Finite Group Databasebeta

← C22×#17988349 #33083379

Subgroups — C22×#17988349 #33083379

Order 18688.

3006 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×#10596831C211yesmaximal, characteristic
2C23×C4⋊Dic73C211yesmaximal, characteristic
3C2×#17988349C2112yesmaximal, direct product factor
4C23×C4⋊C4×C73C211yesmaximal, characteristic
5C24×Dic73—21no—
6C23×#10596831—24no—
7C23×#10596831—24no—
8C23×#10596831C418yescomplemented
9C23×#10596831C2216yes—
10C22×C4⋊Dic73—24no—
11C22×C4⋊Dic73—23no—
12C22×C4⋊Dic73C418yescomplemented
13C22×C4⋊Dic73C2216yes—
14#17988349C22116yesdirect product factor
15C24×C4×C73—21no—
16C24×C4×C73C2211yescharacteristic
17C22×C4⋊C4×C73—23no—
18C22×C4⋊C4×C73—24no—
19C22×C4⋊C4×C73C418yescomplemented
20C22×C4⋊C4×C73C2216yes—
21C23×Dic73—28no—
22C23×Dic73—26no—
23C23×Dic73—44no—
24C23×Dic73—44no—
25C22×#10596831—232no—
26C22×#10596831—212no—
27C22×#10596831—212no—
28C22×#10596831C2×C4124yescomplemented
29C22×#10596831C2314yes—
30C2×C4⋊Dic73—224no—
31C2×C4⋊Dic73—26no—
32C2×C4⋊Dic73—212no—
33C2×C4⋊Dic73C2×C4124yescomplemented
34C2×C4⋊Dic73C2314yes—
35C25×C73D411yescharacteristic
36C23×C4×C73—28no—
37C23×C4×C73—26no—
38C23×C4×C73—44no—
39C23×C4×C73—44no—
40C23×C4×C73C2×C414yes—
41C23×C4×C73C2×C414yes—
42C23×C4×C73C2×C414yes—
43C23×C4×C73D413yes—
44C23×C4×C73D414yes—
45C23×C4×C73D414yes—
46C23×C4×C73Q814yes—
47C23×C4×C73C2313yes—
48C2×C4⋊C4×C73—224no—
49C2×C4⋊C4×C73—26no—
50C2×C4⋊C4×C73—212no—
51C2×C4⋊C4×C73C2×C4124yescomplemented
52C2×C4⋊C4×C73C2314yes—
53C22×Dic73—224no—
54C22×Dic73—24no—
55C22×Dic73—432no—
56C22×Dic73—412no—
57C22×Dic73—412no—
58C2×#10596831—248no—
59C2×#10596831—24no—
60C2×#10596831—24no—
61C2×#10596831C22×C418yescomplemented
62C4⋊Dic73—224no—
63C4⋊Dic73—24no—
64C4⋊Dic73C22×C418yescomplemented
65C24×C73C22⋊C414yes—
66C24×C73C22⋊C414yes—
67C24×C73C4⋊C414yes—
68C24×C73D814yes—
69C24×C73SD1614yes—
70C24×C73SD1614yes—
71C24×C73Q1614yes—
72C24×C73C2×D413yes—
73C22×C4×C73—224no—
74C22×C4×C73—24no—
75C22×C4×C73—432no—
76C22×C4×C73—412no—
77C22×C4×C73—412no—
78C22×C4×C73C42116yes—
79C22×C4×C73C22⋊C4112yes—
80C22×C4×C73C22⋊C4116yes—
81C22×C4×C73C22⋊C4112yes—
82C22×C4×C73C4⋊C4112yes—
83C22×C4×C73C4⋊C4116yes—
84C22×C4×C73C4⋊C4116yes—
85C22×C4×C73C22×C416yes—
86C22×C4×C73C22×C416yes—
87C22×C4×C73C22×C416yes—
88C22×C4×C73C2×D413yes—
89C22×C4×C73C2×D416yes—
90C22×C4×C73C2×D416yes—
91C22×C4×C73C2×Q816yes—
92C22×C4×C73C2411yescharacteristic
93C4⋊C4×C73—224no—
94C4⋊C4×C73—24no—
95C4⋊C4×C73C22×C418yescomplemented
96C23×C73#95116yes—
97C23×C73#102116yes—
98C23×C73#102116yes—
99C23×C73#103116yes—
100C23×C73#103116yes—
101C23×C73#106116yes—
102C23×C73#107116yes—
103C23×C73C2×C22⋊C416yes—
104C23×C73C2×C22⋊C416yes—
105C23×C73C2×C4⋊C416yes—
106C23×C73C2×D816yes—
107C23×C73C2×SD1616yes—
108C23×C73C2×SD1616yes—
109C23×C73C2×Q1616yes—
110C23×C73C22×D411yescharacteristic
111C2×C4×C73—28no—
112C2×C4×C73—44no—
113C2×C4×C73—44no—
114C2×C4×C73—448no—
115C2×C4×C73#95148yes—
116C2×C4×C73C2×C42112yes—
117C2×C4×C73C2×C22⋊C4112yes—
118C2×C4×C73C2×C22⋊C416yes—
119C2×C4×C73C2×C22⋊C416yes—
120C2×C4×C73C2×C4⋊C4112yes—
121C2×C4×C73C2×C4⋊C416yes—
122C2×C4×C73C2×C4⋊C4112yes—
123C2×C4×C73C23×C411yescharacteristic
