Finite Group Databasebeta

← #34057371

Subgroups — #34057371

Order 19072.

336 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750351C211yesmaximal, characteristic, complemented
2#23750344C211yesmaximal, characteristic
3#23749979C211yesmaximal, characteristic
4#23749978C211yesmaximal, characteristic
5#23749974C211yesmaximal, characteristic, complemented
6#23749933C211yesmaximal, characteristic, complemented
7#23749930C211yesmaximal, characteristic, complemented
8#23749903C211yesmaximal, characteristic
9#23749845C211yesmaximal, characteristic
10#23749833C211yesmaximal, characteristic, complemented
11#23749749C211yesmaximal, characteristic, complemented
12Q16×Dic149C211yesmaximal, characteristic, complemented
13C4×#14558726C211yesmaximal, characteristic, complemented
14SD16×Dic149C211yesmaximal, characteristic
15#464×C149C211yesmaximal, characteristic
16C2×#14558726C2211yescharacteristic
17#18011910—21no—
18#18011910C2211yescharacteristic
19#18011909C2211yescharacteristic
20#18011904—21no—
21#18011904—21no—
22#18011903—21no—
23#18011903C2211yescharacteristic
24#18011902—21no—
25#18011902C2211yescharacteristic
26#18011898C2211yescharacteristic
27#18011888—21no—
28Q8×Dic149C2211yescharacteristic
29Q8×Dic149C2211yescharacteristic
30Q8×Dic149C2211yescharacteristic
31C4×Dic298—21no—
32C4×Dic298C2211yescharacteristic
33C4×Dic298C2211yescharacteristic
34D4×Dic149C2211yescharacteristic
35#18011867—21no—
36#18011845C2211yescharacteristic
37#18011844C2211yescharacteristic
38#18011843C2211yescharacteristic
39#18011840C2211yescharacteristic
40#18011840C2211yescharacteristic
41#18011836C2211yescharacteristic
42#18011836C2211yescharacteristic
43#18011835C2211yescharacteristic
44#18011835C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011832C2211yescharacteristic
49C4×#11924746C2211yescharacteristic
50C8×Dic149C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×Q16×C149C2211yescharacteristic
53C2×SD16×C149C2211yescharacteristic
54#124×C149C2211yescharacteristic
55C4×Q8×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298D411yescharacteristic
61C2×Dic298C2311yescharacteristic
62C22×Dic149—21no—
63#14558726—22no—
64C2×#11924746C2311yescharacteristic
65C2×#11924746C2311yescharacteristic
66C4⋊Dic149—21no—
67C4⋊Dic149—21no—
68C4⋊Dic149—21no—
69C4⋊Dic149—21no—
70C4⋊Dic149D411yescharacteristic
71C4⋊Dic149C2311yescharacteristic
72C4⋊Dic149C2311yescharacteristic
73C4⋊Dic149C2311yescharacteristic
74#14558715—21no—
75#14558715—21no—
76#14558715—21no—
77#14558715—21no—
78#14558715—21no—
79#14558715—21no—
80#14558715—21no—
81#14558715D411yescharacteristic
82#14558715D411yescharacteristic
83C22⋊Dic149—21no—
84C22⋊Dic149—21no—
85C22⋊Dic149—21no—
86C4×Dic149—21no—
87C4×Dic149—21no—
88C4×Dic149—21no—
89C4×Dic149—21no—
90C4×Dic149C2311yescharacteristic
91C4×Dic149C2311yescharacteristic
92C2×Q8×C149C2311yescharacteristic
93C2×Q8×C149C2311yescharacteristic
94C2×D4×C149C2311yescharacteristic
95Q16×C149—22no—
96SD16×C149—22no—
97C2×C8×C149C2311yescharacteristic
98C2×C8×C149C2311yescharacteristic
99C4⋊C4×C149—21no—
100C4⋊C4×C149C2311yescharacteristic
101C22⋊C4×C149—21no—
102C22⋊C4×C149—21no—
103C42×C149—21no—
104C42×C149C2311yescharacteristic
105Dic298—22no—
106Dic298—21no—
107Dic298—21no—
108Dic298—42no—
109C2×Dic149—21no—
110C2×Dic149—21no—
111C2×Dic149—21no—
112C2×Dic149—21no—
113C2×Dic149—42no—
114C2×Dic149C2×D411yescharacteristic
115C2×Dic149C2×D411yescharacteristic
116C2×Dic149C2×D411yescharacteristic
117C2×Dic149C2×D411yescharacteristic
118#11924746—21no—
119#11924746—21no—
120C23×C149—21no—
121Q8×C149—21no—
122Q8×C149—21no—
123Q8×C149—21no—
124Q8×C149#4112yes—
125D4×C149—21no—
126D4×C149—21no—
127C2×C4×C149—21no—
128C2×C4×C149—21no—
129C2×C4×C149—21no—
130C2×C4×C149C2×D411yescharacteristic
131C2×C4×C149C2×D411yescharacteristic
132C2×C4×C149C2411yescharacteristic
133C8×C149—21no—
134C8×C149—21no—
135C22×C149—41no—
136C22×C149—41no—
137C22×C149—41no—
138C22×C149C22×D411yescharacteristic
139C4×C149—22no—
140C4×C149—21no—
