Finite Group Databasebeta

← C2×#20245276 #26369708

Subgroups — C2×#20245276 #26369708

Order 12032.

646 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689563C211yesmaximal, characteristic
2C2×#15689245C211yesmaximal, characteristic
3C2×#15689229C211yesmaximal, characteristic, complemented
4#20245276C218yesmaximal, direct product factor
5C2×#15688945C211yesmaximal, characteristic, complemented
6C2×#15688940C211yesmaximal, characteristic, complemented
7C2×#15688900C211yesmaximal, characteristic, complemented
8C2×C47×#360C211yesmaximal, characteristic
9C22×Dic188C2211yescharacteristic
10C2×#13094031—21no—
11C2×#13093989—21no—
12#15689563C414yescomplemented
13#15689563C2214yes—
14C2×#13093970C412yescomplemented
15C2×#13093968C412yescomplemented
16C2×#13093964C2211yescharacteristic
17#15689245—22no—
18#15689245C2214yes—
19#15689229—22no—
20#15689229C2214yescomplemented
21C2×#13093960C2211yescharacteristic
22C2×#13093951—21no—
23C2×#13093947—21no—
24C2×#13093934C2211yescharacteristic
25#15688945C2214yescomplemented
26#15688940C2214yescomplemented
27#15688900C2214yescomplemented
28C2×#135×C47C2211yescharacteristic
29C2×M32×C47C2211yescharacteristic
30C2×#106×C47C2211yescharacteristic
31C47×#360C2214yes—
32C22×Dic94—21no—
33C2×Dic188—21no—
34C2×Dic188—21no—
35C2×Dic188—21no—
36C2×Dic188C2×C412yes—
37C2×Dic188C2×C412yes—
38C2×Dic188C2312yes—
39#13094031—24no—
40#13094031—42no—
41C2×#10625329—21no—
42C2×#10625329—41no—
43C22×C47⋊C8—41no—
44C22×C47⋊C8D411yescharacteristic
45#13093989—24no—
46#13093989—42no—
47C2×Dic47⋊C4—41no—
48C2×C4×Dic47—41no—
49C2×C4×Dic47D411yescharacteristic
50#13093970C2×C418yescomplemented
51#13093968C2×C418yescomplemented
52#13093964C2×C412yes—
53#13093964C2312yes—
54C2×C47⋊C16C2×C412yes—
55#13093960—21no—
56#13093960C2312yes—
57#13093951—24no—
58#13093947—24no—
59#13093934D412yes—
60#13093934C2312yes—
61C2×#41×C47—21no—
62#135×C47—21no—
63#135×C47—21no—
64#135×C47C2×C412yes—
65#135×C47C2312yes—
66C2×Q16×C47C2×C411yescharacteristic
67C2×SD16×C47—21no—
68C2×D8×C47C2×C411yescharacteristic
69C22×C8×C47C2311yescharacteristic
70C2×C4⋊C4×C47—21no—
71M32×C47—21no—
72M32×C47C2312yes—
73C2×C16×C47—21no—
74#106×C47—21no—
75#106×C47C2312yes—
76#41×C47—22no—
77#41×C47—22no—
78#41×C47—41no—
79#41×C47—41no—
80C2×Q8×C47—21no—
81C2×D4×C47—21no—
82C2×D4×C47—41no—
83C22×C4×C47—41no—
84C22×C4×C47—41no—
85C22×C4×C47C2×D411yescharacteristic
86C22×Dic47—21no—
87C22×Dic47—41no—
88C2×Dic94—22no—
89C2×Dic94—22no—
90C2×Dic94—22no—
91C2×Dic94—41no—
92C2×Dic94—41no—
93C2×Dic94—41no—
94Q16×C47—21no—
95Q16×C47C22×C412yes—
96SD16×C47—22no—
97SD16×C47—22no—
98D8×C47—21no—
99D8×C47C22×C412yes—
100C2×C8×C47C22×C411yescharacteristic
101C2×C8×C47C22×C411yescharacteristic
102C2×C8×C47C2×D411yescharacteristic
103C2×C8×C47#4111yescharacteristic
104C2×C8×C47#4111yescharacteristic
105C2×C8×C47C2411yescharacteristic
106C4⋊C4×C47—22no—
107C4⋊C4×C47—41no—
108Dic47⋊C4—44no—
109C4×Dic47—21no—
110C4×Dic47—44no—
111C4×Dic47C2×D412yes—
112#10625329—22no—
113#10625329—44no—
