Finite Group Databasebeta

← #72312549

Subgroups — #72312549

Order 1024.

Only the 34371 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 522 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63090C214yesmaximal, complemented
2#10576179C2132yesmaximal, complemented
3#10576178C2132yesmaximal, complemented
4#10576177C2116yesmaximal, complemented
5#10576173C2132yesmaximal, complemented
6#10575251C211yesmaximal, characteristic, complemented
7C2×#60469C214yesmaximal, complemented
8C2×#60387C214yesmaximal, complemented
9C2×#60182C212yesmaximal, complemented
10C22×#585C2214yescomplemented
11#63090C22164yescomplemented
12#63090C22132yescomplemented
13#63090C22132yescomplemented
14C2×#3586C22132yescomplemented
15C2×#3585C22132yescomplemented
16C2×#3584C22132yescomplemented
17C22×#575C2212yes—
18C22×#575C2214yescomplemented
19C22×#575C2218yescomplemented
20C22×#568C2214yescomplemented
21C2×#3449C2212yescomplemented
22#61111C221128yescomplemented
23#61110C221128yescomplemented
24#61109C221256yescomplemented
25#61108C221256yescomplemented
26#61107C221512yescomplemented
27#61106C221256yescomplemented
28#61105C221128yescomplemented
29#61100C221128yescomplemented
30#60645C22116yescomplemented
31#60644C22116yescomplemented
32#60643C22116yescomplemented
33#60639C2218yescomplemented
34#60469C22132yescomplemented
35#60469C22132yescomplemented
36#60469C22164yescomplemented
37C2×#3069C22132yescomplemented
38C2×#3068C22132yescomplemented
39C2×#3067C22132yescomplemented
40#60387C22164yescomplemented
41#60387C22164yescomplemented
42C2×#3022C22116yescomplemented
43C2×#3021C22116yescomplemented
44C2×#3020C22116yescomplemented
45C2×#3019C22116yescomplemented
46C2×#3018C22132yescomplemented
47#60182C22164yescomplemented
48C2×#2957C22116yescomplemented
49C2×#2956C22116yescomplemented
50C2×#2955C22116yescomplemented
51C22×#430C2212yescomplemented
52C22×#421C2214yescomplemented
53C22×#413C2214yescomplemented
54C2×#2873C2211yescharacteristic, complemented
55C2×#585C23116yes—
56C2×#585C23116yescomplemented
57C2×#585C23132yescomplemented
58C2×#585C23132yescomplemented
59C22×2−1+4C2318yescomplemented
60C22×H(5,𝔽2)C2318yescomplemented
61C23×#41C2314yes—
62C23×#41C2314yes—
63#3586C231256yescomplemented
64#3586C231256yescomplemented
65#3585C231256yescomplemented
66#3585C231256yescomplemented
67#3584C231256yescomplemented
68#3584C231256yescomplemented
69C2×#578C23164yescomplemented
70C2×#577C231128yescomplemented
71C2×#576C23164yescomplemented
72C2×#575D4116yescomplemented
73C2×#575D4116yescomplemented
74C2×#575D4116yescomplemented
75C2×#575C2318yes—
76C2×#575C2318yes—
77C2×#575C23132yes—
78C2×#575C23132yes—
79C2×#575C23132yescomplemented
80C2×#575C23116yescomplemented
81C2×#575C23116yescomplemented
82C2×#575C23132yescomplemented
83C2×#575C23132yescomplemented
84C2×#575C23132yescomplemented
85C2×#575C23132yescomplemented
86C2×#575C23132yescomplemented
