Finite Group Databasebeta

← #47982475

Subgroups — #47982475

Order 35456.

228 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 45 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#31800744C211yesmaximal, characteristic
2#31800396C211yesmaximal, characteristic, complemented
3#31800362C211yesmaximal, characteristic, complemented
4#31800361C211yesmaximal, characteristic, complemented
5#31799741C211yesmaximal, characteristic, complemented
6#31799741C211yesmaximal, characteristic, complemented
7#329×C277C211yesmaximal, characteristic, complemented
8C2×Dic1108—21no—
9C2×#17984552—21no—
10#22579880C2211yescharacteristic, complemented
11#22579869—21no—
12#22579868C2211yescharacteristic
13#22579868C2211yescharacteristic
14#22579866—21no—
15#22579866—21no—
16#22579850—21no—
17#22579850—21no—
18#22579848—21no—
19#22579805—21no—
20#22579804—21no—
21#22579802—21no—
22#22579801—21no—
23#22579791C2211yescharacteristic, complemented
24#124×C277C2211yescharacteristic
25#97×C277C2211yescharacteristic, complemented
26#97×C277C2211yescharacteristic, complemented
27C23×D277—21no—
28C2×Dic554—21no—
29C2×Dic554D411yescharacteristic
30C2×Dic554D411yescharacteristic
31C2×D1108—21no—
32C2×D1108D411yescharacteristic
33C2×D1108D411yescharacteristic
34C2×C22⋊D277—21no—
35C2×C22⋊D277—21no—
36Dic1108—42no—
37#17984552—42no—
38C2×#14555660—21no—
39C4⋊Dic277—21no—
40C4⋊Dic277—21no—
41C22⋊Dic277—21no—
42#17984540—21no—
43#17984540—21no—
44#17984540—21no—
45#17984540—21no—
46#17984540—21no—
47#17984540—21no—
48C4×Dic277—21no—
49C2×Q8×C277D411yescharacteristic
50C2×D4×C277D411yescharacteristic
51C2×C8×C277—21no—
52C2×C8×C277—21no—
53C22⋊C4×C277—21no—
54C22⋊C4×C277—21no—
55C42×C277C2311yescharacteristic
56C22×D277—21no—
57C22×D277—21no—
58C22×D277—81no—
59C22×D277—81no—
60C22×D277—81no—
61Dic554—41no—
62Dic554—41no—
63Dic554—41no—
64Dic554—41no—
65D1108—41no—
66D1108—41no—
67D1108—81no—
68C22⋊D277—81no—
69C22⋊D277—81no—
70C2×Dic277—21no—
71C2×Dic277—21no—
72C2×Dic277—41no—
73#14555660—41no—
74C23×C277—21no—
75Q8×C277—41no—
76D4×C277—41no—
77C2×C4×C277—21no—
78C2×C4×C277C2×D411yescharacteristic
79C2×C4×C277C2×D411yescharacteristic
80C2×C4×C277C2×D411yescharacteristic
81C8×C277—22no—
82C8×C277—41no—
83C22×C277—41no—
84C22×C277—41no—
85C22×C277—41no—
86C22×C277#12011yescharacteristic
87C2×D277—41no—
88C2×D277—41no—
89C2×D277—41no—
90C2×D277—41no—
91C2×D277—41no—
92C2×D277—41no—
93C2×D277—84no—
94C4×C277—21no—
95C4×C277—21no—
96C4×C277—21no—
97C4×C277—41no—
98Dic277—41no—
99Dic277—41no—
100Dic277—81no—
101C2×C277—81no—
102C2×C277#45311yescharacteristic
103C2×C277#45511yescharacteristic
104C2×C277#45511yescharacteristic
105D277—81no—
106D277—81no—
107C277#165911yescharacteristic, complemented, Sylow
108#1659—2771nomaximal, Sylow
109H(3,𝔽4)—2771no—
110#497—2771no—
111#489—2771no—
112#489—2771no—
113#329—2771no—
114#329—2771no—
115#329D27711yescharacteristic, complemented
116C2×Q16—5541no—
117C2×SD16—5541no—
118C4⋊Q8—2771no—
119#124—2771no—
120#124—2771no—
121#124—5541no—
122#124—5541no—
123#124—5541no—
124#124C2×D27711yescharacteristic
125#120—5541no—
126#120—5541no—
127#120—5541no—
128#103—5541no—
129#103—5541no—
130#102—5541no—
131#102—5541no—
132#97—2771no—
133#97C2×D27711yescharacteristic, complemented
134#97C2×D27711yescharacteristic, complemented
135C24—5541no—
136C2×Q8—2771no—
137C2×Q8—2771no—
138C2×Q8—5541no—
139C2×Q8D110811yescharacteristic
140C2×D4—2771no—
141C2×D4—2771no—
142C2×D4—5541no—
143C2×D4—5541no—
144C2×D4—5541no—
145C2×D4D110811yescharacteristic
146Q16—11082no—
147SD16—11082no—
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—5541no—
151C4⋊C4—5541no—
152C4⋊C4—5541no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C22⋊C4—5541no—
156C22⋊C4—5541no—
157C22⋊C4—5541no—
158C22⋊C4—5541no—
159C22⋊C4—5541no—
160C22⋊C4—5541no—
161C22⋊C4—5541no—
162C42—5541no—
163C42C22×D27711yescharacteristic
164C23—21no—
165C23—5541no—
166C23—5541no—
167C23—22161no—
168C23—22161no—
169C23—22161no—
170Q8—41no—
171Q8—11081no—
172Q8—11081no—
173Q8—11081no—
174Q8—11081no—
175D4—41no—
176D4—11081no—
177D4—11081no—
178D4—22161no—
179D4—22161no—
180D4—22161no—
181C2×C4—21no—
182C2×C4—5541no—
183C2×C4—5541no—
184C2×C4—11081no—
185C2×C4D4×D27711yescharacteristic
186C2×C4D4×D27711yescharacteristic
187C2×C4C2×D110811yescharacteristic
188C8—22no—
189C8—41no—
190C8—11081no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—11081no—
195C22—11081no—
196C22—11081no—
197C22—11081no—
198C22—11081no—
199C22—11081no—
200C22—22164no—
201C22#2257985011yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—11081no—
207C4—11081no—
208C4—22161no—
209C2—81no—
210C2—22161no—
211C2—22161no—
212C2#3180017111yescharacteristic
213C2#3180018111yescharacteristic
214C2#3180018211yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#329×C277C2
socleC22×C277#120
prime radical#31800744C2
hypercenter#329D277
hypocenterC277#1659
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #31800396C2semidirect
3. #31800362C2semidirect
4. #31800361C2semidirect
5. #31799741C2semidirect
6. #31799741C2semidirect
7. #329×C277C2semidirect
10. #22579880C22semidirect
23. #22579791C22semidirect
25. #97×C277C22semidirect
26. #97×C277C22semidirect
107. C277#1659semidirect
115. #329D277semidirect
133. #97C2×D277semidirect
134. #97C2×D277semidirect

Maximal subgroups

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

subgroupindex
#318007442
#318003962
#318003622
#318003612
#317997412
#329×C2772
#1659277