Finite Group Databasebeta

← #34054274

Subgroups — #34054274

Order 19072.

520 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 133 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×#18011934C211yesmaximal, characteristic, complemented
2C22×C8×D149C211yesmaximal, characteristic, complemented
3#23750138C212yesmaximal, complemented
4#23749863C211yesmaximal, characteristic, complemented
5#23749862C211yesmaximal, characteristic, complemented
6#23749861C211yesmaximal, characteristic, complemented
7#23749857C212yesmaximal, complemented
8#23749856C212yesmaximal, complemented
9#23749662C211yesmaximal, characteristic, complemented
10#23749620C212yesmaximal, complemented
11#467×C149C211yesmaximal, characteristic, complemented
12C2×#14558737C2212yes—
13C22×C4×D149C2211yescharacteristic
14#18011934—24no—
15C2×#14558723C2212yescomplemented
16C2×D1192C2211yescharacteristic, complemented
17C22×#11924746C2211yescharacteristic
18C2×C8×D149—24no—
19C2×C8×D149C2211yescharacteristic
20C2×C8×D149C2211yescharacteristic
21C2×C8×D149C2211yescharacteristic
22C2×C8×D149C2211yescharacteristic
23#18011896—22no—
24#18011887C2212yes—
25#18011886C2212yes—
26#18011885C2212yes—
27#18011881—22no—
28#18011873—22no—
29#18011871—22no—
30#18011869C2212yes—
31#18011845C2211yescharacteristic, complemented
32#18011842C2212yescomplemented
33#18011835C2212yescomplemented
34#18011833C2212yescomplemented
35#18011831C2212yescomplemented
36C2×Q16×C149C2211yescharacteristic, complemented
37C22×C8×C149C2211yescharacteristic
38C22⋊Q8×C149C2212yes—
39#107×C149C2211yescharacteristic, complemented
40#103×C149C2212yescomplemented
41C23×D149D411yescharacteristic
42#14558737—24no—
43#14558737—24no—
44C2×D596—22no—
45C2×D596—22no—
46C2×D596C2312yes—
47C2×C22⋊D149—22no—
48C22×Dic149D411yescharacteristic
49C2×C4×D149—22no—
50C2×C4×D149—22no—
51C2×C4×D149—22no—
52C2×C4×D149D411yescharacteristic
53C2×C4×D149D411yescharacteristic
54C2×C4×D149C2311yescharacteristic
55C2×C4×D149C2311yescharacteristic
56#14558723—24no—
57D1192—22no—
58C2×#11924746—22no—
59C2×#11924746C2311yescharacteristic
60C2×#11924746C2311yescharacteristic
61C8×D149—22no—
62C8×D149—22no—
63C8×D149—22no—
64C8×D149D414yescomplemented
65C4⋊Dic149C2312yes—
66#14558715—22no—
67#14558713—22no—
68#14558713—22no—
69#14558713—22no—
70#14558713—22no—
71C4×Dic149—22no—
72C2×Q8×C149C2312yes—
73C22×C4×C149C2311yescharacteristic
74Q16×C149—22no—
75C2×C8×C149—22no—
76C2×C8×C149C2311yescharacteristic
77C2×C8×C149C2311yescharacteristic
78C4⋊C4×C149—22no—
79C4⋊C4×C149C2312yes—
80C22⋊C4×C149—22no—
81C22×D149—22no—
82C22×D149—22no—
83C22×D149—22no—
84C22×D149—22no—
85C22×D149C2×D411yescharacteristic
86C22×D149C2×D411yescharacteristic
87D596—22no—
88D596—22no—
89D596—44no—
90D596—44no—
91C22⋊D149—44no—
92C2×Dic149—22no—
93C2×Dic149—22no—
94C2×Dic149C2×D411yescharacteristic
95C2×Dic149C2×D411yescharacteristic
96C4×D149—22no—
97C4×D149—21no—
98C4×D149—21no—
99C4×D149—22no—
100C4×D149—44no—
101C4×D149C2×D412yes—
102C4×D149#4112yes—
103#11924746—21no—
104#11924746C2×D412yes—
105C23×C149C2×D411yescharacteristic
106Q8×C149—22no—
107Q8×C149—22no—
108C2×C4×C149—21no—
109C2×C4×C149—21no—
110C2×C4×C149—22no—
111C2×C4×C149—22no—
112C2×C4×C149C2×D411yescharacteristic
113C2×C4×C149C2411yescharacteristic
114C8×C149—21no—
115C8×C149C2×D412yes—
116C22×C149—21no—
117C22×C149—21no—
118C22×C149#13512yescomplemented
119C22×C149C22×D411yescharacteristic
120C2×D149—28no—
121C2×D149—21no—
122C2×D149—21no—
123C2×D149—21no—
124C2×D149—21no—
125C2×D149—42no—
126C2×D149—42no—
127C2×D149—42no—
128C2×D149#12112yes—
129C2×D149#13512yescomplemented
130C4×C149—21no—
131C4×C149—42no—
132C4×C149—42no—
133C4×C149C22×D411yescharacteristic
134C4×C149C2×#4111yescharacteristic
135Dic149—21no—
136Dic149—42no—
137Dic149#12112yes—
138C2×C149—22no—
139C2×C149C2×#12111yescharacteristic
140C2×C149C2×#13511yescharacteristic
141C2×C149C2×#13511yescharacteristic
142D149—22no—
143D149—22no—
144D149—82no—