114#10625329—41no—
115C2×C47⋊C8—21no—
116C2×C47⋊C8—21no—
117C2×C47⋊C8—44no—
118C2×C47⋊C8—41no—
119C2×C47⋊C8C2×D412yes—
120Dic188—22no—
121Dic188—22no—
122Dic188—22no—
123Dic188C22×C414yes—
124C16×C47—22no—
125C47⋊C16C22×C414yes—
126C23×C47—41no—
127C23×C47AGL(1,ℤ/8)11yescharacteristic
128Q8×C47—22no—
129Q8×C47—41no—
130D4×C47—22no—
131D4×C47—42no—
132D4×C47—42no—
133D4×C47—41no—
134C2×C4×C47—41no—
135C2×C4×C47—42no—
136C2×C4×C47—42no—
137C2×C4×C47—42no—
138C2×C4×C47—82no—
139C2×C4×C47C4×D411yescharacteristic
140C2×C4×C47C4×D411yescharacteristic
141C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C47C22×D411yescharacteristic
145C2×Dic47—22no—
146C2×Dic47—42no—
147C2×Dic47—42no—
148C2×Dic47—42no—
149C2×Dic47—42no—
150Dic94—24no—
151Dic94—42no—
152Dic94—42no—
153Dic94—42no—
154C8×C47C4×D411yescharacteristic
155C8×C47C4×D411yescharacteristic
156C8×C47C23×C411yescharacteristic
157C8×C47C2×#4111yescharacteristic
158C47⋊C8—22no—
159C47⋊C8—42no—
160C2×#2180—471nomaximal, Sylow
161C22×C47—22no—
162C22×C47—42no—
163C22×C47—82no—
164C22×C47#44211yescharacteristic
165C22×C47#44211yescharacteristic
166C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
167C4×C47—42no—
168C4×C47—82no—
169C4×C47#44211yescharacteristic
170C4×C47#44211yescharacteristic
171C4×C47C2×C4×D411yescharacteristic
172C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
173Dic47—42no—
174Dic47—44no—
175C2×#510—471no—
176C2×#444—471no—
177C2×#441—471no—
178#2180—478no—
179C2×#365—471no—
180C2×#362—471no—
181C2×#360D4711yescharacteristic
182C2×#347—471no—
183C2×C47—21no—
184C2×C47—21no—
185C2×C47—82no—
186C2×C47#218012yescomplemented
187C2×C47C2×#44211yescharacteristic
188C2×#135C2×D4711yescharacteristic
189C22×Q16—471no—
190C2×#131—941no—
191C2×C4×Q8—941no—
192#510—474no—
193#510—474no—
194C2×Q32—472no—
195C2×SD32—472no—
196C2×M32—471no—
197C2×M32C2×D4711yescharacteristic
198#444—474no—
199#444—942no—
200#441—474no—
201#441—942no—
202C2×#108—471no—
203C2×#106C2×D4711yescharacteristic
204C2×#104—941no—
205C2×#103—941no—
206C2×#97—471no—
207#365—474no—
208#362—474no—
209#360C2×D4714yes—
210#347—474no—
211C47C2×#218011yescharacteristic, complemented, Sylow
212C2×#41—21no—
213C22×Q8—941no—
214#135—21no—
215#135—21no—
216#135C4×D4712yes—
217#135C22×D4712yes—
218C2×Q16—472no—
219C2×Q16—472no—
220C2×Q16—472no—
221C2×Q16—941no—
222C2×Q16—941no—
223C2×Q16—941no—
224C2×Q16C4×D4711yescharacteristic
225C2×SD16—21no—
226C2×D8C4×D4711yescharacteristic
227#131—944no—
228#131—1882no—
229C2×M16—941no—
230C2×M16—1881no—
231C22×C8—471no—
232C22×C8—1881no—
233C22×C8C22×D4711yescharacteristic
234C4×Q8—944no—
235C4×Q8—1882no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—1881no—
238C2×C42—471no—
239C2×C42—1881no—
240Q32—478no—
241SD32—478no—
242M32—21no—
243M32—472no—
244M32—472no—
245M32C22×D4712yes—
246C2×C16—21no—
247C2×C16—472no—
248#108—472no—
249#108—941no—
250#106—21no—
251#106C22×D4712yes—
252#104—944no—
253#103—944no—
254#97—472no—
255#97—472no—
256#41—22no—
257#41—22no—
258#41—41no—
259#41—41no—
