Finite Group Databasebeta

← #34079979

Subgroups — #34079979

Order 19328.

410 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752785C211yesmaximal, characteristic, complemented
2#23752779C211yesmaximal, characteristic
3#23752554C211yesmaximal, characteristic, complemented
4#23752550C211yesmaximal, characteristic, complemented
5#23752535C211yesmaximal, characteristic, complemented
6#23752534C211yesmaximal, characteristic, complemented
7#23752457C211yesmaximal, characteristic, complemented
8#23752455C211yesmaximal, characteristic, complemented
9#23752440C211yesmaximal, characteristic, complemented
10#23752438C211yesmaximal, characteristic, complemented
11#23752363C211yesmaximal, characteristic, complemented
12#23752349C211yesmaximal, characteristic, complemented
13#23752349C211yesmaximal, characteristic, complemented
14#23752177C211yesmaximal, characteristic, complemented
15#450×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×Q8×D151C2211yescharacteristic, complemented
18C2×#14558992C2211yescharacteristic
19C2×#14558992C2211yescharacteristic
20C2×#14558987C2211yescharacteristic, complemented
21C2×C8×D151C2211yescharacteristic, complemented
22#18012738—21no—
23#18012735—21no—
24#18012726—21no—
25#18012725—21no—
26#18012724—21no—
27#18012721—21no—
28#18012719C2211yescharacteristic, complemented
29#18012718C2211yescharacteristic
30#18012715C2211yescharacteristic, complemented
31#18012710C2211yescharacteristic
32#18012710C2211yescharacteristic
33#18012710C2211yescharacteristic
34#18012710C2211yescharacteristic
35#18012708—21no—
36#18012708—21no—
37#18012698C2211yescharacteristic
38#18012697C2211yescharacteristic, complemented
39#18012673C2211yescharacteristic, complemented
40#18012672C2211yescharacteristic, complemented
41#18012671C2211yescharacteristic, complemented
42#18012670C2211yescharacteristic, complemented
43#18012664C2211yescharacteristic, complemented
44#18012664C2211yescharacteristic, complemented
45#18012663C2211yescharacteristic, complemented
46#18012663C2211yescharacteristic, complemented
47#18012660C2211yescharacteristic
48#18012660C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic, complemented
51(C2×D151)⋊C8C2211yescharacteristic, complemented
52C22×D4×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic
54C2×SD16×C151C2211yescharacteristic
55C22⋊Q8×C151C2211yescharacteristic
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59#14559004—41no—
60#14559004—41no—
61C2×Dic302—21no—
62C2×Dic302D411yescharacteristic
63C2×Dic302C2311yescharacteristic
64Q8×D151—41no—
65Q8×D151—41no—
66C2×D604D411yescharacteristic
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151D411yescharacteristic
72C2×C22⋊D151D411yescharacteristic
73C2×C4×D151—21no—
74C2×C4×D151C2311yescharacteristic
75C2×C4×D151C2311yescharacteristic
76#14558992—41no—
77#14558992—41no—
78#14558987—41no—
79C2×C151⋊C8C2311yescharacteristic
80C2×C151⋊C8C2311yescharacteristic
81C8×D151—41no—
82C4⋊Dic151—21no—
83C4⋊Dic151C2311yescharacteristic
84C4⋊Dic151C2311yescharacteristic
85C4⋊Dic151C2311yescharacteristic
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90C22⋊Dic151—21no—
91C22⋊Dic151—21no—
92C22⋊Dic151—21no—
93C22⋊Dic151—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—21no—
97C4×Dic151—21no—
98C4×Dic151—21no—
99C24×C151—21no—
100C2×Q8×C151C2311yescharacteristic
101C2×D4×C151—21no—
102C2×D4×C151—41no—
103C2×D4×C151—41no—
