Finite Group Databasebeta

← C2×#23749940 #34054564

Subgroups — C2×#23749940 #34054564

Order 19072.

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

normal subgroups only

This group has 512 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×#18011886C211yesmaximal, characteristic
2C2×C4⋊C4×D149C211yesmaximal, characteristic, complemented
3#23749940C218yesmaximal, direct product factor
4C2×#18011844C211yesmaximal, characteristic, complemented
5C2×#18011833C211yesmaximal, characteristic, complemented
6C2×#18011831C211yesmaximal, characteristic, complemented
7C2×#18011823C211yesmaximal, characteristic, complemented
8C2×#107×C149C211yesmaximal, characteristic, complemented
9C22×D596—21no—
10C22×D596C2211yescharacteristic
11C22×C4×D149—21no—
12C22×C4×D149C2211yescharacteristic
13C22×#11924746C2211yescharacteristic
14#18011886—22no—
15#18011886C2214yes—
16C2×C4⋊Dic149C2211yescharacteristic
17C2×#14558715—21no—
18C4⋊C4×D149—22no—
19C4⋊C4×D149C2214yescomplemented
20C2×#14558713—21no—
21#18011844C2214yescomplemented
22#18011833C2214yescomplemented
23#18011831C2214yescomplemented
24#18011823C2214yescomplemented
25C22×C8×C149C2211yescharacteristic
26C2×C4⋊C4×C149C2211yescharacteristic
27C2×C4⋊C4×C149C2211yescharacteristic
28#107×C149C2214yescomplemented
29C23×D149—21no—
30C23×D149D411yescharacteristic
31C2×D596—24no—
32C2×D596—21no—
33C2×D596—22no—
34C2×D596—22no—
35C2×D596—44no—
36C2×D596C2312yes—
37C22×Dic149—21no—
38C22×Dic149D411yescharacteristic
39C2×C4×D149—24no—
40C2×C4×D149—22no—
41C2×C4×D149—22no—
42C2×C4×D149—44no—
43C2×C4×D149D412yes—
44C2×C4×D149C2312yes—
45C2×#11924746—22no—
46C2×#11924746C2312yes—
47C4⋊Dic149—21no—
48C4⋊Dic149C2312yes—
49#14558715—24no—
50#14558713—24no—
51C22×C4×C149—21no—
52C22×C4×C149—21no—
53C22×C4×C149C2311yescharacteristic
54C2×C8×C149—22no—
55C2×C8×C149C2312yes—
56C4⋊C4×C149—21no—
57C4⋊C4×C149—21no—
58C4⋊C4×C149C2312yes—
59C4⋊C4×C149C2312yes—
60C22×D149—22no—
61C22×D149—22no—
62C22×D149—22no—
63C22×D149—42no—
64C22×D149—42no—
65C22×D149—42no—
66C22×D149D814yes—
67C22×D149C2×D412yes—
68D596—22no—
69D596—22no—
70D596—48no—
71D596—42no—
72C2×Dic149—22no—
73C2×Dic149—22no—
74C2×Dic149—42no—
75C2×Dic149C2×D412yes—
76C4×D149—24no—
77C4×D149—22no—
78C4×D149—22no—
79C4×D149—48no—
80#11924746—22no—
81C23×C149C2×D411yescharacteristic
82C2×C4×C149—22no—
83C2×C4×C149—22no—
84C2×C4×C149—42no—
85C2×C4×C149—42no—
86C2×C4×C149C2×D411yescharacteristic
87C2×C4×C149#4112yes—
88C2×C4×C149#4112yes—
89C2×C4×C149C2411yescharacteristic
90C8×C149—22no—
91C22×C149#12312yes—
92C22×C149C2×D812yes—
93C22×C149#13712yes—
94C22×C149C22×D411yescharacteristic
95C2×D149—22no—
96C2×D149—22no—
97C2×D149—28no—
98C2×D149—42no—
99C2×D149—42no—
100C2×D149—42no—
101C2×D149—84no—
102C2×D149C2×D814yes—
103C4×C149—42no—
104C4×C149—42no—
105C4×C149#12312yes—
106C4×C149C2×#4111yescharacteristic
107C4×C149C2×#4111yescharacteristic
108Dic149—22no—
109Dic149—42no—
110C2×C149#48014yescomplemented
111C2×C149C2×#12311yescharacteristic
112C2×C149C22×D811yescharacteristic
113C2×C149C2×#13711yescharacteristic
114D149—24no—
115D149—82no—
116C149C2×#48011yescharacteristic, complemented, Sylow
117C2×#480—1491nomaximal, Sylow
