Finite Group Databasebeta

← #47982182

Subgroups — #47982182

Order 35456.

232 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 49 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#31800589C211yesmaximal, characteristic
2#31800333C211yesmaximal, characteristic, complemented
3#31800313C211yesmaximal, characteristic, complemented
4#31799929C211yesmaximal, characteristic, complemented
5#31799738C211yesmaximal, characteristic, complemented
6#31799725C211yesmaximal, characteristic, complemented
7#327×C277C211yesmaximal, characteristic, complemented
8#22579875—21no—
9#22579866—21no—
10#22579864—21no—
11#22579859C2211yescharacteristic
12#22579852—21no—
13#22579848—21no—
14D4×Dic277—21no—
15C2×C4⋊Dic277C2211yescharacteristic
16C2×#17984540—21no—
17C2×#17984540C2211yescharacteristic
18#22579813—21no—
19#22579812—21no—
20#22579805—21no—
21#22579801—21no—
22C22⋊#14555660C2211yescharacteristic
23#22579787—21no—
24#121×C277C2211yescharacteristic
25C22⋊C8×C277C2211yescharacteristic
26#95×C277C2211yescharacteristic
27C23×D277D411yescharacteristic
28C2×Dic554D411yescharacteristic
29C2×C22⋊D277—21no—
30C2×C22⋊D277—21no—
31C22×Dic277—21no—
32C22×Dic277—21no—
33C22×Dic277D411yescharacteristic
34C2×#14555660—21no—
35C4⋊Dic277—21no—
36C4⋊Dic277—21no—
37C4⋊Dic277—21no—
38C4⋊Dic277D411yescharacteristic
39#17984542—21no—
40C22⋊Dic277—21no—
41C22⋊Dic277—21no—
42#17984540—21no—
43#17984540—21no—
44#17984540—21no—
45#17984540—21no—
46#17984540—42no—
47C4×Dic277—21no—
48C2×D4×C277—21no—
49C2×D4×C277D411yescharacteristic
50C22×C4×C277—21no—
51C22×C4×C277C2311yescharacteristic
52C2×C8×C277—21no—
53C4⋊C4×C277D411yescharacteristic
54C22⋊C4×C277—21no—
55C22×D277—21no—
56C22×D277—21no—
57C22×D277—21no—
58C22×D277—41no—
59C22×D277—41no—
60Dic554—41no—
61C22⋊D277—81no—
62C22⋊D277—81no—
63C2×Dic277—21no—
64C2×Dic277—21no—
65C2×Dic277—21no—
66C2×Dic277—41no—
67C2×Dic277—41no—
68C2×Dic277—41no—
69C2×Dic277—41no—
70C2×Dic277—81no—
71#14555660—41no—
72C23×C277—21no—
73C23×C277C2×D411yescharacteristic
74D4×C277—41no—
75D4×C277—41no—
76D4×C277—41no—
77C2×C4×C277—21no—
78C2×C4×C277—41no—
79C2×C4×C277—41no—
80C2×C4×C277—41no—
81C2×C4×C277—41no—
82C2×C4×C277C2×D411yescharacteristic
83C2×C4×C277C2×D411yescharacteristic
84C8×C277—41no—
85C22×C277—21no—
86C22×C277—21no—
87C22×C277—41no—
88C22×C277—41no—
89C22×C277—41no—
90C22×C277#12011yescharacteristic
91C22×C277#13511yescharacteristic
92C22×C277AGL(1,ℤ/8)11yescharacteristic
93C2×D277—42no—
94C2×D277—41no—
95C2×D277—41no—
96C2×D277—41no—
97C2×D277—81no—
98C4×C277—21no—
99C4×C277—21no—
100C4×C277—41no—
101C4×C277—81no—
102Dic277—41no—
103Dic277—41no—
104Dic277—41no—
105Dic277—81no—
106C2×C277—21no—
107C2×C277—21no—
108C2×C277—81no—
109C2×C277#44911yescharacteristic
110C2×C277#45511yescharacteristic
111C2×C277#45811yescharacteristic
112D277—81no—
113C277#161211yescharacteristic, complemented, Sylow
114#1612—2771nomaximal, Sylow
115#538—2771no—
116#483—2771no—
117#480—2771no—
118#397—2771no—
119#328—2771no—
120#327D27711yescharacteristic, complemented
121#323—2771no—
122#126—5541no—
123#124—5541no—
124#123—5541no—
125C22⋊Q8—2771no—
126#121—5541no—
127#121C2×D27711yescharacteristic
128#120—5541no—
129C4×D4—5541no—
130C2×C4⋊C4—2771no—
131C2×C22⋊C4—2771no—
132C2×C22⋊C4—5541no—
133#107—5541no—
134#106—5541no—
135#103—5541no—
136#102—5541no—
137C22⋊C8—2771no—
138C22⋊C8C2×D27711yescharacteristic
139#95—5541no—
140#95C2×D27711yescharacteristic
141C24—2771no—
142C2×Q8—2771no—
143C2×D4—21no—
144C2×D4—5541no—
145C2×D4—5541no—
146C2×D4D110811yescharacteristic
147C22×C4—21no—
148C22×C4—2771no—
149C22×C4—5541no—
150C22×C4—5541no—
151C22×C4C22×D27711yescharacteristic
152C2×C8—21no—
153C2×C8—5541no—
154C4⋊C4—2771no—
155C4⋊C4—5541no—
156C4⋊C4—5541no—
157C4⋊C4—5541no—
158C4⋊C4—5541no—
159C4⋊C4D110811yescharacteristic
160C22⋊C4—21no—
161C22⋊C4—5541no—
162C22⋊C4—5541no—
163C22⋊C4—5541no—
164C22⋊C4—5541no—
165C22⋊C4—5541no—
166C22⋊C4—5541no—
167C22⋊C4—11082no—
168C42—5541no—
169C23—21no—
170C23—5541no—
171C23—5541no—
172C23—5541no—
173C23—11081no—
174C23—11081no—
175C23D4×D27711yescharacteristic
176Q8—11081no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—22161no—
181D4—22161no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—5541no—
188C2×C4—5541no—
189C2×C4—5541no—
190C2×C4—11081no—
191C2×C4—11081no—
192C2×C4—11081no—
193C2×C4—11081no—
194C2×C4—22161no—
195C2×C4D4×D27711yescharacteristic
196C2×C4C2×D110811yescharacteristic
197C8—41no—
198C8—11081no—
199C22—21no—
200C22—21no—
201C22—41no—
202C22—41no—
203C22—41no—
204C22—11082no—
205C22—11081no—
206C22—11081no—
207C22—11081no—
208C22—22161no—
209C22#2257985011yescharacteristic
210C22#2257990111yescharacteristic
211C22#2257990411yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—11081no—
217C4—11081no—
218C4—11081no—
219C4—22161no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—22161no—
224C2#3180014811yescharacteristic
225C2#3180018111yescharacteristic
226C2#3180019311yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting#327×C277C2
socleC22×C277#120
prime radical#31800589C2
hypercenter#327D277
hypocenterC277#1612
LCSG ▷ C22×C4×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #31800333C2semidirect
3. #31800313C2semidirect
4. #31799929C2semidirect
5. #31799738C2semidirect
6. #31799725C2semidirect
7. #327×C277C2semidirect
113. C277#1612semidirect
120. #327D277semidirect

Maximal subgroups

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

subgroupindex
#318005892
#318003332
#318003132
#317999292
#317997382
#317997252
#327×C2772
#1612277