Finite Group Databasebeta

← #34010169

Subgroups — #34010169

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#22624873C212yesmaximal, complemented
3#22624860C212yesmaximal
4#22612642C211yesmaximal, characteristic
5#17989608—22no—
6#17989433—22no—
7#17989432C2214yes—
8C2×#14556579C411yescharacteristic
9C2×C4×Dic146C2211yescharacteristic
10C2×C4×D292C411yescharacteristic
11#17988493C411yescharacteristic
12#17988489C2211yescharacteristic
13#17988479—22no—
14#17988461—22no—
15#17988457C2211yescharacteristic
16#376×C73C411yescharacteristic
17C4⋊#10596833—42no—
18C22⋊#10596833—24no—
19#14556646—42no—
20C22×Dic146C2×C411yescharacteristic
21C22×D292C2×C411yescharacteristic
22C22×C4×D73—21no—
23#14556579—22no—
24#14556579—22no—
25C4×Dic146—42no—
26C4×D292—42no—
27C2×C4⋊Dic73—22no—
28C2×C4⋊Dic73C2×C411yescharacteristic
29C2×C4⋊Dic73C2311yescharacteristic
30C2×#11924007D412yes—
31C2×#11924005—22no—
32C2×#11924005—22no—
33C2×#11924005—21no—
34C2×C4×Dic73D412yes—
35#14556498—22no—
36C2×C42×C73C2×C411yescharacteristic
37C2×C42×C73C2×C411yescharacteristic
38C2×C42×C73C2×C411yescharacteristic
39#95×C73—21no—
40#95×C73—21no—
41C2×#10596833—44no—
42C23×D73—21no—
43C2×Dic146—21no—
44C2×Dic146—21no—
45C2×Dic146—41no—
46C2×Dic146—41no—
47C2×D292—21no—
48C2×D292—41no—
49C2×D292—41no—
50C2×D292M1612yes—
51C22×Dic73—21no—
52C22×Dic73C22⋊C412yes—
53C22×Dic73C2×D412yes—
54C2×C4×D73—42no—
55C2×C4×D73—82no—
56C4⋊Dic73—41no—
57C4⋊Dic73—41no—
58C4⋊Dic73—82no—
59#11924007—42no—
60#11924005—28no—
61#11924005—42no—
62#11924005—82no—
63C4×Dic73—22no—
64C4×Dic73—22no—
65C22×C4×C73—21no—
66C22×C4×C73—21no—
67C22×C4×C73C22⋊C411yescharacteristic
68C22×C4×C73C22⋊C411yescharacteristic
69C22×C4×C73C22×C411yescharacteristic
70C42×C73—22no—
71C42×C73—21no—
72C42×C73—41no—
73C42×C73M1612yes—
74C23×C73C2×C22⋊C411yescharacteristic
75C22×D73—22no—
76C22×D73—42no—
77C22×D73—42no—
78C22×D73—41no—
79C22×D73—41no—
80C2×C4×C73—21no—
81C2×C4×C73—21no—
82C2×C4×C73—22no—
83C2×C4×C73—21no—
84C2×C4×C73—41no—
85C2×C4×C73—41no—
86C2×C4×C73—41no—
87C2×C4×C73—41no—
88C2×C4×C73—41no—
89C2×C4×C73—41no—
90C2×C4×C73—41no—
91C2×C4×C73#9912yes—
92C2×C4×C73C2×M1611yescharacteristic
93C2×C4×C73C2×M1611yescharacteristic
94C2×Dic73—22no—
95C2×Dic73—22no—
96C2×Dic73—22no—
97C2×Dic73—22no—
98C2×Dic73—42no—
99C2×Dic73—42no—
100C2×Dic73—41no—
101D292—42no—
102D292—42no—
103C4×D73—84no—
104Dic146—42no—
105Dic146—42no—
106#10596833—84no—
107C22×C73—21no—
108C22×C73—21no—
109C22×C73#40711yescharacteristic
110C22×C73C2×#9911yescharacteristic
111C22×C73#41311yescharacteristic
112C2×D73—44no—
113C2×D73—42no—
114C2×D73—82no—
115C2×D73—81no—
116C2×D73—81no—
117C4×C73—22no—
118C4×C73—21no—
119C4×C73—21no—
120C4×C73—42no—
121C4×C73—41no—
122C4×C73—81no—
123Dic73—42no—
124Dic73—42no—
125Dic73—81no—
126#11534—731nomaximal, Sylow
127C2×C73—21no—
128C2×C73—21no—
