Finite Group Databasebeta

← #32995640

Subgroups — #32995640

Order 18688.

350 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 91 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#22608275C211yesmaximal, characteristic
2#22608255C211yesmaximal, characteristic
3#22607877C212yesmaximal
4#22607875C212yesmaximal
5C73×#2565C211yesmaximal, characteristic
6#17988644—21no—
7#17988640—21no—
8#17988313—21no—
9#17988313—21no—
10#17988313C2212yes—
11#17988313C2212yes—
12C2×#125×C73C411yescharacteristic
13C2×C4×Q8×C73C2211yescharacteristic
14#398×C73—21no—
15#398×C73—21no—
16#391×C73C411yescharacteristic
17#391×C73C411yescharacteristic
18#387×C73—21no—
19#387×C73—21no—
20#384×C73C2211yescharacteristic
21#382×C73C2211yescharacteristic
22C4×C4⋊C4×C73C411yescharacteristic
23C4⋊#10596831—41no—
24C4⋊#10596831—41no—
25C22⋊#10596831—22no—
26C22⋊#10596831—22no—
27#14556502—41no—
28C4×#10596831—41no—
29C22×Q8×C73C2×C411yescharacteristic
30#125×C73—41no—
31#125×C73—41no—
32C4×Q8×C73—41no—
33C4×Q8×C73—41no—
34C2×C4⋊C4×C73—21no—
35C2×C4⋊C4×C73—21no—
36C2×C4⋊C4×C73—21no—
37C2×C4⋊C4×C73—21no—
38C2×C4⋊C4×C73—21no—
39C2×C4⋊C4×C73C2×C411yescharacteristic
40C2×C4⋊C4×C73C2×C411yescharacteristic
41C2×C4⋊C4×C73D411yescharacteristic
42C2×C4⋊C4×C73D411yescharacteristic
43C2×C4⋊C4×C73C2311yescharacteristic
44C2×C42×C73C2×C411yescharacteristic
45C2×C42×C73C2×C411yescharacteristic
46C2×C42×C73C2×C411yescharacteristic
47C2×C42×C73D411yescharacteristic
48C2×C42×C73D411yescharacteristic
49#95×C73—21no—
50#95×C73—21no—
51#95×C73—21no—
52#95×C73—21no—
53#95×C73—21no—
54#95×C73—21no—
55#95×C73—21no—
56C2×#10596831—42no—
57C2×#10596831—42no—
58C2×Q8×C73—22no—
59C2×Q8×C73—22no—
60C2×Q8×C73—41no—
61C22×C4×C73—21no—
62C22×C4×C73—21no—
63C22×C4×C73—21no—
64C22×C4×C73—21no—
65C22×C4×C73C22⋊C411yescharacteristic
66C22×C4×C73C22⋊C411yescharacteristic
67C22×C4×C73C22⋊C411yescharacteristic
68C22×C4×C73C22⋊C411yescharacteristic
69C22×C4×C73C22×C411yescharacteristic
70C22×C4×C73C2×D411yescharacteristic
71C22×C4×C73C2×D411yescharacteristic
72C4⋊C4×C73—41no—
73C4⋊C4×C73—41no—
74C4⋊C4×C73—41no—
75C4⋊C4×C73—41no—
76C4⋊C4×C73—41no—
77C4⋊C4×C73—42no—
78C4⋊C4×C73—42no—
79C4⋊C4×C73—42no—
80C4⋊C4×C73—42no—
81C4⋊C4×C73—41no—
82C4⋊C4×C73—41no—
83C42×C73—21no—
84C42×C73—21no—
85C42×C73—21no—
86C42×C73—21no—
87C42×C73—21no—
88C42×C73—21no—
89C42×C73—22no—
90C42×C73—22no—
91C23×C73C2×C22⋊C411yescharacteristic
92Q8×C73—44no—
93C2×C4×C73—21no—
94C2×C4×C73—21no—
95C2×C4×C73—21no—
96C2×C4×C73—21no—
97C2×C4×C73—22no—
98C2×C4×C73—21no—
99C2×C4×C73—21no—
100C2×C4×C73—21no—
101C2×C4×C73—21no—
102C2×C4×C73—21no—
103C2×C4×C73—21no—
104C2×C4×C73—41no—
105C2×C4×C73—41no—
106C2×C4×C73—41no—
107C2×C4×C73—41no—
108C2×C4×C73—41no—
109C2×C4×C73—41no—
110C2×C4×C73—41no—
111C2×C4×C73—41no—
112C2×C4×C73—41no—
113C2×C4×C73—41no—
114C2×C4×C73—42no—
115C2×C4×C73—41no—
116C2×C4×C73—41no—
117C2×C4×C73—41no—
118C2×C4×C73#9911yescharacteristic
119C2×C4×C73#9911yescharacteristic
120C2×C4×C73#10112yes—
121C2×C4×C73#13112yes—
122#10596831—82no—
123#10596831—82no—
124C22×C73—21no—
125C22×C73—21no—
126C22×C73#40811yescharacteristic
127C22×C73C2×#9911yescharacteristic
128C22×C73C2×#10111yescharacteristic
129C4×C73—21no—
130C4×C73—21no—
131C4×C73—22no—
132C4×C73—22no—
133C4×C73—42no—
