Finite Group Databasebeta

← #34053569

Subgroups — #34053569

Order 19072.

484 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011932C211yesmaximal, characteristic
2#23750107C211yesmaximal, characteristic, complemented
3#23750104C211yesmaximal, characteristic, complemented
4#23749735C211yesmaximal, characteristic, complemented
5#23749734C211yesmaximal, characteristic, complemented
6#23749730C211yesmaximal, characteristic, complemented
7#23749729C211yesmaximal, characteristic, complemented
8C4×#14558725C211yesmaximal, characteristic, complemented
9SD16×Dic149C211yesmaximal, characteristic, complemented
10#23749712C211yesmaximal, characteristic, complemented
11#106×D149C211yesmaximal, characteristic, complemented
12#23749625C211yesmaximal, characteristic, complemented
13#23749623C211yesmaximal, characteristic, complemented
14#23749579C211yesmaximal, characteristic, complemented
15C4×SD16×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558735C2211yescharacteristic
18#18011932C418yescomplemented
19C2×#14558726C2211yescharacteristic
20C2×#14558725C2211yescharacteristic
21C2×#14558721C2211yescharacteristic
22C2×#14558719C2211yescharacteristic
23C2×C8×D149C2211yescharacteristic
24Q8×Dic149C2211yescharacteristic
25C4×Dic298C2211yescharacteristic
26#18011876C2211yescharacteristic
27C4×D596—21no—
28C4×D596C2211yescharacteristic
29D4×Dic149C2211yescharacteristic
30#18011873—21no—
31#18011873C2211yescharacteristic
32C4×C22⋊D149—21no—
33#18011871—21no—
34#18011868—21no—
35#18011868C2211yescharacteristic
36#18011867—21no—
37C2×#14558715—21no—
38C4⋊C4×D149—21no—
39C4⋊C4×D149C2211yescharacteristic
40C4⋊C4×D149C2211yescharacteristic
41#18011843C2211yescharacteristic
42#18011842C2211yescharacteristic
43#18011842C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011832C2211yescharacteristic
49#18011831C2211yescharacteristic
50#18011822C2211yescharacteristic
51#18011821C2211yescharacteristic
52C8×Dic149C2211yescharacteristic
53C2×SD16×C149C2211yescharacteristic
54C4×Q8×C149C2211yescharacteristic
55C4×D4×C149C2211yescharacteristic
56#106×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59C4×C8×C149C2211yescharacteristic
60#14558737—22no—
61#14558737C2×C414yescomplemented
62#14558735—22no—
63#14558735C2×C414yescomplemented
64C2×Dic298C2311yescharacteristic
65C2×D596—21no—
66C2×D596C2311yescharacteristic
67C2×C22⋊D149—21no—
68C22×Dic149—21no—
69C22×Dic149—21no—
70C2×C4×D149—21no—
71C2×C4×D149—21no—
72C2×C4×D149—21no—
73C2×C4×D149—21no—
74C2×C4×D149—21no—
75C2×C4×D149C2311yescharacteristic
76#14558726C2×C414yescomplemented
77#14558725C2×C414yescomplemented
78#14558721C2×C414yescomplemented
79#14558719—22no—
80C2×#11924746C2311yescharacteristic
81C2×#11924746C2311yescharacteristic
82C8×D149C2×C414yescomplemented
83C4⋊Dic149—21no—
84C4⋊Dic149C2311yescharacteristic
85C4⋊Dic149C2311yescharacteristic
86#14558715—21no—
87#14558715—21no—
88#14558715—21no—
89#14558715—21no—
90#14558715D411yescharacteristic
91#14558715D411yescharacteristic
92C22⋊Dic149—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713D411yescharacteristic
96#14558713D411yescharacteristic
97C4×Dic149—21no—
98C4×Dic149—21no—
99C4×Dic149—21no—
100C4×Dic149C2311yescharacteristic