118C2×#121—1491no—
119C22×C4⋊C4—1491no—
120#480—1498no—
121C2×#107—1491no—
122C2×#107D14911yescharacteristic, complemented
123C2×#102—1491no—
124C2×#102—1491no—
125C2×C22⋊C8—1491no—
126C22×D4—2981no—
127C22×D4—1491no—
128C23×C4—2981no—
129C23×C4—1491no—
130C22×C8—1491no—
131C22×C8C2×D14911yescharacteristic
132#121—2982no—
133#121—1494no—
134C2×C4⋊C4—2982no—
135C2×C4⋊C4—2981no—
136C2×C4⋊C4—1491no—
137C2×C4⋊C4—1494no—
138C2×C4⋊C4C2×D14911yescharacteristic
139C2×C4⋊C4C2×D14911yescharacteristic
140C2×C22⋊C4—2981no—
141#107—1494no—
142#107C2×D14914yescomplemented
143#102—1494no—
144#102—1494no—
145C22⋊C8—1494no—
146C24—2981no—
147C24—1491no—
148C2×D4—2984no—
149C2×D4—2981no—
150C2×D4—2982no—
151C2×D4—2982no—
152C2×D4—5964no—
153C2×D4—1492no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—2984no—
157C22×C4—2982no—
158C22×C4—2982no—
159C22×C4—2981no—
160C22×C4—5964no—
161C22×C4—1491no—
162C22×C4—1492no—
163C22×C4—1492no—
164C22×C4C22×D14911yescharacteristic
165C2×C8—22no—
166C2×C8—2982no—
167C2×C8—1492no—
168C2×C8C22×D14912yes—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—2984no—
172C4⋊C4—2981no—
173C4⋊C4—1492no—
174C4⋊C4C22×D14912yes—
175C4⋊C4C22×D14912yes—
176C22⋊C4—2984no—
177C23—2982no—
178C23—2982no—
179C23—2982no—
180C23—5962no—
181C23—5962no—
182C23—5962no—
183C23—1494no—
184C23—1492no—
185C23D4×D14911yescharacteristic
186D4—2982no—
187D4—2982no—
188D4—5968no—
189D4—5962no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—2982no—
195C2×C4—2982no—
196C2×C4—2982no—
197C2×C4—2984no—
198C2×C4—2982no—
199C2×C4—5968no—
200C2×C4—5962no—
201C2×C4—1492no—
202C2×C4D4×D14911yescharacteristic
203C2×C4#1455873612yes—
204C2×C4#1455873712yes—
205C2×C4C23×D14911yescharacteristic
206C8—22no—
207C8—2982no—
208C22—2982no—
209C22—2988no—
210C22—2982no—
211C22—5962no—
212C22—5962no—
213C22—5962no—
214C22—1494no—
215C22—11924no—
216C22#1801189612yes—
217C22D8×D14912yes—
218C22#1801194312yes—
219C22C2×D4×D14911yescharacteristic
220C4—42no—
221C4—42no—
222C4—2982no—
223C4—5962no—
224C4#1801189612yes—
225C4C2×#1455873611yescharacteristic
226C4C2×#1455873711yescharacteristic
227C2—2984no—
228C2—11922no—
229C2#2374994014yesdirect product factor
230C2C2×#1801189611yescharacteristic
231C2C2×D8×D14911yescharacteristic
232C2C2×#1801194311yescharacteristic
subgroupG/H
centerC23D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#107×C149C2
socleC23×C149C2×D4
prime radicalC2×#18011886C2
hypercenterC2×#107D149
hypocenterC149C2×#480
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D149C2semidirect
3. #23749940C2direct (N × H)
4. C2×#18011844C2semidirect
5. C2×#18011833C2semidirect
6. C2×#18011831C2semidirect
7. C2×#18011823C2semidirect
8. C2×#107×C149C2semidirect
19. C4⋊C4×D149C22semidirect
21. #18011844C22semidirect
22. #18011833C22semidirect
23. #18011831C22semidirect
24. #18011823C22semidirect
28. #107×C149C22semidirect
110. C2×C149#480semidirect
116. C149C2×#480semidirect
122. C2×#107D149semidirect
142. #107C2×D149semidirect
229. C2#23749940direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#180118862
C2×C4⋊C4×D1492
#237499402
C2×#180118442
C2×#180118332
C2×#180118312
C2×#180118232
C2×#107×C1492
C2×#480149