Finite Group Databasebeta

← C2×#72237526 #72312943

Subgroups — C2×#72237526 #72312943

Order 2048.

At least 7146 conjugacy classes of subgroups; only the 4464 normal subgroups are shown.

The subgroup lattice has 692 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#495753C211yesmaximal, characteristic, complemented
2C2×#503232C211yesmaximal, characteristic, complemented
3C2×#499886C212yesmaximal, complemented
4C2×#500801C212yesmaximal, complemented
5C2×#501188C214yesmaximal, complemented
6C2×#497323C212yesmaximal, complemented
7C2×#503225C212yesmaximal, complemented
8C2×#497333C211yesmaximal, characteristic, complemented
9C2×#6573705C211yesmaximal, characteristic, complemented
10C2×#501108C212yesmaximal, complemented
11C2×#500810C211yesmaximal, characteristic, complemented
12C2×#10583198C211yesmaximal, characteristic, complemented
13C2×#511930C211yesmaximal, characteristic, complemented
14C2×#499819C214yesmaximal, complemented
15C2×#6573729C212yesmaximal, complemented
16#72237526C2132yesmaximal, direct product factor
17C2×#7622880C212yesmaximal, complemented
18C2×#511819C212yesmaximal, complemented
19C2×#63091C2211yescharacteristic, complemented
20C2×#63011C2212yescomplemented
21#10583198C22116yescomplemented
22C2×#62328C2211yescharacteristic, complemented
23C2×#62270C2212yescomplemented
24C2×#61661C2212yescomplemented
25C2×#61630C2214yescomplemented
26C2×#61089C2211yescharacteristic
27C2×#61049C2212yes—
28C2×#60399C2214yescomplemented
29C2×#60388C2212yescomplemented
30C2×#60305C2211yescharacteristic, complemented
31C2×#33570C2212yescomplemented
32#7622880C22132yescomplemented
33C2×#33559C2212yescomplemented
34C2×#33559C2212yescomplemented
35C2×#33553C2214yescomplemented
36C2×#33553C2214yescomplemented
37C2×#33553C2214yescomplemented
38C2×#33546C2211yescharacteristic
39C2×#33546C2212yescomplemented
40C2×#33359C2212yescomplemented
41C2×#33348C2214yescomplemented
42C2×#32951C2211yescharacteristic, complemented
43C2×#32948C2212yescomplemented
44C2×#32894C2212yescomplemented
45C2×#32894C2214yescomplemented
46#6573729C22132yescomplemented
47#6573705C22116yescomplemented
48C2×#25799C2211yescharacteristic, complemented
49C2×#25799C2212yescomplemented
50C2×#24285C2212yescomplemented
51C2×#24287C2211yescharacteristic, complemented
52C2×#24408C2214yescomplemented
53C2×#24420C2212yescomplemented
54C2×#23872C2212yescomplemented
55C2×#23882C2214yescomplemented
56C2×#22458C2211yescharacteristic, complemented
57C2×#22455C2212yescomplemented
58C2×#21483C2212yescomplemented
59C2×#21477C2211yescharacteristic, complemented
60#511930C22116yescomplemented
61#511819C22132yescomplemented
62#503232C22116yescomplemented
63#503225C22132yescomplemented
64#501188C22164yescomplemented
65#501108C22132yescomplemented
66#500810C22116yescomplemented
67#500801C22132yescomplemented
68#499886C22132yescomplemented
69#499819C22164yescomplemented
70C2×#13432C2214yescomplemented
71C2×#13436C2212yescomplemented
72C2×#13353C2214yescomplemented
73C2×#13353C2214yescomplemented
