Finite Group Databasebeta

← C2×#72216323 #72275364

Subgroups — C2×#72216323 #72275364

Order 2048.

Only the 6696 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 515 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#187940C212yesmaximal, complemented
2C2×#347047C214yesmaximal, complemented
3C2×#347043C218yesmaximal, complemented
4C2×#187928C214yesmaximal, complemented
5C2×#10586472C211yesmaximal, characteristic, complemented
6C2×#188035C211yesmaximal, characteristic, complemented
7C2×#647656C211yesmaximal, characteristic, complemented
8C22×#23900C214yesmaximal, complemented
9C2×#6499867C212yesmaximal, complemented
10#72216323C2132yesmaximal, direct product factor
11C2×#347042C214yesmaximal, complemented
12#10586472C22116yescomplemented
13C2×#62832C2212yescomplemented
14C2×#62818C2214yescomplemented
15C2×#62817C2212yes—
16C2×#62817C2212yescomplemented
17C22×#3484C2214yes—
18C23×D42C2211yescharacteristic
19C24×#120C2212yescomplemented
20C22×#2846C2214yescomplemented
21C22×#2846C2211yescharacteristic, complemented
22#6499867C22132yescomplemented
23C2×#23984C2218yescomplemented
24C2×#23900C22164yescomplemented
25C2×#23900C2218yescomplemented
26C2×#23900C22116yescomplemented
27C2×#23900C22116yescomplemented
28C2×#21746C2212yescomplemented
29C2×#21746C2214yescomplemented
30C22×#1898C2218yescomplemented
31C22×#1781C2214yescomplemented
32#647656C22116yescomplemented
33C2×#15947C2212yescomplemented
34C2×#15258C2212yescomplemented
35C2×#15257C2214yescomplemented
36C2×#14134C2211yescharacteristic, complemented
37C2×#13867C2212yescomplemented
38#347047C22164yescomplemented
39#347043C221128yescomplemented
40#347042C22164yescomplemented
41#188035C22116yescomplemented
42C2×#8546C2212yescomplemented
43C2×#8542C2214yescomplemented
44C2×#8541C2212yescomplemented
45#187940C22132yescomplemented
46#187928C22164yescomplemented
47C2×#8535C2218yescomplemented
48C2×#8534C22116yescomplemented
49C2×#8534C22116yescomplemented
50C2×#8534C2218yescomplemented
51C28C2311yescharacteristic, complemented
52C23×H(5,𝔽2)D414yescomplemented
53C25×D4D412yescomplemented
54C25×D4C2312yes—
55#62832C23116yescomplemented
56#62818C23132yescomplemented
57#62817D4116yescomplemented
58#62817C23116yes—
59#62817C23116yescomplemented
60C2×#3490D418yescomplemented
61C2×#3490C2314yes—
62C2×#3484D418yescomplemented
63C2×#3484D418yescomplemented
64C2×#3484D418yescomplemented
65C2×#3484D4132yescomplemented
66C2×#3484C2314yes—
67C2×#3484C2318yes—
68C2×#3484C2318yes—
69C2×#3484C23132yes—
70C22×D42D418yescomplemented
71C22×D42C2318yes—
72C22×#534D418yescomplemented
73C23×#127C2311yescharacteristic
74C23×#121D412yescomplemented
75C23×#121C2312yes—
76C23×#120D412yescomplemented
77C23×#120C2314yes—
78C23×#120C2311yescharacteristic
79C23×#120C2311yescharacteristic
80C23×#120C2314yescomplemented
81C23×#120C2314yescomplemented
82C23×#120C2312yescomplemented
83C23×#120C23116yescomplemented