87C22×#137D418yescomplemented
88C22×#137C23116yescomplemented
89C22×#137C23116yescomplemented
90C22×AGL(1,ℤ/8)D418yescomplemented
91C22×AGL(1,ℤ/8)C23116yescomplemented
92C22×AGL(1,ℤ/8)C23116yescomplemented
93C22×#135C2318yes—
94C22×#135C23116yescomplemented
95C2×#568C23132yescomplemented
96C2×#568C23116yescomplemented
97C2×#568C23116yescomplemented
98C2×#568C23132yescomplemented
99C22×#131C23116yescomplemented
100C23×M16C2312yes—
101C23×M16C2314yes—
102#3449C23116yescomplemented
103#3449C23116yescomplemented
104C2×#536C2318yescomplemented
105C2×#535C2318yescomplemented
106C2×#532C2318yescomplemented
107C22×#117C2311yescharacteristic
108#3293C231256yescomplemented
109#3292C231256yescomplemented
110#3291C231512yescomplemented
111#3290C2311024yescomplemented
112#3289C2311024yescomplemented
113#3288C2311024yescomplemented
114#3156C23164yescomplemented
115#3155C23164yescomplemented
116#3154C231128yescomplemented
117#3153C23164yescomplemented
118#3152C23132yescomplemented
119#3151C23132yescomplemented
120#3150C23132yescomplemented
121#3147C23132yescomplemented
122#3069C231256yescomplemented
123#3069C231256yescomplemented
124#3068C231256yescomplemented
125#3068C231256yescomplemented
126#3067C231256yescomplemented
127#3067C231256yescomplemented
128C2×#473C23164yescomplemented
129C2×#472C23164yescomplemented
130C2×#471C231128yescomplemented
131#3022C231256yescomplemented
132#3021C231256yescomplemented
133#3020C231256yescomplemented
134#3019C231256yescomplemented
135#3018C231256yescomplemented
136#3018C231256yescomplemented
137C2×#456C23164yescomplemented
138C2×#454C23164yescomplemented
139C2×#455C23164yescomplemented
140C2×#453C23164yescomplemented
141#2957C231256yescomplemented
142#2956C231256yescomplemented
143#2955C231256yescomplemented
144C2×#444C23164yescomplemented
145C2×#443C23164yescomplemented
146C2×#430C2318yescomplemented
147C2×#430C2318yescomplemented
148C2×#430C23132yescomplemented
149C22×#108C2318yescomplemented
150C2×#421C23116yescomplemented
151C2×#421C23132yescomplemented
152C2×#421C23116yescomplemented
153C2×#421C23132yescomplemented
154C22×#104C23116yescomplemented
155C2×#413C23132yescomplemented
156C2×#413C23132yescomplemented
157C2×#413C23116yescomplemented
158C2×#413C23116yescomplemented
159C22×#101C2318yescomplemented
160C22×#100C2318yescomplemented
161#2873C23116yescomplemented
162C2×#405C2318yescomplemented
163C2×C4×M16C2314yescomplemented
164#585C241128yes—
165#585C24164yescomplemented
166#585C24164yescomplemented
167C2×2−1+4C24132yes—
168C2×2−1+4C24164yescomplemented
169C2×H(5,𝔽2)C24132yes—
170C2×H(5,𝔽2)C24164yescomplemented
171C22×#41C2×D418yes—
172C22×#41C2×D418yes—
173C22×#41C2×D418yes—
174C22×#41C2×D4116yes—
175C22×#41C2×D4116yes—
176C22×#41C24116yes—
177C22×#41C24116yes—
178C22×#41C2418yes—
179C22×#41C2418yes—
180C22×#41C2418yes—
181C22×#41C2418yes—
182C22×#41C2418yes—
