Finite Group Databasebeta

← C2×#21423667 #28571356

Subgroups — C2×#21423667 #28571356

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×#16837750C211yesmaximal, characteristic
2C2×#16837609C211yesmaximal, characteristic, complemented
3C2×#16837603C211yesmaximal, characteristic
4C2×#16837529C211yesmaximal, characteristic, complemented
5#21423667C218yesmaximal, direct product factor
6C2×#16837152C211yesmaximal, characteristic, complemented
7C2×#16837145C211yesmaximal, characteristic
8C2×C59×#332C211yesmaximal, characteristic, complemented
9C22×#11745672—21no—
10C22×#11745660—21no—
11C2×#14273724C2211yescharacteristic
12C2×C4×Dic118C2211yescharacteristic
13#16837750—22no—
14#16837750C2214yes—
15#16837609—22no—
16#16837609C2214yescomplemented
17#16837603—22no—
18#16837603C2214yes—
19#16837529—22no—
20#16837529C2214yescomplemented
21C2×C4⋊(C59⋊C8)C2211yescharacteristic
22C2×Dic59⋊C8—21no—
23C2×#14273651—21no—
24C2×#14273649—21no—
25C2×#14273647—21no—
26C2×#14273647—21no—
27C2×#14273637—21no—
28C2×C4×C59⋊C8C2211yescharacteristic
29#16837152C2214yescomplemented
30#16837145C2214yes—
31C2×C4⋊Q8×C59C2211yescharacteristic
32C2×C4⋊C8×C59C2211yescharacteristic
33C2×C4⋊C8×C59C2211yescharacteristic
34C59×#332C2214yescomplemented
35C22×Dic118D411yescharacteristic
36C22×D236—21no—
37C22×D236—21no—
38C22×D236—21no—
39C2×#11745672—24no—
40C2×#11745672—44no—
41C2×#11745660—24no—
42C2×#11745660—44no—
43C22×C59⋊C8—21no—
44C22×C59⋊C8D411yescharacteristic
45C22×C59⋊C8D411yescharacteristic
46#14273724—21no—
47#14273724—21no—
48#14273724—21no—
49#14273724C2312yes—
50C4×Dic118—21no—
51C4×Dic118—21no—
52C4×Dic118D412yes—
53C4×Dic118C2312yes—
54C2×C4⋊Dic59D411yescharacteristic
55C2×Dic59⋊C4—21no—
56C2×C4×Dic59—21no—
57C4⋊(C59⋊C8)—21no—
58C4⋊(C59⋊C8)C2312yes—
59Dic59⋊C8—24no—
60#14273651—24no—
61#14273649—24no—
62#14273647—24no—
63#14273647—24no—
64#14273637—24no—
65C4×C59⋊C8D412yes—
66C4×C59⋊C8C2312yes—
67C22×Q8×C59—21no—
68C22×C8×C59—21no—
69C22×C8×C59—21no—
70C4⋊Q8×C59—21no—
71C4⋊Q8×C59—21no—
72C4⋊Q8×C59—21no—
73C4⋊Q8×C59C2312yes—
74C2×C4⋊C4×C59—21no—
75C2×C4⋊C4×C59—21no—
76C2×C42×C59C2311yescharacteristic
77C4⋊C8×C59—21no—
78C4⋊C8×C59—21no—
79C4⋊C8×C59C2312yes—
80C4⋊C8×C59C2312yes—
81C23×D59—41no—
82C2×Q8×C59—22no—
83C2×Q8×C59—41no—
84C2×Q8×C59—42no—
85C2×Q8×C59—42no—
86C22×C4×C59—41no—
87C22×C4×C59C2×D411yescharacteristic
88C22×C4×C59C2×D411yescharacteristic
89C22×C4×C59#4111yescharacteristic
90C22×Dic59—21no—
91C22×Dic59—21no—
92C2×D236—22no—
93C2×D236—22no—
94C2×D236—22no—
95C2×D236—42no—
96C2×D236—42no—
97C2×D236—42no—
98C2×D236—42no—
99C2×D236—41no—
100C2×D236—41no—
101C2×D236—41no—
102C2×D236—82no—
103C2×Dic118—22no—
104C2×Dic118—22no—
105C2×Dic118—21no—
106C2×Dic118C2×D412yes—
107C2×C8×C59—22no—
