Finite Group Databasebeta

← C2×#34036515 #49169216

Subgroups — C2×#34036515 #49169216

Order 37504.

668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C22×#17989789C211yesmaximal, characteristic, complemented
2C22×D2344C211yesmaximal, characteristic, complemented
3C22×#17989787C211yesmaximal, characteristic, complemented
4C2×#22627620C211yesmaximal, characteristic, complemented
5C2×#22627613C211yesmaximal, characteristic, complemented
6#34036515C218yesmaximal, direct product factor
7C2×#22627534C211yesmaximal, characteristic, complemented
8C22×SD16×C293C211yesmaximal, characteristic, complemented
9C22×D1172C2211yescharacteristic
10C22×D1172C2211yescharacteristic
11C22×C22⋊D293—22no—
12C2×#17989789—24no—
13C2×#17989789C2214yescomplemented
14C2×D2344—24no—
15C2×D2344C2214yescomplemented
16C2×#17989787—24no—
17C2×#17989787C2214yescomplemented
18C22×#14556873C2211yescharacteristic
19#22627620—22no—
20#22627620C2214yescomplemented
21#22627613—22no—
22#22627613C2214yescomplemented
23C2×#17989779—22no—
24C2×C4×Dic293C2211yescharacteristic
25#22627534C2214yescomplemented
26C22×Q8×C293C2211yescharacteristic
27C22×D4×C293C2211yescharacteristic
28C2×SD16×C293—24no—
29C2×SD16×C293C2214yescomplemented
30C22×C8×C293C2211yescharacteristic
31C23×D293—21no—
32C23×D293—21no—
33C2×D1172—22no—
34C2×D1172—22no—
35C2×D1172—22no—
36C2×D1172—22no—
37C2×D1172—21no—
38C2×D1172—21no—
39C2×D1172C2312yes—
40C2×D1172C2312yes—
41C2×C22⋊D293—28no—
42C2×C22⋊D293—48no—
43C22×Dic293D412yes—
44#17989789—28no—
45D2344—28no—
46#17989787—28no—
47C2×#14556873D414yescomplemented
48C2×#14556873C2312yes—
49#17989779—28no—
50C4×Dic293D412yes—
51C4×Dic293C2312yes—
52C24×C293—21no—
53C2×Q8×C293—21no—
54C2×Q8×C293—22no—
55C2×Q8×C293—22no—
56C2×Q8×C293C2312yes—
57C2×D4×C293—22no—
58C2×D4×C293—22no—
59C2×D4×C293—21no—
60C2×D4×C293C2312yes—
61C22×C4×C293—21no—
62C22×C4×C293C2311yescharacteristic
63SD16×C293—28no—
64C2×C8×C293D414yescomplemented
65C2×C8×C293C2312yes—
66C22×D293—22no—
67C22×D293—22no—
68C22×D293—42no—
69C22×D293—42no—
70C22×D293—44no—
71C22×D293—44no—
72D1172—22no—
73D1172—22no—
74D1172—22no—
75D1172—22no—
76D1172—42no—
77D1172—42no—
78C22⋊D293—416no—
79C2×Dic293—24no—
80C2×Dic293C2×D414yes—
81#14556873C2×D414yescomplemented
82C23×C293—22no—
83C23×C293—42no—
84C23×C293—44no—
85C23×C293C2×D411yescharacteristic
86Q8×C293—22no—
87Q8×C293—22no—
88Q8×C293—42no—
89D4×C293—22no—
90D4×C293—22no—
91D4×C293—42no—
92C2×C4×C293—22no—
93C2×C4×C293—42no—
94C2×C4×C293C2×D411yescharacteristic
95C2×C4×C293C2×D412yes—
96C2×C4×C293C2×D412yes—
97C2×C4×C293C2411yescharacteristic
98C8×C293C2×D414yescomplemented
99C22×C293—42no—
100C22×C293—44no—
101C22×C293—84no—
102C22×C293#12712yes—
103C22×C293AGL(1,ℤ/8)14yes—
104C22×C293C22×D411yescharacteristic
105C2×D293—42no—
106C2×D293—42no—
107C2×D293—44no—
108C2×D293—44no—
109C2×D293—84no—
110C2×D293—84no—
111C4×C293—42no—
112C4×C293#12712yes—
113C4×C293C22×D411yescharacteristic
114C4×C293C22×D411yescharacteristic
115Dic293—24no—
116C2×C293—82no—
117C2×C293#49614yescomplemented
118C2×C293C2×#12711yescharacteristic
119C2×C293C2×AGL(1,ℤ/8)12yes—
120D293—82no—
121D293—82no—
122C293C2×#49611yescharacteristic, complemented, Sylow
123C2×#496—2931nomaximal, Sylow
124C22×SD16—2931no—
125C22×SD16D29311yescharacteristic, complemented
126C22×D8—2931no—
