Finite Group Databasebeta

← #32980928

Subgroups — #32980928

Order 18688.

458 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 115 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×#17988957C211yesmaximal, characteristic
2#22610903C212yesmaximal
3C2×#17988329C211yesmaximal, characteristic
4#22607812C212yesmaximal
5C73×#2382C211yesmaximal, characteristic
6C2×#14556591C2211yescharacteristic
7#17988957—22no—
8#17988957C414yescomplemented
9C2×#14556514—22no—
10C2×#14556502C2212yes—
11C2×#14556502C2211yescharacteristic
12#17988349—22no—
13#17988349—22no—
14#17988329—22no—
15C2×#125×C73C2211yescharacteristic
16#389×C73—22no—
17#387×C73—22no—
18#387×C73—22no—
19#382×C73C2212yes—
20C22×Dic146—21no—
21C22×#10596831—21no—
22C22×#10596831—22no—
23#14556591—21no—
24#14556591—22no—
25#14556591C2×C412yes—
26C2×C4⋊Dic73—22no—
27#14556514—28no—
28#14556502—21no—
29#14556502—22no—
30#14556502—22no—
31#14556502C2×C412yes—
32#125×C73—22no—
33#125×C73C2×C412yes—
34#125×C73D412yes—
35C2×C4⋊C4×C73—22no—
36C2×C4⋊C4×C73—22no—
37C2×C4⋊C4×C73D412yes—
38C2×C4⋊C4×C73D412yes—
39C2×C4⋊C4×C73D412yes—
40C2×C42×C73—22no—
41C2×C42×C73C2311yescharacteristic
42#95×C73—22no—
43#95×C73—22no—
44#95×C73—22no—
45#95×C73—22no—
46C2×Dic146—22no—
47C2×Dic146—42no—
48C2×Dic146—42no—
49C2×Dic146—41no—
50C22×Dic73—41no—
51C2×#10596831—24no—
52C2×#10596831—22no—
53C2×#10596831—41no—
54C2×#10596831—41no—
55C2×#10596831—42no—
56C2×#10596831—42no—
57C4⋊Dic73—24no—
58C4⋊Dic73—42no—
59C22×C4×C73—22no—
60C22×C4×C73—22no—
61C22×C4×C73—22no—
62C22×C4×C73C2×D411yescharacteristic
63C22×C4×C73C2×D412yes—
64C4⋊C4×C73—24no—
65C4⋊C4×C73—24no—
66C4⋊C4×C73—22no—
67C4⋊C4×C73—42no—
68C4⋊C4×C73—42no—
69C4⋊C4×C73—82no—
70C4⋊C4×C73C22⋊C414yes—
71C42×C73—82no—
72C42×C73C22×C411yescharacteristic
73C42×C73C2×D411yescharacteristic
74C42×C73#4112yes—
75C23×C73#12011yescharacteristic
76C2×C4×C73—21no—
77C2×C4×C73—21no—
78C2×C4×C73—22no—
79C2×C4×C73—22no—
80C2×C4×C73—24no—
81C2×C4×C73—42no—
82C2×C4×C73—42no—
83C2×C4×C73—42no—
84C2×C4×C73—42no—
85C2×C4×C73—42no—
86C2×C4×C73—42no—
87C2×C4×C73—42no—
88C2×C4×C73—42no—
89C2×C4×C73C2×C22⋊C411yescharacteristic
90C2×C4×C73C4×D412yes—
91C2×C4×C73#12112yes—
92C2×C4×C73#12311yescharacteristic
93C2×Dic73—42no—
94C2×Dic73—81no—
95C2×Dic73—81no—
96Dic146—44no—
97Dic146—82no—
98#10596831—44no—
99#10596831—42no—
100C22×C73#38611yescharacteristic
101C22×C73#45411yescharacteristic
102C22×C73#45411yescharacteristic
103C22×C73#45512yes—
104C22×C73#45612yes—
105C4×C73—22no—
106C4×C73—22no—
107C4×C73—21no—
108C4×C73—21no—
109C4×C73—44no—
110C4×C73—82no—
111C4×C73—82no—
112Dic73—82no—
113#9004—731nomaximal, Sylow
114C2×C73#166211yescharacteristic
115C2×C73#166311yescharacteristic
116C2×C73#166412yes—
117C2×C73#188212yes—
