Finite Group Databasebeta

← C4×#17988963 #33094412

Subgroups — C4×#17988963 #33094412

Order 18688.

1422 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988963C211yesmaximal, characteristic
2C2×C4×#11924013C214yesmaximal, complemented
3C4×#14556588C211yesmaximal, characteristic, complemented
4#22610796C214yesmaximal, complemented
5#22610738C211yesmaximal, characteristic, complemented
6#22610736C211yesmaximal, characteristic, complemented
7#22610090C211yesmaximal, characteristic, complemented
8C42×#10596831C211yesmaximal, characteristic, complemented
9C4×#127×C73C211yesmaximal, characteristic, complemented
10C22×#11924013C2214yes—
11C2×#14556588C2211yescharacteristic
12C2×C4×D292—22no—
13C2×C4×D292C2212yes—
14#17988963C418yesdirect product factor
15C4×#11924013—216no—
16C2×#14556524C2214yes—
17C2×#14556512C2214yes—
18C2×#14556511C2214yes—
19C2×C4×#10596831C2211yescharacteristic
20C2×C4×#10596831C2212yes—
21C2×C4×#10596831C2211yescharacteristic
22C2×C4×#10596831C2212yes—
23#17988489—22no—
24#17988489C2212yes—
25#17988457C2211yescharacteristic
26C2×#127×C73C2211yescharacteristic
27C2×C4×D4×C73—22no—
28C2×C4×D4×C73C2212yes—
29#390×C73—22no—
30#390×C73C2212yes—
31#384×C73C2211yescharacteristic
32C43×C73C2211yescharacteristic
33C22×D292—22no—
34C22×D292C2312yes—
35C22×C4×D73—22no—
36C2×#11924013—28no—
37C2×#11924013—28no—
38C2×#11924013C2×C4116yescomplemented
39C22×#10596831C2312yes—
40C22×#10596831C2312yes—
41#14556588—22no—
42#14556588C2×C414yescomplemented
43C4×D292—28no—
44C4×D292—48no—
45C2×C4⋊Dic73—22no—
46C2×C4⋊Dic73C2312yes—
47C2×#11924005—22no—
48C2×#11924005—24no—
49#14556524—28no—
50#14556512—28no—
51#14556511—28no—
52C4×#10596831—24no—
53C4×#10596831—22no—
54C4×#10596831C2×C414yescomplemented
55C4×#10596831D418yescomplemented
56C22×D4×C73—22no—
57C22×D4×C73C2312yes—
58C23×C4×C73—22no—
59#127×C73—22no—
60#127×C73C2×C414yescomplemented
61C4×D4×C73—28no—
62C4×D4×C73—48no—
63C2×C4⋊C4×C73—22no—
64C2×C4⋊C4×C73C2312yes—
65C2×C22⋊C4×C73—22no—
66C2×C22⋊C4×C73—24no—
67C2×C42×C73D412yes—
68C2×C42×C73D412yes—
69C2×C42×C73C2311yescharacteristic
70C2×C42×C73C2311yescharacteristic
71C2×C42×C73C2311yescharacteristic
72C23×D73—22no—
73C2×D292—24no—
74C2×D292—24no—
75C2×D292—28no—
76C2×D292—22no—
77C2×D292—44no—
78C2×D292—44no—
79C2×D292C22×C414yes—
80C22×Dic73—22no—
81C2×C4×D73—44no—
82C2×C4×D73—48no—
83#11924013—232no—
84C2×#10596831—22no—
85C2×#10596831—22no—
86C2×#10596831C22×C414yes—
87C2×#10596831C2×D414yes—
88C2×#10596831C2×D414yes—
89C2×#10596831#4114yes—
90C4⋊Dic73—24no—
91C4⋊Dic73—44no—
92#11924005—44no—
93#11924005—48no—
94C24×C73—22no—
95C2×D4×C73—28no—
96C2×D4×C73—24no—
97C2×D4×C73—24no—
98C2×D4×C73—22no—
99C2×D4×C73—44no—
100C2×D4×C73—44no—
101C2×D4×C73C22×C414yes—
102C22×C4×C73—22no—
103C22×C4×C73—44no—
104C22×C4×C73—48no—
105C22×C4×C73C2×D411yescharacteristic
106C22×C4×C73C2×D412yes—
107C22×C4×C73C2×D412yes—
108C22×C4×C73C2×D411yescharacteristic
109C22×C4×C73C2411yescharacteristic
110C4⋊C4×C73—24no—
111C4⋊C4×C73—44no—
112C22⋊C4×C73—44no—
113C22⋊C4×C73—48no—
114C42×C73—24no—
115C42×C73—22no—
116C42×C73D818yescomplemented
117C42×C73C22×C412yes—
118C42×C73C2×D414yes—
119C42×C73#4112yes—
120C23×C73—24no—
121C23×C73—42no—