145C149#305011yescharacteristic, complemented, Sylow
146#3050—1491nomaximal, Sylow
147C2×#135—1491no—
148C23×C8—1491no—
149#525—1492no—
150#467—1491no—
151#467D14911yescharacteristic, complemented
152#466—1491no—
153#466—1491no—
154#465—1492no—
155#465—1492no—
156#427—1491no—
157#416—1492no—
158C2×#41—1492no—
159C23×C4—1491no—
160#135—2984no—
161C2×Q16C2×D14911yescharacteristic, complemented
162C2×SD16—1492no—
163C2×D8—1491no—
164C22×C8—2984no—
165C22×C8—1491no—
166C22×C8—1491no—
167C22×C8—1491no—
168C22×C8—1491no—
169C22×C8—1491no—
170C22×C8C2×D14911yescharacteristic
171#123—2982no—
172C22⋊Q8—1492no—
173C22⋊Q8C2×D14912yes—
174#121—1492no—
175#121—1492no—
176#120—2982no—
177C4×D4—2982no—
178C4×D4—2982no—
179#117—1492no—
180#107—1491no—
181#107C2×D14911yescharacteristic, complemented
182#106—1492no—
183#103—1492no—
184#103C2×D14912yescomplemented
185#102—1492no—
186#102—1492no—
187C24—1491no—
188#41—2984no—
189#41—2984no—
190C2×Q8C22×D14912yes—
191C2×D4—2982no—
192C2×D4—2982no—
193C2×D4—2982no—
194C2×D4—1492no—
195C22×C4—2982no—
196C22×C4—2982no—
197C22×C4—2982no—
198C22×C4—1491no—
199C22×C4—1491no—
200C22×C4—1491no—
201C22×C4—1491no—
202C22×C4—1491no—
203C22×C4C22×D14911yescharacteristic
204Q16—22no—
205SD16—2984no—
206D8—2982no—
207C2×C8—22no—
208C2×C8—2982no—
209C2×C8—2982no—
210C2×C8—2982no—
211C2×C8—2982no—
212C2×C8—1491no—
213C2×C8—1491no—
214C2×C8—1494no—
215C2×C8C22×D14911yescharacteristic
216C2×C8C22×D14911yescharacteristic
217C4⋊C4—22no—
218C4⋊C4—2982no—
219C4⋊C4—1492no—
220C4⋊C4C22×D14912yes—
221C22⋊C4—22no—
222C22⋊C4—2982no—
223C22⋊C4—2982no—
224C22⋊C4—2982no—
225C22⋊C4—2982no—
226C42—2982no—
227C23—2982no—
228C23—2982no—
229C23—2982no—
230C23—2982no—
231C23—1491no—
232C23—1491no—
233C23D4×D14911yescharacteristic
234Q8—22no—
235Q8—22no—
236D4—2982no—
237D4—2982no—
238D4—5964no—
239D4—5964no—
240D4—5964no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—2982no—
246C2×C4—2982no—
247C2×C4—2982no—
248C2×C4—2981no—
249C2×C4—2981no—
250C2×C4—2982no—
251C2×C4—5964no—
252C2×C4—1491no—
253C2×C4—1491no—
254C2×C4—1492no—
255C2×C4—1492no—
256C2×C4D4×D14911yescharacteristic
257C2×C4C23×D14911yescharacteristic
258C8—21no—
259C8—2981no—
260C8—1492no—
261C8D4×D14912yes—
262C22—21no—
263C22—21no—
264C22—2988no—
265C22—2981no—
266C22—2981no—
267C22—2981no—
268C22—2981no—
269C22—5962no—
270C22—5962no—
271C22—5962no—
272C22—1492no—
273C22—1492no—
274C22#1801193412yescomplemented
275C22C2×D4×D14911yescharacteristic
276C4—21no—
277C4—42no—
278C4—42no—
279C4—2981no—
280C4—5962no—
281C4—1492no—
282C4C2×D4×D14911yescharacteristic
283C4#41×D14911yescharacteristic
284C2—22no—
285C2—2982no—
286C2—2982no—
287C2—11922no—
288C2#121×D14911yescharacteristic
289C2#135×D14911yescharacteristic
290C2C2×#1801193411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#467×C149C2
socleC22×C149C22×D4
hypercenter#467D149
hypocenterC149#3050
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. C2×#18011934C2semidirect
2. C22×C8×D149C2semidirect
3. #23750138C2semidirect
4. #23749863C2semidirect
5. #23749862C2semidirect
6. #23749861C2semidirect
7. #23749857C2semidirect
8. #23749856C2semidirect
9. #23749662C2semidirect
10. #23749620C2semidirect
11. #467×C149C2semidirect
15. C2×#14558723C22semidirect
16. C2×D1192C22semidirect
31. #18011845C22semidirect
32. #18011842C22semidirect
33. #18011835C22semidirect
34. #18011833C22semidirect
35. #18011831C22semidirect
36. C2×Q16×C149C22semidirect
39. #107×C149C22semidirect
40. #103×C149C22semidirect
64. C8×D149D4semidirect
118. C22×C149#135semidirect
129. C2×D149#135semidirect
145. C149#3050semidirect
151. #467D149semidirect
161. C2×Q16C2×D149semidirect
181. #107C2×D149semidirect
184. #103C2×D149semidirect
274. C22#18011934semidirect

Maximal subgroups

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

subgroupindex
C2×#180119342
C22×C8×D1492
#237501382
#237498632
#237498622
#237498612
#237498572
#237498562
#237496622
#237496202
#467×C1492
#3050149