Finite Group Databasebeta

← C2×#23752394 #34078451

Subgroups — C2×#23752394 #34078451

Order 19328.

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

normal subgroups only

This group has 708 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
2C2×#18012770C212yesmaximal, complemented
3#23752394C218yesmaximal, direct product factor
4C2×#18012667C212yesmaximal, complemented
5C2×#18012658C211yesmaximal, characteristic, complemented
6C2×C4⋊Q8×C151C211yesmaximal, characteristic, complemented
7#18012787—24no—
8#18012787—22no—
9#18012787C2214yes—
10C2×#14559005—22no—
11C2×#14559004—22no—
12C2×#14559004C2212yes—
13C2×Q8×D151—22no—
14#18012770—24no—
15#18012770C2218yescomplemented
16C2×#14558994—22no—
17C2×#14558991—22no—
18C2×#14558988C2212yes—
19#18012667C2218yescomplemented
20#18012658C2214yescomplemented
21C22×Q8×C151C2211yescharacteristic
22C22×Q8×C151C2211yescharacteristic
23C4⋊Q8×C151—22no—
24C4⋊Q8×C151C2214yescomplemented
25C2×C4⋊C4×C151—22no—
26C2×C42×C151C2211yescharacteristic
27#14559005—28no—
28#14559005—28no—
29#14559004—28no—
30#14559004—28no—
31#14559004—22no—
32#14559004—22no—
33#14559004D414yes—
34#14559004C2314yes—
35C2×Dic302—22no—
36C2×Dic302D412yes—
37Q8×D151—28no—
38Q8×D151—28no—
39C2×D604—22no—
40C2×D604D412yes—
41C2×C22⋊D151—22no—
42C2×C4×D151—24no—
43C2×C4×D151—22no—
44#14558994—28no—
45#14558991—28no—
46#14558988—22no—
47#14558988C2314yes—
48C2×C151⋊C8—22no—
49C2×Q8×C151—22no—
50C2×Q8×C151—22no—
51C2×Q8×C151—21no—
52C2×Q8×C151—22no—
53C2×Q8×C151—22no—
54C2×Q8×C151D412yes—
55C2×Q8×C151C2312yes—
56C2×Q8×C151C2312yes—
57C22×C4×C151—21no—
58C22×C4×C151—21no—
59C22×C4×C151D412yes—
60C22×C4×C151C2311yescharacteristic
61C4⋊C4×C151—28no—
62C42×C151—21no—
63C42×C151C2312yes—
64C22×D151—22no—
65Dic302—28no—
66Dic302—22no—
67Dic302C2×D414yes—
68D604—28no—
69D604—22no—
70D604C2×D414yes—
71C22⋊D151—24no—
72C22⋊D151—24no—
73C2×Dic151—22no—
74C4×D151—216no—
75C4×D151—24no—
76C4×D151—24no—
77C151⋊C8—24no—
78C23×C151C2×D411yescharacteristic
79Q8×C151—24no—
80Q8×C151—24no—
81Q8×C151—24no—
82Q8×C151—42no—
83C2×C4×C151—24no—
84C2×C4×C151—22no—
85C2×C4×C151—22no—
86C2×C4×C151—22no—
87C2×C4×C151—22no—
88C2×C4×C151—41no—
89C2×C4×C151—41no—
90C2×C4×C151C2×D412yes—
91C2×C4×C151C2×D412yes—
92C2×C4×C151C2×D414yes—
93C2×C4×C151C2×D411yescharacteristic
94C2×C4×C151C2411yescharacteristic
95C22×C151—22no—
96C22×C151#12011yescharacteristic
97C22×C151#12011yescharacteristic
98C22×C151C22×D411yescharacteristic
99C2×D151—24no—
100C2×D151—44no—
101C4×C151—24no—
102C4×C151—24no—
103C4×C151—42no—
104C4×C151#12012yes—
105C4×C151C22×D412yes—
106Dic151—24no—
107C2×C151—21no—
108C2×C151—21no—
109C2×C151#45612yescomplemented
110C2×C151C2×#12011yescharacteristic
111D151—44no—
112C151C2×#45611yescharacteristic, complemented, Sylow
113C2×#456—1511nomaximal, Sylow
