Finite Group Databasebeta

← #32983663

Subgroups — #32983663

Order 18688.

518 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 107 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#22614923C211yesmaximal, characteristic
2#22608656C212yesmaximal, complemented
3#22608272C211yesmaximal, characteristic
4#22607788C212yesmaximal, complemented
5C73×#2973C211yesmaximal, characteristic
6C2×#14556591C2211yescharacteristic
7C2×#14556578C412yes—
8#17988644C2212yes—
9#17988512—21no—
10#17988512—21no—
11#17988492C412yes—
12#17988447—21no—
13#17988447—21no—
14C4×C4⋊Dic73C2211yescharacteristic
15#17988335—24no—
16#17988311—21no—
17#17988311—21no—
18C2×C4×D4×C73C2211yescharacteristic
19#435×C73—24no—
20#432×C73C2212yes—
21#407×C73—21no—
22C2×C22⋊C8×C73—21no—
23C22×Dic146C2×C412yes—
24#14556591—22no—
25#14556591—22no—
26#14556578—44no—
27C2×C4⋊Dic73—21no—
28C2×C4⋊Dic73—21no—
29C2×C4⋊Dic73—21no—
30C2×C22⋊Dic73—22no—
31C2×C22⋊Dic73—22no—
32C2×C4×Dic73C2×C412yes—
33C4⋊#10596831—22no—
34C22⋊#10596831—22no—
35#14556502—22no—
36#14556498—22no—
37#14556498—22no—
38#14556498—21no—
39C22×D4×C73C2×C411yescharacteristic
40C23×C4×C73D411yescharacteristic
41C23×C4×C73D411yescharacteristic
42C2×M16×C73—22no—
43C22×C8×C73—22no—
44C4×D4×C73—22no—
45C4×D4×C73—22no—
46C2×C4⋊C4×C73C2×C411yescharacteristic
47C2×C22⋊C4×C73D411yescharacteristic
48C2×C22⋊C4×C73D411yescharacteristic
49C2×C42×C73C2311yescharacteristic
50C4⋊C8×C73D414yes—
51C22⋊C8×C73—22no—
52C22⋊C8×C73—22no—
53C22⋊C8×C73—22no—
54#97×C73—22no—
55C2×Dic146—24no—
56C2×Dic146—42no—
57C2×Dic146—42no—
58C22×Dic73—22no—
59C22×Dic73—22no—
60C2×#10596831—42no—
61C4⋊Dic73—42no—
62C4⋊Dic73—41no—
63C4⋊Dic73—42no—
64C4⋊Dic73—41no—
65C22⋊Dic73—44no—
66C22⋊Dic73—44no—
67C4×Dic73—42no—
68C24×C73C22⋊C411yescharacteristic
69C24×C73C22⋊C411yescharacteristic
70C2×D4×C73—22no—
71C2×D4×C73—22no—
72C2×D4×C73—41no—
73C22×C4×C73—21no—
74C22×C4×C73—21no—
75C22×C4×C73—21no—
76C22×C4×C73—21no—
77C22×C4×C73—42no—
78C22×C4×C73—42no—
79C22×C4×C73C22⋊C411yescharacteristic
80C22×C4×C73C22⋊C411yescharacteristic
81C22×C4×C73C22×C411yescharacteristic
82C22×C4×C73C2×D411yescharacteristic
83C22×C4×C73C2×D411yescharacteristic
84M16×C73—82no—
85C2×C8×C73—24no—
86C2×C8×C73—82no—
87C4⋊C4×C73—22no—
88C22⋊C4×C73—22no—
89C22⋊C4×C73—22no—
90C42×C73C2×D412yes—
91C42×C73#4112yes—
92C23×C73—21no—
93C23×C73—21no—
94C23×C73—21no—
95C23×C73—21no—
96C23×C73—21no—
97C23×C73—41no—
98C23×C73—41no—
99C23×C73—41no—
100C23×C73—41no—
101C23×C73#10012yes—
102C23×C73C2×C22⋊C411yescharacteristic
103D4×C73—44no—
104C2×C4×C73—21no—
105C2×C4×C73—21no—
106C2×C4×C73—22no—
107C2×C4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73—41no—
110C2×C4×C73—42no—
111C2×C4×C73—42no—
112C2×C4×C73—41no—
113C2×C4×C73—41no—
114C2×C4×C73—81no—
115C2×C4×C73—81no—
116C2×C4×C73C4×D412yes—
117C2×C4×C73#12011yescharacteristic
118C2×C4×C73#12112yes—
119C2×C4×C73#12311yescharacteristic
120C2×Dic73—42no—
121C2×Dic73—42no—
122C2×Dic73—42no—
123C2×Dic73—42no—
124C2×Dic73—42no—
125C2×Dic73—42no—
126Dic146—84no—
127C8×C73—44no—
128#10596831—82no—
129C22×C73—21no—
130C22×C73—21no—
131C22×C73—22no—
132C22×C73—42no—
133C22×C73—42no—
134C22×C73—41no—
135C22×C73—41no—
136C22×C73—41no—
137C22×C73—41no—
138C22×C73—41no—
139C22×C73—81no—
140C22×C73—81no—
141C22×C73#38611yescharacteristic
142C22×C73C2×#10011yescharacteristic
143C22×C73#41311yescharacteristic
144C4×C73—21no—
145C4×C73—22no—
146C4×C73—22no—
147C4×C73—41no—
148C4×C73—41no—
149C4×C73#45512yes—
150Dic73—82no—
151Dic73—82no—
