Finite Group Databasebeta

← #34081007

Subgroups — #34081007

Order 19328.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752909C211yesmaximal, characteristic, complemented
2#23752872C211yesmaximal, characteristic, complemented
3#23752568C211yesmaximal, characteristic, complemented
4#23752550C211yesmaximal, characteristic, complemented
5#23752532C211yesmaximal, characteristic, complemented
6#23752522C211yesmaximal, characteristic, complemented
7#23752447C211yesmaximal, characteristic, complemented
8#23752429C211yesmaximal, characteristic, complemented
9#23752355C211yesmaximal, characteristic, complemented
10#23752349C211yesmaximal, characteristic, complemented
11#23752303C211yesmaximal, characteristic, complemented
12C8×C22⋊D151C211yesmaximal, characteristic, complemented
13#23752209C211yesmaximal, characteristic, complemented
14#103×D151C211yesmaximal, characteristic, complemented
15#465×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×Q8×D151C2211yescharacteristic
18C2×#14558992C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20C2×C8×D151C2211yescharacteristic
21#18012732—21no—
22#18012730C2211yescharacteristic
23#18012728C2211yescharacteristic
24#18012725—21no—
25#18012720—21no—
26#18012717—21no—
27#18012714C2211yescharacteristic
28#18012712—21no—
29#18012710—21no—
30#18012710C2211yescharacteristic
31#18012704C2211yescharacteristic
32D4×Dic151C2211yescharacteristic
33#18012701—21no—
34C4×C22⋊D151C2211yescharacteristic
35(C22⋊D151)⋊C4—21no—
36#18012698C2211yescharacteristic
37C4⋊C4×D151C2211yescharacteristic
38#18012672C2211yescharacteristic
39#18012670C2211yescharacteristic
40Dic151⋊C8C2211yescharacteristic
41#18012664C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012663C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012662C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012659C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×SD16×C151C2211yescharacteristic
53C22×C8×C151C2211yescharacteristic
54C22⋊Q8×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic
56#106×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59#14559004—22no—
60#14559004—41no—
61C2×Dic302—21no—
62C2×Dic302C2311yescharacteristic
63Q8×D151—22no—
64Q8×D151—41no—
65C2×D604—21no—
66C2×D604C2311yescharacteristic
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151D411yescharacteristic
70C22×Dic151—21no—
71C2×C4×D151—21no—
72C2×C4×D151—21no—
73C2×C4×D151—21no—
74C2×C4×D151C2311yescharacteristic
75#14558992—22no—
76#14558989—41no—
77C2×C151⋊C8C2311yescharacteristic
78C2×C151⋊C8C2311yescharacteristic
79C8×D151—41no—
80C4⋊Dic151—21no—
81C4⋊Dic151C2311yescharacteristic
82C4⋊Dic151C2311yescharacteristic
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4D411yescharacteristic
87C22⋊Dic151—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90C22⋊Dic151D411yescharacteristic
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4D411yescharacteristic
95C4×Dic151—21no—
96C4×Dic151—21no—
97C4×Dic151C2311yescharacteristic
98C2×Q8×C151C2311yescharacteristic
99C2×D4×C151—21no—
100C2×D4×C151C2311yescharacteristic
101C22×C4×C151C2311yescharacteristic
102SD16×C151—41no—
103C2×C8×C151—41no—
104C2×C8×C151C2311yescharacteristic
105C2×C8×C151C2311yescharacteristic
106C4⋊C4×C151—21no—
107C4⋊C4×C151C2311yescharacteristic
108C4⋊C4×C151C2311yescharacteristic
109C22⋊C4×C151—21no—
110C22⋊C4×C151—21no—
111C22×D151—21no—
112C22×D151C2×D411yescharacteristic
113Dic302—21no—
114Dic302—42no—
115Dic302#4112yes—
116D604—21no—
117D604—21no—
118D604—42no—
119C22⋊D151—22no—
120C22⋊D151—42no—
121C22⋊D151—42no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C2×Dic151—81no—
126C2×Dic151C2×D411yescharacteristic
127C2×Dic151C2×D411yescharacteristic
128C2×Dic151C2×D411yescharacteristic
129C4×D151—21no—
130C4×D151—21no—
131C4×D151—42no—
132C4×D151—42no—
133C4×D151—81no—
134C151⋊C8—21no—
135C151⋊C8—21no—
136C23×C151—21no—
137C23×C151C2×D411yescharacteristic
138Q8×C151—21no—
139Q8×C151—21no—
140D4×C151—21no—
141D4×C151—21no—
142D4×C151—81no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151C2×D411yescharacteristic
149C2×C4×C151C2411yescharacteristic
150C8×C151—21no—
151C8×C151—21no—
152C22×C151—21no—
153C22×C151—21no—
154C22×C151—21no—
155C22×C151—41no—
156C22×C151—41no—
157C22×C151—41no—
158C22×C151C22×D411yescharacteristic
159C2×D151—21no—
160C2×D151—21no—
161C2×D151—41no—
162C2×D151—41no—
163C2×D151—41no—
164C2×D151#13512yes—
165C4×C151—21no—
166C4×C151—41no—
167C4×C151—41no—
168C4×C151—41no—
169C4×C151C2×#4111yescharacteristic
