Finite Group Databasebeta

← #34080210

Subgroups — #34080210

Order 19328.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752835C211yesmaximal, characteristic, complemented
2#23752776C211yesmaximal, characteristic, complemented
3#23752598C211yesmaximal, characteristic, complemented
4#23752597C211yesmaximal, characteristic, complemented
5#23752573C211yesmaximal, characteristic, complemented
6#23752557C211yesmaximal, characteristic, complemented
7#23752436C211yesmaximal, characteristic, complemented
8#23752430C211yesmaximal, characteristic, complemented
9#23752410C211yesmaximal, characteristic, complemented
10#23752406C211yesmaximal, characteristic, complemented
11#23752362C211yesmaximal, characteristic, complemented
12#23752357C211yesmaximal, characteristic, complemented
13#23752348C211yesmaximal, characteristic, complemented
14#23752270C211yesmaximal, characteristic, complemented
15#452×C151C211yesmaximal, characteristic, complemented
16C22×D604C2211yescharacteristic
17C2×#14558991C2211yescharacteristic
18C2×#14558991C2211yescharacteristic
19C2×#14558991C2211yescharacteristic, complemented
20C2×D1208C2211yescharacteristic
21C2×D1208C2211yescharacteristic
22C2×#14558989C2211yescharacteristic, complemented
23#18012738C2211yescharacteristic, complemented
24#18012735C2211yescharacteristic
25#18012735C2211yescharacteristic
26#18012734—21no—
27#18012728C2211yescharacteristic
28#18012728C2211yescharacteristic
29#18012728C2211yescharacteristic, complemented
30#18012725—21no—
31#18012721—21no—
32#18012719—21no—
33#18012713—21no—
34#18012713—21no—
35#18012713C2211yescharacteristic
36#18012707—21no—
37#18012707—21no—
38Q8×Dic151C2211yescharacteristic, complemented
39#18012701C2211yescharacteristic, complemented
40#18012698C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic, complemented
42Dic151⋊C8C2211yescharacteristic, complemented
43#18012663C2211yescharacteristic, complemented
44#18012661C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012660C2211yescharacteristic, complemented
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50#18012649C2211yescharacteristic, complemented
51C8×Dic151C2211yescharacteristic, complemented
52C2×#41×C151C2211yescharacteristic
53C2×Q16×C151C2211yescharacteristic, complemented
54C2×SD16×C151C2211yescharacteristic, complemented
55C22⋊Q8×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic, complemented
57#102×C151C2211yescharacteristic, complemented
58C22⋊C8×C151C2211yescharacteristic
59C23×D151—21no—
60C2×Dic302—21no—
61C2×D604—21no—
62C2×D604—41no—
63C2×D604—41no—
64C2×D604C2311yescharacteristic
65C2×D604C2311yescharacteristic
66C2×D604C2311yescharacteristic
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C4×D151—21no—
73#14558991—41no—
74#14558991—41no—
75#14558991—41no—
76D1208—41no—
77D1208—41no—
78#14558989—41no—
79C2×C151⋊C8C2311yescharacteristic
80C2×C151⋊C8C2311yescharacteristic
81C4⋊Dic151—21no—
82C4⋊Dic151D411yescharacteristic
83C4⋊Dic151D411yescharacteristic
84C4⋊Dic151C2311yescharacteristic
85Dic151⋊C4—21no—
86C22⋊Dic151D411yescharacteristic
87C22⋊Dic151D411yescharacteristic
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—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96C4×Dic151—21no—
97C4×Dic151C2311yescharacteristic
98C4×Dic151C2311yescharacteristic
99#41×C151—41no—
100#41×C151—41no—
101C2×Q8×C151C2311yescharacteristic
102C2×Q8×C151C2311yescharacteristic
103C2×D4×C151—21no—
