Finite Group Databasebeta

← #34081075

Subgroups — #34081075

Order 19328.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752862C211yesmaximal, characteristic, complemented
2#23752856C211yesmaximal, characteristic, complemented
3#23752570C211yesmaximal, characteristic, complemented
4#23752543C211yesmaximal, characteristic, complemented
5#23752529C211yesmaximal, characteristic, complemented
6#23752500C211yesmaximal, characteristic, complemented
7#23752462C211yesmaximal, characteristic, complemented
8#23752439C211yesmaximal, characteristic, complemented
9#23752425C211yesmaximal, characteristic, complemented
10#23752354C211yesmaximal, characteristic, complemented
11#23752324C211yesmaximal, characteristic, complemented
12#23752280C211yesmaximal, characteristic, complemented
13#23752210C211yesmaximal, characteristic, complemented
14C2×#18012660C211yesmaximal, characteristic, complemented
15#447×C151C211yesmaximal, characteristic, complemented
16C2×#14559003—21no—
17C2×#14559003C2211yescharacteristic
18C2×#14558992C2211yescharacteristic, complemented
19C2×#14558987C2211yescharacteristic, complemented
20C22×C151⋊C8C2211yescharacteristic
21#18012738C2211yescharacteristic, complemented
22#18012726C2211yescharacteristic
23#18012721—21no—
24#18012720—21no—
25#18012720—21no—
26#18012718C2211yescharacteristic
27#18012716—21no—
28#18012711—21no—
29#18012710C2211yescharacteristic
30#18012710C2211yescharacteristic, complemented
31#18012708—21no—
32D4×Dic151C2211yescharacteristic
33D4×Dic151C2211yescharacteristic, complemented
34C4×C22⋊D151C2211yescharacteristic
35C2×C4⋊Dic151C2211yescharacteristic
36C4⋊C4×D151C2211yescharacteristic, complemented
37C2×C22⋊Dic151—21no—
38#18012671C2211yescharacteristic, complemented
39#18012671C2211yescharacteristic, complemented
40#18012670C2211yescharacteristic, complemented
41Dic151⋊C8C2211yescharacteristic, complemented
42#18012664C2211yescharacteristic, complemented
43#18012664C2211yescharacteristic, complemented
44#18012662C2211yescharacteristic, complemented
45#18012660C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012660C2211yescharacteristic
49#18012660C2211yescharacteristic, complemented
50(C2×D151)⋊C8C2211yescharacteristic, complemented
51#18012649C2211yescharacteristic, complemented
52C22×D4×C151C2211yescharacteristic
53C2×D8×C151C2211yescharacteristic
54C2×D8×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59#14559003—22no—
60#14559003—41no—
61#14559003—44no—
62C2×Dic302—21no—
63C2×Dic302C2311yescharacteristic
64C2×C22⋊D151—21no—
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67C2×C22⋊D151D411yescharacteristic
68C22×Dic151—21no—
69C22×Dic151—21no—
70C22×Dic151—21no—
71C22×Dic151—21no—
72C2×C4×D151—21no—
73C2×C4×D151C2311yescharacteristic
74#14558992—41no—
75#14558987—41no—
76C2×C151⋊C8—41no—
77C2×C151⋊C8C2311yescharacteristic
78C2×C151⋊C8C2311yescharacteristic
79C4⋊Dic151—21no—
80C4⋊Dic151C2311yescharacteristic
81C4⋊Dic151C2311yescharacteristic
82C4⋊Dic151C2311yescharacteristic
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4D411yescharacteristic
87C22⋊Dic151—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90C22⋊Dic151—21no—
91C22⋊Dic151—21no—
92C22⋊Dic151—21no—
93C22⋊Dic151—21no—
94C22⋊Dic151D411yescharacteristic
95(C2×D151)⋊C4D411yescharacteristic
96C4×Dic151C2311yescharacteristic
97C24×C151—21no—
98C2×D4×C151—22no—
99C2×D4×C151—21no—
100C2×D4×C151—21no—
101C2×D4×C151—41no—
