Finite Group Databasebeta

← #44550326

Subgroups — #44550326

Order 32128.

552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#22548763C211yesmaximal, characteristic
2C2×#22548641C212yesmaximal, complemented
3#30631689C212yesmaximal, complemented
4#30631594C211yesmaximal, characteristic, complemented
5C2×#101×C251C211yesmaximal, characteristic, complemented
6#22548763—24no—
7#22548763—22no—
8#22548763C414yescomplemented
9C2×#16860811—22no—
10C2×#16860810—22no—
11C2×#16860810C2212yes—
12C2×Q8×D251—22no—
13C2×C4⋊Dic251C2211yescharacteristic
14C2×C4×Dic251C2211yescharacteristic
15#22548641—24no—
16#22548640—22no—
17#22548637—22no—
18C251⋊#95—22no—
19C22×Q8×C251C2211yescharacteristic
20C2×M16×C251C2212yes—
21#101×C251—22no—
22#16860811—28no—
23#16860811—28no—
24#16860810—28no—
25#16860810—28no—
26#16860810—22no—
27#16860810—22no—
28#16860810C2×C414yes—
29#16860810D414yes—
30C2×Dic502—22no—
31C2×Dic502D412yes—
32Q8×D251—28no—
33Q8×D251—28no—
34C2×D1004—22no—
35C2×D1004D412yes—
36C2×C22⋊D251—22no—
37C22×Dic251—21no—
38C22×Dic251—21no—
39C2×C4×D251—24no—
40C2×C4×D251—22no—
41C4⋊Dic251—22no—
42C4×Dic251—22no—
43C2×Q8×C251—22no—
44C2×Q8×C251—22no—
45C2×Q8×C251C2×C412yes—
46C2×Q8×C251D412yes—
47C22×C4×C251D412yes—
48C22×C4×C251C2311yescharacteristic
49M16×C251—22no—
50M16×C251—22no—
51C2×C8×C251—22no—
52C22×D251—22no—
53Dic502—28no—
54Dic502—22no—
55Dic502C22⋊C414yes—
56D1004—28no—
57D1004—22no—
58D1004C22⋊C414yes—
59C22⋊D251—24no—
60C22⋊D251—24no—
61C2×Dic251—22no—
62C2×Dic251—22no—
63C2×Dic251—41no—
64C2×Dic251—41no—
65C2×Dic251—42no—
66C2×Dic251—41no—
67C4×D251—216no—
68C4×D251—24no—
69C4×D251—24no—
70C23×C251C2×D411yescharacteristic
71Q8×C251—24no—
72Q8×C251—24no—
73C2×C4×C251—22no—
74C2×C4×C251—22no—
75C2×C4×C251C22⋊C414yes—
76C2×C4×C251C22×C411yescharacteristic
77C2×C4×C251C2×D412yes—
78C2×C4×C251C2×D412yes—
79C2×C4×C251C2×D411yescharacteristic
80C8×C251—42no—
81C22×C251—21no—
82C22×C251—21no—
83C22×C251C2×C22⋊C411yescharacteristic
84C22×C251#12011yescharacteristic
85C22×C251#12011yescharacteristic
86C2×D251—24no—
87C2×D251—42no—
88C2×D251—42no—
89C4×C251—24no—
90C4×C251C2×C22⋊C412yes—
91C4×C251#12012yes—
92Dic251—24no—
93Dic251—42no—
94Dic251—81no—
95C2×C251—21no—
96C2×C251—21no—
97C2×C251#37911yescharacteristic
98C2×C251#45411yescharacteristic
99C2×C251#45611yescharacteristic
100D251—44no—
101C251#179311yescharacteristic, complemented, Sylow
102#1793—2511nomaximal, Sylow
103C2×2−1+4—2511no—
104C2×#104—2512no—
105#417—2512no—
106C2×#101D25111yescharacteristic, complemented
107#391—2511no—
1082−1+4—5024no—
1092−1+4—5022no—
1102−1+4—2514no—
111C2×#41—5022no—
112C2×#41—5022no—
113C2×#41—2512no—
114C22×Q8—5022no—
115C22×Q8C2×D25111yescharacteristic
116C2×M16C2×D25112yes—
117C2×C4⋊C4—2511no—
118C2×C42—2511no—
119#104—5024no—
120#103—5022no—
121#102—5022no—
122#101—22no—
123#95—5022no—
124#41—5028no—
125#41—5028no—
126#41—5028no—
127#41—5028no—
128#41—5022no—
129#41—5022no—
130#41—2514no—
131#41—2514no—
132C2×Q8—22no—
133C2×Q8—22no—
134C2×Q8—5022no—
135C2×Q8—5028no—
136C2×Q8—5028no—
137C2×Q8—2512no—
138C2×Q8C4×D25112yes—
139C2×Q8C22⋊D25112yes—
140C2×D4—5022no—
141C2×D4—5022no—
142C2×D4—2512no—
143C22×C4—5024no—
144C22×C4—5021no—
145C22×C4—5021no—
146C22×C4—5022no—
147C22×C4D100412yes—
148C22×C4C22×D25111yescharacteristic
149M16—22no—
150M16—22no—
151C2×C8—22no—
152C4⋊C4—5022no—
153C42—5022no—
154C23—5022no—
155C23C2×D100411yescharacteristic
156Q8—24no—
157Q8—24no—
158Q8—5028no—
159Q8—5022no—
160Q8—2514no—
161D4—5028no—
162D4—5024no—
163D4—5024no—
164D4—5022no—
165D4—2514no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—10042no—
169C2×C4—10041no—
170C2×C4—10041no—
171C2×C4—10041no—
172C2×C4—50216no—
173C2×C4—5022no—
174C2×C4—5022no—
175C2×C4—5024no—
176C2×C4—5024no—
177C2×C4(C2×D251)⋊C414yes—
178C2×C4C2×C4×D25111yescharacteristic
179C2×C4D4×D25112yes—
180C2×C4D4×D25112yes—
181C2×C4C2×C22⋊D25111yescharacteristic
182C8—42no—
183C22—21no—
184C22—21no—
185C22—10042no—
186C22—10042no—
187C22—5024no—
188C22C2×(C2×D251)⋊C411yescharacteristic
189C22#2254868511yescharacteristic
190C22#2254868511yescharacteristic
191C4—24no—
192C4—20081no—
193C4—10042no—
194C4—5024no—
195C4C22⋊C4×D25112yes—
196C4#2254868312yes—
197C2—21no—
198C2—21no—
199C2—10044no—
200C2#3063154211yescharacteristic
201C2#3063186211yescharacteristic
202C2#3063187211yescharacteristic
subgroupG/H
centerC22#22548685
commutatorC2×C4×C251C22×C4
FrattiniC22×C4C22×D251
FittingC2×#101×C251C2
socleC22×C251#120
prime radicalC2×#22548763C2
cosocleC22×C4×C251C23
hypercenterC2×#101D251
hypocenterC251#1793
LCSG ▷ C2×C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#22548641C2semidirect
3. #30631689C2semidirect
4. #30631594C2semidirect
5. C2×#101×C251C2semidirect
8. #22548763C4semidirect
101. C251#1793semidirect
106. C2×#101D251semidirect

Maximal subgroups

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

subgroupindex
C2×#225487632
C2×#225486412
#306316892
#306315942
C2×#101×C2512
#1793251