Finite Group Databasebeta

← #34080204

Subgroups — #34080204

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#23752833C211yesmaximal, characteristic, complemented
2#23752599C211yesmaximal, characteristic, complemented
3#23752594C211yesmaximal, characteristic, complemented
4#23752571C211yesmaximal, characteristic, complemented
5#23752558C211yesmaximal, characteristic, complemented
6#23752431C211yesmaximal, characteristic, complemented
7#23752424C211yesmaximal, characteristic, complemented
8#23752409C211yesmaximal, characteristic, complemented
9#23752404C211yesmaximal, characteristic, complemented
10#23752374C211yesmaximal, characteristic, complemented
11#23752363C211yesmaximal, characteristic, complemented
12#23752357C211yesmaximal, characteristic, complemented
13#23752346C211yesmaximal, characteristic, complemented
14#23752273C211yesmaximal, characteristic, complemented
15#535×C151C211yesmaximal, characteristic, complemented
16C2×#14558994C2211yescharacteristic, complemented
17C2×#14558992C2211yescharacteristic
18C2×#14558992C2211yescharacteristic
19C2×#14558992C2211yescharacteristic, complemented
20C2×#14558991C2211yescharacteristic, complemented
21C2×#14558989C2211yescharacteristic
22C2×#14558989C2211yescharacteristic
23C2×#14558989C2211yescharacteristic, complemented
24#18012739C2211yescharacteristic, complemented
25#18012734—21no—
26#18012727C2211yescharacteristic, complemented
27#18012725—21no—
28#18012721—21no—
29#18012718C2211yescharacteristic
30#18012717—21no—
31#18012713C2211yescharacteristic
32C4×Dic302C2211yescharacteristic, complemented
33C4×D604C2211yescharacteristic, complemented
34C4⋊(C151⋊C8)C2211yescharacteristic, complemented
35C4⋊(C151⋊C8)C2211yescharacteristic, complemented
36#18012663C2211yescharacteristic, complemented
37#18012663C2211yescharacteristic, complemented
38#18012660C2211yescharacteristic
39#18012660C2211yescharacteristic
40#18012660C2211yescharacteristic
41#18012660C2211yescharacteristic
42#18012660C2211yescharacteristic, complemented
43#18012660C2211yescharacteristic, complemented
44C22⋊(C151⋊C8)C2211yescharacteristic
45C22⋊(C151⋊C8)C2211yescharacteristic
46#18012650C2211yescharacteristic, complemented
47C4×C151⋊C8C2211yescharacteristic, complemented
48C2×#41×C151C2211yescharacteristic
49C22×D4×C151C2211yescharacteristic
50#127×C151C2211yescharacteristic
51#127×C151C2211yescharacteristic
52#124×C151C2211yescharacteristic
53#124×C151C2211yescharacteristic
54#121×C151—21no—
55#121×C151—21no—
56#120×C151—21no—
57#120×C151—21no—
58#117×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302C2311yescharacteristic
61C2×D604C2311yescharacteristic
62C2×C22⋊D151—21no—
63C2×C4×D151—21no—
64#14558994—41no—
65#14558992—41no—
66#14558992—41no—
67#14558992—41no—
68#14558991—41no—
69#14558989—41no—
70#14558989—41no—
71#14558989—41no—
72C2×C151⋊C8C2311yescharacteristic
73C2×C151⋊C8C2311yescharacteristic
74C2×C151⋊C8C2311yescharacteristic
75C2×C151⋊C8C2311yescharacteristic
76C4⋊Dic151—21no—
77C4⋊Dic151C2311yescharacteristic
78C4⋊Dic151C2311yescharacteristic
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81C22⋊Dic151—21no—
82(C2×D151)⋊C4—21no—
83(C2×D151)⋊C4—21no—
84(C2×D151)⋊C4—21no—
85(C2×D151)⋊C4—21no—
86C4×Dic151—21no—
87C24×C151—21no—
88#41×C151—41no—
89#41×C151—41no—
90C2×Q8×C151C2311yescharacteristic
91C2×D4×C151—21no—
92C2×D4×C151—21no—
93C2×D4×C151—21no—
94C2×D4×C151—21no—
95C2×D4×C151—21no—
96C2×D4×C151—21no—
97C2×D4×C151—41no—
98C2×D4×C151—41no—
99C2×D4×C151C2311yescharacteristic
100C2×D4×C151C2311yescharacteristic
101C2×D4×C151C2311yescharacteristic
102C22×C4×C151—21no—
103C22×C4×C151C2311yescharacteristic
104C4⋊C4×C151D411yescharacteristic
105C4⋊C4×C151D411yescharacteristic
106C22⋊C4×C151—21no—
107C22⋊C4×C151—21no—
108C22⋊C4×C151—21no—
109C22⋊C4×C151—21no—
110C22⋊C4×C151D411yescharacteristic
111C22⋊C4×C151D411yescharacteristic
112C42×C151C2311yescharacteristic
113C42×C151C2311yescharacteristic
114C22×D151—21no—
115Dic302—21no—
116Dic302—21no—
117Dic302—81no—
118D604—21no—
119D604—21no—
120C22⋊D151—81no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C4×D151—81no—
125C151⋊C8—21no—
126C151⋊C8—21no—
127C151⋊C8—21no—
128C151⋊C8—21no—
129C23×C151—21no—
130C23×C151—21no—
131C23×C151—21no—
132C23×C151—42no—
133C23×C151—81no—
134C23×C151—81no—
135C23×C151C2×D411yescharacteristic
136Q8×C151—21no—
137Q8×C151—21no—
138D4×C151—21no—
139D4×C151—21no—
140D4×C151—21no—
141D4×C151—21no—
142D4×C151—21no—
143D4×C151—21no—