102C2×D4×C151C2311yescharacteristic
103C2×D4×C151C2311yescharacteristic
104C2×D4×C151C2311yescharacteristic
105C22×C4×C151C2311yescharacteristic
106D8×C151—22no—
107D8×C151—41no—
108C2×C8×C151C2311yescharacteristic
109C2×C8×C151C2311yescharacteristic
110C4⋊C4×C151C2311yescharacteristic
111C22⋊C4×C151—21no—
112C22×D151C2×D411yescharacteristic
113Dic302—21no—
114Dic302—21no—
115Dic302—42no—
116C22⋊D151—22no—
117C22⋊D151—42no—
118C22⋊D151—42no—
119C22⋊D151—81no—
120C2×Dic151—21no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151—42no—
125C2×Dic151—42no—
126C2×Dic151—42no—
127C2×Dic151—81no—
128C2×Dic151C2×D411yescharacteristic
129C2×Dic151C2×D411yescharacteristic
130C2×Dic151C2×D411yescharacteristic
131C4×D151—21no—
132C4×D151—21no—
133C4×D151—42no—
134C151⋊C8—21no—
135C151⋊C8—21no—
136C23×C151—21no—
137C23×C151—21no—
138C23×C151—21no—
139C23×C151—42no—
140C23×C151—42no—
141C23×C151—81no—
142C23×C151C2×D411yescharacteristic
143D4×C151—21no—
144D4×C151—21no—
145D4×C151—21no—
146D4×C151—21no—
147D4×C151—21no—
148D4×C151—42no—
149D4×C151—42no—
150D4×C151#4112yescomplemented
151C2×C4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151—21no—
154C2×C4×C151C2×D411yescharacteristic
155C2×C4×C151C2411yescharacteristic
156C8×C151—21no—
157C8×C151—21no—
158C22×C151—21no—
159C22×C151—21no—
160C22×C151—22no—
161C22×C151—41no—
162C22×C151—41no—
163C22×C151—41no—
164C22×C151—41no—
165C22×C151—41no—
166C22×C151—41no—
167C22×C151—41no—
168C22×C151—41no—
169C22×C151—84no—
170C22×C151AGL(1,ℤ/8)12yes—
171C22×C151C22×D411yescharacteristic
172C2×D151—21no—
173C2×D151—21no—
174C2×D151—21no—
175C4×C151—21no—
176C4×C151—41no—
177C4×C151C2×#4111yescharacteristic
178C4×C151H(5,𝔽2)11yescharacteristic
179Dic151—21no—
180Dic151—21no—
181Dic151—21no—
182Dic151—41no—
183Dic151—41no—
184Dic151—41no—
185Dic151—41no—
186C2×C151—22no—
187C2×C151—42no—
188C2×C151—81no—
189C2×C151—81no—
190C2×C151#54611yescharacteristic
191C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C151#57711yescharacteristic
193D151—41no—
194C151#330611yescharacteristic, complemented, Sylow
195#3306—1511nomaximal, Sylow
196#547—1511no—
197#546—1511no—
198#489—1511no—
199#483—1511no—
200#481—1511no—
201#476—1511no—
202#469—1511no—
203#465—1511no—
204#463—1511no—
205#449—1511no—
206#447D15111yescharacteristic, complemented
207#442—1511no—
208#435—1511no—
209#417—1511no—
210C2×#102—1511no—
211C2×#41—3021no—
212C2×#41—1511no—
213C22×D4C2×D15111yescharacteristic
214C2×SD16—1511no—
215C2×D8C2×D15111yescharacteristic
216C2×D8C2×D15111yescharacteristic
217C2×M16—1511no—
218C22×C8—1511no—
219C4⋊Q8—1511no—
220#124—1511no—
221#123—3021no—
222#123—3021no—
223#123—3021no—
224C22⋊Q8—3021no—
225C22⋊Q8—1511no—
226#121—3021no—
227#121—1511no—
228#121—1511no—
229#121C2×D15111yescharacteristic
230#120—3021no—
231C4×D4—1511no—
232C4×D4—1511no—
233C4×D4—1511no—
234C2×C4⋊C4—1511no—
235C2×C4⋊C4—1511no—
236C2×C22⋊C4—3021no—
237#106—1511no—
238#106—1511no—
239#106—1511no—
240C4⋊C8—1511no—
241#103—1511no—
242#103—1511no—
243#103—1511no—
244#102—1511no—
245#102—1511no—
246#102—1511no—
247#102—1511no—
248#102—1511no—
249#102C2×D15111yescharacteristic
250#102C2×D15111yescharacteristic
251C22⋊C8—1511no—
252C22⋊C8C2×D15111yescharacteristic
253#97—1511no—
254C24—21no—
255#41—3022no—
256#41—6041no—
257#41—6044no—
258C2×Q8—3021no—
259C2×Q8—1511no—
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—3021no—
265C2×D4—3021no—
266C2×D4—3021no—
