Finite Group Databasebeta

← #34054875

Subgroups — #34054875

Order 19072.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750246C211yesmaximal, characteristic, complemented
2#23749966C211yesmaximal, characteristic, complemented
3#23749949C211yesmaximal, characteristic, complemented
4#23749915C211yesmaximal, characteristic, complemented
5#23749905C211yesmaximal, characteristic, complemented
6#23749840C211yesmaximal, characteristic, complemented
7#23749840C211yesmaximal, characteristic, complemented
8#23749776C211yesmaximal, characteristic, complemented
9#23749759C211yesmaximal, characteristic
10#23749735C211yesmaximal, characteristic, complemented
11#23749725C211yesmaximal, characteristic, complemented
12C4×#14558724C211yesmaximal, characteristic, complemented
13C4×#14558721C211yesmaximal, characteristic, complemented
14#23749686C211yesmaximal, characteristic, complemented
15#518×C149C211yesmaximal, characteristic, complemented
16C2×#14558724C2211yescharacteristic
17C2×#14558724C2211yescharacteristic
18C2×#14558721C2211yescharacteristic
19C2×#14558721C2211yescharacteristic
20#18011911C2211yescharacteristic, complemented
21#18011906—21no—
22#18011899C2211yescharacteristic, complemented
23#18011897—21no—
24#18011893—21no—
25#18011890C2211yescharacteristic
26#18011889—21no—
27#18011885C2211yescharacteristic
28C4×Dic298C2211yescharacteristic, complemented
29C4×D596C2211yescharacteristic, complemented
30#18011844C2211yescharacteristic, complemented
31#18011844C2211yescharacteristic, complemented
32#18011842C2211yescharacteristic, complemented
33#18011842C2211yescharacteristic, complemented
34C4⋊#11924746C2211yescharacteristic, complemented
35C4⋊#11924746C2211yescharacteristic, complemented
36#18011834C2211yescharacteristic, complemented
37#18011834C2211yescharacteristic, complemented
38#18011832C2211yescharacteristic
39#18011832C2211yescharacteristic
40#18011832C2211yescharacteristic
41#18011832C2211yescharacteristic
42#18011831C2211yescharacteristic, complemented
43#18011831C2211yescharacteristic, complemented
44C22⋊#11924746C2211yescharacteristic
45C22⋊#11924746C2211yescharacteristic
46#18011822C2211yescharacteristic, complemented
47C4×#11924746C2211yescharacteristic, complemented
48C22×D4×C149C2211yescharacteristic
49C4×D4×C149—21no—
50C4×D4×C149—21no—
51C4×D4×C149C2211yescharacteristic
52C4×D4×C149C2211yescharacteristic
53C4×D4×C149C2211yescharacteristic
54C4×D4×C149C2211yescharacteristic
55#117×C149C2211yescharacteristic
56#117×C149C2211yescharacteristic
57C2×C22⋊C4×C149—21no—
58C2×C22⋊C4×C149—21no—
59C2×Dic298—21no—
60C2×Dic298C2311yescharacteristic
61C2×D596C2311yescharacteristic
62C2×C22⋊D149—21no—
63C2×C4×D149—21no—
64#14558724—22no—
65#14558724—22no—
66#14558721—22no—
67#14558721—22no—
68C2×#11924746C2311yescharacteristic
69C2×#11924746C2311yescharacteristic
70C2×#11924746C2311yescharacteristic
71C2×#11924746C2311yescharacteristic
72C4⋊Dic149—21no—
73C4⋊Dic149C2311yescharacteristic
74C4⋊Dic149C2311yescharacteristic
75#14558715—21no—
76#14558715—21no—
77C22⋊Dic149—21no—
78#14558713—21no—
79#14558713—21no—
80#14558713—21no—
81#14558713—21no—
82C4×Dic149—21no—
83C24×C149—21no—
84C2×D4×C149—22no—
85C2×D4×C149—22no—
86C2×D4×C149—21no—
87C2×D4×C149C2311yescharacteristic
88C2×D4×C149C2311yescharacteristic
