Finite Group Databasebeta

← #34081113

Subgroups — #34081113

Order 19328.

404 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#23752915C211yesmaximal, characteristic, complemented
2#23752884C211yesmaximal, characteristic, complemented
3#23752578C211yesmaximal, characteristic, complemented
4#23752538C211yesmaximal, characteristic, complemented
5#23752527C211yesmaximal, characteristic, complemented
6#23752466C211yesmaximal, characteristic, complemented
7#23752449C211yesmaximal, characteristic, complemented
8#23752408C211yesmaximal, characteristic, complemented
9#23752360C211yesmaximal, characteristic, complemented
10#23752360C211yesmaximal, characteristic, complemented
11#23752310C211yesmaximal, characteristic, complemented
12#23752282C211yesmaximal, characteristic, complemented
13#23752212C211yesmaximal, characteristic, complemented
14#23752207C211yesmaximal, characteristic, complemented
15#479×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559005C2211yescharacteristic
18C2×#14558991C2211yescharacteristic
19C2×D1208C2211yescharacteristic
20C2×D1208C2211yescharacteristic
21C2×#14558987C2211yescharacteristic
22C2×C8×D151C2211yescharacteristic
23#18012736—21no—
24#18012736C2211yescharacteristic
25#18012734—21no—
26#18012724—21no—
27#18012714—21no—
28#18012714—21no—
29#18012714—21no—
30#18012714C2211yescharacteristic
31#18012714C2211yescharacteristic
32#18012714C2211yescharacteristic
33#18012714C2211yescharacteristic
34C4×D604—21no—
35C4×D604C2211yescharacteristic
36C4×D604C2211yescharacteristic
37#18012701—21no—
38#18012697C2211yescharacteristic
39C4⋊C4×D151C2211yescharacteristic
40#18012672C2211yescharacteristic
41#18012663C2211yescharacteristic
42#18012661C2211yescharacteristic
43#18012661C2211yescharacteristic
44#18012659C2211yescharacteristic
45#18012659C2211yescharacteristic
46#18012659C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51#18012650C2211yescharacteristic
52#125×C151C2211yescharacteristic
53C4×Q8×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic
55#106×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#103×C151C2211yescharacteristic
59#14559005—22no—
60#14559005—22no—
61#14559005—41no—
62#14559005—41no—
63C2×D604—21no—
64C2×D604—21no—
65C2×D604—21no—
66C2×D604—21no—
67C2×D604—21no—
68C2×D604—21no—
69C2×D604—21no—
70C2×D604—21no—
71C2×D604D411yescharacteristic
72C2×D604C2311yescharacteristic
73C2×D604C2311yescharacteristic
74C2×D604C2311yescharacteristic
75C2×C4×D151—21no—
76C2×C4×D151—21no—
77C2×C4×D151—21no—
78C2×C4×D151—21no—
79C2×C4×D151C2311yescharacteristic
80C2×C4×D151C2311yescharacteristic
81#14558991—22no—
82D1208—41no—
83D1208—41no—
84#14558987—41no—
85C2×C151⋊C8C2311yescharacteristic
86C2×C151⋊C8C2311yescharacteristic
87C8×D151—41no—
88C4⋊Dic151D411yescharacteristic
89C4⋊Dic151C2311yescharacteristic
90Dic151⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—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—
100C2×Q8×C151C2311yescharacteristic
101C2×C8×C151C2311yescharacteristic
102C2×C8×C151C2311yescharacteristic
103C4⋊C4×C151—21no—