74C2×#13360C2214yescomplemented
75C2×#13350C2214yescomplemented
76C2×#13350C2212yescomplemented
77#497333C22116yescomplemented
78#497323C22132yescomplemented
79#495753C22116yescomplemented
80C2×#13234C2212yescomplemented
81C2×#13231C2212yescomplemented
82C2×#13231C2212yescomplemented
83C2×#13102C2214yescomplemented
84C2×#13102C2214yescomplemented
85C2×#13099C2214yescomplemented
86C2×#13054C2212yescomplemented
87C2×#13051C2211yescharacteristic, complemented
88C2×#13045C2214yescomplemented
89C2×#13045C2212yescomplemented
90C2×#12968C2211yescharacteristic, complemented
91C2×#12962C2212yescomplemented
92C2×#12807C2211yescharacteristic, complemented
93C2×#12805C2212yescomplemented
94C2×#12778C2212yescomplemented
95C2×#12765C2211yescharacteristic, complemented
96C2×#12755C2214yescomplemented
97C2×#12718C2212yescomplemented
98C2×#12711C2214yescomplemented
99C2×#12633C2211yescharacteristic, complemented
100C2×#12623C2212yescomplemented
101C2×H(7,𝔽2)C2312yescomplemented
102#63091C2318yescomplemented
103C2×#3585C2312yescomplemented
104C2×#3584C2311yescharacteristic, complemented
105C22×#576D411yescharacteristic, complemented
106C22×#576C2311yescharacteristic
107C24×D8D412yescomplemented
108C2×#3573C2311yescharacteristic, complemented
109#63011C23116yescomplemented
110C2×#3498C2312yes—
111C2×#3484C2314yes—
112C2×#3549C2312yes—
113C2×#3537C2314yes—
114C2×#3481C2311yescharacteristic
115#62328C2318yescomplemented
116#62270C23116yescomplemented
117#61661C23116yescomplemented
118#61630C23132yescomplemented
119#61089D418yescomplemented
120#61089C2318yes—
121#61049D4116yescomplemented
122#61049C23116yes—
123C2×#3199C2312yes—
124C2×#3199C2314yes—
125C2×#3155D412yescomplemented
126C22×#493D411yescharacteristic, complemented
127C2×#3058D411yescharacteristic, complemented
128C2×#3058C2311yescharacteristic
129C2×#3058C2312yes—
130C2×#3050D412yescomplemented
131C2×#3041D414yescomplemented
132C2×#3038D412yescomplemented
133#60399C23132yescomplemented
134C2×#3027C2314yescomplemented
135C2×#3027C2314yescomplemented
136C2×#3027C2312yescomplemented
137C2×#3025C2314yes—
138C2×#3025C2312yes—
139#60388C23116yescomplemented
140C2×#3021C2312yescomplemented
141C2×#3021C2312yescomplemented
142C2×#3021C2314yescomplemented
143C2×#3018C2312yes—
144C2×#3018C2311yescharacteristic
145C2×#3008D412yescomplemented
146C2×#3008C2312yes—
147C2×#3008C2314yes—
148C2×#3003D414yescomplemented
149#60305C2318yescomplemented
150C2×#2979C2311yescharacteristic
151C2×#2977C2312yes—
152C2×#2948D412yescomplemented
153C2×C4×#135D411yescharacteristic, complemented
154C2×#2931C2311yescharacteristic
155C2×#2929C2312yes—
156C2×#2888C2312yescomplemented
157C2×#2883C2314yescomplemented
158#33570C23116yescomplemented
159#33559C23116yescomplemented
160#33559C23116yescomplemented
161#33553C23132yescomplemented
162#33553C23132yescomplemented
163#33553C23132yescomplemented
164#33546D418yescomplemented
165#33546C2318yes—
166#33546C23116yescomplemented
167C2×#2198D412yescomplemented
168C2×#2197D414yescomplemented