124C2×C4×C73C23×C411yescharacteristic
125C2×C4×C73C23×C411yescharacteristic
126C2×C4×C73C22×D411yescharacteristic
127C2×C4×C73C22×D411yescharacteristic
128C2×C4×C73C22×Q811yescharacteristic
129C2×Dic73—28no—
130C2×Dic73—44no—
131C2×Dic73—44no—
132C2×Dic73—448no—
133#10596831—28no—
134C22×C73#340164yescomplemented
135C22×C73C2×#95112yes—
136C22×C73C2×#102112yes—
137C22×C73C2×#102112yes—
138C22×C73C2×#103112yes—
139C22×C73C2×#103112yes—
140C22×C73C2×#106112yes—
141C22×C73C2×#107112yes—
142C22×C73C22×C22⋊C411yescharacteristic
143C22×C73C22×C22⋊C411yescharacteristic
144C22×C73C22×C4⋊C411yescharacteristic
145C22×C73C22×D811yescharacteristic
146C22×C73C22×SD1611yescharacteristic
147C22×C73C22×SD1611yescharacteristic
148C22×C73C22×Q1611yescharacteristic
149C4×C73—48no—
150C4×C73C2×#95112yes—
151C4×C73C22×C4211yescharacteristic
152C4×C73C22×C22⋊C411yescharacteristic
153C4×C73C22×C4⋊C411yescharacteristic
154C4×C73C22×C4⋊C411yescharacteristic
155Dic73—48no—
156C22×#340—731nomaximal, Sylow
157C2×C73C2×#340124yescomplemented
158C2×C73C22×#9511yescharacteristic
159C2×C73C22×#10211yescharacteristic
160C2×C73C22×#10211yescharacteristic
161C2×C73C22×#10311yescharacteristic
162C2×C73C22×#10311yescharacteristic
163C2×C73C22×#10611yescharacteristic
164C2×C73C22×#10711yescharacteristic
165C24×C8—731no—
166C23×C4⋊C4—731no—
167C23×C4⋊C4D7311yescharacteristic
168C2×#340—7312no—
169C73C22×#34011yescharacteristic, complemented, Sylow
170C24×C4—21no—
171C24×C4—1461no—
172C24×C4C2×D7311yescharacteristic
173C23×C8—738no—
174C23×C8—736no—
175C23×C8—1464no—
176C23×C8—1464no—
177C22×C4⋊C4—23no—
178C22×C4⋊C4—24no—
179C22×C4⋊C4—738no—
180C22×C4⋊C4—736no—
181C22×C4⋊C4—1464no—
182C22×C4⋊C4—1463no—
183C22×C4⋊C4Dic7318yescomplemented
184C22×C4⋊C4C2×D7316yes—
185#340—7316no—
186C25C22⋊D7311yescharacteristic
187C23×C4—28no—
188C23×C4—26no—
189C23×C4—44no—
190C23×C4—44no—
191C23×C4—2924no—
192C23×C4—2924no—
193C23×C4—1468no—
194C23×C4—1466no—
195C23×C4Dic14614yes—
196C23×C4C4×D7314yes—
197C23×C4C4×D7314yes—
198C23×C4D29214yes—
199C23×C4C2×Dic7314yes—
200C23×C4C22⋊D7313yes—
201C23×C4C22⋊D7314yes—
202C23×C4C22×D7313yes—
203C22×C8—7324no—
204C22×C8—734no—
205C22×C8—14632no—
206C22×C8—14612no—
207C22×C8—14612no—
208C2×C4⋊C4—224no—
209C2×C4⋊C4—26no—
210C2×C4⋊C4—212no—
211C2×C4⋊C4—7324no—
212C2×C4⋊C4—734no—
213C2×C4⋊C4—14624no—
214C2×C4⋊C4—1466no—
215C2×C4⋊C4—14612no—
216C2×C4⋊C4C2×Dic73124yescomplemented
217C2×C4⋊C4C22×D7314yes—
218C24#1192400514yes—
219C24C22⋊Dic7314yes—
220C24#1192400714yes—
221C24#1192401314yes—
222C24#1192401514yes—
223C24#1192401614yes—
224C24#1192401814yes—
225C24C2×C22⋊D7313yes—
226C22×C4—224no—
227C22×C4—24no—
228C22×C4—432no—
229C22×C4—412no—
230C22×C4—412no—
231C22×C4—29232no—
232C22×C4—29212no—
233C22×C4—29212no—
234C22×C4—14624no—
235C22×C4—1464no—
236C22×C4C4×Dic73116yes—
237C22×C4#11924005112yes—
238C22×C4#11924005116yes—
239C22×C4C22⋊Dic73112yes—
240C22×C4#11924007112yes—
241C22×C4#11924007116yes—
242C22×C4C4⋊Dic73116yes—
243C22×C4C2×C4×D7316yes—
244C22×C4C2×C4×D7316yes—
245C22×C4C22×Dic7316yes—
246C22×C4C2×C22⋊D7313yes—
247C22×C4C2×C22⋊D7316yes—
248C22×C4C2×D29216yes—
249C22×C4C2×Dic14616yes—
250C22×C4C23×D7311yescharacteristic
251C2×C8—738no—
