Finite Group Databasebeta

← #34079061

Subgroups — #34079061

Order 19328.

418 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752778C211yesmaximal, characteristic
2#23752693C211yesmaximal, characteristic, complemented
3#23752539C211yesmaximal, characteristic, complemented
4#23752537C211yesmaximal, characteristic, complemented
5#23752534C211yesmaximal, characteristic, complemented
6#23752533C211yesmaximal, characteristic, complemented
7#23752530C211yesmaximal, characteristic, complemented
8#23752529C211yesmaximal, characteristic, complemented
9#23752527C211yesmaximal, characteristic, complemented
10#23752253C211yesmaximal, characteristic, complemented
11#23752249C211yesmaximal, characteristic, complemented
12#23752215C211yesmaximal, characteristic, complemented
13#102×D151C211yesmaximal, characteristic, complemented
14#23752177C211yesmaximal, characteristic, complemented
15#480×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×D4×D151C2211yescharacteristic
18C2×#14558987C2211yescharacteristic
19C2×C8×D151C2211yescharacteristic
20#18012735—21no—
21#18012725—21no—
22#18012714C2211yescharacteristic
23#18012713C2211yescharacteristic
24#18012710C2211yescharacteristic
25#18012709—21no—
26#18012707—21no—
27#18012704—21no—
28#18012701—21no—
29C4×C22⋊D151—21no—
30C4×C22⋊D151—21no—
31#18012698C2211yescharacteristic, complemented
32#18012697C2211yescharacteristic
33#18012697C2211yescharacteristic
34#18012697C2211yescharacteristic, complemented
35C4⋊C4×D151C2211yescharacteristic
36C4⋊C4×D151C2211yescharacteristic, complemented
37#18012673C2211yescharacteristic, complemented
38#18012672C2211yescharacteristic, complemented
39#18012671C2211yescharacteristic, complemented
40#18012670C2211yescharacteristic, complemented
41#18012670C2211yescharacteristic, complemented
42#18012670C2211yescharacteristic, complemented
43#18012661C2211yescharacteristic
44#18012661C2211yescharacteristic
45#18012660C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic, complemented
50(C2×D151)⋊C8C2211yescharacteristic, complemented
51(C2×D151)⋊C8C2211yescharacteristic, complemented
52#121×C151C2211yescharacteristic
53C2×C4⋊C4×C151C2211yescharacteristic, complemented
54#107×C151C2211yescharacteristic, complemented
55#107×C151C2211yescharacteristic, complemented
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60#14559004—22no—
61#14559004—22no—
62C2×Dic302D411yescharacteristic
63C2×D604—21no—
64C2×D604D411yescharacteristic
65C2×D604C2311yescharacteristic
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151D411yescharacteristic
70C2×C22⋊D151D411yescharacteristic
71D4×D151—22no—
72D4×D151—22no—
73C2×C4×D151—21no—
74C2×C4×D151—21no—
75C2×C4×D151C2311yescharacteristic
76C2×C4×D151C2311yescharacteristic
77#14558987—22no—
78C2×C151⋊C8C2311yescharacteristic
79C2×C151⋊C8C2311yescharacteristic
80C8×D151—22no—
81C4⋊Dic151C2311yescharacteristic
82C4⋊Dic151C2311yescharacteristic
83C4⋊Dic151C2311yescharacteristic
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86C22⋊Dic151—21no—
87C22⋊Dic151—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93C4×Dic151—21no—
94C4×Dic151—21no—
95C4×Dic151—21no—
96C4×Dic151—21no—
97C2×D4×C151—21no—
98C2×D4×C151C2311yescharacteristic
99C22×C4×C151—21no—
100C22×C4×C151C2311yescharacteristic
101C2×C8×C151C2311yescharacteristic