144D4×C151—42no—
145D4×C151—42no—
146D4×C151—81no—
147D4×C151—81no—
148D4×C151—81no—
149D4×C151—81no—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151—42no—
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×C151—41no—
167C22×C151—41no—
168C22×C151—41no—
169C22×C151—41no—
170C22×C151—41no—
171C22×C151—41no—
172C22×C151—84no—
173C22×C151C22×D411yescharacteristic
174C2×D151—41no—
175C2×D151—41no—
176C2×D151—41no—
177C4×C151—21no—
178C4×C151—21no—
179C4×C151—21no—
180C4×C151—21no—
181C4×C151—21no—
182C4×C151—41no—
183C4×C151H(5,𝔽2)11yescharacteristic
184C4×C151H(5,𝔽2)11yescharacteristic
185Dic151—41no—
186Dic151—41no—
187Dic151—41no—
188C2×C151—41no—
189C2×C151—81no—
190C2×C151—81no—
191C2×C151—81no—
192C2×C151#53511yescharacteristic
193C2×C151#57611yescharacteristic
194C2×C151#57711yescharacteristic
195D151—81no—
196C151#322411yescharacteristic, complemented, Sylow
197#3224—1511nomaximal, Sylow
198#542—1511no—
199#535D15111yescharacteristic, complemented
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×#41C2×D15111yescharacteristic
214C22×D4C2×D15111yescharacteristic
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⋊Q8—1511no—
224#127C2×D15111yescharacteristic
225#127C2×D15111yescharacteristic
226#126—3021no—
227#124—3021no—
228#124—1511no—
229#124C2×D15111yescharacteristic
230#124C2×D15111yescharacteristic
231#123—3021no—
232C22⋊Q8—3021no—
233C22⋊Q8—1511no—
234#121—21no—
235#121—21no—
236#121—1511no—
237#120—21no—
238#120—21no—
239C4×Q8—1511no—
240C4×D4—1511no—
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—21no—
257#41—41no—
258#41—41no—
259C2×Q8—3021no—
260C2×Q8—1511no—
261C2×Q8C22×D15111yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—3021no—
271C2×D4—1511no—
272C2×D4C22×D15111yescharacteristic
273C2×D4C22×D15111yescharacteristic
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—3021no—
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—21no—
300C22⋊C4—21no—
301C22⋊C4—3021no—
302C22⋊C4—3021no—
303C22⋊C4—3021no—
304C22⋊C4—3021no—
305C22⋊C4—3021no—
306C22⋊C4C22⋊D15111yescharacteristic
307C22⋊C4C22⋊D15111yescharacteristic
308C42—3021no—
309C42C22×D15111yescharacteristic
310C42C22×D15111yescharacteristic
311C23—21no—
312C23—21no—
313C23—21no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—3021no—
318C23C2×C22⋊D15111yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—3021no—
322Q8—3021no—
323Q8—12081no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4—81no—
334D4—81no—
335D4—81no—
336D4—3021no—
337D4—3021no—
338D4—12081no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—3021no—
344C2×C4—3021no—
345C2×C4—3021no—
346C2×C4—12081no—
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—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—84no—
370C22—6041no—
371C22—6041no—
372C22—6041no—
373C22C22×C22⋊D15111yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—6041no—
381C4—6041no—
382C4—6041no—
383C4#1801278411yescharacteristic
384C4#1801278411yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—81no—
389C2—12081no—
390C2#2375277911yescharacteristic
391C2#2375301511yescharacteristic
392C2#2375302311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#535×C151C2
socleC22×C151C22×D4
hypercenter#535D151
hypocenterC151#3224
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #23752833C2semidirect
2. #23752599C2semidirect
3. #23752594C2semidirect
4. #23752571C2semidirect
5. #23752558C2semidirect
6. #23752431C2semidirect
7. #23752424C2semidirect
8. #23752409C2semidirect
9. #23752404C2semidirect
10. #23752374C2semidirect
11. #23752363C2semidirect
12. #23752357C2semidirect
13. #23752346C2semidirect
14. #23752273C2semidirect
15. #535×C151C2semidirect
16. C2×#14558994C22semidirect
19. C2×#14558992C22semidirect
20. C2×#14558991C22semidirect
23. C2×#14558989C22semidirect
24. #18012739C22semidirect
26. #18012727C22semidirect
32. C4×Dic302C22semidirect
33. C4×D604C22semidirect
34. C4⋊(C151⋊C8)C22semidirect
35. C4⋊(C151⋊C8)C22semidirect
36. #18012663C22semidirect
37. #18012663C22semidirect
42. #18012660C22semidirect
43. #18012660C22semidirect
46. #18012650C22semidirect
47. C4×C151⋊C8C22semidirect
196. C151#3224semidirect
199. #535D151semidirect

Maximal subgroups

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

subgroupindex
#237528332
#237525992
#237525942
#237525712
#237525582
#237524312
#237524242
#237524092
#237524042
#237523742
#237523632
#237523572
#237523462
#237522732
#535×C1512
#3224151