Finite Group Databasebeta

← #34080181

Subgroups — #34080181

Order 19328.

396 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752820C211yesmaximal, characteristic, complemented
2#23752775C211yesmaximal, characteristic
3#23752603C211yesmaximal, characteristic, complemented
4#23752583C211yesmaximal, characteristic, complemented
5#23752575C211yesmaximal, characteristic, complemented
6#23752565C211yesmaximal, characteristic, complemented
7#23752435C211yesmaximal, characteristic, complemented
8#23752434C211yesmaximal, characteristic, complemented
9#23752409C211yesmaximal, characteristic, complemented
10#23752375C211yesmaximal, characteristic, complemented
11#23752371C211yesmaximal, characteristic, complemented
12#23752364C211yesmaximal, characteristic, complemented
13#23752361C211yesmaximal, characteristic, complemented
14#23752272C211yesmaximal, characteristic, complemented
15#460×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×D4×D151C2211yescharacteristic
18C2×Dic604C2211yescharacteristic, complemented
19C2×#14558994C2211yescharacteristic, complemented
20C2×#14558993C2211yescharacteristic
21C2×#14558992C2211yescharacteristic
22C2×#14558992C2211yescharacteristic, complemented
23C2×#14558991C2211yescharacteristic
24#18012737C2211yescharacteristic, complemented
25#18012735C2211yescharacteristic
26#18012734—21no—
27#18012733—21no—
28#18012731—21no—
29#18012730C2211yescharacteristic, complemented
30#18012729—21no—
31#18012727C2211yescharacteristic
32#18012726C2211yescharacteristic
33#18012719C2211yescharacteristic
34#18012715C2211yescharacteristic
35#18012711—21no—
36#18012711—21no—
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×SD16×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic, complemented
54#127×C151C2211yescharacteristic
55C4×Q8×C151C2211yescharacteristic, complemented
56C4⋊C8×C151C2211yescharacteristic, complemented
57#102×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60#14559003—41no—
61#14559003—41no—
62C2×Dic302C2311yescharacteristic
63C2×Dic302C2311yescharacteristic
64C2×D604C2311yescharacteristic
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69D4×D151—41no—
70D4×D151—41no—
71C22×Dic151—21no—
72C2×C4×D151C2311yescharacteristic
73Dic604—41no—
74#14558994—41no—
75#14558993—41no—
76#14558992—41no—
77#14558992—41no—
78#14558991—41no—
79C2×C151⋊C8C2311yescharacteristic
80C2×C151⋊C8C2311yescharacteristic
81C4⋊Dic151—21no—
82C4⋊Dic151—21no—
83C4⋊Dic151C2311yescharacteristic
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88Dic151⋊C4—21no—
89Dic151⋊C4D411yescharacteristic
90Dic151⋊C4D411yescharacteristic
91C22⋊Dic151—21no—
92C22⋊Dic151—21no—
93(C2×D151)⋊C4—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×Q8×C151C2311yescharacteristic
102C2×D4×C151—21no—
103C2×D4×C151—21no—
104C2×D4×C151C2311yescharacteristic
105C2×D4×C151C2311yescharacteristic
106SD16×C151—41no—
107SD16×C151—41no—
108C2×C8×C151C2311yescharacteristic
109C2×C8×C151C2311yescharacteristic
110C4⋊C4×C151—21no—
111C4⋊C4×C151C2311yescharacteristic
112C42×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—
123D604—21no—
124D604—21no—
