Finite Group Databasebeta

← #34078783

Subgroups — #34078783

Order 19328.

504 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012766C211yesmaximal, characteristic, complemented
2C2×#18012745C211yesmaximal, characteristic, complemented
3#23752792C211yesmaximal, characteristic, complemented
4#23752778C211yesmaximal, characteristic, complemented
5#23752466C211yesmaximal, characteristic, complemented
6#23752463C211yesmaximal, characteristic, complemented
7#23752460C211yesmaximal, characteristic, complemented
8#23752455C211yesmaximal, characteristic, complemented
9#23752448C211yesmaximal, characteristic, complemented
10#23752447C211yesmaximal, characteristic, complemented
11#23752444C211yesmaximal, characteristic, complemented
12#23752251C211yesmaximal, characteristic, complemented
13#23752207C211yesmaximal, characteristic, complemented
14#102×D151C211yesmaximal, characteristic, complemented
15#465×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559004C2211yescharacteristic
18C2×D4×D151C2211yescharacteristic
19#18012766—24no—
20C2×#14558991C2211yescharacteristic
21C2×D1208C2211yescharacteristic
22C2×#14558989C2211yescharacteristic
23#18012745—24no—
24C2×#14558988C2211yescharacteristic, complemented
25C2×#14558987C2211yescharacteristic
26C2×#14558987C2211yescharacteristic, complemented
27C2×C8×D151C2211yescharacteristic
28C2×C8×D151C2211yescharacteristic, complemented
29#18012735—21no—
30#18012725—21no—
31#18012717—21no—
32#18012715C2211yescharacteristic, complemented
33#18012714—21no—
34#18012714C2211yescharacteristic
35#18012714C2211yescharacteristic, complemented
36#18012713C2211yescharacteristic
37#18012713C2211yescharacteristic, complemented
38#18012712—21no—
39#18012712—21no—
40#18012710C2211yescharacteristic
41#18012709—21no—
42#18012707—21no—
43#18012697C2211yescharacteristic
44C4⋊C4×D151C2211yescharacteristic
45#18012673C2211yescharacteristic, complemented
46#18012672C2211yescharacteristic, complemented
47#18012670C2211yescharacteristic, complemented
48#18012663C2211yescharacteristic, complemented
49#18012661C2211yescharacteristic
50#18012661C2211yescharacteristic, complemented
51#18012660C2211yescharacteristic
52#18012659C2211yescharacteristic
53#18012659C2211yescharacteristic, complemented
54C2×SD16×C151C2211yescharacteristic
55C22×C8×C151C2211yescharacteristic, complemented
56C22⋊Q8×C151C2211yescharacteristic, complemented
57#121×C151C2211yescharacteristic
58#106×C151C2211yescharacteristic, complemented
59#103×C151C2211yescharacteristic, complemented
60#102×C151C2211yescharacteristic
61C23×D151—21no—
62#14559005—22no—
63#14559005—22no—
64#14559004—22no—
65#14559004—22no—
66C2×Dic302D411yescharacteristic
67C2×D604—21no—
68C2×D604—21no—
69C2×D604—21no—
70C2×D604D411yescharacteristic
71C2×D604C2311yescharacteristic
72C2×D604C2311yescharacteristic
73C2×C22⋊D151—21no—
74C2×C22⋊D151—21no—
75C2×C22⋊D151—21no—
76C2×C22⋊D151—21no—
77C2×C22⋊D151D411yescharacteristic
78C2×C22⋊D151D411yescharacteristic
79D4×D151—22no—
80D4×D151—22no—
81C2×C4×D151—21no—
82C2×C4×D151—21no—
83C2×C4×D151C2311yescharacteristic
84C2×C4×D151C2311yescharacteristic
85#14558991—22no—
86D1208—22no—
87#14558989—22no—
88#14558988—22no—
89#14558987—22no—
90#14558987D414yescomplemented
91C2×C151⋊C8C2311yescharacteristic
92C2×C151⋊C8C2311yescharacteristic
93C8×D151—22no—
94C8×D151—22no—
95C4⋊Dic151C2311yescharacteristic
96C4⋊Dic151C2311yescharacteristic
97Dic151⋊C4—21no—
98Dic151⋊C4—21no—
99C22⋊Dic151—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)⋊C4—21no—
106C4×Dic151—21no—
107C2×Q8×C151C2311yescharacteristic
