Finite Group Databasebeta

← #34079057

Subgroups — #34079057

Order 19328.

410 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×D151C211yesmaximal, characteristic
2#117×D151C211yesmaximal, characteristic
3#23752554C211yesmaximal, characteristic, complemented
4#23752553C211yesmaximal, characteristic, complemented
5#23752550C211yesmaximal, characteristic, complemented
6#23752549C211yesmaximal, characteristic, complemented
7#23752546C211yesmaximal, characteristic, complemented
8#23752544C211yesmaximal, characteristic, complemented
9#23752541C211yesmaximal, characteristic, complemented
10#23752253C211yesmaximal, characteristic, complemented
11#23752251C211yesmaximal, characteristic, complemented
12#23752219C211yesmaximal, characteristic, complemented
13#23752219C211yesmaximal, characteristic, complemented
14#23752174C211yesmaximal, characteristic
15#485×C151C211yesmaximal, characteristic, complemented
16C2×Q8×D151C2211yescharacteristic
17C22×C4×D151C2211yescharacteristic
18C2×#14558987C2211yescharacteristic
19C2×#14558987C2211yescharacteristic
20#18012719C2211yescharacteristic
21#18012718C2211yescharacteristic
22#18012717—21no—
23#18012716—21no—
24#18012715C2211yescharacteristic
25#18012698C2211yescharacteristic
26#18012697C2211yescharacteristic
27#18012697C2211yescharacteristic
28#18012696—21no—
29#18012695—21no—
30C4⋊C4×D151—21no—
31C4⋊C4×D151C2211yescharacteristic
32C4⋊C4×D151C2211yescharacteristic
33C4⋊C4×D151C2211yescharacteristic
34C22⋊C4×D151—21no—
35C22⋊C4×D151—21no—
36C42×D151—21no—
37#18012673C2211yescharacteristic, complemented
38#18012672C2211yescharacteristic, complemented
39#18012672C2211yescharacteristic, complemented
40#18012671C2211yescharacteristic, complemented
41#18012670C2211yescharacteristic, complemented
42#18012670C2211yescharacteristic, complemented
43#18012664C2211yescharacteristic, complemented
44#18012664C2211yescharacteristic, complemented
45#18012663C2211yescharacteristic, complemented
46#18012663C2211yescharacteristic, complemented
47#18012662C2211yescharacteristic, complemented
48#18012662C2211yescharacteristic, complemented
49C22⋊(C151⋊C8)C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
52C22⋊Q8×C151C2211yescharacteristic
53#117×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic, complemented
55#106×C151C2211yescharacteristic, complemented
56#103×C151C2211yescharacteristic, complemented
57#103×C151C2211yescharacteristic, complemented
58C22⋊C8×C151C2211yescharacteristic
59C23×D151D411yescharacteristic
60C2×Dic302—21no—
61C2×Dic302C2311yescharacteristic
62Q8×D151—22no—
63Q8×D151—22no—
64C22×Dic151D411yescharacteristic
65C2×C4×D151—22no—
66C2×C4×D151—22no—
67C2×C4×D151—21no—
68C2×C4×D151—21no—
69C2×C4×D151—21no—
70C2×C4×D151—21no—
71C2×C4×D151D411yescharacteristic
72C2×C4×D151D411yescharacteristic
73C2×C4×D151C2311yescharacteristic
74C2×C4×D151C2311yescharacteristic
75#14558987—22no—
76#14558987—22no—
77C2×C151⋊C8C2311yescharacteristic
78C2×C151⋊C8C2311yescharacteristic
79C4⋊Dic151—21no—
80C4⋊Dic151C2311yescharacteristic
81C4⋊Dic151C2311yescharacteristic
82C4⋊Dic151C2311yescharacteristic
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94C4×Dic151—21no—
95C4×Dic151—21no—
