Finite Group Databasebeta

← C2×#21423546 #28570989

Subgroups — C2×#21423546 #28570989

Order 15104.

726 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837752C211yesmaximal, characteristic, complemented
2C2×#16837693C211yesmaximal, characteristic
3C2×#16837679C211yesmaximal, characteristic
4C2×#16837467C211yesmaximal, characteristic
5#21423546C218yesmaximal, direct product factor
6C2×#16837154C211yesmaximal, characteristic, complemented
7C2×#16837150C211yesmaximal, characteristic, complemented
8C2×C59×#332C211yesmaximal, characteristic, complemented
9C22×C8×D59—21no—
10C2×#14273727C2211yescharacteristic
11C2×C4×D236C2211yescharacteristic
12#16837752—22no—
13#16837752C2214yescomplemented
14#16837693—22no—
15#16837693C2214yes—
16#16837679—22no—
17#16837679C2214yes—
18#16837467—22no—
19#16837467C2214yes—
20C2×#14273660—21no—
21C2×#14273659—21no—
22C2×C4⋊(C59⋊C8)C2211yescharacteristic
23C2×#14273651—21no—
24C2×#14273651—21no—
25C2×#14273649—21no—
26C2×#14273647—21no—
27C2×(C2×D59)⋊C8—21no—
28C2×C4×C59⋊C8C2211yescharacteristic
29#16837154C2214yescomplemented
30#16837150C2214yescomplemented
31C2×C4⋊Q8×C59C2211yescharacteristic
32C2×C4⋊C8×C59C2211yescharacteristic
33C2×C4⋊C8×C59C2211yescharacteristic
34C59×#332C2214yescomplemented
35C22×Dic118—21no—
36C22×D236D411yescharacteristic
37C22×C4×D59—21no—
38C22×C59⋊C8—21no—
39C22×C59⋊C8D411yescharacteristic
40C22×C59⋊C8D411yescharacteristic
41C2×C8×D59—24no—
42C2×C8×D59—44no—
43#14273727—21no—
44#14273727—21no—
45#14273727—21no—
46#14273727C2312yes—
47C4×D236—21no—
48C4×D236—21no—
49C4×D236D412yes—
50C4×D236C2312yes—
51C2×C4⋊Dic59—21no—
52C2×C4⋊Dic59—21no—
53C2×C4⋊Dic59D411yescharacteristic
54C2×(C2×D59)⋊C4—21no—
55#14273660—24no—
56#14273659—24no—
57C4⋊(C59⋊C8)—21no—
58C4⋊(C59⋊C8)C2312yes—
59#14273651—24no—
60#14273651—24no—
61#14273649—24no—
62#14273647—24no—
63(C2×D59)⋊C8—24no—
64C4×C59⋊C8D412yes—
65C4×C59⋊C8C2312yes—
66C22×Q8×C59—21no—
67C22×C8×C59—21no—
68C22×C8×C59—21no—
69C4⋊Q8×C59—21no—
70C4⋊Q8×C59—21no—
71C4⋊Q8×C59—21no—
72C4⋊Q8×C59C2312yes—
73C2×C4⋊C4×C59—21no—
74C2×C4⋊C4×C59—21no—
75C2×C42×C59C2311yescharacteristic
76C4⋊C8×C59—21no—
77C4⋊C8×C59—21no—
78C4⋊C8×C59C2312yes—
79C4⋊C8×C59C2312yes—
80C23×D59—21no—
81C2×Q8×C59—22no—
82C2×Q8×C59—41no—
83C2×Q8×C59—42no—
84C2×Q8×C59—42no—
85C22×C4×C59—41no—
86C22×C4×C59C2×D411yescharacteristic
87C22×C4×C59C2×D411yescharacteristic
88C22×C4×C59#4111yescharacteristic
89C22×Dic59—21no—
90C22×Dic59—41no—
91C2×D236—21no—
92C2×D236—22no—
93C2×D236Q1614yes—
94C2×D236C2×D412yes—
95C2×C4×D59—22no—
96C2×C4×D59—22no—
97C2×C4×D59—42no—
98C2×C4×D59—42no—
99C2×Dic118—22no—
100C2×Dic118—41no—
101C2×Dic118—82no—
102C2×C8×C59—22no—
103C2×C8×C59—22no—
104C2×C8×C59—42no—
105C2×C8×C59—42no—
106C4⋊C4×C59—22no—
107C4⋊C4×C59—22no—
108C4⋊C4×C59—41no—
109C4⋊C4×C59—41no—
110C42×C59C2×D411yescharacteristic
111C42×C59C2×D411yescharacteristic
112C42×C59#4111yescharacteristic
113C42×C59C2411yescharacteristic
114(C2×D59)⋊C4—22no—
115(C2×D59)⋊C4—22no—
116C4⋊Dic59—21no—
117C4⋊Dic59—22no—
118C4⋊Dic59—22no—
119C4⋊Dic59—41no—
120C4⋊Dic59—41no—
121C4⋊Dic59C2×D412yes—
