Finite Group Databasebeta

← #34081034

Subgroups — #34081034

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#23752925C211yesmaximal, characteristic, complemented
2#23752861C211yesmaximal, characteristic, complemented
3#23752561C211yesmaximal, characteristic, complemented
4#23752553C211yesmaximal, characteristic, complemented
5#23752551C211yesmaximal, characteristic, complemented
6#23752500C211yesmaximal, characteristic, complemented
7#23752444C211yesmaximal, characteristic, complemented
8#23752441C211yesmaximal, characteristic, complemented
9#23752416C211yesmaximal, characteristic, complemented
10#23752358C211yesmaximal, characteristic, complemented
11#23752357C211yesmaximal, characteristic, complemented
12#23752292C211yesmaximal, characteristic, complemented
13C8×C22⋊D151C211yesmaximal, characteristic, complemented
14#23752205C211yesmaximal, characteristic, complemented
15#416×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×#14558993C2211yescharacteristic
18C2×#14558991C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20C2×C8×D151C2211yescharacteristic
21#18012738C2211yescharacteristic
22#18012737C2211yescharacteristic
23#18012727—21no—
24#18012725—21no—
25#18012722—21no—
26#18012720—21no—
27#18012718C2211yescharacteristic
28#18012715C2211yescharacteristic
29#18012714C2211yescharacteristic
30#18012713C2211yescharacteristic
31#18012712—21no—
32#18012711—21no—
33D4×Dic151C2211yescharacteristic
34#18012701C2211yescharacteristic
35C4×C22⋊D151C2211yescharacteristic
36#18012697C2211yescharacteristic
37#18012696—21no—
38C2×Dic151⋊C4—21no—
39#18012672C2211yescharacteristic
40#18012671C2211yescharacteristic
41#18012670C2211yescharacteristic
42Dic151⋊C8C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012662C2211yescharacteristic
46#18012662C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012660C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×#41×C151C2211yescharacteristic
53C22×C8×C151C2211yescharacteristic
54#117×C151C2211yescharacteristic
55#103×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59#14559003—22no—
60#14559003—41no—
61C2×Dic302—21no—
62C2×Dic302C2311yescharacteristic
63C2×D604—21no—
64C2×D604C2311yescharacteristic
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67C2×C22⋊D151D411yescharacteristic
68C22×Dic151—21no—
69C22×Dic151—21no—
70C2×C4×D151—21no—
71C2×C4×D151C2311yescharacteristic
72#14558993—41no—
73#14558991—41no—
74#14558989—22no—
75C2×C151⋊C8C2311yescharacteristic
76C2×C151⋊C8C2311yescharacteristic
77C8×D151—41no—
78C4⋊Dic151C2311yescharacteristic
79C4⋊Dic151C2311yescharacteristic
80Dic151⋊C4—21no—
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4D411yescharacteristic
86C22⋊Dic151—21no—
87C22⋊Dic151—21no—
88C22⋊Dic151D411yescharacteristic
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)⋊C4D411yescharacteristic
95C4×Dic151—21no—
96C4×Dic151C2311yescharacteristic
97#41×C151—22no—
98#41×C151—41no—
99C2×Q8×C151C2311yescharacteristic
100C2×D4×C151—21no—
101C2×D4×C151C2311yescharacteristic
102C22×C4×C151—21no—
103C22×C4×C151C2311yescharacteristic
104C2×C8×C151—41no—
105C2×C8×C151C2311yescharacteristic
106C2×C8×C151C2311yescharacteristic
107C4⋊C4×C151C2311yescharacteristic
108C4⋊C4×C151C2311yescharacteristic
109C22⋊C4×C151—21no—
110C42×C151—21no—
111C22×D151—21no—
112C22×D151C2×D411yescharacteristic
113Dic302—21no—
114Dic302—21no—
115Dic302—81no—
116D604—21no—
117D604—21no—
118D604—81no—
119C22⋊D151—22no—
120C22⋊D151—42no—
121C22⋊D151—81no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C2×Dic151—42no—
126C2×Dic151—42no—
127C2×Dic151C2×D411yescharacteristic
128C2×Dic151C2×D411yescharacteristic
129C2×Dic151C2×D411yescharacteristic
130C4×D151—21no—
131C4×D151—21no—
132C4×D151—42no—
133C151⋊C8—21no—
134C151⋊C8—21no—
