Finite Group Databasebeta

← #49134351

Subgroups — #49134351

Order 36224.

380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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#31827200C212yesmaximal, complemented
2#31826854C212yesmaximal, complemented
3#31826849C211yesmaximal, characteristic, complemented
4#31826688C212yesmaximal, complemented
5#31826681C212yesmaximal, complemented
6#31826661C212yesmaximal, complemented
7#31826567C212yesmaximal, complemented
8C4×D2264C211yesmaximal, characteristic, complemented
9#446×C283C211yesmaximal, characteristic, complemented
10C2×Dic1132C2211yescharacteristic
11C2×#17985381C2212yes—
12C2×#17985381C2212yes—
13C2×D2264C2211yescharacteristic
14C2×D2264C2211yescharacteristic
15C2×D2264C2212yes—
16#22583607C2212yes—
17#22583599—22no—
18#22583598C2212yes—
19#22583598C2212yes—
20#22583595—22no—
21#22583595—22no—
22C4×Dic566C2212yes—
23C4×D1132C2212yes—
24C4×D1132C2212yes—
25#22583572—22no—
26#22583544C2211yescharacteristic
27#22583535C2212yes—
28#22583532C2212yes—
29#22583532C2212yes—
30C4×Q8×C283C2211yescharacteristic
31C4⋊C8×C283C2212yes—
32C4⋊C8×C283C2211yescharacteristic
33#97×C283C2212yes—
34C4×C8×C283C2211yescharacteristic
35C2×Dic566C2312yes—
36C2×D1132—22no—
37C2×D1132—22no—
38C2×D1132C2312yes—
39C2×D1132C2312yes—
40C2×C4×D283—22no—
41C2×C4×D283—22no—
42Dic1132—41no—
43#17985381—24no—
44#17985381—42no—
45D2264—22no—
46D2264—42no—
47D2264—41no—
48C4⋊Dic283C2312yes—
49Dic283⋊C4—22no—
50(C2×D283)⋊C4—22no—
51(C2×D283)⋊C4—22no—
52(C2×D283)⋊C4—22no—
53(C2×D283)⋊C4—22no—
54(C2×D283)⋊C4—22no—
55(C2×D283)⋊C4—22no—
56C4×Dic283—22no—
57C2×Q8×C283D411yescharacteristic
58C2×C8×C283C2312yes—
59C2×C8×C283C2311yescharacteristic
60C2×C8×C283C2311yescharacteristic
61C4⋊C4×C283D412yes—
62C4⋊C4×C283D411yescharacteristic
63C42×C283C2311yescharacteristic
64C42×C283C2312yes—
65C22×D283—22no—
66C22×D283—22no—
67Dic566—22no—
68Dic566—22no—
69D1132—22no—
70D1132—22no—
71D1132—22no—
72D1132—22no—
73D1132—44no—
74D1132—82no—
75C2×Dic283—22no—
76C2×Dic283—22no—
77C4×D283—82no—
78C4×D283—82no—
79Q8×C283—41no—
80C2×C4×C283C2×D411yescharacteristic
81C2×C4×C283C2×D412yes—
82C2×C4×C283C2×D412yes—
83C2×C4×C283C2×D411yescharacteristic
84C2×C4×C283C2411yescharacteristic
85C8×C283—22no—
86C8×C283—21no—
87C8×C283#4112yes—
88C22×C283C22×D411yescharacteristic
89C2×D283—42no—
90C2×D283—42no—
91C2×D283—42no—
92C2×D283—42no—
93C2×D283—42no—
94C2×D283—42no—
95C4×C283—21no—
96C4×C283—22no—
97C4×C283—21no—
98C4×C283—22no—
99C4×C283C2×#4111yescharacteristic
100C4×C283H(5,𝔽2)11yescharacteristic
101Dic283—42no—
102Dic283—42no—
103C2×C283#55011yescharacteristic
104C2×C283#57511yescharacteristic
105C2×C283#57611yescharacteristic
106D283—82no—
107D283—82no—
108C283#340311yescharacteristic, complemented, Sylow
