Finite Group Databasebeta

← C2×#21423665 #28571354

Subgroups — C2×#21423665 #28571354

Order 15104.

734 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837749C211yesmaximal, characteristic
2C2×#16837613C211yesmaximal, characteristic, complemented
3C2×#16837603C211yesmaximal, characteristic
4C2×#16837532C211yesmaximal, characteristic, complemented
5#21423665C218yesmaximal, direct product factor
6C2×#16837149C211yesmaximal, characteristic, complemented
7C2×#16837145C211yesmaximal, characteristic
8C2×C59×#334C211yesmaximal, characteristic, complemented
9C22×Dic236—21no—
10C22×#11745660—21no—
11C2×#14273727C2211yescharacteristic
12C2×#14273724C2211yescharacteristic
13C2×C4×Dic118C2211yescharacteristic
14#16837749—22no—
15#16837749C2214yes—
16#16837613—22no—
17#16837613C2214yescomplemented
18#16837603—22no—
19#16837603C2214yes—
20#16837532—22no—
21#16837532C2214yescomplemented
22C2×C4⋊(C59⋊C8)C2211yescharacteristic
23C2×Dic59⋊C8—21no—
24C2×#14273652—21no—
25C2×#14273649—21no—
26C2×#14273649—21no—
27C2×#14273649—21no—
28C2×#14273637—21no—
29#16837149C2214yescomplemented
30#16837145C2214yes—
31C2×C4⋊C8×C59C2211yescharacteristic
32C2×C4⋊C8×C59C2211yescharacteristic
33C2×C4×C8×C59C2211yescharacteristic
34C59×#334C2214yescomplemented
35C22×Dic118—21no—
36C22×Dic118D411yescharacteristic
37C22×D236—21no—
38C22×D236—21no—
39C22×D236—21no—
40C2×Dic236—24no—
41C2×Dic236—44no—
42C2×#11745660—24no—
43C2×#11745660—44no—
44C22×C59⋊C8—21no—
45#14273727—21no—
46#14273727—21no—
47#14273727—21no—
48#14273727C2312yes—
49#14273724—21no—
50#14273724—21no—
51#14273724—21no—
52#14273724C2312yes—
53C4×Dic118—21no—
54C4×Dic118—21no—
55C4×Dic118D412yes—
56C4×Dic118C2312yes—
57C2×C4⋊Dic59—21no—
58C2×C4⋊Dic59—21no—
59C2×C4⋊Dic59D411yescharacteristic
60C2×Dic59⋊C4—21no—
61C2×C4×Dic59—21no—
62C4⋊(C59⋊C8)—21no—
63C4⋊(C59⋊C8)C2312yes—
64Dic59⋊C8—24no—
65#14273652—24no—
66#14273649—24no—
67#14273649—24no—
68#14273649—24no—
69#14273637—24no—
70C22×C8×C59—21no—
71C22×C8×C59—21no—
72C22×C8×C59D411yescharacteristic
73C22×C8×C59D411yescharacteristic
74C2×C42×C59C2311yescharacteristic
75C4⋊C8×C59—21no—
76C4⋊C8×C59—21no—
77C4⋊C8×C59C2312yes—
78C4⋊C8×C59C2312yes—
79C4×C8×C59D412yes—
80C4×C8×C59C2312yes—
81C23×D59—41no—
82C22×C4×C59C2×D411yescharacteristic
83C22×C4×C59C2×D411yescharacteristic
84C22×C4×C59#4111yescharacteristic
85C22×Dic59—21no—
86C22×Dic59—21no—
87C22×Dic59—41no—
88C2×D236—22no—
89C2×D236—22no—
90C2×D236—22no—
91C2×D236—42no—
92C2×D236—42no—
93C2×D236—42no—
94C2×D236—42no—
95C2×D236—41no—
96C2×D236—41no—
97C2×D236—41no—
98C2×D236—82no—
99C2×Dic118—22no—
100C2×Dic118—22no—
101C2×Dic118—21no—
102C2×Dic118—22no—
103C2×Dic118—42no—
104C2×Dic118—42no—
105C2×Dic118—41no—
106C2×Dic118C2×D412yes—
107C2×C8×C59—22no—
108C2×C8×C59—22no—
109C2×C8×C59—22no—
110C2×C8×C59—22no—
111C2×C8×C59—42no—
112C2×C8×C59—42no—
113C2×C8×C59C2×D412yes—
114C2×C8×C59C2×D412yes—
115C42×C59C2×D411yescharacteristic
116C42×C59C2×D411yescharacteristic
117C42×C59#4111yescharacteristic
118C42×C59C2411yescharacteristic
119C4⋊Dic59—21no—
120C4⋊Dic59—22no—
121C4⋊Dic59—22no—
122C4⋊Dic59—41no—
123C4⋊Dic59—41no—
124C4⋊Dic59C2×D412yes—
125Dic59⋊C4—22no—
126Dic59⋊C4—22no—
