Finite Group Databasebeta

← C2×#20276606 #27537525

Subgroups — C2×#20276606 #27537525

Order 13568.

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×#16811063C211yesmaximal, characteristic
2C2×#16810731C211yesmaximal, characteristic, complemented
3#20276606C218yesmaximal, direct product factor
4C2×#16810447C211yesmaximal, characteristic, complemented
5C2×#16810438C211yesmaximal, characteristic, complemented
6C2×#16810433C211yesmaximal, characteristic
7C2×#16810401C211yesmaximal, characteristic, complemented
8C2×C53×#444C211yesmaximal, characteristic
9C22×Dic212C2211yescharacteristic
10C2×C4×Dic106—21no—
11#16811063C414yescomplemented
12#16811063C2214yes—
13C2×#13133163C412yescomplemented
14C2×#13133161C412yescomplemented
15C2×#13133157C2211yescharacteristic
16C2×#13133157C2211yescharacteristic
17#16810731—22no—
18#16810731C2214yescomplemented
19C2×#13133149C2211yescharacteristic
20C2×#13133142—21no—
21#16810447C2214yescomplemented
22#16810438C2214yescomplemented
23#16810433C2214yes—
24#16810401C2214yescomplemented
25C2×#135×C53C2211yescharacteristic
26C2×#131×C53—21no—
27C53×#444—22no—
28C53×#444C2214yes—
29C2×#108×C53C2211yescharacteristic
30C2×#104×C53—21no—
31C2×#97×C53C2211yescharacteristic
32C22×Dic106—21no—
33C2×Dic212—21no—
34C2×Dic212—21no—
35C2×Dic212—21no—
36C2×Dic212C2×C412yes—
37C2×Dic212C2×C412yes—
38C2×Dic212C2312yes—
39C4×Dic106—24no—
40C4×Dic106—42no—
41C2×C4⋊Dic53—21no—
42C2×#11719919—41no—
43C2×C4×Dic53—41no—
44#13133163C2×C418yescomplemented
45#13133161C2×C418yescomplemented
46#13133157—21no—
47#13133157C2×C412yes—
48#13133157C2312yes—
49#13133157C2312yes—
50C2×#11719908—21no—
51C2×#11719908C2×C412yes—
52#13133149—21no—
53#13133149C2312yes—
54#13133142—24no—
55C2×#41×C53—21no—
56#135×C53—21no—
57#135×C53—21no—
58#135×C53C2×C412yes—
59#135×C53C2312yes—
60C2×Q16×C53C2×C411yescharacteristic
61C2×SD16×C53—21no—
62C2×D8×C53C2×C411yescharacteristic
63#131×C53—24no—
64#131×C53—42no—
65C2×M16×C53—21no—
66C2×M16×C53—41no—
67C22×C8×C53—41no—
68C22×C8×C53D411yescharacteristic
69C22×C8×C53C2311yescharacteristic
70C2×C42×C53D411yescharacteristic
71#108×C53—21no—
72#108×C53C2312yes—
73#104×C53—24no—
74#97×C53D412yes—
75#97×C53C2312yes—
76#41×C53—22no—
77#41×C53—22no—
78#41×C53—41no—
79#41×C53—41no—
80C2×Q8×C53—21no—
81C2×D4×C53—21no—
82C2×D4×C53—41no—
83C22×C4×C53—21no—
84C22×C4×C53—41no—
85C22×C4×C53C2×D411yescharacteristic
86C22×Dic53—41no—
87C22×Dic53—41no—
88C2×Dic106—22no—
89C2×Dic106—22no—
90C2×Dic106—22no—
91C2×Dic106—41no—
92C2×Dic106—41no—
93C2×Dic106—41no—
94Q16×C53—21no—
95Q16×C53C22×C412yes—
96SD16×C53—22no—
97SD16×C53—22no—
98D8×C53—21no—
99D8×C53C22×C412yes—
100M16×C53—22no—
101M16×C53—44no—
102M16×C53—41no—
103C2×C8×C53—21no—
104C2×C8×C53—21no—
105C2×C8×C53—44no—
106C2×C8×C53—41no—
107C2×C8×C53C22×C411yescharacteristic
108C2×C8×C53C22×C411yescharacteristic
109C2×C8×C53C2×D412yes—
110C2×C8×C53C2×D411yescharacteristic
111C2×C8×C53#4111yescharacteristic
112C2×C8×C53#4111yescharacteristic
113C2×C8×C53C2411yescharacteristic
114C42×C53—21no—
