Finite Group Databasebeta

← #34010153

Subgroups — #34010153

Order 18688.

444 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 78 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#22624871C212yesmaximal, complemented
3#22624860C212yesmaximal
4C4×#14556579C211yesmaximal, characteristic
5#17989608—22no—
6#17989433—22no—
7#17989432C2214yes—
8C2×#14556579C411yescharacteristic
9C2×C4×Dic146C2211yescharacteristic
10C2×C4×D292C411yescharacteristic
11#17988493C411yescharacteristic
12#17988489C2211yescharacteristic
13#17988478—22no—
14#17988453C2211yescharacteristic
15C4×#11924005—22no—
16C43×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—41no—
26C4×Dic146—41no—
27C4×D292—41no—
28C4×D292—41no—
29C2×C4⋊Dic73C2×C411yescharacteristic
30C2×C4⋊Dic73C2311yescharacteristic
31C2×#11924007D412yes—
32C2×#11924005—22no—
33C2×#11924005—22no—
34C2×#11924005—21no—
35C2×C4×Dic73D412yes—
36#14556498—22no—
37#14556498—22no—
38C2×C42×C73—21no—
39C2×C42×C73—21no—
40C2×C42×C73C2×C411yescharacteristic
41C2×C42×C73C2×C411yescharacteristic
42C2×C42×C73C2×C411yescharacteristic
43C2×#10596833—44no—
44C23×D73—21no—
45C2×Dic146—21no—
46C2×Dic146—21no—
47C2×Dic146—41no—
48C2×Dic146—41no—
49C2×D292—21no—
50C2×D292—41no—
51C2×D292—41no—
52C2×D292M1612yes—
53C22×Dic73—21no—
54C22×Dic73C22⋊C412yes—
55C22×Dic73C2×D412yes—
56C2×C4×D73—44no—
57C2×C4×D73—41no—
58C2×C4×D73—41no—
59C4⋊Dic73—41no—
60C4⋊Dic73—41no—
61#11924007—42no—
62#11924005—28no—
63#11924005—44no—
64#11924005—42no—
65C4×Dic73—22no—
66C4×Dic73—22no—
67C22×C4×C73—21no—
68C22×C4×C73—21no—
69C22×C4×C73C22⋊C411yescharacteristic
70C22×C4×C73C22⋊C411yescharacteristic
71C22×C4×C73C22×C411yescharacteristic
72C42×C73—21no—
73C42×C73—21no—
74C42×C73—21no—
75C42×C73—41no—
76C42×C73—42no—
77C42×C73—42no—
78C42×C73M1612yes—
79C23×C73C2×C22⋊C411yescharacteristic
80C22×D73—22no—
81C22×D73—42no—
82C22×D73—42no—
83C22×D73—41no—
84C22×D73—41no—
85C2×C4×C73—21no—
86C2×C4×C73—21no—
87C2×C4×C73—22no—
88C2×C4×C73—22no—
89C2×C4×C73—22no—
90C2×C4×C73—21no—
91C2×C4×C73—41no—
92C2×C4×C73—41no—
93C2×C4×C73—41no—
94C2×C4×C73—41no—
95C2×C4×C73—41no—
96C2×C4×C73#9911yescharacteristic
97C2×C4×C73#9911yescharacteristic
98C2×C4×C73C2×M1611yescharacteristic
99C2×C4×C73C2×M1611yescharacteristic
100C2×Dic73—22no—
101C2×Dic73—22no—
102C2×Dic73—22no—
103C2×Dic73—22no—
104C2×Dic73—42no—
105C2×Dic73—42no—
106C2×Dic73—41no—
107D292—42no—
108D292—42no—
109C4×D73—82no—
110C4×D73—82no—
111Dic146—42no—
112Dic146—42no—
113#10596833—84no—
114C22×C73—21no—
115C22×C73—21no—
116C22×C73#40711yescharacteristic
117C22×C73C2×#9911yescharacteristic
118C22×C73#41311yescharacteristic
119C2×D73—44no—
120C2×D73—42no—
121C2×D73—82no—
122C2×D73—81no—
123C2×D73—81no—
124C4×C73—21no—
125C4×C73—21no—
126C4×C73—21no—
127C4×C73—42no—
128C4×C73—42no—
129C4×C73—41no—
130C4×C73#35512yes—
131Dic73—42no—
132Dic73—42no—
133Dic73—81no—
134#11530—731nomaximal, Sylow
135C2×C73—21no—
136C2×C73—21no—
137C2×C73#146511yescharacteristic
138C2×C73#212611yescharacteristic
139C2×C73C2×#35511yescharacteristic
140D73—82no—
141C4×#124—731no—
142#1467—732no—
