Finite Group Databasebeta

← #34080198

Subgroups — #34080198

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#23752781C211yesmaximal, characteristic, complemented
2#23752602C211yesmaximal, characteristic, complemented
3#23752594C211yesmaximal, characteristic, complemented
4#23752574C211yesmaximal, characteristic, complemented
5#23752560C211yesmaximal, characteristic, complemented
6#23752434C211yesmaximal, characteristic, complemented
7#23752427C211yesmaximal, characteristic, complemented
8#23752412C211yesmaximal, characteristic, complemented
9#23752407C211yesmaximal, characteristic, complemented
10#23752372C211yesmaximal, characteristic, complemented
11#23752362C211yesmaximal, characteristic, complemented
12#23752355C211yesmaximal, characteristic, complemented
13#23752345C211yesmaximal, characteristic, complemented
14#23752273C211yesmaximal, characteristic, complemented
15#542×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C22×D604C2211yescharacteristic
18C2×#14558994C2211yescharacteristic, complemented
19C2×#14558992C2211yescharacteristic, complemented
20C2×#14558991C2211yescharacteristic
21C2×#14558991C2211yescharacteristic
22C2×#14558991C2211yescharacteristic, complemented
23C2×#14558989C2211yescharacteristic
24C2×#14558989C2211yescharacteristic
25C2×#14558989C2211yescharacteristic, complemented
26#18012736C2211yescharacteristic
27#18012736C2211yescharacteristic
28#18012727C2211yescharacteristic
29#18012727C2211yescharacteristic
30#18012714—21no—
31#18012714—21no—
32#18012709—21no—
33#18012709—21no—
34C4⋊(C151⋊C8)C2211yescharacteristic, complemented
35C4⋊(C151⋊C8)C2211yescharacteristic, complemented
36#18012662C2211yescharacteristic, complemented
37#18012662C2211yescharacteristic, complemented
38#18012659C2211yescharacteristic
39#18012659C2211yescharacteristic
40#18012659C2211yescharacteristic
41#18012659C2211yescharacteristic
42#18012659C2211yescharacteristic, complemented
43#18012659C2211yescharacteristic, complemented
44C22⋊(C151⋊C8)C2211yescharacteristic
45C22⋊(C151⋊C8)C2211yescharacteristic
46#18012650C2211yescharacteristic, complemented
47C4×C151⋊C8C2211yescharacteristic, complemented
48C4⋊Q8×C151C2211yescharacteristic, complemented
49#126×C151—21no—
50#124×C151—21no—
51#124×C151C2211yescharacteristic, complemented
52#123×C151—21no—
53C22⋊Q8×C151—21no—
54C22⋊Q8×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic
56C4×Q8×C151C2211yescharacteristic, complemented
57C4×D4×C151C2211yescharacteristic, complemented
58#117×C151C2211yescharacteristic
59C23×D151—21no—
60#14559004—41no—
61#14559004—41no—
62C2×Dic302C2311yescharacteristic
63C2×D604—21no—
64C2×D604—21no—
65C2×D604—21no—
66C2×D604—21no—
67C2×D604—21no—
68C2×D604—41no—
69C2×D604—41no—
70C2×D604C2311yescharacteristic
71C2×D604C2311yescharacteristic
72C2×D604C2311yescharacteristic
73C2×C22⋊D151—21no—
74C2×C4×D151—21no—
75#14558994—41no—
76#14558992—41no—
77#14558991—41no—
78#14558991—41no—
79#14558991—41no—
80#14558989—41no—
81#14558989—41no—
82#14558989—41no—
83C2×C151⋊C8C2311yescharacteristic
84C2×C151⋊C8C2311yescharacteristic
85C2×C151⋊C8C2311yescharacteristic
86C2×C151⋊C8C2311yescharacteristic
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91C2×Q8×C151—21no—
92C2×Q8×C151C2311yescharacteristic
93C2×D4×C151—21no—
94C2×D4×C151C2311yescharacteristic
95C22×C4×C151—21no—
96C22×C4×C151C2311yescharacteristic
97C4⋊C4×C151—21no—
98C4⋊C4×C151—21no—
99C4⋊C4×C151—21no—
100C4⋊C4×C151D411yescharacteristic
101C4⋊C4×C151D411yescharacteristic
102C4⋊C4×C151C2311yescharacteristic
103C4⋊C4×C151C2311yescharacteristic
104C22⋊C4×C151—21no—
105C22⋊C4×C151—21no—
106C22⋊C4×C151—21no—
107C22⋊C4×C151—21no—
108C22⋊C4×C151—21no—
109C22⋊C4×C151D411yescharacteristic
110C22⋊C4×C151D411yescharacteristic
111C42×C151—21no—
112C42×C151C2311yescharacteristic
113C42×C151C2311yescharacteristic
114C22×D151—21no—
115C22×D151—21no—
116C22×D151—21no—
117C22×D151—42no—
118C22×D151—81no—
119C22×D151—81no—
120Dic302—21no—
121Dic302—21no—
122D604—21no—
123D604—21no—
124D604—21no—
125D604—21no—
126D604—21no—
127D604—21no—
128D604—42no—
129D604—81no—
130D604—81no—
131D604—81no—
132D604—81no—
133C22⋊D151—42no—
134C2×Dic151—21no—
135C4×D151—42no—
136C151⋊C8—21no—
137C151⋊C8—21no—
138C151⋊C8—21no—
139C151⋊C8—21no—
140C23×C151—21no—
141C23×C151C2×D411yescharacteristic
142Q8×C151—21no—
143Q8×C151—21no—
144Q8×C151—81no—
145D4×C151—21no—
146D4×C151—21no—
