Finite Group Databasebeta

← #34054936

Subgroups — #34054936

Order 19072.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750231C211yesmaximal, characteristic, complemented
2#23750097C211yesmaximal, characteristic, complemented
3#23749952C211yesmaximal, characteristic, complemented
4#23749951C211yesmaximal, characteristic, complemented
5#23749922C211yesmaximal, characteristic, complemented
6#23749821C211yesmaximal, characteristic, complemented
7#23749820C211yesmaximal, characteristic, complemented
8#23749760C211yesmaximal, characteristic, complemented
9#23749760C211yesmaximal, characteristic, complemented
10#23749736C211yesmaximal, characteristic, complemented
11#23749734C211yesmaximal, characteristic, complemented
12#23749707C211yesmaximal, characteristic, complemented
13#23749705C211yesmaximal, characteristic, complemented
14#23749685C211yesmaximal, characteristic, complemented
15#478×C149C211yesmaximal, characteristic, complemented
16C2×D4×D149C2211yescharacteristic
17C2×D1192C2211yescharacteristic
18C2×D1192C2211yescharacteristic
19C2×#14558721C2211yescharacteristic
20C2×#14558721C2211yescharacteristic
21#18011908C2211yescharacteristic, complemented
22#18011896—21no—
23#18011896—21no—
24#18011886—21no—
25#18011886—21no—
26#18011886C2211yescharacteristic
27#18011886C2211yescharacteristic
28C4×D596C2211yescharacteristic
29D4×Dic149C2211yescharacteristic
30#18011873C2211yescharacteristic
31#18011873C2211yescharacteristic, complemented
32#18011873C2211yescharacteristic, complemented
33C4×C22⋊D149—21no—
34#18011871—21no—
35#18011869C2211yescharacteristic
36#18011868C2211yescharacteristic
37C2×#14558713—21no—
38C22⋊C4×D149—21no—
39#18011844C2211yescharacteristic, complemented
40#18011842C2211yescharacteristic, complemented
41C4⋊#11924746C2211yescharacteristic, complemented
42#18011833C2211yescharacteristic, complemented
43#18011833C2211yescharacteristic, complemented
44#18011831C2211yescharacteristic
45#18011831C2211yescharacteristic
46#18011831C2211yescharacteristic, complemented
47#18011831C2211yescharacteristic, complemented
48#18011823C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011821C2211yescharacteristic, complemented
51C8×Dic149C2211yescharacteristic, complemented
52#125×C149C2211yescharacteristic, complemented
53C4×D4×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic, complemented
55#106×C149C2211yescharacteristic, complemented
56C4⋊C8×C149C2211yescharacteristic, complemented
57#102×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59C23×D149—21no—
60C2×D596—21no—
61C2×D596—21no—
62C2×D596—21no—
63C2×D596—21no—
64C2×D596C2311yescharacteristic
65C2×D596C2311yescharacteristic
66C2×D596C2311yescharacteristic
67C2×C22⋊D149—21no—
68D4×D149—22no—
69D4×D149—22no—
70C22×Dic149—21no—
71C2×C4×D149—21no—
72C2×C4×D149—21no—
73C2×C4×D149—21no—
74C2×C4×D149—21no—
75C2×C4×D149C2311yescharacteristic
76D1192—22no—
77D1192—22no—
78#14558721—22no—
79#14558721—22no—
80C2×#11924746C2311yescharacteristic
81C2×#11924746C2311yescharacteristic
82C4⋊Dic149C2311yescharacteristic
83#14558715D411yescharacteristic
84#14558715D411yescharacteristic
85C22⋊Dic149—21no—
86#14558713—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713D411yescharacteristic
94#14558713D411yescharacteristic
95C4×Dic149—21no—
96C4×Dic149C2311yescharacteristic
97C2×D4×C149C2311yescharacteristic
98C22×C4×C149—21no—