89C22×C4×C149—21no—
90C22×C4×C149—21no—
91C22×C4×C149—21no—
92C22×C4×C149—21no—
93C22×C4×C149C2311yescharacteristic
94C4⋊C4×C149D411yescharacteristic
95C4⋊C4×C149D411yescharacteristic
96C4⋊C4×C149C2311yescharacteristic
97C4⋊C4×C149C2311yescharacteristic
98C22⋊C4×C149—21no—
99C22⋊C4×C149—21no—
100C22⋊C4×C149—21no—
101C22⋊C4×C149—21no—
102C22⋊C4×C149—21no—
103C22⋊C4×C149D411yescharacteristic
104C22⋊C4×C149D411yescharacteristic
105C42×C149—21no—
106C42×C149C2311yescharacteristic
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109Dic298—21no—
110Dic298—21no—
111Dic298—81no—
112D596—21no—
113D596—21no—
114C22⋊D149—81no—
115C2×Dic149—21no—
116C2×Dic149—21no—
117C2×Dic149—21no—
118C4×D149—81no—
119#11924746—21no—
120#11924746—21no—
121#11924746—21no—
122#11924746—21no—
123C23×C149—24no—
124C23×C149—21no—
125C23×C149—21no—
126C23×C149—81no—
127C23×C149—81no—
128C23×C149C2×D411yescharacteristic
129D4×C149—24no—
130D4×C149—21no—
131D4×C149—21no—
132D4×C149#4112yes—
133D4×C149#4112yes—
134C2×C4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149—21no—
137C2×C4×C149—21no—
138C2×C4×C149—81no—
139C2×C4×C149—81no—
140C2×C4×C149—81no—
141C2×C4×C149—81no—
142C2×C4×C149C2×D411yescharacteristic
143C2×C4×C149C2×D411yescharacteristic
144C2×C4×C149C2×D411yescharacteristic
145C2×C4×C149C2×D411yescharacteristic
146C2×C4×C149C2×D411yescharacteristic
147C2×C4×C149C2411yescharacteristic
148C22×C149—21no—
149C22×C149—22no—
150C22×C149—22no—
151C22×C149—21no—
152C22×C149—21no—
153C22×C149—41no—
154C22×C149—41no—
155C22×C149—41no—
156C22×C149—41no—
157C22×C149—84no—
158C22×C149C22×D411yescharacteristic
159C2×D149—41no—
160C2×D149—41no—
161C2×D149—41no—
162C4×C149—21no—
163C4×C149—21no—
164C4×C149—21no—
165C4×C149—21no—
166C4×C149—21no—
167C4×C149—41no—
168C4×C149—41no—
169C4×C149C2×#4111yescharacteristic
170C4×C149C2×#4111yescharacteristic
171Dic149—41no—
172Dic149—41no—
173Dic149—41no—
174C2×C149—41no—
175C2×C149—42no—
176C2×C149—42no—
177C2×C149#52511yescharacteristic
178C2×C149#57611yescharacteristic
179C2×C149#57711yescharacteristic
180D149—81no—
181C149#311811yescharacteristic, complemented, Sylow
182#3118—1491nomaximal, Sylow
183#542—1491no—
184#518D14911yescharacteristic, complemented
185#485—1491no—
186#482—1491no—
187#476—1491no—
188#474—1491no—
189#463—1491no—
190#463—1491no—
191#450—1491no—
192#447—1491no—
193#442—1491no—
194#440—1491no—
195C4×SD16—1491no—
196C4×D8—1491no—
197#433—1491no—
198C22×D4C2×D14911yescharacteristic
199C2×SD16—1491no—
200C2×SD16—1491no—
201C2×D8—1491no—
202C2×D8—1491no—
203C4⋊Q8—1491no—
204#126—2981no—
205#124—2981no—
206#124—1491no—
207#123—2981no—
208C22⋊Q8—2981no—
209C22⋊Q8—1491no—
210#121—1491no—
211C4×Q8—1491no—
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—1491no—
215C4×D4C2×D14911yescharacteristic
216C4×D4C2×D14911yescharacteristic
217C4×D4C2×D14911yescharacteristic
218C4×D4C2×D14911yescharacteristic
219#117C2×D14911yescharacteristic
220#117C2×D14911yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223#107—1491no—
224#107—1491no—
225#106—1491no—
226#106—1491no—
227C4⋊C8—1491no—
228C4⋊C8—1491no—
229#103—1491no—
230#103—1491no—
231#102—1491no—
232#102—1491no—
233#102—1491no—
234#102—1491no—
235#102—1491no—
236#102—1491no—
237C22⋊C8—1491no—
238C22⋊C8—1491no—
239#97—1491no—
