Finite Group Databasebeta

← #34081009

Subgroups — #34081009

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#23752915C211yesmaximal, characteristic, complemented
2#23752874C211yesmaximal, characteristic, complemented
3#23752569C211yesmaximal, characteristic, complemented
4#23752555C211yesmaximal, characteristic, complemented
5#23752532C211yesmaximal, characteristic, complemented
6#23752449C211yesmaximal, characteristic, complemented
7#23752442C211yesmaximal, characteristic, complemented
8#23752428C211yesmaximal, characteristic, complemented
9#23752360C211yesmaximal, characteristic, complemented
10#23752352C211yesmaximal, characteristic, complemented
11C4×#14558991C211yesmaximal, characteristic, complemented
12#23752277C211yesmaximal, characteristic, complemented
13#23752207C211yesmaximal, characteristic, complemented
14#103×D151C211yesmaximal, characteristic, complemented
15#479×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×Q8×D151C2211yescharacteristic
18C2×#14558993C2211yescharacteristic
19C2×#14558991C2211yescharacteristic
20C2×D1208C2211yescharacteristic
21C2×C8×D151C2211yescharacteristic
22C2×C8×D151C2211yescharacteristic
23#18012734—21no—
24#18012727—21no—
25#18012727C2211yescharacteristic
26#18012724—21no—
27#18012719—21no—
28#18012719C2211yescharacteristic
29#18012714—21no—
30#18012714—21no—
31#18012714C2211yescharacteristic
32#18012714C2211yescharacteristic
33#18012714C2211yescharacteristic
34C4×D604—21no—
35C4×D604C2211yescharacteristic
36C4×D604C2211yescharacteristic
37#18012701—21no—
38#18012697C2211yescharacteristic
39C4⋊C4×D151C2211yescharacteristic
40#18012670C2211yescharacteristic
41#18012664C2211yescharacteristic
42#18012663C2211yescharacteristic
43#18012662C2211yescharacteristic
44#18012662C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012659C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C4×C151⋊C8C2211yescharacteristic
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—41no—
61C2×Dic302—21no—
62C2×Dic302C2311yescharacteristic
63Q8×D151—22no—
64Q8×D151—41no—
65C2×D604—21no—
66C2×D604—21no—
67C2×D604—21no—
68C2×D604—21no—
69C2×D604D411yescharacteristic
70C2×D604C2311yescharacteristic
71C2×D604C2311yescharacteristic
72C2×C4×D151—21no—
73C2×C4×D151—21no—
74C2×C4×D151—21no—
75C2×C4×D151—21no—
76C2×C4×D151C2311yescharacteristic
77C2×C4×D151C2311yescharacteristic
78#14558993—41no—
79#14558991—22no—
80D1208—41no—
81C2×C151⋊C8C2311yescharacteristic
82C2×C151⋊C8C2311yescharacteristic
83C8×D151—41no—
84C8×D151—41no—
85C4⋊Dic151—21no—
86C4⋊Dic151D411yescharacteristic
87C4⋊Dic151C2311yescharacteristic
88Dic151⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊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×D151C2×D411yescharacteristic
114C22×D151C2×D411yescharacteristic
115Dic302—21no—
116Dic302—21no—
117Dic302—42no—
118D604—22no—
119D604—21no—
120D604—21no—
121D604—21no—
122D604—21no—
123D604—42no—
124D604—42no—
125D604—42no—
126D604—81no—
127C2×Dic151—21no—
128C2×Dic151—21no—
129C2×Dic151C2×D411yescharacteristic
130C2×Dic151C2×D411yescharacteristic
131C4×D151—21no—
132C4×D151—21no—
133C4×D151—21no—
134C4×D151—21no—
135C4×D151—42no—
136C4×D151—42no—
137C4×D151—81no—
138C4×D151—81no—
139C151⋊C8—21no—
140C151⋊C8—21no—
141Q8×C151—21no—
142Q8×C151#4112yes—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151C2×D411yescharacteristic
148C2×C4×C151C2×D411yescharacteristic
149C2×C4×C151C2411yescharacteristic
150C8×C151—21no—
151C8×C151—21no—
152C22×C151C22×D411yescharacteristic
153C2×D151—21no—
154C2×D151—21no—
155C2×D151—21no—
156C2×D151—21no—
157C2×D151—21no—
158C2×D151—41no—
159C2×D151—41no—
160C2×D151—41no—
161C2×D151—41no—
162C2×D151—41no—
163C2×D151—41no—
164C2×D151#13512yes—
165C4×C151—22no—
166C4×C151—21no—
167C4×C151—21no—
168C4×C151—41no—
169C4×C151—41no—
170C4×C151—41no—
171C4×C151C2×#4111yescharacteristic
172C4×C151H(5,𝔽2)11yescharacteristic
173Dic151—21no—
