Finite Group Databasebeta

← C2×C47×#2349 #26073809

Subgroups — C2×C47×#2349 #26073809

Order 12032.

4198 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C47C212yesmaximal
2C22×C4×D4×C47C211yesmaximal, characteristic
3C47×#2349C2116yesmaximal, direct product factor
4C2×C47×#389C212yesmaximal, complemented
5C2×C47×#385C214yesmaximal, complemented
6C2×C47×#382C211yesmaximal, characteristic, complemented
7C2×C47×#380C212yesmaximal, complemented
8C2×C4×C4⋊C4×C47C211yesmaximal, characteristic, complemented
9C22×#95×C47C212yesmaximal, complemented
10C23×D4×C47C2211yescharacteristic
11C24×C4×C47C2214yes—
12C24×C4×C47C2212yes—
13C2×C4×D4×C47—216no—
14C2×C4×D4×C47C4116yescomplemented
15C2×C4×D4×C47C22116yes—
16C2×C4×D4×C47C2218yes—
17C22×C4⋊C4×C47C2212yes—
18C22×C4⋊C4×C47C2212yes—
19C22×C4⋊C4×C47C2214yes—
20C22×C4⋊C4×C47C2211yescharacteristic
21C22×C22⋊C4×C47C2214yes—
22C22×C22⋊C4×C47C2212yes—
23C22×C42×C47C2212yes—
24C22×C42×C47C2211yescharacteristic
25C47×#389C22116yescomplemented
26C47×#385C22132yescomplemented
27C47×#382C2218yescomplemented
28C47×#380C22116yescomplemented
29C4×C4⋊C4×C47C2218yescomplemented
30C2×#95×C47C2211yescharacteristic
31C2×#95×C47C2212yes—
32C2×#95×C47C2214yes—
33C2×#95×C47C2211yescharacteristic
34C2×#95×C47C2212yes—
35C2×#95×C47C22116yescomplemented
36C25×C47C2312yes—
37C22×D4×C47C2×C418yes—
38C22×D4×C47D418yes—
39C22×D4×C47Q818yes—
40C22×D4×C47C2314yes—
41C23×C4×C47—216no—
42C23×C4×C47—216no—
43C23×C4×C47—48no—
44C23×C4×C47—48no—
45C23×C4×C47C2×C4116yescomplemented
46C23×C4×C47C2312yes—
47C23×C4×C47C2314yes—
48C23×C4×C47C23116yes—
49C23×C4×C47C2311yescharacteristic
50C23×C4×C47C2311yescharacteristic
51C23×C4×C47C2312yes—
52C23×C4×C47C2312yes—
53C23×C4×C47C2318yes—
54C23×C4×C47C2311yescharacteristic
55C4×D4×C47—264no—
56C4×D4×C47C2×C4164yescomplemented
57C2×C4⋊C4×C47—28no—
58C2×C4⋊C4×C47—28no—
59C2×C4⋊C4×C47—48no—
60C2×C4⋊C4×C47C2×C418yescomplemented
61C2×C4⋊C4×C47C2318yes—
62C2×C4⋊C4×C47C2318yes—
63C2×C4⋊C4×C47C23116yes—
64C2×C4⋊C4×C47C2314yes—
65C2×C22⋊C4×C47—216no—
66C2×C22⋊C4×C47C2×C4116yescomplemented
67C2×C22⋊C4×C47C23116yes—
68C2×C22⋊C4×C47C2318yes—
69C2×C42×C47—28no—
70C2×C42×C47C2×C418yescomplemented
71C2×C42×C47C2318yes—
72C2×C42×C47C2314yes—
73#95×C47C2314yes—
74#95×C47C2318yes—
75#95×C47C23116yes—
76#95×C47C2314yes—
77#95×C47C2318yes—
78C24×C47—28no—
79C24×C47—28no—
80C24×C47C22×C418yes—
81C24×C47C2×D418yes—
