Finite Group Databasebeta

← #34078327

Subgroups — #34078327

Order 19328.

764 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 764 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14559005C211yesmaximal, characteristic, complemented
2C2×#18012760C212yesmaximal, complemented
3#23752722C211yesmaximal, characteristic, complemented
4#23752377C212yesmaximal, complemented
5#23752368C211yesmaximal, characteristic, complemented
6#23752365C211yesmaximal, characteristic, complemented
7#23752356C212yesmaximal, complemented
8#23752345C211yesmaximal, characteristic, complemented
9#23752207C212yesmaximal, complemented
10C22⋊C8×D151C211yesmaximal, characteristic, complemented
11#448×C151C211yesmaximal, characteristic, complemented
12C2×#14559005—28no—
13C2×#14559005—21no—
14C2×#14559005—21no—
15C2×#14559005C2212yes—
16C2×#14559005C2212yes—
17C2×#14559003C2211yescharacteristic, complemented
18C22×D604—21no—
19C22×D604C2211yescharacteristic
20C22×C4×D151—21no—
21C22×C4×D151C2211yescharacteristic
22#18012760—28no—
23C2×#14558994C2212yescomplemented
24C2×#14558993C2212yescomplemented
25C2×#14558989C2212yescomplemented
26C2×C8×D151C2212yescomplemented
27#18012721—21no—
28#18012719C2211yescharacteristic, complemented
29#18012718C2211yescharacteristic
30#18012710C2211yescharacteristic, complemented
31#18012707—21no—
32D4×Dic151—21no—
33(C22⋊D151)⋊C4—21no—
34#18012697C2211yescharacteristic, complemented
35#18012663C2212yescomplemented
36#18012661C2212yescomplemented
37#18012659C2212yescomplemented
38C22⋊(C151⋊C8)C2211yescharacteristic
39(C2×D151)⋊C8C2212yescomplemented
40C22×Q8×C151C2211yescharacteristic
41C2×SD16×C151C2212yescomplemented
42#121×C151C2211yescharacteristic
43#103×C151C2212yescomplemented
44C22⋊C8×C151C2211yescharacteristic
45C23×D151—21no—
46C23×D151D411yescharacteristic
47#14559005—28no—
48#14559005—28no—
49#14559005—24no—
50#14559005—24no—
51#14559005—24no—
52#14559005D418yescomplemented
53#14559003—24no—
54C2×Dic302C2311yescharacteristic
55C2×D604—28no—
56C2×D604—22no—
57C2×D604—22no—
58C2×D604—24no—
59C2×D604—21no—
60C2×D604C2312yes—
61C2×C22⋊D151—21no—
62C2×C22⋊D151—21no—
63C22×Dic151—21no—
64C22×Dic151D411yescharacteristic
65C2×C4×D151—28no—
66C2×C4×D151—22no—
67C2×C4×D151—22no—
68C2×C4×D151—24no—
69C2×C4×D151D411yescharacteristic
70C2×C4×D151D411yescharacteristic
71C2×C4×D151C2311yescharacteristic
72C2×C4×D151C2311yescharacteristic
73#14558994—24no—
74#14558993—24no—
75#14558989—24no—
76C2×C151⋊C8C2312yes—
77C8×D151—24no—
78C4⋊Dic151—21no—
79C4⋊Dic151C2311yescharacteristic
80Dic151⋊C4—21no—
81C22⋊Dic151—21no—
82C22⋊Dic151—21no—
83(C2×D151)⋊C4—21no—
84(C2×D151)⋊C4—21no—
85C4×Dic151—21no—
86C2×Q8×C151—24no—
87C2×Q8×C151—21no—
88C2×Q8×C151C2312yes—
89C2×D4×C151—21no—
90C2×D4×C151C2311yescharacteristic
91C22×C4×C151—21no—
92C22×C4×C151C2311yescharacteristic
93SD16×C151—24no—
94C2×C8×C151C2312yes—
95C4⋊C4×C151C2311yescharacteristic
96C22⋊C4×C151—21no—
97C22×D151—24no—
98C22×D151—22no—
99C22×D151—22no—
100C22×D151—22no—
