Finite Group Databasebeta

← #34047192

Subgroups — #34047192

Order 19072.

1224 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×D149C211yesmaximal, characteristic, complemented
2C2×#18011881C211yesmaximal, characteristic
3C2×#18011873C212yesmaximal, complemented
4C2×#18011871C211yesmaximal, characteristic, complemented
5#23749504C211yesmaximal, characteristic, complemented
6#23749503C212yesmaximal, complemented
7#23749496C212yesmaximal, complemented
8#23749480C211yesmaximal, characteristic, complemented
9C22⋊C4×Dic149C211yesmaximal, characteristic, complemented
10#23749472C212yesmaximal, complemented
11#385×C149C211yesmaximal, characteristic, complemented
12C24×D149C2211yescharacteristic
13C22×D596C2212yes—
14C22×C22⋊D149C2211yescharacteristic
15C23×Dic149C2211yescharacteristic
16C22×C4×D149—24no—
17C22×C4×D149—28no—
18C22×C4×D149C2212yes—
19C22×C4×D149C2212yes—
20C22×C4×D149C2211yescharacteristic, complemented
21#18011881C418yescomplemented
22#18011873—28no—
23#18011871—24no—
24C2×#14558715C2211yescharacteristic, complemented
25C2×C22⋊Dic149C2211yescharacteristic
26C2×#14558713C2212yes—
27C2×#14558713C2212yes—
28C2×#14558713C2212yes—
29C2×#14558713C2211yescharacteristic, complemented
30C2×#14558713C2212yescomplemented
31C2×C4×Dic149C2211yescharacteristic, complemented
32C2×C4×Dic149C2212yescomplemented
33#18011818C2212yescomplemented
34#18011818C2212yescomplemented
35C23×C4×C149C2211yescharacteristic
36C2×C4⋊C4×C149C2212yescomplemented
37C2×C22⋊C4×C149C2211yescharacteristic
38C2×C22⋊C4×C149C2211yescharacteristic
39#95×C149C2212yescomplemented
40C23×D149—24no—
41C23×D149—24no—
42C23×D149—22no—
43C23×D149—22no—
44C23×D149C2×C414yescomplemented
45C23×D149C2311yescharacteristic
46C23×D149C2312yes—
47C2×D596—24no—
48C2×D596—24no—
49C2×D596C2×C418yescomplemented
50C2×C22⋊D149—22no—
51C2×C22⋊D149—22no—
52C2×C22⋊D149C2×C414yescomplemented
53C22×Dic149—24no—
54C22×Dic149D414yescomplemented
55C22×Dic149C2312yes—
56C22×Dic149C2311yescharacteristic
57C22×Dic149C2311yescharacteristic
58C22×Dic149C2311yescharacteristic
59C2×C4×D149—232no—
60C2×C4×D149—24no—
61C2×C4×D149—24no—
62C2×C4×D149—24no—
63C2×C4×D149—24no—
64C2×C4×D149—22no—
65C2×C4×D149—24no—
66C2×C4×D149—24no—
67C2×C4×D149D418yescomplemented
68#14558715—22no—
69C22⋊Dic149—22no—
70#14558713—24no—
71#14558713—24no—
72#14558713—22no—
73#14558713—24no—
74#14558713C2×C418yescomplemented
75C4×Dic149—22no—
76C4×Dic149—24no—
77C24×C149C2311yescharacteristic
78C22×C4×C149—22no—
79C22×C4×C149—24no—
80C22×C4×C149C2311yescharacteristic
81C22×C4×C149C2311yescharacteristic
82C22×C4×C149C2312yes—
83C22×C4×C149C2312yes—
84C4⋊C4×C149—24no—
85C22⋊C4×C149—22no—
86C22⋊C4×C149C2×C414yescomplemented
87C22×D149—28no—
88C22×D149—216no—
89C22×D149—28no—
90C22×D149—28no—
91C22×D149—22no—
92C22×D149—22no—
93C22×D149—22no—
94C22×D149—22no—
95C22×D149—216no—
96C22×D149—21no—
97C22×D149—22no—
98C22×D149—21no—
99C22×D149—22no—
100C22×D149C22×C414yes—
101C22×D149C22×C412yescomplemented
102C22×D149C2×D414yes—
103C22×D149#4114yes—
104D596—216no—
105C22⋊D149—28no—
106C2×Dic149—22no—
107C2×Dic149—21no—
108C2×Dic149—21no—
109C2×Dic149—28no—
110C2×Dic149—22no—
