Finite Group Databasebeta

← #34056046

Subgroups — #34056046

Order 19072.

392 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750170C211yesmaximal, characteristic, complemented
2#23750156C211yesmaximal, characteristic, complemented
3#23749924C211yesmaximal, characteristic, complemented
4#23749923C211yesmaximal, characteristic, complemented
5#23749909C211yesmaximal, characteristic, complemented
6#23749903C211yesmaximal, characteristic, complemented
7#23749876C211yesmaximal, characteristic, complemented
8#23749871C211yesmaximal, characteristic, complemented
9#23749869C211yesmaximal, characteristic, complemented
10#23749839C211yesmaximal, characteristic, complemented
11#23749838C211yesmaximal, characteristic, complemented
12#23749824C211yesmaximal, characteristic, complemented
13#23749818C211yesmaximal, characteristic, complemented
14#23749648C211yesmaximal, characteristic, complemented
15#469×C149C211yesmaximal, characteristic, complemented
16C2×#14558735—21no—
17C2×#14558725C2211yescharacteristic
18C2×#14558724C2211yescharacteristic
19C2×#14558721C2211yescharacteristic
20C2×#14558720C2211yescharacteristic
21#18011910C2211yescharacteristic
22#18011907C2211yescharacteristic
23#18011904—21no—
24#18011902C2211yescharacteristic
25#18011898C2211yescharacteristic
26#18011897—21no—
27#18011892—21no—
28#18011890C2211yescharacteristic
29#18011885C2211yescharacteristic
30#18011883—21no—
31#18011876C2211yescharacteristic
32D4×Dic149—21no—
33D4×Dic149C2211yescharacteristic
34D4×Dic149C2211yescharacteristic
35#18011873C2211yescharacteristic
36#18011871—21no—
37#18011867—21no—
38C2×C4×Dic149C2211yescharacteristic
39#18011845C2211yescharacteristic
40#18011844C2211yescharacteristic
41#18011842C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011840C2211yescharacteristic
44#18011840C2211yescharacteristic
45#18011840C2211yescharacteristic
46#18011836C2211yescharacteristic
47#18011834C2211yescharacteristic
48#18011833C2211yescharacteristic
49#18011832C2211yescharacteristic
50#18011832C2211yescharacteristic
51#18011831C2211yescharacteristic
52C2×D8×C149C2211yescharacteristic
53C2×M16×C149C2211yescharacteristic
54#121×C149C2211yescharacteristic
55#121×C149C2211yescharacteristic
56#106×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59#14558735—44no—
60C2×Dic298—21no—
61C2×Dic298C2311yescharacteristic
62C2×D596C2311yescharacteristic
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66C22×Dic149—21no—
67C22×Dic149—21no—
68C22×Dic149D411yescharacteristic
69C22×Dic149D411yescharacteristic
70C2×C4×D149—21no—
71#14558725—41no—
72#14558724—41no—
73#14558721—41no—
74#14558720—41no—
75C2×#11924746C2311yescharacteristic
76C2×#11924746C2311yescharacteristic
77C4⋊Dic149—21no—
78C4⋊Dic149C2311yescharacteristic
79C4⋊Dic149C2311yescharacteristic
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84C22⋊Dic149—21no—
85C22⋊Dic149—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88C22⋊Dic149—21no—
89#14558713—21no—
90#14558713—21no—
91C4×Dic149—21no—
92C4×Dic149D411yescharacteristic
