Finite Group Databasebeta

← #34045757

Subgroups — #34045757

Order 19072.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#23750137C211yesmaximal, characteristic, complemented
3#23750132C211yesmaximal, characteristic, complemented
4#23749641C211yesmaximal, characteristic, complemented
5#23749588C211yesmaximal, characteristic, complemented
6#23749381C211yesmaximal, characteristic, complemented
7#421×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2211yescharacteristic
9C22×C4×D149C2211yescharacteristic
10#18011942—21no—
11#18011941—21no—
12#18011937—21no—
13#18011936—21no—
14#18011931—22no—
15C2×#14558720C2211yescharacteristic
16#18011895—21no—
17#18011892—21no—
18#18011891—21no—
19#18011887—21no—
20#18011886—21no—
21#18011882—21no—
22#18011881—21no—
23#18011879—21no—
24C4×D596—22no—
25C4×C22⋊D149—22no—
26#18011870C2211yescharacteristic
27#18011837—22no—
28#18011823—22no—
29C2×#41×C149C2211yescharacteristic
30C2×M16×C149C2211yescharacteristic
31#117×C149C2211yescharacteristic
32#104×C149—22no—
33C23×D149D411yescharacteristic
34#14558736—21no—
35#14558736—21no—
36#14558736—21no—
37#14558736—21no—
38C2×Dic298D411yescharacteristic, complemented
39C2×D596—22no—
40C2×D596D411yescharacteristic, complemented
41C2×C22⋊D149—22no—
42C2×C22⋊D149—21no—
43C22×Dic149D411yescharacteristic
44C2×C4×D149—21no—
45C2×C4×D149—21no—
46C2×C4×D149—21no—
47C2×C4×D149—21no—
48C2×C4×D149—21no—
49C2×C4×D149—21no—
50C2×C4×D149—21no—
51#14558726—22no—
52#14558724—22no—
53#14558723—22no—
54#14558721—22no—
55#14558720—21no—
56#14558720—21no—
57C2×#11924746D412yescomplemented
58C4⋊Dic149—22no—
59C4⋊Dic149—21no—
60#14558715—22no—
61C22⋊Dic149—22no—
62C22⋊Dic149—21no—
63#14558713—22no—
64#14558713—22no—
65#14558713—22no—
66C4×Dic149D412yescomplemented
67#41×C149—21no—
68#41×C149—21no—
69#41×C149—21no—
70#41×C149—21no—
71C2×Q8×C149D411yescharacteristic, complemented
72C2×D4×C149—21no—
73C2×D4×C149D411yescharacteristic, complemented
74C22×C4×C149—21no—
75C22×C4×C149C2311yescharacteristic
76M16×C149—21no—
77M16×C149—21no—
78C2×C8×C149—21no—
79C4⋊C4×C149—21no—
80C22⋊C4×C149—21no—
81C42×C149D412yescomplemented
82C22×D149—21no—
83C22×D149—21no—
84C22×D149—21no—
85C22×D149—21no—
86C22×D149—42no—
87Dic298—21no—
88Dic298—21no—
89D596—21no—
90D596—21no—
91D596—44no—
92C22⋊D149—44no—
93C22⋊D149—41no—
94C22⋊D149—41no—
95C2×Dic149—21no—
96C2×Dic149—21no—
97C2×Dic149—21no—
98C2×Dic149—22no—
99C2×Dic149—21no—
100C4×D149—41no—
101C4×D149—41no—
102C4×D149—41no—
103C4×D149—41no—
104C4×D149—41no—
105C4×D149—41no—
106#11924746—22no—
107C23×C149—21no—
108C23×C149C2×D411yescharacteristic
109Q8×C149—21no—
110Q8×C149—21no—
111D4×C149—21no—
112D4×C149—21no—
113D4×C149—41no—
114D4×C149—41no—
115C2×C4×C149—22no—
116C2×C4×C149—21no—
117C2×C4×C149—41no—
118C2×C4×C149—41no—
119C2×C4×C149C2×D411yescharacteristic
120C2×C4×C149C2×D411yescharacteristic
121C2×C4×C149C2×D411yescharacteristic
122C2×C4×C149C2×D411yescharacteristic
123C2×C4×C149C2×D411yescharacteristic
124C2×C4×C149#4111yescharacteristic
125C8×C149—41no—
126C22×C149—41no—
127C22×C149—42no—
128C22×C149—41no—
129C22×C149#12011yescharacteristic
130C22×C149#12011yescharacteristic
131C22×C149#12111yescharacteristic
132C2×D149—22no—
133C2×D149—22no—
134C2×D149—22no—
135C2×D149—41no—
136C2×D149—41no—
137C2×D149—41no—
138C2×D149—41no—
139C2×D149—42no—
140C2×D149—41no—
141C4×C149—42no—
142C4×C149—41no—
143C4×C149#12011yescharacteristic
144C4×C149#12111yescharacteristic
145C4×C149#12111yescharacteristic
146C4×C149#12711yescharacteristic
147Dic149—42no—
148Dic149—41no—
149Dic149—41no—
150C2×C149—21no—
151C2×C149—21no—
152C2×C149—21no—
153C2×C149—81no—
154C2×C149#39211yescharacteristic
155D149—42no—
156D149—81no—