101C2×Q8×C149C2311yescharacteristic
102C2×D4×C149C2311yescharacteristic
103C22×C4×C149—21no—
104SD16×C149C2×C414yescomplemented
105C2×C8×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C4⋊C4×C149—21no—
108C4⋊C4×C149C2311yescharacteristic
109C4⋊C4×C149C2311yescharacteristic
110C22⋊C4×C149—21no—
111C42×C149—21no—
112C42×C149C2311yescharacteristic
113C22×D149—21no—
114C22×D149C2×D411yescharacteristic
115Dic298—21no—
116Dic298C22×C412yes—
117D596—24no—
118D596—21no—
119D596C22×C412yes—
120C22⋊D149—24no—
121C2×Dic149—21no—
122C2×Dic149—24no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C2×Dic149—81no—
126C2×Dic149C2×D411yescharacteristic
127C2×Dic149C2×D411yescharacteristic
128C2×Dic149C2×D411yescharacteristic
129C4×D149—24no—
130C4×D149—81no—
131C4×D149—81no—
132C4×D149—81no—
133C4×D149—81no—
134C4×D149C22×C412yes—
135C4×D149#4112yes—
136#11924746—21no—
137#11924746C22×C412yes—
138C23×C149—21no—
139Q8×C149—21no—
140Q8×C149C22×C412yes—
141D4×C149—21no—
142D4×C149C22×C412yes—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—81no—
147C2×C4×C149C2×D411yescharacteristic
148C2×C4×C149C2×D411yescharacteristic
149C2×C4×C149C2411yescharacteristic
150C8×C149—21no—
151C8×C149C22×C412yes—
152C22×C149—22no—
153C22×C149—41no—
154C22×C149—41no—
155C22×C149C22×D411yescharacteristic
156C2×D149—21no—
157C2×D149—21no—
158C2×D149—22no—
159C2×D149—41no—
160C2×D149—41no—
161C2×D149C4×D412yes—
162C4×C149—22no—
163C4×C149—21no—
164C4×C149—21no—
165C4×C149—41no—
166C4×C149—41no—
167C4×C149C23×C411yescharacteristic
168C4×C149C2×#4111yescharacteristic
169Dic149—22no—
170Dic149—21no—
171Dic149—21no—
172Dic149—41no—
173Dic149—41no—
174Dic149C4×D412yes—
175C2×C149—42no—
176C2×C149C2×C4×D411yescharacteristic
177C2×C149#57711yescharacteristic
178C2×C149#57711yescharacteristic
179D149—22no—
180D149—42no—
181C149#295211yescharacteristic, complemented, Sylow
182#2952—1491nomaximal, Sylow
183C2×#135—1491no—
184#520—1491no—
185#520—1491no—
186#442—1491no—
187#442—1491no—
188#441—1491no—
189#441—1491no—
190C4×SD16—1491no—
191C4×SD16—1491no—
192C4×SD16—1491no—
193C4×SD16D14911yescharacteristic, complemented
194C2×#106—1491no—
195#417—1491no—
196#417—1491no—
197#405—1491no—
198C2×#41—1491no—
199C2×#41—1491no—
200#135—1498no—
201C2×Q16—1491no—
202C2×SD16—1491no—
203C2×SD16C2×D14911yescharacteristic
204C2×D8—1491no—
205C2×M16—1491no—
206C22×C8—1491no—
207C4×Q8—1491no—
208C4×Q8—1491no—
209C4×Q8—1491no—
210C4×Q8C2×D14911yescharacteristic
211C4×D4—2981no—
212C4×D4—2981no—
213C4×D4—2981no—
214C4×D4—2981no—
215C4×D4—1491no—
216C4×D4—1491no—
217C4×D4—1491no—
218C4×D4C2×D14911yescharacteristic
219#117—2981no—
220#117—2981no—
221#117—1491no—
222C2×C4⋊C4—2981no—
223C2×C4⋊C4—2981no—
224C2×C4⋊C4—1491no—
225C2×C4⋊C4—1491no—
226#106—1491no—
227#106—1491no—
228#106—1491no—
229#106C2×D14911yescharacteristic
230#103—1491no—
231#103—1491no—
232#103—1491no—
233#103C2×D14911yescharacteristic
234#102—1491no—
235#102—1491no—
236#102—1491no—
237#102C2×D14911yescharacteristic
238#97—1491no—
239#97—1491no—
240C4×C8—1491no—
241C4×C8C2×D14911yescharacteristic
242#41—2982no—
243#41—2982no—
244#41—1494no—
245#41—1494no—
246C2×Q8—1491no—
247C2×Q8C22×D14911yescharacteristic
248C2×D4—2981no—
249C2×D4—2981no—
250C2×D4—1491no—
