Finite Group Databasebeta

← #34081031

Subgroups — #34081031

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#23752926C211yesmaximal, characteristic, complemented
2#23752861C211yesmaximal, characteristic, complemented
3#23752561C211yesmaximal, characteristic, complemented
4#23752554C211yesmaximal, characteristic, complemented
5#23752552C211yesmaximal, characteristic, complemented
6#23752500C211yesmaximal, characteristic, complemented
7#23752439C211yesmaximal, characteristic, complemented
8#23752438C211yesmaximal, characteristic, complemented
9#23752415C211yesmaximal, characteristic, complemented
10#23752354C211yesmaximal, characteristic, complemented
11D8×Dic151C211yesmaximal, characteristic, complemented
12(C22⋊D151)⋊C8C211yesmaximal, characteristic, complemented
13#23752208C211yesmaximal, characteristic, complemented
14#23752205C211yesmaximal, characteristic, complemented
15#449×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×#14558992C2211yescharacteristic
18C22×C151⋊C8C2211yescharacteristic
19C2×C8×D151C2211yescharacteristic
20#18012738C2211yescharacteristic
21#18012737C2211yescharacteristic
22#18012726—21no—
23#18012725—21no—
24#18012722—21no—
25#18012720—21no—
26#18012718C2211yescharacteristic
27#18012715C2211yescharacteristic
28#18012711—21no—
29#18012711—21no—
30#18012710C2211yescharacteristic
31D4×Dic151C2211yescharacteristic
32D4×Dic151C2211yescharacteristic
33C4×C22⋊D151C2211yescharacteristic
34#18012698C2211yescharacteristic
35#18012697C2211yescharacteristic
36#18012695—21no—
37C2×Dic151⋊C4—21no—
38#18012673C2211yescharacteristic
39#18012671C2211yescharacteristic
40#18012670C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012662C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012660C2211yescharacteristic
49#18012660C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×#41×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic
54C2×D8×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59#14559003—22no—
60#14559003—41no—
61C2×Dic302—21no—
62C2×Dic302C2311yescharacteristic
63C2×C22⋊D151—21no—
64C2×C22⋊D151—21no—
65C2×C22⋊D151D411yescharacteristic
66C22×Dic151—21no—
67C22×Dic151—21no—
68C22×Dic151—21no—
69C2×C4×D151C2311yescharacteristic
70#14558992—41no—
71C2×C151⋊C8—41no—
72C2×C151⋊C8C2311yescharacteristic
73C2×C151⋊C8C2311yescharacteristic
74C8×D151—41no—
75C4⋊Dic151C2311yescharacteristic
76C4⋊Dic151C2311yescharacteristic
77C4⋊Dic151C2311yescharacteristic
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4D411yescharacteristic
84C22⋊Dic151—21no—
85C22⋊Dic151—21no—
86C22⋊Dic151—21no—
87C22⋊Dic151—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151D411yescharacteristic
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4D411yescharacteristic
93C4×Dic151—21no—
94C4×Dic151—21no—
95C4×Dic151C2311yescharacteristic
96#41×C151—22no—
97#41×C151—41no—
98C2×Q8×C151C2311yescharacteristic
99C2×D4×C151—21no—
100C2×D4×C151—21no—
101C2×D4×C151C2311yescharacteristic
102C2×D4×C151C2311yescharacteristic
103C22×C4×C151—21no—
104C22×C4×C151C2311yescharacteristic
105SD16×C151—41no—
106D8×C151—22no—
107C2×C8×C151C2311yescharacteristic
108C2×C8×C151C2311yescharacteristic
109C4⋊C4×C151C2311yescharacteristic
110C22⋊C4×C151—21no—
111C22×D151C2×D411yescharacteristic
112Dic302—21no—
113Dic302—21no—
114Dic302—81no—
115C22⋊D151—22no—
116C22⋊D151—42no—
117C22⋊D151—81no—
118C2×Dic151—21no—
119C2×Dic151—21no—
120C2×Dic151—21no—
121C2×Dic151—21no—
122C2×Dic151—42no—
123C2×Dic151—42no—
124C2×Dic151—42no—
125C2×Dic151C2×D411yescharacteristic
126C2×Dic151C2×D411yescharacteristic
127C2×Dic151C2×D411yescharacteristic
128C4×D151—21no—
129C4×D151—21no—
130C151⋊C8—21no—
131C151⋊C8—21no—
132C23×C151—21no—
133C23×C151—21no—
134C23×C151C2×D411yescharacteristic
135Q8×C151—21no—
136Q8×C151—21no—
137D4×C151—21no—
138D4×C151—21no—
139D4×C151—21no—
140D4×C151—42no—
141D4×C151—81no—
142D4×C151#4112yes—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151—42no—
148C2×C4×C151C2×D411yescharacteristic
149C2×C4×C151C2411yescharacteristic
150C8×C151—21no—
151C8×C151—21no—
152C22×C151—21no—
153C22×C151—22no—
154C22×C151—21no—
155C22×C151—21no—
156C22×C151—41no—
157C22×C151—41no—
158C22×C151—41no—
159C22×C151—41no—
160C22×C151—41no—
161C22×C151C22×D411yescharacteristic
162C2×D151—21no—
163C2×D151—21no—
164C2×D151—21no—
