Finite Group Databasebeta

← #11782009

Subgroups — #11782009

Order 1152.

264 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 45 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#10593359C212yesmaximal
2#10590902C211yesmaximal, characteristic, complemented
3#10590733C211yesmaximal, characteristic
4#10590170C211yesmaximal, characteristic, complemented
5#10590040C212yesmaximal, complemented
6C2×C3×ΓL(1,𝔽25)—21no—
7#63919C2212yes—
8C4×#625C2211yescharacteristic
9C4⋊#622C2212yes—
10#63742—22no—
11#63739—22no—
12C8×C3⋊Dic3C2211yescharacteristic
13C3×#818—21no—
14#63576—21no—
15#63572C2211yescharacteristic
16(C2×D3)⋊(C3⋊C8)—21no—
17#5128—61no—
18#4874—61no—
19C2×C3×C4×D3—21no—
20C2×#627—22no—
21C2×#625D411yescharacteristic
22C2×#622—22no—
23C2×C32×C8D411yescharacteristic
24C4×C3⋊Dic3C2311yescharacteristic
25C2×C3⋊(C3⋊C8)D411yescharacteristic
26C3×C4⋊Dic3—22no—
27C2×C3×C3⋊C8—21no—
28C3×ΓL(1,𝔽25)—42no—
29#3724—22no—
30#3724D411yescharacteristic
31(C2×D3)⋊Dic3—21no—
32#1695—91nomaximal, Sylow
33C2×C3×M16—61no—
34C4×#67—61no—
35C2×ΓL(1,𝔽25)—21no—
36#888—62no—
37C3×#107—61no—
38#830—61no—
39(C2×D3)⋊C8—61no—
40#818—21no—
41Dic3⋊C8—61no—
42C8×Dic3—61no—
43C8×Dic3—61no—
44#807—62no—
45C22×C3×D3—21no—
46C2×C32×C4C2×D411yescharacteristic
47C2×C3⋊Dic3C2×D411yescharacteristic
48C2×C3⋊Dic3#4111yescharacteristic
49C2×C3×Dic3—21no—
50C2×C3×Dic3—42no—
51C3×C4×D3—41no—
52C3×C4×D3—41no—
53#627—82no—
54#625—22no—
55#622—42no—
56C32×C8SD1612yes—
57C3⋊(C3⋊C8)—21no—
58C3×C3⋊C8—41no—
59#500—91no—
60#476—92no—
61#436—91no—
62#334—91no—
63#333—92no—
64C22×C3×C4—61no—
65C2×#67—61no—
66C2×C4×D3—21no—
67C2×Dic6—122no—
68C3×M16—122no—
69C2×C3×C8—21no—
70C2×C3×C8—21no—
71C2×C3×C8—61no—
72C3×C4⋊C4—62no—
73#217—61no—
74(C2×D3)⋊C4—61no—
75C4⋊Dic3—22no—
76Dic3⋊C4—61no—
77Dic3⋊C4—122no—
78C4×Dic3—61no—
79C4×Dic3—61no—
80C2×C3⋊C8—21no—
81C2×C3⋊C8—61no—
82C2×C3⋊C8—61no—
83ΓL(1,𝔽25)—42no—
84C22×C32#12111yescharacteristic
85C2×C3×D3—41no—
86C2×C3×D3—41no—
87C2×C3×D3—41no—
88C32×C4C2×SD1611yescharacteristic
89C32×C4#13711yescharacteristic
90C3⋊Dic3—21no—
91C3⋊Dic3#13712yes—
92C3×Dic3—41no—
93C3×Dic3—82no—
94C2×M16—61no—
95C4⋊Q8—92no—
96C4×D4—91no—
97#107—61no—
98#107—181no—
99#106—182no—
100C4⋊C8—91no—
101C4⋊C8—92no—
102#102—182no—
103C22⋊C8—181no—
104C4×C8—91no—
105C23×C3—61no—
106C22×D3—21no—
107C2×C3×C4—21no—
108C2×C3×C4—21no—
109C2×C3×C4—61no—
110C2×C3×C4—121no—
111C2×C3×C4—121no—
112C2×C3×C4—122no—
113#67—122no—
114C2×Dic3—21no—
115C2×Dic3—42no—
116C2×Dic3—61no—
117C2×Dic3—61no—
118C2×Dic3—61no—
119C2×Dic3—61no—
120C4×D3—41no—
121C4×D3—41no—
122Dic6—244no—
123C3×C8—22no—
124C3×C8—22no—
125C3×C8—121no—
126C3⋊C8—41no—
127C3⋊C8—62no—
128C3⋊C8—121no—
129C2×C32#46111yescharacteristic
130C2×C32#47011yescharacteristic
131C2×C32#47211yescharacteristic
132C3×D3—81no—
133C2×Q8—182no—
134C2×D4—91no—
135C22×C4—61no—
136M16—122no—
137C2×C8—61no—
138C2×C8—91no—
139C2×C8—182no—
140C2×C8GO+(4,𝔽2)11yescharacteristic
141C4⋊C4—62no—
142C4⋊C4—91no—
143C4⋊C4—182no—
144C22⋊C4—181no—
145C42—91no—
146C22×C3—21no—
147C22×C3—21no—
148C22×C3—121no—
149C22×C3—121no—
150C22×C3—121no—
151C2×D3—41no—
152C2×D3—41no—
153C2×D3—41no—
154C3×C4—21no—
155C3×C4—21no—
156C3×C4—21no—
157C3×C4—21no—
158C3×C4—121no—
159C3×C4—242no—
160Dic3—41no—
161Dic3—62no—
162Dic3—62no—
163Dic3—62no—
164Dic3—82no—
165Dic3—121no—
166C32#169511yescharacteristic, complemented, Sylow
167C23—61no—
168Q8—722no—
169D4—182no—
170C2×C4—61no—
171C2×C4—91no—
172C2×C4—91no—
173C2×C4—121no—
174C2×C4—121no—
175C2×C4—122no—
176C2×C4C2×GO+(4,𝔽2)11yescharacteristic
177C8—121no—
178C8—181no—
179C8—362no—
180C8#377512yes—
181C2×C3—21no—
182C2×C3—21no—
183C2×C3—21no—
184C2×C3—21no—
185C2×C3—21no—
186C2×C3—21no—
187C2×C3—241no—
188D3—81no—
189C22—121no—
190C22—121no—
191C22—121no—
192C22#6423011yescharacteristic
193C4—92no—
194C4—121no—
195C4—181no—
196C4—242no—
197C4#6422611yescharacteristic
198C4C2×#377511yescharacteristic
199C3—21no—
200C3—21no—
201C2—241no—
202C2#1059328911yescharacteristic
203C2#1059330311yescharacteristic
204C2#1059343711yescharacteristic
subgroupG/H
centerC22#64230
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#121
prime radicalC2×#625D4
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1695
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #10590902C2semidirect
4. #10590170C2semidirect
5. #10590040C2semidirect
166. C32#1695semidirect

Maximal subgroups

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

subgroupindex
#105933592
#105909022
#105907332
#105901702
#105900402
#16959