Finite Group Databasebeta

← #32990885

Subgroups — #32990885

Order 18688.

236 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 69 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#22608702C211yesmaximal, characteristic
2#22608662C211yesmaximal, characteristic
3#22608632C211yesmaximal, characteristic
4#22608405C211yesmaximal, characteristic
5#22607841C211yesmaximal, characteristic
6#22607800C211yesmaximal, characteristic
7C73×#1287C211yesmaximal, characteristic
8#17989144C2211yescharacteristic
9#17988644C2211yescharacteristic
10#17988611C2211yescharacteristic
11C2×C4⋊#10596831C2211yescharacteristic
12#17988338—22no—
13#17988335—21no—
14#17988334—21no—
15#17988332—21no—
16#17988332—21no—
17#17988319—22no—
18#432×C73C2211yescharacteristic
19#432×C73C2211yescharacteristic
20#431×C73C2211yescharacteristic
21C2×#11924012—21no—
22C22×#10596831—21no—
23#14556591D411yescharacteristic
24#14556591D411yescharacteristic
25#14556583—21no—
26#14556570—21no—
27#14556570—21no—
28C4×Dic146—21no—
29C4×Dic146—21no—
30#14556550—21no—
31C4⋊#10596831—21no—
32C4⋊#10596831—21no—
33C4⋊#10596831—21no—
34C4⋊#10596831—21no—
35C4⋊#10596831—21no—
36C22⋊#10596831—21no—
37#14556502—21no—
38C2×C42×C73C2311yescharacteristic
39C4⋊C8×C73—21no—
40C4⋊C8×C73—21no—
41C4⋊C8×C73—21no—
42C22⋊C8×C73—21no—
43C22⋊C8×C73—21no—
44C22⋊C8×C73—21no—
45#97×C73—21no—
46#97×C73—21no—
47C4×C8×C73D412yes—
48C2×Dic146—21no—
49C2×Dic146—21no—
50#11924012—81no—
51C2×#10596831—41no—
52C2×#10596831—41no—
53C2×#10596831—41no—
54C2×#10596831—81no—
55C4⋊Dic73—21no—
56C4⋊Dic73—21no—
57C4⋊Dic73—21no—
58C4⋊Dic73—21no—
59#11924007—41no—
60#11924007—41no—
61C22⋊Dic73—41no—
62C4×Dic73—41no—
63C22×C4×C73#4111yescharacteristic
64C22×C4×C73#4111yescharacteristic
65C22×C4×C73#4111yescharacteristic
66C2×C8×C73—22no—
67C2×C8×C73—41no—
68C2×C8×C73—41no—
69C42×C73C2×D411yescharacteristic
70C42×C73C2×D411yescharacteristic
71C42×C73#4111yescharacteristic
72C42×C73#4111yescharacteristic
73C23×C73#12611yescharacteristic
74C2×C4×C73—21no—
75C2×C4×C73—21no—
76C2×C4×C73—41no—
77C2×C4×C73—41no—
78C2×C4×C73#12111yescharacteristic
79C2×C4×C73#12311yescharacteristic
80C2×C4×C73#12311yescharacteristic
81C2×C4×C73#12311yescharacteristic
82C2×C4×C73#12411yescharacteristic
83C2×C4×C73#12611yescharacteristic
84C2×Dic73—41no—
85C2×Dic73—41no—
86Dic146—41no—
87Dic146—41no—
88Dic146—81no—
89C8×C73—42no—
90C8×C73—81no—
91C8×C73—81no—
92#10596831—81no—
93#10596831—81no—
94#10596831—81no—
95C22×C73—21no—
96C22×C73—21no—
97C22×C73—21no—
98C22×C73#39711yescharacteristic
99C4×C73—21no—
100C4×C73—21no—
101C4×C73—21no—
102C4×C73—21no—
103C4×C73—21no—
104C4×C73#47111yescharacteristic
105C4×C73#47111yescharacteristic
106Dic73—81no—
107Dic73—81no—
108#10648—731nomaximal, Sylow
109C2×C73—41no—
110C2×C73#207911yescharacteristic
111C2×C73#208011yescharacteristic