122C2×C59⋊C8—22no—
123C2×C59⋊C8—22no—
124C2×C59⋊C8—22no—
125C2×C59⋊C8—42no—
126C2×C59⋊C8C2×D412yes—
127C2×C59⋊C8C2×D412yes—
128C8×D59—48no—
129C23×C59#12111yescharacteristic
130C22×D59—22no—
131C22×D59—24no—
132C22×D59—42no—
133C22×D59—42no—
134Q8×C59—42no—
135Q8×C59—42no—
136Q8×C59—82no—
137C2×C4×C59—22no—
138C2×C4×C59—42no—
139C2×C4×C59—82no—
140C2×C4×C59#12111yescharacteristic
141C2×C4×C59#12111yescharacteristic
142C2×C4×C59#12111yescharacteristic
143C2×C4×C59C2×Q1612yes—
144C2×C4×C59#13512yes—
145C2×C4×C59#13512yes—
146C2×C4×C59AGL(1,ℤ/8)12yes—
147C2×C4×C59C22×D411yescharacteristic
148C2×C4×C59C22×D411yescharacteristic
149C2×C4×C59C2×#4111yescharacteristic
150C2×Dic59—22no—
151C2×Dic59—42no—
152C2×Dic59—42no—
153C2×Dic59—82no—
154D236—22no—
155D236—24no—
156D236C2×Q1614yes—
157C4×D59—42no—
158C4×D59—42no—
159C4×D59—44no—
160Dic118—82no—
161Dic118—82no—
162C8×C59—42no—
163C8×C59—42no—
164C59⋊C8—22no—
165C59⋊C8—22no—
166C59⋊C8—42no—
167C2×#1683—591nomaximal, Sylow
168C22×C59#46312yes—
169C22×C59#46712yes—
170C22×C59#47112yes—
171C22×C59C2×#12111yescharacteristic
172C2×D59—24no—
173C2×D59—48no—
174C2×D59—42no—
175C2×D59—42no—
176C4×C59—21no—
177C4×C59—21no—
178C4×C59—82no—
179C4×C59#46312yes—
180C4×C59#46712yes—
181C4×C59C22×Q1611yescharacteristic
182C4×C59C2×#13511yescharacteristic
183C4×C59C2×#13511yescharacteristic
184C4×C59C2×AGL(1,ℤ/8)11yescharacteristic
185Dic59—42no—
186Dic59—82no—
187C2×#487—591no—
188C2×#476—591no—
189C2×#474—591no—
190C2×C8×D4—591no—
191#1683—598no—
192C2×#335—591no—
193C2×#333—591no—
194C2×#332D5911yescharacteristic, complemented
195C2×C59#168314yescomplemented
196C2×C59C2×#46311yescharacteristic
197C2×C59C2×#46711yescharacteristic
198C2×C59C2×#47111yescharacteristic
199D59—44no—
200C23×C8—1181no—
201C2×C4⋊Q8—591no—
202C2×C4⋊Q8C2×D5911yescharacteristic
203C2×C4×D4—591no—
204#487—594no—
205#487—1182no—
206#476—594no—
207#476—1182no—
208#474—594no—
209#474—1182no—
210C8×D4—594no—
211C8×D4—1182no—
212C2×#107—1181no—
213C2×#106—1181no—
214C2×C4⋊C8—591no—
215C2×C4⋊C8C2×D5911yescharacteristic
216C2×C4⋊C8C2×D5911yescharacteristic
217C2×#103—1181no—
218C2×#103—1181no—
219C2×#102—1181no—
220C2×#102—1181no—
221C2×C22⋊C8—1181no—
222C2×C4×C8—591no—
223#335—594no—
224#333—594no—
225#332C2×D5914yescomplemented
226C59C2×#168311yescharacteristic, complemented, Sylow
227C22×Q8—21no—
228C22×Q8—1181no—
229C22×D4—591no—
230C23×C4—1181no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—591no—
234C22×C8—591no—
235C22×C8—1184no—
236C22×C8—1181no—
237C22×C8—2364no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—592no—
242C4⋊Q8—1181no—
243C4⋊Q8—1181no—
244C4⋊Q8—1181no—
245C4⋊Q8C22×D5912yes—
246C4×D4—592no—
247C4×D4—592no—
248C4×D4—1181no—
249C4×D4—1181no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—591no—
253C2×C4⋊C4—1181no—
254C2×C4⋊C4—1181no—
255C2×C22⋊C4—1181no—
256C2×C42C22×D5911yescharacteristic
257#107—1184no—
258#106—1184no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—592no—
262C4⋊C8—1181no—
263C4⋊C8C22×D5912yes—
264C4⋊C8C22×D5912yes—
265#103—1184no—
266#103—1184no—
267#102—1184no—
268#102—1184no—