143#1324—732no—
144#1318—732no—
145C73#1153011yescharacteristic, complemented, Sylow
146C2×#124—731no—
147C2×C4×Q8—731no—
148C2×C4×D4—731no—
149#432—1462no—
150#391—731no—
151#390—731no—
152#388—1462no—
153#382—731no—
154C4×C22⋊C4—1462no—
155C43#6440811yescharacteristic
156#324—734no—
157#324—1462no—
158C22×Q8—731no—
159C22×D4—731no—
160C23×C4—1461no—
161#124—1462no—
162#124—1462no—
163C4×Q8—2921no—
164C4×Q8—2921no—
165C4×D4—2921no—
166C4×D4—2921no—
167C2×C4⋊C4—732no—
168C2×C4⋊C4—731no—
169C2×C4⋊C4—731no—
170C2×C22⋊C4—1462no—
171C2×C22⋊C4—1461no—
172C2×C22⋊C4—1462no—
173C2×C42—21no—
174C2×C42—21no—
175C2×C42—732no—
176C2×C42C2×#6440811yescharacteristic
177C2×C42C2×#6440811yescharacteristic
178C2×C42C2×#6440811yescharacteristic
179C4⋊C8—2922no—
180C22⋊C8—1464no—
181#97—2922no—
182#95—1462no—
183#95—1462no—
184C24—1461no—
185C2×Q8—2921no—
186C2×Q8—2921no—
187C2×Q8—1461no—
188C2×Q8—1461no—
189C2×D4—2921no—
190C2×D4—2921no—
191C2×D4—732no—
192C2×D4—1461no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—2924no—
196C22×C4—2921no—
197C22×C4—2921no—
198C22×C4—732no—
199C22×C4—732no—
200C22×C4—1461no—
201C22×C4C22⋊#6440811yescharacteristic
202C22×C4C22⋊#6440811yescharacteristic
203C22×C4C22×#6440811yescharacteristic
204C2×C8—2924no—
205C4⋊C4—2921no—
206C4⋊C4—2922no—
207C4⋊C4—2921no—
208C22⋊C4—2924no—
209C22⋊C4—2922no—
210C22⋊C4—1468no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—41no—
215C42—42no—
216C42—42no—
217C42—1462no—
218C42—1462no—
219C42#1192403812yes—
220C23—2922no—
221C23—2922no—
222C23—2921no—
223C23—2921no—
224C23—1462no—
225C23C2×C22⋊#6440811yescharacteristic
226Q8—2922no—
227Q8—2922no—
228D4—2922no—
229D4—2922no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—2922no—
242C2×C4—2922no—
243C2×C4—2921no—
244C2×C4—5842no—
245C2×C4—5842no—
246C2×C4—1462no—
247C2×C4—1462no—
248C2×C4—1462no—
249C2×C4—1462no—
250C2×C4#1455665011yescharacteristic
251C2×C4#1455665011yescharacteristic
252C2×C4D73⋊M1611yescharacteristic
253C2×C4C2×#1192403811yescharacteristic
254C8—5844no—
255C22—21no—
256C22—21no—
257C22—2924no—
258C22—2922no—
259C22—5842no—
260C22—5841no—
261C22—5841no—
262C22#1798955811yescharacteristic
263C22C2×#1455665011yescharacteristic
264C22#1798957311yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—42no—
269C4—42no—
270C4—41no—
271C4—2922no—
272C4—2922no—
273C4—5841no—
274C4#1798949612yes—
275C2—21no—
276C2—21no—
277C2—5842no—
278C2#2262518811yescharacteristic
279C2#2262620411yescharacteristic
280C2C2×#1798949611yescharacteristic
subgroupG/H
centerC22C2×#14556650
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
FittingC43×C73C4
socleC22×C73C2×#99
prime radicalC22×D292C2×C4
cosocleC2×C4⋊Dic73C23
hypercenterC43#64408
hypocenterC73#11530
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C43

Complements

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

NH ≅ G/Ntype
1. #22625193C2semidirect
2. #22624871C2semidirect
145. C73#11530semidirect

Maximal subgroups

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

subgroupindex
#226251932
#226248712
#226248602
C4×#145565792
#1153073