Finite Group Databasebeta

← #22611279

Subgroups — #22611279

Order 9344.

230 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 73 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#17988627C211yesmaximal, characteristic
3#17988452C211yesmaximal, characteristic
4#17988355C211yesmaximal, characteristic
5#17988348C211yesmaximal, characteristic
6#17988346C211yesmaximal, characteristic
7#428×C73C211yesmaximal, characteristic
8C2×#11924012C2211yescharacteristic
9#14556591—21no—
10#14556590—21no—
11#14556583—21no—
12#14556582—21no—
13#14556568—22no—
14#14556550C2211yescharacteristic
15C2×C4⋊Dic73C2211yescharacteristic
16C2×C4×Dic73C2211yescharacteristic
17#14556524—21no—
18#14556522—21no—
19#14556498—22no—
20C2×M16×C73C2211yescharacteristic
21#117×C73C2211yescharacteristic
22C2×C4⋊C4×C73C2211yescharacteristic
23#107×C73—21no—
24#106×C73—21no—
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⋊Dic73D411yescharacteristic
35C4⋊Dic73D411yescharacteristic
36#11924007—22no—
37#11924007—22no—
38C22⋊Dic73—21no—
39C4×Dic73—21no—
40C4×Dic73—21no—
41C4×Dic73Q812yescomplemented
42C22×C4×C73—21no—
43C22×C4×C73C2311yescharacteristic
44M16×C73—21no—
45M16×C73Q812yescomplemented
46C2×C8×C73—21no—
47C4⋊C4×C73—21no—
48C4⋊C4×C73—21no—
49C4⋊C4×C73D411yescharacteristic
50C4⋊C4×C73D411yescharacteristic
51C22⋊C4×C73—21no—
52C42×C73—21no—
53C23×C73C2×D411yescharacteristic
54C2×C4×C73—21no—
55C2×C4×C73—21no—
56C2×C4×C73—42no—
57C2×C4×C73—41no—
58C2×C4×C73C2×D411yescharacteristic
59C2×C4×C73C2×D411yescharacteristic
60C2×C4×C73C2×Q811yescharacteristic
61C2×C4×C73C2×Q811yescharacteristic
62C2×C4×C73C2×Q811yescharacteristic
63C2×C4×C73#4111yescharacteristic
64C2×Dic73—21no—
65C2×Dic73—21no—
66C2×Dic73—22no—
67C2×Dic73—22no—
68C2×Dic73—41no—
69C2×Dic73—41no—
70C2×Dic73—42no—
71Dic146—82no—
72C8×C73—22no—
73#10596831—22no—
74C22×C73—21no—
75C22×C73—21no—
76C22×C73#12011yescharacteristic
77C22×C73C22⋊Q811yescharacteristic
78C22×C73C4⋊Q811yescharacteristic
79C4×C73—41no—
80C4×C73—41no—
81C4×C73—81no—
82C4×C73C22⋊Q811yescharacteristic
83C4×C73C22⋊Q811yescharacteristic
84C4×C73C4⋊Q811yescharacteristic
85C4×C73C4⋊Q811yescharacteristic
86Dic73—42no—
87Dic73—41no—
88Dic73—41no—
89Dic73—42no—
90C2×C73—21no—
91C2×C73—21no—
92C2×C73#39511yescharacteristic
93C2×C73#45411yescharacteristic
94C2×C73#45511yescharacteristic
95#2061—731nomaximal, Sylow
96C73#206111yescharacteristic, complemented, Sylow
97#544—731no—
98#428—731no—
99#428D7311yescharacteristic
100#382—731no—
101#343—731no—
102#339—731no—
103#339—731no—
104C2×M16—731no—
105C2×M16C2×D7311yescharacteristic
106C4⋊Q8—1461no—
107C4⋊Q8—1461no—
108#125—1461no—
109#125—1461no—
110C22⋊Q8—1462no—
111#117—731no—
112#117C2×D7311yescharacteristic
113C2×C4⋊C4—731no—
114C2×C4⋊C4C2×D7311yescharacteristic
115C2×C42—731no—
116#107—21no—
117#107—1461no—
118#106—21no—
119#106—1461no—
120#95—1462no—
121C2×Q8—1462no—
122C22×C4—21no—
123C22×C4—732no—
124C22×C4—1461no—
125C22×C4C22×D7311yescharacteristic
126M16—21no—
127M16—732no—
128M16—1461no—
129M16Dic14612yescomplemented
130C2×C8—21no—
131C2×C8—1461no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—731no—
135C4⋊C4—731no—
136C4⋊C4—1462no—
137C4⋊C4—1462no—
138C4⋊C4—1462no—
139C4⋊C4—1461no—
140C4⋊C4—1461no—
141C4⋊C4C22⋊D7311yescharacteristic
142C4⋊C4C22⋊D7311yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—1461no—
145C42—21no—
146C42—732no—
147C42—1461no—
148C42—1461no—
149C23D4×D7311yescharacteristic
150Q8—5842no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—42no—
154C2×C4—41no—
155C2×C4—2921no—
156C2×C4—2921no—
157C2×C4—2922no—
158C2×C4—1461no—
159C2×C4—1461no—
160C2×C4—1462no—
161C2×C4—1462no—
162C2×C4D4×D7311yescharacteristic
163C2×C4C2×C22⋊D7311yescharacteristic
164C2×C4Q8×D7311yescharacteristic
165C2×C4Q8×D7311yescharacteristic
166C2×C4C2×Dic14611yescharacteristic
167C2×C4#1192402811yescharacteristic
168C8—22no—
169C8—1462no—
170C22—21no—
171C22—21no—
172C22#1455655911yescharacteristic
173C22#1455656911yescharacteristic
174C22#1455659011yescharacteristic
175C4—41no—
176C4—41no—
177C4—81no—
178C4—2922no—
179C4—2921no—
180C4—2922no—
181C4—2921no—
182C4#1455656911yescharacteristic
183C4#1455657011yescharacteristic
184C4#1455658911yescharacteristic
185C4#1455659011yescharacteristic
186C2—21no—
187C2—21no—
188C2#1798850711yescharacteristic
189C2#1798875811yescharacteristic
190C2#1798876311yescharacteristic
subgroupG/H
centerC22#14556559
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#428×C73C2
socleC22×C73#120
hypercenter#428D73
hypocenterC73#2061
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
29. #11924012Q8semidirect
41. C4×Dic73Q8semidirect
45. M16×C73Q8semidirect
96. C73#2061semidirect
129. M16Dic146semidirect