269C22⋊C8—1184no—
270C4×C8—592no—
271C4×C8—592no—
272C24—1181no—
273C2×Q8—22no—
274C2×Q8—41no—
275C2×Q8—42no—
276C2×Q8—42no—
277C2×Q8—1182no—
278C2×Q8—4722no—
279C2×Q8—2361no—
280C2×D4—594no—
281C2×D4—592no—
282C2×D4—1181no—
283C2×D4—1182no—
284C22×C4—41no—
285C22×C4—1181no—
286C22×C4—1182no—
287C22×C4—1182no—
288C22×C4—2361no—
289C22×C4—2362no—
290C22×C4—2362no—
291C22×C4#1174568511yescharacteristic
292C22×C4D4×D5911yescharacteristic
293C22×C4D4×D5911yescharacteristic
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—42no—
297C2×C8—42no—
298C2×C8—592no—
299C2×C8—592no—
300C2×C8—1182no—
301C2×C8—1182no—
302C2×C8—1182no—
303C2×C8—2368no—
304C2×C8—2362no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—592no—
310C4⋊C4—1181no—
311C4⋊C4—1182no—
312C4⋊C4—1182no—
313C4⋊C4—2361no—
314C4⋊C4—2361no—
315C22⋊C4—1182no—
316C22⋊C4—1182no—
317C42#1174568511yescharacteristic
318C42D4×D5911yescharacteristic
319C42D4×D5911yescharacteristic
320C42C23×D5911yescharacteristic
321C23—1182no—
322C23—1184no—
323C23—2362no—
324C23—2362no—
325C23#1427370011yescharacteristic
326Q8—42no—
327Q8—42no—
328Q8—82no—
329Q8—4722no—
330Q8—4722no—
331D4—594no—
332D4—1184no—
333D4—1182no—
334C2×C4—22no—
335C2×C4—42no—
336C2×C4—82no—
337C2×C4—1182no—
338C2×C4—4722no—
339C2×C4—2362no—
340C2×C4—2362no—
341C2×C4—2362no—
342C2×C4—2362no—
343C2×C4—2364no—
344C2×C4#1427370011yescharacteristic
345C2×C4#1427370011yescharacteristic
346C2×C4#1427370011yescharacteristic
347C2×C4Q16×D5912yes—
348C2×C4#1427374812yes—
349C2×C4#1427374812yes—
350C2×C4#1427375112yes—
351C2×C4C2×D4×D5911yescharacteristic
352C2×C4C2×D4×D5911yescharacteristic
353C2×C4C2×#1174568511yescharacteristic
354C8—42no—
355C8—42no—
356C8—1182no—
357C8—1182no—
358C8—2362no—
359C22—1184no—
360C22—2362no—
361C22—2368no—
362C22—2362no—
363C22#1683761612yes—
364C22#1683764212yes—
365C22#1683766812yes—
366C22C2×#1427370011yescharacteristic
367C4—21no—
368C4—21no—
369C4—82no—
370C4—4722no—
371C4—2362no—
372C4#1683761612yes—
373C4#1683764212yes—
374C4C2×Q16×D5911yescharacteristic
375C4C2×#1427374811yescharacteristic
376C4C2×#1427374811yescharacteristic
377C4C2×#1427375111yescharacteristic
378C2—2364no—
379C2#2142354614yesdirect product factor
380C2C2×#1683761611yescharacteristic
381C2C2×#1683764211yescharacteristic
382C2C2×#1683766811yescharacteristic
subgroupG/H
centerC23#14273700
commutator, cosocleC42×C59C24
FrattiniC42C23×D59
FittingC2×C59×#332C2
socleC23×C59#121
prime radicalC22×D236D4
hypercenterC2×#332D59
hypocenterC59C2×#1683
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
1. C2×#16837752C2semidirect
5. #21423546C2direct (N × H)
6. C2×#16837154C2semidirect
7. C2×#16837150C2semidirect
8. C2×C59×#332C2semidirect
13. #16837752C22semidirect
29. #16837154C22semidirect
30. #16837150C22semidirect
34. C59×#332C22semidirect
194. C2×#332D59semidirect
195. C2×C59#1683semidirect
225. #332C2×D59semidirect
226. C59C2×#1683semidirect
379. C2#21423546direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168377522
C2×#168376932
C2×#168376792
C2×#168374672
#214235462
C2×#168371542
C2×#168371502
C2×C59×#3322
C2×#168359