Finite Group Databasebeta

← C2×#23752387 #34078448

Subgroups — C2×#23752387 #34078448

Order 19328.

728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 728 conjugacy classes of subgroups — too many to draw. Only its 149 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×#18012787C211yesmaximal, characteristic, complemented
2C2×#18012767C212yesmaximal, complemented
3C2×#18012728C211yesmaximal, characteristic, complemented
4#23752387C218yesmaximal, direct product factor
5C2×#18012665C212yesmaximal, complemented
6C2×#101×C151C211yesmaximal, characteristic, complemented
7#18012787—24no—
8#18012787—22no—
9#18012787C2214yescomplemented
10C2×#14559005—22no—
11C2×#14559004—22no—
12C2×#14559004C2212yes—
13C2×Q8×D151—22no—
14C22×D604C2211yescharacteristic
15#18012767—24no—
16#18012767C2218yescomplemented
17C2×#14558993—22no—
18C2×D1208—22no—
19#18012728—22no—
20#18012728C2214yescomplemented
21C2×(C2×D151)⋊C4—22no—
22C2×C4×Dic151C2211yescharacteristic
23#18012665C2218yescomplemented
24C22×Q8×C151C2211yescharacteristic
25C2×M16×C151C2212yes—
26#101×C151C2214yescomplemented
27C23×D151—21no—
28#14559005—28no—
29#14559005—28no—
30#14559004—28no—
31#14559004—28no—
32#14559004—22no—
33#14559004—22no—
34#14559004D414yes—
35#14559004C2314yes—
36C2×Dic302—22no—
37C2×Dic302D412yes—
38Q8×D151—28no—
39Q8×D151—28no—
40C2×D604—22no—
41C2×D604—22no—
42C2×D604—22no—
43C2×D604—21no—
44C2×D604D412yes—
45C2×D604C2312yes—
46C2×C22⋊D151—22no—
47C22×Dic151—21no—
48C2×C4×D151—24no—
49C2×C4×D151—22no—
50#14558993—28no—
51D1208—28no—
52(C2×D151)⋊C4—28no—
53C4×Dic151—21no—
54C4×Dic151C2312yes—
55C2×Q8×C151—22no—
56C2×Q8×C151—22no—
57C2×Q8×C151D412yes—
58C2×Q8×C151C2312yes—
59C22×C4×C151D412yes—
60C22×C4×C151C2311yescharacteristic
61M16×C151—22no—
62M16×C151C2314yes—
63C2×C8×C151—22no—
64C22×D151—22no—
65C22×D151—22no—
66C22×D151—44no—
67C22×D151—41no—
68C22×D151—41no—
69Dic302—28no—
70Dic302—22no—
71Dic302C2×D414yes—
72D604—28no—
73D604—22no—
74D604—24no—
75D604—42no—
76D604C2×D414yes—
77C22⋊D151—24no—
78C22⋊D151—24no—
79C2×Dic151—22no—
80C2×Dic151—22no—
81C2×Dic151—42no—
82C4×D151—216no—
83C4×D151—24no—
84C4×D151—24no—
85C23×C151C2×D411yescharacteristic
86Q8×C151—24no—
87Q8×C151—24no—
88C2×C4×C151—22no—
89C2×C4×C151—22no—
90C2×C4×C151C2×D412yes—
91C2×C4×C151C2×D412yes—
92C2×C4×C151C2×D414yes—
93C2×C4×C151C2×D411yescharacteristic
94C2×C4×C151C2411yescharacteristic
95C8×C151—24no—
96C22×C151—22no—
97C22×C151#12011yescharacteristic
98C22×C151#12011yescharacteristic
99C22×C151C22×D411yescharacteristic
100C2×D151—24no—
101C2×D151—44no—
102C2×D151—44no—
103C2×D151—42no—
104C2×D151—82no—
105C2×D151—82no—
106C4×C151—24no—
107C4×C151#12012yes—
108C4×C151C22×D412yes—
109Dic151—24no—
110Dic151—42no—
111C2×C151—21no—
112C2×C151—21no—
113C2×C151#45412yescomplemented
114C2×C151C2×#12011yescharacteristic
115D151—44no—
116D151—82no—
117C151C2×#45411yescharacteristic, complemented, Sylow
118C2×#454—1511nomaximal, Sylow
