Finite Group Databasebeta

← C2×#31826634 #49130586

Subgroups — C2×#31826634 #49130586

Order 36224.

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×#22583656C211yesmaximal, characteristic, complemented
2C2×#22583638C211yesmaximal, characteristic, complemented
3C2×#22583635C211yesmaximal, characteristic, complemented
4C2×#22583607C211yesmaximal, characteristic, complemented
5#31826634C218yesmaximal, direct product factor
6C2×#22583538C211yesmaximal, characteristic, complemented
7C2×#22583526C211yesmaximal, characteristic, complemented
8C2×#104×C283C211yesmaximal, characteristic, complemented
9#22583656—22no—
10#22583656—22no—
11#22583656—22no—
12#22583656C2214yescomplemented
13C2×#17985393—21no—
14C2×#17985392—21no—
15C2×#17985392C2211yescharacteristic
16C22×D1132—21no—
17C22×D1132—22no—
18C22×D1132C2211yescharacteristic
19C22×D1132C2211yescharacteristic, complemented
20C2×D4×D283—22no—
21C2×D4×D283—21no—
22#22583638—22no—
23#22583638C2214yescomplemented
24#22583635—22no—
25#22583635C2214yescomplemented
26C2×#17985381—21no—
27C2×#17985379—21no—
28C2×D2264—21no—
29C2×#17985377—21no—
30C2×#17985376C2211yescharacteristic, complemented
31#22583607—22no—
32#22583607C2214yescomplemented
33#22583538C2214yescomplemented
34#22583526C2214yescomplemented
35C2×#41×C283C2211yescharacteristic
36C2×M16×C283C2211yescharacteristic, complemented
37C2×C42×C283C2211yescharacteristic, complemented
38#104×C283C2214yescomplemented
39C23×D283—22no—
40C23×D283—21no—
41C23×D283D412yes—
42#17985393—24no—
43#17985393—24no—
44#17985392—24no—
45#17985392—24no—
46#17985392—21no—
47#17985392—21no—
48#17985392D412yescomplemented
49#17985392C2312yes—
50C2×Dic566D411yescharacteristic, complemented
51C2×D1132—22no—
52C2×D1132—24no—
53C2×D1132—24no—
54C2×D1132—28no—
55C2×D1132—21no—
56C2×D1132—21no—
57C2×D1132—21no—
58C2×D1132—21no—
59C2×D1132—21no—
60C2×D1132—21no—
61C2×D1132—21no—
62C2×D1132—21no—
63C2×D1132—21no—
64C2×D1132—48no—
65C2×D1132D412yes—
66C2×D1132D411yescharacteristic, complemented
67C2×D1132C2312yes—
68C2×D1132C2312yescomplemented
69C2×C22⋊D283—22no—
70C2×C22⋊D283—21no—
71D4×D283—28no—
72D4×D283—24no—
73D4×D283—28no—
74D4×D283—24no—
75C2×C4×D283—22no—
76C2×C4×D283—21no—
77#17985381—24no—
78#17985379—24no—
79D2264—24no—
80#17985377—24no—
81#17985376—21no—
82#17985376C2312yescomplemented
83C2×C283⋊C8—21no—
84#41×C283—21no—
85#41×C283—21no—
86#41×C283D412yescomplemented
87#41×C283C2312yes—
88C2×Q8×C283D411yescharacteristic, complemented
89C2×D4×C283—21no—
90C2×D4×C283D411yescharacteristic, complemented
91C22×C4×C283—21no—
92C22×C4×C283—21no—
93C22×C4×C283C2311yescharacteristic
94M16×C283—21no—
95M16×C283C2312yescomplemented
96C2×C8×C283—21no—
97C42×C283—21no—
98C42×C283C2312yescomplemented
99C22×D283—22no—
100C22×D283—21no—
101C22×D283—28no—
102C22×D283—22no—
103C22×D283—22no—
104C22×D283—44no—
105C22×D283—44no—
106C22×D283—41no—
107C22×D283—41no—
108C22×D283—84no—
109C22×D283C2×D414yes—
110Dic566—21no—
111Dic566C2×D412yescomplemented
112D1132—28no—
113D1132—22no—
114D1132—22no—
115D1132—21no—
116D1132—22no—
117D1132—22no—
118D1132—22no—
119D1132—22no—
120D1132—416no—
121D1132—41no—
122D1132—41no—
123D1132C2×D412yescomplemented
124C22⋊D283—28no—
125C22⋊D283—22no—
126C22⋊D283—22no—
127C2×Dic283—21no—
128C4×D283—28no—
