Finite Group Databasebeta

← #49121677

Subgroups — #49121677

Order 36224.

342 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 85 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#31827232C211yesmaximal, characteristic, complemented
2#31826972C211yesmaximal, characteristic
3#31826428C212yesmaximal, complemented
4#31826237C212yesmaximal, complemented
5#413×C283C211yesmaximal, characteristic, complemented
6C22×C4×D283C2211yescharacteristic
7#22583617—24no—
8C2×#17985376—22no—
9C2×#17985376C2212yes—
10#22583591C412yes—
11#22583586—21no—
12#22583581—21no—
13#22583578C412yes—
14C4×C22⋊D283—22no—
15#22583569C2211yescharacteristic
16(C2×D283)⋊C8—24no—
17C2×#41×C283C2211yescharacteristic
18C2×M16×C283C2212yes—
19#101×C283—21no—
20#100×C283—21no—
21C23×D283C2×C411yescharacteristic
22C2×C22⋊D283—22no—
23C22×Dic283C2×C411yescharacteristic
24C2×C4×D283—21no—
25C2×C4×D283—21no—
26C2×C4×D283—22no—
27C2×C4×D283—22no—
28#17985376—24no—
29#17985376—22no—
30#17985376—22no—
31C2×C283⋊C8—24no—
32C2×C283⋊C8D414yescomplemented
33C4⋊Dic283—21no—
34Dic283⋊C4—22no—
35C22⋊Dic283—22no—
36C22⋊Dic283C2×C412yes—
37(C2×D283)⋊C4—22no—
38C4×Dic283—21no—
39#41×C283—22no—
40#41×C283—22no—
41C2×Q8×C283D411yescharacteristic
42C2×D4×C283C2×C412yes—
43C2×D4×C283D411yescharacteristic
44C22×C4×C283D412yes—
45C22×C4×C283C2311yescharacteristic
46M16×C283—22no—
47M16×C283—22no—
48C2×C8×C283—22no—
49C22×D283—21no—
50C22×D283—22no—
51C22×D283—42no—
52C22⋊D283—44no—
53C2×Dic283—22no—
54C2×Dic283—21no—
55C2×Dic283—22no—
56C4×D283—41no—
57C4×D283—42no—
58C4×D283—41no—
59C283⋊C8—24no—
60C23×C283C22⋊C412yes—
61C23×C283C22×C411yescharacteristic
62Q8×C283—22no—
63D4×C283—24no—
64D4×C283—22no—
65C2×C4×C283—22no—
66C2×C4×C283—22no—
67C2×C4×C283C22⋊C412yes—
68C2×C4×C283C2×D412yes—
69C2×C4×C283C2×D411yescharacteristic
70C2×C4×C283C2×D411yescharacteristic
71C2×C4×C283#4112yes—
72C8×C283—42no—
73C22×C283—22no—
74C22×C283—41no—
75C22×C283—42no—
76C22×C283C2×C22⋊C411yescharacteristic
77C22×C283C4×D412yes—
78C2×D283—22no—
79C2×D283—24no—
80C2×D283—41no—
81C2×D283—42no—
82C2×D283—41no—
83C4×C283—22no—
84C4×C283#12011yescharacteristic
85C4×C283#12112yes—
86C4×C283#12311yescharacteristic
87Dic283—42no—
88Dic283—41no—
89C2×C283—21no—
90C2×C283—22no—
91C2×C283—42no—
92C2×C283#38611yescharacteristic
93D283—42no—
94C283#189111yescharacteristic, complemented, Sylow
95#1891—2831nomaximal, Sylow
96#568—2831no—
97#525—2831no—
98#413D28311yescharacteristic, complemented
99#407—2832no—
100#344—2832no—
101C2×#41C2×D28311yescharacteristic
102C23×C4—2831no—
103#131—5664no—
104C2×M16—2832no—
105C2×M16—5662no—
106C2×M16C2×D28312yes—
107#123—2832no—
108C22⋊Q8—5661no—
109#121—5661no—
110#120—2832no—
111C4×D4—5662no—
112#117—2831no—
113#101—21no—
114#100—21no—
115C22⋊C8—5664no—
116C24—2831no—
117#41—22no—
118#41—22no—
119C2×Q8C22⋊D28311yescharacteristic
120C2×D4—5662no—
121C2×D4C4×D28312yes—
122C2×D4C22⋊D28311yescharacteristic
123C22×C4—2831no—
124C22×C4—5662no—
125C22×C4—5661no—
126C22×C4—5661no—
127C22×C4—5662no—
128C22×C4D113212yes—
129C22×C4C22×D28311yescharacteristic
130M16—22no—
131M16—22no—
132M16—5664no—
133M16—5662no—
134M16—5662no—
135C2×C8—22no—
136C2×C8—2834no—
137C2×C8—5664no—
138C4⋊C4—5662no—
139C4⋊C4—5661no—
140C22⋊C4—2832no—
141C22⋊C4—5662no—
142C22⋊C4—5662no—
143C42—5661no—
144C23—5661no—
145C23—5662no—
146C23—11322no—
147C23(C2×D283)⋊C412yes—
148C23C2×C4×D28311yescharacteristic
149Q8—22no—
150D4—24no—
151D4—22no—
152D4—11324no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—5662no—
156C2×C4—5661no—
157C2×C4—5662no—
158C2×C4—11321no—
159C2×C4—11322no—
160C2×C4—11321no—
161C2×C4(C2×D283)⋊C412yes—
162C2×C4D4×D28312yes—
163C2×C4C2×C22⋊D28311yescharacteristic
164C2×C4C2×D113211yescharacteristic
165C2×C4#1798539112yes—
166C8—42no—
167C8—5664no—
168C22—22no—
169C22—41no—
170C22—42no—
171C22—5662no—
172C22—5664no—
173C22—11321no—
174C22—11322no—
175C22—11321no—
176C22C2×(C2×D283)⋊C411yescharacteristic
177C22(C22⋊D283)⋊C412yes—
178C4—22no—
179C4—11322no—
180C4—11321no—
181C4#2258358011yescharacteristic
182C4#2258358212yes—
183C4#2258359411yescharacteristic
184C2—21no—
185C2—22no—
186C2—42no—
187C2—11322no—
188C2#3182634211yescharacteristic
subgroupG/H
centerC4#22583580
commutatorC23×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#413×C283C2
socleC2×C283#386
prime radical#31826972C2
cosocleC22×C4×C283C23
hypercenter#413D283
hypocenterC283#1891
LCSG ▷ C23×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #31827232C2semidirect
3. #31826428C2semidirect
4. #31826237C2semidirect
5. #413×C283C2semidirect
32. C2×C283⋊C8D4semidirect
94. C283#1891semidirect
98. #413D283semidirect

Maximal subgroups

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

subgroupindex
#318272322
#318269722
#318264282
#318262372
#413×C2832
#1891283