82C24×C47C2×Q818yes—
83C24×C47C2414yes—
84C24×C47C2411yescharacteristic
85C2×D4×C47C4⋊C4164yescomplemented
86C2×D4×C47C22×C4116yes—
87C2×D4×C47C2×D4116yes—
88C2×D4×C47C2×Q8116yes—
89C22×C4×C47—24no—
90C22×C4×C47—24no—
91C22×C4×C47—28no—
92C22×C4×C47—24no—
93C22×C4×C47—24no—
94C22×C4×C47—24no—
95C22×C4×C47—28no—
96C22×C4×C47—232no—
97C22×C4×C47—24no—
98C22×C4×C47—28no—
99C22×C4×C47—24no—
100C22×C4×C47—28no—
101C22×C4×C47—232no—
102C22×C4×C47—432no—
103C22×C4×C47—416no—
104C22×C4×C47—416no—
105C22×C4×C47—464no—
106C22×C4×C47C22×C414yes—
107C22×C4×C47C22×C414yes—
108C22×C4×C47C22×C418yes—
109C22×C4×C47C22×C414yes—
110C22×C4×C47C22×C4132yescomplemented
111C22×C4×C47C2×D414yes—
112C22×C4×C47C2×Q814yes—
113C22×C4×C47#4118yes—
114C22×C4×C47C2414yes—
115C22×C4×C47C2418yes—
116C22×C4×C47C2412yes—
117C22×C4×C47C2412yes—
118C22×C4×C47C2414yes—
119C22×C4×C47C2414yes—
120C22×C4×C47C2412yes—
121C4⋊C4×C47—216no—
122C4⋊C4×C47—216no—
123C4⋊C4×C47—416no—
124C4⋊C4×C47C22×C4116yescomplemented
125C22⋊C4×C47—232no—
126C22⋊C4×C47C22×C4132yescomplemented
127C42×C47—216no—
128C42×C47C22×C4116yescomplemented
129C23×C47—216no—
130C23×C47—216no—
131C23×C47—232no—
132C23×C47—232no—
133C23×C47—28no—
134C23×C47—28no—
135C23×C47C2×C4⋊C4132yes—
136C23×C47C23×C418yes—
137C23×C47C23×C412yes—
138C23×C47C22×D418yes—
139C23×C47C22×D412yes—
140C23×C47C22×Q818yes—
141C23×C47C22×Q812yes—
142C23×C47C2×#4114yes—
143C23×C47H(5,𝔽2)14yes—
144C23×C47C2511yescharacteristic
145D4×C47C2×C4⋊C4164yescomplemented
146C2×C4×C47—28no—
147C2×C4×C47—28no—
148C2×C4×C47—216no—
149C2×C4×C47—216no—
150C2×C4×C47—24no—
151C2×C4×C47—24no—
152C2×C4×C47—28no—
153C2×C4×C47—24no—
154C2×C4×C47—24no—
155C2×C4×C47—24no—
156C2×C4×C47—28no—
157C2×C4×C47—24no—
158C2×C4×C47—28no—
159C2×C4×C47—24no—
160C2×C4×C47—28no—
161C2×C4×C47—432no—
162C2×C4×C47—464no—
163C2×C4×C47—48no—
164C2×C4×C47—416no—
165C2×C4×C47C2×C4⋊C4116yes—
166C2×C4×C47C23×C414yes—
167C2×C4×C47C23×C414yes—
168C2×C4×C47C23×C418yes—
169C2×C4×C47C23×C414yes—
170C2×C4×C47C22×D414yes—
171C2×C4×C47C22×Q814yes—
172C2×C4×C47C2×#4118yes—
173C2×#2349C4711yesmaximal, characteristic, direct product factor, Sylow
174C22×C47—264no—
175C22×C47—28no—
176C22×C47—28no—
177C22×C47—216no—
178C22×C47—216no—
179C22×C47C22×C4⋊C4116yes—
180C22×C47C22×C4⋊C414yes—
181C22×C47C4×#4114yes—
182C22×C47#51814yes—
183C22×C47#54618yes—
184C22×C47#55418yes—
185C22×C47C24×C411yescharacteristic
