Finite Group Databasebeta

← #34081790

Subgroups — #34081790

Order 19328.

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#23752938C211yesmaximal, characteristic, complemented
2#23752931C211yesmaximal, characteristic
3#23752566C211yesmaximal, characteristic
4#23752565C211yesmaximal, characteristic
5#23752561C211yesmaximal, characteristic, complemented
6#23752520C211yesmaximal, characteristic, complemented
7#23752517C211yesmaximal, characteristic, complemented
8#23752490C211yesmaximal, characteristic
9#23752432C211yesmaximal, characteristic
10#23752420C211yesmaximal, characteristic, complemented
11#23752336C211yesmaximal, characteristic, complemented
12Q16×Dic151C211yesmaximal, characteristic, complemented
13C4×#14558994C211yesmaximal, characteristic, complemented
14SD16×Dic151C211yesmaximal, characteristic
15#464×C151C211yesmaximal, characteristic
16C2×#14558994C2211yescharacteristic
17#18012738—21no—
18#18012738C2211yescharacteristic
19#18012737C2211yescharacteristic
20#18012732—21no—
21#18012732—21no—
22#18012731—21no—
23#18012731C2211yescharacteristic
24#18012730—21no—
25#18012730C2211yescharacteristic
26#18012726C2211yescharacteristic
27#18012716—21no—
28Q8×Dic151C2211yescharacteristic
29Q8×Dic151C2211yescharacteristic
30Q8×Dic151C2211yescharacteristic
31C4×Dic302—21no—
32C4×Dic302C2211yescharacteristic
33C4×Dic302C2211yescharacteristic
34D4×Dic151C2211yescharacteristic
35#18012695—21no—
36#18012673C2211yescharacteristic
37#18012672C2211yescharacteristic
38#18012671C2211yescharacteristic
39Dic151⋊C8C2211yescharacteristic
40Dic151⋊C8C2211yescharacteristic
41#18012664C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012663C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012662C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012660C2211yescharacteristic
49C4×C151⋊C8C2211yescharacteristic
50C8×Dic151C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×Q16×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic
54#124×C151C2211yescharacteristic
55C4×Q8×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302D411yescharacteristic
61C2×Dic302C2311yescharacteristic
62C22×Dic151—21no—
63#14558994—22no—
64C2×C151⋊C8C2311yescharacteristic
65C2×C151⋊C8C2311yescharacteristic
66C4⋊Dic151—21no—
67C4⋊Dic151—21no—
68C4⋊Dic151—21no—
69C4⋊Dic151—21no—
70C4⋊Dic151D411yescharacteristic
71C4⋊Dic151C2311yescharacteristic
72C4⋊Dic151C2311yescharacteristic
73C4⋊Dic151C2311yescharacteristic
74Dic151⋊C4—21no—
75Dic151⋊C4—21no—
76Dic151⋊C4—21no—
77Dic151⋊C4—21no—
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4D411yescharacteristic
82Dic151⋊C4D411yescharacteristic
83C22⋊Dic151—21no—
84C22⋊Dic151—21no—
85C22⋊Dic151—21no—
86C4×Dic151—21no—
87C4×Dic151—21no—
88C4×Dic151—21no—
89C4×Dic151—21no—
90C4×Dic151C2311yescharacteristic
91C4×Dic151C2311yescharacteristic
92C2×Q8×C151C2311yescharacteristic
93C2×Q8×C151C2311yescharacteristic
94C2×D4×C151C2311yescharacteristic
95Q16×C151—22no—
96SD16×C151—22no—
97C2×C8×C151C2311yescharacteristic
98C2×C8×C151C2311yescharacteristic
99C4⋊C4×C151—21no—
100C4⋊C4×C151C2311yescharacteristic
101C22⋊C4×C151—21no—
102C22⋊C4×C151—21no—
103C42×C151—21no—
104C42×C151C2311yescharacteristic
105Dic302—22no—
106Dic302—21no—
107Dic302—21no—
108Dic302—42no—
109C2×Dic151—21no—
110C2×Dic151—21no—
111C2×Dic151—21no—
112C2×Dic151—21no—
113C2×Dic151—42no—
114C2×Dic151C2×D411yescharacteristic
115C2×Dic151C2×D411yescharacteristic
116C2×Dic151C2×D411yescharacteristic
117C2×Dic151C2×D411yescharacteristic
118C151⋊C8—21no—
119C151⋊C8—21no—
120C23×C151—21no—
121Q8×C151—21no—
122Q8×C151—21no—
123Q8×C151—21no—
124Q8×C151#4112yes—
125D4×C151—21no—
126D4×C151—21no—
127C2×C4×C151—21no—
128C2×C4×C151—21no—
129C2×C4×C151—21no—
130C2×C4×C151C2×D411yescharacteristic
131C2×C4×C151C2×D411yescharacteristic
132C2×C4×C151C2411yescharacteristic
133C8×C151—21no—
134C8×C151—21no—
135C22×C151—41no—
136C22×C151—41no—
137C22×C151—41no—
138C22×C151C22×D411yescharacteristic
139C4×C151—22no—
140C4×C151—21no—
141C4×C151—21no—
142C4×C151—41no—
143C4×C151—41no—