147D4×C151—81no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151—81no—
154C2×C4×C151C2×D411yescharacteristic
155C2×C4×C151C2×D411yescharacteristic
156C2×C4×C151C2×D411yescharacteristic
157C2×C4×C151C2×D411yescharacteristic
158C2×C4×C151C2×D411yescharacteristic
159C2×C4×C151C2411yescharacteristic
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—21no—
179C4×C151—21no—
180C4×C151—21no—
181C4×C151—21no—
182C4×C151—41no—
183C4×C151—41no—
184C4×C151—41no—
185C4×C151H(5,𝔽2)11yescharacteristic
186C4×C151H(5,𝔽2)11yescharacteristic
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#542D15111yescharacteristic, complemented
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#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—21no—
227#124—21no—
228#124—1511no—
229#124—1511no—
230#124C2×D15111yescharacteristic, complemented
231#123—21no—
232C22⋊Q8—21no—
233C22⋊Q8C2×D15111yescharacteristic
234#121—3021no—
235#121—3021no—
236#121C2×D15111yescharacteristic
237#120—3021no—
238#120—3021no—
239C4×Q8C2×D15111yescharacteristic, complemented
240C4×D4C2×D15111yescharacteristic, complemented
241#117C2×D15111yescharacteristic
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×C8—1511no—
256C24—3021no—
257#41—6041no—
258#41—6041no—
259C2×Q8—21no—
260C2×Q8—1511no—
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—6041no—
279SD16—6041no—
280SD16—6041no—
281SD16—6041no—
282SD16—6041no—
283D8—6041no—
284D8—6041no—
285D8—6041no—
286C2×C8—1511no—
287C2×C8—1511no—
288C2×C8—1511no—
289C2×C8—1511no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4C22⋊D15111yescharacteristic
294C4⋊C4C22⋊D15111yescharacteristic
295C4⋊C4C22×D15111yescharacteristic
296C4⋊C4C22×D15111yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—3021no—
303C22⋊C4—3021no—
304C22⋊C4—3021no—
305C22⋊C4—3021no—
306C22⋊C4C22⋊D15111yescharacteristic
307C22⋊C4C22⋊D15111yescharacteristic
308C42—21no—
309C42C22×D15111yescharacteristic
310C42C22×D15111yescharacteristic
311C23—21no—
312C23—3021no—
313C23—3021no—
314C23—3021no—
315C23—6042no—
316C23—12081no—
317C23—12081no—
318C23C2×C22⋊D15111yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—81no—
322Q8—3021no—
323Q8—3021no—
324D4—21no—
325D4—21no—
326D4—81no—
327D4—3021no—
328D4—3021no—
329D4—3021no—
330D4—3021no—
331D4—3021no—
332D4—3021no—
333D4—6042no—
334D4—6042no—
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—81no—
345C2×C4—3021no—
346C2×C4—6042no—
347C2×C4C2×C22⋊D15111yescharacteristic
348C2×C4C2×C22⋊D15111yescharacteristic
349C2×C4C2×C22⋊D15111yescharacteristic
350C2×C4C2×C22⋊D15111yescharacteristic
351C2×C4C2×C22⋊D15111yescharacteristic
352C2×C4C23×D15111yescharacteristic
353C8—3021no—
354C8—3021no—
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—
373C22C22×C22⋊D15111yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—6041no—
383C4#1801278511yescharacteristic
384C4#1801278511yescharacteristic
385C2—41no—
386C2—81no—
387C2—12081no—
388C2—12081no—
389C2—12081no—
390C2#2375277611yescharacteristic
391C2#2375301511yescharacteristic
392C2#2375302011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#542×C151C2
socleC22×C151C22×D4
hypercenter#542D151
hypocenterC151#3224
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #23752781C2semidirect
2. #23752602C2semidirect
3. #23752594C2semidirect
4. #23752574C2semidirect
5. #23752560C2semidirect
6. #23752434C2semidirect
7. #23752427C2semidirect
8. #23752412C2semidirect
9. #23752407C2semidirect
10. #23752372C2semidirect
11. #23752362C2semidirect
12. #23752355C2semidirect
13. #23752345C2semidirect
14. #23752273C2semidirect
15. #542×C151C2semidirect
18. C2×#14558994C22semidirect
19. C2×#14558992C22semidirect
22. C2×#14558991C22semidirect
25. C2×#14558989C22semidirect
34. C4⋊(C151⋊C8)C22semidirect
35. C4⋊(C151⋊C8)C22semidirect
36. #18012662C22semidirect
37. #18012662C22semidirect
42. #18012659C22semidirect
43. #18012659C22semidirect
46. #18012650C22semidirect
47. C4×C151⋊C8C22semidirect
48. C4⋊Q8×C151C22semidirect
51. #124×C151C22semidirect
56. C4×Q8×C151C22semidirect
57. C4×D4×C151C22semidirect
196. C151#3224semidirect
198. #542D151semidirect
223. C4⋊Q8C2×D151semidirect
230. #124C2×D151semidirect
239. C4×Q8C2×D151semidirect
240. C4×D4C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527812
#237526022
#237525942
#237525742
#237525602
#237524342
#237524272
#237524122
#237524072
#237523722
#237523622
#237523552
#237523452
#237522732
#542×C1512
#3224151