Finite Group Databasebeta

← #34055462

Subgroups — #34055462

Order 19072.

416 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 121 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⋊Q8×D149C212yesmaximal
2#23749962C212yesmaximal, complemented
3#23749959C212yesmaximal, complemented
4#23749866C211yesmaximal, characteristic, complemented
5#23749864C212yesmaximal, complemented
6#23749782C212yesmaximal, complemented
7#23749779C212yesmaximal, complemented
8C2×#18011823C211yesmaximal, characteristic
9#467×C149C211yesmaximal, characteristic, complemented
10C2×Q8×D149C2212yes—
11C22×C4×D149C2211yescharacteristic
12C2×Dic596C2211yescharacteristic, complemented
13C2×#14558726C2212yescomplemented
14C22×#11924746C2211yescharacteristic
15#18011891C2212yes—
16#18011890C2212yes—
17#18011889—22no—
18#18011888—22no—
19#18011887C2212yes—
20C4⋊C4×D149—22no—
21C4⋊C4×D149C2212yes—
22C22⋊C4×D149—22no—
23#18011845C2211yescharacteristic, complemented
24#18011844C2212yescomplemented
25#18011836C2212yescomplemented
26#18011835C2212yescomplemented
27#18011834C2212yescomplemented
28#18011823C2212yes—
29#18011823C2212yes—
30C2×Q16×C149C2211yescharacteristic, complemented
31C22×C8×C149C2211yescharacteristic
32C22⋊Q8×C149C2212yes—
33#107×C149C2211yescharacteristic, complemented
34#103×C149C2212yescomplemented
35C23×D149D411yescharacteristic
36C2×Dic298—22no—
37C2×Dic298C2312yes—
38Q8×D149—42no—
39Q8×D149—42no—
40C22×Dic149D411yescharacteristic
41C2×C4×D149—22no—
42C2×C4×D149—22no—
43C2×C4×D149—41no—
44C2×C4×D149—41no—
45C2×C4×D149D412yes—
46C2×C4×D149C2312yes—
47Dic596—41no—
48#14558726—42no—
49C2×#11924746—41no—
50C2×#11924746C2312yes—
51C4⋊Dic149—22no—
52C4⋊Dic149C2312yes—
53#14558715—22no—
54#14558715—22no—
55#14558715—22no—
56C22⋊Dic149—22no—
57#14558713—22no—
58#14558713—22no—
59C2×Q8×C149C2312yes—
60C22×C4×C149C2311yescharacteristic
61Q16×C149—41no—
62C2×C8×C149—41no—
63C2×C8×C149C2311yescharacteristic
64C2×C8×C149C2311yescharacteristic
65C4⋊C4×C149—22no—
66C4⋊C4×C149C2312yes—
67C22⋊C4×C149—22no—
68C22×D149—41no—
69C22×D149—41no—
70C22×D149Q1614yescomplemented
71C22×D149C2×D412yes—
72Dic298—22no—
73Dic298—22no—
74Dic298—44no—
75C2×Dic149—22no—
76C2×Dic149—22no—
77C2×Dic149—41no—
78C2×Dic149C2×D412yes—
79C4×D149—22no—
80C4×D149—22no—
81C4×D149—42no—
82C4×D149—44no—
83C4×D149—44no—
84#11924746—22no—
85C23×C149C2×D411yescharacteristic
86Q8×C149—22no—
87Q8×C149—22no—
88C2×C4×C149—21no—
89C2×C4×C149—21no—
90C2×C4×C149—22no—
91C2×C4×C149—22no—
92C2×C4×C149C2×D411yescharacteristic
93C2×C4×C149C2411yescharacteristic
94C8×C149—21no—
95C8×C149—21no—
96C22×C149—21no—
97C22×C149—21no—
98C22×C149C2×Q1612yes—
99C22×C149C22×D411yescharacteristic
100C2×D149—22no—
101C2×D149—22no—
102C2×D149—44no—
103C2×D149C2×Q1614yes—
104C4×C149—21no—
105C4×C149—42no—
106C4×C149—42no—
107C4×C149H(5,𝔽2)11yescharacteristic
108C4×C149H(5,𝔽2)11yescharacteristic
109Dic149—22no—
110Dic149—42no—
111Dic149—42no—
112C2×C149—22no—
113C2×C149#53411yescharacteristic
114C2×C149C22×Q1611yescharacteristic
115C2×C149#57511yescharacteristic
116D149—24no—
117C149#318911yescharacteristic, complemented, Sylow
118#3189—1491nomaximal, Sylow
119C2×C22⋊Q8—1492no—
