Finite Group Databasebeta

← #47985111

Subgroups — #47985111

Order 35456.

226 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 47 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#31800799C211yesmaximal, characteristic, complemented
2#31800438C211yesmaximal, characteristic, complemented
3#31800252C211yesmaximal, characteristic, complemented
4#31799813C211yesmaximal, characteristic, complemented
5#31799812C211yesmaximal, characteristic, complemented
6#31799783C211yesmaximal, characteristic, complemented
7#509×C277C211yesmaximal, characteristic, complemented
8#41×D277—21no—
9#22579912—21no—
10#22579909—21no—
11#22579907—21no—
12#22579904—21no—
13#22579902C2211yescharacteristic
14#22579900—21no—
15C2×#17984546C2211yescharacteristic
16#22579851—21no—
17#22579824—21no—
18#22579821—21no—
19#22579820C2211yescharacteristic, complemented
20#22579812C2211yescharacteristic, complemented
21#22579801—21no—
22#135×C277C2211yescharacteristic
23C2×D8×C277C2211yescharacteristic, complemented
24SD32×C277—21no—
25D16×C277—21no—
26M32×C277C2211yescharacteristic, complemented
27#17984564—21no—
28#17984563—21no—
29#17984563—41no—
30#17984562—21no—
31#17984562—41no—
32Q8×D277—21no—
33C2×C22⋊D277—41no—
34D4×D277—21no—
35D4×D277—41no—
36C2×C4×D277—41no—
37C2×C4×D277D411yescharacteristic
38Dic1108D411yescharacteristic, complemented
39#17984553—21no—
40#17984552—21no—
41#17984551—21no—
42#17984550—21no—
43D2216D411yescharacteristic, complemented
44#17984548—21no—
45#17984546—21no—
46#17984546—21no—
47C2×#14555660D411yescharacteristic
48C4⋊Dic277—21no—
49C22⋊Dic277—41no—
50#17984538—21no—
51#41×C277—21no—
52C2×D4×C277—21no—
53Q16×C277D411yescharacteristic, complemented
54SD16×C277—21no—
55D8×C277—21no—
56D8×C277—21no—
57D8×C277D411yescharacteristic, complemented
58C2×C8×C277C2311yescharacteristic
59C16×C277—21no—
60C22×D277—41no—
61C22×D277D811yescharacteristic
62Dic554—21no—
63Dic554—41no—
64D1108—21no—
65D1108—41no—
66C22⋊D277—41no—
67C22⋊D277—41no—
68C22⋊D277—41no—
69C22⋊D277—82no—
70C2×Dic277—41no—
71C2×Dic277—41no—
72C2×Dic277D811yescharacteristic
73C4×D277—21no—
74C4×D277—21no—
75C4×D277—41no—
76C4×D277—41no—
77C4×D277—41no—
78#14555660—21no—
79C23×C277—41no—
80Q8×C277—21no—
81D4×C277—21no—
82D4×C277—41no—
83D4×C277—41no—
84D4×C277—41no—
85C2×C4×C277—41no—
86C2×C4×C277C2×D411yescharacteristic
87C8×C277C2×D411yescharacteristic
88C8×C277C2×D411yescharacteristic
89C22×C277—41no—
90C22×C277—81no—
91C22×C277—81no—
92C22×C277—81no—
93C22×C277C2×D811yescharacteristic
94C2×D277—21no—
95C2×D277—41no—
96C2×D277—41no—
97C2×D277—82no—
98C4×C277—41no—
99C4×C277#12011yescharacteristic
100C4×C277AGL(1,ℤ/8)11yescharacteristic
101Dic277—21no—
102Dic277—41no—
103Dic277—81no—
104C2×C277—21no—
105C2×C277—81no—
106C2×C277—161no—
107C2×C277#44711yescharacteristic
108D277—41no—
109D277—81no—
110C277#219011yescharacteristic, complemented, Sylow
111#2190—2771nomaximal, Sylow
112#575—2771no—
113#509—2771no—
