Finite Group Databasebeta

← #34080960

Subgroups — #34080960

Order 19328.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752908C211yesmaximal, characteristic, complemented
2#23752566C211yesmaximal, characteristic, complemented
3#23752545C211yesmaximal, characteristic, complemented
4#23752533C211yesmaximal, characteristic, complemented
5#23752512C211yesmaximal, characteristic, complemented
6#23752446C211yesmaximal, characteristic, complemented
7#23752443C211yesmaximal, characteristic, complemented
8#23752424C211yesmaximal, characteristic, complemented
9#23752357C211yesmaximal, characteristic, complemented
10#23752346C211yesmaximal, characteristic, complemented
11C4×#14558989C211yesmaximal, characteristic, complemented
12D4×C151⋊C8C211yesmaximal, characteristic, complemented
13#23752208C211yesmaximal, characteristic, complemented
14C2×#18012660C211yesmaximal, characteristic, complemented
15#546×C151C211yesmaximal, characteristic, complemented
16C2×#14558991C2211yescharacteristic, complemented
17C2×#14558989C2211yescharacteristic
18C2×#14558989C2211yescharacteristic
19C22×C151⋊C8C2211yescharacteristic
20C22×C151⋊C8C2211yescharacteristic, complemented
21#18012734—21no—
22#18012731C2211yescharacteristic, complemented
23#18012721—21no—
24#18012713C2211yescharacteristic
25#18012713C2211yescharacteristic, complemented
26#18012711—21no—
27C4×D604C2211yescharacteristic, complemented
28(C22⋊D151)⋊C4—21no—
29#18012698C2211yescharacteristic, complemented
30C2×C4⋊Dic151C2211yescharacteristic
31#18012672C2211yescharacteristic, complemented
32#18012672C2211yescharacteristic, complemented
33#18012670C2211yescharacteristic, complemented
34C4⋊(C151⋊C8)C2211yescharacteristic, complemented
35#18012663C2211yescharacteristic, complemented
36#18012663C2211yescharacteristic, complemented
37#18012663C2211yescharacteristic, complemented
38#18012660C2211yescharacteristic
39#18012660C2211yescharacteristic
40#18012660C2211yescharacteristic
41#18012660C2211yescharacteristic
42#18012660C2211yescharacteristic
43#18012660C2211yescharacteristic
44#18012659C2211yescharacteristic, complemented
45C22⋊(C151⋊C8)C2211yescharacteristic
46C22⋊(C151⋊C8)C2211yescharacteristic, complemented
47C4×C151⋊C8C2211yescharacteristic, complemented
48C2×#41×C151C2211yescharacteristic
49C22×D4×C151C2211yescharacteristic
50#124×C151C2211yescharacteristic
51#123×C151—21no—
52C22⋊Q8×C151C2211yescharacteristic
53#121×C151—21no—
54#121×C151C2211yescharacteristic
55#120×C151—21no—
56C4×D4×C151C2211yescharacteristic
57C4×D4×C151C2211yescharacteristic
58C2×C22⋊C4×C151—21no—
59C2×D604C2311yescharacteristic
60C2×C22⋊D151—21no—
61C2×C22⋊D151—21no—
62C22×Dic151—21no—
63C2×C4×D151—21no—
64#14558991—41no—
65#14558989—22no—
66#14558989—41no—
67C2×C151⋊C8—41no—
68C2×C151⋊C8—41no—
69C2×C151⋊C8C2311yescharacteristic
70C2×C151⋊C8C2311yescharacteristic
71C2×C151⋊C8C2311yescharacteristic
72C2×C151⋊C8C2311yescharacteristic
73C4⋊Dic151—21no—
74C4⋊Dic151C2311yescharacteristic
75C4⋊Dic151C2311yescharacteristic
76C4⋊Dic151C2311yescharacteristic
77Dic151⋊C4—21no—
78Dic151⋊C4—21no—
79C22⋊Dic151—21no—
80(C2×D151)⋊C4—21no—
81(C2×D151)⋊C4—21no—
82(C2×D151)⋊C4—21no—
83C4×Dic151—21no—
84C24×C151—21no—
85#41×C151—22no—
86#41×C151—41no—
87C2×Q8×C151C2311yescharacteristic
88C2×D4×C151—22no—
89C2×D4×C151—21no—
90C2×D4×C151—21no—
91C2×D4×C151—21no—
92C2×D4×C151—41no—
93C2×D4×C151D411yescharacteristic
94C2×D4×C151C2311yescharacteristic
