Finite Group Databasebeta

← #485×D149 #34054579

Subgroups — #485×D149 #34054579

Order 19072.

416 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×D149C211yesmaximal, characteristic
2#117×D149C211yesmaximal, characteristic
3#23749969C211yesmaximal, characteristic, complemented
4#23749968C211yesmaximal, characteristic, complemented
5#23749967C211yesmaximal, characteristic, complemented
6#23749966C211yesmaximal, characteristic, complemented
7#23749965C211yesmaximal, characteristic, complemented
8#23749964C211yesmaximal, characteristic, complemented
9#23749963C211yesmaximal, characteristic, complemented
10#107×D149C211yesmaximal, characteristic, complemented
11#106×D149C211yesmaximal, characteristic, complemented
12#103×D149C211yesmaximal, characteristic, complemented
13#103×D149C211yesmaximal, characteristic, complemented
14C22⋊C8×D149C211yesmaximal, characteristic
15#485×C149C211yesmaximal, characteristic, complemented
16C2×Q8×D149C2211yescharacteristic
17C22×C4×D149C2211yescharacteristic
18C2×C8×D149C2211yescharacteristic
19C2×C8×D149C2211yescharacteristic
20#18011891C2211yescharacteristic
21#18011890C2211yescharacteristic
22#18011889—21no—
23#18011888—21no—
24#18011887C2211yescharacteristic
25#18011870C2211yescharacteristic
26#18011869C2211yescharacteristic
27#18011869C2211yescharacteristic
28#18011868—21no—
29#18011867—21no—
30C4⋊C4×D149—21no—
31C4⋊C4×D149C2211yescharacteristic
32C4⋊C4×D149C2211yescharacteristic
33C4⋊C4×D149C2211yescharacteristic
34C22⋊C4×D149—21no—
35C22⋊C4×D149—21no—
36C42×D149—21no—
37#18011845C2211yescharacteristic, complemented
38#18011844C2211yescharacteristic, complemented
39#18011844C2211yescharacteristic, complemented
40#18011843C2211yescharacteristic, complemented
41#18011842C2211yescharacteristic, complemented
42#18011842C2211yescharacteristic, complemented
43#18011836C2211yescharacteristic, complemented
44#18011836C2211yescharacteristic, complemented
45#18011835C2211yescharacteristic, complemented
46#18011835C2211yescharacteristic, complemented
47#18011834C2211yescharacteristic, complemented
48#18011834C2211yescharacteristic, complemented
49C22⋊#11924746C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011823C2211yescharacteristic
52C22⋊Q8×C149C2211yescharacteristic
53#117×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic, complemented
55#106×C149C2211yescharacteristic, complemented
56#103×C149C2211yescharacteristic, complemented
57#103×C149C2211yescharacteristic, complemented
58C22⋊C8×C149C2211yescharacteristic
59C23×D149D411yescharacteristic
60C2×Dic298—21no—
61C2×Dic298C2311yescharacteristic
62Q8×D149—22no—
63Q8×D149—22no—
64C22×Dic149D411yescharacteristic
65C2×C4×D149—22no—
66C2×C4×D149—22no—
67C2×C4×D149—21no—
68C2×C4×D149—21no—
69C2×C4×D149—21no—
70C2×C4×D149—21no—
71C2×C4×D149D411yescharacteristic
72C2×C4×D149D411yescharacteristic
73C2×C4×D149C2311yescharacteristic
74C2×C4×D149C2311yescharacteristic
75C2×#11924746C2311yescharacteristic
76C2×#11924746C2311yescharacteristic
77C8×D149—22no—
78C8×D149—22no—
79C4⋊Dic149—21no—
80C4⋊Dic149C2311yescharacteristic
81C4⋊Dic149C2311yescharacteristic
82C4⋊Dic149C2311yescharacteristic
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94C4×Dic149—21no—
95C4×Dic149—21no—
96C4×Dic149—21no—
97C2×Q8×C149C2311yescharacteristic