252C2×C8—14648no—
253C2×C8—1464no—
254C2×C8—1464no—
255C4⋊C4—224no—
256C4⋊C4—24no—
257C4⋊C4—738no—
258C4⋊C4—14624no—
259C4⋊C4—1464no—
260C4⋊C4C22×Dic7318yescomplemented
261C23#14556498116yes—
262C23#14556511116yes—
263C23#14556512116yes—
264C23#14556514116yes—
265C23#14556515116yes—
266C23#14556522116yes—
267C23#14556524116yes—
268C23C2×#1192400516yes—
269C23C2×C22⋊Dic7316yes—
270C23C2×#1192400716yes—
271C23C2×#1192401316yes—
272C23C2×#1192401516yes—
273C23C2×#1192401616yes—
274C23C2×#1192401816yes—
275C23C22×C22⋊D7311yescharacteristic
276C2×C4—28no—
277C2×C4—448no—
278C2×C4—44no—
279C2×C4—44no—
280C2×C4—29248no—
281C2×C4—2924no—
282C2×C4—2924no—
283C2×C4—1468no—
284C2×C4#14556498148yes—
285C2×C4C2×C4×Dic73112yes—
286C2×C4C2×#1192400516yes—
287C2×C4C2×#11924005112yes—
288C2×C4C2×C22⋊Dic7316yes—
289C2×C4C2×#1192400716yes—
290C2×C4C2×#11924007112yes—
291C2×C4C2×C4⋊Dic73112yes—
292C2×C4C22×C4×D7311yescharacteristic
293C2×C4C22×C4×D7311yescharacteristic
294C2×C4C23×Dic7311yescharacteristic
295C2×C4C22×C22⋊D7311yescharacteristic
296C2×C4C22×D29211yescharacteristic
297C2×C4C22×Dic14611yescharacteristic
298C8—1468no—
299C22#17988349164yesdirect product factor
300C22C2×#14556498112yes—
301C22C2×#14556511112yes—
302C22C2×#14556512112yes—
303C22C2×#14556514112yes—
304C22C2×#14556515112yes—
305C22C2×#14556522112yes—
306C22C2×#14556524112yes—
307C22C22×#1192400511yescharacteristic
308C22C22×C22⋊Dic7311yescharacteristic
309C22C22×#1192400711yescharacteristic
310C22C22×#1192401311yescharacteristic
311C22C22×#1192401511yescharacteristic
312C22C22×#1192401611yescharacteristic
313C22C22×#1192401811yescharacteristic
314C4—48no—
315C4—2928no—
316C4C2×#14556498112yes—
317C4C22×C4×Dic7311yescharacteristic
318C4C22×#1192400511yescharacteristic
319C4C22×#1192400711yescharacteristic
320C4C22×C4⋊Dic7311yescharacteristic
321C2C2×#17988349124yesdirect product factor
322C2C22×#1455649811yescharacteristic
323C2C22×#1455651111yescharacteristic
324C2C22×#1455651211yescharacteristic
325C2C22×#1455651411yescharacteristic
326C2C22×#1455651511yescharacteristic
327C2C22×#1455652211yescharacteristic
328C2C22×#1455652411yescharacteristic
subgroupG/H
centerC25C22⋊D73
commutatorC4×C73C22×C42
FrattiniC22×C4C23×D73
FittingC23×C4⋊C4×C73C2
socle, prime radicalC25×C73D4
cosocleC22×C4×C73C24
hypercenterC23×C4⋊C4D73
hypocenterC73C22×#340
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C25 ◁ C24×C4 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#17988349C2direct (N × H)
8. C23×#10596831C4semidirect
12. C22×C4⋊Dic73C4semidirect
14. #17988349C22direct (N × H)
19. C22×C4⋊C4×C73C4semidirect
28. C22×#10596831C2×C4semidirect
33. C2×C4⋊Dic73C2×C4semidirect
51. C2×C4⋊C4×C73C2×C4semidirect
61. C2×#10596831C22×C4semidirect
64. C4⋊Dic73C22×C4semidirect
95. C4⋊C4×C73C22×C4semidirect
134. C22×C73#340semidirect
157. C2×C73C2×#340semidirect
169. C73C22×#340semidirect
183. C22×C4⋊C4Dic73semidirect
216. C2×C4⋊C4C2×Dic73semidirect
260. C4⋊C4C22×Dic73semidirect
299. C22#17988349direct (N × H)
321. C2C2×#17988349direct (N × H)

Maximal subgroups

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

subgroupindex
C24×#105968312
C23×C4⋊Dic732
C2×#179883492
C23×C4⋊C4×C732
C22×#34073