Finite Group Databasebeta

← #49096955

Subgroups — #49096955

Order 35968.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#31824035C211yesmaximal, characteristic
2#31823444C211yesmaximal, characteristic
3#31823435C211yesmaximal, characteristic
4#31823254C211yesmaximal, characteristic, complemented
5#31823253C211yesmaximal, characteristic, complemented
6#31823252C211yesmaximal, characteristic, complemented
7#352×C281C211yesmaximal, characteristic, complemented
8C2×#17985137C2211yescharacteristic
9C22×Dic562C411yescharacteristic, complemented
10M16×D281—21no—
11#22582878—21no—
12#22582865—21no—
13#22582863C411yescharacteristic, complemented
14#22582862C411yescharacteristic, complemented
15#22582860C2211yescharacteristic
16#22582857—21no—
17#22582856—21no—
18#22582835—21no—
19#22582835C411yescharacteristic, complemented
20#22582797—21no—
21#22582796C2211yescharacteristic
22#22582794C2211yescharacteristic
23#22582793—21no—
24#123×C281C2211yescharacteristic
25#100×C281C2211yescharacteristic
26#99×C281C2211yescharacteristic
27#17985137—41no—
28#17985137—41no—
29C2×Dic562—21no—
30C2×Dic562—21no—
31C2×Dic562—41no—
32C2×Dic562—41no—
33C2×Dic562D411yescharacteristic
34C2×C22⋊D281C2×C411yescharacteristic
35C2×C22⋊D281D411yescharacteristic
36C22×Dic281C2×C411yescharacteristic
37C22×Dic281C2×C411yescharacteristic
38C22×Dic281D411yescharacteristic
39C2×C4×D281D411yescharacteristic
40#17985122—21no—
41#17985121—41no—
42C8×D281—41no—
43C4⋊Dic281—21no—
44#17985117—21no—
45#17985117—21no—
46#17985117—21no—
47#17985117—41no—
48C22⋊Dic281—21no—
49C22⋊Dic281—21no—
50C22⋊Dic281C2×C411yescharacteristic
51#17985115—21no—
52#17985115—21no—
53C4×Dic281—21no—
54C4×Dic281—41no—
55C2×D4×C281C2311yescharacteristic
56C22×C4×C281C2×C411yescharacteristic
57M16×C281—21no—
58C4⋊C4×C281—21no—
59C22⋊C4×C281—21no—
60C22⋊C4×C281—21no—
61C22⋊C4×C281C2×C411yescharacteristic
62C22×D281C22⋊C411yescharacteristic
63Dic562—41no—
64Dic562—42no—
65Dic562—41no—
66Dic562—41no—
67C22⋊D281—41no—
68C22⋊D281—41no—
69C2×Dic281—21no—
70C2×Dic281—21no—
71C2×Dic281—21no—
72C2×Dic281—21no—
73C2×Dic281—21no—
74C2×Dic281—21no—
75C2×Dic281—41no—
76C2×Dic281—41no—
77C2×Dic281C22⋊C411yescharacteristic
78C2×Dic281C22⋊C411yescharacteristic
79C2×Dic281C22⋊C411yescharacteristic
80C4×D281—21no—
81C4×D281—21no—
82#14555886—41no—
83C23×C281C22×C411yescharacteristic
84C23×C281C2×D411yescharacteristic
85D4×C281—41no—
86C2×C4×C281—21no—
87C2×C4×C281—21no—
88C2×C4×C281—41no—
89C2×C4×C281—41no—
90C2×C4×C281C2×D411yescharacteristic
91C8×C281—41no—
92C22×C281—21no—
93C22×C281—21no—
94C22×C281—41no—
95C22×C281—41no—
96C22×C281C2×C22⋊C411yescharacteristic
97C2×D281—21no—
98C2×D281—41no—
99C4×C281—21no—
100C4×C281—41no—
101C4×C281—41no—
102C4×C281—81no—
103Dic281—21no—
104Dic281—21no—
105Dic281—41no—
106Dic281—41no—
107Dic281—81no—
108Dic281#9911yescharacteristic
109Dic281#9911yescharacteristic
110C2×C281—21no—
