Finite Group Databasebeta

← C2×#20276847 #27538663

Subgroups — C2×#20276847 #27538663

Order 13568.

658 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133160C211yesmaximal, characteristic, complemented
2C2×#16811040C211yesmaximal, characteristic, complemented
3C2×#16810893C211yesmaximal, characteristic
4#20276847C218yesmaximal, direct product factor
5C2×#16810452C211yesmaximal, characteristic, complemented
6C2×#16810439C211yesmaximal, characteristic, complemented
7C2×#16810435C211yesmaximal, characteristic, complemented
8C2×C53×#473C211yesmaximal, characteristic, complemented
9C2×#13133242—21no—
10C22×D424C2211yescharacteristic
11C2×#13133160—21no—
12C2×#13133160—21no—
13C2×#13133160—22no—
14C2×#13133160C2214yescomplemented
15#16811040—22no—
16#16811040C2214yescomplemented
17C2×#13133157—21no—
18C2×#13133157C2211yescharacteristic
19C22×#11719908—21no—
20C22×#11719908C2211yescharacteristic
21#16810893—22no—
22#16810893C2214yes—
23C2×#13133153C2211yescharacteristic
24C2×#13133133—21no—
25#16810452C2214yescomplemented
26#16810439C2214yescomplemented
27#16810435C2214yescomplemented
28C2×#137×C53—21no—
29C22×Q16×C53C2211yescharacteristic
30C2×#131×C53C2211yescharacteristic
31C53×#473—22no—
32C53×#473C2214yescomplemented
33C2×#108×C53C2211yescharacteristic
34C2×#101×C53—21no—
35C22×D212—21no—
36#13133242—24no—
37#13133242—42no—
38C2×#11719924—41no—
39C2×D424—21no—
40C2×D424—21no—
41C2×D424—21no—
42C2×D424—21no—
43C2×D424—21no—
44C2×D424C2312yes—
45C2×#11719922—41no—
46C2×#11719917—21no—
47#13133160—24no—
48#13133160—24no—
49#13133157—21no—
50#13133157—24no—
51#13133157C2312yes—
52C2×#11719908—21no—
53C2×#11719908—24no—
54C2×#11719908D411yescharacteristic
55C2×#11719908D411yescharacteristic
56C2×#11719908D412yes—
57C2×#11719908C2312yes—
58#13133153—21no—
59#13133153C2312yes—
60#13133133—24no—
61C2×#41×C53D411yescharacteristic
62C22×Q8×C53—21no—
63#137×C53—24no—
64#137×C53—42no—
65C2×Q16×C53—21no—
66C2×Q16×C53—21no—
67C2×Q16×C53—21no—
68C2×Q16×C53—21no—
69C2×Q16×C53—21no—
70C2×Q16×C53—41no—
71C2×Q16×C53C2312yes—
72C2×SD16×C53—41no—
73#131×C53—21no—
74#131×C53—21no—
75#131×C53D412yes—
76#131×C53C2312yes—
77C2×M16×C53—21no—
78C2×M16×C53—21no—
79C2×M16×C53D411yescharacteristic
80C22×C8×C53—21no—
81C22×C8×C53C2311yescharacteristic
82#108×C53—21no—
83#108×C53C2312yes—
84#101×C53—24no—
85C23×D53—41no—
86#41×C53—21no—
87#41×C53—21no—
88#41×C53D812yes—
89#41×C53C2×D412yes—
90C2×Q8×C53—22no—
91C2×Q8×C53—41no—
92C2×Q8×C53—41no—
93C2×Q8×C53—41no—
94C2×Q8×C53—41no—
95C2×Q8×C53—41no—
96C2×Q8×C53D811yescharacteristic
97C2×D4×C53—21no—
98C2×D4×C53D811yescharacteristic
99C22×C4×C53—21no—
100C22×C4×C53—41no—
101C22×C4×C53C2×D411yescharacteristic
102C2×D212—22no—
103C2×D212—41no—
104C2×D212—41no—
105C2×D212—41no—
106C2×D212—41no—
107C2×D212—41no—
108Q16×C53—22no—
109Q16×C53—22no—
110Q16×C53—44no—
111Q16×C53—41no—
112Q16×C53—41no—
113SD16×C53—44no—
114M16×C53—21no—
115M16×C53—22no—
116M16×C53—22no—
117M16×C53—22no—
118M16×C53—41no—
119M16×C53C2×D412yes—
120C2×C8×C53—21no—
121C2×C8×C53—22no—
122C2×C8×C53—22no—
123C2×C8×C53—41no—
124C2×C8×C53C2×D411yescharacteristic
125C2×C8×C53C2×D411yescharacteristic
126C2×C8×C53C2×D411yescharacteristic
127C2×C8×C53#4111yescharacteristic
128C2×C8×C53#4111yescharacteristic
129C2×C8×C53C2411yescharacteristic
130#11719924—44no—