104C2×D4×C151C2311yescharacteristic
105C2×D4×C151C2311yescharacteristic
106C22×C4×C151C2311yescharacteristic
107SD16×C151—41no—
108SD16×C151—41no—
109C2×C8×C151C2311yescharacteristic
110C2×C8×C151C2311yescharacteristic
111C4⋊C4×C151—21no—
112C4⋊C4×C151C2311yescharacteristic
113C22⋊C4×C151—21no—
114C22×D151C2×D411yescharacteristic
115C22×D151C2×D411yescharacteristic
116Dic302—21no—
117Dic302—21no—
118Dic302—41no—
119Dic302—42no—
120D604—41no—
121C22⋊D151—41no—
122C22⋊D151—41no—
123C22⋊D151—81no—
124C22⋊D151—81no—
125C22⋊D151—81no—
126C22⋊D151—81no—
127C2×Dic151—21no—
128C2×Dic151—21no—
129C2×Dic151—21no—
130C2×Dic151—21no—
131C2×Dic151C2×D411yescharacteristic
132C2×Dic151C2×D411yescharacteristic
133C4×D151—21no—
134C4×D151—21no—
135C4×D151—21no—
136C4×D151—21no—
137C4×D151—42no—
138C151⋊C8—21no—
139C151⋊C8—21no—
140C23×C151—21no—
141C23×C151—21no—
142C23×C151—42no—
143C23×C151—81no—
144C23×C151—81no—
145C23×C151C2×D411yescharacteristic
146Q8×C151—21no—
147Q8×C151—21no—
148D4×C151—21no—
149D4×C151—21no—
150D4×C151—21no—
151D4×C151—21no—
152D4×C151—42no—
153C2×C4×C151—21no—
154C2×C4×C151—21no—
155C2×C4×C151—21no—
156C2×C4×C151—21no—
157C2×C4×C151C2×D411yescharacteristic
158C2×C4×C151C2411yescharacteristic
159C8×C151—21no—
160C8×C151—21no—
161C22×C151—21no—
162C22×C151—21no—
163C22×C151—21no—
164C22×C151—41no—
165C22×C151—41no—
166C22×C151—41no—
167C22×C151—41no—
168C22×C151—41no—
169C22×C151—41no—
170C22×C151—84no—
171C22×C151C22×D411yescharacteristic
172C2×D151—21no—
173C2×D151—21no—
174C2×D151—21no—
175C2×D151—21no—
176C2×D151—21no—
177C2×D151—21no—
178C4×C151—21no—
179C4×C151—41no—
180C4×C151—41no—
181C4×C151H(5,𝔽2)11yescharacteristic
182C4×C151H(5,𝔽2)11yescharacteristic
183Dic151—21no—
184Dic151—21no—
185Dic151—41no—
186Dic151—41no—
187Dic151—41no—
188Dic151—41no—
189C2×C151—41no—
190C2×C151—81no—
191C2×C151—81no—
192C2×C151#53411yescharacteristic
193C2×C151#57711yescharacteristic
194C2×C151#57711yescharacteristic
195D151—41no—
196D151—41no—
197C151#320011yescharacteristic, complemented, Sylow
198#3200—1511nomaximal, Sylow
199#536—1511no—
200#535—1511no—
201#485—1511no—
202#485—1511no—
203#482—1511no—
204#482—1511no—
205#468—1511no—
206#468—1511no—
207#465—1511no—
208#465—1511no—
209#450—1511no—
210#450D15111yescharacteristic, complemented
211#448—1511no—
212#448—1511no—
213#408—1511no—
214C2×#41—1511no—
215C22×Q8—1511no—
216C22×D4C2×D15111yescharacteristic
217C2×SD16—1511no—
218C2×SD16—1511no—
219C2×SD16C2×D15111yescharacteristic
220C2×SD16C2×D15111yescharacteristic
221C2×M16—1511no—
222C22×C8—1511no—
223C4⋊Q8—3021no—
224#127—3021no—
225#124—3021no—
226#124—3021no—
227#123—3021no—
228#123—3021no—
229C22⋊Q8—1511no—
230C22⋊Q8—1511no—
231C22⋊Q8—1511no—
232C22⋊Q8C2×D15111yescharacteristic
233#121—1511no—
234#121—1511no—
235#121—1511no—
236#121—1511no—
237#120—3021no—
238#120—3021no—
239#117—1511no—
240#117—1511no—
241#107—1511no—
242#107—1511no—
243#106—1511no—
244#106—1511no—
245#103—1511no—
246#103—1511no—
247#103—1511no—
248#103—1511no—
249#102—1511no—
250#102—1511no—
251#102C2×D15111yescharacteristic
252#102C2×D15111yescharacteristic
253C22⋊C8—1511no—
254C22⋊C8—1511no—
255C22⋊C8—1511no—
256C22⋊C8C2×D15111yescharacteristic
257C24—21no—
258#41—6041no—
259#41—6041no—
260C2×Q8—3021no—
261C2×Q8—6041no—
262C2×Q8—6041no—
263C2×Q8—1511no—
264C2×Q8—1511no—
265C2×Q8C22×D15111yescharacteristic
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—3021no—