111C2×C281—41no—
112C2×C281—41no—
113C2×C281C2×#9911yescharacteristic
114D281—41no—
115C281#212311yescharacteristic, complemented, Sylow
116#2123—2811nomaximal, Sylow
117#536—2811no—
118#413—2811no—
119#410—2811no—
120#352—2811no—
121#352—2811no—
122#352—2811no—
123#352D28111yescharacteristic, complemented
124C2×#41—2811no—
125C22×Q8—2811no—
126C2×M16—5621no—
127C4⋊Q8—5621no—
128#124—5621no—
129#123—2811no—
130#123—2811no—
131#123—2811no—
132#123C2×D28111yescharacteristic
133C22⋊Q8—5621no—
134C22⋊Q8—5621no—
135#117—2811no—
136#117—5621no—
137#101—5621no—
138#100—2811no—
139#100C2×D28111yescharacteristic
140#99—2811no—
141#99—5621no—
142#99C2×D28111yescharacteristic
143#41—11241no—
144#41—11241no—
145C2×Q8—2811no—
146C2×Q8—5621no—
147C2×Q8—5621no—
148C2×Q8—11241no—
149C2×Q8—11241no—
150C2×D4—2811no—
151C2×D4—2811no—
152C2×D4C22×D28111yescharacteristic
153C22×C4—2811no—
154C22×C4—2811no—
155C22×C4—2811no—
156C22×C4—2811no—
157C22×C4C4×D28111yescharacteristic
158M16—21no—
159M16—5621no—
160M16—11241no—
161C2×C8—11241no—
162C4⋊C4—21no—
163C4⋊C4—5621no—
164C4⋊C4—5621no—
165C4⋊C4—5621no—
166C4⋊C4—5621no—
167C4⋊C4—11241no—
168C22⋊C4—21no—
169C22⋊C4—21no—
170C22⋊C4—2811no—
171C22⋊C4—5621no—
172C22⋊C4—5621no—
173C22⋊C4—5621no—
174C22⋊C4—5621no—
175C22⋊C4C4×D28111yescharacteristic
176C42—5621no—
177C42—11241no—
178C23—2811no—
179C23C2×C4×D28111yescharacteristic
180C23D4×D28111yescharacteristic
181Q8—11241no—
182Q8—11241no—
183Q8—11241no—
184Q8—11242no—
185D4—41no—
186D4—11241no—
187D4—11241no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—2811no—
193C2×C4—2811no—
194C2×C4—2811no—
195C2×C4—5621no—
196C2×C4—5621no—
197C2×C4—5621no—
198C2×C4—5621no—
199C2×C4—5621no—
200C2×C4—5621no—
201C2×C4—5621no—
202C2×C4—5621no—
203C2×C4—11241no—
204C2×C4—11241no—
205C2×C4D4×D28111yescharacteristic
206C8—41no—
207C8—11241no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—5621no—
213C22—11241no—
214C22C22⋊C4×D28111yescharacteristic
215C4—21no—
216C4—41no—
217C4—41no—
218C4—81no—
219C4—2811no—
220C4—2811no—
221C4—5621no—
222C4—5621no—
223C4—11241no—
224C4—11241no—
225C4—22481no—
226C2—21no—
227C2—41no—
228C2—41no—
229C2—11241no—
230C2#99×D28111yescharacteristic
subgroupG/H
centerC2#99×D281
commutatorC23×C281C22×C4
FrattiniC2×D4C22×D281
Fitting#352×C281C2
socleC2×C281C2×#99
prime radicalC2×#17985137C22
cosocleC2×D4×C281C23
hypercenter#352D281
hypocenterC281#2123
LCSG ▷ C23×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
4. #31823254C2semidirect
5. #31823253C2semidirect
6. #31823252C2semidirect
7. #352×C281C2semidirect
9. C22×Dic562C4semidirect
13. #22582863C4semidirect
14. #22582862C4semidirect
19. #22582835C4semidirect
115. C281#2123semidirect
123. #352D281semidirect

Maximal subgroups

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

subgroupindex
#318240352
#318234442
#318234352
#318232542
#318232532
#318232522
#352×C2812
#2123281