Finite Group Databasebeta

← #34056506

Subgroups — #34056506

Order 19072.

494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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#23750280C211yesmaximal, characteristic, complemented
2D4×D596C211yesmaximal, characteristic, complemented
3#23749972C211yesmaximal, characteristic, complemented
4#23749940C212yesmaximal, complemented
5#23749905C211yesmaximal, characteristic, complemented
6#23749860C212yesmaximal, complemented
7#23749820C211yesmaximal, characteristic, complemented
8#23749757C212yesmaximal, complemented
9C8×D596C211yesmaximal, characteristic, complemented
10#102×D149C212yesmaximal, complemented
11C4×D8×C149C211yesmaximal, characteristic, complemented
12C2×#14558736—21no—
13C22×D596—21no—
14C2×D4×D149C2212yes—
15C2×#14558721C2212yescomplemented
16C2×C8×D149C2212yescomplemented
17#18011911C2211yescharacteristic, complemented
18#18011908C2211yescharacteristic
19#18011893—22no—
20#18011890—21no—
21#18011886C2212yes—
22#18011885—21no—
23#18011882C2212yescomplemented
24#18011881—22no—
25C4×D596C2211yescharacteristic
26C4⋊C4×D149C2212yescomplemented
27#18011844C2212yescomplemented
28C4⋊#11924746C2211yescharacteristic, complemented
29#18011833C2212yescomplemented
30#18011833C2212yescomplemented
31#18011832C2212yes—
32#18011831C2212yescomplemented
33#18011823C2212yescomplemented
34C2×D8×C149C2211yescharacteristic
35C4×D4×C149C2211yescharacteristic
36C4×D4×C149C2211yescharacteristic, complemented
37#107×C149C2211yescharacteristic, complemented
38#102×C149C2211yescharacteristic
39#102×C149C2211yescharacteristic, complemented
40C4×C8×C149C2211yescharacteristic, complemented
41C23×D149—22no—
42#14558736—44no—
43C2×Dic298—21no—
44C2×D596—22no—
45C2×D596—21no—
46C2×D596—21no—
47C2×D596—44no—
48C2×D596D411yescharacteristic
49C2×D596C2312yes—
50C2×C22⋊D149—22no—
51C2×C22⋊D149—22no—
52D4×D149—24no—
53D4×D149—42no—
54C2×C4×D149—22no—
55C2×C4×D149C2312yes—
56#14558721—42no—
57C2×#11924746C2312yes—
58C8×D149—42no—
59C4⋊Dic149—21no—
60C4⋊Dic149D411yescharacteristic
61C4⋊Dic149C2312yes—
62#14558715—22no—
63C22⋊Dic149—22no—
64#14558713—22no—
65#14558713D412yes—
66C2×D4×C149C2311yescharacteristic
67C2×D4×C149C2311yescharacteristic
68C22×C4×C149—21no—
69C22×C4×C149—21no—
70D8×C149—22no—
71C2×C8×C149C2311yescharacteristic
72C2×C8×C149C2311yescharacteristic
73C4⋊C4×C149C2311yescharacteristic
74C4⋊C4×C149C2311yescharacteristic
75C22⋊C4×C149—21no—
76C22⋊C4×C149—21no—
77C42×C149C2311yescharacteristic
78C22×D149—22no—
79C22×D149—44no—
80C22×D149—44no—
81C22×D149—82no—
82C22×D149C2×D412yes—
83Dic298—42no—
84D596—22no—
85D596—22no—
86D596—44no—
87D596—42no—
88D596—81no—
89D596D814yescomplemented
90C22⋊D149—44no—
91C22⋊D149—44no—
92C2×Dic149—22no—
93C2×Dic149C2×D412yes—
94C4×D149—22no—
95C4×D149—22no—
96C4×D149—44no—
97#11924746—22no—
98C23×C149—21no—
99C23×C149—21no—
100D4×C149—21no—
101D4×C149—21no—
102D4×C149—21no—
103D4×C149#4112yescomplemented
104C2×C4×C149—21no—
105C2×C4×C149—21no—
106C2×C4×C149—42no—
107C2×C4×C149—42no—
108C2×C4×C149C2×D411yescharacteristic
109C2×C4×C149C2×D411yescharacteristic
110C2×C4×C149C2411yescharacteristic
111C8×C149—21no—
112C8×C149—21no—
113C22×C149—22no—
114C22×C149—41no—
115C22×C149—41no—
116C22×C149—41no—
117C22×C149—41no—
118C22×C149—41no—
119C22×C149C22×D411yescharacteristic
120C2×D149—22no—
121C2×D149—22no—
122C2×D149—42no—
123C2×D149—42no—
124C2×D149—42no—
125C2×D149—88no—
126C2×D149C2×D814yes—
127C4×C149—21no—
128C4×C149—41no—
129C4×C149—41no—
130C4×C149C2×D812yes—
131C4×C149C2×#4111yescharacteristic
132C4×C149H(5,𝔽2)11yescharacteristic
133Dic149—22no—
134Dic149—42no—
135C2×C149—42no—
136C2×C149—81no—
137C2×C149#54611yescharacteristic
138C2×C149C22×D811yescharacteristic
139C2×C149#57711yescharacteristic
140D149—24no—
141D149—82no—
142C149#329411yescharacteristic, complemented, Sylow
143#3294—1491nomaximal, Sylow
144#547—1491no—
145D42—1491no—
146#486—1491no—
147#480—1492no—
148#474—1491no—
149#466—1492no—