109#3403—2831nomaximal, Sylow
110#559—2832no—
111#496—2832no—
112#495—2831no—
113#464—2832no—
114#463—2832no—
115#459—2832no—
116#446D28311yescharacteristic, complemented
117#440—2832no—
118C4×D8—2831no—
119C2×Q16—2831no—
120C2×SD16—2832no—
121C2×SD16—2832no—
122C2×D8—2831no—
123C2×D8—2831no—
124C2×D8—2832no—
125#127—2832no—
126#124—2832no—
127#124—2832no—
128#124—5662no—
129#123—5662no—
130#123—5662no—
131C4×Q8—2832no—
132C4×Q8C2×D28311yescharacteristic
133C4×D4—2832no—
134C4×D4—2832no—
135C4×D4—5662no—
136#107—2831no—
137C4⋊C8C2×D28312yes—
138C4⋊C8C2×D28311yescharacteristic
139#103—2832no—
140#102—2832no—
141#102—2832no—
142#97C2×D28312yes—
143C4×C8C2×D28311yescharacteristic
144C2×Q8—2832no—
145C2×Q8D113211yescharacteristic
146C2×D4—2832no—
147C2×D4—2832no—
148C2×D4—5662no—
149C2×D4—5662no—
150C22×C4—5662no—
151C22×C4—5662no—
152Q16—11321no—
153SD16—5664no—
154SD16—11322no—
155D8—5662no—
156D8—11322no—
157D8—11321no—
158C2×C8C22×D28311yescharacteristic
159C2×C8C22×D28312yes—
160C2×C8C22×D28311yescharacteristic
161C4⋊C4—2832no—
162C4⋊C4—5662no—
163C4⋊C4D113212yes—
164C4⋊C4D113211yescharacteristic
165C22⋊C4—5662no—
166C22⋊C4—5662no—
167C22⋊C4—5662no—
168C22⋊C4—5662no—
169C22⋊C4—5662no—
170C22⋊C4—5662no—
171C42—5662no—
172C42C22×D28311yescharacteristic
173C42C22×D28312yes—
174C23—5662no—
175C23—5662no—
176Q8—41no—
177Q8—5662no—
178Q8—5662no—
179D4—5662no—
180D4—5662no—
181D4—5662no—
182D4—5662no—
183D4—11324no—
184D4—22642no—
185C2×C4—5662no—
186C2×C4—5662no—
187C2×C4—22642no—
188C2×C4—22642no—
189C2×C4C2×D113212yes—
190C2×C4C2×D113211yescharacteristic
191C2×C4C2×D113211yescharacteristic
192C2×C4C2×D113212yes—
193C2×C4C23×D28311yescharacteristic
194C8—22no—
195C8—21no—
196C8#1798539312yes—
197C22—11322no—
198C22—11322no—
199C22—11322no—
200C22—11322no—
201C22—11322no—
202C22—11322no—
203C22C22×D113211yescharacteristic
204C4—22no—
205C4—21no—
206C4—21no—
207C4—22no—
208C4—11322no—
209C4—11322no—
210C4C2×#1798539311yescharacteristic
211C4#2258365611yescharacteristic
212C2—22642no—
213C2—22642no—
214C2#3182713711yescharacteristic
215C2#3182726511yescharacteristic
216C2#3182727011yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#446×C283C2
socleC22×C283C22×D4
hypercenter#446D283
hypocenterC283#3403
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #31827200C2semidirect
2. #31826854C2semidirect
3. #31826849C2semidirect
4. #31826688C2semidirect
5. #31826681C2semidirect
6. #31826661C2semidirect
7. #31826567C2semidirect
8. C4×D2264C2semidirect
9. #446×C283C2semidirect
108. C283#3403semidirect
116. #446D283semidirect

Maximal subgroups

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

subgroupindex
#318272002
#318268542
#318268492
#318266882
#318266812
#318266612
#318265672
C4×D22642
#446×C2832
#3403283