Finite Group Databasebeta

← #49130934

Subgroups — #49130934

Order 36224.

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×#22583637C211yesmaximal, characteristic, complemented
2C2×#22583616C211yesmaximal, characteristic, complemented
3#31827045C211yesmaximal, characteristic, complemented
4#31827031C211yesmaximal, characteristic, complemented
5#31826719C211yesmaximal, characteristic, complemented
6#31826716C211yesmaximal, characteristic, complemented
7#31826713C211yesmaximal, characteristic, complemented
8#31826708C211yesmaximal, characteristic, complemented
9#31826701C211yesmaximal, characteristic, complemented
10#31826700C211yesmaximal, characteristic, complemented
11#31826697C211yesmaximal, characteristic, complemented
12#31826504C211yesmaximal, characteristic, complemented
13#31826460C211yesmaximal, characteristic, complemented
14#102×D283C211yesmaximal, characteristic, complemented
15#465×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×#17985392C2211yescharacteristic
18C2×D4×D283C2211yescharacteristic
19#22583637—24no—
20C2×#17985379C2211yescharacteristic
21C2×D2264C2211yescharacteristic
22C2×#17985377C2211yescharacteristic
23#22583616—24no—
24C2×#17985376C2211yescharacteristic, complemented
25C2×#17985375C2211yescharacteristic
26C2×#17985375C2211yescharacteristic, complemented
27C2×C8×D283C2211yescharacteristic
28C2×C8×D283C2211yescharacteristic, complemented
29#22583606—21no—
30#22583596—21no—
31#22583588—21no—
32#22583586C2211yescharacteristic, complemented
33#22583585—21no—
34#22583585C2211yescharacteristic
35#22583585C2211yescharacteristic, complemented
36#22583584C2211yescharacteristic
37#22583584C2211yescharacteristic, complemented
38#22583583—21no—
39#22583583—21no—
40#22583581C2211yescharacteristic
41#22583580—21no—
42#22583578—21no—
43#22583568C2211yescharacteristic
44C4⋊C4×D283C2211yescharacteristic
45#22583544C2211yescharacteristic, complemented
46#22583543C2211yescharacteristic, complemented
47#22583541C2211yescharacteristic, complemented
48#22583534C2211yescharacteristic, complemented
49#22583532C2211yescharacteristic
50#22583532C2211yescharacteristic, complemented
51#22583531C2211yescharacteristic
52#22583530C2211yescharacteristic
53#22583530C2211yescharacteristic, complemented
54C2×SD16×C283C2211yescharacteristic
55C22×C8×C283C2211yescharacteristic, complemented
56C22⋊Q8×C283C2211yescharacteristic, complemented
57#121×C283C2211yescharacteristic
58#106×C283C2211yescharacteristic, complemented
59#103×C283C2211yescharacteristic, complemented
60#102×C283C2211yescharacteristic
61C23×D283—21no—
62#17985393—22no—
63#17985393—22no—
64#17985392—22no—
65#17985392—22no—
66C2×Dic566D411yescharacteristic
67C2×D1132—21no—
68C2×D1132—21no—
69C2×D1132—21no—
70C2×D1132D411yescharacteristic
71C2×D1132C2311yescharacteristic
72C2×D1132C2311yescharacteristic
73C2×C22⋊D283—21no—
74C2×C22⋊D283—21no—
75C2×C22⋊D283—21no—
76C2×C22⋊D283—21no—
77C2×C22⋊D283D411yescharacteristic
78C2×C22⋊D283D411yescharacteristic
79D4×D283—22no—
80D4×D283—22no—
81C2×C4×D283—21no—
82C2×C4×D283—21no—
83C2×C4×D283C2311yescharacteristic
84C2×C4×D283C2311yescharacteristic
85#17985379—22no—
86D2264—22no—
87#17985377—22no—
88#17985376—22no—
89#17985375—22no—
90#17985375D414yescomplemented
91C2×C283⋊C8C2311yescharacteristic
92C2×C283⋊C8C2311yescharacteristic
93C8×D283—22no—
94C8×D283—22no—
95C4⋊Dic283C2311yescharacteristic
96C4⋊Dic283C2311yescharacteristic
97Dic283⋊C4—21no—
98Dic283⋊C4—21no—
99C22⋊Dic283—21no—
100(C2×D283)⋊C4—21no—
101(C2×D283)⋊C4—21no—
102(C2×D283)⋊C4—21no—
103(C2×D283)⋊C4—21no—
104(C2×D283)⋊C4—21no—
105(C2×D283)⋊C4—21no—
106C4×Dic283—21no—
107C2×Q8×C283C2311yescharacteristic
108C2×D4×C283—21no—
