Finite Group Databasebeta

← #34080205

Subgroups — #34080205

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#23752836C211yesmaximal, characteristic, complemented
2#23752780C211yesmaximal, characteristic, complemented
3#23752601C211yesmaximal, characteristic, complemented
4#23752594C211yesmaximal, characteristic, complemented
5#23752560C211yesmaximal, characteristic, complemented
6#23752437C211yesmaximal, characteristic, complemented
7#23752430C211yesmaximal, characteristic, complemented
8#23752411C211yesmaximal, characteristic, complemented
9#23752406C211yesmaximal, characteristic, complemented
10#23752377C211yesmaximal, characteristic, complemented
11#23752364C211yesmaximal, characteristic, complemented
12#23752360C211yesmaximal, characteristic, complemented
13#23752347C211yesmaximal, characteristic, complemented
14#23752274C211yesmaximal, characteristic, complemented
15#489×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×D4×D151C2211yescharacteristic
18C2×#14558994C2211yescharacteristic, complemented
19C2×#14558993C2211yescharacteristic
20C2×#14558993C2211yescharacteristic, complemented
21C2×#14558992C2211yescharacteristic
22C2×#14558991C2211yescharacteristic, complemented
23C2×D1208C2211yescharacteristic
24C2×D1208C2211yescharacteristic, complemented
25C2×#14558989C2211yescharacteristic
26#18012736C2211yescharacteristic
27#18012735C2211yescharacteristic
28#18012734—21no—
29#18012728—21no—
30#18012728C2211yescharacteristic
31#18012727C2211yescharacteristic, complemented
32#18012724—21no—
33#18012719C2211yescharacteristic
34#18012715—21no—
35#18012714C2211yescharacteristic
36#18012712—21no—
37#18012712—21no—
38#18012709—21no—
39#18012709—21no—
40#18012704C2211yescharacteristic, complemented
41#18012701C2211yescharacteristic, complemented
42#18012696C2211yescharacteristic
43Dic151⋊C8C2211yescharacteristic, complemented
44Dic151⋊C8C2211yescharacteristic, complemented
45#18012659C2211yescharacteristic
46#18012659C2211yescharacteristic
47#18012659C2211yescharacteristic, complemented
48#18012659C2211yescharacteristic, complemented
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C4×C151⋊C8C2211yescharacteristic, complemented
52C4⋊Q8×C151C2211yescharacteristic, complemented
53#124×C151C2211yescharacteristic
54#103×C151C2211yescharacteristic, complemented
55#103×C151C2211yescharacteristic, complemented
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#97×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60#14559005—41no—
61#14559005—41no—
62C2×Dic302C2311yescharacteristic
63C2×D604—21no—
64C2×D604—21no—
65C2×D604—21no—
66C2×D604—21no—
67C2×D604C2311yescharacteristic
68C2×D604C2311yescharacteristic
69C2×D604C2311yescharacteristic
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73D4×D151—41no—
74D4×D151—41no—
75C2×C4×D151—21no—
76C2×C4×D151—21no—
77C2×C4×D151C2311yescharacteristic
78#14558994—41no—
79#14558993—41no—
80#14558993—41no—
81#14558992—41no—
82#14558991—41no—
83D1208—41no—
84D1208—41no—
85#14558989—41no—
86C2×C151⋊C8C2311yescharacteristic
87C2×C151⋊C8C2311yescharacteristic
88C4⋊Dic151—21no—
89Dic151⋊C4—21no—
90Dic151⋊C4D411yescharacteristic
91Dic151⋊C4D411yescharacteristic
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4—21no—
98(C2×D151)⋊C4—21no—
99(C2×D151)⋊C4D411yescharacteristic
100(C2×D151)⋊C4D411yescharacteristic
101C4×Dic151—21no—
102C4×Dic151C2311yescharacteristic
103C2×Q8×C151—21no—
104C2×Q8×C151C2311yescharacteristic
105C2×D4×C151C2311yescharacteristic
106C2×C8×C151C2311yescharacteristic
107C2×C8×C151C2311yescharacteristic
108C4⋊C4×C151—21no—
109C4⋊C4×C151C2311yescharacteristic
110C4⋊C4×C151C2311yescharacteristic
111C22⋊C4×C151—21no—
112C22⋊C4×C151—21no—
113C42×C151C2311yescharacteristic
114C22×D151—21no—
115C22×D151—21no—
116C22×D151—21no—
117C22×D151—42no—
118C22×D151—81no—
119C22×D151—81no—
120C22×D151C2×D411yescharacteristic
121Dic302—21no—
122Dic302—21no—
123D604—21no—
124D604—21no—
125D604—21no—
126D604—21no—
127D604—21no—
128D604—21no—
129D604—42no—
130D604—81no—
131D604—81no—
132D604—81no—
133C22⋊D151—42no—
134C22⋊D151—81no—
135C22⋊D151—81no—
136C2×Dic151—21no—
137C2×Dic151C2×D411yescharacteristic
138C2×Dic151C2×D411yescharacteristic
139C2×Dic151C2×D411yescharacteristic
140C4×D151—21no—
141C4×D151—21no—
142C4×D151—42no—
143C4×D151—81no—
144C151⋊C8—21no—
145C151⋊C8—21no—
146C23×C151—21no—
147Q8×C151—21no—
148Q8×C151—21no—
149Q8×C151—81no—
150D4×C151—21no—
151D4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151—21no—
154C2×C4×C151—21no—
155C2×C4×C151C2×D411yescharacteristic
156C2×C4×C151C2×D411yescharacteristic
157C2×C4×C151C2411yescharacteristic
158C8×C151—21no—
159C8×C151—21no—
