Finite Group Databasebeta

← #34054895

Subgroups — #34054895

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#23750231C211yesmaximal, characteristic, complemented
2#23750104C211yesmaximal, characteristic, complemented
3#23749945C211yesmaximal, characteristic, complemented
4#23749940C211yesmaximal, characteristic, complemented
5#23749929C211yesmaximal, characteristic, complemented
6#23749826C211yesmaximal, characteristic, complemented
7#23749820C211yesmaximal, characteristic, complemented
8#23749771C211yesmaximal, characteristic, complemented
9#23749771C211yesmaximal, characteristic, complemented
10#23749734C211yesmaximal, characteristic, complemented
11#23749724C211yesmaximal, characteristic, complemented
12#23749712C211yesmaximal, characteristic, complemented
13#23749705C211yesmaximal, characteristic, complemented
14#23749685C211yesmaximal, characteristic, complemented
15#478×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C2×#14558725C2211yescharacteristic
18C2×#14558725C2211yescharacteristic
19C2×#14558721C2211yescharacteristic
20C2×#14558721C2211yescharacteristic
21#18011908C2211yescharacteristic
22#18011896—21no—
23#18011896—21no—
24#18011886—21no—
25#18011886—21no—
26#18011886C2211yescharacteristic
27#18011886C2211yescharacteristic
28C4×Dic298C2211yescharacteristic
29#18011876C2211yescharacteristic
30D4×Dic149C2211yescharacteristic
31#18011873C2211yescharacteristic
32#18011873C2211yescharacteristic
33C4×C22⋊D149—21no—
34#18011871—21no—
35#18011868C2211yescharacteristic
36#18011867—21no—
37C2×#14558715—21no—
38C4⋊C4×D149C2211yescharacteristic
39#18011844C2211yescharacteristic
40#18011842C2211yescharacteristic
41C4⋊#11924746C2211yescharacteristic
42#18011834C2211yescharacteristic
43#18011834C2211yescharacteristic
44#18011833C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011831C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011823C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52#125×C149C2211yescharacteristic
53C4×D4×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59#14558735—22no—
60#14558735—22no—
61C2×Dic298C2311yescharacteristic
62C2×D596—21no—
63C2×D596—21no—
64C2×D596—21no—
65C2×D596—21no—
66C2×D596C2311yescharacteristic
67C2×D596C2311yescharacteristic
68C2×C22⋊D149—21no—
69C22×Dic149—21no—
70C22×Dic149—21no—
71C2×C4×D149—21no—
72C2×C4×D149—21no—
73C2×C4×D149—21no—
74C2×C4×D149C2311yescharacteristic
75#14558725—22no—
76#14558725—22no—
77#14558721—22no—
78#14558721—22no—
79C2×#11924746C2311yescharacteristic
80C2×#11924746C2311yescharacteristic
81C4⋊Dic149C2311yescharacteristic
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715D411yescharacteristic
86#14558715D411yescharacteristic
87C22⋊Dic149—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713D411yescharacteristic
93#14558713D411yescharacteristic
94C4×Dic149—21no—
95C4×Dic149—21no—
96C4×Dic149C2311yescharacteristic
97C2×D4×C149C2311yescharacteristic
98C22×C4×C149—21no—
99C2×C8×C149C2311yescharacteristic
100C2×C8×C149C2311yescharacteristic
101C4⋊C4×C149—21no—
102C4⋊C4×C149—21no—
103C4⋊C4×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
105C4⋊C4×C149C2311yescharacteristic
106C22⋊C4×C149—21no—
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109C22×D149—21no—
110C22×D149C2×D411yescharacteristic
111Dic298—21no—
112Dic298#4112yes—
113D596—21no—
114D596—21no—
115D596—21no—
116D596—21no—
117D596—81no—
118D596—81no—
119D596—81no—
120D596—81no—
121C22⋊D149—24no—
122C2×Dic149—24no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C2×Dic149—81no—
126C2×Dic149C2×D411yescharacteristic
127C2×Dic149C2×D411yescharacteristic
128C2×Dic149C2×D411yescharacteristic
