Finite Group Databasebeta

← #34044992

Subgroups — #34044992

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#23750137C211yesmaximal, characteristic
3C2×#18011839C211yesmaximal, characteristic, complemented
4C2×#18011837C211yesmaximal, characteristic, complemented
5C4×#14558713C211yesmaximal, characteristic, complemented
6#23749384C211yesmaximal, characteristic, complemented
7#339×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2211yescharacteristic
9C22×C4×D149C2211yescharacteristic
10C2×#14558720C2211yescharacteristic
11C2×#14558719—21no—
12M16×D149—22no—
13M16×D149—22no—
14C2×C8×D149—21no—
15#18011895—21no—
16#18011891C411yescharacteristic, complemented
17#18011891C411yescharacteristic, complemented
18#18011886C411yescharacteristic, complemented
19#18011886C411yescharacteristic, complemented
20#18011881—21no—
21C4×D596—21no—
22C4×D596—21no—
23C2×#14558713—21no—
24C2×C4×Dic149C2211yescharacteristic
25#18011839—22no—
26#18011837—22no—
27#18011818—21no—
28C2×M16×C149C2211yescharacteristic
29#117×C149C2211yescharacteristic
30C2×C42×C149C2211yescharacteristic
31C23×D149D411yescharacteristic
32#14558736—21no—
33#14558736—21no—
34#14558736—21no—
35#14558736—21no—
36C2×Dic298C2×C411yescharacteristic
37C2×D596—21no—
38C2×D596—21no—
39C2×D596C2×C411yescharacteristic
40C2×C22⋊D149—21no—
41C22×Dic149—21no—
42C22×Dic149D411yescharacteristic
43C2×C4×D149—21no—
44C2×C4×D149—21no—
45C2×C4×D149—21no—
46C2×C4×D149—21no—
47C2×C4×D149—21no—
48C2×C4×D149C2×C411yescharacteristic
49C2×C4×D149C2×C411yescharacteristic
50C2×C4×D149D411yescharacteristic
51C2×C4×D149D411yescharacteristic
52#14558720—21no—
53#14558720D412yescomplemented
54#14558719—24no—
55C2×#11924746—21no—
56C8×D149—24no—
57C4⋊Dic149—21no—
58C4⋊Dic149—21no—
59#14558713—24no—
60#14558713—21no—
61#14558713—21no—
62#14558713—21no—
63#14558713—21no—
64C4×Dic149—21no—
65C4×Dic149—21no—
66C22×C4×C149—21no—
67C22×C4×C149C2311yescharacteristic
68M16×C149—21no—
69M16×C149D412yescomplemented
70C2×C8×C149—21no—
71C4⋊C4×C149C2×C411yescharacteristic
72C4⋊C4×C149C2×C411yescharacteristic
73C22⋊C4×C149—21no—
74C42×C149—21no—
75C42×C149—21no—
76C42×C149—21no—
77C22×D149—21no—
78C22×D149—21no—
79C22×D149—22no—
80C22×D149—21no—
81C22×D149—41no—
82C22×D149C22⋊C411yescharacteristic
83C22×D149C22⋊C411yescharacteristic
84Dic298—21no—
85Dic298—21no—
86D596—21no—
87D596—21no—
88D596—42no—
89D596—42no—
90C22⋊D149—41no—
91C22⋊D149—41no—
92C2×Dic149—21no—
93C2×Dic149—21no—
94C2×Dic149—22no—
95C2×Dic149—21no—
96C2×Dic149—41no—
97C2×Dic149—41no—
98C2×Dic149C22⋊C411yescharacteristic
99C2×Dic149C22⋊C411yescharacteristic
100C4×D149—21no—
101C4×D149—21no—
102C4×D149—21no—
103C4×D149—21no—
104C4×D149—21no—
105C4×D149—21no—
106C4×D149—21no—
107C4×D149—21no—
108C4×D149—41no—
109C4×D149—41no—
110#11924746—22no—
111C23×C149C2×D411yescharacteristic
112C2×C4×C149—22no—
113C2×C4×C149—21no—
114C2×C4×C149—21no—
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×C149C2×C22⋊C411yescharacteristic
127C22×C149#12111yescharacteristic
128C22×C149#12111yescharacteristic
129C2×D149—21no—
130C2×D149—21no—
131C2×D149—21no—
132C2×D149—21no—
133C2×D149—21no—
134C2×D149—42no—
135C2×D149—42no—
136C2×D149—41no—
137C2×D149—41no—
138C2×D149—41no—
139C2×D149#10412yescomplemented
140C4×C149—42no—
141C4×C149—41no—
142C4×C149—41no—
143C4×C149C4×D411yescharacteristic
144C4×C149C4×D411yescharacteristic
145C4×C149#12011yescharacteristic
146C4×C149#12311yescharacteristic
147Dic149—21no—
148Dic149—21no—
149Dic149—42no—
150Dic149—41no—
151C2×C149—21no—
152C2×C149—21no—