240C4×C8—1491no—
241C24—21no—
242C2×Q8—2981no—
243C2×Q8—1491no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—2981no—
248C2×D4—1491no—
249C2×D4C22×D14911yescharacteristic
250C2×D4C22×D14911yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—2981no—
256C22×C4C22×D14911yescharacteristic
257SD16—2982no—
258SD16—2982no—
259D8—2982no—
260D8—2982no—
261C2×C8—1491no—
262C2×C8—1491no—
263C2×C8—1491no—
264C2×C8—1491no—
265C4⋊C4—2981no—
266C4⋊C4—2981no—
267C4⋊C4—2981no—
268C4⋊C4—1491no—
269C4⋊C4—1491no—
270C4⋊C4C22⋊D14911yescharacteristic
271C4⋊C4C22⋊D14911yescharacteristic
272C4⋊C4C22×D14911yescharacteristic
273C4⋊C4C22×D14911yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4—2981no—
284C22⋊C4C22⋊D14911yescharacteristic
285C22⋊C4C22⋊D14911yescharacteristic
286C42—21no—
287C42—2981no—
288C42C22×D14911yescharacteristic
289C42C22×D14911yescharacteristic
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—2981no—
296C23C2×C22⋊D14911yescharacteristic
297Q8—2981no—
298Q8—2981no—
299Q8—11921no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—2981no—
304D4—2981no—
305D4—11921no—
306D4#1455873612yes—
307D4#1455873612yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—2981no—
317C2×C4—2981no—
318C2×C4—2981no—
319C2×C4—11921no—
320C2×C4C2×C22⋊D14911yescharacteristic
321C2×C4C2×C22⋊D14911yescharacteristic
322C2×C4C2×C22⋊D14911yescharacteristic
323C2×C4C2×C22⋊D14911yescharacteristic
324C2×C4C2×C22⋊D14911yescharacteristic
325C2×C4C23×D14911yescharacteristic
326C8—2981no—
327C8—2981no—
328C8—2981no—
329C8—2981no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—84no—
340C22—5961no—
341C22—5961no—
342C22—5961no—
343C22C22×C22⋊D14911yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—5961no—
352C4—5961no—
353C4—5961no—
354C4C2×#1455873611yescharacteristic
355C4C2×#1455873611yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—11921no—
360C2#2375013611yescharacteristic
361C2#2375042811yescharacteristic
362C2#2375043611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#518×C149C2
socleC22×C149C22×D4
prime radical#23749759C2
hypercenter#518D149
hypocenterC149#3118
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #23750246C2semidirect
2. #23749966C2semidirect
3. #23749949C2semidirect
4. #23749915C2semidirect
5. #23749905C2semidirect
6. #23749840C2semidirect
7. #23749840C2semidirect
8. #23749776C2semidirect
10. #23749735C2semidirect
11. #23749725C2semidirect
12. C4×#14558724C2semidirect
13. C4×#14558721C2semidirect
14. #23749686C2semidirect
15. #518×C149C2semidirect
20. #18011911C22semidirect
22. #18011899C22semidirect
28. C4×Dic298C22semidirect
29. C4×D596C22semidirect
30. #18011844C22semidirect
31. #18011844C22semidirect
32. #18011842C22semidirect
33. #18011842C22semidirect
34. C4⋊#11924746C22semidirect
35. C4⋊#11924746C22semidirect
36. #18011834C22semidirect
37. #18011834C22semidirect
42. #18011831C22semidirect
43. #18011831C22semidirect
46. #18011822C22semidirect
47. C4×#11924746C22semidirect
181. C149#3118semidirect
184. #518D149semidirect

Maximal subgroups

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

subgroupindex
#237502462
#237499662
#237499492
#237499152
#237499052
#237498402
#237497762
#237497592
#237497352
#237497252
C4×#145587242
C4×#145587212
#237496862
#518×C1492
#3118149