183C22×#41C24116yes—
184C22×#41C24116yes—
185C23×Q8C2×D414yes—
186C23×Q8C2414yes—
187C23×D4C2×D414yes—
188C23×D4C2414yes—
189C24×C4C2411yescharacteristic
190#578C241512yescomplemented
191#577C2411024yescomplemented
192#576C241512yescomplemented
193#575C2×D4164yes—
194#575C2×D4132yescomplemented
195#575C2×D4132yescomplemented
196#575C2×D41128yescomplemented
197#575C2×D41128yescomplemented
198#575C24164yes—
199#575C24164yes—
200#575C241128yes—
201#575C241128yes—
202#575C241128yescomplemented
203#575C241128yescomplemented
204C2×#137C2×D4132yes—
205C2×#137C2×D4132yescomplemented
206C2×#137C2×D4164yescomplemented
207C2×#137C2×D4164yescomplemented
208C2×#137C24164yes—
209C2×#137C24164yescomplemented
210C2×#137C24164yescomplemented
211C2×#137C24164yescomplemented
212C2×#137C24164yescomplemented
213C2×AGL(1,ℤ/8)C2×D4132yes—
214C2×AGL(1,ℤ/8)C2×D4132yescomplemented
215C2×AGL(1,ℤ/8)C2×D4164yescomplemented
216C2×AGL(1,ℤ/8)C2×D4164yescomplemented
217C2×AGL(1,ℤ/8)C24164yes—
218C2×AGL(1,ℤ/8)C24164yescomplemented
219C2×AGL(1,ℤ/8)C24164yescomplemented
220C2×AGL(1,ℤ/8)C24164yescomplemented
221C2×AGL(1,ℤ/8)C24164yescomplemented
222C2×#135C2×D4132yescomplemented
223C2×#135C2×D4164yescomplemented
224C2×#135C24132yes—
225C2×#135C24164yes—
226C2×#135C24164yes—
227C2×#135C24164yescomplemented
228C22×Q16C2×D418yescomplemented
229C22×Q16C24116yescomplemented
230C22×SD16C2×D4116yescomplemented
231C22×SD16C24132yescomplemented
232C22×D8C2×D418yescomplemented
233C22×D8C24116yescomplemented
234#568C241128yescomplemented
235#568C241128yescomplemented
236C2×#131C24164yes—
237C2×#131C24164yescomplemented
238C2×#131C24164yescomplemented
239C22×M16C2×D418yes—
240C22×M16C2×D418yes—
241C22×M16C2×D418yes—
242C22×M16C2×D418yes—
243C22×M16C2414yes—
244C22×M16C2414yes—
245C22×M16C24116yes—
246C22×M16C24116yes—
247C22×M16C2418yes—
248C22×M16C2418yes—
249C22×M16C2418yes—
250C22×M16C24116yes—
251C23×C8C2414yes—
252#536C24164yescomplemented
253#535C24164yescomplemented
254#532C24132yes—
255#532C24132yescomplemented
256C2×C4⋊Q8C2418yescomplemented
257C2×#127C2418yescomplemented
258C2×#124C24116yescomplemented
259C2×#117C2414yes—
260C2×#117C2418yes—
261C22×C42C2412yes—
262#497C241128yescomplemented
263#496C241128yescomplemented
264#495C241128yescomplemented
265#494C24132yescomplemented
266#493C24132yescomplemented
267#492C24164yescomplemented
268#473C241512yescomplemented
269#472C241512yescomplemented
270#471C2411024yescomplemented
271#456C241512yescomplemented
272#455C241512yescomplemented
273#454C241512yescomplemented
274#453C241512yescomplemented
275#444C241512yescomplemented
276#443C241512yescomplemented
277#430C24164yescomplemented
278#430C24164yescomplemented
279C2×#108C24132yescomplemented
280C2×#108C24164yescomplemented
281#421C24164yes—
282#421C24164yescomplemented
283#421C241128yescomplemented
284C2×#104C24164yescomplemented
285C2×#104C241128yescomplemented
