Finite Group Databasebeta

← #34055470

Subgroups — #34055470

Order 19072.

420 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750132C211yesmaximal, characteristic
2C22⋊Q8×D149C211yesmaximal, characteristic, complemented
3#23749967C211yesmaximal, characteristic, complemented
4#23749963C211yesmaximal, characteristic, complemented
5#23749954C211yesmaximal, characteristic, complemented
6#23749937C211yesmaximal, characteristic, complemented
7#23749865C211yesmaximal, characteristic, complemented
8#23749863C211yesmaximal, characteristic, complemented
9#23749853C211yesmaximal, characteristic, complemented
10#23749851C211yesmaximal, characteristic, complemented
11#23749787C211yesmaximal, characteristic, complemented
12#23749779C211yesmaximal, characteristic, complemented
13#23749762C211yesmaximal, characteristic, complemented
14C22⋊C8×D149C211yesmaximal, characteristic, complemented
15#452×C149C211yesmaximal, characteristic, complemented
16C2×Q8×D149C2211yescharacteristic
17C22×C4×D149C2211yescharacteristic
18C2×#14558726C2211yescharacteristic, complemented
19C2×#14558724C2211yescharacteristic, complemented
20C2×C8×D149C2211yescharacteristic
21C2×C8×D149C2211yescharacteristic
22#18011892—21no—
23#18011891C2211yescharacteristic
24#18011890C2211yescharacteristic
25#18011889—21no—
26#18011888—21no—
27#18011887C2211yescharacteristic
28#18011887C2211yescharacteristic
29#18011887C2211yescharacteristic
30#18011882C2211yescharacteristic
31#18011882C2211yescharacteristic
32#18011879—21no—
33C4×C22⋊D149—21no—
34C4×C22⋊D149—21no—
35#18011870C2211yescharacteristic
36C4⋊C4×D149—21no—
37C4⋊C4×D149C2211yescharacteristic
38C22⋊C4×D149—21no—
39#18011845C2211yescharacteristic, complemented
40#18011844C2211yescharacteristic, complemented
41#18011843C2211yescharacteristic, complemented
42#18011842C2211yescharacteristic, complemented
43#18011836C2211yescharacteristic, complemented
44#18011836C2211yescharacteristic, complemented
45#18011835C2211yescharacteristic, complemented
46#18011835C2211yescharacteristic, complemented
47#18011835C2211yescharacteristic, complemented
48#18011832C2211yescharacteristic, complemented
49C22⋊#11924746C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011823C2211yescharacteristic
52C2×#41×C149C2211yescharacteristic
53C2×Q16×C149C2211yescharacteristic, complemented
54C2×SD16×C149C2211yescharacteristic, complemented
55C22⋊Q8×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic, complemented
57#102×C149C2211yescharacteristic, complemented
58C22⋊C8×C149C2211yescharacteristic
59C23×D149D411yescharacteristic
60C2×Dic298—21no—
61C2×Dic298C2311yescharacteristic
62Q8×D149—41no—
63Q8×D149—41no—
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66C22×Dic149D411yescharacteristic
67C2×C4×D149—21no—
68C2×C4×D149—21no—
69C2×C4×D149—41no—
70C2×C4×D149—41no—
71C2×C4×D149D411yescharacteristic
72C2×C4×D149D411yescharacteristic
73C2×C4×D149C2311yescharacteristic
74C2×C4×D149C2311yescharacteristic
75#14558726—41no—
76#14558724—41no—
77C2×#11924746C2311yescharacteristic
78C2×#11924746C2311yescharacteristic
79C8×D149—41no—
80C8×D149—41no—
81C4⋊Dic149—21no—
82C4⋊Dic149C2311yescharacteristic
83C4⋊Dic149C2311yescharacteristic
84C4⋊Dic149C2311yescharacteristic
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88#14558715—21no—
89#14558715—21no—
90C22⋊Dic149—21no—
91C22⋊Dic149—21no—
92C22⋊Dic149—21no—
93C22⋊Dic149—21no—
94#14558713—21no—
95#14558713—21no—
96#14558713—21no—
97#14558713—21no—
98C4×Dic149—21no—
99#41×C149—41no—
100#41×C149—41no—