108C2×D4×C151—21no—
109C2×D4×C151C2311yescharacteristic
110C22×C4×C151C2311yescharacteristic
111SD16×C151—22no—
112C2×C8×C151—22no—
113C2×C8×C151C2311yescharacteristic
114C2×C8×C151C2311yescharacteristic
115C4⋊C4×C151—21no—
116C4⋊C4×C151C2311yescharacteristic
117C4⋊C4×C151C2311yescharacteristic
118C22⋊C4×C151—21no—
119C22⋊C4×C151—21no—
120C22×D151—21no—
121C22×D151—21no—
122C22×D151—42no—
123C22×D151—81no—
124C22×D151—81no—
125C22×D151C2×D411yescharacteristic
126C22×D151C2×D411yescharacteristic
127Dic302—22no—
128D604—22no—
129D604—21no—
130D604—21no—
131D604—21no—
132D604—21no—
133D604—42no—
134D604—81no—
135D604—81no—
136C22⋊D151—22no—
137C22⋊D151—22no—
138C22⋊D151—42no—
139C22⋊D151—81no—
140C22⋊D151—81no—
141C22⋊D151—81no—
142C2×Dic151—21no—
143C2×Dic151—21no—
144C2×Dic151C2×D411yescharacteristic
145C2×Dic151C2×D411yescharacteristic
146C4×D151—21no—
147C4×D151—21no—
148C4×D151—42no—
149C4×D151—81no—
150C4×D151C2×D412yes—
151C4×D151#4112yes—
152C151⋊C8—21no—
153C151⋊C8C2×D412yes—
154C23×C151—21no—
155C23×C151C2×D411yescharacteristic
156Q8×C151—21no—
157Q8×C151—21no—
158D4×C151—21no—
159D4×C151—21no—
160D4×C151—81no—
161C2×C4×C151—21no—
162C2×C4×C151—21no—
163C2×C4×C151—21no—
164C2×C4×C151—21no—
165C2×C4×C151—21no—
166C2×C4×C151C2×D411yescharacteristic
167C2×C4×C151C2411yescharacteristic
168C8×C151—21no—
169C8×C151C2×D412yes—
170C22×C151—21no—
171C22×C151—21no—
172C22×C151—21no—
173C22×C151—41no—
174C22×C151—41no—
175C22×C151—41no—
176C22×C151C22×D411yescharacteristic
177C2×D151—21no—
178C2×D151—21no—
179C2×D151—21no—
180C2×D151—21no—
181C2×D151—21no—
182C2×D151—41no—
183C2×D151—41no—
184C2×D151—41no—
185C2×D151—41no—
186C2×D151—41no—
187C2×D151—41no—
188C2×D151—84no—
189C2×D151#12112yes—
190C4×C151—21no—
191C4×C151—41no—
192C4×C151—41no—
193C4×C151—41no—
194C4×C151C22×D411yescharacteristic
195C4×C151C2×#4111yescharacteristic
196Dic151—21no—
197Dic151—41no—
198Dic151—41no—
199Dic151#12112yes—
200C2×C151—41no—
201C2×C151—81no—
202C2×C151C2×#12111yescharacteristic
203C2×C151#57611yescharacteristic
204C2×C151#57711yescharacteristic
205D151—22no—
206D151—41no—
207D151—81no—
208D151—81no—
209C151#306211yescharacteristic, complemented, Sylow
210#3062—1511nomaximal, Sylow
211C2×AGL(1,ℤ/8)—1511no—
212C2×#131—1511no—
213#537—1511no—
214#535—1511no—
215#469—1511no—
216#469—1511no—
217#468—1511no—
218#468—1511no—
219#466—1511no—
220#466—1511no—
221#465—1511no—
222#465D15111yescharacteristic, complemented
223#428—1511no—
224#416—1511no—
225C2×#102—1511no—
226C2×#41—1511no—
227C2×#41—1511no—
228C22×D4—1511no—
229AGL(1,ℤ/8)—3024no—
230C2×SD16—1511no—
231C2×SD16C2×D15111yescharacteristic
232C2×D8—1511no—
233C2×D8—1511no—
234#131—3024no—
235C2×M16—1511no—
236C2×M16—1511no—
237C2×M16—1511no—
238C22×C8—1511no—
239C22×C8—1511no—
240C22×C8C2×D15111yescharacteristic, complemented
241#127—3021no—
242#124—3021no—
243C22⋊Q8—3021no—
244C22⋊Q8—1511no—
245C22⋊Q8C2×D15111yescharacteristic, complemented
246#121—3021no—
247#121—3021no—
248#121—3021no—
249#121—1511no—
250#121—1511no—
251#121—1511no—
252#121—1511no—
253#121—1511no—
254#121C2×D15111yescharacteristic
255#120—3021no—
256#120—3021no—
257#117—1511no—
258C2×C4⋊C4—1511no—
259#107—1511no—
260#107—1511no—
261#106—1511no—
262#106C2×D15111yescharacteristic, complemented
263#103—1511no—
264#103C2×D15111yescharacteristic, complemented
265#102—1511no—
266#102—1511no—
267#102—1511no—
268#102—1511no—
269#102—1511no—
270#102C2×D15111yescharacteristic
271C24—3021no—
272#41—3022no—
273#41—3022no—
274#41—3022no—
275#41—3022no—
276C2×Q8—1511no—
277C2×Q8C22×D15111yescharacteristic
