Finite Group Databasebeta

← #34080810

Subgroups — #34080810

Order 19328.

504 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012762C211yesmaximal, characteristic, complemented
2C22×#14558991C211yesmaximal, characteristic, complemented
3#23752873C211yesmaximal, characteristic, complemented
4#23752853C211yesmaximal, characteristic, complemented
5#23752597C211yesmaximal, characteristic, complemented
6#23752444C211yesmaximal, characteristic, complemented
7#23752443C211yesmaximal, characteristic, complemented
8#23752436C211yesmaximal, characteristic, complemented
9#23752430C211yesmaximal, characteristic, complemented
10#23752373C211yesmaximal, characteristic, complemented
11#23752360C211yesmaximal, characteristic, complemented
12#23752348C211yesmaximal, characteristic, complemented
13#23752297C211yesmaximal, characteristic, complemented
14(C22⋊D151)⋊C8C211yesmaximal, characteristic, complemented
15#451×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559005C2211yescharacteristic, complemented
18C22×D604C2211yescharacteristic
19#18012762—24no—
20C2×#14558991—24no—
21C2×#14558991C2211yescharacteristic
22C2×#14558991C2211yescharacteristic
23C2×#14558991C2211yescharacteristic
24C2×#14558991C2211yescharacteristic
25C2×#14558991C2211yescharacteristic, complemented
26C2×D1208C2211yescharacteristic
27C2×D1208C2211yescharacteristic
28C22×C151⋊C8C2211yescharacteristic
29C2×C8×D151C2211yescharacteristic, complemented
30#18012728—21no—
31#18012728C2211yescharacteristic
32#18012728C2211yescharacteristic, complemented
33#18012724—21no—
34#18012715—21no—
35#18012715C2211yescharacteristic, complemented
36#18012714—21no—
37#18012714C2211yescharacteristic
38#18012713—21no—
39#18012713C2211yescharacteristic
40#18012709—21no—
41Q8×Dic151C2211yescharacteristic, complemented
42#18012701C2211yescharacteristic
43C4×C22⋊D151—21no—
44C4×C22⋊D151C2211yescharacteristic
45C22⋊C4×D151—21no—
46#18012670C2211yescharacteristic, complemented
47Dic151⋊C8C2211yescharacteristic, complemented
48#18012663C2211yescharacteristic, complemented
49#18012661C2211yescharacteristic
50#18012661C2211yescharacteristic
51#18012659C2211yescharacteristic, complemented
52(C2×D151)⋊C8C2211yescharacteristic, complemented
53C8×Dic151C2211yescharacteristic, complemented
54C22×Q8×C151C2211yescharacteristic
55C2×Q16×C151C2211yescharacteristic, complemented
56C2×Q16×C151C2211yescharacteristic, complemented
57C22⋊Q8×C151C2211yescharacteristic
58#103×C151C2211yescharacteristic, complemented
59#103×C151C2211yescharacteristic, complemented
60C22⋊C8×C151C2211yescharacteristic
61C23×D151—21no—
62#14559005—22no—
63#14559005—22no—
64#14559005—41no—
65#14559005—41no—
66C2×D604—22no—
67C2×D604—21no—
68C2×D604—21no—
69C2×D604—21no—
70C2×D604—21no—
71C2×D604—41no—
72C2×D604C2311yescharacteristic
