Finite Group Databasebeta

← #47982487

Subgroups — #47982487

Order 35456.

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

normal subgroups only

This group has 208 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#31800746C211yesmaximal, characteristic
2#31800411C211yesmaximal, characteristic, complemented
3#31800396C211yesmaximal, characteristic, complemented
4#31800361C211yesmaximal, characteristic, complemented
5#31799743C211yesmaximal, characteristic, complemented
6#31799741C211yesmaximal, characteristic, complemented
7#329×C277C211yesmaximal, characteristic, complemented
8C2×Dic1108—21no—
9C2×#17984552—21no—
10#22579880C2211yescharacteristic
11#22579872C2211yescharacteristic
12#22579868C2211yescharacteristic
13#22579864—21no—
14#22579862—21no—
15#22579857—21no—
16#22579856—21no—
17#22579853—21no—
18#22579852—21no—
19#22579814—21no—
20#22579812—21no—
21#22579804—21no—
22#22579801—21no—
23#22579791C2211yescharacteristic
24#124×C277C2211yescharacteristic
25#97×C277C2211yescharacteristic
26#97×C277C2211yescharacteristic
27C2×Dic554—21no—
28C2×Dic554D411yescharacteristic
29C2×D1108D411yescharacteristic
30C2×C22⋊D277—21no—
31C2×C22⋊D277—21no—
32C22×Dic277—21no—
33C2×C4×D277—21no—
34Dic1108—42no—
35#17984552—42no—
36C2×#14555660—21no—
37C4⋊Dic277—21no—
38C4⋊Dic277—21no—
39C4⋊Dic277—21no—
40C4⋊Dic277D411yescharacteristic
41C4⋊Dic277D411yescharacteristic
42#17984542—21no—
43#17984542—21no—
44#17984542—21no—
45C22⋊Dic277—21no—
46#17984540—21no—
47#17984540—21no—
48#17984540—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—
57Dic554—41no—
58Dic554—41no—
59Dic554—41no—
60D1108—41no—
61C22⋊D277—81no—
62C22⋊D277—81no—
63C2×Dic277—21no—
64C2×Dic277—21no—
65C2×Dic277—21no—
66C2×Dic277—41no—
67C2×Dic277—81no—
68C4×D277—81no—
69#14555660—41no—
70C23×C277—21no—
71Q8×C277—41no—
72D4×C277—41no—
73C2×C4×C277—21no—
74C2×C4×C277C2×D411yescharacteristic
75C2×C4×C277C2×D411yescharacteristic
76C2×C4×C277C2×D411yescharacteristic
77C8×C277—22no—
78C8×C277—22no—
79C22×C277—41no—
80C22×C277—41no—
81C22×C277—41no—
82C22×C277#12011yescharacteristic
83C2×D277—41no—
84C2×D277—41no—
85C2×D277—41no—
86C4×C277—21no—
87C4×C277—21no—
88C4×C277—21no—
89C4×C277—41no—
90Dic277—41no—
91Dic277—41no—
92Dic277—41no—
93Dic277—81no—
94C2×C277—81no—
95C2×C277#45311yescharacteristic
96C2×C277#45511yescharacteristic
97C2×C277#45611yescharacteristic
98D277—81no—
99C277#166111yescharacteristic, complemented, Sylow
100#1661—2771nomaximal, Sylow
101#562—2771no—
102#501—2771no—
103#497—2771no—
104#489—2771no—
105#330—2771no—
106#329—2771no—
107#329D27711yescharacteristic, complemented
108C2×Q16—5541no—
109C2×SD16—5541no—
110C4⋊Q8—2771no—
111#125—2771no—
112#124—2771no—
113#124C2×D27711yescharacteristic
114#123—5541no—
115#123—5541no—
116C22⋊Q8—5541no—
117C22⋊Q8—5541no—
118#121—5541no—
119#121—5541no—
120#107—5541no—
121#106—5541no—
122#103—5541no—
123#102—5541no—
124#97—2771no—
125#97C2×D27711yescharacteristic
126#97C2×D27711yescharacteristic
127C2×Q8—2771no—
128C2×Q8—5541no—
129C2×Q8D110811yescharacteristic
130C2×D4—2771no—
131C2×D4—5541no—
132C2×D4—5541no—
133C2×D4D110811yescharacteristic
134C22×C4—5541no—
135C22×C4—5541no—
136Q16—11082no—
137SD16—11082no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—5541no—
141C4⋊C4—2771no—
142C4⋊C4—2771no—
143C4⋊C4—5541no—
144C4⋊C4—5541no—
145C4⋊C4—5541no—
146C4⋊C4—5541no—
147C4⋊C4—5541no—
148C4⋊C4—5541no—
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—5541no—
152C22⋊C4—5541no—
153C22⋊C4—5541no—
154C22⋊C4—5541no—
155C42C22×D27711yescharacteristic
156C23—21no—
157C23—5541no—
158Q8—41no—
159Q8—11081no—
160Q8—11081no—
161Q8—11081no—
162D4—41no—
163D4—11081no—
164D4—22161no—
165D4—22161no—
166C2×C4—21no—
167C2×C4—5541no—
168C2×C4—5541no—
169C2×C4—5541no—
170C2×C4—11081no—
171C2×C4—22161no—
172C2×C4—22161no—
173C2×C4D4×D27711yescharacteristic
174C2×C4D4×D27711yescharacteristic
175C2×C4C2×D110811yescharacteristic
176C8—22no—
177C8—22no—
178C8—11081no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—11081no—
183C22—11081no—
184C22—11081no—
185C22#2257985011yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—11081no—
191C4—11081no—
192C4—11081no—
193C4—22161no—
194C2—81no—
195C2—22161no—
196C2#3180017111yescharacteristic
197C2#3180018211yescharacteristic
198C2#3180018611yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#329×C277C2
socleC22×C277#120
prime radical#31800746C2
hypercenter#329D277
hypocenterC277#1661
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. #31800411C2semidirect
3. #31800396C2semidirect
4. #31800361C2semidirect
5. #31799743C2semidirect
6. #31799741C2semidirect
7. #329×C277C2semidirect
99. C277#1661semidirect
107. #329D277semidirect

Maximal subgroups

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

subgroupindex
#318007462
#318004112
#318003962
#318003612
#317997432
#317997412
#329×C2772
#1661277