Finite Group Databasebeta

← #34010167

Subgroups — #34010167

Order 18688.

424 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 74 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#22625193C212yesmaximal, complemented
2#22624874C212yesmaximal, complemented
3#22624859C212yesmaximal
4#22612643C211yesmaximal, characteristic
5#17989608—22no—
6#17989433—22no—
7#17989432C2214yes—
8C2×#14556578C411yescharacteristic
9C2×C4×Dic146C2211yescharacteristic
10#17988492C411yescharacteristic
11#17988490C2211yescharacteristic
12#17988475—22no—
13#17988460—22no—
14#17988456C2211yescharacteristic
15#17988433C411yescharacteristic
16C2×C4×D4×C73C411yescharacteristic
17C4⋊#10596833—42no—
18C22⋊#10596833—24no—
19#14556646—42no—
20C22×Dic146C2×C411yescharacteristic
21#14556578—22no—
22#14556578—22no—
23C4×Dic146—42no—
24C2×C4⋊Dic73C2311yescharacteristic
25C2×#11924007—22no—
26C2×#11924007D412yes—
27C2×C22⋊Dic73—22no—
28C2×C22⋊Dic73—22no—
29C2×C4×Dic73C2×C411yescharacteristic
30C2×C4×Dic73C2×C411yescharacteristic
31C2×C4×Dic73D412yes—
32#14556498—22no—
33#14556498—21no—
34#14556498—21no—
35C22×D4×C73C2×C411yescharacteristic
36C23×C4×C73—21no—
37C4×D4×C73—42no—
38C2×C4⋊C4×C73C2×C411yescharacteristic
39C2×C22⋊C4×C73—21no—
40C2×C42×C73C2×C411yescharacteristic
41C2×#10596833—44no—
42C2×Dic146—21no—
43C2×Dic146—21no—
44C2×Dic146—41no—
45C2×Dic146—41no—
46C22×Dic73—21no—
47C22×Dic73—21no—
48C22×Dic73C22⋊C412yes—
49C22×Dic73C2×D412yes—
50C4⋊Dic73—41no—
51#11924007—42no—
52#11924007—82no—
53C22⋊Dic73—28no—
54C22⋊Dic73—82no—
55C4×Dic73—22no—
56C4×Dic73—22no—
57C4×Dic73—21no—
58C4×Dic73—41no—
59C4×Dic73M1612yes—
60C24×C73—21no—
61C2×D4×C73—21no—
62C2×D4×C73—41no—
63C2×D4×C73—41no—
64C2×D4×C73M1612yes—
65C22×C4×C73—21no—
66C22×C4×C73—42no—
67C22×C4×C73—82no—
68C22×C4×C73C22⋊C411yescharacteristic
69C22×C4×C73C22⋊C411yescharacteristic
70C22×C4×C73C22×C411yescharacteristic
71C4⋊C4×C73—41no—
72C22⋊C4×C73—42no—
73C42×C73—22no—
74C23×C73—22no—
75C23×C73—42no—
76C23×C73—42no—
77C23×C73—41no—
78C23×C73—41no—
79C23×C73C2×C22⋊C411yescharacteristic
80D4×C73—42no—
81D4×C73—42no—
82C2×C4×C73—21no—
83C2×C4×C73—21no—
84C2×C4×C73—21no—
85C2×C4×C73—41no—
86C2×C4×C73—41no—
87C2×C4×C73—42no—
88C2×C4×C73—41no—
89C2×C4×C73—84no—
90C2×C4×C73#9912yes—
91C2×C4×C73C2×M1611yescharacteristic
92C2×C4×C73C2×M1611yescharacteristic
93C2×Dic73—22no—
94C2×Dic73—22no—
95C2×Dic73—22no—
96C2×Dic73—22no—
97C2×Dic73—22no—
98C2×Dic73—41no—
99C2×Dic73—41no—
100C2×Dic73—42no—
101C2×Dic73—41no—
102C2×Dic73—41no—
103C2×Dic73—41no—
104Dic146—42no—
105Dic146—42no—
106#10596833—84no—
107C22×C73—21no—
108C22×C73—21no—
109C22×C73—44no—
110C22×C73—42no—
111C22×C73—82no—
112C22×C73—81no—
113C22×C73—81no—
114C22×C73#40711yescharacteristic
115C22×C73C2×#9911yescharacteristic
116C22×C73#41311yescharacteristic
117C4×C73—22no—
118C4×C73—21no—
119C4×C73—21no—
120C4×C73—41no—
121C4×C73—81no—
122Dic73—42no—
123Dic73—42no—
124Dic73—42no—
125Dic73—81no—
126#11534—731nomaximal, Sylow
127C2×C73—21no—
128C2×C73—21no—