104C2×D4×C151C2311yescharacteristic
105C22×C4×C151—21no—
106C22×C4×C151C2311yescharacteristic
107Q16×C151—41no—
108SD16×C151—41no—
109C2×C8×C151C2311yescharacteristic
110C2×C8×C151C2311yescharacteristic
111C4⋊C4×C151—21no—
112C4⋊C4×C151C2311yescharacteristic
113C22⋊C4×C151—21no—
114C22×D151—21no—
115C22×D151—21no—
116C22×D151—21no—
117C22×D151—42no—
118C22×D151—81no—
119C22×D151—81no—
120Dic302—81no—
121D604—21no—
122D604—21no—
123D604—21no—
124D604—21no—
125D604—21no—
126D604—21no—
127D604—42no—
128C22⋊D151—81no—
129C22⋊D151—81no—
130C22⋊D151—81no—
131C22⋊D151—81no—
132C22⋊D151—81no—
133C2×Dic151—21no—
134C2×Dic151C2×D411yescharacteristic
135C2×Dic151C2×D411yescharacteristic
136C2×Dic151C2×D411yescharacteristic
137C2×Dic151C2×D411yescharacteristic
138C4×D151—81no—
139C151⋊C8—21no—
140C151⋊C8—21no—
141C23×C151—21no—
142C23×C151C2×D411yescharacteristic
143Q8×C151—21no—
144Q8×C151—21no—
145Q8×C151—21no—
146Q8×C151—21no—
147D4×C151—21no—
148D4×C151—21no—
149D4×C151—42no—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151—21no—
154C2×C4×C151—21no—
155C2×C4×C151—42no—
156C2×C4×C151C2×D411yescharacteristic
157C2×C4×C151C2411yescharacteristic
158C8×C151—21no—
159C8×C151—21no—
160C22×C151—21no—
161C22×C151—21no—
162C22×C151—21no—
163C22×C151—41no—
164C22×C151—41no—
165C22×C151—41no—
166C22×C151C22×D411yescharacteristic
167C2×D151—41no—
168C2×D151—41no—
169C2×D151—41no—
170C2×D151—41no—
171C2×D151—41no—
172C2×D151—41no—
173C2×D151—41no—
174C2×D151—41no—
175C2×D151—41no—
176C2×D151—84no—
177C4×C151—21no—
178C4×C151—41no—
179C4×C151—41no—
180C4×C151—41no—
181C4×C151H(5,𝔽2)11yescharacteristic
182C4×C151H(5,𝔽2)11yescharacteristic
183Dic151—21no—
184Dic151—21no—
185Dic151—21no—
186Dic151—21no—
187Dic151—41no—
188C2×C151—41no—
189C2×C151—81no—
190C2×C151#53511yescharacteristic
191C2×C151#57611yescharacteristic
192C2×C151#57711yescharacteristic
193D151—81no—
194D151—81no—
195D151—81no—
196C151#322411yescharacteristic, complemented, Sylow
197#3224—1511nomaximal, Sylow
198#542—1511no—
199#535—1511no—
200#496—1511no—
201#495—1511no—
202#489—1511no—
203#486—1511no—
204#464—1511no—
205#463—1511no—
206#460—1511no—
207#459—1511no—
208#452D15111yescharacteristic, complemented
209#450—1511no—
210#449—1511no—
211#447—1511no—
212#433—1511no—
213C2×#41C2×D15111yescharacteristic
214C22×D4—1511no—
215C2×Q16C2×D15111yescharacteristic, complemented
216C2×SD16—1511no—
217C2×SD16—1511no—
218C2×SD16—1511no—
219C2×SD16C2×D15111yescharacteristic, complemented
220C2×D8—1511no—
221C2×D8—1511no—
222C2×D8—1511no—
223C4⋊Q8—1511no—
224#127—1511no—
225#127—1511no—
226#126—3021no—
227#124—3021no—
228#124—1511no—
229#124—1511no—
230#124—1511no—
231#123—3021no—
232C22⋊Q8—3021no—
233C22⋊Q8C2×D15111yescharacteristic
234#121—3021no—
235#121—3021no—
236#121—1511no—
237#120—3021no—
238#120—3021no—
239C4×Q8—1511no—
240C4×D4—1511no—
241#117—1511no—
242C4⋊C8—1511no—
243C4⋊C8—1511no—
244#103—1511no—
245#103C2×D15111yescharacteristic, complemented
246#102—1511no—
247#102—1511no—
248#102—1511no—
249#102—1511no—
250#102—1511no—
251#102C2×D15111yescharacteristic, complemented
252C22⋊C8—1511no—
253C22⋊C8C2×D15111yescharacteristic
254#97—1511no—
255C4×C8—1511no—
256C24—3021no—
257#41—41no—
258#41—41no—
259C2×Q8—3021no—
260C2×Q8C22×D15111yescharacteristic
261C2×Q8C22×D15111yescharacteristic
262C2×D4—21no—
263C2×D4—3021no—
264C2×D4—3021no—
265C2×D4—3021no—
266C2×D4—3021no—
267C2×D4—3021no—
