Finite Group Databasebeta

← #34055961

Subgroups — #34055961

Order 19072.

308 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750253C211yesmaximal, characteristic
2#23750237C211yesmaximal, characteristic
3#23750034C211yesmaximal, characteristic, complemented
4#23750027C211yesmaximal, characteristic, complemented
5#23749994C211yesmaximal, characteristic, complemented
6#23749976C211yesmaximal, characteristic, complemented
7#23749967C211yesmaximal, characteristic
8#23749967C211yesmaximal, characteristic
9#23749961C211yesmaximal, characteristic
10#23749956C211yesmaximal, characteristic
11#23749933C211yesmaximal, characteristic, complemented
12#23749933C211yesmaximal, characteristic, complemented
13#23749921C211yesmaximal, characteristic, complemented
14#23749911C211yesmaximal, characteristic, complemented
15#433×C149C211yesmaximal, characteristic
16#18011911C2211yescharacteristic
17#18011911C2211yescharacteristic
18#18011911C2211yescharacteristic
19#18011910—21no—
20#18011904—21no—
21#18011904—21no—
22#18011903C2211yescharacteristic
23#18011903C2211yescharacteristic
24#18011903C2211yescharacteristic
25#18011902—21no—
26#18011901—21no—
27#18011901—21no—
28#18011890C2211yescharacteristic
29#18011890C2211yescharacteristic
30#18011888—21no—
31#18011888—21no—
32C4×Dic298C2211yescharacteristic
33C4×Dic298C2211yescharacteristic
34#18011870C2211yescharacteristic
35C2×C4⋊Dic149C2211yescharacteristic
36#18011845C2211yescharacteristic
37#18011845C2211yescharacteristic
38#18011845C2211yescharacteristic
39#18011845C2211yescharacteristic
40#18011843C2211yescharacteristic
41#18011843C2211yescharacteristic
42#18011843C2211yescharacteristic
43#18011843C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011836C2211yescharacteristic
46#18011836C2211yescharacteristic
47#18011836C2211yescharacteristic
48#18011836C2211yescharacteristic
49#18011836C2211yescharacteristic
50#18011836C2211yescharacteristic
51#18011836C2211yescharacteristic
52#117×C149C2211yescharacteristic
53C4⋊C8×C149C2211yescharacteristic
54C4⋊C8×C149C2211yescharacteristic
55C22⋊C8×C149C2211yescharacteristic
56C22⋊C8×C149C2211yescharacteristic
57#97×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298—21no—
61C2×Dic298C2311yescharacteristic
62C2×Dic298C2311yescharacteristic
63C22×Dic149—21no—
64C4⋊Dic149—21no—
65C4⋊Dic149—21no—
66C4⋊Dic149—21no—
67C4⋊Dic149—21no—
68C4⋊Dic149—21no—
69C4⋊Dic149C2311yescharacteristic
70C4⋊Dic149C2311yescharacteristic
71C4⋊Dic149C2311yescharacteristic
72C4⋊Dic149C2311yescharacteristic
73C4⋊Dic149C2311yescharacteristic
74C4⋊Dic149C2311yescharacteristic
75#14558715—21no—
76#14558715—21no—
77#14558715—21no—
78#14558715—21no—
79#14558715—21no—
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85C22⋊Dic149—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88C4×Dic149—21no—
89C4×Dic149—21no—
90C4×Dic149—21no—
91C22×C4×C149C2311yescharacteristic
92C2×C8×C149C2311yescharacteristic
93C2×C8×C149C2311yescharacteristic
94C2×C8×C149C2311yescharacteristic
95C2×C8×C149C2311yescharacteristic
96C4⋊C4×C149D411yescharacteristic
97C4⋊C4×C149D411yescharacteristic
98C22⋊C4×C149D411yescharacteristic
99C22⋊C4×C149D411yescharacteristic
100C42×C149C2311yescharacteristic
101C42×C149C2311yescharacteristic
102Dic298—21no—
103Dic298—21no—
104Dic298—21no—
105Dic298—21no—
106Dic298—81no—
107Dic298—81no—
108C2×Dic149—21no—
109C2×Dic149—21no—
110C2×Dic149—21no—
111C2×Dic149—21no—
112C2×Dic149—21no—
113C2×Dic149—21no—
114C2×Dic149—21no—
115C2×Dic149—21no—
116C2×Dic149—81no—
117C23×C149C2×D411yescharacteristic
118C2×C4×C149—21no—
119C2×C4×C149—21no—
120C2×C4×C149C2×D411yescharacteristic
121C2×C4×C149C2×D411yescharacteristic
122C2×C4×C149C2×D411yescharacteristic
123C2×C4×C149C2×D411yescharacteristic
124C2×C4×C149C2×D411yescharacteristic
125C2×C4×C149C2411yescharacteristic
126C8×C149—21no—
127C8×C149—21no—
128C8×C149—21no—
129C8×C149—21no—
130C22×C149—21no—
131C22×C149—21no—
132C22×C149—21no—
133C22×C149C22×D411yescharacteristic
134C4×C149—21no—
135C4×C149—21no—
136C4×C149—21no—
137C4×C149—21no—
138C4×C149—21no—
