Finite Group Databasebeta

← #34055965

Subgroups — #34055965

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#23750235C211yesmaximal, characteristic
3#23750033C211yesmaximal, characteristic, complemented
4#23750025C211yesmaximal, characteristic, complemented
5#23749992C211yesmaximal, characteristic, complemented
6#23749974C211yesmaximal, characteristic, complemented
7#23749966C211yesmaximal, characteristic
8#23749958C211yesmaximal, characteristic
9#23749956C211yesmaximal, characteristic
10#23749935C211yesmaximal, characteristic, complemented
11#23749930C211yesmaximal, characteristic, complemented
12#23749919C211yesmaximal, characteristic, complemented
13#23749908C211yesmaximal, characteristic, complemented
14#23749683C211yesmaximal, characteristic
15#485×C149C211yesmaximal, characteristic
16#18011911—21no—
17#18011910C2211yescharacteristic
18#18011910C2211yescharacteristic
19#18011909C2211yescharacteristic
20#18011904—21no—
21#18011904—21no—
22#18011903—21no—
23#18011902—21no—
24#18011902C2211yescharacteristic
25#18011902C2211yescharacteristic
26#18011902C2211yescharacteristic
27#18011901—21no—
28#18011890C2211yescharacteristic
29#18011888—21no—
30#18011888—21no—
31Q8×Dic149C2211yescharacteristic
32#18011876C2211yescharacteristic
33#18011870C2211yescharacteristic
34C2×C4⋊Dic149C2211yescharacteristic
35#18011844C2211yescharacteristic
36#18011844C2211yescharacteristic
37#18011844C2211yescharacteristic
38#18011843C2211yescharacteristic
39#18011843C2211yescharacteristic
40#18011842C2211yescharacteristic
41#18011840C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011835C2211yescharacteristic
47#18011834C2211yescharacteristic
48#18011834C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C22⋊Q8×C149C2211yescharacteristic
53#117×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298—21no—
61C2×Dic298C2311yescharacteristic
62C22×Dic149—21no—
63C2×#11924746C2311yescharacteristic
64C2×#11924746C2311yescharacteristic
65C4⋊Dic149—21no—
66C4⋊Dic149—21no—
67C4⋊Dic149—21no—
68C4⋊Dic149—21no—
69C4⋊Dic149—21no—
70C4⋊Dic149D411yescharacteristic
71C4⋊Dic149D411yescharacteristic
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—
84C22⋊Dic149—21no—
85C22⋊Dic149D411yescharacteristic
86C22⋊Dic149D411yescharacteristic
87C4×Dic149—21no—
88C4×Dic149—21no—
89C4×Dic149C2311yescharacteristic
90C4×Dic149C2311yescharacteristic
91C2×Q8×C149C2311yescharacteristic
92C22×C4×C149C2311yescharacteristic
93C2×C8×C149C2311yescharacteristic
94C2×C8×C149C2311yescharacteristic
95C4⋊C4×C149—21no—
96C4⋊C4×C149C2311yescharacteristic
97C4⋊C4×C149C2311yescharacteristic
98C4⋊C4×C149C2311yescharacteristic
99C22⋊C4×C149—21no—
100C22⋊C4×C149—21no—
101C42×C149—21no—
102Dic298—21no—
103Dic298—21no—
104Dic298—81no—
105Dic298—81no—
106C2×Dic149—21no—
107C2×Dic149—21no—
108C2×Dic149—21no—
109C2×Dic149—21no—
110C2×Dic149—81no—
111C2×Dic149C2×D411yescharacteristic
112C2×Dic149C2×D411yescharacteristic
113C2×Dic149C2×D411yescharacteristic
114C2×Dic149C2×D411yescharacteristic
115#11924746—21no—
116#11924746—21no—
117C23×C149C2×D411yescharacteristic
118Q8×C149—21no—
119Q8×C149—21no—
120C2×C4×C149—21no—
121C2×C4×C149—21no—
122C2×C4×C149—21no—
123C2×C4×C149—21no—
124C2×C4×C149—21no—
125C2×C4×C149—21no—
126C2×C4×C149C2×D411yescharacteristic
