Finite Group Databasebeta

← Q16×C22⋊D197 #38754458

Subgroups — Q16×C22⋊D197 #38754458

Order 25216.

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

normal subgroups only

This group has 472 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×Q16×D197C211yesmaximal, characteristic, complemented
2Q8×C22⋊D197C212yesmaximal
3#27161457C211yesmaximal, characteristic, complemented
4#27161320C211yesmaximal, characteristic, complemented
5#27161317C211yesmaximal, characteristic, complemented
6#27161287C212yesmaximal, complemented
7#27161235C212yesmaximal, complemented
8#27161233C212yesmaximal, complemented
9Q16×Dic197C211yesmaximal, characteristic, complemented
10C8×C22⋊D197C211yesmaximal, characteristic
11C22×Q16×C197C211yesmaximal, characteristic, complemented
12C2×Q8×D197C2212yes—
13C2×Dic788C2211yescharacteristic
14C2×#15691348C2212yes—
15C2×#15691348C2212yes—
16Q16×D197—24no—
17C2×C8×D197C2211yescharacteristic
18#20263324—22no—
19#20263324C2212yes—
20#20263305—22no—
21#20263305C2212yes—
22#20263302—22no—
23#20263302C2212yes—
24Q8×Dic197C2212yes—
25C4×C22⋊D197—22no—
26C4×C22⋊D197C2211yescharacteristic
27#20263260C2211yescharacteristic
28#20263255C2211yescharacteristic
29#20263251C2212yes—
30#20263250C2212yes—
31#20263250C2212yes—
32C22⋊#13096802C2211yescharacteristic
33#20263238C2211yescharacteristic
34C8×Dic197C2211yescharacteristic
35C22×Q8×C197C2212yes—
36C2×Q16×C197—24no—
37C2×Q16×C197C2211yescharacteristic
38C2×Q16×C197C2212yes—
39C2×Q16×C197C2211yescharacteristic
40C22×C8×C197C2211yescharacteristic
41C2×Dic394—22no—
42C2×Dic394C2312yes—
43Q8×D197—24no—
44Q8×D197—42no—
45C2×C22⋊D197D411yescharacteristic
46C2×C4×D197—22no—
47C2×C4×D197C2311yescharacteristic
48Dic788—22no—
49#15691348—24no—
50#15691348—42no—
51C2×#13096802C2311yescharacteristic
52C2×#13096802C2311yescharacteristic
53C8×D197—22no—
54C4⋊Dic197—22no—
55C4⋊Dic197C2312yes—
56#15691337—22no—
57#15691337—22no—
58#15691337—22no—
59#15691337—22no—
60#15691337D411yescharacteristic
61C22⋊Dic197—22no—
62C22⋊Dic197D411yescharacteristic
63#15691335—22no—
64#15691335D411yescharacteristic
65C4×Dic197—22no—
66C4×Dic197C2311yescharacteristic
67C2×Q8×C197—22no—
68C2×Q8×C197—24no—
69C2×Q8×C197—42no—
70C2×Q8×C197C2312yes—
71C2×Q8×C197C2312yes—
72C22×C4×C197—22no—
73C22×C4×C197C2311yescharacteristic
74Q16×C197—24no—
75Q16×C197—22no—
76Q16×C197D414yescomplemented
77C2×C8×C197—22no—
78C2×C8×C197C2311yescharacteristic
79C2×C8×C197C2311yescharacteristic
80C22×D197C2×D411yescharacteristic
81Dic394—22no—
82Dic394—22no—
83Dic394—44no—
84C22⋊D197Q1614yesdirect product factor
85C2×Dic197—22no—
86C2×Dic197—22no—
87C2×Dic197C2×D411yescharacteristic
88C2×Dic197C2×D411yescharacteristic
89C2×Dic197C2×D411yescharacteristic
90C4×D197—21no—
91C4×D197—21no—
92C4×D197—44no—
93#13096802—21no—
94#13096802—21no—
95C23×C197C2×D411yescharacteristic
96Q8×C197—22no—
97Q8×C197—22no—
98Q8×C197—22no—
99Q8×C197—44no—
100Q8×C197C2×D414yes—
101C2×C4×C197—22no—
102C2×C4×C197—21no—
103C2×C4×C197—21no—
104C2×C4×C197—22no—
105C2×C4×C197—44no—
106C2×C4×C197C2×D411yescharacteristic
107C2×C4×C197C2411yescharacteristic
108C8×C197—21no—
109C8×C197C2×D412yes—
110C22×C197—21no—
111C22×C197—21no—
112C22×C197C2×Q1612yescomplemented
113C22×C197C22×D411yescharacteristic
114C2×D197—21no—
115C2×D197—21no—
116C2×D197C2×Q1612yescomplemented
117C4×C197—21no—
118C4×C197—24no—
119C4×C197—42no—
120C4×C197C22×D411yescharacteristic
121C4×C197H(5,𝔽2)11yescharacteristic
122Dic197—21no—
123Dic197—21no—
124Dic197—42no—
125Dic197—42no—
126Dic197C2×Q1612yescomplemented
127C2×C197—22no—
128C2×C197D4211yescharacteristic
