Finite Group Databasebeta

← C2×#22590241 #32150896

Subgroups — C2×#22590241 #32150896

Order 18176.

710 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986435C211yesmaximal, characteristic
2C2×#17986120C211yesmaximal, characteristic, complemented
3C2×#17986111C211yesmaximal, characteristic, complemented
4#22590241C218yesmaximal, direct product factor
5C2×#17985823C211yesmaximal, characteristic, complemented
6C2×#17985810C211yesmaximal, characteristic, complemented
7C2×#17985776C211yesmaximal, characteristic, complemented
8C2×#361×C71C211yesmaximal, characteristic, complemented
9C2×#14556150C2211yescharacteristic
10C2×#14556136—21no—
11C2×D4×Dic71—21no—
12#17986435C414yescomplemented
13#17986435C2214yes—
14C2×#14556072C412yescomplemented
15C2×#14556069C412yescomplemented
16C2×#14556068C2211yescharacteristic
17#17986120—22no—
18#17986120C2214yescomplemented
19#17986111—22no—
20#17986111C2214yescomplemented
21C2×#14556060C2211yescharacteristic
22C2×#14556054—21no—
23C2×#14556049—21no—
24C2×#14556038C2211yescharacteristic
25#17985823C2214yescomplemented
26#17985810C2214yescomplemented
27#17985776C2214yescomplemented
28C22×D8×C71C2211yescharacteristic
29C2×M32×C71C2211yescharacteristic
30C2×#108×C71C2211yescharacteristic
31#361×C71C2214yescomplemented
32C2×#11765865—21no—
33C23×Dic71—41no—
34#14556150—21no—
35#14556150—21no—
36#14556150C2×C412yescomplemented
37#14556150C2312yes—
38C2×Dic284C2×C411yescharacteristic, complemented
39C2×#11765854—21no—
40C2×D568C2×C411yescharacteristic, complemented
41#14556136—24no—
42#14556136—42no—
43C2×#11765848—41no—
44C22×C71⋊C8D411yescharacteristic
45C2×C8×D71—41no—
46D4×Dic71—24no—
47D4×Dic71—42no—
48C2×C4⋊Dic71—21no—
49C2×C22⋊Dic71—41no—
50C2×C4×Dic71D411yescharacteristic
51#14556072C2×C418yescomplemented
52#14556069C2×C418yescomplemented
53#14556068C2×C412yescomplemented
54#14556068C2312yes—
55C2×C71⋊C16C2×C412yescomplemented
56#14556060—21no—
57#14556060C2312yes—
58#14556054—24no—
59#14556049—24no—
60#14556038D412yes—
61#14556038C2312yes—
62C22×D4×C71—21no—
63C2×D8×C71—21no—
64C2×D8×C71—21no—
65C2×D8×C71—21no—
66C2×D8×C71C2×C412yes—
67C2×D8×C71C2×C412yes—
68C2×D8×C71C2312yes—
69C2×M16×C71—21no—
70C22×C8×C71C2311yescharacteristic
71M32×C71—21no—
72M32×C71C2312yes—
73C2×C16×C71—21no—
74#108×C71—21no—
75#108×C71C2312yes—
76#11765865—22no—
77#11765865—22no—
78#11765865—41no—
79#11765865—41no—
80C2×Dic142—21no—
81C2×D284—21no—
82C2×C22⋊D71—41no—
83C22×Dic71—21no—
84C22×Dic71—44no—
85C22×Dic71—41no—
86C22×Dic71—84no—
87C2×C4×D71—41no—
88Dic284—21no—
89Dic284C22×C412yescomplemented
90#11765854—22no—
91#11765854—22no—
92D568—21no—
93D568C22×C412yescomplemented
94#11765848—44no—
95C2×C71⋊C8—21no—
96C2×C71⋊C8—21no—
97C2×C71⋊C8C2×D412yes—
98C8×D71—44no—
99C4⋊Dic71—22no—
100C4⋊Dic71—41no—
101C22⋊Dic71—44no—
102C4×Dic71—21no—
103C4×Dic71C2×D412yes—
104C71⋊C16C22×C414yescomplemented
105C24×C71—41no—
106C2×D4×C71—22no—
107C2×D4×C71—22no—
108C2×D4×C71—22no—
109C2×D4×C71—41no—
110C2×D4×C71—41no—
111C2×D4×C71—41no—
112C22×C4×C71C2×D411yescharacteristic
113D8×C71—22no—
114D8×C71—22no—
115D8×C71—22no—
116D8×C71C22×C414yes—
117M16×C71—22no—
118M16×C71—41no—
119C2×C8×C71—41no—
120C2×C8×C71C22×C411yescharacteristic
121C2×C8×C71C22×C411yescharacteristic
122C2×C8×C71C2×D411yescharacteristic
123C2×C8×C71#4111yescharacteristic
124C2×C8×C71#4111yescharacteristic
125C2×C8×C71C2411yescharacteristic
126C16×C71—22no—
127C23×C71—42no—
128C23×C71—42no—
129C23×C71—42no—
130C23×C71—82no—
131C23×C71—82no—
132C23×C71AGL(1,ℤ/8)11yescharacteristic
133C22×D71—41no—
134D4×C71—24no—
135D4×C71—42no—
136D4×C71—42no—
137D4×C71—42no—
138C2×C4×C71C4×D411yescharacteristic
139C2×C4×C71C4×D411yescharacteristic
140C2×C4×C71AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C71AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C71AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C71C22×D411yescharacteristic
144C22⋊D71—42no—
145C22⋊D71—42no—
146C2×Dic71—22no—
147C2×Dic71—42no—
148C2×Dic71—41no—
149C2×Dic71—42no—
150C2×Dic71—88no—
151C2×Dic71—82no—
152D284—22no—
153D284—41no—
154C4×D71—42no—
155C4×D71—42no—
156Dic142—22no—
157Dic142—41no—
158C8×C71—42no—
159C8×C71C4×D411yescharacteristic
160C8×C71C4×D411yescharacteristic
161C8×C71C23×C411yescharacteristic
162C8×C71C2×#4111yescharacteristic
163C71⋊C8—22no—
164C22×C71—22no—
165C22×C71—44no—
166C22×C71—82no—
167C22×C71—82no—
168C22×C71—84no—
169C22×C71—84no—
170C22×C71#44211yescharacteristic
171C22×C71#44211yescharacteristic