95C2×D4×C151C2311yescharacteristic
96C22×C4×C151—21no—
97C22×C4×C151—21no—
98C22×C4×C151C2311yescharacteristic
99C22×C4×C151C2311yescharacteristic
100C4⋊C4×C151—21no—
101C4⋊C4×C151D411yescharacteristic
102C4⋊C4×C151C2311yescharacteristic
103C22⋊C4×C151—21no—
104C22⋊C4×C151—21no—
105C22⋊C4×C151—21no—
106C22⋊C4×C151—21no—
107C22⋊C4×C151—21no—
108C22⋊C4×C151D411yescharacteristic
109C22⋊C4×C151D411yescharacteristic
110C42×C151C2311yescharacteristic
111C22×D151—21no—
112D604—21no—
113D604—21no—
114C22⋊D151—42no—
115C22⋊D151—81no—
116C2×Dic151—21no—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151—81no—
120C4×D151—81no—
121C151⋊C8—21no—
122C151⋊C8—21no—
123C151⋊C8—21no—
124C151⋊C8—21no—
125C23×C151—21no—
126C23×C151—21no—
127C23×C151—42no—
128C23×C151—42no—
129C23×C151—81no—
130C23×C151C2×D411yescharacteristic
131C23×C151C2×D411yescharacteristic
132Q8×C151—21no—
133Q8×C151—21no—
134D4×C151—22no—
135D4×C151—21no—
136D4×C151—21no—
137D4×C151—21no—
138D4×C151—42no—
139D4×C151—42no—
140D4×C151—81no—
141D4×C151#4112yes—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—42no—
149C2×C4×C151—81no—
150C2×C4×C151C2×D411yescharacteristic
151C2×C4×C151C2×D411yescharacteristic
152C2×C4×C151C2×D411yescharacteristic
153C2×C4×C151C2×D411yescharacteristic
154C2×C4×C151C2411yescharacteristic
155C22×C151—21no—
156C22×C151—21no—
157C22×C151—21no—
158C22×C151—22no—
159C22×C151—21no—
160C22×C151—21no—
161C22×C151—41no—
162C22×C151—41no—
163C22×C151—41no—
164C22×C151—41no—
165C22×C151—41no—
166C22×C151—84no—
167C22×C151#13512yes—
168C22×C151C22×D411yescharacteristic
169C2×D151—41no—
170C2×D151—41no—
171C2×D151—41no—
172C4×C151—21no—
173C4×C151—21no—
174C4×C151—21no—
175C4×C151—21no—
176C4×C151—41no—
177C4×C151—41no—
178C4×C151C2×#4111yescharacteristic
179C4×C151H(5,𝔽2)11yescharacteristic
180Dic151—41no—
181Dic151—41no—
182Dic151—41no—
183C2×C151—22no—
184C2×C151—41no—
185C2×C151—42no—
186C2×C151—81no—
187C2×C151#54611yescharacteristic
188C2×C151C2×#13511yescharacteristic
189C2×C151#57611yescharacteristic
190D151—81no—
191C151#329711yescharacteristic, complemented, Sylow
192#3297—1511nomaximal, Sylow
193#553—1511no—
194#546D15111yescharacteristic, complemented
195#488—1511no—
196#484—1511no—
197#482—1511no—
198#478—1511no—
199#466—1511no—
200#465—1511no—
201#463—1511no—
202#449—1511no—
203#447—1511no—
204C4×D8—1511no—
205C8×D4—1511no—
206#416—1511no—
207C2×#102—1511no—
208C2×#41C2×D15111yescharacteristic
209C22×D4C2×D15111yescharacteristic
210C2×SD16—1511no—
211C2×D8—1511no—
212C2×D8—1511no—
213C22×C8—1511no—
214C22×C8—1511no—
215#126—3021no—
216#125—1511no—
217#124C2×D15111yescharacteristic
218#123—21no—
219#123—3021no—
220C22⋊Q8C2×D15111yescharacteristic
221#121—21no—
222#121—3021no—
223#121—1511no—
224#121—1511no—
225#121C2×D15111yescharacteristic
226#120—21no—
227C4×D4—3021no—
228C4×D4—1511no—
229C4×D4C2×D15111yescharacteristic
230C4×D4C2×D15111yescharacteristic
231#117—1511no—
232C2×C4⋊C4—1511no—
233C2×C22⋊C4—21no—
234#107—1511no—
235#107—1511no—
236#106—1511no—
237C4⋊C8—1511no—
238#103—1511no—
239#103—1511no—
240#103—1511no—
241#102—1511no—
242#102—1511no—
243#102—1511no—
244#102—1511no—
245#102—1511no—
246#102—1511no—
247#102—1511no—
248C22⋊C8—1511no—
249C22⋊C8—1511no—
250C4×C8—1511no—
251C24—21no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D15111yescharacteristic
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—41no—
260C2×D4—3021no—