260C2×Q8—21no—
261C2×Q8—942no—
262C2×Q8—942no—
263C2×Q8—942no—
264C2×Q8—1881no—
265C2×Q8—1881no—
266C2×Q8—1881no—
267C2×D4—21no—
268C2×D4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—941no—
272C22×C4—1881no—
273C22×C4D4×D4711yescharacteristic
274Q16—21no—
275Q16—474no—
276Q16—942no—
277Q16—942no—
278Q16—942no—
279Q16C2×C4×D4712yes—
280SD16—22no—
281SD16—22no—
282D8—21no—
283D8C2×C4×D4712yes—
284M16—942no—
285M16—1884no—
286M16—1881no—
287C2×C8—472no—
288C2×C8—941no—
289C2×C8—941no—
290C2×C8—1884no—
291C2×C8—1881no—
292C2×C8C2×C4×D4711yescharacteristic
293C2×C8C2×C4×D4711yescharacteristic
294C2×C8D4×D4711yescharacteristic
295C2×C8#1062535211yescharacteristic
296C2×C8#1062535211yescharacteristic
297C2×C8C23×D4711yescharacteristic
298C4⋊C4—22no—
299C4⋊C4—41no—
300C4⋊C4—1884no—
301C42—472no—
302C42—941no—
303C42—1884no—
304C16—22no—
305C16—474no—
306C23—41no—
307C23#1309404811yescharacteristic
308Q8—22no—
309Q8—41no—
310Q8—944no—
311Q8—1882no—
312Q8—1882no—
313Q8—1882no—
314D4—22no—
315D4—42no—
316D4—42no—
317D4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—82no—
323C2×C4—942no—
324C2×C4—1882no—
325C2×C4—1882no—
326C2×C4—1882no—
327C2×C4—1882no—
328C2×C4(C22⋊D47)⋊C411yescharacteristic
329C2×C4(C22⋊D47)⋊C411yescharacteristic
330C2×C4#1309404811yescharacteristic
331C2×C4#1309405111yescharacteristic
332C2×C4#1309405111yescharacteristic
333C2×C4C2×D4×D4711yescharacteristic
334C8—942no—
335C8—1882no—
336C8(C22⋊D47)⋊C411yescharacteristic
337C8(C22⋊D47)⋊C411yescharacteristic
338C8C22×C4×D4711yescharacteristic
339C8C2×#1062535211yescharacteristic
340C22—22no—
341C22—42no—
342C22—82no—
343C22#1568923211yescharacteristic
344C22#1568923211yescharacteristic
345C22C2×#1309404811yescharacteristic
346C4—42no—
347C4—82no—
348C4—1882no—
349C4—1884no—
350C4#1568923211yescharacteristic
351C4#1568923211yescharacteristic
352C4C2×(C22⋊D47)⋊C411yescharacteristic
353C4C2×#1309405111yescharacteristic
354C2—21no—
355C2—21no—
356C2—82no—
357C2#2024527612yesdirect product factor
358C2C2×#1568923211yescharacteristic
subgroupG/H
centerC22#15689232
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC2×C47×#360C2
socleC22×C47#442
prime radicalC2×#135×C47C22
cosocleC2×C8×C47C24
hypercenterC2×#360D47
hypocenterC47C2×#2180
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#360

Complements

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

NH ≅ G/Ntype
3. C2×#15689229C2semidirect
4. #20245276C2direct (N × H)
5. C2×#15688945C2semidirect
6. C2×#15688940C2semidirect
7. C2×#15688900C2semidirect
12. #15689563C4semidirect
14. C2×#13093970C4semidirect
15. C2×#13093968C4semidirect
20. #15689229C22semidirect
25. #15688945C22semidirect
26. #15688940C22semidirect
27. #15688900C22semidirect
50. #13093970C2×C4semidirect
51. #13093968C2×C4semidirect
186. C2×C47#2180semidirect
211. C47C2×#2180semidirect
357. C2#20245276direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156895632
C2×#156892452
C2×#156892292
#202452762
C2×#156889452
C2×#156889402
C2×#156889002
C2×C47×#3602
C2×#218047