96C4×Dic151—21no—
97C2×Q8×C151C2311yescharacteristic
98C22×C4×C151C2311yescharacteristic
99C2×C8×C151C2311yescharacteristic
100C2×C8×C151C2311yescharacteristic
101C4⋊C4×C151—21no—
102C4⋊C4×C151C2311yescharacteristic
103C4⋊C4×C151C2311yescharacteristic
104C4⋊C4×C151C2311yescharacteristic
105C22⋊C4×C151—21no—
106C22⋊C4×C151—21no—
107C42×C151—21no—
108C22×D151—22no—
109C22×D151—22no—
110C22×D151—41no—
111C22×D151C2×D411yescharacteristic
112C22×D151C2×D411yescharacteristic
113Dic302—21no—
114Dic302—21no—
115Dic302—42no—
116C2×Dic151—22no—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151—21no—
120C2×Dic151—21no—
121C2×Dic151C2×D411yescharacteristic
122C2×Dic151C2×D411yescharacteristic
123C4×D151—22no—
124C4×D151—21no—
125C4×D151—21no—
126C4×D151—22no—
127C4×D151—42no—
128C4×D151—42no—
129C4×D151—42no—
130C4×D151—42no—
131C4×D151#4112yes—
132C4×D151#4112yes—
133C151⋊C8—21no—
134C151⋊C8—21no—
135C23×C151C2×D411yescharacteristic
136Q8×C151—21no—
137Q8×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2411yescharacteristic
146C8×C151—21no—
147C8×C151—21no—
148C22×C151—21no—
149C22×C151—21no—
150C22×C151—21no—
151C22×C151C22×D411yescharacteristic
152C2×D151—21no—
153C2×D151—21no—
154C2×D151—21no—
155C2×D151—21no—
156C2×D151—44no—
157C2×D151#12312yes—
158C2×D151#13712yes—
159C4×C151—21no—
160C4×C151—41no—
161C4×C151—41no—
162C4×C151—41no—
163C4×C151—41no—
164C4×C151C2×#4111yescharacteristic
165C4×C151C2×#4111yescharacteristic
166Dic151—21no—
167Dic151—41no—
168Dic151—41no—
169Dic151—41no—
170Dic151—41no—
171Dic151#12312yes—
172C2×C151—41no—
173C2×C151C2×#12311yescharacteristic
174C2×C151C2×#13711yescharacteristic
175C2×C151#57511yescharacteristic
176D151—22no—
177D151—22no—
178C151#309511yescharacteristic, complemented, Sylow
179#3095—1511nomaximal, Sylow
180C2×C22⋊Q8—1511no—
181C2×#117—1511no—
182#485—1511no—
183#485—1511no—
184#485—1511no—
185#485D15111yescharacteristic, complemented
186#484—1511no—
187#484—1511no—
188#483—1511no—
189#483—1511no—
190#428—1511no—
191#428—1511no—
192#419—1511no—
193#419—1511no—
194#407—1511no—
195C22×Q8—1511no—
196C23×C4—1511no—
197C2×M16—1511no—
198C2×M16—1511no—
199C22⋊Q8—3021no—
200C22⋊Q8—3021no—
201C22⋊Q8—1511no—
202C22⋊Q8—1511no—
203C22⋊Q8—1511no—
204C22⋊Q8C2×D15111yescharacteristic
205#117—3021no—
206#117—3021no—
207#117—1511no—
208#117—1511no—
209#117—1511no—
210#117C2×D15111yescharacteristic
211C2×C4⋊C4—3021no—
212C2×C4⋊C4—1511no—
213C2×C4⋊C4—1511no—
214C2×C4⋊C4—1511no—
215C2×C22⋊C4—3021no—
216C2×C22⋊C4—3021no—
217C2×C42—3021no—
218#107—1511no—
219#107—1511no—
220#107—1511no—
221#107C2×D15111yescharacteristic, complemented
222#106—1511no—
223#106—1511no—
224#106—1511no—
225#106C2×D15111yescharacteristic, complemented
226#103—1511no—
227#103—1511no—
228#103—1511no—
229#103—1511no—
230#103—1511no—
231#103—1511no—
232#103C2×D15111yescharacteristic, complemented
233#103C2×D15111yescharacteristic, complemented
234C22⋊C8—1511no—
235C22⋊C8—1511no—
236C22⋊C8—1511no—
237C22⋊C8C2×D15111yescharacteristic
238C24—1511no—
239C2×Q8—3021no—
240C2×Q8—3022no—
241C2×Q8—3022no—
242C2×Q8—1511no—
243C2×Q8C22×D15111yescharacteristic
244C22×C4—3022no—
245C22×C4—3022no—
246C22×C4—3021no—
