Finite Group Databasebeta

← #32975225

Subgroups — #32975225

Order 18688.

434 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 83 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#22616861C211yesmaximal, characteristic
2#22611408C212yesmaximal, complemented
3#22607755C212yesmaximal, complemented
4#22607752C211yesmaximal, characteristic
5C73×#2093C211yesmaximal, characteristic
6C2×#14556572—21no—
7C2×#14556522—22no—
8#17988517—21no—
9#17988512—22no—
10#17988485C2212yes—
11#17988462—22no—
12#17988349—22no—
13#17988342C2212yes—
14C2×#107×C73—21no—
15C2×#102×C73—21no—
16#390×C73C2211yescharacteristic
17#384×C73C2211yescharacteristic
18#336×C73C2211yescharacteristic
19C23×Dic73—21no—
20C22×#10596831—22no—
21#14556572—42no—
22#14556572—42no—
23C2×C4⋊Dic73—21no—
24C2×C4⋊Dic73D412yes—
25C2×C4⋊Dic73D412yes—
26C2×#11924007—22no—
27C2×C22⋊Dic73—22no—
28C2×C22⋊Dic73—21no—
29#14556522—44no—
30#14556498—22no—
31#14556498—21no—
32#14556498—22no—
33C22×D4×C73D411yescharacteristic
34C22×C8×C73—21no—
35C2×C4⋊C4×C73—22no—
36C2×C4⋊C4×C73—21no—
37C2×C4⋊C4×C73D411yescharacteristic
38C2×C22⋊C4×C73—22no—
39C2×C42×C73C2311yescharacteristic
40#107×C73—42no—
41#102×C73—42no—
42C22×Dic73—22no—
43C22×Dic73—22no—
44C22×Dic73—42no—
45C22×Dic73—81no—
46C22×Dic73—81no—
47C2×#10596831—24no—
48C2×#10596831—42no—
49C2×#10596831—42no—
50C4⋊Dic73—22no—
51C4⋊Dic73—22no—
52C4⋊Dic73—42no—
53C4⋊Dic73—81no—
54#11924007—42no—
55#11924007—42no—
56C22⋊Dic73—42no—
57C22⋊Dic73—44no—
58C24×C73—21no—
59C2×D4×C73—21no—
60C2×D4×C73—41no—
61C2×D4×C73—41no—
62C2×D4×C73SD1612yes—
63C22×C4×C73—21no—
64C22×C4×C73—41no—
65C22×C4×C73C2×D412yes—
66C22×C4×C73C2×D411yescharacteristic
67C2×C8×C73—22no—
68C2×C8×C73—41no—
69C2×C8×C73—41no—
70C4⋊C4×C73—41no—
71C4⋊C4×C73—41no—
72C4⋊C4×C73—41no—
73C4⋊C4×C73—42no—
74C4⋊C4×C73—42no—
75C22⋊C4×C73—42no—
76C22⋊C4×C73—42no—
77C42×C73—41no—
78C23×C73—22no—
79C23×C73—42no—
80C23×C73—41no—
81C23×C73—42no—
82C23×C73—41no—
83C23×C73#12011yescharacteristic
84D4×C73—42no—
85D4×C73—81no—
86C2×C4×C73—21no—
87C2×C4×C73—22no—
88C2×C4×C73—21no—
89C2×C4×C73—22no—
90C2×C4×C73—42no—
91C2×C4×C73—41no—
92C2×C4×C73—82no—
93C2×C4×C73—81no—
94C2×C4×C73C2×SD1611yescharacteristic
95C2×C4×C73#13512yes—
96C2×C4×C73AGL(1,ℤ/8)12yes—
97C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
98C2×Dic73—42no—
99C2×Dic73—42no—
100C2×Dic73—42no—
101C2×Dic73—42no—
102C2×Dic73—42no—
103C2×Dic73—42no—
104C2×Dic73—84no—
105C8×C73—42no—
106#10596831—44no—
107C22×C73—42no—
108C22×C73—44no—
109C22×C73—82no—
110C22×C73—81no—
111C22×C73—81no—
112C22×C73#44912yes—
113C22×C73#45011yescharacteristic
114C22×C73#45311yescharacteristic
115C22×C73#45612yes—
116C22×C73#45811yescharacteristic
117C4×C73—22no—
118C4×C73—22no—
119C4×C73—21no—
120C4×C73—21no—
121C4×C73—81no—
122C4×C73—161no—
123Dic73—82no—
124Dic73—82no—
125#7819—731nomaximal, Sylow
126C2×C73—82no—
127C2×C73#160912yes—
128C2×C73#161311yescharacteristic
129C2×C73#162011yescharacteristic
130C2×C73#165412yes—
131C2×C73#166011yescharacteristic
