Finite Group Databasebeta

← #34055675

Subgroups — #34055675

Order 19072.

444 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 113 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#23750170C211yesmaximal, characteristic, complemented
2C2×#18011898C211yesmaximal, characteristic, complemented
3#23750013C212yesmaximal, complemented
4#23749983C212yesmaximal, complemented
5#23749839C212yesmaximal, complemented
6#23749838C212yesmaximal, complemented
7#23749766C211yesmaximal, characteristic, complemented
8#23749763C211yesmaximal, characteristic, complemented
9#23749759C211yesmaximal, characteristic, complemented
10#23749679C211yesmaximal, characteristic, complemented
11#447×C149C211yesmaximal, characteristic, complemented
12C2×#14558735—21no—
13C22×Dic298C2211yescharacteristic
14C2×#14558725C2212yescomplemented
15C2×#14558724C2212yescomplemented
16C2×#14558721C2212yes—
17#18011910C2211yescharacteristic, complemented
18#18011907C2211yescharacteristic, complemented
19#18011898—21no—
20#18011898—21no—
21#18011898C2212yes—
22#18011898C2212yes—
23#18011897—21no—
24#18011885C2211yescharacteristic
25#18011883—21no—
26D4×Dic149C2211yescharacteristic, complemented
27#18011873C2211yescharacteristic, complemented
28#18011871—21no—
29C2×C22⋊Dic149—21no—
30C2×C22⋊Dic149—21no—
31C2×C4×Dic149C2211yescharacteristic
32#18011840C2212yescomplemented
33#18011836C2212yescomplemented
34#18011834C2212yescomplemented
35#18011832C2212yes—
36C22⋊#11924746C2211yescharacteristic
37#18011821C2212yescomplemented
38C22×D4×C149C2211yescharacteristic
39C2×D8×C149C2212yes—
40#121×C149C2211yescharacteristic
41#102×C149C2212yes—
42C22⋊C8×C149C2211yescharacteristic
43#14558735—44no—
44C2×Dic298—21no—
45C2×Dic298—21no—
46C2×Dic298—42no—
47C2×Dic298C2312yes—
48C2×D596C2311yescharacteristic
49C2×C22⋊D149—21no—
50C2×C22⋊D149—21no—
51C2×C22⋊D149—21no—
52C22×Dic149—21no—
53C22×Dic149—21no—
54C22×Dic149D411yescharacteristic
55C22×Dic149D411yescharacteristic
56C2×C4×D149—21no—
57#14558725—42no—
58#14558724—42no—
59#14558721—42no—
60C2×#11924746C2312yes—
61C4⋊Dic149C2311yescharacteristic
62#14558715—21no—
63C22⋊Dic149—22no—
64C22⋊Dic149—22no—
65C22⋊Dic149—22no—
66C22⋊Dic149—22no—
67C22⋊Dic149—21no—
68#14558713—21no—
69#14558713—21no—
70C4×Dic149D411yescharacteristic
71C4×Dic149D411yescharacteristic
72C4×Dic149C2311yescharacteristic
73C4×Dic149C2311yescharacteristic
74C24×C149—21no—
75C2×D4×C149—21no—
76C2×D4×C149—21no—
77C2×D4×C149—42no—
78C2×D4×C149C2311yescharacteristic
79C2×D4×C149C2312yes—
80C22×C4×C149C2311yescharacteristic
81D8×C149—42no—
82C2×C8×C149C2312yes—
83C4⋊C4×C149C2311yescharacteristic
84C22⋊C4×C149—21no—
85C22×D149—21no—
86Dic298—22no—
87Dic298—22no—
88Dic298—42no—
89Dic298—42no—
90D596—22no—
91C22⋊D149—42no—
92C22⋊D149—42no—
93C22⋊D149—42no—
94C2×Dic149—22no—
95C2×Dic149—21no—
96C2×Dic149—22no—
97C2×Dic149—41no—
98C2×Dic149—42no—
99C2×Dic149—42no—
100C2×Dic149C2×D411yescharacteristic
101C2×Dic149C2×D411yescharacteristic
102C2×Dic149C2×D411yescharacteristic
103C2×Dic149C2×D411yescharacteristic
104C4×D149—42no—
105#11924746—22no—
106C23×C149—21no—
107C23×C149—22no—
108C23×C149—42no—
109C23×C149—42no—
110C23×C149—42no—
111C23×C149C2×D411yescharacteristic
112D4×C149—22no—
113D4×C149—22no—
114D4×C149—22no—
115D4×C149—42no—
116D4×C149—42no—
117C2×C4×C149—22no—
118C2×C4×C149—21no—
119C2×C4×C149C2×D411yescharacteristic
120C2×C4×C149C2411yescharacteristic
121C8×C149—22no—
122C22×C149—21no—
123C22×C149—21no—
124C22×C149—42no—
125C22×C149—41no—
126C22×C149—41no—
127C22×C149—42no—
128C22×C149—42no—
129C22×C149—41no—
130C22×C149—84no—
131C22×C149AGL(1,ℤ/8)12yes—
132C22×C149C22×D411yescharacteristic
133C2×D149—41no—
134C2×D149—41no—
135C2×D149—41no—
136C4×C149—21no—
137C4×C149—41no—
138C4×C149H(5,𝔽2)12yes—
139Dic149—21no—
140Dic149—21no—
141Dic149—21no—
142Dic149—21no—
143Dic149—42no—
144Dic149—41no—
145C2×C149—22no—
146C2×C149—81no—
147C2×C149—82no—