125C22⋊D151—42no—
126C22⋊D151—42no—
127C22⋊D151—81no—
128C22⋊D151—81no—
129C2×Dic151—21no—
130C2×Dic151—21no—
131C2×Dic151—21no—
132C2×Dic151—42no—
133C2×Dic151C2×D411yescharacteristic
134C2×Dic151C2×D411yescharacteristic
135C2×Dic151C2×D411yescharacteristic
136C4×D151—21no—
137C4×D151—21no—
138C151⋊C8—21no—
139C151⋊C8—21no—
140C23×C151—21no—
141C23×C151—21no—
142Q8×C151—21no—
143Q8×C151—21no—
144D4×C151—21no—
145D4×C151—21no—
146D4×C151—21no—
147D4×C151—21no—
148D4×C151—81no—
149D4×C151—81no—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151C2×D411yescharacteristic
153C2×C4×C151C2×D411yescharacteristic
154C2×C4×C151C2411yescharacteristic
155C8×C151—21no—
156C8×C151—21no—
157C22×C151—41no—
158C22×C151—41no—
159C22×C151—41no—
160C22×C151—41no—
161C22×C151—41no—
162C22×C151—41no—
163C22×C151C22×D411yescharacteristic
164C2×D151—21no—
165C2×D151—21no—
166C2×D151—21no—
167C2×D151—41no—
168C2×D151—41no—
169C2×D151—41no—
170C2×D151—84no—
171C4×C151—21no—
172C4×C151—21no—
173C4×C151—41no—
174C4×C151—41no—
175C4×C151H(5,𝔽2)11yescharacteristic
176C4×C151H(5,𝔽2)11yescharacteristic
177Dic151—21no—
178Dic151—21no—
179Dic151—21no—
180Dic151—41no—
181Dic151—41no—
182Dic151—41no—
183C2×C151—81no—
184C2×C151—81no—
185C2×C151#53511yescharacteristic
186C2×C151#57711yescharacteristic
187C2×C151#57711yescharacteristic
188D151—41no—
189D151—81no—
190C151#322211yescharacteristic, complemented, Sylow
191#3222—1511nomaximal, Sylow
192#541—1511no—
193#535—1511no—
194#497—1511no—
195#492—1511no—
196#490—1511no—
197#488—1511no—
198#464—1511no—
199#464—1511no—
200#460—1511no—
201#460D15111yescharacteristic, complemented
202#452—1511no—
203#452—1511no—
204#450—1511no—
205#450—1511no—
206#433—1511no—
207C2×#41—1511no—
208C22×D4—1511no—
209C2×Q16—1511no—
210C2×Q16—1511no—
211C2×SD16—1511no—
212C2×SD16—1511no—
213C2×SD16—1511no—
214C2×SD16—1511no—
215C2×SD16C2×D15111yescharacteristic
216C2×SD16C2×D15111yescharacteristic, complemented
217C4⋊Q8—1511no—
218#127—1511no—
219#127C2×D15111yescharacteristic
220#126—3021no—
221#126—3021no—
222#125—3021no—
223#125—3021no—
224#125—1511no—
225#124—1511no—
226#124—1511no—
227C22⋊Q8—1511no—
228C22⋊Q8—1511no—
229#121—3021no—
230#121—3021no—
231#120—3021no—
232#120—3021no—
233C4×Q8—1511no—
234C4×Q8C2×D15111yescharacteristic, complemented
235#117—1511no—
236C4⋊C8—1511no—
237C4⋊C8C2×D15111yescharacteristic, complemented
238#103—1511no—
239#103—1511no—
240#102—1511no—
241#102—1511no—
242#102—1511no—
243#102—1511no—
244#102C2×D15111yescharacteristic
245#102C2×D15111yescharacteristic, complemented
246C22⋊C8—1511no—
247C22⋊C8—1511no—
248#97—1511no—
249C4×C8—1511no—
250C24—3021no—
251#41—6041no—
252#41—6041no—
253C2×Q8—1511no—
254C2×Q8—1511no—
255C2×Q8C22×D15111yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—3021no—
259C2×D4—3021no—
260C2×D4—3021no—
261C2×D4—3021no—
262C2×D4—6041no—
263C2×D4—6041no—
264C2×D4—1511no—
265C2×D4C22×D15111yescharacteristic
266C2×D4C22×D15111yescharacteristic
267C22×C4—3021no—
268C22×C4—1511no—
269Q16—6041no—
270Q16—6041no—
271SD16—41no—
272SD16—41no—
273SD16—6041no—
274SD16—6041no—
275SD16—6041no—
276SD16—6041no—
