Finite Group Databasebeta

← #34057780

Subgroups — #34057780

Order 19072.

380 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#23750360C211yesmaximal, characteristic, complemented
2#23750358C211yesmaximal, characteristic, complemented
3#23750014C211yesmaximal, characteristic, complemented
4#23750011C211yesmaximal, characteristic, complemented
5#23750006C211yesmaximal, characteristic, complemented
6#23749850C211yesmaximal, characteristic, complemented
7#23749847C211yesmaximal, characteristic, complemented
8#23749843C211yesmaximal, characteristic, complemented
9#23749839C211yesmaximal, characteristic, complemented
10#23749820C211yesmaximal, characteristic, complemented
11#23749819C211yesmaximal, characteristic, complemented
12#23749753C211yesmaximal, characteristic, complemented
13#23749724C211yesmaximal, characteristic, complemented
14#23749707C211yesmaximal, characteristic, complemented
15#440×C149C211yesmaximal, characteristic, complemented
16C2×#14558726C2211yescharacteristic
17C2×#14558725C2211yescharacteristic
18C2×#14558725C2211yescharacteristic
19C2×#14558723C2211yescharacteristic
20C2×D1192C2211yescharacteristic
21C2×D1192C2211yescharacteristic
22C2×#14558721C2211yescharacteristic
23C2×#14558721C2211yescharacteristic
24#18011908C2211yescharacteristic
25#18011907C2211yescharacteristic
26#18011900C2211yescharacteristic
27#18011900C2211yescharacteristic
28#18011899—21no—
29#18011899C2211yescharacteristic
30#18011898C2211yescharacteristic
31#18011897—21no—
32#18011896—21no—
33#18011896—21no—
34#18011894—21no—
35#18011893—21no—
36C4×Dic298C2211yescharacteristic
37#18011876C2211yescharacteristic
38C4×D596—21no—
39#18011873C2211yescharacteristic
40#18011873C2211yescharacteristic
41#18011873C2211yescharacteristic
42C4×C22⋊D149—21no—
43C4⋊#11924746C2211yescharacteristic
44#18011840C2211yescharacteristic
45#18011840C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49#18011831C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×SD16×C149C2211yescharacteristic
53C4×Q8×C149C2211yescharacteristic
54C4×D4×C149C2211yescharacteristic
55#107×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#97×C149C2211yescharacteristic
59C2×Dic298D411yescharacteristic
60C2×Dic298C2311yescharacteristic
61C2×D596—21no—
62C2×D596—21no—
63C2×D596C2311yescharacteristic
64C2×D596C2311yescharacteristic
65C2×D596C2311yescharacteristic
66C2×C22⋊D149—21no—
67C2×C22⋊D149—21no—
68C2×C4×D149—21no—
69C2×C4×D149—21no—
70C2×C4×D149—21no—
71#14558726—41no—
72#14558725—22no—
73#14558725—41no—
74#14558723—41no—
75D1192—22no—
76D1192—41no—
77#14558721—41no—
78#14558721—41no—
79C2×#11924746C2311yescharacteristic
80C2×#11924746C2311yescharacteristic
81C4⋊Dic149D411yescharacteristic
82#14558715—21no—
83#14558715D411yescharacteristic
84#14558715D411yescharacteristic
85C22⋊Dic149—21no—
86C22⋊Dic149—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713—21no—
96C4×Dic149—21no—
97C4×Dic149C2311yescharacteristic
98C4×Dic149C2311yescharacteristic
99C2×Q8×C149C2311yescharacteristic
100C2×D4×C149C2311yescharacteristic
101C22×C4×C149—21no—
102SD16×C149—22no—
103C2×C8×C149C2311yescharacteristic
104C2×C8×C149C2311yescharacteristic
105C4⋊C4×C149—21no—
106C4⋊C4×C149C2311yescharacteristic
107C4⋊C4×C149C2311yescharacteristic
108C22⋊C4×C149—21no—
109C42×C149—21no—
110C42×C149C2311yescharacteristic
111C22×D149—21no—
112C22×D149—21no—
113C22×D149—21no—
114Dic298—21no—
115Dic298—21no—
116Dic298—41no—
117D596—21no—
118D596—21no—
119D596—21no—
120D596—21no—
121D596—21no—
122D596—21no—
123D596—42no—
124D596—81no—
125C22⋊D149—42no—
126C22⋊D149—81no—
127C2×Dic149—21no—
128C2×Dic149C2×D411yescharacteristic
129C2×Dic149C2×D411yescharacteristic
130C2×Dic149C2×D411yescharacteristic
131C2×Dic149C2×D411yescharacteristic
132C4×D149—81no—
133C4×D149—81no—
134C4×D149—81no—
135#11924746—21no—
136#11924746—21no—
137C23×C149—21no—
138Q8×C149—21no—
139Q8×C149—21no—
140D4×C149—21no—
141D4×C149—21no—
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#4112yes—
151C22×C149—41no—
152C22×C149—41no—
153C22×C149—41no—
154C22×C149C22×D411yescharacteristic
155C2×D149—41no—
156C2×D149—41no—
157C2×D149—41no—
158C2×D149—41no—
159C2×D149—41no—
160C2×D149—41no—
161C2×D149—41no—
162C2×D149—41no—
163C2×D149—41no—
164C4×C149—21no—
165C4×C149—21no—
166C4×C149—41no—
167C4×C149—41no—
168C4×C149—41no—
169C4×C149C2×#4111yescharacteristic
170C4×C149H(5,𝔽2)11yescharacteristic
171Dic149—21no—
172Dic149—21no—
