Finite Group Databasebeta

← #34056405

Subgroups — #34056405

Order 19072.

504 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011933C211yesmaximal, characteristic, complemented
2C2×SD16×D149C211yesmaximal, characteristic, complemented
3#23750285C211yesmaximal, characteristic, complemented
4#23750272C211yesmaximal, characteristic, complemented
5#23750006C211yesmaximal, characteristic, complemented
6#23749855C211yesmaximal, characteristic, complemented
7#23749846C211yesmaximal, characteristic, complemented
8#23749843C211yesmaximal, characteristic, complemented
9#23749785C211yesmaximal, characteristic, complemented
10#23749782C211yesmaximal, characteristic, complemented
11#23749768C211yesmaximal, characteristic, complemented
12#23749760C211yesmaximal, characteristic, complemented
13#23749712C211yesmaximal, characteristic, complemented
14C8×C22⋊D149C211yesmaximal, characteristic, complemented
15#465×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×#14558736C2211yescharacteristic, complemented
18C2×Q8×D149C2211yescharacteristic
19C2×D4×D149C2211yescharacteristic
20#18011933—24no—
21C2×Dic596C2211yescharacteristic, complemented
22C2×#14558726C2211yescharacteristic, complemented
23C2×#14558725C2211yescharacteristic
24C2×#14558725C2211yescharacteristic, complemented
25C2×#14558724C2211yescharacteristic
26C2×#14558723C2211yescharacteristic
27SD16×D149—24no—
28C2×D1192C2211yescharacteristic
29C2×#14558721C2211yescharacteristic
30C2×C8×D149C2211yescharacteristic
31#18011900C2211yescharacteristic, complemented
32#18011898C2211yescharacteristic
33#18011897—21no—
34#18011893—21no—
35#18011891C2211yescharacteristic
36#18011889—21no—
37#18011886C2211yescharacteristic
38#18011884—21no—
39#18011882—21no—
40#18011879—21no—
41#18011876C2211yescharacteristic, complemented
42#18011873—21no—
43#18011873C2211yescharacteristic
44C4×C22⋊D149C2211yescharacteristic
45C22⋊C4×D149—21no—
46#18011840C2211yescharacteristic, complemented
47#18011834C2211yescharacteristic, complemented
48#18011834C2211yescharacteristic, complemented
49#18011831C2211yescharacteristic
50#18011831C2211yescharacteristic, complemented
51C22⋊#11924746C2211yescharacteristic, complemented
52#18011823C2211yescharacteristic
53C8×Dic149C2211yescharacteristic, complemented
54C2×SD16×C149C2211yescharacteristic
55C22×C8×C149C2211yescharacteristic, complemented
56C22⋊Q8×C149C2211yescharacteristic, complemented
57#121×C149C2211yescharacteristic
58#106×C149C2211yescharacteristic, complemented
59#103×C149C2211yescharacteristic, complemented
60#102×C149C2211yescharacteristic
61C23×D149—21no—
62#14558736—22no—
63#14558736—22no—
64#14558736—41no—
65#14558736—41no—
66C2×Dic298—21no—
67C2×Dic298C2311yescharacteristic
68C2×Dic298C2311yescharacteristic
69Q8×D149—22no—
70Q8×D149—41no—
71C2×D596—21no—
72C2×D596C2311yescharacteristic
73C2×D596C2311yescharacteristic
74C2×C22⋊D149—21no—
75C2×C22⋊D149—21no—
76C2×C22⋊D149—21no—
77C2×C22⋊D149D411yescharacteristic
78D4×D149—22no—
79D4×D149—41no—
80C2×C4×D149—21no—
81C2×C4×D149—21no—
82C2×C4×D149—21no—
83C2×C4×D149—21no—
84C2×C4×D149C2311yescharacteristic
85Dic596—22no—
86#14558726—41no—
87#14558725—22no—
88#14558725D414yescomplemented
89#14558724—22no—
90#14558723—22no—
91D1192—22no—
92#14558721—41no—
93C2×#11924746C2311yescharacteristic
94C2×#11924746C2311yescharacteristic
95C8×D149—22no—
96C4⋊Dic149—21no—
97#14558715—21no—
98#14558715D411yescharacteristic
99C22⋊Dic149—21no—
100C22⋊Dic149—21no—
101C22⋊Dic149D411yescharacteristic
102#14558713—21no—
103#14558713—21no—
104#14558713—21no—
105#14558713—21no—
106#14558713—21no—
107#14558713D411yescharacteristic
108C4×Dic149—21no—
109C4×Dic149C2311yescharacteristic
110C2×Q8×C149C2311yescharacteristic