109C2×D4×C283C2311yescharacteristic
110C22×C4×C283C2311yescharacteristic
111SD16×C283—22no—
112C2×C8×C283—22no—
113C2×C8×C283C2311yescharacteristic
114C2×C8×C283C2311yescharacteristic
115C4⋊C4×C283—21no—
116C4⋊C4×C283C2311yescharacteristic
117C4⋊C4×C283C2311yescharacteristic
118C22⋊C4×C283—21no—
119C22⋊C4×C283—21no—
120C22×D283—21no—
121C22×D283—21no—
122C22×D283—42no—
123C22×D283—81no—
124C22×D283—81no—
125C22×D283C2×D411yescharacteristic
126C22×D283C2×D411yescharacteristic
127Dic566—22no—
128D1132—22no—
129D1132—21no—
130D1132—21no—
131D1132—21no—
132D1132—21no—
133D1132—42no—
134D1132—81no—
135D1132—81no—
136C22⋊D283—22no—
137C22⋊D283—22no—
138C22⋊D283—42no—
139C22⋊D283—81no—
140C22⋊D283—81no—
141C22⋊D283—81no—
142C2×Dic283—21no—
143C2×Dic283—21no—
144C2×Dic283C2×D411yescharacteristic
145C2×Dic283C2×D411yescharacteristic
146C4×D283—21no—
147C4×D283—21no—
148C4×D283—42no—
149C4×D283—81no—
150C4×D283C2×D412yes—
151C4×D283#4112yes—
152C283⋊C8—21no—
153C283⋊C8C2×D412yes—
154C23×C283—21no—
155C23×C283C2×D411yescharacteristic
156Q8×C283—21no—
157Q8×C283—21no—
158D4×C283—21no—
159D4×C283—21no—
160D4×C283—81no—
161C2×C4×C283—21no—
162C2×C4×C283—21no—
163C2×C4×C283—21no—
164C2×C4×C283—21no—
165C2×C4×C283—21no—
166C2×C4×C283C2×D411yescharacteristic
167C2×C4×C283C2411yescharacteristic
168C8×C283—21no—
169C8×C283C2×D412yes—
170C22×C283—21no—
171C22×C283—21no—
172C22×C283—21no—
173C22×C283—41no—
174C22×C283—41no—
175C22×C283—41no—
176C22×C283C22×D411yescharacteristic
177C2×D283—21no—
178C2×D283—21no—
179C2×D283—21no—
180C2×D283—21no—
181C2×D283—21no—
182C2×D283—41no—
183C2×D283—41no—
184C2×D283—41no—
185C2×D283—41no—
186C2×D283—41no—
187C2×D283—41no—
188C2×D283—84no—
189C2×D283#12112yes—
190C4×C283—21no—
191C4×C283—41no—
192C4×C283—41no—
193C4×C283—41no—
194C4×C283C22×D411yescharacteristic
195C4×C283C2×#4111yescharacteristic
196Dic283—21no—
197Dic283—41no—
198Dic283—41no—
199Dic283#12112yes—
200C2×C283—41no—
201C2×C283—81no—
202C2×C283C2×#12111yescharacteristic
203C2×C283#57611yescharacteristic
204C2×C283#57711yescharacteristic
205D283—22no—
206D283—41no—
207D283—81no—
208D283—81no—
209C283#306211yescharacteristic, complemented, Sylow
210#3062—2831nomaximal, Sylow
211C2×AGL(1,ℤ/8)—2831no—
212C2×#131—2831no—
213#537—2831no—
214#535—2831no—
215#469—2831no—
216#469—2831no—
217#468—2831no—
218#468—2831no—
219#466—2831no—
220#466—2831no—
221#465—2831no—
222#465D28311yescharacteristic, complemented
223#428—2831no—
224#416—2831no—
225C2×#102—2831no—
226C2×#41—2831no—
227C2×#41—2831no—
228C22×D4—2831no—
229AGL(1,ℤ/8)—5664no—
230C2×SD16—2831no—
231C2×SD16C2×D28311yescharacteristic
232C2×D8—2831no—
233C2×D8—2831no—
234#131—5664no—
235C2×M16—2831no—
236C2×M16—2831no—
237C2×M16—2831no—
238C22×C8—2831no—
239C22×C8—2831no—
240C22×C8C2×D28311yescharacteristic, complemented
241#127—5661no—
242#124—5661no—
243C22⋊Q8—2831no—
244C22⋊Q8—5661no—
245C22⋊Q8C2×D28311yescharacteristic, complemented
246#121—2831no—
247#121—2831no—
248#121—2831no—
249#121—2831no—
250#121—2831no—
251#121—5661no—
252#121—5661no—
253#121—5661no—
254#121C2×D28311yescharacteristic
255#120—5661no—
256#120—5661no—
257#117—2831no—
258C2×C4⋊C4—2831no—
259#107—2831no—
260#107—2831no—
261#106—2831no—
262#106C2×D28311yescharacteristic, complemented
263#103—2831no—
264#103C2×D28311yescharacteristic, complemented
265#102—2831no—
266#102—2831no—
267#102—2831no—
268#102—2831no—
269#102—2831no—
270#102C2×D28311yescharacteristic
271C24—5661no—
272#41—5662no—
273#41—5662no—
274#41—5662no—
275#41—5662no—
276C2×Q8—2831no—
277C2×Q8C22×D28311yescharacteristic
278C2×D4—21no—
279C2×D4—2831no—
280C2×D4—2831no—
281C2×D4—2831no—
282C2×D4—2831no—
283C2×D4—2831no—
284C2×D4—5661no—