129C4×D283—22no—
130C4×D283—22no—
131C283⋊C8—22no—
132C23×C283—21no—
133C23×C283C2×D411yescharacteristic
134Q8×C283—21no—
135Q8×C283C2×D412yescomplemented
136D4×C283—22no—
137D4×C283—22no—
138D4×C283—21no—
139D4×C283C2×D412yescomplemented
140C2×C4×C283—24no—
141C2×C4×C283—21no—
142C2×C4×C283—22no—
143C2×C4×C283—22no—
144C2×C4×C283—22no—
145C2×C4×C283C2×D411yescharacteristic
146C2×C4×C283C2×D411yescharacteristic
147C2×C4×C283C2×D411yescharacteristic
148C2×C4×C283C2×D411yescharacteristic
149C2×C4×C283C2×D411yescharacteristic
150C2×C4×C283C2411yescharacteristic
151C8×C283—22no—
152C22×C283—22no—
153C22×C283—22no—
154C22×C283—42no—
155C22×C283#12011yescharacteristic
156C22×C283#12011yescharacteristic
157C22×C283C22×D411yescharacteristic
158C2×D283—24no—
159C2×D283—22no—
160C2×D283—44no—
161C2×D283—42no—
162C2×D283—44no—
163C2×D283—44no—
164C2×D283—42no—
165C2×D283—82no—
166C2×D283—88no—
167C2×D283—82no—
168C2×D283—82no—
169C4×C283—24no—
170C4×C283—22no—
171C4×C283#12011yescharacteristic
172C4×C283#12011yescharacteristic
173C4×C283C22×D411yescharacteristic
174C4×C283C22×D411yescharacteristic
175Dic283—22no—
176C2×C283—21no—
177C2×C283—21no—
178C2×C283—42no—
179C2×C283#45312yescomplemented
180C2×C283C2×#12011yescharacteristic
181D283—44no—
182D283—42no—
183D283—82no—
184C283C2×#45311yescharacteristic, complemented, Sylow
185C2×#453—2831nomaximal, Sylow
186C2×H(5,𝔽2)—2831no—
187C2×AGL(1,ℤ/8)—2831no—
188C2×AGL(1,ℤ/8)—2831no—
189C2×#127—2831no—
190#453—2838no—
191C2×#104—2831no—
192C2×#104D28311yescharacteristic, complemented
193C2×#100—2831no—
194H(5,𝔽2)—2834no—
195H(5,𝔽2)—5662no—
196H(5,𝔽2)—5662no—
197H(5,𝔽2)—5662no—
198C2×#41—2831no—
199C2×#41—5661no—
200C2×#41—5661no—
201C2×#41C2×D28311yescharacteristic
202C22×D4—2831no—
203C22×D4—2831no—
204C22×D4—5661no—
205C22×D4—5662no—
206C22×D4—5662no—
207C22×D4—5661no—
208AGL(1,ℤ/8)—2834no—
209AGL(1,ℤ/8)—2834no—
210AGL(1,ℤ/8)—5662no—
211AGL(1,ℤ/8)—5662no—
212C2×SD16—5661no—
213C2×SD16—5661no—
214C2×D8—5661no—
215C2×D8—5661no—
216C2×M16—2831no—
217C2×M16C2×D28311yescharacteristic, complemented
218#127—2834no—
219#127—5662no—
220C2×C42C2×D28311yescharacteristic, complemented
221#104—2834no—
222#104C2×D28314yescomplemented
223#100—2834no—
224C24—2832no—
225C24—5662no—
226C24—5661no—
227#41—21no—
228#41—21no—
229#41—2832no—
230#41—2832no—
231#41—5664no—
232#41—5664no—
233#41—5664no—
234#41—5664no—
235#41—5661no—
236#41—5661no—
237#41D113212yescomplemented
238#41C22×D28312yes—
239C2×Q8—2831no—
240C2×Q8D113211yescharacteristic, complemented
241C2×D4—21no—
242C2×D4—2831no—
243C2×D4—2832no—
244C2×D4—2832no—
245C2×D4—2832no—
246C2×D4—5664no—
247C2×D4—5662no—
248C2×D4—5664no—
249C2×D4—5668no—
250C2×D4—5668no—
251C2×D4—5668no—
252C2×D4—5664no—
253C2×D4—5662no—
254C2×D4—5661no—
255C2×D4—5664no—
256C2×D4—5661no—
257C2×D4—5661no—
258C2×D4—5661no—
259C2×D4—5661no—
260C2×D4—5661no—
261C2×D4—5661no—
262C2×D4—5661no—
263C2×D4—5661no—
264C2×D4—5661no—
265C2×D4—11328no—
266C2×D4D113211yescharacteristic, complemented
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—5662no—
270C22×C4—5661no—
271C22×C4C22×D28311yescharacteristic
272SD16—5664no—
273SD16—5664no—
274D8—5664no—
275D8—5664no—
276M16—21no—
277M16—2832no—
278M16—5661no—
279M16C22×D28312yescomplemented
