Finite Group Databasebeta

← C2×#31826644 #49130592

Subgroups — C2×#31826644 #49130592

Order 36224.

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

normal subgroups only

This group has 760 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
2C2×#22583643C211yesmaximal, characteristic, complemented
3C2×#22583640C211yesmaximal, characteristic, complemented
4C2×#22583598C211yesmaximal, characteristic, complemented
5#31826644C218yesmaximal, 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#22583656C2214yes—
13C2×#17985393—21no—
14C2×#17985392—21no—
15C2×#17985392C2211yescharacteristic
16C22×Dic566C2211yescharacteristic, complemented
17C22×D1132—21no—
18C22×D1132C2211yescharacteristic
19C2×D4×D283—22no—
20C2×D4×D283—21no—
21#22583643—22no—
22#22583643C2214yescomplemented
23#22583640—22no—
24#22583640C2214yescomplemented
25C2×Dic1132—21no—
26C2×#17985382—21no—
27C2×#17985381—21no—
28C2×#17985380—21no—
29C2×#17985376C2211yescharacteristic, complemented
30#22583598—22no—
31#22583598C2214yescomplemented
32C2×(C2×D283)⋊C4—22no—
33#22583538C2214yescomplemented
34#22583526C2214yescomplemented
35C2×#41×C283C2211yescharacteristic
36C2×M16×C283C2211yescharacteristic, complemented
37C2×C42×C283C2211yescharacteristic, complemented
38#104×C283C2214yescomplemented
39C23×D283—22no—
40C23×D283D412yes—
41#17985393—24no—
42#17985393—24no—
43#17985392—24no—
44#17985392—24no—
45#17985392—21no—
46#17985392—21no—
47#17985392D412yes—
48#17985392C2312yes—
49C2×Dic566—21no—
50C2×Dic566—21no—
51C2×Dic566—21no—
52C2×Dic566—21no—
53C2×Dic566—21no—
54C2×Dic566D411yescharacteristic
55C2×Dic566C2312yescomplemented
56C2×D1132—22no—
57C2×D1132—24no—
58C2×D1132—24no—
59C2×D1132—21no—
60C2×D1132—21no—
61C2×D1132—21no—
62C2×D1132—21no—
63C2×D1132D412yes—
64C2×D1132D411yescharacteristic
65C2×D1132C2312yes—
66C2×C22⋊D283—22no—
67C2×C22⋊D283—21no—
68D4×D283—28no—
69D4×D283—24no—
70D4×D283—28no—
71D4×D283—24no—
72C22×Dic283—21no—
73C2×C4×D283—22no—
74C2×C4×D283—21no—
75Dic1132—24no—
76#17985382—24no—
77#17985381—24no—
78#17985380—24no—
79#17985376—21no—
80#17985376C2312yescomplemented
81C2×C283⋊C8—21no—
82(C2×D283)⋊C4—28no—
83#41×C283—21no—
84#41×C283—21no—
85#41×C283D412yes—
86#41×C283C2312yes—
87C2×Q8×C283D411yescharacteristic
88C2×D4×C283—21no—
89C2×D4×C283D411yescharacteristic
90C22×C4×C283—21no—
91C22×C4×C283—21no—
92C22×C4×C283C2311yescharacteristic
93M16×C283—21no—
94M16×C283C2312yescomplemented
95C2×C8×C283—21no—
96C42×C283—21no—
97C42×C283C2312yescomplemented
98C22×D283—22no—
99C22×D283—21no—
100C22×D283—28no—
101C22×D283—22no—
102C22×D283—44no—
103C22×D283—84no—
104C22×D283C2×D414yes—
105Dic566—21no—
106Dic566—22no—
107Dic566—22no—
108Dic566—41no—
109Dic566—41no—
110Dic566C2×D412yes—
111D1132—28no—
112D1132—22no—
113D1132—22no—
114D1132—21no—
115D1132—22no—
116D1132—22no—
117D1132C2×D412yes—
118C22⋊D283—28no—
119C22⋊D283—22no—
120C22⋊D283—22no—
121C2×Dic283—21no—
122C2×Dic283—22no—