153C2×C149#38611yescharacteristic
154C2×C149C2×#10411yescharacteristic
155C2×C149#42111yescharacteristic
156D149—22no—
157D149—41no—
158D149—81no—
159C149#187111yescharacteristic, complemented, Sylow
160#1871—1491nomaximal, Sylow
161C22×M16—1491no—
162#525—1491no—
163C2×#104—1491no—
164C2×#104—1491no—
165C4×C22⋊C4—1491no—
166#339—1491no—
167#339D14911yescharacteristic, complemented
168C2×#41—1491no—
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#117C2×D14911yescharacteristic
185C2×C22⋊C4—2981no—
186C2×C42—1491no—
187C2×C42C2×D14911yescharacteristic
188#104—2982no—
189#104—2982no—
190#95—2981no—
191C24—1491no—
192#41—2981no—
193#41—2981no—
194#41—2981no—
195#41—2981no—
196C2×Q8—1491no—
197C2×D4—2981no—
198C2×D4—2981no—
199C2×D4—2981no—
200C2×D4—1491no—
201C22×C4—21no—
202C22×C4—2981no—
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—
218M16D59612yescomplemented
219C2×C8—21no—
220C2×C8—2984no—
221C2×C8—2981no—
222C4⋊C4—2981no—
223C4⋊C4—2981no—
224C4⋊C4C4×D14911yescharacteristic
225C4⋊C4C4×D14911yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—2984no—
228C22⋊C4—2981no—
229C22⋊C4—2981no—
230C22⋊C4—2981no—
231C22⋊C4—2981no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—2981no—
236C42—2981no—
237C23—2982no—
238C23—2981no—
239C23—2981no—
240C23—2981no—
241C23—5961no—
242C23—1491no—
243C23—1491no—
244C23D4×D14911yescharacteristic
245Q8—2981no—
246Q8—2981no—
247D4—2981no—
248D4—2981no—
249D4—5962no—
250D4—5962no—
251D4—5961no—
252D4—5961no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—2981no—
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—2982no—
269C2×C4—2981no—
270C2×C4—5961no—
271C2×C4—5961no—
272C2×C4—5961no—
273C2×C4—5961no—
274C2×C4—1491no—
275C2×C4—1491no—
276C2×C4C2×C4×D14911yescharacteristic
277C2×C4D4×D14911yescharacteristic
278C2×C4D4×D14911yescharacteristic
279C2×C4C2×D59611yescharacteristic
280C2×C4#1455873611yescharacteristic
281C2×C4#1455873711yescharacteristic
282C8—22no—
283C8—2982no—
284C22—21no—
285C22—21no—
286C22—2981no—
287C22—2981no—
288C22—2981no—
289C22—2981no—
290C22—2981no—
291C22—5962no—
292C22—5962no—
293C22—5961no—
294C22—5961no—
295C22—5961no—
296C22—1492no—
297C22C22⋊C4×D14911yescharacteristic
298C22#1801188411yescharacteristic
299C22#1801188611yescharacteristic
300C4—42no—
301C4—41no—
302C4—41no—
303C4—2981no—
304C4—2981no—
305C4—5962no—
306C4—5961no—
307C4#1801187311yescharacteristic
308C4C4×D59611yescharacteristic
309C4#1801188111yescharacteristic
310C4#1801189611yescharacteristic
311C2—21no—
312C2—21no—
313C2—2982no—
314C2—5961no—
315C2—11921no—
316C2#2374950311yescharacteristic
317C2#104×D14911yescharacteristic
318C2#2374964011yescharacteristic
subgroupG/H
centerC2×C4D4×D149
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
Fitting#339×C149C2
socleC22×C149C2×C22⋊C4
prime radical#23750137C2
cosocleC22×C4×C149C23
hypercenter#339D149
hypocenterC149#1871
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. C2×M16×D149C2semidirect
3. C2×#18011839C2semidirect
4. C2×#18011837C2semidirect
5. C4×#14558713C2semidirect
6. #23749384C2semidirect
7. #339×C149C2semidirect
16. #18011891C4semidirect
17. #18011891C4semidirect
18. #18011886C4semidirect
19. #18011886C4semidirect
53. #14558720D4semidirect
69. M16×C149D4semidirect
139. C2×D149#104semidirect
159. C149#1871semidirect
167. #339D149semidirect
218. M16D596semidirect

Maximal subgroups

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

subgroupindex
C2×M16×D1492
#237501372
C2×#180118392
C2×#180118372
C4×#145587132
#237493842
#339×C1492
#1871149