Finite Group Databasebeta

← #34056892

Subgroups — #34056892

Order 19072.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750321C211yesmaximal, characteristic, complemented
2#23749979C211yesmaximal, characteristic, complemented
3#23749963C211yesmaximal, characteristic, complemented
4#23749936C211yesmaximal, characteristic, complemented
5#23749925C211yesmaximal, characteristic, complemented
6#23749876C211yesmaximal, characteristic, complemented
7#23749873C211yesmaximal, characteristic, complemented
8#23749837C211yesmaximal, characteristic, complemented
9#23749770C211yesmaximal, characteristic, complemented
10#23749759C211yesmaximal, characteristic, complemented
11C4×#14558721C211yesmaximal, characteristic, complemented
12#23749703C211yesmaximal, characteristic, complemented
13#23749630C211yesmaximal, characteristic, complemented
14#23749626C211yesmaximal, characteristic, complemented
15#546×C149C211yesmaximal, characteristic, complemented
16C2×#14558723C2211yescharacteristic, complemented
17C2×#14558721C2211yescharacteristic
18C2×#14558721C2211yescharacteristic
19C2×#14558720C2211yescharacteristic
20C2×#14558720C2211yescharacteristic, complemented
21#18011906—21no—
22#18011903C2211yescharacteristic, complemented
23#18011893—21no—
24#18011885C2211yescharacteristic
25#18011885C2211yescharacteristic, complemented
26#18011883—21no—
27C4×D596C2211yescharacteristic, complemented
28#18011871—21no—
29#18011870C2211yescharacteristic
30C2×C4⋊Dic149C2211yescharacteristic, complemented
31#18011844C2211yescharacteristic, complemented
32#18011844C2211yescharacteristic, complemented
33#18011842C2211yescharacteristic, complemented
34C4⋊#11924746C2211yescharacteristic, complemented
35#18011835C2211yescharacteristic, complemented
36#18011835C2211yescharacteristic, complemented
37#18011835C2211yescharacteristic, complemented
38#18011832C2211yescharacteristic
39#18011832C2211yescharacteristic
40#18011832C2211yescharacteristic
41#18011832C2211yescharacteristic
42#18011832C2211yescharacteristic
43#18011832C2211yescharacteristic
44#18011831C2211yescharacteristic, complemented
45C22⋊#11924746C2211yescharacteristic
46C22⋊#11924746C2211yescharacteristic, complemented
47C4×#11924746C2211yescharacteristic, complemented
48C2×#41×C149C2211yescharacteristic
49C22×D4×C149C2211yescharacteristic
50#124×C149C2211yescharacteristic
51#123×C149—21no—
52C22⋊Q8×C149C2211yescharacteristic
53#121×C149—21no—
54#121×C149C2211yescharacteristic
55#120×C149—21no—
56C4×D4×C149C2211yescharacteristic
57C4×D4×C149C2211yescharacteristic
58C2×C22⋊C4×C149—21no—
59C2×D596C2311yescharacteristic
60C2×C22⋊D149—21no—
61C2×C22⋊D149—21no—
62C22×Dic149—21no—
63C2×C4×D149—21no—
64#14558723—41no—
65#14558721—22no—
66#14558721—41no—
67#14558720—41no—
68#14558720—41no—
69C2×#11924746C2311yescharacteristic
70C2×#11924746C2311yescharacteristic
71C2×#11924746C2311yescharacteristic
72C2×#11924746C2311yescharacteristic
73C4⋊Dic149—21no—
74C4⋊Dic149C2311yescharacteristic
75C4⋊Dic149C2311yescharacteristic
76C4⋊Dic149C2311yescharacteristic
77#14558715—21no—
78#14558715—21no—
79C22⋊Dic149—21no—
80#14558713—21no—
81#14558713—21no—
82#14558713—21no—
83C4×Dic149—21no—
84C24×C149—21no—
85#41×C149—22no—
86#41×C149—41no—
87C2×Q8×C149C2311yescharacteristic
88C2×D4×C149—22no—
89C2×D4×C149—21no—
90C2×D4×C149—21no—
91C2×D4×C149—21no—
92C2×D4×C149—41no—
93C2×D4×C149D411yescharacteristic
94C2×D4×C149C2311yescharacteristic
