Finite Group Databasebeta

← #22626047

Subgroups — #22626047

Order 9344.

200 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 72 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×#14556662C211yesmaximal, characteristic
2C2×#14556661C211yesmaximal, characteristic
3#17989592C211yesmaximal, characteristic
4C4×#11924038C211yesmaximal, characteristic
5#17989463C211yesmaximal, characteristic
6#17989463C211yesmaximal, characteristic
7C4⋊C8×D73C211yesmaximal, characteristic
8C2×#11924038C2211yescharacteristic
9C2×#11924038C2211yescharacteristic
10C2×#11924038C2211yescharacteristic
11C2×#11924038C2211yescharacteristic
12#14556662—22no—
13#14556661—22no—
14#14556658—21no—
15#14556658—21no—
16#14556646—21no—
17C4×#10596833—21no—
18C2×C8×D73C2211yescharacteristic
19C2×C8×D73C2211yescharacteristic
20C42×D73C2211yescharacteristic
21C4⋊#10596831C411yescharacteristic
22#14556520C411yescharacteristic
23#14556520C411yescharacteristic
24C4⋊C8×C73C411yescharacteristic
25#11924038—21no—
26#11924038—21no—
27#11924038—21no—
28#11924038—21no—
29#11924038—21no—
30#11924038—21no—
31#11924038D412yes—
32#11924038Q812yes—
33C2×#10596833—21no—
34C2×#10596833—21no—
35C2×#10596833—21no—
36C2×#10596833—21no—
37C2×C4×D73Q811yescharacteristic
38C2×C4×D73Q811yescharacteristic
39C2×C4×D73C2311yescharacteristic
40C2×#10596831C2×C411yescharacteristic
41C2×#10596831C2×C411yescharacteristic
42C8×D73—21no—
43C8×D73—21no—
44C8×D73—21no—
45C8×D73—21no—
46C4×Dic73C2×C411yescharacteristic
47C4×Dic73D411yescharacteristic
48C4×Dic73D411yescharacteristic
49C2×C8×C73C2×C411yescharacteristic
50C2×C8×C73C2×C411yescharacteristic
51C42×C73C2×C411yescharacteristic
52C22×D73C2×Q811yescharacteristic
53C2×C4×C73C4⋊C411yescharacteristic
54C2×C4×C73C4⋊C411yescharacteristic
55C2×C4×C73C22×C411yescharacteristic
56C2×Dic73C4⋊C411yescharacteristic
57C2×Dic73C4⋊C411yescharacteristic
58C2×Dic73C2×D411yescharacteristic
59C4×D73—22no—
60C4×D73—41no—
61C4×D73C2×D411yescharacteristic
62C4×D73C2×Q811yescharacteristic
63C4×D73#4111yescharacteristic
64C4×D73#4111yescharacteristic
65#10596833—22no—
66#10596833—22no—
67#10596833—41no—
68#10596833—41no—
69C8×C73—21no—
70C8×C73—21no—
71#10596831—21no—
72#10596831—21no—
73C22×C73C2×C4⋊C411yescharacteristic
74C2×D73—21no—
75C2×D73—21no—
76C2×D73#12511yescharacteristic
77C2×D73C4⋊Q811yescharacteristic
78C4×C73—21no—
79C4×C73—21no—
80C4×C73C4×D411yescharacteristic
81C4×C73C4×Q811yescharacteristic
82Dic73—21no—
83Dic73#10812yescomplemented
84Dic73#12111yescharacteristic
85Dic73C22⋊Q811yescharacteristic
86C2×C73#38911yescharacteristic
87C2×C73C2×#10811yescharacteristic
88C2×C73#43011yescharacteristic
89D73—21no—
90D73—21no—
91#1950—731nomaximal, Sylow
92C73#195011yescharacteristic, complemented, Sylow
93C2×#108—731no—
94C2×#108—731no—
95#423—731no—
96C2×C4⋊C8—731no—
97C4×M16—731no—
98#341—731no—
99#341—731no—
100C2×M16—731no—
101C2×M16—731no—
102C2×M16—731no—
103C2×M16—731no—
104C22×C8—731no—
105C22×C8—731no—
106C2×C42—731no—
107#108—1462no—
108#108—1462no—
109C4⋊C8—731no—
110C4⋊C8—731no—
111C4⋊C8—731no—
112C4⋊C8—1461no—
113C4⋊C8—1461no—
114C4⋊C8#6440811yescharacteristic
115#97—1461no—
116C4×C8—1461no—
117C22×C4—731no—
118C22×C4—731no—
119C22×C4—731no—
120M16—732no—
121M16—732no—
122M16—1461no—
123M16—1461no—
124M16—1461no—
125M16—1461no—
126M16—1461no—
127M16—1461no—
128C2×C8—731no—
129C2×C8—731no—
130C2×C8—1461no—
131C2×C8—1461no—
132C2×C8—1461no—
133C2×C8—1461no—
134C2×C8—1461no—
135C2×C8—1461no—
136C2×C8—1461no—
137C2×C8—1461no—
138C2×C8C2×#6440811yescharacteristic
139C2×C8C2×#6440811yescharacteristic
140C42—731no—
141C42—731no—
142C42—731no—
143C42C2×#6440811yescharacteristic
144C23—731no—
145C2×C4—2921no—
146C2×C4—731no—
147C2×C4—731no—
148C2×C4—731no—
149C2×C4—731no—
150C2×C4—731no—
151C2×C4—731no—
152C2×C4—731no—
153C2×C4—1462no—
154C2×C4C4⋊#6440811yescharacteristic
155C2×C4C4⋊#6440811yescharacteristic
156C2×C4C22×#6440811yescharacteristic
157C8—21no—
158C8—21no—
159C8—2921no—
160C8—2921no—
161C8—1462no—
162C8—1462no—
163C8—1461no—
164C8—1461no—
165C22—731no—
166C22—731no—
167C22—1461no—
168C22—1461no—
169C22C2×C4⋊#6440811yescharacteristic
170C4—21no—
171C4—21no—
172C4—731no—
173C4—731no—
174C4—732no—
175C4—1461no—
176C4D4×#6440811yescharacteristic
177C4Q8×#6440811yescharacteristic
178C2—1461no—
179C2—1461no—
180C2#1798953811yescharacteristic
181C2D73⋊#10811yescharacteristic
182C2#1798960211yescharacteristic
subgroupG/H
centerC22C2×C4⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4⋊C8×C73C4
socleC22×C73C2×C4⋊C4
hypercenterC4⋊C8#64408
hypocenterC73#1950
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
83. Dic73#108semidirect
92. C73#1950semidirect