Finite Group Databasebeta

← #49130933

Subgroups — #49130933

Order 36224.

484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22583632C211yesmaximal, characteristic, complemented
2C2×#22583616C211yesmaximal, characteristic, complemented
3#31827046C212yesmaximal, complemented
4#31826712C214yesmaximal, complemented
5#31826707C212yesmaximal, complemented
6#31826702C212yesmaximal, complemented
7#31826464C212yesmaximal, complemented
8C2×#107×C283C211yesmaximal, characteristic, complemented
9C2×#17985392C2212yes—
10C2×#17985392C2211yescharacteristic
11#22583632—24no—
12C2×Dic1132C2211yescharacteristic
13C2×#17985381C2212yes—
14C2×D2264C2211yescharacteristic
15#22583616—24no—
16C2×#17985376C2211yescharacteristic
17C2×#17985375C2212yes—
18C2×C8×D283C2212yes—
19#22583590—22no—
20#22583590C2214yes—
21#22583585—22no—
22#22583585C2214yes—
23#22583584—24no—
24#22583533C2214yes—
25#22583530C2214yes—
26C22×C8×C283C2211yescharacteristic
27C2×C4⋊C4×C283C2212yes—
28#107×C283C2212yes—
29#107×C283C2212yes—
30#17985392—22no—
31#17985392—24no—
32#17985392—22no—
33#17985392—24no—
34C2×Dic566D411yescharacteristic
35C2×Dic566C2312yes—
36C2×D1132—24no—
37C2×D1132D411yescharacteristic
38C2×D1132C2312yes—
39C2×C22⋊D283—22no—
40C2×C22⋊D283D412yes—
41C2×C4×D283—22no—
42C2×C4×D283C2312yes—
43Dic1132—22no—
44#17985381—24no—
45D2264—22no—
46#17985376—22no—
47#17985375—24no—
48C2×C283⋊C8C2312yes—
49C8×D283—24no—
50C4⋊Dic283—24no—
51(C2×D283)⋊C4—24no—
52(C2×D283)⋊C4—24no—
53C22×C4×C283—22no—
54C22×C4×C283C2311yescharacteristic
55C2×C8×C283D414yescomplemented
56C2×C8×C283C2311yescharacteristic
57C2×C8×C283C2311yescharacteristic
58C4⋊C4×C283—22no—
59C4⋊C4×C283C2314yes—
60C22×D283—22no—
61C22×D283C2×D412yes—
62Dic566—22no—
63Dic566—22no—
64Dic566—22no—
65D1132—22no—
66D1132—22no—
67D1132—22no—
68D1132—84no—
69C22⋊D283—24no—
70C22⋊D283—44no—
71C2×Dic283—22no—
72C2×Dic283C2×D412yes—
73C4×D283—22no—
74C4×D283—22no—
75C4×D283—44no—
76C283⋊C8—22no—
77C23×C283C2×D411yescharacteristic
78C2×C4×C283—24no—
79C2×C4×C283—82no—
80C2×C4×C283C2×D411yescharacteristic
81C2×C4×C283C2×D412yes—
82C2×C4×C283#4112yes—
83C2×C4×C283C2411yescharacteristic
84C8×C283C2×D412yes—
85C8×C283C2×D412yes—
86C22×C283—21no—
87C22×C283—21no—
88C22×C283#12112yes—
89C22×C283C22×D411yescharacteristic
90C2×D283—22no—
91C2×D283—22no—
92C2×D283—22no—
93C2×D283—42no—
94C2×D283—42no—
95C2×D283—42no—
96C4×C283—44no—
97C4×C283#12112yes—
98C4×C283C22×D411yescharacteristic
99C4×C283C2×#4111yescharacteristic
100Dic283—22no—
101Dic283—42no—
102C2×C283—22no—
103C2×C283C2×#12111yescharacteristic
104C2×C283#57611yescharacteristic
105C2×C283#57811yescharacteristic
106D283—42no—
107D283—82no—
108C283#306111yescharacteristic, complemented, Sylow
109#3061—2831nomaximal, Sylow