280C2×C8—21no—
281C2×C8—5661no—
282C42—21no—
283C42C22×D28312yescomplemented
284C23—21no—
285C23—2834no—
286C23—5668no—
287C23—5661no—
288C23—5662no—
289C23—5662no—
290C23—5662no—
291C23—11324no—
292C23—11324no—
293C23—11321no—
294C23—11321no—
295C23—22644no—
296C23D4×D28311yescharacteristic
297Q8—21no—
298Q8—2832no—
299Q8—5661no—
300Q8C2×D113212yescomplemented
301D4—22no—
302D4—22no—
303D4—21no—
304D4—2832no—
305D4—5668no—
306D4—5668no—
307D4—5662no—
308D4—5662no—
309D4—5661no—
310D4—5662no—
311D4—5662no—
312D4—5662no—
313D4—5662no—
314D4—5662no—
315D4—5662no—
316D4—113216no—
317D4—11321no—
318D4—11321no—
319D4C2×D113212yescomplemented
320C2×C4—24no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—5668no—
326C2×C4—5661no—
327C2×C4—5662no—
328C2×C4—5662no—
329C2×C4D4×D28311yescharacteristic
330C2×C4D4×D28311yescharacteristic
331C2×C4D4×D28311yescharacteristic
332C2×C4C2×D113211yescharacteristic
333C2×C4C2×D113211yescharacteristic
334C2×C4C23×D28311yescharacteristic
335C8—22no—
336C8—5662no—
337C22—22no—
338C22—22no—
339C22—42no—
340C22—5662no—
341C22—5664no—
342C22—11324no—
343C22—11324no—
344C22—11324no—
345C22—11322no—
346C22—11322no—
347C22—22642no—
348C22—22642no—
349C22—22648no—
350C22—22642no—
351C22#2258358011yescharacteristic
352C22#2258358011yescharacteristic
353C22C2×D4×D28311yescharacteristic
354C4—24no—
355C4—22no—
356C4—5662no—
357C4#2258358011yescharacteristic
358C4#2258358011yescharacteristic
359C4C2×D4×D28311yescharacteristic
360C4C22×D113211yescharacteristic
361C2—21no—
362C2—21no—
363C2—42no—
364C2—11324no—
365C2—11322no—
366C2—22642no—
367C2#3182663412yesdirect product factor
368C2C2×#2258358011yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#104×C283C2
socleC22×C283#120
hypercenterC2×#104D283
hypocenterC283C2×#453
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×#22583656C2semidirect
2. C2×#22583638C2semidirect
3. C2×#22583635C2semidirect
4. C2×#22583607C2semidirect
5. #31826634C2direct (N × H)
6. C2×#22583538C2semidirect
7. C2×#22583526C2semidirect
8. C2×#104×C283C2semidirect
12. #22583656C22semidirect
19. C22×D1132C22semidirect
23. #22583638C22semidirect
25. #22583635C22semidirect
30. C2×#17985376C22semidirect
32. #22583607C22semidirect
33. #22583538C22semidirect
34. #22583526C22semidirect
36. C2×M16×C283C22semidirect
37. C2×C42×C283C22semidirect
38. #104×C283C22semidirect
48. #17985392D4semidirect
50. C2×Dic566D4semidirect
66. C2×D1132D4semidirect
68. C2×D1132C23semidirect
82. #17985376C23semidirect
86. #41×C283D4semidirect
88. C2×Q8×C283D4semidirect
90. C2×D4×C283D4semidirect
95. M16×C283C23semidirect
98. C42×C283C23semidirect
111. Dic566C2×D4semidirect
123. D1132C2×D4semidirect
135. Q8×C283C2×D4semidirect
139. D4×C283C2×D4semidirect
179. C2×C283#453semidirect
184. C283C2×#453semidirect
192. C2×#104D283semidirect
217. C2×M16C2×D283semidirect
220. C2×C42C2×D283semidirect
222. #104C2×D283semidirect
237. #41D1132semidirect
240. C2×Q8D1132semidirect
266. C2×D4D1132semidirect
279. M16C22×D283semidirect
283. C42C22×D283semidirect
300. Q8C2×D1132semidirect
319. D4C2×D1132semidirect
367. C2#31826634direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#225836562
C2×#225836382
C2×#225836352
C2×#225836072
#318266342
C2×#225835382
C2×#225835262
C2×#104×C2832
C2×#453283