104C4⋊C4×C151—21no—
105C4⋊C4×C151—21no—
106C4⋊C4×C151C2311yescharacteristic
107C4⋊C4×C151C2311yescharacteristic
108C4⋊C4×C151C2311yescharacteristic
109C42×C151—21no—
110C42×C151C2311yescharacteristic
111C22×D151—21no—
112C22×D151—21no—
113C22×D151—21no—
114C22×D151C2×D411yescharacteristic
115C22×D151C2×D411yescharacteristic
116D604—21no—
117D604—21no—
118D604—21no—
119D604—21no—
120D604—21no—
121D604—21no—
122D604—41no—
123D604—42no—
124D604—42no—
125D604—42no—
126D604—42no—
127D604—81no—
128D604—81no—
129D604—81no—
130D604—81no—
131C2×Dic151—21no—
132C2×Dic151C2×D411yescharacteristic
133C2×Dic151C2×D411yescharacteristic
134C4×D151—21no—
135C4×D151—21no—
136C4×D151—21no—
137C4×D151—21no—
138C4×D151—42no—
139C4×D151—42no—
140C4×D151—81no—
141C4×D151—81no—
142C151⋊C8—21no—
143C151⋊C8—21no—
144Q8×C151—21no—
145Q8×C151#4112yes—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151C2×D411yescharacteristic
151C2×C4×C151C2×D411yescharacteristic
152C2×C4×C151C2411yescharacteristic
153C8×C151—21no—
154C8×C151—21no—
155C22×C151C22×D411yescharacteristic
156C2×D151—21no—
157C2×D151—21no—
158C2×D151—21no—
159C2×D151—21no—
160C2×D151—21no—
161C2×D151—21no—
162C2×D151—41no—
163C2×D151—41no—
164C2×D151—41no—
165C2×D151—41no—
166C2×D151—41no—
167C2×D151—41no—
168C2×D151—41no—
169C2×D151—41no—
170C2×D151—41no—
171C4×C151—22no—
172C4×C151—21no—
173C4×C151—21no—
174C4×C151—41no—
175C4×C151—41no—
176C4×C151—41no—
177C4×C151C2×#4111yescharacteristic
178C4×C151H(5,𝔽2)11yescharacteristic
179Dic151—21no—
180Dic151—21no—
181Dic151—41no—
182C2×C151#54611yescharacteristic
183C2×C151#57511yescharacteristic
184C2×C151#57611yescharacteristic
185D151—41no—
186D151—41no—
187D151—81no—
188D151—81no—
189D151—81no—
190C151#330911yescharacteristic, complemented, Sylow
191#3309—1511nomaximal, Sylow
192#553—1511no—
193#550—1511no—
194#490—1511no—
195#482—1511no—
196#480—1511no—
197#479D15111yescharacteristic, complemented
198#469—1511no—
199#466—1511no—
200#459—1511no—
201#449—1511no—
202#449—1511no—
203#440—1511no—
204#435—1511no—
205#417—1511no—
206#416—1511no—
207C2×#41—1511no—
208C2×#41—1511no—
209C2×SD16—1511no—
210C2×D8—1511no—
211C2×D8—1511no—
212C2×M16—1511no—
213C22×C8—1511no—
214#127—3021no—
215#127—1511no—
216#126—3021no—
217#125C2×D15111yescharacteristic
218#123—3021no—
219#121—3021no—
220#121—3021no—
221#121—3021no—
222#121—1511no—
223#121—1511no—
224#121—1511no—
225#121—1511no—
226C4×Q8C2×D15111yescharacteristic
227C4×D4—3021no—
228C4×D4—3021no—
229C4×D4—1511no—
230C4×D4—1511no—
231#117—1511no—
232C2×C4⋊C4—1511no—
233#107—1511no—
234#107C2×D15111yescharacteristic
235#106C2×D15111yescharacteristic
236C4⋊C8C2×D15111yescharacteristic
237#103—1511no—
238#103C2×D15111yescharacteristic
239#103C2×D15111yescharacteristic
240#102—1511no—
241#102—1511no—
242#102—1511no—
243#102—1511no—
244#102—1511no—
245#102—1511no—
246#102—1511no—
247C22⋊C8—1511no—
248C22⋊C8—1511no—
249#97—1511no—
250#41—3022no—
251#41—3022no—
252#41—6041no—
253#41—6041no—
254C2×Q8C22×D15111yescharacteristic
255C2×D4—3021no—
256C2×D4—3021no—
