Finite Group Databasebeta

← #46822421

Subgroups — #46822421

Order 34432.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575479C211yesmaximal, characteristic, complemented
2C2×#22575473C211yesmaximal, characteristic, complemented
3#31771276C211yesmaximal, characteristic, complemented
4#31770995C211yesmaximal, characteristic, complemented
5#31770853C211yesmaximal, characteristic, complemented
6#31770839C211yesmaximal, characteristic, complemented
7#31770824C211yesmaximal, characteristic, complemented
8#31770800C211yesmaximal, characteristic, complemented
9#31770765C211yesmaximal, characteristic, complemented
10#31770750C211yesmaximal, characteristic, complemented
11#31770748C211yesmaximal, characteristic, complemented
12#31770739C211yesmaximal, characteristic, complemented
13#31770705C211yesmaximal, characteristic, complemented
14#31770677C211yesmaximal, characteristic, complemented
15#546×C269C211yesmaximal, characteristic, complemented
16C2×#16864402C2211yescharacteristic
17C2×#16864402C2211yescharacteristic, complemented
18#22575479—24no—
19#22575473—24no—
20C2×#16864392C2211yescharacteristic, complemented
21C2×#16864390C2211yescharacteristic
22C2×#16864390C2211yescharacteristic
23C2×#16864389C2211yescharacteristic, complemented
24C2×#16864389C2211yescharacteristic, complemented
25C2×#16864387C2211yescharacteristic
26C2×#16864387C2211yescharacteristic
27C2×#16864387C2211yescharacteristic
28C2×#16864387C2211yescharacteristic
29C2×#16864386C2211yescharacteristic
30C22×#14524130C2211yescharacteristic, complemented
31#22575450C2211yescharacteristic, complemented
32#22575449—21no—
33#22575427C2211yescharacteristic
34#22575427C2211yescharacteristic, complemented
35#22575426—21no—
36#22575426—21no—
37C4×Dic538C2211yescharacteristic, complemented
38#22575415—21no—
39#22575386C2211yescharacteristic, complemented
40C4⋊#14524130C2211yescharacteristic, complemented
41#22575377C2211yescharacteristic, complemented
42#22575376C2211yescharacteristic, complemented
43#22575374C2211yescharacteristic
44#22575374C2211yescharacteristic
45#22575373C2211yescharacteristic, complemented
46#22575373C2211yescharacteristic, complemented
47C22⋊#14524130C2211yescharacteristic
48C22⋊#14524130C2211yescharacteristic, complemented
49#22575364C2211yescharacteristic, complemented
50C2×#41×C269C2211yescharacteristic
51C22×D4×C269C2211yescharacteristic
52#124×C269C2211yescharacteristic
53#123×C269—21no—
54C22⋊Q8×C269C2211yescharacteristic
55#121×C269—21no—
56#121×C269C2211yescharacteristic
57#120×C269—21no—
58C4×D4×C269C2211yescharacteristic
59C4×D4×C269C2211yescharacteristic
60C2×C22⋊C4×C269—21no—
61#16864402—22no—
62#16864402—22no—
63#16864402—41no—
64#16864402—41no—
65C2×Dic538C2311yescharacteristic
66C2×D1076—21no—
67C2×D1076—21no—
68C2×D1076C2311yescharacteristic
69C2×D1076C2311yescharacteristic
70C2×C22⋊D269—21no—
71C2×C22⋊D269—21no—
72C2×C22⋊D269—21no—
73C2×C22⋊D269—21no—
74C2×C4×D269—21no—
75C2×C4×D269—21no—
76#16864392—22no—
77#16864390—22no—
78#16864390D414yescomplemented
79#16864389—22no—
80#16864389—41no—
81#16864387—22no—
82#16864387—22no—
83#16864387—22no—
84#16864387—41no—
85#16864386—22no—
86C2×#14524130—22no—
87C2×#14524130C2311yescharacteristic
88C2×#14524130C2311yescharacteristic
89C2×#14524130C2311yescharacteristic
90C2×#14524130C2311yescharacteristic
91C4⋊Dic269C2311yescharacteristic
92#16864381—21no—
93#16864379—21no—
94#16864379—21no—
95C4×Dic269—21no—
96C24×C269—21no—
97#41×C269—22no—
98#41×C269—41no—
99C2×Q8×C269C2311yescharacteristic
100C2×D4×C269—22no—
101C2×D4×C269—21no—
102C2×D4×C269—21no—
103C2×D4×C269—21no—
104C2×D4×C269—41no—
105C2×D4×C269D411yescharacteristic
106C2×D4×C269C2311yescharacteristic
107C2×D4×C269C2311yescharacteristic
