Finite Group Databasebeta

← #47982101

Subgroups — #47982101

Order 35456.

310 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 53 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#31800583C211yesmaximal, characteristic, complemented
2#31800136C212yesmaximal, complemented
3#31799735C212yesmaximal, complemented
4#31799728C211yesmaximal, characteristic, complemented
5#394×C277C211yesmaximal, characteristic, complemented
6C2×#17984563—21no—
7C2×#17984548—22no—
8#22579860—22no—
9#22579855—22no—
10#22579854—21no—
11#22579854C2212yes—
12#22579801—22no—
13C22⋊#14555660C2212yes—
14C22×D4×C277C2211yescharacteristic
15C2×C4⋊C4×C277C2211yescharacteristic
16C2×C22⋊C4×C277—21no—
17C2×C22⋊C4×C277—21no—
18#95×C277C2211yescharacteristic
19#17984563—42no—
20#17984563—42no—
21C2×Dic554—21no—
22C2×D1108—21no—
23C2×D1108—21no—
24C2×D1108D412yes—
25C2×C22⋊D277—22no—
26C2×C4×D277—22no—
27#17984548—44no—
28C2×#14555660—22no—
29C4⋊Dic277—21no—
30C4⋊Dic277D412yes—
31#17984540—22no—
32#17984540—22no—
33C24×C277—21no—
34C2×D4×C277—22no—
35C2×D4×C277—42no—
36C22×C4×C277—21no—
37C22×C4×C277D411yescharacteristic
38C22×C4×C277D411yescharacteristic
39C22×C4×C277C2311yescharacteristic
40C4⋊C4×C277—22no—
41C22⋊C4×C277—42no—
42C22⋊C4×C277—42no—
43C22×D277—22no—
44Dic554—42no—
45D1108—42no—
46D1108—42no—
47D1108—81no—
48C22⋊D277—42no—
49C22⋊D277—42no—
50C2×Dic277—22no—
51C4×D277—44no—
52#14555660—42no—
53C23×C277—22no—
54C23×C277—41no—
55C23×C277—41no—
56C23×C277—41no—
57C23×C277—41no—
58C23×C277—41no—
59C23×C277—41no—
60C23×C277C2×D411yescharacteristic
61D4×C277—24no—
62D4×C277—42no—
63C2×C4×C277—21no—
64C2×C4×C277—21no—
65C2×C4×C277—21no—
66C2×C4×C277—41no—
67C2×C4×C277—41no—
68C2×C4×C277—41no—
69C2×C4×C277—41no—
70C2×C4×C277—41no—
71C2×C4×C277D812yescomplemented
72C2×C4×C277C2×D412yes—
73C22×C277—21no—
74C22×C277—21no—
75C22×C277—42no—
76C22×C277—42no—
77C22×C277—42no—
78C22×C277—81no—
79C22×C277—81no—
80C22×C277—81no—
81C22×C277—81no—
82C22×C277#12011yescharacteristic
83C22×C277C2×D811yescharacteristic
84C22×C277AGL(1,ℤ/8)11yescharacteristic
85C2×D277—42no—
86C2×D277—42no—
87C2×D277—42no—
88C4×C277—22no—
89C4×C277—22no—
90C4×C277—41no—
91C4×C277—81no—
92Dic277—42no—
93C2×C277—21no—
94C2×C277—21no—
95C2×C277—82no—
96C2×C277#44711yescharacteristic
97C2×C277#45411yescharacteristic
98C2×C277B(4,𝔽2)11yescharacteristic
99D277—82no—
100C277#159811yescharacteristic, complemented, Sylow
101#1598—2771nomaximal, Sylow
102#537—2771no—
103#447—2772no—
104#394D27711yescharacteristic, complemented
105#327—2772no—
106#324—2771no—
107C2×#41—5541no—
108C22×D4C2×D27711yescharacteristic
109C2×D8—5542no—
110C22⋊Q8—5542no—
111#121—2772no—
112#121—5542no—
113#121—5541no—
114C2×C4⋊C4C2×D27711yescharacteristic
115C2×C22⋊C4—21no—
116C2×C22⋊C4—21no—
117#102—5542no—
118C22⋊C8—2772no—
119#95C2×D27711yescharacteristic
120C24—21no—
121#41—11082no—
122#41—11082no—
123C2×Q8—5541no—
124C2×D4—22no—
125C2×D4—42no—
126C2×D4—2772no—
127C2×D4—5541no—
128C2×D4—5541no—
129C2×D4—5542no—
130C22×C4—21no—
131C22×C4—5542no—
132C22×C4C22⋊D27711yescharacteristic
133C22×C4C22⋊D27711yescharacteristic
134C22×C4C22×D27711yescharacteristic
135D8—11084no—
136C2×C8—5542no—
137C4⋊C4—22no—
138C4⋊C4—2772no—
139C4⋊C4—5541no—
140C22⋊C4—42no—
141C22⋊C4—42no—
142C22⋊C4—5542no—
143C22⋊C4—5542no—
144C23—22no—
145C23—41no—
146C23—41no—
147C23—41no—
148C23—41no—
149C23—41no—
150C23—41no—
151C23—5542no—
152C23C2×C22⋊D27711yescharacteristic
153Q8—11082no—
154D4—24no—
155D4—42no—
156D4—11082no—
157D4—11082no—
158D4—11082no—
159D4—11082no—
160D4—22161no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—5542no—
170C2×C4—11084no—
171C2×C4#1798454812yescomplemented
172C2×C4D4×D27712yes—
173C8—11082no—
174C22—21no—
175C22—21no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—81no—
180C22—81no—
181C22—81no—
182C22—81no—
183C22—11082no—
184C22—11082no—
185C22—11082no—
186C22#2257984811yescharacteristic
187C22C2×#1798454811yescharacteristic
188C22#2257990511yescharacteristic
189C4—22no—
190C4—22no—
191C4—41no—
192C4—81no—
193C4—11082no—
194C2—21no—
195C2—21no—
196C2—82no—
197C2—22162no—
198C2#3180013511yescharacteristic
199C2#3180017411yescharacteristic
200C2#3180018811yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting#394×C277C2
socleC22×C277#120
hypercenter#394D277
hypocenterC277#1598
LCSG ▷ C22×C4×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #31800583C2semidirect
2. #31800136C2semidirect
3. #31799735C2semidirect
4. #31799728C2semidirect
5. #394×C277C2semidirect
71. C2×C4×C277D8semidirect
100. C277#1598semidirect
104. #394D277semidirect
171. C2×C4#17984548semidirect

Maximal subgroups

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

subgroupindex
#318005832
#318001362
#317997352
#317997282
#394×C2772
#1598277