Finite Group Databasebeta

← #34080578

Subgroups — #34080578

Order 19328.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752834C211yesmaximal, characteristic, complemented
2#23752831C211yesmaximal, characteristic, complemented
3#23752503C211yesmaximal, characteristic, complemented
4#23752500C211yesmaximal, characteristic, complemented
5#23752497C211yesmaximal, characteristic, complemented
6#23752495C211yesmaximal, characteristic, complemented
7#23752467C211yesmaximal, characteristic, complemented
8#23752464C211yesmaximal, characteristic
9#23752444C211yesmaximal, characteristic, complemented
10#23752438C211yesmaximal, characteristic, complemented
11#23752436C211yesmaximal, characteristic, complemented
12#23752429C211yesmaximal, characteristic, complemented
13#23752424C211yesmaximal, characteristic, complemented
14#23752237C211yesmaximal, characteristic, complemented
15#464×C151C211yesmaximal, characteristic, complemented
16C2×#14558991C2211yescharacteristic
17C2×#14558989C2211yescharacteristic
18C2×#14558987C2211yescharacteristic
19C2×C8×D151C2211yescharacteristic
20#18012739C2211yescharacteristic
21#18012738C2211yescharacteristic
22#18012733—21no—
23#18012732—21no—
24#18012728C2211yescharacteristic
25#18012727—21no—
26#18012725—21no—
27#18012724—21no—
28#18012723—21no—
29#18012717—21no—
30#18012716—21no—
31#18012715C2211yescharacteristic
32#18012715C2211yescharacteristic
33#18012714C2211yescharacteristic
34#18012710C2211yescharacteristic
35Q8×Dic151C2211yescharacteristic
36C4×D604C2211yescharacteristic
37D4×Dic151C2211yescharacteristic
38#18012696C2211yescharacteristic
39#18012671C2211yescharacteristic
40#18012671C2211yescharacteristic
41#18012670C2211yescharacteristic
42#18012670C2211yescharacteristic
43C4⋊(C151⋊C8)C2211yescharacteristic
44Dic151⋊C8C2211yescharacteristic
45Dic151⋊C8C2211yescharacteristic
46#18012663C2211yescharacteristic
47#18012663C2211yescharacteristic
48#18012663C2211yescharacteristic
49#18012661C2211yescharacteristic
50#18012661C2211yescharacteristic
51#18012660C2211yescharacteristic
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×Dic302—21no—
61C2×D604—21no—
62C2×D604C2311yescharacteristic
63C2×C22⋊D151—21no—
64C22×Dic151—21no—
65C2×C4×D151—21no—
66C2×C4×D151C2311yescharacteristic
67#14558991—41no—
68#14558989—41no—
69#14558987—41no—
70C2×C151⋊C8C2311yescharacteristic
71C2×C151⋊C8C2311yescharacteristic
72C8×D151—41no—
73C4⋊Dic151—21no—
74C4⋊Dic151—21no—
75C4⋊Dic151C2311yescharacteristic
76C4⋊Dic151C2311yescharacteristic
77C4⋊Dic151C2311yescharacteristic
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4D411yescharacteristic
82Dic151⋊C4D411yescharacteristic
83C22⋊Dic151—21no—
84C22⋊Dic151—21no—
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4D411yescharacteristic
92(C2×D151)⋊C4D411yescharacteristic
93C4×Dic151—21no—
94C4×Dic151C2311yescharacteristic
95C2×Q8×C151C2311yescharacteristic
96C2×Q8×C151C2311yescharacteristic
97C2×D4×C151C2311yescharacteristic
98Q16×C151—41no—
99SD16×C151—41no—
100C2×C8×C151C2311yescharacteristic
101C2×C8×C151C2311yescharacteristic
102C4⋊C4×C151—21no—
103C4⋊C4×C151C2311yescharacteristic
104C22⋊C4×C151—21no—
105C22⋊C4×C151—21no—
106C42×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151C2×D411yescharacteristic
110Dic302—81no—
111Dic302—81no—
112D604—21no—
113D604—21no—
114D604—81no—
115C22⋊D151—81no—
116C2×Dic151—21no—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151—81no—
120C2×Dic151C2×D411yescharacteristic
121C2×Dic151C2×D411yescharacteristic
122C2×Dic151C2×D411yescharacteristic
123C4×D151—21no—
124C4×D151—21no—
125C4×D151—81no—
126C151⋊C8—21no—
127C151⋊C8—21no—
128C23×C151—21no—
129Q8×C151—21no—
130Q8×C151—21no—
131Q8×C151—21no—
132Q8×C151—21no—
133D4×C151—21no—
134D4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151C2×D411yescharacteristic
139C2×C4×C151C2×D411yescharacteristic
140C2×C4×C151C2411yescharacteristic
141C8×C151—21no—
142C8×C151—21no—
143C22×C151—41no—
144C22×C151—41no—
145C22×C151—41no—
146C22×C151C22×D411yescharacteristic
147C2×D151—21no—
148C2×D151—21no—
149C2×D151—21no—
150C2×D151—41no—
151C2×D151—41no—
152C2×D151—41no—
153C4×C151—21no—
154C4×C151—21no—
155C4×C151—41no—
156C4×C151—41no—
157C4×C151—41no—
158C4×C151H(5,𝔽2)11yescharacteristic
159C4×C1512−1+411yescharacteristic
160Dic151—21no—
161Dic151—21no—
