Finite Group Databasebeta

← #34080201

Subgroups — #34080201

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#23752827C211yesmaximal, characteristic, complemented
2#23752775C211yesmaximal, characteristic, complemented
3#23752600C211yesmaximal, characteristic, complemented
4#23752595C211yesmaximal, characteristic, complemented
5#23752570C211yesmaximal, characteristic, complemented
6#23752557C211yesmaximal, characteristic, complemented
7#23752435C211yesmaximal, characteristic, complemented
8#23752427C211yesmaximal, characteristic, complemented
9#23752409C211yesmaximal, characteristic, complemented
10#23752375C211yesmaximal, characteristic, complemented
11#23752364C211yesmaximal, characteristic, complemented
12#23752354C211yesmaximal, characteristic, complemented
13#23752344C211yesmaximal, characteristic, complemented
14#23752272C211yesmaximal, characteristic, complemented
15#459×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×D4×D151C2211yescharacteristic
18C2×Dic604C2211yescharacteristic, complemented
19C2×#14558993C2211yescharacteristic
20C2×#14558992C2211yescharacteristic
21C2×#14558992C2211yescharacteristic, complemented
22C2×#14558992C2211yescharacteristic, complemented
23C2×#14558989C2211yescharacteristic
24#18012738C2211yescharacteristic, complemented
25#18012735C2211yescharacteristic
26#18012732—21no—
27#18012727C2211yescharacteristic
28#18012726C2211yescharacteristic
29#18012726C2211yescharacteristic, complemented
30#18012725—21no—
31#18012722—21no—
32#18012719C2211yescharacteristic
33#18012718—21no—
34#18012711—21no—
35#18012711—21no—
36#18012710C2211yescharacteristic
37#18012707—21no—
38#18012707—21no—
39C4×Dic302C2211yescharacteristic, complemented
40#18012696C2211yescharacteristic
41C4⋊(C151⋊C8)C2211yescharacteristic, complemented
42#18012664C2211yescharacteristic, complemented
43#18012662C2211yescharacteristic, complemented
44#18012661C2211yescharacteristic
45#18012660C2211yescharacteristic
46#18012660C2211yescharacteristic, complemented
47#18012659C2211yescharacteristic
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50#18012649C2211yescharacteristic, complemented
51C8×Dic151C2211yescharacteristic, complemented
52C2×D8×C151C2211yescharacteristic
53C2×D8×C151C2211yescharacteristic, complemented
54#127×C151C2211yescharacteristic
55C4×D4×C151C2211yescharacteristic, complemented
56C4⋊C8×C151C2211yescharacteristic, complemented
57#102×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60#14559003—41no—
61#14559003—41no—
62C2×Dic302—21no—
63C2×Dic302C2311yescharacteristic
64C2×Dic302C2311yescharacteristic
65C2×D604C2311yescharacteristic
66C2×C22⋊D151—21no—
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×D151C2311yescharacteristic
75Dic604—41no—
76#14558993—41no—
77#14558992—41no—
78#14558992—41no—
79#14558992—41no—
80#14558989—41no—
81C2×C151⋊C8C2311yescharacteristic
82C2×C151⋊C8C2311yescharacteristic
83C4⋊Dic151—21no—
84C4⋊Dic151C2311yescharacteristic
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4D411yescharacteristic
88Dic151⋊C4D411yescharacteristic
89C22⋊Dic151—21no—
90C22⋊Dic151—21no—
91C22⋊Dic151—21no—
92C22⋊Dic151—21no—
93C22⋊Dic151—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4D411yescharacteristic
98(C2×D151)⋊C4D411yescharacteristic
99C4×Dic151—21no—
100C4×Dic151C2311yescharacteristic
101C2×D4×C151—21no—
102C2×D4×C151—21no—
103C2×D4×C151C2311yescharacteristic
104C2×D4×C151C2311yescharacteristic
105C2×D4×C151C2311yescharacteristic
106C22×C4×C151—21no—
107D8×C151—41no—
108D8×C151—41no—
109C2×C8×C151C2311yescharacteristic
110C2×C8×C151C2311yescharacteristic
111C4⋊C4×C151C2311yescharacteristic
112C22⋊C4×C151—21no—
113C42×C151C2311yescharacteristic
114C22×D151—21no—
115C22×D151—42no—
116C22×D151—81no—
117C22×D151—81no—
118C22×D151C2×D411yescharacteristic
119Dic302—21no—
120Dic302—21no—
121Dic302—21no—
122Dic302—21no—
123Dic302—81no—
124D604—21no—
125D604—21no—
126C22⋊D151—42no—
127C22⋊D151—42no—
128C22⋊D151—81no—
129C22⋊D151—81no—
130C22⋊D151—81no—
131C2×Dic151—21no—
132C2×Dic151—21no—
133C2×Dic151—21no—
134C2×Dic151—42no—
135C2×Dic151C2×D411yescharacteristic
136C2×Dic151C2×D411yescharacteristic
137C2×Dic151C2×D411yescharacteristic
138C4×D151—21no—
139C4×D151—21no—
140C151⋊C8—21no—
141C151⋊C8—21no—
142C23×C151—21no—
143C23×C151—21no—
144C23×C151—21no—
145D4×C151—21no—
146D4×C151—21no—
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—81no—
