Finite Group Databasebeta

← #34045756

Subgroups — #34045756

Order 19072.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#23750423C211yesmaximal, characteristic, complemented
2#23750136C211yesmaximal, characteristic, complemented
3#23749643C211yesmaximal, characteristic, complemented
4#23749642C211yesmaximal, characteristic, complemented
5#23749589C211yesmaximal, characteristic, complemented
6#23749381C211yesmaximal, characteristic, complemented
7#525×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2211yescharacteristic
9#18011942—21no—
10#18011941—21no—
11#18011937—21no—
12#18011936—21no—
13#18011931—22no—
14C2×#14558720C2211yescharacteristic
15C2×#14558720C2211yescharacteristic
16#18011894—21no—
17#18011890—21no—
18#18011885—21no—
19#18011880—21no—
20C4×C22⋊D149—22no—
21#18011870C2211yescharacteristic
22#18011839—22no—
23#18011838—22no—
24C22⋊#11924746—22no—
25C2×#41×C149C2211yescharacteristic
26C23×C4×C149C2211yescharacteristic
27#123×C149—21no—
28C22⋊Q8×C149—21no—
29#121×C149—21no—
30#120×C149—21no—
31C4×D4×C149—22no—
32#117×C149C2211yescharacteristic
33#14558736—21no—
34#14558736—21no—
35#14558736—21no—
36#14558736—21no—
37C2×Dic298D411yescharacteristic, complemented
38C2×D596D411yescharacteristic, complemented
39C2×C22⋊D149—22no—
40C2×C22⋊D149—21no—
41C2×C4×D149—21no—
42#14558726—22no—
43#14558724—22no—
44#14558723—22no—
45#14558721—22no—
46#14558720—21no—
47#14558720—21no—
48#14558720—21no—
49#14558720—21no—
50C2×#11924746—21no—
51C2×#11924746D412yescomplemented
52C4⋊Dic149—21no—
53#14558715—22no—
54C22⋊Dic149—22no—
55C22⋊Dic149—21no—
56#14558713—22no—
57C4×Dic149D412yescomplemented
58C24×C149D411yescharacteristic
59#41×C149—21no—
60#41×C149—21no—
61#41×C149—21no—
62#41×C149—21no—
63C2×Q8×C149D411yescharacteristic, complemented
64C2×D4×C149—22no—
65C2×D4×C149—21no—
66C2×D4×C149D411yescharacteristic, complemented
67C22×C4×C149—21no—
68C22×C4×C149—21no—
69C22×C4×C149—21no—
70C22×C4×C149—21no—
71C22×C4×C149—21no—
72C22×C4×C149—21no—
73C22×C4×C149—21no—
74C22×C4×C149D411yescharacteristic
75C22×C4×C149C2311yescharacteristic
76C4⋊C4×C149—22no—
77C4⋊C4×C149—21no—
78C22⋊C4×C149—22no—
79C22⋊C4×C149—22no—
80C22⋊C4×C149—21no—
81C42×C149D412yescomplemented
82C22×D149—21no—
83Dic298—21no—
84Dic298—21no—
85D596—21no—
86D596—21no—
87C22⋊D149—44no—
88C22⋊D149—41no—
89C22⋊D149—41no—
90C2×Dic149—21no—
91C2×Dic149—22no—
92C4×D149—41no—
93C4×D149—41no—
94#11924746—22no—
95#11924746—41no—
96C23×C149—21no—
97C23×C149—21no—
98C23×C149—21no—
99C23×C149—21no—
100C23×C149—42no—
101C23×C149C2×D411yescharacteristic
102Q8×C149—21no—
103Q8×C149—21no—
104D4×C149—21no—
105D4×C149—21no—
106D4×C149—44no—
107D4×C149—41no—
108D4×C149—41no—
109C2×C4×C149—22no—
110C2×C4×C149—21no—
111C2×C4×C149—21no—
112C2×C4×C149—21no—
113C2×C4×C149—21no—
114C2×C4×C149—41no—
115C2×C4×C149—41no—
116C2×C4×C149—41no—
117C2×C4×C149—41no—
118C2×C4×C149—41no—
119C2×C4×C149—41no—
120C2×C4×C149C2×D411yescharacteristic
121C2×C4×C149C2×D411yescharacteristic
122C2×C4×C149C2×D411yescharacteristic
123C2×C4×C149C2×D411yescharacteristic
124C2×C4×C149C2×D411yescharacteristic
125C2×C4×C149#4111yescharacteristic
126C22×C149—22no—
127C22×C149—22no—
128C22×C149—22no—
129C22×C149—41no—
130C22×C149—41no—
131C22×C149—41no—
132C22×C149—41no—
133C22×C149—42no—
134C22×C149—41no—
135C22×C149—41no—
136C22×C149#12011yescharacteristic
137C22×C149#12011yescharacteristic
138C22×C149#12111yescharacteristic
139C2×D149—42no—
140C2×D149—41no—
141C4×C149—42no—
142C4×C149—41no—
143C4×C149—41no—
144C4×C149#12011yescharacteristic
145C4×C149#12111yescharacteristic
146C4×C149#12111yescharacteristic
147C4×C149#12711yescharacteristic
148Dic149—42no—
149Dic149—41no—
150C2×C149—21no—