169C2×#2196D412yescomplemented
170C2×#2134C2314yescomplemented
171C2×#2132C2311yescharacteristic
172#33359C23116yescomplemented
173C2×#2128C2314yescomplemented
174C2×#2128C2314yescomplemented
175C2×#2126C2312yes—
176C2×#2126C2311yescharacteristic
177#33348C23132yescomplemented
178C2×#2122C2314yescomplemented
179C2×#2122C2314yescomplemented
180C2×#2122C2314yescomplemented
181C2×#2120C2312yes—
182C2×#2120C2314yes—
183C2×#2120C2312yes—
184#32951C2318yescomplemented
185#32948C23116yescomplemented
186#32894C23116yescomplemented
187#32894C23132yescomplemented
188#25799C2318yescomplemented
189#25799C23116yescomplemented
190#24420C23116yescomplemented
191#24408C23132yescomplemented
192#24287C2318yescomplemented
193#24285C23116yescomplemented
194#23882C23132yescomplemented
195#23872C23116yescomplemented
196#22458C2318yescomplemented
197#22455C23116yescomplemented
198#21483C23116yescomplemented
199#21477C2318yescomplemented
200C2×#1914C2312yescomplemented
201C2×#1910C2314yescomplemented
202C2×#1891C2312yes—
203C2×#1884C2311yescharacteristic
204C2×#1868C2312yescomplemented
205C2×#1858C2311yescharacteristic, complemented
206C2×#1813C2311yescharacteristic, complemented
207C2×#1812C2312yescomplemented
208C2×#1795C2312yescomplemented
209C2×#1795C2314yescomplemented
210C2×#1794C2311yescharacteristic, complemented
211C2×#1794C2314yescomplemented
212C2×#1791C2312yescomplemented
213C2×#1791C2312yescomplemented
214C2×#1757C2311yescharacteristic, complemented
215C2×#1757C2312yescomplemented
216#13436C23116yescomplemented
217#13432C23132yescomplemented
218#13360C23132yescomplemented
219#13353C23132yescomplemented
220#13353C23132yescomplemented
221#13350C23116yescomplemented
222#13350C23132yescomplemented
223#13234C23116yescomplemented
224#13231C23116yescomplemented
225#13231C23116yescomplemented
226#13102C23132yescomplemented
227#13102C23132yescomplemented
228#13099C23132yescomplemented
229#13054C23116yescomplemented
230#13051C2318yescomplemented
231#13045C23116yescomplemented
232#13045C23132yescomplemented
233#12968C2318yescomplemented
234#12962C23116yescomplemented
235#12807C2318yescomplemented
236#12805C23116yescomplemented
237#12778C23116yescomplemented
238#12765C2318yescomplemented
239#12755C23132yescomplemented
240#12718C23116yescomplemented
241#12711C23132yescomplemented
242#12633C2318yescomplemented
243#12623C23116yescomplemented
244C2×#1395C2314yescomplemented
245C2×#1395C2312yescomplemented
246C2×#1392C2312yescomplemented
247C2×#1391C2312yescomplemented
248C2×#1391C2312yescomplemented
249H(7,𝔽2)C2418yescomplemented
250C2×#585C2411yescharacteristic
251C2×#585C2412yes—
252C22×H(5,𝔽2)C2×D412yescomplemented
253C22×H(5,𝔽2)C2412yes—
254C24×D4C2×D414yescomplemented
255#3585C2418yescomplemented
256#3584C2414yescomplemented
257C2×#576C2×D414yes—
258C2×#576C2×D418yes—
259C2×#576C2×D418yescomplemented
260C2×#576C2414yes—
261C22×AGL(1,ℤ/8)C2×D414yes—
262C22×AGL(1,ℤ/8)C2×D412yes—
263C22×AGL(1,ℤ/8)C2×D412yescomplemented
264C22×AGL(1,ℤ/8)C2×D414yescomplemented