120#484—1492no—
121#484—1492no—
122#467—1491no—
123#467—1492no—
124#467D14911yescharacteristic, complemented
125#451—1492no—
126#451—1492no—
127C2×C22⋊C8—1491no—
128C22×Q8—1492no—
129C23×C4—1491no—
130C2×Q16—1492no—
131C2×Q16—1491no—
132C2×Q16C2×D14911yescharacteristic, complemented
133C22×C8—1491no—
134C22×C8C2×D14911yescharacteristic
135C22⋊Q8—2982no—
136C22⋊Q8—2982no—
137C22⋊Q8—1492no—
138C22⋊Q8—1492no—
139C22⋊Q8—1492no—
140C22⋊Q8C2×D14912yes—
141C2×C4⋊C4—2982no—
142C2×C4⋊C4—1492no—
143C2×C22⋊C4—2982no—
144#107—1491no—
145#107—1492no—
146#107C2×D14911yescharacteristic, complemented
147#103—1492no—
148#103—1492no—
149#103—1492no—
150#103C2×D14912yescomplemented
151C22⋊C8—1492no—
152C22⋊C8—1492no—
153C24—1491no—
154C2×Q8—2982no—
155C2×Q8—5962no—
156C2×Q8—5962no—
157C2×Q8—1492no—
158C2×Q8C22×D14912yes—
159C22×C4—2982no—
160C22×C4—2982no—
161C22×C4—5961no—
162C22×C4—5961no—
163C22×C4—1492no—
164C22×C4—1491no—
165C22×C4—1492no—
166C22×C4C22×D14911yescharacteristic
167Q16—41no—
168Q16—5961no—
169Q16—5962no—
170C2×C8—41no—
171C2×C8—5961no—
172C2×C8—1492no—
173C2×C8C22×D14911yescharacteristic
174C2×C8C22×D14911yescharacteristic
175C4⋊C4—22no—
176C4⋊C4—2982no—
177C4⋊C4—2982no—
178C4⋊C4—2982no—
179C4⋊C4—2982no—
180C4⋊C4—1492no—
181C4⋊C4C22×D14912yes—
182C22⋊C4—22no—
183C22⋊C4—2982no—
184C22⋊C4—2982no—
185C22⋊C4—2982no—
186C23—5961no—
187C23—5961no—
188C23—1492no—
189C23—1494no—
190C23D4×D14911yescharacteristic
191Q8—22no—
192Q8—22no—
193Q8—2982no—
194Q8—2982no—
195Q8—5964no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—2982no—
201C2×C4—2982no—
202C2×C4—2982no—
203C2×C4—2982no—
204C2×C4—5962no—
205C2×C4—5964no—
206C2×C4—5964no—
207C2×C4—5961no—
208C2×C4—1492no—
209C2×C4D4×D14911yescharacteristic
210C2×C4C23×D14911yescharacteristic
211C8—21no—
212C8—21no—
213C8—2982no—
214C22—21no—
215C22—21no—
216C22—2982no—
217C22—2982no—
218C22—5964no—
219C22—1494no—
220C22Q16×D14912yes—
221C22C2×D4×D14911yescharacteristic
222C4—21no—
223C4—42no—
224C4—42no—
225C4—2982no—
226C4—5962no—
227C4—5962no—
228C4#1801195611yescharacteristic
229C4#1801195711yescharacteristic
230C2—22no—
231C2—2984no—
232C2#2375018311yescharacteristic
233C2C2×Q16×D14911yescharacteristic
234C2#2375042211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#467×C149C2
socleC22×C149C22×D4
prime radicalC23×D149D4
hypercenter#467D149
hypocenterC149#3189
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #23749962C2semidirect
3. #23749959C2semidirect
4. #23749866C2semidirect
5. #23749864C2semidirect
6. #23749782C2semidirect
7. #23749779C2semidirect
9. #467×C149C2semidirect
12. C2×Dic596C22semidirect
13. C2×#14558726C22semidirect
23. #18011845C22semidirect
24. #18011844C22semidirect
25. #18011836C22semidirect
26. #18011835C22semidirect
27. #18011834C22semidirect
30. C2×Q16×C149C22semidirect
33. #107×C149C22semidirect
34. #103×C149C22semidirect
70. C22×D149Q16semidirect
117. C149#3189semidirect
124. #467D149semidirect
132. C2×Q16C2×D149semidirect
146. #107C2×D149semidirect
150. #103C2×D149semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D1492
#237499622
#237499592
#237498662
#237498642
#237497822
#237497792
C2×#180118232
#467×C1492
#3189149