Finite Group Databasebeta

← #34057750

Subgroups — #34057750

Order 19072.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750361C211yesmaximal, characteristic, complemented
2#23750347C211yesmaximal, characteristic, complemented
3#23750016C211yesmaximal, characteristic, complemented
4#23750012C211yesmaximal, characteristic
5#23750006C211yesmaximal, characteristic, complemented
6#23749848C211yesmaximal, characteristic, complemented
7#23749846C211yesmaximal, characteristic, complemented
8#23749842C211yesmaximal, characteristic, complemented
9#23749839C211yesmaximal, characteristic, complemented
10#23749828C211yesmaximal, characteristic, complemented
11#23749754C211yesmaximal, characteristic, complemented
12#23749734C211yesmaximal, characteristic, complemented
13#23749730C211yesmaximal, characteristic, complemented
14#23749716C211yesmaximal, characteristic, complemented
15#460×C149C211yesmaximal, characteristic, complemented
16C2×Dic596C2211yescharacteristic
17C2×#14558726C2211yescharacteristic
18C2×#14558725C2211yescharacteristic
19C2×#14558724C2211yescharacteristic
20C2×#14558724C2211yescharacteristic
21C2×#14558721C2211yescharacteristic
22C2×#14558721C2211yescharacteristic
23#18011909C2211yescharacteristic
24#18011906—21no—
25#18011905—21no—
26#18011900C2211yescharacteristic
27#18011899C2211yescharacteristic
28#18011898—21no—
29#18011898C2211yescharacteristic
30#18011898C2211yescharacteristic
31#18011892—21no—
32#18011892—21no—
33#18011889—21no—
34C4×Dic298C2211yescharacteristic
35C4×Dic298C2211yescharacteristic
36#18011876C2211yescharacteristic
37D4×Dic149—21no—
38D4×Dic149C2211yescharacteristic
39D4×Dic149C2211yescharacteristic
40#18011873C2211yescharacteristic
41#18011868—21no—
42#18011842C2211yescharacteristic
43#18011840C2211yescharacteristic
44#18011840C2211yescharacteristic
45#18011836C2211yescharacteristic
46#18011835C2211yescharacteristic
47#18011834C2211yescharacteristic
48#18011833C2211yescharacteristic
49#18011822C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×SD16×C149C2211yescharacteristic
53C2×SD16×C149C2211yescharacteristic
54#127×C149C2211yescharacteristic
55C4×Q8×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59C2×Dic298D411yescharacteristic
60C2×Dic298C2311yescharacteristic
61C2×Dic298C2311yescharacteristic
62C2×D596C2311yescharacteristic
63C22×Dic149—21no—
64C22×Dic149—21no—
65C2×C4×D149—21no—
66Dic596—41no—
67#14558726—22no—
68#14558725—41no—
69#14558724—22no—
70#14558724—41no—
71#14558721—22no—
72#14558721—41no—
73C2×#11924746C2311yescharacteristic
74C2×#11924746C2311yescharacteristic
75C4⋊Dic149D411yescharacteristic
76C4⋊Dic149C2311yescharacteristic
77#14558715—21no—
78#14558715—21no—
79#14558715—21no—
80#14558715—21no—
81#14558715D411yescharacteristic
82#14558715D411yescharacteristic
83C22⋊Dic149—21no—
84C22⋊Dic149—21no—
85C22⋊Dic149—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88C22⋊Dic149—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94C4×Dic149—21no—
95C4×Dic149—21no—
96C4×Dic149C2311yescharacteristic
97C4×Dic149C2311yescharacteristic
98C2×Q8×C149C2311yescharacteristic
99C2×D4×C149—21no—
100C2×D4×C149—21no—
101C2×D4×C149C2311yescharacteristic
102C2×D4×C149C2311yescharacteristic
103SD16×C149—41no—
104SD16×C149—41no—
105C2×C8×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C4⋊C4×C149—21no—
108C4⋊C4×C149C2311yescharacteristic
109C42×C149—21no—
110C42×C149C2311yescharacteristic
111C22×D149—21no—
112Dic298—21no—
113Dic298—21no—
114Dic298—21no—
115Dic298—21no—
116Dic298—41no—
117D596—21no—
118D596—21no—
119C2×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149—21no—
122C2×Dic149—81no—
123C2×Dic149—81no—
124C2×Dic149C2×D411yescharacteristic
125C2×Dic149C2×D411yescharacteristic
126C2×Dic149C2×D411yescharacteristic
127C2×Dic149C2×D411yescharacteristic
128C4×D149—42no—
129#11924746—21no—
130#11924746#4112yes—
131C23×C149—21no—
132C23×C149—21no—
133Q8×C149—21no—
134Q8×C149—21no—
135D4×C149—21no—
136D4×C149—21no—
137D4×C149—21no—
138D4×C149—21no—
139D4×C149—42no—
140D4×C149—81no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149C2×D411yescharacteristic
144C2×C4×C149C2×D411yescharacteristic
145C2×C4×C149C2411yescharacteristic
146C8×C149—21no—
147C8×C149—21no—
148C22×C149—41no—
149C22×C149—41no—
150C22×C149—41no—
151C22×C149—41no—
152C22×C149—41no—
153C22×C149—41no—
154C22×C149C22×D411yescharacteristic
155C2×D149—41no—
156C2×D149—41no—
157C2×D149—41no—
158C4×C149—21no—
159C4×C149—21no—
160C4×C149—41no—
161C4×C149—41no—
