Finite Group Databasebeta

← #34055983

Subgroups — #34055983

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#23750031C211yesmaximal, characteristic, complemented
3#23750021C211yesmaximal, characteristic, complemented
4#23749984C211yesmaximal, characteristic, complemented
5#23749979C211yesmaximal, characteristic, complemented
6#23749963C211yesmaximal, characteristic, complemented
7#23749953C211yesmaximal, characteristic, complemented
8#23749946C211yesmaximal, characteristic
9#23749941C211yesmaximal, characteristic
10#23749932C211yesmaximal, characteristic, complemented
11#23749925C211yesmaximal, characteristic, complemented
12#23749915C211yesmaximal, characteristic, complemented
13#23749910C211yesmaximal, characteristic, complemented
14#23749686C211yesmaximal, characteristic, complemented
15#542×C149C211yesmaximal, characteristic
16#18011911C2211yescharacteristic
17#18011911C2211yescharacteristic
18#18011910—21no—
19#18011903C2211yescharacteristic
20#18011903C2211yescharacteristic
21#18011902—21no—
22#18011888—21no—
23#18011888—21no—
24#18011870C2211yescharacteristic
25C2×C4⋊Dic149C2211yescharacteristic
26#18011844C2211yescharacteristic
27#18011844C2211yescharacteristic
28#18011842C2211yescharacteristic
29#18011842C2211yescharacteristic
30#18011842C2211yescharacteristic
31#18011842C2211yescharacteristic
32#18011842C2211yescharacteristic
33#18011842C2211yescharacteristic
34C4⋊#11924746C2211yescharacteristic
35C4⋊#11924746C2211yescharacteristic
36#18011835C2211yescharacteristic
37#18011835C2211yescharacteristic
38#18011835C2211yescharacteristic
39#18011835C2211yescharacteristic
40#18011832C2211yescharacteristic
41#18011832C2211yescharacteristic
42#18011832C2211yescharacteristic
43#18011832C2211yescharacteristic
44C22⋊#11924746C2211yescharacteristic
45C22⋊#11924746C2211yescharacteristic
46#18011822C2211yescharacteristic
47C4×#11924746C2211yescharacteristic
48C4⋊Q8×C149C2211yescharacteristic
49#126×C149—21no—
50#124×C149—21no—
51#124×C149C2211yescharacteristic
52#123×C149—21no—
53C22⋊Q8×C149—21no—
54C22⋊Q8×C149C2211yescharacteristic
55#121×C149C2211yescharacteristic
56C4×Q8×C149C2211yescharacteristic
57C4×D4×C149C2211yescharacteristic
58#117×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298—21no—
61C22×Dic149—21no—
62C2×#11924746C2311yescharacteristic
63C2×#11924746C2311yescharacteristic
64C2×#11924746C2311yescharacteristic
65C2×#11924746C2311yescharacteristic
66C4⋊Dic149—21no—
67C4⋊Dic149—21no—
68C4⋊Dic149—21no—
69C4⋊Dic149C2311yescharacteristic
70C4⋊Dic149C2311yescharacteristic
71C4⋊Dic149C2311yescharacteristic
72C4⋊Dic149C2311yescharacteristic
73#14558715—21no—
74#14558715—21no—
75#14558715—21no—
76#14558715—21no—
77C22⋊Dic149—21no—
78C4×Dic149—21no—
79C2×Q8×C149—21no—
80C2×Q8×C149C2311yescharacteristic
81C2×D4×C149—21no—
82C2×D4×C149C2311yescharacteristic
83C22×C4×C149—21no—
84C22×C4×C149C2311yescharacteristic
85C4⋊C4×C149—21no—
86C4⋊C4×C149—21no—
87C4⋊C4×C149—21no—
88C4⋊C4×C149D411yescharacteristic
89C4⋊C4×C149D411yescharacteristic
90C4⋊C4×C149C2311yescharacteristic
91C4⋊C4×C149C2311yescharacteristic
92C22⋊C4×C149—21no—
93C22⋊C4×C149—21no—
94C22⋊C4×C149—21no—
95C22⋊C4×C149—21no—
96C22⋊C4×C149—21no—
97C22⋊C4×C149D411yescharacteristic
98C22⋊C4×C149D411yescharacteristic
99C42×C149—21no—
100C42×C149C2311yescharacteristic
101C42×C149C2311yescharacteristic
102Dic298—81no—
103Dic298—81no—
104C2×Dic149—21no—
105C2×Dic149—21no—
106C2×Dic149—21no—
107C2×Dic149—21no—
108C2×Dic149—81no—
109#11924746—21no—
110#11924746—21no—
111#11924746—21no—
112#11924746—21no—
113C23×C149—21no—
114C23×C149C2×D411yescharacteristic
115Q8×C149—21no—
116Q8×C149—21no—
117Q8×C149—81no—
118D4×C149—21no—
119D4×C149—21no—
120D4×C149—81no—
121C2×C4×C149—21no—
122C2×C4×C149—21no—
123C2×C4×C149—21no—
124C2×C4×C149—21no—
125C2×C4×C149—21no—
126C2×C4×C149—81no—
127C2×C4×C149C2×D411yescharacteristic
128C2×C4×C149C2×D411yescharacteristic
129C2×C4×C149C2×D411yescharacteristic
130C2×C4×C149C2×D411yescharacteristic
131C2×C4×C149C2×D411yescharacteristic