270C2×D4—3021no—
271C2×D4—3021no—
272C2×D4—3021no—
273C2×D4—1511no—
274C2×D4—1511no—
275C2×D4—1511no—
276C2×D4C22×D15111yescharacteristic
277C2×D4C22×D15111yescharacteristic
278C22×C4—3021no—
279C22×C4—1511no—
280C22×C4—1511no—
281C22×C4C22×D15111yescharacteristic
282SD16—41no—
283SD16—41no—
284SD16—6041no—
285SD16—6041no—
286M16—6041no—
287C2×C8—6041no—
288C2×C8—1511no—
289C2×C8—1511no—
290C2×C8C22×D15111yescharacteristic
291C2×C8C22×D15111yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—3021no—
294C4⋊C4—3021no—
295C4⋊C4—3021no—
296C4⋊C4—1511no—
297C4⋊C4—1511no—
298C4⋊C4—1511no—
299C4⋊C4C22×D15111yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—3021no—
302C22⋊C4—3021no—
303C22⋊C4—3021no—
304C22⋊C4—3021no—
305C22⋊C4—3021no—
306C22⋊C4—3021no—
307C22⋊C4—3021no—
308C22⋊C4—3021no—
309C22⋊C4—3021no—
310C42—3021no—
311C42—3021no—
312C23—21no—
313C23—21no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—1511no—
318C23—1511no—
319C23D4×D15111yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—3021no—
323Q8—3021no—
324Q8—6041no—
325Q8—6042no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—6041no—
332D4—6041no—
333D4—6041no—
334D4—12081no—
335D4—12081no—
336D4—12081no—
337D4—12081no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—3021no—
343C2×C4—3021no—
344C2×C4—3021no—
345C2×C4—3021no—
346C2×C4—3021no—
347C2×C4—3021no—
348C2×C4—3021no—
349C2×C4—3021no—
350C2×C4—6042no—
351C2×C4—1511no—
352C2×C4—1511no—
353C2×C4D4×D15111yescharacteristic
354C2×C4C23×D15111yescharacteristic
355C8—21no—
356C8—21no—
357C8—3021no—
358C8—3021no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—3021no—
370C22—3021no—
371C22—3021no—
372C22—3021no—
373C22—3021no—
374C22—3021no—
375C22C2×D4×D15111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—3021no—
380C4—3021no—
381C4—6041no—
382C4—6041no—
383C4—6041no—
384C4—6041no—
385C4#1801278411yescharacteristic
386C4#1801278411yescharacteristic
387C2—41no—
388C2—81no—
389C2—81no—
390C2—6041no—
391C2—6041no—
392C2#2375277211yescharacteristic
393C2#2375301811yescharacteristic
394C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#450×C151C2
socleC22×C151C22×D4
prime radical#23752779C2
hypercenter#450D151
hypocenterC151#3200
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #23752785C2semidirect
3. #23752554C2semidirect
4. #23752550C2semidirect
5. #23752535C2semidirect
6. #23752534C2semidirect
7. #23752457C2semidirect
8. #23752455C2semidirect
9. #23752440C2semidirect
10. #23752438C2semidirect
11. #23752363C2semidirect
12. #23752349C2semidirect
13. #23752349C2semidirect
14. #23752177C2semidirect
15. #450×C151C2semidirect
17. C2×Q8×D151C22semidirect
20. C2×#14558987C22semidirect
21. C2×C8×D151C22semidirect
28. #18012719C22semidirect
30. #18012715C22semidirect
38. #18012697C22semidirect
39. #18012673C22semidirect
40. #18012672C22semidirect
41. #18012671C22semidirect
42. #18012670C22semidirect
43. #18012664C22semidirect
44. #18012664C22semidirect
45. #18012663C22semidirect
46. #18012663C22semidirect
50. (C2×D151)⋊C8C22semidirect
51. (C2×D151)⋊C8C22semidirect
197. C151#3200semidirect
210. #450D151semidirect

Maximal subgroups

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

subgroupindex
#237527852
#237527792
#237525542
#237525502
#237525352
#237525342
#237524572
#237524552
#237524402
#237524382
#237523632
#237523492
#237521772
#450×C1512
#3200151