Finite Group Databasebeta

← #72234382

Subgroups — #72234382

Order 1024.

536 conjugacy classes of subgroups.

The subgroup lattice has 517 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#513005C211yesmaximal, characteristic
2#484130C211yesmaximal, characteristic, complemented
3#484074C211yesmaximal, characteristic, complemented
4#151128C211yesmaximal, characteristic, complemented
5#151127C211yesmaximal, characteristic, complemented
6#151118C211yesmaximal, characteristic, complemented
7#151116C211yesmaximal, characteristic, complemented
8#151116C211yesmaximal, characteristic, complemented
9#151115C211yesmaximal, characteristic, complemented
10#151085C211yesmaximal, characteristic, complemented
11#151083C211yesmaximal, characteristic, complemented
12#151066C211yesmaximal, characteristic, complemented
13#150162C211yesmaximal, characteristic, complemented
14#150063C211yesmaximal, characteristic, complemented
15#149509C211yesmaximal, characteristic, complemented
16#33735C2211yescharacteristic
17C4×#508C2211yescharacteristic
18#18087—21no—
19#18035—21no—
20#13716C411yescharacteristic
21#13713C411yescharacteristic
22#13708C411yescharacteristic
23#13707C411yescharacteristic
24#13690C411yescharacteristic
25#13689C411yescharacteristic
26#13666C411yescharacteristic
27#13663C411yescharacteristic
28#13654C2211yescharacteristic
29#13653C2211yescharacteristic
30#13652C2211yescharacteristic
31#13652C2211yescharacteristic
32#13640C2211yescharacteristic
33C4×M64C2211yescharacteristic
34#12086C2211yescharacteristic
35#12085C2211yescharacteristic
36#12085C2211yescharacteristic
37#12085C2211yescharacteristic
38#12074—21no—
39#12074—21no—
40#12071—21no—
41#12070—21no—
42#12045C2211yescharacteristic
43#12045C2211yescharacteristic
44#12045C2211yescharacteristic
45#12044C2211yescharacteristic
46#12024C2211yescharacteristic
47C2×#1372C2211yescharacteristic
48#11659—21no—
49#11648—21no—
50#11408C2211yescharacteristic
51#7463C2211yescharacteristic
52#7463C2211yescharacteristic
53#7463C2211yescharacteristic
54#7463C2211yescharacteristic
55#7386C2211yescharacteristic
56#7386C2211yescharacteristic
57#7386C2211yescharacteristic
58#7386C2211yescharacteristic
59#7385C2211yescharacteristic
60#7385C2211yescharacteristic
61#7385C2211yescharacteristic
62#7385C2211yescharacteristic
63#7332C2211yescharacteristic
64#7332C2211yescharacteristic
65#7330C2211yescharacteristic
66#7330C2211yescharacteristic
67C2×#508C2×C411yescharacteristic
68#3168—21no—
69#2994—41no—
70#2970—41no—
71C4×#135—21no—
72C2×Q64C2×C411yescharacteristic
73C2×SD64C2×C411yescharacteristic
74C2×SD64C2×C411yescharacteristic
75C2×D32C2×C411yescharacteristic
76C2×M64—21no—
77#2253C2×C411yescharacteristic
78#2249C2×C411yescharacteristic
79#2242—21no—
80#2217—21no—
81#2216C2×C411yescharacteristic
82#2215C2×C411yescharacteristic
83C4×Q32C2×C411yescharacteristic
84C4×Q32C2311yescharacteristic
85C4×Q32C2311yescharacteristic
86C4×SD32—21no—
87C4×SD32—21no—