114#509D27711yescharacteristic, complemented
115#469—2771no—
116#360—2771no—
117#360—2771no—
118#349—2771no—
119C2×#41—5541no—
120#137—5541no—
121#137—5541no—
122AGL(1,ℤ/8)—5541no—
123AGL(1,ℤ/8)—5541no—
124#135—2771no—
125#135—5541no—
126#135C2×D27711yescharacteristic
127C2×D8C2×D27711yescharacteristic, complemented
128C2×M16—2771no—
129#121—5541no—
130SD32—21no—
131SD32—5541no—
132D16—21no—
133D16—5541no—
134M32—2771no—
135M32C2×D27711yescharacteristic, complemented
136#106—2771no—
137#102—5541no—
138#41—21no—
139#41—5541no—
140#41—5541no—
141#41—5541no—
142#41—11081no—
143#41—11081no—
144C2×Q8—5541no—
145C2×D4—21no—
146C2×D4—5541no—
147C2×D4—11081no—
148C2×D4—11081no—
149C22×C4—2771no—
150C22×C4—11081no—
151Q16—2771no—
152Q16—5541no—
153Q16C22⋊D27711yescharacteristic, complemented
154SD16—21no—
155SD16—5541no—
156SD16—5541no—
157SD16—5541no—
158D8—21no—
159D8—21no—
160D8—2771no—
161D8—5541no—
162D8C22⋊D27711yescharacteristic, complemented
163M16—5541no—
164M16—5541no—
165C2×C8—2771no—
166C2×C8C22×D27711yescharacteristic
167C4⋊C4—5541no—
168C22⋊C4—11081no—
169C16—21no—
170C16—5541no—
171C23—41no—
172C23—2771no—
173C23—11081no—
174Q8—21no—
175Q8—5541no—
176Q8—11081no—
177D4—21no—
178D4—41no—
179D4—41no—
180D4—41no—
181D4—5541no—
182D4—11081no—
183D4—11081no—
184D4—11081no—
185D4—11081no—
186D4—22162no—
187C2×C4—41no—
188C2×C4—2771no—
189C2×C4—5541no—
190C2×C4—5541no—
191C2×C4—11081no—
192C2×C4—11081no—
193C2×C4—11081no—
194C2×C4—11081no—
195C2×C4—11081no—
196C2×C4D4×D27711yescharacteristic
197C8—5541no—
198C8D4×D27711yescharacteristic
199C8C2×C22⋊D27711yescharacteristic
200C22—41no—
201C22—81no—
202C22—81no—
203C22—81no—
204C22—5541no—
205C22—11081no—
206C22—11081no—
207C22—22162no—
208C22D8×D27711yescharacteristic
209C4—41no—
210C4—5541no—
211C4—11081no—
212C4—22161no—
213C4#2257984811yescharacteristic
214C4#2257990411yescharacteristic
215C2—21no—
216C2—81no—
217C2—161no—
218C2—11081no—
219C2—22161no—
220C2#3180013411yescharacteristic
subgroupG/H
centerC2#31800134
commutator, cosocleC2×C8×C277C23
FrattiniC2×C8C22×D277
Fitting#509×C277C2
socleC2×C277#447
hypercenter#509D277
hypocenterC277#2190
LCSG ▷ C2×C8×C277 ▷ C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #31800799C2semidirect
2. #31800438C2semidirect
3. #31800252C2semidirect
4. #31799813C2semidirect
5. #31799812C2semidirect
6. #31799783C2semidirect
7. #509×C277C2semidirect
19. #22579820C22semidirect
20. #22579812C22semidirect
23. C2×D8×C277C22semidirect
26. M32×C277C22semidirect
38. Dic1108D4semidirect
43. D2216D4semidirect
53. Q16×C277D4semidirect
57. D8×C277D4semidirect
110. C277#2190semidirect
114. #509D277semidirect
127. C2×D8C2×D277semidirect
135. M32C2×D277semidirect
153. Q16C22⋊D277semidirect
162. D8C22⋊D277semidirect

Maximal subgroups

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

subgroupindex
#318007992
#318004382
#318002522
#317998132
#317998122
#317997832
#509×C2772
#2190277