101C22×D151—41no—
102C22×D151—42no—
103C22×D151—42no—
104C22×D151C2×D411yescharacteristic
105C22×D151C2×D411yescharacteristic
106Dic302—22no—
107D604—28no—
108D604—24no—
109D604—28no—
110D604—22no—
111D604C2×D414yes—
112C22⋊D151—42no—
113C22⋊D151—42no—
114C2×Dic151—22no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151—42no—
118C2×Dic151C2×D411yescharacteristic
119C2×Dic151C2×D411yescharacteristic
120C4×D151—28no—
121C4×D151—22no—
122C4×D151—22no—
123C4×D151—28no—
124C4×D151—22no—
125C4×D151C2×D414yes—
126C151⋊C8—22no—
127C23×C151—21no—
128C23×C151C2×D411yescharacteristic
129Q8×C151—24no—
130Q8×C151—22no—
131Q8×C151C2×D414yes—
132D4×C151—22no—
133D4×C151—42no—
134C2×C4×C151—24no—
135C2×C4×C151—22no—
136C2×C4×C151—22no—
137C2×C4×C151—21no—
138C2×C4×C151C2×D411yescharacteristic
139C2×C4×C151C2411yescharacteristic
140C8×C151—22no—
141C22×C151—21no—
142C22×C151—21no—
143C22×C151—41no—
144C22×C151—41no—
145C22×C151—41no—
146C22×C151#13512yescomplemented
147C22×C151C22×D411yescharacteristic
148C2×D151—21no—
149C2×D151—21no—
150C2×D151—21no—
151C2×D151—24no—
152C2×D151—21no—
153C2×D151—21no—
154C2×D151—44no—
155C2×D151—48no—
156C2×D151—42no—
157C2×D151—42no—
158C2×D151#12012yes—
159C4×C151—24no—
160C4×C151—21no—
161C4×C151—41no—
162C4×C151C22×D412yes—
163Dic151—21no—
164Dic151—41no—
165Dic151—41no—
166Dic151#12012yes—
167C2×C151—22no—
168C2×C151—81no—
169C2×C151C2×#12011yescharacteristic
170C2×C151C2×#13511yescharacteristic
171C2×C151#57511yescharacteristic
172D151—22no—
173D151—41no—
174D151—44no—
175C151#300211yescharacteristic, complemented, Sylow
176#3002—1511nomaximal, Sylow
177C22×#41—1511no—
178C2×#135—1512no—
179#525—1511no—
180#452—1512no—
181#451—1511no—
182#450—1511no—
183#449—1512no—
184#448D15111yescharacteristic, complemented
185#447—1511no—
186#416—1512no—
187C2×C22⋊C8—1511no—
188C2×#41—3028no—
189C2×#41—3021no—
190C2×#41—3021no—
191C2×#41—1512no—
192C2×#41—1512no—
193C2×#41—1511no—
194C22×Q8C2×D15111yescharacteristic
195C22×D4—3021no—
196C22×D4—1511no—
197C23×C4—3021no—
198C23×C4—1511no—
199#135—3028no—
200C2×Q16—1512no—
201C2×SD16—1512no—
202C2×SD16C2×D15112yescomplemented
203C2×D8—1512no—
204C22×C8—1512no—
205#123—3021no—
206C22⋊Q8—1511no—
207C22⋊Q8—1511no—
208#121—1511no—
209#121C2×D15111yescharacteristic
210#120—3021no—
211C4×D4—3021no—
212C4×D4—3021no—
213#117—1511no—
214#103—1512no—
215#103C2×D15112yescomplemented
216#102—1512no—
217#102—1512no—
218C22⋊C8—1511no—
219C22⋊C8—1512no—
220C22⋊C8C2×D15111yescharacteristic
221C24—3021no—
222C24—1511no—
223#41—3028no—
224#41—3028no—
225#41—3024no—
226#41—3024no—
227#41—3024no—
228#41—3024no—
229#41—1518no—
230C2×Q8—24no—
231C2×Q8—21no—
232C2×Q8—1511no—
233C2×Q8C22×D15112yes—
234C2×D4—21no—
235C2×D4—3028no—
236C2×D4—3022no—
237C2×D4—3022no—
238C2×D4—3024no—
239C2×D4—3021no—
240C2×D4—3021no—
241C2×D4—3021no—
242C2×D4—1512no—
243C2×D4C22×D15111yescharacteristic
244C22×C4—21no—
245C22×C4—3028no—
246C22×C4—3022no—
247C22×C4—3022no—
248C22×C4—3024no—
249C22×C4—3021no—
