Finite Group Databasebeta

← #34045868

Subgroups — #34045868

Order 19072.

278 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 65 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
1#23750251C211yesmaximal, characteristic, complemented
2C2×#18011826C211yesmaximal, characteristic
3C2×#18011826C211yesmaximal, characteristic
4#23749392C211yesmaximal, characteristic, complemented
5#23749391C211yesmaximal, characteristic, complemented
6#23749391C211yesmaximal, characteristic, complemented
7C2×#99×C149C211yesmaximal, characteristic
8#18011890—22no—
9#18011888—22no—
10#18011888—22no—
11C2×C22⋊Dic149C2211yescharacteristic
12C2×C22⋊Dic149C2211yescharacteristic
13C2×C22⋊Dic149C2211yescharacteristic
14C2×C22⋊Dic149C2211yescharacteristic
15#18011826—22no—
16#18011826—22no—
17C22×D4×C149C2211yescharacteristic
18C2×C22⋊C4×C149C2211yescharacteristic
19C2×C22⋊C4×C149C2211yescharacteristic
20#99×C149—22no—
21C2×Dic298—22no—
22C22×Dic149—21no—
23C22×Dic149—21no—
24C22×Dic149—21no—
25C22×Dic149—21no—
26C4⋊Dic149—22no—
27#14558715—24no—
28C22⋊Dic149—21no—
29C22⋊Dic149—21no—
30C22⋊Dic149—21no—
31C22⋊Dic149—21no—
32C22⋊Dic149—21no—
33C22⋊Dic149—21no—
34C22⋊Dic149D412yes—
35C22⋊Dic149D412yes—
36C24×C149Q811yescharacteristic, complemented
37C24×C149C2311yescharacteristic
38C2×D4×C149—21no—
39C2×D4×C149—21no—
40C2×D4×C149—21no—
41C2×D4×C149—21no—
42C2×D4×C149—21no—
43C2×D4×C149—21no—
44C22×C4×C149—21no—
45C22×C4×C149—21no—
46C22×C4×C149Q811yescharacteristic, complemented
47C22⋊C4×C149—21no—
48C22⋊C4×C149—21no—
49C22⋊C4×C149—21no—
50C22⋊C4×C149D412yes—
51Dic298—82no—
52C2×Dic149—22no—
53C2×Dic149—22no—
54C2×Dic149—41no—
55C2×Dic149—41no—
56C2×Dic149—81no—
57C2×Dic149—81no—
58C2×Dic149—81no—
59C2×Dic149—81no—
60C23×C149—21no—
61C23×C149—21no—
62C23×C149—21no—
63C23×C149—81no—
64C23×C149—81no—
65C23×C149C2×D411yescharacteristic
66C23×C149C2×D411yescharacteristic
67C23×C149C2×D411yescharacteristic
68C23×C149C2×Q811yescharacteristic
69C23×C149#4111yescharacteristic
70C23×C149#4111yescharacteristic
71C23×C149#4111yescharacteristic
72D4×C149—41no—
73D4×C149—41no—
74D4×C149—41no—
75D4×C149—41no—
76C2×C4×C149—22no—
77C2×C4×C149—21no—
78C2×C4×C149—21no—
79C2×C4×C149—21no—
80C2×C4×C149—41no—
81C2×C4×C149—81no—
82C2×C4×C149—81no—
83C22×C149—41no—
84C22×C149—41no—
85C22×C149—41no—
86C22×C149—41no—
87C22×C149—41no—
88C22×C149—41no—
89C22×C149—41no—
90C22×C149—41no—
91C22×C149—81no—
92C22×C149—81no—
93C22×C149—81no—
94C22×C149#12011yescharacteristic
95C22×C149C22⋊Q811yescharacteristic
96C22×C149C22⋊Q811yescharacteristic
97C22×C149C22⋊Q811yescharacteristic
98C22×C149#12411yescharacteristic
99C22×C149#12411yescharacteristic
100C22×C149#12411yescharacteristic
101C4×C149—42no—
102C4×C149—41no—
103C4×C149—81no—
104Dic149—42no—
105Dic149—42no—
106Dic149—81no—
107Dic149—81no—
108C2×C149—21no—
109C2×C149—21no—
110C2×C149—21no—
111C2×C149—21no—
112C2×C149—21no—
113C2×C149—21no—
