Finite Group Databasebeta

← #34045749

Subgroups — #34045749

Order 19072.

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

normal subgroups only

This group has 348 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
2#23750199C211yesmaximal, characteristic, complemented
3#23749641C211yesmaximal, characteristic, complemented
4#23749634C211yesmaximal, characteristic, complemented
5#23749599C211yesmaximal, characteristic, complemented
6#23749397C211yesmaximal, characteristic, complemented
7C2×#137×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2211yescharacteristic
9#18011942—21no—
10#18011941—21no—
11#18011937—21no—
12#18011936—21no—
13#18011931—22no—
14C2×#14558720C2211yescharacteristic
15#18011909—21no—
16#18011900—21no—
17#18011894—22no—
18#18011887—22no—
19#18011870C2211yescharacteristic
20#18011870C2211yescharacteristic
21#18011837—22no—
22#18011835—22no—
23#18011826—22no—
24C2×#41×C149C2211yescharacteristic
25C22×Q8×C149C2211yescharacteristic
26#137×C149—22no—
27#137×C149—22no—
28C2×Q16×C149—21no—
29C2×SD16×C149—21no—
30C2×M16×C149C2211yescharacteristic
31#14558736—21no—
32#14558736—21no—
33#14558736—21no—
34#14558736—21no—
35C2×Dic298D411yescharacteristic
36C2×D596D411yescharacteristic
37C2×C22⋊D149—21no—
38C2×C4×D149—21no—
39#14558726—22no—
40#14558724—22no—
41#14558723—22no—
42#14558721—22no—
43#14558720—21no—
44#14558720—21no—
45C2×#11924746D412yes—
46C4⋊Dic149—21no—
47C4⋊Dic149—21no—
48#14558715—24no—
49C22⋊Dic149—21no—
50C22⋊Dic149D412yes—
51#14558713—24no—
52C4×Dic149—21no—
53C4×Dic149—21no—
54#41×C149—21no—
55#41×C149—21no—
56#41×C149—21no—
57#41×C149—21no—
58C2×Q8×C149—21no—
59C2×Q8×C149—21no—
60C2×Q8×C149—21no—
61C2×Q8×C149—21no—
62C2×Q8×C149—21no—
63C2×Q8×C149D411yescharacteristic
64C2×Q8×C149D412yes—
65C2×D4×C149—21no—
66C2×D4×C149D411yescharacteristic
67C22×C4×C149—21no—
68C22×C4×C149—21no—
69C22×C4×C149C2311yescharacteristic
70Q16×C149—24no—
71SD16×C149—24no—
72M16×C149—21no—
73M16×C149D412yes—
74C2×C8×C149—21no—
75C22×D149—21no—
76Dic298—21no—
77Dic298—21no—
78D596—21no—
79D596—21no—
80C22⋊D149—41no—
81C22⋊D149—41no—
82C2×Dic149—21no—
83C2×Dic149—22no—
84C2×Dic149—41no—
85C4×D149—41no—
86C4×D149—41no—
87#11924746—22no—
88C23×C149—21no—
89C23×C149C2×D411yescharacteristic
90Q8×C149—21no—
91Q8×C149—22no—
92Q8×C149—21no—
93Q8×C149—22no—
94Q8×C149—41no—
95Q8×C149—41no—
96D4×C149—21no—
97D4×C149—21no—
98D4×C149—41no—
99D4×C149—41no—
100C2×C4×C149—22no—
101C2×C4×C149—21no—
102C2×C4×C149—41no—
103C2×C4×C149—41no—
104C2×C4×C149—41no—
105C2×C4×C149—41no—
106C2×C4×C149C2×D411yescharacteristic
107C2×C4×C149C2×D411yescharacteristic
108C2×C4×C149C2×D411yescharacteristic
109C2×C4×C149C2×D411yescharacteristic
110C2×C4×C149C2×D411yescharacteristic
111C2×C4×C149#4111yescharacteristic
112C8×C149—22no—
113C22×C149—41no—
114C22×C149—41no—
115C22×C149—81no—
116C22×C149#12011yescharacteristic
117C22×C149#12111yescharacteristic
118C22×C149#12711yescharacteristic
119C2×D149—42no—
120C2×D149—41no—
121C4×C149—41no—
122C4×C149—42no—
123C4×C149#12011yescharacteristic
124C4×C149#12011yescharacteristic
125C4×C149#12111yescharacteristic
126C4×C149#12111yescharacteristic
127Dic149—42no—
128Dic149—41no—
129Dic149—81no—
130C2×C149—21no—
131C2×C149—21no—
132C2×C149—21no—