127C22×D8—2931no—
128C2×#127—2931no—
129C2×#124—2931no—
130#496—2938no—
131C2×#97—2931no—
132C22×Q8C2×D29311yescharacteristic
133C22×D4—2931no—
134C22×D4—2931no—
135C22×D4—5862no—
136C22×D4C2×D29311yescharacteristic
137C2×SD16—24no—
138C2×SD16—2934no—
139C2×SD16—5864no—
140C2×SD16C2×D29314yescomplemented
141C2×D8—2934no—
142C2×D8—2934no—
143C2×D8—5864no—
144C2×D8—5864no—
145C22×C8—2931no—
146C22×C8C2×D29311yescharacteristic
147#127—2934no—
148#127—5862no—
149#124—2934no—
150#124—5862no—
151C2×C22⋊C4—5862no—
152C2×C42—2931no—
153#97—2934no—
154C24—21no—
155C24—5861no—
156C24—5861no—
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D29312yes—
161C2×D4—22no—
162C2×D4—21no—
163C2×D4—22no—
164C2×D4—2932no—
165C2×D4—2932no—
166C2×D4—5868no—
167C2×D4—5862no—
168C2×D4—5862no—
169C2×D4—5861no—
170C2×D4—5861no—
171C2×D4—5862no—
172C2×D4—5862no—
173C2×D4—11728no—
174C2×D4C22×D29312yes—
175C22×C4—21no—
176C22×C4—2932no—
177C22×C4C22×D29311yescharacteristic
178SD16—28no—
179SD16—5868no—
180D8—5868no—
181D8—5868no—
182C2×C8—2934no—
183C2×C8—2932no—
184C2×C8C22⋊D29314yescomplemented
185C2×C8C22×D29312yes—
186C22⋊C4—5868no—
187C42—2932no—
188C42—2932no—
189C23—22no—
190C23—42no—
191C23—44no—
192C23—5862no—
193C23—5862no—
194C23—11722no—
195C23—11722no—
196C23—11724no—
197C23—11724no—
198C23D4×D29311yescharacteristic
199Q8—22no—
200Q8—22no—
201Q8—42no—
202D4—22no—
203D4—22no—
204D4—42no—
205D4—5862no—
206D4—5862no—
207D4—5862no—
208D4—5862no—
209D4—117216no—
210D4—11722no—
211D4—11722no—
212C2×C4—22no—
213C2×C4—42no—
214C2×C4—2934no—
215C2×C4—5864no—
216C2×C4D4×D29311yescharacteristic
217C2×C4D4×D29312yes—
218C2×C4C2×C22⋊D29312yes—
219C2×C4C23×D29311yescharacteristic
220C8—2934no—
221C8C2×C22⋊D29314yescomplemented
222C22—44no—
223C22—42no—
224C22—84no—
225C22—23444no—
226C22—23444no—
227C22—11724no—
228C22—11724no—
229C22—11722no—
230C22—11722no—
231C22#2262762012yes—
232C22#2262765114yes—
233C22C2×D4×D29311yescharacteristic
234C4—42no—
235C4—5864no—
236C4#2262762012yes—
237C4C2×D4×D29311yescharacteristic
238C4C22×C22⋊D29311yescharacteristic
239C2—82no—
240C2—23442no—
241C2—23442no—
242C2#3403651514yesdirect product factor
243C2C2×#2262762011yescharacteristic
244C2C2×#2262765112yes—
subgroupG/H
centerC23D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC22×SD16×C293C2
socleC23×C293C2×D4
hypercenterC22×SD16D293
hypocenterC293C2×#496
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×#17989789C2semidirect
2. C22×D2344C2semidirect
3. C22×#17989787C2semidirect
4. C2×#22627620C2semidirect
5. C2×#22627613C2semidirect
6. #34036515C2direct (N × H)
7. C2×#22627534C2semidirect
8. C22×SD16×C293C2semidirect
13. C2×#17989789C22semidirect
15. C2×D2344C22semidirect
17. C2×#17989787C22semidirect
20. #22627620C22semidirect
22. #22627613C22semidirect
25. #22627534C22semidirect
29. C2×SD16×C293C22semidirect
47. C2×#14556873D4semidirect
64. C2×C8×C293D4semidirect
81. #14556873C2×D4semidirect
98. C8×C293C2×D4semidirect
117. C2×C293#496semidirect
122. C293C2×#496semidirect
125. C22×SD16D293semidirect
140. C2×SD16C2×D293semidirect
184. C2×C8C22⋊D293semidirect
221. C8C2×C22⋊D293semidirect
242. C2#34036515direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#179897892
C22×D23442
C22×#179897872
C2×#226276202
C2×#226276132
#340365152
C2×#226275342
C22×SD16×C2932
C2×#496293