101C2×Q8×C149C2311yescharacteristic
102C2×Q8×C149C2311yescharacteristic
103C2×D4×C149—21no—
104C2×D4×C149C2311yescharacteristic
105C22×C4×C149—21no—
106C22×C4×C149C2311yescharacteristic
107Q16×C149—41no—
108SD16×C149—41no—
109C2×C8×C149C2311yescharacteristic
110C2×C8×C149C2311yescharacteristic
111C4⋊C4×C149—21no—
112C4⋊C4×C149C2311yescharacteristic
113C22⋊C4×C149—21no—
114C22×D149—22no—
115C22×D149—22no—
116C22×D149—41no—
117C22×D149C2×D411yescharacteristic
118C22×D149C2×D411yescharacteristic
119Dic298—21no—
120Dic298—21no—
121Dic298—42no—
122C22⋊D149—42no—
123C22⋊D149—42no—
124C2×Dic149—21no—
125C2×Dic149—21no—
126C2×Dic149—21no—
127C2×Dic149—21no—
128C2×Dic149—41no—
129C2×Dic149C2×D411yescharacteristic
130C2×Dic149C2×D411yescharacteristic
131C4×D149—21no—
132C4×D149—21no—
133C4×D149—21no—
134C4×D149—21no—
135C4×D149—41no—
136C4×D149—41no—
137C4×D149—42no—
138C4×D149—42no—
139#11924746—21no—
140#11924746—21no—
141C23×C149—21no—
142C23×C149C2×D411yescharacteristic
143Q8×C149—21no—
144Q8×C149—21no—
145Q8×C149—21no—
146Q8×C149—21no—
147D4×C149—21no—
148D4×C149—21no—
149D4×C149—42no—
150C2×C4×C149—21no—
151C2×C4×C149—21no—
152C2×C4×C149—21no—
153C2×C4×C149—21no—
154C2×C4×C149—21no—
155C2×C4×C149—42no—
156C2×C4×C149C2×D411yescharacteristic
157C2×C4×C149C2411yescharacteristic
158C8×C149—21no—
159C8×C149—21no—
160C22×C149—21no—
161C22×C149—21no—
162C22×C149—21no—
163C22×C149—41no—
164C22×C149—41no—
165C22×C149—41no—
166C22×C149C22×D411yescharacteristic
167C2×D149—21no—
168C2×D149—21no—
169C2×D149—21no—
170C2×D149—21no—
171C2×D149—44no—
172C2×D149#13512yes—
173C2×D149#13712yes—
174C4×C149—21no—
175C4×C149—41no—
176C4×C149—41no—
177C4×C149—41no—
178C4×C149H(5,𝔽2)11yescharacteristic
179C4×C149H(5,𝔽2)11yescharacteristic
180Dic149—21no—
181Dic149—21no—
182Dic149—41no—
183Dic149—41no—
184Dic149—41no—
185Dic149—41no—
186C2×C149—41no—
187C2×C149—81no—
188C2×C149#53411yescharacteristic
189C2×C149C2×#13511yescharacteristic
190C2×C149C2×#13711yescharacteristic
191D149—22no—
192D149—22no—
193C149#319011yescharacteristic, complemented, Sylow
194#3190—1491nomaximal, Sylow
195#525—1491no—
196C2×C22⋊Q8—1491no—
197#485—1491no—
198#485—1491no—
199#483—1491no—
200#480—1491no—
201#467—1491no—
202#467—1491no—
203#465—1491no—
204#465—1491no—
205#452—1491no—
206#452D14911yescharacteristic, complemented
207#451—1491no—
208#448—1491no—
209C2×C22⋊C8—1491no—
210C2×#41C2×D14911yescharacteristic
211C22×Q8—1491no—
212C23×C4—1491no—
213C2×Q16—1491no—
214C2×Q16C2×D14911yescharacteristic, complemented
215C2×SD16—1491no—
216C2×SD16C2×D14911yescharacteristic, complemented
217C22×C8—1491no—
218C22×C8—1491no—
219#123—2981no—
220C22⋊Q8—2981no—
221C22⋊Q8—2981no—
222C22⋊Q8—1491no—
223C22⋊Q8—1491no—
224C22⋊Q8—1491no—
225C22⋊Q8—1491no—
226C22⋊Q8—1491no—
227C22⋊Q8C2×D14911yescharacteristic
228#121—1491no—
229#121—1491no—
230#120—2981no—
231C4×D4—2981no—
232C4×D4—2981no—
233#117—1491no—
234C2×C4⋊C4—2981no—
235C2×C4⋊C4—1491no—
236C2×C22⋊C4—2981no—
237#107—1491no—
238#107—1491no—
239#106—1491no—
240#106—1491no—
241#103—1491no—
242#103—1491no—
243#103—1491no—
244#103—1491no—
245#103—1491no—
246#103C2×D14911yescharacteristic, complemented
247#102—1491no—
248#102C2×D14911yescharacteristic, complemented
249C22⋊C8—1491no—
250C22⋊C8—1491no—
251C22⋊C8—1491no—
252C22⋊C8C2×D14911yescharacteristic
253C24—1491no—
254#41—41no—
255#41—41no—
256C2×Q8—2981no—
257C2×Q8—5961no—
258C2×Q8—5961no—
259C2×Q8—1491no—
260C2×Q8C22×D14911yescharacteristic
261C2×Q8C22×D14911yescharacteristic
262C2×D4—21no—
