Finite Group Databasebeta

← #34081731

Subgroups — #34081731

Order 19328.

354 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752926C211yesmaximal, characteristic
2#23752920C211yesmaximal, characteristic, complemented
3#23752616C211yesmaximal, characteristic, complemented
4#23752551C211yesmaximal, characteristic, complemented
5#23752550C211yesmaximal, characteristic, complemented
6#23752524C211yesmaximal, characteristic, complemented
7#23752523C211yesmaximal, characteristic, complemented
8#23752505C211yesmaximal, characteristic, complemented
9#23752500C211yesmaximal, characteristic, complemented
10#23752455C211yesmaximal, characteristic, complemented
11SD16×Dic151C211yesmaximal, characteristic, complemented
12#23752288C211yesmaximal, characteristic, complemented
13#23752254C211yesmaximal, characteristic, complemented
14#23752253C211yesmaximal, characteristic, complemented
15#468×C151C211yesmaximal, characteristic, complemented
16C2×#14558987C2211yescharacteristic
17#18012738C2211yescharacteristic
18#18012738C2211yescharacteristic
19#18012729—21no—
20#18012726—21no—
21#18012725—21no—
22#18012719—21no—
23#18012716—21no—
24#18012715C2211yescharacteristic
25#18012711—21no—
26#18012710C2211yescharacteristic
27Q8×Dic151C2211yescharacteristic
28D4×Dic151C2211yescharacteristic
29C4×C22⋊D151C2211yescharacteristic
30(C22⋊D151)⋊C4—21no—
31#18012698C2211yescharacteristic
32#18012697C2211yescharacteristic
33#18012695—21no—
34C2×C4⋊Dic151C2211yescharacteristic
35C4⋊C4×D151C2211yescharacteristic
36#18012673C2211yescharacteristic
37#18012673C2211yescharacteristic
38#18012672C2211yescharacteristic
39#18012672C2211yescharacteristic
40#18012672C2211yescharacteristic
41#18012671C2211yescharacteristic
42#18012671C2211yescharacteristic
43#18012670C2211yescharacteristic
44Dic151⋊C8C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012663C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012660C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×SD16×C151C2211yescharacteristic
53C2×M16×C151C2211yescharacteristic
54C22⋊Q8×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic
56#107×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302—21no—
61C2×C22⋊D151—21no—
62C2×C22⋊D151D411yescharacteristic
63C22×Dic151—21no—
64C22×Dic151—21no—
65C2×C4×D151—21no—
66C2×C4×D151C2311yescharacteristic
67#14558987—22no—
68C2×C151⋊C8C2311yescharacteristic
69C2×C151⋊C8C2311yescharacteristic
70C4⋊Dic151—21no—
71C4⋊Dic151—21no—
72C4⋊Dic151C2311yescharacteristic
73C4⋊Dic151C2311yescharacteristic
74C4⋊Dic151C2311yescharacteristic
75C4⋊Dic151C2311yescharacteristic
76Dic151⋊C4—21no—
77Dic151⋊C4—21no—
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4D411yescharacteristic
81C22⋊Dic151—21no—
82C22⋊Dic151—21no—
83C22⋊Dic151—21no—
84C22⋊Dic151D411yescharacteristic
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4D411yescharacteristic
88C4×Dic151—21no—
89C4×Dic151—21no—
90C4×Dic151—21no—
91C4×Dic151C2311yescharacteristic
92C2×Q8×C151C2311yescharacteristic
93C2×D4×C151—21no—
94C2×D4×C151C2311yescharacteristic
95C22×C4×C151C2311yescharacteristic
96SD16×C151—22no—
97M16×C151—22no—
98C2×C8×C151C2311yescharacteristic
99C2×C8×C151C2311yescharacteristic
100C4⋊C4×C151—21no—
101C4⋊C4×C151C2311yescharacteristic
102C4⋊C4×C151C2311yescharacteristic
103C22⋊C4×C151—21no—
104C22⋊C4×C151—21no—
105C22×D151C2×D411yescharacteristic
106Dic302—81no—
107Dic302—81no—
108C22⋊D151—22no—
109C22⋊D151—81no—
110C2×Dic151—21no—
111C2×Dic151—21no—
112C2×Dic151—21no—
113C2×Dic151—21no—
114C2×Dic151—42no—
115C2×Dic151—81no—
116C2×Dic151C2×D411yescharacteristic
117C2×Dic151C2×D411yescharacteristic
118C2×Dic151C2×D411yescharacteristic
119C4×D151—21no—
120C4×D151—21no—
121C4×D151—81no—
122C151⋊C8—21no—
123C151⋊C8—21no—
124C23×C151—21no—
125C23×C151C2×D411yescharacteristic
126Q8×C151—21no—
127Q8×C151—21no—
128D4×C151—21no—
129D4×C151—21no—
130D4×C151—81no—
131C2×C4×C151—21no—
132C2×C4×C151—21no—
133C2×C4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151C2×D411yescharacteristic
137C2×C4×C151C2411yescharacteristic
138C8×C151—21no—
139C8×C151#4112yes—
140C22×C151—21no—
141C22×C151—21no—
142C22×C151—21no—
143C22×C151—41no—
144C22×C151—41no—
145C22×C151—41no—
146C22×C151C22×D411yescharacteristic
147C2×D151—21no—
148C2×D151—21no—
149C2×D151—21no—
150C4×C151—21no—
151C4×C151—41no—
152C4×C151—41no—
153C4×C151—41no—
