Finite Group Databasebeta

← #1794×C179 #37505016

Subgroups — #1794×C179 #37505016

Order 22912.

548 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 132 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#585×C179C211yesmaximal, characteristic
2#421×C179C212yesmaximal, complemented
3#416×C179C212yesmaximal, complemented
4#410×C179C211yesmaximal, characteristic, complemented
5#408×C179C211yesmaximal, characteristic, complemented
62−1+4×C179—22no—
72−1+4×C179C412yescomplemented
8H(5,𝔽2)×C179—22no—
9H(5,𝔽2)×C179—22no—
10H(5,𝔽2)×C179C412yescomplemented
11C2×#41×C179—24no—
12C2×#41×C179—22no—
13C2×#41×C179C2212yes—
14C2×#41×C179C2211yescharacteristic
15C2×M16×C179C2211yescharacteristic, complemented
16C22×C8×C179C2211yescharacteristic, complemented
17#117×C179C2212yescomplemented
18#104×C179—24no—
19#103×C179—22no—
20#102×C179—22no—
21#99×C179—22no—
22C22⋊C8×C179—22no—
23#41×C179—24no—
24#41×C179—28no—
25#41×C179—24no—
26#41×C179—24no—
27#41×C179—24no—
28#41×C179—24no—
29#41×C179—22no—
30#41×C179—22no—
31#41×C179—22no—
32#41×C179—22no—
33#41×C179C2×C414yes—
34#41×C179D414yes—
35C2×Q8×C179—22no—
36C2×Q8×C179—24no—
37C2×Q8×C179C2×C411yescharacteristic
38C2×Q8×C179D412yes—
39C2×D4×C179—28no—
40C2×D4×C179—22no—
41C2×D4×C179—24no—
42C2×D4×C179—22no—
43C2×D4×C179—24no—
44C2×D4×C179C2×C411yescharacteristic
45C2×D4×C179D412yes—
46C2×D4×C179D412yes—
47C22×C4×C179—24no—
48C22×C4×C179—22no—
49C22×C4×C179D412yes—
50C22×C4×C179C2311yescharacteristic
51M16×C179—22no—
52C2×C8×C179—21no—
53C2×C8×C179—21no—
54C2×C8×C179—22no—
55C4⋊C4×C179—22no—
56C22⋊C4×C179—22no—
57C42×C179—22no—
58C23×C179—24no—
59C23×C179—22no—
60C23×C179C22⋊C412yes—
61C23×C179C2×D411yescharacteristic
62Q8×C179—24no—
63Q8×C179—22no—
64Q8×C179—22no—
65Q8×C179C22⋊C414yes—
66D4×C179—28no—
67D4×C179—24no—
68D4×C179—24no—
69D4×C179—24no—
70D4×C179—24no—
71D4×C179—22no—
72D4×C179—22no—
73D4×C179C22⋊C414yes—
74C2×C4×C179—24no—
75C2×C4×C179—28no—
76C2×C4×C179—22no—
77C2×C4×C179—24no—
78C2×C4×C179—22no—
79C2×C4×C179—24no—
80C2×C4×C179—22no—
81C2×C4×C179—42no—
82C2×C4×C179C22⋊C412yes—
83C2×C4×C179C22×C411yescharacteristic
84C2×C4×C179C2×D412yes—
85C2×C4×C179C2×D412yes—
86C2×C4×C179C2×D411yescharacteristic
87C8×C179—41no—
88C8×C179—41no—
89C22×C179—22no—
90C22×C179—24no—
91C22×C179—41no—
92C22×C179—42no—
93C22×C179—82no—
94C22×C179—84no—
95C22×C179C2×C22⋊C411yescharacteristic
96C22×C179#12012yes—
97C4×C179—24no—
98C4×C179—22no—
99C4×C179—82no—
100C4×C179C2×C22⋊C412yes—
101C4×C179#12011yescharacteristic
102C4×C179#12011yescharacteristic
103C2×C179—22no—
104C2×C179—21no—
105C2×C179—42no—
106C2×C179—44no—
107C2×C179#37911yescharacteristic
108C179#179411yescharacteristic, direct product factor, Sylow
109#1794C17911yesmaximal, characteristic, direct product factor, Sylow
110#585C2×C17911yescharacteristic
111#421C2×C17912yescomplemented
112#416C2×C17912yescomplemented
113#410C2×C17911yescharacteristic, complemented
114#408C2×C17911yescharacteristic, complemented