84C22×#518D414yescomplemented
85C23×C4×D4D412yescomplemented
86C24×C22⋊C4C2312yescomplemented
87C2×#2846C23116yescomplemented
88C2×#2846C23132yescomplemented
89C2×#2846C2318yescomplemented
90C22×#379C2312yescomplemented
91C22×#379C2311yescharacteristic, complemented
92C22×#379C2314yescomplemented
93#23984C23164yescomplemented
94#23900C23164yescomplemented
95#23900C231128yescomplemented
96#23900C231128yescomplemented
97#21746C23116yescomplemented
98#21746C23132yescomplemented
99C2×#1898C23116yescomplemented
100C2×#1898C23132yescomplemented
101C2×#1898C23164yescomplemented
102C2×#1819C2314yescomplemented
103C2×#1781C2318yescomplemented
104C2×#1781C2314yescomplemented
105C2×#1781C2318yescomplemented
106C2×#1781C23132yescomplemented
107#15947C23116yescomplemented
108#15258C23116yescomplemented
109#15257C23132yescomplemented
110#14134C2318yescomplemented
111#13867C23116yescomplemented
112C2×#1440C2312yescomplemented
113C2×#1438C2312yescomplemented
114C2×#1438C2314yescomplemented
115C2×#1438C2314yescomplemented
116#8546C23116yescomplemented
117#8542C23132yescomplemented
118#8541C23116yescomplemented
119#8535C23164yescomplemented
120#8534C231128yescomplemented
121#8534C231128yescomplemented
122#8534C23164yescomplemented
123C27C2×D412yes—
124C27C2×D411yescharacteristic, complemented
125C27C2412yes—
126C27C2411yescharacteristic
127C27C2414yescomplemented
128C22×H(5,𝔽2)C2×D414yescomplemented
129C22×H(5,𝔽2)C2×D418yescomplemented
130C22×H(5,𝔽2)C2×D418yescomplemented
131C22×H(5,𝔽2)C2×D4132yescomplemented
132C24×D4C2×D414yes—
133C24×D4C2×D4116yes—
134C24×D4C2×D414yes—
135C24×D4C2×D414yes—
136C24×D4C2×D414yes—
137C24×D4C2×D414yes—
138C24×D4C2×D418yes—
139C24×D4C2×D412yes—
140C24×D4C2×D412yes—
141C24×D4C2×D412yes—
142C24×D4C2×D418yes—
143C24×D4C2×D412yescomplemented
144C24×D4C2×D412yescomplemented
145C24×D4C2×D411yescharacteristic, complemented
146C24×D4C2×D4116yescomplemented
147C24×D4C2412yes—
148C24×D4C2412yes—
149C24×D4C2411yescharacteristic
150C24×D4C2418yes—
151C25×C4C2×D412yes—
152C25×C4C2×D412yescomplemented
153#3490C2×D4164yescomplemented
154#3490C2×D4116yescomplemented
155#3490C24116yes—
156#3484C2×D4132yescomplemented
157#3484C2×D4132yescomplemented
158#3484C2×D4164yescomplemented
159#3484C2×D4164yescomplemented
160#3484C2×D4164yescomplemented
161#3484C2×D4116yescomplemented
162#3484C24132yes—
163#3484C24132yes—
164#3484C24116yes—
165C2×#543C2×D414yescomplemented
166C2×#534C2×D414yescomplemented
167C2×#534C2×D418yescomplemented
168C2×#534C2×D4116yescomplemented
169C2×#534C2×D4116yescomplemented
170C2×#534C2×D4164yescomplemented
171C22×#127C2×D414yescomplemented
172C22×#127C2414yes—
173C22×#121C2×D418yescomplemented
174C22×#121C2×D4116yescomplemented
175C22×#121C2418yes—
176C22×#120C2×D418yes—
177C22×#120C2×D418yes—
178C22×#120C2×D4132yes—
179C22×#120C2×D4116yes—
180C22×#120C2×D418yes—
181C22×#120C2×D4116yes—
182C22×#120C2×D414yes—
