Finite Group Databasebeta

← C2×#14521218 #16855036

Subgroups — C2×#14521218 #16855036

Order 3968.

844 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 844 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758566C211yesmaximal, characteristic, complemented
2C2×#11758485C211yesmaximal, characteristic, complemented
3C2×#11758526C211yesmaximal, characteristic, complemented
4C2×#11758451C211yesmaximal, characteristic, complemented
5#14521218C218yesmaximal, direct product factor
6C2×#11758393C211yesmaximal, characteristic, complemented
7C2×#11758411C211yesmaximal, characteristic, complemented
8C2×C31×#104C211yesmaximal, characteristic, complemented
9C2×#41×C31C2211yescharacteristic
10#11758566—22no—
11#11758566—22no—
12#11758566—22no—
13#11758566C2214yescomplemented
14C2×#92499—21no—
15C2×D4×D31—22no—
16C2×D4×D31—21no—
17C2×#92495—21no—
18C2×#92495C2211yescharacteristic
19C22×D124—21no—
20C22×D124—22no—
21C22×D124C2211yescharacteristic
22C22×D124C2211yescharacteristic, complemented
23C2×M16×C31C2211yescharacteristic, complemented
24C2×C42×C31C2211yescharacteristic, complemented
25#11758526—22no—
26#11758526C2214yescomplemented
27C2×#92481—21no—
28C2×#92479—21no—
29C2×#92474C2211yescharacteristic, complemented
30#11758485—22no—
31#11758485C2214yescomplemented
32C2×D248—21no—
33C2×#92470—21no—
34#11758451—22no—
35#11758451C2214yescomplemented
36C31×#104C2214yescomplemented
37#11758411C2214yescomplemented
38#11758393C2214yescomplemented
39C23×D31—22no—
40C23×D31—21no—
41C23×D31D412yes—
42#41×C31—21no—
43#41×C31—21no—
44#41×C31D412yescomplemented
45#41×C31C2312yes—
46C2×Q8×C31D411yescharacteristic, complemented
47C2×D4×C31—21no—
48C2×D4×C31D411yescharacteristic, complemented
49C22×C4×C31—21no—
50C22×C4×C31—21no—
51C22×C4×C31C2311yescharacteristic
52C2×C22⋊D31—22no—
53C2×C22⋊D31—21no—
54#92499—24no—
55#92499—24no—
56D4×D31—28no—
57D4×D31—24no—
58D4×D31—28no—
59D4×D31—24no—
60#92495—24no—
61#92495—21no—
62#92495—21no—
63#92495—24no—
64#92495D412yescomplemented
65#92495C2312yes—
66C2×D124—22no—
67C2×D124—24no—
68C2×D124—21no—
69C2×D124—21no—
70C2×D124—21no—
71C2×D124—21no—
72C2×D124—24no—
73C2×D124—21no—
74C2×D124—21no—
75C2×D124—21no—
76C2×D124—21no—
77C2×D124—28no—
78C2×D124—21no—
79C2×D124—48no—
80C2×D124D412yes—
81C2×D124D411yescharacteristic, complemented
82C2×D124C2312yes—
83C2×D124C2312yescomplemented
84C2×C4×D31—22no—
85C2×C4×D31—21no—
86C2×Dic62D411yescharacteristic, complemented
87M16×C31—21no—
88M16×C31C2312yescomplemented
89C2×C8×C31—21no—
90C42×C31—21no—
91C42×C31C2312yescomplemented
92#92481—24no—
93#92479—24no—
94#92474—21no—
95#92474C2312yescomplemented
96C2×C31⋊C8—21no—
97D248—24no—
98#92470—24no—
99C23×C31—21no—
100C23×C31C2×D411yescharacteristic
101C22×D31—22no—
102C22×D31—21no—
103C22×D31—28no—
104C22×D31—22no—
105C22×D31—22no—
106C22×D31—44no—
107C22×D31—44no—
108C22×D31—41no—
109C22×D31—41no—
110C22×D31—84no—
111C22×D31C2×D414yes—
112Q8×C31—21no—
113Q8×C31C2×D412yescomplemented
114D4×C31—22no—
115D4×C31—22no—
116D4×C31—21no—
117D4×C31C2×D412yescomplemented
118C2×C4×C31—24no—
119C2×C4×C31—21no—
120C2×C4×C31—22no—
121C2×C4×C31—22no—
122C2×C4×C31—22no—
