Finite Group Databasebeta

← #34055656

Subgroups — #34055656

Order 19072.

410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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#23750159C211yesmaximal, characteristic, complemented
2#23750007C212yesmaximal, complemented
3#23749979C212yesmaximal, complemented
4#23749844C212yesmaximal, complemented
5#23749837C212yesmaximal, complemented
6#23749781C211yesmaximal, characteristic, complemented
7#23749776C211yesmaximal, characteristic, complemented
8#23749764C211yesmaximal, characteristic, complemented
9#23749759C211yesmaximal, characteristic
10#23749678C211yesmaximal, characteristic, complemented
11C2×#124×C149C211yesmaximal, characteristic, complemented
12C2×#14558726C2212yescomplemented
13C2×#14558724C2212yes—
14C2×#14558723C2212yescomplemented
15C2×#14558721C2212yes—
16#18011905—21no—
17#18011903C2211yescharacteristic, complemented
18#18011899C2211yescharacteristic, complemented
19#18011894—21no—
20#18011890C2211yescharacteristic
21#18011885C2211yescharacteristic
22C4×Dic298C2211yescharacteristic, complemented
23C4×D596C2211yescharacteristic, complemented
24C4×C22⋊D149—21no—
25#18011868—21no—
26C4⋊#11924746C2212yescomplemented
27#18011835C2212yescomplemented
28#18011835C2212yescomplemented
29#18011832C2212yes—
30#18011832C2212yes—
31C22⋊#11924746C2211yescharacteristic
32C22⋊#11924746C2211yescharacteristic
33C4×#11924746C2212yescomplemented
34C22×Q8×C149C2211yescharacteristic
35C22×D4×C149C2211yescharacteristic
36#124×C149—21no—
37#124×C149—21no—
38#124×C149C2212yes—
39#124×C149C2212yes—
40C2×C22⋊C4×C149—21no—
41C2×C22⋊C4×C149—21no—
42C2×C42×C149C2211yescharacteristic
43C2×Dic298C2311yescharacteristic
44C2×D596C2311yescharacteristic
45C2×C22⋊D149—21no—
46C2×C4×D149—21no—
47#14558726—42no—
48#14558724—42no—
49#14558723—42no—
50#14558721—42no—
51C2×#11924746C2312yes—
52C2×#11924746C2312yes—
53C4⋊Dic149C2311yescharacteristic
54C4⋊Dic149C2311yescharacteristic
55#14558715—21no—
56#14558715—21no—
57#14558715—21no—
58#14558715—21no—
59C22⋊Dic149—21no—
60#14558713—21no—
61#14558713—21no—
62#14558713—21no—
63#14558713—21no—
64C4×Dic149—21no—
65C24×C149—21no—
66C2×Q8×C149—21no—
67C2×Q8×C149—42no—
68C2×Q8×C149C2312yes—
69C2×D4×C149—21no—
70C2×D4×C149—42no—
71C2×D4×C149C2312yes—
72C22×C4×C149—21no—
73C22×C4×C149D411yescharacteristic
74C22×C4×C149D411yescharacteristic
75C22×C4×C149C2311yescharacteristic
76C22⋊C4×C149—22no—
77C22⋊C4×C149—22no—
78C22⋊C4×C149—22no—
79C22⋊C4×C149—22no—
80C42×C149D411yescharacteristic
81C42×C149D411yescharacteristic
82C42×C149C2311yescharacteristic
83C42×C149C2311yescharacteristic
84C22×D149—21no—
85Dic298—22no—
86D596—22no—
87C22⋊D149—42no—
88C2×Dic149—21no—
89C2×Dic149—21no—
90C2×Dic149—21no—
91C4×D149—42no—
92#11924746—22no—
93#11924746—22no—
94C23×C149—22no—
95C23×C149—42no—
96C23×C149—42no—
97C23×C149—42no—
98C23×C149C2×D411yescharacteristic
99Q8×C149—22no—
100Q8×C149—22no—
101Q8×C149—42no—
102D4×C149—22no—
103D4×C149—22no—
104D4×C149—42no—
105C2×C4×C149—22no—
106C2×C4×C149—22no—
107C2×C4×C149—22no—
108C2×C4×C149—41no—
109C2×C4×C149—42no—
110C2×C4×C149C2×D411yescharacteristic
111C2×C4×C149C2×D411yescharacteristic
112C2×C4×C149C2×D411yescharacteristic
113C2×C4×C149C2×D411yescharacteristic
114C2×C4×C149C2×D411yescharacteristic
115C2×C4×C149C2411yescharacteristic
116C22×C149—21no—
117C22×C149—21no—
118C22×C149—42no—
119C22×C149—42no—
120C22×C149—42no—
121C22×C149—84no—
122C22×C149#13512yes—
123C22×C149C22×D411yescharacteristic
124C2×D149—41no—
125C2×D149—41no—
126C2×D149—41no—
127C4×C149—21no—
128C4×C149—21no—
129C4×C149—21no—
130C4×C149—21no—
131C4×C149—21no—
132C4×C149—42no—
133C4×C149H(5,𝔽2)12yes—
134Dic149—41no—
135Dic149—41no—
136Dic149—41no—
137C2×C149—22no—
138C2×C149—82no—
139C2×C149#53511yescharacteristic
140C2×C149C2×#13511yescharacteristic
