Finite Group Databasebeta

← #34045709

Subgroups — #34045709

Order 19072.

478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×#18011939C211yesmaximal, characteristic, complemented
2#23750194C211yesmaximal, characteristic, complemented
3C2×#18011908C211yesmaximal, characteristic, complemented
4C2×#18011839C211yesmaximal, characteristic, complemented
5#23749629C211yesmaximal, characteristic, complemented
6C2×#18011827C211yesmaximal, characteristic, complemented
7#339×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2211yescharacteristic
9C22×D596—22no—
10C22×D596C2211yescharacteristic
11C22×D596C2211yescharacteristic
12#18011939—22no—
13#18011939—22no—
14C2×#14558725—21no—
15C2×D1192—21no—
16C2×#14558720C2211yescharacteristic
17#18011908—22no—
18#18011908—22no—
19#18011908—21no—
20#18011899—21no—
21#18011886—22no—
22#18011881—22no—
23#18011839—22no—
24#18011831—22no—
25#18011827—22no—
26C2×M16×C149C2211yescharacteristic
27#117×C149C2211yescharacteristic
28C2×C42×C149C2211yescharacteristic
29C23×D149—21no—
30C23×D149D412yes—
31#14558736—21no—
32#14558736—21no—
33#14558736—21no—
34#14558736—21no—
35C2×Dic298D411yescharacteristic, complemented
36C2×D596—28no—
37C2×D596—24no—
38C2×D596—21no—
39C2×D596—21no—
40C2×D596—21no—
41C2×D596—21no—
42C2×D596—21no—
43C2×D596—21no—
44C2×D596—21no—
45C2×D596—21no—
46C2×D596—21no—
47C2×D596—21no—
48C2×D596—21no—
49C2×D596—48no—
50C2×D596D411yescharacteristic, complemented
51C2×D596D412yescomplemented
52C2×C22⋊D149—21no—
53C2×C4×D149—21no—
54#14558725—24no—
55D1192—24no—
56#14558720—21no—
57#14558720—21no—
58C2×#11924746—21no—
59#14558713—24no—
60C22×C4×C149—21no—
61C22×C4×C149C2311yescharacteristic
62M16×C149—21no—
63M16×C149D412yescomplemented
64C2×C8×C149—21no—
65C4⋊C4×C149D412yescomplemented
66C22⋊C4×C149—21no—
67C42×C149—21no—
68C42×C149—21no—
69C42×C149D412yescomplemented
70C22×D149—21no—
71C22×D149—22no—
72C22×D149—22no—
73C22×D149—22no—
74C22×D149—22no—
75C22×D149—44no—
76C22×D149—44no—
77C22×D149—41no—
78C22×D149—41no—
79Dic298—21no—
80Dic298—21no—
81D596—21no—
82D596—22no—
83D596—22no—
84D596—21no—
85D596—416no—
86D596—41no—
87D596—41no—
88D596—41no—
89D596—41no—
90D596—41no—
91D596—41no—
92D596—84no—
93C22⋊D149—41no—
94C22⋊D149—41no—
95C2×Dic149—21no—
96C4×D149—41no—
97C4×D149—41no—
98#11924746—41no—
99C23×C149C2×D411yescharacteristic
100C2×C4×C149—24no—
101C2×C4×C149—22no—
102C2×C4×C149—22no—
103C2×C4×C149C2×D411yescharacteristic
104C2×C4×C149C2×D411yescharacteristic
105C2×C4×C149C2×D411yescharacteristic
106C2×C4×C149C2×D411yescharacteristic
107C2×C4×C149C2×D411yescharacteristic
108C2×C4×C149#4111yescharacteristic
109C8×C149—22no—
110C22×C149—22no—
111C22×C149#12011yescharacteristic
112C22×C149#12011yescharacteristic
113C22×C149#12111yescharacteristic
114C2×D149—44no—
115C2×D149—44no—
116C2×D149—41no—
117C2×D149—42no—
118C2×D149—42no—
119C2×D149—42no—
120C2×D149—44no—
121C2×D149—82no—
122C2×D149—82no—
123C2×D149—82no—
124C4×C149—24no—
125C4×C149—42no—
126C4×C149#12011yescharacteristic
127C4×C149#12111yescharacteristic
128C4×C149#12111yescharacteristic
129C4×C149#12711yescharacteristic
130Dic149—41no—
131C2×C149—21no—
132C2×C149—21no—
133C2×C149#39211yescharacteristic
134C2×C149#45312yes—
135D149—81no—
136D149—82no—
137D149—82no—
138C149#200211yescharacteristic, complemented, Sylow
139#2002—1491nomaximal, Sylow
140C2×AGL(1,ℤ/8)—1491no—
141#535—1491no—
142C2×#127—1491no—
