Finite Group Databasebeta

← #34055560

Subgroups — #34055560

Order 19072.

410 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750198C211yesmaximal, characteristic, complemented
2#23750192C211yesmaximal, characteristic
3#23749967C211yesmaximal, characteristic, complemented
4#23749963C211yesmaximal, characteristic, complemented
5#23749948C211yesmaximal, characteristic, complemented
6#23749947C211yesmaximal, characteristic, complemented
7#23749870C211yesmaximal, characteristic, complemented
8#23749868C211yesmaximal, characteristic, complemented
9#23749853C211yesmaximal, characteristic, complemented
10#23749851C211yesmaximal, characteristic, complemented
11#23749776C211yesmaximal, characteristic, complemented
12#23749762C211yesmaximal, characteristic, complemented
13#23749762C211yesmaximal, characteristic, complemented
14#23749590C211yesmaximal, characteristic, complemented
15#450×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×Q8×D149C2211yescharacteristic, complemented
18C2×#14558724C2211yescharacteristic
19C2×#14558724C2211yescharacteristic
20C2×#14558719C2211yescharacteristic, complemented
21C2×C8×D149C2211yescharacteristic, complemented
22#18011910—21no—
23#18011907—21no—
24#18011898—21no—
25#18011897—21no—
26#18011896—21no—
27#18011893—21no—
28#18011891C2211yescharacteristic, complemented
29#18011890C2211yescharacteristic
30#18011887C2211yescharacteristic, complemented
31#18011882C2211yescharacteristic
32#18011882C2211yescharacteristic
33#18011882C2211yescharacteristic
34#18011882C2211yescharacteristic
35#18011880—21no—
36#18011880—21no—
37#18011870C2211yescharacteristic
38#18011869C2211yescharacteristic, complemented
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#18011832C2211yescharacteristic
48#18011832C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011823C2211yescharacteristic, complemented
51#18011823C2211yescharacteristic, complemented
52C22×D4×C149C2211yescharacteristic
53C2×SD16×C149C2211yescharacteristic
54C2×SD16×C149C2211yescharacteristic
55C22⋊Q8×C149C2211yescharacteristic
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59#14558736—41no—
60#14558736—41no—
61C2×Dic298—21no—
62C2×Dic298D411yescharacteristic
63C2×Dic298C2311yescharacteristic
64Q8×D149—41no—
65Q8×D149—41no—
66C2×D596D411yescharacteristic
67C2×C22⋊D149—21no—
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C2×C22⋊D149D411yescharacteristic
72C2×C22⋊D149D411yescharacteristic
73C2×C4×D149—21no—
74C2×C4×D149C2311yescharacteristic
75C2×C4×D149C2311yescharacteristic
76#14558724—41no—
77#14558724—41no—
78#14558719—41no—
79C2×#11924746C2311yescharacteristic
80C2×#11924746C2311yescharacteristic
81C8×D149—41no—
82C4⋊Dic149—21no—
83C4⋊Dic149C2311yescharacteristic
84C4⋊Dic149C2311yescharacteristic
85C4⋊Dic149C2311yescharacteristic
86#14558715—21no—
87#14558715—21no—
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90C22⋊Dic149—21no—
91C22⋊Dic149—21no—
92C22⋊Dic149—21no—
93C22⋊Dic149—21no—
94#14558713—21no—
95#14558713—21no—
96#14558713—21no—
97C4×Dic149—21no—
98C4×Dic149—21no—
99C24×C149—21no—
100C2×Q8×C149C2311yescharacteristic
101C2×D4×C149—21no—
102C2×D4×C149—41no—
103C2×D4×C149—41no—
104C2×D4×C149C2311yescharacteristic
105C2×D4×C149C2311yescharacteristic
106C22×C4×C149C2311yescharacteristic
107SD16×C149—41no—
108SD16×C149—41no—
