Finite Group Databasebeta

← #47982205

Subgroups — #47982205

Order 35456.

246 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 51 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#31800579C211yesmaximal, characteristic
2#31800321C211yesmaximal, characteristic, complemented
3#31800318C211yesmaximal, characteristic, complemented
4#31799942C211yesmaximal, characteristic, complemented
5#31799735C211yesmaximal, characteristic, complemented
6#31799727C211yesmaximal, characteristic, complemented
7#327×C277C211yesmaximal, characteristic, complemented
8C2×#17984562—21no—
9#22579858—21no—
10#22579857—21no—
11#22579854C2211yescharacteristic
12#22579853—21no—
13#22579852—21no—
14#22579852—21no—
15C2×C4⋊Dic277C2211yescharacteristic
16C2×#17984542C2211yescharacteristic
17#22579812—21no—
18#22579811—21no—
19#22579802—21no—
20#22579801—21no—
21C22⋊#14555660C2211yescharacteristic
22#22579787—21no—
23#22579787—21no—
24#121×C277C2211yescharacteristic
25C22⋊C8×C277C2211yescharacteristic
26#95×C277C2211yescharacteristic
27#17984562—42no—
28#17984562—42no—
29C2×Dic554—21no—
30C2×D1108D411yescharacteristic
31C2×C22⋊D277—21no—
32C2×C22⋊D277—21no—
33C2×C22⋊D277—21no—
34C22×Dic277—21no—
35C22×Dic277—21no—
36C22×Dic277D411yescharacteristic
37C22×Dic277D411yescharacteristic
38C2×C4×D277—21no—
39C2×#14555660—21no—
40C4⋊Dic277—21no—
41C4⋊Dic277—21no—
42C4⋊Dic277D411yescharacteristic
43#17984542—21no—
44#17984542—21no—
45#17984542—21no—
46C22⋊Dic277—21no—
47#17984540—21no—
48#17984540—21no—
49C2×D4×C277—21no—
50C2×D4×C277D411yescharacteristic
51C22×C4×C277—21no—
52C22×C4×C277C2311yescharacteristic
53C2×C8×C277—21no—
54C4⋊C4×C277D411yescharacteristic
55C22⋊C4×C277—21no—
56C22×D277—21no—
57Dic554—42no—
58D1108—41no—
59C22⋊D277—42no—
60C22⋊D277—41no—
61C22⋊D277—41no—
62C22⋊D277—81no—
63C2×Dic277—21no—
64C2×Dic277—21no—
65C2×Dic277—21no—
66C2×Dic277—21no—
67C2×Dic277—42no—
68C2×Dic277—41no—
69C2×Dic277—42no—
70C2×Dic277—41no—
71C2×Dic277SD1612yes—
72C4×D277—42no—
73#14555660—41no—
74C23×C277—21no—
75C23×C277C2×D411yescharacteristic
76D4×C277—41no—
77D4×C277—41no—
78D4×C277—41no—
79C2×C4×C277—21no—
80C2×C4×C277—41no—
81C2×C4×C277—41no—
82C2×C4×C277—41no—
83C2×C4×C277—41no—
84C2×C4×C277C2×D411yescharacteristic
85C2×C4×C277C2×D411yescharacteristic
86C8×C277—41no—
87C22×C277—21no—
88C22×C277—21no—
89C22×C277—41no—
90C22×C277—41no—
91C22×C277—41no—
92C22×C277#12011yescharacteristic
93C22×C277C2×SD1611yescharacteristic
94C22×C277AGL(1,ℤ/8)11yescharacteristic
95C2×D277—41no—
96C2×D277—41no—
97C2×D277—41no—
98C4×C277—21no—
99C4×C277—21no—
100C4×C277—41no—
101C4×C277—81no—
102Dic277—22no—
103Dic277—41no—
104Dic277—41no—
105Dic277—81no—
106C2×C277—21no—
107C2×C277—21no—
108C2×C277—81no—
109C2×C277#45011yescharacteristic
110C2×C277#45411yescharacteristic
111C2×C277#45811yescharacteristic
112D277—81no—
113C277#161611yescharacteristic, complemented, Sylow
114#1616—2771nomaximal, Sylow
115#537—2771no—
116#481—2771no—
117#481—2771no—
118#400—2771no—
119#327—2771no—
120#327D27711yescharacteristic, complemented
121#324—2771no—
122C2×#41—5541no—
123C22⋊Q8—5541no—
124C22⋊Q8—5541no—
125#121—2771no—
126#121—5541no—
127#121—5541no—
128#121—5541no—
129#121C2×D27711yescharacteristic
130C2×C4⋊C4—2771no—
131C2×C4⋊C4—2771no—
132#106—5541no—
133#106—5541no—
134#102—5541no—
135#102—5541no—
136C22⋊C8—2771no—
137C22⋊C8C2×D27711yescharacteristic
138#95—5541no—
139#95—5541no—
140#95C2×D27711yescharacteristic
141#41—11082no—
142#41—11082no—
143C2×Q8—5541no—
144C2×D4—21no—
145C2×D4—2771no—
146C2×D4—5541no—
147C2×D4—5541no—
148C2×D4—5541no—
149C2×D4D110811yescharacteristic
150C22×C4—21no—
151C22×C4—2771no—
152C22×C4—2771no—
153C22×C4—5541no—
154C22×C4—5541no—
155C22×C4—5541no—
156C22×C4C22×D27711yescharacteristic
157C2×C8—21no—
158C2×C8—5541no—
159C4⋊C4—2771no—
160C4⋊C4—5541no—
161C4⋊C4—5541no—
162C4⋊C4—5541no—
163C4⋊C4—5541no—
164C4⋊C4—5541no—
165C4⋊C4D110811yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—5541no—
168C22⋊C4—5541no—
169C22⋊C4—5541no—
170C23—21no—
171C23—5541no—
172C23D4×D27711yescharacteristic
173Q8—11082no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—11081no—
178D4—11082no—
179D4—11081no—
180D4—11081no—
181D4—22161no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—2772no—
188C2×C4—5541no—
189C2×C4—5541no—
190C2×C4—5541no—
191C2×C4—5541no—
192C2×C4—11082no—
193C2×C4—11082no—
194C2×C4—11081no—
195C2×C4—11082no—
196C2×C4—11081no—
197C2×C4D4×D27711yescharacteristic
198C2×C4C2×D110811yescharacteristic
199C8—41no—
200C8—11081no—
201C22—21no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—11081no—
207C22—11081no—
208C22—11081no—
209C22#2257985011yescharacteristic
210C22SD16×D27711yescharacteristic
211C22#2257990411yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—5542no—
217C4—11081no—
218C4—11081no—
219C4—22161no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—22161no—
224C2#3180015411yescharacteristic
225C2#3180017611yescharacteristic
226C2#3180019311yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting#327×C277C2
socleC22×C277#120
prime radical#31800579C2
hypercenter#327D277
hypocenterC277#1616
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. #31800321C2semidirect
3. #31800318C2semidirect
4. #31799942C2semidirect
5. #31799735C2semidirect
6. #31799727C2semidirect
7. #327×C277C2semidirect
113. C277#1616semidirect
120. #327D277semidirect

Maximal subgroups

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

subgroupindex
#318005792
#318003212
#318003182
#317999422
#317997352
#317997272
#327×C2772
#1616277