Finite Group Databasebeta

← C2×#31826649 #49130604

Subgroups — C2×#31826649 #49130604

Order 36224.

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

normal subgroups only

This group has 708 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×#22583657C211yesmaximal, characteristic
2C2×#22583643C211yesmaximal, characteristic, complemented
3C2×#22583640C211yesmaximal, characteristic, complemented
4C2×#22583610C211yesmaximal, characteristic, complemented
5#31826649C218yesmaximal, direct product factor
6C2×#22583538C211yesmaximal, characteristic, complemented
7C2×#22583528C211yesmaximal, characteristic, complemented
8C2×#104×C283C211yesmaximal, characteristic, complemented
9#22583657—22no—
10#22583657—22no—
11#22583657—22no—
12#22583657C2214yes—
13C2×#17985392—21no—
14C2×#17985392C2211yescharacteristic
15C2×#17985391—22no—
16C2×#17985391—21no—
17C22×Dic566—21no—
18C22×Dic566C2211yescharacteristic
19C22×Dic566C2211yescharacteristic
20C2×Q8×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
30#22583610—22no—
31#22583610C2214yescomplemented
32C2×C4⋊Dic283—22no—
33#22583538C2214yescomplemented
34#22583528C2214yescomplemented
35C2×#41×C283C2211yescharacteristic
36C2×M16×C283C2211yescharacteristic
37C2×C42×C283C2211yescharacteristic
38#104×C283C2214yescomplemented
39#17985392—24no—
40#17985392—24no—
41#17985392—21no—
42#17985392—21no—
43#17985392D412yes—
44#17985392C2312yes—
45#17985391—28no—
46#17985391—24no—
47#17985391—28no—
48#17985391—24no—
49C2×Dic566—22no—
50C2×Dic566—24no—
51C2×Dic566—24no—
52C2×Dic566—21no—
53C2×Dic566—21no—
54C2×Dic566—21no—
55C2×Dic566—21no—
56C2×Dic566—21no—
57C2×Dic566—21no—
58C2×Dic566—21no—
59C2×Dic566—21no—
60C2×Dic566—21no—
61C2×Dic566D411yescharacteristic
62C2×Dic566D412yes—
63C2×Dic566C2312yes—
64C2×Dic566C2312yes—
65Q8×D283—24no—
66Q8×D283—24no—
67C2×D1132D411yescharacteristic
68C2×C22⋊D283—22no—
69C2×C22⋊D283—21no—
70C22×Dic283—22no—
71C22×Dic283—21no—
72C22×Dic283D412yes—
73C2×C4×D283—22no—
74C2×C4×D283—21no—
75Dic1132—24no—
76#17985382—24no—
77#17985381—24no—
78#17985380—24no—
79#17985376—21no—
80#17985376C2312yes—
81C2×C283⋊C8—21no—
82C4⋊Dic283—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×C283C2312yes—
95C2×C8×C283—21no—
96C42×C283—21no—
97C42×C283C2312yes—
98C22×D283—21no—
99Dic566—28no—
100Dic566—22no—
101Dic566—21no—
102Dic566—22no—
103Dic566—22no—
104Dic566—22no—
105Dic566—22no—
106Dic566—22no—
107Dic566—41no—
108Dic566—41no—
109Dic566C2×D412yes—
110D1132—21no—
111D1132C2×D412yes—
112C22⋊D283—28no—
113C22⋊D283—22no—
114C22⋊D283—22no—
115C2×Dic283—28no—
116C2×Dic283—21no—
117C2×Dic283—22no—
118C2×Dic283—22no—
119C2×Dic283—22no—
120C2×Dic283—41no—
121C2×Dic283—41no—
122C2×Dic283C2×D414yes—
123C4×D283—28no—
124C4×D283—22no—
125C4×D283—22no—
126C283⋊C8—22no—
127C23×C283—21no—
128C23×C283C2×D411yescharacteristic
129Q8×C283—21no—
130Q8×C283C2×D412yes—
131D4×C283—22no—
132D4×C283—22no—
133D4×C283—21no—
134D4×C283C2×D412yes—
135C2×C4×C283—24no—
136C2×C4×C283—21no—
137C2×C4×C283—22no—
138C2×C4×C283—22no—
139C2×C4×C283—22no—
140C2×C4×C283C2×D411yescharacteristic
141C2×C4×C283C2×D411yescharacteristic
142C2×C4×C283C2×D411yescharacteristic
143C2×C4×C283C2×D411yescharacteristic
144C2×C4×C283C2×D411yescharacteristic
145C2×C4×C283C2411yescharacteristic
146C8×C283—22no—
147C22×C283—22no—
148C22×C283—22no—
149C22×C283—42no—
150C22×C283#12011yescharacteristic
151C22×C283#12011yescharacteristic
152C22×C283C22×D411yescharacteristic
153C2×D283—22no—
154C2×D283—42no—
155C4×C283—24no—
156C4×C283—22no—
157C4×C283#12011yescharacteristic
158C4×C283#12011yescharacteristic
159C4×C283C22×D411yescharacteristic
160C4×C283C22×D411yescharacteristic
161Dic283—22no—
162Dic283—24no—
163Dic283—42no—
164C2×C283—21no—
165C2×C283—21no—
166C2×C283—42no—
167C2×C283#45612yescomplemented
168C2×C283C2×#12011yescharacteristic
169D283—42no—
170C283C2×#45611yescharacteristic, complemented, Sylow
171C2×#456—2831nomaximal, Sylow
172C2×2−1+4—2831no—