108C2×C8×C59—22no—
109C2×C8×C59—42no—
110C2×C8×C59—42no—
111C4⋊C4×C59—22no—
112C4⋊C4×C59—22no—
113C4⋊C4×C59—41no—
114C4⋊C4×C59—41no—
115C42×C59C2×D411yescharacteristic
116C42×C59C2×D411yescharacteristic
117C42×C59#4111yescharacteristic
118C42×C59C2411yescharacteristic
119#11745672—48no—
120C4⋊Dic59—21no—
121C4⋊Dic59C2×D412yes—
122Dic59⋊C4—22no—
123Dic59⋊C4—22no—
124C4×Dic59—22no—
125C4×Dic59—22no—
126C2×C59⋊C8—22no—
127C2×C59⋊C8—22no—
128C2×C59⋊C8—22no—
129C2×C59⋊C8—42no—
130C2×C59⋊C8C2×D412yes—
131C2×C59⋊C8C2×D412yes—
132#11745660—48no—
133C23×C59#12111yescharacteristic
134C22×D59—42no—
135C22×D59—82no—
136C22×D59—82no—
137C22×D59—82no—
138Q8×C59—42no—
139Q8×C59—42no—
140Q8×C59—82no—
141C2×C4×C59—22no—
142C2×C4×C59—42no—
143C2×C4×C59—82no—
144C2×C4×C59#12111yescharacteristic
145C2×C4×C59#12111yescharacteristic
146C2×C4×C59#12111yescharacteristic
147C2×C4×C59#13512yes—
148C2×C4×C59AGL(1,ℤ/8)12yes—
149C2×C4×C59AGL(1,ℤ/8)12yes—
150C2×C4×C59#13712yes—
151C2×C4×C59C22×D411yescharacteristic
152C2×C4×C59C22×D411yescharacteristic
153C2×C4×C59C2×#4111yescharacteristic
154C2×Dic59—22no—
155C2×Dic59—22no—
156C2×Dic59—42no—
157C2×Dic59—42no—
158D236—42no—
159D236—42no—
160D236—42no—
161D236—42no—
162D236—82no—
163D236—82no—
164D236—82no—
165D236—82no—
166Dic118—22no—
167Dic118—22no—
168Dic118—42no—
169C8×C59—42no—
170C8×C59—42no—
171C59⋊C8—22no—
172C59⋊C8—22no—
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—82no—
186C4×C59#46412yes—
187C4×C59#46912yes—
188C4×C59C2×#13511yescharacteristic
189C4×C59C2×AGL(1,ℤ/8)11yescharacteristic
190C4×C59C2×AGL(1,ℤ/8)11yescharacteristic
191C4×C59C2×#13711yescharacteristic
192Dic59—42no—
193Dic59—42no—
194C2×#486—591no—
195C2×#462—591no—
196C2×#460—591no—
197C2×#446—591no—
198#1702—598no—
199C2×#334—591no—
200C2×#332D5911yescharacteristic, complemented
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⋊Q8C2×D5911yescharacteristic
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×C8—591no—
230#334—594no—
231#332C2×D5914yescomplemented
232#331—594no—
233C59C2×#170211yescharacteristic, complemented, Sylow
234C22×Q8—21no—
235C22×Q8—591no—
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—591no—
246C22×C8—591no—
247C22×C8—1181no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8C22×D5912yes—
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—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—591no—
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×C8—592no—
279C4×C8—592no—
280C24—2361no—
281C2×Q8—22no—
282C2×Q8—41no—
283C2×Q8—42no—
284C2×Q8—42no—
285C2×Q8—592no—
286C2×Q8—1181no—
287C2×Q8—1182no—
288C2×Q8—1182no—
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—41no—
301C22×C4—1181no—
302C22×C4—1181no—