265C22×#135C2×D411yescharacteristic
266C22×#135C2×D412yes—
267C23×D8C2×D412yes—
268C23×D8C2×D411yescharacteristic
269C23×D8C2×D414yescomplemented
270C23×D8C2×D412yescomplemented
271C23×D8C2×D411yescharacteristic, complemented
272C23×D8C2×D412yescomplemented
273C23×D8C2×D4116yescomplemented
274#3573C2414yescomplemented
275C2×#568C2411yescharacteristic
276C22×#131C2×D411yescharacteristic, complemented
277C22×#131C2411yescharacteristic
278C24×C8C2×D412yescomplemented
279#3549C2418yes—
280#3537C24116yes—
281#3498C2×D418yescomplemented
282#3498C2418yes—
283#3484C2×D4116yescomplemented
284#3484C24116yes—
285#3481C2×D414yes—
286#3481C2414yes—
287C2×#559C2×D411yescharacteristic
288C2×#551C2×D412yes—
289C2×D42C2×D411yescharacteristic
290C2×#535C2×D414yescomplemented
291C2×#535C2×D412yescomplemented
292C2×#535C2412yes—
293C2×#535C2414yes—
294C2×#532C2411yescharacteristic
295C22×#127C2×D412yescomplemented
296C2×#525C2×D414yescomplemented
297C2×#525C2412yes—
298C2×#518C2×D414yescomplemented
299C2×C4×#41C2×D412yescomplemented
300#3199C2418yes—
301#3199C24116yes—
302#3155C2×D4116yescomplemented
303C2×#493C2×D418yescomplemented
304#3058C2×D414yescomplemented
305#3058C2×D418yescomplemented
306#3058C2×D418yescomplemented
307#3058C2414yes—
308#3058C2418yes—
309#3050C2×D4116yescomplemented
310#3041C2×D4132yescomplemented
311#3038C2×D4116yescomplemented
312#3027C24116yescomplemented
313#3027C24116yescomplemented
314#3027C2418yescomplemented
315#3025C2×D418yes—
316#3025C24116yes—
317#3025C2418yes—
318C2×#458C2×D414yes—
319C2×B(4,𝔽2)C2×D414yes—
320#3021C2418yescomplemented
321#3021C2418yescomplemented
322#3021C24116yescomplemented
323#3018C2×D414yes—
324#3018C2418yes—
325#3018C2414yes—
326C2×#455C2×D412yes—
327C2×#453C2×D412yes—
328#3008C2×D4116yescomplemented
329#3008C2×D418yescomplemented
330#3008C2×D4116yescomplemented
331#3008C24116yes—
332#3008C2418yes—
333#3003C2×D4132yescomplemented
334#2979C2414yes—
335#2977C2418yes—
336#2948C2×D4116yescomplemented
337C4×#135C2×D418yescomplemented
338#2931C2×D414yescomplemented
339#2931C2414yes—
340#2929C2×D418yescomplemented
341#2929C2418yes—
342C2×#427C2×D412yescomplemented
343C2×#427C2×D411yescharacteristic, complemented
344C2×#424C2×D412yescomplemented
345C2×#423C2×D411yescharacteristic, complemented
346C2×#418C2×D414yescomplemented
347C2×#418C2×D412yescomplemented
348C2×#418C2×D414yescomplemented
349C2×#418C2×D412yescomplemented
350C2×#416C2×D414yescomplemented
351C2×#416C2×D412yescomplemented
352#2888C2418yescomplemented
353C2×#413C2412yes—
354C2×#413C2412yes—
355C2×#413C2411yescharacteristic
356#2883C24116yescomplemented
357C2×#410C2414yes—
358C2×#410C2411yescharacteristic
359C2×#410C2412yes—
360C2×#408C2×D411yescharacteristic, complemented
361C2×#408C2411yescharacteristic
362C2×#408C2412yes—
363C2×#407C2×D412yescomplemented
364C2×#405C2×D412yescomplemented
365C22×C4×C8C2×D411yescharacteristic, complemented
366#2198C2×D4116yescomplemented
367#2197C2×D4132yescomplemented
368#2196C2×D4116yescomplemented