154C4×C151C2×#4111yescharacteristic
155C4×C1512−1+411yescharacteristic
156Dic151—21no—
157Dic151—21no—
158Dic151—41no—
159Dic151—41no—
160Dic151—41no—
161Dic151—41no—
162Dic151#13712yes—
163C2×C151—41no—
164C2×C151—81no—
165C2×C151#54711yescharacteristic
166C2×C151C2×#13711yescharacteristic
167C2×C151#57611yescharacteristic
168D151—41no—
169C151#335711yescharacteristic, complemented, Sylow
170#3357—1511nomaximal, Sylow
171#555—1511no—
172#554—1511no—
173#500—1511no—
174#485—1511no—
175#485—1511no—
176#480—1511no—
177#480—1511no—
178#477—1511no—
179#476—1511no—
180#468—1511no—
181#468D15111yescharacteristic, complemented
182C4×SD16—1511no—
183#436—1511no—
184#428—1511no—
185#428—1511no—
186C2×SD16C2×D15111yescharacteristic
187C2×M16—1511no—
188C2×M16C2×D15111yescharacteristic
189C4⋊Q8—1511no—
190C4⋊Q8—1511no—
191#125—3021no—
192#124—3021no—
193#124—3021no—
194C22⋊Q8—3021no—
195C22⋊Q8—3021no—
196C22⋊Q8—1511no—
197C22⋊Q8C2×D15111yescharacteristic
198#121—3021no—
199#121—1511no—
200#121C2×D15111yescharacteristic
201C4×Q8—1511no—
202C4×D4—3021no—
203C4×D4—1511no—
204C4×D4—1511no—
205#117—3021no—
206#117—1511no—
207#117—1511no—
208C2×C4⋊C4—1511no—
209C2×C4⋊C4—1511no—
210#107—1511no—
211#107—1511no—
212#107—1511no—
213#107—1511no—
214#107—1511no—
215#107C2×D15111yescharacteristic
216#106—1511no—
217#106—1511no—
218#106—1511no—
219C4⋊C8—1511no—
220#103—1511no—
221#103—1511no—
222#103C2×D15111yescharacteristic
223#102—1511no—
224#102—1511no—
225#102C2×D15111yescharacteristic
226C22⋊C8—1511no—
227C22⋊C8—1511no—
228C4×C8—1511no—
229C2×Q8—3021no—
230C2×Q8—3021no—
231C2×Q8C22×D15111yescharacteristic
232C2×D4—21no—
233C2×D4—3021no—
234C2×D4—1511no—
235C2×D4C22×D15111yescharacteristic
236C22×C4—3021no—
237C22×C4—3021no—
238C22×C4—3021no—
239C22×C4—1511no—
240C22×C4C22×D15111yescharacteristic
241SD16—22no—
242M16—22no—
243M16—3022no—
244C2×C8—1511no—
245C2×C8—1511no—
246C2×C8C22×D15111yescharacteristic
247C2×C8C22×D15111yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—3021no—
250C4⋊C4—3021no—
251C4⋊C4—3021no—
252C4⋊C4—3021no—
253C4⋊C4—3021no—
254C4⋊C4—3021no—
255C4⋊C4—1511no—
256C4⋊C4—1511no—
257C4⋊C4—1511no—
258C4⋊C4—1511no—
259C4⋊C4—1511no—
260C4⋊C4C22×D15111yescharacteristic
261C4⋊C4C22×D15111yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—3021no—
265C22⋊C4—3021no—
266C22⋊C4—3021no—
267C22⋊C4—3021no—
268C22⋊C4—3021no—
269C22⋊C4—1511no—
270C22⋊C4—1511no—
271C42—3021no—
272C42—3021no—
273C42—3021no—
274C42—1511no—
275C23—21no—
276C23—1511no—
277C23D4×D15111yescharacteristic
278Q8—21no—
279Q8—21no—
280Q8—12081no—
281Q8—12081no—
282D4—21no—
283D4—21no—
284D4—81no—
285D4—3022no—
286D4—12081no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—3021no—
293C2×C4—3021no—
294C2×C4—3021no—
295C2×C4—3021no—
296C2×C4—3021no—
297C2×C4—3021no—
298C2×C4—6042no—
299C2×C4—1511no—
300C2×C4—1511no—
301C2×C4—1511no—
302C2×C4—12081no—
303C2×C4—12081no—
304C2×C4D4×D15111yescharacteristic
305C2×C4C23×D15111yescharacteristic
306C8—21no—
307C8—3021no—
308C8—3021no—
309C8#1455900312yes—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—3021no—
317C22—3021no—
318C22—3021no—
319C22C2×D4×D15111yescharacteristic
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—3021no—
325C4—3021no—
326C4—6041no—
327C4—6041no—
328C4—6041no—
329C4—6041no—
330C4—1512no—
331C4C2×#1455900311yescharacteristic
332C4#1801278611yescharacteristic
333C2—41no—
334C2—81no—
335C2—6041no—
336C2#2375286211yescharacteristic
337C2#137×D15111yescharacteristic
338C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#468×C151C2
socleC22×C151C22×D4
prime radical#23752926C2
hypercenter#468D151
hypocenterC151#3357
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
2. #23752920C2semidirect
3. #23752616C2semidirect
4. #23752551C2semidirect
5. #23752550C2semidirect
6. #23752524C2semidirect
7. #23752523C2semidirect
8. #23752505C2semidirect
9. #23752500C2semidirect
10. #23752455C2semidirect
11. SD16×Dic151C2semidirect
12. #23752288C2semidirect
13. #23752254C2semidirect
14. #23752253C2semidirect
15. #468×C151C2semidirect
169. C151#3357semidirect
181. #468D151semidirect

Maximal subgroups

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

subgroupindex
#237529262
#237529202
#237526162
#237525512
#237525502
#237525242
#237525232
#237525052
#237525002
#237524552
SD16×Dic1512
#237522882
#237522542
#237522532
#468×C1512
#3357151