134C4×C73—41no—
135C4×C73—41no—
136C4×C73—41no—
137C4×C73—41no—
138C4×C73—81no—
139C4×C73—81no—
140C4×C73—81no—
141#11571—731nomaximal, Sylow
142C2×C73—21no—
143C2×C73—21no—
144C2×C73#147211yescharacteristic
145C2×C73#212611yescharacteristic
146C2×C73#213311yescharacteristic
147#2565D7311yescharacteristic
148#1467—731no—
149#1461—731no—
150#1325—732no—
151#1324—732no—
152C73#1157111yescharacteristic, complemented, Sylow
153C2×#125Dic7311yescharacteristic
154C2×C4×Q8C2×D7311yescharacteristic
155#432—1461no—
156#431—1461no—
157#398—21no—
158#398—21no—
159#391Dic7311yescharacteristic
160#391Dic7311yescharacteristic
161#387—21no—
162#387—21no—
163#384C2×D7311yescharacteristic
164#382C2×D7311yescharacteristic
165C4×C4⋊C4Dic7311yescharacteristic
166#324—732no—
167#324—732no—
168#324—1461no—
169#324—1461no—
170C22×Q8C2×Dic7311yescharacteristic
171#125—41no—
172#125—41no—
173C4×Q8—41no—
174C4×Q8—41no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4C2×Dic7311yescharacteristic
181C2×C4⋊C4C2×Dic7311yescharacteristic
182C2×C4⋊C4C22⋊D7311yescharacteristic
183C2×C4⋊C4C22⋊D7311yescharacteristic
184C2×C4⋊C4C22×D7311yescharacteristic
185C2×C42C2×Dic7311yescharacteristic
186C2×C42C2×Dic7311yescharacteristic
187C2×C42C2×Dic7311yescharacteristic
188C2×C42C22⋊D7311yescharacteristic
189C2×C42C22⋊D7311yescharacteristic
190C4⋊C8—2921no—
191C4⋊C8—2921no—
192C22⋊C8—1462no—
193C22⋊C8—1462no—
194#97—2921no—
195C4×C8—2921no—
196#95—21no—
197#95—21no—
198#95—21no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95—21no—
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8—41no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4C22⋊Dic7311yescharacteristic
211C22×C4C22⋊Dic7311yescharacteristic
212C22×C4C22⋊Dic7311yescharacteristic
213C22×C4C22⋊Dic7311yescharacteristic
214C22×C4C22×Dic7311yescharacteristic
215C22×C4C2×C22⋊D7311yescharacteristic
216C22×C4C2×C22⋊D7311yescharacteristic
217C2×C8—2922no—
218C2×C8—2922no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—22no—
237C42—22no—
238C23C2×C22⋊Dic7311yescharacteristic
239Q8—44no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—42no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4#1455650611yescharacteristic
266C2×C4#1455650611yescharacteristic
267C2×C4#1455651012yes—
268C2×C4#1455659812yes—
269C8—5842no—
270C8—5842no—
271C22—21no—
272C22—21no—
273C22#1798855411yescharacteristic
274C22C2×#1455650611yescharacteristic
275C22C2×#1455651011yescharacteristic
276C4—21no—
277C4—21no—
278C4—22no—
279C4—22no—
280C4—42no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—41no—
285C4—81no—
286C4—81no—
287C4—81no—
288C2—21no—
289C2—21no—
290C2#2260829511yescharacteristic
291C2#2261159611yescharacteristic
292C2#2261162011yescharacteristic
subgroupG/H
centerC22C2×#14556506
commutatorC22×C4×C73C22×C4
FrattiniC2×C4⋊C4C22×D73
FittingC73×#2565C2
socleC22×C73C2×#99
prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4⋊C4×C73C23
hypercenter#2565D73
hypocenterC73#11571
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2565

Complements

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

NH ≅ G/Ntype
152. C73#11571semidirect

Maximal subgroups

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

subgroupindex
#226082752
#226082552
#226078772
#226078752
C73×#25652
#1157173