Finite Group Databasebeta

← #37510139

Subgroups — #37510139

Order 22912.

290 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 89 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×#19153112C211yesmaximal, characteristic
2C2×#19153037C211yesmaximal, characteristic
3#26038346C211yesmaximal, characteristic
4#26038202C211yesmaximal, characteristic
5#26038201C211yesmaximal, characteristic
6#26038193C211yesmaximal, characteristic
7C2×#103×C179C211yesmaximal, characteristic
8C22×Dic358—21no—
9C22×C179⋊C8C2211yescharacteristic
10#19153112—22no—
11#19153112—22no—
12C2×C4⋊Dic179C2211yescharacteristic
13C2×C4⋊Dic179C2211yescharacteristic
14C2×Dic179⋊C4—21no—
15C2×C4×Dic179C2211yescharacteristic
16#19153037—22no—
17C179⋊#95—21no—
18C179⋊#95—21no—
19C22×Q8×C179C2211yescharacteristic
20C22×C8×C179C2211yescharacteristic
21C2×C4⋊C4×C179C2211yescharacteristic
22#103×C179—22no—
23C2×Dic358—24no—
24C2×Dic358—42no—
25C2×Dic358—42no—
26C22×Dic179—21no—
27C22×Dic179—21no—
28C22×Dic179D411yescharacteristic
29C22×Dic179D411yescharacteristic
30C2×C179⋊C8—21no—
31C2×C179⋊C8—21no—
32C2×C179⋊C8—21no—
33C4⋊Dic179—21no—
34C4⋊Dic179—21no—
35C4⋊Dic179—21no—
36C4⋊Dic179D412yes—
37Dic179⋊C4—24no—
38C4×Dic179—21no—
39C4×Dic179—21no—
40C2×Q8×C179—21no—
41C2×Q8×C179—21no—
42C2×Q8×C179—21no—
43C2×Q8×C179—21no—
44C2×Q8×C179—21no—
45C2×Q8×C179Q812yescomplemented
46C22×C4×C179—21no—
47C22×C4×C179—21no—
48C22×C4×C179C2311yescharacteristic
49C2×C8×C179—21no—
50C2×C8×C179—21no—
51C2×C8×C179—21no—
52C4⋊C4×C179—21no—
53C4⋊C4×C179D412yes—
54Dic358—48no—
55C2×Dic179—21no—
56C2×Dic179—21no—
57C2×Dic179—21no—
58C2×Dic179—21no—
59C2×Dic179—22no—
60C2×Dic179—41no—
61C2×Dic179—41no—
62C2×Dic179—41no—
63C2×Dic179—41no—
64C2×Dic179—41no—
65C2×Dic179SD1612yes—
66C2×Dic179Q1612yes—
67C179⋊C8—41no—
68C23×C179C2×D411yescharacteristic
69Q8×C179—22no—
70Q8×C179—22no—
71Q8×C179—41no—
72Q8×C179—41no—
73C2×C4×C179—22no—
74C2×C4×C179—22no—
75C2×C4×C179—41no—
76C2×C4×C179—41no—
77C2×C4×C179—41no—
78C2×C4×C179—41no—
79C2×C4×C179C2×D411yescharacteristic
80C2×C4×C179C2×D411yescharacteristic
81C2×C4×C179C2×Q811yescharacteristic
82C2×C4×C179#4111yescharacteristic
83C2×C4×C179#4111yescharacteristic
84C2×C4×C179#4111yescharacteristic
85C8×C179—41no—
86C22×C179#12011yescharacteristic
87C22×C179C22⋊Q811yescharacteristic
88C22×C179#12411yescharacteristic
89C22×C179C2×SD1611yescharacteristic
90C22×C179C2×Q1611yescharacteristic
91C22×C179AGL(1,ℤ/8)11yescharacteristic
92C22×C179#13711yescharacteristic
93C4×C179—42no—
94C4×C179—42no—
95C4×C179C22⋊Q811yescharacteristic
96C4×C179C22⋊Q811yescharacteristic
97C4×C179#12411yescharacteristic
98C4×C179#12411yescharacteristic
99Dic179—22no—
100Dic179—22no—
101Dic179—42no—
102Dic179—81no—
103C2×C179#39311yescharacteristic
104C2×C179#45011yescharacteristic
105C2×C179#45111yescharacteristic
106C2×C179#47511yescharacteristic
107C2×C179#47711yescharacteristic
108C2×C179#48711yescharacteristic
