Finite Group Databasebeta

← #34047587

Subgroups — #34047587

Order 19072.

776 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D149C211yesmaximal, characteristic
2C2×#18011871C212yesmaximal
3C22×C4⋊Dic149C211yesmaximal, characteristic, complemented
4C2×C4⋊C4×D149C211yesmaximal, characteristic, complemented
5#23749522C212yesmaximal, complemented
6#23749499C212yesmaximal, complemented
7#23749497C212yesmaximal, complemented
8#23749494C211yesmaximal, characteristic, complemented
9#23749482C211yesmaximal, characteristic, complemented
10C4⋊C4×Dic149C211yesmaximal, characteristic, complemented
11#380×C149C211yesmaximal, characteristic, complemented
12C22×C22⋊D149C2211yescharacteristic
13C23×Dic149C2212yes—
14C22×C4×D149C2212yes—
15C22×C4×D149C2211yescharacteristic
16C4×C22⋊D149C418yescomplemented
17#18011871—28no—
18C2×C4⋊Dic149—24no—
19C2×C4⋊Dic149C2211yescharacteristic
20C2×C4⋊Dic149C2212yes—
21C2×C4⋊Dic149C2211yescharacteristic
22C2×#14558715C2212yes—
23C2×#14558715C2212yes—
24C2×#14558715C2212yes—
25C2×#14558715C2211yescharacteristic
26C4⋊C4×D149—24no—
27C2×C22⋊Dic149C2211yescharacteristic
28C2×#14558713C2212yes—
29C2×#14558713C2211yescharacteristic
30C2×C4×Dic149C2212yes—
31C2×C4×Dic149C2211yescharacteristic
32#18011818C2212yes—
33#18011818C2212yes—
34C23×C4×C149C2211yescharacteristic
35C2×C4⋊C4×C149C2211yescharacteristic
36C2×C4⋊C4×C149C2211yescharacteristic
37C2×C22⋊C4×C149C2212yes—
38#95×C149C2212yes—
39C23×D149C2311yescharacteristic
40C2×C22⋊D149C2×C414yes—
41C2×C22⋊D149D414yes—
42C2×C22⋊D149Q814yes—
43C22×Dic149—24no—
44C22×Dic149—24no—
45C22×Dic149—42no—
46C22×Dic149C2312yes—
47C22×Dic149C2311yescharacteristic
48C22×Dic149C2311yescharacteristic
49C22×Dic149C2312yes—
50C22×Dic149C2311yescharacteristic
51C2×C4×D149—24no—
52C2×C4×D149—24no—
53C2×C4×D149—22no—
54C2×C4×D149—22no—
55C2×C4×D149—42no—
56C2×C4×D149C2×C414yescomplemented
57C4⋊Dic149—24no—
58C4⋊Dic149—22no—
59C4⋊Dic149D414yescomplemented
60#14558715—24no—
61#14558715—24no—
62#14558715—42no—
63#14558715C2×C414yescomplemented
64C22⋊Dic149C2×C414yescomplemented
65#14558713—24no—
66#14558713C2×C414yescomplemented
67C4×Dic149—24no—
68C4×Dic149C2×C414yescomplemented
69C24×C149C2311yescharacteristic
70C22×C4×C149—22no—
71C22×C4×C149—22no—
72C22×C4×C149C2×C414yescomplemented
73C22×C4×C149C2312yes—
74C22×C4×C149C2312yes—
75C22×C4×C149C2311yescharacteristic
76C22×C4×C149C2311yescharacteristic
77C4⋊C4×C149—22no—
78C4⋊C4×C149—22no—
79C22⋊C4×C149—24no—
80C22×D149—21no—
81C22×D149—21no—
82C22×D149—21no—
83C22×D149—21no—
84C22×D149C22×C412yes—
85C22×D149C2×D412yes—
86C22×D149C2×Q812yes—
87C22⋊D149C4⋊C4116yescomplemented
88C2×Dic149—22no—
89C2×Dic149—21no—
90C2×Dic149—21no—
91C2×Dic149—22no—
92C2×Dic149—21no—
93C2×Dic149—21no—
94C2×Dic149—22no—
95C2×Dic149—22no—
96C2×Dic149—22no—
97C2×Dic149—48no—
98C2×Dic149C22×C412yes—
99C2×Dic149C22×C412yes—
100C2×Dic149C22×C412yes—
101C2×Dic149C2×D414yes—
102C2×Dic149C2×D412yes—
103C2×Dic149C2×Q812yes—
104C4×D149—28no—
