Finite Group Databasebeta

← #27170194

Subgroups — #27170194

Order 12928.

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#20265847C211yesmaximal, characteristic, complemented
2#20265374C211yesmaximal, characteristic, complemented
3#20265369C211yesmaximal, characteristic, complemented
4#20264921C211yesmaximal, characteristic, complemented
5#20264909C211yesmaximal, characteristic, complemented
6#20264906C211yesmaximal, characteristic, complemented
7#493×C101C211yesmaximal, characteristic, complemented
8C2×#13108073—21no—
9C2×#13108062—21no—
10C2×#13108059—21no—
11#15692251—21no—
12#15692227—22no—
13#15692226—21no—
14C4×Dic202C2211yescharacteristic
15C4×D404C2211yescharacteristic
16D4×Dic101—21no—
17C4⋊#11717579C2211yescharacteristic
18C4⋊#11717579C2211yescharacteristic
19#15692176—21no—
20#15692176—21no—
21C2×D8×C101—22no—
22#127×C101C2211yescharacteristic
23#127×C101C2211yescharacteristic
24C4×C8×C101C2211yescharacteristic
25#13108073—42no—
26#13108073—42no—
27C2×Dic202D411yescharacteristic
28C2×D404D411yescharacteristic
29C2×C22⋊D101—22no—
30C2×C22⋊D101—22no—
31C22×Dic101—22no—
32C2×C4×D101—21no—
33#13108062—42no—
34#13108059—42no—
35C2×#11717579—21no—
36C2×#11717579—21no—
37C4⋊Dic101D411yescharacteristic
38C4⋊Dic101D411yescharacteristic
39#13108053—21no—
40C22⋊Dic101—22no—
41#13108051—21no—
42C4×Dic101—21no—
43C2×D4×C101—21no—
44C2×D4×C101—21no—
45C2×D4×C101—21no—
46C2×D4×C101—21no—
47C2×D4×C101—21no—
48C2×D4×C101D412yes—
49D8×C101—44no—
50C2×C8×C101—21no—
51C42×C101C2311yescharacteristic
52C23×C101—22no—
53C23×C101—41no—
54C22×D101—21no—
55D4×C101—42no—
56D4×C101—42no—
57D4×C101—41no—
58D4×C101—41no—
59D4×C101—41no—
60D4×C101—41no—
61D4×C101—41no—
62D4×C101—41no—
63D4×C101—41no—
64D4×C101—41no—
65C2×C4×C101C2×D411yescharacteristic
66C2×C4×C101C2×D411yescharacteristic
67C2×C4×C101C2×D411yescharacteristic
68C22⋊D101—44no—
69C22⋊D101—82no—
70C2×Dic101—21no—
71C2×Dic101—21no—
72C2×Dic101—21no—
73C2×Dic101—44no—
74D404—21no—
75D404—21no—
76C4×D101—41no—
77C4×D101—41no—
78Dic202—21no—
79Dic202D812yescomplemented
80C8×C101—22no—
81#11717579—41no—
82#11717579—41no—
83C22×C101—42no—
84C22×C101—42no—
85C22×C101—42no—
86C22×C101—81no—
87C22×C101—81no—
88C22×C101—81no—
89C22×C101#12011yescharacteristic
90C2×D101—41no—
91C2×D101—41no—
92C2×D101—41no—
93C4×C101—21no—
94C4×C101C2×D811yescharacteristic
95C4×C101#13511yescharacteristic
96C4×C101AGL(1,ℤ/8)11yescharacteristic
97C4×C101AGL(1,ℤ/8)11yescharacteristic
98Dic101—22no—
99Dic101—41no—
100Dic101—41no—
101C2×C101—82no—
102C2×C101—161no—
103C2×C101#44711yescharacteristic
104C2×C101#44911yescharacteristic
105C2×C101#45311yescharacteristic
106D101—81no—
107#1621—1011nomaximal, Sylow
108C101#162111yescharacteristic, complemented, Sylow
109#550—1011no—
110#493D10111yescharacteristic, complemented
111#460—1011no—
112#459—1011no—
113#331—1011no—
114Q8⋊C8—1011no—
115D4⋊C8—1011no—
116C2×#41—2021no—
117C2×SD16—2021no—
118C2×D8—22no—
119C2×D8—2021no—
120#127—2021no—
121#127C2×D10111yescharacteristic
122#127C2×D10111yescharacteristic
123#121—2021no—
124#121—2022no—
125C4×Q8—1011no—
126C4×D4—1011no—
127C4×D4—2021no—
128C4⋊C8—1011no—
129C4⋊C8—1011no—
130#102—2021no—
131#102—2021no—
132C4×C8C2×D10111yescharacteristic
133#41—4042no—
134#41—4042no—
135C2×Q8—1011no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—21no—
141C2×D4—1011no—
142C2×D4—2022no—
143C2×D4—2022no—
144C2×D4C22⋊D10112yes—
145C22×C4—2022no—
146C22×C4—2021no—
147SD16—4042no—
148D8—44no—
149D8—4042no—
150C2×C8—21no—
151C2×C8—2021no—
152C2×C8—2021no—
153C4⋊C4—1011no—
154C4⋊C4—1011no—
155C4⋊C4—2021no—
156C22⋊C4—2022no—
157C22⋊C4—2021no—
158C42—2021no—
159C42C22×D10111yescharacteristic
160C23—22no—
161C23—41no—
162C23—2021no—
163Q8—1012no—
164Q8—2021no—
165D4—42no—
166D4—42no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—41no—
171D4—41no—
172D4—41no—
173D4—41no—
174D4—41no—
175D4—8082no—
176D4—4044no—
177D4—2021no—
178D4—2021no—
179C2×C4—4044no—
180C2×C4—4041no—
181C2×C4—4041no—
182C2×C4—2021no—
183C2×C4—2021no—
184C2×C4—2021no—
185C2×C4D4×D10111yescharacteristic
186C2×C4D4×D10111yescharacteristic
187C2×C4C2×C22⋊D10111yescharacteristic
188C8—22no—
189C8—4041no—
190C8—4041no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—81no—
195C22—81no—
196C22—81no—
197C22—4041no—
198C22—4041no—
199C22—4041no—
200C22#1569222311yescharacteristic
201C4—21no—
202C4—4041no—
203C4—4041no—
204C4—2022no—
205C4D8×D10111yescharacteristic
206C4#1569227411yescharacteristic
207C4#1569227911yescharacteristic
208C4#1569227911yescharacteristic
209C2—82no—
210C2—161no—
211C2—8081no—
212C2#2026530911yescharacteristic
213C2#2026531911yescharacteristic
214C2#2026534411yescharacteristic
subgroupG/H
centerC22#15692223
commutator, cosocleC42×C101C23
FrattiniC42C22×D101
Fitting#493×C101C2
socleC22×C101#120
hypercenter#493D101
hypocenterC101#1621
LCSG ▷ C42×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #20265847C2semidirect
2. #20265374C2semidirect
3. #20265369C2semidirect
4. #20264921C2semidirect
5. #20264909C2semidirect
6. #20264906C2semidirect
7. #493×C101C2semidirect
79. Dic202D8semidirect
108. C101#1621semidirect
110. #493D101semidirect

Maximal subgroups

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

subgroupindex
#202658472
#202653742
#202653692
#202649212
#202649092
#202649062
#493×C1012
#1621101