Finite Group Databasebeta

← #34080197

Subgroups — #34080197

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#23752831C211yesmaximal, characteristic, complemented
2#23752780C211yesmaximal, characteristic, complemented
3#23752602C211yesmaximal, characteristic, complemented
4#23752571C211yesmaximal, characteristic, complemented
5#23752559C211yesmaximal, characteristic, complemented
6#23752436C211yesmaximal, characteristic, complemented
7#23752429C211yesmaximal, characteristic, complemented
8#23752410C211yesmaximal, characteristic, complemented
9#23752405C211yesmaximal, characteristic, complemented
10#23752373C211yesmaximal, characteristic, complemented
11#23752361C211yesmaximal, characteristic, complemented
12#23752356C211yesmaximal, characteristic, complemented
13#23752344C211yesmaximal, characteristic, complemented
14#23752271C211yesmaximal, characteristic, complemented
15#495×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×D4×D151C2211yescharacteristic
18C2×#14558991C2211yescharacteristic
19C2×#14558991C2211yescharacteristic, complemented
20C2×#14558989C2211yescharacteristic
21C2×#14558989C2211yescharacteristic, complemented
22#18012739C2211yescharacteristic, complemented
23#18012736C2211yescharacteristic
24#18012735C2211yescharacteristic
25#18012732—21no—
26#18012728C2211yescharacteristic
27#18012725—21no—
28#18012723—21no—
29#18012716—21no—
30#18012715C2211yescharacteristic
31#18012712—21no—
32#18012712—21no—
33#18012710C2211yescharacteristic
34#18012709—21no—
35#18012709—21no—
36Q8×Dic151C2211yescharacteristic, complemented
37D4×Dic151C2211yescharacteristic, complemented
38#18012696C2211yescharacteristic
39Dic151⋊C8C2211yescharacteristic, complemented
40Dic151⋊C8C2211yescharacteristic, complemented
41#18012663C2211yescharacteristic, complemented
42#18012663C2211yescharacteristic, complemented
43#18012661C2211yescharacteristic
44#18012661C2211yescharacteristic
45#18012661C2211yescharacteristic, complemented
46#18012661C2211yescharacteristic, complemented
47#18012660C2211yescharacteristic
48#18012660C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51#18012650C2211yescharacteristic, complemented
52C2×Q16×C151C2211yescharacteristic, complemented
53C2×SD16×C151C2211yescharacteristic
54C2×SD16×C151C2211yescharacteristic, complemented
55C2×D8×C151C2211yescharacteristic
56#124×C151C2211yescharacteristic
57#124×C151C2211yescharacteristic, complemented
58C4×C8×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60#14559005—41no—
61#14559005—41no—
62C2×Dic302—21no—
63C2×D604—21no—
64C2×D604—21no—
65C2×D604—21no—
66C2×D604C2311yescharacteristic
67C2×D604C2311yescharacteristic
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72D4×D151—41no—
73D4×D151—41no—
74C22×Dic151—21no—
75C2×C4×D151—21no—
76C2×C4×D151C2311yescharacteristic
77#14558991—41no—
78#14558991—41no—
79#14558989—41no—
80#14558989—41no—
81C2×C151⋊C8C2311yescharacteristic
82C2×C151⋊C8C2311yescharacteristic
83C4⋊Dic151—21no—
84C4⋊Dic151—21no—
85C4⋊Dic151C2311yescharacteristic
86C4⋊Dic151C2311yescharacteristic
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)⋊C4D411yescharacteristic
96(C2×D151)⋊C4D411yescharacteristic
97C4×Dic151—21no—
98C4×Dic151C2311yescharacteristic
99C2×Q8×C151C2311yescharacteristic
100C2×Q8×C151C2311yescharacteristic
101C2×D4×C151C2311yescharacteristic
102C2×D4×C151C2311yescharacteristic
103Q16×C151—41no—
104SD16×C151—41no—
105SD16×C151—41no—
106D8×C151—41no—
107C2×C8×C151C2311yescharacteristic
108C2×C8×C151C2311yescharacteristic
109C22⋊C4×C151—21no—
110C22⋊C4×C151—21no—
111C22⋊C4×C151—21no—
112C22⋊C4×C151—21no—
113C42×C151C2311yescharacteristic
114C22×D151—21no—
115C22×D151—21no—
116C22×D151—42no—
117C22×D151—81no—
118C22×D151—81no—
119C22×D151C2×D411yescharacteristic
120Dic302—81no—
121D604—21no—
122D604—21no—
123D604—21no—
124D604—21no—
125D604—42no—
126D604—81no—
127D604—81no—