165C4×C151—21no—
166C4×C151—41no—
167C4×C151—41no—
168C4×C151C2×#4111yescharacteristic
169C4×C151H(5,𝔽2)11yescharacteristic
170Dic151—21no—
171Dic151—21no—
172Dic151—41no—
173Dic151—41no—
174Dic151—41no—
175Dic151—41no—
176Dic151#13512yes—
177C2×C151—41no—
178C2×C151—42no—
179C2×C151—81no—
180C2×C151#54611yescharacteristic
181C2×C151C2×#13511yescharacteristic
182C2×C151#57711yescharacteristic
183D151—41no—
184C151#330311yescharacteristic, complemented, Sylow
185#3303—1511nomaximal, Sylow
186#555—1511no—
187#547—1511no—
188#487—1511no—
189#485—1511no—
190#485—1511no—
191#476—1511no—
192#465—1511no—
193#465—1511no—
194#461—1511no—
195#449—1511no—
196#449D15111yescharacteristic, complemented
197C4×D8—1511no—
198C8×D4—1511no—
199#416—1511no—
200#416—1511no—
201C2×#41—1511no—
202C2×#41C2×D15111yescharacteristic
203C2×SD16—1511no—
204C2×SD16C2×D15111yescharacteristic
205C2×D8C2×D15111yescharacteristic
206C22×C8—1511no—
207C22×C8—1511no—
208C4⋊Q8—1511no—
209C4⋊Q8—1511no—
210#124—3021no—
211#124—3021no—
212#123—3021no—
213#123—3021no—
214C22⋊Q8—1511no—
215C22⋊Q8—1511no—
216#121—3021no—
217#121—3021no—
218#121—1511no—
219#121C2×D15111yescharacteristic
220C4×D4—1511no—
221C4×D4—1511no—
222C4×D4—1511no—
223#117—3021no—
224#117—1511no—
225#117—1511no—
226C2×C4⋊C4—3021no—
227#107—1511no—
228#106—1511no—
229#106—1511no—
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⋊C8C2×D15111yescharacteristic
243C4×C8—1511no—
244#41—22no—
245#41—41no—
246#41—3022no—
247#41—6041no—
248C2×Q8—3021no—
249C2×Q8—1511no—
250C2×Q8C22×D15111yescharacteristic
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—3021no—
254C2×D4—3021no—
255C2×D4—1511no—
256C2×D4C22×D15111yescharacteristic
257C2×D4C22×D15111yescharacteristic
258C22×C4—21no—
259C22×C4—3021no—
260C22×C4—3021no—
261C22×C4—3021no—
262C22×C4—1511no—
263C22×C4C22×D15111yescharacteristic
264SD16—41no—
265SD16—6041no—
266D8—22no—
267C2×C8—6041no—
268C2×C8—6041no—
269C2×C8—1511no—
270C2×C8—1511no—
271C2×C8C22×D15111yescharacteristic
272C2×C8C22×D15111yescharacteristic
273C4⋊C4—3021no—
274C4⋊C4—3021no—
275C4⋊C4—3021no—
276C4⋊C4—3021no—
277C4⋊C4—3021no—
278C4⋊C4—1511no—
279C4⋊C4—1511no—
280C4⋊C4—1511no—
281C4⋊C4—1511no—
282C4⋊C4C22×D15111yescharacteristic
283C22⋊C4—21no—
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—3021no—
294C42—3021no—
295C42—1511no—
296C23—21no—
297C23—21no—
298C23—1511no—
299C23D4×D15111yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—3021no—
303Q8—3021no—
304Q8—12081no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—3022no—
311D4—6042no—
312D4—12081no—
313D4#1455900312yes—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—3021no—
320C2×C4—3021no—
321C2×C4—3021no—
322C2×C4—3021no—
323C2×C4—3021no—
324C2×C4—3021no—
325C2×C4—6042no—
326C2×C4—6042no—
327C2×C4—6042no—
328C2×C4—1511no—
329C2×C4—1511no—
330C2×C4—1511no—
331C2×C4D4×D15111yescharacteristic
332C2×C4C23×D15111yescharacteristic
333C8—21no—
334C8—21no—
335C8—3021no—
336C8—3021no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—3021no—
347C22—3021no—
348C22—3021no—
349C22C2×D4×D15111yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—3021no—
354C4—3021no—
355C4—6041no—
356C4—6041no—
357C4—6041no—
358C4—6041no—
359C4—1512no—
360C4C2×#1455900311yescharacteristic
361C4#1801278411yescharacteristic
362C2—41no—
363C2—42no—
364C2—81no—
365C2—6041no—
366C2#2375284911yescharacteristic
367C2#135×D15111yescharacteristic
368C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#449×C151C2
socleC22×C151C22×D4
hypercenter#449D151
hypocenterC151#3303
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. #23752926C2semidirect
2. #23752861C2semidirect
3. #23752561C2semidirect
4. #23752554C2semidirect
5. #23752552C2semidirect
6. #23752500C2semidirect
7. #23752439C2semidirect
8. #23752438C2semidirect
9. #23752415C2semidirect
10. #23752354C2semidirect
11. D8×Dic151C2semidirect
12. (C22⋊D151)⋊C8C2semidirect
13. #23752208C2semidirect
14. #23752205C2semidirect
15. #449×C151C2semidirect
184. C151#3303semidirect
196. #449D151semidirect

Maximal subgroups

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

subgroupindex
#237529262
#237528612
#237525612
#237525542
#237525522
#237525002
#237524392
#237524382
#237524152
#237523542
D8×Dic1512
(C22⋊D151)⋊C82
#237522082
#237522052
#449×C1512
#3303151