Finite Group Databasebeta

← #32981018

Subgroups — #32981018

Order 18688.

572 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 131 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×#17988526C211yesmaximal, characteristic
2#22610019C212yesmaximal
3C2×#17988313C211yesmaximal, characteristic
4#22607809C212yesmaximal
5C73×#2313C211yesmaximal, characteristic
6C22×C4⋊Dic73C2211yescharacteristic
7C2×C22⋊#10596831C2212yes—
8#17988526—22no—
9#17988526C414yescomplemented
10C2×#14556498—21no—
11C2×#14556498—21no—
12C2×#14556498C2211yescharacteristic
13#17988349—24no—
14#17988313—22no—
15C22×C4⋊C4×C73C2211yescharacteristic
16#387×C73—24no—
17#381×C73—21no—
18#380×C73C2212yes—
19C4×C22⋊C4×C73—21no—
20C23×Dic73—21no—
21C23×Dic73—21no—
22C22×#10596831—22no—
23C2×C4⋊Dic73—22no—
24C2×C4⋊Dic73—21no—
25C2×C4⋊Dic73—22no—
26C2×C4⋊Dic73C2×C412yes—
27C22⋊#10596831—22no—
28C22⋊#10596831—22no—
29#14556498—24no—
30#14556498—24no—
31#14556498—21no—
32#14556498C2×C412yes—
33C23×C4×C73D411yescharacteristic
34C23×C4×C73D411yescharacteristic
35C23×C4×C73C2311yescharacteristic
36C2×C4⋊C4×C73—22no—
37C2×C4⋊C4×C73—22no—
38C2×C4⋊C4×C73C2×C412yes—
39C2×C4⋊C4×C73D412yes—
40C2×C4⋊C4×C73D414yes—
41C2×C22⋊C4×C73—22no—
42C2×C42×C73—22no—
43#95×C73—22no—
44#95×C73—24no—
45#95×C73—22no—
46C22×Dic73—22no—
47C22×Dic73—22no—
48C22×Dic73—42no—
49C22×Dic73—42no—
50C22×Dic73—44no—
51C22×Dic73—41no—
52C22×Dic73—41no—
53C22×Dic73—42no—
54C2×#10596831—44no—
55C2×#10596831—42no—
56C4⋊Dic73—24no—
57C4⋊Dic73—42no—
58C24×C73C2×D411yescharacteristic
59C22×C4×C73—21no—
60C22×C4×C73—21no—
61C22×C4×C73—21no—
62C22×C4×C73—22no—
63C22×C4×C73—22no—
64C22×C4×C73—21no—
65C22×C4×C73—24no—
66C22×C4×C73—42no—
67C22×C4×C73—42no—
68C22×C4×C73C22⋊C412yes—
69C22×C4×C73C22⋊C412yes—
70C22×C4×C73C22×C411yescharacteristic
71C22×C4×C73C2×D412yes—
72C22×C4×C73C2×D411yescharacteristic
73C22×C4×C73#4112yes—
74C4⋊C4×C73—24no—
75C4⋊C4×C73—24no—
76C4⋊C4×C73—44no—
77C22⋊C4×C73—42no—
78C22⋊C4×C73—42no—
79C42×C73—82no—
80C23×C73—22no—
81C23×C73—22no—
82C23×C73C2×C22⋊C411yescharacteristic
83C23×C73#12011yescharacteristic
84C23×C73#12311yescharacteristic
85C23×C73#13512yes—
86C23×C73#13712yes—
87C2×C4×C73—24no—
88C2×C4×C73—22no—
89C2×C4×C73—22no—
90C2×C4×C73—22no—
91C2×C4×C73—22no—
92C2×C4×C73—41no—
93C2×C4×C73—41no—
94C2×C4×C73—42no—
95C2×C4×C73—42no—
96C2×C4×C73—42no—
97C2×C4×C73—42no—
98C2×C4×C73—42no—
99C2×C4×C73—44no—
100C2×C4×C73—44no—
101C2×C4×C73—44no—
102C2×C4×C73—81no—
103C2×C4×C73C4×D412yes—
104C2×C4×C73#12112yes—
105C2×Dic73—42no—
106C2×Dic73—42no—
107C2×Dic73—44no—
108C2×Dic73—42no—
109C2×Dic73—42no—
110C2×Dic73—84no—
111C2×Dic73—82no—
112C2×Dic73—82no—
113#10596831—82no—
114C22×C73—24no—
115C22×C73—24no—
116C22×C73—21no—
117C22×C73—21no—
118C22×C73—21no—
119C22×C73—21no—
120C22×C73#38611yescharacteristic
121C22×C73#41611yescharacteristic
122C22×C73#41911yescharacteristic
123C22×C73#45212yes—
124C22×C73#45412yes—
125C22×C73#45812yes—
126C22×C73#48512yes—
127C4×C73—22no—
128C4×C73—22no—
129C4×C73—42no—
130C4×C73—42no—
131C4×C73—84no—
132Dic73—82no—
133Dic73—82no—
134#9022—731nomaximal, Sylow
135C2×C73—21no—
136C2×C73—21no—
137C2×C73—22no—
138C2×C73#161514yes—
139C2×C73#187311yescharacteristic