267C2×D4—1511no—
268C2×D4C22×D15111yescharacteristic
269C2×D4C22×D15111yescharacteristic
270C2×D4C22×D15111yescharacteristic
271C22×C4—3021no—
272C22×C4—3021no—
273C22×C4—3021no—
274C22×C4—3021no—
275C22×C4—3021no—
276C22×C4—1511no—
277C22×C4C22×D15111yescharacteristic
278SD16—6041no—
279D8—22no—
280D8—41no—
281M16—6041no—
282C2×C8—6041no—
283C2×C8—1511no—
284C2×C8—1511no—
285C2×C8C22×D15111yescharacteristic
286C2×C8C22×D15111yescharacteristic
287C4⋊C4—3021no—
288C4⋊C4—3021no—
289C4⋊C4—3021no—
290C4⋊C4—3021no—
291C4⋊C4—1511no—
292C4⋊C4—1511no—
293C4⋊C4—1511no—
294C4⋊C4—1511no—
295C4⋊C4C22×D15111yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—3021no—
298C22⋊C4—3021no—
299C22⋊C4—3021no—
300C22⋊C4—3021no—
301C22⋊C4—3021no—
302C22⋊C4—3021no—
303C22⋊C4—3021no—
304C22⋊C4—1511no—
305C22⋊C4—1511no—
306C42—1511no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—1511no—
314C23D4×D15111yescharacteristic
315Q8—3021no—
316Q8—3021no—
317Q8—6042no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—42no—
324D4—42no—
325D4—3022no—
326D4—6042no—
327D4—6042no—
328D4—12081no—
329D4#1455900312yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—3021no—
334C2×C4—3021no—
335C2×C4—3021no—
336C2×C4—3021no—
337C2×C4—3021no—
338C2×C4—3021no—
339C2×C4—6042no—
340C2×C4—6042no—
341C2×C4—6042no—
342C2×C4—6042no—
343C2×C4—1511no—
344C2×C4—1511no—
345C2×C4—1511no—
346C2×C4—12081no—
347C2×C4D4×D15111yescharacteristic
348C2×C4C23×D15111yescharacteristic
349C8—21no—
350C8—21no—
351C8—3021no—
352C8—3021no—
353C22—21no—
354C22—21no—
355C22—22no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—84no—
365C22—3021no—
366C22—3021no—
367C22—3021no—
368C22#1801276312yes—
369C22C2×D4×D15111yescharacteristic
370C4—21no—
371C4—41no—
372C4—3021no—
373C4—3021no—
374C4—3021no—
375C4—6041no—
376C4—6041no—
377C4—6041no—
378C4—6041no—
379C4C2×#1455900311yescharacteristic
380C4#1801278411yescharacteristic
381C2—22no—
382C2—42no—
383C2—81no—
384C2—81no—
385C2—6041no—
386C2#2375284911yescharacteristic
387C2C2×#1801276311yescharacteristic
388C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#447×C151C2
socleC22×C151C22×D4
hypercenter#447D151
hypocenterC151#3306
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #23752862C2semidirect
2. #23752856C2semidirect
3. #23752570C2semidirect
4. #23752543C2semidirect
5. #23752529C2semidirect
6. #23752500C2semidirect
7. #23752462C2semidirect
8. #23752439C2semidirect
9. #23752425C2semidirect
10. #23752354C2semidirect
11. #23752324C2semidirect
12. #23752280C2semidirect
13. #23752210C2semidirect
14. C2×#18012660C2semidirect
15. #447×C151C2semidirect
18. C2×#14558992C22semidirect
19. C2×#14558987C22semidirect
21. #18012738C22semidirect
30. #18012710C22semidirect
33. D4×Dic151C22semidirect
36. C4⋊C4×D151C22semidirect
38. #18012671C22semidirect
39. #18012671C22semidirect
40. #18012670C22semidirect
41. Dic151⋊C8C22semidirect
42. #18012664C22semidirect
43. #18012664C22semidirect
44. #18012662C22semidirect
49. #18012660C22semidirect
50. (C2×D151)⋊C8C22semidirect
51. #18012649C22semidirect
150. D4×C151#41semidirect
194. C151#3306semidirect
206. #447D151semidirect
329. D4#14559003semidirect

Maximal subgroups

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

subgroupindex
#237528622
#237528562
#237525702
#237525432
#237525292
#237525002
#237524622
#237524392
#237524252
#237523542
#237523242
#237522802
#237522102
C2×#180126602
#447×C1512
#3306151