369#2134C24116yescomplemented
370#2132C2414yes—
371#2128C24116yescomplemented
372#2128C24116yescomplemented
373#2126C2×D414yes—
374#2126C2418yes—
375#2126C2414yes—
376C2×#354C2×D412yes—
377C2×#353C2×D412yes—
378#2122C24116yescomplemented
379#2122C24116yescomplemented
380#2122C24116yescomplemented
381#2120C2×D418yes—
382#2120C24116yes—
383#2120C2418yes—
384#2120C2418yes—
385C2×#352C2×D414yes—
386C2×AΣL(1,𝔽16)C2×D414yes—
387#1914C2418yescomplemented
388#1910C24116yescomplemented
389#1891C2418yes—
390#1884C2414yes—
391#1868C2418yescomplemented
392#1858C2414yescomplemented
393#1813C2414yescomplemented
394#1812C2418yescomplemented
395#1795C24116yescomplemented
396#1795C2418yescomplemented
397#1794C2414yescomplemented
398#1794C24116yescomplemented
399#1791C2418yescomplemented
400#1791C2418yescomplemented
401#1757C2414yescomplemented
402#1757C2418yescomplemented
403#1395C24116yescomplemented
404#1395C2418yescomplemented
405#1392C2418yescomplemented
406#1391C2418yescomplemented
407#1391C2418yescomplemented
408#585C22×D412yes—
409#585C2512yes—
410#585C2514yes—
411C2×H(5,𝔽2)C22×D418yes—
412C2×H(5,𝔽2)C22×D414yes—
413C2×H(5,𝔽2)C22×D412yes—
414C2×H(5,𝔽2)C22×D418yescomplemented
415C2×H(5,𝔽2)C2514yes—
416C22×#41C22×D412yes—
417C22×#41C22×D414yes—
418C22×#41C22×D411yescharacteristic
419C22×#41C2511yescharacteristic
420C23×D4C22×D414yes—
421C23×D4C22×D414yes—
422C23×D4C22×D412yes—
423C23×D4C22×D412yes—
424C23×D4C22×D4116yescomplemented
425C24×C4C22×D412yes—
426C2×AGL(1,ℤ/8)#120116yes—
427C2×AGL(1,ℤ/8)#12018yes—
428C2×AGL(1,ℤ/8)C22×D418yes—
429C2×AGL(1,ℤ/8)C22×D4116yes—
430C2×AGL(1,ℤ/8)C22×D418yescomplemented
431C2×AGL(1,ℤ/8)C22×D4116yescomplemented
432C2×#135#12014yes—
433C2×#135#12018yes—
434C2×#135C22×D414yes—
435C2×#135C22×D418yes—
436C22×Q16#12011yescharacteristic
437C22×SD16#12012yes—
438C22×SD16#12014yes—
439C22×D8#12012yes—
440C22×D8#12014yes—
441C22×D8#12018yes—
442C22×D8#12012yes—
443C22×D8#12014yes—
444C22×D8#12011yescharacteristic
445C22×D8C22×D418yes—
446C22×D8C22×D414yes—
447C22×D8C22×D414yescomplemented
448C22×D8C22×D418yescomplemented
449C22×D8C22×D4116yescomplemented
450C22×D8C22×D418yescomplemented
451#568C2512yes—
452C2×#131C22×D414yes—
453C2×#131C22×D412yes—
454C2×#131C22×D414yescomplemented
455C2×#131C2512yes—
456C22×M16C22×D412yes—
457C22×M16C22×D411yescharacteristic
458C22×M16C22×D412yes—
459C22×M16C22×D411yescharacteristic
460C23×C8C22×D411yescharacteristic
461C23×C8C22×D412yes—
462C23×C8C22×D411yescharacteristic
463C23×C8C22×D412yes—
464C23×C8C22×D418yescomplemented
465#559C22×D414yes—
466#551C22×D418yes—
467D42C22×D414yes—
468#535C22×D418yes—
469#535C22×D414yes—
470#535C22×D4116yescomplemented
471#535C22×D418yescomplemented
472#535C2514yes—
473#535C2518yes—
474#532C22×D412yes—
475#532C22×D412yes—
476#532H(5,𝔽2)12yes—
477#532C2512yes—
478C2×C4⋊Q8H(5,𝔽2)11yescharacteristic
479C2×#127C22×D411yescharacteristic
480C2×#127C22×D418yescomplemented
481C2×#124C22×D411yescharacteristic
482C2×#124H(5,𝔽2)11yescharacteristic
483#525C22×D414yes—