111C2×Dic149—22no—
112C2×Dic149—22no—
113C2×Dic149C22×C412yescomplemented
114C2×Dic149C2×D412yes—
115C2×Dic149C2×D412yes—
116C2×Dic149C2×D414yes—
117C4×D149—216no—
118C4×D149—216no—
119C4×D149—44no—
120C23×C149—22no—
121C23×C149—22no—
122C23×C149C22×C412yes—
123C23×C149C2×D412yes—
124C23×C149#4112yes—
125C23×C149C2411yescharacteristic
126C2×C4×C149—28no—
127C2×C4×C149—22no—
128C2×C4×C149—22no—
129C2×C4×C149—22no—
130C2×C4×C149—22no—
131C2×C4×C149—21no—
132C2×C4×C149—22no—
133C2×C4×C149—21no—
134C2×C4×C149—22no—
135C2×C4×C149C22×C414yescomplemented
136C2×C4×C149C2×D414yes—
137C22×C149—24no—
138C22×C149—22no—
139C22×C149—22no—
140C22×C149—24no—
141C22×C149C4×D414yescomplemented
142C22×C149C23×C411yescharacteristic
143C22×C149C22×D411yescharacteristic
144C22×C149C22×D412yes—
145C22×C149C2×#4112yes—
146C22×C149C2×#4111yescharacteristic
147C2×D149—232no—
148C2×D149—24no—
149C2×D149—24no—
150C2×D149—24no—
151C2×D149—24no—
152C2×D149—24no—
153C2×D149—24no—
154C2×D149—22no—
155C2×D149—24no—
156C2×D149—41no—
157C2×D149—41no—
158C2×D149—42no—
159C2×D149C4×D418yescomplemented
160C4×C149—24no—
161C4×C149—24no—
162C4×C149—41no—
163C4×C149—41no—
164Dic149—22no—
165Dic149—22no—
166Dic149—42no—
167Dic149#12014yescomplemented
168C2×C149—24no—
169C2×C149C2×C4×D412yes—
170C2×C149C2×C4×D411yescharacteristic
171C2×C149C2×#12011yescharacteristic
172C2×C149#52511yescharacteristic
173C2×C149#52512yes—
174D149—28no—
175D149—42no—
176C149C4×#12011yescharacteristic, complemented, Sylow
177C4×#120—1491nomaximal, Sylow
178C24×C4—1491no—
179C2×#120—1491no—
180C2×C4×D4—1492no—
181C2×C4×D4—1491no—
182#386—1491no—
183#386—1492no—
184#385—1492no—
185#385D14911yescharacteristic, complemented
186#379—1491no—
187C4×C22⋊C4—1491no—
188C4×C22⋊C4—1492no—
189C25—1491no—
190C22×D4—1491no—
191C22×D4—1492no—
192C23×C4—2984no—
193C23×C4—2988no—
194C23×C4—1491no—
195C23×C4—1492no—
196C23×C4—1491no—
197C23×C4—1492no—
198C23×C4C2×D14911yescharacteristic
199#120—1498no—
200C4×D4—2984no—
201C4×D4—2988no—
202C2×C4⋊C4—1491no—
203C2×C4⋊C4C2×D14912yescomplemented
204C2×C22⋊C4—1491no—
205C2×C22⋊C4—1492no—
206C2×C22⋊C4—1491no—
207C2×C22⋊C4—1492no—
208C2×C22⋊C4—1492no—
209C2×C22⋊C4—1492no—
210C2×C22⋊C4C2×D14911yescharacteristic
211C2×C22⋊C4C2×D14911yescharacteristic
212C2×C42—1492no—
213C2×C42—1491no—
214#95—1492no—
215#95—1492no—
216#95C2×D14912yescomplemented
217C24—2984no—
218C24—2984no—
219C24—2982no—
220C24—2982no—
221C24—1494no—
222C24—1491no—
223C24—1492no—
224C24C22×D14911yescharacteristic
225C2×D4—2984no—
226C2×D4—2984no—
227C2×D4—2982no—
228C2×D4—2982no—
229C2×D4—1494no—
230C2×D4—1498no—
231C22×C4—22no—
232C22×C4—24no—
233C22×C4—29832no—
234C22×C4—2984no—
235C22×C4—2984no—
236C22×C4—2984no—
237C22×C4—2984no—
238C22×C4—2982no—
239C22×C4—2984no—
240C22×C4—2984no—
241C22×C4—2984no—
242C22×C4—1492no—
243C22×C4—1494no—
244C22×C4—1491no—
245C22×C4—1491no—
246C22×C4—1498no—
247C22×C4—1491no—
248C22×C4C22×D14911yescharacteristic
249C22×C4C22×D14911yescharacteristic
250C22×C4C22×D14912yes—
251C22×C4C22×D14912yes—
252C4⋊C4—24no—
253C4⋊C4—2982no—
254C22⋊C4—22no—
255C22⋊C4—2984no—
256C22⋊C4—2984no—
257C22⋊C4—2982no—
258C22⋊C4—2982no—
