Finite Group Databasebeta

← #34057262

Subgroups — #34057262

Order 19072.

336 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750314C211yesmaximal, characteristic
2#23750310C211yesmaximal, characteristic
3#23750025C211yesmaximal, characteristic, complemented
4#23749969C211yesmaximal, characteristic, complemented
5#23749966C211yesmaximal, characteristic, complemented
6#23749962C211yesmaximal, characteristic, complemented
7#23749960C211yesmaximal, characteristic, complemented
8#23749935C211yesmaximal, characteristic, complemented
9#23749931C211yesmaximal, characteristic, complemented
10#23749884C211yesmaximal, characteristic, complemented
11#23749883C211yesmaximal, characteristic, complemented
12#23749719C211yesmaximal, characteristic, complemented
13#23749701C211yesmaximal, characteristic
14#23749666C211yesmaximal, characteristic, complemented
15#428×C149C211yesmaximal, characteristic, complemented
16C2×Dic596C2211yescharacteristic
17C2×#14558719C2211yescharacteristic
18#18011906—21no—
19#18011904—21no—
20#18011903—21no—
21#18011902C2211yescharacteristic
22#18011902C2211yescharacteristic
23#18011901—21no—
24#18011894—21no—
25#18011893—21no—
26#18011891C2211yescharacteristic
27#18011891C2211yescharacteristic
28#18011890C2211yescharacteristic
29#18011890C2211yescharacteristic
30#18011876C2211yescharacteristic
31#18011876C2211yescharacteristic
32C4×C22⋊D149C2211yescharacteristic
33#18011870—21no—
34#18011869C2211yescharacteristic
35#18011868—21no—
36C4⋊C4×D149C2211yescharacteristic
37#18011844C2211yescharacteristic
38#18011844C2211yescharacteristic
39#18011844C2211yescharacteristic
40#18011843C2211yescharacteristic
41#18011842C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011834C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011834C2211yescharacteristic
48#18011834C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011823C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×M16×C149C2211yescharacteristic
53#117×C149C2211yescharacteristic
54C2×C4⋊C4×C149C2211yescharacteristic
55#107×C149C2211yescharacteristic
56#107×C149C2211yescharacteristic
57#106×C149C2211yescharacteristic
58#106×C149C2211yescharacteristic
59C2×Dic298C2311yescharacteristic
60C2×Dic298C2311yescharacteristic
61C2×C22⋊D149D411yescharacteristic
62C2×C4×D149—21no—
63C2×C4×D149C2311yescharacteristic
64Dic596—22no—
65#14558719—22no—
66C2×#11924746C2311yescharacteristic
67C2×#11924746C2311yescharacteristic
68C4⋊Dic149—21no—
69C4⋊Dic149—21no—
70C4⋊Dic149—21no—
71C4⋊Dic149—21no—
72C4⋊Dic149C2311yescharacteristic
73C4⋊Dic149C2311yescharacteristic
74#14558715—21no—
75#14558715—21no—
76#14558715—21no—
77#14558715—21no—
78#14558715—21no—
79#14558715—21no—
80#14558715—21no—
81#14558715D411yescharacteristic
82C22⋊Dic149—21no—
83C22⋊Dic149—21no—
84C22⋊Dic149D411yescharacteristic
85#14558713—21no—
86#14558713—21no—
87#14558713—21no—
88#14558713D411yescharacteristic
89C4×Dic149—21no—
90C4×Dic149—21no—
91C4×Dic149—21no—
92C4×Dic149C2311yescharacteristic
93C22×C4×C149—21no—
94C22×C4×C149C2311yescharacteristic
95M16×C149—22no—
96C2×C8×C149C2311yescharacteristic
97C2×C8×C149C2311yescharacteristic
98C4⋊C4×C149—21no—
99C4⋊C4×C149C2311yescharacteristic
100C4⋊C4×C149C2311yescharacteristic
101C4⋊C4×C149C2311yescharacteristic
102C4⋊C4×C149C2311yescharacteristic
103C22⋊C4×C149—21no—
104C42×C149—21no—
105C22×D149C2×D411yescharacteristic
106Dic298—21no—
107Dic298—21no—
108Dic298—21no—
109Dic298—21no—
110C22⋊D149—41no—
111C2×Dic149—21no—
112C2×Dic149—21no—
113C2×Dic149—21no—
114C2×Dic149—21no—
115C2×Dic149C2×D411yescharacteristic
116C2×Dic149C2×D411yescharacteristic
117C2×Dic149C2×D411yescharacteristic
118C4×D149—21no—
119C4×D149—21no—
120C4×D149—42no—
121#11924746—21no—
122#11924746—21no—
123C23×C149C2×D411yescharacteristic
124C2×C4×C149—21no—
125C2×C4×C149—21no—
126C2×C4×C149—21no—
127C2×C4×C149—21no—
128C2×C4×C149—21no—
129C2×C4×C149—21no—
130C2×C4×C149—42no—
131C2×C4×C149C2×D411yescharacteristic
132C2×C4×C149C2411yescharacteristic
133C8×C149—21no—
134C8×C149#4112yes—
135C22×C149—21no—
136C22×C149—21no—
137C22×C149—21no—
138C22×C149C22×D411yescharacteristic
139C2×D149—21no—
140C2×D149—21no—
141C2×D149—21no—
142C4×C149—21no—
143C4×C149—41no—
144C4×C149—41no—
