Finite Group Databasebeta

← #34011073

Subgroups — #34011073

Order 18688.

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

normal subgroups only

This group has 394 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
1C4×#14556652C211yesmaximal, characteristic
2#22625193C211yesmaximal, characteristic
3#22624931C214yesmaximal
4#22615139C211yesmaximal, characteristic
5#17989608—21no—
6C2×#14556652—21no—
7C4×#11924037—21no—
8#17989467C2212yes—
9#17989433C2212yes—
10#17989432—21no—
11C2×#14556591C411yescharacteristic
12C2×C4×Dic146C2211yescharacteristic
13#17988508C412yes—
14#17988508C2212yes—
15#17988493—21no—
16#17988486—21no—
17#17988486—21no—
18#17988457—21no—
19C4×C4⋊C4×C73C411yescharacteristic
20C2×#11924037—22no—
21C4⋊#10596833—41no—
22#14556652—24no—
23C22⋊#10596833—22no—
24#14556646—41no—
25#14556646—41no—
26C4×#10596833—41no—
27C22×Dic146C2×C412yes—
28C22×Dic146D411yescharacteristic
29#14556591—41no—
30#14556591—41no—
31C4×Dic146—41no—
32C4×Dic146—41no—
33C2×C4⋊Dic73—22no—
34C2×C4⋊Dic73—22no—
35C2×C4⋊Dic73—21no—
36C2×C4⋊Dic73—21no—
37C2×C4⋊Dic73D411yescharacteristic
38C2×#11924007C2×C411yescharacteristic
39C2×#11924007C2311yescharacteristic
40C2×C4×Dic73D411yescharacteristic
41C2×C4×Dic73D411yescharacteristic
42#14556498—22no—
43#14556498—22no—
44C2×C4⋊C4×C73—21no—
45C2×C42×C73—21no—
46C2×C42×C73C2×C411yescharacteristic
47#95×C73C2×C412yes—
48#11924037—24no—
49#11924037—42no—
50C2×#10596833—42no—
51C2×#10596833—42no—
52C2×Dic146—22no—
53C2×Dic146—22no—
54C2×Dic146—41no—
55C2×Dic146—42no—
56C2×Dic146—82no—
57C22×Dic73—22no—
58C22×Dic73C22⋊C411yescharacteristic
59C22×Dic73C22⋊C411yescharacteristic
60C22×Dic73C2×D411yescharacteristic
61C22×Dic73C2×D411yescharacteristic
62C4⋊Dic73—41no—
63C4⋊Dic73—42no—
64C4⋊Dic73—41no—
65C4⋊Dic73—41no—
66C4⋊Dic73—82no—
67C4⋊Dic73—82no—
68#11924007—41no—
69#11924007—41no—
70C4×Dic73—21no—
71C4×Dic73—21no—
72C4×Dic73—21no—
73C4×Dic73—21no—
74C22×C4×C73—22no—
75C22×C4×C73C22⋊C411yescharacteristic
76C22×C4×C73C22⋊C411yescharacteristic
77C22×C4×C73C22×C411yescharacteristic
78C4⋊C4×C73—24no—
79C42×C73—21no—
80C42×C73—21no—
81C42×C73—42no—
82C23×C73C2×C22⋊C411yescharacteristic
83C2×C4×C73—21no—
84C2×C4×C73—21no—
85C2×C4×C73—22no—
86C2×C4×C73—24no—
87C2×C4×C73—21no—
88C2×C4×C73—42no—
89C2×C4×C73—42no—
90C2×C4×C73—41no—
91C2×C4×C73#9911yescharacteristic
92C2×C4×C73#9911yescharacteristic
93C2×C4×C73#10412yes—
94C2×Dic73—21no—
95C2×Dic73—21no—
96C2×Dic73—21no—
97C2×Dic73—21no—
98C2×Dic73—21no—
99C2×Dic73—21no—
100C2×Dic73—21no—
101C2×Dic73—41no—
102C2×Dic73—41no—
103C2×Dic73—42no—
104C2×Dic73—42no—
105C2×Dic73—42no—
106C2×Dic73#13712yes—
107Dic146—44no—
108Dic146—84no—
109#10596833—44no—
110#10596833—82no—
111C22×C73—21no—
112C22×C73—21no—
113C22×C73C2×#9911yescharacteristic
114C22×C73#41911yescharacteristic
115C22×C73C2×#10411yescharacteristic
116C4×C73—21no—
117C4×C73—22no—
118C4×C73—44no—
119C4×C73—41no—
120C4×C73#35612yes—
121Dic73—22no—
122Dic73—41no—
123Dic73—41no—
124Dic73—41no—
125Dic73—82no—
126#11795—731nomaximal, Sylow
127C2×C73—21no—