114C2×2−1+4—1511no—
115C2×#137—1512no—
116C2×C4⋊Q8D15111yescharacteristic, complemented
117#456—1518no—
118C2×#104—1512no—
119C2×#101—1511no—
1202−1+4—3024no—
1212−1+4—3022no—
1222−1+4—1514no—
123C2×#41—3022no—
124C2×#41—3022no—
125C2×#41—1512no—
126C22×Q8—3022no—
127C22×Q8C2×D15111yescharacteristic
128C22×Q8C2×D15111yescharacteristic
129#137—3024no—
130#137—1518no—
131C2×Q16—3022no—
132C2×SD16—3022no—
133C2×M16—1512no—
134C4⋊Q8—22no—
135C4⋊Q8C2×D15114yescomplemented
136C2×C4⋊C4—22no—
137C2×C42C2×D15111yescharacteristic
138#104—1518no—
139#101—1514no—
140#41—3028no—
141#41—3028no—
142#41—3028no—
143#41—3022no—
144#41—3028no—
145#41—3022no—
146#41—1514no—
147#41—1514no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—21no—
151C2×Q8—22no—
152C2×Q8—22no—
153C2×Q8—3022no—
154C2×Q8—3028no—
155C2×Q8—3028no—
156C2×Q8—1512no—
157C2×Q8C22⋊D15112yes—
158C2×Q8C22×D15112yes—
159C2×Q8C22×D15112yes—
160C2×D4—3022no—
161C2×D4—3022no—
162C2×D4—1512no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—3024no—
166C22×C4—3022no—
167C22×C4C22⋊D15112yes—
168C22×C4C22×D15111yescharacteristic
169Q16—3028no—
170SD16—3028no—
171M16—3022no—
172M16—1514no—
173C2×C8—3022no—
174C4⋊C4—28no—
175C42—21no—
176C42C22×D15112yes—
177C23—3022no—
178C23C2×C22⋊D15111yescharacteristic
179Q8—24no—
180Q8—24no—
181Q8—24no—
182Q8—42no—
183Q8—3028no—
184Q8—3022no—
185Q8—1514no—
186D4—3028no—
187D4—3024no—
188D4—3024no—
189D4—3022no—
190D4—1514no—
191C2×C4—24no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—30216no—
199C2×C4—3022no—
200C2×C4—3024no—
201C2×C4—3024no—
202C2×C4D4×D15112yes—
203C2×C4D4×D15112yes—
204C2×C4C2×C22⋊D15114yes—
205C2×C4C2×C22⋊D15111yescharacteristic
206C2×C4C23×D15111yescharacteristic
207C8—3024no—
208C22—22no—
209C22—3024no—
210C22—6044no—
211C22#1801270711yescharacteristic
212C22#1801270711yescharacteristic
213C22C22×C22⋊D15111yescharacteristic
214C4—24no—
215C4—24no—
216C4—42no—
217C4—3024no—
218C4#1801270712yes—
219C4C2×D4×D15112yes—
220C2—21no—
221C2—21no—
222C2—6044no—
223C2#2375239412yesdirect product factor
224C2C2×#1801270711yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×C4⋊Q8×C151C2
socleC22×C151#120
prime radicalC2×#18012787C2
hypercenterC2×C4⋊Q8D151
hypocenterC151C2×#456
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#18012770C2semidirect
3. #23752394C2direct (N × H)
4. C2×#18012667C2semidirect
5. C2×#18012658C2semidirect
6. C2×C4⋊Q8×C151C2semidirect
15. #18012770C22semidirect
19. #18012667C22semidirect
20. #18012658C22semidirect
24. C4⋊Q8×C151C22semidirect
109. C2×C151#456semidirect
112. C151C2×#456semidirect
116. C2×C4⋊Q8D151semidirect
135. C4⋊Q8C2×D151semidirect
223. C2#23752394direct (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×#180127702
#237523942
C2×#180126672
C2×#180126582
C2×C4⋊Q8×C1512
C2×#456151