186C22×C47C23×D411yescharacteristic
187C22×C47C23×Q811yescharacteristic
188C22×C47C22×#4112yes—
189C22×C47C2×H(5,𝔽2)12yes—
190C4×C47—24no—
191C4×C47—24no—
192C4×C47—28no—
193C4×C47—28no—
194C4×C47—44no—
195C4×C47—48no—
196C4×C47C22×C4⋊C418yes—
197C22×C4×D4C2×C4712yes—
198C22×C4×D4C2×C4711yescharacteristic
199#2349C2×C47116yesdirect product factor
200C2×#389C2×C4712yescomplemented
201C2×#385C2×C4714yescomplemented
202C2×#382C2×C4711yescharacteristic, complemented
203C2×#380C2×C4712yescomplemented
204C2×C4×C4⋊C4C2×C4711yescharacteristic, complemented
205C22×#95C2×C4712yescomplemented
206C2×C47—216no—
207C2×C47#234918yesdirect product factor
208C2×C47C23×C4⋊C411yescharacteristic
209C2×C47C2×C4×#4111yescharacteristic
210C2×C47C2×#51811yescharacteristic
211C2×C47C2×#54612yes—
212C2×C47C2×#55412yes—
213C23×D4C22×C4711yescharacteristic
214C24×C4C22×C4714yes—
215C24×C4C22×C4712yes—
216C2×C4×D4—216no—
217C2×C4×D4C4×C47116yescomplemented
218C2×C4×D4C22×C47116yes—
219C2×C4×D4C22×C4718yes—
220C22×C4⋊C4C22×C4712yes—
221C22×C4⋊C4C22×C4712yes—
222C22×C4⋊C4C22×C4714yes—
223C22×C4⋊C4C22×C4711yescharacteristic
224C22×C22⋊C4C22×C4714yes—
225C22×C22⋊C4C22×C4712yes—
226C22×C42C22×C4712yes—
227C22×C42C22×C4711yescharacteristic
228#389C22×C47116yescomplemented
229#385C22×C47132yescomplemented
230#382C22×C4718yescomplemented
231#380C22×C47116yescomplemented
232C4×C4⋊C4C22×C4718yescomplemented
233C2×#95C22×C4711yescharacteristic
234C2×#95C22×C4712yes—
235C2×#95C22×C4714yes—
236C2×#95C22×C4711yescharacteristic
237C2×#95C22×C4712yes—
238C2×#95C22×C47116yescomplemented
239C47C2×#234911yescharacteristic, direct product factor, Sylow
240C25C23×C4712yes—
241C22×D4C2×C4×C4718yes—
242C22×D4D4×C4718yes—
243C22×D4Q8×C4718yes—
244C22×D4C23×C4714yes—
245C23×C4—216no—
246C23×C4—216no—
247C23×C4—48no—
248C23×C4—48no—
249C23×C4C2×C4×C47116yescomplemented
250C23×C4C23×C4712yes—
251C23×C4C23×C4714yes—
252C23×C4C23×C47116yes—
253C23×C4C23×C4711yescharacteristic
254C23×C4C23×C4712yes—
255C23×C4C23×C4711yescharacteristic
256C23×C4C23×C4712yes—
257C23×C4C23×C4718yes—
258C23×C4C23×C4711yescharacteristic
259C4×D4—264no—
260C4×D4C2×C4×C47164yescomplemented
261C2×C4⋊C4—28no—
262C2×C4⋊C4—28no—
263C2×C4⋊C4—48no—
264C2×C4⋊C4C2×C4×C4718yescomplemented
265C2×C4⋊C4C23×C4718yes—
266C2×C4⋊C4C23×C4718yes—
267C2×C4⋊C4C23×C47116yes—
268C2×C4⋊C4C23×C4714yes—
269C2×C22⋊C4—216no—
270C2×C22⋊C4C2×C4×C47116yescomplemented
271C2×C22⋊C4C23×C47116yes—
