Finite Group Databasebeta

← #34056128

Subgroups — #34056128

Order 19072.

370 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750229C211yesmaximal, characteristic, complemented
2#23750226C211yesmaximal, characteristic, complemented
3#23749927C211yesmaximal, characteristic, complemented
4#23749926C211yesmaximal, characteristic, complemented
5#23749925C211yesmaximal, characteristic, complemented
6#23749923C211yesmaximal, characteristic, complemented
7#23749877C211yesmaximal, characteristic, complemented
8#23749875C211yesmaximal, characteristic, complemented
9#23749860C211yesmaximal, characteristic, complemented
10#23749858C211yesmaximal, characteristic, complemented
11#23749818C211yesmaximal, characteristic, complemented
12#23749818C211yesmaximal, characteristic, complemented
13#23749817C211yesmaximal, characteristic, complemented
14#23749650C211yesmaximal, characteristic, complemented
15#459×C149C211yesmaximal, characteristic, complemented
16C2×#14558721C2211yescharacteristic
17C2×#14558721C2211yescharacteristic
18C2×#14558719C2211yescharacteristic
19C2×C8×D149C2211yescharacteristic
20#18011907C2211yescharacteristic
21#18011903C2211yescharacteristic
22#18011902C2211yescharacteristic
23#18011894—21no—
24#18011893—21no—
25#18011892—21no—
26#18011892—21no—
27#18011886C2211yescharacteristic
28#18011885—21no—
29#18011884—21no—
30#18011883—21no—
31#18011883—21no—
32#18011882C2211yescharacteristic
33#18011882C2211yescharacteristic
34#18011882C2211yescharacteristic
35C4×D596C2211yescharacteristic
36D4×Dic149C2211yescharacteristic
37D4×Dic149C2211yescharacteristic
38#18011868C2211yescharacteristic
39#18011845C2211yescharacteristic
40#18011844C2211yescharacteristic
41#18011843C2211yescharacteristic
42#18011842C2211yescharacteristic
43C4⋊#11924746C2211yescharacteristic
44#18011840C2211yescharacteristic
45#18011840C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011832C2211yescharacteristic
49#18011832C2211yescharacteristic
50#18011832C2211yescharacteristic
51#18011832C2211yescharacteristic
52C2×D8×C149C2211yescharacteristic
53C2×D8×C149C2211yescharacteristic
54#127×C149C2211yescharacteristic
55C4×D4×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59C2×D596—21no—
60C2×D596C2311yescharacteristic
61C2×C22⋊D149—21no—
62C2×C22⋊D149—21no—
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66C22×Dic149—21no—
67C22×Dic149—21no—
68C2×C4×D149—21no—
69C2×C4×D149C2311yescharacteristic
70#14558721—41no—
71#14558721—41no—
72#14558719—41no—
73C2×#11924746C2311yescharacteristic
74C2×#11924746C2311yescharacteristic
75C8×D149—41no—
76C4⋊Dic149—21no—
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79C4⋊Dic149C2311yescharacteristic
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715D411yescharacteristic
84#14558715D411yescharacteristic
85C22⋊Dic149—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713D411yescharacteristic
93#14558713D411yescharacteristic
94C4×Dic149C2311yescharacteristic
95C2×D4×C149—21no—
96C2×D4×C149—21no—
97C2×D4×C149C2311yescharacteristic
98C2×D4×C149C2311yescharacteristic
99C2×D4×C149C2311yescharacteristic
100C22×C4×C149—21no—
101D8×C149—41no—
102D8×C149—41no—
103C2×C8×C149C2311yescharacteristic
104C2×C8×C149C2311yescharacteristic
105C4⋊C4×C149C2311yescharacteristic
106C22⋊C4×C149—21no—
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109C22×D149C2×D411yescharacteristic
110D596—21no—
111D596—21no—
112D596—81no—
113C22⋊D149—81no—
114C22⋊D149—81no—
115C22⋊D149—81no—
116C22⋊D149—81no—
117C22⋊D149—81no—
118C2×Dic149—21no—
119C2×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149—81no—
122C2×Dic149—81no—
123C2×Dic149C2×D411yescharacteristic
124C2×Dic149C2×D411yescharacteristic
125C2×Dic149C2×D411yescharacteristic
126C4×D149—21no—
127C4×D149—21no—
128C4×D149—81no—
129#11924746—21no—
130#11924746—21no—
131C23×C149—21no—
132C23×C149—21no—
133C23×C149—21no—
134D4×C149—21no—
135D4×C149—21no—
136D4×C149—21no—
137D4×C149—21no—
138D4×C149—21no—
139D4×C149—21no—
140D4×C149—81no—
141D4×C149—81no—
142C2×C4×C149—21no—
143C2×C4×C149—81no—
144C2×C4×C149C2×D411yescharacteristic
145C2×C4×C149C2×D411yescharacteristic
146C2×C4×C149C2411yescharacteristic
147C8×C149—21no—
148C8×C149—21no—
149C22×C149—41no—
150C22×C149—41no—
151C22×C149—41no—
152C22×C149—41no—
153C22×C149—41no—
154C22×C149—41no—
155C22×C149—41no—
156C22×C149—41no—
157C22×C149—41no—
158C22×C149C22×D411yescharacteristic
159C2×D149—21no—
160C2×D149—21no—
161C2×D149—21no—
162C2×D149—41no—
163C2×D149—41no—
