Finite Group Databasebeta

← #34056498

Subgroups — #34056498

Order 19072.

494 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 139 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
1D4×D596C211yesmaximal, characteristic, complemented
2#23749973C211yesmaximal, characteristic, complemented
3#23749938C212yesmaximal, complemented
4#23749902C211yesmaximal, characteristic, complemented
5#23749859C212yesmaximal, complemented
6#23749820C211yesmaximal, characteristic, complemented
7#23749758C212yesmaximal, complemented
8C4×#14558721C211yesmaximal, characteristic, complemented
9D4×#11924746C211yesmaximal, characteristic, complemented
10C2×#18011831C212yesmaximal, complemented
11#547×C149C211yesmaximal, characteristic, complemented
12C22×D596C2212yes—
13C2×D4×D149—21no—
14C2×#14558721C2211yescharacteristic
15C2×#14558721C2212yescomplemented
16C22×#11924746C2212yescomplemented
17#18011908C2211yescharacteristic
18#18011886—21no—
19#18011885C2212yes—
20#18011881—22no—
21C4×D596C2211yescharacteristic
22#18011844C2212yescomplemented
23#18011844C2211yescharacteristic, complemented
24C4⋊#11924746C2211yescharacteristic, complemented
25#18011832C2211yescharacteristic, complemented
26#18011831C2212yes—
27#18011831C2211yescharacteristic
28#18011831C2212yescomplemented
29#18011831C2212yescomplemented
30#18011831C2212yescomplemented
31C22⋊#11924746C2212yescomplemented
32C4×#11924746C2211yescharacteristic, complemented
33C2×#41×C149—21no—
34C4⋊Q8×C149C2211yescharacteristic, complemented
35#123×C149—22no—
36C22⋊Q8×C149—21no—
37#121×C149C2212yescomplemented
38C4×D4×C149C2211yescharacteristic
39C4×D4×C149C2211yescharacteristic, complemented
40C2×C4⋊C4×C149C2212yescomplemented
41C23×D149—22no—
42C2×D596—24no—
43C2×D596—21no—
44C2×D596—22no—
45C2×D596—21no—
46C2×D596—42no—
47C2×D596C2312yes—
48C2×D596C2311yescharacteristic
49C2×C22⋊D149—22no—
50D4×D149—44no—
51C2×C4×D149—21no—
52#14558721—22no—
53#14558721—42no—
54C2×#11924746—42no—
55C2×#11924746C2311yescharacteristic
56C2×#11924746C2312yes—
57C2×#11924746C2311yescharacteristic
58C4⋊Dic149C2311yescharacteristic
59#14558713—21no—
60#14558713—22no—
61#41×C149—44no—
62C2×Q8×C149—21no—
63C2×D4×C149—22no—
64C2×D4×C149D411yescharacteristic
65C2×D4×C149C2311yescharacteristic
66C22×C4×C149—22no—
67C22×C4×C149—21no—
68C22×C4×C149C2312yes—
69C4⋊C4×C149—22no—
70C4⋊C4×C149—21no—
71C4⋊C4×C149D411yescharacteristic
72C4⋊C4×C149C2311yescharacteristic
73C4⋊C4×C149C2312yes—
74C22⋊C4×C149—21no—
75C22⋊C4×C149—22no—
76C22⋊C4×C149D412yes—
77C42×C149C2311yescharacteristic
78C22×D149—21no—
79C22×D149—22no—
80C22×D149—44no—
81C22×D149—44no—
82C22×D149—82no—
83D596—22no—
84D596—21no—
85D596—22no—
86D596—44no—
87D596—42no—
88D596—81no—
89D596#4112yescomplemented
90C22⋊D149—44no—
91C2×Dic149—21no—
92C4×D149—42no—
93#11924746—21no—
94#11924746—22no—
95#11924746—21no—
96C23×C149—21no—
97C23×C149C2×D412yes—
98Q8×C149—42no—
99D4×C149—21no—
100D4×C149—21no—
101D4×C149—44no—
102D4×C149D814yescomplemented
103C2×C4×C149—22no—
104C2×C4×C149—22no—
105C2×C4×C149—21no—
106C2×C4×C149—22no—
107C2×C4×C149—44no—
108C2×C4×C149—42no—
109C2×C4×C149C2×D411yescharacteristic
110C2×C4×C149C2×D412yes—
111C2×C4×C149C2×D411yescharacteristic
112C2×C4×C149C2411yescharacteristic
113C22×C149—22no—
114C22×C149—22no—
115C22×C149—41no—
116C22×C149—41no—
117C22×C149—41no—
118C22×C149C2×D814yes—
119C22×C149C22×D411yescharacteristic
120C2×D149—22no—
121C2×D149—41no—
122C2×D149—41no—
123C2×D149—42no—
124C2×D149—42no—
125C2×D149—42no—
126C2×D149—88no—
127C4×C149—22no—
128C4×C149—21no—
129C4×C149—41no—
130C4×C149—42no—
131C4×C149C2×D812yes—
132C4×C149C2×#4111yescharacteristic
133C4×C149H(5,𝔽2)11yescharacteristic
134Dic149—41no—
135C2×C149—24no—
136C2×C149—81no—
137C2×C149#54611yescharacteristic
138C2×C149C22×D811yescharacteristic
139C2×C149#57711yescharacteristic
140D149—42no—
141D149—82no—
142C149#329411yescharacteristic, complemented, Sylow
143#3294—1491nomaximal, Sylow
144#547D14911yescharacteristic, complemented