285C2×D4—5661no—
286C2×D4—5661no—
287C2×D4—5662no—
288C2×D4—5662no—
289C2×D4—5661no—
290C2×D4—5661no—
291C2×D4—5661no—
292C2×D4—5661no—
293C2×D4C22×D28311yescharacteristic
294C22×C4—2831no—
295C22×C4—2831no—
296C22×C4—5661no—
297C22×C4—5661no—
298C22×C4C22×D28311yescharacteristic
299SD16—22no—
300SD16—5662no—
301D8—5662no—
302D8—5662no—
303M16—2834no—
304M16—5662no—
305M16—5662no—
306C2×C8—22no—
307C2×C8—2831no—
308C2×C8—2831no—
309C2×C8—5662no—
310C2×C8—5662no—
311C2×C8C22×D28311yescharacteristic
312C2×C8C22×D28311yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—2831no—
315C4⋊C4—2831no—
316C4⋊C4—5661no—
317C4⋊C4—5661no—
318C4⋊C4C22×D28311yescharacteristic
319C4⋊C4C22×D28311yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—5661no—
323C22⋊C4—5661no—
324C22⋊C4—5661no—
325C22⋊C4—5661no—
326C22⋊C4—5661no—
327C22⋊C4—5661no—
328C22⋊C4—5661no—
329C42—5661no—
330C23—21no—
331C23—2831no—
332C23—2831no—
333C23—5661no—
334C23—5661no—
335C23—11322no—
336C23—22641no—
337C23—22641no—
338C23D4×D28311yescharacteristic
339Q8—21no—
340Q8—21no—
341Q8—5662no—
342D4—21no—
343D4—21no—
344D4—81no—
345D4—5662no—
346D4—5662no—
347D4—5662no—
348D4—5661no—
349D4—5661no—
350D4—5661no—
351D4—5661no—
352D4—11322no—
353D4—11322no—
354D4—22641no—
355D4—22641no—
356D4—22641no—
357D4—22641no—
358D4—22641no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—2831no—
365C2×C4—2832no—
366C2×C4—2832no—
367C2×C4—2831no—
368C2×C4—5661no—
369C2×C4—5661no—
370C2×C4—5661no—
371C2×C4—5661no—
372C2×C4—11322no—
373C2×C4—22641no—
374C2×C4D4×D28311yescharacteristic
375C2×C4C23×D28311yescharacteristic
376C8—21no—
377C8—2832no—
378C8—5661no—
379C8D4×D28312yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—2832no—
387C22—5661no—
388C22—5661no—
389C22—5661no—
390C22—5661no—
391C22—5661no—
392C22—11321no—
393C22—11321no—
394C22—11321no—
395C22—11321no—
396C22—11321no—
397C22—11321no—
398C22—22644no—
399C22C2×D4×D28311yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—2832no—
405C4—5661no—
406C4—11321no—
407C4—11321no—
408C4C2×D4×D28311yescharacteristic
409C4#41×D28311yescharacteristic
410C2—41no—
411C2—81no—
412C2—5662no—
413C2—11321no—
414C2—22641no—
415C2—22641no—
416C2#121×D28311yescharacteristic
417C2#3182726711yescharacteristic
418C2#3182727111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#465×C283C2
socleC22×C283C22×D4
hypercenter#465D283
hypocenterC283#3062
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#22583637C2semidirect
2. C2×#22583616C2semidirect
3. #31827045C2semidirect
4. #31827031C2semidirect
5. #31826719C2semidirect
6. #31826716C2semidirect
7. #31826713C2semidirect
8. #31826708C2semidirect
9. #31826701C2semidirect
10. #31826700C2semidirect
11. #31826697C2semidirect
12. #31826504C2semidirect
13. #31826460C2semidirect
14. #102×D283C2semidirect
15. #465×C283C2semidirect
24. C2×#17985376C22semidirect
26. C2×#17985375C22semidirect
28. C2×C8×D283C22semidirect
32. #22583586C22semidirect
35. #22583585C22semidirect
37. #22583584C22semidirect
45. #22583544C22semidirect
46. #22583543C22semidirect
47. #22583541C22semidirect
48. #22583534C22semidirect
50. #22583532C22semidirect
53. #22583530C22semidirect
55. C22×C8×C283C22semidirect
56. C22⋊Q8×C283C22semidirect
58. #106×C283C22semidirect
59. #103×C283C22semidirect
90. #17985375D4semidirect
209. C283#3062semidirect
222. #465D283semidirect
240. C22×C8C2×D283semidirect
245. C22⋊Q8C2×D283semidirect
262. #106C2×D283semidirect
264. #103C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836372
C2×#225836162
#318270452
#318270312
#318267192
#318267162
#318267132
#318267082
#318267012
#318267002
#318266972
#318265042
#318264602
#102×D2832
#465×C2832
#3062283