110C2×#135—2831no—
111C2×#131—2831no—
112#537—2832no—
113#468—2834no—
114#467—2832no—
115#466—2832no—
116C2×#107D28311yescharacteristic, complemented
117#417—2832no—
118C2×#41—2831no—
119C2×#41—2832no—
120#135—5664no—
121C2×Q16—2831no—
122C2×SD16—2832no—
123C2×D8—2831no—
124#131—5664no—
125C2×M16—2831no—
126C2×M16—2832no—
127C22×C8—2832no—
128C22×C8C2×D28311yescharacteristic
129C22⋊Q8—2834no—
130C22⋊Q8—5662no—
131#121—2834no—
132#121—5662no—
133#121—5664no—
134C2×C4⋊C4C2×D28312yes—
135#107C2×D28312yes—
136#107C2×D28312yes—
137#103—2834no—
138#102—2834no—
139#41—5662no—
140#41—5662no—
141#41—5664no—
142#41—5664no—
143C2×Q8—2831no—
144C2×Q8—2832no—
145C2×D4—2832no—
146C2×D4—2831no—
147C2×D4—2832no—
148C2×D4—5664no—
149C2×D4—5662no—
150C22×C4—22no—
151C22×C4—2832no—
152C22×C4—5662no—
153C22×C4C22×D28311yescharacteristic
154Q16—5662no—
155SD16—5664no—
156D8—5662no—
157M16—5662no—
158M16—5664no—
159C2×C8—2832no—
160C2×C8—5664no—
161C2×C8D113214yescomplemented
162C2×C8C22×D28311yescharacteristic
163C2×C8C22×D28311yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—5664no—
166C4⋊C4C22×D28314yes—
167C22⋊C4—5664no—
168C22⋊C4—5664no—
169C23—2832no—
170C23—5662no—
171C23D4×D28311yescharacteristic
172Q8—5662no—
173Q8—5662no—
174Q8—5662no—
175D4—5664no—
176D4—5662no—
177D4—5662no—
178D4—5662no—
179D4—11324no—
180D4—22644no—
181C2×C4—24no—
182C2×C4—82no—
183C2×C4—2832no—
184C2×C4—5662no—
185C2×C4—5662no—
186C2×C4—5662no—
187C2×C4—11324no—
188C2×C4D4×D28311yescharacteristic
189C2×C4C2×D113212yes—
190C2×C4#1798539312yes—
191C2×C4C23×D28311yescharacteristic
192C8—5662no—
193C8C2×D113212yes—
194C8C2×D113212yes—
195C22—21no—
196C22—21no—
197C22—5662no—
198C22—5662no—
199C22—5662no—
200C22—11322no—
201C22—11322no—
202C22—11322no—
203C22#2258358512yes—
204C22C2×D4×D28311yescharacteristic
205C4—44no—
206C4—5662no—
207C4—11322no—
208C4#2258358512yes—
209C4C22×D113211yescharacteristic
210C4C2×#1798539311yescharacteristic
211C2—22no—
212C2—11322no—
213C2—22642no—
214C2C2×#2258358511yescharacteristic
215C2#3182726611yescharacteristic
216C2#3182727811yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#107×C283C2
socleC22×C283C22×D4
hypercenterC2×#107D283
hypocenterC283#3061
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
1. C2×#22583632C2semidirect
2. C2×#22583616C2semidirect
3. #31827046C2semidirect
4. #31826712C2semidirect
5. #31826707C2semidirect
6. #31826702C2semidirect
7. #31826464C2semidirect
8. C2×#107×C283C2semidirect
55. C2×C8×C283D4semidirect
108. C283#3061semidirect
116. C2×#107D283semidirect
161. C2×C8D1132semidirect

Maximal subgroups

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

subgroupindex
C2×#225836322
C2×#225836162
#318270462
#318267122
#318267072
#318267022
#318264642
C2×#107×C2832
#3061283