132#2724—731no—
133#2093D7311yescharacteristic
134#2084—732no—
135#1271—732no—
136#1270—731no—
137C73#781911yescharacteristic, complemented, Sylow
138C2×#123—1461no—
139C2×#107—21no—
140C2×#106—1462no—
141C2×#102—21no—
142#398—1461no—
143#397—1462no—
144#390C2×D7311yescharacteristic
145#389—732no—
146#385—1462no—
147#384C2×D7311yescharacteristic
148#340—1462no—
149#336—732no—
150#336C2×D7311yescharacteristic
151C22×D4C22⋊D7311yescharacteristic
152C23×C4—1461no—
153C22×C8—21no—
154C22×C8—1462no—
155#123—2922no—
156#123—2922no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—732no—
160C2×C4⋊C4—732no—
161C2×C4⋊C4—1462no—
162C2×C4⋊C4—1461no—
163C2×C4⋊C4C22⋊D7311yescharacteristic
164C2×C22⋊C4—22no—
165C2×C22⋊C4—1462no—
166C2×C22⋊C4—1461no—
167C2×C42C22×D7311yescharacteristic
168#107—42no—
169#106—2924no—
170#102—42no—
171#95—1462no—
172#95—1461no—
173#95—1462no—
174C24—21no—
175C2×D4—21no—
176C2×D4—41no—
177C2×D4—41no—
178C2×D4#1192401512yes—
179C22×C4—21no—
180C22×C4—41no—
181C22×C4—2922no—
182C22×C4—5841no—
183C22×C4—5841no—
184C22×C4—1462no—
185C22×C4—1462no—
186C22×C4D4×D7312yes—
187C22×C4C2×C22⋊D7311yescharacteristic
188C2×C8—22no—
189C2×C8—41no—
190C2×C8—41no—
191C2×C8—2922no—
192C2×C8—2922no—
193C2×C8—1464no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—42no—
198C4⋊C4—42no—
199C4⋊C4—2922no—
200C4⋊C4—2922no—
201C4⋊C4—2922no—
202C4⋊C4—5841no—
203C4⋊C4—1462no—
204C4⋊C4—1462no—
205C22⋊C4—42no—
206C22⋊C4—42no—
207C22⋊C4—2922no—
208C22⋊C4—2924no—
209C42—41no—
210C23—22no—
211C23—42no—
212C23—41no—
213C23—42no—
214C23—41no—
215C23#1455655911yescharacteristic
216D4—42no—
217D4—81no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—82no—
225C2×C4—81no—
226C2×C4—2922no—
227C2×C4—2922no—
228C2×C4—2922no—
229C2×C4—2922no—
230C2×C4—2922no—
231C2×C4—2922no—
232C2×C4—5844no—
233C2×C4C2×#1192401511yescharacteristic
234C2×C4#1455661012yes—
235C2×C4#1455661512yes—
236C2×C4#1455661611yescharacteristic
237C8—42no—
238C8—2924no—
239C22—42no—
240C22—44no—
241C22—82no—
242C22—81no—
243C22—81no—
244C22#1798872912yes—
245C22#1798873711yescharacteristic
246C22#1798875411yescharacteristic
247C22#1798876812yes—
248C22#1798877611yescharacteristic
249C4—22no—
250C4—22no—
251C4—21no—
252C4—21no—
253C4—81no—
254C4—161no—
255C4—5842no—
256C4—5842no—
257C2—82no—
258C2#2260892512yes—
259C2#2260895011yescharacteristic
260C2#2260898811yescharacteristic
261C2#2260921412yes—
262C2#2260924011yescharacteristic
subgroupG/H
centerC23#14556559
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#2093C2
socleC23×C73#120
prime radicalC22×D4×C73D4
hypercenter#2093D73
hypocenterC73#7819
LCSG ▷ C2×C42×C73 ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2093

Complements

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

NH ≅ G/Ntype
2. #22611408C2semidirect
3. #22607755C2semidirect
137. C73#7819semidirect

Maximal subgroups

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

subgroupindex
#226168612
#226114082
#226077552
#226077522
C73×#20932
#781973