Finite Group Databasebeta

← #34045723

Subgroups — #34045723

Order 19072.

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

normal subgroups only

This group has 394 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×#18011944C211yesmaximal, characteristic, complemented
2#23750194C211yesmaximal, characteristic
3C2×#18011899C211yesmaximal, characteristic, complemented
4C2×#18011839C211yesmaximal, characteristic, complemented
5#23749633C211yesmaximal, characteristic, complemented
6C2×#18011827C211yesmaximal, characteristic, complemented
7#339×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2211yescharacteristic
9C22×Dic298C2211yescharacteristic
10C22×D596C2211yescharacteristic
11#18011944—22no—
12#18011944—22no—
13C2×Dic596—21no—
14C2×#14558725—21no—
15C2×#14558720C2211yescharacteristic
16#18011908—21no—
17#18011899—22no—
18#18011899—21no—
19#18011899—22no—
20#18011886—22no—
21#18011881—22no—
22C2×#14558713—22no—
23#18011839—22no—
24#18011834—22no—
25#18011827—22no—
26C2×M16×C149C2211yescharacteristic
27#117×C149C2211yescharacteristic
28C2×C42×C149C2211yescharacteristic
29C23×D149D412yes—
30#14558736—21no—
31#14558736—21no—
32#14558736—21no—
33#14558736—21no—
34C2×Dic298—21no—
35C2×Dic298—21no—
36C2×Dic298—21no—
37C2×Dic298—21no—
38C2×Dic298—21no—
39C2×Dic298D411yescharacteristic
40C2×Dic298D412yescomplemented
41C2×D596—24no—
42C2×D596—21no—
43C2×D596—21no—
44C2×D596—21no—
45C2×D596—21no—
46C2×D596—21no—
47C2×D596—21no—
48C2×D596D411yescharacteristic
49C2×C22⋊D149—21no—
50C22×Dic149—21no—
51C2×C4×D149—21no—
52Dic596—24no—
53#14558725—24no—
54#14558720—21no—
55#14558720—21no—
56C2×#11924746—21no—
57#14558713—28no—
58#14558713—24no—
59C22×C4×C149—21no—
60C22×C4×C149C2311yescharacteristic
61M16×C149—21no—
62M16×C149D412yescomplemented
63C2×C8×C149—21no—
64C4⋊C4×C149D412yes—
65C22⋊C4×C149—21no—
66C42×C149—21no—
67C42×C149—21no—
68C42×C149D412yescomplemented
69C22×D149—21no—
70C22×D149—22no—
71C22×D149—22no—
72C22×D149—22no—
73C22×D149—44no—
74Dic298—22no—
75Dic298—21no—
76Dic298—22no—
77Dic298—21no—
78Dic298—41no—
79Dic298—41no—
80D596—21no—
81D596—21no—
82D596—41no—
83D596—41no—
84D596—41no—
85D596—41no—
86D596—84no—
87C22⋊D149—41no—
88C22⋊D149—41no—
89C2×Dic149—21no—
90C2×Dic149—22no—
91C2×Dic149—41no—
92C2×Dic149—41no—
93C4×D149—41no—
94C4×D149—41no—
95#11924746—41no—
96C23×C149C2×D411yescharacteristic
97C2×C4×C149—22no—
98C2×C4×C149—22no—
99C2×C4×C149—42no—
100C2×C4×C149C2×D411yescharacteristic
101C2×C4×C149C2×D411yescharacteristic
102C2×C4×C149C2×D411yescharacteristic
103C2×C4×C149C2×D411yescharacteristic
104C2×C4×C149C2×D411yescharacteristic
105C2×C4×C149#4111yescharacteristic
106C8×C149—22no—
107C22×C149—22no—
108C22×C149#12011yescharacteristic
109C22×C149#12011yescharacteristic
110C22×C149#12111yescharacteristic
111C2×D149—44no—
112C2×D149—41no—
113C2×D149—42no—
114C2×D149—42no—
115C2×D149—44no—
116C2×D149—82no—
117C4×C149—42no—
118C4×C149—42no—
119C4×C149#12011yescharacteristic
120C4×C149#12111yescharacteristic
121C4×C149#12111yescharacteristic
122C4×C149#12711yescharacteristic
123Dic149—41no—
124Dic149—42no—
125C2×C149—21no—
126C2×C149—21no—
127C2×C149#39211yescharacteristic
128C2×C149#45512yes—
129D149—81no—
130D149—82no—
131C149#200411yescharacteristic, complemented, Sylow