143C2×#104—1491no—
144#418—1491no—
145C2×#100—1491no—
146#339D14911yescharacteristic, complemented
147C2×#41—1491no—
148C22×D4—2982no—
149C22×D4—1491no—
150C22×D4—1491no—
151AGL(1,ℤ/8)—2982no—
152AGL(1,ℤ/8)—2982no—
153C2×SD16—2981no—
154C2×D8—2981no—
155C2×M16—1491no—
156C2×M16C2×D14911yescharacteristic
157#127—2982no—
158#127—2981no—
159#127—2982no—
160#124—2981no—
161#121—2982no—
162#120—2982no—
163#117C2×D14911yescharacteristic
164C2×C42C2×D14911yescharacteristic
165#104—2982no—
166#102—2982no—
167#100—2982no—
168C24—2981no—
169C24—1492no—
170#41—2981no—
171#41—2981no—
172#41—2981no—
173#41—2981no—
174C2×Q8—1491no—
175C2×D4—2988no—
176C2×D4—2984no—
177C2×D4—2981no—
178C2×D4—2981no—
179C2×D4—2981no—
180C2×D4—2981no—
181C2×D4—2981no—
182C2×D4—2981no—
183C2×D4—2981no—
184C2×D4—2981no—
185C2×D4—2981no—
186C2×D4—2981no—
187C2×D4—2981no—
188C2×D4—2981no—
189C2×D4—5968no—
190C2×D4—1491no—
191C2×D4—1492no—
192C22×C4—21no—
193C22×C4—2981no—
194C22×C4C22×D14911yescharacteristic
195SD16—2984no—
196D8—2984no—
197M16—21no—
198M16—2981no—
199M16—2981no—
200M16D59612yescomplemented
201C2×C8—21no—
202C2×C8—2981no—
203C4⋊C4D59612yescomplemented
204C22⋊C4—21no—
205C22⋊C4—2984no—
206C42—21no—
207C42—21no—
208C42D59612yescomplemented
209C23—2982no—
210C23—2982no—
211C23—2982no—
212C23—2981no—
213C23—2982no—
214C23—5964no—
215C23—5964no—
216C23—5961no—
217C23—5961no—
218C23D4×D14911yescharacteristic
219Q8—2981no—
220Q8—2981no—
221D4—2981no—
222D4—2982no—
223D4—2982no—
224D4—2981no—
225D4—59616no—
226D4—5961no—
227D4—5961no—
228D4—5961no—
229D4—5961no—
230D4—5961no—
231D4—5961no—
232D4—5961no—
233D4—5961no—
234D4—11924no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—2981no—
239C2×C4—5961no—
240C2×C4—5961no—
241C2×C4D4×D14911yescharacteristic
242C2×C4D4×D14911yescharacteristic
243C2×C4C2×D59611yescharacteristic
244C2×C4C2×D59611yescharacteristic
245C2×C4C2×D59611yescharacteristic
246C2×C4#1455873711yescharacteristic
247C8—22no—
248C8—5961no—
249C22—22no—
250C22—5964no—
251C22—5964no—
252C22—5961no—
253C22—5962no—
254C22—5962no—
255C22—5962no—
256C22—5964no—
257C22—11922no—
258C22—11922no—
259C22—11922no—
260C22#1801188111yescharacteristic
261C22#1801188111yescharacteristic
262C22#1801188611yescharacteristic
263C4—24no—
264C4—42no—
265C4—5961no—
266C4#1801188111yescharacteristic
267C4#1801188611yescharacteristic
268C4#1801188611yescharacteristic
269C4#1801190811yescharacteristic
270C2—21no—
271C2—21no—
272C2—11922no—
273C2—11922no—
274C2—11921no—
275C2#2374953511yescharacteristic
276C2#2374979412yes—
subgroupG/H
centerC22#18011881
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#339×C149C2
socleC22×C149#120
hypercenter#339D149
hypocenterC149#2002
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. C2×#18011939C2semidirect
2. #23750194C2semidirect
3. C2×#18011908C2semidirect
4. C2×#18011839C2semidirect
5. #23749629C2semidirect
6. C2×#18011827C2semidirect
7. #339×C149C2semidirect
35. C2×Dic298D4semidirect
50. C2×D596D4semidirect
51. C2×D596D4semidirect
63. M16×C149D4semidirect
65. C4⋊C4×C149D4semidirect
69. C42×C149D4semidirect
138. C149#2002semidirect
146. #339D149semidirect
200. M16D596semidirect
203. C4⋊C4D596semidirect
208. C42D596semidirect

Maximal subgroups

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

subgroupindex
C2×#180119392
#237501942
C2×#180119082
C2×#180118392
#237496292
C2×#180118272
#339×C1492
#2002149