183C22×#120C2×D4116yescomplemented
184C22×#120C2×D414yescomplemented
185C22×#120C2418yes—
186C22×#120C24116yes—
187C22×#120C2414yes—
188C22×#120C2414yes—
189C22×#120C2418yescomplemented
190C22×#120C24116yescomplemented
191C22×#120C24116yescomplemented
192C2×#518C2×D418yescomplemented
193C2×#518C2×D418yescomplemented
194C2×#518C2×D4132yescomplemented
195C2×#518C2×D418yescomplemented
196C2×#518C2×D414yescomplemented
197C22×C4×D4C2×D4116yescomplemented
198C23×C4⋊C4C2×D412yescomplemented
199C23×C22⋊C4C2×D412yes—
200C23×C22⋊C4C2×D414yes—
201C23×C22⋊C4C2×D418yes—
202C23×C22⋊C4C2×D412yescomplemented
203C23×C22⋊C4C2×D412yescomplemented
204C23×C22⋊C4C2×D411yescharacteristic, complemented
205C23×C22⋊C4C2411yescharacteristic
206C23×C22⋊C4C2412yes—
207C23×C22⋊C4C2414yes—
208C23×C22⋊C4C2418yescomplemented
209C23×C42C2×D411yescharacteristic, complemented
210#2846C24164yescomplemented
211C2×#379C2418yes—
212C2×#379C2414yescomplemented
213C2×#379C2418yescomplemented
214C2×#379C24116yescomplemented
215#1898C24164yescomplemented
216#1898C241128yescomplemented
217#1819C24116yescomplemented
218#1781C24132yescomplemented
219#1781C24116yescomplemented
220#1781C24132yescomplemented
221#1440C2418yescomplemented
222#1438C24116yescomplemented
223#1438C24116yescomplemented
224#1438C2418yescomplemented
225C26#12018yes—
226C26#12014yes—
227C26#12014yes—
228C26#12014yescomplemented
229C26C22×D412yes—
230C26C22×D414yes—
231C26C22×D412yes—
232C26C22×D418yes—
233C26C22×D414yes—
234C26C22×D414yes—
235C26C22×D414yes—
236C26C22×D412yes—
237C26C22×D411yescharacteristic
238C26C22×D412yes—
239C26C22×D418yes—
240C26C22×D414yescomplemented
241C26C2511yescharacteristic
242C26C2512yes—
243C26C2514yes—
244C2×H(5,𝔽2)C22×D4132yescomplemented
245C2×H(5,𝔽2)C22×D4132yescomplemented
246C2×H(5,𝔽2)C22×D4116yescomplemented
247C23×D4#12012yes—
248C23×D4#12012yes—
249C23×D4#12018yes—
250C23×D4#120116yes—
251C23×D4#12018yes—
252C23×D4#12014yes—
253C23×D4#120116yes—
254C23×D4#120116yes—
255C23×D4#120116yes—
256C23×D4#12012yes—
257C23×D4#12014yes—
258C23×D4#12012yes—
259C23×D4#12018yes—
260C23×D4#12018yes—
261C23×D4#12018yescomplemented
262C23×D4#120116yescomplemented
263C23×D4#120116yescomplemented
264C23×D4#120132yescomplemented
265C23×D4C22×D414yes—
266C23×D4C22×D4116yes—
267C23×D4C22×D414yes—
268C23×D4C22×D414yes—
269C23×D4C22×D414yes—
270C23×D4C22×D4116yes—
271C23×D4C22×D418yes—
272C23×D4C22×D418yes—
273C23×D4C22×D4116yes—
274C23×D4C22×D4116yes—
275C23×D4C22×D4116yes—
276C23×D4C22×D418yes—
277C23×D4C22×D414yes—
278C23×D4C22×D414yes—
279C23×D4C22×D4132yes—
280C23×D4C22×D4116yes—
281C23×D4C22×D418yes—
282C23×D4C22×D414yes—
283C23×D4C22×D418yes—
284C23×D4C22×D414yes—
285C23×D4C22×D418yes—
286C23×D4C22×D412yes—
287C23×D4C22×D418yescomplemented
288C23×D4C22×D418yescomplemented
289C23×D4C22×D414yescomplemented
290C23×D4C2514yes—
291C23×D4C2514yes—
292C23×D4C2512yes—
293C24×C4#12014yes—
