Finite Group Databasebeta

← #34045742

Subgroups — #34045742

Order 19072.

380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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#23750423C211yesmaximal, characteristic, complemented
2#23750192C211yesmaximal, characteristic, complemented
3#23749641C211yesmaximal, characteristic, complemented
4#23749630C211yesmaximal, characteristic, complemented
5#23749599C211yesmaximal, characteristic, complemented
6#23749397C211yesmaximal, characteristic, complemented
7C2×AGL(1,ℤ/8)×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2211yescharacteristic
9#18011942—21no—
10#18011941—21no—
11#18011937—21no—
12#18011936—21no—
13#18011931—22no—
14C2×#14558720C2211yescharacteristic
15#18011907—21no—
16#18011898—21no—
17#18011882—22no—
18#18011880—22no—
19#18011870C2211yescharacteristic
20#18011870C2211yescharacteristic
21#18011837—22no—
22#18011832—22no—
23#18011826—22no—
24C2×#41×C149C2211yescharacteristic
25C22×D4×C149C2211yescharacteristic
26AGL(1,ℤ/8)×C149—22no—
27AGL(1,ℤ/8)×C149—22no—
28C2×SD16×C149—21no—
29C2×D8×C149—21no—
30C2×M16×C149C2211yescharacteristic
31#14558736—21no—
32#14558736—21no—
33#14558736—21no—
34#14558736—21no—
35C2×Dic298D411yescharacteristic
36C2×D596D411yescharacteristic
37C2×C22⋊D149—24no—
38C2×C22⋊D149—21no—
39C2×C4×D149—21no—
40#14558726—22no—
41#14558724—22no—
42#14558723—22no—
43#14558721—22no—
44#14558720—21no—
45#14558720—21no—
46C2×#11924746D412yescomplemented
47C4⋊Dic149—21no—
48C4⋊Dic149—21no—
49C22⋊Dic149—24no—
50C22⋊Dic149—21no—
51C22⋊Dic149D412yes—
52C4×Dic149—21no—
53C4×Dic149—21no—
54C24×C149—21no—
55#41×C149—21no—
56#41×C149—21no—
57#41×C149—21no—
58#41×C149—21no—
59C2×Q8×C149D411yescharacteristic, complemented
60C2×D4×C149—21no—
61C2×D4×C149—21no—
62C2×D4×C149—21no—
63C2×D4×C149—21no—
64C2×D4×C149—21no—
65C2×D4×C149—21no—
66C2×D4×C149D412yes—
67C2×D4×C149D411yescharacteristic, complemented
68C22×C4×C149—21no—
69C22×C4×C149C2311yescharacteristic
70SD16×C149—24no—
71D8×C149—24no—
72M16×C149—21no—
73M16×C149D412yescomplemented
74C2×C8×C149—21no—
75C22×D149—21no—
76Dic298—21no—
77Dic298—21no—
78D596—21no—
79D596—21no—
80C22⋊D149—41no—
81C22⋊D149—41no—
82C22⋊D149—84no—
83C2×Dic149—21no—
84C2×Dic149—22no—
85C2×Dic149—41no—
86C4×D149—41no—
87C4×D149—41no—
88#11924746—22no—
89C23×C149—22no—
90C23×C149—21no—
91C23×C149—41no—
92C23×C149—41no—
93C23×C149—82no—
94C23×C149C2×D411yescharacteristic
95Q8×C149—21no—
96Q8×C149—21no—
97D4×C149—21no—
98D4×C149—21no—
99D4×C149—22no—
100D4×C149—22no—
101D4×C149—41no—
102D4×C149—41no—
103D4×C149—41no—
104D4×C149—41no—
105C2×C4×C149—21no—
106C2×C4×C149—41no—
107C2×C4×C149—41no—
108C2×C4×C149C2×D411yescharacteristic
109C2×C4×C149C2×D411yescharacteristic
110C2×C4×C149C2×D411yescharacteristic
111C2×C4×C149C2×D411yescharacteristic
112C2×C4×C149C2×D411yescharacteristic
113C2×C4×C149#4111yescharacteristic
114C8×C149—22no—
115C22×C149—41no—
116C22×C149—44no—
117C22×C149—41no—
118C22×C149—42no—
119C22×C149—81no—
120C22×C149—82no—
121C22×C149—82no—
122C22×C149#12011yescharacteristic
123C22×C149#12111yescharacteristic
124C22×C149#12711yescharacteristic
125C2×D149—42no—
126C2×D149—41no—
127C4×C149—41no—
128C4×C149#12011yescharacteristic
129C4×C149#12011yescharacteristic
130C4×C149#12111yescharacteristic
131C4×C149#12111yescharacteristic
132Dic149—42no—
133Dic149—41no—
134Dic149—81no—
135C2×C149—21no—
136C2×C149—21no—
137C2×C149—21no—
138C2×C149—82no—
139C2×C149—81no—
140C2×C149#39211yescharacteristic
141D149—81no—