127C4×Dic59—22no—
128C4×Dic59—22no—
129C2×C59⋊C8—22no—
130C2×C59⋊C8—42no—
131Dic236—48no—
132#11745660—48no—
133C23×C59#12111yescharacteristic
134C22×D59—42no—
135C22×D59—82no—
136C22×D59—82no—
137C22×D59—82no—
138C2×C4×C59—22no—
139C2×C4×C59#12111yescharacteristic
140C2×C4×C59#12111yescharacteristic
141C2×C4×C59#12111yescharacteristic
142C2×C4×C59#13512yes—
143C2×C4×C59AGL(1,ℤ/8)12yes—
144C2×C4×C59AGL(1,ℤ/8)12yes—
145C2×C4×C59#13712yes—
146C2×C4×C59C22×D411yescharacteristic
147C2×C4×C59C22×D411yescharacteristic
148C2×C4×C59C2×#4111yescharacteristic
149C2×Dic59—22no—
150C2×Dic59—22no—
151C2×Dic59—42no—
152C2×Dic59—42no—
153C2×Dic59—42no—
154C2×Dic59—82no—
155D236—42no—
156D236—42no—
157D236—42no—
158D236—42no—
159D236—82no—
160D236—82no—
161D236—82no—
162D236—82no—
163Dic118—22no—
164Dic118—22no—
165Dic118—42no—
166Dic118—42no—
167Dic118—42no—
168Dic118—82no—
169C8×C59—22no—
170C8×C59—22no—
171C8×C59—42no—
172C8×C59—42no—
173C59⋊C8—42no—
174C2×#1702—591nomaximal, Sylow
175C22×C59#46412yes—
176C22×C59#46912yes—
177C22×C59#47112yes—
178C22×C59C2×#12111yescharacteristic
179C2×D59—82no—
180C2×D59—82no—
181C2×D59—82no—
182C2×D59—164no—
183C4×C59—21no—
184C4×C59—21no—
185C4×C59#46412yes—
186C4×C59#46912yes—
187C4×C59C2×#13511yescharacteristic
188C4×C59C2×AGL(1,ℤ/8)11yescharacteristic
189C4×C59C2×AGL(1,ℤ/8)11yescharacteristic
190C4×C59C2×#13711yescharacteristic
191Dic59—42no—
192Dic59—42no—
193Dic59—82no—
194C2×#486—591no—
195C2×#462—591no—
196C2×#460—591no—
197C2×#446—591no—
198#1702—598no—
199C2×#334D5911yescharacteristic, complemented
200C2×#332—591no—
201C2×#331—591no—
202C2×C59#170214yescomplemented
203C2×C59C2×#46411yescharacteristic
204C2×C59C2×#46911yescharacteristic
205C2×C59C2×#47111yescharacteristic
206D59—162no—
207C22×Q16—1181no—
208C22×SD16—1181no—
209C2×C4⋊Q8—591no—
210C2×#127—591no—
211C2×C4×Q8—591no—
212#486—594no—
213#486—1182no—
214#462—594no—
215#462—1182no—
216#460—594no—
217#460—1182no—
218#446—594no—
219#446—1182no—
220C2×C4⋊C8—591no—
221C2×C4⋊C8—1181no—
222C2×C4⋊C8C2×D5911yescharacteristic
223C2×C4⋊C8C2×D5911yescharacteristic
224C2×#103—1181no—
225C2×#102—1181no—
226C2×#102—1181no—
227C2×#102—1181no—
228C2×#97—1181no—
229C2×C4×C8C2×D5911yescharacteristic
230#334C2×D5914yescomplemented
231#332—594no—
232#331—594no—
233C59C2×#170211yescharacteristic, complemented, Sylow
234C22×Q8—591no—
235C22×Q8—1181no—
236C22×D4—1181no—
237C22×D4—1181no—
238C22×D4—1181no—
239C2×Q16—1184no—
240C2×Q16—2364no—
241C2×SD16—1184no—
242C2×SD16—2364no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—1181no—
246C22×C8D23611yescharacteristic
247C22×C8D23611yescharacteristic
248C4⋊Q8—592no—
249C4⋊Q8—1181no—
250C4⋊Q8—1181no—
251C4⋊Q8—1181no—
252#127—592no—
253#127—1181no—
254#127—1181no—
255#127—1181no—
256C4×Q8—592no—
257C4×Q8—592no—
258C4×Q8—1181no—
259C4×Q8—1181no—
260C2×C4⋊C4—591no—
261C2×C4⋊C4—1181no—
262C2×C4⋊C4—1181no—
263C2×C4⋊C4—1181no—
264C2×C42—1181no—
265C2×C42C22×D5911yescharacteristic
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—592no—
269C4⋊C8—1184no—
270C4⋊C8—1181no—
271C4⋊C8C22×D5912yes—
272C4⋊C8C22×D5912yes—
273#103—1184no—
274#102—1184no—
275#102—1184no—
276#102—1184no—
277#97—1184no—
278C4×C8D23612yes—