109C2×C8×C149C2311yescharacteristic
110C2×C8×C149C2311yescharacteristic
111C4⋊C4×C149—21no—
112C4⋊C4×C149C2311yescharacteristic
113C22⋊C4×C149—21no—
114C22×D149C2×D411yescharacteristic
115C22×D149C2×D411yescharacteristic
116Dic298—21no—
117Dic298—21no—
118Dic298—41no—
119Dic298—42no—
120D596—41no—
121C22⋊D149—41no—
122C22⋊D149—41no—
123C22⋊D149—81no—
124C22⋊D149—81no—
125C22⋊D149—81no—
126C22⋊D149—81no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C2×Dic149—21no—
131C2×Dic149C2×D411yescharacteristic
132C2×Dic149C2×D411yescharacteristic
133C4×D149—21no—
134C4×D149—21no—
135C4×D149—21no—
136C4×D149—21no—
137C4×D149—42no—
138#11924746—21no—
139#11924746—21no—
140C23×C149—21no—
141C23×C149—21no—
142C23×C149—42no—
143C23×C149—81no—
144C23×C149—81no—
145C23×C149C2×D411yescharacteristic
146Q8×C149—21no—
147Q8×C149—21no—
148D4×C149—21no—
149D4×C149—21no—
150D4×C149—21no—
151D4×C149—21no—
152D4×C149—42no—
153C2×C4×C149—21no—
154C2×C4×C149—21no—
155C2×C4×C149—21no—
156C2×C4×C149—21no—
157C2×C4×C149C2×D411yescharacteristic
158C2×C4×C149C2411yescharacteristic
159C8×C149—21no—
160C8×C149—21no—
161C22×C149—21no—
162C22×C149—21no—
163C22×C149—21no—
164C22×C149—41no—
165C22×C149—41no—
166C22×C149—41no—
167C22×C149—41no—
168C22×C149—41no—
169C22×C149—41no—
170C22×C149—84no—
171C22×C149C22×D411yescharacteristic
172C2×D149—21no—
173C2×D149—21no—
174C2×D149—21no—
175C2×D149—21no—
176C2×D149—21no—
177C2×D149—21no—
178C4×C149—21no—
179C4×C149—41no—
180C4×C149—41no—
181C4×C149H(5,𝔽2)11yescharacteristic
182C4×C149H(5,𝔽2)11yescharacteristic
183Dic149—21no—
184Dic149—21no—
185Dic149—41no—
186Dic149—41no—
187Dic149—41no—
188Dic149—41no—
189C2×C149—41no—
190C2×C149—81no—
191C2×C149—81no—
192C2×C149#53411yescharacteristic
193C2×C149#57711yescharacteristic
194C2×C149#57711yescharacteristic
195D149—41no—
196D149—41no—
197C149#320011yescharacteristic, complemented, Sylow
198#3200—1491nomaximal, Sylow
199#536—1491no—
200#535—1491no—
201#485—1491no—
202#485—1491no—
203#482—1491no—
204#482—1491no—
205#468—1491no—
206#468—1491no—
207#465—1491no—
208#465—1491no—
209#450—1491no—
210#450D14911yescharacteristic, complemented
211#448—1491no—
212#448—1491no—
213#408—1491no—
214C2×#41—1491no—
215C22×Q8—1491no—
216C22×D4C2×D14911yescharacteristic
217C2×SD16—1491no—
218C2×SD16—1491no—
219C2×SD16C2×D14911yescharacteristic
220C2×SD16C2×D14911yescharacteristic
221C2×M16—1491no—
222C22×C8—1491no—
223C4⋊Q8—2981no—
224#127—2981no—
225#124—2981no—
226#124—2981no—
227#123—2981no—
228#123—2981no—
229C22⋊Q8—1491no—
230C22⋊Q8—1491no—
231C22⋊Q8—1491no—
232C22⋊Q8C2×D14911yescharacteristic
233#121—1491no—
234#121—1491no—
235#121—1491no—
236#121—1491no—
237#120—2981no—
238#120—2981no—
239#117—1491no—
240#117—1491no—
241#107—1491no—
242#107—1491no—
243#106—1491no—
244#106—1491no—
245#103—1491no—
246#103—1491no—
247#103—1491no—
248#103—1491no—
249#102—1491no—
250#102—1491no—
251#102C2×D14911yescharacteristic
252#102C2×D14911yescharacteristic
253C22⋊C8—1491no—
254C22⋊C8—1491no—
255C22⋊C8—1491no—
256C22⋊C8C2×D14911yescharacteristic
257C24—21no—
258#41—5961no—
259#41—5961no—
260C2×Q8—2981no—
261C2×Q8—5961no—
262C2×Q8—5961no—
263C2×Q8—1491no—
264C2×Q8—1491no—
265C2×Q8C22×D14911yescharacteristic
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—2981no—
270C2×D4—2981no—
271C2×D4—2981no—
272C2×D4—2981no—
273C2×D4—1491no—