141C4×C149—21no—
142C4×C149—41no—
143C4×C149—41no—
144C4×C149C2×#4111yescharacteristic
145C4×C1492−1+411yescharacteristic
146Dic149—21no—
147Dic149—21no—
148Dic149—21no—
149Dic149—41no—
150Dic149—41no—
151Dic149—41no—
152Dic149—41no—
153Dic149#13512yes—
154C2×C149—81no—
155C2×C149#54811yescharacteristic
156C2×C149C2×#13511yescharacteristic
157C2×C149#57811yescharacteristic
158C149#336411yescharacteristic, complemented, Sylow
159#3364—1491nomaximal, Sylow
160#557—1491no—
161#556—1491no—
162#488—1491no—
163#488—1491no—
164#487—1491no—
165#479—1491no—
166#479—1491no—
167#474—1491no—
168#464—1491no—
169#464D14911yescharacteristic
170#462—1491no—
171C8×Q8—1491no—
172C4×Q16—1491no—
173C4×Q16—1491no—
174C4×SD16—1491no—
175C2×Q16—1491no—
176C2×Q16C2×D14911yescharacteristic
177C2×SD16C2×D14911yescharacteristic
178C4⋊Q8—2981no—
179C4⋊Q8—1491no—
180C4⋊Q8—1491no—
181#126—2981no—
182#126—2981no—
183#125—2981no—
184#125—2981no—
185#125—1491no—
186#125—1491no—
187#124—1491no—
188#124C2×D14911yescharacteristic
189C22⋊Q8—2981no—
190C4×Q8—2981no—
191C4×Q8—1491no—
192C4×Q8—1491no—
193C4×Q8—1491no—
194C4×Q8—1491no—
195C4×Q8—1491no—
196C4×Q8C2×D14911yescharacteristic
197C4×D4—1491no—
198#117—2981no—
199#107—1491no—
200#107—1491no—
201#106—1491no—
202C4⋊C8—1491no—
203C4⋊C8—1491no—
204C4⋊C8C2×D14911yescharacteristic
205#103—1491no—
206#103—1491no—
207#103—1491no—
208#103—1491no—
209#103—1491no—
210#103—1491no—
211#103C2×D14911yescharacteristic
212#102—1491no—
213#102—1491no—
214#102C2×D14911yescharacteristic
215C4×C8—1491no—
216C4×C8—1491no—
217C4×C8—1491no—
218C2×Q8—2981no—
219C2×Q8—1491no—
220C2×Q8—1491no—
221C2×Q8C22×D14911yescharacteristic
222C2×Q8C22×D14911yescharacteristic
223C2×D4C22×D14911yescharacteristic
224C22×C4—2981no—
225Q16—22no—
226Q16—2982no—
227SD16—22no—
228C2×C8—1491no—
229C2×C8—1491no—
230C2×C8C22×D14911yescharacteristic
231C2×C8C22×D14911yescharacteristic
232C4⋊C4—21no—
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—2981no—
243C4⋊C4—2981no—
244C4⋊C4—1491no—
245C4⋊C4—1491no—
246C4⋊C4—1491no—
247C4⋊C4—1491no—
248C4⋊C4—1491no—
249C4⋊C4—1491no—
250C4⋊C4C22×D14911yescharacteristic
251C22⋊C4—21no—
252C22⋊C4—21no—
253C22⋊C4—2981no—
254C22⋊C4—2981no—
255C22⋊C4—2981no—
256C42—21no—
257C42—2981no—
258C42—2981no—
259C42—2981no—
260C42—2981no—
261C42—1491no—
262C42—1491no—
263C42C22×D14911yescharacteristic
264C23—21no—
265Q8—21no—
266Q8—21no—
267Q8—21no—
268Q8—2982no—
269Q8—2981no—
270Q8—2981no—
271Q8—5962no—
272Q8#1455873512yes—
273D4—21no—
274D4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—2981no—
279C2×C4—2981no—
280C2×C4—2981no—
281C2×C4—2981no—
282C2×C4—5962no—
283C2×C4—1491no—
284C2×C4—1491no—
285C2×C4—1491no—
286C2×C4—1491no—
287C2×C4D4×D14911yescharacteristic
288C2×C4D4×D14911yescharacteristic
289C2×C4C23×D14911yescharacteristic
290C8—21no—
291C8—21no—
292C8—2981no—
293C8—2981no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22C2×D4×D14911yescharacteristic
298C4—21no—
299C4—21no—
300C4—22no—
301C4—41no—
302C4—41no—
303C4—2981no—
304C4—2981no—
305C4—2981no—
306C4—5961no—
307C4—5961no—
308C4—5961no—
309C4—5961no—
310C4—1492no—
311C4C2×#1455873511yescharacteristic
312C4#1801195811yescharacteristic
313C2—81no—
314C2#2375028111yescharacteristic
315C2#135×D14911yescharacteristic
316C2#2375044111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#464×C149C2
socleC22×C149C22×D4
prime radicalC2×D4×C149C23
hypercenter#464D149
hypocenterC149#3364
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #23750351C2semidirect
5. #23749974C2semidirect
6. #23749933C2semidirect
7. #23749930C2semidirect
10. #23749833C2semidirect
11. #23749749C2semidirect
12. Q16×Dic149C2semidirect
13. C4×#14558726C2semidirect
158. C149#3364semidirect

Maximal subgroups

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

subgroupindex
#237503512
#237503442
#237499792
#237499782
#237499742
#237499332
#237499302
#237499032
#237498452
#237498332
#237497492
Q16×Dic1492
C4×#145587262
SD16×Dic1492
#464×C1492
#3364149