Finite Group Databasebeta

← #47984209

Subgroups — #47984209

Order 35456.

406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×#22579905C212yesmaximal, complemented
2C2×#22579807C212yesmaximal, complemented
3#31799903C211yesmaximal, characteristic, complemented
4#31799771C211yesmaximal, characteristic, complemented
5#537×C277C211yesmaximal, characteristic, complemented
6C22×D1108C2211yescharacteristic
7#22579905—24no—
8#22579905—24no—
9C2×#17984550—22no—
10C2×#17984548—22no—
11C2×#17984547C2212yes—
12C2×#17984540—22no—
13C2×C4×Dic277C2211yescharacteristic
14#22579807—24no—
15C2×#41×C277C2212yes—
16C22⋊Q8×C277—22no—
17#121×C277—22no—
18#121×C277—22no—
19C2×C4⋊C4×C277C2211yescharacteristic
20C23×D277—21no—
21C2×D1108—22no—
22C2×D1108—22no—
23C2×D1108—21no—
24C2×D1108D412yescomplemented
25C22×Dic277—21no—
26#17984550—28no—
27#17984548—28no—
28#17984547—22no—
29#17984547D414yescomplemented
30C2×#14555660—22no—
31#17984540—44no—
32C4×Dic277—22no—
33#41×C277—22no—
34#41×C277—22no—
35#41×C277—22no—
36#41×C277—22no—
37C2×Q8×C277D412yes—
38C2×D4×C277—22no—
39C2×D4×C277—22no—
40C2×D4×C277D412yes—
41C22×C4×C277—22no—
42C22×C4×C277D412yes—
43C22×C4×C277C2311yescharacteristic
44C4⋊C4×C277—22no—
45C4⋊C4×C277—22no—
46C22⋊C4×C277—24no—
47C22×D277—22no—
48C22×D277—42no—
49C22×D277—42no—
50C22×D277—41no—
51C22×D277—41no—
52D1108—24no—
53D1108—42no—
54C2×Dic277—22no—
55C2×Dic277—41no—
56C2×Dic277—41no—
57#14555660—24no—
58C23×C277—22no—
59C23×C277C2×D411yescharacteristic
60Q8×C277—22no—
61Q8×C277—22no—
62D4×C277—22no—
63D4×C277—22no—
64D4×C277—42no—
65D4×C277—42no—
66D4×C277—82no—
67C2×C4×C277—22no—
68C2×C4×C277—22no—
69C2×C4×C277—42no—
70C2×C4×C277—42no—
71C2×C4×C277—42no—
72C2×C4×C277C2×D411yescharacteristic
73C2×C4×C277C2×D412yes—
74C2×C4×C277C2×D412yes—
75C2×C4×C277#4111yescharacteristic
76C22×C277—21no—
77C22×C277—21no—
78C22×C277—42no—
79C22×C277—42no—
80C22×C277—42no—
81C22×C277#12011yescharacteristic
82C22×C277#12111yescharacteristic
83C22×C277#12711yescharacteristic
84C2×D277—44no—
85C2×D277—42no—
86C2×D277—82no—
87C2×D277—81no—
88C2×D277—81no—
89C4×C277—42no—
90C4×C277—42no—
91C4×C277#12012yes—
92C4×C277#12112yes—
93Dic277—42no—
94C2×C277—21no—
95C2×C277—21no—
96C2×C277—82no—
97C2×C277#39211yescharacteristic
98C2×C277#45311yescharacteristic
99C2×C277#45411yescharacteristic
100D277—82no—
101C277#200611yescharacteristic, complemented, Sylow
102#2006—2771nomaximal, Sylow
103C2×AGL(1,ℤ/8)—2772no—
104#537D27711yescharacteristic, complemented
105C2×#104—2772no—
106#390—2771no—
107#343—2771no—
108C2×#41C2×D27712yes—
109C22×D4—2771no—
110AGL(1,ℤ/8)—5544no—
111AGL(1,ℤ/8)—5544no—
112C2×SD16—5542no—
113C2×D8—5542no—
114C2×M16—2772no—
115C22⋊Q8—22no—
116#121—22no—
117#121—22no—
118C2×C4⋊C4C2×D27711yescharacteristic
119C2×C22⋊C4—5542no—
120C2×C42—2771no—
121#104—5544no—
122C24—5541no—
123#41—22no—
124#41—22no—
125#41—22no—
126#41—22no—
127C2×Q8C22⋊D27712yes—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—2772no—
131C2×D4—5542no—
132C2×D4—5542no—
133C2×D4—5541no—
134C2×D4C22⋊D27712yes—
135C22×C4—22no—
136C22×C4—5541no—
137C22×C4C22⋊D27712yes—
138C22×C4C22×D27711yescharacteristic
139SD16—5548no—
140D8—5548no—
141M16—2774no—
142M16—5542no—
143C2×C8—5542no—
144C4⋊C4—22no—
145C4⋊C4—22no—
146C22⋊C4—24no—
147C22⋊C4—11084no—
148C42—5542no—
149C23—22no—
150C23—5542no—
151C23—11082no—
152C23—11082no—
153C23—11081no—
154C23—11081no—
155C23C2×C22⋊D27711yescharacteristic
156Q8—22no—
157Q8—22no—
158D4—22no—
159D4—22no—
160D4—42no—
161D4—42no—
162D4—82no—
163D4—5544no—
164D4—11082no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—5542no—
171C2×C4—11081no—
172C2×C4—11081no—
173C2×C4D4×D27711yescharacteristic
174C2×C4D4×D27712yes—
175C2×C4C2×C22⋊D27712yes—
176C2×C4#1798456211yescharacteristic
177C8—5544no—
178C22—21no—
179C22—21no—
180C22—42no—
181C22—42no—
182C22—42no—
183C22—11084no—
184C22—11082no—
185C22—22162no—
186C22—22161no—
187C22—22161no—
188C22#2257984911yescharacteristic
189C22#2257985111yescharacteristic
190C22#2257987611yescharacteristic
191C4—42no—
192C4—42no—
193C4—11082no—
194C4#2257984812yes—
195C4#2257985212yes—
196C2—21no—
197C2—21no—
198C2—82no—
199C2—22162no—
200C2#3179991011yescharacteristic
201C2#3180017011yescharacteristic
202C2#3180017511yescharacteristic
subgroupG/H
centerC22#22579849
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting#537×C277C2
socleC22×C277#120
hypercenter#537D277
hypocenterC277#2006
LCSG ▷ C22×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#22579905C2semidirect
2. C2×#22579807C2semidirect
3. #31799903C2semidirect
4. #31799771C2semidirect
5. #537×C277C2semidirect
24. C2×D1108D4semidirect
29. #17984547D4semidirect
101. C277#2006semidirect
104. #537D277semidirect

Maximal subgroups

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

subgroupindex
C2×#225799052
C2×#225798072
#317999032
#317997712
#537×C2772
#2006277