Finite Group Databasebeta

← #32995600

Subgroups — #32995600

Order 18688.

444 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 87 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#22614239C211yesmaximal, characteristic
2#22608269C211yesmaximal, characteristic
3#22607860C214yesmaximal, complemented
4C73×#1460C211yesmaximal, characteristic
5C2×#14556572C412yes—
6C22×C4⋊Dic73C411yescharacteristic
7#17988551—21no—
8#17988517—21no—
9#17988512—21no—
10#17988485—21no—
11#17988448C2212yes—
12#17988447—21no—
13#17988447C411yescharacteristic
14#17988313—21no—
15#17988311C2212yes—
16C2×C4×D4×C73C2211yescharacteristic
17#431×C73—21no—
18#323×C73—21no—
19#323×C73C2212yes—
20C23×Dic73C2×C412yes—
21C2×#11924012—41no—
22#14556572—44no—
23C2×C4⋊Dic73—21no—
24C2×C4⋊Dic73—21no—
25C2×C4⋊Dic73—21no—
26C2×C4⋊Dic73—41no—
27C2×C4⋊Dic73—41no—
28C2×#11924007—22no—
29C2×C22⋊Dic73—22no—
30C2×C22⋊Dic73C2×C412yes—
31C22⋊#10596831—22no—
32C22⋊#10596831—41no—
33#14556498—21no—
34#14556498—22no—
35#14556498—22no—
36C22×D4×C73C2×C411yescharacteristic
37C23×C4×C73C2×C411yescharacteristic
38C23×C4×C73D411yescharacteristic
39C4×D4×C73—41no—
40C4×D4×C73—41no—
41C2×C4⋊C4×C73D411yescharacteristic
42C2×C22⋊C4×C73D411yescharacteristic
43C2×C22⋊C4×C73C2311yescharacteristic
44C2×C42×C73D411yescharacteristic
45C4⋊C8×C73—41no—
46C22⋊C8×C73—22no—
47C4×C8×C73—41no—
48C22×Dic73—22no—
49C22×Dic73—22no—
50C22×Dic73—24no—
51C22×Dic73—42no—
52C22×Dic73—42no—
53#11924012—82no—
54C2×#10596831—42no—
55C4⋊Dic73—42no—
56C4⋊Dic73—42no—
57C4⋊Dic73—41no—
58C4⋊Dic73—41no—
59#11924007—44no—
60C22⋊Dic73—44no—
61C22⋊Dic73—42no—
62C24×C73C22⋊C411yescharacteristic
63C24×C73C22×C411yescharacteristic
64C2×D4×C73—22no—
65C2×D4×C73—22no—
66C2×D4×C73—41no—
67C22×C4×C73—21no—
68C22×C4×C73—21no—
69C22×C4×C73—21no—
70C22×C4×C73—21no—
71C22×C4×C73—42no—
72C22×C4×C73—42no—
73C22×C4×C73C22⋊C411yescharacteristic
74C22×C4×C73C22⋊C411yescharacteristic
75C22×C4×C73C22⋊C411yescharacteristic
76C22×C4×C73C2×D411yescharacteristic
77C22×C4×C73C2×D411yescharacteristic
78C2×C8×C73—42no—
79C4⋊C4×C73—41no—
80C22⋊C4×C73—41no—
81C22⋊C4×C73—41no—
82C42×C73—21no—
83C42×C73—21no—
84C23×C73—21no—
85C23×C73—21no—
86C23×C73—21no—
87C23×C73—21no—
88C23×C73—21no—
89C23×C73—41no—
90C23×C73—41no—
91C23×C73—41no—
92C23×C73—41no—
93C23×C73C2×C22⋊C411yescharacteristic
94C23×C73#13112yes—
95D4×C73—44no—
96C2×C4×C73—21no—
97C2×C4×C73—21no—
98C2×C4×C73—22no—
99C2×C4×C73—21no—
100C2×C4×C73—21no—
101C2×C4×C73—21no—
102C2×C4×C73—42no—
103C2×C4×C73—42no—
104C2×C4×C73—42no—
105C2×C4×C73—41no—
106C2×C4×C73—41no—
107C2×C4×C73—41no—
108C2×C4×C73—81no—
109C2×C4×C73#9911yescharacteristic
110C2×C4×C73#9911yescharacteristic
111C2×C4×C73#10012yes—
112C2×Dic73—42no—
113C2×Dic73—42no—
114C2×Dic73—42no—
115C2×Dic73—42no—
116C2×Dic73—42no—
117C2×Dic73—42no—
118C2×Dic73—84no—
119C8×C73—82no—
120#10596831—82no—
121C22×C73—21no—
122C22×C73—21no—
123C22×C73—22no—
124C22×C73—42no—
125C22×C73—42no—
126C22×C73—42no—
127C22×C73—41no—
128C22×C73—41no—
129C22×C73—41no—
130C22×C73—41no—
131C22×C73—41no—
132C22×C73—81no—
133C22×C73#40811yescharacteristic
134C22×C73C2×#9911yescharacteristic
135C22×C73C2×#10011yescharacteristic
136C4×C73—21no—
137C4×C73—22no—
138C4×C73—41no—
139C4×C73—41no—
140C4×C73—41no—
141C4×C73#35212yes—
142Dic73—82no—
143Dic73—82no—
144#11562—731nomaximal, Sylow
145C2×C73—21no—
146C2×C73—21no—
