Finite Group Databasebeta

← C2×#21425867 #28741699

Subgroups — C2×#21425867 #28741699

Order 15104.

658 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D59C211yesmaximal, characteristic
2C2×#108×D59C211yesmaximal, characteristic
3C2×#16837437C211yesmaximal, characteristic
4#21425867C218yesmaximal, direct product factor
5C2×#16837226C211yesmaximal, characteristic, complemented
6C2×#16837225C211yesmaximal, characteristic, complemented
7C2×#16837224C211yesmaximal, characteristic, complemented
8C2×C59×#365C211yesmaximal, characteristic, complemented
9C2×M16×D59—21no—
10C22×C8×D59C2211yescharacteristic
11C2×#14273685—21no—
12C2×#14273667C2211yescharacteristic
13C2×#14273666C412yescomplemented
14M32×D59C414yescomplemented
15M32×D59C2214yes—
16C2×C16×D59C412yescomplemented
17C2×#14273663C2211yescharacteristic
18C2×#14273662—21no—
19#108×D59—22no—
20#108×D59C2214yes—
21#16837437—22no—
22#16837437C2214yes—
23C2×#14273660—21no—
24C2×#14273659C2211yescharacteristic
25#16837226C2214yescomplemented
26#16837225C2214yescomplemented
27#16837224C2214yescomplemented
28C2×M32×C59C2211yescharacteristic
29C2×#108×C59C2211yescharacteristic
30C2×#106×C59C2211yescharacteristic
31C59×#365C2214yescomplemented
32C22×C4×D59D411yescharacteristic
33C2×#11745664—21no—
34C2×#11745659—41no—
35M16×D59—24no—
36M16×D59—42no—
37C22×C59⋊C8D411yescharacteristic
38C2×C8×D59—41no—
39C2×C8×D59C2×C411yescharacteristic
40C2×C8×D59C2×C412yes—
41C2×C8×D59C2×C411yescharacteristic
42C2×C8×D59D412yes—
43C2×C8×D59Q812yes—
44C2×C8×D59Q811yescharacteristic
45C2×C8×D59Q811yescharacteristic
46C2×C8×D59C2312yes—
47#14273685—24no—
48#14273685—42no—
49C2×C4⋊Dic59—21no—
50C2×(C2×D59)⋊C4—41no—
51C2×C4×Dic59—41no—
52#14273667C2×C412yes—
53#14273667C2312yes—
54#14273666C2×C418yescomplemented
55C2×C59⋊C16C2×C412yes—
56C16×D59C2×C418yescomplemented
57#14273663—21no—
58#14273663C2312yes—
59#14273662—24no—
60#14273660—24no—
61#14273659—21no—
62#14273659C2312yes—
63C2×M16×C59—21no—
64C22×C8×C59C2311yescharacteristic
65C2×C4⋊C4×C59—21no—
66M32×C59C2×C412yes—
67M32×C59C2312yes—
68C2×C16×C59C2×C412yes—
69#108×C59—21no—
70#108×C59C2312yes—
71#106×C59—21no—
72#106×C59C2312yes—
73C23×D59SD1611yescharacteristic
74C22×C4×C59—41no—
75C22×C4×C59C2×D411yescharacteristic
76C22×Dic59—41no—
77C22×Dic59SD1611yescharacteristic
78C2×C4×D59C4⋊C411yescharacteristic
79C2×C4×D59C4⋊C411yescharacteristic
80C2×C4×D59C4⋊C412yes—
81C2×C4×D59SD1612yes—
82C2×C4×D59SD1611yescharacteristic
83C2×C4×D59SD1612yes—
84C2×C4×D59SD1611yescharacteristic
85C2×C4×D59C2×D412yes—
86M16×C59—22no—
87M16×C59—41no—
88C2×C8×C59—41no—
89C2×C8×C59C22×C411yescharacteristic
90C2×C8×C59C22×C411yescharacteristic
91C2×C8×C59C2×D411yescharacteristic
92C2×C8×C59C2×Q811yescharacteristic
93C2×C8×C59C2×Q811yescharacteristic
94C2×C8×C59C2411yescharacteristic
95C4⋊C4×C59—22no—
96C4⋊C4×C59—41no—
97(C2×D59)⋊C4—44no—
98C4⋊Dic59—22no—
99C4⋊Dic59—41no—
100C4×Dic59—44no—
101#11745664—22no—
102#11745664—41no—
103C2×C59⋊C8—41no—
104C2×C59⋊C8C4⋊C411yescharacteristic
105C2×C59⋊C8C4⋊C412yes—
106C2×C59⋊C8C4⋊C411yescharacteristic
107C2×C59⋊C8C2×D412yes—
108#11745659—44no—
109C8×D59—44no—
110C8×D59C4⋊C412yes—
111C8×D59C4⋊C412yes—
112C8×D59C4⋊C412yes—
113C8×D59C4⋊C412yes—
114C8×D59C22×C412yes—