303C22×C4#1174568511yescharacteristic
304C22×C4D4×D5911yescharacteristic
305C22×C4D4×D5911yescharacteristic
306Q16—2368no—
307SD16—2368no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—42no—
311C2×C8—42no—
312C2×C8—592no—
313C2×C8—592no—
314C2×C8—1182no—
315C2×C8—1182no—
316C2×C8—1182no—
317C2×C8—2362no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—592no—
323C4⋊C4—1181no—
324C4⋊C4—1182no—
325C4⋊C4—1182no—
326C42—1182no—
327C42—1182no—
328C42#1174568511yescharacteristic
329C42D4×D5911yescharacteristic
330C42D4×D5911yescharacteristic
331C42C23×D5911yescharacteristic
332C23—4722no—
333C23—4722no—
334C23—4722no—
335C23—2362no—
336C23#1427370011yescharacteristic
337Q8—42no—
338Q8—42no—
339Q8—82no—
340Q8—1182no—
341Q8—1182no—
342Q8—2362no—
343D4—4722no—
344D4—4722no—
345D4—4722no—
346D4—4722no—
347D4—2362no—
348D4—2362no—
349D4—2362no—
350D4—2362no—
351C2×C4—22no—
352C2×C4—42no—
353C2×C4—82no—
354C2×C4—1182no—
355C2×C4—1182no—
356C2×C4—2362no—
357C2×C4—2362no—
358C2×C4#1427370011yescharacteristic
359C2×C4#1427370011yescharacteristic
360C2×C4#1427370011yescharacteristic
361C2×C4#1427374812yes—
362C2×C4#1427375112yes—
363C2×C4#1427375412yes—
364C2×C4#1427375912yes—
365C2×C4C2×D4×D5911yescharacteristic
366C2×C4C2×D4×D5911yescharacteristic
367C2×C4C2×#1174568511yescharacteristic
368C8—42no—
369C8—42no—
370C8—1182no—
371C8—1182no—
372C8—2362no—
373C22—9444no—
374C22—4722no—
375C22—4722no—
376C22—4722no—
377C22#1683762712yes—
378C22#1683765412yes—
379C22#1683766812yes—
380C22C2×#1427370011yescharacteristic
381C4—21no—
382C4—21no—
383C4—82no—
384C4—2362no—
385C4—2362no—
386C4#1683762712yes—
387C4#1683765412yes—
388C4C2×#1427374811yescharacteristic
389C4C2×#1427375111yescharacteristic
390C4C2×#1427375411yescharacteristic
391C4C2×#1427375911yescharacteristic
392C2—9442no—
393C2#2142366714yesdirect product factor
394C2C2×#1683762711yescharacteristic
395C2C2×#1683765411yescharacteristic
396C2C2×#1683766811yescharacteristic
subgroupG/H
centerC23#14273700
commutator, cosocleC42×C59C24
FrattiniC42C23×D59
FittingC2×C59×#332C2
socleC23×C59#121
prime radicalC2×#14273724C22
hypercenterC2×#332D59
hypocenterC59C2×#1702
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. C2×#16837609C2semidirect
4. C2×#16837529C2semidirect
5. #21423667C2direct (N × H)
6. C2×#16837152C2semidirect
8. C2×C59×#332C2semidirect
16. #16837609C22semidirect
20. #16837529C22semidirect
29. #16837152C22semidirect
34. C59×#332C22semidirect
200. C2×#332D59semidirect
202. C2×C59#1702semidirect
231. #332C2×D59semidirect
233. C59C2×#1702semidirect
393. C2#21423667direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168377502
C2×#168376092
C2×#168376032
C2×#168375292
#214236672
C2×#168371522
C2×#168371452
C2×C59×#3322
C2×#170259