129C2×C73—82no—
130C2×C73#146511yescharacteristic
131C2×C73#212811yescharacteristic
132C2×C73#213311yescharacteristic
133#2326—731no—
134#1467—732no—
135#1325—732no—
136#1318—732no—
137C73#1153411yescharacteristic, complemented, Sylow
138C2×#124—731no—
139C2×C4×Q8—731no—
140C2×C4×D4#6440811yescharacteristic
141#432—1462no—
142#391—731no—
143#390—731no—
144#388—1462no—
145#385—1462no—
146#384—731no—
147#376—731no—
148#324—734no—
149#324—1462no—
150C22×Q8—731no—
151C22×D4C2×#6440811yescharacteristic
152C23×C4—21no—
153#124—1462no—
154#124—1462no—
155C4×Q8—2922no—
156C4×D4—42no—
157C2×C4⋊C4—732no—
158C2×C4⋊C4—731no—
159C2×C4⋊C4—1462no—
160C2×C4⋊C4C2×#6440811yescharacteristic
161C2×C22⋊C4—21no—
162C2×C22⋊C4—1462no—
163C2×C22⋊C4—1462no—
164C2×C42—731no—
165C2×C42—731no—
166C2×C42—732no—
167C2×C42C2×#6440811yescharacteristic
168C4⋊C8—2922no—
169C22⋊C8—1464no—
170#97—2922no—
171#95—1462no—
172#95—1461no—
173#95—1461no—
174C24—21no—
175C2×Q8—2921no—
176C2×Q8—2921no—
177C2×Q8—1461no—
178C2×Q8—1461no—
179C2×D4—21no—
180C2×D4—41no—
181C2×D4—41no—
182C2×D4#1192403812yes—
183C22×C4—21no—
184C22×C4—42no—
185C22×C4—82no—
186C22×C4—732no—
187C22×C4—732no—
188C22×C4—1461no—
189C22×C4—1461no—
190C22×C4C22⋊#6440811yescharacteristic
191C22×C4C22⋊#6440811yescharacteristic
192C22×C4C22×#6440811yescharacteristic
193C2×C8—2924no—
194C4⋊C4—41no—
195C4⋊C4—2922no—
196C4⋊C4—2921no—
197C4⋊C4—5842no—
198C22⋊C4—42no—
199C22⋊C4—5842no—
200C22⋊C4—1468no—
201C42—22no—
202C42—2921no—
203C42—732no—
204C42—1461no—
205C42—1462no—
206C42—1462no—
207C23—22no—
208C23—42no—
209C23—42no—
210C23—41no—
211C23—41no—
212C23C2×C22⋊#6440811yescharacteristic
213Q8—2922no—
214Q8—2922no—
215D4—42no—
216D4—42no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—84no—
225C2×C4—2921no—
226C2×C4—2921no—
227C2×C4—2922no—
228C2×C4—2921no—
229C2×C4—2921no—
230C2×C4—2921no—
231C2×C4—1462no—
232C2×C4—1462no—
233C2×C4—1462no—
234C2×C4—1462no—
235C2×C4—1462no—
236C2×C4#1455664912yes—
237C2×C4D73⋊M1611yescharacteristic
238C2×C4C2×#1192403811yescharacteristic
239C8—5844no—
240C22—21no—
241C22—21no—
242C22—44no—
243C22—42no—
244C22—82no—
245C22—81no—
246C22—81no—
247C22#1798955811yescharacteristic
248C22C2×#1455664911yescharacteristic
249C22#1798957311yescharacteristic
250C4—21no—
251C4—21no—
252C4—22no—
253C4—41no—
254C4—81no—
255C4—2922no—
256C4—2922no—
257C4—2922no—
258C4—5841no—
259C2—21no—
260C2—21no—
261C2—82no—
262C2#2262518611yescharacteristic
263C2#2262621011yescharacteristic
264C2#2262622611yescharacteristic
subgroupG/H
centerC22C2×#14556649
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
FittingC2×C4×D4×C73C4
socleC22×C73C2×#99
prime radicalC22×D4×C73C2×C4
cosocleC2×C4⋊Dic73C23
hypercenterC2×C4×D4#64408
hypocenterC73#11534
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #22625193C2semidirect
2. #22624874C2semidirect
137. C73#11534semidirect

Maximal subgroups

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

subgroupindex
#226251932
#226248742
#226248592
#226126432
#1153473