Finite Group Databasebeta

← #34045753

Subgroups — #34045753

Order 19072.

348 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 69 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#23750425C211yesmaximal, characteristic
2C2×#18011942C211yesmaximal, characteristic, complemented
3#23750199C211yesmaximal, characteristic, complemented
4#23749643C211yesmaximal, characteristic, complemented
5#23749598C211yesmaximal, characteristic, complemented
6#23749396C211yesmaximal, characteristic, complemented
7#419×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2211yescharacteristic
9C2×#14558736C2211yescharacteristic
10#18011944—21no—
11#18011944—21no—
12#18011942—22no—
13#18011942—22no—
14#18011939—21no—
15#18011939—21no—
16#18011933—22no—
17C2×#14558726—21no—
18C2×#14558723—21no—
19C2×#14558720C2211yescharacteristic
20#18011909—21no—
21#18011900—21no—
22#18011894—22no—
23#18011887—22no—
24#18011870C2211yescharacteristic
25#18011839—22no—
26#18011825—22no—
27C22×Q8×C149C2211yescharacteristic
28C2×M16×C149C2211yescharacteristic
29#117×C149C2211yescharacteristic
30#103×C149—22no—
31#14558736—21no—
32#14558736—21no—
33#14558736—21no—
34#14558736—21no—
35#14558736—21no—
36#14558736—21no—
37#14558736—21no—
38#14558736—21no—
39C2×Dic298D411yescharacteristic
40C2×Dic298D411yescharacteristic
41C2×D596D411yescharacteristic
42C2×D596D411yescharacteristic
43C2×C22⋊D149—21no—
44C2×C22⋊D149—21no—
45C2×C4×D149—21no—
46C2×C4×D149—21no—
47Dic596—22no—
48#14558726—24no—
49#14558725—22no—
50#14558725—22no—
51#14558723—24no—
52D1192—22no—
53#14558720—21no—
54#14558720D412yes—
55C2×#11924746—21no—
56C4⋊Dic149—21no—
57#14558715—24no—
58C22⋊Dic149D412yes—
59#14558713—24no—
60C4×Dic149—21no—
61C2×Q8×C149—21no—
62C2×Q8×C149—21no—
63C2×Q8×C149—21no—
64C2×Q8×C149—21no—
65C2×Q8×C149—21no—
66C2×Q8×C149D412yes—
67C22×C4×C149—21no—
68C22×C4×C149C2311yescharacteristic
69M16×C149—21no—
70M16×C149—21no—
71C2×C8×C149D412yes—
72C4⋊C4×C149—21no—
73C22⋊C4×C149—21no—
74C42×C149—21no—
75C22×D149—21no—
76C22×D149—21no—
77Dic298—21no—
78Dic298—21no—
79Dic298—21no—
80Dic298—21no—
81D596—21no—
82D596—21no—
83D596—21no—
84D596—21no—
85C22⋊D149—41no—
86C22⋊D149—41no—
87C22⋊D149—41no—
88C22⋊D149—41no—
89C2×Dic149—21no—
90C2×Dic149—22no—
91C2×Dic149—21no—
92C4×D149—41no—
93C4×D149—41no—
94C4×D149—41no—
95C4×D149—41no—
96#11924746—22no—
97C23×C149C2×D411yescharacteristic
98Q8×C149—22no—
99Q8×C149—22no—
100Q8×C149—41no—
101Q8×C149—41no—
102C2×C4×C149—22no—
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#12011yescharacteristic
115C22×C149#12111yescharacteristic
116C22×C149#12711yescharacteristic
117C2×D149—42no—
118C2×D149—41no—
119C2×D149—41no—
120C2×D149—81no—
121C4×C149—42no—
122C4×C149—81no—
123C4×C149#12011yescharacteristic
124C4×C149#12011yescharacteristic
125C4×C149#12111yescharacteristic
126C4×C149#12111yescharacteristic
127Dic149—42no—
128Dic149—41no—
129Dic149—41no—
130C2×C149—21no—
131C2×C149—21no—
132C2×C149—21no—
133C2×C149#39211yescharacteristic
134D149—81no—
135D149—81no—
136C149#200911yescharacteristic, complemented, Sylow
