Finite Group Databasebeta

← #34055046

Subgroups — #34055046

Order 19072.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750255C211yesmaximal, characteristic, complemented
2#23750188C211yesmaximal, characteristic
3#23749988C211yesmaximal, characteristic, complemented
4#23749985C211yesmaximal, characteristic, complemented
5#23749983C211yesmaximal, characteristic, complemented
6#23749982C211yesmaximal, characteristic, complemented
7#23749978C211yesmaximal, characteristic, complemented
8#23749971C211yesmaximal, characteristic, complemented
9#23749970C211yesmaximal, characteristic, complemented
10#23749628C211yesmaximal, characteristic, complemented
11#23749623C211yesmaximal, characteristic, complemented
12#23749618C211yesmaximal, characteristic, complemented
13#102×D149C211yesmaximal, characteristic, complemented
14#23749582C211yesmaximal, characteristic, complemented
15#490×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C2×D4×D149C2211yescharacteristic
18C2×#14558719C2211yescharacteristic
19C2×C8×D149C2211yescharacteristic
20#18011911C2211yescharacteristic, complemented
21#18011910—21no—
22#18011910C2211yescharacteristic, complemented
23#18011907C2211yescharacteristic
24#18011902C2211yescharacteristic, complemented
25#18011901—21no—
26#18011899C2211yescharacteristic
27#18011898C2211yescharacteristic
28#18011891—21no—
29#18011889—21no—
30#18011883—21no—
31#18011883—21no—
32#18011879—21no—
33#18011879—21no—
34#18011869C2211yescharacteristic
35#18011868C2211yescharacteristic
36C4⋊C4×D149C2211yescharacteristic
37#18011836C2211yescharacteristic, complemented
38#18011836C2211yescharacteristic, complemented
39#18011834C2211yescharacteristic, complemented
40#18011834C2211yescharacteristic, complemented
41#18011833C2211yescharacteristic
42#18011833C2211yescharacteristic
43#18011832C2211yescharacteristic
44#18011832C2211yescharacteristic
45#18011832C2211yescharacteristic, complemented
46#18011832C2211yescharacteristic, complemented
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49#18011821C2211yescharacteristic, complemented
50C4×#11924746C2211yescharacteristic, complemented
51C8×Dic149C2211yescharacteristic, complemented
52#127×C149C2211yescharacteristic
53#125×C149C2211yescharacteristic, complemented
54#102×C149C2211yescharacteristic
55#102×C149C2211yescharacteristic
56#102×C149C2211yescharacteristic, complemented
57#102×C149C2211yescharacteristic, complemented
58#97×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60#14558735—22no—
61#14558735—22no—
62C2×Dic298—21no—
63C2×Dic298—21no—
64C2×Dic298C2311yescharacteristic
65C2×D596C2311yescharacteristic
66C2×C22⋊D149—21no—
67C2×C22⋊D149—21no—
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70D4×D149—22no—
71D4×D149—22no—
72C22×Dic149—21no—
73C2×C4×D149—21no—
74C2×C4×D149C2311yescharacteristic
75#14558719—22no—
76C2×#11924746C2311yescharacteristic
77C2×#11924746C2311yescharacteristic
78C8×D149—22no—
79C4⋊Dic149—21no—
80C4⋊Dic149—21no—
81C4⋊Dic149C2311yescharacteristic
82C4⋊Dic149C2311yescharacteristic
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86#14558715D411yescharacteristic
87#14558715D411yescharacteristic
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713D411yescharacteristic
94#14558713D411yescharacteristic
95C4×Dic149—21no—
96C4×Dic149C2311yescharacteristic
97C2×D4×C149—21no—