484#525C22×D414yes—
485#525C22×D4116yescomplemented
486#525H(5,𝔽2)14yes—
487#525C2514yes—
488C2×#123C22×D412yes—
489C2×#123H(5,𝔽2)12yes—
490C2×#120C22×D412yes—
491C2×#120H(5,𝔽2)12yes—
492#518C22×D4116yescomplemented
493C4×#41C22×D418yescomplemented
494C2×#117C22×D414yes—
495C2×#117C22×D412yes—
496C2×#117C22×D412yes—
497C22×C42C22×D411yescharacteristic
498#458C22×D4116yes—
499B(4,𝔽2)C22×D4116yes—
500#455C22×D418yes—
501#453C22×D418yes—
502#427C22×D414yescomplemented
503#427C22×D418yescomplemented
504#424C22×D418yescomplemented
505#423C22×D414yescomplemented
506#418C22×D418yescomplemented
507#418C22×D4116yescomplemented
508#418C22×D418yescomplemented
509#418C22×D4116yescomplemented
510#416C22×D4116yescomplemented
511#416C22×D418yescomplemented
512#413C22×D412yes—
513#413C2514yes—
514#413C2514yes—
515#413C2512yes—
516C2×#100C22×D412yes—
517#410C22×D414yes—
518#410C2512yes—
519#410C2518yes—
520#410C2514yes—
521C2×#99C22×D414yes—
522#408C22×D414yes—
523#408C22×D412yes—
524#408C22×D414yescomplemented
525#408C2514yes—
526#408C2512yes—
527#407C22×D418yescomplemented
528#405C22×D418yescomplemented
529C2×C4×C8C22×D414yescomplemented
530#354C22×D418yes—
531#353C22×D418yes—
532#352C22×D4116yes—
533AΣL(1,𝔽16)C22×D4116yes—
534C25D4212yes—
535H(5,𝔽2)C23×D414yes—
536C2×#41C2×#12014yes—
537C2×#41C2×#12018yes—
538C2×#41D4212yes—
539C2×#41C23×D414yes—
540C2×#41C23×D418yes—
541C2×#41C23×D412yes—
542C2×#41C23×D412yes—
543C2×#41C23×D411yescharacteristic
544C2×#41C23×D411yescharacteristic
545C2×#41C2×H(5,𝔽2)12yes—
546C2×#41C2×H(5,𝔽2)11yescharacteristic
547C2×#41C2611yescharacteristic
548C22×Q8C2×#12012yes—
549C22×Q8D4211yescharacteristic
550C22×Q8C2×H(5,𝔽2)11yescharacteristic
551C22×D4C2×#12018yes—
552C22×D4C2×#12014yes—
553C22×D4C2×#12014yes—
554C22×D4C2×#12012yes—
555C22×D4D4211yescharacteristic
556C22×D4C23×D418yes—
557C22×D4C23×D414yes—
558C22×D4C23×D418yes—
559C22×D4C23×D414yes—
560C22×D4C23×D411yescharacteristic
561C22×D4C2×H(5,𝔽2)12yes—
562C23×C4D4212yes—
563C23×C4D4214yes—
564C23×C4C23×D411yescharacteristic
565C23×C4C23×D412yes—
566C23×C4C23×D414yes—
567C2×Q16C2×#12014yes—
568C2×SD16C2×#12018yes—
569C2×SD16C2×#120116yes—
570C2×D8B(4,𝔽2)12yes—
571C2×D8B(4,𝔽2)12yes—
572C2×D8B(4,𝔽2)14yes—
573C2×D8C2×#12018yes—
574C2×D8C2×#120116yes—
575C2×D8C2×#12018yes—
576C2×D8C2×#12014yes—
577C2×M16C2×#12014yes—
578C2×M16C2×#12012yes—
579C2×M16C23×D412yes—
580C2×M16C23×D414yes—
581C2×M16C23×D414yes—
582C2×M16C23×D412yes—
583C22×C8C2×#12014yes—
584C22×C8C2×#12012yes—
585C22×C8C2×#12012yes—
586C22×C8C2×#12011yescharacteristic
587C22×C8C2×#12011yescharacteristic
588C22×C8C23×D414yes—
589C22×C8C23×D412yes—
590C22×C8C23×D414yes—
591C22×C8C23×D412yes—
592C4⋊Q8D4212yes—
593C4⋊Q8C2×H(5,𝔽2)12yes—
594#127D4212yes—
595#127C23×D412yes—
596#124D4212yes—
597#124D4212yes—
598#124C23×D412yes—
599#124C2×H(5,𝔽2)12yes—
600#123D4214yes—
601#123D4214yes—
602#123C23×D414yes—
603#123C2×H(5,𝔽2)14yes—
604#120D4214yes—
605#120D4214yes—
606#120C23×D414yes—
607#120C2×H(5,𝔽2)14yes—