172C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
173C2×D71—42no—
174C2×D71—82no—
175C4×C71#44211yescharacteristic
176C4×C71#44211yescharacteristic
177C4×C71C2×C4×D411yescharacteristic
178C4×C71C2×AGL(1,ℤ/8)11yescharacteristic
179Dic71—42no—
180Dic71—42no—
181Dic71—82no—
182C2×AGL(1,ℤ/16)—711nomaximal, Sylow
183C2×C71—21no—
184C2×C71—21no—
185C2×C71—84no—
186C2×C71AGL(1,ℤ/16)12yescomplemented
187C2×C71C2×#44211yescharacteristic
188D71—82no—
189C2×#509—711no—
190C2×#444—711no—
191C2×#442—711no—
192AGL(1,ℤ/16)—718no—
193C2×#365—711no—
194C2×#361D7111yescharacteristic, complemented
195C2×#360—711no—
196C2×#347—711no—
197C71C2×AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
198C2×#135—711no—
199C22×D8C2×D7111yescharacteristic
200C2×#131—1421no—
201C2×C4×D4—1421no—
202#509—714no—
203#509—714no—
204C2×SD32—712no—
205C2×D16—712no—
206C2×M32—711no—
207C2×M32C2×D7111yescharacteristic
208#444—714no—
209#444—1422no—
210#442—714no—
211#442—1422no—
212C2×#108C2×D7111yescharacteristic
213C2×#106—711no—
214C2×#104—1421no—
215C2×#102—1421no—
216C2×#97—711no—
217#365—714no—
218#361C2×D7114yescomplemented
219#360—714no—
220#347—714no—
221C2×#41—1421no—
222C22×D4—21no—
223C23×C4—2841no—
224#135—712no—
225#135—712no—
226#135—1421no—
227#135—1421no—
228C2×Q16—711no—
229C2×SD16—1421no—
230C2×D8—21no—
231C2×D8—21no—
232C2×D8—21no—
233C2×D8—711no—
234C2×D8C4×D7112yes—
235C2×D8C4×D7112yes—
236C2×D8C22×D7112yes—
237#131—2842no—
238#131—1424no—
239C2×M16—21no—
240C2×M16—2841no—
241C22×C8—2841no—
242C22×C8—711no—
243C22×C8C22×D7111yescharacteristic
244C4×D4—2842no—
245C4×D4—1424no—
246C2×C4⋊C4—1421no—
247C2×C22⋊C4—2841no—
248C2×C42—711no—
249SD32—718no—
250D16—718no—
251M32—21no—
252M32—712no—
253M32—712no—
254M32C22×D7112yes—
255C2×C16—21no—
256C2×C16—712no—
257#108—21no—
258#108C22×D7112yes—
259#106—712no—
260#106—1421no—
261#104—1424no—
262#102—1424no—
263#97—712no—
264#97—712no—
265C24—41no—
266#41—2841no—
267#41—2841no—
268#41—1422no—
269#41—1422no—
270C2×Q8—1421no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—22no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—2841no—
278C2×D4—1421no—
279C22×C4—2841no—
280C22×C4—2841no—
281C22×C4—2844no—
282C22×C4—5684no—
283C22×C4—1421no—
284C22×C4D4×D7111yescharacteristic
285Q16—712no—
286Q16—1421no—
287SD16—1422no—
288SD16—1422no—
289D8—22no—
290D8—22no—
291D8—22no—
292D8—712no—
293D8—1421no—
294D8C2×C4×D7114yes—
295M16—22no—
296M16—41no—
297M16—2844no—
298C2×C8—41no—
299C2×C8—2844no—
300C2×C8—712no—
301C2×C8—1421no—
302C2×C8—1421no—
303C2×C8C2×C4×D7111yescharacteristic
304C2×C8C2×C4×D7111yescharacteristic
305C2×C8D4×D7111yescharacteristic
306C2×C8#1176586411yescharacteristic
307C2×C8#1176586411yescharacteristic
308C2×C8C23×D7111yescharacteristic
309C4⋊C4—2841no—
310C4⋊C4—1422no—
311C22⋊C4—2844no—
312C42—712no—
313C42—1421no—
314C16—22no—
315C16—714no—
316C23—42no—
317C23—42no—
318C23—42no—
319C23—82no—
320C23—82no—
321C23—2841no—
322C23#1455615511yescharacteristic
323Q8—2841no—
324Q8—1422no—
325D4—24no—
326D4—42no—
327D4—42no—
328D4—42no—
329D4—2842no—
330D4—2842no—
331D4—2841no—
332D4—1422no—
333C2×C4—2842no—
334C2×C4—2841no—
335C2×C4—2842no—
336C2×C4—2842no—
337C2×C4—2842no—
338C2×C4—5688no—
339C2×C4—5682no—
340C2×C4—1422no—
341C2×C4(C22⋊D71)⋊C411yescharacteristic
342C2×C4(C22⋊D71)⋊C411yescharacteristic
343C2×C4#1455615211yescharacteristic
344C2×C4#1455615211yescharacteristic
345C2×C4#1455615511yescharacteristic
346C2×C4C2×D4×D7111yescharacteristic
347C8—42no—
348C8—1422no—
349C8(C22⋊D71)⋊C411yescharacteristic
350C8(C22⋊D71)⋊C411yescharacteristic
351C8C22×C4×D7111yescharacteristic
352C8C2×#1176586411yescharacteristic
353C22—22no—
354C22—44no—
355C22—82no—
356C22—82no—
357C22—84no—
358C22—84no—
359C22—2842no—
360C22—5682no—
361C22#1798610811yescharacteristic
362C22#1798610811yescharacteristic
363C22C2×#1455615511yescharacteristic
364C4—2842no—
365C4—2842no—
366C4—5682no—
367C4#1798610811yescharacteristic
368C4#1798610811yescharacteristic
369C4C2×(C22⋊D71)⋊C411yescharacteristic
370C4C2×#1455615211yescharacteristic
371C2—21no—
372C2—21no—
373C2—84no—
374C2—5682no—
375C2#2259024112yesdirect product factor
376C2C2×#1798610811yescharacteristic
subgroupG/H
centerC22#17986108
commutatorC8×C71C23×C4
FrattiniC2×C8C23×D71
FittingC2×#361×C71C2
socleC22×C71#442
prime radicalC2×#17986435C2
cosocleC2×C8×C71C24
hypercenterC2×#361D71
hypocenterC71C2×AGL(1,ℤ/16)
LCSG ▷ C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