145C4×C149—41no—
146C4×C149—41no—
147C4×C149C2×#4111yescharacteristic
148C4×C1492−1+411yescharacteristic
149Dic149—21no—
150Dic149—21no—
151Dic149—21no—
152Dic149—41no—
153Dic149—41no—
154Dic149—41no—
155Dic149—41no—
156C2×C149—41no—
157C2×C149#54711yescharacteristic
158C2×C149#57511yescharacteristic
159C2×C149#57811yescharacteristic
160D149—41no—
161C149#335211yescharacteristic, complemented, Sylow
162#3352—1491nomaximal, Sylow
163#552—1491no—
164#552—1491no—
165#499—1491no—
166#485—1491no—
167#485—1491no—
168#484—1491no—
169#484—1491no—
170#479—1491no—
171#479—1491no—
172#470—1491no—
173#470—1491no—
174C4×Q16—1491no—
175#436—1491no—
176#428—1491no—
177#428D14911yescharacteristic, complemented
178C2×Q16—1491no—
179C2×M16—1491no—
180C2×M16C2×D14911yescharacteristic
181#126—2981no—
182#126—2981no—
183#125—2981no—
184#125—2981no—
185#125—1491no—
186#125—1491no—
187#123—2981no—
188#123—2981no—
189C22⋊Q8—1491no—
190C22⋊Q8—1491no—
191C22⋊Q8—1491no—
192C22⋊Q8—1491no—
193C4×Q8—1491no—
194C4×Q8—1491no—
195C4×D4—1491no—
196#117—2981no—
197#117—2981no—
198#117—1491no—
199#117C2×D14911yescharacteristic
200C2×C4⋊C4—1491no—
201C2×C4⋊C4C2×D14911yescharacteristic
202#107—1491no—
203#107—1491no—
204#107—1491no—
205#107C2×D14911yescharacteristic
206#107C2×D14911yescharacteristic
207#106—1491no—
208#106—1491no—
209#106C2×D14911yescharacteristic
210#106C2×D14911yescharacteristic
211C4⋊C8—1491no—
212#103—1491no—
213#103—1491no—
214#103—1491no—
215#103—1491no—
216#103—1491no—
217#103—1491no—
218C22⋊C8—1491no—
219C22⋊C8—1491no—
220C4×C8—1491no—
221C2×Q8—1491no—
222C2×Q8—1491no—
223C2×D4—1491no—
224C22×C4—21no—
225C22×C4—2981no—
226C22×C4—1491no—
227C22×C4C22×D14911yescharacteristic
228Q16—2982no—
229M16—22no—
230M16—2982no—
231C2×C8—1491no—
232C2×C8—1491no—
233C2×C8C22×D14911yescharacteristic
234C2×C8C22×D14911yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—2981no—
237C4⋊C4—2981no—
238C4⋊C4—2981no—
239C4⋊C4—2981no—
240C4⋊C4—2981no—
241C4⋊C4—2981no—
242C4⋊C4—2981no—
243C4⋊C4—2981no—
244C4⋊C4—2981no—
245C4⋊C4—2981no—
246C4⋊C4—2981no—
247C4⋊C4—1491no—
248C4⋊C4—1491no—
249C4⋊C4—1491no—
250C4⋊C4C22×D14911yescharacteristic
251C4⋊C4C22×D14911yescharacteristic
252C4⋊C4C22×D14911yescharacteristic
253C4⋊C4C22×D14911yescharacteristic
254C22⋊C4—21no—
255C22⋊C4—2981no—
256C22⋊C4—2981no—
257C22⋊C4—2981no—
258C22⋊C4—2981no—
259C22⋊C4—2981no—
260C22⋊C4—1491no—
261C22⋊C4—1491no—
262C42—21no—
263C42—2981no—
264C42—2981no—
265C42—2981no—
266C42—1491no—
267C23—1491no—
268C23D4×D14911yescharacteristic
269Q8—2981no—
270Q8—2981no—
271Q8—2981no—
272Q8—2981no—
273D4—5961no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—2981no—
282C2×C4—2981no—
283C2×C4—2981no—
284C2×C4—2981no—
285C2×C4—2981no—
286C2×C4—2981no—
287C2×C4—5962no—
288C2×C4—1491no—
289C2×C4—1491no—
290C2×C4—1491no—
291C2×C4D4×D14911yescharacteristic
292C2×C4C23×D14911yescharacteristic
293C8—21no—
294C8—2981no—
295C8—2981no—
296C8#1455873612yes—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—2981no—
301C22—2981no—
302C22—2981no—
303C22C2×D4×D14911yescharacteristic
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—2981no—
310C4—2981no—
311C4—2981no—
312C4—5961no—
313C4—5961no—
314C4—5961no—
315C4—5961no—
316C4C2×#1455873611yescharacteristic
317C4#1801195911yescharacteristic
318C2—41no—
319C2—5961no—
320C2#2375027611yescharacteristic
321C2#2375042111yescharacteristic
322C2#2375044111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#428×C149C2
socleC22×C149C22×D4
prime radicalC2×C22⋊D149D4
hypercenter#428D149
hypocenterC149#3352
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. #23750025C2semidirect
4. #23749969C2semidirect
5. #23749966C2semidirect
6. #23749962C2semidirect
7. #23749960C2semidirect
8. #23749935C2semidirect
9. #23749931C2semidirect
10. #23749884C2semidirect
11. #23749883C2semidirect
12. #23749719C2semidirect
14. #23749666C2semidirect
15. #428×C149C2semidirect
161. C149#3352semidirect
177. #428D149semidirect

Maximal subgroups

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

subgroupindex
#237503142
#237503102
#237500252
#237499692
#237499662
#237499622
#237499602
#237499352
#237499312
#237498842
#237498832
#237497192
#237497012
#237496662
#428×C1492
#3352149