Finite Group Databasebeta

← #49121737

Subgroups — #49121737

Order 36224.

304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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×#22583641C211yesmaximal, characteristic
2#31827231C211yesmaximal, characteristic
3#31826481C211yesmaximal, characteristic
4#31826474C211yesmaximal, characteristic, complemented
5#31826237C211yesmaximal, characteristic, complemented
6C283⋊#338C211yesmaximal, characteristic, complemented
7C2×#101×C283C211yesmaximal, characteristic, complemented
8C2×#17985392C2211yescharacteristic
9#22583641—22no—
10#22583641—22no—
11C2×#17985382C412yescomplemented
12C2×#17985379C412yescomplemented
13#22583618—22no—
14#22583616—22no—
15C2×#17985376C2211yescharacteristic
16C2×#17985376C2211yescharacteristic
17M16×D283—22no—
18#22583569C2211yescharacteristic
19#22583536—22no—
20#22583534—22no—
21C22×Q8×C283C2211yescharacteristic
22C2×M16×C283C2211yescharacteristic
23C2×M16×C283C2211yescharacteristic
24#101×C283—22no—
25#17985392—21no—
26#17985392—21no—
27#17985392D412yes—
28#17985392D412yes—
29C2×Dic566C2×C411yescharacteristic
30C2×D1132C2×C411yescharacteristic
31C2×C22⋊D283—21no—
32C2×C4×D283—21no—
33#17985382—24no—
34#17985379—24no—
35#17985376—21no—
36#17985376—21no—
37#17985376—21no—
38#17985376—21no—
39#17985375—24no—
40C2×C283⋊C8C2×C412yes—
41C2×C283⋊C8D412yes—
42C8×D283—24no—
43C4⋊Dic283—21no—
44C22⋊Dic283—21no—
45C4×Dic283—21no—
46C2×Q8×C283—21no—
47C2×Q8×C283—21no—
48C2×Q8×C283—21no—
49C2×Q8×C283—21no—
50C2×Q8×C283—21no—
51C2×Q8×C283C2×C412yes—
52C22×C4×C283—21no—
53C22×C4×C283C2311yescharacteristic
54M16×C283—21no—
55M16×C283—21no—
56M16×C283—21no—
57M16×C283D412yes—
58C2×C8×C283—21no—
59C2×C8×C283—21no—
60C22×D283—21no—
61Dic566—21no—
62Dic566C22⋊C412yes—
63D1132—21no—
64D1132C22⋊C412yes—
65C22⋊D283—22no—
66C22⋊D283—22no—
67C2×Dic283—21no—
68C2×Dic283—41no—
69C4×D283—22no—
70C4×D283—22no—
71C283⋊C8—22no—
72C283⋊C8—22no—
73C23×C283#4111yescharacteristic
74Q8×C283—22no—
75Q8×C283—22no—
76Q8×C283—41no—
77Q8×C283—41no—
78C2×C4×C283—22no—
79C2×C4×C283—41no—
80C2×C4×C283—41no—
81C2×C4×C283C22×C411yescharacteristic
82C2×C4×C283C2×D411yescharacteristic
83C2×C4×C283C2×D411yescharacteristic
84C2×C4×C283C2×D411yescharacteristic
85C2×C4×C283C2×D411yescharacteristic
86C2×C4×C283#4111yescharacteristic
87C8×C283—22no—
88C8×C283—41no—
89C22×C283—41no—
90C22×C283C4×D411yescharacteristic
91C22×C283#12111yescharacteristic
92C22×C283#12311yescharacteristic
93C2×D283—22no—
94C2×D283—81no—
95C4×C283—42no—
96C4×C283C2×C22⋊C411yescharacteristic
97C4×C283C4×D411yescharacteristic
98C4×C283#12011yescharacteristic
99C4×C283#12111yescharacteristic
100Dic283—22no—
101Dic283—81no—
102C2×C283—21no—
103C2×C283—21no—
104C2×C283—21no—
105C2×C283#38611yescharacteristic
106D283—42no—
107C283#190211yescharacteristic, complemented, Sylow
108#1902—2831nomaximal, Sylow
109C2×#137—2831no—
110#568—2831no—
111#421—2831no—
112#419—2831no—
113C2×#101D28311yescharacteristic, complemented
114#344—2831no—
115#338—2831no—
116C2×#41—2831no—
117C22×Q8C2×D28311yescharacteristic
118#137—5662no—
119#137—5662no—
120C2×Q16—2832no—
121C2×SD16—2832no—
122#131—5662no—
123#131—5662no—
124C2×M16—2831no—
125C2×M16—2831no—
126C2×M16—5662no—
127C2×M16C2×D28311yescharacteristic
128C2×M16C2×D28311yescharacteristic
129#117—2831no—
130#104—5662no—
131#103—5662no—
132#101—22no—
133#41—2832no—
134#41—2832no—
135#41—5661no—
136#41—5661no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—2831no—
143C2×Q8C4×D28312yes—
144C2×D4—2831no—
145C2×D4—5661no—
146C22×C4—21no—
147C22×C4—5661no—
148C22×C4C22×D28311yescharacteristic
149Q16—5664no—
150SD16—5664no—
151M16—21no—
152M16—21no—
153M16—21no—
154M16—5664no—
155M16—5661no—
156M16—5661no—
157M16—5661no—
158M16—5661no—
159M16C22⋊D28312yes—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—2832no—
163C2×C8—2832no—
164C2×C8—5664no—
165C4⋊C4—5661no—
166C22⋊C4—5661no—
167C42—5661no—
168C23—5661no—
169C23#1798539211yescharacteristic
170Q8—22no—
171Q8—22no—
172Q8—41no—
173Q8—41no—
174Q8—2832no—
175Q8—5661no—
176D4—2832no—
177D4—5662no—
178D4—5662no—
179D4—5661no—
180C2×C4—22no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—5661no—
184C2×C4—5662no—
185C2×C4—5662no—
186C2×C4—11321no—
187C2×C4C2×C4×D28311yescharacteristic
188C2×C4D4×D28311yescharacteristic
189C2×C4D4×D28311yescharacteristic
190C2×C4D4×D28311yescharacteristic
191C2×C4C2×C22⋊D28311yescharacteristic
192C2×C4#1798539111yescharacteristic
193C8—22no—
194C8—41no—
195C8—5662no—
196C8—5662no—
197C22—41no—
198C22—5662no—
199C22—22641no—
200C22C4×C22⋊D28311yescharacteristic
201C22#2258358311yescharacteristic
202C22#2258359211yescharacteristic
203C4—42no—
204C4—5662no—
205C4—22641no—
206C4C22⋊C4×D28311yescharacteristic
207C4(C22⋊D283)⋊C411yescharacteristic
208C4#2258357811yescharacteristic
209C4#2258358111yescharacteristic
210C2—21no—
211C2—21no—
212C2—21no—
213C2—11322no—
214C2#3182634111yescharacteristic
subgroupG/H
centerC2#31826341
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
FittingC2×#101×C283C2
socleC2×C283#386
prime radicalC2×#17985392C22
cosocleC22×C4×C283C23
hypercenterC2×#101D283
hypocenterC283#1902
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
4. #31826474C2semidirect
5. #31826237C2semidirect
6. C283⋊#338C2semidirect
7. C2×#101×C283C2semidirect
11. C2×#17985382C4semidirect
12. C2×#17985379C4semidirect
107. C283#1902semidirect
113. C2×#101D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836412
#318272312
#318264812
#318264742
#318262372
C283⋊#3382
C2×#101×C2832
#1902283