141C2×C149#57511yescharacteristic
142D149—81no—
143C149#321111yescharacteristic, complemented, Sylow
144#3211—1491nomaximal, Sylow
145#529—1491no—
146C2×#124D14911yescharacteristic, complemented
147#495—1492no—
148#488—1492no—
149#464—1492no—
150#463—1492no—
151#451—1491no—
152#450—1491no—
153#448—1491no—
154#447—1491no—
155#431—1491no—
156C22×Q8C2×D14911yescharacteristic
157C22×D4C2×D14911yescharacteristic
158C2×Q16—1492no—
159C2×SD16—1492no—
160C2×SD16—1492no—
161C2×D8—1492no—
162#126—2981no—
163#125—1491no—
164#124—21no—
165#124—21no—
166#124—1491no—
167#124C2×D14912yes—
168#124C2×D14912yes—
169#123—2981no—
170C22⋊Q8—1491no—
171#121—1491no—
172C4×Q8—1491no—
173C4×D4—2981no—
174C4×D4—1491no—
175#117—2981no—
176C2×C22⋊C4—21no—
177C2×C22⋊C4—21no—
178C2×C42C2×D14911yescharacteristic
179C4⋊C8—1492no—
180#103—1492no—
181#103—1492no—
182#102—1492no—
183#102—1492no—
184C22⋊C8—1491no—
185C22⋊C8—1491no—
186C4×C8—1492no—
187C24—21no—
188C2×Q8—21no—
189C2×Q8—42no—
190C2×Q8—1491no—
191C2×Q8C22×D14912yes—
192C2×D4—21no—
193C2×D4—42no—
194C2×D4—2981no—
195C2×D4—1491no—
196C2×D4C22×D14912yes—
197C22×C4—21no—
198C22×C4—2981no—
199C22×C4C22⋊D14911yescharacteristic
200C22×C4C22⋊D14911yescharacteristic
201C22×C4C22×D14911yescharacteristic
202Q16—5962no—
203SD16—5962no—
204SD16—5962no—
205D8—5962no—
206C2×C8—1492no—
207C2×C8—1492no—
208C4⋊C4—2981no—
209C4⋊C4—2981no—
210C4⋊C4—2981no—
211C4⋊C4—2981no—
212C4⋊C4—1491no—
213C4⋊C4—1491no—
214C22⋊C4—22no—
215C22⋊C4—22no—
216C22⋊C4—22no—
217C22⋊C4—22no—
218C22⋊C4—2981no—
219C22⋊C4—2981no—
220C22⋊C4—2981no—
221C22⋊C4—2981no—
222C22⋊C4—2981no—
223C42—2981no—
224C42C22⋊D14911yescharacteristic
225C42C22⋊D14911yescharacteristic
226C42C22×D14911yescharacteristic
227C42C22×D14911yescharacteristic
228C23—22no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23—2981no—
233C23C2×C22⋊D14911yescharacteristic
234Q8—22no—
235Q8—22no—
236Q8—42no—
237Q8—2982no—
238D4—22no—
239D4—22no—
240D4—42no—
241D4—2982no—
242D4—5962no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—2981no—
249C2×C4—2981no—
250C2×C4—2981no—
251C2×C4—5962no—
252C2×C4C2×C22⋊D14911yescharacteristic
253C2×C4C2×C22⋊D14911yescharacteristic
254C2×C4C2×C22⋊D14911yescharacteristic
255C2×C4C2×C22⋊D14911yescharacteristic
256C2×C4C2×C22⋊D14911yescharacteristic
257C2×C4C23×D14911yescharacteristic
258C8—2982no—
259C8—2982no—
260C22—21no—
261C22—21no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—84no—
266C22—5961no—
267C22—5961no—
268C22—5961no—
269C22#1801193112yes—
270C22C22×C22⋊D14911yescharacteristic
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—21no—
276C4—42no—
277C4—5961no—
278C4—5961no—
279C4—5961no—
280C4#1801195612yes—
281C2—22no—
282C2—82no—
283C2—11921no—
284C2#2375019211yescharacteristic
285C2C2×#1801193111yescharacteristic
286C2#2375042311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#124×C149C2
socleC22×C149C22×D4
prime radical#23749759C2
hypercenterC2×#124D149
hypocenterC149#3211
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #23750159C2semidirect
2. #23750007C2semidirect
3. #23749979C2semidirect
4. #23749844C2semidirect
5. #23749837C2semidirect
6. #23749781C2semidirect
7. #23749776C2semidirect
8. #23749764C2semidirect
10. #23749678C2semidirect
11. C2×#124×C149C2semidirect
12. C2×#14558726C22semidirect
14. C2×#14558723C22semidirect
17. #18011903C22semidirect
18. #18011899C22semidirect
22. C4×Dic298C22semidirect
23. C4×D596C22semidirect
26. C4⋊#11924746C22semidirect
27. #18011835C22semidirect
28. #18011835C22semidirect
33. C4×#11924746C22semidirect
143. C149#3211semidirect
146. C2×#124D149semidirect

Maximal subgroups

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

subgroupindex
#237501592
#237500072
#237499792
#237498442
#237498372
#237497812
#237497762
#237497642
#237497592
#237496782
C2×#124×C1492
#3211149