108C22×C4×C269—21no—
109C22×C4×C269—21no—
110C22×C4×C269C2311yescharacteristic
111C22×C4×C269C2311yescharacteristic
112C4⋊C4×C269—21no—
113C4⋊C4×C269D411yescharacteristic
114C4⋊C4×C269C2311yescharacteristic
115C22⋊C4×C269—21no—
116C22⋊C4×C269—21no—
117C22⋊C4×C269—21no—
118C22⋊C4×C269—21no—
119C22⋊C4×C269—21no—
120C22⋊C4×C269D411yescharacteristic
121C22⋊C4×C269D411yescharacteristic
122C42×C269C2311yescharacteristic
123C22×D269—21no—
124C22×D269—21no—
125Dic538—21no—
126Dic538C2×D412yes—
127D1076—21no—
128D1076—21no—
129D1076—21no—
130D1076—21no—
131D1076—42no—
132D1076—81no—
133C22⋊D269—42no—
134C22⋊D269—42no—
135C22⋊D269—81no—
136C22⋊D269—81no—
137C2×Dic269—21no—
138C2×Dic269—21no—
139C4×D269—42no—
140C4×D269—42no—
141#14524130—21no—
142#14524130—21no—
143#14524130—21no—
144#14524130C2×D412yes—
145C23×C269—21no—
146C23×C269—21no—
147C23×C269—42no—
148C23×C269—42no—
149C23×C269—81no—
150C23×C269C2×D411yescharacteristic
151C23×C269C2×D411yescharacteristic
152Q8×C269—21no—
153Q8×C269—21no—
154D4×C269—21no—
155D4×C269—21no—
156D4×C269—21no—
157D4×C269—41no—
158D4×C269—42no—
159D4×C269—42no—
160D4×C269—81no—
161D4×C269C2×D412yes—
162C2×C4×C269—21no—
163C2×C4×C269—21no—
164C2×C4×C269—21no—
165C2×C4×C269—21no—
166C2×C4×C269—21no—
167C2×C4×C269—21no—
168C2×C4×C269—42no—
169C2×C4×C269—81no—
170C2×C4×C269C2×D411yescharacteristic
171C2×C4×C269C2×D411yescharacteristic
172C2×C4×C269C2×D411yescharacteristic
173C2×C4×C269C2×D411yescharacteristic
174C2×C4×C269C2411yescharacteristic
175C22×C269—21no—
176C22×C269—21no—
177C22×C269—22no—
178C22×C269—21no—
179C22×C269—21no—
180C22×C269—21no—
181C22×C269—21no—
182C22×C269—41no—
183C22×C269—41no—
184C22×C269—41no—
185C22×C269—41no—
186C22×C269—41no—
187C22×C269—84no—
188C22×C269C22×D411yescharacteristic
189C2×D269—41no—
190C2×D269—41no—
191C2×D269—41no—
192C2×D269—41no—
193C2×D269—41no—
194C2×D269—41no—
195C4×C269—21no—
196C4×C269—21no—
197C4×C269—21no—
198C4×C269—21no—
199C4×C269—41no—
200C4×C269—41no—
201C4×C269C22×D411yescharacteristic
202C4×C269H(5,𝔽2)11yescharacteristic
203Dic269—22no—
204Dic269—41no—
205C2×C269—41no—
206C2×C269—41no—
207C2×C269—42no—
208C2×C269—81no—
209C2×C269D4211yescharacteristic
210C2×C269#57511yescharacteristic
211C2×C269#57611yescharacteristic
212D269—81no—
213D269—81no—
214C269#326811yescharacteristic, complemented, Sylow
215#3268—2691nomaximal, Sylow
216C2×AGL(1,ℤ/8)—2691no—
217C2×#135—2691no—
218#550—2691no—
219#546D26911yescharacteristic, complemented
220#496—2691no—
221#468—2691no—
222#466—2691no—
223#464—2691no—
224#459—2691no—
225#452—2691no—
226#449—2691no—
227#449—2691no—
228#447—2691no—
229#440—2691no—
230#435—2691no—
231C2×#41—2691no—
232C2×#41—2691no—
233C2×#41C2×D26911yescharacteristic
234C22×D4C2×D26911yescharacteristic
235AGL(1,ℤ/8)—5384no—
236#135—5384no—
237C2×Q16—2691no—
238C2×SD16—2691no—
239C2×SD16—2691no—
240C2×SD16—2691no—
241C2×SD16—2691no—
242C2×D8—2691no—
243C2×D8—2691no—
244C2×D8—2691no—
245C2×D8—2691no—
246C2×M16—2691no—
247C22×C8—2691no—
248#127—2691no—
249#127—5381no—
250#124C2×D26911yescharacteristic
251#123—21no—
252C22⋊Q8C2×D26911yescharacteristic
253#121—21no—
254#121—2691no—
255#121—2691no—
256#121—5381no—
257#121—5381no—
258#121C2×D26911yescharacteristic
259#120—21no—
260C4×Q8—2691no—
261C4×D4—5381no—
262C4×D4C2×D26911yescharacteristic
263C4×D4C2×D26911yescharacteristic
264C2×C22⋊C4—21no—
265#107—2691no—
266C4⋊C8—2691no—
267#103—2691no—
268#103—2691no—
269#102—2691no—
270#102—2691no—
271#102—2691no—
272#102—2691no—
273C22⋊C8—2691no—
274C22⋊C8—2691no—
275#97—2691no—
276C24—21no—
277#41—22no—
278#41—41no—
279#41—5382no—
280#41—5382no—
281#41—10761no—
282#41—10761no—
283C2×Q8—2691no—
284C2×Q8C22×D26911yescharacteristic