73C2×D604C2311yescharacteristic
74C2×D604C2311yescharacteristic
75C2×C22⋊D151—21no—
76C2×C22⋊D151D411yescharacteristic
77C2×C4×D151—21no—
78C2×C4×D151—21no—
79C2×C4×D151—21no—
80C2×C4×D151C2311yescharacteristic
81#14558991—22no—
82#14558991—22no—
83#14558991—22no—
84#14558991—22no—
85#14558991D414yescomplemented
86D1208—22no—
87D1208—41no—
88C2×C151⋊C8—22no—
89C2×C151⋊C8C2311yescharacteristic
90C2×C151⋊C8C2311yescharacteristic
91C8×D151—22no—
92C4⋊Dic151—21no—
93C4⋊Dic151C2311yescharacteristic
94Dic151⋊C4—21no—
95Dic151⋊C4D411yescharacteristic
96C22⋊Dic151D411yescharacteristic
97(C2×D151)⋊C4—21no—
98(C2×D151)⋊C4—21no—
99(C2×D151)⋊C4—21no—
100(C2×D151)⋊C4—21no—
101(C2×D151)⋊C4—21no—
102(C2×D151)⋊C4—21no—
103(C2×D151)⋊C4—21no—
104(C2×D151)⋊C4—21no—
105(C2×D151)⋊C4D411yescharacteristic
106C4×Dic151—21no—
107C4×Dic151C2311yescharacteristic
108C2×Q8×C151—21no—
109C2×Q8×C151—22no—
110C2×Q8×C151—41no—
111C2×Q8×C151C2311yescharacteristic
112C2×Q8×C151C2311yescharacteristic
113C2×Q8×C151C2311yescharacteristic
114C22×C4×C151—21no—
115C22×C4×C151C2311yescharacteristic
116Q16×C151—22no—
117Q16×C151—41no—
118C2×C8×C151C2311yescharacteristic
119C2×C8×C151C2311yescharacteristic
120C4⋊C4×C151—21no—
121C4⋊C4×C151C2311yescharacteristic
122C22⋊C4×C151—21no—
123C22×D151—21no—
124C22×D151—21no—
125C22×D151—21no—
126C22×D151—42no—
127C22×D151—42no—
128C22×D151—81no—
129C22×D151C2×D411yescharacteristic
130D604—21no—
131D604—21no—
132D604—21no—
133D604—21no—
134D604—21no—
135D604—42no—
136D604—42no—
137D604—42no—
138D604—81no—
139D604C2×D412yes—
140C22⋊D151—22no—
141C22⋊D151—42no—
142C2×Dic151—21no—
143C2×Dic151C2×D411yescharacteristic
144C2×Dic151C2×D411yescharacteristic
145C2×Dic151C2×D411yescharacteristic
146C4×D151—21no—
147C4×D151—21no—
148C4×D151—42no—
149C4×D151—42no—
150C4×D151—81no—
151C151⋊C8—21no—
152C151⋊C8C2×D412yes—
153C23×C151C2×D411yescharacteristic
154Q8×C151—21no—
155Q8×C151—21no—
156Q8×C151—21no—
157Q8×C151—21no—
158Q8×C151—21no—
159Q8×C151—42no—
160Q8×C151C2×D412yes—
161C2×C4×C151—21no—
162C2×C4×C151—21no—
163C2×C4×C151—21no—
164C2×C4×C151—21no—
165C2×C4×C151—21no—
166C2×C4×C151—21no—
167C2×C4×C151—42no—
168C2×C4×C151C2×D411yescharacteristic
169C2×C4×C151C2411yescharacteristic
170C8×C151—21no—
171C8×C151—21no—
172C22×C151—21no—
173C22×C151—21no—
174C22×C151#13512yescomplemented
175C22×C151C22×D411yescharacteristic
176C2×D151—21no—
177C2×D151—22no—
178C2×D151—21no—
179C2×D151—21no—
180C2×D151—41no—
181C2×D151—41no—
182C2×D151—41no—
183C2×D151—41no—
184C2×D151—41no—
185C2×D151—41no—
186C2×D151—41no—
187C2×D151—41no—
188C2×D151—84no—
189C4×C151—21no—
190C4×C151—22no—
191C4×C151—41no—
192C4×C151—41no—
193C4×C151—41no—
194C4×C151C22×D411yescharacteristic
195C4×C151H(5,𝔽2)11yescharacteristic
196Dic151—21no—
197Dic151—21no—
198Dic151—21no—