268C2×D4—3021no—
269C2×D4—6041no—
270C2×D4—6041no—
271C2×D4—1511no—
272C2×D4—1511no—
273C2×D4—1511no—
274C2×D4C22×D15111yescharacteristic
275C22×C4—21no—
276C22×C4—3021no—
277C22×C4C22×D15111yescharacteristic
278Q16—41no—
279SD16—41no—
280SD16—6041no—
281SD16—6041no—
282SD16—6041no—
283D8—6041no—
284D8—6041no—
285D8—6041no—
286C2×C8—1511no—
287C2×C8—1511no—
288C2×C8C22×D15111yescharacteristic
289C2×C8C22×D15111yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—3021no—
292C4⋊C4—3021no—
293C4⋊C4—1511no—
294C4⋊C4—1511no—
295C4⋊C4—1511no—
296C4⋊C4C22×D15111yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—3021no—
299C22⋊C4—3021no—
300C22⋊C4—3021no—
301C22⋊C4—3021no—
302C22⋊C4—3021no—
303C22⋊C4—3021no—
304C22⋊C4—3021no—
305C22⋊C4—3021no—
306C22⋊C4—1511no—
307C22⋊C4—1511no—
308C42—3021no—
309C42—1511no—
310C42—1511no—
311C23—21no—
312C23—3021no—
313C23—3021no—
314C23—3021no—
315C23—6042no—
316C23—12081no—
317C23—12081no—
318C23D4×D15111yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—12081no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—3021no—
328D4—3021no—
329D4—3021no—
330D4—3021no—
331D4—3021no—
332D4—3021no—
333D4—6042no—
334D4—12081no—
335D4—12081no—
336D4—12081no—
337D4—12081no—
338D4—12081no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—3021no—
346C2×C4—1511no—
347C2×C4—1511no—
348C2×C4—1511no—
349C2×C4—1511no—
350C2×C4—12081no—
351C2×C4D4×D15111yescharacteristic
352C2×C4C23×D15111yescharacteristic
353C8—21no—
354C8—21no—
355C8—3021no—
356C8—3021no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—6041no—
364C22—6041no—
365C22—6041no—
366C22—6041no—
367C22—6041no—
368C22—6041no—
369C22—6041no—
370C22—6041no—
371C22—6041no—
372C22—12084no—
373C22C2×D4×D15111yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—3021no—
379C4—3021no—
380C4—3021no—
381C4—3021no—
382C4—6041no—
383C4#1801278411yescharacteristic
384C4#1801278411yescharacteristic
385C2—41no—
386C2—81no—
387C2—12081no—
388C2—12081no—
389C2—12081no—
390C2#2375277711yescharacteristic
391C2#2375301411yescharacteristic
392C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#452×C151C2
socleC22×C151C22×D4
hypercenter#452D151
hypocenterC151#3224
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #23752835C2semidirect
2. #23752776C2semidirect
3. #23752598C2semidirect
4. #23752597C2semidirect
5. #23752573C2semidirect
6. #23752557C2semidirect
7. #23752436C2semidirect
8. #23752430C2semidirect
9. #23752410C2semidirect
10. #23752406C2semidirect
11. #23752362C2semidirect
12. #23752357C2semidirect
13. #23752348C2semidirect
14. #23752270C2semidirect
15. #452×C151C2semidirect
19. C2×#14558991C22semidirect
22. C2×#14558989C22semidirect
23. #18012738C22semidirect
29. #18012728C22semidirect
38. Q8×Dic151C22semidirect
39. #18012701C22semidirect
41. Dic151⋊C8C22semidirect
42. Dic151⋊C8C22semidirect
43. #18012663C22semidirect
46. #18012660C22semidirect
50. #18012649C22semidirect
51. C8×Dic151C22semidirect
53. C2×Q16×C151C22semidirect
54. C2×SD16×C151C22semidirect
56. #103×C151C22semidirect
57. #102×C151C22semidirect
196. C151#3224semidirect
208. #452D151semidirect
215. C2×Q16C2×D151semidirect
219. C2×SD16C2×D151semidirect
245. #103C2×D151semidirect
251. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528352
#237527762
#237525982
#237525972
#237525732
#237525572
#237524362
#237524302
#237524102
#237524062
#237523622
#237523572
#237523482
#237522702
#452×C1512
#3224151