Finite Group Databasebeta

← #34080207

Subgroups — #34080207

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#23752775C211yesmaximal, characteristic, complemented
3#23752599C211yesmaximal, characteristic, complemented
4#23752596C211yesmaximal, characteristic, complemented
5#23752574C211yesmaximal, characteristic, complemented
6#23752433C211yesmaximal, characteristic, complemented
7#23752426C211yesmaximal, characteristic, complemented
8#23752411C211yesmaximal, characteristic, complemented
9#23752406C211yesmaximal, characteristic, complemented
10#23752375C211yesmaximal, characteristic, complemented
11#23752364C211yesmaximal, characteristic, complemented
12#23752358C211yesmaximal, characteristic, complemented
13#23752347C211yesmaximal, characteristic, complemented
14#23752271C211yesmaximal, characteristic, complemented
15#486×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×D4×D151C2211yescharacteristic
18C2×Dic604C2211yescharacteristic, complemented
19C2×#14558993C2211yescharacteristic
20C2×#14558993C2211yescharacteristic, complemented
21C2×#14558992C2211yescharacteristic
22C2×#14558992C2211yescharacteristic, complemented
23C2×D1208C2211yescharacteristic
24C2×#14558989C2211yescharacteristic
25C2×#14558989C2211yescharacteristic, complemented
26#18012735C2211yescharacteristic
27#18012734—21no—
28#18012728—21no—
29#18012727C2211yescharacteristic
30#18012727C2211yescharacteristic, complemented
31#18012726C2211yescharacteristic
32#18012724—21no—
33#18012719C2211yescharacteristic
34#18012715—21no—
35#18012714C2211yescharacteristic
36#18012711—21no—
37#18012711—21no—
38#18012707—21no—
39#18012707—21no—
40#18012704C2211yescharacteristic, complemented
41#18012701C2211yescharacteristic, complemented
42#18012696C2211yescharacteristic
43Dic151⋊C8C2211yescharacteristic, complemented
44Dic151⋊C8C2211yescharacteristic, complemented
45#18012662C2211yescharacteristic, complemented
46#18012662C2211yescharacteristic, complemented
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51#18012650C2211yescharacteristic, complemented
52C4⋊Q8×C151C2211yescharacteristic, complemented
53#127×C151C2211yescharacteristic
54#102×C151C2211yescharacteristic
55#102×C151C2211yescharacteristic
56#102×C151C2211yescharacteristic, complemented
57#102×C151C2211yescharacteristic, complemented
58C4×C8×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60#14559003—41no—
61#14559003—41no—
62C2×Dic302C2311yescharacteristic
63C2×Dic302C2311yescharacteristic
64C2×D604—21no—
65C2×D604C2311yescharacteristic
66C2×D604C2311yescharacteristic
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71D4×D151—41no—
72D4×D151—41no—
73C22×Dic151—21no—
74C2×C4×D151—21no—
75C2×C4×D151C2311yescharacteristic
76Dic604—41no—
77#14558993—41no—
78#14558993—41no—
79#14558992—41no—
80#14558992—41no—
81D1208—41no—
82#14558989—41no—
83#14558989—41no—
84C2×C151⋊C8C2311yescharacteristic
85C2×C151⋊C8C2311yescharacteristic
86C4⋊Dic151—21no—
87Dic151⋊C4—21no—
88Dic151⋊C4D411yescharacteristic
89Dic151⋊C4D411yescharacteristic
90C22⋊Dic151—21no—
91C22⋊Dic151—21no—
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×D4×C151—21no—
105C2×D4×C151—21no—
106C2×D4×C151C2311yescharacteristic
107C2×D4×C151C2311yescharacteristic
108C2×C8×C151C2311yescharacteristic
109C2×C8×C151C2311yescharacteristic
110C4⋊C4×C151—21no—
111C4⋊C4×C151C2311yescharacteristic
112C4⋊C4×C151C2311yescharacteristic
113C42×C151C2311yescharacteristic
114C22×D151—21no—
115C22×D151—21no—
116C22×D151—42no—
117C22×D151—81no—
118C22×D151—81no—
119C22×D151C2×D411yescharacteristic
120Dic302—21no—
121Dic302—21no—
122Dic302—21no—
123Dic302—21no—
124D604—21no—
125D604—21no—
126D604—21no—
127D604—21no—
128D604—81no—
129C22⋊D151—42no—
130C22⋊D151—42no—
131C22⋊D151—81no—
132C22⋊D151—81no—
133C2×Dic151—21no—
134C2×Dic151—21no—
135C2×Dic151—42no—
136C2×Dic151C2×D411yescharacteristic
137C2×Dic151C2×D411yescharacteristic
138C2×Dic151C2×D411yescharacteristic
139C4×D151—21no—
140C4×D151—21no—
141C4×D151—81no—
142C151⋊C8—21no—