88C4×SD32—21no—
89C4×D16C2×C411yescharacteristic
90C4×D16C2311yescharacteristic
91C4×D16C2311yescharacteristic
92#2162D411yescharacteristic
93#2158C2×C411yescharacteristic
94#2138—21no—
95C2×C4×C16C2311yescharacteristic
96#1591—21no—
97#1591—21no—
98#1591—21no—
99#1589—21no—
100#1588—41no—
101#1585—41no—
102#1582—41no—
103#1582—41no—
104C8×Q16—21no—
105C8×D8—21no—
106C8×D8—21no—
107C8×D8—21no—
108#1568—21no—
109C2×#335—21no—
110#1488—41no—
111#1483—41no—
112C8×M16D411yescharacteristic
113#1424C2×C411yescharacteristic
114#1424C2×C411yescharacteristic
115#1423C2×C411yescharacteristic
116#1423C2×C411yescharacteristic
117C4⋊C32C2×C411yescharacteristic
118C4⋊C32C2×C411yescharacteristic
119#1416C2×C411yescharacteristic
120#1416C2×C411yescharacteristic
121#1416C2×C411yescharacteristic
122#1416C2×C411yescharacteristic
123#1415C2×C411yescharacteristic
124#1415C2×C411yescharacteristic
125#1415C2×C411yescharacteristic
126#1415C2×C411yescharacteristic
127C22⋊C32C2×C411yescharacteristic
128C22⋊C32C2×C411yescharacteristic
129#1397C2311yescharacteristic
130#1397C2311yescharacteristic
131#1397C2311yescharacteristic
132#1397C2311yescharacteristic
133C4×C32—21no—
134#1372—21no—
135#1372C2311yescharacteristic
136#1372C2311yescharacteristic
137#1372C2311yescharacteristic
138#1372C2311yescharacteristic
139#1371—21no—
140#1332—21no—
141#1332—21no—
142#1332—21no—
143#1332—21no—
144#1331—21no—
145#1331—21no—
146#1331—21no—
147#1331—21no—
148#1312D411yescharacteristic
149#1312D411yescharacteristic
150#1311C2311yescharacteristic
151#1311C2311yescharacteristic
152C2×#135—21no—
153#529—41no—
154C4×#41—41no—
155#508—22no—
156#508—41no—
157C2×Q32C22×C411yescharacteristic
158C2×Q32C22×C411yescharacteristic
159C2×SD32—21no—
160C2×SD32—21no—
161C2×D16C22×C411yescharacteristic
162C2×D16C22×C411yescharacteristic
163C22×C16C22×C411yescharacteristic
164C22×C16#4111yescharacteristic
165#499—21no—
166#495—21no—
167#488—41no—
168#467—21no—
169#466—21no—
170#465—41no—
171#446—41no—
172#446—41no—
173#446—41no—
174C8×Q8—41no—
175C4×Q16—21no—
176C4×Q16—21no—
177C4×Q16—21no—
178C4×SD16—41no—
179C4×SD16—41no—
180C4×SD16—41no—
181C4×D8—21no—
182C4×D8—21no—
183C4×D8—21no—
184#436—41no—
185#435—81no—
186#435—81no—
187#435—81no—
188C8×D4—41no—
189C8×D4—41no—
190C8×D4—41no—
191C8×D4—81no—
192#433—81no—
193#432—41no—
194#432—81no—
195#431D811yescharacteristic
196#427—21no—
197#424—81no—
198C2×C4⋊C8—41no—
199#416—41no—
200C4×M16D811yescharacteristic
201C2×#97—81no—
202C2×C4×C8C2×D411yescharacteristic
203Q64—41no—
204SD64—22no—
205SD64—41no—
206D32—22no—
207M64—42no—
208C2×C32—21no—
209C2×C32—21no—
210C2×C32C22×C411yescharacteristic
211C2×C32C22×C411yescharacteristic
212C2×C32C22×C411yescharacteristic
213C2×C32C22×C411yescharacteristic
214#367—21no—
215#367—21no—
216#366C22×C411yescharacteristic
217#366C22×C411yescharacteristic
218#366C22×C411yescharacteristic
219#366C22×C411yescharacteristic
220C4⋊C16—21no—
221#358—21no—
222#358—21no—
