Finite Group Databasebeta

← #34054887

Subgroups — #34054887

Order 19072.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750229C211yesmaximal, characteristic, complemented
2#23750104C211yesmaximal, characteristic, complemented
3#23749942C211yesmaximal, characteristic, complemented
4#23749937C211yesmaximal, characteristic, complemented
5#23749933C211yesmaximal, characteristic, complemented
6#23749925C211yesmaximal, characteristic, complemented
7#23749822C211yesmaximal, characteristic, complemented
8#23749767C211yesmaximal, characteristic, complemented
9#23749767C211yesmaximal, characteristic, complemented
10#23749737C211yesmaximal, characteristic, complemented
11#23749722C211yesmaximal, characteristic, complemented
12#23749716C211yesmaximal, characteristic, complemented
13D8×Dic149C211yesmaximal, characteristic, complemented
14#23749685C211yesmaximal, characteristic, complemented
15#459×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C2×#14558724C2211yescharacteristic
18C2×#14558724C2211yescharacteristic
19#18011903C2211yescharacteristic
20#18011892—21no—
21#18011892—21no—
22#18011883—21no—
23#18011883—21no—
24#18011882C2211yescharacteristic
25#18011882C2211yescharacteristic
26C4×Dic298C2211yescharacteristic
27#18011876C2211yescharacteristic
28D4×Dic149C2211yescharacteristic
29D4×Dic149C2211yescharacteristic
30D4×Dic149C2211yescharacteristic
31C4×C22⋊D149—21no—
32#18011871—21no—
33#18011868C2211yescharacteristic
34#18011867—21no—
35C2×#14558715—21no—
36C4⋊C4×D149C2211yescharacteristic
37#18011845C2211yescharacteristic
38#18011844C2211yescharacteristic
39#18011843C2211yescharacteristic
40#18011842C2211yescharacteristic
41C4⋊#11924746C2211yescharacteristic
42#18011836C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011832C2211yescharacteristic
45#18011832C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011823C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×D8×C149C2211yescharacteristic
53C2×D8×C149C2211yescharacteristic
54#127×C149C2211yescharacteristic
55C4×D4×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59#14558735—22no—
60#14558735—22no—
61C2×Dic298C2311yescharacteristic
62C2×C22⋊D149—21no—
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65C22×Dic149—21no—
66C22×Dic149—21no—
67C22×Dic149—21no—
68C22×Dic149—21no—
69C2×C4×D149—21no—
70C2×C4×D149C2311yescharacteristic
71#14558724—22no—
72#14558724—22no—
73C2×#11924746C2311yescharacteristic
74C2×#11924746C2311yescharacteristic
75C4⋊Dic149C2311yescharacteristic
76C4⋊Dic149C2311yescharacteristic
77C4⋊Dic149C2311yescharacteristic
78#14558715—21no—
79#14558715—21no—
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#14558713D411yescharacteristic
91#14558713D411yescharacteristic
92C4×Dic149—21no—
93C4×Dic149—21no—
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—22no—
102D8×C149—22no—
103C2×C8×C149C2311yescharacteristic
104C2×C8×C149C2311yescharacteristic
105C4⋊C4×C149C2311yescharacteristic
106C22⋊C4×C149—21no—
107C42×C149C2311yescharacteristic
108C22×D149C2×D411yescharacteristic
109Dic298—21no—
110Dic298#4112yes—
111C22⋊D149—24no—
112C22⋊D149—81no—
113C22⋊D149—81no—
114C2×Dic149—24no—
115C2×Dic149—21no—
116C2×Dic149—21no—
117C2×Dic149—21no—
118C2×Dic149—21no—
119C2×Dic149—81no—
120C2×Dic149—81no—
121C2×Dic149—81no—
122C2×Dic149C2×D411yescharacteristic
123C2×Dic149C2×D411yescharacteristic
124C2×Dic149C2×D411yescharacteristic
125C4×D149—21no—
126C4×D149—21no—
127C4×D149—81no—
128#11924746—21no—
129#11924746—21no—
130C23×C149—21no—
131C23×C149—21no—
132C23×C149—21no—
133D4×C149—21no—
134D4×C149—21no—
135D4×C149—21no—
136D4×C149—21no—
137D4×C149—21no—
138D4×C149—81no—
139D4×C149—81no—
140D4×C149#4112yes—
141C2×C4×C149—21no—
142C2×C4×C149—81no—
143C2×C4×C149C2×D411yescharacteristic
144C2×C4×C149C2×D411yescharacteristic
145C2×C4×C149C2411yescharacteristic
146C8×C149—21no—
147C8×C149—21no—
148C22×C149—22no—
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×C149C22×D411yescharacteristic
158C2×D149—21no—
159C2×D149—21no—
160C2×D149—21no—
161C4×C149—21no—
162C4×C149—21no—
163C4×C149—41no—
164C4×C149C2×#4111yescharacteristic
165C4×C149C2×#4111yescharacteristic
166Dic149—21no—
167Dic149—22no—
168Dic149—21no—
169Dic149—21no—
170Dic149—41no—
171Dic149—41no—
172Dic149—41no—
173C2×C149—42no—