286#413C24164yescomplemented
287#413C24164yescomplemented
288#413C241128yescomplemented
289C2×#101C24132yescomplemented
290C2×#101C24164yescomplemented
291C2×#100C24132yescomplemented
292C2×#100C24164yescomplemented
293#405C24164yescomplemented
294C4×M16C24132yescomplemented
295C2×#97C2418yescomplemented
296C2×C4×C8C2418yescomplemented
297C25H(5,𝔽2)11yescharacteristic
2982−1+4C251128yes—
299H(5,𝔽2)C251128yes—
300C2×#41C22×D4116yes—
301C2×#41C22×D4132yes—
302C2×#41C22×D4116yes—
303C2×#41C22×D4132yes—
304C2×#41C22×D4132yes—
305C2×#41C22×D4116yes—
306C2×#41C22×D4132yes—
307C2×#41C22×D4132yes—
308C2×#41C22×D4132yes—
309C2×#41C22×D4132yes—
310C2×#41C22×D4132yes—
311C2×#41C22×D4116yes—
312C2×#41C22×D4116yes—
313C2×#41C25116yes—
314C2×#41C25116yes—
315C2×#41C25116yes—
316C2×#41C25132yes—
317C2×#41C25132yes—
318C2×#41C25116yes—
319C2×#41C25116yes—
320C2×#41C25132yes—
321C22×Q8C22×D418yes—
322C22×Q8C22×D418yes—
323C22×Q8C22×D4116yes—
324C22×Q8C22×D4116yes—
325C22×Q8C22×D418yes—
326C22×Q8C2518yes—
327C22×Q8C25116yes—
328C22×D4C22×D418yes—
329C22×D4C22×D418yes—
330C22×D4C22×D4116yes—
331C22×D4C22×D4116yes—
332C22×D4C22×D418yes—
333C22×D4C2518yes—
334C22×D4C25116yes—
335C23×C4C22×D414yes—
336C23×C4C22×D414yes—
337C23×C4C22×D414yes—
338C23×C4C22×D414yes—
339C23×C4H(5,𝔽2)14yes—
340C23×C4H(5,𝔽2)11yescharacteristic
341C23×C4H(5,𝔽2)12yes—
342C23×C4C2512yes—
343C23×C4C2514yes—
344C23×C4C2511yescharacteristic
345#137C22×D41256yes—
346#137C22×D41128yes—
347#137C22×D41128yes—
348#137C251256yes—
349AGL(1,ℤ/8)C22×D41256yes—
350AGL(1,ℤ/8)C22×D41128yes—
351AGL(1,ℤ/8)C22×D41128yes—
352AGL(1,ℤ/8)C251256yes—
353#135C22×D41128yes—
354#135C22×D41256yes—
355#135C251128yes—
356C2×Q16C22×D4132yes—
357C2×Q16C22×D4164yes—
358C2×Q16C25164yes—
359C2×SD16C22×D4164yes—
360C2×SD16C22×D41128yes—
361C2×SD16C251128yes—
362C2×D8C22×D4132yes—
363C2×D8C22×D4164yes—
364C2×D8C25164yes—
365#131C251256yes—
366C2×M16C22×D4116yes—
367C2×M16C22×D4116yes—
368C2×M16C22×D4132yes—
369C2×M16C22×D4132yes—
370C2×M16C22×D4116yes—
371C2×M16C22×D418yes—
372C2×M16C22×D418yes—
373C2×M16C22×D4132yes—
374C2×M16C22×D4132yes—
375C2×M16C25116yes—
376C2×M16C25116yes—
377C2×M16C25116yes—
378C2×M16C25116yes—
379C2×M16C25116yes—
380C2×M16C25132yes—
381C2×M16C25132yes—
382C22×C8C22×D418yes—
383C22×C8C22×D4116yes—
384C22×C8C22×D418yes—
385C22×C8C25116yes—
386C22×C8C2518yes—
387C4⋊Q8C25132yes—
388#127C25132yes—
389#124C25164yes—
390#117C25116yes—
391C2×C42C2518yes—
392C2×C42C2514yes—
393#108C251128yes—
394#104C251256yes—
395#101C251128yes—
396#100C251128yes—
397#97C25132yes—
398C4×C8C25132yes—
399C24D4214yes—
400C24D4214yes—
401C24C2×H(5,𝔽2)12yes—
402C24C2×H(5,𝔽2)14yes—
403C24C2×H(5,𝔽2)11yescharacteristic
404#41C23×D4164yes—
405#41C23×D4132yes—
406#41C23×D4164yes—
407#41C23×D4132yes—
408#41C23×D4132yes—
409#41C26132yes—
410C2×Q8C23×D4116yes—
411C2×Q8C23×D4132yes—
412C2×Q8C23×D4132yes—