119C2×2−1+4—1511no—
120C2×AGL(1,ℤ/8)—1512no—
121C2×#124—1511no—
122#454—1518no—
123C2×#104—1512no—
124C2×#101D15111yescharacteristic, complemented
1252−1+4—3024no—
1262−1+4—3022no—
1272−1+4—1514no—
128C2×#41—3022no—
129C2×#41—3022no—
130C2×#41—1512no—
131C22×Q8—3022no—
132C22×Q8C2×D15111yescharacteristic
133C22×D4—1511no—
134AGL(1,ℤ/8)—3024no—
135AGL(1,ℤ/8)—1518no—
136C2×SD16—3022no—
137C2×D8—3022no—
138C2×M16C2×D15112yes—
139#124—3022no—
140#124—1514no—
141C2×C22⋊C4—3022no—
142C2×C42—1511no—
143#104—1518no—
144#101C2×D15114yescomplemented
145C24—3021no—
146#41—3028no—
147#41—3028no—
148#41—3028no—
149#41—3022no—
150#41—3028no—
151#41—3022no—
152#41—1514no—
153#41—1514no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—3022no—
157C2×Q8—3028no—
158C2×Q8—3028no—
159C2×Q8—1512no—
160C2×Q8D60412yes—
161C2×Q8C22×D15112yes—
162C2×D4—3022no—
163C2×D4—3022no—
164C2×D4—3022no—
165C2×D4—3022no—
166C2×D4—3021no—
167C2×D4—1512no—
168C2×D4—1512no—
169C22×C4—3024no—
170C22×C4—3022no—
171C22×C4—3021no—
172C22×C4D60412yes—
173C22×C4C22×D15111yescharacteristic
174SD16—3028no—
175D8—3028no—
176M16—22no—
177M16C22×D15114yes—
178C2×C8—22no—
179C22⋊C4—3028no—
180C42—3021no—
181C42—1512no—
182C23—3022no—
183C23—3022no—
184C23—6044no—
185C23—6041no—
186C23—6041no—
187C23C2×D60411yescharacteristic
188Q8—24no—
189Q8—24no—
190Q8—3028no—
191Q8—3022no—
192Q8—1514no—
193D4—3028no—
194D4—3024no—
195D4—3024no—
196D4—3022no—
197D4—3024no—
198D4—6042no—
199D4—1514no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—30216no—
203C2×C4—3022no—
204C2×C4—3024no—
205C2×C4—3024no—
206C2×C4—3022no—
207C2×C4—6042no—
208C2×C4D4×D15112yes—
209C2×C4D4×D15112yes—
210C2×C4C2×D60414yes—
211C2×C4C2×D60411yescharacteristic
212C2×C4C23×D15111yescharacteristic
213C8—24no—
214C22—22no—
215C22—3024no—
216C22—6044no—
217C22—6044no—
218C22—6042no—
219C22—12082no—
220C22—12082no—
221C22#1801270911yescharacteristic
222C22#1801270911yescharacteristic
223C22C22×D60411yescharacteristic
224C4—24no—
225C4—3024no—
226C4—6042no—
227C4#1801270912yes—
228C4C2×D4×D15112yes—
229C2—21no—
230C2—21no—
231C2—6044no—
232C2—12082no—
233C2#2375238712yesdirect product factor
234C2C2×#1801270911yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×#101×C151C2
socleC22×C151#120
hypercenterC2×#101D151
hypocenterC151C2×#454
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
1. C2×#18012787C2semidirect
2. C2×#18012767C2semidirect
3. C2×#18012728C2semidirect
4. #23752387C2direct (N × H)
5. C2×#18012665C2semidirect
6. C2×#101×C151C2semidirect
9. #18012787C22semidirect
16. #18012767C22semidirect
20. #18012728C22semidirect
23. #18012665C22semidirect
26. #101×C151C22semidirect
113. C2×C151#454semidirect
117. C151C2×#454semidirect
124. C2×#101D151semidirect
144. #101C2×D151semidirect
233. C2#23752387direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#180127872
C2×#180127672
C2×#180127282
#237523872
C2×#180126652
C2×#101×C1512
C2×#454151