Finite Group Databasebeta

← #49131244

Subgroups — #49131244

Order 36224.

398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#31827046C211yesmaximal, characteristic
2#31826946C211yesmaximal, characteristic, complemented
3#31826808C212yesmaximal, complemented
4#31826802C212yesmaximal, complemented
5#31826792C212yesmaximal, complemented
6#31826780C212yesmaximal, complemented
7#31826505C211yesmaximal, characteristic, complemented
8#31826464C211yesmaximal, characteristic, complemented
9#31826462C211yesmaximal, characteristic, complemented
10#31826431C211yesmaximal, characteristic, complemented
11C2×#107×C283C211yesmaximal, characteristic, complemented
12C2×#17985392C2211yescharacteristic
13C2×#17985392C2211yescharacteristic
14C2×#17985376C2211yescharacteristic
15#22583590—21no—
16#22583590C2212yes—
17#22583585—21no—
18#22583585C2212yes—
19#22583584—22no—
20#22583575—21no—
21#22583572—21no—
22C4×C22⋊D283—22no—
23#22583569C2211yescharacteristic
24#22583568C2212yes—
25C4⋊C4×D283C2212yes—
26#22583543C2212yes—
27#22583541C2212yes—
28#22583535C2211yescharacteristic
29#22583535C2211yescharacteristic
30#22583533C2212yes—
31#22583532C2211yescharacteristic
32#22583532C2211yescharacteristic
33#22583530C2212yes—
34(C2×D283)⋊C8C2212yes—
35(C2×D283)⋊C8C2212yes—
36C22×C8×C283C2211yescharacteristic
37C2×C4⋊C4×C283C2211yescharacteristic
38C2×C4⋊C4×C283C2211yescharacteristic
39#107×C283C2212yes—
40#107×C283C2212yes—
41#17985392—22no—
42#17985392—22no—
43#17985392—22no—
44#17985392—22no—
45C2×Dic566D411yescharacteristic
46C2×Dic566C2311yescharacteristic
47C2×D1132—22no—
48C2×D1132D411yescharacteristic
49C2×D1132C2311yescharacteristic
50C2×C22⋊D283—21no—
51C2×C22⋊D283D412yes—
52C2×C4×D283—22no—
53C2×C4×D283—21no—
54C2×C4×D283C2312yes—
55#17985376—22no—
56C2×C283⋊C8C2312yes—
57C4⋊Dic283—22no—
58C4⋊Dic283C2311yescharacteristic
59C4⋊Dic283C2311yescharacteristic
60Dic283⋊C4—22no—
61C22⋊Dic283—21no—
62(C2×D283)⋊C4—22no—
63(C2×D283)⋊C4—22no—
64(C2×D283)⋊C4—22no—
65C4×Dic283—22no—
66C4×Dic283—21no—
67C22×C4×C283—21no—
68C22×C4×C283—21no—
69C22×C4×C283C2311yescharacteristic
70C2×C8×C283—22no—
71C2×C8×C283C2311yescharacteristic
72C2×C8×C283C2311yescharacteristic
73C4⋊C4×C283—21no—
74C4⋊C4×C283—21no—
75C4⋊C4×C283C2312yes—
76C4⋊C4×C283C2312yes—
77C22×D283—21no—
78C22×D283C2×D412yes—
79Dic566—22no—
80Dic566—21no—
81Dic566—21no—
82D1132—22no—
83D1132—21no—
84D1132—21no—
85D1132—82no—
86C22⋊D283—24no—
87C22⋊D283—42no—
88C2×Dic283—21no—
89C2×Dic283—21no—
90C2×Dic283—21no—
91C2×Dic283C2×D412yes—
92C4×D283—22no—
93C4×D283—22no—
94C4×D283—42no—
95C4×D283—82no—
96C283⋊C8—22no—
97C23×C283C2×D411yescharacteristic
98C2×C4×C283—22no—
99C2×C4×C283—22no—
100C2×C4×C283—81no—
101C2×C4×C283—81no—
102C2×C4×C283C2×D411yescharacteristic
103C2×C4×C283#4112yes—
104C2×C4×C283#4112yes—
105C2×C4×C283C2411yescharacteristic
106C8×C283—21no—
107C8×C283—21no—
108C22×C283—21no—
109C22×C283—21no—
110C22×C283#12312yes—
111C22×C283C22×D411yescharacteristic
112C2×D283—22no—
113C2×D283—22no—
114C2×D283—22no—
115C2×D283—41no—
116C2×D283—41no—
117C2×D283—41no—
118C4×C283—42no—
119C4×C283—42no—
120C4×C283#12312yes—
121C4×C283C2×#4111yescharacteristic
122C4×C283C2×#4111yescharacteristic
123Dic283—22no—
124Dic283—41no—
125Dic283—41no—
126Dic283—41no—
127C2×C283—22no—
128C2×C283C2×#12311yescharacteristic
129C2×C283#57611yescharacteristic
130C2×C283#57811yescharacteristic