413C2×Q8C23×D4116yes—
414C2×Q8C23×D4116yes—
415C2×Q8C26116yes—
416C2×D4C23×D4116yes—
417C2×D4C23×D4132yes—
418C2×D4C23×D4132yes—
419C2×D4C23×D4116yes—
420C2×D4C23×D4116yes—
421C2×D4C26116yes—
422C22×C4D4214yes—
423C22×C4D4218yes—
424C22×C4D4214yes—
425C22×C4D4214yes—
426C22×C4D4214yes—
427C22×C4D4214yes—
428C22×C4D4214yes—
429C22×C4D4214yes—
430C22×C4D4214yes—
431C22×C4D4214yes—
432C22×C4D4218yes—
433C22×C4D4214yes—
434C22×C4C23×D412yes—
435C22×C4C23×D412yes—
436C22×C4C23×D414yes—
437C22×C4C23×D414yes—
438C22×C4C23×D414yes—
439C22×C4C23×D418yes—
440C22×C4C23×D418yes—
441C22×C4C23×D418yes—
442C22×C4C23×D418yes—
443C22×C4C23×D414yes—
444C22×C4C23×D412yes—
445C22×C4C23×D412yes—
446C22×C4C2×H(5,𝔽2)12yes—
447C22×C4C2×H(5,𝔽2)18yes—
448C22×C4C2×H(5,𝔽2)14yes—
449C22×C4C2×H(5,𝔽2)11yescharacteristic
450C22×C4C2×H(5,𝔽2)14yes—
451C22×C4C2×H(5,𝔽2)12yes—
452C22×C4C2611yescharacteristic
453C22×C4C2612yes—
454C22×C4C2614yes—
455Q16C23×D41128yes—
456SD16C23×D41256yes—
457D8C23×D41128yes—
458M16C23×D4164yes—
459M16C23×D4132yes—
460M16C23×D4132yes—
461M16C26132yes—
462C2×C8C23×D4132yes—
463C2×C8C23×D4116yes—
464C2×C8C23×D4132yes—
465C2×C8C23×D4116yes—
466C2×C8C26116yes—
467C42C2618yes—
468C23C2×D4212yes—
469C23C2×D4214yes—
470C23C2×D4212yes—
471C23C2×D4214yes—
472C23C2×D4218yes—
473C23C2×D4214yes—
474C23C2×D4214yes—
475C23C22×H(5,𝔽2)11yescharacteristic
476C23C22×H(5,𝔽2)12yes—
477C23C22×H(5,𝔽2)14yes—
478Q8C24×D4132yes—
479D4C24×D4132yes—
480C2×C4C2×D4214yes—
481C2×C4C2×D4212yes—
482C2×C4C2×D4214yes—
483C2×C4C2×D4214yes—
484C2×C4C2×D4212yes—
485C2×C4C2×D4214yes—
486C2×C4C2×D4214yes—
487C2×C4C2×D4218yes—
488C2×C4C2×D4218yes—
489C2×C4C2×D4218yes—
490C2×C4C2×D4218yes—
491C2×C4C2×D4214yes—
492C2×C4C2×D4214yes—
493C2×C4C2×D4218yes—
494C2×C4C2×D4214yes—
495C2×C4C2×D4214yes—
496C2×C4C2×D4214yes—
497C2×C4C24×D412yes—
498C2×C4C24×D414yes—
499C2×C4C24×D414yes—
500C2×C4C24×D418yes—
501C2×C4C24×D414yes—
502C2×C4C24×D414yes—
503C2×C4C24×D412yes—
504C2×C4C22×H(5,𝔽2)12yes—
505C2×C4C22×H(5,𝔽2)14yes—
506C2×C4C22×H(5,𝔽2)11yescharacteristic
507C2×C4C2711yescharacteristic
508C8C24×D4132yes—
509C22C22×D4214yes—
510C22C22×D4212yes—
511C22C22×D4214yes—
512C22C22×D4214yes—
513C22C23×H(5,𝔽2)11yescharacteristic
514C4C22×D4211yescharacteristic
515C4C22×D4214yes—
516C4C22×D4214yes—
517C4C22×D4214yes—
518C4C22×D4211yescharacteristic
519C4C25×D412yes—
520C2C23×D4211yescharacteristic
subgroupG/H
centerC4C22×D42
commutator, Frattini, cosocleC2×C4C27
socleC2C23×D42
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4 ◁ C24×C4 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#63090C2semidirect
2. #10576179C2semidirect
3. #10576178C2semidirect
4. #10576177C2semidirect
5. #10576173C2semidirect
6. #10575251C2semidirect
7. C2×#60469C2semidirect
8. C2×#60387C2semidirect
9. C2×#60182C2semidirect
10. C22×#585C22semidirect
11. #63090C22semidirect
12. #63090C22semidirect
