Finite Group Databasebeta

← #34044990

Subgroups — #34044990

Order 19072.

376 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C2×M16×D149C211yesmaximal, characteristic, complemented
2#23750132C211yesmaximal, characteristic
3C2×#18011838C211yesmaximal, characteristic, complemented
4C4×#14558713C211yesmaximal, characteristic, complemented
5#23749386C211yesmaximal, characteristic, complemented
6#23749385C211yesmaximal, characteristic, complemented
7C2×#104×C149C211yesmaximal, characteristic, complemented
8C22×C4×D149C2211yescharacteristic
9C2×#14558720C2211yescharacteristic
10C2×#14558719—21no—
11M16×D149—22no—
12M16×D149—22no—
13C2×C8×D149—21no—
14#18011892—21no—
15#18011887C411yescharacteristic, complemented
16#18011887C411yescharacteristic, complemented
17#18011882C411yescharacteristic, complemented
18#18011882C411yescharacteristic, complemented
19#18011879—21no—
20C4×C22⋊D149—21no—
21C4×C22⋊D149—21no—
22#18011870C2211yescharacteristic
23C2×#14558713—21no—
24C2×C4×Dic149C2211yescharacteristic
25#18011838—22no—
26#18011818—21no—
27C2×#41×C149C2211yescharacteristic
28C2×M16×C149C2211yescharacteristic
29C2×C42×C149C2211yescharacteristic
30#104×C149—22no—
31C23×D149D411yescharacteristic
32C2×C22⋊D149—21no—
33C2×C22⋊D149—21no—
34C22×Dic149—21no—
35C22×Dic149D411yescharacteristic
36C2×C4×D149—21no—
37C2×C4×D149—21no—
38C2×C4×D149—21no—
39C2×C4×D149—21no—
40C2×C4×D149C2×C411yescharacteristic
41C2×C4×D149C2×C411yescharacteristic
42C2×C4×D149D411yescharacteristic
43C2×C4×D149D411yescharacteristic
44#14558720—21no—
45#14558720D412yescomplemented
46#14558719—24no—
47C2×#11924746—21no—
48C8×D149—24no—
49C4⋊Dic149C2×C411yescharacteristic
50C4⋊Dic149C2×C411yescharacteristic
51#14558715—21no—
52#14558715—21no—
53C22⋊Dic149—21no—
54C22⋊Dic149—21no—
55C22⋊Dic149—21no—
56#14558713—24no—
57#14558713—21no—
58#14558713—21no—
59C4×Dic149—21no—
60C4×Dic149—21no—
61C4×Dic149—21no—
62#41×C149—21no—
63#41×C149—21no—
64#41×C149—21no—
65#41×C149—21no—
66C2×Q8×C149C2×C411yescharacteristic
67C2×D4×C149—21no—
68C2×D4×C149C2×C411yescharacteristic
69C22×C4×C149—21no—
70C22×C4×C149—21no—
71C22×C4×C149C2311yescharacteristic
72M16×C149—21no—
73M16×C149D412yescomplemented
74C2×C8×C149—21no—
75C42×C149—21no—
76C42×C149—21no—
77C22×D149—21no—
78C22×D149—21no—
79C22×D149—22no—
80C22×D149—41no—
81C22×D149C22⋊C411yescharacteristic
82C22×D149C22⋊C411yescharacteristic
83C22⋊D149—42no—
84C22⋊D149—42no—
85C2×Dic149—21no—
86C2×Dic149—21no—
87C2×Dic149—22no—
88C2×Dic149—21no—
89C2×Dic149—21no—
90C2×Dic149—41no—
91C2×Dic149—41no—
92C2×Dic149C22⋊C411yescharacteristic
93C2×Dic149C22⋊C411yescharacteristic
94C4×D149—21no—
95C4×D149—21no—
96C4×D149—21no—
97C4×D149—21no—
98C4×D149—21no—
99C4×D149—21no—
100C4×D149—21no—
101C4×D149—21no—
102#11924746—22no—
103C23×C149—21no—
104C23×C149C2×D411yescharacteristic
105Q8×C149—21no—
106Q8×C149—21no—
107D4×C149—21no—
108D4×C149—21no—
109D4×C149—41no—
110D4×C149—41no—
111C2×C4×C149—22no—
112C2×C4×C149—21no—
113C2×C4×C149—41no—
114C2×C4×C149—41no—
115C2×C4×C149—41no—
116C2×C4×C149—41no—
117C2×C4×C149C22×C411yescharacteristic
118C2×C4×C149C2×D411yescharacteristic
119C2×C4×C149C2×D411yescharacteristic
120C2×C4×C149C2×D411yescharacteristic
121C2×C4×C149#4111yescharacteristic
122C2×C4×C149#4111yescharacteristic
123C8×C149—22no—
124C22×C149—21no—
125C22×C149—21no—
126C22×C149—41no—
127C22×C149—41no—
128C22×C149—41no—
129C22×C149C2×C22⋊C411yescharacteristic
130C22×C149#12111yescharacteristic
131C22×C149#12111yescharacteristic
132C2×D149—21no—
133C2×D149—21no—
134C2×D149—21no—
135C2×D149—21no—
136C2×D149—21no—
137C2×D149—42no—
138C2×D149—42no—
139C2×D149#10412yescomplemented
140C4×C149—42no—
141C4×C149—41no—
142C4×C149C4×D411yescharacteristic
143C4×C149C4×D411yescharacteristic
144C4×C149#12011yescharacteristic
145C4×C149#12311yescharacteristic
146Dic149—21no—
147Dic149—21no—
148Dic149—42no—
149Dic149—41no—
150Dic149—41no—
151C2×C149—21no—
152C2×C149—21no—
153C2×C149—81no—
154C2×C149#38611yescharacteristic