105C4×D149—48no—
106C23×C149—21no—
107C23×C149—21no—
108C23×C149—21no—
109C23×C149—21no—
110C23×C149C22×C412yes—
111C23×C149C2×D412yes—
112C23×C149C2×Q812yes—
113C23×C149C2411yescharacteristic
114C2×C4×C149—21no—
115C2×C4×C149—21no—
116C2×C4×C149—28no—
117C2×C4×C149—22no—
118C2×C4×C149—22no—
119C2×C4×C149—22no—
120C2×C4×C149—22no—
121C2×C4×C149—22no—
122C2×C4×C149—22no—
123C2×C4×C149C22×C412yes—
124C2×C4×C149C22×C412yes—
125C2×C4×C149C2×D412yes—
126C2×C4×C149#4112yes—
127C22×C149—22no—
128C22×C149—22no—
129C22×C149—22no—
130C22×C149—22no—
131C22×C149—22no—
132C22×C149—22no—
133C22×C149C2×C4⋊C414yescomplemented
134C22×C149C23×C411yescharacteristic
135C22×C149C22×D411yescharacteristic
136C22×C149C22×D411yescharacteristic
137C22×C149C22×Q811yescharacteristic
138C22×C149C2×#4111yescharacteristic
139C22×C149H(5,𝔽2)11yescharacteristic
140C22×C1492−1+411yescharacteristic
141C2×D149—22no—
142C2×D149—22no—
143C2×D149—22no—
144C2×D149—22no—
145C2×D149—22no—
146C2×D149—22no—
147C2×D149C2×C4⋊C414yescomplemented
148C4×C149—22no—
149C4×C149—42no—
150C4×C149—42no—
151C4×C149C4×D414yescomplemented
152Dic149—22no—
153Dic149—22no—
154Dic149—24no—
155Dic149—42no—
156Dic149C2×C4⋊C414yescomplemented
157C2×C149—24no—
158C2×C149C22×C4⋊C411yescharacteristic
159C2×C149C2×C4×D411yescharacteristic
160C2×C149#52011yescharacteristic
161C2×C149D4211yescharacteristic
162C2×C149#54711yescharacteristic
163C2×C149D4×Q811yescharacteristic
164C2×C149#55411yescharacteristic
165D149—24no—
166C149D4×C4⋊C411yescharacteristic, complemented, Sylow
167D4×C4⋊C4—1491nomaximal, Sylow
168C2×C4×D4—1491no—
169C2×C4×D4—1492no—
170C22×C4⋊C4—1491no—
171C22×C4⋊C4—1491no—
172#389—1492no—
173#385—1492no—
174#385—1492no—
175#384—1491no—
176#380—1491no—
177#380D14911yescharacteristic, complemented
178C4×C4⋊C4—1491no—
179C22×D4—1491no—
180C23×C4—1492no—
181C23×C4—1492no—
182C23×C4—1491no—
183C23×C4C2×D14911yescharacteristic
184C4×D4—2988no—
185C4×D4—1498no—
186C2×C4⋊C4—2984no—
187C2×C4⋊C4—2984no—
188C2×C4⋊C4—1491no—
189C2×C4⋊C4—1492no—
190C2×C4⋊C4—1492no—
191C2×C4⋊C4—1492no—
192C2×C4⋊C4—1492no—
193C2×C4⋊C4—1491no—
194C2×C4⋊C4—1491no—
195C2×C4⋊C4C2×D14911yescharacteristic
196C2×C4⋊C4C2×D14911yescharacteristic
197C2×C22⋊C4—1492no—
198C2×C22⋊C4—1491no—
199C2×C22⋊C4—1491no—
200C2×C22⋊C4C2×D14912yes—
201C2×C42—1492no—
202C2×C42—1491no—
203#95—1492no—
204#95—1492no—
205#95C2×D14912yes—
206C24—1491no—
207C24C22×D14911yescharacteristic
208C2×D4—1494no—
209C2×D4—1494no—
210C2×D4—1494no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—2984no—
214C22×C4—2984no—
215C22×C4—2982no—
216C22×C4—2982no—
217C22×C4—2984no—
218C22×C4—2984no—
219C22×C4—5962no—
220C22×C4—5962no—
221C22×C4—1492no—
222C22×C4—1491no—
223C22×C4—1491no—
224C22×C4—1492no—
225C22×C4—1494no—
226C22×C4—1491no—
227C22×C4C4×D14914yescomplemented
228C22×C4C22×D14912yes—
229C22×C4C22×D14912yes—
230C22×C4C22×D14911yescharacteristic
231C22×C4C22×D14911yescharacteristic
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4—2984no—