279C4×C8C22×D5912yes—
280C24—2361no—
281C2×Q8—592no—
282C2×Q8—1181no—
283C2×Q8—1182no—
284C2×Q8—1182no—
285C2×Q8—1182no—
286C2×Q8—2362no—
287C2×Q8—2362no—
288C2×Q8—2361no—
289C2×D4—1182no—
290C2×D4—1182no—
291C2×D4—1182no—
292C2×D4—4722no—
293C2×D4—2361no—
294C2×D4—2361no—
295C2×D4—2361no—
296C2×D4—2362no—
297C2×D4—2362no—
298C2×D4—2362no—
299C2×D4—2362no—
300C22×C4—1181no—
301C22×C4—1181no—
302C22×C4—2361no—
303C22×C4C2×D23611yescharacteristic
304C22×C4D4×D5911yescharacteristic
305C22×C4#1174568911yescharacteristic
306Q16—2368no—
307SD16—2368no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—42no—
313C2×C8—42no—
314C2×C8—1182no—
315C2×C8—2362no—
316C2×C8C2×D23612yes—
317C2×C8C2×D23612yes—
318C4⋊C4—592no—
319C4⋊C4—1181no—
320C4⋊C4—1182no—
321C4⋊C4—1182no—
322C4⋊C4—1182no—
323C4⋊C4—1182no—
324C4⋊C4—2361no—
325C4⋊C4—2361no—
326C42—1182no—
327C42—1182no—
328C42C2×D23611yescharacteristic
329C42D4×D5911yescharacteristic
330C42#1174568911yescharacteristic
331C42C23×D5911yescharacteristic
332C23—4722no—
333C23—4722no—
334C23—4722no—
335C23—2362no—
336C23#1427370211yescharacteristic
337Q8—1182no—
338Q8—1182no—
339Q8—4722no—
340Q8—2362no—
341Q8—2362no—
342Q8—2362no—
343D4—4722no—
344D4—4722no—
345D4—4722no—
346D4—4722no—
347D4—2362no—
348D4—2362no—
349D4—2362no—
350D4—2362no—
351C2×C4—22no—
352C2×C4—1182no—
353C2×C4—1182no—
354C2×C4—4722no—
355C2×C4—2362no—
356C2×C4—2362no—
357C2×C4—2362no—
358C2×C4#1427370211yescharacteristic
359C2×C4#1427370211yescharacteristic
360C2×C4#1427370211yescharacteristic
361C2×C4#1427374912yes—
362C2×C4#1427375412yes—
363C2×C4#1427375412yes—
364C2×C4#1427376012yes—
365C2×C4C2×D4×D5911yescharacteristic
366C2×C4C22×D23611yescharacteristic
367C2×C4C2×#1174568911yescharacteristic
368C8—22no—
369C8—22no—
370C8—42no—
371C8—42no—
372C8—2362no—
373C22—9444no—
374C22—4722no—
375C22—4722no—
376C22—4722no—
377C22#1683762512yes—
378C22#1683765612yes—
379C22#1683766612yes—
380C22C2×#1427370211yescharacteristic
381C4—21no—
382C4—21no—
383C4—4722no—
384C4—2362no—
385C4—2362no—
386C4#1683762512yes—
387C4#1683765612yes—
388C4C2×#1427374911yescharacteristic
389C4C2×#1427375411yescharacteristic
390C4C2×#1427375411yescharacteristic
391C4C2×#1427376011yescharacteristic
392C2—9442no—
393C2#2142366514yesdirect product factor
394C2C2×#1683762511yescharacteristic
395C2C2×#1683765611yescharacteristic
396C2C2×#1683766611yescharacteristic
subgroupG/H
centerC23#14273702
commutator, cosocleC42×C59C24
FrattiniC42C23×D59
FittingC2×C59×#334C2
socleC23×C59#121
prime radicalC2×#14273724C22
hypercenterC2×#334D59
hypocenterC59C2×#1702
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
2. C2×#16837613C2semidirect
4. C2×#16837532C2semidirect
5. #21423665C2direct (N × H)
6. C2×#16837149C2semidirect
8. C2×C59×#334C2semidirect
17. #16837613C22semidirect
21. #16837532C22semidirect
29. #16837149C22semidirect
34. C59×#334C22semidirect
199. C2×#334D59semidirect
202. C2×C59#1702semidirect
230. #334C2×D59semidirect
233. C59C2×#1702semidirect
393. C2#21423665direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168377492
C2×#168376132
C2×#168376032
C2×#168375322
#214236652
C2×#168371492
C2×#168371452
C2×C59×#3342
C2×#170259