112C2×C73#208211yescharacteristic
113#1570—731no—
114#1559—731no—
115#1552—731no—
116#1497—731no—
117#1307—731no—
118#1290—731no—
119#1287D7311yescharacteristic
120C73#1064811yescharacteristic, complemented, Sylow
121#533—731no—
122#432—731no—
123#432C2×D7311yescharacteristic
124#432C2×D7311yescharacteristic
125#431C2×D7311yescharacteristic
126#423—731no—
127C2×C4⋊C8—731no—
128#334—1462no—
129#333—1461no—
130#332—1461no—
131#332—1461no—
132#332—1461no—
133Q8⋊C8—1462no—
134C2×M16—1461no—
135C22×C8—1461no—
136C4⋊Q8—731no—
137C4⋊Q8—731no—
138#125—1461no—
139C22⋊Q8—1461no—
140C22⋊Q8—1461no—
141C4×Q8—1461no—
142C4×Q8—1461no—
143#117—1461no—
144C2×C42C22×D7311yescharacteristic
145C4⋊C8—21no—
146C4⋊C8—21no—
147C4⋊C8—21no—
148C4⋊C8—1461no—
149C4⋊C8—1461no—
150C4⋊C8—1461no—
151C4⋊C8—1461no—
152C4⋊C8—1461no—
153C22⋊C8—21no—
154C22⋊C8—21no—
155C22⋊C8—21no—
156C22⋊C8—1461no—
157#97—21no—
158#97—21no—
159#97—1461no—
160C4×C8D29212yes—
161C2×Q8—1461no—
162C2×Q8—1461no—
163C22×C4#1192402711yescharacteristic
164C22×C4#1192402811yescharacteristic
165C22×C4#1192402911yescharacteristic
166M16—5841no—
167C2×C8—22no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—2921no—
171C2×C8—2921no—
172C2×C8—2921no—
173C2×C8—5841no—
174C4⋊C4—2921no—
175C4⋊C4—2921no—
176C4⋊C4—1461no—
177C4⋊C4—1461no—
178C4⋊C4—1461no—
179C4⋊C4—1461no—
180C22⋊C4—2921no—
181C42—2921no—
182C42D4×D7311yescharacteristic
183C42C2×D29211yescharacteristic
184C42#1192402711yescharacteristic
185C42#1192402811yescharacteristic
186C23#1455658611yescharacteristic
187Q8—2921no—
188Q8—2921no—
189Q8—5841no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—2921no—
195C2×C4—2921no—
196C2×C4#1455656611yescharacteristic
197C2×C4#1455657311yescharacteristic
198C2×C4#1455657311yescharacteristic
199C2×C4#1455657511yescharacteristic
200C2×C4#1455657911yescharacteristic
201C2×C4#1455658611yescharacteristic
202C8—42no—
203C8—81no—
204C8—81no—
205C8—5841no—
206C8—5841no—
207C8—5841no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22#1798851411yescharacteristic
212C4—21no—
213C4—21no—
214C4—21no—
215C4—21no—
216C4—21no—
217C4—5841no—
218C4—5841no—
219C4#1798885111yescharacteristic
220C4#1798885111yescharacteristic
221C2—41no—
222C2#2261137811yescharacteristic
223C2#2261138311yescharacteristic
224C2#2261139711yescharacteristic
subgroupG/H
centerC22#17988514
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1287C2
socleC22×C73#397
prime radicalC23×C73#126
hypercenter#1287D73
hypocenterC73#10648
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1287

Complements

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

NH ≅ G/Ntype
120. C73#10648semidirect

Maximal subgroups

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

subgroupindex
#226087022
#226086622
#226086322
#226084052
#226078412
#226078002
C73×#12872
#1064873