261C2×D4—3021no—
262C2×D4—1511no—
263C2×D4C22⋊D15111yescharacteristic
264C2×D4C22×D15111yescharacteristic
265C2×D4C22×D15111yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—3021no—
269C22×C4—3021no—
270C22×C4C22×D15111yescharacteristic
271C22×C4C22×D15111yescharacteristic
272SD16—6041no—
273D8—3022no—
274D8—6041no—
275C2×C8—6041no—
276C2×C8—6041no—
277C2×C8—1511no—
278C2×C8—1511no—
279C2×C8—1511no—
280C2×C8—1511no—
281C4⋊C4—21no—
282C4⋊C4—3021no—
283C4⋊C4—3021no—
284C4⋊C4—3021no—
285C4⋊C4—1511no—
286C4⋊C4—1511no—
287C4⋊C4—1511no—
288C4⋊C4C22⋊D15111yescharacteristic
289C4⋊C4C22×D15111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—3021no—
296C22⋊C4—3021no—
297C22⋊C4—3021no—
298C22⋊C4—3021no—
299C22⋊C4C22⋊D15111yescharacteristic
300C22⋊C4C22⋊D15111yescharacteristic
301C42—3021no—
302C42C22×D15111yescharacteristic
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—3021no—
309C23C2×C22⋊D15111yescharacteristic
310C23C2×C22⋊D15111yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—22no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—42no—
318D4—42no—
319D4—81no—
320D4—3021no—
321D4—3021no—
322D4—6042no—
323D4—12081no—
324D4#1455900312yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—81no—
333C2×C4—3021no—
334C2×C4—3021no—
335C2×C4—3021no—
336C2×C4—12081no—
337C2×C4—12081no—
338C2×C4C2×C22⋊D15111yescharacteristic
339C2×C4C2×C22⋊D15111yescharacteristic
340C2×C4C2×C22⋊D15111yescharacteristic
341C2×C4C2×C22⋊D15111yescharacteristic
342C2×C4C23×D15111yescharacteristic
343C8—3021no—
344C8—3021no—
345C8—3021no—
346C8—3021no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—22no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—84no—
359C22—6041no—
360C22—6041no—
361C22—6041no—
362C22#1801275912yes—
363C22C22×C22⋊D15111yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—6041no—
371C4—6041no—
372C4—6041no—
373C4C2×#1455900311yescharacteristic
374C4#1801278411yescharacteristic
375C2—22no—
376C2—41no—
377C2—42no—
378C2—81no—
379C2—12081no—
380C2#2375285611yescharacteristic
381C2C2×#1801275911yescharacteristic
382C2#2375301511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#546×C151C2
socleC22×C151C22×D4
hypercenter#546D151
hypocenterC151#3297
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #23752908C2semidirect
2. #23752566C2semidirect
3. #23752545C2semidirect
4. #23752533C2semidirect
5. #23752512C2semidirect
6. #23752446C2semidirect
7. #23752443C2semidirect
8. #23752424C2semidirect
9. #23752357C2semidirect
10. #23752346C2semidirect
11. C4×#14558989C2semidirect
12. D4×C151⋊C8C2semidirect
13. #23752208C2semidirect
14. C2×#18012660C2semidirect
15. #546×C151C2semidirect
16. C2×#14558991C22semidirect
20. C22×C151⋊C8C22semidirect
22. #18012731C22semidirect
25. #18012713C22semidirect
27. C4×D604C22semidirect
29. #18012698C22semidirect
31. #18012672C22semidirect
32. #18012672C22semidirect
33. #18012670C22semidirect
34. C4⋊(C151⋊C8)C22semidirect
35. #18012663C22semidirect
36. #18012663C22semidirect
37. #18012663C22semidirect
44. #18012659C22semidirect
46. C22⋊(C151⋊C8)C22semidirect
47. C4×C151⋊C8C22semidirect
191. C151#3297semidirect
194. #546D151semidirect

Maximal subgroups

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

subgroupindex
#237529082
#237525662
#237525452
#237525332
#237525122
#237524462
#237524432
#237524242
#237523572
#237523462
C4×#145589892
D4×C151⋊C82
#237522082
C2×#180126602
#546×C1512
#3297151