109C2×C179#48911yescharacteristic
110C179#202411yescharacteristic, complemented, Sylow
111#2024—1791nomaximal, Sylow
112C2×C4⋊Q8—1791no—
113C2×#103—1791no—
114C2×#103D17911yescharacteristic
115#391—1791no—
116#340—1791no—
117#340—1791no—
118#336—1791no—
119C22×Q8—3581no—
120C22×Q8C2×D17911yescharacteristic
121C22×C8—1791no—
122C22×C8C2×D17911yescharacteristic
123C4⋊Q8—3582no—
124C4⋊Q8—3582no—
125C2×C4⋊C4—3581no—
126C2×C4⋊C4—1791no—
127C2×C4⋊C4—1791no—
128C2×C4⋊C4C2×D17911yescharacteristic
129C2×C42—1791no—
130#103—22no—
131#103—3582no—
132#95—3581no—
133#95—3581no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—3584no—
140C2×Q8—7162no—
141C2×Q8—7162no—
142C2×Q8Dic35812yescomplemented
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—3581no—
146C22×C4—3581no—
147C22×C4—1791no—
148C22×C4—1791no—
149C22×C4C22×D17911yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—3581no—
154C2×C8—3581no—
155C2×C8—3581no—
156C4⋊C4—21no—
157C4⋊C4—3584no—
158C4⋊C4—3581no—
159C4⋊C4—3581no—
160C4⋊C4—3581no—
161C4⋊C4—1792no—
162C4⋊C4C22⋊D17912yes—
163C42—3581no—
164C42—3581no—
165C23D4×D17911yescharacteristic
166Q8—22no—
167Q8—22no—
168Q8—41no—
169Q8—41no—
170Q8—7168no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—3581no—
178C2×C4—3581no—
179C2×C4—3581no—
180C2×C4—3581no—
181C2×C4—3582no—
182C2×C4—1792no—
183C2×C4—1792no—
184C2×C4—7161no—
185C2×C4—7161no—
186C2×C4—7161no—
187C2×C4—7161no—
188C2×C4—7161no—
189C2×C4D4×D17911yescharacteristic
190C2×C4C2×C22⋊D17911yescharacteristic
191C2×C4C2×Dic35811yescharacteristic
192C2×C4#1566825811yescharacteristic
193C2×C4#1566825811yescharacteristic
194C2×C4#1566825911yescharacteristic
195C8—41no—
196C8—7161no—
197C22#1915308111yescharacteristic
198C22#1915309011yescharacteristic
199C22#1915309911yescharacteristic
200C22SD16×D17911yescharacteristic
201C22Q16×D17911yescharacteristic
202C22#1915314011yescharacteristic
203C22#1915314511yescharacteristic
204C4—42no—
205C4—42no—
206C4—3582no—
207C4—3582no—
208C4—14321no—
209C4—7162no—
210C4#1915309011yescharacteristic
211C4#1915309211yescharacteristic
212C4#1915309911yescharacteristic
213C4#1915310011yescharacteristic
214C2#2603835111yescharacteristic
215C2#2603858811yescharacteristic
216C2#2603859311yescharacteristic
217C2#2603872211yescharacteristic
218C2#2603873211yescharacteristic
219C2#2603878811yescharacteristic
220C2#2603880011yescharacteristic
subgroupG/H
centerC23D4×D179
commutator, cosocleC22×C4×C179C23
FrattiniC22×C4C22×D179
FittingC2×#103×C179C2
socle, prime radicalC23×C179C2×D4
hypercenterC2×#103D179
hypocenterC179#2024
LCSG ▷ C22×C4×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
45. C2×Q8×C179Q8semidirect
110. C179#2024semidirect
142. C2×Q8Dic358semidirect

Maximal subgroups

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

subgroupindex
C2×#191531122
C2×#191530372
#260383462
#260382022
#260382012
#260381932
C2×#103×C1792
#2024179