Finite Group Databasebeta

← #34080202

Subgroups — #34080202

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#23752829C211yesmaximal, characteristic, complemented
2#23752776C211yesmaximal, characteristic, complemented
3#23752600C211yesmaximal, characteristic, complemented
4#23752593C211yesmaximal, characteristic, complemented
5#23752573C211yesmaximal, characteristic, complemented
6#23752557C211yesmaximal, characteristic, complemented
7#23752437C211yesmaximal, characteristic, complemented
8#23752429C211yesmaximal, characteristic, complemented
9#23752411C211yesmaximal, characteristic, complemented
10#23752405C211yesmaximal, characteristic, complemented
11#23752374C211yesmaximal, characteristic, complemented
12#23752365C211yesmaximal, characteristic, complemented
13#23752345C211yesmaximal, characteristic, complemented
14#23752270C211yesmaximal, characteristic, complemented
15#449×C151C211yesmaximal, characteristic, complemented
16C22×D604C2211yescharacteristic
17C2×#14558994C2211yescharacteristic, complemented
18C2×#14558993C2211yescharacteristic
19C2×#14558993C2211yescharacteristic
20C2×#14558992C2211yescharacteristic, complemented
21C2×#14558989C2211yescharacteristic
22C2×#14558989C2211yescharacteristic
23#18012738C2211yescharacteristic, complemented
24#18012735C2211yescharacteristic
25#18012735C2211yescharacteristic
26#18012732—21no—
27#18012728C2211yescharacteristic
28#18012728C2211yescharacteristic
29#18012726—21no—
30#18012726C2211yescharacteristic, complemented
31#18012720—21no—
32#18012718C2211yescharacteristic
33#18012716—21no—
34#18012713—21no—
35#18012713—21no—
36#18012707—21no—
37#18012707—21no—
38#18012704C2211yescharacteristic, complemented
39D4×Dic151C2211yescharacteristic, complemented
40#18012698C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic, complemented
42Dic151⋊C8C2211yescharacteristic, complemented
43#18012663C2211yescharacteristic, complemented
44#18012661C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012660C2211yescharacteristic, complemented
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50#18012649C2211yescharacteristic, complemented
51C8×Dic151C2211yescharacteristic, complemented
52C2×#41×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic, complemented
54C2×D8×C151C2211yescharacteristic, complemented
55#121×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic, complemented
57#102×C151C2211yescharacteristic, complemented
58C22⋊C8×C151C2211yescharacteristic
59C23×D151—21no—
60C2×Dic302—21no—
61C2×Dic302C2311yescharacteristic
62C2×D604—21no—
63C2×D604—41no—
64C2×D604—41no—
65C2×D604C2311yescharacteristic
66C2×D604C2311yescharacteristic
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C22×Dic151—21no—
72#14558994—41no—
73#14558993—41no—
74#14558993—41no—
75#14558992—41no—
76#14558989—41no—
77#14558989—41no—
78C2×C151⋊C8C2311yescharacteristic
79C2×C151⋊C8C2311yescharacteristic
80C4⋊Dic151D411yescharacteristic
81C4⋊Dic151D411yescharacteristic
82C4⋊Dic151C2311yescharacteristic
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86C22⋊Dic151—21no—
87C22⋊Dic151—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90C22⋊Dic151D411yescharacteristic
91C22⋊Dic151D411yescharacteristic
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96C4×Dic151—21no—
97C4×Dic151C2311yescharacteristic
98C4×Dic151C2311yescharacteristic
99#41×C151—41no—
100#41×C151—41no—
101C2×Q8×C151C2311yescharacteristic
102C2×D4×C151—21no—
103C2×D4×C151—21no—
104C2×D4×C151C2311yescharacteristic
105C2×D4×C151C2311yescharacteristic
106C22×C4×C151—21no—
107C22×C4×C151C2311yescharacteristic
108SD16×C151—41no—
109D8×C151—41no—
110C2×C8×C151C2311yescharacteristic
111C2×C8×C151C2311yescharacteristic
112C4⋊C4×C151C2311yescharacteristic
113C22⋊C4×C151—21no—
114C22×D151—21no—
115C22×D151—21no—
116C22×D151—42no—
117C22×D151—81no—
118C22×D151—81no—
119Dic302—21no—
120Dic302—21no—
121Dic302—81no—
122D604—21no—
123D604—21no—
124D604—21no—
125D604—21no—
126D604—42no—
127C22⋊D151—81no—
128C22⋊D151—81no—
129C22⋊D151—81no—
130C22⋊D151—81no—
131C2×Dic151—21no—
132C2×Dic151—21no—
133C2×Dic151—81no—
134C2×Dic151C2×D411yescharacteristic
135C2×Dic151C2×D411yescharacteristic
136C2×Dic151C2×D411yescharacteristic
137C2×Dic151C2×D411yescharacteristic
138C151⋊C8—21no—
139C151⋊C8—21no—
140C23×C151—21no—
141C23×C151—21no—
142C23×C151C2×D411yescharacteristic
143Q8×C151—21no—
144Q8×C151—21no—
145D4×C151—21no—
146D4×C151—21no—
147D4×C151—21no—
148D4×C151—21no—
149D4×C151—42no—
150D4×C151—81no—
151C2×C4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151—21no—