98C22×C4×C149C2311yescharacteristic
99C2×C8×C149C2311yescharacteristic
100C2×C8×C149C2311yescharacteristic
101C4⋊C4×C149—21no—
102C4⋊C4×C149C2311yescharacteristic
103C4⋊C4×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
105C22⋊C4×C149—21no—
106C22⋊C4×C149—21no—
107C42×C149—21no—
108C22×D149—22no—
109C22×D149—22no—
110C22×D149—22no—
111C22×D149C2×D411yescharacteristic
112C22×D149C2×D411yescharacteristic
113Dic298—21no—
114Dic298—21no—
115Dic298—42no—
116C2×Dic149—22no—
117C2×Dic149—21no—
118C2×Dic149—21no—
119C2×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149C2×D411yescharacteristic
122C2×Dic149C2×D411yescharacteristic
123C4×D149—22no—
124C4×D149—21no—
125C4×D149—21no—
126C4×D149—22no—
127C4×D149—42no—
128C4×D149—42no—
129C4×D149—42no—
130C4×D149—42no—
131C4×D149#4112yes—
132C4×D149#4112yes—
133#11924746—21no—
134#11924746—21no—
135C23×C149C2×D411yescharacteristic
136Q8×C149—21no—
137Q8×C149—21no—
138C2×C4×C149—21no—
139C2×C4×C149—21no—
140C2×C4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149C2×D411yescharacteristic
145C2×C4×C149C2411yescharacteristic
146C8×C149—21no—
147C8×C149—21no—
148C22×C149—21no—
149C22×C149—21no—
150C22×C149—21no—
151C22×C149C22×D411yescharacteristic
152C2×D149—21no—
153C2×D149—21no—
154C2×D149—21no—
155C2×D149—44no—
156C2×D149#12312yes—
157C2×D149#13512yes—
158C2×D149#13712yes—
159C4×C149—21no—
160C4×C149—41no—
161C4×C149—41no—
162C4×C149—41no—
163C4×C149—41no—
164C4×C149C2×#4111yescharacteristic
165C4×C149C2×#4111yescharacteristic
166Dic149—21no—
167Dic149—41no—
168Dic149—41no—
169Dic149—41no—
170Dic149—41no—
171Dic149#12312yes—
172C2×C149—41no—
173C2×C149C2×#12311yescharacteristic
174C2×C149C2×#13511yescharacteristic
175C2×C149C2×#13711yescharacteristic
176D149—41no—
177D149#48514yesdirect product factor
178C149C2×#48511yescharacteristic, complemented, Sylow
179C2×#485—1491nomaximal, Sylow
180C2×C22⋊Q8—1491no—
181C2×#117—1491no—
182#485—1491no—
183#485—1491no—
184#485—1491no—
185#485—1491no—
186#485—1491no—
187#485—1491no—
188#485—1491no—
189#485D14911yescharacteristic, direct product factor
190C2×#107—1491no—
191C2×#106—1491no—
192C2×#103—1491no—
193C2×#103—1491no—
194C2×C22⋊C8—1491no—
195C22×Q8—1491no—
196C23×C4—1491no—
197C22×C8—1491no—
198C22×C8—1491no—
199C22⋊Q8—2981no—
200C22⋊Q8—2981no—
201C22⋊Q8—1491no—
202C22⋊Q8—1491no—
203C22⋊Q8—1491no—
204C22⋊Q8C2×D14911yescharacteristic
205#117—2981no—
206#117—2981no—
207#117—1491no—
208#117—1491no—
209#117—1491no—
210#117C2×D14911yescharacteristic
211C2×C4⋊C4—2981no—
212C2×C4⋊C4—1491no—
213C2×C4⋊C4—1491no—
214C2×C4⋊C4—1491no—
215C2×C22⋊C4—2981no—
216C2×C22⋊C4—2981no—
217C2×C42—2981no—
218#107—1491no—
219#107—1491no—
220#107—1491no—
221#107C2×D14911yescharacteristic, complemented
222#106—1491no—
223#106—1491no—
224#106—1491no—
225#106C2×D14911yescharacteristic, complemented
226#103—1491no—
227#103—1491no—
228#103—1491no—
229#103—1491no—
230#103—1491no—
231#103—1491no—
232#103C2×D14911yescharacteristic, complemented
233#103C2×D14911yescharacteristic, complemented
234C22⋊C8—1491no—
235C22⋊C8—1491no—
236C22⋊C8—1491no—
237C22⋊C8C2×D14911yescharacteristic
238C24—1491no—
239C2×Q8—2981no—
240C2×Q8—2982no—
241C2×Q8—2982no—
242C2×Q8—1491no—
243C2×Q8C22×D14911yescharacteristic
244C22×C4—2982no—
245C22×C4—2982no—
