Finite Group Databasebeta

← #22610922

Subgroups — #22610922

Order 9344.

228 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#14556582C211yesmaximal, characteristic
2#17988610C211yesmaximal, characteristic
3M16×Dic73C211yesmaximal, characteristic
4#17988356C211yesmaximal, characteristic
5#17988355C211yesmaximal, characteristic
6#17988355C211yesmaximal, characteristic
7#343×C73C211yesmaximal, characteristic
8C2×#11924012C2211yescharacteristic
9C2×#11924012C2211yescharacteristic
10#14556582—21no—
11#14556582—21no—
12#14556582—21no—
13#14556582—21no—
14C2×C4⋊Dic73C412yes—
15C2×C4⋊Dic73C2211yescharacteristic
16C2×#11924007C412yes—
17C2×C4×Dic73C2211yescharacteristic
18#14556520—21no—
19#14556520—21no—
20#14556501—21no—
21C8×Dic73—21no—
22C2×M16×C73C2211yescharacteristic
23C2×M16×C73C2211yescharacteristic
24C2×C4⋊C4×C73C2211yescharacteristic
25C22×Dic73C2×C412yes—
26C22×Dic73C2×C411yescharacteristic
27C22×Dic73C2×C411yescharacteristic
28#11924012—21no—
29#11924012—21no—
30#11924012—21no—
31#11924012Q812yes—
32C2×#10596831—21no—
33C2×#10596831—21no—
34C4⋊Dic73—21no—
35C4⋊Dic73—21no—
36C4⋊Dic73—22no—
37C4⋊Dic73—22no—
38#11924007—22no—
39#11924007—22no—
40C4×Dic73D411yescharacteristic
41C4×Dic73D411yescharacteristic
42C4×Dic73D411yescharacteristic
43C4×Dic73D411yescharacteristic
44C22×C4×C73C2×C412yes—
45C22×C4×C73C2311yescharacteristic
46M16×C73—21no—
47M16×C73—21no—
48M16×C73—21no—
49M16×C73Q812yes—
50C2×C8×C73—21no—
51C2×C8×C73—21no—
52C4⋊C4×C73—21no—
53C4⋊C4×C73—21no—
54C23×C73C22×C411yescharacteristic
55C2×C4×C73—22no—
56C2×C4×C73—42no—
57C2×C4×C73C2×D411yescharacteristic
58C2×C4×C73C2×D411yescharacteristic
59C2×C4×C73C2×Q811yescharacteristic
60C2×C4×C73C2×Q811yescharacteristic
61C2×C4×C73#4111yescharacteristic
62C2×C4×C73#4111yescharacteristic
63C2×Dic73—22no—
64C2×Dic73—41no—
65C2×Dic73—41no—
66C2×Dic73—42no—
67C2×Dic73C22⋊C411yescharacteristic
68C2×Dic73C22⋊C411yescharacteristic
69C2×Dic73C22⋊C411yescharacteristic
70C2×Dic73C22⋊C411yescharacteristic
71C8×C73—22no—
72C8×C73—41no—
73#10596831—22no—
74#10596831—41no—
75C22×C73—21no—
76C22×C73—21no—
77C22×C73C2×C22⋊C411yescharacteristic
78C22×C73C4×Q811yescharacteristic
79C22×C73C4×Q811yescharacteristic
80C4×C73—42no—
81C4×C73C22⋊Q811yescharacteristic
82C4×C73C22⋊Q811yescharacteristic
83C4×C73#12411yescharacteristic
84C4×C73C4⋊Q811yescharacteristic
85Dic73—21no—
86Dic73—21no—
87Dic73—21no—
88Dic73—21no—
89Dic73—42no—
90C2×C73—21no—
91C2×C73—21no—
92C2×C73#39111yescharacteristic
93C2×C73#41311yescharacteristic
94C2×C73#41311yescharacteristic
95#1998—731nomaximal, Sylow
96C73#199811yescharacteristic, complemented, Sylow
97C2×#125—731no—
98#423—731no—
99C4×M16—731no—
100#343—731no—
101#343—731no—
102#343—731no—
103#343D7311yescharacteristic
104C2×M16—731no—
105C2×M16—731no—
106C2×M16C2×D7311yescharacteristic
107C2×M16C2×D7311yescharacteristic
108#125—1461no—
109#125—1461no—
110#125—1461no—
111#125—1461no—
112C2×C4⋊C4—732no—
113C2×C4⋊C4—732no—
114C2×C4⋊C4—731no—
115C2×C4⋊C4C2×D7311yescharacteristic
116C2×C42—731no—
117C4⋊C8—1461no—
118C4⋊C8—1461no—
119#97—1461no—
120C4×C8—1461no—
121C22×C4—731no—
122C22×C4—731no—
123C22×C4—732no—
124C22×C4C4×D7312yes—
125C22×C4C22×D7311yescharacteristic
126M16—21no—
127M16—21no—
128M16—21no—
129M16—732no—
130M16—1461no—
131M16—1461no—
132M16—1461no—
133M16Dic14612yes—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—1461no—
137C2×C8—1461no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—1462no—
141C4⋊C4—1462no—
142C4⋊C4—1462no—
143C4⋊C4—1462no—
144C4⋊C4—1461no—
145C4⋊C4—1461no—
146C42—731no—
147C42—731no—
148C42—731no—
149C42—731no—
150C23C2×C4×D7311yescharacteristic
151C2×C4—22no—
152C2×C4—42no—
153C2×C4—2922no—
154C2×C4—2921no—
155C2×C4—2921no—
156C2×C4—731no—
157C2×C4—731no—
158C2×C4—731no—
159C2×C4—731no—
160C2×C4—1462no—
161C2×C4D4×D7311yescharacteristic
162C2×C4D4×D7311yescharacteristic
163C2×C4Q8×D7311yescharacteristic
164C2×C4C2×Dic14611yescharacteristic
165C2×C4#1192402711yescharacteristic
166C2×C4#1192402811yescharacteristic
167C8—22no—
168C8—41no—
169C8—2921no—
170C8—1462no—
171C22—21no—
172C22—21no—
173C22C22⋊C4×D7311yescharacteristic
174C22#1455655611yescharacteristic
175C22C4×Dic14611yescharacteristic
176C4—42no—
177C4—2922no—
178C4—1461no—
179C4—1461no—
180C4—1461no—
181C4—1461no—
182C4#1455656811yescharacteristic
183C4#1455656911yescharacteristic
184C4#1455657711yescharacteristic
185C4#1455659011yescharacteristic
186C2—21no—
187C2—21no—
188C2#1798849111yescharacteristic
189C2#1798856811yescharacteristic
190C2#1798857011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D73
commutatorC23×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#343×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#343D73
hypocenterC73#1998
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
96. C73#1998semidirect