143C151⋊C8—21no—
144C23×C151—21no—
145C23×C151—21no—
146Q8×C151—81no—
147D4×C151—21no—
148D4×C151—21no—
149D4×C151—21no—
150D4×C151—21no—
151D4×C151—81no—
152D4×C151—81no—
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×C151—41no—
164C22×C151—41no—
165C22×C151—41no—
166C22×C151C22×D411yescharacteristic
167C2×D151—21no—
168C2×D151—21no—
169C2×D151—21no—
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×C151H(5,𝔽2)11yescharacteristic
182C4×C151H(5,𝔽2)11yescharacteristic
183Dic151—21no—
184Dic151—21no—
185Dic151—21no—
186Dic151—41no—
187Dic151—41no—
188C2×C151—81no—
189C2×C151—81no—
190C2×C151#53511yescharacteristic
191C2×C151#57611yescharacteristic
192C2×C151#57711yescharacteristic
193D151—41no—
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#486D15111yescharacteristic, complemented
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#127C2×D15111yescharacteristic
226#126—3021no—
227#124—3021no—
228#124—1511no—
229#124—1511no—
230#124—1511no—
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#103—1511no—
245#103—1511no—
246#102—1511no—
247#102—1511no—
248#102C2×D15111yescharacteristic
249#102C2×D15111yescharacteristic
250#102C2×D15111yescharacteristic, complemented
251#102C2×D15111yescharacteristic, complemented
252C22⋊C8—1511no—
253C22⋊C8—1511no—
254#97—1511no—
255C4×C8C2×D15111yescharacteristic, complemented
256C24—3021no—
257#41—6041no—
258#41—6041no—
259C2×Q8—21no—
260C2×Q8—1511no—
261C2×Q8—1511no—
262C2×D4—21no—
263C2×D4—21no—
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×D4C22×D15111yescharacteristic
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—3021no—
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—
310C42C22×D15111yescharacteristic
311C23—21no—
312C23—21no—
313C23—3021no—
314C23—3021no—
315C23—6042no—
316C23—1511no—
317C23—12081no—
318C23—12081no—
319Q8—81no—
320Q8—3021no—
321Q8—3021no—
322Q8—3021no—
323Q8—3021no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—81no—
329D4—81no—
330D4—3021no—
331D4—3021no—
332D4—3021no—
333D4—3021no—
334D4—6042no—
335D4—6042no—
336D4—12081no—
337D4—12081no—
338D4—12081no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—3021no—
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—41no—
361C22—41no—
362C22—41no—
363C22—3021no—
364C22—3021no—
365C22—3021no—
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—3021no—
379C4—3021no—
380C4—3021no—
381C4—6041no—
382C4—6041no—
383C4#1801278511yescharacteristic
384C4#1801278511yescharacteristic
385C2—81no—
386C2—81no—
387C2—6041no—
388C2—12081no—
389C2—12081no—
390C2#2375278011yescharacteristic
391C2#2375301311yescharacteristic
392C2#2375301811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#486×C151C2
socleC22×C151C22×D4
hypercenter#486D151
hypocenterC151#3224
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #23752836C2semidirect
2. #23752775C2semidirect
3. #23752599C2semidirect
4. #23752596C2semidirect
5. #23752574C2semidirect
6. #23752433C2semidirect
7. #23752426C2semidirect
8. #23752411C2semidirect
9. #23752406C2semidirect
10. #23752375C2semidirect
11. #23752364C2semidirect
12. #23752358C2semidirect
13. #23752347C2semidirect
14. #23752271C2semidirect
15. #486×C151C2semidirect
18. C2×Dic604C22semidirect
20. C2×#14558993C22semidirect
22. C2×#14558992C22semidirect
25. C2×#14558989C22semidirect
30. #18012727C22semidirect
40. #18012704C22semidirect
41. #18012701C22semidirect
43. Dic151⋊C8C22semidirect
44. Dic151⋊C8C22semidirect
45. #18012662C22semidirect
46. #18012662C22semidirect
51. #18012650C22semidirect
52. C4⋊Q8×C151C22semidirect
56. #102×C151C22semidirect
57. #102×C151C22semidirect
58. C4×C8×C151C22semidirect
196. C151#3224semidirect
203. #486D151semidirect
223. C4⋊Q8C2×D151semidirect
250. #102C2×D151semidirect
251. #102C2×D151semidirect
255. C4×C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528362
#237527752
#237525992
#237525962
#237525742
#237524332
#237524262
#237524112
#237524062
#237523752
#237523642
#237523582
#237523472
#237522712
#486×C1512
#3224151