98C2×D4×C149—21no—
99C2×D4×C149C2311yescharacteristic
100C2×D4×C149C2311yescharacteristic
101C2×C8×C149C2311yescharacteristic
102C2×C8×C149C2311yescharacteristic
103C4⋊C4×C149—21no—
104C4⋊C4×C149—21no—
105C4⋊C4×C149C2311yescharacteristic
106C4⋊C4×C149C2311yescharacteristic
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109C22×D149—42no—
110C22×D149—81no—
111C22×D149—81no—
112C22×D149C2×D411yescharacteristic
113Dic298—21no—
114Dic298—21no—
115Dic298—81no—
116Dic298—81no—
117D596—21no—
118D596—21no—
119C22⋊D149—42no—
120C22⋊D149—42no—
121C22⋊D149—81no—
122C22⋊D149—81no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C2×Dic149—21no—
126C2×Dic149—42no—
127C2×Dic149C2×D411yescharacteristic
128C2×Dic149C2×D411yescharacteristic
129C2×Dic149C2×D411yescharacteristic
130C4×D149—81no—
131C4×D149#4112yes—
132C4×D149#4112yes—
133#11924746—21no—
134#11924746—21no—
135C23×C149—21no—
136C23×C149—21no—
137D4×C149—21no—
138D4×C149—21no—
139D4×C149—21no—
140D4×C149—21no—
141D4×C149—81no—
142D4×C149—81no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149C2×D411yescharacteristic
146C2×C4×C149C2×D411yescharacteristic
147C2×C4×C149C2411yescharacteristic
148C8×C149—21no—
149C8×C149—21no—
150C22×C149—41no—
151C22×C149—41no—
152C22×C149—41no—
153C22×C149—41no—
154C22×C149—41no—
155C22×C149—41no—
156C22×C149C22×D411yescharacteristic
157C2×D149—21no—
158C2×D149—21no—
159C2×D149—41no—
160C2×D149—41no—
161C2×D149—41no—
162C2×D149—84no—
163C2×D149#12412yes—
164C4×C149—21no—
165C4×C149—21no—
166C4×C149—41no—
167C4×C149—41no—
168C4×C149C2×#4111yescharacteristic
169C4×C149C2×#4111yescharacteristic
170Dic149—21no—
171Dic149—21no—
172Dic149—41no—
173Dic149—41no—
174Dic149—41no—
175Dic149#12412yes—
176C2×C149—81no—
177C2×C149—81no—
178C2×C149C2×#12411yescharacteristic
179C2×C149#57611yescharacteristic
180C2×C149#57711yescharacteristic
181D149—22no—
182D149—81no—
183C149#313611yescharacteristic, complemented, Sylow
184#3136—1491nomaximal, Sylow
185#544—1491no—
186#535—1491no—
187#490—1491no—
188#490D14911yescharacteristic, complemented
189#489—1491no—
190#489—1491no—
191#488—1491no—
192#488—1491no—
193#486—1491no—
194#486—1491no—
195#418—1491no—
196#417—1491no—
197#416—1491no—
198C2×#102—1491no—
199#405—1491no—
200C2×#41—1491no—
201C22×D4—1491no—
202C2×M16—1491no—
203C22×C8—1491no—
204C4⋊Q8—2981no—
205C4⋊Q8—1491no—
206C4⋊Q8—1491no—
207#127—1491no—
208#127C2×D14911yescharacteristic
209#125—2981no—
210#125—1491no—
211#125C2×D14911yescharacteristic, complemented
212#124—1491no—
213#124—1491no—
214C22⋊Q8—2981no—
215C22⋊Q8—2981no—
216#121—2981no—
217#121—2981no—
218#120—2981no—
219#120—2981no—
220#117—1491no—
221#117—1491no—
222C2×C4⋊C4—1491no—
223#103—1491no—
224#103—1491no—
225#103—1491no—
226#103—1491no—
227#102—1491no—
228#102—1491no—
229#102—1491no—
230#102—1491no—
231#102—1491no—
232#102—1491no—
233#102—1491no—
234#102—1491no—
235#102C2×D14911yescharacteristic
236#102C2×D14911yescharacteristic
237#102C2×D14911yescharacteristic, complemented
238#102C2×D14911yescharacteristic, complemented
239#97—1491no—
240#97C2×D14911yescharacteristic, complemented
241C4×C8—1491no—
242C4×C8—1491no—
243C24—2981no—
244#41—2982no—
245#41—2982no—
246C2×Q8—2981no—
247C2×Q8—2981no—
248C2×Q8—1491no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—2981no—
252C2×D4—2982no—
253C2×D4—2982no—