114C2×C149—21no—
115C2×C149—81no—
116C2×C149#39311yescharacteristic
117C149#203211yescharacteristic, complemented, Sylow
118#2032—1491nomaximal, Sylow
119#543—1491no—
120C2×#99—1491no—
121C2×#99—1491no—
122C2×#99D14911yescharacteristic
123#342—1491no—
124#342—1491no—
125#342—1491no—
126C22×D4C2×D14911yescharacteristic
127C22⋊Q8—2982no—
128C22⋊Q8—2982no—
129C22⋊Q8—2982no—
130C2×C22⋊C4—1491no—
131C2×C22⋊C4—1491no—
132C2×C22⋊C4—1491no—
133C2×C22⋊C4—1491no—
134C2×C22⋊C4C2×D14911yescharacteristic
135C2×C22⋊C4C2×D14911yescharacteristic
136#99—22no—
137#99—2982no—
138#99—2982no—
139C24Dic29811yescharacteristic, complemented
140C24C22×D14911yescharacteristic
141C2×Q8—2982no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—2981no—
151C22×C4—2981no—
152C22×C4—2981no—
153C22×C4—2981no—
154C22×C4Dic29811yescharacteristic, complemented
155C4⋊C4—2984no—
156C4⋊C4—2982no—
157C22⋊C4—21no—
158C22⋊C4—21no—
159C22⋊C4—21no—
160C22⋊C4—2981no—
161C22⋊C4—2981no—
162C22⋊C4—2981no—
163C22⋊C4—2981no—
164C22⋊C4—2981no—
165C22⋊C4—2981no—
166C22⋊C4—1492no—
167C22⋊C4—1492no—
168C22⋊C4C22⋊D14912yes—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—81no—
173C23—81no—
174C23D4×D14911yescharacteristic
175C23D4×D14911yescharacteristic
176C23C2×C22⋊D14911yescharacteristic
177C23C2×Dic29811yescharacteristic
178C23#1455873511yescharacteristic
179C23#1455873511yescharacteristic
180C23#1455873611yescharacteristic
181Q8—11922no—
182D4—41no—
183D4—41no—
184D4—41no—
185D4—41no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—81no—
192C2×C4—81no—
193C2×C4—2982no—
194C2×C4—2982no—
195C2×C4—5961no—
196C2×C4—5961no—
197C2×C4—11921no—
198C2×C4—11921no—
199C2×C4—11921no—
200C2×C4—11921no—
201C22—41no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22—81no—
210C22—81no—
211C22—81no—
212C22#1801187911yescharacteristic
213C22#1801188811yescharacteristic
214C22#1801188811yescharacteristic
215C22#1801189011yescharacteristic
216C22#1801189711yescharacteristic
217C22#1801189711yescharacteristic
218C22#1801189811yescharacteristic
219C4—42no—
220C4—41no—
221C4—81no—
222C4—5962no—
223C4—5962no—
224C4—11921no—
225C4—11921no—
226C2—21no—
227C2—21no—
228C2—21no—
229C2—21no—
230C2—21no—
231C2—21no—
232C2—21no—
233C2—81no—
234C2#2374953711yescharacteristic
subgroupG/H
centerC2#23749537
commutator, cosocleC24×C149C23
FrattiniC24C22×D149
FittingC2×#99×C149C2
socleC2×C149#393
prime radicalC22×D4×C149C22
hypercenterC2×#99D149
hypocenterC149#2032
LCSG ▷ C24×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
1. #23750251C2semidirect
4. #23749392C2semidirect
5. #23749391C2semidirect
6. #23749391C2semidirect
36. C24×C149Q8semidirect
46. C22×C4×C149Q8semidirect
117. C149#2032semidirect
139. C24Dic298semidirect
154. C22×C4Dic298semidirect

Maximal subgroups

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

subgroupindex
#237502512
C2×#180118262
#237493922
#237493912
C2×#99×C1492
#2032149