118C2×C73#188811yescharacteristic
119C2×#491—731no—
120#2382D7311yescharacteristic
121#1993—732no—
122C2×#330—731no—
123#1295—732no—
124C73#900411yescharacteristic, complemented, Sylow
125C2×C4⋊Q8—731no—
126C2×#125C2×D7311yescharacteristic
127#491—734no—
128#491—1462no—
129C2×#103—1462no—
130C2×#97—731no—
131C2×#97—732no—
132#389—22no—
133#387—22no—
134#387—22no—
135#382C2×D7312yes—
136#340—1462no—
137#340—1462no—
138#330—1462no—
139C22×Q8—1461no—
140C22×C8—1462no—
141C22×C8—1461no—
142C4⋊Q8—732no—
143C4⋊Q8—1461no—
144C4⋊Q8—1462no—
145#125—22no—
146#125C4×D7312yes—
147#125D29212yes—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—1462no—
151C2×C4⋊C4C22⋊D7312yes—
152C2×C4⋊C4C22⋊D7312yes—
153C2×C4⋊C4C22⋊D7312yes—
154C2×C42—22no—
155C2×C42C22×D7311yescharacteristic
156#103—1468no—
157#97—732no—
158#97—1462no—
159#97—1461no—
160#97—1462no—
161#95—22no—
162#95—22no—
163#95—22no—
164#95—22no—
165C2×Q8—2922no—
166C2×Q8—2922no—
167C2×Q8—2921no—
168C2×Q8—1462no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—2921no—
173C22×C4C2×C22⋊D7311yescharacteristic
174C22×C4C2×C22⋊D7312yes—
175C2×C8—2921no—
176C2×C8—2921no—
177C2×C8—2922no—
178C2×C8—2922no—
179C2×C8—1464no—
180C2×C8—1462no—
181C4⋊C4—24no—
182C4⋊C4—24no—
183C4⋊C4—22no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C4⋊C4—82no—
187C4⋊C4—2922no—
188C4⋊C4—1464no—
189C4⋊C4#1192400514yes—
190C42—82no—
191C42C2×C4×D7311yescharacteristic
192C42C2×D29211yescharacteristic
193C42#1192402812yes—
194C23#1455656011yescharacteristic
195Q8—2924no—
196Q8—5842no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—2922no—
211C2×C4—5841no—
212C2×C4—5841no—
213C2×C4C2×#1192400511yescharacteristic
214C2×C4C4×C22⋊D7312yes—
215C2×C4#1455656512yes—
216C2×C4#1455657411yescharacteristic
217C8—2924no—
218C8—2922no—
219C22#1798846611yescharacteristic
220C22#1798876011yescharacteristic
221C22#1798876011yescharacteristic
222C22#1798876512yes—
223C22#1798877012yes—
224C4—22no—
225C4—22no—
226C4—21no—
227C4—21no—
228C4—44no—
229C4—82no—
230C4—82no—
231C4—5842no—
232C2#2260925411yescharacteristic
233C2#2260925911yescharacteristic
234C2#2260926512yes—
235C2#2261030012yes—
236C2#2261033411yescharacteristic
subgroupG/H
centerC23#14556560
commutatorC42×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#2382C2
socle, prime radicalC23×C73#120
cosocleC2×C42×C73C23
hypercenter#2382D73
hypocenterC73#9004
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2382

Complements

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

NH ≅ G/Ntype
8. #17988957C4semidirect
124. C73#9004semidirect

Maximal subgroups

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

subgroupindex
C2×#179889572
#226109032
C2×#179883292
#226078122
C73×#23822
#900473