132#2004—1491nomaximal, Sylow
133C2×#137—1491no—
134#535—1491no—
135C2×#124—1491no—
136C2×#104—1491no—
137#419—1491no—
138C2×#100—1491no—
139#339D14911yescharacteristic, complemented
140C2×#41—1491no—
141C22×Q8—1491no—
142C22×D4—1491no—
143#137—2982no—
144#137—2982no—
145C2×Q16—2981no—
146C2×SD16—2981no—
147C2×M16—1491no—
148C2×M16C2×D14911yescharacteristic
149#127—2981no—
150#124—2982no—
151#124—2981no—
152#124—2982no—
153#121—2982no—
154#120—2982no—
155#117C2×D14911yescharacteristic
156C2×C22⋊C4—2982no—
157C2×C42C2×D14911yescharacteristic
158#104—2982no—
159#103—2982no—
160#100—2982no—
161C24—1492no—
162#41—2981no—
163#41—2981no—
164#41—2981no—
165#41—2981no—
166C2×Q8—2981no—
167C2×Q8—2981no—
168C2×Q8—2981no—
169C2×Q8—2981no—
170C2×Q8—2981no—
171C2×Q8—1491no—
172C2×Q8—1492no—
173C2×D4—2984no—
174C2×D4—2981no—
175C2×D4—2981no—
176C2×D4—2981no—
177C2×D4—2981no—
178C2×D4—2981no—
179C2×D4—2981no—
180C2×D4—2981no—
181C2×D4—1491no—
182C22×C4—21no—
183C22×C4—2981no—
184C22×C4—2981no—
185C22×C4C22×D14911yescharacteristic
186Q16—2984no—
187SD16—2984no—
188M16—21no—
189M16—2981no—
190M16—2981no—
191M16D59612yescomplemented
192C2×C8—21no—
193C2×C8—2981no—
194C4⋊C4D59612yes—
195C22⋊C4—21no—
196C22⋊C4—2988no—
197C22⋊C4—2984no—
198C42—21no—
199C42—21no—
200C42D59612yescomplemented
201C23—2982no—
202C23—2982no—
203C23—2981no—
204C23—2982no—
205C23—5964no—
206C23D4×D14911yescharacteristic
207Q8—2982no—
208Q8—2981no—
209Q8—2982no—
210Q8—2981no—
211Q8—5961no—
212Q8—5961no—
213D4—2981no—
214D4—2981no—
215D4—5961no—
216D4—5961no—
217D4—5961no—
218D4—5961no—
219D4—5961no—
220D4—5961no—
221D4—11924no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—2982no—
226C2×C4—2981no—
227C2×C4—5961no—
228C2×C4—5961no—
229C2×C4—5961no—
230C2×C4—5961no—
231C2×C4D4×D14911yescharacteristic
232C2×C4D4×D14911yescharacteristic
233C2×C4C2×D59611yescharacteristic
234C2×C4C2×D59611yescharacteristic
235C2×C4C2×D59611yescharacteristic
236C2×C4#1455873711yescharacteristic
237C8—22no—
238C8—5961no—
239C22—22no—
240C22—5964no—
241C22—5961no—
242C22—5962no—
243C22—5962no—
244C22—5964no—
245C22—11922no—
246C22#1801188111yescharacteristic
247C22#1801188111yescharacteristic
248C22#1801188611yescharacteristic
249C4—42no—
250C4—42no—
251C4—5961no—
252C4—5962no—
253C4#1801188111yescharacteristic
254C4#1801188611yescharacteristic
255C4#1801188611yescharacteristic
256C4#1801190811yescharacteristic
257C2—21no—
258C2—21no—
259C2—11922no—
260C2—11921no—
261C2#2374953511yescharacteristic
262C2#2374980412yes—
subgroupG/H
centerC22#18011881
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#339×C149C2
socleC22×C149#120
prime radical#23750194C2
hypercenter#339D149
hypocenterC149#2004
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×#18011944C2semidirect
3. C2×#18011899C2semidirect
4. C2×#18011839C2semidirect
5. #23749633C2semidirect
6. C2×#18011827C2semidirect
7. #339×C149C2semidirect
40. C2×Dic298D4semidirect
62. M16×C149D4semidirect
68. C42×C149D4semidirect
131. C149#2004semidirect
139. #339D149semidirect
191. M16D596semidirect
200. C42D596semidirect

Maximal subgroups

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

subgroupindex
C2×#180119442
#237501942
C2×#180118992
C2×#180118392
#237496332
C2×#180118272
#339×C1492
#2004149