Finite Group Databasebeta

← C2×#27132923 #37582216

Subgroups — C2×#27132923 #37582216

Order 24448.

468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 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×#20259353C211yesmaximal, characteristic, complemented
2C2×#20259348C211yesmaximal, characteristic
3C2×#20259328C211yesmaximal, characteristic, complemented
4#27132923C218yesmaximal, direct product factor
5C2×#20259258C211yesmaximal, characteristic, complemented
6C2×#20259241C211yesmaximal, characteristic, complemented
7C2×#20259239C211yesmaximal, characteristic, complemented
8C22×SD16×C191C211yesmaximal, characteristic, complemented
9C2×#15690287C2211yescharacteristic
10#20259353—22no—
11#20259353C2214yescomplemented
12#20259348—22no—
13#20259348C2214yes—
14C2×#15690277—21no—
15C2×#15690275—21no—
16C2×#15690274—21no—
17C2×#15690272—21no—
18#20259328—22no—
19#20259328C2214yescomplemented
20C2×#15690271C2211yescharacteristic
21C2×#15690271C2211yescharacteristic
22C2×#15690271C2211yescharacteristic
23C2×#15690270—21no—
24C2×C8×D191—21no—
25#20259258C2214yescomplemented
26#20259241C2214yescomplemented
27#20259239C2214yescomplemented
28C22×Q8×C191C2211yescharacteristic
29C22×D4×C191C2211yescharacteristic
30C2×SD16×C191—22no—
31C2×SD16×C191—21no—
32C2×SD16×C191—21no—
33C2×SD16×C191C2214yescomplemented
34C22×C8×C191C2211yescharacteristic
35#15690287—21no—
36#15690287—21no—
37#15690287D412yes—
38#15690287C2312yes—
39C2×Dic382D411yescharacteristic
40C2×D764D411yescharacteristic
41C2×C22⋊D191—21no—
42C2×C4×D191—21no—
43#15690277—24no—
44#15690275—24no—
45#15690274—24no—
46#15690272—24no—
47#15690271—21no—
48#15690271—21no—
49#15690271—21no—
50#15690271C2312yes—
51#15690271C2312yes—
52#15690271C2312yes—
53#15690270—24no—
54C2×C191⋊C8—21no—
55C2×C191⋊C8—21no—
56C2×C191⋊C8—21no—
57C8×D191—24no—
58C24×C191—21no—
59C2×Q8×C191—21no—
60C2×Q8×C191—21no—
61C2×Q8×C191—21no—
62C2×Q8×C191—21no—
63C2×Q8×C191—21no—
64C2×Q8×C191C2312yes—
65C2×D4×C191—21no—
66C2×D4×C191—21no—
67C2×D4×C191—21no—
68C2×D4×C191—21no—
69C2×D4×C191—21no—
70C2×D4×C191C2312yes—
71C22×C4×C191—21no—
72C22×C4×C191C2311yescharacteristic
73SD16×C191—24no—
74SD16×C191—24no—
75C2×C8×C191D412yes—
76C2×C8×C191D411yescharacteristic
77C2×C8×C191D411yescharacteristic
78C2×C8×C191C2312yes—
79C22×D191—21no—
80Dic382—21no—
81Dic382C2×D412yes—
82D764—21no—
83D764C2×D412yes—
84C22⋊D191—22no—
85C22⋊D191—22no—
86C2×Dic191—21no—
87C4×D191—22no—
88C4×D191—22no—
89C191⋊C8—22no—
90C191⋊C8—22no—
91C191⋊C8—22no—
92C23×C191—22no—
93C23×C191—41no—
94C23×C191—41no—
95C23×C191—82no—
96C23×C191#4111yescharacteristic
97Q8×C191—22no—
98Q8×C191—22no—
99Q8×C191—41no—
100Q8×C191—41no—
101D4×C191—22no—
102D4×C191—22no—
103D4×C191—41no—
104D4×C191—41no—
105C2×C4×C191—22no—
106C2×C4×C191—41no—
107C2×C4×C191—41no—
108C2×C4×C191C2×D411yescharacteristic
109C2×C4×C191C2×D411yescharacteristic
110C2×C4×C191C2×D411yescharacteristic
111C2×C4×C191C2×D411yescharacteristic
112C2×C4×C191#4111yescharacteristic
113C2×C4×C191C2411yescharacteristic
114C8×C191C2×D412yes—
115C8×C191C2×D412yes—
116C22×C191—22no—
117C22×C191—42no—
118C22×C191—82no—
119C22×C191—82no—
120C22×C191—82no—
121C22×C191#12111yescharacteristic
122C22×C191#12111yescharacteristic
123C22×C191C2×#4111yescharacteristic
124C2×D191—22no—
125C2×D191—42no—
126C4×C191—42no—
127C4×C191#12111yescharacteristic
128C4×C191#12111yescharacteristic
129C4×C191C22×D411yescharacteristic
130C4×C191C22×D411yescharacteristic
131Dic191—22no—
132C2×C191—21no—
133C2×C191—21no—
134C2×C191—82no—
135C2×C191#47112yescomplemented
136C2×C191C2×#12111yescharacteristic
137D191—42no—
138C191C2×#47111yescharacteristic, complemented, Sylow