247C22×C4—3021no—
248C22×C4—3021no—
249C22×C4—3021no—
250C22×C4—1511no—
251C22×C4—1511no—
252C22×C4—1511no—
253C22×C4—1511no—
254C22×C4—1511no—
255C22×C4C22×D15111yescharacteristic
256M16—3022no—
257M16—3022no—
258C2×C8—1511no—
259C2×C8—1511no—
260C2×C8C22×D15111yescharacteristic
261C2×C8C22×D15111yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—3021no—
264C4⋊C4—3021no—
265C4⋊C4—3021no—
266C4⋊C4—3021no—
267C4⋊C4—3021no—
268C4⋊C4—3021no—
269C4⋊C4—1511no—
270C4⋊C4—1511no—
271C4⋊C4—1511no—
272C4⋊C4C22×D15111yescharacteristic
273C4⋊C4C22×D15111yescharacteristic
274C4⋊C4C22×D15111yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—3021no—
278C22⋊C4—3021no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C42—21no—
284C42—3021no—
285C42—3021no—
286C42—3021no—
287C23—3022no—
288C23—3022no—
289C23—6041no—
290C23—1511no—
291C23—1511no—
292C23D4×D15111yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—3021no—
296Q8—3021no—
297Q8—6042no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—3022no—
305C2×C4—3022no—
306C2×C4—3022no—
307C2×C4—3021no—
308C2×C4—3021no—
309C2×C4—3021no—
310C2×C4—3021no—
311C2×C4—3021no—
312C2×C4—3021no—
313C2×C4—6042no—
314C2×C4—6042no—
315C2×C4—6042no—
316C2×C4—6042no—
317C2×C4—1511no—
318C2×C4—1511no—
319C2×C4—1512no—
320C2×C4—1512no—
321C2×C4D4×D15111yescharacteristic
322C2×C4C23×D15111yescharacteristic
323C8—21no—
324C8—21no—
325C8—3021no—
326C8—3021no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—3021no—
331C22—3021no—
332C22—3021no—
333C22—3021no—
334C22—6044no—
335C22—1512no—
336C22—1512no—
337C22C2×D4×D15111yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—3021no—
344C4—6041no—
345C4—6041no—
346C4—6041no—
347C4—6041no—
348C4—1512no—
349C4#41×D15111yescharacteristic
350C4#41×D15111yescharacteristic
351C2—41no—
352C2—3022no—
353C2—3022no—
354C2#123×D15111yescharacteristic
355C2#137×D15111yescharacteristic
356C2#2375300911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#485×C151C2
socleC22×C151C22×D4
prime radicalC23×D151D4
hypercenter#485D151
hypocenterC151#3095
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #23752554C2semidirect
4. #23752553C2semidirect
5. #23752550C2semidirect
6. #23752549C2semidirect
7. #23752546C2semidirect
8. #23752544C2semidirect
9. #23752541C2semidirect
10. #23752253C2semidirect
11. #23752251C2semidirect
12. #23752219C2semidirect
13. #23752219C2semidirect
15. #485×C151C2semidirect
37. #18012673C22semidirect
38. #18012672C22semidirect
39. #18012672C22semidirect
40. #18012671C22semidirect
41. #18012670C22semidirect
42. #18012670C22semidirect
43. #18012664C22semidirect
44. #18012664C22semidirect
45. #18012663C22semidirect
46. #18012663C22semidirect
47. #18012662C22semidirect
48. #18012662C22semidirect
54. #107×C151C22semidirect
55. #106×C151C22semidirect
56. #103×C151C22semidirect
57. #103×C151C22semidirect
178. C151#3095semidirect
185. #485D151semidirect
221. #107C2×D151semidirect
225. #106C2×D151semidirect
232. #103C2×D151semidirect
233. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D1512
#117×D1512
#237525542
#237525532
#237525502
#237525492
#237525462
#237525442
#237525412
#237522532
#237522512
#237522192
#237521742
#485×C1512
#3095151