Finite Group Databasebeta

← #37510015

Subgroups — #37510015

Order 22912.

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

normal subgroups only

This group has 478 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×#19153139C211yesmaximal, characteristic, complemented
2#26039006C211yesmaximal, characteristic, complemented
3C2×#19153041C211yesmaximal, characteristic, complemented
4#26038444C211yesmaximal, characteristic, complemented
5C2×#19153030C211yesmaximal, characteristic, complemented
6#26038199C211yesmaximal, characteristic, complemented
7C2×#127×C179C211yesmaximal, characteristic, complemented
8C2×#15668259C2211yescharacteristic
9#19153139—22no—
10#19153139—22no—
11C2×#15668247—21no—
12C2×#15668244—21no—
13C2×#15668243C2211yescharacteristic
14C2×#15668243C2211yescharacteristic
15#19153109—21no—
16#19153100—21no—
17#19153084—22no—
18#19153082—22no—
19#19153072C2211yescharacteristic
20#19153041—22no—
21#19153034—22no—
22#19153030—22no—
23C22×D4×C179—22no—
24C22×D4×C179C2211yescharacteristic
25C22×D4×C179C2211yescharacteristic
26#127×C179—22no—
27#127×C179—22no—
28C2×C42×C179C2211yescharacteristic
29#15668259—21no—
30#15668259—21no—
31#15668259—21no—
32#15668259—21no—
33C2×Dic358D411yescharacteristic, complemented
34C2×D716D411yescharacteristic, complemented
35C2×C22⋊D179—24no—
36C2×C22⋊D179—21no—
37C2×C4×D179—21no—
38#15668247—24no—
39#15668244—24no—
40#15668243—21no—
41#15668243—21no—
42#15668243—21no—
43#15668243D412yescomplemented
44C2×C179⋊C8—21no—
45C2×C179⋊C8—21no—
46C4⋊Dic179D412yescomplemented
47C22⋊Dic179—24no—
48C22⋊Dic179—21no—
49C4×Dic179—21no—
50C24×C179—21no—
51C24×C179D412yes—
52C2×D4×C179—28no—
53C2×D4×C179—21no—
54C2×D4×C179—21no—
55C2×D4×C179—21no—
56C2×D4×C179—21no—
57C2×D4×C179—21no—
58C2×D4×C179—21no—
59C2×D4×C179—21no—
60C2×D4×C179—21no—
61C2×D4×C179—21no—
62C2×D4×C179—21no—
63C2×D4×C179—21no—
64C2×D4×C179—48no—
65C2×D4×C179D412yescomplemented
66C22×C4×C179—21no—
67C22×C4×C179C2311yescharacteristic
68C42×C179—21no—
69C42×C179D412yescomplemented
70C22×D179—21no—
71Dic358—21no—
72Dic358—21no—
73D716—21no—
74D716—21no—
75C22⋊D179—41no—
76C22⋊D179—41no—
77C22⋊D179—84no—
78C2×Dic179—22no—
79C2×Dic179—21no—
80C4×D179—41no—
81C4×D179—41no—
82C179⋊C8—22no—
83C179⋊C8—41no—
84C23×C179—22no—
85C23×C179—22no—
86C23×C179—22no—
87C23×C179—22no—
88C23×C179—44no—
89C23×C179—44no—
90C23×C179—41no—
91C23×C179—41no—
92C23×C179C2×D411yescharacteristic
93D4×C179—22no—
94D4×C179—22no—
95D4×C179—416no—
96D4×C179—41no—
97D4×C179—41no—
98D4×C179—41no—
99D4×C179—41no—
100D4×C179—41no—
101D4×C179—41no—
102C2×C4×C179—24no—
103C2×C4×C179—22no—
104C2×C4×C179C2×D411yescharacteristic
105C2×C4×C179C2×D411yescharacteristic
106C2×C4×C179C2×D411yescharacteristic
107C2×C4×C179C2×D411yescharacteristic
108C2×C4×C179C2×D411yescharacteristic
109C2×C4×C179#4111yescharacteristic
110C22×C179—22no—
111C22×C179—44no—
112C22×C179—44no—
113C22×C179—42no—
114C22×C179—42no—
115C22×C179—44no—
116C22×C179—82no—
117C22×C179—82no—
118C22×C179—82no—
119C22×C179#12011yescharacteristic
120C22×C179#12011yescharacteristic
121C22×C179#12111yescharacteristic
122C2×D179—41no—
123C2×D179—42no—
124C4×C179—24no—
125C4×C179#12011yescharacteristic
126C4×C179#12111yescharacteristic
127C4×C179#12111yescharacteristic
128C4×C179#12711yescharacteristic
129Dic179—41no—
130Dic179—42no—
131C2×C179—21no—
132C2×C179—21no—
133C2×C179—82no—
134C2×C179—82no—
135C2×C179#39211yescharacteristic
136C2×C179#45312yes—
137D179—81no—