145D42—1491no—
146#486—1491no—
147#480—1492no—
148#474—1491no—
149#466—1492no—
150#459—1491no—
151#447—1492no—
152C4×D8—1491no—
153C8×D4—1491no—
154C2×#102—1492no—
155C2×#41—21no—
156C22×D4—2981no—
157C22×D4—1492no—
158C2×D8—1491no—
159C2×D8—1492no—
160C22×C8—1492no—
161C4⋊Q8C2×D14911yescharacteristic, complemented
162#127—1491no—
163#123—22no—
164C22⋊Q8—21no—
165#121—2981no—
166#121—1492no—
167#121C2×D14912yescomplemented
168#120—2982no—
169C4×D4—1491no—
170C4×D4C2×D14911yescharacteristic
171C4×D4C2×D14911yescharacteristic, complemented
172C2×C4⋊C4C2×D14912yescomplemented
173#107—1491no—
174#107—1492no—
175C4⋊C8—1491no—
176#102—1491no—
177#102—1491no—
178#102—1492no—
179#102—1492no—
180#102—1492no—
181#102—1492no—
182C22⋊C8—1492no—
183C4×C8—1491no—
184C24—2982no—
185#41—44no—
186C2×Q8—21no—
187C2×D4—22no—
188C2×D4—2984no—
189C2×D4—2982no—
190C2×D4—2982no—
191C2×D4—2981no—
192C2×D4—2981no—
193C2×D4—5962no—
194C2×D4—5964no—
195C2×D4—1492no—
196C2×D4—1491no—
197C2×D4C22⋊D14911yescharacteristic
198C2×D4C22×D14911yescharacteristic
199C22×C4—22no—
200C22×C4—21no—
201C22×C4—2981no—
202C22×C4C22×D14912yes—
203D8—2982no—
204D8—5962no—
205C2×C8—5962no—
206C2×C8—1491no—
207C2×C8—1491no—
208C2×C8—1492no—
209C4⋊C4—22no—
210C4⋊C4—21no—
211C4⋊C4—1491no—
212C4⋊C4C22⋊D14911yescharacteristic
213C4⋊C4C22×D14911yescharacteristic
214C4⋊C4C22×D14912yes—
215C22⋊C4—21no—
216C22⋊C4—22no—
217C22⋊C4—2981no—
218C22⋊C4—2982no—
219C22⋊C4C22⋊D14912yes—
220C42C22×D14911yescharacteristic
221C23—21no—
222C23—2981no—
223C23—2982no—
224C23—5964no—
225C23—5964no—
226C23—11922no—
227C23C2×C22⋊D14912yes—
228Q8—42no—
229D4—21no—
230D4—21no—
231D4—44no—
232D4—2982no—
233D4—2981no—
234D4—2982no—
235D4—5964no—
236D4—5964no—
237D4—5962no—
238D4—1492no—
239D4—11921no—
240D4#1455872114yescomplemented
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—44no—
246C2×C4—42no—
247C2×C4—2981no—
248C2×C4—5962no—
249C2×C4C2×C22⋊D14911yescharacteristic
250C2×C4C2×C22⋊D14912yes—
251C2×C4C2×C22⋊D14911yescharacteristic
252C2×C4C23×D14911yescharacteristic
253C8—2981no—
254C8—2981no—
255C8—2982no—
256C22—22no—
257C22—22no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—2982no—
262C22—5961no—
263C22—5961no—
264C22—5962no—
265C22—5962no—
266C22—5962no—
267C22—11928no—
268C22C2×#1455872114yes—
269C22C22×C22⋊D14911yescharacteristic
270C4—21no—
271C4—22no—
272C4—41no—
273C4—42no—
274C4—5961no—
275C4C2×#1455872112yes—
276C4#41×D14911yescharacteristic
277C4#1801195711yescharacteristic
278C2—24no—
279C2—81no—
280C2—5962no—
281C2—11922no—
282C2#2375026311yescharacteristic
283C2C22×#1455872111yescharacteristic
284C2#2375043311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#547×C149C2
socleC22×C149C22×D4
hypercenter#547D149
hypocenterC149#3294
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. D4×D596C2semidirect
2. #23749973C2semidirect
3. #23749938C2semidirect
4. #23749902C2semidirect
5. #23749859C2semidirect
6. #23749820C2semidirect
7. #23749758C2semidirect
8. C4×#14558721C2semidirect
9. D4×#11924746C2semidirect
10. C2×#18011831C2semidirect
11. #547×C149C2semidirect
15. C2×#14558721C22semidirect
16. C22×#11924746C22semidirect
22. #18011844C22semidirect
23. #18011844C22semidirect
24. C4⋊#11924746C22semidirect
25. #18011832C22semidirect
28. #18011831C22semidirect
29. #18011831C22semidirect
30. #18011831C22semidirect
31. C22⋊#11924746C22semidirect
32. C4×#11924746C22semidirect
34. C4⋊Q8×C149C22semidirect
37. #121×C149C22semidirect
39. C4×D4×C149C22semidirect
40. C2×C4⋊C4×C149C22semidirect
89. D596#41semidirect
102. D4×C149D8semidirect
142. C149#3294semidirect
144. #547D149semidirect
161. C4⋊Q8C2×D149semidirect
167. #121C2×D149semidirect
171. C4×D4C2×D149semidirect
172. C2×C4⋊C4C2×D149semidirect
240. D4#14558721semidirect

Maximal subgroups

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

subgroupindex
D4×D5962
#237499732
#237499382
#237499022
#237498592
#237498202
#237497582
C4×#145587212
D4×#119247462
C2×#180118312
#547×C1492
#3294149