123C2×C4×C31C2×D411yescharacteristic
124C2×C4×C31C2×D411yescharacteristic
125C2×C4×C31C2×D411yescharacteristic
126C2×C4×C31C2×D411yescharacteristic
127C2×C4×C31C2×D411yescharacteristic
128C2×C4×C31C2411yescharacteristic
129C22⋊D31—28no—
130C22⋊D31—22no—
131C22⋊D31—22no—
132C2×Dic31—21no—
133D124—28no—
134D124—22no—
135D124—21no—
136D124—22no—
137D124—22no—
138D124—22no—
139D124—22no—
140D124—22no—
141D124—416no—
142D124—41no—
143D124—41no—
144D124C2×D412yescomplemented
145C4×D31—28no—
146C4×D31—22no—
147C4×D31—22no—
148Dic62—21no—
149Dic62C2×D412yescomplemented
150C8×C31—22no—
151C31⋊C8—22no—
152C2×#453—311nomaximal, Sylow
153C22×C31—22no—
154C22×C31—22no—
155C22×C31—42no—
156C22×C31#12011yescharacteristic
157C22×C31#12011yescharacteristic
158C22×C31C22×D411yescharacteristic
159C2×D31—24no—
160C2×D31—22no—
161C2×D31—44no—
162C2×D31—42no—
163C2×D31—44no—
164C2×D31—44no—
165C2×D31—42no—
166C2×D31—82no—
167C2×D31—88no—
168C2×D31—82no—
169C2×D31—82no—
170C4×C31—24no—
171C4×C31—22no—
172C4×C31#12011yescharacteristic
173C4×C31#12011yescharacteristic
174C4×C31C22×D411yescharacteristic
175C4×C31C22×D411yescharacteristic
176Dic31—22no—
177C2×H(5,𝔽2)—311no—
178C2×AGL(1,ℤ/8)—311no—
179C2×AGL(1,ℤ/8)—311no—
180C2×#127—311no—
181#453—318no—
182C2×#104—311no—
183C2×#104D3111yescharacteristic, complemented
184C2×#100—311no—
185C2×C31—21no—
186C2×C31—21no—
187C2×C31—42no—
188C2×C31#45312yescomplemented
189C2×C31C2×#12011yescharacteristic
190D31—44no—
191D31—42no—
192D31—82no—
193H(5,𝔽2)—314no—
194H(5,𝔽2)—622no—
195H(5,𝔽2)—622no—
196H(5,𝔽2)—622no—
197C2×#41—311no—
198C2×#41—621no—
199C2×#41—621no—
200C2×#41C2×D3111yescharacteristic
201C22×D4—311no—
202C22×D4—311no—
203C22×D4—621no—
204C22×D4—622no—
205C22×D4—622no—
206C22×D4—621no—
207AGL(1,ℤ/8)—314no—
208AGL(1,ℤ/8)—314no—
209AGL(1,ℤ/8)—622no—
210AGL(1,ℤ/8)—622no—
211C2×SD16—621no—
212C2×SD16—621no—
213C2×D8—621no—
214C2×D8—621no—
215C2×M16—311no—
216C2×M16C2×D3111yescharacteristic, complemented
217#127—314no—
218#127—622no—
219C2×C42C2×D3111yescharacteristic, complemented
220#104—314no—
221#104C2×D3114yescomplemented
222#100—314no—
223C31C2×#45311yescharacteristic, complemented, Sylow
224C24—312no—
225C24—622no—
226C24—621no—
227#41—21no—
228#41—21no—
229#41—312no—
230#41—312no—
231#41—624no—
232#41—624no—
233#41—624no—
234#41—624no—
235#41—621no—
236#41—621no—
237#41D12412yescomplemented
238#41C22×D3112yes—
239C2×Q8—311no—
240C2×Q8D12411yescharacteristic, complemented
241C2×D4—21no—
242C2×D4—311no—
243C2×D4—312no—
244C2×D4—312no—
245C2×D4—312no—
246C2×D4—624no—
247C2×D4—622no—
248C2×D4—624no—
249C2×D4—628no—
250C2×D4—628no—
251C2×D4—628no—
252C2×D4—624no—
253C2×D4—622no—
254C2×D4—621no—
255C2×D4—624no—
256C2×D4—621no—
257C2×D4—621no—
258C2×D4—621no—
259C2×D4—621no—
260C2×D4—621no—
261C2×D4—621no—
262C2×D4—621no—
263C2×D4—621no—
264C2×D4—621no—
265C2×D4—1248no—
266C2×D4D12411yescharacteristic, complemented
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—622no—
270C22×C4—621no—
271C22×C4C22×D3111yescharacteristic
272SD16—624no—
273SD16—624no—
274D8—624no—
275D8—624no—
276M16—21no—
277M16—312no—
278M16—621no—
279M16C22×D3112yescomplemented
280C2×C8—21no—