259C22⋊C4—2984no—
260C22⋊C4—1498no—
261C22⋊C4C4×D14914yescomplemented
262C42—2984no—
263C42—2982no—
264C23—22no—
265C23—22no—
266C23—2988no—
267C23—2988no—
268C23—29816no—
269C23—29816no—
270C23—2982no—
271C23—2982no—
272C23—2982no—
273C23—2982no—
274C23—2988no—
275C23—2982no—
276C23—2981no—
277C23—2982no—
278C23—2981no—
279C23—1492no—
280C23—1494no—
281C23—1494no—
282C23—1494no—
283C23C2×C4×D14912yes—
284C23D4×D14912yes—
285C23#1455873712yes—
286C23C23×D14911yescharacteristic
287D4—29816no—
288D4—2988no—
289C2×C4—28no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—29816no—
299C2×C4—29816no—
300C2×C4—2981no—
301C2×C4—2982no—
302C2×C4—2981no—
303C2×C4—2988no—
304C2×C4—2982no—
305C2×C4—2982no—
306C2×C4—2982no—
307C2×C4—5964no—
308C2×C4—1492no—
309C2×C4—1492no—
310C2×C4—1494no—
311C2×C4—1492no—
312C2×C4C2×C4×D14914yescomplemented
313C2×C4D4×D14914yes—
314C22—24no—
315C22—22no—
316C22—22no—
317C22—24no—
318C22—29832no—
319C22—2984no—
320C22—2984no—
321C22—2984no—
322C22—2984no—
323C22—2984no—
324C22—2984no—
325C22—2984no—
326C22—2982no—
327C22—5961no—
328C22—5961no—
329C22—5962no—
330C22—1498no—
331C22#1801187314yescomplemented
332C22C22×C4×D14911yescharacteristic
333C22C2×D4×D14912yes—
334C22C2×D4×D14911yescharacteristic
335C22#41×D14912yes—
336C22C2×#1455873711yescharacteristic
337C4—24no—
338C4—24no—
339C4—41no—
340C4—41no—
341C4—2982no—
342C4—2982no—
343C4—5962no—
344C4—1494no—
345C2—24no—
346C2—2988no—
347C2—5962no—
348C2C4×D4×D14912yes—
349C2C2×#1801187311yescharacteristic
350C2#120×D14911yescharacteristic
351C2#2375013311yescharacteristic
352C2#2375013812yes—
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#385×C149C2
socle, cosocleC23×C149C24
prime radicalC2×#18011881C2
hypercenter#385D149
hypocenterC149C4×#120
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C23×C4×D149C2semidirect
3. C2×#18011873C2semidirect
4. C2×#18011871C2semidirect
5. #23749504C2semidirect
6. #23749503C2semidirect
7. #23749496C2semidirect
8. #23749480C2semidirect
9. C22⋊C4×Dic149C2semidirect
10. #23749472C2semidirect
11. #385×C149C2semidirect
20. C22×C4×D149C22semidirect
21. #18011881C4semidirect
24. C2×#14558715C22semidirect
29. C2×#14558713C22semidirect
30. C2×#14558713C22semidirect
31. C2×C4×Dic149C22semidirect
32. C2×C4×Dic149C22semidirect
33. #18011818C22semidirect
34. #18011818C22semidirect
36. C2×C4⋊C4×C149C22semidirect
39. #95×C149C22semidirect
44. C23×D149C2×C4semidirect
49. C2×D596C2×C4semidirect
52. C2×C22⋊D149C2×C4semidirect
54. C22×Dic149D4semidirect
67. C2×C4×D149D4semidirect
74. #14558713C2×C4semidirect
86. C22⋊C4×C149C2×C4semidirect
101. C22×D149C22×C4semidirect
113. C2×Dic149C22×C4semidirect
135. C2×C4×C149C22×C4semidirect
141. C22×C149C4×D4semidirect
159. C2×D149C4×D4semidirect
167. Dic149#120semidirect
176. C149C4×#120semidirect
185. #385D149semidirect
203. C2×C4⋊C4C2×D149semidirect
216. #95C2×D149semidirect
261. C22⋊C4C4×D149semidirect
312. C2×C4C2×C4×D149semidirect
331. C22#18011873semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D1492
C2×#180118812
C2×#180118732
C2×#180118712
#237495042
#237495032
#237494962
#237494802
C22⋊C4×Dic1492
#237494722
#385×C1492
C4×#120149