137#2009—1491nomaximal, Sylow
138#575—1491no—
139C2×#137—1491no—
140#536—1491no—
141#421—1491no—
142#419D14911yescharacteristic, complemented
143#410—1491no—
144#344—1491no—
145C2×#41—1491no—
146C2×#41—1491no—
147C22×Q8C2×D14911yescharacteristic
148#137—2981no—
149#137—2981no—
150#137—2982no—
151#137—2982no—
152AGL(1,ℤ/8)—2981no—
153AGL(1,ℤ/8)—2981no—
154#135—2982no—
155C2×Q16—2981no—
156C2×SD16—2981no—
157C2×M16—1491no—
158C2×M16C2×D14911yescharacteristic
159C4⋊Q8—2981no—
160#124—2981no—
161#123—2982no—
162C22⋊Q8—2982no—
163#117—1491no—
164#117C2×D14911yescharacteristic
165#104—2982no—
166#103—22no—
167#99—2982no—
168#41—2981no—
169#41—2981no—
170#41—2981no—
171#41—2981no—
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×Q8—1491no—
183C2×Q8D59612yes—
184C2×D4—2981no—
185C2×D4—2981no—
186C2×D4—1491no—
187C2×D4—1491no—
188C22×C4—21no—
189C22×C4—2981no—
190C22×C4—2981no—
191C22×C4C22×D14911yescharacteristic
192Q16—2982no—
193Q16—2984no—
194SD16—2982no—
195SD16—2982no—
196SD16—2984no—
197D8—2982no—
198M16—21no—
199M16—21no—
200M16—2981no—
201M16—1492no—
202C2×C8—2981no—
203C2×C8C22⋊D14912yes—
204C4⋊C4—21no—
205C4⋊C4—2984no—
206C4⋊C4—2981no—
207C22⋊C4—21no—
208C22⋊C4—2984no—
209C22⋊C4—1492no—
210C42—21no—
211C42—2981no—
212C23—2981no—
213C23—2981no—
214C23D4×D14911yescharacteristic
215Q8—22no—
216Q8—22no—
217Q8—41no—
218Q8—41no—
219Q8—2981no—
220Q8—2981no—
221Q8—2981no—
222Q8—2981no—
223D4—2981no—
224D4—2981no—
225D4—2981no—
226D4—2981no—
227D4—5961no—
228D4—5961no—
229D4—5961no—
230D4—5961no—
231C2×C4—22no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—2982no—
236C2×C4—2981no—
237C2×C4—2981no—
238C2×C4—5961no—
239C2×C4—5961no—
240C2×C4—5961no—
241C2×C4—5961no—
242C2×C4D4×D14911yescharacteristic
243C2×C4D4×D14911yescharacteristic
244C2×C4D4×D14911yescharacteristic
245C2×C4C2×C22⋊D14911yescharacteristic
246C2×C4C2×D59611yescharacteristic
247C2×C4#1455873611yescharacteristic
248C8—22no—
249C8—2982no—
250C22—41no—
251C22—5962no—
252C22—5961no—
253C22—5961no—
254C22—11921no—
255C22#1801188111yescharacteristic
256C22#1801188411yescharacteristic
257C22#1801190711yescharacteristic
258C4—42no—
259C4—81no—
260C4—5962no—
261C4—5961no—
262C4—5961no—
263C4#1801187911yescharacteristic
264C4#1801188111yescharacteristic
265C4#1801188411yescharacteristic
266C4#1801188511yescharacteristic
267C2—21no—
268C2—21no—
269C2—21no—
270C2—11921no—
271C2—11921no—
272C2#2374953411yescharacteristic
subgroupG/H
centerC2#23749534
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#419×C149C2
socleC2×C149#392
prime radical#23750425C2
hypercenter#419D149
hypocenterC149#2009
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
2. C2×#18011942C2semidirect
3. #23750199C2semidirect
4. #23749643C2semidirect
5. #23749598C2semidirect
6. #23749396C2semidirect
7. #419×C149C2semidirect
136. C149#2009semidirect
142. #419D149semidirect

Maximal subgroups

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

subgroupindex
#237504252
C2×#180119422
#237501992
#237496432
#237495982
#237493962
#419×C1492
#2009149