Finite Group Databasebeta

← #34057454

Subgroups — #34057454

Order 19072.

344 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750361C211yesmaximal, characteristic
2#23750352C211yesmaximal, characteristic, complemented
3#23749983C211yesmaximal, characteristic, complemented
4#23749978C211yesmaximal, characteristic, complemented
5#23749929C211yesmaximal, characteristic, complemented
6#23749927C211yesmaximal, characteristic, complemented
7#23749913C211yesmaximal, characteristic, complemented
8#23749846C211yesmaximal, characteristic, complemented
9#23749846C211yesmaximal, characteristic, complemented
10#23749822C211yesmaximal, characteristic
11#23749753C211yesmaximal, characteristic, complemented
12#23749733C211yesmaximal, characteristic, complemented
13#23749722C211yesmaximal, characteristic, complemented
14#23749716C211yesmaximal, characteristic, complemented
15#490×C149C211yesmaximal, characteristic
16C2×Dic596C2211yescharacteristic
17C2×#14558724C2211yescharacteristic
18C2×#14558724C2211yescharacteristic
19#18011910—21no—
20#18011910C2211yescharacteristic
21#18011902C2211yescharacteristic
22#18011901—21no—
23#18011901—21no—
24#18011898—21no—
25#18011898C2211yescharacteristic
26#18011898C2211yescharacteristic
27#18011892—21no—
28#18011892—21no—
29C4×Dic298C2211yescharacteristic
30C4×Dic298C2211yescharacteristic
31C4×Dic298C2211yescharacteristic
32#18011876—21no—
33#18011876C2211yescharacteristic
34#18011876C2211yescharacteristic
35D4×Dic149—21no—
36D4×Dic149C2211yescharacteristic
37D4×Dic149C2211yescharacteristic
38#18011844C2211yescharacteristic
39#18011843C2211yescharacteristic
40#18011842C2211yescharacteristic
41C4⋊#11924746C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011840C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011836C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011834C2211yescharacteristic
48#18011832C2211yescharacteristic
49#18011832C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52#127×C149C2211yescharacteristic
53#125×C149C2211yescharacteristic
54#102×C149C2211yescharacteristic
55#102×C149C2211yescharacteristic
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#97×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298D411yescharacteristic
61C2×Dic298C2311yescharacteristic
62C2×Dic298C2311yescharacteristic
63C22×Dic149—21no—
64C22×Dic149—21no—
65Dic596—22no—
66#14558724—22no—
67#14558724—22no—
68C2×#11924746C2311yescharacteristic
69C2×#11924746C2311yescharacteristic
70C4⋊Dic149—21no—
71C4⋊Dic149D411yescharacteristic
72C4⋊Dic149C2311yescharacteristic
73C4⋊Dic149C2311yescharacteristic
74#14558715—21no—
75#14558715—21no—
76#14558715—21no—
77#14558715—21no—
78#14558715—21no—
79#14558715—21no—
80#14558715D411yescharacteristic
81#14558715D411yescharacteristic
82C22⋊Dic149—21no—
83C22⋊Dic149—21no—
84C22⋊Dic149—21no—
85C22⋊Dic149—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88C4×Dic149—21no—
89C4×Dic149—21no—
90C4×Dic149—21no—
91C4×Dic149—21no—
92C4×Dic149C2311yescharacteristic
93C4×Dic149C2311yescharacteristic
94C2×D4×C149—21no—
95C2×D4×C149—21no—
96C2×D4×C149C2311yescharacteristic
97C2×D4×C149C2311yescharacteristic
98C2×C8×C149C2311yescharacteristic
99C2×C8×C149C2311yescharacteristic
100C4⋊C4×C149—21no—
101C4⋊C4×C149—21no—
102C4⋊C4×C149C2311yescharacteristic
103C4⋊C4×C149C2311yescharacteristic
104C42×C149C2311yescharacteristic
105Dic298—21no—
106Dic298—21no—
107Dic298—21no—
108Dic298—41no—
109Dic298—42no—
110Dic298#4112yes—
111C2×Dic149—21no—
112C2×Dic149—21no—
113C2×Dic149—21no—
114C2×Dic149—21no—
115C2×Dic149—81no—
116C2×Dic149—81no—
117C2×Dic149C2×D411yescharacteristic
118C2×Dic149C2×D411yescharacteristic
119C2×Dic149C2×D411yescharacteristic
120C2×Dic149C2×D411yescharacteristic
121#11924746—21no—
122#11924746—21no—
123C23×C149—21no—
124C23×C149—21no—
125D4×C149—21no—
126D4×C149—21no—
127D4×C149—21no—
128D4×C149—21no—
129D4×C149—42no—
130D4×C149—81no—
131C2×C4×C149—21no—
132C2×C4×C149—21no—
133C2×C4×C149C2×D411yescharacteristic
134C2×C4×C149C2×D411yescharacteristic
135C2×C4×C149C2411yescharacteristic
136C8×C149—21no—
137C8×C149—21no—
138C22×C149—41no—
139C22×C149—41no—
140C22×C149—41no—
141C22×C149—41no—
142C22×C149—41no—
143C22×C149—41no—
144C22×C149C22×D411yescharacteristic