170C4×C151H(5,𝔽2)11yescharacteristic
171Dic151—21no—
172Dic151—22no—
173Dic151—21no—
174Dic151—21no—
175Dic151—41no—
176Dic151—41no—
177C2×C151—41no—
178C2×C151—81no—
179C2×C151#54611yescharacteristic
180C2×C151C2×#13511yescharacteristic
181C2×C151#57711yescharacteristic
182D151—22no—
183D151—81no—
184C151#330111yescharacteristic, complemented, Sylow
185#3301—1511nomaximal, Sylow
186#553—1511no—
187#548—1511no—
188#488—1511no—
189#485—1511no—
190#481—1511no—
191#479—1511no—
192#466—1511no—
193#465D15111yescharacteristic, complemented
194#463—1511no—
195#449—1511no—
196#448—1511no—
197C4×SD16—1511no—
198C8×D4—1511no—
199#416—1511no—
200C2×#103—1511no—
201C2×#41—1511no—
202C22×Q8—1511no—
203C2×SD16—1511no—
204C2×SD16C2×D15111yescharacteristic
205C2×D8—1511no—
206C22×C8—1511no—
207C22×C8C2×D15111yescharacteristic
208#126—3021no—
209#125—1511no—
210#124—3021no—
211#124—1511no—
212#123—3021no—
213C22⋊Q8—3021no—
214C22⋊Q8C2×D15111yescharacteristic
215#121—3021no—
216#121—3021no—
217#121—1511no—
218#121—1511no—
219#121C2×D15111yescharacteristic
220C4×Q8—1511no—
221C4×D4—3021no—
222C4×D4—3021no—
223C4×D4—1511no—
224C4×D4—1511no—
225#117—1511no—
226C2×C4⋊C4—1511no—
227#107—1511no—
228#106—1511no—
229#106C2×D15111yescharacteristic
230C4⋊C8—1511no—
231#103—1511no—
232#103—1511no—
233#103—1511no—
234#103—1511no—
235#103—1511no—
236#103C2×D15111yescharacteristic
237#102—1511no—
238#102—1511no—
239#102—1511no—
240#102C2×D15111yescharacteristic
241C22⋊C8—1511no—
242C22⋊C8—1511no—
243C4×C8—1511no—
244#41—3022no—
245#41—6041no—
246C2×Q8—3021no—
247C2×Q8—3022no—
248C2×Q8—6041no—
249C2×Q8—1511no—
250C2×Q8C22×D15111yescharacteristic
251C2×D4—21no—
252C2×D4—3021no—
253C2×D4—3021no—
254C2×D4—3021no—
255C2×D4—1511no—
256C2×D4—1511no—
257C2×D4C22×D15111yescharacteristic
258C22×C4—3021no—
259C22×C4—3021no—
260C22×C4—3021no—
261C22×C4—3021no—
262C22×C4—1511no—
263C22×C4C22×D15111yescharacteristic
264SD16—41no—
265SD16—3022no—
266D8—6041no—
267C2×C8—41no—
268C2×C8—6041no—
269C2×C8—1511no—
270C2×C8—1511no—
271C2×C8C22×D15111yescharacteristic
272C2×C8C22×D15111yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—3021no—
275C4⋊C4—3021no—
276C4⋊C4—3021no—
277C4⋊C4—3021no—
278C4⋊C4—1511no—
279C4⋊C4—1511no—
280C4⋊C4—1511no—
281C4⋊C4C22×D15111yescharacteristic
282C4⋊C4C22×D15111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—3021no—
286C22⋊C4—3021no—
287C22⋊C4—3021no—
288C22⋊C4—3021no—
289C22⋊C4—3021no—
290C22⋊C4—3021no—
291C22⋊C4—1511no—
292C22⋊C4—1511no—
293C42—3021no—
294C42—3021no—
295C42—1511no—
296C23—21no—
297C23—3021no—
298C23—1511no—
299C23D4×D15111yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—3021no—
303Q8—6042no—
304Q8—1512no—
305D4—21no—
306D4—21no—
307D4—81no—
308D4—3022no—
309D4—3021no—
310D4—3021no—
311D4—6042no—
312D4—6042no—
313D4—6042no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—3021no—
320C2×C4—3021no—
321C2×C4—3021no—
322C2×C4—3021no—
323C2×C4—3021no—
324C2×C4—6042no—
325C2×C4—6042no—
326C2×C4—1511no—
327C2×C4—1511no—
328C2×C4—1511no—
329C2×C4—12081no—
330C2×C4—12081no—
331C2×C4D4×D15111yescharacteristic
332C2×C4C23×D15111yescharacteristic
333C8—21no—
334C8—21no—
335C8—3021no—
336C8—3021no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—3021no—
344C22—3021no—
345C22—6041no—
346C22—6041no—
347C22—6041no—
348C22—1512no—
349C22C2×D4×D15111yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—3021no—
355C4—3021no—
356C4—3021no—
357C4—3022no—
358C4—6041no—
359C4—6041no—
360C4#41×D15111yescharacteristic
361C4#1801278411yescharacteristic
362C2—41no—
363C2—81no—
364C2—3022no—
365C2—12081no—
366C2#2375285111yescharacteristic
367C2#135×D15111yescharacteristic
368C2#2375301811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#465×C151C2
socleC22×C151C22×D4
hypercenter#465D151
hypocenterC151#3301
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #23752909C2semidirect
2. #23752872C2semidirect
3. #23752568C2semidirect
4. #23752550C2semidirect
5. #23752532C2semidirect
6. #23752522C2semidirect
7. #23752447C2semidirect
8. #23752429C2semidirect
9. #23752355C2semidirect
10. #23752349C2semidirect
11. #23752303C2semidirect
12. C8×C22⋊D151C2semidirect
13. #23752209C2semidirect
14. #103×D151C2semidirect
15. #465×C151C2semidirect
184. C151#3301semidirect
193. #465D151semidirect

Maximal subgroups

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

subgroupindex
#237529092
#237528722
#237525682
#237525502
#237525322
#237525222
#237524472
#237524292
#237523552
#237523492
#237523032
C8×C22⋊D1512
#237522092
#103×D1512
#465×C1512
#3301151