123C2×Dic283—41no—
124C2×Dic283—41no—
125C4×D283—28no—
126C4×D283—22no—
127C4×D283—22no—
128C283⋊C8—22no—
129C23×C283—21no—
130C23×C283C2×D411yescharacteristic
131Q8×C283—21no—
132Q8×C283C2×D412yes—
133D4×C283—22no—
134D4×C283—22no—
135D4×C283—21no—
136D4×C283C2×D412yes—
137C2×C4×C283—21no—
138C2×C4×C283—22no—
139C2×C4×C283—22no—
140C2×C4×C283—22no—
141C2×C4×C283—42no—
142C2×C4×C283C2×D411yescharacteristic
143C2×C4×C283C2×D411yescharacteristic
144C2×C4×C283C2×D411yescharacteristic
145C2×C4×C283C2×D411yescharacteristic
146C2×C4×C283C2×D411yescharacteristic
147C2×C4×C283C2411yescharacteristic
148C8×C283—22no—
149C22×C283—22no—
150C22×C283—22no—
151C22×C283—42no—
152C22×C283#12011yescharacteristic
153C22×C283#12011yescharacteristic
154C22×C283C22×D411yescharacteristic
155C2×D283—24no—
156C2×D283—22no—
157C2×D283—44no—
158C2×D283—42no—
159C2×D283—44no—
160C2×D283—82no—
161C2×D283—88no—
162C4×C283—22no—
163C4×C283—42no—
164C4×C283#12011yescharacteristic
165C4×C283#12011yescharacteristic
166C4×C283C22×D411yescharacteristic
167C4×C283C22×D411yescharacteristic
168Dic283—22no—
169Dic283—42no—
170C2×C283—21no—
171C2×C283—21no—
172C2×C283—42no—
173C2×C283#45512yescomplemented
174C2×C283C2×#12011yescharacteristic
175D283—44no—
176D283—42no—
177C283C2×#45511yescharacteristic, complemented, Sylow
178C2×#455—2831nomaximal, Sylow
179C2×H(5,𝔽2)—2831no—
180C2×#137—2831no—
181C2×#137—2831no—
182C2×#124—2831no—
183#455—2838no—
184C2×#104—2831no—
185C2×#104D28311yescharacteristic, complemented
186C2×#100—2831no—
187H(5,𝔽2)—2834no—
188H(5,𝔽2)—5662no—
189H(5,𝔽2)—5662no—
190H(5,𝔽2)—5662no—
191C2×#41—2831no—
192C2×#41—5661no—
193C2×#41—5661no—
194C2×#41C2×D28311yescharacteristic
195C22×Q8—2831no—
196C22×D4—2831no—
197C22×D4—5661no—
198C22×D4—5662no—
199C22×D4—5661no—
200#137—2834no—
201#137—2834no—
202#137—5662no—
203#137—5662no—
204C2×Q16—5661no—
205C2×Q16—5661no—
206C2×SD16—5661no—
207C2×SD16—5661no—
208C2×M16—2831no—
209C2×M16C2×D28311yescharacteristic, complemented
210#124—2834no—
211#124—5662no—
212C2×C22⋊C4—5662no—
213C2×C42C2×D28311yescharacteristic, complemented
214#104—2834no—
215#104C2×D28314yescomplemented
216#100—2834no—
217C24—2832no—
218C24—5662no—
219#41—21no—
220#41—21no—
221#41—2832no—
222#41—2832no—
223#41—5664no—
224#41—5664no—
225#41—5664no—
226#41—5664no—
227#41—5661no—
228#41—5661no—
229#41D113212yes—
230#41C22×D28312yes—
231C2×Q8—2831no—
232C2×Q8—2832no—
233C2×Q8—5661no—
234C2×Q8—5661no—
235C2×Q8—5661no—
236C2×Q8—5661no—
237C2×Q8—5661no—
238C2×Q8D113211yescharacteristic
239C2×D4—21no—
240C2×D4—2831no—
241C2×D4—2832no—
242C2×D4—2832no—
243C2×D4—5664no—
244C2×D4—5662no—
245C2×D4—5664no—
246C2×D4—5668no—
247C2×D4—5668no—
248C2×D4—5664no—
249C2×D4—5662no—
250C2×D4—5661no—
251C2×D4—5664no—
252C2×D4—5661no—
253C2×D4—5661no—
254C2×D4—5661no—
255C2×D4—5661no—
256C2×D4D113211yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—5662no—
260C22×C4—5661no—
261C22×C4—5661no—