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×C151—41no—
167C22×C151—41no—
168C22×C151—41no—
169C22×C151C22×D411yescharacteristic
170C2×D151—21no—
171C2×D151—21no—
172C2×D151—21no—
173C2×D151—41no—
174C2×D151—41no—
175C2×D151—41no—
176C2×D151—84no—
177C4×C151—21no—
178C4×C151—21no—
179C4×C151—41no—
180C4×C151H(5,𝔽2)11yescharacteristic
181C4×C151H(5,𝔽2)11yescharacteristic
182Dic151—21no—
183Dic151—21no—
184Dic151—21no—
185Dic151—41no—
186Dic151—41no—
187Dic151—41no—
188C2×C151—81no—
189C2×C151—81no—
190C2×C151—81no—
191C2×C151#53511yescharacteristic
192C2×C151#57611yescharacteristic
193C2×C151#57711yescharacteristic
194D151—41no—
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#486—1511no—
204#464—1511no—
205#463—1511no—
206#460—1511no—
207#459D15111yescharacteristic, complemented
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×D8C2×D15111yescharacteristic
222C2×D8C2×D15111yescharacteristic, complemented
223C4⋊Q8—1511no—
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×D4C2×D15111yescharacteristic, complemented
241#117—1511no—
242C4⋊C8—1511no—
243C4⋊C8C2×D15111yescharacteristic, complemented
244#103—1511no—
245#103—1511no—
246#102—1511no—
247#102—1511no—
248#102—1511no—
249#102—1511no—
250#102C2×D15111yescharacteristic
251#102C2×D15111yescharacteristic, complemented
252C22⋊C8—1511no—
253C22⋊C8—1511no—
254#97—1511no—
255C4×C8—1511no—
256C24—3021no—
257#41—6041no—
258#41—6041no—
259C2×Q8—3021no—
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×D4C22×D15111yescharacteristic
273C2×D4C22×D15111yescharacteristic
274C2×D4C22×D15111yescharacteristic
275C22×C4—21no—
276C22×C4—3021no—
277C22×C4—1511no—
278Q16—6041no—
279SD16—6041no—
280SD16—6041no—
281SD16—6041no—
282SD16—6041no—
283D8—41no—
284D8—41no—
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⋊C4C22×D15111yescharacteristic
297C22⋊C4—21no—
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—21no—
314C23—3021no—
315C23—6042no—
316C23—1511no—
317C23—12081no—
318C23—12081no—
319Q8—3021no—
320Q8—3021no—
321Q8—3021no—
322Q8—3021no—
323Q8—12081no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—81no—
331D4—81no—
332D4—3021no—
333D4—3021no—
334D4—6042no—
335D4—6042no—
336D4—12081no—
337D4—12081no—
338D4—12081no—
339C2×C4—21no—
340C2×C4—81no—
341C2×C4—3021no—
342C2×C4—3021no—
343C2×C4—3021no—
344C2×C4—3021no—
345C2×C4—3021no—
346C2×C4—6042no—
347C2×C4—1511no—
348C2×C4—1511no—
349C2×C4—1511no—
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—41no—
364C22—41no—
365C22—41no—
366C22—3021no—
367C22—3021no—
368C22—3021no—
369C22—6041no—
370C22—6041no—
371C22—6041no—
372C22—12084no—
373C22C2×D4×D15111yescharacteristic
374C4—21no—
375C4—21no—
376C4—41no—
377C4—3021no—
378C4—3021no—
379C4—3021no—
380C4—6041no—
381C4—6041no—
382C4—6041no—
383C4#1801278411yescharacteristic
384C4#1801278511yescharacteristic
385C2—81no—
386C2—81no—
387C2—81no—
388C2—6041no—
389C2—12081no—
390C2#2375277811yescharacteristic
391C2#2375301311yescharacteristic
392C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#459×C151C2
socleC22×C151C22×D4
hypercenter#459D151
hypocenterC151#3224
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #23752827C2semidirect
2. #23752775C2semidirect
3. #23752600C2semidirect
4. #23752595C2semidirect
5. #23752570C2semidirect
6. #23752557C2semidirect
7. #23752435C2semidirect
8. #23752427C2semidirect
9. #23752409C2semidirect
10. #23752375C2semidirect
11. #23752364C2semidirect
12. #23752354C2semidirect
13. #23752344C2semidirect
14. #23752272C2semidirect
15. #459×C151C2semidirect
18. C2×Dic604C22semidirect
21. C2×#14558992C22semidirect
22. C2×#14558992C22semidirect
24. #18012738C22semidirect
29. #18012726C22semidirect
39. C4×Dic302C22semidirect
41. C4⋊(C151⋊C8)C22semidirect
42. #18012664C22semidirect
43. #18012662C22semidirect
46. #18012660C22semidirect
50. #18012649C22semidirect
51. C8×Dic151C22semidirect
53. C2×D8×C151C22semidirect
55. C4×D4×C151C22semidirect
56. C4⋊C8×C151C22semidirect
58. #102×C151C22semidirect
196. C151#3224semidirect
207. #459D151semidirect
222. C2×D8C2×D151semidirect
240. C4×D4C2×D151semidirect
243. C4⋊C8C2×D151semidirect
251. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528272
#237527752
#237526002
#237525952
#237525702
#237525572
#237524352
#237524272
#237524092
#237523752
#237523642
#237523542
#237523442
#237522722
#459×C1512
#3224151