254C2×D4—2981no—
255C2×D4—2981no—
256C2×D4—2981no—
257C2×D4—1491no—
258C2×D4C22×D14911yescharacteristic
259C2×D4C22×D14911yescharacteristic
260C22×C4—2981no—
261C22×C4—2981no—
262C22×C4—1491no—
263M16—2982no—
264C2×C8—2982no—
265C2×C8—1491no—
266C2×C8—1491no—
267C2×C8C22×D14911yescharacteristic
268C2×C8C22×D14911yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—2981no—
272C4⋊C4—2981no—
273C4⋊C4—2981no—
274C4⋊C4—2981no—
275C4⋊C4—2981no—
276C4⋊C4—1491no—
277C4⋊C4—1491no—
278C4⋊C4—1491no—
279C4⋊C4—1491no—
280C4⋊C4C22×D14911yescharacteristic
281C4⋊C4C22×D14911yescharacteristic
282C22⋊C4—2981no—
283C22⋊C4—2981no—
284C22⋊C4—2981no—
285C22⋊C4—2981no—
286C22⋊C4—2981no—
287C22⋊C4—1491no—
288C22⋊C4—1491no—
289C42—2981no—
290C42—1491no—
291C42C22×D14911yescharacteristic
292C23—21no—
293C23—21no—
294C23—2981no—
295C23—5962no—
296C23—1491no—
297C23—11921no—
298C23—11921no—
299Q8—2981no—
300Q8—2981no—
301Q8—11921no—
302Q8—11921no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—81no—
308D4—81no—
309D4—2981no—
310D4—2981no—
311D4—5962no—
312D4—5962no—
313D4—11921no—
314D4—11921no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—2981no—
318C2×C4—2981no—
319C2×C4—2981no—
320C2×C4—5962no—
321C2×C4—1491no—
322C2×C4—1491no—
323C2×C4—1491no—
324C2×C4—1492no—
325C2×C4—1492no—
326C2×C4—11921no—
327C2×C4D4×D14911yescharacteristic
328C2×C4D4×D14911yescharacteristic
329C2×C4C23×D14911yescharacteristic
330C8—21no—
331C8—21no—
332C8—2981no—
333C8—2981no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—2981no—
341C22—2981no—
342C22—5961no—
343C22—5961no—
344C22—5961no—
345C22—1492no—
346C22—11924no—
347C22C2×D4×D14911yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—2981no—
353C4—2981no—
354C4—5961no—
355C4—5961no—
356C4—5961no—
357C4—1492no—
358C4#41×D14911yescharacteristic
359C4#41×D14911yescharacteristic
360C2—81no—
361C2—81no—
362C2—2982no—
363C2—11921no—
364C2#124×D14911yescharacteristic
365C2#2375042911yescharacteristic
366C2#2375043511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#490×C149C2
socleC22×C149C22×D4
prime radical#23750188C2
hypercenter#490D149
hypocenterC149#3136
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #23750255C2semidirect
3. #23749988C2semidirect
4. #23749985C2semidirect
5. #23749983C2semidirect
6. #23749982C2semidirect
7. #23749978C2semidirect
8. #23749971C2semidirect
9. #23749970C2semidirect
10. #23749628C2semidirect
11. #23749623C2semidirect
12. #23749618C2semidirect
13. #102×D149C2semidirect
14. #23749582C2semidirect
15. #490×C149C2semidirect
20. #18011911C22semidirect
22. #18011910C22semidirect
24. #18011902C22semidirect
37. #18011836C22semidirect
38. #18011836C22semidirect
39. #18011834C22semidirect
40. #18011834C22semidirect
45. #18011832C22semidirect
46. #18011832C22semidirect
49. #18011821C22semidirect
50. C4×#11924746C22semidirect
51. C8×Dic149C22semidirect
53. #125×C149C22semidirect
56. #102×C149C22semidirect
57. #102×C149C22semidirect
58. #97×C149C22semidirect
183. C149#3136semidirect
188. #490D149semidirect
211. #125C2×D149semidirect
237. #102C2×D149semidirect
238. #102C2×D149semidirect
240. #97C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237502552
#237501882
#237499882
#237499852
#237499832
#237499822
#237499782
#237499712
#237499702
#237496282
#237496232
#237496182
#102×D1492
#237495822
#490×C1492
#3136149