294C24×C4#12018yes—
295C24×C4#12014yes—
296C24×C4#12014yescomplemented
297C24×C4#12018yescomplemented
298C24×C4C22×D412yes—
299C24×C4C22×D412yes—
300C24×C4C22×D418yes—
301C24×C4C22×D412yes—
302C24×C4C22×D411yescharacteristic
303C24×C4C22×D418yescomplemented
304#543C22×D4116yescomplemented
305#534C22×D4164yescomplemented
306#534C22×D4164yescomplemented
307#534C22×D4116yescomplemented
308#534C22×D4132yescomplemented
309C2×#120#120132yes—
310C2×#120#120132yescomplemented
311C2×#120#120164yescomplemented
312C2×#120C22×D4132yes—
313C2×#120C22×D4132yes—
314C2×#120C22×D4116yes—
315C2×#120C22×D4164yes—
316C2×#120C22×D4132yes—
317C2×#120C25116yes—
318#518C22×D4132yescomplemented
319#518C22×D4132yescomplemented
320#518C22×D4132yescomplemented
321#518C22×D4116yescomplemented
322C22×C4⋊C4C22×D418yescomplemented
323C22×C22⋊C4#12018yes—
324C22×C22⋊C4#12018yes—
325C22×C22⋊C4#120116yescomplemented
326C22×C22⋊C4#120132yescomplemented
327C22×C22⋊C4#12018yescomplemented
328C22×C22⋊C4#120116yescomplemented
329C22×C22⋊C4C22×D418yes—
330C22×C22⋊C4C22×D412yes—
331C22×C22⋊C4C22×D4116yes—
332C22×C22⋊C4C22×D418yes—
333C22×C22⋊C4C22×D414yes—
334C22×C22⋊C4C22×D414yes—
335C22×C22⋊C4C22×D4132yes—
336C22×C22⋊C4C22×D4116yes—
337C22×C22⋊C4C22×D418yescomplemented
338C22×C22⋊C4C22×D418yescomplemented
339C22×C22⋊C4C22×D414yescomplemented
340C22×C22⋊C4C2512yes—
341C22×C22⋊C4C2518yes—
342C22×C22⋊C4C2514yes—
343C22×C42C22×D414yescomplemented
344#379C25116yes—
345C25C2×#12014yes—
346C25C2×#12014yes—
347C25C2×#12018yes—
348C25C2×#120116yes—
349C25C2×#12014yes—
350C25C2×#12018yes—
351C25C2×#12018yes—
352C25C2×#12018yes—
353C25C2×#120116yes—
354C25C2×#12014yes—
355C25C2×#12014yes—
356C25C2×#12014yes—
357C25C2×#12018yes—
358C25C2×#12014yes—
359C25C2×#12018yes—
360C25C2×#12012yes—
361C25C2×#12012yes—
362C25C2×#12012yes—
363C25C2×#12012yes—
364C25C2×#120116yes—
365C25C2×#12014yes—
366C25C2×#120116yes—
367C25C2×#12014yes—
368C25C2×#12014yes—
369C25C2×#12012yes—
370C25C2×#12018yes—
371C25C2×#12012yes—
372C25C2×#120116yescomplemented
373C25C23×D414yes—
374C25C23×D412yes—
375C25C23×D414yes—
376C25C23×D412yes—
377C25C23×D414yes—
378C25C23×D418yes—
379C25C23×D412yes—
380C25C23×D418yes—
381C25C23×D414yes—
382C25C23×D411yescharacteristic
383C25C23×D414yes—
384C25C23×D418yes—
385C25C23×D411yescharacteristic
386C25C2611yescharacteristic
387C22×D4B(4,𝔽2)116yescomplemented
388C22×D4C2×#12018yes—
389C22×D4C2×#12018yes—
390C22×D4C2×#120132yes—
391C22×D4C2×#120116yes—
392C22×D4C2×#120132yes—
393C22×D4C2×#12018yes—
394C22×D4C2×#12018yes—
395C22×D4C2×#12018yes—
396C22×D4C2×#12018yes—
397C22×D4C2×#120116yes—
398C22×D4C2×#12018yes—
399C22×D4C2×#12018yes—
400C22×D4C2×#120116yes—
401C22×D4C2×#12018yes—
402C22×D4C2×#120132yescomplemented
403C22×D4C2×#120164yescomplemented
404C22×D4C23×D418yes—
405C22×D4C23×D418yes—
406C22×D4C23×D418yes—
407C22×D4C23×D4116yes—
408C22×D4C23×D4132yes—