122C23×C73—42no—
123C23×C73—44no—
124C23×C73—44no—
125C23×C73C22×D411yescharacteristic
126C22×D73—24no—
127C22×D73—42no—
128C22×D73—42no—
129C22×D73—44no—
130C22×D73—44no—
131D4×C73—28no—
132D4×C73—44no—
133D4×C73—416no—
134C2×C4×C73—22no—
135C2×C4×C73—22no—
136C2×C4×C73—22no—
137C2×C4×C73—42no—
138C2×C4×C73—44no—
139C2×C4×C73—88no—
140C2×C4×C73C4×D414yes—
141C2×C4×C73#12712yes—
142C2×C4×C73#12712yes—
143C2×C4×C73C2×D814yes—
144C2×C4×C73C2×D814yes—
145C2×C4×C73C2×D814yes—
146C2×C4×C73#13514yes—
147C2×C4×C73C23×C411yescharacteristic
148C2×C4×C73C22×D412yes—
149C2×C4×C73C2×#4112yes—
150C2×C4×C73C2×#4111yescharacteristic
151C2×Dic73—42no—
152C2×Dic73—44no—
153D292—28no—
154D292—44no—
155D292—416no—
156C4×D73—88no—
157#10596831—24no—
158#10596831C4×D418yescomplemented
159C22×C73—44no—
160C22×C73—48no—
161C22×C73—82no—
162C22×C73—82no—
163C22×C73—84no—
164C22×C73C2×C4×D411yescharacteristic
165C22×C73C2×#12711yescharacteristic
166C22×C73#53211yescharacteristic
167C22×C73C22×D812yes—
168C22×C73C2×#13512yes—
169C2×D73—44no—
170C2×D73—48no—
171C2×D73—82no—
172C2×D73—82no—
173C2×D73—84no—
174C4×C73—22no—
175C4×C73—24no—
176C4×C73—82no—
177C4×C73C4×D818yescomplemented
178C4×C73#49314yescomplemented
179C4×C73C2×C4×D412yes—
180C4×C73#53212yes—
181Dic73—82no—
182C4×#493—731nomaximal, Sylow
183C2×C73—84no—
184C2×C73C4×#12711yescharacteristic
185C2×C73C2×C4×D812yes—
186C2×C73C2×#49311yescharacteristic
187C2×C73#314711yescharacteristic
188C2×C73#316912yes—
189D73—84no—
190C2×#493—731no—
191C2×C4×D8—734no—
192C4×#127—731no—
193C4×#127D7311yescharacteristic, complemented
194#1970—734no—
195#1957—731no—
196#1957—731no—
197#1845—731no—
198C42×C8—731no—
199C73C4×#49311yescharacteristic, complemented, Sylow
200C22×D8—734no—
201C2×#127—731no—
202C2×#127C2×D7311yescharacteristic
203C2×C4×D4—22no—
204C2×C4×D4—732no—
205C2×C4×D4—1462no—
206C2×C4×D4C2×D7312yes—
207#493—738no—
208C4×D8—14616no—
209C2×#107—734no—
210C2×#102—734no—
211C2×#102—734no—
212C2×C4×C8—731no—
213C2×C4×C8—732no—
214C2×C4×C8—731no—
215C2×C4×C8—732no—
216#390—22no—
217#390—732no—
218#390—1462no—
219#390C2×D7312yes—
220#384—731no—
221#384C2×D7311yescharacteristic
222C43C2×D7311yescharacteristic
223C22×D4—22no—
224C22×D4—732no—
225C22×D4—1462no—
226C22×D4C22×D7312yes—
227C23×C4—22no—
228C23×C4—1462no—
229C2×D8—7316no—
230C2×D8—1468no—
231C2×D8—1468no—
232C22×C8—732no—
233C22×C8—732no—
234#127—22no—
235#127—734no—
236#127—1462no—
237#127C4×D7314yescomplemented
238C4×D4—28no—
239C4×D4—48no—
240C4×D4—2928no—
241C4×D4—1468no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—732no—
244C2×C4⋊C4—1462no—
245C2×C4⋊C4C22×D7312yes—
246C2×C22⋊C4—24no—
247C2×C22⋊C4—22no—
248C2×C22⋊C4—1462no—
249C2×C22⋊C4—1464no—
250C2×C42C22⋊D7312yes—
251C2×C42C22⋊D7312yes—
252C2×C42C22×D7311yescharacteristic
253C2×C42C22×D7311yescharacteristic
254C2×C42C22×D7311yescharacteristic
255#107—1468no—
256#102—1468no—
257#102—1468no—
258C4×C8—734no—
259C4×C8—738no—
260C4×C8—1464no—
261C4×C8—1462no—
262C24—22no—
263C24—1462no—
264C2×D4—28no—
265C2×D4—24no—
266C2×D4—24no—
267C2×D4—22no—
268C2×D4—44no—
269C2×D4—44no—
270C2×D4—2924no—
271C2×D4—2924no—
272C2×D4—734no—
273C2×D4—1468no—
274C2×D4—1464no—
275C2×D4—1464no—
276C2×D4—1462no—