155C2×C149C2×#10411yescharacteristic
156C2×C149#42111yescharacteristic
157D149—22no—
158D149—41no—
159C149#187111yescharacteristic, complemented, Sylow
160#1871—1491nomaximal, Sylow
161C22×M16—1491no—
162#525—1491no—
163C2×#104—1491no—
164C2×#104D14911yescharacteristic, complemented
165C4×C22⋊C4—1491no—
166#339—1491no—
167#339—1491no—
168C2×#41C2×D14911yescharacteristic
169C23×C4—1491no—
170C2×M16—2981no—
171C2×M16—2982no—
172C2×M16—2982no—
173C2×M16—1491no—
174C2×M16C2×D14911yescharacteristic
175C22×C8—2981no—
176#123—2981no—
177C22⋊Q8—1491no—
178C22⋊Q8—1491no—
179#121—1491no—
180#121—1491no—
181#120—2981no—
182C4×D4—2981no—
183C4×D4—2981no—
184#117—1491no—
185C2×C22⋊C4—2981no—
186C2×C42—1491no—
187C2×C42C2×D14911yescharacteristic
188#104—22no—
189#104—2982no—
190#95—2981no—
191C24—1491no—
192#41—21no—
193#41—21no—
194#41—21no—
195#41—21no—
196C2×Q8C4×D14911yescharacteristic
197C2×D4—21no—
198C2×D4—2981no—
199C2×D4—2981no—
200C2×D4C4×D14911yescharacteristic
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—2981no—
204C22×C4—2981no—
205C22×C4—2981no—
206C22×C4—2981no—
207C22×C4—2981no—
208C22×C4—1491no—
209C22×C4—1491no—
210C22×C4—1491no—
211C22×C4—1491no—
212C22×C4—1491no—
213C22×C4C22×D14911yescharacteristic
214M16—21no—
215M16—2984no—
216M16—2981no—
217M16—1492no—
218M16C22⋊D14912yescomplemented
219C2×C8—21no—
220C2×C8—2984no—
221C2×C8—2981no—
222C4⋊C4—2981no—
223C4⋊C4—2981no—
224C4⋊C4—1491no—
225C4⋊C4—1491no—
226C22⋊C4—2984no—
227C22⋊C4—2981no—
228C22⋊C4—2981no—
229C22⋊C4—2981no—
230C22⋊C4—2981no—
231C22⋊C4—2981no—
232C42—21no—
233C42—21no—
234C42—2981no—
235C42—2981no—
236C42—2981no—
237C23—21no—
238C23—2982no—
239C23—2981no—
240C23—2981no—
241C23—5961no—
242C23—1491no—
243C23—1491no—
244C23D4×D14911yescharacteristic
245Q8—21no—
246Q8—21no—
247D4—21no—
248D4—21no—
249D4—41no—
250D4—41no—
251D4—5962no—
252D4—5962no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—2981no—
260C2×C4—2981no—
261C2×C4—2981no—
262C2×C4—2981no—
263C2×C4—2981no—
264C2×C4—2981no—
265C2×C4—2981no—
266C2×C4—2981no—
267C2×C4—2981no—
268C2×C4—2981no—
269C2×C4—2982no—
270C2×C4—2981no—
271C2×C4—2981no—
272C2×C4—5961no—
273C2×C4—5961no—
274C2×C4—1491no—
275C2×C4—1491no—
276C2×C4C2×C4×D14911yescharacteristic
277C2×C4D4×D14911yescharacteristic
278C2×C4D4×D14911yescharacteristic
279C2×C4C2×C22⋊D14911yescharacteristic
280C2×C4#1455873511yescharacteristic
281C2×C4#1455873611yescharacteristic
282C8—22no—
283C8—2982no—
284C22—21no—
285C22—21no—
286C22—41no—
287C22—41no—
288C22—41no—
289C22—2981no—
290C22—2981no—
291C22—2981no—
292C22—2981no—
293C22—2981no—
294C22—5962no—
295C22—5962no—
296C22—1492no—
297C22C22⋊C4×D14911yescharacteristic
298C22#1801188211yescharacteristic
299C22#1801188411yescharacteristic
300C4—42no—
301C4—41no—
302C4—2981no—
303C4—2981no—
304C4—5962no—
305C4—5961no—
306C4—5961no—
307C4#1801187111yescharacteristic
308C4C4×C22⋊D14911yescharacteristic
309C4#1801187911yescharacteristic
310C4#1801189311yescharacteristic
311C2—21no—
312C2—21no—
313C2—81no—
314C2—2982no—
315C2—5961no—
316C2#2374950111yescharacteristic
317C2#104×D14911yescharacteristic
318C2#2374964011yescharacteristic
subgroupG/H
centerC2×C4D4×D149
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
FittingC2×#104×C149C2
socleC22×C149C2×C22⋊C4
prime radical#23750132C2
cosocleC22×C4×C149C23
hypercenterC2×#104D149
hypocenterC149#1871
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×M16×D149C2semidirect
3. C2×#18011838C2semidirect
4. C4×#14558713C2semidirect
5. #23749386C2semidirect
6. #23749385C2semidirect
7. C2×#104×C149C2semidirect
15. #18011887C4semidirect
16. #18011887C4semidirect
17. #18011882C4semidirect
18. #18011882C4semidirect
45. #14558720D4semidirect
73. M16×C149D4semidirect
139. C2×D149#104semidirect
159. C149#1871semidirect
164. C2×#104D149semidirect
218. M16C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
C2×M16×D1492
#237501322
C2×#180118382
C4×#145587132
#237493862
#237493852
C2×#104×C1492
#1871149