Finite Group Databasebeta

← #34079900

Subgroups — #34079900

Order 19328.

424 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#23752722C211yesmaximal, characteristic, complemented
2#23752719C211yesmaximal, characteristic, complemented
3#23752554C211yesmaximal, characteristic, complemented
4#23752552C211yesmaximal, characteristic, complemented
5#23752535C211yesmaximal, characteristic, complemented
6#23752533C211yesmaximal, characteristic, complemented
7#23752452C211yesmaximal, characteristic, complemented
8#23752445C211yesmaximal, characteristic, complemented
9#23752440C211yesmaximal, characteristic, complemented
10#23752438C211yesmaximal, characteristic, complemented
11#23752374C211yesmaximal, characteristic, complemented
12#23752371C211yesmaximal, characteristic, complemented
13#23752354C211yesmaximal, characteristic, complemented
14C22⋊C8×D151C211yesmaximal, characteristic, complemented
15#449×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C22×C4×D151C2211yescharacteristic
18C2×#14558994C2211yescharacteristic, complemented
19C2×#14558992C2211yescharacteristic, complemented
20C2×C8×D151C2211yescharacteristic
21C2×C8×D151C2211yescharacteristic
22#18012721—21no—
23#18012720—21no—
24#18012719C2211yescharacteristic
25#18012718C2211yescharacteristic
26#18012715C2211yescharacteristic
27#18012715C2211yescharacteristic
28#18012710C2211yescharacteristic
29#18012710C2211yescharacteristic
30#18012710C2211yescharacteristic
31#18012707—21no—
32#18012707—21no—
33D4×Dic151—21no—
34C4×C22⋊D151—21no—
35C4×C22⋊D151—21no—
36(C22⋊D151)⋊C4—21no—
37#18012698C2211yescharacteristic
38#18012697C2211yescharacteristic
39#18012673C2211yescharacteristic, complemented
40#18012672C2211yescharacteristic, complemented
41#18012671C2211yescharacteristic, complemented
42#18012670C2211yescharacteristic, complemented
43#18012664C2211yescharacteristic, complemented
44#18012664C2211yescharacteristic, complemented
45#18012663C2211yescharacteristic, complemented
46#18012660C2211yescharacteristic, complemented
47#18012660C2211yescharacteristic, complemented
48#18012660C2211yescharacteristic, complemented
49C22⋊(C151⋊C8)C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
52C2×#41×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic, complemented
54C2×D8×C151C2211yescharacteristic, complemented
55#121×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic, complemented
57#102×C151C2211yescharacteristic, complemented
58C22⋊C8×C151C2211yescharacteristic
59C23×D151D411yescharacteristic
60#14559003—41no—
61#14559003—41no—
62C2×Dic302C2311yescharacteristic
63C2×C22⋊D151—21no—
64C2×C22⋊D151—21no—
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67C22×Dic151—21no—
68C22×Dic151D411yescharacteristic
69C2×C4×D151—41no—
70C2×C4×D151—41no—
71C2×C4×D151D411yescharacteristic
72C2×C4×D151D411yescharacteristic
73C2×C4×D151C2311yescharacteristic
74C2×C4×D151C2311yescharacteristic
75#14558994—41no—
76#14558992—41no—
77C2×C151⋊C8C2311yescharacteristic
78C2×C151⋊C8C2311yescharacteristic
79C8×D151—41no—
80C8×D151—41no—
81C4⋊Dic151—21no—
82C4⋊Dic151C2311yescharacteristic
83C4⋊Dic151C2311yescharacteristic
84C4⋊Dic151C2311yescharacteristic
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90C22⋊Dic151—21no—
91C22⋊Dic151—21no—
92C22⋊Dic151—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—21no—
97C4×Dic151—21no—
98C4×Dic151—21no—
99#41×C151—41no—
100#41×C151—41no—
101C2×Q8×C151C2311yescharacteristic
102C2×D4×C151—21no—
103C2×D4×C151—21no—
104C2×D4×C151C2311yescharacteristic
105C2×D4×C151C2311yescharacteristic
106C22×C4×C151—21no—
107C22×C4×C151C2311yescharacteristic
108SD16×C151—41no—
109D8×C151—41no—
110C2×C8×C151C2311yescharacteristic
111C2×C8×C151C2311yescharacteristic
112C4⋊C4×C151C2311yescharacteristic
113C22⋊C4×C151—21no—
114C22×D151—22no—
115C22×D151—41no—
116C22×D151—41no—
117C22×D151C2×D411yescharacteristic
118C22×D151C2×D411yescharacteristic
119Dic302—21no—
120Dic302—21no—
121C22⋊D151—42no—
122C22⋊D151—42no—
123C22⋊D151—42no—
124C22⋊D151—42no—
125C2×Dic151—21no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—21no—
129C2×Dic151—41no—
130C2×Dic151—42no—
131C2×Dic151C2×D411yescharacteristic
132C2×Dic151C2×D411yescharacteristic
133C4×D151—21no—
134C4×D151—21no—
135C4×D151—21no—
136C4×D151—21no—
137C4×D151—41no—
138C4×D151—41no—
139C151⋊C8—21no—
140C151⋊C8—21no—
141C23×C151—21no—
142C23×C151—21no—
143C23×C151C2×D411yescharacteristic
144Q8×C151—21no—
145Q8×C151—21no—
146D4×C151—21no—
147D4×C151—21no—
148D4×C151—21no—
149D4×C151—21no—
150D4×C151—42no—
151D4×C151—42no—
152C2×C4×C151—21no—
