Finite Group Databasebeta

← #47982343

Subgroups — #47982343

Order 35456.

308 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 57 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#31800637C211yesmaximal, characteristic
2#31800279C211yesmaximal, characteristic, complemented
3#31800204C211yesmaximal, characteristic, complemented
4#31799746C211yesmaximal, characteristic, complemented
5#31799731C211yesmaximal, characteristic, complemented
6#31799731C211yesmaximal, characteristic, complemented
7#486×C277C211yesmaximal, characteristic, complemented
8C2×D4×D277—21no—
9C2×D4×D277—21no—
10C2×#17984550—21no—
11#22579851—21no—
12#22579851—21no—
13#22579848—22no—
14C4×D1108C2211yescharacteristic
15C4×D1108C2211yescharacteristic
16#22579813—21no—
17C4⋊#14555660C2211yescharacteristic, complemented
18C4⋊#14555660C2211yescharacteristic, complemented
19#22579804—21no—
20#22579800—21no—
21C4⋊Q8×C277C2211yescharacteristic, complemented
22#127×C277C2211yescharacteristic
23#102×C277—22no—
24C4×C8×C277C2211yescharacteristic, complemented
25C23×D277—22no—
26C2×D1108D411yescharacteristic
27C2×D1108D411yescharacteristic
28C2×C22⋊D277—22no—
29C2×C22⋊D277—22no—
30D4×D277—42no—
31D4×D277—42no—
32D4×D277—42no—
33D4×D277—42no—
34C2×C4×D277—21no—
35C2×C4×D277—21no—
36#17984550—42no—
37C2×#14555660—21no—
38C2×#14555660—21no—
39C4⋊Dic277D411yescharacteristic
40C4⋊Dic277D411yescharacteristic
41C22⋊Dic277—22no—
42#17984540—21no—
43#17984540—21no—
44C2×Q8×C277—21no—
45C2×D4×C277—21no—
46C2×D4×C277—21no—
47C2×D4×C277D412yes—
48C2×C8×C277—21no—
49C4⋊C4×C277—21no—
50C4⋊C4×C277—21no—
51C42×C277C2311yescharacteristic
52C22×D277—21no—
53C22×D277—21no—
54C22×D277—44no—
55C22×D277—44no—
56C22×D277—82no—
57D1108—21no—
58D1108—21no—
59D1108D812yes—
60D1108SD1612yescomplemented
61C22⋊D277—44no—
62C22⋊D277—44no—
63C2×Dic277—21no—
64C2×Dic277—21no—
65C4×D277—41no—
66C4×D277—41no—
67C4×D277—41no—
68C4×D277—41no—
69#14555660—41no—
70#14555660—41no—
71C23×C277—22no—
72Q8×C277—41no—
73Q8×C277—41no—
74D4×C277—42no—
75D4×C277—41no—
76D4×C277—41no—
77D4×C277—41no—
78D4×C277—41no—
79C2×C4×C277—41no—
80C2×C4×C277C2×D411yescharacteristic
81C2×C4×C277C2×D411yescharacteristic
82C2×C4×C277C2×D411yescharacteristic
83C8×C277—41no—
84C22×C277—42no—
85C22×C277—42no—
86C22×C277—42no—
87C22×C277#12011yescharacteristic
88C2×D277—22no—
89C2×D277—22no—
90C2×D277—41no—
91C2×D277—41no—
92C2×D277—41no—
93C2×D277—41no—
94C2×D277—88no—
95C4×C277—21no—
96C4×C277—81no—
97C4×C277C2×D811yescharacteristic
98C4×C277C2×SD1611yescharacteristic
99C4×C277AGL(1,ℤ/8)11yescharacteristic
100C4×C277AGL(1,ℤ/8)11yescharacteristic
101Dic277—41no—
102Dic277—41no—
103C2×C277—82no—
104C2×C277#44711yescharacteristic
105C2×C277#45011yescharacteristic
106C2×C277#45511yescharacteristic
107D277—42no—
108D277—42no—
109C277#163911yescharacteristic, complemented, Sylow