140C2×C73#188811yescharacteristic
141C2×C73#189011yescharacteristic
142C2×#400—731no—
143#2313D7311yescharacteristic
144#1824—732no—
145C2×#324—731no—
146#1294—732no—
147C73#902211yescharacteristic, complemented, Sylow
148C22×C4⋊C4—731no—
149C22×C4⋊C4C2×D7311yescharacteristic
150C2×C22⋊C8—732no—
151#400—734no—
152#400—1462no—
153#387—24no—
154#381—21no—
155#380C2×D7312yes—
156C4×C22⋊C4—21no—
157C2×#95—731no—
158C2×#95—1461no—
159C2×#95—1461no—
160#340—1464no—
161#324—1462no—
162C23×C4—1461no—
163C23×C4—1461no—
164C23×C4C22⋊D7311yescharacteristic
165C23×C4C22⋊D7311yescharacteristic
166C23×C4C22×D7311yescharacteristic
167C22×C8—1462no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—732no—
171C2×C4⋊C4—1461no—
172C2×C4⋊C4—1462no—
173C2×C4⋊C4—1462no—
174C2×C4⋊C4C4×D7312yes—
175C2×C4⋊C4D29212yes—
176C2×C4⋊C4C22⋊D7314yes—
177C2×C22⋊C4—22no—
178C2×C42—22no—
179C22⋊C8—1462no—
180C22⋊C8—1462no—
181#95—22no—
182#95—24no—
183#95—22no—
184#95—732no—
185#95—1464no—
186#95—1464no—
187#95—1461no—
188C24C2×C22⋊D7311yescharacteristic
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—21no—
195C22×C4—24no—
196C22×C4—42no—
197C22×C4—42no—
198C22×C4—2922no—
199C22×C4—2922no—
200C22×C4—2924no—
201C22×C4—2921no—
202C22×C4—2921no—
203C22×C4—2922no—
204C22×C4—1462no—
205C22×C4—1462no—
206C22×C4#1192400512yes—
207C22×C4#1192400512yes—
208C22×C4C2×C4×D7311yescharacteristic
209C22×C4C2×C22⋊D7312yes—
210C22×C4C2×D29211yescharacteristic
211C22×C4#1192402812yes—
212C2×C8—2924no—
213C2×C8—2922no—
214C4⋊C4—24no—
215C4⋊C4—24no—
216C4⋊C4—44no—
217C4⋊C4—2922no—
218C4⋊C4—1464no—
219C22⋊C4—42no—
220C22⋊C4—42no—
221C42—82no—
222C23—22no—
223C23—22no—
224C23C2×#1192400511yescharacteristic
225C23#1455656011yescharacteristic
226C23#1455657411yescharacteristic
227C23#1455661112yes—
228C23#1455662112yes—
229C2×C4—24no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—44no—
242C2×C4—44no—
243C2×C4—44no—
244C2×C4—81no—
245C2×C4—2922no—
246C2×C4—2922no—
247C2×C4—2924no—
248C2×C4—2922no—
249C2×C4—2922no—
250C2×C4—5844no—
251C2×C4—5842no—
252C2×C4—5842no—
253C2×C4C4×C22⋊D7312yes—
254C2×C4#1455656512yes—
255C8—5842no—
256C22—24no—
257C22—24no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22#1798846611yescharacteristic
263C22#1798858111yescharacteristic
264C22#1798859511yescharacteristic
265C22#1798874912yes—
266C22#1798876012yes—
267C22#1798877712yes—
268C22#1798892812yes—
269C4—22no—
270C4—22no—
271C4—42no—
272C4—42no—
273C4—84no—
274C4—5842no—
275C4—5842no—
276C2—21no—
277C2—22no—
278C2—21no—
279C2#2260896214yes—
280C2#2261024311yescharacteristic
281C2#2261033411yescharacteristic
282C2#2261034411yescharacteristic
subgroupG/H
centerC23#14556560
commutatorC22×C4×C73C22×C4
FrattiniC23×C4C22×D73
FittingC73×#2313C2
socleC23×C73#120
prime radicalC24×C73C2×D4
cosocleC23×C4×C73C23
hypercenter#2313D73
hypocenterC73#9022
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2313

Complements

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

NH ≅ G/Ntype
9. #17988526C4semidirect
147. C73#9022semidirect

Maximal subgroups

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

subgroupindex
C2×#179885262
#226100192
C2×#179883132
#226078092
C73×#23132
#902273