93C4×Dic149D411yescharacteristic
94C4×Dic149C2311yescharacteristic
95C4×Dic149C2311yescharacteristic
96C2×D4×C149—21no—
97C2×D4×C149—21no—
98C2×D4×C149C2311yescharacteristic
99C2×D4×C149C2311yescharacteristic
100C22×C4×C149C2311yescharacteristic
101D8×C149—41no—
102M16×C149—41no—
103C2×C8×C149C2311yescharacteristic
104C2×C8×C149C2311yescharacteristic
105C4⋊C4×C149C2311yescharacteristic
106C4⋊C4×C149C2311yescharacteristic
107C22⋊C4×C149—21no—
108C22⋊C4×C149—21no—
109C22×D149—21no—
110Dic298—21no—
111Dic298—21no—
112Dic298—42no—
113D596—21no—
114D596—21no—
115C22⋊D149—42no—
116C22⋊D149—42no—
117C22⋊D149—42no—
118C2×Dic149—22no—
119C2×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149—21no—
122C2×Dic149—41no—
123C2×Dic149—42no—
124C2×Dic149—42no—
125C2×Dic149C2×D411yescharacteristic
126C2×Dic149C2×D411yescharacteristic
127C2×Dic149C2×D411yescharacteristic
128C2×Dic149C2×D411yescharacteristic
129C4×D149—42no—
130#11924746—21no—
131#11924746—21no—
132C23×C149—21no—
133C23×C149—21no—
134C23×C149C2×D411yescharacteristic
135D4×C149—21no—
136D4×C149—21no—
137D4×C149—21no—
138D4×C149—21no—
139D4×C149—42no—
140D4×C149—42no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149C2×D411yescharacteristic
146C2×C4×C149C2411yescharacteristic
147C8×C149—21no—
148C8×C149—21no—
149C22×C149—21no—
150C22×C149—21no—
151C22×C149—21no—
152C22×C149—41no—
153C22×C149—41no—
154C22×C149—41no—
155C22×C149—41no—
156C22×C149—41no—
157C22×C149—41no—
158C22×C149C22×D411yescharacteristic
159C2×D149—41no—
160C2×D149—41no—
161C2×D149—41no—
162C4×C149—21no—
163C4×C149—41no—
164C4×C149—41no—
165C4×C149H(5,𝔽2)11yescharacteristic
166C4×C1492−1+411yescharacteristic
167Dic149—21no—
168Dic149—21no—
169Dic149—21no—
170Dic149—41no—
171Dic149—41no—
172Dic149—41no—
173Dic149AGL(1,ℤ/8)12yes—
174C2×C149—41no—
175C2×C149—81no—
176C2×C149—81no—
177C2×C149#53711yescharacteristic
178C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
179C2×C149#57511yescharacteristic
180D149—81no—
181C149#325111yescharacteristic, complemented, Sylow
182#3251—1491nomaximal, Sylow
183#532—1491no—
184#529—1491no—
185#478—1491no—
186#478—1491no—
187#475—1491no—
188#474—1491no—
189#469—1491no—
190#469D14911yescharacteristic, complemented
191#468—1491no—
192#468—1491no—
193#463—1491no—
194#463—1491no—
195#460—1491no—
196#459—1491no—
197#423—1491no—
198C2×#41—2981no—
199C2×SD16—1491no—
200C2×SD16—1491no—
201C2×D8—1491no—
202C2×D8C2×D14911yescharacteristic
203C2×M16—1491no—
204C2×M16C2×D14911yescharacteristic
205C4⋊Q8—1491no—
206#127—1491no—
207#126—2981no—
208#125—1491no—
209#124—2981no—
210#124—1491no—
211#123—2981no—
212C22⋊Q8—1491no—
213#121—2981no—
214#121—1491no—
215#121C2×D14911yescharacteristic
216#121C2×D14911yescharacteristic
217C4×Q8—1491no—
218C4×D4—2981no—
219C4×D4—2981no—
220C4×D4—1491no—
221C4×D4—1491no—
222C4×D4—1491no—
223#117—2981no—
224C2×C42—1491no—
225#107—1491no—
226#107—1491no—
227#106—1491no—
228#106C2×D14911yescharacteristic
229C4⋊C8—1491no—
230C4⋊C8—1491no—
231C4⋊C8—1491no—
232C4⋊C8—1491no—