409C22×D4C23×D418yes—
410C22×D4C23×D418yes—
411C23×C4C2×#12012yes—
412C23×C4C2×#12012yes—
413C23×C4C2×#12012yes—
414C23×C4C2×#12014yes—
415C23×C4C2×#12014yes—
416C23×C4C2×#12018yes—
417C23×C4C2×#120116yes—
418C23×C4C2×#12014yes—
419C23×C4C2×#120116yes—
420C23×C4C2×#12014yes—
421C23×C4C2×#120116yes—
422C23×C4C2×#12012yes—
423C23×C4C2×#12014yes—
424C23×C4C2×#120116yescomplemented
425C23×C4C2×#120132yescomplemented
426C23×C4C23×D412yes—
427C23×C4C23×D414yes—
428C23×C4C23×D414yes—
429C23×C4C23×D414yes—
430C2×C22⋊C4C2×#120132yes—
431C2×C22⋊C4C2×#120132yes—
432C2×C22⋊C4C2×#120116yes—
433C2×C22⋊C4C2×#12018yes—
434C2×C22⋊C4C2×#120164yescomplemented
435C2×C22⋊C4C2×#120132yescomplemented
436C2×C22⋊C4C23×D4132yes—
437C2×C22⋊C4C23×D4116yes—
438C2×C22⋊C4C23×D418yes—
439C24#284618yes—
440C24#284618yes—
441C24#284618yes—
442C24#284614yes—
443C24#2846116yes—
444C24#284618yes—
445C24#284614yes—
446C24#284614yes—
447C24#284614yes—
448C24C2×B(4,𝔽2)18yes—
449C24C2×B(4,𝔽2)18yescomplemented
450C24#302618yes—
451C24C22×#12018yes—
452C24C22×#12018yes—
453C24C22×#12014yes—
454C24C22×#12012yes—
455C24C22×#120116yes—
456C24C22×#12018yes—
457C24C22×#12011yescharacteristic
458C24C22×#12012yes—
459C24C22×#12018yes—
460C24C22×#12018yes—
461C24C22×#12014yes—
462C24C22×#12014yes—
463C24C22×#12014yes—
464C24C22×#12014yes—
465C24C22×#12012yes—
466C24C22×#12011yescharacteristic
467C24C22×#12014yes—
468C24C22×#12018yes—
469C24C22×#12014yes—
470C24C22×#120116yes—
471C24C22×#12014yes—
472C24C24×D412yes—
473C24C24×D414yes—
474C24C24×D411yescharacteristic
475C2×D4C2×B(4,𝔽2)132yescomplemented
476C22×C4C2×B(4,𝔽2)18yescomplemented
477C22×C4C22×#12014yes—
478C22×C4C22×#12014yes—
479C22×C4C22×#12018yes—
480C22×C4C22×#120116yes—
481C22×C4C22×#120132yes—
482C22×C4C22×#12018yes—
483C22×C4C22×#12014yes—
484C23#32898116yes—
485C23#32898116yes—
486C23C2×#284612yes—
487C23C2×#284618yes—
488C23C2×#284611yescharacteristic
489C23C2×#284614yes—
490C23C2×#284618yes—
491C23C2×#284611yescharacteristic
492C23C22×B(4,𝔽2)14yes—
493C23C22×B(4,𝔽2)18yes—
494C23C22×B(4,𝔽2)18yescomplemented
495C23C2×#302614yes—
496C23C2×#302618yes—
497C23#6039914yes—
498C23C23×#12012yes—
499C23C23×#12011yescharacteristic
500C23C23×#12014yes—
501C2×C4C22×B(4,𝔽2)18yescomplemented
502C22C2×#3289814yes—
503C22C2×#3289814yes—
504C22C2×#32898116yes—
505C22#662889612yes—
506C22#662889612yes—
507C22C22×#284611yescharacteristic
508C22C23×B(4,𝔽2)12yes—
509C22C22×#302612yes—
510C22C2×#6039912yes—
511C2#7221632314yesdirect product factor
512C2C22×#3289812yes—
513C2C2×#662889611yescharacteristic
subgroupG/H
center, socleC23C2×#2846
commutator, Frattini, cosocleC25C26
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C27 ◁ G
LECSG ▷ C25 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#187940C2semidirect
2. C2×#347047C2semidirect
3. C2×#347043C2semidirect
4. C2×#187928C2semidirect
5. C2×#10586472C2semidirect
6. C2×#188035C2semidirect