129C2×C197C22×Q1611yescharacteristic
130C2×C197#57811yescharacteristic
131D197—22no—
132C197D4×Q1611yescharacteristic, complemented, Sylow
133D4×Q16—1971nomaximal, Sylow
134C22×Q16—1971no—
135C22×Q16D19711yescharacteristic, complemented
136D4×Q8—1972no—
137#494—1971no—
138#467—1971no—
139#467—1971no—
140#462—1972no—
141#451—1972no—
142#451—1972no—
143C4×Q16—1971no—
144C8×D4—1971no—
145C22×Q8—1972no—
146C22×Q8C2×D19712yes—
147C2×Q16—24no—
148C2×Q16—3944no—
149C2×Q16—1972no—
150C2×Q16—1972no—
151C2×Q16—1971no—
152C2×Q16C2×D19712yes—
153C2×Q16C2×D19711yescharacteristic
154C2×Q16C2×D19711yescharacteristic
155C22×C8—1971no—
156C22×C8C2×D19711yescharacteristic
157C4⋊Q8—3942no—
158C4⋊Q8—1972no—
159C22⋊Q8—3942no—
160C22⋊Q8—3942no—
161C22⋊Q8—1972no—
162C22⋊Q8—1972no—
163C4×Q8—1972no—
164C4×D4—3942no—
165C4×D4—1971no—
166#107—1971no—
167C4⋊C8—1971no—
168#103—1972no—
169#103—1972no—
170#103—1972no—
171C22⋊C8—1971no—
172C22⋊C8—1971no—
173C4×C8—1971no—
174C2×Q8—22no—
175C2×Q8—24no—
176C2×Q8—42no—
177C2×Q8—7882no—
178C2×Q8—3942no—
179C2×Q8—3944no—
180C2×Q8—1972no—
181C2×Q8C22×D19712yes—
182C2×Q8C22×D19712yes—
183C2×D4—1971no—
184C22×C4—22no—
185C22×C4—3942no—
186C22×C4—1971no—
187C22×C4C22×D19711yescharacteristic
188Q16—24no—
189Q16—22no—
190Q16—7882no—
191Q16—3944no—
192Q16—3942no—
193Q16C22⋊D19714yesdirect product factor
194C2×C8—22no—
195C2×C8—3942no—
196C2×C8—1971no—
197C2×C8—1971no—
198C2×C8C22×D19711yescharacteristic
199C2×C8C22×D19711yescharacteristic
200C4⋊C4—3942no—
201C4⋊C4—3942no—
202C4⋊C4—3942no—
203C4⋊C4—3942no—
204C4⋊C4—3942no—
205C4⋊C4—1972no—
206C4⋊C4—1971no—
207C22⋊C4—3942no—
208C22⋊C4—3942no—
209C22⋊C4—1971no—
210C22⋊C4—1971no—
211C42—3942no—
212C42—1971no—
213C23—1971no—
214C23D4×D19711yescharacteristic
215Q8—22no—
216Q8—22no—
217Q8—22no—
218Q8—44no—
219Q8—7884no—
220Q8—3942no—
221Q8—3942no—
222Q8C2×C22⋊D19714yes—
223D4—1974no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—44no—
229C2×C4—7884no—
230C2×C4—3942no—
231C2×C4—3942no—
232C2×C4—3941no—
233C2×C4—3941no—
234C2×C4—1971no—
235C2×C4—1971no—
236C2×C4—1971no—
237C2×C4D4×D19711yescharacteristic
238C2×C4C23×D19711yescharacteristic
239C8—21no—
240C8—3941no—
241C8—3941no—
242C8C2×C22⋊D19712yes—
243C22—21no—
244C22—21no—
245C22—3941no—
246C22—3941no—
247C22—1972no—
248C22Q16×D19712yescomplemented
249C22C2×D4×D19711yescharacteristic
250C4—21no—
251C4—24no—
252C4—42no—
253C4—7882no—
254C4—7882no—
255C4—3941no—
256C4—3941no—
257C4—1972no—
258C4C22×C22⋊D19711yescharacteristic
259C4#2026337111yescharacteristic
260C2—22no—
261C2—3942no—
262C2D4×C22⋊D19711yescharacteristic
263C2C2×Q16×D19711yescharacteristic
264C2#2716189211yescharacteristic
subgroupG/H
centerC22C2×D4×D197
commutator, cosocleC2×C4×C197C24
FrattiniC2×C4C23×D197
FittingC22×Q16×C197C2
socleC22×C197C22×D4
prime radicalC2×C22⋊D197D4
hypercenterC22×Q16D197
hypocenterC197D4×Q16
LCSG ▷ C2×C4×C197 ▷ C2×C197 ▷ C197
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D197C2semidirect
3. #27161457C2semidirect
4. #27161320C2semidirect
5. #27161317C2semidirect
6. #27161287C2semidirect
7. #27161235C2semidirect
8. #27161233C2semidirect
9. Q16×Dic197C2semidirect
11. C22×Q16×C197C2semidirect
76. Q16×C197D4semidirect
84. C22⋊D197Q16direct (N × H)
112. C22×C197C2×Q16semidirect
116. C2×D197C2×Q16semidirect
126. Dic197C2×Q16semidirect
132. C197D4×Q16semidirect
135. C22×Q16D197semidirect
193. Q16C22⋊D197direct (N × H)
248. C22Q16×D197semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D1972
Q8×C22⋊D1972
#271614572
#271613202
#271613172
#271612872
#271612352
#271612332
Q16×Dic1972
C8×C22⋊D1972
C22×Q16×C1972
D4×Q16197