131#11719922—44no—
132#11719917—22no—
133#11719917—41no—
134C2×#88322—41no—
135D424—22no—
136D424—22no—
137D424—41no—
138D424—41no—
139#11719908—22no—
140#11719908C2×D412yes—
141#11719908C2×D412yes—
142C23×C53—21no—
143C23×C53#13511yescharacteristic
144C22×D53—42no—
145C22×D53—81no—
146C22×D53—81no—
147C22×D53—162no—
148Q8×C53—21no—
149Q8×C53—42no—
150Q8×C53—42no—
151Q8×C53—81no—
152Q8×C53—81no—
153Q8×C53C2×D812yes—
154D4×C53—22no—
155D4×C53—22no—
156D4×C53—21no—
157D4×C53C2×D812yes—
158C2×C4×C53—21no—
159C2×C4×C53—22no—
160C2×C4×C53—22no—
161C2×C4×C53—42no—
162C2×C4×C53—81no—
163C2×C4×C53—81no—
164C2×C4×C53#12111yescharacteristic
165C2×C4×C53#12111yescharacteristic
166C2×C4×C53C2×D811yescharacteristic
167C2×C4×C53C2×D811yescharacteristic
168C2×C4×C53#13511yescharacteristic
169C2×C4×C53C22×D411yescharacteristic
170D212—42no—
171D212—42no—
172D212—81no—
173D212—81no—
174C8×C53—22no—
175C8×C53—42no—
176C8×C53#12111yescharacteristic
177C8×C53#12111yescharacteristic
178C8×C53C22×D411yescharacteristic
179C8×C53C2×#4111yescharacteristic
180#88322—42no—
181C2×#2223—531nomaximal, Sylow
182C22×C53—22no—
183C22×C53—22no—
184C22×C53—42no—
185C22×C53#46611yescharacteristic
186C22×C53#46611yescharacteristic
187C22×C53C2×#13511yescharacteristic
188C2×D53—82no—
189C2×D53—162no—
190C2×D53—162no—
191C2×D53—162no—
192C4×C53—22no—
193C4×C53—82no—
194C4×C53#46611yescharacteristic
195C4×C53#46611yescharacteristic
196C4×C53C2×#12111yescharacteristic
197C4×C53C22×D811yescharacteristic
198C22×SD32—531no—
199C2×#504—531no—
200C2×#473D5311yescharacteristic, complemented
201C2×#472—531no—
202#2223—538no—
203C2×#368—531no—
204C2×#362—531no—
205C2×#361—531no—
206C2×C53—21no—
207C2×C53—21no—
208C2×C53—42no—
209C2×C53#222312yescomplemented
210C2×C53C2×#46611yescharacteristic
211D53—162no—
212C2×#137—21no—
213C2×AGL(1,ℤ/8)—1061no—
214C22×Q16C2×D5311yescharacteristic
215C22×D8—531no—
216C2×#131C2×D5311yescharacteristic
217C2×SD32—534no—
218C2×SD32—1061no—
219C2×SD32—1061no—
220C2×SD32—1062no—
221#504—534no—
222#504—1062no—
223C2×M32—531no—
224C2×M32—1061no—
225C22×C16—531no—
226C22×C16—1061no—
227#473—22no—
228#473C2×D5314yescomplemented
229#472—534no—
230#472—1062no—
231C2×#108—531no—
232C2×#108C2×D5311yescharacteristic
233C2×#101—21no—
234C2×#100—1061no—
235#368—534no—
236#362—534no—
237#361—534no—
238C53C2×#222311yescharacteristic, complemented, Sylow
239C2×#41C22⋊D5311yescharacteristic
240C22×Q8—21no—
241C22×D4—1061no—
242#137—24no—
243#137—42no—
244AGL(1,ℤ/8)—1064no—
245AGL(1,ℤ/8)—2122no—
246C2×Q16—21no—
247C2×Q16—21no—
248C2×Q16—21no—
249C2×Q16—21no—
250C2×Q16—21no—
251C2×Q16—41no—
252C2×Q16C22×D5312yes—
253C2×SD16—41no—
254C2×SD16—2121no—
255C2×D8—532no—
256C2×D8—1061no—
257C2×D8—1061no—
258C2×D8—1061no—
259C2×D8—1061no—
260C2×D8—1061no—
261C2×D8—2121no—
262#131—21no—
263#131—21no—
264#131C22⋊D5312yes—
265#131C22×D5312yes—
266C2×M16—21no—
267C2×M16—21no—
268C2×M16—1061no—
269C2×M16C22⋊D5311yescharacteristic
270C22×C8—21no—
271C22×C8C22×D5311yescharacteristic
272SD32—1064no—
273SD32—1064no—
274M32—532no—
275M32—1064no—
276M32—1061no—
277C2×C16—531no—
278C2×C16—531no—
279C2×C16—532no—
280C2×C16—532no—
281C2×C16—1064no—
282C2×C16—1061no—
283#108—21no—
284#108—532no—
285#108—1061no—
286#108C22×D5312yes—
287#101—24no—
288#100—1064no—
289C24—2121no—
290#41—21no—
291#41—21no—
292#41#1171992212yes—
