Finite Group Databasebeta

← #34045768

Subgroups — #34045768

Order 19072.

426 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 91 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×#14558723C211yesmaximal, characteristic, complemented
2C22×#14558721C211yesmaximal, characteristic
3C2×#18011835C211yesmaximal, characteristic, complemented
4C2×#18011832C211yesmaximal, characteristic, complemented
5#23749527C211yesmaximal, characteristic, complemented
6#23749380C211yesmaximal, characteristic, complemented
7C2×#124×C149C211yesmaximal, characteristic, complemented
8C22×D596C2211yescharacteristic
9C2×#14558723—22no—
10C2×#14558723—22no—
11C2×#14558723—22no—
12C2×#14558721—22no—
13C2×#14558721—22no—
14C2×#14558721—22no—
15C22×#11924746C2211yescharacteristic
16C22×#11924746C2211yescharacteristic
17C2×C4⋊Dic149C2211yescharacteristic
18C2×#14558713—22no—
19#18011835—22no—
20#18011832—22no—
21C22×Q8×C149C2211yescharacteristic
22C22×D4×C149C2211yescharacteristic
23#124×C149—22no—
24#124×C149—22no—
25C2×C22⋊C4×C149—22no—
26C2×C42×C149C2211yescharacteristic
27C23×D149—21no—
28C2×D596—21no—
29C2×D596—21no—
30C2×D596—21no—
31C2×D596—21no—
32C2×D596—21no—
33C2×D596D412yes—
34C22×Dic149—21no—
35#14558723—28no—
36#14558721—28no—
37C2×#11924746—21no—
38C2×#11924746—21no—
39C2×#11924746—21no—
40C2×#11924746—21no—
41C2×#11924746D412yes—
42C2×#11924746D412yes—
43C4⋊Dic149—21no—
44C4⋊Dic149—21no—
45#14558713—44no—
46C24×C149—21no—
47C2×Q8×C149—21no—
48C2×Q8×C149—21no—
49C2×Q8×C149—21no—
50C2×Q8×C149—21no—
51C2×Q8×C149—21no—
52C2×Q8×C149D412yes—
53C2×D4×C149—21no—
54C2×D4×C149—21no—
55C2×D4×C149—21no—
56C2×D4×C149—21no—
57C2×D4×C149—21no—
58C2×D4×C149D412yes—
59C22×C4×C149—21no—
60C22×C4×C149D412yes—
61C22×C4×C149C2311yescharacteristic
62C22⋊C4×C149—28no—
63C42×C149—21no—
64C42×C149—21no—
65C22×D149—22no—
66C22×D149—41no—
67C22×D149—41no—
68C22×D149—42no—
69C22×D149—42no—
70D596—22no—
71D596—22no—
72D596—41no—
73D596—41no—
74C2×Dic149—41no—
75C2×Dic149—42no—
76#11924746—22no—
77#11924746—22no—
78C23×C149—22no—
79C23×C149—41no—
80C23×C149—41no—
81C23×C149—42no—
82C23×C149—42no—
83C23×C149C2×D411yescharacteristic
84Q8×C149—22no—
85Q8×C149—22no—
86Q8×C149—41no—
87Q8×C149—41no—
88D4×C149—22no—
89D4×C149—22no—
90D4×C149—41no—
91D4×C149—41no—
92C2×C4×C149—22no—
93C2×C4×C149—22no—
94C2×C4×C149—22no—
95C2×C4×C149—22no—
96C2×C4×C149—41no—
97C2×C4×C149—41no—
98C2×C4×C149C2×D411yescharacteristic
99C2×C4×C149C2×D411yescharacteristic
100C2×C4×C149C2×D411yescharacteristic
101C2×C4×C149C2×D411yescharacteristic
102C2×C4×C149C2×D411yescharacteristic
103C2×C4×C149#4111yescharacteristic
104C22×C149—42no—
105C22×C149—44no—
106C22×C149—82no—
107C22×C149—81no—
108C22×C149—81no—
109C22×C149#12011yescharacteristic
110C22×C149#12111yescharacteristic
111C22×C149#12711yescharacteristic
112C22×C149#13512yes—
113C22×C149AGL(1,ℤ/8)12yes—
114C2×D149—42no—
115C2×D149—44no—
116C2×D149—82no—
117C2×D149—81no—
118C2×D149—81no—
119C4×C149—42no—
120C4×C149—42no—
121C4×C149#12011yescharacteristic
122C4×C149#12011yescharacteristic
123C4×C149#12111yescharacteristic
124C4×C149#12111yescharacteristic
125Dic149—81no—
126C2×C149—82no—
127C2×C149#39211yescharacteristic
128C2×C149#44912yes—
129C2×C149#46312yes—
130C2×C149#49511yescharacteristic
