Finite Group Databasebeta

← #1654×C179 #37504876

Subgroups — #1654×C179 #37504876

Order 22912.

240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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#547×C179C211yesmaximal, characteristic
2#498×C179C211yesmaximal, characteristic, complemented
3#474×C179C211yesmaximal, characteristic, complemented
4#461×C179C211yesmaximal, characteristic, complemented
5#332×C179C211yesmaximal, characteristic, complemented
6D4⋊C8×C179C211yesmaximal, characteristic, complemented
7D4⋊C8×C179C211yesmaximal, characteristic, complemented
8C2×#41×C179—21no—
9C2×SD16×C179—21no—
10C4⋊Q8×C179C2211yescharacteristic
11C4⋊Q8×C179C2211yescharacteristic
12#123×C179—22no—
13C22⋊Q8×C179—21no—
14#121×C179—21no—
15C4×D4×C179C2211yescharacteristic
16C4×D4×C179C2211yescharacteristic
17C2×C4⋊C4×C179—21no—
18#107×C179—21no—
19#106×C179—22no—
20C4⋊C8×C179C2211yescharacteristic
21C4⋊C8×C179C2211yescharacteristic
22#103×C179—21no—
23#102×C179—21no—
24C4×C8×C179C2211yescharacteristic
25#41×C179—42no—
26#41×C179—42no—
27C2×Q8×C179—21no—
28C2×Q8×C179—21no—
29C2×D4×C179—22no—
30C2×D4×C179D411yescharacteristic
31C2×D4×C179D411yescharacteristic
32C22×C4×C179—22no—
33C22×C4×C179—21no—
34C22×C4×C179—21no—
35SD16×C179—42no—
36C2×C8×C179—21no—
37C2×C8×C179—21no—
38C2×C8×C179—21no—
39C4⋊C4×C179—22no—
40C4⋊C4×C179—21no—
41C4⋊C4×C179—21no—
42C4⋊C4×C179—21no—
43C4⋊C4×C179D411yescharacteristic
44C4⋊C4×C179D412yes—
45C4⋊C4×C179D411yescharacteristic
46C22⋊C4×C179—22no—
47C22⋊C4×C179—21no—
48C22⋊C4×C179—21no—
49C42×C179C2311yescharacteristic
50C23×C179—21no—
51C23×C179—21no—
52Q8×C179—41no—
53Q8×C179—41no—
54Q8×C179—41no—
55Q8×C179—41no—
56D4×C179—21no—
57D4×C179—21no—
58D4×C179—21no—
59D4×C179—44no—
60D4×C179SD1612yescomplemented
61C2×C4×C179—21no—
62C2×C4×C179—22no—
63C2×C4×C179—21no—
64C2×C4×C179—44no—
65C2×C4×C179—41no—
66C2×C4×C179—41no—
67C2×C4×C179—41no—
68C2×C4×C179—41no—
69C2×C4×C179—41no—
70C2×C4×C179C2×D411yescharacteristic
71C2×C4×C179C2×D411yescharacteristic
72C2×C4×C179C2×D411yescharacteristic
73C8×C179—22no—
74C8×C179—41no—
75C8×C179—41no—
76C22×C179—22no—
77C22×C179—41no—
78C22×C179—41no—
79C22×C179—41no—
80C22×C179—41no—
81C22×C179—41no—
82C22×C179#12011yescharacteristic
83C4×C179—21no—
84C4×C179—41no—
85C4×C179—41no—
86C4×C179—42no—
87C4×C179—81no—
88C4×C179C2×SD1611yescharacteristic
89C4×C179#13511yescharacteristic
90C4×C179AGL(1,ℤ/8)11yescharacteristic
91C4×C179AGL(1,ℤ/8)11yescharacteristic
92C2×C179—42no—
93C2×C179—81no—
94C2×C179#44911yescharacteristic
95C2×C179#45011yescharacteristic
96C2×C179#45611yescharacteristic
97C179#165411yescharacteristic, direct product factor, Sylow
98#1654C17911yesmaximal, characteristic, direct product factor, Sylow
99#547C2×C17911yescharacteristic
100#498C2×C17911yescharacteristic, complemented
101#474C2×C17911yescharacteristic, complemented