223#358—21no—
224#358—21no—
225#357—21no—
226#357—21no—
227#357—21no—
228#357—21no—
229C22⋊C16—21no—
230C4×C16C22×C411yescharacteristic
231C4×C16C2×D411yescharacteristic
232C4×C16C2×D411yescharacteristic
233C4×C16C2×D411yescharacteristic
234C4×C16#4111yescharacteristic
235C4×C16C2411yescharacteristic
236#335—21no—
237#335—21no—
238#335—21no—
239#335—21no—
240#335—41no—
241#334—41no—
242Q8⋊C8—41no—
243Q8⋊C8—41no—
244Q8⋊C8—41no—
245Q8⋊C8—41no—
246D4⋊C8—41no—
247D4⋊C8—41no—
248D4⋊C8—41no—
249D4⋊C8—41no—
250#322D811yescharacteristic
251#322D811yescharacteristic
252C82C2×D411yescharacteristic
253C82C2×D411yescharacteristic
254C2×#41—41no—
255#135—42no—
256#135—81no—
257C2×Q16—21no—
258C2×Q16—21no—
259C2×SD16—41no—
260C2×SD16—41no—
261C2×D8—21no—
262C2×D8—21no—
263C2×M16—21no—
264C2×M16—81no—
265C22×C8—81no—
266C22×C8—81no—
267C22×C8—81no—
268C22×C8—81no—
269C22×C8C4×D411yescharacteristic
270C22×C8#13511yescharacteristic
271#126—81no—
272#125—41no—
273#124—41no—
274#123—81no—
275C22⋊Q8—41no—
276#121—41no—
277C4×Q8—41no—
278C4×Q8—41no—
279C4×Q8—41no—
280C4×D4—41no—
281C4×D4—41no—
282C4×D4—41no—
283C4×D4—81no—
284C4×D4—81no—
285C4×D4—81no—
286#117—41no—
287#117—81no—
288#117—81no—
289C2×C42—81no—
290C2×C42C2×D811yescharacteristic
291Q32—21no—
292Q32—21no—
293Q32—21no—
294Q32—21no—
295SD32—42no—
296SD32—81no—
297D16—21no—
298D16—21no—
299D16—21no—
300D16#13112yes—
301C2×C16—21no—
302C2×C16—21no—
303C2×C16—21no—
304C2×C16—21no—
305C2×C16—41no—
306C2×C16C4×D411yescharacteristic
307C2×C16C4×D411yescharacteristic
308C2×C16C23×C411yescharacteristic
309C2×C16C2×#4111yescharacteristic
310#107—21no—
311#107—21no—
312#107—21no—
313#107—21no—
314#106—41no—
315#106—41no—
316C4⋊C8—21no—
317C4⋊C8—41no—
318C4⋊C8—41no—
319C4⋊C8—41no—
320C4⋊C8—41no—
321C4⋊C8—81no—
322C4⋊C8—81no—
323C4⋊C8—81no—
324C4⋊C8—81no—
325C4⋊C8—81no—
326#103—41no—
327#103—41no—
328#103—41no—
329#103—41no—
330#102—41no—
331#102—41no—
332#102—41no—
333#102—41no—
334C22⋊C8—21no—
335C22⋊C8—81no—
336C22⋊C8—81no—
337C22⋊C8—81no—
338C22⋊C8—81no—
339C22⋊C8—81no—
340#97—21no—
341#97—81no—
342#97—81no—
343#97—81no—
344#97—81no—
345C4×C8—81no—
346C4×C8C4×D411yescharacteristic
347C4×C8C2×D811yescharacteristic
348C4×C8C2×D811yescharacteristic
349C4×C8C2×D811yescharacteristic
350C4×C8C2×D811yescharacteristic
351C4×C8C2×D811yescharacteristic
352C4×C8#13511yescharacteristic
353C4×C8C22×D411yescharacteristic
354C32—22no—
355C32—21no—
356C32—21no—
357C32—21no—
358C32—21no—
359C32—41no—
360#41—82no—
361#41—161no—
362C2×Q8—41no—
363C2×Q8—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—81no—
367C2×D4—81no—
368C22×C4—81no—
369C22×C4—81no—
370C22×C4—81no—
371C22×C4—81no—
372C22×C4C4×D811yescharacteristic
373C22×C4#50911yescharacteristic
374C22×C4#50911yescharacteristic
375Q16—41no—
376Q16—41no—
377Q16—41no—
378Q16—41no—
379SD16—82no—
380SD16—161no—
381D8—22no—
382D8—41no—
383D8—41no—
384D8—41no—
385M16—81no—
386M16—321no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—41no—