174C2×C149—81no—
175C2×C149—81no—
176C2×C149#52511yescharacteristic
177C2×C149#57611yescharacteristic
178C2×C149#57711yescharacteristic
179D149—41no—
180C149#311911yescharacteristic, complemented, Sylow
181#3119—1491nomaximal, Sylow
182#540—1491no—
183#520—1491no—
184#481—1491no—
185#480—1491no—
186#479—1491no—
187#478—1491no—
188#460—1491no—
189#459D14911yescharacteristic, complemented
190#449—1491no—
191#449—1491no—
192#442—1491no—
193#440—1491no—
194C4×SD16—1491no—
195C4×D8—1491no—
196#433—1491no—
197C2×#41—1491no—
198C2×SD16—1491no—
199C2×SD16—1491no—
200C2×D8C2×D14911yescharacteristic
201C2×D8C2×D14911yescharacteristic
202#127C2×D14911yescharacteristic
203#125—1491no—
204#123—2981no—
205#123—2981no—
206#121—2981no—
207#121—2981no—
208#121—1491no—
209#121—1491no—
210C4×Q8—1491no—
211C4×Q8—1491no—
212C4×D4—2981no—
213C4×D4—2981no—
214C4×D4—1491no—
215C4×D4—1491no—
216C4×D4—1491no—
217C4×D4C2×D14911yescharacteristic
218#117—2981no—
219#117—1491no—
220C2×C4⋊C4—2981no—
221C2×C4⋊C4—1491no—
222#107—1491no—
223#107—1491no—
224#106—1491no—
225#106—1491no—
226C4⋊C8—1491no—
227C4⋊C8C2×D14911yescharacteristic
228#103—1491no—
229#103—1491no—
230#102—1491no—
231#102—1491no—
232#102—1491no—
233#102—1491no—
234#102C2×D14911yescharacteristic
235#102C2×D14911yescharacteristic
236C22⋊C8—1491no—
237C22⋊C8—1491no—
238#97—1491no—
239C4×C8—1491no—
240#41—2982no—
241#41—2982no—
242C2×Q8—1491no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—2981no—
246C2×D4—2981no—
247C2×D4—2981no—
248C2×D4C22×D14911yescharacteristic
249C2×D4C22×D14911yescharacteristic
250C2×D4C22×D14911yescharacteristic
251C22×C4—21no—
252C22×C4—2981no—
253C22×C4—2981no—
254C22×C4—2981no—
255C22×C4—2981no—
256C22×C4—2981no—
257C22×C4—1491no—
258SD16—2982no—
259SD16—2982no—
260D8—22no—
261D8—22no—
262C2×C8—1491no—
263C2×C8—1491no—
264C2×C8C22×D14911yescharacteristic
265C2×C8C22×D14911yescharacteristic
266C4⋊C4—2981no—
267C4⋊C4—2981no—
268C4⋊C4—2981no—
269C4⋊C4—2981no—
270C4⋊C4—2981no—
271C4⋊C4—1491no—
272C4⋊C4—1491no—
273C4⋊C4—1491no—
274C4⋊C4—1491no—
275C4⋊C4—1491no—
276C4⋊C4C22×D14911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—2981no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4—1491no—
284C22⋊C4—1491no—
285C42—2981no—
286C42—2981no—
287C42—1491no—
288C42C22×D14911yescharacteristic
289C23—21no—
290C23—21no—
291C23—21no—
292C23—1491no—
293Q8—2981no—
294Q8—1492no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—21no—
300D4—81no—
301D4—81no—
302D4—2984no—
303D4—11921no—
304D4—11921no—
305D4#1455873512yes—
306C2×C4—21no—
307C2×C4—81no—
308C2×C4—2984no—
309C2×C4—2981no—
310C2×C4—2981no—
311C2×C4—2981no—
312C2×C4—2981no—
313C2×C4—2981no—
314C2×C4—2981no—
315C2×C4—1491no—
316C2×C4—1491no—
317C2×C4—1491no—
318C2×C4—11921no—
319C2×C4—11921no—
320C2×C4—11921no—
321C2×C4—11921no—
322C2×C4D4×D14911yescharacteristic
323C2×C4D4×D14911yescharacteristic
324C2×C4C23×D14911yescharacteristic
325C8—21no—
326C8—21no—
327C8—2981no—
328C8—2981no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—2981no—
339C22—2981no—
340C22—2981no—
341C22C2×D4×D14911yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—2981no—
346C4—2981no—
347C4—2981no—
348C4—2982no—
349C4—5961no—
350C4—5961no—
351C4—5961no—
352C4#41×D14911yescharacteristic
353C4C2×#1455873511yescharacteristic
354C2—42no—
355C2—81no—
356C2—81no—
357C2—5961no—
358C2#2375013511yescharacteristic
359C2#2375042611yescharacteristic
360C2#2375043511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#459×C149C2
socleC22×C149C22×D4
hypercenter#459D149
hypocenterC149#3119
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. #23750104C2semidirect
3. #23749942C2semidirect
4. #23749937C2semidirect
5. #23749933C2semidirect
6. #23749925C2semidirect
7. #23749822C2semidirect
8. #23749767C2semidirect
9. #23749767C2semidirect
10. #23749737C2semidirect
11. #23749722C2semidirect
12. #23749716C2semidirect
13. D8×Dic149C2semidirect
14. #23749685C2semidirect
15. #459×C149C2semidirect
180. C149#3119semidirect
189. #459D149semidirect

Maximal subgroups

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

subgroupindex
#237502292
#237501042
#237499422
#237499372
#237499332
#237499252
#237498222
#237497672
#237497372
#237497222
#237497162
D8×Dic1492
#237496852
#459×C1492
#3119149