Finite Group Databasebeta

← #34055902

Subgroups — #34055902

Order 19072.

322 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750178C211yesmaximal, characteristic
2#23750177C211yesmaximal, characteristic
3#23750033C211yesmaximal, characteristic, complemented
4#23750032C211yesmaximal, characteristic, complemented
5#23749992C211yesmaximal, characteristic, complemented
6#23749992C211yesmaximal, characteristic, complemented
7#23749967C211yesmaximal, characteristic
8#23749966C211yesmaximal, characteristic
9#23749963C211yesmaximal, characteristic
10#23749919C211yesmaximal, characteristic, complemented
11#23749918C211yesmaximal, characteristic, complemented
12#23749909C211yesmaximal, characteristic, complemented
13#23749908C211yesmaximal, characteristic, complemented
14#23749679C211yesmaximal, characteristic
15#485×C149C211yesmaximal, characteristic
16#18011910C2211yescharacteristic
17#18011910C2211yescharacteristic
18#18011910C2211yescharacteristic
19#18011909C2211yescharacteristic
20#18011902C2211yescharacteristic
21#18011902C2211yescharacteristic
22#18011901—21no—
23#18011890C2211yescharacteristic
24#18011888—21no—
25#18011888—21no—
26#18011888—21no—
27Q8×Dic149C2211yescharacteristic
28C4×Dic298—21no—
29C4×Dic298—21no—
30#18011876—21no—
31#18011876C2211yescharacteristic
32#18011870C2211yescharacteristic
33#18011867—21no—
34C2×C4×Dic149C2211yescharacteristic
35#18011845C2211yescharacteristic
36#18011844C2211yescharacteristic
37#18011844C2211yescharacteristic
38#18011843C2211yescharacteristic
39#18011842C2211yescharacteristic
40#18011842C2211yescharacteristic
41#18011840C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011835C2211yescharacteristic
47#18011834C2211yescharacteristic
48#18011834C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011821C2211yescharacteristic
51#18011821C2211yescharacteristic
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×Dic298—21no—
62C2×Dic298C2311yescharacteristic
63C22×Dic149D411yescharacteristic
64C22×Dic149D411yescharacteristic
65C2×#11924746C2311yescharacteristic
66C2×#11924746C2311yescharacteristic
67C4⋊Dic149—21no—
68C4⋊Dic149—21no—
69C4⋊Dic149—21no—
70C4⋊Dic149C2311yescharacteristic
71C4⋊Dic149C2311yescharacteristic
72C4⋊Dic149C2311yescharacteristic
73#14558715—21no—
74#14558715—21no—
75#14558715—21no—
76#14558715—21no—
77#14558715—21no—
78#14558715—21no—
79#14558715—21no—
80#14558715—21no—
81#14558715—21no—
82C22⋊Dic149—21no—
83C22⋊Dic149—21no—
84C4×Dic149—21no—
85C4×Dic149—21no—
86C4×Dic149—21no—
87C4×Dic149D411yescharacteristic
88C4×Dic149D411yescharacteristic
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—42no—
105Dic298—42no—
106Dic298—42no—
107C2×Dic149—22no—
108C2×Dic149—21no—
109C2×Dic149—21no—
110C2×Dic149—21no—
111C2×Dic149—21no—
112C2×Dic149—41no—
113C2×Dic149C2×D411yescharacteristic
114C2×Dic149C2×D411yescharacteristic
115C2×Dic149C2×D411yescharacteristic
116C2×Dic149C2×D411yescharacteristic
117#11924746—21no—
118#11924746—21no—
119C23×C149C2×D411yescharacteristic
120Q8×C149—21no—
121Q8×C149—21no—
122C2×C4×C149—21no—
123C2×C4×C149—21no—
124C2×C4×C149—21no—
125C2×C4×C149—21no—
126C2×C4×C149—21no—
127C2×C4×C149—21no—
128C2×C4×C149C2×D411yescharacteristic
129C2×C4×C149C2411yescharacteristic
130C8×C149—21no—
131C8×C149—21no—
132C22×C149—21no—
133C22×C149—21no—
134C22×C149—21no—
135C22×C149C22×D411yescharacteristic
136C4×C149—21no—
137C4×C149—41no—
138C4×C149—41no—
139C4×C149—41no—
140C4×C149—41no—
141C4×C1492−1+411yescharacteristic
