Finite Group Databasebeta

← #34055972

Subgroups — #34055972

Order 19072.

320 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750253C211yesmaximal, characteristic, complemented
2#23750242C211yesmaximal, characteristic
3#23750032C211yesmaximal, characteristic, complemented
4#23750029C211yesmaximal, characteristic, complemented
5#23749983C211yesmaximal, characteristic, complemented
6#23749978C211yesmaximal, characteristic, complemented
7#23749966C211yesmaximal, characteristic, complemented
8#23749961C211yesmaximal, characteristic, complemented
9#23749936C211yesmaximal, characteristic
10#23749935C211yesmaximal, characteristic, complemented
11#23749923C211yesmaximal, characteristic, complemented
12#23749919C211yesmaximal, characteristic, complemented
13#23749903C211yesmaximal, characteristic, complemented
14#23749683C211yesmaximal, characteristic, complemented
15#482×C149C211yesmaximal, characteristic
16#18011911—21no—
17#18011910C2211yescharacteristic
18#18011910C2211yescharacteristic
19#18011910C2211yescharacteristic
20#18011904—21no—
21#18011903—21no—
22#18011902C2211yescharacteristic
23#18011902C2211yescharacteristic
24#18011898—21no—
25#18011898C2211yescharacteristic
26#18011892—21no—
27#18011890C2211yescharacteristic
28#18011888—21no—
29#18011888—21no—
30#18011888—21no—
31#18011876C2211yescharacteristic
32D4×Dic149C2211yescharacteristic
33#18011870C2211yescharacteristic
34C2×C4⋊Dic149C2211yescharacteristic
35#18011845C2211yescharacteristic
36#18011845C2211yescharacteristic
37#18011844C2211yescharacteristic
38#18011844C2211yescharacteristic
39#18011844C2211yescharacteristic
40#18011842C2211yescharacteristic
41#18011840C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011834C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011832C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52#121×C149C2211yescharacteristic
53#117×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298—21no—
61C2×Dic298—21no—
62C2×Dic298C2311yescharacteristic
63C22×Dic149—21no—
64C22×Dic149—21no—
65C2×#11924746C2311yescharacteristic
66C2×#11924746C2311yescharacteristic
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—
82C22⋊Dic149—21no—
83C22⋊Dic149—21no—
84C22⋊Dic149—21no—
85C22⋊Dic149—21no—
86C22⋊Dic149D411yescharacteristic
87C22⋊Dic149D411yescharacteristic
88C4×Dic149—21no—
89C4×Dic149C2311yescharacteristic
90C4×Dic149C2311yescharacteristic
91C2×D4×C149—21no—
92C2×D4×C149C2311yescharacteristic
93C22×C4×C149C2311yescharacteristic
94C2×C8×C149C2311yescharacteristic
95C2×C8×C149C2311yescharacteristic
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—
106Dic298—81no—
107C2×Dic149—21no—
108C2×Dic149—21no—
109C2×Dic149—21no—
110C2×Dic149—21no—
111C2×Dic149—81no—
112C2×Dic149—81no—
113C2×Dic149C2×D411yescharacteristic
114C2×Dic149C2×D411yescharacteristic
115C2×Dic149C2×D411yescharacteristic
116C2×Dic149C2×D411yescharacteristic
117#11924746—21no—
118#11924746—21no—
119C23×C149—21no—
120C23×C149C2×D411yescharacteristic
121D4×C149—21no—
122D4×C149—21no—
123D4×C149—81no—
124C2×C4×C149—21no—
125C2×C4×C149—21no—
126C2×C4×C149—21no—
127C2×C4×C149—21no—
128C2×C4×C149—21no—
129C2×C4×C149C2×D411yescharacteristic
130C2×C4×C149C2411yescharacteristic
131C8×C149—21no—
132C8×C149—21no—
133C22×C149—21no—
134C22×C149—21no—
135C22×C149—21no—
136C22×C149—41no—
137C22×C149—41no—
138C22×C149—41no—
139C22×C149C22×D411yescharacteristic
140C4×C149—21no—
141C4×C149—41no—
142C4×C149—41no—
143C4×C149—41no—
144C4×C1492−1+411yescharacteristic
145C4×C1492−1+411yescharacteristic
146Dic149—21no—
147Dic149—21no—
148Dic149—21no—
149Dic149—21no—
150Dic149—41no—
151Dic149—41no—
152Dic149—41no—
153Dic149—41no—
154C2×C149—41no—
155C2×C149—81no—
156C2×C149#53611yescharacteristic