272C2×C22⋊C4C23×C4718yes—
273C2×C42—28no—
274C2×C42C2×C4×C4718yescomplemented
275C2×C42C23×C4718yes—
276C2×C42C23×C4714yes—
277#95C23×C4714yes—
278#95C23×C4718yes—
279#95C23×C47116yes—
280#95C23×C4714yes—
281#95C23×C4718yes—
282C24—28no—
283C24—28no—
284C24C22×C4×C4718yes—
285C24C2×D4×C4718yes—
286C24C2×Q8×C4718yes—
287C24C24×C4714yes—
288C24C24×C4711yescharacteristic
289C2×D4C4⋊C4×C47164yescomplemented
290C2×D4C22×C4×C47116yes—
291C2×D4C2×D4×C47116yes—
292C2×D4C2×Q8×C47116yes—
293C22×C4—24no—
294C22×C4—24no—
295C22×C4—28no—
296C22×C4—24no—
297C22×C4—24no—
298C22×C4—24no—
299C22×C4—28no—
300C22×C4—232no—
301C22×C4—24no—
302C22×C4—28no—
303C22×C4—24no—
304C22×C4—28no—
305C22×C4—232no—
306C22×C4—432no—
307C22×C4—416no—
308C22×C4—416no—
309C22×C4—464no—
310C22×C4C22×C4×C4714yes—
311C22×C4C22×C4×C4714yes—
312C22×C4C22×C4×C4718yes—
313C22×C4C22×C4×C4714yes—
314C22×C4C22×C4×C47132yescomplemented
315C22×C4C2×D4×C4714yes—
316C22×C4C2×Q8×C4714yes—
317C22×C4#41×C4718yes—
318C22×C4C24×C4718yes—
319C22×C4C24×C4714yes—
320C22×C4C24×C4712yes—
321C22×C4C24×C4712yes—
322C22×C4C24×C4714yes—
323C22×C4C24×C4714yes—
324C22×C4C24×C4712yes—
325C4⋊C4—216no—
326C4⋊C4—216no—
327C4⋊C4—416no—
328C4⋊C4C22×C4×C47116yescomplemented
329C22⋊C4—232no—
330C22⋊C4C22×C4×C47132yescomplemented
331C42—216no—
332C42C22×C4×C47116yescomplemented
333C23—216no—
334C23—216no—
335C23—232no—
336C23—232no—
337C23—28no—
338C23—28no—
339C23C2×C4⋊C4×C47132yes—
340C23C23×C4×C4718yes—
341C23C23×C4×C4712yes—
342C23C22×D4×C4718yes—
343C23C22×D4×C4712yes—
344C23C22×Q8×C4718yes—
345C23C22×Q8×C4712yes—
346C23C2×#41×C4714yes—
347C23H(5,𝔽2)×C4714yes—
348C23C25×C4711yescharacteristic
349D4C2×C4⋊C4×C47164yescomplemented
350C2×C4—28no—
351C2×C4—28no—
352C2×C4—216no—
353C2×C4—216no—
354C2×C4—24no—
355C2×C4—24no—
356C2×C4—28no—
357C2×C4—24no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—28no—
361C2×C4—24no—
362C2×C4—28no—
363C2×C4—24no—
364C2×C4—28no—
365C2×C4—432no—
366C2×C4—464no—
367C2×C4—48no—
368C2×C4—416no—
369C2×C4C2×C4⋊C4×C47116yes—
370C2×C4C23×C4×C4714yes—
371C2×C4C23×C4×C4714yes—
372C2×C4C23×C4×C4718yes—
373C2×C4C23×C4×C4714yes—
374C2×C4C22×D4×C4714yes—
375C2×C4C22×Q8×C4714yes—
376C2×C4C2×#41×C4718yes—
377C22—264no—
378C22—28no—
379C22—28no—
380C22—216no—
381C22—216no—
382C22C22×C4⋊C4×C47116yes—
383C22C22×C4⋊C4×C4714yes—
384C22C4×#41×C4714yes—
385C22C47×#51814yes—
386C22C47×#54618yes—