111C2×D4×C149—21no—
112C2×D4×C149C2311yescharacteristic
113C22×C4×C149C2311yescharacteristic
114SD16×C149—22no—
115C2×C8×C149—22no—
116C2×C8×C149C2311yescharacteristic
117C2×C8×C149C2311yescharacteristic
118C4⋊C4×C149—21no—
119C4⋊C4×C149C2311yescharacteristic
120C4⋊C4×C149C2311yescharacteristic
121C22⋊C4×C149—21no—
122C22⋊C4×C149—21no—
123C22×D149—21no—
124C22×D149—21no—
125C22×D149—42no—
126C22×D149—42no—
127C22×D149—81no—
128C22×D149C2×D411yescharacteristic
129Dic298—21no—
130Dic298—21no—
131Dic298—21no—
132Dic298—42no—
133Dic298C2×D412yes—
134D596—21no—
135D596—21no—
136D596—21no—
137D596—42no—
138D596C2×D412yes—
139C22⋊D149—22no—
140C22⋊D149—42no—
141C22⋊D149—42no—
142C22⋊D149—42no—
143C2×Dic149—21no—
144C2×Dic149—21no—
145C2×Dic149C2×D411yescharacteristic
146C2×Dic149C2×D411yescharacteristic
147C2×Dic149C2×D411yescharacteristic
148C4×D149—21no—
149C4×D149—21no—
150C4×D149—42no—
151C4×D149—42no—
152C4×D149—42no—
153C4×D149—81no—
154#11924746—21no—
155#11924746—21no—
156C23×C149—21no—
157C23×C149C2×D411yescharacteristic
158Q8×C149—21no—
159Q8×C149—21no—
160D4×C149—21no—
161D4×C149—21no—
162D4×C149—81no—
163C2×C4×C149—21no—
164C2×C4×C149—21no—
165C2×C4×C149—21no—
166C2×C4×C149—21no—
167C2×C4×C149—21no—
168C2×C4×C149C2×D411yescharacteristic
169C2×C4×C149C2411yescharacteristic
170C8×C149—21no—
171C8×C149C2×D412yes—
172C22×C149—21no—
173C22×C149—21no—
174C22×C149—21no—
175C22×C149—41no—
176C22×C149—41no—
177C22×C149—41no—
178C22×C149C22×D411yescharacteristic
179C2×D149—21no—
180C2×D149—21no—
181C2×D149—22no—
182C2×D149—41no—
183C2×D149—41no—
184C2×D149—41no—
185C2×D149—41no—
186C2×D149—41no—
187C2×D149—84no—
188C2×D149#13512yescomplemented
189C4×C149—21no—
190C4×C149—41no—
191C4×C149—41no—
192C4×C149—41no—
193C4×C149C22×D411yescharacteristic
194C4×C149H(5,𝔽2)11yescharacteristic
195Dic149—21no—
196Dic149—22no—
197Dic149—21no—
198Dic149—21no—
199Dic149—41no—
200C2×C149—41no—
201C2×C149—81no—
202C2×C149D4211yescharacteristic
203C2×C149C2×#13511yescharacteristic
204C2×C149#57711yescharacteristic
205D149—22no—
206D149—42no—
207D149—81no—
208C149#328211yescharacteristic, complemented, Sylow
209#3282—1491nomaximal, Sylow
210C2×#135—1491no—
211C22×SD16—1491no—
212#548—1491no—
213#546—1491no—
214#495—1491no—
215#465—1491no—
216#465D14911yescharacteristic, complemented
217#464—1491no—
218#463—1491no—
219#452—1491no—
220#451—1491no—
221#449—1491no—
222#447—1491no—
223C4×SD16—1491no—
224C8×D4—1491no—
225C2×#41—1491no—
226C2×#41—1491no—
227C22×Q8—1491no—
228C22×D4—1491no—
229#135—2984no—
230C2×Q16—1491no—
231C2×Q16—1491no—
232C2×SD16—2984no—
233C2×SD16—1491no—
234C2×SD16—1491no—
235C2×SD16—1491no—
236C2×SD16—1491no—
237C2×SD16C2×D14911yescharacteristic
238C2×D8—1491no—
239C2×D8—1491no—
240C22×C8—1491no—
241C22×C8C2×D14911yescharacteristic, complemented
242#124—2981no—
243#124—1491no—
244#124—1491no—
245#123—2981no—
246C22⋊Q8—2981no—
247C22⋊Q8—1491no—
248C22⋊Q8C2×D14911yescharacteristic, complemented
249#121—2981no—
250#121—2981no—
251#121—1491no—
252#121C2×D14911yescharacteristic
253#120—2981no—
254C4×Q8—1491no—
255C4×D4—2981no—
256C4×D4—1491no—
257C4×D4—1491no—
258C2×C22⋊C4—2981no—
259#106C2×D14911yescharacteristic, complemented
260C4⋊C8—1491no—
261#103—1491no—
262#103—1491no—
263#103C2×D14911yescharacteristic, complemented
264#102—1491no—
265#102—1491no—
266#102C2×D14911yescharacteristic
267C22⋊C8—1491no—
268C22⋊C8—1491no—
269C4×C8—1491no—
270C24—2981no—
271#41—2982no—
272#41—2982no—
273#41—5961no—
274#41—5961no—
275C2×Q8—2981no—
276C2×Q8—2982no—
277C2×Q8—5961no—
278C2×Q8—1491no—
279C2×Q8—1491no—
280C2×Q8C22×D14911yescharacteristic
281C2×D4—21no—
282C2×D4—2981no—
283C2×D4—2982no—
284C2×D4—2981no—
