Finite Group Databasebeta

← #49094365

Subgroups — #49094365

Order 35968.

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#31824133C211yesmaximal, characteristic, complemented
2#31823660C211yesmaximal, characteristic, complemented
3#31823655C211yesmaximal, characteristic, complemented
4#31823207C211yesmaximal, characteristic, complemented
5#31823195C211yesmaximal, characteristic, complemented
6#31823192C211yesmaximal, characteristic, complemented
7#493×C281C211yesmaximal, characteristic, complemented
8C2×#17985137—21no—
9C2×#17985126—21no—
10C2×#17985123—21no—
11#22582875—21no—
12#22582851—22no—
13#22582850—21no—
14C4×Dic562C2211yescharacteristic
15C4×D1124C2211yescharacteristic
16D4×Dic281—21no—
17C4⋊#14555886C2211yescharacteristic
18C4⋊#14555886C2211yescharacteristic
19#22582800—21no—
20#22582800—21no—
21C2×D8×C281—22no—
22#127×C281C2211yescharacteristic
23#127×C281C2211yescharacteristic
24C4×C8×C281C2211yescharacteristic
25#17985137—42no—
26#17985137—42no—
27C2×Dic562D411yescharacteristic
28C2×D1124D411yescharacteristic
29C2×C22⋊D281—22no—
30C2×C22⋊D281—22no—
31C22×Dic281—22no—
32C2×C4×D281—21no—
33#17985126—42no—
34#17985123—42no—
35C2×#14555886—21no—
36C2×#14555886—21no—
37C4⋊Dic281D411yescharacteristic
38C4⋊Dic281D411yescharacteristic
39#17985117—21no—
40C22⋊Dic281—22no—
41#17985115—21no—
42C4×Dic281—21no—
43C2×D4×C281—21no—
44C2×D4×C281—21no—
45C2×D4×C281—21no—
46C2×D4×C281—21no—
47C2×D4×C281—21no—
48C2×D4×C281D412yes—
49D8×C281—44no—
50C2×C8×C281—21no—
51C42×C281C2311yescharacteristic
52C22×D281—21no—
53Dic562—21no—
54Dic562D812yescomplemented
55D1124—21no—
56D1124—21no—
57C22⋊D281—44no—
58C22⋊D281—82no—
59C2×Dic281—21no—
60C2×Dic281—21no—
61C2×Dic281—21no—
62C2×Dic281—44no—
63C4×D281—41no—
64C4×D281—41no—
65#14555886—41no—
66#14555886—41no—
67C23×C281—22no—
68C23×C281—41no—
69D4×C281—42no—
70D4×C281—42no—
71D4×C281—41no—
72D4×C281—41no—
73D4×C281—41no—
74D4×C281—41no—
75D4×C281—41no—
76D4×C281—41no—
77D4×C281—41no—
78D4×C281—41no—
79C2×C4×C281C2×D411yescharacteristic
80C2×C4×C281C2×D411yescharacteristic
81C2×C4×C281C2×D411yescharacteristic
82C8×C281—22no—
83C22×C281—42no—
84C22×C281—42no—
85C22×C281—42no—
86C22×C281—81no—
87C22×C281—81no—
88C22×C281—81no—
89C22×C281#12011yescharacteristic
90C2×D281—41no—
91C2×D281—41no—
92C2×D281—41no—
93C4×C281—21no—
94C4×C281C2×D811yescharacteristic
95C4×C281#13511yescharacteristic
96C4×C281AGL(1,ℤ/8)11yescharacteristic
97C4×C281AGL(1,ℤ/8)11yescharacteristic
98Dic281—22no—
99Dic281—41no—
100Dic281—41no—
101C2×C281—82no—
102C2×C281—161no—
103C2×C281#44711yescharacteristic
104C2×C281#44911yescharacteristic
105C2×C281#45311yescharacteristic
106D281—81no—
107C281#162111yescharacteristic, complemented, Sylow
108#1621—2811nomaximal, Sylow
109#550—2811no—
110#493D28111yescharacteristic, complemented
111#460—2811no—
112#459—2811no—
113#331—2811no—
114Q8⋊C8—2811no—
115D4⋊C8—2811no—
116C2×#41—5621no—
117C2×SD16—5621no—
118C2×D8—22no—
119C2×D8—5621no—
120#127—5621no—
121#127C2×D28111yescharacteristic
122#127C2×D28111yescharacteristic
123#121—5621no—
124#121—5622no—
125C4×Q8—2811no—
126C4×D4—2811no—
127C4×D4—5621no—
128C4⋊C8—2811no—
129C4⋊C8—2811no—
130#102—5621no—
131#102—5621no—
132C4×C8C2×D28111yescharacteristic
133#41—11242no—
134#41—11242no—
135C2×Q8—2811no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—21no—
141C2×D4—2811no—
142C2×D4—5622no—
143C2×D4—5622no—
144C2×D4C22⋊D28112yes—
145C22×C4—5622no—
146C22×C4—5621no—
147SD16—11242no—
148D8—44no—
149D8—11242no—
150C2×C8—21no—
151C2×C8—5621no—
152C2×C8—5621no—
153C4⋊C4—2811no—
154C4⋊C4—2811no—
155C4⋊C4—5621no—
156C22⋊C4—5622no—
157C22⋊C4—5621no—
158C42—5621no—
159C42C22×D28111yescharacteristic
160C23—22no—
161C23—41no—
162C23—5621no—
163Q8—2812no—
164Q8—5621no—
165D4—42no—
166D4—42no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—41no—
171D4—41no—
172D4—41no—
173D4—41no—
174D4—41no—
175D4—5621no—
176D4—5621no—
177D4—11244no—
178D4—22482no—
179C2×C4—5621no—
180C2×C4—5621no—
181C2×C4—5621no—
182C2×C4—11244no—
183C2×C4—11241no—
184C2×C4—11241no—
185C2×C4D4×D28111yescharacteristic
186C2×C4D4×D28111yescharacteristic
187C2×C4C2×C22⋊D28111yescharacteristic
188C8—22no—
189C8—11241no—
190C8—11241no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—81no—
195C22—81no—
196C22—81no—
197C22—11241no—
198C22—11241no—
199C22—11241no—
200C22#2258284711yescharacteristic
201C4—21no—
202C4—5622no—
203C4—11241no—
204C4—11241no—
205C4D8×D28111yescharacteristic
206C4#2258289811yescharacteristic
207C4#2258290311yescharacteristic
208C4#2258290311yescharacteristic
209C2—82no—
210C2—161no—
211C2—22481no—
212C2#3182359511yescharacteristic
213C2#3182360511yescharacteristic
214C2#3182363011yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#493×C281C2
socleC22×C281#120
hypercenter#493D281
hypocenterC281#1621
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #31824133C2semidirect
2. #31823660C2semidirect
3. #31823655C2semidirect
4. #31823207C2semidirect
5. #31823195C2semidirect
6. #31823192C2semidirect
7. #493×C281C2semidirect
54. Dic562D8semidirect
107. C281#1621semidirect
110. #493D281semidirect

Maximal subgroups

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

subgroupindex
#318241332
#318236602
#318236552
#318232072
#318231952
#318231922
#493×C2812
#1621281