139C2×#471—1911nomaximal, Sylow
140C2×#137—1911no—
141C2×AGL(1,ℤ/8)—1911no—
142C22×SD16D19111yescharacteristic, complemented
143C2×#131—1911no—
144#471—1918no—
145C2×#108—1911no—
146C2×#101—1911no—
147C2×#100—1911no—
148C2×#41—1911no—
149C22×Q8C2×D19111yescharacteristic
150C22×D4C2×D19111yescharacteristic
151#137—3822no—
152#137—1914no—
153AGL(1,ℤ/8)—3822no—
154AGL(1,ℤ/8)—1914no—
155C2×Q16—3821no—
156C2×SD16—21no—
157C2×SD16—21no—
158C2×SD16—22no—
159C2×SD16—3821no—
160C2×SD16—3821no—
161C2×SD16C2×D19114yescomplemented
162C2×D8—3821no—
163#131—3822no—
164#131—1914no—
165C2×M16—3821no—
166C2×M16—1911no—
167C2×M16—1911no—
168C2×M16—1911no—
169C22×C8—3821no—
170C22×C8C2×D19111yescharacteristic
171#108—1914no—
172#101—1914no—
173#100—1914no—
174C24—21no—
175#41—3821no—
176#41—3821no—
177#41—1912no—
178#41—1912no—
179C2×Q8—21no—
180C2×Q8—21no—
181C2×Q8—21no—
182C2×Q8—21no—
183C2×Q8—21no—
184C2×Q8—1911no—
185C2×Q8C22×D19112yes—
186C2×D4—21no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—21no—
190C2×D4—21no—
191C2×D4—3821no—
192C2×D4—1911no—
193C2×D4C22×D19112yes—
194C22×C4—21no—
195C22×C4—3821no—
196C22×C4C22×D19111yescharacteristic
197Q16—3824no—
198SD16—24no—
199SD16—24no—
200SD16—3824no—
201SD16—3824no—
202D8—3824no—
203M16—3821no—
204M16—3821no—
205M16—3821no—
206M16—3824no—
207M16—1912no—
208M16—1912no—
209M16—1912no—
210C2×C8—3821no—
211C2×C8—3821no—
212C2×C8—3821no—
213C2×C8—3824no—
214C2×C8C22⋊D19111yescharacteristic
215C2×C8C22⋊D19111yescharacteristic
216C2×C8C22⋊D19112yes—
217C2×C8C22×D19112yes—
218C23—22no—
219C23—41no—
220C23—41no—
221C23—82no—
222C23—3821no—
223C23#1569028611yescharacteristic
224Q8—22no—
225Q8—22no—
226Q8—41no—
227Q8—41no—
228Q8—3821no—
229Q8—1912no—
230D4—22no—
231D4—22no—
232D4—41no—
233D4—41no—
234D4—3822no—
235D4—3822no—
236D4—3821no—
237D4—1912no—
238C2×C4—22no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—3821no—
242C2×C4—3822no—
243C2×C4—3822no—
244C2×C4D4×D19111yescharacteristic
245C2×C4D4×D19111yescharacteristic
246C2×C4C2×C22⋊D19111yescharacteristic
247C2×C4C2×C22⋊D19111yescharacteristic
248C2×C4#1569028611yescharacteristic
249C2×C4C23×D19111yescharacteristic
250C8—3822no—
251C8—3822no—
252C8—3822no—
253C8C2×C22⋊D19112yes—
254C8C2×C22⋊D19112yes—
255C22—22no—
256C22—42no—
257C22—82no—
258C22—82no—
259C22—82no—
260C22—3822no—
261C22—7642no—
262C22#2025929311yescharacteristic
263C22#2025929311yescharacteristic
264C22C2×#1569028611yescharacteristic
265C4—42no—
266C4—3822no—
267C4#2025929311yescharacteristic
268C4#2025929311yescharacteristic
269C4C2×D4×D19111yescharacteristic
270C4C22×C22⋊D19111yescharacteristic
271C2—21no—
272C2—21no—
273C2—82no—
274C2—7642no—
275C2#2713292312yesdirect product factor
276C2C2×#2025929311yescharacteristic
subgroupG/H
centerC22#20259293
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
FittingC22×SD16×C191C2
socleC22×C191#121
prime radicalC2×#20259348C2
hypercenterC22×SD16D191
hypocenterC191C2×#471
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#20259353C2semidirect
3. C2×#20259328C2semidirect
4. #27132923C2direct (N × H)
5. C2×#20259258C2semidirect
6. C2×#20259241C2semidirect
7. C2×#20259239C2semidirect
8. C22×SD16×C191C2semidirect
11. #20259353C22semidirect
19. #20259328C22semidirect
25. #20259258C22semidirect
26. #20259241C22semidirect
27. #20259239C22semidirect
33. C2×SD16×C191C22semidirect
135. C2×C191#471semidirect
138. C191C2×#471semidirect
142. C22×SD16D191semidirect
161. C2×SD16C2×D191semidirect
275. C2#27132923direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#202593532
C2×#202593482
C2×#202593282
#271329232
C2×#202592582
C2×#202592412
C2×#202592392
C22×SD16×C1912
C2×#471191