281C2×C8—621no—
282C42—21no—
283C42C22×D3112yescomplemented
284C23—21no—
285C23—314no—
286C23—628no—
287C23—621no—
288C23—622no—
289C23—622no—
290C23—622no—
291C23—1244no—
292C23—1244no—
293C23—1241no—
294C23—1241no—
295C23—2484no—
296C23D4×D3111yescharacteristic
297Q8—21no—
298Q8—312no—
299Q8—621no—
300Q8C2×D12412yescomplemented
301D4—22no—
302D4—22no—
303D4—21no—
304D4—312no—
305D4—628no—
306D4—628no—
307D4—622no—
308D4—622no—
309D4—621no—
310D4—622no—
311D4—622no—
312D4—622no—
313D4—622no—
314D4—622no—
315D4—622no—
316D4—12416no—
317D4—1241no—
318D4—1241no—
319D4C2×D12412yescomplemented
320C2×C4—24no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—628no—
326C2×C4—621no—
327C2×C4—622no—
328C2×C4—622no—
329C2×C4C2×D12411yescharacteristic
330C2×C4C2×D12411yescharacteristic
331C2×C4D4×D3111yescharacteristic
332C2×C4D4×D3111yescharacteristic
333C2×C4D4×D3111yescharacteristic
334C2×C4C23×D3111yescharacteristic
335C8—22no—
336C8—622no—
337C22—22no—
338C22—22no—
339C22—42no—
340C22—622no—
341C22—624no—
342C22—1244no—
343C22—1244no—
344C22—1244no—
345C22—1242no—
346C22—1242no—
347C22—2482no—
348C22—2482no—
349C22—2488no—
350C22—2482no—
351C22#1175845911yescharacteristic
352C22#1175845911yescharacteristic
353C22C2×D4×D3111yescharacteristic
354C4—24no—
355C4—22no—
356C4—622no—
357C4#1175845911yescharacteristic
358C4#1175845911yescharacteristic
359C4C22×D12411yescharacteristic
360C4C2×D4×D3111yescharacteristic
361C2—21no—
362C2—21no—
363C2—42no—
364C2—1244no—
365C2—1242no—
366C2—2482no—
367C2#1452121812yesdirect product factor
368C2C2×#1175845911yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#104C2
socleC22×C31#120
hypercenterC2×#104D31
hypocenterC31C2×#453
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×#11758566C2semidirect
2. C2×#11758485C2semidirect
3. C2×#11758526C2semidirect
4. C2×#11758451C2semidirect
5. #14521218C2direct (N × H)
6. C2×#11758393C2semidirect
7. C2×#11758411C2semidirect
8. C2×C31×#104C2semidirect
13. #11758566C22semidirect
22. C22×D124C22semidirect
23. C2×M16×C31C22semidirect
24. C2×C42×C31C22semidirect
26. #11758526C22semidirect
29. C2×#92474C22semidirect
31. #11758485C22semidirect
35. #11758451C22semidirect
36. C31×#104C22semidirect
37. #11758411C22semidirect
38. #11758393C22semidirect
44. #41×C31D4semidirect
46. C2×Q8×C31D4semidirect
48. C2×D4×C31D4semidirect
64. #92495D4semidirect
81. C2×D124D4semidirect
83. C2×D124C23semidirect
86. C2×Dic62D4semidirect
88. M16×C31C23semidirect
91. C42×C31C23semidirect
95. #92474C23semidirect
113. Q8×C31C2×D4semidirect
117. D4×C31C2×D4semidirect
144. D124C2×D4semidirect
149. Dic62C2×D4semidirect
183. C2×#104D31semidirect
188. C2×C31#453semidirect
216. C2×M16C2×D31semidirect
219. C2×C42C2×D31semidirect
221. #104C2×D31semidirect
223. C31C2×#453semidirect
237. #41D124semidirect
240. C2×Q8D124semidirect
266. C2×D4D124semidirect
279. M16C22×D31semidirect
283. C42C22×D31semidirect
300. Q8C2×D124semidirect
319. D4C2×D124semidirect
367. C2#14521218direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117585662
C2×#117584852
C2×#117585262
C2×#117584512
#145212182
C2×#117583932
C2×#117584112
C2×C31×#1042
C2×#45331