162Dic151—21no—
163Dic151—41no—
164Dic151—41no—
165Dic151—41no—
166C2×C151—81no—
167C2×C151#53711yescharacteristic
168C2×C151#57711yescharacteristic
169C2×C151#57711yescharacteristic
170D151—41no—
171D151—81no—
172C151#326311yescharacteristic, complemented, Sylow
173#3263—1511nomaximal, Sylow
174#542—1511no—
175#542—1511no—
176#476—1511no—
177#476—1511no—
178#475—1511no—
179#475—1511no—
180#470—1511no—
181#469—1511no—
182#465—1511no—
183#465—1511no—
184#464—1511no—
185#464D15111yescharacteristic, complemented
186#463—1511no—
187#463—1511no—
188#424—1511no—
189C2×Q16C2×D15111yescharacteristic
190C2×SD16—1511no—
191C2×SD16C2×D15111yescharacteristic
192C2×D8—1511no—
193C2×M16—1511no—
194C22×C8—1511no—
195C4⋊Q8—1511no—
196C4⋊Q8—1511no—
197#126—3021no—
198#126—3021no—
199#124—3021no—
200#124—3021no—
201#124—1511no—
202#124C2×D15111yescharacteristic
203#123—3021no—
204#123—3021no—
205C22⋊Q8—3021no—
206C22⋊Q8—3021no—
207C22⋊Q8—1511no—
208C22⋊Q8—1511no—
209#121—1511no—
210#121—1511no—
211C4×Q8—1511no—
212C4×Q8C2×D15111yescharacteristic
213C4×D4—1511no—
214C4×D4—1511no—
215#117—1511no—
216#106—1511no—
217#106—1511no—
218#106—1511no—
219#106—1511no—
220C4⋊C8—1511no—
221C4⋊C8—1511no—
222C4⋊C8—1511no—
223C4⋊C8C2×D15111yescharacteristic
224#103—1511no—
225#103—1511no—
226#103—1511no—
227#103C2×D15111yescharacteristic
228#102—1511no—
229#102—1511no—
230#102—1511no—
231#102C2×D15111yescharacteristic
232C2×Q8—3021no—
233C2×Q8—3021no—
234C2×Q8C22×D15111yescharacteristic
235C2×Q8C22×D15111yescharacteristic
236C2×D4—3021no—
237C2×D4—3021no—
238C2×D4—1511no—
239C2×D4C22×D15111yescharacteristic
240C22×C4—3021no—
241C22×C4—3021no—
242C22×C4—1511no—
243Q16—41no—
244SD16—41no—
245SD16—6041no—
246D8—6041no—
247M16—6041no—
248C2×C8—6041no—
249C2×C8—1511no—
250C2×C8—1511no—
251C2×C8C22×D15111yescharacteristic
252C2×C8C22×D15111yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—3021no—
255C4⋊C4—3021no—
256C4⋊C4—3021no—
257C4⋊C4—3021no—
258C4⋊C4—3021no—
259C4⋊C4—1511no—
260C4⋊C4—1511no—
261C4⋊C4—1511no—
262C4⋊C4—1511no—
263C4⋊C4—1511no—
264C4⋊C4C22×D15111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—3021no—
268C22⋊C4—3021no—
269C22⋊C4—3021no—
270C22⋊C4—3021no—
271C22⋊C4—3021no—
272C22⋊C4—3021no—
273C22⋊C4—3021no—
274C22⋊C4—3021no—
275C22⋊C4—1511no—
276C22⋊C4—1511no—
277C42—21no—
278C42—3021no—
279C42—1511no—
280C42C22×D15111yescharacteristic
281C23—21no—
282C23—3021no—
283C23—1511no—
284Q8—21no—
285Q8—21no—
286Q8—21no—
287Q8—21no—
288Q8—12081no—
289Q8—12081no—
290D4—21no—
291D4—21no—
292D4—3021no—
293D4—3021no—
294D4—12081no—
295D4—12081no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—3021no—
300C2×C4—3021no—
301C2×C4—3021no—
302C2×C4—3021no—
303C2×C4—3021no—
304C2×C4—1511no—
305C2×C4—1511no—
306C2×C4—1511no—
307C2×C4—12081no—
308C2×C4—12081no—
309C2×C4D4×D15111yescharacteristic
310C2×C4D4×D15111yescharacteristic
311C2×C4C23×D15111yescharacteristic
312C8—21no—
313C8—21no—
314C8—3021no—
315C8—3021no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—3021no—
320C22—3021no—
321C22—3021no—
322C22—6041no—
323C22—6041no—
324C22—6041no—
325C22C2×D4×D15111yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—3021no—
332C4—3021no—
333C4—3021no—
334C4—6041no—
335C4—6041no—
336C4—6041no—
337C4#1801278411yescharacteristic
338C4#1801278611yescharacteristic
339C2—81no—
340C2—6041no—
341C2—12081no—
342C2#2375279111yescharacteristic
343C2#2375301911yescharacteristic
344C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#464×C151C2
socleC22×C151C22×D4
prime radical#23752464C2
hypercenter#464D151
hypocenterC151#3263
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. #23752834C2semidirect
2. #23752831C2semidirect
3. #23752503C2semidirect
4. #23752500C2semidirect
5. #23752497C2semidirect
6. #23752495C2semidirect
7. #23752467C2semidirect
9. #23752444C2semidirect
10. #23752438C2semidirect
11. #23752436C2semidirect
12. #23752429C2semidirect
13. #23752424C2semidirect
14. #23752237C2semidirect
15. #464×C151C2semidirect
172. C151#3263semidirect
185. #464D151semidirect

Maximal subgroups

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

subgroupindex
#237528342
#237528312
#237525032
#237525002
#237524972
#237524952
#237524672
#237524642
#237524442
#237524382
#237524362
#237524292
#237524242
#237522372
#464×C1512
#3263151