131C2×C149#49611yescharacteristic
132D149—82no—
133C149#201211yescharacteristic, complemented, Sylow
134#2012—1491nomaximal, Sylow
135C22×SD16—1491no—
136C22×D8—1491no—
137C2×#124D14911yescharacteristic, complemented
138C2×#103—1491no—
139C2×#102—1491no—
140#390—1491no—
141#336—1491no—
142C22×Q8C2×D14911yescharacteristic
143C22×D4—1491no—
144C22×D4C2×D14911yescharacteristic
145C2×SD16—2982no—
146C2×SD16—2982no—
147C2×SD16—2982no—
148C2×D8—2982no—
149C2×D8—2982no—
150C2×D8—2982no—
151C22×C8—1491no—
152C22×C8—1491no—
153#124—22no—
154#124—22no—
155C2×C4⋊C4—1491no—
156C2×C22⋊C4—22no—
157C2×C22⋊C4—2982no—
158C2×C42C2×D14911yescharacteristic
159#103—2982no—
160#102—2982no—
161C24—21no—
162C24—2981no—
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8C22⋊D14912yes—
169C2×D4—21no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—2981no—
175C2×D4—2981no—
176C2×D4—2981no—
177C2×D4—2981no—
178C2×D4—2981no—
179C2×D4—1492no—
180C2×D4C22⋊D14912yes—
181C22×C4—21no—
182C22×C4—2981no—
183C22×C4C22⋊D14912yes—
184C22×C4C22×D14911yescharacteristic
185SD16—2988no—
186D8—2988no—
187C2×C8—2981no—
188C2×C8—2981no—
189C2×C8—2981no—
190C2×C8—2981no—
191C2×C8—1492no—
192C2×C8—1492no—
193C4⋊C4—2981no—
194C4⋊C4—2981no—
195C22⋊C4—28no—
196C22⋊C4—5964no—
197C42—21no—
198C42—21no—
199C23—22no—
200C23—41no—
201C23—42no—
202C23—42no—
203C23—41no—
204C23—2982no—
205C23—5961no—
206C23—5962no—
207C23—5962no—
208C23—5961no—
209C23C2×C22⋊D14911yescharacteristic
210Q8—22no—
211Q8—22no—
212Q8—41no—
213Q8—41no—
214D4—22no—
215D4—22no—
216D4—41no—
217D4—41no—
218D4—2982no—
219D4—2982no—
220D4—5961no—
221D4—5961no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—5961no—
229C2×C4—5962no—
230C2×C4D4×D14911yescharacteristic
231C2×C4D4×D14911yescharacteristic
232C2×C4D4×D14911yescharacteristic
233C2×C4C2×C22⋊D14911yescharacteristic
234C2×C4C2×C22⋊D14911yescharacteristic
235C2×C4#1455873511yescharacteristic
236C8—2982no—
237C8—2982no—
238C22—44no—
239C22—42no—
240C22—81no—
241C22—81no—
242C22—82no—
243C22—5962no—
244C22—5964no—
245C22—11921no—
246C22—11921no—
247C22—11922no—
248C22#1801188011yescharacteristic
249C22#1801188211yescharacteristic
250C22#1801190711yescharacteristic
251C22#1801193112yes—
252C22#1801193612yes—
253C4—42no—
254C4—42no—
255C4—11921no—
256C4#1801187911yescharacteristic
257C4#1801187911yescharacteristic
258C4#1801188311yescharacteristic
259C4#1801188311yescharacteristic
260C2—82no—
261C2—11922no—
262C2#2374953311yescharacteristic
263C2#2374977012yes—
264C2#2374983712yes—
265C2#2375000711yescharacteristic
266C2#2375001511yescharacteristic
subgroupG/H
centerC23C2×C22⋊D149
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
FittingC2×#124×C149C2
socleC23×C149C2×D4
prime radicalC22×#14558721C2
hypercenterC2×#124D149
hypocenterC149#2012
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C22×#14558723C2semidirect
3. C2×#18011835C2semidirect
4. C2×#18011832C2semidirect
5. #23749527C2semidirect
6. #23749380C2semidirect
7. C2×#124×C149C2semidirect
133. C149#2012semidirect
137. C2×#124D149semidirect

Maximal subgroups

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

subgroupindex
C22×#145587232
C22×#145587212
C2×#180118352
C2×#180118322
#237495272
#237493802
C2×#124×C1492
#2012149