137M16—21no—
138M16—1461no—
139M16—1461no—
140C2×C8—21no—
141C2×C8—1461no—
142C4⋊C4—21no—
143C4⋊C4—1464no—
144C4⋊C4—1462no—
145C4⋊C4—1461no—
146C4⋊C4—1461no—
147C22⋊C4—21no—
148C22⋊C4—732no—
149C22⋊C4—1461no—
150C42—21no—
151C42—21no—
152C42—732no—
153C42—1461no—
154C42D29211yescharacteristic
155C42D29211yescharacteristic
156C23—1461no—
157C23D4×D7311yescharacteristic
158Q8—2924no—
159Q8—1461no—
160Q8—1461no—
161D4—2921no—
162D4—2921no—
163D4—1461no—
164D4—1461no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—42no—
168C2×C4—41no—
169C2×C4—2921no—
170C2×C4—2921no—
171C2×C4—1462no—
172C2×C4—1462no—
173C2×C4—1461no—
174C2×C4D4×D7311yescharacteristic
175C2×C4C2×D29211yescharacteristic
176C2×C4Q8×D7311yescharacteristic
177C2×C4#1192402711yescharacteristic
178C2×C4#1192402811yescharacteristic
179C2×C4#1192402811yescharacteristic
180C8—41no—
181C8—2921no—
182C22—41no—
183C22—2921no—
184C22—5841no—
185C22#1455656111yescharacteristic
186C22#1455656911yescharacteristic
187C22#1455657711yescharacteristic
188C4—22no—
189C4—41no—
190C4—81no—
191C4—2922no—
192C4—2922no—
193C4—2921no—
194C4#1455656911yescharacteristic
195C4#1455657111yescharacteristic
196C4#1455657711yescharacteristic
197C4#1455657911yescharacteristic
198C2—21no—
199C2—21no—
200C2—21no—
201C2—5841no—
202C2#1798850011yescharacteristic
subgroupG/H
centerC4#14556577
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#339×C73C2
socleC2×C73#393
hypercenter#339D73
hypocenterC73#2031
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. #17989144C2semidirect
5. #17988358C2semidirect
6. #17988343C2semidirect
7. #339×C73C2semidirect
28. C2×Dic146Q8semidirect
29. C2×D292Q8semidirect
102. C73#2031semidirect
108. #339D73semidirect