127C2×C4×C149C2411yescharacteristic
128C8×C149—21no—
129C8×C149—21no—
130C22×C149—21no—
131C22×C149—21no—
132C22×C149—21no—
133C22×C149C22×D411yescharacteristic
134C4×C149—21no—
135C4×C149—41no—
136C4×C149—41no—
137C4×C149—41no—
138C4×C149—41no—
139C4×C1492−1+411yescharacteristic
140C4×C1492−1+411yescharacteristic
141Dic149—21no—
142Dic149—21no—
143Dic149—21no—
144Dic149—21no—
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#485D14911yescharacteristic
163#484—1491no—
164#483—1491no—
165#479—1491no—
166#479—1491no—
167#477—1491no—
168#475—1491no—
169#433—1491no—
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⋊Q8C2×D14911yescharacteristic
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#107C2×D14911yescharacteristic
195#106—1491no—
196#106—1491no—
197#106—1491no—
198#106C2×D14911yescharacteristic
199C4⋊C8—1491no—
200C4⋊C8—1491no—
201#103—1491no—
202#103—1491no—
203#103—1491no—
204#103—1491no—
205#103—1491no—
206#103—1491no—
207#103C2×D14911yescharacteristic
208#103C2×D14911yescharacteristic
209C22⋊C8—1491no—
210C22⋊C8C2×D14911yescharacteristic
211#97—1491no—
212C4×C8—1491no—
213C2×Q8—2981no—
214C2×Q8—2981no—
215C2×Q8—1491no—
216C2×Q8C22×D14911yescharacteristic
217C22×C4—2981no—
218C22×C4C22×D14911yescharacteristic
219C2×C8—1491no—
220C2×C8—1491no—
221C2×C8C22×D14911yescharacteristic
222C2×C8C22×D14911yescharacteristic
223C4⋊C4—21no—
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⋊C4C22×D14911yescharacteristic
244C4⋊C4C22×D14911yescharacteristic
245C4⋊C4C22×D14911yescharacteristic
246C22⋊C4—21no—
247C22⋊C4—21no—
248C22⋊C4—2981no—
249C22⋊C4—1491no—
250C22⋊C4—1491no—
251C42—21no—
252C42—2981no—
253C42—2981no—
254C42—1491no—
255C42—1491no—
256C23D4×D14911yescharacteristic
257Q8—21no—
258Q8—21no—
259Q8—2981no—
260Q8—2981no—
261Q8—11921no—
262Q8—11921no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—2981no—
270C2×C4—2981no—
271C2×C4—2981no—
272C2×C4—2981no—
273C2×C4—1491no—
274C2×C4—1491no—
275C2×C4—1491no—
276C2×C4—1491no—
277C2×C4—11921no—
278C2×C4D4×D14911yescharacteristic
279C2×C4C23×D14911yescharacteristic
280C8—21no—
281C8—21no—
282C8—2981no—
283C8—2981no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22C2×D4×D14911yescharacteristic
288C4—21no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—2981no—
294C4—2981no—
295C4—2981no—
296C4—2981no—
297C4—5961no—
298C4—5961no—
299C4—5961no—
300C4—5961no—
301C4#1801195811yescharacteristic
302C4#1801195811yescharacteristic
303C2—41no—
304C2#2375019711yescharacteristic
305C2#2375043211yescharacteristic
306C2#2375044111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#485×C149C2
socleC22×C149C22×D4
prime radicalC23×C149C2×D4
hypercenter#485D149
hypocenterC149#3242
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #23750033C2semidirect
4. #23750025C2semidirect
5. #23749992C2semidirect
6. #23749974C2semidirect
10. #23749935C2semidirect
11. #23749930C2semidirect
12. #23749919C2semidirect
13. #23749908C2semidirect
153. C149#3242semidirect

Maximal subgroups

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

subgroupindex
#237502532
#237502352
#237500332
#237500252
#237499922
#237499742
#237499662
#237499582
#237499562
#237499352
#237499302
#237499192
#237499082
#237496832
#485×C1492
#3242149