151C2×C149—21no—
152C2×C149—21no—
153C2×C149—42no—
154C2×C149—81no—
155C2×C149#39211yescharacteristic
156D149—81no—
157C149#201011yescharacteristic, complemented, Sylow
158#2010—1491nomaximal, Sylow
159#575—1491no—
160#525—1491no—
161#525D14911yescharacteristic, complemented
162#421—1491no—
163#421—1491no—
164#407—1491no—
165H(3,ℤ/4)—1491no—
166C2×#41—1491no—
167C2×#41C2×D14911yescharacteristic
168C23×C4C2×D14911yescharacteristic
169#137—2981no—
170#137—2981no—
171AGL(1,ℤ/8)—2981no—
172AGL(1,ℤ/8)—2981no—
173#135—2982no—
174C2×M16—1491no—
175C2×M16—1491no—
176#123—21no—
177#123—2981no—
178C22⋊Q8—21no—
179C22⋊Q8—2981no—
180#121—21no—
181#121—2981no—
182#120—21no—
183#120—2981no—
184C4×D4—22no—
185C4×D4—2982no—
186#117—1491no—
187#117C2×D14911yescharacteristic
188#104—2982no—
189#104—2982no—
190C22⋊C8—2982no—
191C24C22⋊D14911yescharacteristic
192#41—21no—
193#41—21no—
194#41—21no—
195#41—21no—
196#41—2981no—
197#41—2981no—
198#41—2981no—
199#41—2981no—
200C2×Q8—1491no—
201C2×Q8C22⋊D14911yescharacteristic, complemented
202C2×D4—22no—
203C2×D4—21no—
204C2×D4—2982no—
205C2×D4—2981no—
206C2×D4—1491no—
207C2×D4C22⋊D14911yescharacteristic, complemented
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—2981no—
216C22×C4C22⋊D14911yescharacteristic
217C22×C4C22×D14911yescharacteristic
218Q16—2982no—
219SD16—2982no—
220SD16—2982no—
221D8—2982no—
222M16—2981no—
223M16—2981no—
224M16—2981no—
225M16—2981no—
226C2×C8—2981no—
227C2×C8—1492no—
228C4⋊C4—22no—
229C4⋊C4—21no—
230C4⋊C4—2982no—
231C4⋊C4—2981no—
232C22⋊C4—22no—
233C22⋊C4—22no—
234C22⋊C4—21no—
235C22⋊C4—2982no—
236C22⋊C4—2982no—
237C22⋊C4—2981no—
238C42—1492no—
239C42C22⋊D14912yescomplemented
240C23—21no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—42no—
245C23—2981no—
246C23C2×C22⋊D14911yescharacteristic
247Q8—21no—
248Q8—21no—
249Q8—2981no—
250Q8—2981no—
251D4—21no—
252D4—21no—
253D4—44no—
254D4—41no—
255D4—41no—
256D4—2981no—
257D4—2981no—
258D4—5964no—
259D4—5961no—
260D4—5961no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—2982no—
273C2×C4—2981no—
274C2×C4—5961no—
275C2×C4—5961no—
276C2×C4D4×D14911yescharacteristic
277C2×C4D4×D14911yescharacteristic
278C2×C4D4×D14911yescharacteristic
279C2×C4C2×C22⋊D14911yescharacteristic
280C2×C4C2×C22⋊D14911yescharacteristic
281C2×C4#1455873511yescharacteristic
282C8—2982no—
283C8—5961no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—42no—
292C22—41no—
293C22—41no—
294C22—5962no—
295C22—5961no—
296C22#1801187911yescharacteristic
297C22#1801188011yescharacteristic
298C22#1801188311yescharacteristic
299C4—42no—
300C4—41no—
301C4—41no—
302C4—5962no—
303C4—5961no—
304C4#1801187911yescharacteristic
305C4#1801188211yescharacteristic
306C4#1801188311yescharacteristic
307C4#1801190711yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—42no—
312C2—81no—
313C2—11921no—
314C2#2374953311yescharacteristic
subgroupG/H
centerC4#18011907
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#525×C149C2
socleC2×C149#392
hypercenter#525D149
hypocenterC149#2010
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #23750423C2semidirect
2. #23750136C2semidirect
3. #23749643C2semidirect
4. #23749642C2semidirect
5. #23749589C2semidirect
6. #23749381C2semidirect
7. #525×C149C2semidirect
37. C2×Dic298D4semidirect
38. C2×D596D4semidirect
51. C2×#11924746D4semidirect
57. C4×Dic149D4semidirect
63. C2×Q8×C149D4semidirect
66. C2×D4×C149D4semidirect
81. C42×C149D4semidirect
157. C149#2010semidirect
161. #525D149semidirect
201. C2×Q8C22⋊D149semidirect
207. C2×D4C22⋊D149semidirect
239. C42C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
#237504232
#237501362
#237496432
#237496422
#237495892
#237493812
#525×C1492
#2010149