250C22×C4—1511no—
251C22×C4—1511no—
252C22×C4—1511no—
253C22×C4—1511no—
254C22×C4—1511no—
255C22×C4C22×D15111yescharacteristic
256Q16—3024no—
257SD16—24no—
258SD16—3024no—
259D8—3024no—
260C2×C8—3024no—
261C2×C8—1512no—
262C2×C8C22×D15112yes—
263C4⋊C4—3021no—
264C4⋊C4—3021no—
265C4⋊C4—1511no—
266C4⋊C4C22×D15111yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—3021no—
269C22⋊C4—3021no—
270C22⋊C4—3021no—
271C22⋊C4—3021no—
272C42—3021no—
273C23—21no—
274C23—3024no—
275C23—3022no—
276C23—3022no—
277C23—3022no—
278C23—6041no—
279C23—6042no—
280C23—6042no—
281C23—1511no—
282C23—1511no—
283C23D4×D15111yescharacteristic
284Q8—24no—
285Q8—22no—
286Q8—3022no—
287Q8D4×D15114yes—
288D4—22no—
289D4—42no—
290D4—3028no—
291D4—3024no—
292D4—3028no—
293D4—3022no—
294D4—6042no—
295D4—6042no—
296D4—1514no—
297C2×C4—24no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—3028no—
302C2×C4—3022no—
303C2×C4—3028no—
304C2×C4—3022no—
305C2×C4—3022no—
306C2×C4—3022no—
307C2×C4—3021no—
308C2×C4—3021no—
309C2×C4—6042no—
310C2×C4—1511no—
311C2×C4—1511no—
312C2×C4—1514no—
313C2×C4D4×D15111yescharacteristic
314C2×C4C23×D15111yescharacteristic
315C8—22no—
316C8—3022no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—3021no—
323C22—3021no—
324C22—3021no—
325C22—3021no—
326C22—3021no—
327C22—3024no—
328C22—6044no—
329C22—6048no—
330C22—6042no—
331C22—6042no—
332C22—1512no—
333C22#1801276012yescomplemented
334C22C2×D4×D15111yescharacteristic
335C4—24no—
336C4—21no—
337C4—41no—
338C4—3021no—
339C4—6041no—
340C4—6041no—
341C4—1512no—
342C4C2×D4×D15112yes—
343C2—22no—
344C2—81no—
345C2—3022no—
346C2—6041no—
347C2—6044no—
348C2#120×D15111yescharacteristic
349C2C2×#1801276011yescharacteristic
350C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#448×C151C2
socleC22×C151C22×D4
hypercenter#448D151
hypocenterC151#3002
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C22×#14559005C2semidirect
2. C2×#18012760C2semidirect
3. #23752722C2semidirect
4. #23752377C2semidirect
5. #23752368C2semidirect
6. #23752365C2semidirect
7. #23752356C2semidirect
8. #23752345C2semidirect
9. #23752207C2semidirect
10. C22⋊C8×D151C2semidirect
11. #448×C151C2semidirect
17. C2×#14559003C22semidirect
23. C2×#14558994C22semidirect
24. C2×#14558993C22semidirect
25. C2×#14558989C22semidirect
26. C2×C8×D151C22semidirect
28. #18012719C22semidirect
30. #18012710C22semidirect
34. #18012697C22semidirect
35. #18012663C22semidirect
36. #18012661C22semidirect
37. #18012659C22semidirect
39. (C2×D151)⋊C8C22semidirect
41. C2×SD16×C151C22semidirect
43. #103×C151C22semidirect
52. #14559005D4semidirect
146. C22×C151#135semidirect
175. C151#3002semidirect
184. #448D151semidirect
202. C2×SD16C2×D151semidirect
215. #103C2×D151semidirect
333. C22#18012760semidirect

Maximal subgroups

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

subgroupindex
C22×#145590052
C2×#180127602
#237527222
#237523772
#237523682
#237523652
#237523562
#237523452
#237522072
C22⋊C8×D1512
#448×C1512
#3002151