95C2×D4×C149C2311yescharacteristic
96C22×C4×C149—21no—
97C22×C4×C149—21no—
98C22×C4×C149C2311yescharacteristic
99C22×C4×C149C2311yescharacteristic
100C4⋊C4×C149—21no—
101C4⋊C4×C149D411yescharacteristic
102C4⋊C4×C149C2311yescharacteristic
103C22⋊C4×C149—21no—
104C22⋊C4×C149—21no—
105C22⋊C4×C149—21no—
106C22⋊C4×C149—21no—
107C22⋊C4×C149—21no—
108C22⋊C4×C149D411yescharacteristic
109C22⋊C4×C149D411yescharacteristic
110C42×C149C2311yescharacteristic
111C22×D149—21no—
112D596—21no—
113D596—21no—
114C22⋊D149—42no—
115C22⋊D149—81no—
116C2×Dic149—21no—
117C2×Dic149—21no—
118C2×Dic149—21no—
119C2×Dic149—81no—
120C4×D149—81no—
121#11924746—21no—
122#11924746—21no—
123#11924746—21no—
124#11924746—21no—
125C23×C149—21no—
126C23×C149—21no—
127C23×C149—42no—
128C23×C149—42no—
129C23×C149—81no—
130C23×C149C2×D411yescharacteristic
131C23×C149C2×D411yescharacteristic
132Q8×C149—21no—
133Q8×C149—21no—
134D4×C149—21no—
135D4×C149—21no—
136D4×C149—21no—
137D4×C149—41no—
138D4×C149—42no—
139D4×C149—42no—
140D4×C149—81no—
141D4×C149#4112yes—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—21no—
147C2×C4×C149—21no—
148C2×C4×C149—42no—
149C2×C4×C149—81no—
150C2×C4×C149C2×D411yescharacteristic
151C2×C4×C149C2×D411yescharacteristic
152C2×C4×C149C2×D411yescharacteristic
153C2×C4×C149C2×D411yescharacteristic
154C2×C4×C149C2411yescharacteristic
155C22×C149—21no—
156C22×C149—21no—
157C22×C149—22no—
158C22×C149—21no—
159C22×C149—21no—
160C22×C149—21no—
161C22×C149—21no—
162C22×C149—41no—
163C22×C149—41no—
164C22×C149—41no—
165C22×C149—41no—
166C22×C149—41no—
167C22×C149—84no—
168C22×C149C22×D411yescharacteristic
169C2×D149—41no—
170C2×D149—41no—
171C2×D149—41no—
172C4×C149—21no—
173C4×C149—21no—
174C4×C149—21no—
175C4×C149—21no—
176C4×C149—41no—
177C4×C149—41no—
178C4×C149C2×#4111yescharacteristic
179C4×C149H(5,𝔽2)11yescharacteristic
180Dic149—41no—
181Dic149—41no—
182Dic149—41no—
183C2×C149—41no—
184C2×C149—41no—
185C2×C149—42no—
186C2×C149—81no—
187C2×C149#54611yescharacteristic
188C2×C149#57511yescharacteristic
189C2×C149#57611yescharacteristic
190D149—81no—
191C149#332211yescharacteristic, complemented, Sylow
192#3322—1491nomaximal, Sylow
193#553—1491no—
194#546D14911yescharacteristic, complemented
195#488—1491no—
196#485—1491no—
197#480—1491no—
198#478—1491no—
199#469—1491no—
200#468—1491no—
201#463—1491no—
202#449—1491no—
203#447—1491no—
204C4×D8—1491no—
205#436—1491no—
206#418—1491no—
207#417—1491no—
208C2×#41C2×D14911yescharacteristic
209C22×D4C2×D14911yescharacteristic
210C2×SD16—1491no—
211C2×D8—1491no—
212C2×D8—1491no—
213C2×M16—1491no—
214C2×M16—1491no—
215#126—2981no—
216#125—1491no—
217#124C2×D14911yescharacteristic
218#123—21no—
219#123—2981no—
220C22⋊Q8C2×D14911yescharacteristic
221#121—21no—
222#121—2981no—
223#121—1491no—
224#121—1491no—
225#121C2×D14911yescharacteristic
226#120—21no—
227C4×D4—2981no—
228C4×D4—1491no—
229C4×D4C2×D14911yescharacteristic
230C4×D4C2×D14911yescharacteristic
231#117—1491no—
232C2×C4⋊C4—1491no—
233C2×C22⋊C4—21no—
234#107—1491no—
235#107—1491no—
236#106—1491no—
237C4⋊C8—1491no—
238#103—1491no—
239#103—1491no—
240#103—1491no—
241#102—1491no—
242#102—1491no—
243#102—1491no—
244#102—1491no—
245#102—1491no—
246#102—1491no—
247#102—1491no—
248C22⋊C8—1491no—
249C22⋊C8—1491no—
250C4×C8—1491no—
251C24—21no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D14911yescharacteristic