274C2×D4—1491no—
275C2×D4—1491no—
276C2×D4C22×D14911yescharacteristic
277C2×D4C22×D14911yescharacteristic
278C22×C4—2981no—
279C22×C4—1491no—
280C22×C4—1491no—
281C22×C4C22×D14911yescharacteristic
282SD16—41no—
283SD16—41no—
284SD16—5961no—
285SD16—5961no—
286M16—5961no—
287C2×C8—5961no—
288C2×C8—1491no—
289C2×C8—1491no—
290C2×C8C22×D14911yescharacteristic
291C2×C8C22×D14911yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—2981no—
294C4⋊C4—2981no—
295C4⋊C4—2981no—
296C4⋊C4—1491no—
297C4⋊C4—1491no—
298C4⋊C4—1491no—
299C4⋊C4C22×D14911yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—2981no—
302C22⋊C4—2981no—
303C22⋊C4—2981no—
304C22⋊C4—2981no—
305C22⋊C4—2981no—
306C22⋊C4—2981no—
307C22⋊C4—2981no—
308C22⋊C4—2981no—
309C22⋊C4—2981no—
310C42—2981no—
311C42—2981no—
312C23—21no—
313C23—21no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—1491no—
318C23—1491no—
319C23D4×D14911yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—2981no—
323Q8—2981no—
324Q8—5961no—
325Q8—5962no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—5961no—
332D4—5961no—
333D4—5961no—
334D4—11921no—
335D4—11921no—
336D4—11921no—
337D4—11921no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—2981no—
343C2×C4—2981no—
344C2×C4—2981no—
345C2×C4—2981no—
346C2×C4—2981no—
347C2×C4—2981no—
348C2×C4—2981no—
349C2×C4—2981no—
350C2×C4—5962no—
351C2×C4—1491no—
352C2×C4—1491no—
353C2×C4D4×D14911yescharacteristic
354C2×C4C23×D14911yescharacteristic
355C8—21no—
356C8—21no—
357C8—2981no—
358C8—2981no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—2981no—
370C22—2981no—
371C22—2981no—
372C22—2981no—
373C22—2981no—
374C22—2981no—
375C22C2×D4×D14911yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—2981no—
380C4—2981no—
381C4—5961no—
382C4—5961no—
383C4—5961no—
384C4—5961no—
385C4#1801195611yescharacteristic
386C4#1801195611yescharacteristic
387C2—41no—
388C2—81no—
389C2—81no—
390C2—5961no—
391C2—5961no—
392C2#2375018511yescharacteristic
393C2#2375043111yescharacteristic
394C2#2375043511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#450×C149C2
socleC22×C149C22×D4
prime radical#23750192C2
hypercenter#450D149
hypocenterC149#3200
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #23750198C2semidirect
3. #23749967C2semidirect
4. #23749963C2semidirect
5. #23749948C2semidirect
6. #23749947C2semidirect
7. #23749870C2semidirect
8. #23749868C2semidirect
9. #23749853C2semidirect
10. #23749851C2semidirect
11. #23749776C2semidirect
12. #23749762C2semidirect
13. #23749762C2semidirect
14. #23749590C2semidirect
15. #450×C149C2semidirect
17. C2×Q8×D149C22semidirect
20. C2×#14558719C22semidirect
21. C2×C8×D149C22semidirect
28. #18011891C22semidirect
30. #18011887C22semidirect
38. #18011869C22semidirect
39. #18011845C22semidirect
40. #18011844C22semidirect
41. #18011843C22semidirect
42. #18011842C22semidirect
43. #18011836C22semidirect
44. #18011836C22semidirect
45. #18011835C22semidirect
46. #18011835C22semidirect
50. #18011823C22semidirect
51. #18011823C22semidirect
197. C149#3200semidirect
210. #450D149semidirect

Maximal subgroups

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

subgroupindex
#237501982
#237501922
#237499672
#237499632
#237499482
#237499472
#237498702
#237498682
#237498532
#237498512
#237497762
#237497622
#237495902
#450×C1492
#3200149