132C2×C4×C149C2411yescharacteristic
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—21no—
142C4×C149—21no—
143C4×C149—21no—
144C4×C149—21no—
145C4×C149—41no—
146C4×C149—41no—
147C4×C149—41no—
148C4×C1492−1+411yescharacteristic
149C4×C1492−1+411yescharacteristic
150Dic149—41no—
151Dic149—41no—
152Dic149—41no—
153Dic149—41no—
154C2×C149—41no—
155C2×C149—81no—
156C2×C149#53611yescharacteristic
157C2×C149#57711yescharacteristic
158C2×C149#57711yescharacteristic
159C149#324411yescharacteristic, complemented, Sylow
160#3244—1491nomaximal, Sylow
161#544—1491no—
162#542D14911yescharacteristic
163#501—1491no—
164#498—1491no—
165#489—1491no—
166#488—1491no—
167#485—1491no—
168#483—1491no—
169#482—1491no—
170#481—1491no—
171#479—1491no—
172#478—1491no—
173#476—1491no—
174#475—1491no—
175#433—1491no—
176C4⋊Q8—2981no—
177C4⋊Q8—1491no—
178C4⋊Q8—1491no—
179C4⋊Q8C2×D14911yescharacteristic
180#126—21no—
181#125—2981no—
182#125—1491no—
183#125—1491no—
184#124—21no—
185#124C2×D14911yescharacteristic
186#123—21no—
187C22⋊Q8—21no—
188C22⋊Q8—2981no—
189C22⋊Q8—2981no—
190C22⋊Q8C2×D14911yescharacteristic
191#121C2×D14911yescharacteristic
192C4×Q8C2×D14911yescharacteristic
193C4×D4C2×D14911yescharacteristic
194#117—1491no—
195#117C2×D14911yescharacteristic
196C2×C4⋊C4—1491no—
197#107—1491no—
198#107—1491no—
199#106—1491no—
200#106—1491no—
201#106—1491no—
202#106—1491no—
203#106—1491no—
204#106—1491no—
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#102—1491no—
214#102—1491no—
215C22⋊C8—1491no—
216C22⋊C8—1491no—
217#97—1491no—
218C4×C8—1491no—
219C2×Q8—21no—
220C2×Q8—2981no—
221C2×Q8—2981no—
222C2×Q8C22×D14911yescharacteristic
223C2×D4—21no—
224C2×D4C22×D14911yescharacteristic
225C22×C4—21no—
226C22×C4—2981no—
227C22×C4C22×D14911yescharacteristic
228C2×C8—1491no—
229C2×C8—1491no—
230C2×C8—1491no—
231C2×C8—1491no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
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⋊C4C22⋊D14911yescharacteristic
247C4⋊C4C22⋊D14911yescharacteristic
248C4⋊C4C22×D14911yescharacteristic
249C4⋊C4C22×D14911yescharacteristic
250C22⋊C4—21no—
251C22⋊C4—21no—
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—21no—
255C22⋊C4—2981no—
256C22⋊C4C22⋊D14911yescharacteristic
257C22⋊C4C22⋊D14911yescharacteristic
258C42—21no—
259C42—2981no—
260C42C22×D14911yescharacteristic
261C42C22×D14911yescharacteristic
262C23—21no—
263C23C2×C22⋊D14911yescharacteristic
264Q8—21no—
265Q8—21no—
266Q8—81no—
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—81no—
278C2×C4—2981no—
279C2×C4—2981no—
280C2×C4—2981no—
281C2×C4—2981no—
282C2×C4—11921no—
283C2×C4C2×C22⋊D14911yescharacteristic
284C2×C4C2×C22⋊D14911yescharacteristic
285C2×C4C2×C22⋊D14911yescharacteristic
286C2×C4C2×C22⋊D14911yescharacteristic
287C2×C4C2×C22⋊D14911yescharacteristic
288C2×C4C23×D14911yescharacteristic
289C8—2981no—
290C8—2981no—
291C8—2981no—
292C8—2981no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22C22×C22⋊D14911yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—5961no—
309C4—5961no—
310C4—5961no—
311C4—5961no—
312C4#1801195811yescharacteristic
313C4#1801195811yescharacteristic
314C2—41no—
315C2—81no—
316C2#2375019611yescharacteristic
317C2#2375043311yescharacteristic
318C2#2375043611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#542×C149C2
socleC22×C149C22×D4
prime radical#121×C149C22
hypercenter#542D149
hypocenterC149#3244
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #23750253C2semidirect
2. #23750031C2semidirect
3. #23750021C2semidirect
4. #23749984C2semidirect
5. #23749979C2semidirect
6. #23749963C2semidirect
7. #23749953C2semidirect
10. #23749932C2semidirect
11. #23749925C2semidirect
12. #23749915C2semidirect
13. #23749910C2semidirect
14. #23749686C2semidirect
159. C149#3244semidirect

Maximal subgroups

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

subgroupindex
#237502532
#237500312
#237500212
#237499842
#237499792
#237499632
#237499532
#237499462
#237499412
#237499322
#237499252
#237499152
#237499102
#237496862
#542×C1492
#3244149