145C4×C149—21no—
146C4×C149—21no—
147C4×C149—41no—
148C4×C149—41no—
149C4×C149C2×#4111yescharacteristic
150C4×C1492−1+411yescharacteristic
151Dic149—22no—
152Dic149—21no—
153Dic149—21no—
154Dic149—21no—
155Dic149—21no—
156Dic149—41no—
157Dic149—41no—
158Dic149—41no—
159C2×C149—81no—
160C2×C149—81no—
161C2×C149#54811yescharacteristic
162C2×C149#57511yescharacteristic
163C2×C149#57711yescharacteristic
164C149#337111yescharacteristic, complemented, Sylow
165#3371—1491nomaximal, Sylow
166#559—1491no—
167#557—1491no—
168#490D14911yescharacteristic
169#489—1491no—
170#488—1491no—
171#479—1491no—
172#478—1491no—
173#476—1491no—
174#464—1491no—
175#464—1491no—
176#460—1491no—
177#446—1491no—
178#441—1491no—
179#440—1491no—
180C4×SD16—1491no—
181C2×Q16—1491no—
182C2×SD16—1491no—
183C2×SD16—1491no—
184C4⋊Q8—2981no—
185C4⋊Q8—1491no—
186#127C2×D14911yescharacteristic
187#125—2981no—
188#125—2981no—
189#125—1491no—
190#125C2×D14911yescharacteristic
191#124—2981no—
192#124—1491no—
193#124—1491no—
194#123—2981no—
195#123—2981no—
196C4×Q8—2981no—
197C4×Q8—1491no—
198C4×Q8—1491no—
199C4×Q8—1491no—
200C4×Q8—1491no—
201C4×Q8—1491no—
202C4×D4—2981no—
203C4×D4—1491no—
204C4×D4—1491no—
205#107—1491no—
206#106—1491no—
207#106—1491no—
208C4⋊C8—1491no—
209C4⋊C8—1491no—
210C4⋊C8—1491no—
211#103—1491no—
212#103—1491no—
213#103—1491no—
214#103—1491no—
215#102—1491no—
216#102—1491no—
217#102C2×D14911yescharacteristic
218#102C2×D14911yescharacteristic
219#102C2×D14911yescharacteristic
220#102C2×D14911yescharacteristic
221#97—1491no—
222#97C2×D14911yescharacteristic
223C4×C8—1491no—
224C2×Q8—2981no—
225C2×Q8—1491no—
226C2×Q8—1491no—
227C2×Q8—1491no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4C22×D14911yescharacteristic
231C2×D4C22×D14911yescharacteristic
232C22×C4—2981no—
233C22×C4—2981no—
234Q16—2982no—
235SD16—2982no—
236SD16—2982no—
237C2×C8—1491no—
238C2×C8—1491no—
239C2×C8C22×D14911yescharacteristic
240C2×C8C22×D14911yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—2981no—
244C4⋊C4—2981no—
245C4⋊C4—2981no—
246C4⋊C4—2981no—
247C4⋊C4—2981no—
248C4⋊C4—2981no—
249C4⋊C4—2981no—
250C4⋊C4—1491no—
251C4⋊C4—1491no—
252C4⋊C4—1491no—
253C4⋊C4—1491no—
254C4⋊C4—1491no—
255C4⋊C4C22×D14911yescharacteristic
256C4⋊C4C22×D14911yescharacteristic
257C22⋊C4—2981no—
258C22⋊C4—2981no—
259C22⋊C4—2981no—
260C22⋊C4—2981no—
261C22⋊C4—2981no—
262C22⋊C4—2981no—
263C42—2981no—
264C42—2981no—
265C42—2981no—
266C42—2981no—
267C42—1491no—
268C42—1491no—
269C42C22×D14911yescharacteristic
270C23—21no—
271C23—21no—
272Q8—2981no—
273Q8—2981no—
274Q8—2981no—
275Q8—5961no—
276Q8—5962no—
277Q8—1492no—
278D4—21no—
279D4—21no—
280D4—21no—
281D4—21no—
282D4—42no—
283D4—81no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—2981no—
287C2×C4—2981no—
288C2×C4—2981no—
289C2×C4—2981no—
290C2×C4—1491no—
291C2×C4—1491no—
292C2×C4—1491no—
293C2×C4—1491no—
294C2×C4—11921no—
295C2×C4—11921no—
296C2×C4D4×D14911yescharacteristic
297C2×C4D4×D14911yescharacteristic
298C2×C4C23×D14911yescharacteristic
299C8—21no—
300C8—21no—
301C8—2981no—
302C8—2981no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22C2×D4×D14911yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—2981no—
315C4—2981no—
316C4—2981no—
317C4—2981no—
318C4—2982no—
319C4—5961no—
320C4—5961no—
321C4—5961no—
322C4#41×D14911yescharacteristic
323C4#1801195811yescharacteristic
324C2—81no—
325C2—81no—
326C2#2375028311yescharacteristic
327C2#2375042111yescharacteristic
328C2#2375043511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#490×C149C2
socleC22×C149C22×D4
prime radical#127×C149C22
hypercenter#490D149
hypocenterC149#3371
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #23750352C2semidirect
3. #23749983C2semidirect
4. #23749978C2semidirect
5. #23749929C2semidirect
6. #23749927C2semidirect
7. #23749913C2semidirect
8. #23749846C2semidirect
9. #23749846C2semidirect
11. #23749753C2semidirect
12. #23749733C2semidirect
13. #23749722C2semidirect
14. #23749716C2semidirect
164. C149#3371semidirect

Maximal subgroups

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

subgroupindex
#237503612
#237503522
#237499832
#237499782
#237499292
#237499272
#237499132
#237498462
#237498222
#237497532
#237497332
#237497222
#237497162
#490×C1492
#3371149