Finite Group Databasebeta

← #33095459

Subgroups — #33095459

Order 18688.

914 conjugacy classes of subgroups; only the 235 normal subgroups are shown.

normal subgroups only

This group has 914 conjugacy classes of subgroups — too many to draw. Only its 235 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×#17989218C211yesmaximal, characteristic
2#22618566C212yesmaximal
3#22610922C214yesmaximal, complemented
4#22610918C214yesmaximal, complemented
5#22610012C212yesmaximal
6#22610011C211yesmaximal, characteristic
7C73×#1821C211yesmaximal, characteristic
8#17989218—28no—
9C2×#14556590C412yes—
10C2×#14556590C2212yes—
11C2×#14556582C412yes—
12C2×#14556582C2212yes—
13C2×#14556570C414yes—
14C2×#14556550C2211yescharacteristic
15C2×#14556550C2211yescharacteristic
16#17988645—28no—
17#17988610C2214yes—
18#17988551C2212yes—
19M16×Dic73C2214yes—
20#17988356C2214yes—
21#17988355C2214yes—
22#17988355C2214yes—
23C22×C4⋊C4×C73C2211yescharacteristic
24#407×C73C2212yes—
25#343×C73C2214yes—
26C22×Dic146C2×C414yes—
27C2×#11924012C2314yes—
28#14556590—28no—
29#14556590—24no—
30#14556590—24no—
31#14556582—28no—
32#14556582—24no—
33#14556582—24no—
34#14556570—216no—
35#14556550—24no—
36#14556550D418yes—
37C2×C4⋊Dic73C2×C414yes—
38C2×C4⋊Dic73C2×C411yescharacteristic
39C2×C4⋊Dic73C2×C411yescharacteristic
40C2×C4⋊Dic73C2311yescharacteristic
41C2×C4⋊Dic73C2311yescharacteristic
42C2×#11924007C2×C414yes—
43C2×#11924007C2×C414yes—
44C2×C22⋊Dic73C2×C412yes—
45C2×C22⋊Dic73C2×C412yes—
46C2×C4×Dic73C2×C412yes—
47C2×C4×Dic73C2312yes—
48#14556520—28no—
49C22⋊#10596831—24no—
50#14556501—24no—
51C8×Dic73—24no—
52C23×C4×C73C2×C412yes—
53C23×C4×C73C2311yescharacteristic
54C2×M16×C73C2314yes—
55C2×C4⋊C4×C73—24no—
56C2×C4⋊C4×C73C2×C412yes—
57C2×C4⋊C4×C73C2312yes—
58C22⋊C8×C73—24no—
59C2×Dic146—28no—
60C2×Dic146—84no—
61C22×Dic73C22×C412yes—
62C22×Dic73C22×C412yes—
63C22×Dic73C22×C412yes—
64C22×Dic73C22×C412yes—
65#11924012—28no—
66C2×#10596831—24no—
67C4⋊Dic73—22no—
68C4⋊Dic73—22no—
69C4⋊Dic73—28no—
70C4⋊Dic73C22⋊C414yes—
71C4⋊Dic73C22⋊C414yes—
72#11924007—28no—
73#11924007—28no—
74C22⋊Dic73—24no—
75C22⋊Dic73C22⋊C418yes—
76C4×Dic73—24no—
77C4×Dic73C2×D414yes—
78C4×Dic73C2×D414yes—
79C24×C73C22×C411yescharacteristic
80C22×C4×C73—24no—
81C22×C4×C73—24no—
82C22×C4×C73—82no—
83C22×C4×C73C22×C411yescharacteristic
84C22×C4×C73C22×C414yes—
85C22×C4×C73C2×D414yes—
86C22×C4×C73C2411yescharacteristic
87M16×C73—28no—
88C2×C8×C73—24no—
89C4⋊C4×C73—24no—
90C4⋊C4×C73—22no—
91C4⋊C4×C73—22no—
92C23×C73—22no—
93C23×C73—41no—
94C23×C73—41no—
95C23×C73C2×C22⋊C412yes—
96C23×C73C23×C411yescharacteristic
97C2×C4×C73—22no—
98C2×C4×C73—28no—
99C2×C4×C73—24no—
100C2×C4×C73—44no—
101C2×C4×C73—84no—
102C2×C4×C73C2×C22⋊C412yes—
103C2×C4×C73C22×D412yes—
104C2×C4×C732−1+414yes—
105C2×Dic73—22no—
106C2×Dic73—22no—
107C2×Dic73—42no—
108C2×Dic73—42no—
109C2×Dic73—42no—
110C2×Dic73—42no—
111C2×Dic73C2×C22⋊C414yes—
112C2×Dic73C2×C22⋊C414yes—
113Dic146—88no—
114C8×C73—44no—
115#10596831—44no—
116C22×C73—21no—
117C22×C73—21no—
118C22×C73—22no—
119C22×C73—22no—
120C22×C73—22no—
121C22×C73—44no—
122C22×C73C22×C22⋊C411yescharacteristic
123C22×C73#51912yes—
124C4×C73—22no—
125C4×C73—44no—
126C4×C73#53614yes—
127Dic73—24no—
128Dic73—24no—
129Dic73—42no—