99C2×C8×C149C2311yescharacteristic
100C2×C8×C149C2311yescharacteristic
101C4⋊C4×C149—21no—
102C4⋊C4×C149—21no—
103C4⋊C4×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
105C4⋊C4×C149C2311yescharacteristic
106C22⋊C4×C149—21no—
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109C22×D149—24no—
110C22×D149—21no—
111C22×D149—21no—
112C22×D149—81no—
113C22×D149—81no—
114C22×D149C2×D411yescharacteristic
115D596—21no—
116D596—21no—
117D596—21no—
118D596—21no—
119D596—21no—
120D596—81no—
121D596—81no—
122D596—81no—
123D596—81no—
124D596#4112yes—
125C22⋊D149—24no—
126C2×Dic149—21no—
127C2×Dic149—81no—
128C2×Dic149C2×D411yescharacteristic
129C2×Dic149C2×D411yescharacteristic
130C2×Dic149C2×D411yescharacteristic
131C4×D149—21no—
132C4×D149—21no—
133C4×D149—81no—
134C4×D149—81no—
135C4×D149—81no—
136C4×D149—81no—
137#11924746—21no—
138#11924746—21no—
139C23×C149—21no—
140D4×C149—21no—
141D4×C149#4112yes—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—81no—
146C2×C4×C149C2×D411yescharacteristic
147C2×C4×C149C2×D411yescharacteristic
148C2×C4×C149C2411yescharacteristic
149C8×C149—21no—
150C8×C149—21no—
151C22×C149—22no—
152C22×C149—41no—
153C22×C149—41no—
154C22×C149C22×D411yescharacteristic
155C2×D149—21no—
156C2×D149—22no—
157C2×D149—21no—
158C2×D149—21no—
159C2×D149—41no—
160C2×D149—41no—
161C2×D149—41no—
162C2×D149—41no—
163C2×D149—41no—
164C2×D149—41no—
165C2×D149—41no—
166C2×D149—41no—
167C2×D149—84no—
168C4×C149—21no—
169C4×C149—21no—
170C4×C149—41no—
171C4×C149—41no—
172C4×C149—41no—
173C4×C149C2×#4111yescharacteristic
174C4×C149C2×#4111yescharacteristic
175Dic149—21no—
176Dic149—21no—
177Dic149—21no—
178Dic149—41no—
179C2×C149—42no—
180C2×C149#52511yescharacteristic
181C2×C149#57611yescharacteristic
182C2×C149#57611yescharacteristic
183D149—41no—
184D149—42no—
185D149—81no—
186D149—81no—
187C149#312211yescharacteristic, complemented, Sylow
188#3122—1491nomaximal, Sylow
189#540—1491no—
190#518—1491no—
191#482—1491no—
192#482—1491no—
193#478—1491no—
194#478D14911yescharacteristic, complemented
195#459—1491no—
196#459—1491no—
197#447—1491no—
198#447—1491no—
199#442—1491no—
200#442—1491no—
201C4×D8—1491no—
202C4×D8—1491no—
203#433—1491no—
204C22×D4—1491no—
205C2×D8—1491no—
206C2×D8—1491no—
207C2×D8—1491no—
208C2×D8—1491no—
209#127—1491no—
210#125C2×D14911yescharacteristic, complemented
211#123—2981no—
212#123—2981no—
213#121—2981no—
214#121—2981no—
215#121—1491no—
216#121—1491no—
217C4×D4—2981no—
218C4×D4—2981no—
219C4×D4—1491no—
220C4×D4—1491no—
221C4×D4—1491no—
222C4×D4—1491no—
223C4×D4—1491no—
224C4×D4C2×D14911yescharacteristic
225#117—1491no—
226#117—1491no—
227C2×C22⋊C4—2981no—
228C2×C22⋊C4—2981no—
229#107—1491no—
230#107C2×D14911yescharacteristic, complemented
231#106—1491no—
232#106C2×D14911yescharacteristic, complemented
233C4⋊C8—1491no—
234C4⋊C8C2×D14911yescharacteristic, complemented
235#102—1491no—
236#102—1491no—
237#102—1491no—
238#102—1491no—
239#102—1491no—
240#102—1491no—
241#102C2×D14911yescharacteristic
242#102C2×D14911yescharacteristic
243C22⋊C8—1491no—
244C22⋊C8—1491no—
245#97—1491no—
246C4×C8—1491no—
247C24—2981no—
248C2×D4—2981no—
249C2×D4—2981no—
250C2×D4—2982no—
251C2×D4—2982no—
252C2×D4—2981no—
253C2×D4—2981no—
254C2×D4—2981no—
255C2×D4—1491no—
256C2×D4—1491no—
257C2×D4—1491no—
258C2×D4C22×D14911yescharacteristic
259C22×C4—21no—
260C22×C4—2981no—
