Finite Group Databasebeta

← #38767912

Subgroups — #38767912

Order 25472.

278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 55 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#27164688C211yesmaximal, characteristic, complemented
2#27164215C211yesmaximal, characteristic, complemented
3#27164210C211yesmaximal, characteristic, complemented
4#27163762C211yesmaximal, characteristic, complemented
5#27163750C211yesmaximal, characteristic, complemented
6#27163747C211yesmaximal, characteristic, complemented
7#493×C199C211yesmaximal, characteristic, complemented
8C2×#15691885—21no—
9C2×#15691874—21no—
10C2×#15691871—21no—
11#20263951—21no—
12#20263927—22no—
13#20263926—21no—
14C4×Dic398C2211yescharacteristic
15C4×D796C2211yescharacteristic
16D4×Dic199—21no—
17C4⋊(C199⋊C8)C2211yescharacteristic
18C4⋊(C199⋊C8)C2211yescharacteristic
19#20263876—21no—
20#20263876—21no—
21C2×D8×C199—22no—
22#127×C199C2211yescharacteristic
23#127×C199C2211yescharacteristic
24C4×C8×C199C2211yescharacteristic
25#15691885—42no—
26#15691885—42no—
27C2×Dic398D411yescharacteristic
28C2×D796D411yescharacteristic
29C2×C22⋊D199—22no—
30C2×C22⋊D199—22no—
31C22×Dic199—22no—
32C2×C4×D199—21no—
33#15691874—42no—
34#15691871—42no—
35C2×C199⋊C8—21no—
36C2×C199⋊C8—21no—
37C4⋊Dic199D411yescharacteristic
38C4⋊Dic199D411yescharacteristic
39Dic199⋊C4—21no—
40C22⋊Dic199—22no—
41(C2×D199)⋊C4—21no—
42C4×Dic199—21no—
43C2×D4×C199—21no—
44C2×D4×C199—21no—
45C2×D4×C199—21no—
46C2×D4×C199—21no—
47C2×D4×C199—21no—
48C2×D4×C199D412yes—
49D8×C199—44no—
50C2×C8×C199—21no—
51C42×C199C2311yescharacteristic
52C22×D199—21no—
53Dic398—21no—
54Dic398D812yescomplemented
55D796—21no—
56D796—21no—
57C22⋊D199—44no—
58C22⋊D199—82no—
59C2×Dic199—21no—
60C2×Dic199—21no—
61C2×Dic199—21no—
62C2×Dic199—44no—
63C4×D199—41no—
64C4×D199—41no—
65C199⋊C8—41no—
66C199⋊C8—41no—
67C23×C199—22no—
68C23×C199—41no—
69D4×C199—42no—
70D4×C199—42no—
71D4×C199—41no—
72D4×C199—41no—
73D4×C199—41no—
74D4×C199—41no—
75D4×C199—41no—
76D4×C199—41no—
77D4×C199—41no—
78D4×C199—41no—
79C2×C4×C199C2×D411yescharacteristic
80C2×C4×C199C2×D411yescharacteristic
81C2×C4×C199C2×D411yescharacteristic
82C8×C199—22no—
83C22×C199—42no—
84C22×C199—42no—
85C22×C199—42no—
86C22×C199—81no—
87C22×C199—81no—
88C22×C199—81no—
89C22×C199#12011yescharacteristic
90C2×D199—41no—
91C2×D199—41no—
92C2×D199—41no—
93C4×C199—21no—
94C4×C199C2×D811yescharacteristic
95C4×C199#13511yescharacteristic
96C4×C199AGL(1,ℤ/8)11yescharacteristic
97C4×C199AGL(1,ℤ/8)11yescharacteristic
98Dic199—22no—
99Dic199—41no—
100Dic199—41no—
101C2×C199—82no—
102C2×C199—161no—
103C2×C199#44711yescharacteristic
104C2×C199#44911yescharacteristic
105C2×C199#45311yescharacteristic
106D199—81no—
107C199#162111yescharacteristic, complemented, Sylow
108#1621—1991nomaximal, Sylow
109#550—1991no—
110#493D19911yescharacteristic, complemented
111#460—1991no—
112#459—1991no—
113#331—1991no—
114Q8⋊C8—1991no—
115D4⋊C8—1991no—
116C2×#41—3981no—
117C2×SD16—3981no—
118C2×D8—22no—
119C2×D8—3981no—
120#127—3981no—
121#127C2×D19911yescharacteristic
122#127C2×D19911yescharacteristic
123#121—3982no—
124#121—3981no—
125C4×Q8—1991no—
126C4×D4—3981no—
127C4×D4—1991no—
128C4⋊C8—1991no—
129C4⋊C8—1991no—
130#102—3981no—
131#102—3981no—
132C4×C8C2×D19911yescharacteristic
133#41—7962no—
134#41—7962no—
135C2×Q8—1991no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—21no—
141C2×D4—3982no—
142C2×D4—3982no—
143C2×D4—1991no—
144C2×D4C22⋊D19912yes—
145C22×C4—3982no—
146C22×C4—3981no—
147SD16—7962no—
148D8—44no—
149D8—7962no—
150C2×C8—21no—
151C2×C8—3981no—
152C2×C8—3981no—
153C4⋊C4—3981no—
154C4⋊C4—1991no—
155C4⋊C4—1991no—
156C22⋊C4—3982no—
157C22⋊C4—3981no—
158C42—3981no—
159C42C22×D19911yescharacteristic
160C23—22no—
161C23—41no—
162C23—3981no—
163Q8—3981no—
164Q8—1992no—
165D4—42no—
166D4—42no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—41no—
171D4—41no—
172D4—41no—
173D4—41no—
174D4—41no—
175D4—7964no—
176D4—15922no—
177D4—3981no—
178D4—3981no—
179C2×C4—7964no—
180C2×C4—7961no—
181C2×C4—7961no—
182C2×C4—3981no—
183C2×C4—3981no—
184C2×C4—3981no—
185C2×C4D4×D19911yescharacteristic
186C2×C4D4×D19911yescharacteristic
187C2×C4C2×C22⋊D19911yescharacteristic
188C8—22no—
189C8—7961no—
190C8—7961no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—81no—
195C22—81no—
196C22—81no—
197C22—7961no—
198C22—7961no—
199C22—7961no—
200C22#2026392311yescharacteristic
201C4—21no—
202C4—7961no—
203C4—7961no—
204C4—3982no—
205C4D8×D19911yescharacteristic
206C4#2026397411yescharacteristic
207C4#2026397911yescharacteristic
208C4#2026397911yescharacteristic
209C2—82no—
210C2—161no—
211C2—15921no—
212C2#2716415011yescharacteristic
213C2#2716416011yescharacteristic
214C2#2716418511yescharacteristic
subgroupG/H
centerC22#20263923
commutator, cosocleC42×C199C23
FrattiniC42C22×D199
Fitting#493×C199C2
socleC22×C199#120
hypercenter#493D199
hypocenterC199#1621
LCSG ▷ C42×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #27164688C2semidirect
2. #27164215C2semidirect
3. #27164210C2semidirect
4. #27163762C2semidirect
5. #27163750C2semidirect
6. #27163747C2semidirect
7. #493×C199C2semidirect
54. Dic398D8semidirect
107. C199#1621semidirect
110. #493D199semidirect

Maximal subgroups

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

subgroupindex
#271646882
#271642152
#271642102
#271637622
#271637502
#271637472
#493×C1992
#1621199