157C149#201011yescharacteristic, complemented, Sylow
158#2010—1491nomaximal, Sylow
159#575—1491no—
160#525—1491no—
161#525—1491no—
162#421—1491no—
163#421D14911yescharacteristic, complemented
164#407—1491no—
165H(3,ℤ/4)—1491no—
166C2×#41—1491no—
167C2×#41C2×D14911yescharacteristic
168C23×C4—1491no—
169#137—2981no—
170#137—2981no—
171AGL(1,ℤ/8)—2981no—
172AGL(1,ℤ/8)—2981no—
173#135—2982no—
174C2×M16—1491no—
175C2×M16C2×D14911yescharacteristic
176#123—2981no—
177#123—2981no—
178C22⋊Q8—2981no—
179C22⋊Q8—2981no—
180#121—2981no—
181#121—2981no—
182#120—2981no—
183#120—2981no—
184C4×D4—2982no—
185C4×D4—2982no—
186#117—1491no—
187#117C2×D14911yescharacteristic
188#104—22no—
189#104—2982no—
190C22⋊C8—2982no—
191C24—1491no—
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×Q8D59611yescharacteristic, complemented
202C2×D4—21no—
203C2×D4—2982no—
204C2×D4—2982no—
205C2×D4—2981no—
206C2×D4—1491no—
207C2×D4D59611yescharacteristic, complemented
208C22×C4—21no—
209C22×C4—2981no—
210C22×C4—2981no—
211C22×C4—2981no—
212C22×C4—2981no—
213C22×C4—2981no—
214C22×C4—2981no—
215C22×C4—2981no—
216C22×C4—1491no—
217C22×C4C22×D14911yescharacteristic
218Q16—2982no—
219SD16—2982no—
220SD16—2982no—
221D8—2982no—
222M16—21no—
223M16—21no—
224M16—2981no—
225M16—2981no—
226C2×C8—21no—
227C2×C8—1492no—
228C4⋊C4—21no—
229C4⋊C4—2982no—
230C4⋊C4—2982no—
231C4⋊C4—2981no—
232C22⋊C4—21no—
233C22⋊C4—2982no—
234C22⋊C4—2982no—
235C22⋊C4—2982no—
236C22⋊C4—2982no—
237C22⋊C4—2981no—
238C42—1492no—
239C42C22⋊D14912yescomplemented
240C23—21no—
241C23—2981no—
242C23—2981no—
243C23—2981no—
244C23—2981no—
245C23—5962no—
246C23D4×D14911yescharacteristic
247Q8—21no—
248Q8—21no—
249Q8—2981no—
250Q8—2981no—
251D4—21no—
252D4—21no—
253D4—41no—
254D4—41no—
255D4—2981no—
256D4—2981no—
257D4—5964no—
258D4—5964no—
259D4—5961no—
260D4—5961no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—2981no—
266C2×C4—2981no—
267C2×C4—2982no—
268C2×C4—2981no—
269C2×C4—2981no—
270C2×C4—5961no—
271C2×C4—5961no—
272C2×C4—5961no—
273C2×C4—5961no—
274C2×C4—5961no—
275C2×C4—5961no—
276C2×C4D4×D14911yescharacteristic
277C2×C4D4×D14911yescharacteristic
278C2×C4D4×D14911yescharacteristic
279C2×C4C2×C22⋊D14911yescharacteristic
280C2×C4C2×D59611yescharacteristic
281C2×C4#1455873611yescharacteristic
282C8—41no—
283C8—2982no—
284C22—41no—
285C22—42no—
286C22—41no—
287C22—2982no—
288C22—2982no—
289C22—2982no—
290C22—5961no—
291C22—5961no—
292C22—5961no—
293C22—5962no—
294C22—5961no—
295C22—5961no—
296C22#1801187911yescharacteristic
297C22#1801188111yescharacteristic
298C22#1801188411yescharacteristic
299C4—42no—
300C4—41no—
301C4—5962no—
302C4—5961no—
303C4—5961no—
304C4#1801188111yescharacteristic
305C4#1801188411yescharacteristic
306C4#1801188511yescharacteristic
307C4#1801190711yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—81no—
312C2—5962no—
313C2—11921no—
314C2#2374953411yescharacteristic
subgroupG/H
centerC4#18011907
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#421×C149C2
socleC2×C149#392
hypercenter#421D149
hypocenterC149#2010
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. #23750423C2semidirect
2. #23750137C2semidirect
3. #23750132C2semidirect
4. #23749641C2semidirect
5. #23749588C2semidirect
6. #23749381C2semidirect
7. #421×C149C2semidirect
38. C2×Dic298D4semidirect
40. C2×D596D4semidirect
57. C2×#11924746D4semidirect
66. C4×Dic149D4semidirect
71. C2×Q8×C149D4semidirect
73. C2×D4×C149D4semidirect
81. C42×C149D4semidirect
157. C149#2010semidirect
163. #421D149semidirect
201. C2×Q8D596semidirect
207. C2×D4D596semidirect
239. C42C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
#237504232
#237501372
#237501322
#237496412
#237495882
#237493812
#421×C1492
#2010149