387C22C47×#55418yes—
388C22C24×C4×C4711yescharacteristic
389C22C23×D4×C4711yescharacteristic
390C22C23×Q8×C4711yescharacteristic
391C22C22×#41×C4712yes—
392C22C2×H(5,𝔽2)×C4712yes—
393C4—24no—
394C4—24no—
395C4—28no—
396C4—28no—
397C4—48no—
398C4—44no—
399C4C22×C4⋊C4×C4718yes—
400C2—216no—
401C2C47×#234918yesdirect product factor
402C2C23×C4⋊C4×C4711yescharacteristic
403C2C2×C4×#41×C4711yescharacteristic
404C2C2×C47×#51811yescharacteristic
405C2C2×C47×#54612yes—
406C2C2×C47×#55412yes—
subgroupG/H
center, socleC24×C47C24
commutatorC22C24×C4×C47
Frattini, cosocleC23C25×C47
prime radicalC23×D4×C47C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C47×#2349C2direct (N × H)
4. C2×C47×#389C2semidirect
5. C2×C47×#385C2semidirect
6. C2×C47×#382C2semidirect
7. C2×C47×#380C2semidirect
8. C2×C4×C4⋊C4×C47C2semidirect
9. C22×#95×C47C2semidirect
14. C2×C4×D4×C47C4semidirect
25. C47×#389C22semidirect
26. C47×#385C22semidirect
27. C47×#382C22semidirect
28. C47×#380C22semidirect
29. C4×C4⋊C4×C47C22semidirect
35. C2×#95×C47C22semidirect
45. C23×C4×C47C2×C4semidirect
56. C4×D4×C47C2×C4semidirect
60. C2×C4⋊C4×C47C2×C4semidirect
66. C2×C22⋊C4×C47C2×C4semidirect
70. C2×C42×C47C2×C4semidirect
85. C2×D4×C47C4⋊C4semidirect
110. C22×C4×C47C22×C4semidirect
124. C4⋊C4×C47C22×C4semidirect
126. C22⋊C4×C47C22×C4semidirect
128. C42×C47C22×C4semidirect
145. D4×C47C2×C4⋊C4semidirect
173. C2×#2349C47direct (N × H)
199. #2349C2×C47direct (N × H)
200. C2×#389C2×C47semidirect
201. C2×#385C2×C47semidirect
202. C2×#382C2×C47semidirect
203. C2×#380C2×C47semidirect
204. C2×C4×C4⋊C4C2×C47semidirect
205. C22×#95C2×C47semidirect
207. C2×C47#2349direct (N × H)
217. C2×C4×D4C4×C47semidirect
228. #389C22×C47semidirect
229. #385C22×C47semidirect
230. #382C22×C47semidirect
231. #380C22×C47semidirect
232. C4×C4⋊C4C22×C47semidirect
238. C2×#95C22×C47semidirect
239. C47C2×#2349direct (N × H)
249. C23×C4C2×C4×C47semidirect
260. C4×D4C2×C4×C47semidirect
264. C2×C4⋊C4C2×C4×C47semidirect
270. C2×C22⋊C4C2×C4×C47semidirect
274. C2×C42C2×C4×C47semidirect
289. C2×D4C4⋊C4×C47semidirect
314. C22×C4C22×C4×C47semidirect
328. C4⋊C4C22×C4×C47semidirect
330. C22⋊C4C22×C4×C47semidirect
332. C42C22×C4×C47semidirect
349. D4C2×C4⋊C4×C47semidirect
401. C2C47×#2349direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D4×C472
C47×#23492
C2×C47×#3892
C2×C47×#3852
C2×C47×#3822
C2×C47×#3802
C2×C4×C4⋊C4×C472
C22×#95×C472
C2×#234947