128C2×C73—21no—
129C2×C73#150811yescharacteristic
130C2×C73#212211yescharacteristic
131C2×C73C2×#35611yescharacteristic
132#2567—731no—
133C4×#101—731no—
134#1467—731no—
135#1354—734no—
136C73#1179511yescharacteristic, complemented, Sylow
137C2×C4⋊Q8—731no—
138C2×C4×Q8—731no—
139#432—1461no—
140C2×#101—1461no—
141C4×M16—1461no—
142#395—732no—
143#395—732no—
144#391—1461no—
145#389—1461no—
146#389—1461no—
147#384—1461no—
148C4×C4⋊C4#6440811yescharacteristic
149#343—732no—
150#324—732no—
151#324—1461no—
152C22×Q8—731no—
153C22×Q8—732no—
154C2×M16—1462no—
155C4⋊Q8—2921no—
156C4⋊Q8—2921no—
157C4×Q8—2921no—
158C4×Q8—2921no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—731no—
161C2×C4⋊C4—731no—
162C2×C4⋊C4—731no—
163C2×C4⋊C4—1461no—
164C2×C4⋊C4—1461no—
165C2×C4⋊C4—1462no—
166C2×C4⋊C4—1462no—
167C2×C42—21no—
168C2×C42—731no—
169C2×C42—731no—
170C2×C42C2×#6440811yescharacteristic
171C4⋊C8—2921no—
172#101—1464no—
173C22⋊C8—1462no—
174#97—2921no—
175#97—2921no—
176C4×C8—2921no—
177#95—1462no—
178#95—1462no—
179#95C2×#6440812yes—
180C2×Q8—2922no—
181C2×Q8—2921no—
182C2×Q8—5842no—
183C2×Q8—1462no—
184C2×Q8—1462no—
185C22×C4—22no—
186C22×C4—731no—
187C22×C4—731no—
188C22×C4—731no—
189C22×C4—731no—
190C22×C4—1462no—
191C22×C4C22⋊#6440811yescharacteristic
192C22×C4C22⋊#6440811yescharacteristic
193C22×C4C22×#6440811yescharacteristic
194M16—2922no—
195M16—1464no—
196C2×C8—2922no—
197C2×C8—2922no—
198C4⋊C4—24no—
199C4⋊C4—2922no—
200C4⋊C4—2921no—
201C4⋊C4—2921no—
202C4⋊C4—2921no—
203C4⋊C4—2921no—
204C4⋊C4—2921no—
205C4⋊C4—5842no—
206C4⋊C4—5842no—
207C42—21no—
208C42—21no—
209C42—42no—
210C42—1461no—
211C42—1461no—
212C42—1461no—
213C42—1461no—
214C23C2×C22⋊#6440811yescharacteristic
215Q8—2924no—
216Q8—5844no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—24no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—41no—
225C2×C4—2921no—
226C2×C4—2921no—
227C2×C4—2922no—
228C2×C4—2922no—
229C2×C4—2922no—
230C2×C4—732no—
231C2×C4—1461no—
232C2×C4—1461no—
233C2×C4—1461no—
234C2×C4—1461no—
235C2×C4—1461no—
236C2×C4—1461no—
237C2×C4—1461no—
238C2×C4#1455665011yescharacteristic
239C2×C4#1455665011yescharacteristic
240C2×C4#1455665512yes—
241C8—2924no—
242C8—5842no—
243C22—21no—
244C22—21no—
245C22C2×#1455665011yescharacteristic
246C22#1798958011yescharacteristic
247C22C2×#1455665511yescharacteristic
248C4—22no—
249C4—21no—
250C4—44no—
251C4—41no—
252C4—2921no—
253C4—2921no—
254C4—2921no—
255C4—5842no—
256C4—1462no—
257C4#1798949812yes—
258C2—21no—
259C2—21no—
260C2#2262533011yescharacteristic
261C2#2262619211yescharacteristic
262C2C2×#1798949811yescharacteristic
subgroupG/H
centerC22C2×#14556650
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
FittingC4×C4⋊C4×C73C4
socleC22×C73C2×#99
prime radicalC23×C73C2×C22⋊C4
cosocleC2×#11924007C23
hypercenterC4×C4⋊C4#64408
hypocenterC73#11795
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
136. C73#11795semidirect

Maximal subgroups

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

subgroupindex
C4×#145566522
#226251932
#226249312
#226151392
#1179573