394C2×C8—81no—
395C2×C8—81no—
396C2×C8—81no—
397C2×C8—81no—
398C2×C8—162no—
399C2×C8—162no—
400C2×C8—321no—
401C2×C8—321no—
402C2×C8C4×D811yescharacteristic
403C2×C8C4×D811yescharacteristic
404C2×C8C2×C4×D411yescharacteristic
405C2×C8C2×#13511yescharacteristic
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—81no—
411C4⋊C4—81no—
412C4⋊C4—81no—
413C4⋊C4—81no—
414C4⋊C4—81no—
415C4⋊C4—81no—
416C22⋊C4—81no—
417C22⋊C4—81no—
418C22⋊C4—81no—
419C22⋊C4—81no—
420C22⋊C4—81no—
421C22⋊C4—81no—
422C22⋊C4—81no—
423C22⋊C4—81no—
424C42—81no—
425C42—81no—
426C42—81no—
427C42—81no—
428C42C4×D811yescharacteristic
429C42#50911yescharacteristic
430C42#50911yescharacteristic
431C42C22×D811yescharacteristic
432C16—21no—
433C16—21no—
434C16—21no—
435C16—41no—
436C16—41no—
437C16C2×#13111yescharacteristic
438C16#56811yescharacteristic
439C23—81no—
440C23—81no—
441C23#217711yescharacteristic
442Q8—81no—
443Q8—81no—
444Q8—81no—
445Q8—81no—
446D4—42no—
447D4—81no—
448D4—81no—
449D4—81no—
450D4—162no—
451D4—162no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—81no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—81no—
461C2×C4—81no—
462C2×C4—162no—
463C2×C4—161no—
464C2×C4—161no—
465C2×C4—161no—
466C2×C4—161no—
467C2×C4—321no—
468C2×C4#217711yescharacteristic
469C2×C4#217711yescharacteristic
470C2×C4#217711yescharacteristic
471C2×C4C2×C4×D811yescharacteristic
472C2×C4C2×#50911yescharacteristic
473C2×C4C2×#50911yescharacteristic
474C8—21no—
475C8—21no—
476C8—21no—
477C8—41no—
478C8—41no—
479C8—41no—
480C8—41no—
481C8—161no—
482C8—161no—
483C8—161no—
484C8—161no—
485C8#293311yescharacteristic
486C8#295611yescharacteristic
487C22—21no—
488C22—21no—
489C22—21no—
490C22—82no—
491C22—161no—
492C22—161no—
493C22—161no—
494C22—161no—
495C22—161no—
496C22C2×#217711yescharacteristic
497C4—21no—
498C4—21no—
499C4—21no—
500C4—21no—
501C4—21no—
502C4—161no—
503C4—161no—
504C4—161no—
505C4—161no—
506C4—161no—
507C4—161no—
508C4#1799411yescharacteristic
509C4#3346411yescharacteristic
510C2—41no—
511C2—162no—
512C2—321no—
513C2#48401211yescharacteristic
514C2#51277811yescharacteristic
515C2#51277911yescharacteristic
subgroupG/H
center, socleC22C2×#2177
commutatorC2×C16C23×C4
Frattini, cosocleC4×C16C24
prime radical#13663C4
LCSG ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ C8×M16 ◁ #11408 ◁ G
LECSG ▷ C4×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #484130C2semidirect
3. #484074C2semidirect
4. #151128C2semidirect
5. #151127C2semidirect
6. #151118C2semidirect
7. #151116C2semidirect
8. #151116C2semidirect
9. #151115C2semidirect
10. #151085C2semidirect
11. #151083C2semidirect
12. #151066C2semidirect
13. #150162C2semidirect
14. #150063C2semidirect
15. #149509C2semidirect

Maximal subgroups

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

subgroupindex
#5130052
#4841302
#4840742
#1511282
#1511272
#1511182
#1511162
#1511152
#1510852
#1510832
#1510662
#1501622
#1500632
#1495092