Finite Group Databasebeta

← #32989483

Subgroups — #32989483

Order 18688.

402 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 91 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#22617999C211yesmaximal, characteristic
2#22610899C212yesmaximal
3C2×#17988328C212yesmaximal
4#22607812C211yesmaximal, characteristic
5C73×#1847C211yesmaximal, characteristic
6C2×#14556583C2212yes—
7C2×#14556502C2212yes—
8#17988527—22no—
9#17988519—22no—
10#17988517—21no—
11#17988517—21no—
12#17988349—22no—
13#17988349—22no—
14#17988328—24no—
15C2×#107×C73—21no—
16C2×#106×C73—21no—
17C2×#97×C73C2211yescharacteristic
18#384×C73C2211yescharacteristic
19#382×C73C2211yescharacteristic
20C22×#10596831—22no—
21#14556583—22no—
22#14556583—22no—
23#14556583—22no—
24#14556583—22no—
25C2×C4⋊Dic73—21no—
26C2×C4⋊Dic73—21no—
27C2×C4⋊Dic73D412yes—
28C2×C4⋊Dic73D412yes—
29C2×#11924007—22no—
30C2×#11924007—22no—
31#14556502—22no—
32#14556502—22no—
33#14556498—22no—
34#14556498—22no—
35#14556498—21no—
36#14556498—21no—
37C22×C8×C73—21no—
38C2×C4⋊C4×C73—21no—
39C2×C4⋊C4×C73—22no—
40C2×C4⋊C4×C73D411yescharacteristic
41C2×C4⋊C4×C73D411yescharacteristic
42C2×C42×C73C2311yescharacteristic
43#107×C73—42no—
44#106×C73—42no—
45#97×C73—21no—
46#97×C73D412yes—
47#95×C73—22no—
48C22×Dic73—22no—
49C22×Dic73—22no—
50C2×#10596831—24no—
51C2×#10596831—42no—
52C2×#10596831—42no—
53C4⋊Dic73—22no—
54C4⋊Dic73—22no—
55C4⋊Dic73—22no—
56C4⋊Dic73—22no—
57C4⋊Dic73—81no—
58C4⋊Dic73—81no—
59#11924007—42no—
60#11924007—42no—
61#11924007—42no—
62#11924007—42no—
63C22×C4×C73—21no—
64C22×C4×C73—21no—
65C22×C4×C73—41no—
66C22×C4×C73C2×D412yes—
67C22×C4×C73C2×D411yescharacteristic
68C2×C8×C73—22no—
69C2×C8×C73—22no—
70C2×C8×C73—22no—
71C4⋊C4×C73—41no—
72C4⋊C4×C73—41no—
73C4⋊C4×C73—41no—
74C4⋊C4×C73—41no—
75C4⋊C4×C73—44no—
76C42×C73C2×D411yescharacteristic
77C42×C73#4111yescharacteristic
78C42×C73#4112yes—
79C23×C73#12011yescharacteristic
80C2×C4×C73—21no—
81C2×C4×C73—22no—
82C2×C4×C73—21no—
83C2×C4×C73—22no—
84C2×C4×C73—41no—
85C2×C4×C73—41no—
86C2×C4×C73—42no—
87C2×C4×C73—42no—
88C2×C4×C73—81no—
89C2×C4×C73—82no—
90C2×C4×C73#12111yescharacteristic
91C2×C4×C73#12112yes—
92C2×C4×C73#12312yes—
93C2×C4×C73#12411yescharacteristic
94C2×Dic73—42no—
95C2×Dic73—42no—
96C2×Dic73—42no—
97C2×Dic73—42no—
98C2×Dic73—42no—
99C2×Dic73—42no—
100C8×C73—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—161no—
114Dic73—82no—
115Dic73—82no—
116#10429—731nomaximal, Sylow
117C2×C73#165711yescharacteristic
118C2×C73#166011yescharacteristic
119C2×C73#166312yes—
120C2×C73#203812yes—
121C2×C73#203911yescharacteristic
122#2822—731no—
123#1992—732no—
124#1847D7311yescharacteristic
125C2×#330—732no—
126#1295—731no—
127C73#1042911yescharacteristic, complemented, Sylow
128C2×#125—732no—
129C2×#107—21no—
130C2×#106—21no—
131C2×#97—732no—
132C2×#97C2×D7311yescharacteristic
133#400—1462no—
134#398—1462no—
135#398—1461no—
136#398—1461no—
137#384C2×D7311yescharacteristic
138#382C2×D7311yescharacteristic
139#340—1462no—
140#340—1462no—
141#330—1464no—
142C22×C8—21no—
143C22×C8—1462no—
144#125—1462no—
145#125—1462no—
146#125—1462no—
147#125—1462no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—732no—
151C2×C4⋊C4—732no—
152C2×C4⋊C4—1462no—
153C2×C4⋊C4—1462no—
154C2×C4⋊C4—1461no—
155C2×C4⋊C4—1461no—
156C2×C4⋊C4C22⋊D7311yescharacteristic
157C2×C4⋊C4C22⋊D7311yescharacteristic
158C2×C42C22×D7311yescharacteristic
159#107—42no—
160#106—42no—
161#97—21no—
162#97—1462no—
163#97—1462no—
164#97D29212yes—
165#95—22no—
166#95—1462no—
167#95—1462no—
168#95—1461no—
169#95—1461no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—41no—
173C22×C4—1462no—
174C22×C4—1462no—
175C22×C4D4×D7312yes—
176C22×C4C2×C22⋊D7311yescharacteristic
177C2×C8—22no—
178C2×C8—22no—
179C2×C8—22no—
180C2×C8—2922no—
181C2×C8—2922no—
182C2×C8—1464no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C4⋊C4—41no—
186C4⋊C4—41no—
187C4⋊C4—44no—
188C4⋊C4—2922no—
189C4⋊C4—2922no—
190C4⋊C4—2922no—
191C4⋊C4—2922no—
192C4⋊C4—5841no—
193C4⋊C4—5841no—
194C4⋊C4—1462no—
195C4⋊C4—1462no—
196C4⋊C4—1462no—
197C4⋊C4—1462no—
198C42C2×D29211yescharacteristic
199C42#1192402811yescharacteristic
200C42#1192402912yes—
201C23#1455655911yescharacteristic
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—81no—
211C2×C4—82no—
212C2×C4—2922no—
213C2×C4—2922no—
214C2×C4—2922no—
215C2×C4—2922no—
216C2×C4—2922no—
217C2×C4—2922no—
218C2×C4#1455656511yescharacteristic
219C2×C4#1455656612yes—
220C2×C4#1455657612yes—
221C2×C4#1455658011yescharacteristic
222C8—24no—
223C8—2924no—
224C22#1798850411yescharacteristic
225C22#1798875411yescharacteristic
226C22#1798875812yes—
227C22#1798876812yes—
228C22#1798876911yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—81no—
234C4—81no—
235C4—161no—
236C4—5842no—
237C4—5842no—
238C2#2260922711yescharacteristic
239C2#2260924011yescharacteristic
240C2#2260925812yes—
241C2#2261115012yes—
242C2#2261115511yescharacteristic
subgroupG/H
centerC23#14556559
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1847C2
socle, prime radicalC23×C73#120
hypercenter#1847D73
hypocenterC73#10429
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

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
#226179992
#226108992
C2×#179883282
#226078122
C73×#18472
#1042973