157C2×C149#57611yescharacteristic
158C2×C149#57811yescharacteristic
159C149#324311yescharacteristic, complemented, Sylow
160#3243—1491nomaximal, Sylow
161#544—1491no—
162#542—1491no—
163#501—1491no—
164#500—1491no—
165#489—1491no—
166#488—1491no—
167#485—1491no—
168#484—1491no—
169#482D14911yescharacteristic
170#480—1491no—
171#479—1491no—
172#478—1491no—
173#477—1491no—
174#474—1491no—
175#433—1491no—
176C4⋊Q8—2981no—
177C4⋊Q8—1491no—
178C4⋊Q8—1491no—
179C4⋊Q8—1491no—
180#126—2981no—
181#125—2981no—
182#125—1491no—
183#125—1491no—
184#124—2981no—
185#124—1491no—
186#123—2981no—
187C22⋊Q8—2981no—
188C22⋊Q8—2981no—
189C22⋊Q8—2981no—
190C22⋊Q8—1491no—
191#121C2×D14911yescharacteristic
192C4×Q8—1491no—
193C4×D4—1491no—
194#117—1491no—
195#117C2×D14911yescharacteristic
196C2×C4⋊C4—1491no—
197#107—1491no—
198#107—1491no—
199#107—1491no—
200#107—1491no—
201#107—1491no—
202#107C2×D14911yescharacteristic
203#106—1491no—
204#106C2×D14911yescharacteristic
205C4⋊C8—1491no—
206C4⋊C8—1491no—
207#103—1491no—
208#103—1491no—
209#103—1491no—
210#103—1491no—
211#102—1491no—
212#102—1491no—
213#102C2×D14911yescharacteristic
214#102C2×D14911yescharacteristic
215C22⋊C8—1491no—
216C22⋊C8C2×D14911yescharacteristic
217#97—1491no—
218C4×C8—1491no—
219C2×Q8—2981no—
220C2×Q8—2981no—
221C2×Q8—2981no—
222C2×Q8—1491no—
223C2×D4—21no—
224C2×D4C22×D14911yescharacteristic
225C22×C4—2981no—
226C22×C4—2981no—
227C22×C4C22×D14911yescharacteristic
228C2×C8—1491no—
229C2×C8—1491no—
230C2×C8C22×D14911yescharacteristic
231C2×C8C22×D14911yescharacteristic
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—2981no—
241C4⋊C4—2981no—
242C4⋊C4—1491no—
243C4⋊C4—1491no—
244C4⋊C4—1491no—
245C4⋊C4—1491no—
246C4⋊C4—1491no—
247C4⋊C4C22×D14911yescharacteristic
248C4⋊C4C22×D14911yescharacteristic
249C4⋊C4C22×D14911yescharacteristic
250C22⋊C4—21no—
251C22⋊C4—21no—
252C22⋊C4—2981no—
253C22⋊C4—2981no—
254C22⋊C4—2981no—
255C22⋊C4—2981no—
256C22⋊C4—1491no—
257C22⋊C4—1491no—
258C42—21no—
259C42—2981no—
260C42—1491no—
261C42—1491no—
262C23—21no—
263C23D4×D14911yescharacteristic
264Q8—2981no—
265Q8—2981no—
266Q8—11921no—
267Q8—11921no—
268Q8—11921no—
269D4—21no—
270D4—21no—
271D4—81no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—2981no—
278C2×C4—2981no—
279C2×C4—2981no—
280C2×C4—2981no—
281C2×C4—1491no—
282C2×C4—1491no—
283C2×C4—1491no—
284C2×C4—1491no—
285C2×C4—11921no—
286C2×C4—11921no—
287C2×C4D4×D14911yescharacteristic
288C2×C4C23×D14911yescharacteristic
289C8—21no—
290C8—21no—
291C8—2981no—
292C8—2981no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22C2×D4×D14911yescharacteristic
300C4—21no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—2981no—
305C4—2981no—
306C4—2981no—
307C4—2981no—
308C4—5961no—
309C4—5961no—
310C4—5961no—
311C4—5961no—
312C4#1801195811yescharacteristic
313C4#1801195811yescharacteristic
314C2—41no—
315C2—81no—
316C2#2375019711yescharacteristic
317C2#2375042911yescharacteristic
318C2#2375043911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#482×C149C2
socleC22×C149C22×D4
prime radical#121×C149C22
hypercenter#482D149
hypocenterC149#3243
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #23750253C2semidirect
3. #23750032C2semidirect
4. #23750029C2semidirect
5. #23749983C2semidirect
6. #23749978C2semidirect
7. #23749966C2semidirect
8. #23749961C2semidirect
10. #23749935C2semidirect
11. #23749923C2semidirect
12. #23749919C2semidirect
13. #23749903C2semidirect
14. #23749683C2semidirect
159. C149#3243semidirect

Maximal subgroups

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

subgroupindex
#237502532
#237502422
#237500322
#237500292
#237499832
#237499782
#237499662
#237499612
#237499362
#237499352
#237499232
#237499192
#237499032
#237496832
#482×C1492
#3243149