102#461C2×C17911yescharacteristic, complemented
103#332C2×C17911yescharacteristic, complemented
104D4⋊C8C2×C17911yescharacteristic, complemented
105D4⋊C8C2×C17911yescharacteristic, complemented
106C2×#41—21no—
107C2×SD16—21no—
108C4⋊Q8C22×C17911yescharacteristic
109C4⋊Q8C22×C17911yescharacteristic
110#123—22no—
111C22⋊Q8—21no—
112#121—21no—
113C4×D4C22×C17911yescharacteristic
114C4×D4C22×C17911yescharacteristic
115C2×C4⋊C4—21no—
116#107—21no—
117#106—22no—
118C4⋊C8C22×C17911yescharacteristic
119C4⋊C8C22×C17911yescharacteristic
120#103—21no—
121#102—21no—
122C4×C8C22×C17911yescharacteristic
123#41—42no—
124#41—42no—
125C2×Q8—21no—
126C2×Q8—21no—
127C2×D4—22no—
128C2×D4D4×C17911yescharacteristic
129C2×D4D4×C17911yescharacteristic
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—21no—
133SD16—42no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—21no—
137C4⋊C4—22no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4D4×C17911yescharacteristic
142C4⋊C4D4×C17912yes—
143C4⋊C4D4×C17911yescharacteristic
144C22⋊C4—22no—
145C22⋊C4—21no—
146C22⋊C4—21no—
147C42C23×C17911yescharacteristic
148C23—21no—
149C23—21no—
150Q8—41no—
151Q8—41no—
152Q8—41no—
153Q8—41no—
154D4—21no—
155D4—21no—
156D4—21no—
157D4—44no—
158D4SD16×C17912yescomplemented
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—44no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4C2×D4×C17911yescharacteristic
169C2×C4C2×D4×C17911yescharacteristic
170C2×C4C2×D4×C17911yescharacteristic
171C8—22no—
172C8—41no—
173C8—41no—
174C22—22no—
175C22—41no—
176C22—41no—
177C22—41no—
178C22—41no—
179C22—41no—
180C22#120×C17911yescharacteristic
181C4—21no—
182C4—41no—
183C4—41no—
184C4—42no—
185C4—81no—
186C4C2×SD16×C17911yescharacteristic
187C4#135×C17911yescharacteristic
188C4AGL(1,ℤ/8)×C17911yescharacteristic
189C4AGL(1,ℤ/8)×C17911yescharacteristic
190C2—42no—
191C2—81no—
192C2#449×C17911yescharacteristic
193C2#450×C17911yescharacteristic
194C2#456×C17911yescharacteristic
subgroupG/H
center, socleC22×C179#120
commutator, Frattini, cosocleC42C23×C179
prime radical#547×C179C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C179 ◁ C42×C179 ◁ G

Complements

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

NH ≅ G/Ntype
2. #498×C179C2semidirect
3. #474×C179C2semidirect
4. #461×C179C2semidirect
5. #332×C179C2semidirect
6. D4⋊C8×C179C2semidirect
7. D4⋊C8×C179C2semidirect
60. D4×C179SD16semidirect
97. C179#1654direct (N × H)
98. #1654C179direct (N × H)
100. #498C2×C179semidirect
101. #474C2×C179semidirect
102. #461C2×C179semidirect
103. #332C2×C179semidirect
104. D4⋊C8C2×C179semidirect
105. D4⋊C8C2×C179semidirect
158. D4SD16×C179semidirect

Maximal subgroups

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

subgroupindex
#547×C1792
#498×C1792
#474×C1792
#461×C1792
#332×C1792
D4⋊C8×C1792
#1654179