164C2×D149—41no—
165C4×C149—21no—
166C4×C149—21no—
167C4×C149—41no—
168C4×C149H(5,𝔽2)11yescharacteristic
169C4×C1492−1+411yescharacteristic
170Dic149—21no—
171Dic149—21no—
172Dic149—21no—
173Dic149—41no—
174Dic149—41no—
175Dic149—41no—
176C2×C149—81no—
177C2×C149—81no—
178C2×C149—81no—
179C2×C149#53711yescharacteristic
180C2×C149#57611yescharacteristic
181C2×C149#57611yescharacteristic
182D149—41no—
183D149—81no—
184C149#325911yescharacteristic, complemented, Sylow
185#3259—1491nomaximal, Sylow
186#540—1491no—
187#540—1491no—
188#478—1491no—
189#478—1491no—
190#478—1491no—
191#478—1491no—
192#469—1491no—
193#469—1491no—
194#466—1491no—
195#466—1491no—
196#459—1491no—
197#459—1491no—
198#459—1491no—
199#459D14911yescharacteristic, complemented
200#424—1491no—
201C2×D8—1491no—
202C2×D8—1491no—
203C2×D8C2×D14911yescharacteristic
204C2×D8C2×D14911yescharacteristic
205C2×M16—1491no—
206C22×C8—1491no—
207#127—1491no—
208#127C2×D14911yescharacteristic
209#125—1491no—
210#125—1491no—
211#123—2981no—
212#123—2981no—
213#123—2981no—
214#123—2981no—
215#121—2981no—
216#121—2981no—
217#121—2981no—
218#121—2981no—
219#121—1491no—
220#121—1491no—
221#121—1491no—
222#121—1491no—
223C4×D4—1491no—
224C4×D4—1491no—
225C4×D4—1491no—
226C4×D4C2×D14911yescharacteristic
227#117—1491no—
228#107—1491no—
229#107—1491no—
230#106—1491no—
231#106—1491no—
232C4⋊C8—1491no—
233C4⋊C8—1491no—
234C4⋊C8—1491no—
235C4⋊C8C2×D14911yescharacteristic
236#102—1491no—
237#102—1491no—
238#102—1491no—
239#102—1491no—
240#102—1491no—
241#102—1491no—
242#102C2×D14911yescharacteristic
243#102C2×D14911yescharacteristic
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—2981no—
247C2×D4—2981no—
248C2×D4—2981no—
249C2×D4—2981no—
250C2×D4—2981no—
251C2×D4—2981no—
252C2×D4—1491no—
253C2×D4C22×D14911yescharacteristic
254C2×D4C22×D14911yescharacteristic
255C2×D4C22×D14911yescharacteristic
256C22×C4—21no—
257C22×C4—2981no—
258C22×C4—2981no—
259C22×C4—2981no—
260C22×C4—1491no—
261D8—41no—
262D8—41no—
263D8—5961no—
264D8—5961no—
265M16—5961no—
266C2×C8—5961no—
267C2×C8—1491no—
268C2×C8—1491no—
269C2×C8C22×D14911yescharacteristic
270C2×C8C22×D14911yescharacteristic
271C4⋊C4—2981no—
272C4⋊C4—2981no—
273C4⋊C4—2981no—
274C4⋊C4—2981no—
275C4⋊C4—1491no—
276C4⋊C4—1491no—
277C4⋊C4—1491no—
278C4⋊C4—1491no—
279C4⋊C4—1491no—
280C4⋊C4C22×D14911yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—2981no—
283C22⋊C4—2981no—
284C22⋊C4—2981no—
285C22⋊C4—2981no—
286C22⋊C4—2981no—
287C22⋊C4—2981no—
288C22⋊C4—2981no—
289C22⋊C4—1491no—
290C22⋊C4—1491no—
291C42—1491no—
292C42C22×D14911yescharacteristic
293C23—21no—
294C23—21no—
295C23—21no—
296C23—2981no—
297C23—1491no—
298D4—21no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—81no—
305D4—81no—
306D4—2981no—
307D4—2981no—
308D4—11921no—
309D4—11921no—
310D4—11921no—
311D4—11921no—
312D4—11921no—
313D4—11921no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—2981no—
317C2×C4—2981no—
318C2×C4—2981no—
319C2×C4—2981no—
320C2×C4—2981no—
321C2×C4—1491no—
322C2×C4—1491no—
323C2×C4—1491no—
324C2×C4—11921no—
325C2×C4—11921no—
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—41no—
341C22—41no—
342C22—41no—
343C22—2981no—
344C22—2981no—
345C22—2981no—
346C22—5961no—
347C22—5961no—
348C22—5961no—
349C22C2×D4×D14911yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—2981no—
354C4—2981no—
355C4—2981no—
356C4—5961no—
357C4—5961no—
358C4—5961no—
359C4#1801195611yescharacteristic
360C4#1801195811yescharacteristic
361C2—81no—
362C2—81no—
363C2—81no—
364C2—5961no—
365C2—11921no—
366C2#2375020411yescharacteristic
367C2#2375042611yescharacteristic
368C2#2375042911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#459×C149C2
socleC22×C149C22×D4
hypercenter#459D149
hypocenterC149#3259
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #23750229C2semidirect
2. #23750226C2semidirect
3. #23749927C2semidirect
4. #23749926C2semidirect
5. #23749925C2semidirect
6. #23749923C2semidirect
7. #23749877C2semidirect
8. #23749875C2semidirect
9. #23749860C2semidirect
10. #23749858C2semidirect
11. #23749818C2semidirect
12. #23749818C2semidirect
13. #23749817C2semidirect
14. #23749650C2semidirect
15. #459×C149C2semidirect
184. C149#3259semidirect
199. #459D149semidirect

Maximal subgroups

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

subgroupindex
#237502292
#237502262
#237499272
#237499262
#237499252
#237499232
#237498772
#237498752
#237498602
#237498582
#237498182
#237498172
#237496502
#459×C1492
#3259149