Finite Group Databasebeta

← #1324×D73 #32995133

Subgroups — #1324×D73 #32995133

Order 18688.

510 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 101 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#382×D73C211yesmaximal, characteristic
2#324×D73C212yesmaximal
3#22607875C211yesmaximal, characteristic, complemented
4#22607874C212yesmaximal, complemented
5C73×#1324C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×D73C411yescharacteristic
7C2×C4⋊C4×D73C2211yescharacteristic
8C2×C42×D73C411yescharacteristic
9C22⋊C8×D73—22no—
10#17988453C411yescharacteristic
11#17988452C411yescharacteristic
12#17988452C2211yescharacteristic
13#17988451—22no—
14#95×D73—22no—
15#17988313C2212yes—
16#17988312—22no—
17#382×C73C2211yescharacteristic
18#324×C73C2212yes—
19C22×C4×D73—21no—
20C22×C4×D73—21no—
21C22×C4×D73C2×C411yescharacteristic
22C22×C4×D73D412yes—
23C2×C8×D73—42no—
24C2×C4⋊Dic73C2×C411yescharacteristic
25C2×C4⋊Dic73C2×C411yescharacteristic
26C2×#11924007—21no—
27C2×#11924007D412yes—
28C4⋊C4×D73—41no—
29C4⋊C4×D73—41no—
30C4⋊C4×D73—41no—
31C4⋊C4×D73—41no—
32C2×C4×Dic73—21no—
33C2×C4×Dic73C2×C411yescharacteristic
34C42×D73—22no—
35C42×D73C814yescomplemented
36C22⋊#10596831—22no—
37#14556503—42no—
38#14556498—22no—
39#14556498—22no—
40#14556498—22no—
41C2×C4⋊C4×C73C2×C411yescharacteristic
42C2×C4⋊C4×C73C2311yescharacteristic
43C2×C42×C73C2×C411yescharacteristic
44C22⋊C8×C73—22no—
45#95×C73—22no—
46C23×D73C22⋊C411yescharacteristic
47C22×Dic73—21no—
48C22×Dic73—21no—
49C22×Dic73C22⋊C411yescharacteristic
50C22×Dic73C22⋊C412yes—
51C2×C4×D73—21no—
52C2×C4×D73—21no—
53C2×C4×D73—22no—
54C2×C4×D73—24no—
55C2×C4×D73—22no—
56C2×C4×D73—22no—
57C2×C4×D73—42no—
58C2×C4×D73—42no—
59C2×C4×D73—44no—
60C2×C4×D73—44no—
61C2×C4×D73—41no—
62C2×C4×D73—41no—
63C2×C4×D73C2×C812yes—
64C2×C4×D73M1612yes—
65C2×#10596831—42no—
66C8×D73—84no—
67C4⋊Dic73—41no—
68C4⋊Dic73—41no—
69#11924007—42no—
70#11924007—42no—
71C4×Dic73—21no—
72C4×Dic73—24no—
73C4×Dic73C2×C812yescomplemented
74C22×C4×C73—21no—
75C22×C4×C73—21no—
76C22×C4×C73C22×C411yescharacteristic
77C22×C4×C73C2×D412yes—
78C2×C8×C73—42no—
79C4⋊C4×C73—41no—
80C4⋊C4×C73—41no—
81C42×C73—21no—
82C42×C73C2×C812yescomplemented
83C23×C73C2×C22⋊C411yescharacteristic
84C22×D73—22no—
85C22×D73—22no—
86C22×D73C22⋊C812yes—
87C22×D73#9911yescharacteristic
88C22×D73#9911yescharacteristic
89C22×D73#10112yes—
90C2×C4×C73—21no—
91C2×C4×C73—21no—
92C2×C4×C73—22no—
93C2×C4×C73—22no—
94C2×C4×C73—41no—
95C2×C4×C73—41no—
96C2×C4×C73—42no—
97C2×C4×C73—42no—
98C2×C4×C73—41no—
99C2×C4×C73C22×C811yescharacteristic
100C2×C4×C73C2×M1611yescharacteristic
101C2×Dic73—21no—
102C2×Dic73—21no—
103C2×Dic73—22no—
104C2×Dic73—22no—
105C2×Dic73—41no—
106C2×Dic73—41no—
107C2×Dic73—42no—
108C2×Dic73—42no—
109C2×Dic73—41no—
110C2×Dic73C22⋊C812yes—
111C4×D73—22no—
112C4×D73—22no—
113C4×D73—22no—
114C4×D73—22no—
115C4×D73—48no—
116C4×D73—44no—
117C4×D73—82no—
118C4×D73—82no—
119C4×D73—82no—
120C8×C73—82no—
121#10596831—82no—
122C22×C73—21no—
123C22×C73—21no—
124C22×C73C2×C22⋊C811yescharacteristic
125C22×C73C2×#9911yescharacteristic
126C22×C73C2×#10111yescharacteristic
127C2×D73—21no—
128C2×D73—21no—
129C2×D73—24no—
130C2×D73—24no—
131C2×D73#32412yes—
132C2×D73#32412yes—
133C2×D73#35412yes—
134C2×D73#35512yes—
135C4×C73—21no—
136C4×C73—21no—
137C4×C73—42no—
138C4×C73—42no—
139C4×C73—81no—
140Dic73—22no—
141Dic73—42no—
142Dic73—42no—
143Dic73—81no—
144C2×#1324—731nomaximal, Sylow
145C2×C73—21no—
146C2×C73—21no—
147C2×C73C2×#32411yescharacteristic
148C2×C73C2×#35411yescharacteristic