263C2×D4—2981no—
264C2×D4—2981no—
265C2×D4C22×D14911yescharacteristic
266C22×C4—21no—
267C22×C4—2981no—
268C22×C4—2981no—
269C22×C4—5961no—
270C22×C4—5961no—
271C22×C4—1491no—
272C22×C4—1491no—
273C22×C4—1491no—
274C22×C4—1491no—
275C22×C4—1491no—
276C22×C4C22×D14911yescharacteristic
277Q16—41no—
278Q16—5961no—
279SD16—41no—
280SD16—5961no—
281C2×C8—5961no—
282C2×C8—5961no—
283C2×C8—1491no—
284C2×C8—1491no—
285C2×C8C22×D14911yescharacteristic
286C2×C8C22×D14911yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—2981no—
289C4⋊C4—2981no—
290C4⋊C4—2981no—
291C4⋊C4—2981no—
292C4⋊C4—2981no—
293C4⋊C4—2981no—
294C4⋊C4—1491no—
295C4⋊C4—1491no—
296C4⋊C4—1491no—
297C4⋊C4C22×D14911yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—2981no—
300C22⋊C4—2981no—
301C22⋊C4—2981no—
302C22⋊C4—2981no—
303C22⋊C4—2981no—
304C22⋊C4—2981no—
305C22⋊C4—2981no—
306C22⋊C4—2981no—
307C42—2981no—
308C23—21no—
309C23—2982no—
310C23—2982no—
311C23—5961no—
312C23—1491no—
313C23—1491no—
314C23D4×D14911yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—21no—
318Q8—21no—
319Q8—2981no—
320Q8—2981no—
321Q8—5962no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—5962no—
326D4—5962no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—42no—
333C2×C4—2981no—
334C2×C4—2981no—
335C2×C4—2981no—
336C2×C4—2981no—
337C2×C4—2981no—
338C2×C4—2981no—
339C2×C4—2981no—
340C2×C4—2981no—
341C2×C4—5961no—
342C2×C4—5961no—
343C2×C4—5962no—
344C2×C4—5962no—
345C2×C4—5961no—
346C2×C4—1491no—
347C2×C4—1491no—
348C2×C4D4×D14911yescharacteristic
349C2×C4C23×D14911yescharacteristic
350C8—21no—
351C8—21no—
352C8—2981no—
353C8—2981no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—2981no—
361C22—2981no—
362C22—2981no—
363C22—2981no—
364C22—5964no—
365C22—1492no—
366C22—1492no—
367C22C2×D4×D14911yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—2981no—
373C4—2981no—
374C4—5961no—
375C4—5961no—
376C4—5961no—
377C4—5961no—
378C4#1801195611yescharacteristic
379C4#1801195611yescharacteristic
380C2—41no—
381C2—81no—
382C2—2982no—
383C2—2982no—
384C2#2375018511yescharacteristic
385C2#135×D14911yescharacteristic
386C2#137×D14911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#452×C149C2
socleC22×C149C22×D4
prime radical#23750132C2
hypercenter#452D149
hypocenterC149#3190
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. C22⋊Q8×D149C2semidirect
3. #23749967C2semidirect
4. #23749963C2semidirect
5. #23749954C2semidirect
6. #23749937C2semidirect
7. #23749865C2semidirect
8. #23749863C2semidirect
9. #23749853C2semidirect
10. #23749851C2semidirect
11. #23749787C2semidirect
12. #23749779C2semidirect
13. #23749762C2semidirect
14. C22⋊C8×D149C2semidirect
15. #452×C149C2semidirect
18. C2×#14558726C22semidirect
19. C2×#14558724C22semidirect
39. #18011845C22semidirect
40. #18011844C22semidirect
41. #18011843C22semidirect
42. #18011842C22semidirect
43. #18011836C22semidirect
44. #18011836C22semidirect
45. #18011835C22semidirect
46. #18011835C22semidirect
47. #18011835C22semidirect
48. #18011832C22semidirect
53. C2×Q16×C149C22semidirect
54. C2×SD16×C149C22semidirect
56. #103×C149C22semidirect
57. #102×C149C22semidirect
193. C149#3190semidirect
206. #452D149semidirect
214. C2×Q16C2×D149semidirect
216. C2×SD16C2×D149semidirect
246. #103C2×D149semidirect
248. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501322
C22⋊Q8×D1492
#237499672
#237499632
#237499542
#237499372
#237498652
#237498632
#237498532
#237498512
#237497872
#237497792
#237497622
C22⋊C8×D1492
#452×C1492
#3190149