261C22×C4—2981no—
262C22×C4—2981no—
263C22×C4—2981no—
264C22×C4—2981no—
265C22×C4—1491no—
266D8—2982no—
267D8—2982no—
268D8—2982no—
269D8—2982no—
270C2×C8—1491no—
271C2×C8—1491no—
272C2×C8C22×D14911yescharacteristic
273C2×C8C22×D14911yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—1491no—
277C4⋊C4—1491no—
278C4⋊C4—1491no—
279C4⋊C4C22×D14911yescharacteristic
280C4⋊C4C22×D14911yescharacteristic
281C4⋊C4C22×D14911yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—2981no—
284C22⋊C4—2981no—
285C22⋊C4—2981no—
286C22⋊C4—2981no—
287C22⋊C4—2981no—
288C22⋊C4—2981no—
289C22⋊C4—2981no—
290C22⋊C4—2981no—
291C22⋊C4—1491no—
292C22⋊C4—1491no—
293C42—2981no—
294C42—1491no—
295C42C22×D14911yescharacteristic
296C23—21no—
297C23—2984no—
298C23—2981no—
299C23—2981no—
300C23—2981no—
301C23—1491no—
302C23—11921no—
303C23—11921no—
304D4—21no—
305D4—2984no—
306D4—2981no—
307D4—2981no—
308D4—2981no—
309D4—2981no—
310D4—2981no—
311D4—1492no—
312D4—11921no—
313D4—11921no—
314D4—11921no—
315D4—11921no—
316D4#1455873712yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—2981no—
322C2×C4—2981no—
323C2×C4—2981no—
324C2×C4—1491no—
325C2×C4—1491no—
326C2×C4—1491no—
327C2×C4—11921no—
328C2×C4—11921no—
329C2×C4—11921no—
330C2×C4—11921no—
331C2×C4—11921no—
332C2×C4D4×D14911yescharacteristic
333C2×C4D4×D14911yescharacteristic
334C2×C4C23×D14911yescharacteristic
335C8—21no—
336C8—21no—
337C8—2981no—
338C8—2981no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—2981no—
343C22—2981no—
344C22—2981no—
345C22—2982no—
346C22—5961no—
347C22—5961no—
348C22—5961no—
349C22—5961no—
350C22—5961no—
351C22—5961no—
352C22—5961no—
353C22—5961no—
354C22—11924no—
355C22C2×D4×D14911yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—2981no—
362C4—2981no—
363C4—2981no—
364C4—5961no—
365C4#41×D14911yescharacteristic
366C4C2×#1455873711yescharacteristic
367C2—42no—
368C2—5961no—
369C2—5962no—
370C2—11921no—
371C2—11921no—
372C2#2375013811yescharacteristic
373C2#2375042711yescharacteristic
374C2#2375042911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#478×C149C2
socleC22×C149C22×D4
hypercenter#478D149
hypocenterC149#3122
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #23750231C2semidirect
2. #23750097C2semidirect
3. #23749952C2semidirect
4. #23749951C2semidirect
5. #23749922C2semidirect
6. #23749821C2semidirect
7. #23749820C2semidirect
8. #23749760C2semidirect
9. #23749760C2semidirect
10. #23749736C2semidirect
11. #23749734C2semidirect
12. #23749707C2semidirect
13. #23749705C2semidirect
14. #23749685C2semidirect
15. #478×C149C2semidirect
21. #18011908C22semidirect
31. #18011873C22semidirect
32. #18011873C22semidirect
39. #18011844C22semidirect
40. #18011842C22semidirect
41. C4⋊#11924746C22semidirect
42. #18011833C22semidirect
43. #18011833C22semidirect
46. #18011831C22semidirect
47. #18011831C22semidirect
50. #18011821C22semidirect
51. C8×Dic149C22semidirect
52. #125×C149C22semidirect
54. #107×C149C22semidirect
55. #106×C149C22semidirect
56. C4⋊C8×C149C22semidirect
187. C149#3122semidirect
194. #478D149semidirect
210. #125C2×D149semidirect
230. #107C2×D149semidirect
232. #106C2×D149semidirect
234. C4⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237502312
#237500972
#237499522
#237499512
#237499222
#237498212
#237498202
#237497602
#237497362
#237497342
#237497072
#237497052
#237496852
#478×C1492
#3122149