174Dic151—21no—
175Dic151—41no—
176Dic151—41no—
177C2×C151#54611yescharacteristic
178C2×C151C2×#13511yescharacteristic
179C2×C151#57711yescharacteristic
180D151—22no—
181D151—41no—
182D151—81no—
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#479D15111yescharacteristic, complemented
192#466—1511no—
193#465—1511no—
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×SD16—1511no—
205C2×D8—1511no—
206C22×C8—1511no—
207C22×C8—1511no—
208#126—3021no—
209#125C2×D15111yescharacteristic
210#124—3021no—
211#124—1511no—
212#123—3021no—
213C22⋊Q8—3021no—
214C22⋊Q8—1511no—
215#121—3021no—
216#121—3021no—
217#121—1511no—
218#121—1511no—
219#121—1511no—
220C4×Q8C2×D15111yescharacteristic
221C4×D4—3021no—
222C4×D4—3021no—
223C4×D4—1511no—
224C4×D4—1511no—
225#117—1511no—
226C2×C4⋊C4—1511no—
227#107C2×D15111yescharacteristic
228#106—1511no—
229#106C2×D15111yescharacteristic
230C4⋊C8C2×D15111yescharacteristic
231#103—1511no—
232#103—1511no—
233#103—1511no—
234#103—1511no—
235#103C2×D15111yescharacteristic
236#103C2×D15111yescharacteristic
237#102—1511no—
238#102—1511no—
239#102—1511no—
240#102—1511no—
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—3021no—
252C2×D4—3021no—
253C2×D4—3021no—
254C2×D4—3021no—
255C2×D4—1511no—
256C2×D4—1511no—
257C2×D4—1511no—
258C22×C4—3021no—
259C22×C4—3021no—
260C22×C4—3021no—
261C22×C4—3021no—
262C22×C4—1511no—
263C22×C4—1511no—
264SD16—3022no—
265SD16—6041no—
266D8—6041no—
267C2×C8—6041no—
268C2×C8—6041no—
269C2×C8—1511no—
270C2×C8—1511no—
271C2×C8C22×D15111yescharacteristic
272C2×C8C22×D15111yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—3021no—
277C4⋊C4—3021no—
278C4⋊C4—1511no—
279C4⋊C4—1511no—
280C4⋊C4C22×D15111yescharacteristic
281C4⋊C4C22×D15111yescharacteristic
282C4⋊C4C22×D15111yescharacteristic
283C22⋊C4—3021no—
284C22⋊C4—3021no—
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—21no—
294C42—3021no—
295C42C22×D15111yescharacteristic
296C23—3021no—
297C23—3021no—
298C23—1511no—
299C23—1511no—
300Q8—21no—
301Q8—3021no—
302Q8—3021no—
303Q8—6042no—
304Q8#1455900512yes—
305D4—3022no—
306D4—3021no—
307D4—3021no—
308D4—3021no—
309D4—3021no—
310D4—6042no—
311D4—6042no—
312D4—6042no—
313D4—12081no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—3021no—
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—12081no—
329C2×C4—12081no—
330C2×C4D4×D15111yescharacteristic
331C2×C4D4×D15111yescharacteristic
332C2×C4C23×D15111yescharacteristic
333C8—21no—
334C8—21no—
335C8—3021no—
336C8—3021no—
337C22—3021no—
338C22—3021no—
339C22—3021no—
340C22—3021no—
341C22—3021no—
342C22—6041no—
343C22—6041no—
344C22—6041no—
345C22—6041no—
346C22—6041no—
347C22—6041no—
348C22—1512no—
349C22C2×D4×D15111yescharacteristic
350C4—21no—
351C4—21no—
352C4—22no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—3021no—
357C4—3021no—
358C4—6041no—
359C4—6041no—
360C4C2×#1455900511yescharacteristic
361C4#1801278511yescharacteristic
362C2—3022no—
363C2—6041no—
364C2—12081no—
365C2—12081no—
366C2#2375285311yescharacteristic
367C2#135×D15111yescharacteristic
368C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#479×C151C2
socleC22×C151C22×D4
hypercenter#479D151
hypocenterC151#3301
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. #23752874C2semidirect
3. #23752569C2semidirect
4. #23752555C2semidirect
5. #23752532C2semidirect
6. #23752449C2semidirect
7. #23752442C2semidirect
8. #23752428C2semidirect
9. #23752360C2semidirect
10. #23752352C2semidirect
11. C4×#14558991C2semidirect
12. #23752277C2semidirect
13. #23752207C2semidirect
14. #103×D151C2semidirect
15. #479×C151C2semidirect
184. C151#3301semidirect
191. #479D151semidirect

Maximal subgroups

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

subgroupindex
#237529152
#237528742
#237525692
#237525552
#237525322
#237524492
#237524422
#237524282
#237523602
#237523522
C4×#145589912
#237522772
#237522072
#103×D1512
#479×C1512
#3301151