262C22×C4C22×D28311yescharacteristic
263Q16—5664no—
264Q16—5664no—
265SD16—5664no—
266SD16—5664no—
267M16—21no—
268M16—2832no—
269M16—5661no—
270M16C22×D28312yescomplemented
271C2×C8—21no—
272C2×C8—5661no—
273C22⋊C4—5668no—
274C42—21no—
275C42C22×D28312yescomplemented
276C23—21no—
277C23—2834no—
278C23—5668no—
279C23—5661no—
280C23—5662no—
281C23—5662no—
282C23—11324no—
283C23—22644no—
284C23D4×D28311yescharacteristic
285Q8—21no—
286Q8—2832no—
287Q8—5661no—
288Q8—5662no—
289Q8—5662no—
290Q8—11321no—
291Q8—11321no—
292Q8C2×D113212yes—
293D4—22no—
294D4—22no—
295D4—21no—
296D4—2832no—
297D4—5668no—
298D4—5668no—
299D4—5662no—
300D4—5662no—
301D4—5661no—
302D4—5662no—
303D4—5662no—
304D4—5662no—
305D4—5662no—
306D4C2×D113212yes—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—42no—
312C2×C4—5668no—
313C2×C4—5661no—
314C2×C4—5662no—
315C2×C4—5662no—
316C2×C4—5662no—
317C2×C4—11321no—
318C2×C4—11321no—
319C2×C4D4×D28311yescharacteristic
320C2×C4D4×D28311yescharacteristic
321C2×C4D4×D28311yescharacteristic
322C2×C4C2×D113211yescharacteristic
323C2×C4C2×D113211yescharacteristic
324C2×C4C23×D28311yescharacteristic
325C8—22no—
326C8—5662no—
327C22—22no—
328C22—22no—
329C22—42no—
330C22—5662no—
331C22—5664no—
332C22—11324no—
333C22—11324no—
334C22—11322no—
335C22—22642no—
336C22—22648no—
337C22#2258358011yescharacteristic
338C22#2258358011yescharacteristic
339C22C2×D4×D28311yescharacteristic
340C4—22no—
341C4—42no—
342C4—5662no—
343C4—11322no—
344C4#2258358011yescharacteristic
345C4#2258358011yescharacteristic
346C4C2×D4×D28311yescharacteristic
347C4C22×D113211yescharacteristic
348C2—21no—
349C2—21no—
350C2—42no—
351C2—11324no—
352C2—11322no—
353C2#3182664412yesdirect product factor
354C2C2×#2258358011yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#104×C283C2
socleC22×C283#120
prime radicalC2×#22583656C2
hypercenterC2×#104D283
hypocenterC283C2×#455
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
2. C2×#22583643C2semidirect
3. C2×#22583640C2semidirect
4. C2×#22583598C2semidirect
5. #31826644C2direct (N × H)
6. C2×#22583538C2semidirect
7. C2×#22583526C2semidirect
8. C2×#104×C283C2semidirect
16. C22×Dic566C22semidirect
22. #22583643C22semidirect
24. #22583640C22semidirect
29. C2×#17985376C22semidirect
31. #22583598C22semidirect
33. #22583538C22semidirect
34. #22583526C22semidirect
36. C2×M16×C283C22semidirect
37. C2×C42×C283C22semidirect
38. #104×C283C22semidirect
55. C2×Dic566C23semidirect
80. #17985376C23semidirect
94. M16×C283C23semidirect
97. C42×C283C23semidirect
173. C2×C283#455semidirect
177. C283C2×#455semidirect
185. C2×#104D283semidirect
209. C2×M16C2×D283semidirect
213. C2×C42C2×D283semidirect
215. #104C2×D283semidirect
270. M16C22×D283semidirect
275. C42C22×D283semidirect
353. C2#31826644direct (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×#225836432
C2×#225836402
C2×#225835982
#318266442
C2×#225835382
C2×#225835262
C2×#104×C2832
C2×#455283