148C2×C149#53511yescharacteristic
149C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
150C2×C149#57511yescharacteristic
151D149—81no—
152C149#321311yescharacteristic, complemented, Sylow
153#3213—1491nomaximal, Sylow
154#532—1491no—
155C2×#124—1491no—
156#496—1492no—
157#489—1492no—
158#463—1492no—
159#463—1492no—
160#448—1491no—
161#448—1491no—
162#447—1491no—
163#447D14911yescharacteristic, complemented
164#432—1491no—
165C2×#41—2981no—
166C22×Q8—1491no—
167C22×D4C2×D14911yescharacteristic
168C2×SD16—1492no—
169C2×SD16—1492no—
170C2×D8—1492no—
171C2×D8C2×D14912yes—
172C4⋊Q8—1491no—
173#127—1491no—
174#124—2981no—
175#124—2981no—
176#124—2981no—
177#124—1492no—
178#124—1492no—
179#121—2981no—
180#121—1491no—
181#121C2×D14911yescharacteristic
182C4×D4—2981no—
183C4×D4—1491no—
184C4×D4—1491no—
185C2×C22⋊C4—2981no—
186C2×C22⋊C4—2981no—
187C2×C42—1491no—
188C4⋊C8—1492no—
189#103—1492no—
190#103—1492no—
191#102—1492no—
192#102C2×D14912yes—
193C22⋊C8—1491no—
194C22⋊C8C2×D14911yescharacteristic
195#97—1492no—
196C24—21no—
197#41—5964no—
198C2×Q8—2981no—
199C2×Q8—2981no—
200C2×Q8—5962no—
201C2×Q8—1492no—
202C2×D4—21no—
203C2×D4—21no—
204C2×D4—42no—
205C2×D4—2981no—
206C2×D4—2981no—
207C2×D4—2981no—
208C2×D4—1491no—
209C2×D4C22×D14912yes—
210C2×D4C22×D14911yescharacteristic
211C22×C4—2981no—
212C22×C4—2981no—
213C22×C4—2981no—
214C22×C4—1491no—
215C22×C4—1491no—
216C22×C4C22×D14911yescharacteristic
217SD16—5962no—
218SD16—5962no—
219D8—42no—
220D8—5962no—
221C2×C8—1492no—
222C2×C8C22×D14912yes—
223C4⋊C4—2981no—
224C4⋊C4—1491no—
225C4⋊C4C22×D14911yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—2981no—
228C22⋊C4—2982no—
229C22⋊C4—2982no—
230C22⋊C4—2982no—
231C22⋊C4—2982no—
232C22⋊C4—2981no—
233C22⋊C4—2981no—
234C42—1491no—
235C42—1491no—
236C42—1491no—
237C42—1491no—
238C23—21no—
239C23—22no—
240C23—42no—
241C23—42no—
242C23—42no—
243C23—2981no—
244C23D4×D14911yescharacteristic
245Q8—2982no—
246Q8—2982no—
247Q8—5962no—
248Q8—5962no—
249D4—22no—
250D4—22no—
251D4—22no—
252D4—42no—
253D4—42no—
254D4—2982no—
255D4—5962no—
256D4—5962no—
257D4—5962no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—2982no—
261C2×C4—2982no—
262C2×C4—2981no—
263C2×C4—5962no—
264C2×C4—5961no—
265C2×C4—5962no—
266C2×C4—5962no—
267C2×C4—1491no—
268C2×C4—1491no—
269C2×C4—1491no—
270C2×C4—1491no—
271C2×C4D4×D14911yescharacteristic
272C2×C4C23×D14911yescharacteristic
273C8—22no—
274C8—2982no—
275C22—21no—
276C22—21no—
277C22—41no—
278C22—42no—
279C22—41no—
280C22—42no—
281C22—42no—
282C22—41no—
283C22—84no—
284C22—5961no—
285C22—5961no—
286C22—5961no—
287C22#1801193512yes—
288C22C2×D4×D14911yescharacteristic
289C4—21no—
290C4—41no—
291C4—2981no—
292C4—2981no—
293C4—2981no—
294C4—2981no—
295C4—5961no—
296C4—5962no—
297C4#1801195612yes—
298C2—22no—
299C2—82no—
300C2—81no—
301C2—11921no—
302C2#2375019011yescharacteristic
303C2C2×#1801193511yescharacteristic
304C2#2375042111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#447×C149C2
socleC22×C149C22×D4
hypercenter#447D149
hypocenterC149#3213
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #23750170C2semidirect
2. C2×#18011898C2semidirect
3. #23750013C2semidirect
4. #23749983C2semidirect
5. #23749839C2semidirect
6. #23749838C2semidirect
7. #23749766C2semidirect
8. #23749763C2semidirect
9. #23749759C2semidirect
10. #23749679C2semidirect
11. #447×C149C2semidirect
14. C2×#14558725C22semidirect
15. C2×#14558724C22semidirect
17. #18011910C22semidirect
18. #18011907C22semidirect
26. D4×Dic149C22semidirect
27. #18011873C22semidirect
32. #18011840C22semidirect
33. #18011836C22semidirect
34. #18011834C22semidirect
37. #18011821C22semidirect
152. C149#3213semidirect
163. #447D149semidirect

Maximal subgroups

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

subgroupindex
#237501702
C2×#180118982
#237500132
#237499832
#237498392
#237498382
#237497662
#237497632
#237497592
#237496792
#447×C1492
#3213149