277C2×C8—1511no—
278C2×C8—1511no—
279C2×C8C22×D15111yescharacteristic
280C2×C8C22×D15111yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—3021no—
283C4⋊C4—3021no—
284C4⋊C4—3021no—
285C4⋊C4—3021no—
286C4⋊C4—3021no—
287C4⋊C4—3021no—
288C4⋊C4—3021no—
289C4⋊C4—1511no—
290C4⋊C4—1511no—
291C4⋊C4—1511no—
292C4⋊C4C22×D15111yescharacteristic
293C22⋊C4—3021no—
294C22⋊C4—3021no—
295C22⋊C4—3021no—
296C22⋊C4—3021no—
297C22⋊C4—3021no—
298C22⋊C4—3021no—
299C22⋊C4—1511no—
300C22⋊C4—1511no—
301C42—21no—
302C42—3021no—
303C42—1511no—
304C42C22×D15111yescharacteristic
305C23—21no—
306C23—21no—
307C23—3021no—
308C23—6042no—
309C23—1511no—
310C23—12081no—
311C23—12081no—
312Q8—21no—
313Q8—21no—
314Q8—3021no—
315Q8—3021no—
316Q8—3021no—
317Q8—3021no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—81no—
323D4—81no—
324D4—3021no—
325D4—3021no—
326D4—6042no—
327D4—6042no—
328D4—12081no—
329D4—12081no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—3021no—
333C2×C4—3021no—
334C2×C4—3021no—
335C2×C4—3021no—
336C2×C4—3021no—
337C2×C4—6042no—
338C2×C4—1511no—
339C2×C4—1511no—
340C2×C4—1511no—
341C2×C4D4×D15111yescharacteristic
342C2×C4D4×D15111yescharacteristic
343C2×C4C23×D15111yescharacteristic
344C8—21no—
345C8—21no—
346C8—3021no—
347C8—3021no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—3021no—
355C22—3021no—
356C22—3021no—
357C22—6041no—
358C22—6041no—
359C22—6041no—
360C22—12084no—
361C22C2×D4×D15111yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—3021no—
367C4—3021no—
368C4—3021no—
369C4—6041no—
370C4—6041no—
371C4—6041no—
372C4#1801278411yescharacteristic
373C4#1801278511yescharacteristic
374C2—81no—
375C2—81no—
376C2—6041no—
377C2—12081no—
378C2#2375277811yescharacteristic
379C2#2375301811yescharacteristic
380C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#460×C151C2
socleC22×C151C22×D4
prime radical#23752775C2
hypercenter#460D151
hypocenterC151#3222
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #23752820C2semidirect
3. #23752603C2semidirect
4. #23752583C2semidirect
5. #23752575C2semidirect
6. #23752565C2semidirect
7. #23752435C2semidirect
8. #23752434C2semidirect
9. #23752409C2semidirect
10. #23752375C2semidirect
11. #23752371C2semidirect
12. #23752364C2semidirect
13. #23752361C2semidirect
14. #23752272C2semidirect
15. #460×C151C2semidirect
18. C2×Dic604C22semidirect
19. C2×#14558994C22semidirect
22. C2×#14558992C22semidirect
24. #18012737C22semidirect
29. #18012730C22semidirect
39. C4×Dic302C22semidirect
41. C4⋊(C151⋊C8)C22semidirect
42. #18012664C22semidirect
43. #18012662C22semidirect
46. #18012660C22semidirect
50. #18012649C22semidirect
51. C8×Dic151C22semidirect
53. C2×SD16×C151C22semidirect
55. C4×Q8×C151C22semidirect
56. C4⋊C8×C151C22semidirect
58. #102×C151C22semidirect
190. C151#3222semidirect
201. #460D151semidirect
216. C2×SD16C2×D151semidirect
234. C4×Q8C2×D151semidirect
237. C4⋊C8C2×D151semidirect
245. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528202
#237527752
#237526032
#237525832
#237525752
#237525652
#237524352
#237524342
#237524092
#237523752
#237523712
#237523642
#237523612
#237522722
#460×C1512
#3222151