110#1639—2771nomaximal, Sylow
111D42—2771no—
112#486D27711yescharacteristic, complemented
113#474—2771no—
114#461—2771no—
115#331—2771no—
116D4⋊C8—2771no—
117D4⋊C8—2771no—
118C22×D4—5541no—
119C22×D4—5541no—
120C2×SD16—5541no—
121C4⋊Q8C2×D27711yescharacteristic, complemented
122#127C2×D27711yescharacteristic
123#121—5541no—
124#121—5541no—
125#120—5542no—
126C4×D4—2771no—
127C4×D4—2771no—
128#107—5541no—
129C4⋊C8—2771no—
130C4⋊C8—2771no—
131#103—5541no—
132#102—22no—
133#102—5541no—
134C4×C8C2×D27711yescharacteristic, complemented
135C24—5542no—
136C2×Q8—21no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—2771no—
140C2×D4—2771no—
141C2×D4—5542no—
142C2×D4—5542no—
143C2×D4—11082no—
144C2×D4—11082no—
145C2×D4—11082no—
146C2×D4—11082no—
147C2×D4C22⋊D27712yes—
148C22×C4—5541no—
149C22×C4—5541no—
150SD16—11082no—
151C2×C8—21no—
152C2×C8—5541no—
153C2×C8—5541no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—2771no—
157C4⋊C4—2771no—
158C22⋊C4—5542no—
159C22⋊C4—5541no—
160C22⋊C4—5541no—
161C42C22×D27711yescharacteristic
162C23—22no—
163C23—5541no—
164C23—5541no—
165C23—11084no—
166C23—11084no—
167C23—22162no—
168Q8—41no—
169Q8—41no—
170D4—42no—
171D4—41no—
172D4—41no—
173D4—41no—
174D4—41no—
175D4—2772no—
176D4—2772no—
177D4—5541no—
178D4—5541no—
179D4—11084no—
180D4—11084no—
181C2×C4—41no—
182C2×C4—5541no—
183C2×C4—5541no—
184C2×C4—11081no—
185C2×C4—11081no—
186C2×C4—11081no—
187C2×C4—11081no—
188C2×C4D4×D27711yescharacteristic
189C2×C4D4×D27711yescharacteristic
190C2×C4C2×C22⋊D27711yescharacteristic
191C8—41no—
192C8—11081no—
193C8—11081no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22—5542no—
198C22—5542no—
199C22—11081no—
200C22—11081no—
201C22—11081no—
202C22—11081no—
203C22—22168no—
204C22#2257984811yescharacteristic
205C4—21no—
206C4—81no—
207C4—11081no—
208C4—11081no—
209C4D8×D27711yescharacteristic
210C4SD16×D27711yescharacteristic
211C4#2257990411yescharacteristic
212C4#2257990711yescharacteristic
213C2—82no—
214C2—11082no—
215C2—11082no—
216C2#3180013411yescharacteristic
217C2#3180015111yescharacteristic
218C2#3180017911yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#486×C277C2
socleC22×C277#120
prime radical#31800637C2
hypercenter#486D277
hypocenterC277#1639
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #31800279C2semidirect
3. #31800204C2semidirect
4. #31799746C2semidirect
5. #31799731C2semidirect
6. #31799731C2semidirect
7. #486×C277C2semidirect
17. C4⋊#14555660C22semidirect
18. C4⋊#14555660C22semidirect
21. C4⋊Q8×C277C22semidirect
24. C4×C8×C277C22semidirect
60. D1108SD16semidirect
109. C277#1639semidirect
112. #486D277semidirect
121. C4⋊Q8C2×D277semidirect
134. C4×C8C2×D277semidirect

Maximal subgroups

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

subgroupindex
#318006372
#318002792
#318002042
#317997462
#317997312
#486×C2772
#1639277