150#459—1491no—
151#447—1492no—
152C4×D8D14911yescharacteristic, complemented
153C8×D4—1491no—
154C2×#102—1492no—
155C2×#41—2981no—
156C22×D4—2981no—
157C22×D4—1492no—
158C2×D8—1492no—
159C2×D8C2×D14911yescharacteristic
160C22×C8—1492no—
161C4⋊Q8—1491no—
162#127—1491no—
163#123—2982no—
164C22⋊Q8—2981no—
165#121—2981no—
166#121—1492no—
167#121—1492no—
168#120—2982no—
169C4×D4—1491no—
170C4×D4C2×D14911yescharacteristic
171C4×D4C2×D14911yescharacteristic, complemented
172C2×C4⋊C4—1492no—
173#107—1492no—
174#107C2×D14911yescharacteristic, complemented
175C4⋊C8—1491no—
176#102—1492no—
177#102—1492no—
178#102—1492no—
179#102—1492no—
180#102C2×D14911yescharacteristic
181#102C2×D14911yescharacteristic, complemented
182C22⋊C8—1492no—
183C4×C8C2×D14911yescharacteristic, complemented
184C24—2982no—
185#41—5964no—
186C2×Q8—2981no—
187C2×D4—2982no—
188C2×D4—2984no—
189C2×D4—2982no—
190C2×D4—2982no—
191C2×D4—2981no—
192C2×D4—2981no—
193C2×D4—5964no—
194C2×D4—5962no—
195C2×D4—1491no—
196C2×D4—1492no—
197C2×D4C22×D14911yescharacteristic
198C2×D4C22×D14911yescharacteristic
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—2982no—
202C22×C4—1492no—
203D8—22no—
204D8—5962no—
205C2×C8—5962no—
206C2×C8—1492no—
207C2×C8C22×D14911yescharacteristic
208C2×C8C22×D14911yescharacteristic
209C4⋊C4—2982no—
210C4⋊C4—2981no—
211C4⋊C4—1492no—
212C4⋊C4—1491no—
213C4⋊C4C22×D14911yescharacteristic
214C4⋊C4C22×D14911yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—21no—
217C22⋊C4—2982no—
218C22⋊C4—2982no—
219C22⋊C4—1492no—
220C42C22×D14911yescharacteristic
221C23—21no—
222C23—21no—
223C23—2982no—
224C23—5964no—
225C23—5964no—
226C23—1492no—
227C23—11922no—
228Q8—5962no—
229D4—21no—
230D4—21no—
231D4—21no—
232D4—2982no—
233D4—2982no—
234D4—5964no—
235D4—5964no—
236D4—5964no—
237D4—5962no—
238D4—1494no—
239D4—11921no—
240D4#1455873612yescomplemented
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—2982no—
246C2×C4—2982no—
247C2×C4—2982no—
248C2×C4—5964no—
249C2×C4—1492no—
250C2×C4D4×D14911yescharacteristic
251C2×C4D4×D14911yescharacteristic
252C2×C4C23×D14911yescharacteristic
253C8—21no—
254C8—21no—
255C8—2982no—
256C22—22no—
257C22—41no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—2982no—
263C22—2982no—
264C22—5962no—
265C22—5962no—
266C22—5962no—
267C22—1494no—
268C22—11928no—
269C22C2×D4×D14911yescharacteristic
270C4—21no—
271C4—41no—
272C4—41no—
273C4—2982no—
274C4—5962no—
275C4D8×D14912yes—
276C4C2×#1455873611yescharacteristic
277C4#1801195711yescharacteristic
278C2—42no—
279C2—81no—
280C2—2984no—
281C2—11922no—
282C2#2375027111yescharacteristic
283C2C2×D8×D14911yescharacteristic
284C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC4×D8×C149C2
socleC22×C149C22×D4
hypercenterC4×D8D149
hypocenterC149#3294
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #23750280C2semidirect
2. D4×D596C2semidirect
3. #23749972C2semidirect
4. #23749940C2semidirect
5. #23749905C2semidirect
6. #23749860C2semidirect
7. #23749820C2semidirect
8. #23749757C2semidirect
9. C8×D596C2semidirect
10. #102×D149C2semidirect
11. C4×D8×C149C2semidirect
15. C2×#14558721C22semidirect
16. C2×C8×D149C22semidirect
17. #18011911C22semidirect
23. #18011882C22semidirect
26. C4⋊C4×D149C22semidirect
27. #18011844C22semidirect
28. C4⋊#11924746C22semidirect
29. #18011833C22semidirect
30. #18011833C22semidirect
32. #18011831C22semidirect
33. #18011823C22semidirect
36. C4×D4×C149C22semidirect
37. #107×C149C22semidirect
39. #102×C149C22semidirect
40. C4×C8×C149C22semidirect
89. D596D8semidirect
103. D4×C149#41semidirect
142. C149#3294semidirect
152. C4×D8D149semidirect
171. C4×D4C2×D149semidirect
174. #107C2×D149semidirect
181. #102C2×D149semidirect
183. C4×C8C2×D149semidirect
240. D4#14558736semidirect

Maximal subgroups

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

subgroupindex
#237502802
D4×D5962
#237499722
#237499402
#237499052
#237498602
#237498202
#237497572
C8×D5962
#102×D1492
C4×D8×C1492
#3294149