139C4×C1492−1+411yescharacteristic
140C4×C1492−1+411yescharacteristic
141Dic149—41no—
142Dic149—41no—
143Dic149—41no—
144Dic149—41no—
145Dic149—41no—
146Dic149—41no—
147Dic149—41no—
148Dic149—41no—
149C2×C149—41no—
150C2×C149#53611yescharacteristic
151C2×C149#57711yescharacteristic
152C2×C149#57811yescharacteristic
153C149#324211yescharacteristic, complemented, Sylow
154#3242—1491nomaximal, Sylow
155#544—1491no—
156#541—1491no—
157#501—1491no—
158#499—1491no—
159#491—1491no—
160#487—1491no—
161#485—1491no—
162#485—1491no—
163#484—1491no—
164#483—1491no—
165#479—1491no—
166#479—1491no—
167#477—1491no—
168#475—1491no—
169#433D14911yescharacteristic
170C4⋊Q8—2981no—
171C4⋊Q8—1491no—
172C4⋊Q8—1491no—
173C4⋊Q8—1491no—
174#126—2981no—
175#126—2981no—
176#125—2981no—
177#125—2981no—
178#125—2981no—
179#125—1491no—
180#125—1491no—
181#125—1491no—
182C22⋊Q8—2981no—
183C22⋊Q8—2981no—
184C22⋊Q8—1491no—
185C22⋊Q8—1491no—
186C4×Q8—1491no—
187C4×Q8—1491no—
188#117—1491no—
189#117C2×D14911yescharacteristic
190C2×C4⋊C4—1491no—
191#107—1491no—
192#107—1491no—
193#107—1491no—
194#107—1491no—
195#106—1491no—
196#106—1491no—
197#106—1491no—
198#106—1491no—
199C4⋊C8C2×D14911yescharacteristic
200C4⋊C8C2×D14911yescharacteristic
201#103—1491no—
202#103—1491no—
203#103—1491no—
204#103—1491no—
205#103—1491no—
206#103—1491no—
207#103—1491no—
208#103—1491no—
209C22⋊C8C2×D14911yescharacteristic
210C22⋊C8C2×D14911yescharacteristic
211#97C2×D14911yescharacteristic
212C4×C8C2×D14911yescharacteristic
213C2×Q8—2981no—
214C2×Q8—2981no—
215C2×Q8—1491no—
216C2×Q8—1491no—
217C22×C4—2981no—
218C22×C4C22×D14911yescharacteristic
219C2×C8C22×D14911yescharacteristic
220C2×C8C22×D14911yescharacteristic
221C2×C8C22×D14911yescharacteristic
222C2×C8C22×D14911yescharacteristic
223C4⋊C4—2981no—
224C4⋊C4—2981no—
225C4⋊C4—2981no—
226C4⋊C4—2981no—
227C4⋊C4—2981no—
228C4⋊C4—2981no—
229C4⋊C4—2981no—
230C4⋊C4—2981no—
231C4⋊C4—2981no—
232C4⋊C4—2981no—
233C4⋊C4—2981no—
234C4⋊C4—2981no—
235C4⋊C4—2981no—
236C4⋊C4—2981no—
237C4⋊C4—2981no—
238C4⋊C4—1491no—
239C4⋊C4—1491no—
240C4⋊C4—1491no—
241C4⋊C4—1491no—
242C4⋊C4—1491no—
243C4⋊C4—1491no—
244C4⋊C4D59611yescharacteristic
245C4⋊C4D59611yescharacteristic
246C22⋊C4—2981no—
247C22⋊C4—2981no—
248C22⋊C4—2981no—
249C22⋊C4D59611yescharacteristic
250C22⋊C4D59611yescharacteristic
251C42—2981no—
252C42—2981no—
253C42—2981no—
254C42C22×D14911yescharacteristic
255C42C22×D14911yescharacteristic
256C23C2×D59611yescharacteristic
257Q8—2981no—
258Q8—2981no—
259Q8—2981no—
260Q8—2981no—
261Q8—11921no—
262Q8—11921no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—2981no—
266C2×C4—2981no—
267C2×C4—2981no—
268C2×C4—2981no—
269C2×C4—2981no—
270C2×C4—2981no—
271C2×C4—2981no—
272C2×C4—2981no—
273C2×C4—11921no—
274C2×C4C2×D59611yescharacteristic
275C2×C4C2×D59611yescharacteristic
276C2×C4C2×D59611yescharacteristic
277C2×C4C2×D59611yescharacteristic
278C2×C4C2×D59611yescharacteristic
279C2×C4C23×D14911yescharacteristic
280C8—21no—
281C8—21no—
282C8—21no—
283C8—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22C22×D59611yescharacteristic
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—5961no—
294C4—5961no—
295C4—5961no—
296C4—5961no—
297C4—5961no—
298C4—5961no—
299C4—5961no—
300C4—5961no—
301C4#1801195811yescharacteristic
302C4#1801195811yescharacteristic
303C2—41no—
304C2#2375020111yescharacteristic
305C2#2375043711yescharacteristic
306C2#2375044211yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#433×C149C2
socleC22×C149C22×D4
prime radicalC23×C149C2×D4
hypercenter#433D149
hypocenterC149#3242
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
3. #23750034C2semidirect
4. #23750027C2semidirect
5. #23749994C2semidirect
6. #23749976C2semidirect
11. #23749933C2semidirect
12. #23749933C2semidirect
13. #23749921C2semidirect
14. #23749911C2semidirect
153. C149#3242semidirect

Maximal subgroups

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

subgroupindex
#237502532
#237502372
#237500342
#237500272
#237499942
#237499762
#237499672
#237499612
#237499562
#237499332
#237499212
#237499112
#433×C1492
#3242149