Finite Group Databasebeta

← #34055676

Subgroups — #34055676

Order 19072.

444 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750172C211yesmaximal, characteristic, complemented
2#124×D149C211yesmaximal, characteristic, complemented
3#23750013C211yesmaximal, characteristic, complemented
4#23750011C211yesmaximal, characteristic, complemented
5#23749986C211yesmaximal, characteristic, complemented
6#23749983C211yesmaximal, characteristic, complemented
7#23749841C211yesmaximal, characteristic, complemented
8#23749840C211yesmaximal, characteristic, complemented
9#23749837C211yesmaximal, characteristic, complemented
10#23749765C211yesmaximal, characteristic, complemented
11#23749762C211yesmaximal, characteristic, complemented
12#23749760C211yesmaximal, characteristic, complemented
13#23749757C211yesmaximal, characteristic, complemented
14#23749681C211yesmaximal, characteristic, complemented
15#463×C149C211yesmaximal, characteristic, complemented
16C2×#14558736—21no—
17C2×Q8×D149C2211yescharacteristic
18C2×D4×D149C2211yescharacteristic
19C2×#14558725C2211yescharacteristic, complemented
20C2×#14558724C2211yescharacteristic, complemented
21C2×#14558723C2211yescharacteristic, complemented
22C2×D1192C2211yescharacteristic
23C2×#14558721C2211yescharacteristic
24C2×#14558721C2211yescharacteristic
25#18011910C2211yescharacteristic, complemented
26#18011907C2211yescharacteristic, complemented
27#18011900C2211yescharacteristic
28#18011899C2211yescharacteristic
29#18011898C2211yescharacteristic
30#18011897—21no—
31#18011897—21no—
32#18011897—21no—
33#18011886C2211yescharacteristic
34#18011884—21no—
35#18011882C2211yescharacteristic
36C4×D596C2211yescharacteristic, complemented
37C4×C22⋊D149—21no—
38C22⋊C4×D149—21no—
39C22⋊C4×D149—21no—
40C42×D149C2211yescharacteristic
41C4⋊#11924746C2211yescharacteristic, complemented
42#18011836C2211yescharacteristic, complemented
43#18011835C2211yescharacteristic, complemented
44#18011834C2211yescharacteristic, complemented
45#18011833C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011823C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011821C2211yescharacteristic, complemented
51#18011821C2211yescharacteristic, complemented
52C2×SD16×C149C2211yescharacteristic, complemented
53C2×D8×C149C2211yescharacteristic
54#124×C149C2211yescharacteristic
55C4×D4×C149C2211yescharacteristic, complemented
56C4⋊C8×C149C2211yescharacteristic, complemented
57#103×C149C2211yescharacteristic, complemented
58#102×C149C2211yescharacteristic
59C23×D149—21no—
60#14558736—44no—
61C2×Dic298—21no—
62C2×Dic298—21no—
63C2×Dic298C2311yescharacteristic
64Q8×D149—41no—
65Q8×D149—41no—
66C2×D596—21no—
67C2×D596C2311yescharacteristic
68C2×D596C2311yescharacteristic
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C2×C22⋊D149—21no—
72C2×C22⋊D149—21no—
73D4×D149—41no—
74D4×D149—41no—
75C2×C4×D149—21no—
76C2×C4×D149—21no—
77C2×C4×D149D411yescharacteristic
78C2×C4×D149D411yescharacteristic
79C2×C4×D149C2311yescharacteristic
80#14558725—41no—
81#14558724—41no—
82#14558723—41no—
83D1192—41no—
84#14558721—41no—
85#14558721—41no—
86C2×#11924746C2311yescharacteristic
87C2×#11924746C2311yescharacteristic
88C4⋊Dic149C2311yescharacteristic
89#14558715—21no—
90C22⋊Dic149—21no—
91C22⋊Dic149—21no—
92C22⋊Dic149—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713—21no—
96#14558713—21no—
97#14558713—21no—
98#14558713—21no—
99C4×Dic149D411yescharacteristic
100C4×Dic149D411yescharacteristic
101C4×Dic149C2311yescharacteristic
102C2×Q8×C149C2311yescharacteristic