277C2×D4C2×C4×D7314yes—
278C22×C4—22no—
279C22×C4—44no—
280C22×C4—48no—
281C22×C4—2924no—
282C22×C4—2928no—
283C22×C4—1462no—
284C22×C4C2×C22⋊D7311yescharacteristic
285C22×C4C2×C22⋊D7312yes—
286C22×C4C2×C22⋊D7312yes—
287C22×C4C2×C22⋊D7311yescharacteristic
288C22×C4C23×D7311yescharacteristic
289D8—14632no—
290C2×C8—734no—
291C2×C8—734no—
292C2×C8—734no—
293C2×C8—734no—
294C2×C8—1462no—
295C2×C8—1462no—
296C4⋊C4—24no—
297C4⋊C4—44no—
298C4⋊C4—2924no—
299C4⋊C4—1464no—
300C22⋊C4—44no—
301C22⋊C4—48no—
302C22⋊C4—2924no—
303C22⋊C4—2928no—
304C42—24no—
305C42—22no—
306C42#1192401318yescomplemented
307C42C2×C4×D7312yes—
308C42D4×D7314yes—
309C42#1192402812yes—
310C23—24no—
311C23—42no—
312C23—42no—
313C23—44no—
314C23—44no—
315C23—2922no—
316C23—2922no—
317C23—2924no—
318C23—2924no—
319C23—1464no—
320C23C22×C22⋊D7311yescharacteristic
321D4—28no—
322D4—44no—
323D4—416no—
324D4—2924no—
325D4—29216no—
326D4—1468no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—42no—
331C2×C4—44no—
332C2×C4—88no—
333C2×C4—2922no—
334C2×C4—2924no—
335C2×C4—5848no—
336C2×C4C4×C22⋊D7314yes—
337C2×C4#1455658712yes—
338C2×C4#1455658712yes—
339C2×C4C2×#1192401314yes—
340C2×C4C2×#1192401314yes—
341C2×C4C2×#1192401314yes—
342C2×C4#1455661114yes—
343C2×C4C22×C4×D7311yescharacteristic
344C2×C4C2×D4×D7312yes—
345C2×C4#41×D7312yes—
346C2×C4C2×#1192402811yescharacteristic
347C8—738no—
348C8—1464no—
349C22—44no—
350C22—48no—
351C22—84no—
352C22—82no—
353C22—82no—
354C22—2924no—
355C22—2928no—
356C22—5844no—
357C22—5842no—
358C22—5842no—
359C22C2×C4×C22⋊D7311yescharacteristic
360C22C2×#1455658711yescharacteristic
361C22#1798913311yescharacteristic
362C22C22×#1192401312yes—
363C22C2×#1455661112yes—
364C4—24no—
365C4—22no—
366C4—82no—
367C4—5842no—
368C4C4×#1192401318yescomplemented
369C4#1798896314yesdirect product factor
370C4C4×D4×D7312yes—
371C4#1798913412yes—
372C2—84no—
373C2—5844no—
374C2C4×#1455658711yescharacteristic
375C2C2×C4×#1192401312yes—
376C2C2×#1798896311yescharacteristic
377C2#2262035711yescharacteristic
378C2#2262050612yes—
subgroupG/H
centerC22×C4C2×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC4×#127×C73C2
socleC23×C73C22×D4
prime radicalC2×#17988963C2
cosocleC22×C4×C73C24
hypercenterC4×#127D73
hypocenterC73C4×#493
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×#127

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11924013C2semidirect
3. C4×#14556588C2semidirect
4. #22610796C2semidirect
5. #22610738C2semidirect
6. #22610736C2semidirect
7. #22610090C2semidirect
8. C42×#10596831C2semidirect
9. C4×#127×C73C2semidirect
14. #17988963C4direct (N × H)
38. C2×#11924013C2×C4semidirect
42. #14556588C2×C4semidirect
54. C4×#10596831C2×C4semidirect
55. C4×#10596831D4semidirect
60. #127×C73C2×C4semidirect
116. C42×C73D8semidirect
158. #10596831C4×D4semidirect
177. C4×C73C4×D8semidirect
178. C4×C73#493semidirect
193. C4×#127D73semidirect
199. C73C4×#493semidirect
237. #127C4×D73semidirect
306. C42#11924013semidirect
368. C4C4×#11924013semidirect
369. C4#17988963direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179889632
C2×C4×#119240132
C4×#145565882
#226107962
#226107382
#226107362
#226100902
C42×#105968312
C4×#127×C732
C4×#49373