153C2×C4×C151—21no—
154C2×C4×C151—21no—
155C2×C4×C151—21no—
156C2×C4×C151—42no—
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×C151C22×D411yescharacteristic
171C2×D151—21no—
172C2×D151—21no—
173C2×D151—21no—
174C2×D151—21no—
175C2×D151—21no—
176C2×D151—44no—
177C2×D151#13512yes—
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×C151C2×#13511yescharacteristic
194C2×C151#57511yescharacteristic
195D151—22no—
196D151—41no—
197C151#319111yescharacteristic, complemented, Sylow
198#3191—1511nomaximal, Sylow
199#525—1511no—
200#525—1511no—
201#485—1511no—
202#485—1511no—
203#482—1511no—
204#482—1511no—
205#467—1511no—
206#466—1511no—
207#465—1511no—
208#465—1511no—
209#452—1511no—
210#452—1511no—
211#449—1511no—
212#449D15111yescharacteristic, complemented
213C2×C22⋊C8—1511no—
214C2×#41—1511no—
215C2×#41C2×D15111yescharacteristic
216C23×C4—1511no—
217C2×Q16—1511no—
218C2×SD16—1511no—
219C2×SD16C2×D15111yescharacteristic, complemented
220C2×D8C2×D15111yescharacteristic, complemented
221C22×C8—1511no—
222C22×C8—1511no—
223#123—3021no—
224#123—3021no—
225C22⋊Q8—1511no—
226C22⋊Q8—1511no—
227C22⋊Q8—1511no—
228C22⋊Q8—1511no—
229#121—1511no—
230#121—1511no—
231#121—1511no—
232#121C2×D15111yescharacteristic
233#120—3021no—
234#120—3021no—
235C4×D4—3021no—
236C4×D4—3021no—
237C4×D4—3021no—
238C4×D4—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#103C2×D15111yescharacteristic, complemented
249#102—1511no—
250#102—1511no—
251#102—1511no—
252#102C2×D15111yescharacteristic, complemented
253C22⋊C8—1511no—
254C22⋊C8—1511no—
255C22⋊C8—1511no—
256C22⋊C8C2×D15111yescharacteristic
257C24—1511no—
258#41—41no—
259#41—41no—
260#41—6041no—
261#41—6041no—
262C2×Q8—1511no—
263C2×Q8C22×D15111yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—3021no—
267C2×D4—3021no—
268C2×D4—3021no—
269C2×D4—3021no—
270C2×D4C22×D15111yescharacteristic
271C2×D4C22×D15111yescharacteristic
272C22×C4—21no—
273C22×C4—3021no—
274C22×C4—6041no—
275C22×C4—6041no—
276C22×C4—1511no—
277C22×C4—1511no—
278C22×C4—1511no—
279C22×C4—1511no—
280C22×C4—1511no—
281C22×C4C22×D15111yescharacteristic
282Q16—6041no—
283SD16—41no—
284SD16—6041no—
285D8—41no—
286C2×C8—6041no—
287C2×C8—6041no—
288C2×C8—1511no—
289C2×C8—1511no—
290C2×C8C22×D15111yescharacteristic
291C2×C8C22×D15111yescharacteristic
292C4⋊C4—3021no—
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—3022no—
315C23—6041no—
316C23—6041no—
317C23—1511no—
318C23—1511no—
319C23D4×D15111yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—3021no—
323Q8—3021no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—42no—
329D4—42no—
330D4—6042no—
331D4—6042no—
332D4—6042no—
333D4—6042no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—3021no—
340C2×C4—3021no—
341C2×C4—3021no—
342C2×C4—3021no—
343C2×C4—3021no—
344C2×C4—3021no—
345C2×C4—3021no—
346C2×C4—3021no—
347C2×C4—6041no—
348C2×C4—6041no—
349C2×C4—6041no—
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—3021no—
369C22—3021no—
370C22—3021no—
371C22—3021no—
372C22—3021no—
373C22—6044no—
374C22—1512no—
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—3022no—
391C2—6041no—
392C2#2375277211yescharacteristic
393C2#135×D15111yescharacteristic
394C2#2375300811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#449×C151C2
socleC22×C151C22×D4
hypercenter#449D151
hypocenterC151#3191
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #23752722C2semidirect
2. #23752719C2semidirect
3. #23752554C2semidirect
4. #23752552C2semidirect
5. #23752535C2semidirect
6. #23752533C2semidirect
7. #23752452C2semidirect
8. #23752445C2semidirect
9. #23752440C2semidirect
10. #23752438C2semidirect
11. #23752374C2semidirect
12. #23752371C2semidirect
13. #23752354C2semidirect
14. C22⋊C8×D151C2semidirect
15. #449×C151C2semidirect
18. C2×#14558994C22semidirect
19. C2×#14558992C22semidirect
39. #18012673C22semidirect
40. #18012672C22semidirect
41. #18012671C22semidirect
42. #18012670C22semidirect
43. #18012664C22semidirect
44. #18012664C22semidirect
45. #18012663C22semidirect
46. #18012660C22semidirect
47. #18012660C22semidirect
48. #18012660C22semidirect
53. C2×SD16×C151C22semidirect
54. C2×D8×C151C22semidirect
56. #103×C151C22semidirect
57. #102×C151C22semidirect
197. C151#3191semidirect
212. #449D151semidirect
219. C2×SD16C2×D151semidirect
220. C2×D8C2×D151semidirect
248. #103C2×D151semidirect
252. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527222
#237527192
#237525542
#237525522
#237525352
#237525332
#237524522
#237524452
#237524402
#237524382
#237523742
#237523712
#237523542
C22⋊C8×D1512
#449×C1512
#3191151