Complements

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

NH ≅ G/Ntype
2. C2×#17986120C2semidirect
3. C2×#17986111C2semidirect
4. #22590241C2direct (N × H)
5. C2×#17985823C2semidirect
6. C2×#17985810C2semidirect
7. C2×#17985776C2semidirect
8. C2×#361×C71C2semidirect
12. #17986435C4semidirect
14. C2×#14556072C4semidirect
15. C2×#14556069C4semidirect
18. #17986120C22semidirect
20. #17986111C22semidirect
25. #17985823C22semidirect
26. #17985810C22semidirect
27. #17985776C22semidirect
31. #361×C71C22semidirect
36. #14556150C2×C4semidirect
38. C2×Dic284C2×C4semidirect
40. C2×D568C2×C4semidirect
51. #14556072C2×C4semidirect
52. #14556069C2×C4semidirect
53. #14556068C2×C4semidirect
55. C2×C71⋊C16C2×C4semidirect
89. Dic284C22×C4semidirect
93. D568C22×C4semidirect
104. C71⋊C16C22×C4semidirect
186. C2×C71AGL(1,ℤ/16)semidirect
194. C2×#361D71semidirect
197. C71C2×AGL(1,ℤ/16)semidirect
218. #361C2×D71semidirect
375. C2#22590241direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179864352
C2×#179861202
C2×#179861112
#225902412
C2×#179858232
C2×#179858102
C2×#179857762
C2×#361×C712
C2×AGL(1,ℤ/16)71