293#41C2×C22⋊D5312yes—
294C2×Q8—22no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8#1171992211yescharacteristic
301C2×D4—21no—
302C2×D4—1062no—
303C2×D4—2121no—
304C2×D4—2121no—
305C2×D4—2121no—
306C2×D4—2121no—
307C2×D4—2121no—
308C2×D4#1171992211yescharacteristic
309C22×C4—21no—
310C22×C4—41no—
311C22×C4C2×C22⋊D5311yescharacteristic
312Q16—22no—
313Q16—22no—
314Q16—44no—
315Q16—41no—
316Q16—41no—
317SD16—44no—
318SD16—2124no—
319D8—1062no—
320D8—1062no—
321D8—2124no—
322D8—2121no—
323D8—2121no—
324M16—21no—
325M16—22no—
326M16—22no—
327M16—22no—
328M16—41no—
329M16—1062no—
330M16—2121no—
331M16C2×C22⋊D5312yes—
332C2×C8—21no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—41no—
336C2×C8—2121no—
337C2×C8D4×D5311yescharacteristic
338C2×C8D4×D5311yescharacteristic
339C2×C8#1171994711yescharacteristic
340C2×C8#1171994711yescharacteristic
341C2×C8C2×C22⋊D5311yescharacteristic
342C2×C8C23×D5311yescharacteristic
343C16—532no—
344C16—532no—
345C16—1062no—
346C23—21no—
347C23—8482no—
348C23—4241no—
349C23—4241no—
350C23—2122no—
351C23#1313323711yescharacteristic
352Q8—21no—
353Q8—42no—
354Q8—42no—
355Q8—81no—
356Q8—81no—
357Q8C2×#1171992212yes—
358D4—22no—
359D4—22no—
360D4—21no—
361D4—4241no—
362D4—4241no—
363D4—2122no—
364D4—2122no—
365D4C2×#1171992212yes—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—42no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4#1313318911yescharacteristic
373C2×C4#1313318911yescharacteristic
374C2×C4C2×#1171992211yescharacteristic
375C2×C4C2×#1171992211yescharacteristic
376C2×C4#1313323711yescharacteristic
377C2×C4C22×C22⋊D5311yescharacteristic
378C8—22no—
379C8—42no—
380C8—2122no—
381C8#1313318911yescharacteristic
382C8#1313318911yescharacteristic
383C8C2×D4×D5311yescharacteristic
384C8C2×#1171994711yescharacteristic
385C22—22no—
386C22—22no—
387C22—42no—
388C22—8482no—
389C22—8482no—
390C22—8482no—
391C22—4242no—
392C22#1681085711yescharacteristic
393C22#1681085711yescharacteristic
394C22C2×#1313323711yescharacteristic
395C4—22no—
396C4—82no—
397C4#1681085711yescharacteristic
398C4#1681085711yescharacteristic
399C4C2×#1313318911yescharacteristic
400C4C22×#1171992211yescharacteristic
401C2—21no—
402C2—21no—
403C2—42no—
404C2—8482no—
405C2#2027684712yesdirect product factor
406C2C2×#1681085711yescharacteristic
subgroupG/H
centerC22#16810857
commutator, cosocleC2×C8×C53C24
FrattiniC2×C8C23×D53
FittingC2×C53×#473C2
socleC22×C53#466
prime radicalC2×#16810893C2
hypercenterC2×#473D53
hypocenterC53C2×#2223
LCSG ▷ C2×C8×C53 ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#473

Complements

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

NH ≅ G/Ntype
1. C22×#13133160C2semidirect
2. C2×#16811040C2semidirect
4. #20276847C2direct (N × H)
5. C2×#16810452C2semidirect
6. C2×#16810439C2semidirect
7. C2×#16810435C2semidirect
8. C2×C53×#473C2semidirect
14. C2×#13133160C22semidirect
16. #16811040C22semidirect
25. #16810452C22semidirect
26. #16810439C22semidirect
27. #16810435C22semidirect
32. C53×#473C22semidirect
200. C2×#473D53semidirect
209. C2×C53#2223semidirect
228. #473C2×D53semidirect
238. C53C2×#2223semidirect
405. C2#20276847direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131331602
C2×#168110402
C2×#168108932
#202768472
C2×#168104522
C2×#168104392
C2×#168104352
C2×C53×#4732
C2×#222353