144C4×C151C2×#4111yescharacteristic
145C4×C1512−1+411yescharacteristic
146Dic151—21no—
147Dic151—21no—
148Dic151—21no—
149Dic151—41no—
150Dic151—41no—
151Dic151—41no—
152Dic151—41no—
153Dic151#13512yes—
154C2×C151—81no—
155C2×C151#54811yescharacteristic
156C2×C151C2×#13511yescharacteristic
157C2×C151#57811yescharacteristic
158C151#336411yescharacteristic, complemented, Sylow
159#3364—1511nomaximal, Sylow
160#557—1511no—
161#556—1511no—
162#488—1511no—
163#488—1511no—
164#487—1511no—
165#479—1511no—
166#479—1511no—
167#474—1511no—
168#464—1511no—
169#464D15111yescharacteristic
170#462—1511no—
171C8×Q8—1511no—
172C4×Q16—1511no—
173C4×Q16—1511no—
174C4×SD16—1511no—
175C2×Q16—1511no—
176C2×Q16C2×D15111yescharacteristic
177C2×SD16C2×D15111yescharacteristic
178C4⋊Q8—3021no—
179C4⋊Q8—1511no—
180C4⋊Q8—1511no—
181#126—3021no—
182#126—3021no—
183#125—3021no—
184#125—3021no—
185#125—1511no—
186#125—1511no—
187#124—1511no—
188#124C2×D15111yescharacteristic
189C22⋊Q8—3021no—
190C4×Q8—3021no—
191C4×Q8—1511no—
192C4×Q8—1511no—
193C4×Q8—1511no—
194C4×Q8—1511no—
195C4×Q8—1511no—
196C4×Q8C2×D15111yescharacteristic
197C4×D4—1511no—
198#117—3021no—
199#107—1511no—
200#107—1511no—
201#106—1511no—
202C4⋊C8—1511no—
203C4⋊C8—1511no—
204C4⋊C8C2×D15111yescharacteristic
205#103—1511no—
206#103—1511no—
207#103—1511no—
208#103—1511no—
209#103—1511no—
210#103—1511no—
211#103C2×D15111yescharacteristic
212#102—1511no—
213#102—1511no—
214#102C2×D15111yescharacteristic
215C4×C8—1511no—
216C4×C8—1511no—
217C4×C8—1511no—
218C2×Q8—3021no—
219C2×Q8—1511no—
220C2×Q8—1511no—
221C2×Q8C22×D15111yescharacteristic
222C2×Q8C22×D15111yescharacteristic
223C2×D4C22×D15111yescharacteristic
224C22×C4—3021no—
225Q16—22no—
226Q16—3022no—
227SD16—22no—
228C2×C8—1511no—
229C2×C8—1511no—
230C2×C8C22×D15111yescharacteristic
231C2×C8C22×D15111yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—3021no—
234C4⋊C4—3021no—
235C4⋊C4—3021no—
236C4⋊C4—3021no—
237C4⋊C4—3021no—
238C4⋊C4—3021no—
239C4⋊C4—3021no—
240C4⋊C4—3021no—
241C4⋊C4—3021no—
242C4⋊C4—3021no—
243C4⋊C4—3021no—
244C4⋊C4—1511no—
245C4⋊C4—1511no—
246C4⋊C4—1511no—
247C4⋊C4—1511no—
248C4⋊C4—1511no—
249C4⋊C4—1511no—
250C4⋊C4C22×D15111yescharacteristic
251C22⋊C4—21no—
252C22⋊C4—21no—
253C22⋊C4—3021no—
254C22⋊C4—3021no—
255C22⋊C4—3021no—
256C42—21no—
257C42—3021no—
258C42—3021no—
259C42—3021no—
260C42—3021no—
261C42—1511no—
262C42—1511no—
263C42C22×D15111yescharacteristic
264C23—21no—
265Q8—21no—
266Q8—21no—
267Q8—21no—
268Q8—3022no—
269Q8—3021no—
270Q8—3021no—
271Q8—6042no—
272Q8#1455900312yes—
273D4—21no—
274D4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—3021no—
279C2×C4—3021no—
280C2×C4—3021no—
281C2×C4—3021no—
282C2×C4—6042no—
283C2×C4—1511no—
284C2×C4—1511no—
285C2×C4—1511no—
286C2×C4—1511no—
287C2×C4D4×D15111yescharacteristic
288C2×C4D4×D15111yescharacteristic
289C2×C4C23×D15111yescharacteristic
290C8—21no—
291C8—21no—
292C8—3021no—
293C8—3021no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22C2×D4×D15111yescharacteristic
298C4—21no—
299C4—21no—
300C4—22no—
301C4—41no—
302C4—41no—
303C4—3021no—
304C4—3021no—
305C4—3021no—
306C4—6041no—
307C4—6041no—
308C4—6041no—
309C4—6041no—
310C4—1512no—
311C4C2×#1455900311yescharacteristic
312C4#1801278611yescharacteristic
313C2—81no—
314C2#2375286811yescharacteristic
315C2#135×D15111yescharacteristic
316C2#2375302811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#464×C151C2
socleC22×C151C22×D4
prime radicalC2×D4×C151C23
hypercenter#464D151
hypocenterC151#3364
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #23752938C2semidirect
5. #23752561C2semidirect
6. #23752520C2semidirect
7. #23752517C2semidirect
10. #23752420C2semidirect
11. #23752336C2semidirect
12. Q16×Dic151C2semidirect
13. C4×#14558994C2semidirect
158. C151#3364semidirect

Maximal subgroups

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

subgroupindex
#237529382
#237529312
#237525662
#237525652
#237525612
#237525202
#237525172
#237524902
#237524322
#237524202
#237523362
Q16×Dic1512
C4×#145589942
SD16×Dic1512
#464×C1512
#3364151