257C2×D4—3021no—
258C2×D4—3021no—
259C2×D4—3021no—
260C2×D4—3021no—
261C2×D4—3021no—
262C2×D4—3021no—
263C2×D4—1511no—
264C2×D4—1511no—
265C2×D4—1511no—
266C2×D4—1511no—
267C22×C4—3021no—
268C22×C4—3021no—
269C22×C4—3021no—
270C22×C4—3021no—
271C22×C4—1511no—
272C22×C4—1511no—
273SD16—3022no—
274D8—6041no—
275D8—6041no—
276M16—6041no—
277C2×C8—6041no—
278C2×C8—1511no—
279C2×C8—1511no—
280C2×C8C22×D15111yescharacteristic
281C2×C8C22×D15111yescharacteristic
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—3021no—
286C4⋊C4—1511no—
287C4⋊C4—1511no—
288C4⋊C4C22×D15111yescharacteristic
289C4⋊C4C22×D15111yescharacteristic
290C4⋊C4C22×D15111yescharacteristic
291C22⋊C4—3021no—
292C22⋊C4—3021no—
293C22⋊C4—3021no—
294C22⋊C4—3021no—
295C22⋊C4—3021no—
296C22⋊C4—3021no—
297C22⋊C4—1511no—
298C22⋊C4—1511no—
299C42—21no—
300C42—3021no—
301C42C22×D15111yescharacteristic
302C23—3021no—
303C23—3021no—
304C23—3021no—
305C23—1511no—
306C23—1511no—
307Q8—21no—
308Q8#1455900512yes—
309D4—3021no—
310D4—3021no—
311D4—3021no—
312D4—3021no—
313D4—3021no—
314D4—3021no—
315D4—6041no—
316D4—6042no—
317D4—6042no—
318D4—6042no—
319D4—6042no—
320D4—12081no—
321D4—12081no—
322D4—12081no—
323D4—12081no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—3021no—
329C2×C4—3021no—
330C2×C4—3021no—
331C2×C4—3021no—
332C2×C4—3021no—
333C2×C4—6042no—
334C2×C4—6042no—
335C2×C4—1511no—
336C2×C4—1511no—
337C2×C4—12081no—
338C2×C4—12081no—
339C2×C4D4×D15111yescharacteristic
340C2×C4D4×D15111yescharacteristic
341C2×C4C23×D15111yescharacteristic
342C8—21no—
343C8—21no—
344C8—3021no—
345C8—3021no—
346C22—3021no—
347C22—3021no—
348C22—3021no—
349C22—3021no—
350C22—3021no—
351C22—3021no—
352C22—6041no—
353C22—6041no—
354C22—6041no—
355C22—6041no—
356C22—6041no—
357C22—6041no—
358C22—6041no—
359C22—6041no—
360C22—6041no—
361C22C2×D4×D15111yescharacteristic
362C4—21no—
363C4—21no—
364C4—22no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—3021no—
369C4—3021no—
370C4—6041no—
371C4C2×#1455900511yescharacteristic
372C4#1801278511yescharacteristic
373C2—6041no—
374C2—6041no—
375C2—12081no—
376C2—12081no—
377C2—12081no—
378C2#2375285311yescharacteristic
379C2#2375301111yescharacteristic
380C2#2375301411yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#479×C151C2
socleC22×C151C22×D4
hypercenter#479D151
hypocenterC151#3309
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #23752915C2semidirect
2. #23752884C2semidirect
3. #23752578C2semidirect
4. #23752538C2semidirect
5. #23752527C2semidirect
6. #23752466C2semidirect
7. #23752449C2semidirect
8. #23752408C2semidirect
9. #23752360C2semidirect
10. #23752360C2semidirect
11. #23752310C2semidirect
12. #23752282C2semidirect
13. #23752212C2semidirect
14. #23752207C2semidirect
15. #479×C151C2semidirect
190. C151#3309semidirect
197. #479D151semidirect

Maximal subgroups

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

subgroupindex
#237529152
#237528842
#237525782
#237525382
#237525272
#237524662
#237524492
#237524082
#237523602
#237523102
#237522822
#237522122
#237522072
#479×C1512
#3309151