251C2×D4C22×D14911yescharacteristic
252C22×C4—21no—
253C22×C4—2981no—
254C22×C4—2981no—
255C22×C4—2981no—
256C22×C4—2981no—
257C22×C4—2981no—
258C22×C4—2981no—
259C22×C4—2981no—
260C22×C4—1491no—
261Q16—1494no—
262SD16—1494no—
263SD16C4×D14914yescomplemented
264D8—1494no—
265M16—2982no—
266C2×C8—1491no—
267C2×C8—1491no—
268C2×C8—1494no—
269C2×C8C22×D14911yescharacteristic
270C2×C8C22×D14911yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—2981no—
273C4⋊C4—2981no—
274C4⋊C4—2981no—
275C4⋊C4—2981no—
276C4⋊C4—2981no—
277C4⋊C4—1491no—
278C4⋊C4—1491no—
279C4⋊C4—1491no—
280C4⋊C4—1491no—
281C4⋊C4C22×D14911yescharacteristic
282C4⋊C4C22×D14911yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—2981no—
285C22⋊C4—2981no—
286C22⋊C4—2981no—
287C22⋊C4—1491no—
288C22⋊C4—1491no—
289C42—21no—
290C42—2981no—
291C42—2981no—
292C42—2981no—
293C42—1491no—
294C42C22×D14911yescharacteristic
295C23—21no—
296C23—2981no—
297C23—1491no—
298Q8—21no—
299Q8—2981no—
300Q8—1492no—
301Q8C2×C4×D14912yes—
302D4—21no—
303D4—2984no—
304D4—2984no—
305D4—2981no—
306D4—1492no—
307D4C2×C4×D14912yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—2984no—
313C2×C4—2981no—
314C2×C4—2984no—
315C2×C4—2981no—
316C2×C4—2981no—
317C2×C4—1491no—
318C2×C4—1491no—
319C2×C4—1491no—
320C2×C4—1492no—
321C2×C4—1492no—
322C2×C4—11921no—
323C2×C4—11921no—
324C2×C4—11921no—
325C2×C4—11921no—
326C2×C4—11921no—
327C2×C4D4×D14911yescharacteristic
328C2×C4D4×D14911yescharacteristic
329C2×C4C23×D14911yescharacteristic
330C8—21no—
331C8—2981no—
332C8—1492no—
333C8C2×C4×D14912yes—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—2981no—
338C22—2981no—
339C22—2982no—
340C22—5961no—
341C22—5961no—
342C22—1492no—
343C22C2×D4×D14911yescharacteristic
344C4—21no—
345C4—21no—
346C4—22no—
347C4—41no—
348C4—41no—
349C4—2981no—
350C4—2981no—
351C4—2982no—
352C4—5961no—
353C4—5961no—
354C4—1492no—
355C4C22×C4×D14911yescharacteristic
356C4#41×D14911yescharacteristic
357C2—42no—
358C2—2982no—
359C2—5962no—
360C2C4×D4×D14911yescharacteristic
361C2#2375043111yescharacteristic
362C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutatorC4×C149C23×C4
FrattiniC2×C4C23×D149
FittingC4×SD16×C149C2
socleC22×C149C22×D4
prime radicalC2×#18011932C2
cosocleC2×C4×C149C24
hypercenterC4×SD16D149
hypocenterC149#2952
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #23750107C2semidirect
3. #23750104C2semidirect
4. #23749735C2semidirect
5. #23749734C2semidirect
6. #23749730C2semidirect
7. #23749729C2semidirect
8. C4×#14558725C2semidirect
9. SD16×Dic149C2semidirect
10. #23749712C2semidirect
11. #106×D149C2semidirect
12. #23749625C2semidirect
13. #23749623C2semidirect
14. #23749579C2semidirect
15. C4×SD16×C149C2semidirect
18. #18011932C4semidirect
61. #14558737C2×C4semidirect
63. #14558735C2×C4semidirect
76. #14558726C2×C4semidirect
77. #14558725C2×C4semidirect
78. #14558721C2×C4semidirect
82. C8×D149C2×C4semidirect
104. SD16×C149C2×C4semidirect
181. C149#2952semidirect
193. C4×SD16D149semidirect
263. SD16C4×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119322
#237501072
#237501042
#237497352
#237497342
#237497302
#237497292
C4×#145587252
SD16×Dic1492
#237497122
#106×D1492
#237496252
#237496232
#237495792
C4×SD16×C1492
#2952149