7. C2×#647656C2semidirect
8. C22×#23900C2semidirect
9. C2×#6499867C2semidirect
10. #72216323C2direct (N × H)
11. C2×#347042C2semidirect
12. #10586472C22semidirect
13. C2×#62832C22semidirect
14. C2×#62818C22semidirect
16. C2×#62817C22semidirect
19. C24×#120C22semidirect
20. C22×#2846C22semidirect
21. C22×#2846C22semidirect
22. #6499867C22semidirect
23. C2×#23984C22semidirect
24. C2×#23900C22semidirect
25. C2×#23900C22semidirect
26. C2×#23900C22semidirect
27. C2×#23900C22semidirect
28. C2×#21746C22semidirect
29. C2×#21746C22semidirect
30. C22×#1898C22semidirect
31. C22×#1781C22semidirect
32. #647656C22semidirect
33. C2×#15947C22semidirect
34. C2×#15258C22semidirect
35. C2×#15257C22semidirect
36. C2×#14134C22semidirect
37. C2×#13867C22semidirect
38. #347047C22semidirect
39. #347043C22semidirect
40. #347042C22semidirect
41. #188035C22semidirect
42. C2×#8546C22semidirect
43. C2×#8542C22semidirect
44. C2×#8541C22semidirect
45. #187940C22semidirect
46. #187928C22semidirect
47. C2×#8535C22semidirect
48. C2×#8534C22semidirect
49. C2×#8534C22semidirect
50. C2×#8534C22semidirect
51. C28C23semidirect
52. C23×H(5,𝔽2)D4semidirect
53. C25×D4D4semidirect
55. #62832C23semidirect
56. #62818C23semidirect
57. #62817D4semidirect
59. #62817C23semidirect
60. C2×#3490D4semidirect
62. C2×#3484D4semidirect
63. C2×#3484D4semidirect
64. C2×#3484D4semidirect
65. C2×#3484D4semidirect
70. C22×D42D4semidirect
72. C22×#534D4semidirect
74. C23×#121D4semidirect
76. C23×#120D4semidirect
80. C23×#120C23semidirect
81. C23×#120C23semidirect
82. C23×#120C23semidirect
83. C23×#120C23semidirect
84. C22×#518D4semidirect
85. C23×C4×D4D4semidirect
86. C24×C22⋊C4C23semidirect
87. C2×#2846C23semidirect
88. C2×#2846C23semidirect
89. C2×#2846C23semidirect
90. C22×#379C23semidirect
91. C22×#379C23semidirect
92. C22×#379C23semidirect
93. #23984C23semidirect
94. #23900C23semidirect
95. #23900C23semidirect
96. #23900C23semidirect
97. #21746C23semidirect
98. #21746C23semidirect
99. C2×#1898C23semidirect
100. C2×#1898C23semidirect
101. C2×#1898C23semidirect
102. C2×#1819C23semidirect
103. C2×#1781C23semidirect
104. C2×#1781C23semidirect
105. C2×#1781C23semidirect
106. C2×#1781C23semidirect
107. #15947C23semidirect
108. #15258C23semidirect
109. #15257C23semidirect
110. #14134C23semidirect
111. #13867C23semidirect
112. C2×#1440C23semidirect
113. C2×#1438C23semidirect
114. C2×#1438C23semidirect
115. C2×#1438C23semidirect
116. #8546C23semidirect
117. #8542C23semidirect
118. #8541C23semidirect
119. #8535C23semidirect
120. #8534C23semidirect
121. #8534C23semidirect
122. #8534C23semidirect
124. C27C2×D4semidirect
127. C27C24semidirect
128. C22×H(5,𝔽2)C2×D4semidirect
129. C22×H(5,𝔽2)C2×D4semidirect
130. C22×H(5,𝔽2)C2×D4semidirect
131. C22×H(5,𝔽2)C2×D4semidirect
143. C24×D4C2×D4semidirect
144. C24×D4C2×D4semidirect
145. C24×D4C2×D4semidirect
146. C24×D4C2×D4semidirect