285C2×D4—2981no—
286C2×D4—2981no—
287C2×D4—5961no—
288C2×D4—1491no—
289C2×D4—1491no—
290C2×D4—1491no—
291C2×D4C22×D14911yescharacteristic
292C22×C4—2981no—
293C22×C4—2981no—
294C22×C4—2981no—
295C22×C4—2981no—
296C22×C4—1491no—
297C22×C4C22×D14911yescharacteristic
298Q16—2982no—
299Q16—5961no—
300SD16—22no—
301SD16—2982no—
302SD16—2982no—
303SD16—2982no—
304SD16—1494no—
305D8—2982no—
306D8—5961no—
307C2×C8—22no—
308C2×C8—2982no—
309C2×C8—1491no—
310C2×C8—1491no—
311C2×C8C22×D14911yescharacteristic
312C2×C8C22×D14911yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—2981no—
315C4⋊C4—2981no—
316C4⋊C4—1491no—
317C4⋊C4C22×D14911yescharacteristic
318C4⋊C4C22×D14911yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—2981no—
322C22⋊C4—2981no—
323C22⋊C4—2981no—
324C22⋊C4—2981no—
325C22⋊C4—2981no—
326C22⋊C4—2981no—
327C22⋊C4—2981no—
328C22⋊C4—1491no—
329C22⋊C4—1491no—
330C42—2981no—
331C42—1491no—
332C23—21no—
333C23—2981no—
334C23—2981no—
335C23—5962no—
336C23—5962no—
337C23—1491no—
338C23—11921no—
339C23D4×D14911yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—2981no—
343Q8—2981no—
344Q8—2981no—
345Q8—5962no—
346Q8—1492no—
347D4—21no—
348D4—21no—
349D4—81no—
350D4—2982no—
351D4—2981no—
352D4—2981no—
353D4—2981no—
354D4—5962no—
355D4—5962no—
356D4—5962no—
357D4—5962no—
358D4—1492no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—2981no—
365C2×C4—2981no—
366C2×C4—2981no—
367C2×C4—2981no—
368C2×C4—5962no—
369C2×C4—5962no—
370C2×C4—5962no—
371C2×C4—1491no—
372C2×C4—1491no—
373C2×C4—1491no—
374C2×C4—11921no—
375C2×C4D4×D14911yescharacteristic
376C2×C4C23×D14911yescharacteristic
377C8—21no—
378C8—2981no—
379C8—2981no—
380C8D4×D14912yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—2981no—
388C22—2981no—
389C22—2982no—
390C22—5961no—
391C22—5961no—
392C22—5961no—
393C22—5961no—
394C22—5961no—
395C22—1492no—
396C22—11924no—
397C22C2×D4×D14911yescharacteristic
398C4—21no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—2981no—
403C4—2981no—
404C4—2981no—
405C4—2982no—
406C4—5961no—
407C4C2×D4×D14911yescharacteristic
408C4#1801195711yescharacteristic
409C2—41no—
410C2—81no—
411C2—2982no—
412C2—5962no—
413C2—11921no—
414C2#2375025911yescharacteristic
415C2#135×D14911yescharacteristic
416C2#2375043111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#465×C149C2
socleC22×C149C22×D4
hypercenter#465D149
hypocenterC149#3282
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#18011933C2semidirect
2. C2×SD16×D149C2semidirect
3. #23750285C2semidirect
4. #23750272C2semidirect
5. #23750006C2semidirect
6. #23749855C2semidirect
7. #23749846C2semidirect
8. #23749843C2semidirect
9. #23749785C2semidirect
10. #23749782C2semidirect
11. #23749768C2semidirect
12. #23749760C2semidirect
13. #23749712C2semidirect
14. C8×C22⋊D149C2semidirect
15. #465×C149C2semidirect
17. C2×#14558736C22semidirect
21. C2×Dic596C22semidirect
22. C2×#14558726C22semidirect
24. C2×#14558725C22semidirect
31. #18011900C22semidirect
41. #18011876C22semidirect
46. #18011840C22semidirect
47. #18011834C22semidirect
48. #18011834C22semidirect
50. #18011831C22semidirect
51. C22⋊#11924746C22semidirect
53. C8×Dic149C22semidirect
55. C22×C8×C149C22semidirect
56. C22⋊Q8×C149C22semidirect
58. #106×C149C22semidirect
59. #103×C149C22semidirect
88. #14558725D4semidirect
188. C2×D149#135semidirect
208. C149#3282semidirect
216. #465D149semidirect
241. C22×C8C2×D149semidirect
248. C22⋊Q8C2×D149semidirect
259. #106C2×D149semidirect
263. #103C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119332
C2×SD16×D1492
#237502852
#237502722
#237500062
#237498552
#237498462
#237498432
#237497852
#237497822
#237497682
#237497602
#237497122
C8×C22⋊D1492
#465×C1492
#3282149