173C2×#137—2831no—
174C2×#137—2831no—
175C2×C4⋊Q8—2831no—
176#456—2838no—
177C2×#104—2831no—
178C2×#104D28311yescharacteristic, complemented
179C2×#101—2831no—
1802−1+4—2834no—
1812−1+4—5662no—
1822−1+4—5662no—
1832−1+4—5662no—
184C2×#41—2831no—
185C2×#41—5661no—
186C2×#41—5662no—
187C2×#41—5661no—
188C2×#41C2×D28311yescharacteristic
189C22×Q8—2831no—
190C22×Q8—2831no—
191C22×Q8—5661no—
192C22×Q8—5661no—
193#137—2834no—
194#137—2834no—
195#137—5662no—
196#137—5662no—
197C2×Q16—5661no—
198C2×Q16—5661no—
199C2×SD16—5661no—
200C2×SD16—5661no—
201C2×M16—2831no—
202C2×M16C2×D28311yescharacteristic
203C4⋊Q8—2834no—
204C4⋊Q8—5662no—
205C2×C4⋊C4—5662no—
206C2×C42C2×D28311yescharacteristic
207#104—2834no—
208#104C2×D28314yescomplemented
209#101—2834no—
210#41—21no—
211#41—21no—
212#41—2832no—
213#41—2832no—
214#41—5664no—
215#41—5664no—
216#41—5668no—
217#41—5668no—
218#41—5664no—
219#41—5664no—
220#41—5661no—
221#41—5661no—
222#41D113212yes—
223#41C22×D28312yes—
224C2×Q8—2832no—
225C2×Q8—2832no—
226C2×Q8—2831no—
227C2×Q8—2832no—
228C2×Q8—5664no—
229C2×Q8—5662no—
230C2×Q8—5664no—
231C2×Q8—5664no—
232C2×Q8—5664no—
233C2×Q8—5661no—
234C2×Q8—5661no—
235C2×Q8—5661no—
236C2×Q8—5661no—
237C2×Q8—5661no—
238C2×Q8—5661no—
239C2×Q8—5661no—
240C2×Q8—5661no—
241C2×Q8—5661no—
242C2×Q8D113211yescharacteristic
243C2×D4—21no—
244C2×D4—2831no—
245C2×D4—5662no—
246C2×D4—5661no—
247C2×D4D113211yescharacteristic
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—2832no—
251C22×C4—5662no—
252C22×C4—5662no—
253C22×C4—5661no—
254C22×C4—5661no—
255C22×C4C22×D28311yescharacteristic
256Q16—5664no—
257Q16—5664no—
258SD16—5664no—
259SD16—5664no—
260M16—21no—
261M16—2832no—
262M16—5661no—
263M16C22×D28312yes—
264C2×C8—21no—
265C2×C8—5661no—
266C4⋊C4—5668no—
267C42—21no—
268C42C22×D28312yes—
269C23—21no—
270C23—5661no—
271C23D4×D28311yescharacteristic
272Q8—21no—
273Q8—2832no—
274Q8—5668no—
275Q8—5662no—
276Q8—5662no—
277Q8—5661no—
278Q8—5662no—
279Q8—5662no—
280Q8—5662no—
281Q8—5662no—
282Q8—11321no—
283Q8—11321no—
284Q8C2×D113212yes—
285D4—22no—
286D4—22no—
287D4—21no—
288D4—2832no—
289D4—5668no—
290D4—5662no—
291D4—5662no—
292D4—5661no—
293D4C2×D113212yes—
294C2×C4—24no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—2834no—
300C2×C4—5668no—
301C2×C4—5668no—
302C2×C4—5662no—
303C2×C4—5662no—
304C2×C4—5661no—
305C2×C4—5662no—
306C2×C4—5662no—
307C2×C4—5662no—
308C2×C4—11321no—
309C2×C4—11321no—
310C2×C4D4×D28311yescharacteristic
311C2×C4D4×D28311yescharacteristic
312C2×C4D4×D28311yescharacteristic
313C2×C4C2×D113211yescharacteristic
314C2×C4C2×D113211yescharacteristic
315C2×C4C23×D28311yescharacteristic
316C8—22no—
317C8—5662no—
318C22—22no—
319C22—22no—
320C22—42no—
321C22—5662no—
322C22—11322no—
323C22#2258358011yescharacteristic
324C22#2258358011yescharacteristic
325C22C2×D4×D28311yescharacteristic
326C4—24no—
327C4—22no—
328C4—5664no—
329C4—5662no—
330C4—11322no—
331C4#2258358011yescharacteristic
332C4#2258358011yescharacteristic
333C4C2×D4×D28311yescharacteristic
334C4C22×D113211yescharacteristic
335C2—21no—
336C2—21no—
337C2—42no—
338C2—11322no—
339C2#3182664912yesdirect product factor
340C2C2×#2258358011yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#104×C283C2
socleC22×C283#120
prime radicalC2×#22583657C2
hypercenterC2×#104D283
hypocenterC283C2×#456
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×#22583610C2semidirect
5. #31826649C2direct (N × H)
6. C2×#22583538C2semidirect
7. C2×#22583528C2semidirect
8. C2×#104×C283C2semidirect
22. #22583643C22semidirect
24. #22583640C22semidirect
31. #22583610C22semidirect
33. #22583538C22semidirect
34. #22583528C22semidirect
38. #104×C283C22semidirect
167. C2×C283#456semidirect
170. C283C2×#456semidirect
178. C2×#104D283semidirect
208. #104C2×D283semidirect
339. C2#31826649direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#225836572
C2×#225836432
C2×#225836402
C2×#225836102
#318266492
C2×#225835382
C2×#225835282
C2×#104×C2832
C2×#456283