129C4×D149—21no—
130C4×D149—21no—
131C4×D149—81no—
132C4×D149—81no—
133C4×D149—81no—
134#11924746—21no—
135#11924746—21no—
136C23×C149—21no—
137D4×C149—21no—
138D4×C149#4112yes—
139C2×C4×C149—21no—
140C2×C4×C149—21no—
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×C149C22×D411yescharacteristic
152C2×D149—21no—
153C2×D149—21no—
154C2×D149—21no—
155C2×D149—41no—
156C2×D149—41no—
157C2×D149—41no—
158C2×D149—41no—
159C2×D149—41no—
160C2×D149—41no—
161C4×C149—21no—
162C4×C149—21no—
163C4×C149—41no—
164C4×C149—41no—
165C4×C149—41no—
166C4×C149C2×#4111yescharacteristic
167C4×C149C2×#4111yescharacteristic
168Dic149—21no—
169Dic149—22no—
170Dic149—21no—
171Dic149—21no—
172Dic149—41no—
173C2×C149—42no—
174C2×C149#52511yescharacteristic
175C2×C149#57611yescharacteristic
176C2×C149#57711yescharacteristic
177D149—41no—
178D149—81no—
179D149—81no—
180C149#311911yescharacteristic, complemented, Sylow
181#3119—1491nomaximal, Sylow
182#540—1491no—
183#520—1491no—
184#481—1491no—
185#480—1491no—
186#479—1491no—
187#478D14911yescharacteristic, complemented
188#460—1491no—
189#459—1491no—
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×D8—1491no—
201C2×D8—1491no—
202#127—1491no—
203#125C2×D14911yescharacteristic
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#107C2×D14911yescharacteristic
224#106—1491no—
225#106C2×D14911yescharacteristic
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—2981no—
244C2×D4—2981no—
245C2×D4—2981no—
246C2×D4—2981no—
247C2×D4—2981no—
248C2×D4—1491no—
249C2×D4—1491no—
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—2982no—
261D8—2982no—
262C2×C8—1491no—
263C2×C8—1491no—
264C2×C8C22×D14911yescharacteristic
265C2×C8C22×D14911yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—2981no—
269C4⋊C4—2981no—
270C4⋊C4—2981no—
271C4⋊C4—1491no—
272C4⋊C4—1491no—
273C4⋊C4—1491no—
274C4⋊C4C22×D14911yescharacteristic
275C4⋊C4C22×D14911yescharacteristic
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—2981no—
291C23—2981no—
292C23—1491no—
293Q8—2981no—
294Q8—1492no—
295D4—21no—
296D4—2984no—
297D4—2981no—
298D4—2981no—
299D4—2981no—
300D4—2981no—
301D4—11921no—
302D4—11921no—
303D4—11921no—
304D4—11921no—
305D4#1455873712yes—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—2984no—
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—2981no—
333C22—2981no—
334C22—2981no—
335C22—5961no—
336C22—5961no—
337C22—5961no—
338C22—5961no—
339C22—5961no—
340C22—5961no—
341C22C2×D4×D14911yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—2981no—
348C4—2981no—
349C4—2981no—
350C4—2982no—
351C4—5961no—
352C4#41×D14911yescharacteristic
353C4C2×#1455873711yescharacteristic
354C2—42no—
355C2—5961no—
356C2—11921no—
357C2—11921no—
358C2#2375013811yescharacteristic
359C2#2375042911yescharacteristic
360C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#478×C149C2
socleC22×C149C22×D4
hypercenter#478D149
hypocenterC149#3119
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #23750231C2semidirect
2. #23750104C2semidirect
3. #23749945C2semidirect
4. #23749940C2semidirect
5. #23749929C2semidirect
6. #23749826C2semidirect
7. #23749820C2semidirect
8. #23749771C2semidirect
9. #23749771C2semidirect
10. #23749734C2semidirect
11. #23749724C2semidirect
12. #23749712C2semidirect
13. #23749705C2semidirect
14. #23749685C2semidirect
15. #478×C149C2semidirect
180. C149#3119semidirect
187. #478D149semidirect

Maximal subgroups

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

subgroupindex
#237502312
#237501042
#237499452
#237499402
#237499292
#237498262
#237498202
#237497712
#237497342
#237497242
#237497122
#237497052
#237496852
#478×C1492
#3119149