278C2×D4—21no—
279C2×D4—3021no—
280C2×D4—3021no—
281C2×D4—3021no—
282C2×D4—3021no—
283C2×D4—3021no—
284C2×D4—3021no—
285C2×D4—3022no—
286C2×D4—3022no—
287C2×D4—3021no—
288C2×D4—1511no—
289C2×D4—1511no—
290C2×D4—1511no—
291C2×D4—1511no—
292C2×D4—1511no—
293C2×D4C22×D15111yescharacteristic
294C22×C4—3021no—
295C22×C4—3021no—
296C22×C4—1511no—
297C22×C4—1511no—
298C22×C4C22×D15111yescharacteristic
299SD16—22no—
300SD16—3022no—
301D8—3022no—
302D8—3022no—
303M16—3022no—
304M16—3022no—
305M16—1514no—
306C2×C8—22no—
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
319C4⋊C4C22×D15111yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—3021no—
323C22⋊C4—3021no—
324C22⋊C4—3021no—
325C22⋊C4—3021no—
326C22⋊C4—3021no—
327C22⋊C4—3021no—
328C22⋊C4—3021no—
329C42—3021no—
330C23—21no—
331C23—3021no—
332C23—3021no—
333C23—6042no—
334C23—1511no—
335C23—1511no—
336C23—12081no—
337C23—12081no—
338C23D4×D15111yescharacteristic
339Q8—21no—
340Q8—21no—
341Q8—3022no—
342D4—21no—
343D4—21no—
344D4—81no—
345D4—3022no—
346D4—3022no—
347D4—3022no—
348D4—3021no—
349D4—3021no—
350D4—3021no—
351D4—3021no—
352D4—6042no—
353D4—6042no—
354D4—12081no—
355D4—12081no—
356D4—12081no—
357D4—12081no—
358D4—12081no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—3021no—
365C2×C4—3021no—
366C2×C4—3021no—
367C2×C4—3021no—
368C2×C4—6042no—
369C2×C4—1511no—
370C2×C4—1511no—
371C2×C4—1512no—
372C2×C4—1512no—
373C2×C4—12081no—
374C2×C4D4×D15111yescharacteristic
375C2×C4C23×D15111yescharacteristic
376C8—21no—
377C8—3021no—
378C8—1512no—
379C8D4×D15112yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—3021no—
387C22—3021no—
388C22—3021no—
389C22—3021no—
390C22—3021no—
391C22—6041no—
392C22—6041no—
393C22—6041no—
394C22—6041no—
395C22—6041no—
396C22—6041no—
397C22—1512no—
398C22—12084no—
399C22C2×D4×D15111yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—3021no—
405C4—6041no—
406C4—6041no—
407C4—1512no—
408C4C2×D4×D15111yescharacteristic
409C4#41×D15111yescharacteristic
410C2—41no—
411C2—81no—
412C2—3022no—
413C2—6041no—
414C2—12081no—
415C2—12081no—
416C2#121×D15111yescharacteristic
417C2#2375301411yescharacteristic
418C2#2375301811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#465×C151C2
socleC22×C151C22×D4
hypercenter#465D151
hypocenterC151#3062
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#18012766C2semidirect
2. C2×#18012745C2semidirect
3. #23752792C2semidirect
4. #23752778C2semidirect
5. #23752466C2semidirect
6. #23752463C2semidirect
7. #23752460C2semidirect
8. #23752455C2semidirect
9. #23752448C2semidirect
10. #23752447C2semidirect
11. #23752444C2semidirect
12. #23752251C2semidirect
13. #23752207C2semidirect
14. #102×D151C2semidirect
15. #465×C151C2semidirect
24. C2×#14558988C22semidirect
26. C2×#14558987C22semidirect
28. C2×C8×D151C22semidirect
32. #18012715C22semidirect
35. #18012714C22semidirect
37. #18012713C22semidirect
45. #18012673C22semidirect
46. #18012672C22semidirect
47. #18012670C22semidirect
48. #18012663C22semidirect
50. #18012661C22semidirect
53. #18012659C22semidirect
55. C22×C8×C151C22semidirect
56. C22⋊Q8×C151C22semidirect
58. #106×C151C22semidirect
59. #103×C151C22semidirect
90. #14558987D4semidirect
209. C151#3062semidirect
222. #465D151semidirect
240. C22×C8C2×D151semidirect
245. C22⋊Q8C2×D151semidirect
262. #106C2×D151semidirect
264. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127662
C2×#180127452
#237527922
#237527782
#237524662
#237524632
#237524602
#237524552
#237524482
#237524472
#237524442
#237522512
#237522072
#102×D1512
#465×C1512
#3062151