115C42×C53C2×D412yes—
116C4⋊Dic53—22no—
117C4⋊Dic53—41no—
118#11719919—44no—
119C4×Dic53—44no—
120Dic212—22no—
121Dic212—22no—
122Dic212—22no—
123Dic212C22×C414yes—
124#11719908—22no—
125#11719908C22×C414yes—
126C23×C53—41no—
127C23×C53AGL(1,ℤ/8)11yescharacteristic
128Q8×C53—22no—
129Q8×C53—41no—
130D4×C53—22no—
131D4×C53—42no—
132D4×C53—42no—
133D4×C53—41no—
134C2×C4×C53—22no—
135C2×C4×C53—42no—
136C2×C4×C53—41no—
137C2×C4×C53—42no—
138C2×C4×C53—42no—
139C2×C4×C53C4×D411yescharacteristic
140C2×C4×C53C4×D411yescharacteristic
141C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C53C22×D411yescharacteristic
145C2×Dic53—42no—
146C2×Dic53—42no—
147C2×Dic53—42no—
148C2×Dic53—42no—
149C2×Dic53—82no—
150Dic106—24no—
151Dic106—42no—
152Dic106—42no—
153Dic106—42no—
154C8×C53—22no—
155C8×C53—42no—
156C8×C53C4×D411yescharacteristic
157C8×C53C4×D411yescharacteristic
158C8×C53C23×C411yescharacteristic
159C8×C53C2×#4111yescharacteristic
160C2×#2180—531nomaximal, Sylow
161C22×C53—22no—
162C22×C53—42no—
163C22×C53—82no—
164C22×C53#44211yescharacteristic
165C22×C53#44211yescharacteristic
166C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
167C4×C53—42no—
168C4×C53—42no—
169C4×C53#44211yescharacteristic
170C4×C53#44211yescharacteristic
171C4×C53C2×C4×D411yescharacteristic
172C4×C53C2×AGL(1,ℤ/8)11yescharacteristic
173Dic53—44no—
174Dic53—82no—
175C2×#510—531no—
176C2×#444D5311yescharacteristic
177C2×#441—531no—
178#2180—538no—
179C2×#365—531no—
180C2×#362—531no—
181C2×#360—531no—
182C2×#347—531no—
183C2×C53—21no—
184C2×C53—21no—
185C2×C53—82no—
186C2×C53#218012yescomplemented
187C2×C53C2×#44211yescharacteristic
188C2×#135C2×D5311yescharacteristic
189C22×Q16—531no—
190C2×#131—21no—
191C2×C4×Q8—1061no—
192#510—534no—
193#510—534no—
194C2×Q32—532no—
195C2×SD32—532no—
196C2×M32—531no—
197C2×M32—531no—
198#444—22no—
199#444C2×D5314yes—
200#441—534no—
201#441—1062no—
202C2×#108C2×D5311yescharacteristic
203C2×#106—531no—
204C2×#104—21no—
205C2×#103—1061no—
206C2×#97C2×D5311yescharacteristic
207#365—534no—
208#362—534no—
209#360—534no—
210#347—534no—
211C53C2×#218011yescharacteristic, complemented, Sylow
212C2×#41—21no—
213C22×Q8—1061no—
214#135—21no—
215#135—21no—
216#135C4×D5312yes—
217#135C22×D5312yes—
218C2×Q16—532no—
219C2×Q16—532no—
220C2×Q16—532no—
221C2×Q16—1061no—
222C2×Q16—1061no—
223C2×Q16—1061no—
224C2×Q16C4×D5311yescharacteristic
225C2×SD16—21no—
226C2×D8C4×D5311yescharacteristic
227#131—24no—
228#131—42no—
229C2×M16—21no—
230C2×M16—41no—
231C22×C8—41no—
232C22×C8C22⋊D5311yescharacteristic
233C22×C8C22×D5311yescharacteristic
234C4×Q8—1064no—
235C4×Q8—2122no—
236C2×C4⋊C4—1061no—
237C2×C4⋊C4—2121no—
238C2×C42—2121no—
239C2×C42C22⋊D5311yescharacteristic
240Q32—538no—
241SD32—538no—
242M32—532no—
243M32—532no—
244M32—532no—
245M32—1061no—
246C2×C16—532no—
247C2×C16—1061no—
248#108—21no—
249#108C22×D5312yes—
250#106—532no—
251#106—1061no—
252#104—24no—
253#103—1064no—
254#97C22⋊D5312yes—
255#97C22×D5312yes—
256#41—22no—
257#41—22no—
258#41—41no—
259#41—41no—
260C2×Q8—21no—
261C2×Q8—1062no—