135C23×C151—21no—
136C23×C151C2×D411yescharacteristic
137Q8×C151—21no—
138Q8×C151—21no—
139D4×C151—21no—
140D4×C151—42no—
141D4×C151#4112yes—
142C2×C4×C151—21no—
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×C151C22×D411yescharacteristic
159C2×D151—21no—
160C2×D151—21no—
161C2×D151—21no—
162C2×D151—41no—
163C2×D151—41no—
164C2×D151—41no—
165C4×C151—21no—
166C4×C151—41no—
167C4×C151—41no—
168C4×C151—41no—
169C4×C151C2×#4111yescharacteristic
170C4×C151H(5,𝔽2)11yescharacteristic
171Dic151—21no—
172Dic151—21no—
173Dic151—41no—
174Dic151—41no—
175Dic151—41no—
176Dic151#13512yes—
177C2×C151—41no—
178C2×C151—42no—
179C2×C151#54611yescharacteristic
180C2×C151C2×#13511yescharacteristic
181C2×C151#57711yescharacteristic
182D151—41no—
183D151—81no—
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#449—1511no—
197C4×D8—1511no—
198C8×D4—1511no—
199#416—1511no—
200#416D15111yescharacteristic, complemented
201C2×#41—1511no—
202C2×#41C2×D15111yescharacteristic
203C2×SD16—1511no—
204C2×SD16—1511no—
205C2×D8—1511no—
206C22×C8—1511no—
207C22×C8C2×D15111yescharacteristic
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#121—1511no—
220C4×D4—1511no—
221C4×D4—1511no—
222C4×D4—1511no—
223#117—3021no—
224#117—1511no—
225#117C2×D15111yescharacteristic
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#103C2×D15111yescharacteristic
236#103C2×D15111yescharacteristic
237#102—1511no—
238#102—1511no—
239#102C2×D15111yescharacteristic
240#102C2×D15111yescharacteristic
241C22⋊C8—1511no—
242C22⋊C8—1511no—
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—3021no—
253C2×D4—3021no—
254C2×D4—3021no—
255C2×D4—1511no—
256C2×D4—1511no—
257C2×D4C22×D15111yescharacteristic
258C22×C4—21no—
259C22×C4—3021no—
260C22×C4—3021no—
261C22×C4—3021no—
262C22×C4—1511no—
263C22×C4C22×D15111yescharacteristic
264SD16—6041no—
265SD16—6041no—
266D8—3022no—
267C2×C8—41no—
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⋊C4C22×D15111yescharacteristic
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—21no—
294C42—3021no—
295C42—1511no—
296C23—21no—
297C23—3021no—
298C23—1511no—
299C23D4×D15111yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—3021no—
303Q8—3021no—
304Q8—12081no—
305D4—21no—
306D4—42no—
307D4—3022no—
308D4—3021no—
309D4—3021no—
310D4—6042no—
311D4—12081no—
312D4—12081no—
313D4#1455900412yes—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
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—3021no—
344C22—3021no—
345C22—3021no—
346C22—6041no—
347C22—6041no—
348C22—6041no—
349C22C2×D4×D15111yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—3021no—
355C4—3021no—
356C4—6041no—
357C4—6041no—
358C4—6041no—
359C4—1512no—
360C4C2×#1455900411yescharacteristic
361C4#1801278411yescharacteristic
362C2—41no—
363C2—42no—
364C2—6041no—
365C2—12081no—
366C2#2375285211yescharacteristic
367C2#135×D15111yescharacteristic
368C2#2375301911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#416×C151C2
socleC22×C151C22×D4
hypercenter#416D151
hypocenterC151#3303
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #23752925C2semidirect
2. #23752861C2semidirect
3. #23752561C2semidirect
4. #23752553C2semidirect
5. #23752551C2semidirect
6. #23752500C2semidirect
7. #23752444C2semidirect
8. #23752441C2semidirect
9. #23752416C2semidirect
10. #23752358C2semidirect
11. #23752357C2semidirect
12. #23752292C2semidirect
13. C8×C22⋊D151C2semidirect
14. #23752205C2semidirect
15. #416×C151C2semidirect
184. C151#3303semidirect
200. #416D151semidirect

Maximal subgroups

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

subgroupindex
#237529252
#237528612
#237525612
#237525532
#237525512
#237525002
#237524442
#237524412
#237524162
#237523582
#237523572
#237522922
C8×C22⋊D1512
#237522052
#416×C1512
#3303151