128C22⋊D151—42no—
129C22⋊D151—81no—
130C22⋊D151—81no—
131C22⋊D151—81no—
132C2×Dic151—21no—
133C2×Dic151—21no—
134C2×Dic151—81no—
135C2×Dic151C2×D411yescharacteristic
136C2×Dic151C2×D411yescharacteristic
137C2×Dic151C2×D411yescharacteristic
138C4×D151—21no—
139C4×D151—21no—
140C4×D151—42no—
141C151⋊C8—21no—
142C151⋊C8—21no—
143C23×C151—21no—
144C23×C151—21no—
145Q8×C151—21no—
146Q8×C151—21no—
147Q8×C151—21no—
148Q8×C151—21no—
149D4×C151—21no—
150D4×C151—21no—
151D4×C151—21no—
152D4×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×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#495D15111yescharacteristic, complemented
202#489—1511no—
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×Q16C2×D15111yescharacteristic, complemented
216C2×SD16—1511no—
217C2×SD16—1511no—
218C2×SD16C2×D15111yescharacteristic
219C2×SD16C2×D15111yescharacteristic, complemented
220C2×D8—1511no—
221C2×D8—1511no—
222C2×D8C2×D15111yescharacteristic
223C4⋊Q8—1511no—
224#127—1511no—
225#127—1511no—
226#126—3021no—
227#124—3021no—
228#124—1511no—
229#124C2×D15111yescharacteristic
230#124C2×D15111yescharacteristic, complemented
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#102—1511no—
249#102—1511no—
250#102—1511no—
251#102—1511no—
252C22⋊C8—1511no—
253C22⋊C8—1511no—
254#97—1511no—
255C4×C8C2×D15111yescharacteristic, complemented
256C24—3021no—
257#41—6041no—
258#41—6041no—
259C2×Q8—3021no—
260C2×Q8C22×D15111yescharacteristic
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×D4C22×D15111yescharacteristic
274C2×D4C22×D15111yescharacteristic
275C22×C4—3021no—
276C22×C4—3021no—
277C22×C4—1511no—
278Q16—41no—
279SD16—41no—
280SD16—41no—
281SD16—6041no—
282SD16—6041no—
283D8—41no—
284D8—6041no—
285D8—6041no—
286C2×C8—1511no—
287C2×C8—1511no—
288C2×C8C22×D15111yescharacteristic
289C2×C8C22×D15111yescharacteristic
290C4⋊C4—3021no—
291C4⋊C4—3021no—
292C4⋊C4—3021no—
293C4⋊C4—1511no—
294C4⋊C4—1511no—
295C4⋊C4—1511no—
296C4⋊C4—1511no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
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—21no—
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—12081no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
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—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#1801278411yescharacteristic
384C4#1801278411yescharacteristic
385C2—81no—
386C2—81no—
387C2—6041no—
388C2—12081no—
389C2—12081no—
390C2#2375277511yescharacteristic
391C2#2375301411yescharacteristic
392C2#2375301911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#495×C151C2
socleC22×C151C22×D4
hypercenter#495D151
hypocenterC151#3224
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #23752831C2semidirect
2. #23752780C2semidirect
3. #23752602C2semidirect
4. #23752571C2semidirect
5. #23752559C2semidirect
6. #23752436C2semidirect
7. #23752429C2semidirect
8. #23752410C2semidirect
9. #23752405C2semidirect
10. #23752373C2semidirect
11. #23752361C2semidirect
12. #23752356C2semidirect
13. #23752344C2semidirect
14. #23752271C2semidirect
15. #495×C151C2semidirect
19. C2×#14558991C22semidirect
21. C2×#14558989C22semidirect
22. #18012739C22semidirect
36. Q8×Dic151C22semidirect
37. D4×Dic151C22semidirect
39. Dic151⋊C8C22semidirect
40. Dic151⋊C8C22semidirect
41. #18012663C22semidirect
42. #18012663C22semidirect
45. #18012661C22semidirect
46. #18012661C22semidirect
51. #18012650C22semidirect
52. C2×Q16×C151C22semidirect
54. C2×SD16×C151C22semidirect
57. #124×C151C22semidirect
58. C4×C8×C151C22semidirect
196. C151#3224semidirect
201. #495D151semidirect
215. C2×Q16C2×D151semidirect
219. C2×SD16C2×D151semidirect
230. #124C2×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
#237528312
#237527802
#237526022
#237525712
#237525592
#237524362
#237524292
#237524102
#237524052
#237523732
#237523612
#237523562
#237523442
#237522712
#495×C1512
#3224151