Finite Group Databasebeta

← #22611500

Subgroups — #22611500

Order 9344.

198 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 79 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#17988485C211yesmaximal, characteristic
2#17988453C211yesmaximal, characteristic
3#17988350C211yesmaximal, characteristic
4#17988350C211yesmaximal, characteristic
5#17988350C211yesmaximal, characteristic
6#17988350C211yesmaximal, characteristic
7#336×C73C211yesmaximal, characteristic
8C2×C4⋊Dic73C2211yescharacteristic
9C2×C4⋊Dic73C2211yescharacteristic
10C2×C4⋊Dic73C2211yescharacteristic
11C2×C4⋊Dic73C2211yescharacteristic
12C2×#11924007—21no—
13#14556498—21no—
14#14556498—21no—
15#14556498—21no—
16C22×C8×C73C2211yescharacteristic
17C22×C8×C73C2211yescharacteristic
18C2×C42×C73C2211yescharacteristic
19C22×Dic73—21no—
20C22×Dic73—21no—
21C22×Dic73—21no—
22C22×Dic73—21no—
23C4⋊Dic73—21no—
24C4⋊Dic73—21no—
25C4⋊Dic73—21no—
26C4⋊Dic73—21no—
27C4⋊Dic73—21no—
28C4⋊Dic73—21no—
29C4⋊Dic73—21no—
30C4⋊Dic73Q812yes—
31#11924007—42no—
32C22×C4×C73D411yescharacteristic
33C22×C4×C73D411yescharacteristic
34C22×C4×C73C2311yescharacteristic
35C2×C8×C73—21no—
36C2×C8×C73—21no—
37C2×C8×C73—21no—
38C2×C8×C73—21no—
39C2×C8×C73—21no—
40C2×C8×C73—21no—
41C42×C73—21no—
42C42×C73—21no—
43C23×C73C2×D411yescharacteristic
44C2×C4×C73—21no—
45C2×C4×C73—21no—
46C2×C4×C73—21no—
47C2×C4×C73—21no—
48C2×C4×C73—21no—
49C2×C4×C73—21no—
50C2×C4×C73C2×Q811yescharacteristic
51C2×C4×C73#4111yescharacteristic
52C2×C4×C73#4111yescharacteristic
53C2×C4×C73#4111yescharacteristic
54C2×C4×C73#4111yescharacteristic
55C2×C4×C73#4111yescharacteristic
56C2×Dic73—22no—
57C2×Dic73—41no—
58C2×Dic73—41no—
59C2×Dic73—41no—
60C2×Dic73—41no—
61C2×Dic73—41no—
62C2×Dic73—41no—
63C2×Dic73—41no—
64C2×Dic73—41no—
65C2×Dic73—41no—
66C2×Dic73—41no—
67C2×Dic73—41no—
68C8×C73—41no—
69C8×C73—41no—
70C22×C73C22⋊Q811yescharacteristic
71C22×C73#12311yescharacteristic
72C22×C73#12411yescharacteristic
73C22×C73#13511yescharacteristic
74C22×C73#13511yescharacteristic
75C22×C73AGL(1,ℤ/8)11yescharacteristic
76C22×C73#13711yescharacteristic
77C4×C73—41no—
78C4×C73—41no—
79C4×C73#12511yescharacteristic
80C4×C73#12511yescharacteristic
81C4×C73#12611yescharacteristic
82C4×C73#12611yescharacteristic
83Dic73—42no—
84Dic73—81no—
85Dic73—81no—
86Dic73—81no—
87C2×C73#40011yescharacteristic
88C2×C73#47811yescharacteristic
89C2×C73#47911yescharacteristic
90C2×C73#48211yescharacteristic
91C2×C73#48511yescharacteristic
92C2×C73#48811yescharacteristic
93C2×C73#48911yescharacteristic
94#2101—731nomaximal, Sylow
95C73#210111yescharacteristic, complemented, Sylow
96#389—731no—
97#382—731no—
98#340—731no—
99#340—731no—
100#340—731no—
101#340—731no—
102#336D7311yescharacteristic
103C22×C8C2×D7311yescharacteristic
104C22×C8C2×D7311yescharacteristic
105C2×C4⋊C4—731no—
106C2×C4⋊C4—731no—
107C2×C4⋊C4—731no—
108C2×C4⋊C4—731no—
109C2×C4⋊C4—1461no—
110C2×C42C2×D7311yescharacteristic
111#95—1461no—
112#95—1461no—
113#95—1461no—
114C22×C4—1461no—
115C22×C4—1461no—
116C22×C4—1461no—
117C22×C4—1461no—
118C22×C4D29211yescharacteristic
119C22×C4D29211yescharacteristic
120C22×C4C22×D7311yescharacteristic
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—21no—
127C4⋊C4—2922no—
128C4⋊C4—732no—
129C4⋊C4—1461no—
130C4⋊C4—1461no—
131C4⋊C4—1461no—
132C4⋊C4—1461no—
133C4⋊C4—1461no—
134C4⋊C4—1461no—
135C4⋊C4—1461no—
136C42—21no—
137C42—21no—
138C23C2×D29211yescharacteristic
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—2921no—
146C2×C4—2921no—
147C2×C4—2921no—
148C2×C4—2921no—
149C2×C4—2921no—
150C2×C4—2921no—
151C2×C4—2921no—
152C2×C4—2921no—
153C2×C4—2921no—
154C2×C4—2921no—
155C2×C4—2921no—
156C2×C4—1462no—
157C2×C4Q8×D7311yescharacteristic
158C2×C4#1192402711yescharacteristic
159C2×C4#1192402711yescharacteristic
160C2×C4#1192402711yescharacteristic
161C2×C4#1192402811yescharacteristic
162C2×C4#1192402811yescharacteristic
163C8—41no—
164C8—41no—
165C22#1455657111yescharacteristic
166C22#1455657511yescharacteristic
167C22#1455657911yescharacteristic
168C22#1455661311yescharacteristic
169C22#1455661311yescharacteristic
170C22#1455661911yescharacteristic
171C22#1455662411yescharacteristic
172C4—41no—
173C4—41no—
174C4—2922no—
175C4—5841no—
176C4—5841no—
177C4—5841no—
178C4#1455658111yescharacteristic
179C4#1455658111yescharacteristic
180C4#1455658411yescharacteristic
181C4#1455658411yescharacteristic
182C2#1798852711yescharacteristic
183C2#1798888811yescharacteristic
184C2#1798889511yescharacteristic
185C2#1798891211yescharacteristic
186C2#1798892911yescharacteristic
187C2#1798894211yescharacteristic
188C2#1798894711yescharacteristic
subgroupG/H
centerC23C2×D292
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#336×C73C2
socleC23×C73C2×D4
hypercenter#336D73
hypocenterC73#2101
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
95. C73#2101semidirect