235C4⋊C4—2984no—
236C4⋊C4—2984no—
237C4⋊C4—2982no—
238C4⋊C4—5962no—
239C4⋊C4—1494no—
240C4⋊C4—1494no—
241C22⋊C4—24no—
242C22⋊C4—2984no—
243C22⋊C4—1494no—
244C22⋊C4—1494no—
245C42—2984no—
246C42—1494no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—2981no—
252C23—2981no—
253C23—2981no—
254C23—2981no—
255C23—1492no—
256C23—1492no—
257C23—1492no—
258C23C2×C4×D14912yes—
259C23D4×D14912yes—
260C23Q8×D14912yes—
261C23C23×D14911yescharacteristic
262D4—14916no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—28no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—2982no—
273C2×C4—2981no—
274C2×C4—2981no—
275C2×C4—2981no—
276C2×C4—2982no—
277C2×C4—2981no—
278C2×C4—2988no—
279C2×C4—2982no—
280C2×C4—2982no—
281C2×C4—2982no—
282C2×C4—5968no—
283C2×C4—5968no—
284C2×C4—1492no—
285C2×C4—1492no—
286C2×C4—1494no—
287C2×C4—1492no—
288C2×C4—1492no—
289C2×C4—1492no—
290C2×C4C2×C4×D14912yes—
291C2×C4C2×C4×D14912yes—
292C2×C4D4×D14912yes—
293C2×C4#1455873512yes—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22—2982no—
301C22—2982no—
302C22—2982no—
303C22—2982no—
304C22—2982no—
305C22—2982no—
306C22—1494no—
307C22C4⋊C4×D14914yescomplemented
308C22C22×C4×D14911yescharacteristic
309C22C2×D4×D14911yescharacteristic
310C22C2×D4×D14911yescharacteristic
311C22C2×Q8×D14911yescharacteristic
312C22C2×#1455873511yescharacteristic
313C22#1801195711yescharacteristic
314C22#1801195811yescharacteristic
315C4—22no—
316C4—42no—
317C4—42no—
318C4—2984no—
319C4—2982no—
320C4—2982no—
321C4—5962no—
322C4—1494no—
323C4#1801187114yescomplemented
324C2—24no—
325C2—2984no—
326C2C2×C4⋊C4×D14911yescharacteristic
327C2C2×#1801187111yescharacteristic
328C2#2375010511yescharacteristic
329C2#2375025911yescharacteristic
330C2#2375027511yescharacteristic
331C2#2375028811yescharacteristic
332C2#2375033311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#380×C149C2
socle, cosocleC23×C149C24
prime radicalC22×C22⋊D149C22
hypercenter#380D149
hypocenterC149D4×C4⋊C4
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊Dic149C2semidirect
4. C2×C4⋊C4×D149C2semidirect
5. #23749522C2semidirect
6. #23749499C2semidirect
7. #23749497C2semidirect
8. #23749494C2semidirect
9. #23749482C2semidirect
10. C4⋊C4×Dic149C2semidirect
11. #380×C149C2semidirect
16. C4×C22⋊D149C4semidirect
56. C2×C4×D149C2×C4semidirect
59. C4⋊Dic149D4semidirect
63. #14558715C2×C4semidirect
64. C22⋊Dic149C2×C4semidirect
66. #14558713C2×C4semidirect
68. C4×Dic149C2×C4semidirect
72. C22×C4×C149C2×C4semidirect
87. C22⋊D149C4⋊C4semidirect
133. C22×C149C2×C4⋊C4semidirect
147. C2×D149C2×C4⋊C4semidirect
151. C4×C149C4×D4semidirect
156. Dic149C2×C4⋊C4semidirect
166. C149D4×C4⋊C4semidirect
177. #380D149semidirect
227. C22×C4C4×D149semidirect
307. C22C4⋊C4×D149semidirect
323. C4#18011871semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D1492
C2×#180118712
C22×C4⋊Dic1492
C2×C4⋊C4×D1492
#237495222
#237494992
#237494972
#237494942
#237494822
C4⋊C4×Dic1492
#380×C1492
D4×C4⋊C4149