103C2×D4×C149C2311yescharacteristic
104C2×D4×C149C2311yescharacteristic
105C22×C4×C149—21no—
106SD16×C149—41no—
107D8×C149—41no—
108C2×C8×C149C2311yescharacteristic
109C2×C8×C149C2311yescharacteristic
110C4⋊C4×C149C2311yescharacteristic
111C22⋊C4×C149—21no—
112C22⋊C4×C149—21no—
113C22⋊C4×C149—21no—
114C42×C149C2311yescharacteristic
115C22×D149—21no—
116C22×D149—21no—
117C22×D149—42no—
118C22×D149—42no—
119C22×D149—42no—
120C22×D149C2×D411yescharacteristic
121Dic298—21no—
122Dic298—21no—
123Dic298—42no—
124Dic298—42no—
125D596—21no—
126D596—21no—
127D596—21no—
128D596—21no—
129D596—42no—
130C22⋊D149—42no—
131C22⋊D149—42no—
132C22⋊D149—42no—
133C22⋊D149—42no—
134C2×Dic149—21no—
135C2×Dic149—21no—
136C2×Dic149C2×D411yescharacteristic
137C2×Dic149C2×D411yescharacteristic
138C2×Dic149C2×D411yescharacteristic
139C4×D149—22no—
140C4×D149—21no—
141C4×D149—21no—
142C4×D149—41no—
143C4×D149—42no—
144C4×D149—42no—
145#11924746—21no—
146#11924746—21no—
147C23×C149—21no—
148C23×C149—21no—
149Q8×C149—21no—
150Q8×C149—21no—
151D4×C149—21no—
152D4×C149—21no—
153D4×C149—21no—
154D4×C149—21no—
155C2×C4×C149—21no—
156C2×C4×C149—21no—
157C2×C4×C149—42no—
158C2×C4×C149C2×D411yescharacteristic
159C2×C4×C149C2×D411yescharacteristic
160C2×C4×C149C2411yescharacteristic
161C8×C149—21no—
162C8×C149—21no—
163C22×C149—41no—
164C22×C149—41no—
165C22×C149—41no—
166C22×C149—41no—
167C22×C149—41no—
168C22×C149—41no—
169C22×C149C22×D411yescharacteristic
170C2×D149—21no—
171C2×D149—21no—
172C2×D149—41no—
173C2×D149—41no—
174C2×D149—41no—
175C2×D149—41no—
176C2×D149—41no—
177C2×D149—41no—
178C2×D149—84no—
179C2×D149AGL(1,ℤ/8)12yes—
180C4×C149—21no—
181C4×C149—21no—
182C4×C149—41no—
183C4×C149—41no—
184C4×C149H(5,𝔽2)11yescharacteristic
185C4×C149H(5,𝔽2)11yescharacteristic
186Dic149—21no—
187Dic149—21no—
188Dic149—21no—
189Dic149—41no—
190Dic149—41no—
191C2×C149—81no—
192C2×C149—81no—
193C2×C149#53511yescharacteristic
194C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
195C2×C149#57511yescharacteristic
196D149—22no—
197D149—81no—
198D149—81no—
199C149#321311yescharacteristic, complemented, Sylow
200#3213—1491nomaximal, Sylow
201#532—1491no—
202C2×#124—1491no—
203#496—1491no—
204#496—1491no—
205#489—1491no—
206#489—1491no—
207#463—1491no—
208#463—1491no—
209#463—1491no—
210#463D14911yescharacteristic, complemented
211#448—1491no—
212#448—1491no—
213#447—1491no—
214#447—1491no—
215#432—1491no—
216C2×#41—2981no—
217C22×Q8—1491no—
218C22×D4—1491no—
219C2×SD16—1491no—
220C2×SD16—1491no—
221C2×SD16—1491no—
222C2×SD16C2×D14911yescharacteristic, complemented
223C2×D8—1491no—
224C2×D8—1491no—
225C2×D8—1491no—
226C2×D8C2×D14911yescharacteristic
227C4⋊Q8—1491no—
228#127—1491no—
229#124—2981no—
230#124—2981no—
231#124—2981no—
232#124—1491no—
233#124—1491no—
234#124—1491no—
235#124C2×D14911yescharacteristic
236#121—2981no—
237#121—1491no—
238#121—1491no—
239C4×D4—2981no—
240C4×D4—1491no—
241C4×D4C2×D14911yescharacteristic, complemented
242C2×C22⋊C4—2981no—
243C2×C22⋊C4—2981no—
244C2×C42—1491no—
245C4⋊C8—1491no—
246C4⋊C8C2×D14911yescharacteristic, complemented
247#103—1491no—
248#103—1491no—
249#103—1491no—
250#103C2×D14911yescharacteristic, complemented
251#102—1491no—
252#102—1491no—
253#102—1491no—
254#102C2×D14911yescharacteristic
255C22⋊C8—1491no—
256C22⋊C8—1491no—
257#97—1491no—
258#97—1491no—
259C24—2981no—
260#41—5964no—
261C2×Q8—2981no—
262C2×Q8—2981no—
263C2×Q8—5961no—
264C2×Q8—5961no—
265C2×Q8—1491no—
266C2×Q8C22×D14911yescharacteristic
267C2×D4—2981no—
268C2×D4—2981no—
269C2×D4—2981no—
270C2×D4—2981no—