262C2×Q8—1062no—
263C2×Q8—1062no—
264C2×Q8—2121no—
265C2×Q8—2121no—
266C2×Q8—2121no—
267C2×D4—21no—
268C2×D4—41no—
269C22×C4—21no—
270C22×C4—41no—
271C22×C4—2121no—
272C22×C4—2121no—
273C22×C4C2×C22⋊D5311yescharacteristic
274Q16—21no—
275Q16—534no—
276Q16—1062no—
277Q16—1062no—
278Q16—1062no—
279Q16C2×C4×D5312yes—
280SD16—22no—
281SD16—22no—
282D8—21no—
283D8C2×C4×D5312yes—
284M16—22no—
285M16—44no—
286M16—41no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—44no—
290C2×C8—41no—
291C2×C8C2×C4×D5311yescharacteristic
292C2×C8C2×C4×D5311yescharacteristic
293C2×C8#1171994511yescharacteristic
294C2×C8#1171994511yescharacteristic
295C2×C8C2×C22⋊D5312yes—
296C2×C8C2×C22⋊D5311yescharacteristic
297C2×C8C23×D5311yescharacteristic
298C4⋊C4—1062no—
299C4⋊C4—2124no—
300C4⋊C4—2121no—
301C42—21no—
302C42—2124no—
303C42C2×C22⋊D5312yes—
304C16—534no—
305C16—1062no—
306C23—41no—
307C23#1313324211yescharacteristic
308Q8—22no—
309Q8—41no—
310Q8—1064no—
311Q8—2122no—
312Q8—2122no—
313Q8—2122no—
314D4—22no—
315D4—42no—
316D4—42no—
317D4—41no—
318C2×C4—22no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—4242no—
324C2×C4—2122no—
325C2×C4—2122no—
326C2×C4—2122no—
327C2×C4—2122no—
328C2×C4C4×C22⋊D5311yescharacteristic
329C2×C4C4×C22⋊D5311yescharacteristic
330C2×C4#1313324211yescharacteristic
331C2×C4#1313324311yescharacteristic
332C2×C4#1313324311yescharacteristic
333C2×C4C22×C22⋊D5311yescharacteristic
334C8—22no—
335C8—42no—
336C8C4×C22⋊D5311yescharacteristic
337C8C4×C22⋊D5311yescharacteristic
338C8C22×C4×D5311yescharacteristic
339C8C2×#1171994511yescharacteristic
340C22—22no—
341C22—42no—
342C22—82no—
343C22#1681073311yescharacteristic
344C22#1681073311yescharacteristic
345C22C2×#1313324211yescharacteristic
346C4—42no—
347C4—42no—
348C4—4242no—
349C4—2124no—
350C4#1681073311yescharacteristic
351C4#1681073311yescharacteristic
352C4C2×C4×C22⋊D5311yescharacteristic
353C4C2×#1313324311yescharacteristic
354C2—21no—
355C2—21no—
356C2—82no—
357C2#2027660612yesdirect product factor
358C2C2×#1681073311yescharacteristic
subgroupG/H
centerC22#16810733
commutatorC8×C53C23×C4
FrattiniC2×C8C23×D53
FittingC2×C53×#444C2
socleC22×C53#442
prime radicalC2×#135×C53C22
cosocleC2×C8×C53C24
hypercenterC2×#444D53
hypocenterC53C2×#2180
LCSG ▷ C8×C53 ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ C2×#444

Complements

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

NH ≅ G/Ntype
2. C2×#16810731C2semidirect
3. #20276606C2direct (N × H)
4. C2×#16810447C2semidirect
5. C2×#16810438C2semidirect
7. C2×#16810401C2semidirect
11. #16811063C4semidirect
13. C2×#13133163C4semidirect
14. C2×#13133161C4semidirect
18. #16810731C22semidirect
21. #16810447C22semidirect
22. #16810438C22semidirect
24. #16810401C22semidirect
44. #13133163C2×C4semidirect
45. #13133161C2×C4semidirect
186. C2×C53#2180semidirect
211. C53C2×#2180semidirect
357. C2#20276606direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168110632
C2×#168107312
#202766062
C2×#168104472
C2×#168104382
C2×#168104332
C2×#168104012
C2×C53×#4442
C2×#218053