160C22×C151—41no—
161C22×C151—41no—
162C22×C151—41no—
163C22×C151C22×D411yescharacteristic
164C2×D151—21no—
165C2×D151—21no—
166C2×D151—21no—
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—21no—
179C4×C151—41no—
180C4×C151—41no—
181C4×C151—41no—
182C4×C151H(5,𝔽2)11yescharacteristic
183C4×C151H(5,𝔽2)11yescharacteristic
184Dic151—21no—
185Dic151—21no—
186Dic151—21no—
187Dic151—41no—
188C2×C151—81no—
189C2×C151#53511yescharacteristic
190C2×C151#57611yescharacteristic
191C2×C151#57711yescharacteristic
192D151—41no—
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#489D15111yescharacteristic, complemented
203#486—1511no—
204#464—1511no—
205#463—1511no—
206#460—1511no—
207#459—1511no—
208#452—1511no—
209#450—1511no—
210#449—1511no—
211#447—1511no—
212#433—1511no—
213C2×#41—1511no—
214C22×D4—1511no—
215C2×Q16—1511no—
216C2×SD16—1511no—
217C2×SD16—1511no—
218C2×SD16—1511no—
219C2×SD16—1511no—
220C2×D8—1511no—
221C2×D8—1511no—
222C2×D8—1511no—
223C4⋊Q8C2×D15111yescharacteristic, complemented
224#127—1511no—
225#127—1511no—
226#126—3021no—
227#124—3021no—
228#124—1511no—
229#124—1511no—
230#124C2×D15111yescharacteristic
231#123—3021no—
232C22⋊Q8—3021no—
233C22⋊Q8—1511no—
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#103C2×D15111yescharacteristic, complemented
245#103C2×D15111yescharacteristic, complemented
246#102—1511no—
247#102—1511no—
248#102—1511no—
249#102—1511no—
250#102C2×D15111yescharacteristic
251#102C2×D15111yescharacteristic
252C22⋊C8—1511no—
253C22⋊C8—1511no—
254#97C2×D15111yescharacteristic, complemented
255C4×C8—1511no—
256C24—3021no—
257#41—6041no—
258#41—6041no—
259C2×Q8—21no—
260C2×Q8—1511no—
261C2×Q8C22×D15111yescharacteristic
262C2×D4—3021no—
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—3021no—
276C22×C4—3021no—
277C22×C4—1511no—
278Q16—6041no—
279SD16—6041no—
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⋊C4C22×D15111yescharacteristic
296C4⋊C4C22×D15111yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
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—
310C42C22×D15111yescharacteristic
311C23—21no—
312C23—3021no—
313C23—3021no—
314C23—3021no—
315C23—6042no—
316C23—1511no—
317C23—12081no—
318C23—12081no—
319Q8—21no—
320Q8—21no—
321Q8—81no—
322Q8—3021no—
323Q8—3021no—
324D4—21no—
325D4—21no—
326D4—3021no—
327D4—3021no—
328D4—3021no—
329D4—3021no—
330D4—3021no—
331D4—3021no—
332D4—6042no—
333D4—6042no—
334D4—12081no—
335D4—12081no—
336D4—12081no—
337D4—12081no—
338D4—12081no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—3021no—
343C2×C4—3021no—
344C2×C4—3021no—
345C2×C4—6042no—
346C2×C4—1511no—
347C2×C4—1511no—
348C2×C4—1511no—
349C2×C4—12081no—
350C2×C4D4×D15111yescharacteristic
351C2×C4D4×D15111yescharacteristic
352C2×C4C23×D15111yescharacteristic
353C8—21no—
354C8—21no—
355C8—3021no—
356C8—3021no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—3021no—
361C22—3021no—
362C22—3021no—
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—21no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—3021no—
380C4—3021no—
381C4—3021no—
382C4—6041no—
383C4#1801278511yescharacteristic
384C4#1801278511yescharacteristic
385C2—81no—
386C2—6041no—
387C2—12081no—
388C2—12081no—
389C2—12081no—
390C2#2375278011yescharacteristic
391C2#2375301611yescharacteristic
392C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#489×C151C2
socleC22×C151C22×D4
hypercenter#489D151
hypocenterC151#3224
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #23752836C2semidirect
2. #23752780C2semidirect
3. #23752601C2semidirect
4. #23752594C2semidirect
5. #23752560C2semidirect
6. #23752437C2semidirect
7. #23752430C2semidirect
8. #23752411C2semidirect
9. #23752406C2semidirect
10. #23752377C2semidirect
11. #23752364C2semidirect
12. #23752360C2semidirect
13. #23752347C2semidirect
14. #23752274C2semidirect
15. #489×C151C2semidirect
18. C2×#14558994C22semidirect
20. C2×#14558993C22semidirect
22. C2×#14558991C22semidirect
24. C2×D1208C22semidirect
31. #18012727C22semidirect
40. #18012704C22semidirect
41. #18012701C22semidirect
43. Dic151⋊C8C22semidirect
44. Dic151⋊C8C22semidirect
47. #18012659C22semidirect
48. #18012659C22semidirect
51. C4×C151⋊C8C22semidirect
52. C4⋊Q8×C151C22semidirect
54. #103×C151C22semidirect
55. #103×C151C22semidirect
58. #97×C151C22semidirect
196. C151#3224semidirect
202. #489D151semidirect
223. C4⋊Q8C2×D151semidirect
244. #103C2×D151semidirect
245. #103C2×D151semidirect
254. #97C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528362
#237527802
#237526012
#237525942
#237525602
#237524372
#237524302
#237524112
#237524062
#237523772
#237523642
#237523602
#237523472
#237522742
#489×C1512
#3224151