199Dic151—41no—
200C2×C151—22no—
201C2×C151D4211yescharacteristic
202C2×C151C2×#13511yescharacteristic
203C2×C151#57711yescharacteristic
204D151—41no—
205D151—42no—
206D151—81no—
207D151—81no—
208C151#328211yescharacteristic, complemented, Sylow
209#3282—1511nomaximal, Sylow
210C2×#135—1511no—
211C22×SD16—1511no—
212#548—1511no—
213#546—1511no—
214#495—1511no—
215#465—1511no—
216#465—1511no—
217#464—1511no—
218#463—1511no—
219#452—1511no—
220#451D15111yescharacteristic, complemented
221#449—1511no—
222#447—1511no—
223C4×SD16—1511no—
224C8×D4—1511no—
225C2×#41—1511no—
226C2×#41—1511no—
227C22×Q8C2×D15111yescharacteristic
228C22×D4—1511no—
229#135—3024no—
230C2×Q16C2×D15111yescharacteristic, complemented
231C2×Q16C2×D15111yescharacteristic, complemented
232C2×SD16—3024no—
233C2×SD16—1511no—
234C2×SD16—1511no—
235C2×SD16—1511no—
236C2×SD16—1511no—
237C2×SD16—1511no—
238C2×D8—1511no—
239C2×D8—1511no—
240C22×C8—1511no—
241C22×C8—1511no—
242#124—3021no—
243#124—1511no—
244#124—1511no—
245#123—3021no—
246C22⋊Q8—3021no—
247C22⋊Q8—1511no—
248C22⋊Q8C2×D15111yescharacteristic
249#121—3021no—
250#121—3021no—
251#121—1511no—
252#121—1511no—
253#120—3021no—
254C4×Q8—1511no—
255C4×D4—3021no—
256C4×D4—1511no—
257C4×D4—1511no—
258C2×C22⋊C4—3021no—
259#106—1511no—
260C4⋊C8—1511no—
261#103—1511no—
262#103C2×D15111yescharacteristic, complemented
263#103C2×D15111yescharacteristic, complemented
264#102—1511no—
265#102—1511no—
266#102—1511no—
267C22⋊C8—1511no—
268C22⋊C8C2×D15111yescharacteristic
269C4×C8—1511no—
270C24—3021no—
271#41—3022no—
272#41—3022no—
273#41—6041no—
274#41—6041no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8C22×D15111yescharacteristic
279C2×Q8C22×D15111yescharacteristic
280C2×Q8C22×D15111yescharacteristic
281C2×D4—3022no—
282C2×D4—3021no—
283C2×D4—3021no—
284C2×D4—3021no—
285C2×D4—3021no—
286C2×D4—3021no—
287C2×D4—6041no—
288C2×D4—1511no—
289C2×D4—1511no—
290C2×D4—1511no—
291C2×D4—1511no—
292C22×C4—21no—
293C22×C4—3021no—
294C22×C4—3021no—
295C22×C4—3021no—
296C22×C4—1511no—
297C22×C4C22×D15111yescharacteristic
298Q16—22no—
299Q16—41no—
300SD16—3022no—
301SD16—3022no—
302SD16—3022no—
303SD16—3022no—
304SD16—1514no—
305D8—3022no—
306D8—6041no—
307C2×C8—3022no—
308C2×C8—3022no—
309C2×C8—1511no—
310C2×C8—1511no—
311C2×C8C22×D15111yescharacteristic
312C2×C8C22×D15111yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—3021no—
315C4⋊C4—3021no—
316C4⋊C4—1511no—
317C4⋊C4—1511no—
318C4⋊C4C22×D15111yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—3021no—
321C22⋊C4—3021no—
322C22⋊C4—3021no—
323C22⋊C4—3021no—
324C22⋊C4—3021no—
325C22⋊C4—3021no—
326C22⋊C4—3021no—
327C22⋊C4—3021no—
328C22⋊C4—1511no—
329C22⋊C4—1511no—
330C42—3021no—
331C42—1511no—
332C23—3021no—
333C23—3021no—
334C23—3021no—
335C23—6042no—
336C23—6042no—
337C23—1511no—