246C22×C4—2981no—
247C22×C4—2981no—
248C22×C4—2981no—
249C22×C4—2981no—
250C22×C4—1491no—
251C22×C4—1491no—
252C22×C4—1491no—
253C22×C4—1491no—
254C22×C4—1491no—
255C22×C4C22×D14911yescharacteristic
256C2×C8—2982no—
257C2×C8—2982no—
258C2×C8—1491no—
259C2×C8—1491no—
260C2×C8C22×D14911yescharacteristic
261C2×C8C22×D14911yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—2981no—
264C4⋊C4—2981no—
265C4⋊C4—2981no—
266C4⋊C4—2981no—
267C4⋊C4—2981no—
268C4⋊C4—2981no—
269C4⋊C4—1491no—
270C4⋊C4—1491no—
271C4⋊C4—1491no—
272C4⋊C4C22×D14911yescharacteristic
273C4⋊C4C22×D14911yescharacteristic
274C4⋊C4C22×D14911yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—2981no—
278C22⋊C4—2981no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C42—21no—
284C42—2981no—
285C42—2981no—
286C42—2981no—
287C23—2982no—
288C23—2982no—
289C23—2982no—
290C23—1491no—
291C23—1491no—
292C23D4×D14911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—2981no—
296Q8—2981no—
297Q8—5962no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—2982no—
305C2×C4—2982no—
306C2×C4—2982no—
307C2×C4—2981no—
308C2×C4—2981no—
309C2×C4—2981no—
310C2×C4—2981no—
311C2×C4—2981no—
312C2×C4—2981no—
313C2×C4—5962no—
314C2×C4—5962no—
315C2×C4—5962no—
316C2×C4—5962no—
317C2×C4—1491no—
318C2×C4—1491no—
319C2×C4—1492no—
320C2×C4—1492no—
321C2×C4D4×D14911yescharacteristic
322C2×C4C23×D14911yescharacteristic
323C8—21no—
324C8—21no—
325C8—2981no—
326C8—2981no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—2981no—
331C22—2981no—
332C22—2981no—
333C22—5964no—
334C22—1492no—
335C22—1492no—
336C22—1492no—
337C22C2×D4×D14911yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—2981no—
344C4—5961no—
345C4—5961no—
346C4—5961no—
347C4—5961no—
348C4—1492no—
349C4#41×D14911yescharacteristic
350C4#41×D14911yescharacteristic
351C2—41no—
352C2—5961no—
353C2—1494no—
354C2#123×D14911yescharacteristic
355C2#135×D14911yescharacteristic
356C2#137×D14911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#485×C149C2
socleC22×C149C22×D4
prime radicalC23×D149D4
hypercenter#485D149
hypocenterC149C2×#485
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #23749969C2semidirect
4. #23749968C2semidirect
5. #23749967C2semidirect
6. #23749966C2semidirect
7. #23749965C2semidirect
8. #23749964C2semidirect
9. #23749963C2semidirect
10. #107×D149C2semidirect
11. #106×D149C2semidirect
12. #103×D149C2semidirect
13. #103×D149C2semidirect
15. #485×C149C2semidirect
37. #18011845C22semidirect
38. #18011844C22semidirect
39. #18011844C22semidirect
40. #18011843C22semidirect
41. #18011842C22semidirect
42. #18011842C22semidirect
43. #18011836C22semidirect
44. #18011836C22semidirect
45. #18011835C22semidirect
46. #18011835C22semidirect
47. #18011834C22semidirect
48. #18011834C22semidirect
54. #107×C149C22semidirect
55. #106×C149C22semidirect
56. #103×C149C22semidirect
57. #103×C149C22semidirect
177. D149#485direct (N × H)
178. C149C2×#485semidirect
189. #485D149direct (N × H)
221. #107C2×D149semidirect
225. #106C2×D149semidirect
232. #103C2×D149semidirect
233. #103C2×D149semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D1492
#117×D1492
#237499692
#237499682
#237499672
#237499662
#237499652
#237499642
#237499632
#107×D1492
#106×D1492
#103×D1492
C22⋊C8×D1492
#485×C1492
C2×#485149