152#9451—731nomaximal, Sylow
153C2×C73—21no—
154C2×C73—21no—
155C2×C73—42no—
156C2×C73—81no—
157C2×C73#188511yescharacteristic
158C2×C73#190011yescharacteristic
159C2×C73#190911yescharacteristic
160#2973D7311yescharacteristic
161#2547—731no—
162#1558—732no—
163#1466—731no—
164#1285—732no—
165C73#945111yescharacteristic, complemented, Sylow
166C2×C4⋊Q8—731no—
167C2×#124—732no—
168C2×C4×D4C2×D7311yescharacteristic
169#435—24no—
170#432—732no—
171#432C2×D7312yes—
172#407—21no—
173C2×C22⋊C8—21no—
174#397—1461no—
175#397—1461no—
176#391—732no—
177#380—1461no—
178#380—1461no—
179C4×C4⋊C4—731no—
180#333—1464no—
181#323—1461no—
182#323—1461no—
183C22×Q8—732no—
184C22×D4C4×D7311yescharacteristic
185C23×C4C22⋊D7311yescharacteristic
186C23×C4C22⋊D7311yescharacteristic
187C2×M16—22no—
188C22×C8—22no—
189C4⋊Q8—1462no—
190C4⋊Q8—1462no—
191#124—2924no—
192C4×D4—22no—
193C4×D4—22no—
194C2×C4⋊C4—1461no—
195C2×C4⋊C4—1461no—
196C2×C4⋊C4—1461no—
197C2×C4⋊C4C4×D7311yescharacteristic
198C2×C22⋊C4—1462no—
199C2×C22⋊C4—1462no—
200C2×C22⋊C4D29211yescharacteristic
201C2×C22⋊C4D29211yescharacteristic
202C2×C42—732no—
203C2×C42C22×D7311yescharacteristic
204C4⋊C8—1462no—
205C4⋊C8C22⋊D7314yes—
206C22⋊C8—22no—
207C22⋊C8—22no—
208C22⋊C8—22no—
209C22⋊C8—1462no—
210#97—22no—
211#97—1462no—
212#95—1462no—
213#95—1462no—
214#95—1461no—
215C24#1192400511yescharacteristic
216C24#1192400511yescharacteristic
217C2×Q8—2922no—
218C2×Q8—2922no—
219C2×Q8—1464no—
220C2×D4—22no—
221C2×D4—22no—
222C2×D4—41no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—1462no—
230C22×C4—1462no—
231C22×C4#1192400511yescharacteristic
232C22×C4#1192400511yescharacteristic
233C22×C4C2×C4×D7311yescharacteristic
234C22×C4C2×C22⋊D7311yescharacteristic
235C22×C4C2×D29211yescharacteristic
236M16—82no—
237C2×C8—24no—
238C2×C8—82no—
239C2×C8—2922no—
240C4⋊C4—22no—
241C4⋊C4—2922no—
242C4⋊C4—2921no—
243C4⋊C4—2922no—
244C4⋊C4—2921no—
245C22⋊C4—22no—
246C22⋊C4—22no—
247C22⋊C4—2924no—
248C22⋊C4—2924no—
249C42—2922no—
250C42C2×C22⋊D7312yes—
251C42#1192402812yes—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—41no—
258C23—41no—
259C23—41no—
260C23—41no—
261C23#1455650712yes—
262C23C2×#1192400511yescharacteristic
263Q8—5844no—
264D4—44no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—2922no—
278C2×C4—2922no—
279C2×C4—2922no—
280C2×C4—2922no—
281C2×C4—2922no—
282C2×C4—2922no—
283C2×C4C4×C22⋊D7312yes—
284C2×C4#1455656011yescharacteristic
285C2×C4#1455656512yes—
286C2×C4#1455657411yescharacteristic
287C8—44no—
288C8—5842no—
289C22—21no—
290C22—21no—
291C22—22no—
292C22—42no—
293C22—42no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22—81no—
300C22—81no—
301C22#1798846611yescharacteristic
302C22C2×#1455650711yescharacteristic
303C22#1798856911yescharacteristic
304C4—22no—
305C4—21no—
306C4—22no—
307C4—41no—
308C4—41no—
309C4—5842no—
310C4—5842no—
311C4#1798876512yes—
312C2—21no—
313C2—21no—
314C2—42no—
315C2—81no—
316C2#2261031911yescharacteristic
317C2#2261039411yescharacteristic
318C2#2261045311yescharacteristic
subgroupG/H
centerC22#17988466
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#2973C2
socleC22×C73#386
prime radicalC22×D4×C73C2×C4
cosocleC2×C42×C73C23
hypercenter#2973D73
hypocenterC73#9451
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #22608656C2semidirect
4. #22607788C2semidirect
165. C73#9451semidirect

Maximal subgroups

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

subgroupindex
#226149232
#226086562
#226082722
#226077882
C73×#29732
#945173