Finite Group Databasebeta

← #32989480

Subgroups — #32989480

Order 18688.

402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 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#22610901C212yesmaximal
2#22610100C211yesmaximal, characteristic
3C2×#17988329C212yesmaximal
4#22607812C211yesmaximal, characteristic
5C73×#2822C211yesmaximal, characteristic
6C2×#14556524—21no—
7C2×#14556522—21no—
8C2×#14556502C2212yes—
9C2×#14556502C2211yescharacteristic
10#17988457C2211yescharacteristic
11#17988349—22no—
12#17988349—22no—
13#17988329—24no—
14C2×#125×C73C2212yes—
15#400×C73—22no—
16#398×C73—21no—
17#398×C73—21no—
18#398×C73—22no—
19#382×C73C2211yescharacteristic
20C22×#10596831—21no—
21C22×#10596831—22no—
22C2×C4⋊Dic73—21no—
23C2×C4⋊Dic73—22no—
24#14556524—42no—
25#14556522—42no—
26#14556502—22no—
27#14556502—21no—
28#14556502—22no—
29#14556502D412yes—
30#125×C73—22no—
31#125×C73—22no—
32#125×C73—22no—
33#125×C73—22no—
34C2×C4⋊C4×C73—22no—
35C2×C4⋊C4×C73—22no—
36C2×C4⋊C4×C73—21no—
37C2×C4⋊C4×C73—21no—
38C2×C4⋊C4×C73D412yes—
39C2×C4⋊C4×C73D412yes—
40C2×C4⋊C4×C73D411yescharacteristic
41C2×C4⋊C4×C73D411yescharacteristic
42C2×C42×C73C2311yescharacteristic
43#95×C73—22no—
44#95×C73—22no—
45#95×C73—21no—
46#95×C73—21no—
47#95×C73—22no—
48C22×Dic73—41no—
49C2×#10596831—22no—
50C2×#10596831—22no—
51C2×#10596831—22no—
52C2×#10596831—24no—
53C2×#10596831—42no—
54C2×#10596831—42no—
55C4⋊Dic73—41no—
56C4⋊Dic73—41no—
57C4⋊Dic73—44no—
58C22×C4×C73—21no—
59C22×C4×C73—21no—
60C22×C4×C73—22no—
61C22×C4×C73—22no—
62C22×C4×C73C2×D412yes—
63C22×C4×C73C2×D411yescharacteristic
64C4⋊C4×C73—22no—
65C4⋊C4×C73—22no—
66C4⋊C4×C73—22no—
67C4⋊C4×C73—22no—
68C4⋊C4×C73—41no—
69C4⋊C4×C73—41no—
70C4⋊C4×C73—42no—
71C4⋊C4×C73—42no—
72C4⋊C4×C73—42no—
73C4⋊C4×C73—42no—
74C4⋊C4×C73—81no—
75C4⋊C4×C73—81no—
76C42×C73C2×D411yescharacteristic
77C42×C73#4111yescharacteristic
78C42×C73#4112yes—
79C23×C73#12011yescharacteristic
80C2×C4×C73—21no—
81C2×C4×C73—22no—
82C2×C4×C73—22no—
83C2×C4×C73—21no—
84C2×C4×C73—42no—
85C2×C4×C73—42no—
86C2×C4×C73—41no—
87C2×C4×C73—41no—
88C2×C4×C73—42no—
89C2×C4×C73—42no—
90C2×C4×C73—42no—
91C2×C4×C73—42no—
92C2×C4×C73—42no—
93C2×C4×C73—42no—
94C2×C4×C73#12111yescharacteristic
95C2×C4×C73#12112yes—
96C2×C4×C73#12312yes—
97C2×C4×C73#12411yescharacteristic
98C2×Dic73—81no—
99C2×Dic73—82no—
100#10596831—24no—
101#10596831—44no—
102C22×C73#39411yescharacteristic
103C22×C73#45311yescharacteristic
104C22×C73#45412yes—
105C22×C73#45612yes—
106C22×C73#45611yescharacteristic
107C4×C73—22no—
108C4×C73—22no—
109C4×C73—21no—
110C4×C73—21no—
111C4×C73—81no—
112C4×C73—81no—
113C4×C73—82no—
114C4×C73—82no—
115Dic73—161no—
116#10429—731nomaximal, Sylow
117C2×C73#165711yescharacteristic
118C2×C73#166011yescharacteristic
119C2×C73#166312yes—
120C2×C73#203812yes—
121C2×C73#203911yescharacteristic
122#2822D7311yescharacteristic
123#1992—732no—
124#1847—731no—
125C2×#330—732no—
126#1295—731no—
127C73#1042911yescharacteristic, complemented, Sylow
128C2×#125C2×D7312yes—
129C2×#107—1461no—
130C2×#106—1461no—
131C2×#97—731no—
132C2×#97—732no—
133#400—22no—
134#398—21no—
135#398—21no—
136#398—22no—
137#384—731no—
138#382C2×D7311yescharacteristic
139#340—1462no—
140#340—1462no—
141#330—1464no—
142C22×C8—1462no—
143C22×C8—1461no—
144#125—22no—
145#125—22no—
146#125—22no—
147#125—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—1462no—
153C2×C4⋊C4—1461no—
154C2×C4⋊C4C22⋊D7312yes—
155C2×C4⋊C4C22⋊D7312yes—
156C2×C4⋊C4C22⋊D7311yescharacteristic
157C2×C4⋊C4C22⋊D7311yescharacteristic
158C2×C42C22×D7311yescharacteristic
159#107—2922no—
160#106—2922no—
161#97—732no—
162#97—1462no—
163#97—1462no—
164#97—1461no—
165#95—22no—
166#95—22no—
167#95—21no—
168#95—21no—
169#95—22no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—2921no—
175C22×C4C2×C22⋊D7311yescharacteristic
176C22×C4C2×C22⋊D7312yes—
177C2×C8—2922no—
178C2×C8—2922no—
179C2×C8—1464no—
180C2×C8—1462no—
181C2×C8—1462no—
182C2×C8—1462no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—22no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—81no—
194C4⋊C4—81no—
195C4⋊C4—2921no—
196C4⋊C4—2921no—
197C4⋊C4—2924no—
198C42D4×D7311yescharacteristic
199C42#1192402711yescharacteristic
200C42#1192402712yes—
201C23#1455656011yescharacteristic
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—5841no—
217C2×C4—5842no—
218C2×C4#1455656211yescharacteristic
219C2×C4#1455656312yes—
220C2×C4#1455657212yes—
221C2×C4#1455657811yescharacteristic
222C8—2924no—
223C8—1464no—
224C22#1798850111yescharacteristic
225C22#1798875511yescharacteristic
226C22#1798876012yes—
227C22#1798877012yes—
228C22#1798877011yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—81no—
234C4—81no—
235C4—82no—
236C4—82no—
237C4—11681no—
238C2#2260922911yescharacteristic
239C2#2260924211yescharacteristic
240C2#2260925912yes—
241C2#2261114512yes—
242C2#2261115211yescharacteristic
subgroupG/H
centerC23#14556560
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#2822C2
socle, prime radicalC23×C73#120
hypercenter#2822D73
hypocenterC73#10429
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2822

Complements

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

NH ≅ G/Ntype
127. C73#10429semidirect

Maximal subgroups

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

subgroupindex
#226109012
#226101002
C2×#179883292
#226078122
C73×#28222
#1042973