1152−1+4—22no—
1162−1+4C4×C17912yescomplemented
117H(5,𝔽2)—22no—
118H(5,𝔽2)—22no—
119H(5,𝔽2)C4×C17912yescomplemented
120C2×#41—24no—
121C2×#41—22no—
122C2×#41C22×C17912yes—
123C2×#41C22×C17911yescharacteristic
124C2×M16C22×C17911yescharacteristic, complemented
125C22×C8C22×C17911yescharacteristic, complemented
126#117C22×C17912yescomplemented
127#104—24no—
128#103—22no—
129#102—22no—
130#99—22no—
131C22⋊C8—22no—
132#41—24no—
133#41—28no—
134#41—24no—
135#41—24no—
136#41—24no—
137#41—22no—
138#41—22no—
139#41—22no—
140#41—22no—
141#41—24no—
142#41C2×C4×C17914yes—
143#41D4×C17914yes—
144C2×Q8—22no—
145C2×Q8—24no—
146C2×Q8C2×C4×C17911yescharacteristic
147C2×Q8D4×C17912yes—
148C2×D4—28no—
149C2×D4—22no—
150C2×D4—22no—
151C2×D4—24no—
152C2×D4—24no—
153C2×D4C2×C4×C17911yescharacteristic
154C2×D4D4×C17912yes—
155C2×D4D4×C17912yes—
156C22×C4—24no—
157C22×C4—22no—
158C22×C4D4×C17912yes—
159C22×C4C23×C17911yescharacteristic
160M16—22no—
161C2×C8—21no—
162C2×C8—21no—
163C2×C8—22no—
164C4⋊C4—22no—
165C22⋊C4—22no—
166C42—22no—
167C23—24no—
168C23—22no—
169C23C22⋊C4×C17912yes—
170C23C2×D4×C17911yescharacteristic
171Q8—24no—
172Q8—22no—
173Q8—22no—
174Q8C22⋊C4×C17914yes—
175D4—28no—
176D4—24no—
177D4—24no—
178D4—24no—
179D4—24no—
180D4—22no—
181D4—22no—
182D4C22⋊C4×C17914yes—
183C2×C4—24no—
184C2×C4—28no—
185C2×C4—22no—
186C2×C4—24no—
187C2×C4—24no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—42no—
191C2×C4C22⋊C4×C17912yes—
192C2×C4C22×C4×C17911yescharacteristic
193C2×C4C2×D4×C17912yes—
194C2×C4C2×D4×C17912yes—
195C2×C4C2×D4×C17911yescharacteristic
196C8—41no—
197C8—41no—
198C22—22no—
199C22—24no—
200C22—41no—
201C22—42no—
202C22—82no—
203C22—84no—
204C22C2×C22⋊C4×C17911yescharacteristic
205C22#120×C17912yes—
206C4—24no—
207C4—22no—
208C4—82no—
209C4C2×C22⋊C4×C17912yes—
210C4#120×C17911yescharacteristic
211C4#120×C17911yescharacteristic
212C2—22no—
213C2—21no—
214C2—42no—
215C2—44no—
216C2#379×C17911yescharacteristic
subgroupG/H
centerC4×C179#120
commutatorC2×C4C22×C4×C179
Frattini, cosocleC22×C4C23×C179
socleC2×C179#379
prime radical#585×C179C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C179 ◁ C22×C4×C179 ◁ G

Complements

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

NH ≅ G/Ntype
2. #421×C179C2semidirect
3. #416×C179C2semidirect
4. #410×C179C2semidirect
5. #408×C179C2semidirect
7. 2−1+4×C179C4semidirect
10. H(5,𝔽2)×C179C4semidirect
15. C2×M16×C179C22semidirect
16. C22×C8×C179C22semidirect
17. #117×C179C22semidirect
108. C179#1794direct (N × H)
109. #1794C179direct (N × H)
111. #421C2×C179semidirect
112. #416C2×C179semidirect
113. #410C2×C179semidirect
114. #408C2×C179semidirect
116. 2−1+4C4×C179semidirect
119. H(5,𝔽2)C4×C179semidirect
124. C2×M16C22×C179semidirect
125. C22×C8C22×C179semidirect
126. #117C22×C179semidirect

Maximal subgroups

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

subgroupindex
#585×C1792
#421×C1792
#416×C1792
#410×C1792
#408×C1792
#1794179