271C2×D4—2981no—
272C2×D4—5961no—
273C2×D4—5961no—
274C2×D4—1491no—
275C2×D4—1491no—
276C2×D4C22×D14911yescharacteristic
277C2×D4C22×D14911yescharacteristic
278C22×C4—21no—
279C22×C4—2981no—
280C22×C4—2981no—
281C22×C4—1491no—
282C22×C4—1491no—
283C22×C4—1491no—
284SD16—41no—
285SD16—5961no—
286SD16—5961no—
287SD16—5961no—
288D8—41no—
289D8—5961no—
290D8—5961no—
291D8—5961no—
292C2×C8—1491no—
293C2×C8—1491no—
294C2×C8C22×D14911yescharacteristic
295C2×C8C22×D14911yescharacteristic
296C4⋊C4—2981no—
297C4⋊C4—1491no—
298C4⋊C4C22×D14911yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—2981no—
303C22⋊C4—2981no—
304C22⋊C4—2981no—
305C22⋊C4—2981no—
306C22⋊C4—2981no—
307C22⋊C4—2981no—
308C22⋊C4—2981no—
309C22⋊C4—2981no—
310C22⋊C4—2981no—
311C42—1491no—
312C42—1491no—
313C42—1491no—
314C42C22×D14911yescharacteristic
315C23—21no—
316C23—21no—
317C23—2981no—
318C23—2981no—
319C23—5962no—
320C23—5962no—
321C23—5962no—
322C23—1491no—
323Q8—21no—
324Q8—21no—
325Q8—2981no—
326Q8—2981no—
327Q8—5962no—
328Q8—5962no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—2981no—
334D4—2981no—
335D4—2981no—
336D4—2981no—
337D4—5962no—
338D4—5962no—
339D4—5962no—
340D4—5962no—
341D4—5962no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—2982no—
346C2×C4—2981no—
347C2×C4—2981no—
348C2×C4—2981no—
349C2×C4—2981no—
350C2×C4—5961no—
351C2×C4—5962no—
352C2×C4—5962no—
353C2×C4—1491no—
354C2×C4—1491no—
355C2×C4—1491no—
356C2×C4D4×D14911yescharacteristic
357C2×C4D4×D14911yescharacteristic
358C2×C4C23×D14911yescharacteristic
359C8—21no—
360C8—21no—
361C8—2981no—
362C8—2981no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—2981no—
370C22—2981no—
371C22—5961no—
372C22—5961no—
373C22—5961no—
374C22—5961no—
375C22—5961no—
376C22—5961no—
377C22—1492no—
378C22—11924no—
379C22C2×D4×D14911yescharacteristic
380C4—21no—
381C4—21no—
382C4—41no—
383C4—41no—
384C4—2981no—
385C4—2981no—
386C4—2981no—
387C4—5961no—
388C4—5961no—
389C4#1801195611yescharacteristic
390C4#1801195711yescharacteristic
391C2—81no—
392C2—81no—
393C2—2982no—
394C2—11921no—
395C2—11921no—
396C2#2375019111yescharacteristic
397C2AGL(1,ℤ/8)×D14911yescharacteristic
398C2#2375042211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#463×C149C2
socleC22×C149C22×D4
hypercenter#463D149
hypocenterC149#3213
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #23750172C2semidirect
2. #124×D149C2semidirect
3. #23750013C2semidirect
4. #23750011C2semidirect
5. #23749986C2semidirect
6. #23749983C2semidirect
7. #23749841C2semidirect
8. #23749840C2semidirect
9. #23749837C2semidirect
10. #23749765C2semidirect
11. #23749762C2semidirect
12. #23749760C2semidirect
13. #23749757C2semidirect
14. #23749681C2semidirect
15. #463×C149C2semidirect
19. C2×#14558725C22semidirect
20. C2×#14558724C22semidirect
21. C2×#14558723C22semidirect
25. #18011910C22semidirect
26. #18011907C22semidirect
36. C4×D596C22semidirect
41. C4⋊#11924746C22semidirect
42. #18011836C22semidirect
43. #18011835C22semidirect
44. #18011834C22semidirect
50. #18011821C22semidirect
51. #18011821C22semidirect
52. C2×SD16×C149C22semidirect
55. C4×D4×C149C22semidirect
56. C4⋊C8×C149C22semidirect
57. #103×C149C22semidirect
199. C149#3213semidirect
210. #463D149semidirect
222. C2×SD16C2×D149semidirect
241. C4×D4C2×D149semidirect
246. C4⋊C8C2×D149semidirect
250. #103C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501722
#124×D1492
#237500132
#237500112
#237499862
#237499832
#237498412
#237498402
#237498372
#237497652
#237497622
#237497602
#237497572
#237496812
#463×C1492
#3213149