338C23—12081no—
339C23D4×D15111yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—21no—
345Q8—42no—
346Q8D4×D15112yes—
347D4—3022no—
348D4—3021no—
349D4—3021no—
350D4—3021no—
351D4—3021no—
352D4—3021no—
353D4—6042no—
354D4—6042no—
355D4—6042no—
356D4—6042no—
357D4—1512no—
358D4—12081no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—42no—
366C2×C4—3021no—
367C2×C4—3021no—
368C2×C4—3021no—
369C2×C4—6042no—
370C2×C4—6042no—
371C2×C4—1511no—
372C2×C4—1511no—
373C2×C4—1511no—
374C2×C4—12081no—
375C2×C4D4×D15111yescharacteristic
376C2×C4C23×D15111yescharacteristic
377C8—21no—
378C8—21no—
379C8—3021no—
380C8—1512no—
381C22—21no—
382C22—21no—
383C22—3021no—
384C22—3021no—
385C22—3021no—
386C22—3022no—
387C22—6041no—
388C22—6041no—
389C22—6041no—
390C22—6041no—
391C22—6041no—
392C22—6041no—
393C22—6041no—
394C22—6041no—
395C22—12084no—
396C22#1801276212yescomplemented
397C22C2×D4×D15111yescharacteristic
398C4—21no—
399C4—22no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—3021no—
404C4—3021no—
405C4—3021no—
406C4—6041no—
407C4C2×D4×D15111yescharacteristic
408C4#1801278411yescharacteristic
409C2—22no—
410C2—6041no—
411C2—6042no—
412C2—12081no—
413C2—12081no—
414C2#2375284411yescharacteristic
415C2C2×#1801276211yescharacteristic
416C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#451×C151C2
socleC22×C151C22×D4
hypercenter#451D151
hypocenterC151#3282
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. C2×#18012762C2semidirect
2. C22×#14558991C2semidirect
3. #23752873C2semidirect
4. #23752853C2semidirect
5. #23752597C2semidirect
6. #23752444C2semidirect
7. #23752443C2semidirect
8. #23752436C2semidirect
9. #23752430C2semidirect
10. #23752373C2semidirect
11. #23752360C2semidirect
12. #23752348C2semidirect
13. #23752297C2semidirect
14. (C22⋊D151)⋊C8C2semidirect
15. #451×C151C2semidirect
17. C2×#14559005C22semidirect
25. C2×#14558991C22semidirect
29. C2×C8×D151C22semidirect
32. #18012728C22semidirect
35. #18012715C22semidirect
41. Q8×Dic151C22semidirect
46. #18012670C22semidirect
47. Dic151⋊C8C22semidirect
48. #18012663C22semidirect
51. #18012659C22semidirect
52. (C2×D151)⋊C8C22semidirect
53. C8×Dic151C22semidirect
55. C2×Q16×C151C22semidirect
56. C2×Q16×C151C22semidirect
58. #103×C151C22semidirect
59. #103×C151C22semidirect
85. #14558991D4semidirect
174. C22×C151#135semidirect
208. C151#3282semidirect
220. #451D151semidirect
230. C2×Q16C2×D151semidirect
231. C2×Q16C2×D151semidirect
262. #103C2×D151semidirect
263. #103C2×D151semidirect
396. C22#18012762semidirect

Maximal subgroups

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

subgroupindex
C2×#180127622
C22×#145589912
#237528732
#237528532
#237525972
#237524442
#237524432
#237524362
#237524302
#237523732
#237523602
#237523482
#237522972
(C22⋊D151)⋊C82
#451×C1512
#3282151