115C8×D59C22×C412yes—
116C8×D59C2×Q812yes—
117C8×D59C2×Q812yes—
118C16×C59C22×C414yes—
119C59⋊C16C22×C414yes—
120C23×C59C2×SD1611yescharacteristic
121C22×D59—42no—
122C22×D59#10611yescharacteristic
123C22×D59#10611yescharacteristic
124C22×D59#10612yes—
125C22×D59C2×SD1612yes—
126C2×C4×C59—42no—
127C2×C4×C59—82no—
128C2×C4×C59C2×C4⋊C411yescharacteristic
129C2×C4×C59C2×C4⋊C411yescharacteristic
130C2×C4×C59C2×SD1611yescharacteristic
131C2×C4×C59C2×SD1611yescharacteristic
132C2×C4×C59C2×SD1611yescharacteristic
133C2×C4×C59C22×D411yescharacteristic
134C2×Dic59—42no—
135C2×Dic59—82no—
136C2×Dic59#10612yes—
137C2×Dic59#10611yescharacteristic
138C2×Dic59#10611yescharacteristic
139C2×Dic59C2×SD1612yes—
140C4×D59#10612yes—
141C4×D59#10612yes—
142C4×D59#10612yes—
143C4×D59#10612yes—
144C4×D59C2×C4⋊C412yes—
145C4×D59C2×C4⋊C412yes—
146C4×D59C2×SD1612yes—
147C4×D59C2×SD1612yes—
148C8×C59—42no—
149C8×C59C2×C4⋊C411yescharacteristic
150C8×C59C2×C4⋊C411yescharacteristic
151C8×C59C23×C411yescharacteristic
152C8×C59C22×Q811yescharacteristic
153C59⋊C8—42no—
154C59⋊C8C2×C4⋊C412yes—
155C59⋊C8C2×C4⋊C412yes—
156C2×#2155—591nomaximal, Sylow
157C22×C59—22no—
158C22×C59C2×#10611yescharacteristic
159C22×C59C2×#10611yescharacteristic
160C22×C59C22×SD1611yescharacteristic
161C2×D59—22no—
162C2×D59—22no—
163C2×D59—42no—
164C2×D59—42no—
165C2×D59C2×#10612yes—
166C2×D59C2×#10612yes—
167C4×C59—82no—
168C4×C59C2×#10611yescharacteristic
169C4×C59C2×#10611yescharacteristic
170C4×C59C22×C4⋊C411yescharacteristic
171C4×C59C22×SD1611yescharacteristic
172Dic59—82no—
173Dic59C2×#10612yes—
174Dic59C2×#10612yes—
175C22×M32—591no—
176C22×#108—591no—
177C2×#427—591no—
178#2155—598no—
179C2×#365—591no—
180C2×#365—591no—
181C2×#365—591no—
182C2×#365D5911yescharacteristic, complemented
183C2×C59—21no—
184C2×C59—21no—
185C2×C59#215512yescomplemented
186C2×C59C22×#10611yescharacteristic
187D59—22no—
188D59—22no—
189C22×M16—1181no—
190C23×C8—591no—
191C2×#117—1181no—
192C2×M32—591no—
193C2×M32—594no—
194C2×M32—594no—
195C2×M32—592no—
196C2×M32C2×D5911yescharacteristic
197C22×C16—592no—
198C2×#108—591no—
199C2×#108—594no—
200C2×#108—1182no—
201C2×#108—1181no—
202C2×#108C2×D5911yescharacteristic
203#427—594no—
204#427—1182no—
205C2×#107—1181no—
206C2×#106—591no—
207C2×#106C2×D5911yescharacteristic
208#365—594no—
209#365—594no—
210#365—594no—
211#365C2×D5914yescomplemented
212C59C2×#215511yescharacteristic, complemented, Sylow
213C23×C4—591no—
214C2×M16—21no—
215C2×M16—1184no—
216C2×M16—1181no—
217C2×M16—2361no—
218C2×M16—2362no—
219C22×C8—591no—
220C22×C8—591no—
221C22×C8—592no—
222C22×C8—591no—
223C22×C8—592no—
224C22×C8—592no—
225C22×C8—591no—
226C22×C8—591no—
227C22×C8—592no—
228C22×C8—2361no—
229C22×C8C22×D5911yescharacteristic
230#117—1184no—
231#117—2362no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—1181no—
234C2×C22⋊C4—2361no—
235C2×C42—2361no—
236M32—592no—
237M32—592no—
238M32—598no—
239M32C4×D5912yes—
240M32C22×D5912yes—
241C2×C16—592no—
242C2×C16—598no—
243C2×C16C4×D5912yes—
244#108—21no—
245#108—592no—
246#108—1184no—
247#108—1181no—
248#108C22×D5912yes—
249#107—1184no—
250#106—21no—
251#106—592no—
252#106—1181no—
253#106C22×D5912yes—
254C24—591no—
255C22×C4—41no—
256C22×C4—591no—
