Finite Group Databasebeta

← #33006804

Subgroups — #33006804

Order 18688.

216 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 51 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#22612246C211yesmaximal, characteristic, complemented
2#22612244C211yesmaximal, characteristic, complemented
3#22612179C211yesmaximal, characteristic, complemented
4#22611811C211yesmaximal, characteristic, complemented
5#22608128C211yesmaximal, characteristic, complemented
6#22608120C211yesmaximal, characteristic, complemented
7C73×#1419C211yesmaximal, characteristic, complemented
8#17989019C2211yescharacteristic
9C2×D1168C2211yescharacteristic
10C2×#14556532—21no—
11#17988962—21no—
12#17988703—21no—
13#17988426—21no—
14#17988425—21no—
15D2336—21no—
16#17988422—21no—
17#17988421C2211yescharacteristic
18#17988393—21no—
19C16×Dic73C2211yescharacteristic
20C2×D16×C73C2211yescharacteristic
21M64×C73C2211yescharacteristic
22#368×C73C2211yescharacteristic
23#14556613—21no—
24C2×D584—21no—
25C2×#11924013—41no—
26#14556599—41no—
27#14556587—41no—
28Dic584D411yescharacteristic, complemented
29#14556536—21no—
30D1168—21no—
31D1168—21no—
32D1168D411yescharacteristic, complemented
33#14556532—42no—
34C2×#11924003D411yescharacteristic
35#14556517—41no—
36C8×Dic73D411yescharacteristic
37#14556497—21no—
38C2×D8×C73—21no—
39D16×C73—21no—
40D16×C73—21no—
41C2×C16×C73C2311yescharacteristic
42#108×C73—21no—
43C32×C73—21no—
44#11924028—41no—
45C2×D292—41no—
46C2×C22⋊D73—82no—
47Dic292—21no—
48#11924017—41no—
49D584—21no—
50D584—41no—
51D584—41no—
52#11924013—81no—
53#11924013—81no—
54#11924011—81no—
55C2×#10596831D811yescharacteristic
56C8×D73—81no—
57C4×Dic73D811yescharacteristic
58#11924003—21no—
59C2×D4×C73—41no—
60D8×C73—41no—
61D8×C73—41no—
62M16×C73—41no—
63C2×C8×C73C2×D411yescharacteristic
64C16×C73C2×D411yescharacteristic
65C16×C73#4111yescharacteristic
66C23×C73—81no—
67C22×D73—81no—
68D4×C73—81no—
69D4×C73—81no—
70C2×C4×C73C2×D811yescharacteristic
71C22⋊D73—81no—
72C22⋊D73—164no—
73C2×Dic73—21no—
74D292—41no—
75D292—81no—
76D292—81no—
77C4×D73—81no—
78Dic146—41no—
79C8×C73—81no—
80C8×C73#12111yescharacteristic
81C8×C73AGL(1,ℤ/8)11yescharacteristic
82#10596831D1611yescharacteristic
83#10596831D1611yescharacteristic
84C22×C73—162no—
85C22×C73—161no—
86C22×C73#50911yescharacteristic
87C2×D73—81no—
88C2×D73—162no—
89C2×D73—161no—
90C4×C73#45911yescharacteristic
91C4×C73C2×D1611yescharacteristic
92Dic73—22no—
93Dic73—81no—
94#13692—731nomaximal, Sylow
95C2×C73—21no—
96C2×C73—321no—
97C2×C73#220611yescharacteristic
98D73—161no—
99D73—321no—
100#2263—731no—
101#2263—731no—
102#2246—731no—
103#2178—731no—
104#1422—731no—
105#1419—731no—
106#1419D7311yescharacteristic, complemented
107C73#1369211yescharacteristic, complemented, Sylow
108#508—731no—
109C2×D16—731no—
110C2×D16—1461no—
111C2×D16C2×D7311yescharacteristic
112#493—1461no—
113#443—1461no—
114SD64—1461no—
115SD64—1461no—
116D32—1461no—
117D32—1461no—
118M64—731no—
119M64C2×D7311yescharacteristic
120#368C2×D7311yescharacteristic
121#359—1461no—
122C4×C16—731no—
123#135—1461no—
124C2×D8—21no—
125C2×D8—2921no—
126C2×D8—1461no—
127#131—2921no—
128#127—2921no—
129Q32—731no—
130SD32—1461no—
131D16—21no—
132D16—21no—
133D16—2922no—
134D16—731no—
135D16—1461no—
136D16—1461no—
137C2×C16—731no—
138C2×C16C22×D7311yescharacteristic
139#108—21no—
140#104—2921no—
141C4×C8—731no—
142C32—21no—
143C32—1461no—
144#41—2921no—
145C2×D4—41no—
146C2×D4—2921no—
147C2×D4—5842no—
148Q16—1461no—
149SD16—2921no—
150D8—41no—
151D8—41no—
152D8—2921no—
153D8—2921no—
154D8—5841no—
155D8—5841no—
156D8—1461no—
157M16—41no—
158M16—5841no—
159C2×C8—5841no—
160C2×C8—731no—
161C2×C8D4×D7311yescharacteristic
162C42—731no—
163C16—1461no—
164C16D4×D7311yescharacteristic
165C16#1192402811yescharacteristic
166C23—81no—
167C23—5841no—
168Q8—2921no—
169D4—81no—
170D4—81no—
171D4—2921no—
172D4—5841no—
173D4—5841no—
174D4—5841no—
175D4—11684no—
176C2×C4—5841no—
177C2×C4—1461no—
178C2×C4D8×D7311yescharacteristic
179C8—81no—
180C8—731no—
181C8—731no—
182C8#1455656411yescharacteristic
183C8#1455661811yescharacteristic
184C22—162no—
185C22—161no—
186C22—5841no—
187C22—11682no—
188C22—11681no—
189C22#1798902411yescharacteristic
190C4—5841no—
191C4—1462no—
192C4#1798878111yescharacteristic
193C4D16×D7311yescharacteristic
194C2—21no—
195C2—321no—
196C2—23361no—
197C2—11681no—
198C2#2261196511yescharacteristic
subgroupG/H
centerC2#22611965
commutator, cosocleC2×C16×C73C23
FrattiniC2×C16C22×D73
FittingC73×#1419C2
socleC2×C73#2206
hypercenter#1419D73
hypocenterC73#13692
LCSG ▷ C2×C16×C73 ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1419

Complements

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

NH ≅ G/Ntype
1. #22612246C2semidirect
2. #22612244C2semidirect
3. #22612179C2semidirect
4. #22611811C2semidirect
5. #22608128C2semidirect
6. #22608120C2semidirect
7. C73×#1419C2semidirect
28. Dic584D4semidirect
32. D1168D4semidirect
106. #1419D73semidirect
107. C73#13692semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226122462
#226122442
#226121792
#226118112
#226081282
#226081202
C73×#14192
#1369273