13. #63090C22semidirect
14. C2×#3586C22semidirect
15. C2×#3585C22semidirect
16. C2×#3584C22semidirect
18. C22×#575C22semidirect
19. C22×#575C22semidirect
20. C22×#568C22semidirect
21. C2×#3449C22semidirect
22. #61111C22semidirect
23. #61110C22semidirect
24. #61109C22semidirect
25. #61108C22semidirect
26. #61107C22semidirect
27. #61106C22semidirect
28. #61105C22semidirect
29. #61100C22semidirect
30. #60645C22semidirect
31. #60644C22semidirect
32. #60643C22semidirect
33. #60639C22semidirect
34. #60469C22semidirect
35. #60469C22semidirect
36. #60469C22semidirect
37. C2×#3069C22semidirect
38. C2×#3068C22semidirect
39. C2×#3067C22semidirect
40. #60387C22semidirect
41. #60387C22semidirect
42. C2×#3022C22semidirect
43. C2×#3021C22semidirect
44. C2×#3020C22semidirect
45. C2×#3019C22semidirect
46. C2×#3018C22semidirect
47. #60182C22semidirect
48. C2×#2957C22semidirect
49. C2×#2956C22semidirect
50. C2×#2955C22semidirect
51. C22×#430C22semidirect
52. C22×#421C22semidirect
53. C22×#413C22semidirect
54. C2×#2873C22semidirect
56. C2×#585C23semidirect
57. C2×#585C23semidirect
58. C2×#585C23semidirect
59. C22×2−1+4C23semidirect
60. C22×H(5,𝔽2)C23semidirect
63. #3586C23semidirect
64. #3586C23semidirect
65. #3585C23semidirect
66. #3585C23semidirect
67. #3584C23semidirect
68. #3584C23semidirect
69. C2×#578C23semidirect
70. C2×#577C23semidirect
71. C2×#576C23semidirect
72. C2×#575D4semidirect
73. C2×#575D4semidirect
74. C2×#575D4semidirect
79. C2×#575C23semidirect
80. C2×#575C23semidirect
81. C2×#575C23semidirect
82. C2×#575C23semidirect
83. C2×#575C23semidirect
84. C2×#575C23semidirect
85. C2×#575C23semidirect
86. C2×#575C23semidirect
87. C22×#137D4semidirect
88. C22×#137C23semidirect
89. C22×#137C23semidirect
90. C22×AGL(1,ℤ/8)D4semidirect
91. C22×AGL(1,ℤ/8)C23semidirect
92. C22×AGL(1,ℤ/8)C23semidirect
94. C22×#135C23semidirect
95. C2×#568C23semidirect
96. C2×#568C23semidirect
97. C2×#568C23semidirect
98. C2×#568C23semidirect
99. C22×#131C23semidirect
102. #3449C23semidirect
103. #3449C23semidirect
104. C2×#536C23semidirect
105. C2×#535C23semidirect
106. C2×#532C23semidirect
108. #3293C23semidirect
109. #3292C23semidirect
110. #3291C23semidirect
111. #3290C23semidirect
112. #3289C23semidirect
113. #3288C23semidirect
114. #3156C23semidirect
115. #3155C23semidirect
116. #3154C23semidirect
117. #3153C23semidirect
118. #3152C23semidirect
119. #3151C23semidirect
120. #3150C23semidirect
121. #3147C23semidirect
122. #3069C23semidirect
123. #3069C23semidirect
124. #3068C23semidirect
125. #3068C23semidirect
126. #3067C23semidirect
127. #3067C23semidirect
128. C2×#473C23semidirect
129. C2×#472C23semidirect
130. C2×#471C23semidirect
131. #3022C23semidirect
132. #3021C23semidirect
133. #3020C23semidirect
134. #3019C23semidirect
135. #3018C23semidirect
136. #3018C23semidirect
137. C2×#456C23semidirect
138. C2×#454C23semidirect