142C149#200811yescharacteristic, complemented, Sylow
143#2008—1491nomaximal, Sylow
144#575—1491no—
145C2×AGL(1,ℤ/8)D14911yescharacteristic, complemented
146#535—1491no—
147#421—1491no—
148#418—1491no—
149#410—1491no—
150#344—1491no—
151C2×#41—1491no—
152C2×#41C2×D14911yescharacteristic
153C22×D4C2×D14911yescharacteristic
154#137—2981no—
155#137—2981no—
156AGL(1,ℤ/8)—22no—
157AGL(1,ℤ/8)—22no—
158AGL(1,ℤ/8)—2981no—
159AGL(1,ℤ/8)—2981no—
160#135—2982no—
161C2×SD16—21no—
162C2×D8—21no—
163C2×M16—1491no—
164C2×M16C2×D14911yescharacteristic
165#127—2981no—
166#124—2981no—
167#121—2982no—
168#120—2982no—
169#117—1491no—
170#117—1491no—
171#104—2982no—
172#102—2982no—
173#99—2982no—
174C24—21no—
175#41—21no—
176#41—21no—
177#41—21no—
178#41—21no—
179#41—2981no—
180#41—2981no—
181#41—2981no—
182#41—2981no—
183C2×Q8—1491no—
184C2×Q8C22⋊D14911yescharacteristic, complemented
185C2×D4—21no—
186C2×D4—21no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—21no—
190C2×D4—21no—
191C2×D4—2981no—
192C2×D4—2984no—
193C2×D4—1491no—
194C2×D4C22⋊D14912yes—
195C2×D4C22⋊D14911yescharacteristic, complemented
196C22×C4—21no—
197C22×C4—2981no—
198C22×C4C22×D14911yescharacteristic
199Q16—2982no—
200SD16—24no—
201SD16—2982no—
202SD16—2982no—
203D8—24no—
204D8—2982no—
205M16—21no—
206M16—2981no—
207M16—2981no—
208M16C22⋊D14912yescomplemented
209C2×C8—21no—
210C2×C8—1492no—
211C4⋊C4—2981no—
212C4⋊C4—2981no—
213C22⋊C4—2984no—
214C22⋊C4—2981no—
215C22⋊C4—1492no—
216C42—2981no—
217C42—2981no—
218C23—22no—
219C23—21no—
220C23—41no—
221C23—41no—
222C23—82no—
223C23—2981no—
224C23D4×D14911yescharacteristic
225Q8—21no—
226Q8—21no—
227Q8—2981no—
228Q8—2981no—
229D4—21no—
230D4—21no—
231D4—22no—
232D4—22no—
233D4—41no—
234D4—41no—
235D4—41no—
236D4—41no—
237D4—2981no—
238D4—2981no—
239D4—5961no—
240D4—5961no—
241D4—11924no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—2982no—
246C2×C4—2981no—
247C2×C4—5961no—
248C2×C4—5961no—
249C2×C4—5961no—
250C2×C4D4×D14911yescharacteristic
251C2×C4D4×D14911yescharacteristic
252C2×C4C2×C22⋊D14911yescharacteristic
253C2×C4C2×C22⋊D14911yescharacteristic
254C2×C4C2×C22⋊D14911yescharacteristic
255C2×C4#1455873511yescharacteristic
256C8—22no—
257C8—2982no—
258C22—41no—
259C22—44no—
260C22—41no—
261C22—42no—
262C22—81no—
263C22—82no—
264C22—82no—
265C22—5962no—
266C22—5961no—
267C22#1801187911yescharacteristic
268C22#1801188311yescharacteristic
269C22#1801190711yescharacteristic
270C4—41no—
271C4—5962no—
272C4—5961no—
273C4—11921no—
274C4#1801187911yescharacteristic
275C4#1801188011yescharacteristic
276C4#1801188211yescharacteristic
277C4#1801188311yescharacteristic
278C2—21no—
279C2—21no—
280C2—21no—
281C2—82no—
282C2—81no—
283C2—11921no—
284C2#2374953311yescharacteristic
subgroupG/H
centerC2#23749533
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
FittingC2×AGL(1,ℤ/8)×C149C2
socleC2×C149#392
hypercenterC2×AGL(1,ℤ/8)D149
hypocenterC149#2008
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #23750423C2semidirect
2. #23750192C2semidirect
3. #23749641C2semidirect
4. #23749630C2semidirect
5. #23749599C2semidirect
6. #23749397C2semidirect
7. C2×AGL(1,ℤ/8)×C149C2semidirect
46. C2×#11924746D4semidirect
59. C2×Q8×C149D4semidirect
67. C2×D4×C149D4semidirect
73. M16×C149D4semidirect
142. C149#2008semidirect
145. C2×AGL(1,ℤ/8)D149semidirect
184. C2×Q8C22⋊D149semidirect
195. C2×D4C22⋊D149semidirect
208. M16C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
#237504232
#237501922
#237496412
#237496302
#237495992
#237493972
C2×AGL(1,ℤ/8)×C1492
#2008149