138C179#200211yescharacteristic, complemented, Sylow
139#2002—1791nomaximal, Sylow
140C2×AGL(1,ℤ/8)—1791no—
141#535—1791no—
142C2×#127D17911yescharacteristic, complemented
143C2×#104—1791no—
144#418—1791no—
145C2×#100—1791no—
146#339—1791no—
147C2×#41—1791no—
148C22×D4—22no—
149C22×D4C2×D17911yescharacteristic
150C22×D4C2×D17911yescharacteristic
151AGL(1,ℤ/8)—3582no—
152AGL(1,ℤ/8)—3582no—
153C2×SD16—3581no—
154C2×D8—3581no—
155C2×M16—1791no—
156C2×M16—1791no—
157#127—22no—
158#127—22no—
159#127—3581no—
160#124—3581no—
161#121—3582no—
162#120—3582no—
163#117—1791no—
164C2×C42C2×D17911yescharacteristic
165#104—3582no—
166#102—3582no—
167#100—3582no—
168C24—21no—
169C24C22⋊D17912yes—
170#41—3581no—
171#41—3581no—
172#41—3581no—
173#41—3581no—
174C2×Q8—1791no—
175C2×D4—28no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—21no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—21no—
187C2×D4—48no—
188C2×D4—3584no—
189C2×D4—3581no—
190C2×D4—1791no—
191C2×D4C22⋊D17912yescomplemented
192C22×C4—21no—
193C22×C4—3581no—
194C22×C4C22×D17911yescharacteristic
195SD16—3584no—
196D8—3584no—
197M16—3581no—
198M16—3581no—
199M16—3581no—
200M16—1792no—
201C2×C8—3581no—
202C2×C8—3581no—
203C4⋊C4—1792no—
204C22⋊C4—3584no—
205C22⋊C4—3581no—
206C42—21no—
207C42—3581no—
208C42C22⋊D17912yescomplemented
209C23—22no—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—44no—
214C23—44no—
215C23—41no—
216C23—41no—
217C23—3581no—
218C23C2×C22⋊D17911yescharacteristic
219Q8—3581no—
220Q8—3581no—
221D4—22no—
222D4—22no—
223D4—416no—
224D4—41no—
225D4—41no—
226D4—41no—
227D4—41no—
228D4—41no—
229D4—41no—
230D4—3581no—
231D4—3581no—
232D4—14324no—
233D4—7161no—
234D4—7161no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—3582no—
238C2×C4—3581no—
239C2×C4—7161no—
240C2×C4—7161no—
241C2×C4D4×D17911yescharacteristic
242C2×C4D4×D17911yescharacteristic
243C2×C4D4×D17911yescharacteristic
244C2×C4C2×C22⋊D17911yescharacteristic
245C2×C4C2×C22⋊D17911yescharacteristic
246C2×C4#1566825811yescharacteristic
247C8—3582no—
248C8—7161no—
249C22—22no—
250C22—44no—
251C22—44no—
252C22—42no—
253C22—42no—
254C22—44no—
255C22—82no—
256C22—82no—
257C22—82no—
258C22—7161no—
259C22—7162no—
260C22#1915308111yescharacteristic
261C22#1915308211yescharacteristic
262C22#1915308511yescharacteristic
263C4—24no—
264C4—7161no—
265C4—7162no—
266C4#1915308111yescharacteristic
267C4#1915308411yescharacteristic
268C4#1915308511yescharacteristic
269C4#1915310911yescharacteristic
270C2—21no—
271C2—21no—
272C2—82no—
273C2—82no—
274C2—14321no—
275C2#2603834711yescharacteristic
276C2#2603860612yes—
subgroupG/H
centerC22#19153081
commutator, cosocleC22×C4×C179C23
FrattiniC22×C4C22×D179
FittingC2×#127×C179C2
socleC22×C179#120
hypercenterC2×#127D179
hypocenterC179#2002
LCSG ▷ C22×C4×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#19153139C2semidirect
2. #26039006C2semidirect
3. C2×#19153041C2semidirect
4. #26038444C2semidirect
5. C2×#19153030C2semidirect
6. #26038199C2semidirect
7. C2×#127×C179C2semidirect
33. C2×Dic358D4semidirect
34. C2×D716D4semidirect
43. #15668243D4semidirect
46. C4⋊Dic179D4semidirect
65. C2×D4×C179D4semidirect
69. C42×C179D4semidirect
138. C179#2002semidirect
142. C2×#127D179semidirect
191. C2×D4C22⋊D179semidirect
208. C42C22⋊D179semidirect

Maximal subgroups

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

subgroupindex
C2×#191531392
#260390062
C2×#191530412
#260384442
C2×#191530302
#260381992
C2×#127×C1792
#2002179