257C22×C4—592no—
258C22×C4—591no—
259C22×C4—591no—
260C22×C4—592no—
261C22×C4—591no—
262C22×C4—592no—
263C22×C4—591no—
264C22×C4—592no—
265C22×C4—2361no—
266C22×C4D4×D5911yescharacteristic
267M16—22no—
268M16—41no—
269M16—1182no—
270M16—2364no—
271M16—2361no—
272C2×C8—41no—
273C2×C8—592no—
274C2×C8—591no—
275C2×C8—591no—
276C2×C8—592no—
277C2×C8—592no—
278C2×C8—592no—
279C2×C8—592no—
280C2×C8—592no—
281C2×C8—592no—
282C2×C8—592no—
283C2×C8—592no—
284C2×C8—592no—
285C2×C8—2364no—
286C2×C8—2361no—
287C2×C8C2×C4×D5911yescharacteristic
288C2×C8C2×C4×D5911yescharacteristic
289C2×C8D4×D5911yescharacteristic
290C2×C8Q8×D5911yescharacteristic
291C2×C8Q8×D5911yescharacteristic
292C2×C8C23×D5911yescharacteristic
293C4⋊C4—22no—
294C4⋊C4—41no—
295C4⋊C4—1182no—
296C4⋊C4—2361no—
297C22⋊C4—2364no—
298C42—2364no—
299C16—594no—
300C16C2×C4×D5914yes—
301C23—591no—
302C23—591no—
303C23—592no—
304C23—592no—
305C23—2362no—
306C23SD16×D5911yescharacteristic
307C2×C4—42no—
308C2×C4—82no—
309C2×C4—592no—
310C2×C4—592no—
311C2×C4—591no—
312C2×C4—591no—
313C2×C4—592no—
314C2×C4—592no—
315C2×C4—592no—
316C2×C4—592no—
317C2×C4—592no—
318C2×C4—592no—
319C2×C4—592no—
320C2×C4—592no—
321C2×C4—4722no—
322C2×C4—2362no—
323C2×C4C4⋊C4×D5911yescharacteristic
324C2×C4C4⋊C4×D5911yescharacteristic
325C2×C4SD16×D5911yescharacteristic
326C2×C4SD16×D5911yescharacteristic
327C2×C4SD16×D5911yescharacteristic
328C2×C4C2×D4×D5911yescharacteristic
329C8—42no—
330C8—592no—
331C8—592no—
332C8—2362no—
333C8C4⋊C4×D5911yescharacteristic
334C8C4⋊C4×D5911yescharacteristic
335C8C22×C4×D5911yescharacteristic
336C8C2×Q8×D5911yescharacteristic
337C22—22no—
338C22—592no—
339C22—592no—
340C22—1182no—
341C22—1182no—
342C22—2362no—
343C22—2362no—
344C22#106×D5911yescharacteristic
345C22#106×D5911yescharacteristic
346C22C2×SD16×D5911yescharacteristic
347C4—82no—
348C4—592no—
349C4—592no—
350C4—4722no—
351C4#106×D5911yescharacteristic
352C4#106×D5911yescharacteristic
353C4C2×C4⋊C4×D5911yescharacteristic
354C4C2×SD16×D5911yescharacteristic
355C2—21no—
356C2—21no—
357C2—1182no—
358C2—1182no—
359C2#2142586712yesdirect product factor
360C2C2×#106×D5911yescharacteristic
subgroupG/H
centerC22#106×D59
commutatorC8×C59C23×C4
FrattiniC2×C8C23×D59
FittingC2×C59×#365C2
socleC22×C59C2×#106
prime radicalC23×D59SD16
cosocleC2×C8×C59C24
hypercenterC2×#365D59
hypocenterC59C2×#2155
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#365

Complements

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

NH ≅ G/Ntype
4. #21425867C2direct (N × H)
5. C2×#16837226C2semidirect
6. C2×#16837225C2semidirect
7. C2×#16837224C2semidirect
8. C2×C59×#365C2semidirect
13. C2×#14273666C4semidirect
14. M32×D59C4semidirect
16. C2×C16×D59C4semidirect
25. #16837226C22semidirect
26. #16837225C22semidirect
27. #16837224C22semidirect
31. C59×#365C22semidirect
54. #14273666C2×C4semidirect
56. C16×D59C2×C4semidirect
182. C2×#365D59semidirect
185. C2×C59#2155semidirect
211. #365C2×D59semidirect
212. C59C2×#2155semidirect
359. C2#21425867direct (N × H)

Maximal subgroups

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

subgroupindex
C2×M32×D592
C2×#108×D592
C2×#168374372
#214258672
C2×#168372262
C2×#168372252
C2×#168372242
C2×C59×#3652
C2×#215559