129C2×C73#146511yescharacteristic
130C2×C73#212811yescharacteristic
131C2×C73#213311yescharacteristic
132D73—82no—
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—731no—
141#432—1462no—
142#391—731no—
143#390—731no—
144#388—1462no—
145#385—1462no—
146#384—731no—
147#376#6440811yescharacteristic
148#324—734no—
149#324—1462no—
150C22×Q8—731no—
151C22×D4—731no—
152C23×C4—1461no—
153#124—1462no—
154#124—1462no—
155C4×Q8—2922no—
156C4×D4—2922no—
157C2×C4⋊C4—732no—
158C2×C4⋊C4—731no—
159C2×C4⋊C4—731no—
160C2×C4⋊C4—1462no—
161C2×C22⋊C4—1461no—
162C2×C22⋊C4—1462no—
163C2×C22⋊C4—1462no—
164C2×C42—732no—
165C2×C42C2×#6440811yescharacteristic
166C2×C42C2×#6440811yescharacteristic
167C2×C42C2×#6440811yescharacteristic
168C4⋊C8—2922no—
169C22⋊C8—1464no—
170#97—2922no—
171#95—21no—
172#95—21no—
173#95—1462no—
174C24—1461no—
175C2×Q8—2921no—
176C2×Q8—2921no—
177C2×Q8—1461no—
178C2×Q8—1461no—
179C2×D4—2921no—
180C2×D4—2921no—
181C2×D4—732no—
182C2×D4—1461no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—2922no—
186C22×C4—5842no—
187C22×C4—732no—
188C22×C4—732no—
189C22×C4—1461no—
190C22×C4C22⋊#6440811yescharacteristic
191C22×C4C22⋊#6440811yescharacteristic
192C22×C4C22×#6440811yescharacteristic
193C2×C8—2924no—
194C4⋊C4—2921no—
195C4⋊C4—2922no—
196C4⋊C4—2921no—
197C4⋊C4—5842no—
198C22⋊C4—2922no—
199C22⋊C4—5842no—
200C22⋊C4—1468no—
201C42—21no—
202C42—22no—
203C42—41no—
204C42—1462no—
205C42—1462no—
206C42#1192403812yes—
207C23—2922no—
208C23—2922no—
209C23—2921no—
210C23—2921no—
211C23—1462no—
212C23C2×C22⋊#6440811yescharacteristic
213Q8—2922no—
214Q8—2922no—
215D4—2922no—
216D4—2922no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—2922no—
229C2×C4—2922no—
230C2×C4—2921no—
231C2×C4—5844no—
232C2×C4—1462no—
233C2×C4—1462no—
234C2×C4—1462no—
235C2×C4—1462no—
236C2×C4#1455665012yes—
237C2×C4D73⋊M1611yescharacteristic
238C2×C4C2×#1192403811yescharacteristic
239C8—5844no—
240C22—21no—
241C22—21no—
242C22—2924no—
243C22—2922no—
244C22—5842no—
245C22—5841no—
246C22—5841no—
247C22#1798955811yescharacteristic
248C22C2×#1455665011yescharacteristic
249C22#1798957311yescharacteristic
250C4—21no—
251C4—21no—
252C4—22no—
253C4—42no—
254C4—41no—
255C4—81no—
256C4—2922no—
257C4—2922no—
258C4—5841no—
259C2—21no—
260C2—21no—
261C2—5842no—
262C2#2262518811yescharacteristic
263C2#2262621211yescharacteristic
264C2#2262622811yescharacteristic
subgroupG/H
centerC22C2×#14556650
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
Fitting#376×C73C4
socleC22×C73C2×#99
prime radicalC22×D292C2×C4
cosocleC2×C4⋊Dic73C23
hypercenter#376#64408
hypocenterC73#11534
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
1. #22625193C2semidirect
2. #22624873C2semidirect
137. C73#11534semidirect

Maximal subgroups

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

subgroupindex
#226251932
#226248732
#226248602
#226126422
#1153473