102C2×C8×C151C2311yescharacteristic
103C4⋊C4×C151—21no—
104C4⋊C4×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C4⋊C4×C151C2311yescharacteristic
107C22⋊C4×C151—21no—
108C22×D151—21no—
109C22×D151—42no—
110C22×D151—81no—
111C22×D151—81no—
112C22×D151C2×D411yescharacteristic
113C22×D151C2×D411yescharacteristic
114Dic302—22no—
115D604—22no—
116D604—21no—
117D604—21no—
118D604—81no—
119C22⋊D151—22no—
120C22⋊D151—22no—
121C22⋊D151—42no—
122C22⋊D151—81no—
123C22⋊D151—81no—
124C2×Dic151—21no—
125C2×Dic151—21no—
126C2×Dic151—21no—
127C2×Dic151C2×D411yescharacteristic
128C2×Dic151C2×D411yescharacteristic
129C4×D151—21no—
130C4×D151—21no—
131C4×D151—81no—
132C4×D151—81no—
133C4×D151#4112yes—
134C4×D151#4112yes—
135C151⋊C8—21no—
136C151⋊C8—21no—
137C23×C151—21no—
138C23×C151C2×D411yescharacteristic
139D4×C151—21no—
140D4×C151—21no—
141D4×C151—81no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151—81no—
148C2×C4×C151C2×D411yescharacteristic
149C2×C4×C151C2411yescharacteristic
150C8×C151—21no—
151C8×C151—21no—
152C22×C151—21no—
153C22×C151—21no—
154C22×C151—21no—
155C22×C151—41no—
156C22×C151—41no—
157C22×C151—41no—
158C22×C151C22×D411yescharacteristic
159C2×D151—21no—
160C2×D151—21no—
161C2×D151—21no—
162C2×D151—21no—
163C2×D151—21no—
164C2×D151—41no—
165C2×D151—41no—
166C2×D151—41no—
167C2×D151—84no—
168C2×D151#12312yes—
169C4×C151—21no—
170C4×C151—41no—
171C4×C151—41no—
172C4×C151—41no—
173C4×C151C2×#4111yescharacteristic
174C4×C151C2×#4111yescharacteristic
175Dic151—21no—
176Dic151—41no—
177Dic151—41no—
178Dic151—41no—
179Dic151#12312yes—
180C2×C151—41no—
181C2×C151—81no—
182C2×C151C2×#12311yescharacteristic
183C2×C151#57611yescharacteristic
184C2×C151#57711yescharacteristic
185D151—22no—
186D151—41no—
187D151—81no—
188C151#309611yescharacteristic, complemented, Sylow
189#3096—1511nomaximal, Sylow
190#535—1511no—
191#520—1511no—
192#482—1511no—
193#482—1511no—
194#482—1511no—
195#482—1511no—
196#481—1511no—
197#481—1511no—
198#480—1511no—
199#480D15111yescharacteristic, complemented
200#428—1511no—
201#427—1511no—
202#418—1511no—
203C2×#102—1511no—
204#408—1511no—
205C2×#41—1511no—
206C22×D4—1511no—
207C2×M16—1511no—
208C22×C8—1511no—
209#127—3021no—
210#124—3021no—
211#121—1511no—
212#121—1511no—
213#121—1511no—
214#121C2×D15111yescharacteristic
215#120—3021no—
216#120—3021no—
217C4×Q8—3021no—
218C4×D4—3021no—
219C4×D4—3021no—
220C4×D4—3021no—
221#117—1511no—
222#117—1511no—
223#117—1511no—
224#117—1511no—
225C2×C4⋊C4—1511no—
226C2×C4⋊C4—1511no—
227C2×C4⋊C4C2×D15111yescharacteristic, complemented
228#107—1511no—
229#107—1511no—
230#107C2×D15111yescharacteristic, complemented
231#107C2×D15111yescharacteristic, complemented
232#106—1511no—
233#106—1511no—
234#106—1511no—
235#106—1511no—
236#102—1511no—
237#102—1511no—
238#102—1511no—
239#102—1511no—
240#102—1511no—
241#102—1511no—
242#102C2×D15111yescharacteristic
243#102C2×D15111yescharacteristic
244C22⋊C8—1511no—
245C22⋊C8—1511no—
246C22⋊C8—1511no—
247C22⋊C8C2×D15111yescharacteristic, complemented
248C24—3021no—
249#41—3022no—
250#41—3022no—
251C2×Q8—1511no—
252C2×D4—21no—
253C2×D4—3021no—
254C2×D4—3021no—
255C2×D4—3021no—
256C2×D4—3022no—
257C2×D4—3022no—
258C2×D4—3021no—
259C2×D4—1511no—
260C2×D4—1511no—
261C2×D4—1511no—
262C2×D4—1511no—
263C2×D4C22×D15111yescharacteristic
264C22×C4—21no—