173Dic149—21no—
174Dic149—21no—
175Dic149—41no—
176C2×C149—81no—
177C2×C149#55011yescharacteristic
178C2×C149#57511yescharacteristic
179C2×C149#57611yescharacteristic
180D149—81no—
181D149—81no—
182D149—81no—
183C149#340311yescharacteristic, complemented, Sylow
184#3403—1491nomaximal, Sylow
185#559—1491no—
186#559—1491no—
187#496—1491no—
188#496—1491no—
189#495—1491no—
190#464—1491no—
191#464—1491no—
192#463—1491no—
193#463—1491no—
194#459—1491no—
195#459—1491no—
196#446—1491no—
197#440—1491no—
198#440D14911yescharacteristic, complemented
199C4×D8—1491no—
200C2×Q16—1491no—
201C2×SD16—1491no—
202C2×SD16—1491no—
203C2×SD16—1491no—
204C2×SD16C2×D14911yescharacteristic
205C2×D8—1491no—
206C2×D8—1491no—
207C2×D8—1491no—
208C2×D8—1491no—
209#127—1491no—
210#127—1491no—
211#124—2981no—
212#124—2981no—
213#124—1491no—
214#124—1491no—
215#124—1491no—
216#124—1491no—
217#123—2981no—
218#123—2981no—
219#123—2981no—
220#123—2981no—
221C4×Q8—1491no—
222C4×Q8—1491no—
223C4×Q8C2×D14911yescharacteristic
224C4×D4—2981no—
225C4×D4—2981no—
226C4×D4—1491no—
227C4×D4—1491no—
228C4×D4—1491no—
229C4×D4C2×D14911yescharacteristic
230#107C2×D14911yescharacteristic
231C4⋊C8—1491no—
232C4⋊C8—1491no—
233C4⋊C8—1491no—
234#103—1491no—
235#103C2×D14911yescharacteristic
236#102—1491no—
237#102—1491no—
238#102—1491no—
239#102C2×D14911yescharacteristic
240#97—1491no—
241#97C2×D14911yescharacteristic
242C4×C8—1491no—
243C2×Q8—1491no—
244C2×Q8—1491no—
245C2×Q8C22×D14911yescharacteristic
246C2×D4—2981no—
247C2×D4—2981no—
248C2×D4—2981no—
249C2×D4—2981no—
250C2×D4—1491no—
251C2×D4—1491no—
252C2×D4—1491no—
253C2×D4C22×D14911yescharacteristic
254C22×C4—21no—
255C22×C4—2981no—
256C22×C4—2981no—
257C22×C4—2981no—
258Q16—5961no—
259SD16—22no—
260SD16—2982no—
261SD16—5961no—
262SD16—5961no—
263D8—2982no—
264D8—5961no—
265D8—5961no—
266D8—5961no—
267C2×C8—1491no—
268C2×C8—1491no—
269C2×C8C22×D14911yescharacteristic
270C2×C8C22×D14911yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—2981no—
273C4⋊C4—1491no—
274C4⋊C4—1491no—
275C4⋊C4—1491no—
276C4⋊C4C22×D14911yescharacteristic
277C4⋊C4C22×D14911yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4—2981no—
284C22⋊C4—2981no—
285C22⋊C4—2981no—
286C22⋊C4—2981no—
287C22⋊C4—2981no—
288C22⋊C4—2981no—
289C22⋊C4—2981no—
290C42—21no—
291C42—2981no—
292C42—1491no—
293C42—1491no—
294C42C22×D14911yescharacteristic
295C23—21no—
296C23—2981no—
297C23—2981no—
298C23—2981no—
299Q8—21no—
300Q8—21no—
301Q8—2981no—
302Q8—2981no—
303Q8—5961no—
304D4—21no—
305D4—21no—
306D4—2981no—
307D4—2981no—
308D4—2981no—
309D4—2981no—
310D4—2981no—
311D4—2981no—
312D4—5962no—
313D4—5962no—
314D4—11921no—
315D4—11921no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—2981no—
321C2×C4—1491no—
322C2×C4—1491no—
323C2×C4—1491no—
324C2×C4—1491no—
325C2×C4—11921no—
326C2×C4—11921no—
327C2×C4—11921no—
328C2×C4D4×D14911yescharacteristic
329C2×C4D4×D14911yescharacteristic
330C2×C4C23×D14911yescharacteristic
331C8—21no—
332C8—2981no—
333C8—2981no—
334C8#1455873612yes—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—5961no—
339C22—5961no—
340C22—5961no—
341C22—5961no—
342C22—5961no—
343C22—5961no—
344C22—5961no—
345C22—5961no—
346C22—5961no—
347C22C2×D4×D14911yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—2981no—
354C4—2981no—
355C4—2981no—
356C4—2981no—
357C4—5961no—
358C4C2×#1455873611yescharacteristic
359C4#1801195711yescharacteristic
360C2—81no—
361C2—11921no—
362C2—11921no—
363C2—11921no—
364C2#2375029611yescharacteristic
365C2#2375042411yescharacteristic
366C2#2375042911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#440×C149C2
socleC22×C149C22×D4
hypercenter#440D149
hypocenterC149#3403
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #23750360C2semidirect
2. #23750358C2semidirect
3. #23750014C2semidirect
4. #23750011C2semidirect
5. #23750006C2semidirect
6. #23749850C2semidirect
7. #23749847C2semidirect
8. #23749843C2semidirect
9. #23749839C2semidirect
10. #23749820C2semidirect
11. #23749819C2semidirect
12. #23749753C2semidirect
13. #23749724C2semidirect
14. #23749707C2semidirect
15. #440×C149C2semidirect
183. C149#3403semidirect
198. #440D149semidirect

Maximal subgroups

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

subgroupindex
#237503602
#237503582
#237500142
#237500112
#237500062
#237498502
#237498472
#237498432
#237498392
#237498202
#237498192
#237497532
#237497242
#237497072
#440×C1492
#3403149