154C2×C4×C151—21no—
155C2×C4×C151—42no—
156C2×C4×C151C2×D411yescharacteristic
157C2×C4×C151C2411yescharacteristic
158C8×C151—21no—
159C8×C151—21no—
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×C151C22×D411yescharacteristic
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—41no—
179C4×C151—41no—
180C4×C151H(5,𝔽2)11yescharacteristic
181C4×C151H(5,𝔽2)11yescharacteristic
182Dic151—21no—
183Dic151—21no—
184Dic151—21no—
185Dic151—21no—
186Dic151—41no—
187Dic151—41no—
188C2×C151—41no—
189C2×C151—81no—
190C2×C151—81no—
191C2×C151#53511yescharacteristic
192C2×C151#57611yescharacteristic
193C2×C151#57711yescharacteristic
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#486—1511no—
204#464—1511no—
205#463—1511no—
206#460—1511no—
207#459—1511no—
208#452—1511no—
209#450—1511no—
210#449D15111yescharacteristic, complemented
211#447—1511no—
212#433—1511no—
213C2×#41C2×D15111yescharacteristic
214C22×D4—1511no—
215C2×Q16—1511no—
216C2×SD16—1511no—
217C2×SD16—1511no—
218C2×SD16—1511no—
219C2×SD16C2×D15111yescharacteristic, complemented
220C2×D8—1511no—
221C2×D8—1511no—
222C2×D8C2×D15111yescharacteristic, complemented
223C4⋊Q8—1511no—
224#127—1511no—
225#127—1511no—
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#121C2×D15111yescharacteristic
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#103C2×D15111yescharacteristic, complemented
246#102—1511no—
247#102—1511no—
248#102—1511no—
249#102—1511no—
250#102—1511no—
251#102C2×D15111yescharacteristic, complemented
252C22⋊C8—1511no—
253C22⋊C8C2×D15111yescharacteristic
254#97—1511no—
255C4×C8—1511no—
256C24—3021no—
257#41—41no—
258#41—41no—
259C2×Q8—3021no—
260C2×Q8—1511no—
261C2×Q8C22×D15111yescharacteristic
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—21no—
276C22×C4—3021no—
277C22×C4C22×D15111yescharacteristic
278Q16—6041no—
279SD16—41no—
280SD16—6041no—
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⋊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—
310C42—1511no—
311C23—21no—
312C23—21no—
313C23—3021no—
314C23—3021no—
315C23—6042no—
316C23—12081no—
317C23—12081no—
318C23D4×D15111yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—3021no—
322Q8—3021no—
323Q8—12081no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—42no—
329D4—81no—
330D4—3021no—
331D4—3021no—
332D4—3021no—
333D4—3021no—
334D4—6042no—
335D4—12081no—
336D4—12081no—
337D4—12081no—
338D4—12081no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—3021no—
345C2×C4—3021no—
346C2×C4—1511no—
347C2×C4—1511no—
348C2×C4—1511no—
349C2×C4—1511no—
350C2×C4—12081no—
351C2×C4D4×D15111yescharacteristic
352C2×C4C23×D15111yescharacteristic
353C8—21no—
354C8—21no—
355C8—3021no—
356C8—3021no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—6041no—
367C22—6041no—
368C22—6041no—
369C22—6041no—
370C22—6041no—
371C22—6041no—
372C22—12084no—
373C22C2×D4×D15111yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—3021no—
378C4—3021no—
379C4—3021no—
380C4—3021no—
381C4—6041no—
382C4—6041no—
383C4#1801278411yescharacteristic
384C4#1801278411yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—12081no—
389C2—12081no—
390C2#2375277711yescharacteristic
391C2#2375301611yescharacteristic
392C2#2375301911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#449×C151C2
socleC22×C151C22×D4
hypercenter#449D151
hypocenterC151#3224
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #23752829C2semidirect
2. #23752776C2semidirect
3. #23752600C2semidirect
4. #23752593C2semidirect
5. #23752573C2semidirect
6. #23752557C2semidirect
7. #23752437C2semidirect
8. #23752429C2semidirect
9. #23752411C2semidirect
10. #23752405C2semidirect
11. #23752374C2semidirect
12. #23752365C2semidirect
13. #23752345C2semidirect
14. #23752270C2semidirect
15. #449×C151C2semidirect
17. C2×#14558994C22semidirect
20. C2×#14558992C22semidirect
23. #18012738C22semidirect
30. #18012726C22semidirect
38. #18012704C22semidirect
39. D4×Dic151C22semidirect
41. Dic151⋊C8C22semidirect
42. Dic151⋊C8C22semidirect
43. #18012663C22semidirect
46. #18012660C22semidirect
50. #18012649C22semidirect
51. C8×Dic151C22semidirect
53. C2×SD16×C151C22semidirect
54. C2×D8×C151C22semidirect
56. #103×C151C22semidirect
57. #102×C151C22semidirect
196. C151#3224semidirect
210. #449D151semidirect
219. C2×SD16C2×D151semidirect
222. C2×D8C2×D151semidirect
245. #103C2×D151semidirect
251. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528292
#237527762
#237526002
#237525932
#237525732
#237525572
#237524372
#237524292
#237524112
#237524052
#237523742
#237523652
#237523452
#237522702
#449×C1512
#3224151