265C22×C4—3021no—
266C22×C4—3021no—
267C22×C4—1511no—
268C22×C4—1511no—
269C22×C4C22×D15111yescharacteristic
270M16—3022no—
271C2×C8—3022no—
272C2×C8—1511no—
273C2×C8—1511no—
274C2×C8C22×D15111yescharacteristic
275C2×C8C22×D15111yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—3021no—
278C4⋊C4—3021no—
279C4⋊C4—1511no—
280C4⋊C4—1511no—
281C4⋊C4—1511no—
282C4⋊C4C22×D15111yescharacteristic
283C4⋊C4C22×D15111yescharacteristic
284C4⋊C4C22×D15111yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—3021no—
287C22⋊C4—3021no—
288C22⋊C4—3021no—
289C22⋊C4—3021no—
290C22⋊C4—3021no—
291C22⋊C4—3021no—
292C22⋊C4—3021no—
293C42—3021no—
294C42—3021no—
295C42—3021no—
296C42—3021no—
297C23—21no—
298C23—3021no—
299C23—6042no—
300C23—1511no—
301C23—1511no—
302C23—12081no—
303C23—12081no—
304C23D4×D15111yescharacteristic
305Q8—3022no—
306D4—21no—
307D4—21no—
308D4—81no—
309D4—3022no—
310D4—3022no—
311D4—3022no—
312D4—3021no—
313D4—3021no—
314D4—6042no—
315D4—12081no—
316D4—12081no—
317D4—12081no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—81no—
324C2×C4—3021no—
325C2×C4—3021no—
326C2×C4—3021no—
327C2×C4—3021no—
328C2×C4—3021no—
329C2×C4—1511no—
330C2×C4—1511no—
331C2×C4—1512no—
332C2×C4—1512no—
333C2×C4—12081no—
334C2×C4—12081no—
335C2×C4D4×D15111yescharacteristic
336C2×C4C23×D15111yescharacteristic
337C8—21no—
338C8—21no—
339C8—3021no—
340C8—3021no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—3021no—
348C22—3021no—
349C22—3021no—
350C22—3021no—
351C22—3021no—
352C22—6041no—
353C22—6041no—
354C22—6041no—
355C22—1512no—
356C22—12084no—
357C22C2×D4×D15111yescharacteristic
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—3021no—
363C4—6041no—
364C4—6041no—
365C4—6041no—
366C4—1512no—
367C4#41×D15111yescharacteristic
368C4#41×D15111yescharacteristic
369C2—41no—
370C2—81no—
371C2—3022no—
372C2—6041no—
373C2—12081no—
374C2#123×D15111yescharacteristic
375C2#2375301311yescharacteristic
376C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#480×C151C2
socleC22×C151C22×D4
prime radical#23752778C2
hypercenter#480D151
hypocenterC151#3096
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #23752693C2semidirect
3. #23752539C2semidirect
4. #23752537C2semidirect
5. #23752534C2semidirect
6. #23752533C2semidirect
7. #23752530C2semidirect
8. #23752529C2semidirect
9. #23752527C2semidirect
10. #23752253C2semidirect
11. #23752249C2semidirect
12. #23752215C2semidirect
13. #102×D151C2semidirect
14. #23752177C2semidirect
15. #480×C151C2semidirect
31. #18012698C22semidirect
34. #18012697C22semidirect
36. C4⋊C4×D151C22semidirect
37. #18012673C22semidirect
38. #18012672C22semidirect
39. #18012671C22semidirect
40. #18012670C22semidirect
41. #18012670C22semidirect
42. #18012670C22semidirect
49. C22⋊(C151⋊C8)C22semidirect
50. (C2×D151)⋊C8C22semidirect
51. (C2×D151)⋊C8C22semidirect
53. C2×C4⋊C4×C151C22semidirect
54. #107×C151C22semidirect
55. #107×C151C22semidirect
58. C22⋊C8×C151C22semidirect
188. C151#3096semidirect
199. #480D151semidirect
227. C2×C4⋊C4C2×D151semidirect
230. #107C2×D151semidirect
231. #107C2×D151semidirect
247. C22⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527782
#237526932
#237525392
#237525372
#237525342
#237525332
#237525302
#237525292
#237525272
#237522532
#237522492
#237522152
#102×D1512
#237521772
#480×C1512
#3096151