152. C25×C4C2×D4semidirect
153. #3490C2×D4semidirect
154. #3490C2×D4semidirect
156. #3484C2×D4semidirect
157. #3484C2×D4semidirect
158. #3484C2×D4semidirect
159. #3484C2×D4semidirect
160. #3484C2×D4semidirect
161. #3484C2×D4semidirect
165. C2×#543C2×D4semidirect
166. C2×#534C2×D4semidirect
167. C2×#534C2×D4semidirect
168. C2×#534C2×D4semidirect
169. C2×#534C2×D4semidirect
170. C2×#534C2×D4semidirect
171. C22×#127C2×D4semidirect
173. C22×#121C2×D4semidirect
174. C22×#121C2×D4semidirect
183. C22×#120C2×D4semidirect
184. C22×#120C2×D4semidirect
189. C22×#120C24semidirect
190. C22×#120C24semidirect
191. C22×#120C24semidirect
192. C2×#518C2×D4semidirect
193. C2×#518C2×D4semidirect
194. C2×#518C2×D4semidirect
195. C2×#518C2×D4semidirect
196. C2×#518C2×D4semidirect
197. C22×C4×D4C2×D4semidirect
198. C23×C4⋊C4C2×D4semidirect
202. C23×C22⋊C4C2×D4semidirect
203. C23×C22⋊C4C2×D4semidirect
204. C23×C22⋊C4C2×D4semidirect
208. C23×C22⋊C4C24semidirect
209. C23×C42C2×D4semidirect
210. #2846C24semidirect
212. C2×#379C24semidirect
213. C2×#379C24semidirect
214. C2×#379C24semidirect
215. #1898C24semidirect
216. #1898C24semidirect
217. #1819C24semidirect
218. #1781C24semidirect
219. #1781C24semidirect
220. #1781C24semidirect
221. #1440C24semidirect
222. #1438C24semidirect
223. #1438C24semidirect
224. #1438C24semidirect
228. C26#120semidirect
240. C26C22×D4semidirect
244. C2×H(5,𝔽2)C22×D4semidirect
245. C2×H(5,𝔽2)C22×D4semidirect
246. C2×H(5,𝔽2)C22×D4semidirect
261. C23×D4#120semidirect
262. C23×D4#120semidirect
263. C23×D4#120semidirect
264. C23×D4#120semidirect
287. C23×D4C22×D4semidirect
288. C23×D4C22×D4semidirect
289. C23×D4C22×D4semidirect
296. C24×C4#120semidirect
297. C24×C4#120semidirect
303. C24×C4C22×D4semidirect
304. #543C22×D4semidirect
305. #534C22×D4semidirect
306. #534C22×D4semidirect
307. #534C22×D4semidirect
308. #534C22×D4semidirect
310. C2×#120#120semidirect
311. C2×#120#120semidirect
318. #518C22×D4semidirect
319. #518C22×D4semidirect
320. #518C22×D4semidirect
321. #518C22×D4semidirect
322. C22×C4⋊C4C22×D4semidirect
325. C22×C22⋊C4#120semidirect
326. C22×C22⋊C4#120semidirect
327. C22×C22⋊C4#120semidirect
328. C22×C22⋊C4#120semidirect
337. C22×C22⋊C4C22×D4semidirect
338. C22×C22⋊C4C22×D4semidirect
339. C22×C22⋊C4C22×D4semidirect
343. C22×C42C22×D4semidirect
372. C25C2×#120semidirect
387. C22×D4B(4,𝔽2)semidirect
402. C22×D4C2×#120semidirect
403. C22×D4C2×#120semidirect
424. C23×C4C2×#120semidirect
425. C23×C4C2×#120semidirect
434. C2×C22⋊C4C2×#120semidirect
435. C2×C22⋊C4C2×#120semidirect
449. C24C2×B(4,𝔽2)semidirect
475. C2×D4C2×B(4,𝔽2)semidirect
476. C22×C4C2×B(4,𝔽2)semidirect
494. C23C22×B(4,𝔽2)semidirect
501. C2×C4C22×B(4,𝔽2)semidirect
511. C2#72216323direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#1879402
C2×#3470472
C2×#3470432
C2×#1879282
C2×#105864722
C2×#1880352
C2×#6476562
C22×#239002
C2×#64998672
#722163232
C2×#3470422