149C2×C73C2×#35511yescharacteristic
150D73—22no—
151D73#132414yesdirect product factor
152C2×#382—731no—
153C2×#324—732no—
154#1324—731no—
155#1324—732no—
156#1324D7311yescharacteristic, direct product factor
157C73C2×#132411yescharacteristic, complemented, Sylow
158C22×C4⋊C4—731no—
159C22×C4⋊C4—731no—
160C22×C42—731no—
161C2×C22⋊C8—1462no—
162#382—731no—
163#382—731no—
164#382—731no—
165#382—1462no—
166#382C2×D7311yescharacteristic
167C2×#95—1462no—
168#324—732no—
169#324—1462no—
170#324C2×D7312yes—
171C23×C4—732no—
172C23×C4—731no—
173C23×C4—1461no—
174C23×C4—1461no—
175C22×C8—2922no—
176C2×C4⋊C4—2921no—
177C2×C4⋊C4—2921no—
178C2×C4⋊C4—2921no—
179C2×C4⋊C4—2921no—
180C2×C4⋊C4—731no—
181C2×C4⋊C4—732no—
182C2×C4⋊C4—731no—
183C2×C4⋊C4—1461no—
184C2×C4⋊C4C4×D7311yescharacteristic
185C2×C4⋊C4C22×D7311yescharacteristic
186C2×C42—731no—
187C2×C42—734no—
188C2×C42—1462no—
189C2×C42—1461no—
190C2×C42C4×D7311yescharacteristic
191C22⋊C8—22no—
192C22⋊C8—2922no—
193C22⋊C8—1462no—
194#95—22no—
195#95—1462no—
196#95—1462no—
197#95—1462no—
198C24—731no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—2922no—
202C22×C4—2922no—
203C22×C4—2924no—
204C22×C4—2921no—
205C22×C4—2921no—
206C22×C4—2924no—
207C22×C4—732no—
208C22×C4—731no—
209C22×C4—732no—
210C22×C4—732no—
211C22×C4—1464no—
212C22×C4—1462no—
213C22×C4—1462no—
214C22×C4—1461no—
215C22×C4—1461no—
216C22×C4—1462no—
217C22×C4—1461no—
218C22×C4—1461no—
219C22×C4C2×C4×D7311yescharacteristic
220C22×C4D4×D7312yes—
221C2×C8—42no—
222C2×C8—2922no—
223C2×C8—5844no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—2921no—
227C4⋊C4—2922no—
228C4⋊C4—2921no—
229C4⋊C4—2922no—
230C42—21no—
231C42—732no—
232C42—1464no—
233C42—1461no—
234C42C8×D7312yescomplemented
235C23—731no—
236C23—732no—
237C23—731no—
238C23—732no—
239C23—1462no—
240C23—1462no—
241C23C22⋊C4×D7311yescharacteristic
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—2924no—
252C2×C4—2928no—
253C2×C4—2921no—
254C2×C4—2921no—
255C2×C4—2922no—
256C2×C4—2922no—
257C2×C4—2921no—
258C2×C4—5842no—
259C2×C4—5842no—
260C2×C4—5842no—
261C2×C4—732no—
262C2×C4—1462no—
263C2×C4—1462no—
264C2×C4—1462no—
265C2×C4—1462no—
266C2×C4—1462no—
267C2×C4—1462no—
268C2×C4—1461no—
269C2×C4—1461no—
270C2×C4C2×C8×D7311yescharacteristic
271C2×C4M16×D7311yescharacteristic
272C8—82no—
273C8—5842no—
274C22—21no—
275C22—21no—
276C22—732no—
277C22—732no—
278C22—732no—
279C22—732no—
280C22—1464no—
281C22—1464no—
282C22—1461no—
283C22—1461no—
284C22C22⋊C8×D7311yescharacteristic
285C22#99×D7311yescharacteristic
286C22#101×D7311yescharacteristic
287C4—21no—
288C4—21no—
289C4—42no—
290C4—42no—
291C4—81no—
292C4—2922no—
293C4—2922no—
294C4—5841no—
295C4—1462no—
296C2—21no—
297C2—21no—
298C2—734no—
299C2—1462no—
300C2#324×D7311yescharacteristic
301C2#354×D7311yescharacteristic
302C2#355×D7311yescharacteristic
subgroupG/H
centerC22#99×D73
commutatorC2×C4×C73C22×C8
FrattiniC2×C4⋊C4C22×D73
FittingC73×#1324C2
socleC22×C73C2×#99
prime radicalC23×D73C22⋊C4
cosocleC2×C4⋊C4×C73C23
hypercenter#1324D73
hypocenterC73C2×#1324
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
3. #22607875C2semidirect
4. #22607874C2semidirect
5. C73×#1324C2semidirect
35. C42×D73C8semidirect
73. C4×Dic73C2×C8semidirect
82. C42×C73C2×C8semidirect
151. D73#1324direct (N × H)
156. #1324D73direct (N × H)
157. C73C2×#1324semidirect
234. C42C8×D73semidirect

Maximal subgroups

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

subgroupindex
#382×D732
#324×D732
#226078752
#226078742
C73×#13242
C2×#132473