142C4×C1492−1+411yescharacteristic
143Dic149—21no—
144Dic149—21no—
145Dic149—21no—
146Dic149—41no—
147Dic149—41no—
148Dic149—41no—
149Dic149—41no—
150Dic149#13712yes—
151C2×C149—41no—
152C2×C149#53611yescharacteristic
153C2×C149C2×#13711yescharacteristic
154C2×C149#57511yescharacteristic
155C149#323711yescharacteristic, complemented, Sylow
156#3237—1491nomaximal, Sylow
157#533—1491no—
158#533—1491no—
159#501—1491no—
160#501—1491no—
161#491—1491no—
162#491—1491no—
163#485—1491no—
164#485—1491no—
165#485—1491no—
166#485D14911yescharacteristic
167#477—1491no—
168#477—1491no—
169#475—1491no—
170#475—1491no—
171#432—1491no—
172C4⋊Q8—1491no—
173C4⋊Q8—1491no—
174C4⋊Q8—1491no—
175C4⋊Q8—1491no—
176#125—2981no—
177#125—1491no—
178#125—1491no—
179C22⋊Q8—2981no—
180C22⋊Q8—2981no—
181C22⋊Q8—2981no—
182C22⋊Q8—1491no—
183C22⋊Q8C2×D14911yescharacteristic
184C4×Q8—2981no—
185C4×Q8—2981no—
186C4×Q8—2981no—
187C4×Q8—1491no—
188C4×Q8—1491no—
189#117—2981no—
190#117—1491no—
191#117C2×D14911yescharacteristic
192C2×C42—1491no—
193#107—1491no—
194#107—1491no—
195#107—1491no—
196#107C2×D14911yescharacteristic
197#106—1491no—
198#106—1491no—
199#106—1491no—
200#106C2×D14911yescharacteristic
201C4⋊C8—1491no—
202C4⋊C8—1491no—
203#103—1491no—
204#103—1491no—
205#103—1491no—
206#103—1491no—
207#103—1491no—
208#103—1491no—
209#103C2×D14911yescharacteristic
210#103C2×D14911yescharacteristic
211C22⋊C8—1491no—
212C22⋊C8C2×D14911yescharacteristic
213#97—1491no—
214#97—1491no—
215C2×Q8—2981no—
216C2×Q8—2981no—
217C2×Q8—2981no—
218C2×Q8—1491no—
219C2×Q8C22×D14911yescharacteristic
220C22×C4—1491no—
221C22×C4—1491no—
222C22×C4C22×D14911yescharacteristic
223C2×C8—1491no—
224C2×C8—1491no—
225C2×C8C22×D14911yescharacteristic
226C2×C8C22×D14911yescharacteristic
227C4⋊C4—21no—
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—2981no—
239C4⋊C4—2981no—
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—2981no—
250C42—21no—
251C42—2981no—
252C42—2981no—
253C42—2981no—
254C42—1491no—
255C42—1491no—
256C42—1491no—
257C42—1491no—
258C23D4×D14911yescharacteristic
259Q8—21no—
260Q8—21no—
261Q8—2981no—
262Q8—2981no—
263Q8—5962no—
264Q8—5962no—
265Q8—5962no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—2982no—
273C2×C4—2981no—
274C2×C4—2981no—
275C2×C4—2981no—
276C2×C4—2981no—
277C2×C4—5961no—
278C2×C4—1491no—
279C2×C4—1491no—
280C2×C4—1491no—
281C2×C4—1491no—
282C2×C4D4×D14911yescharacteristic
283C2×C4C23×D14911yescharacteristic
284C8—21no—
285C8—21no—
286C8—2981no—
287C8—2981no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22C2×D4×D14911yescharacteristic
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—2981no—
298C4—2981no—
299C4—2981no—
300C4—5961no—
301C4—5961no—
302C4—5961no—
303C4—5961no—
304C4—1492no—
305C4#1801195811yescharacteristic
306C4#1801195811yescharacteristic
307C2—41no—
308C2#2375019711yescharacteristic
309C2#137×D14911yescharacteristic
310C2#2375042211yescharacteristic
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#3237
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. #23750032C2semidirect
5. #23749992C2semidirect
6. #23749992C2semidirect
10. #23749919C2semidirect
11. #23749918C2semidirect
12. #23749909C2semidirect
13. #23749908C2semidirect
155. C149#3237semidirect

Maximal subgroups

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

subgroupindex
#237501782
#237501772
#237500332
#237500322
#237499922
#237499672
#237499662
#237499632
#237499192
#237499182
#237499092
#237499082
#237496792
#485×C1492
#3237149