147C2×C73—42no—
148C2×C73—81no—
149C2×C73#147111yescharacteristic
150C2×C73C2×#35211yescharacteristic
151C2×C73#212311yescharacteristic
152#2486—731no—
153#1465—731no—
154#1460D7311yescharacteristic
155#1317—734no—
156C73#1156211yescharacteristic, complemented, Sylow
157C2×#123—732no—
158C2×C4×D4C2×D7311yescharacteristic
159C22×C4⋊C4—731no—
160#431—21no—
161#407—1461no—
162#398—1461no—
163#397—1461no—
164#389—1461no—
165#381—732no—
166#380—731no—
167#380—1461no—
168#324—1461no—
169#323—21no—
170#323—732no—
171#323C2×D7312yes—
172C22×D4C4×D7311yescharacteristic
173C23×C4—732no—
174C23×C4C4×D7311yescharacteristic
175C23×C4D29211yescharacteristic
176C2×M16—2921no—
177#123—2924no—
178C4×D4—41no—
179C4×D4—41no—
180C2×C4⋊C4—2921no—
181C2×C4⋊C4—2921no—
182C2×C4⋊C4—1461no—
183C2×C4⋊C4—1462no—
184C2×C4⋊C4—1461no—
185C2×C4⋊C4—1461no—
186C2×C4⋊C4D29211yescharacteristic
187C2×C22⋊C4—732no—
188C2×C22⋊C4—1462no—
189C2×C22⋊C4C22⋊D7311yescharacteristic
190C2×C22⋊C4C22×D7311yescharacteristic
191C2×C42C22⋊D7311yescharacteristic
192C4⋊C8—41no—
193C22⋊C8—22no—
194C22⋊C8—2921no—
195C22⋊C8—1462no—
196C4×C8—41no—
197#95—1461no—
198#95—1462no—
199#95—1462no—
200C24#1192400511yescharacteristic
201C24C2×C4×D7311yescharacteristic
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—41no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—2922no—
212C22×C4—2922no—
213C22×C4—1462no—
214C22×C4—1462no—
215C22×C4—1464no—
216C22×C4#1192400511yescharacteristic
217C22×C4#1192400511yescharacteristic
218C22×C4#1192400511yescharacteristic
219C22×C4C2×C22⋊D7311yescharacteristic
220C22×C4C2×D29211yescharacteristic
221M16—5842no—
222C2×C8—42no—
223C2×C8—2922no—
224C4⋊C4—41no—
225C4⋊C4—2922no—
226C4⋊C4—2922no—
227C4⋊C4—2921no—
228C4⋊C4—2921no—
229C4⋊C4—2924no—
230C22⋊C4—41no—
231C22⋊C4—41no—
232C22⋊C4—2924no—
233C22⋊C4—2922no—
234C42—21no—
235C42—21no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23—41no—
242C23—41no—
243C23—41no—
244C23—41no—
245C23C2×#1192400511yescharacteristic
246C23#1455659712yes—
247D4—44no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—81no—
261C2×C4—2922no—
262C2×C4—2922no—
263C2×C4—2922no—
264C2×C4—2922no—
265C2×C4—2922no—
266C2×C4—2922no—
267C2×C4—5844no—
268C2×C4#1455650511yescharacteristic
269C2×C4#1455650511yescharacteristic
270C2×C4#1455650712yes—
271C8—82no—
272C8—5842no—
273C22—21no—
274C22—21no—
275C22—22no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—81no—
285C22#1798855311yescharacteristic
286C22C2×#1455650511yescharacteristic
287C22C2×#1455650711yescharacteristic
288C4—21no—
289C4—22no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—5842no—
294C4—5842no—
295C4#1798837812yes—
296C2—21no—
297C2—21no—
298C2—42no—
299C2—81no—
300C2#2260829011yescharacteristic
301C2C2×#1798837811yescharacteristic
302C2#2261158411yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC24×C73C22×C4
FrattiniC2×C22⋊C4C22×D73
FittingC73×#1460C2
socleC22×C73C2×#99
prime radicalC22×D4×C73C2×C4
cosocleC2×C22⋊C4×C73C23
hypercenter#1460D73
hypocenterC73#11562
LCSG ▷ C24×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1460

Complements

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

NH ≅ G/Ntype
3. #22607860C2semidirect
156. C73#11562semidirect

Maximal subgroups

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

subgroupindex
#226142392
#226082692
#226078602
C73×#14602
#1156273