233#103—1491no—
234#103—1491no—
235#102—1491no—
236#102—1491no—
237#102—1491no—
238#102—1491no—
239#102C2×D14911yescharacteristic
240#102C2×D14911yescharacteristic
241#41—5964no—
242C2×Q8—2981no—
243C2×Q8—1491no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—2981no—
247C2×D4—2981no—
248C2×D4—2981no—
249C2×D4—1491no—
250C2×D4C22×D14911yescharacteristic
251C2×D4C22×D14911yescharacteristic
252C22×C4—2981no—
253C22×C4—2981no—
254C22×C4—2981no—
255C22×C4—1491no—
256C22×C4—1491no—
257C22×C4C22×D14911yescharacteristic
258SD16—5961no—
259SD16—5961no—
260D8—41no—
261D8—5961no—
262M16—41no—
263M16—5961no—
264C2×C8—1491no—
265C2×C8—1491no—
266C2×C8C22×D14911yescharacteristic
267C2×C8C22×D14911yescharacteristic
268C4⋊C4—2981no—
269C4⋊C4—2981no—
270C4⋊C4—2981no—
271C4⋊C4—2981no—
272C4⋊C4—2981no—
273C4⋊C4—1491no—
274C4⋊C4—1491no—
275C4⋊C4C22×D14911yescharacteristic
276C4⋊C4C22×D14911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4—2981no—
284C22⋊C4—2981no—
285C22⋊C4—2981no—
286C42—2981no—
287C42—1491no—
288C42—1491no—
289C42—1491no—
290C42—1491no—
291C23—21no—
292C23—21no—
293C23—2981no—
294C23D4×D14911yescharacteristic
295Q8—2981no—
296Q8—2981no—
297Q8—5962no—
298D4—21no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—42no—
304D4—2981no—
305D4—2981no—
306D4—5962no—
307D4—5962no—
308D4—5962no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—2982no—
314C2×C4—2981no—
315C2×C4—2981no—
316C2×C4—2981no—
317C2×C4—5962no—
318C2×C4—5961no—
319C2×C4—5962no—
320C2×C4—5962no—
321C2×C4—1491no—
322C2×C4—1491no—
323C2×C4—1491no—
324C2×C4—1491no—
325C2×C4D4×D14911yescharacteristic
326C2×C4C23×D14911yescharacteristic
327C8—21no—
328C8—21no—
329C8—2981no—
330C8—2981no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—5961no—
341C22—5961no—
342C22—5961no—
343C22C2×D4×D14911yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—2981no—
348C4—2981no—
349C4—2981no—
350C4—5961no—
351C4—5961no—
352C4—5961no—
353C4—1492no—
354C4#1801195611yescharacteristic
355C4#1801195811yescharacteristic
356C2—41no—
357C2—81no—
358C2—81no—
359C2—11921no—
360C2#2375020211yescharacteristic
361C2AGL(1,ℤ/8)×D14911yescharacteristic
362C2#2375042111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#469×C149C2
socleC22×C149C22×D4
hypercenter#469D149
hypocenterC149#3251
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #23750170C2semidirect
2. #23750156C2semidirect
3. #23749924C2semidirect
4. #23749923C2semidirect
5. #23749909C2semidirect
6. #23749903C2semidirect
7. #23749876C2semidirect
8. #23749871C2semidirect
9. #23749869C2semidirect
10. #23749839C2semidirect
11. #23749838C2semidirect
12. #23749824C2semidirect
13. #23749818C2semidirect
14. #23749648C2semidirect
15. #469×C149C2semidirect
181. C149#3251semidirect
190. #469D149semidirect

Maximal subgroups

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

subgroupindex
#237501702
#237501562
#237499242
#237499232
#237499092
#237499032
#237498762
#237498712
#237498692
#237498392
#237498382
#237498242
#237498182
#237496482
#469×C1492
#3251149