131D283—42no—
132D283—81no—
133C283#309811yescharacteristic, complemented, Sylow
134#3098—2831nomaximal, Sylow
135#537—2831no—
136#520—2831no—
137#485—2832no—
138#484—2832no—
139#482—2832no—
140#480—2832no—
141#428—2831no—
142C2×#107D28311yescharacteristic, complemented
143#417—2831no—
144#416—2831no—
145#408—2831no—
146C2×#41—2831no—
147C2×#41—2831no—
148C2×M16—2831no—
149C22×C8C2×D28311yescharacteristic
150C22⋊Q8—2832no—
151C22⋊Q8—5661no—
152#121—2832no—
153#121—5661no—
154#121—5662no—
155C4×Q8—5661no—
156C4×D4—5661no—
157C4×D4—5662no—
158#117—2831no—
159#117—2832no—
160C2×C4⋊C4—2832no—
161C2×C4⋊C4C2×D28311yescharacteristic
162C2×C4⋊C4C2×D28311yescharacteristic
163#107—2832no—
164#107C2×D28312yes—
165#107C2×D28312yes—
166#106—2832no—
167#103—2831no—
168#103—2831no—
169#103—2832no—
170#102—2831no—
171#102—2831no—
172#102—2832no—
173C22⋊C8—2832no—
174C22⋊C8—2832no—
175#41—5662no—
176#41—5662no—
177#41—5662no—
178#41—5662no—
179C2×Q8—2831no—
180C2×Q8—2831no—
181C2×D4—2832no—
182C2×D4—2831no—
183C2×D4—2831no—
184C2×D4—5662no—
185C2×D4—5661no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—2832no—
189C22×C4—5662no—
190C22×C4—5661no—
191C22×C4C22×D28311yescharacteristic
192M16—5662no—
193C2×C8—22no—
194C2×C8—2832no—
195C2×C8C22×D28311yescharacteristic
196C2×C8C22×D28311yescharacteristic
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—2831no—
200C4⋊C4—2831no—
201C4⋊C4—5662no—
202C4⋊C4—5662no—
203C4⋊C4C22×D28312yes—
204C4⋊C4C22×D28312yes—
205C22⋊C4—5662no—
206C22⋊C4—5662no—
207C22⋊C4—5662no—
208C22⋊C4—5661no—
209C42—5662no—
210C42—5661no—
211C23—2832no—
212C23—5661no—
213C23D4×D28311yescharacteristic
214Q8—5662no—
215Q8—5661no—
216Q8—5661no—
217D4—5664no—
218D4—5662no—
219D4—5661no—
220D4—5661no—
221D4—11322no—
222D4—22642no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—81no—
226C2×C4—81no—
227C2×C4—2832no—
228C2×C4—5662no—
229C2×C4—5662no—
230C2×C4—5661no—
231C2×C4—5661no—
232C2×C4—5661no—
233C2×C4—11322no—
234C2×C4—22642no—
235C2×C4D4×D28311yescharacteristic
236C2×C4#1798539212yes—
237C2×C4#1798539312yes—
238C2×C4C23×D28311yescharacteristic
239C8—21no—
240C8—21no—
241C8—5662no—
242C22—21no—
243C22—21no—
244C22—5662no—
245C22—5662no—
246C22—5662no—
247C22—11321no—
248C22—11321no—
249C22—11321no—
250C22#2258359512yes—
251C22C2×D4×D28311yescharacteristic
252C4—42no—
253C4—42no—
254C4—5662no—
255C4—11321no—
256C4—11321no—
257C4—11321no—
258C4#2258359512yes—
259C4C2×#1798539211yescharacteristic
260C4C2×#1798539311yescharacteristic
261C2—22no—
262C2—11322no—
263C2—22641no—
264C2C2×#2258359511yescharacteristic
265C2#3182726611yescharacteristic
266C2#3182727811yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#107×C283C2
socleC22×C283C22×D4
prime radical#31827046C2
hypercenterC2×#107D283
hypocenterC283#3098
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. #31826946C2semidirect
3. #31826808C2semidirect
4. #31826802C2semidirect
5. #31826792C2semidirect
6. #31826780C2semidirect
7. #31826505C2semidirect
8. #31826464C2semidirect
9. #31826462C2semidirect
10. #31826431C2semidirect
11. C2×#107×C283C2semidirect
133. C283#3098semidirect
142. C2×#107D283semidirect

Maximal subgroups

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

subgroupindex
#318270462
#318269462
#318268082
#318268022
#318267922
#318267802
#318265052
#318264642
#318264622
#318264312
C2×#107×C2832
#3098283