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—41no—
260C2×D4—2981no—
261C2×D4—2981no—
262C2×D4—1491no—
263C2×D4C22⋊D14911yescharacteristic
264C2×D4C22×D14911yescharacteristic
265C2×D4C22×D14911yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—2981no—
269C22×C4—2981no—
270C22×C4C22×D14911yescharacteristic
271C22×C4C22×D14911yescharacteristic
272SD16—5961no—
273D8—2982no—
274D8—5961no—
275M16—5961no—
276M16—5961no—
277C2×C8—1491no—
278C2×C8—1491no—
279C2×C8—1491no—
280C2×C8—1491no—
281C4⋊C4—21no—
282C4⋊C4—2981no—
283C4⋊C4—2981no—
284C4⋊C4—2981no—
285C4⋊C4—1491no—
286C4⋊C4—1491no—
287C4⋊C4—1491no—
288C4⋊C4C22⋊D14911yescharacteristic
289C4⋊C4C22×D14911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—2981no—
296C22⋊C4—2981no—
297C22⋊C4—2981no—
298C22⋊C4—2981no—
299C22⋊C4C22⋊D14911yescharacteristic
300C22⋊C4C22⋊D14911yescharacteristic
301C42—2981no—
302C42C22×D14911yescharacteristic
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—2981no—
309C23C2×C22⋊D14911yescharacteristic
310C23C2×C22⋊D14911yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—41no—
317D4—42no—
318D4—42no—
319D4—81no—
320D4—2981no—
321D4—2981no—
322D4—5962no—
323D4—11921no—
324D4#1455873512yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—81no—
333C2×C4—2981no—
334C2×C4—2981no—
335C2×C4—2981no—
336C2×C4—11921no—
337C2×C4—11921no—
338C2×C4C2×C22⋊D14911yescharacteristic
339C2×C4C2×C22⋊D14911yescharacteristic
340C2×C4C2×C22⋊D14911yescharacteristic
341C2×C4C2×C22⋊D14911yescharacteristic
342C2×C4C23×D14911yescharacteristic
343C8—2981no—
344C8—2981no—
345C8—2981no—
346C8—2981no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—22no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—84no—
360C22—5961no—
361C22—5961no—
362C22—5961no—
363C22C22×C22⋊D14911yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—5961no—
371C4—5961no—
372C4—5961no—
373C4C2×#1455873511yescharacteristic
374C4#1801195611yescharacteristic
375C2—41no—
376C2—41no—
377C2—42no—
378C2—81no—
379C2—11921no—
380C2#2375026911yescharacteristic
381C2#2375042311yescharacteristic
382C2#2375042811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#546×C149C2
socleC22×C149C22×D4
hypercenter#546D149
hypocenterC149#3322
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #23750321C2semidirect
2. #23749979C2semidirect
3. #23749963C2semidirect
4. #23749936C2semidirect
5. #23749925C2semidirect
6. #23749876C2semidirect
7. #23749873C2semidirect
8. #23749837C2semidirect
9. #23749770C2semidirect
10. #23749759C2semidirect
11. C4×#14558721C2semidirect
12. #23749703C2semidirect
13. #23749630C2semidirect
14. #23749626C2semidirect
15. #546×C149C2semidirect
16. C2×#14558723C22semidirect
20. C2×#14558720C22semidirect
22. #18011903C22semidirect
25. #18011885C22semidirect
27. C4×D596C22semidirect
30. C2×C4⋊Dic149C22semidirect
31. #18011844C22semidirect
32. #18011844C22semidirect
33. #18011842C22semidirect
34. C4⋊#11924746C22semidirect
35. #18011835C22semidirect
36. #18011835C22semidirect
37. #18011835C22semidirect
44. #18011831C22semidirect
46. C22⋊#11924746C22semidirect
47. C4×#11924746C22semidirect
191. C149#3322semidirect
194. #546D149semidirect

Maximal subgroups

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

subgroupindex
#237503212
#237499792
#237499632
#237499362
#237499252
#237498762
#237498732
#237498372
#237497702
#237497592
C4×#145587212
#237497032
#237496302
#237496262
#546×C1492
#3322149