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—41no—
290C2×D4—2691no—
291C2×D4—2691no—
292C2×D4—5381no—
293C2×D4—5381no—
294C2×D4—5381no—
295C2×D4—5381no—
296C2×D4—5381no—
297C2×D4—5381no—
298C2×D4C22⋊D26911yescharacteristic
299C2×D4C22×D26911yescharacteristic
300C2×D4C22×D26911yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—5381no—
304C22×C4—5381no—
305C22×C4C22×D26911yescharacteristic
306C22×C4C22×D26911yescharacteristic
307Q16—5382no—
308SD16—2694no—
309SD16—5382no—
310SD16—5382no—
311SD16—10761no—
312D8—5382no—
313D8—5382no—
314D8—5382no—
315D8—10761no—
316M16—5382no—
317C2×C8—2691no—
318C2×C8—2691no—
319C2×C8—2691no—
320C2×C8—2691no—
321C2×C8—5382no—
322C4⋊C4—21no—
323C4⋊C4—2691no—
324C4⋊C4—5381no—
325C4⋊C4C22⋊D26911yescharacteristic
326C4⋊C4C22×D26911yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C22⋊C4—21no—
331C22⋊C4—21no—
332C22⋊C4—5381no—
333C22⋊C4—5381no—
334C22⋊C4C22⋊D26911yescharacteristic
335C22⋊C4C22⋊D26911yescharacteristic
336C42—5381no—
337C42C22×D26911yescharacteristic
338C23—21no—
339C23—21no—
340C23—42no—
341C23—42no—
342C23—81no—
343C23—5381no—
344C23—5381no—
345C23C2×C22⋊D26911yescharacteristic
346C23C2×C22⋊D26911yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—2692no—
350Q8—5381no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—41no—
355D4—42no—
356D4—42no—
357D4—81no—
358D4—5381no—
359D4—5381no—
360D4—5381no—
361D4—5381no—
362D4—10762no—
363D4—10762no—
364D4—10762no—
365D4—21521no—
366D4—21521no—
367D4—21521no—
368D4D4×D26912yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—81no—
377C2×C4—5381no—
378C2×C4—5381no—
379C2×C4—10762no—
380C2×C4—10762no—
381C2×C4C2×C22⋊D26911yescharacteristic
382C2×C4C2×C22⋊D26911yescharacteristic
383C2×C4C2×C22⋊D26911yescharacteristic
384C2×C4C2×C22⋊D26911yescharacteristic
385C2×C4C23×D26911yescharacteristic
386C8—2692no—
387C8—5381no—
388C8—5381no—
389C8—5381no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—22no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—84no—
403C22—10761no—
404C22—10761no—
405C22—10761no—
406C22—10761no—
407C22—10761no—
408C22—10761no—
409C22C22×C22⋊D26911yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—5382no—
417C4—10761no—
418C4C2×D4×D26911yescharacteristic
419C4#2257549811yescharacteristic
420C2—41no—
421C2—41no—
422C2—42no—
423C2—81no—
424C2—21521no—
425C2—21521no—
426C2D4×C22⋊D26911yescharacteristic
427C2#3177140311yescharacteristic
428C2#3177140811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#546×C269C2
socleC22×C269C22×D4
hypercenter#546D269
hypocenterC269#3268
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#22575479C2semidirect
2. C2×#22575473C2semidirect
3. #31771276C2semidirect
4. #31770995C2semidirect
5. #31770853C2semidirect
6. #31770839C2semidirect
7. #31770824C2semidirect
8. #31770800C2semidirect
9. #31770765C2semidirect
10. #31770750C2semidirect
11. #31770748C2semidirect
12. #31770739C2semidirect
13. #31770705C2semidirect
14. #31770677C2semidirect
15. #546×C269C2semidirect
17. C2×#16864402C22semidirect
20. C2×#16864392C22semidirect
23. C2×#16864389C22semidirect
24. C2×#16864389C22semidirect
30. C22×#14524130C22semidirect
31. #22575450C22semidirect
34. #22575427C22semidirect
37. C4×Dic538C22semidirect
39. #22575386C22semidirect
40. C4⋊#14524130C22semidirect
41. #22575377C22semidirect
42. #22575376C22semidirect
45. #22575373C22semidirect
46. #22575373C22semidirect
48. C22⋊#14524130C22semidirect
49. #22575364C22semidirect
78. #16864390D4semidirect
214. C269#3268semidirect
219. #546D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754792
C2×#225754732
#317712762
#317709952
#317708532
#317708392
#317708242
#317708002
#317707652
#317707502
#317707482
#317707392
#317707052
#317706772
#546×C2692
#3268269