139. C2×#455C23semidirect
140. C2×#453C23semidirect
141. #2957C23semidirect
142. #2956C23semidirect
143. #2955C23semidirect
144. C2×#444C23semidirect
145. C2×#443C23semidirect
146. C2×#430C23semidirect
147. C2×#430C23semidirect
148. C2×#430C23semidirect
149. C22×#108C23semidirect
150. C2×#421C23semidirect
151. C2×#421C23semidirect
152. C2×#421C23semidirect
153. C2×#421C23semidirect
154. C22×#104C23semidirect
155. C2×#413C23semidirect
156. C2×#413C23semidirect
157. C2×#413C23semidirect
158. C2×#413C23semidirect
159. C22×#101C23semidirect
160. C22×#100C23semidirect
161. #2873C23semidirect
162. C2×#405C23semidirect
163. C2×C4×M16C23semidirect
165. #585C24semidirect
166. #585C24semidirect
168. C2×2−1+4C24semidirect
170. C2×H(5,𝔽2)C24semidirect
190. #578C24semidirect
191. #577C24semidirect
192. #576C24semidirect
194. #575C2×D4semidirect
195. #575C2×D4semidirect
196. #575C2×D4semidirect
197. #575C2×D4semidirect
202. #575C24semidirect
203. #575C24semidirect
205. C2×#137C2×D4semidirect
206. C2×#137C2×D4semidirect
207. C2×#137C2×D4semidirect
209. C2×#137C24semidirect
210. C2×#137C24semidirect
211. C2×#137C24semidirect
212. C2×#137C24semidirect
214. C2×AGL(1,ℤ/8)C2×D4semidirect
215. C2×AGL(1,ℤ/8)C2×D4semidirect
216. C2×AGL(1,ℤ/8)C2×D4semidirect
218. C2×AGL(1,ℤ/8)C24semidirect
219. C2×AGL(1,ℤ/8)C24semidirect
220. C2×AGL(1,ℤ/8)C24semidirect
221. C2×AGL(1,ℤ/8)C24semidirect
222. C2×#135C2×D4semidirect
223. C2×#135C2×D4semidirect
227. C2×#135C24semidirect
228. C22×Q16C2×D4semidirect
229. C22×Q16C24semidirect
230. C22×SD16C2×D4semidirect
231. C22×SD16C24semidirect
232. C22×D8C2×D4semidirect
233. C22×D8C24semidirect
234. #568C24semidirect
235. #568C24semidirect
237. C2×#131C24semidirect
238. C2×#131C24semidirect
252. #536C24semidirect
253. #535C24semidirect
255. #532C24semidirect
256. C2×C4⋊Q8C24semidirect
257. C2×#127C24semidirect
258. C2×#124C24semidirect
262. #497C24semidirect
263. #496C24semidirect
264. #495C24semidirect
265. #494C24semidirect
266. #493C24semidirect
267. #492C24semidirect
268. #473C24semidirect
269. #472C24semidirect
270. #471C24semidirect
271. #456C24semidirect
272. #455C24semidirect
273. #454C24semidirect
274. #453C24semidirect
275. #444C24semidirect
276. #443C24semidirect
277. #430C24semidirect
278. #430C24semidirect
279. C2×#108C24semidirect
280. C2×#108C24semidirect
282. #421C24semidirect
283. #421C24semidirect
284. C2×#104C24semidirect
285. C2×#104C24semidirect
286. #413C24semidirect
287. #413C24semidirect
288. #413C24semidirect
289. C2×#101C24semidirect
290. C2×#101C24semidirect
291. C2×#100C24semidirect
292. C2×#100C24semidirect
293. #405C24semidirect
294. C4×M16C24semidirect
295. C2×#97C24semidirect
296. C2×C4×C8C24semidirect

Maximal subgroups

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

subgroupindex
C2×#630902
#105761792
#105761782
#105761772
#105761732
#105752512
C2×#604692
C2×#603872
C2×#601822