162C4×C149C2×#4111yescharacteristic
163C4×C149H(5,𝔽2)11yescharacteristic
164Dic149—21no—
165Dic149—21no—
166Dic149—21no—
167Dic149—21no—
168Dic149—41no—
169Dic149—41no—
170Dic149—41no—
171C2×C149—81no—
172C2×C149—81no—
173C2×C149#55011yescharacteristic
174C2×C149#57511yescharacteristic
175C2×C149#57711yescharacteristic
176D149—81no—
177C149#340111yescharacteristic, complemented, Sylow
178#3401—1491nomaximal, Sylow
179#559—1491no—
180#556—1491no—
181#497—1491no—
182#496—1491no—
183#495—1491no—
184#464—1491no—
185#464—1491no—
186#463—1491no—
187#463—1491no—
188#461—1491no—
189#460D14911yescharacteristic, complemented
190#446—1491no—
191#442—1491no—
192#441—1491no—
193C4×SD16—1491no—
194C2×Q16—1491no—
195C2×Q16—1491no—
196C2×SD16—1491no—
197C2×SD16—1491no—
198C2×SD16—1491no—
199C2×SD16C2×D14911yescharacteristic
200C2×SD16C2×D14911yescharacteristic
201C2×D8—1491no—
202C2×D8—1491no—
203C4⋊Q8—1491no—
204#127C2×D14911yescharacteristic
205#126—2981no—
206#126—2981no—
207#124—2981no—
208#124—1491no—
209#124—1491no—
210#124—1491no—
211#124—1491no—
212#123—2981no—
213#123—2981no—
214C22⋊Q8—2981no—
215C4×Q8—1491no—
216C4×Q8—1491no—
217C4×Q8—1491no—
218C4×Q8C2×D14911yescharacteristic
219C4×D4—2981no—
220C4×D4—1491no—
221C4×D4—1491no—
222C4×D4—1491no—
223#117—2981no—
224#106—1491no—
225C4⋊C8—1491no—
226C4⋊C8—1491no—
227C4⋊C8C2×D14911yescharacteristic
228#103—1491no—
229#103—1491no—
230#103—1491no—
231#102—1491no—
232#102C2×D14911yescharacteristic
233#102C2×D14911yescharacteristic
234#97—1491no—
235#97—1491no—
236C4×C8—1491no—
237C2×Q8—1491no—
238C2×Q8—1491no—
239C2×Q8—1491no—
240C2×Q8C22×D14911yescharacteristic
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—1491no—
244C2×D4C22×D14911yescharacteristic
245C2×D4C22×D14911yescharacteristic
246C22×C4—2981no—
247C22×C4—2981no—
248C22×C4—2981no—
249Q16—2982no—
250Q16—5961no—
251SD16—41no—
252SD16—41no—
253SD16—2982no—
254SD16—5961no—
255SD16—5961no—
256D8—2982no—
257D8—5961no—
258C2×C8—1491no—
259C2×C8—1491no—
260C2×C8C22×D14911yescharacteristic
261C2×C8C22×D14911yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—2981no—
264C4⋊C4—2981no—
265C4⋊C4—2981no—
266C4⋊C4—2981no—
267C4⋊C4—1491no—
268C4⋊C4—1491no—
269C4⋊C4—1491no—
270C4⋊C4—1491no—
271C4⋊C4C22×D14911yescharacteristic
272C22⋊C4—2981no—
273C22⋊C4—2981no—
274C22⋊C4—2981no—
275C22⋊C4—2981no—
276C22⋊C4—2981no—
277C22⋊C4—2981no—
278C22⋊C4—2981no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C42—21no—
284C42—2981no—
285C42—2981no—
286C42—1491no—
287C42—1491no—
288C42C22×D14911yescharacteristic
289C23—21no—
290C23—21no—
291C23—2981no—
292Q8—21no—
293Q8—21no—
294Q8—2981no—
295Q8—2981no—
296Q8—2981no—
297Q8—2981no—
298Q8—5961no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—42no—
304D4—81no—
305D4—2981no—
306D4—2981no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—2981no—
310C2×C4—2981no—
311C2×C4—2981no—
312C2×C4—5962no—
313C2×C4—1491no—
314C2×C4—1491no—
315C2×C4—1491no—
316C2×C4—1491no—
317C2×C4—11921no—
318C2×C4—11921no—
319C2×C4D4×D14911yescharacteristic
320C2×C4D4×D14911yescharacteristic
321C2×C4C23×D14911yescharacteristic
322C8—21no—
323C8—21no—
324C8—2981no—
325C8—1492no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—5961no—
333C22—5961no—
334C22—5961no—
335C22C2×D4×D14911yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—2981no—
341C4—2981no—
342C4—2981no—
343C4—2981no—
344C4—5961no—
345C4—5961no—
346C4—5961no—
347C4#41×D14911yescharacteristic
348C4#1801195611yescharacteristic
349C2—81no—
350C2—81no—
351C2—11921no—
352C2#2375029311yescharacteristic
353C2#2375042111yescharacteristic
354C2#2375043111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#460×C149C2
socleC22×C149C22×D4
prime radical#23750012C2
hypercenter#460D149
hypocenterC149#3401
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #23750361C2semidirect
2. #23750347C2semidirect
3. #23750016C2semidirect
5. #23750006C2semidirect
6. #23749848C2semidirect
7. #23749846C2semidirect
8. #23749842C2semidirect
9. #23749839C2semidirect
10. #23749828C2semidirect
11. #23749754C2semidirect
12. #23749734C2semidirect
13. #23749730C2semidirect
14. #23749716C2semidirect
15. #460×C149C2semidirect
177. C149#3401semidirect
189. #460D149semidirect

Maximal subgroups

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

subgroupindex
#237503612
#237503472
#237500162
#237500122
#237500062
#237498482
#237498462
#237498422
#237498392
#237498282
#237497542
#237497342
#237497302
#237497162
#460×C1492
#3401149