Finite Group Databasebeta

← #32975180

Subgroups — #32975180

Order 18688.

398 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 87 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#22617924C211yesmaximal, characteristic
2#22611340C212yesmaximal
3#22607757C211yesmaximal, characteristic
4#22607756C212yesmaximal
5C73×#2096C211yesmaximal, characteristic
6C2×#14556514—22no—
7#17988508—22no—
8#17988507—21no—
9#17988494—21no—
10#17988493C2212yes—
11#17988491—22no—
12#17988349—22no—
13#17988342C2212yes—
14C2×#106×C73—21no—
15C2×#103×C73—21no—
16#391×C73C2211yescharacteristic
17#384×C73C2211yescharacteristic
18#336×C73C2211yescharacteristic
19C22×Dic146—21no—
20C22×Dic146D412yes—
21C22×#10596831—22no—
22C2×C4⋊Dic73—21no—
23C2×C4⋊Dic73D412yes—
24C2×#11924007—22no—
25C2×C4×Dic73—21no—
26#14556514—44no—
27#14556498—21no—
28#14556498—22no—
29#14556498—22no—
30#14556498—22no—
31C22×Q8×C73D411yescharacteristic
32C22×C8×C73—21no—
33C2×C4⋊C4×C73—21no—
34C2×C4⋊C4×C73—22no—
35C2×C4⋊C4×C73D411yescharacteristic
36C2×C42×C73C2311yescharacteristic
37#106×C73—42no—
38#103×C73—42no—
39#95×C73—22no—
40C2×Dic146—22no—
41C2×Dic146—42no—
42C2×Dic146—42no—
43C2×Dic146—81no—
44C2×Dic146—82no—
45C2×Dic146SD1614yes—
46C22×Dic73—22no—
47C22×Dic73—22no—
48C2×#10596831—42no—
49C2×#10596831—42no—
50C2×#10596831—42no—
51C4⋊Dic73—42no—
52C4⋊Dic73—81no—
53#11924007—82no—
54C4×Dic73—81no—
55C2×Q8×C73—21no—
56C2×Q8×C73—41no—
57C2×Q8×C73—41no—
58C2×Q8×C73Q1612yes—
59C22×C4×C73—21no—
60C22×C4×C73—21no—
61C22×C4×C73—41no—
62C22×C4×C73C2×D412yes—
63C22×C4×C73C2×D411yescharacteristic
64C2×C8×C73—22no—
65C2×C8×C73—41no—
66C2×C8×C73—41no—
67C4⋊C4×C73—41no—
68C4⋊C4×C73—41no—
69C4⋊C4×C73—41no—
70C4⋊C4×C73—42no—
71C4⋊C4×C73—42no—
72C42×C73—41no—
73C23×C73#12011yescharacteristic
74Q8×C73—42no—
75Q8×C73—81no—
76C2×C4×C73—21no—
77C2×C4×C73—22no—
78C2×C4×C73—21no—
79C2×C4×C73—22no—
80C2×C4×C73—22no—
81C2×C4×C73—41no—
82C2×C4×C73—41no—
83C2×C4×C73—41no—
84C2×C4×C73—42no—
85C2×C4×C73—82no—
86C2×C4×C73—81no—
87C2×C4×C73C2×SD1612yes—
88C2×C4×C73C2×Q1611yescharacteristic
89C2×C4×C73#13712yes—
90C2×C4×C73#13711yescharacteristic
91C2×Dic73—24no—
92C2×Dic73—42no—
93C2×Dic73—42no—
94C2×Dic73—42no—
95C2×Dic73—42no—
96C2×Dic73—42no—
97Dic146—44no—
98Dic146—82no—
99Dic146—84no—
100C8×C73—42no—
101#10596831—82no—
102C22×C73#44812yes—
103C22×C73#45111yescharacteristic
104C22×C73#45311yescharacteristic
105C22×C73#45512yes—
106C22×C73#45811yescharacteristic
107C4×C73—22no—
108C4×C73—22no—
109C4×C73—21no—
110C4×C73—21no—
111C4×C73—42no—
112C4×C73—81no—
113C4×C73—161no—
114Dic73—44no—
115Dic73—82no—
116#7812—731nomaximal, Sylow
117C2×C73#160812yes—
118C2×C73#161411yescharacteristic
119C2×C73#162311yescharacteristic
120C2×C73#164512yes—
121C2×C73#165911yescharacteristic
122#2811—731no—
123#2096D7311yescharacteristic
124#2072—732no—
125#1272—731no—
126#1272—732no—
127C73#781211yescharacteristic, complemented, Sylow
128C2×#106—21no—
129C2×#103—21no—
130C2×#103—1462no—
131#395—1462no—
132#395—1461no—
133#391—732no—
134#391—1462no—
135#391—1461no—
136#391C2×D7311yescharacteristic
137#384C2×D7311yescharacteristic
138#340—1462no—
139#336—732no—
140#336C2×D7311yescharacteristic
141C22×Q8—732no—
142C22×Q8—1461no—
143C22×Q8C22⋊D7311yescharacteristic
144C22×C8—21no—
145C22×C8—1462no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—732no—
149C2×C4⋊C4—1462no—
150C2×C4⋊C4—1461no—
151C2×C4⋊C4C22⋊D7311yescharacteristic
152C2×C42—1461no—
153C2×C42C22×D7311yescharacteristic
154#106—42no—
155#103—42no—
156#103—2924no—
157#95—22no—
158#95—1462no—
159#95—1461no—
160#95—1462no—
161#95—1462no—
162C2×Q8—21no—
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8—2922no—
166C2×Q8—2922no—
167C2×Q8—5841no—
168C2×Q8—5842no—
169C2×Q8—734no—
170C2×Q8—1462no—
171C2×Q8#1192401812yes—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—41no—
175C22×C4—1462no—
176C22×C4—1462no—
177C22×C4D4×D7312yes—
178C22×C4C2×C22⋊D7311yescharacteristic
179C2×C8—22no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—2922no—
183C2×C8—2922no—
184C2×C8—2922no—
185C4⋊C4—41no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—2922no—
191C4⋊C4—5842no—
192C4⋊C4—5841no—
193C42—41no—
194C42—5841no—
195C23#1455655911yescharacteristic
196Q8—42no—
197Q8—81no—
198Q8—2924no—
199Q8—5842no—
200Q8—5844no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—82no—
211C2×C4—81no—
212C2×C4—2922no—
213C2×C4—2922no—
214C2×C4—2922no—
215C2×C4—2922no—
216C2×C4—2922no—
217C2×C4—1464no—
218C2×C4SD16×D7312yes—
219C2×C4C2×#1192401811yescharacteristic
220C2×C4#1455662012yes—
221C2×C4#1455662111yescharacteristic
222C8—42no—
223C8—5842no—
224C22#1798872412yes—
225C22#1798874211yescharacteristic
226C22#1798875411yescharacteristic
227C22#1798876312yes—
228C22#1798877611yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—42no—
234C4—81no—
235C4—161no—
236C4—2924no—
237C4—5842no—
238C2#2260892012yes—
239C2#2260895511yescharacteristic
240C2#2260900711yescharacteristic
241C2#2260915112yes—
242C2#2260923511yescharacteristic
subgroupG/H
centerC23#14556559
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#2096C2
socle, prime radicalC23×C73#120
hypercenter#2096D73
hypocenterC73#7812
LCSG ▷ C2×C42×C73 ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2096

Complements

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

NH ≅ G/Ntype
127. C73#7812semidirect

Maximal subgroups

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

subgroupindex
#226179242
#226113402
#226077572
#226077562
C73×#20962
#781273