133C2×C149—81no—
134C2×C149#39211yescharacteristic
135D149—81no—
136C149#200911yescharacteristic, complemented, Sylow
137#2009—1491nomaximal, Sylow
138#575—1491no—
139C2×#137D14911yescharacteristic, complemented
140#536—1491no—
141#421—1491no—
142#419—1491no—
143#410—1491no—
144#344—1491no—
145C2×#41—1491no—
146C2×#41C2×D14911yescharacteristic
147C22×Q8C2×D14911yescharacteristic
148#137—22no—
149#137—22no—
150#137—2981no—
151#137—2981no—
152AGL(1,ℤ/8)—2981no—
153AGL(1,ℤ/8)—2981no—
154#135—2982no—
155C2×Q16—21no—
156C2×SD16—21no—
157C2×M16—1491no—
158C2×M16C2×D14911yescharacteristic
159C4⋊Q8—2981no—
160#124—2981no—
161#123—2982no—
162C22⋊Q8—2982no—
163#117—1491no—
164#117—1491no—
165#104—2982no—
166#103—2982no—
167#99—2982no—
168#41—21no—
169#41—21no—
170#41—21no—
171#41—21no—
172#41—2981no—
173#41—2981no—
174#41—2981no—
175#41—2981no—
176C2×Q8—21no—
177C2×Q8—21no—
178C2×Q8—21no—
179C2×Q8—21no—
180C2×Q8—21no—
181C2×Q8—1491no—
182C2×Q8C22⋊D14912yes—
183C2×Q8C22⋊D14911yescharacteristic
184C2×D4—21no—
185C2×D4—2981no—
186C2×D4—1491no—
187C2×D4C22⋊D14911yescharacteristic
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—2981no—
191C22×C4C22×D14911yescharacteristic
192Q16—24no—
193Q16—2982no—
194SD16—24no—
195SD16—2982no—
196SD16—2982no—
197D8—2982no—
198M16—21no—
199M16—2981no—
200M16—2981no—
201M16C22⋊D14912yes—
202C2×C8—21no—
203C2×C8—1492no—
204C4⋊C4—2984no—
205C4⋊C4—2981no—
206C4⋊C4—2981no—
207C22⋊C4—2984no—
208C22⋊C4—2981no—
209C22⋊C4—1492no—
210C42—2981no—
211C42—2981no—
212C23—21no—
213C23—2981no—
214C23D4×D14911yescharacteristic
215Q8—21no—
216Q8—22no—
217Q8—21no—
218Q8—22no—
219Q8—41no—
220Q8—41no—
221Q8—2981no—
222Q8—2981no—
223D4—21no—
224D4—21no—
225D4—41no—
226D4—41no—
227D4—2981no—
228D4—2981no—
229D4—5961no—
230D4—5961no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—2982no—
238C2×C4—2981no—
239C2×C4—5961no—
240C2×C4—5961no—
241C2×C4—5961no—
242C2×C4D4×D14911yescharacteristic
243C2×C4D4×D14911yescharacteristic
244C2×C4C2×C22⋊D14911yescharacteristic
245C2×C4C2×C22⋊D14911yescharacteristic
246C2×C4C2×C22⋊D14911yescharacteristic
247C2×C4#1455873511yescharacteristic
248C8—22no—
249C8—2982no—
250C22—41no—
251C22—41no—
252C22—81no—
253C22—5962no—
254C22—5961no—
255C22#1801187911yescharacteristic
256C22#1801188311yescharacteristic
257C22#1801190711yescharacteristic
258C4—41no—
259C4—42no—
260C4—5962no—
261C4—5961no—
262C4—11921no—
263C4#1801187911yescharacteristic
264C4#1801188011yescharacteristic
265C4#1801188211yescharacteristic
266C4#1801188311yescharacteristic
267C2—21no—
268C2—21no—
269C2—21no—
270C2—81no—
271C2—11921no—
272C2#2374953311yescharacteristic
subgroupG/H
centerC2#23749533
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
FittingC2×#137×C149C2
socleC2×C149#392
prime radical#23750423C2
hypercenterC2×#137D149
hypocenterC149#2009
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. #23750199C2semidirect
3. #23749641C2semidirect
4. #23749634C2semidirect
5. #23749599C2semidirect
6. #23749397C2semidirect
7. C2×#137×C149C2semidirect
136. C149#2009semidirect
139. C2×#137D149semidirect

Maximal subgroups

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

subgroupindex
#237504232
#237501992
#237496412
#237496342
#237495992
#237493972
C2×#137×C1492
#2009149