130Dic73—42no—
131#21832—731nomaximal, Sylow
132C2×C73—22no—
133C2×C73—42no—
134C2×C73#231011yescharacteristic
135C2×C73#288811yescharacteristic
136C2×C73#288911yescharacteristic
137C2×#544—731no—
138#2921—732no—
139#1998—734no—
140#1997—734no—
141#1822—732no—
142#1821—731no—
143#1821D7311yescharacteristic
144C73#2183211yescharacteristic, complemented, Sylow
145#544—1468no—
146C2×C4⋊Q8—732no—
147C2×C4⋊Q8—732no—
148C2×#125—732no—
149C2×#125—732no—
150C2×C22⋊Q8—734no—
151C2×#117—731no—
152C2×#117—731no—
153C22×C4⋊C4C2×D7311yescharacteristic
154#433—1468no—
155#423—734no—
156#407—732no—
157#407C2×D7312yes—
158C4×M16—734no—
159#343—734no—
160#343—734no—
161#343—734no—
162#343C2×D7314yes—
163C22×Q8—734no—
164C23×C4C4×D7312yes—
165C23×C4C22×D7311yescharacteristic
166C2×M16—734no—
167C2×M16C22×D7314yes—
168C4⋊Q8—1464no—
169C4⋊Q8—1464no—
170C4⋊Q8—1468no—
171#125—1464no—
172#125—1464no—
173#125—1468no—
174C22⋊Q8—14616no—
175#117—738no—
176#117—1464no—
177C2×C4⋊C4—24no—
178C2×C4⋊C4—731no—
179C2×C4⋊C4—731no—
180C2×C4⋊C4—734no—
181C2×C4⋊C4—734no—
182C2×C4⋊C4—734no—
183C2×C4⋊C4—731no—
184C2×C4⋊C4—731no—
185C2×C4⋊C4C4×D7312yes—
186C2×C4⋊C4C22×D7312yes—
187C2×C22⋊C4—732no—
188C2×C22⋊C4—732no—
189C2×C42—732no—
190C2×C42—732no—
191C4⋊C8—1468no—
192C22⋊C8—24no—
193C22⋊C8—1464no—
194#97—1464no—
195C4×C8—1464no—
196C24C2×C4×D7311yescharacteristic
197C2×Q8—5844no—
198C2×Q8—1468no—
199C22×C4—24no—
200C22×C4—24no—
201C22×C4—82no—
202C22×C4—732no—
203C22×C4—732no—
204C22×C4—732no—
205C22×C4—732no—
206C22×C4C2×C4×D7311yescharacteristic
207C22×C4C2×C4×D7314yes—
208C22×C4D4×D7314yes—
209C22×C4C23×D7311yescharacteristic
210M16—28no—
211M16—1468no—
212C2×C8—24no—
213C2×C8—1464no—
214C4⋊C4—24no—
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—734no—
218C4⋊C4—734no—
219C4⋊C4—1468no—
220C4⋊C4—1468no—
221C4⋊C4—1468no—
222C4⋊C4—1462no—
223C4⋊C4—1462no—
224C22⋊C4—738no—
225C22⋊C4—1464no—
226C42—734no—
227C42—734no—
228C42—1464no—
229C23—22no—
230C23—41no—
231C23—41no—
232C23C22⋊C4×D7312yes—
233C23C22×C4×D7311yescharacteristic
234Q8—5848no—
235C2×C4—22no—
236C2×C4—28no—
237C2×C4—24no—
238C2×C4—44no—
239C2×C4—84no—
240C2×C4—2922no—
241C2×C4—2922no—
242C2×C4—2922no—
243C2×C4—2922no—
244C2×C4—734no—
245C2×C4—734no—
246C2×C4—1462no—
247C2×C4—1462no—
248C2×C4C22⋊C4×D7312yes—
249C2×C4C2×D4×D7312yes—
250C2×C4#1455663814yes—
251C8—44no—
252C8—2924no—
253C22—21no—
254C22—21no—
255C22—22no—
256C22—22no—
257C22—22no—
258C22—44no—
259C22C2×C22⋊C4×D7311yescharacteristic
260C22#1798906412yes—
261C4—22no—
262C4—44no—
263C4—2922no—
264C4—2922no—
265C4—1464no—
266C4—1464no—
267C4#1798915914yes—
268C2—22no—
269C2—42no—
270C2#2261251611yescharacteristic
271C2#2261840711yescharacteristic
272C2#2261841111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D73
commutatorC23×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1821C2
socleC22×C73C22×C22⋊C4
prime radicalC24×C73C22×C4
cosocleC22×C4×C73C24
hypercenter#1821D73
hypocenterC73#21832
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
3. #22610922C2semidirect
4. #22610918C2semidirect
144. C73#21832semidirect

Maximal subgroups

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

subgroupindex
C2×#179892182
#226185662
#226109222
#226109182
#226100122
#226100112
C73×#18212
#2183273