608#117D4214yes—
609#117C23×D414yes—
610#117C23×D418yes—
611#117C23×D414yes—
612C2×C22⋊C4D4212yes—
613C2×C22⋊C4D4212yes—
614C2×C42D4211yescharacteristic
615C2×C42D4211yescharacteristic
616C2×C42D4212yes—
617C2×C42C23×D412yes—
618#100C23×D414yes—
619#99C23×D418yes—
620C24C2×D4212yes—
621C24C2×D4214yes—
622C24#348411yescharacteristic
623C2×Q8C22×#12014yes—
624C2×Q8C2×D4212yes—
625C2×Q8C2×D4211yescharacteristic
626C2×Q8#348412yes—
627C2×Q8C22×H(5,𝔽2)11yescharacteristic
628C2×D4C2×B(4,𝔽2)14yes—
629C2×D4C2×B(4,𝔽2)14yes—
630C2×D4C22×#12018yes—
631C2×D4C22×#12014yes—
632C2×D4C2×D4212yes—
633C2×D4C2×D4211yescharacteristic
634C2×D4C2×D4212yes—
635C2×D4C2×D4212yes—
636C2×D4#348412yes—
637C2×D4#348412yes—
638C2×D4C24×D411yescharacteristic
639C2×D4C22×H(5,𝔽2)12yes—
640C22×C4C22×#12011yescharacteristic
641C22×C4C22×#12012yes—
642C22×C4C22×#12011yescharacteristic
643C22×C4C2×D4211yescharacteristic
644C22×C4C2×D4211yescharacteristic
645C22×C4C2×D4212yes—
646C22×C4C2×D4214yes—
647C22×C4#348412yes—
648C22×C4#348412yes—
649C22×C4#348411yescharacteristic
650C22×C4C24×D412yes—
651C22×C4C24×D411yescharacteristic
652D8C2×B(4,𝔽2)18yes—
653D8C2×B(4,𝔽2)18yes—
654C2×C8C2×B(4,𝔽2)11yescharacteristic
655C2×C8C2×B(4,𝔽2)11yescharacteristic
656C2×C8C2×B(4,𝔽2)12yes—
657C2×C8C22×#12012yes—
658C2×C8C22×#12014yes—
659C2×C8C22×#12012yes—
660C22⋊C4C2×D4214yes—
661C22⋊C4C2×D4214yes—
662C42C2×D4212yes—
663C42C2×D4212yes—
664C23D4×#12011yescharacteristic
665C23D4×#12012yes—
666C23D4×#12011yescharacteristic
667C23C22×D4212yes—
668C23C2×#348411yescharacteristic
669D4C22×B(4,𝔽2)18yes—
670C2×C4D4×#12011yescharacteristic
671C2×C4D4×#12012yes—
672C2×C4D4×#12011yescharacteristic
673C2×C4C22×B(4,𝔽2)11yescharacteristic
674C2×C4C22×B(4,𝔽2)11yescharacteristic
675C2×C4#6039911yescharacteristic
676C2×C4#6039911yescharacteristic
677C2×C4C23×#12011yescharacteristic
678C2×C4C22×D4211yescharacteristic
679C2×C4C2×#348412yes—
680C8C22×B(4,𝔽2)12yes—
681C8C22×B(4,𝔽2)12yes—
682C22D4×B(4,𝔽2)11yescharacteristic
683C22D4×B(4,𝔽2)11yescharacteristic
684C22C2×D4×#12011yescharacteristic
685C4D4×B(4,𝔽2)11yescharacteristic
686C4D4×B(4,𝔽2)11yescharacteristic
687C4C23×B(4,𝔽2)11yescharacteristic
688C4C2×#6039911yescharacteristic
689C2#7223752612yesdirect product factor
690C2C2×D4×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22D4×B(4,𝔽2)
commutator, Frattini, cosocleC2×#41C26
LCSG ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#576 ◁ G
LECSG ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#495753C2semidirect
2. C2×#503232C2semidirect
3. C2×#499886C2semidirect
4. C2×#500801C2semidirect
5. C2×#501188C2semidirect
6. C2×#497323C2semidirect
7. C2×#503225C2semidirect
8. C2×#497333C2semidirect
9. C2×#6573705C2semidirect
10. C2×#501108C2semidirect
11. C2×#500810C2semidirect
12. C2×#10583198C2semidirect
13. C2×#511930C2semidirect
14. C2×#499819C2semidirect
15. C2×#6573729C2semidirect
16. #72237526C2direct (N × H)
17. C2×#7622880C2semidirect
18. C2×#511819C2semidirect
19. C2×#63091C22semidirect
20. C2×#63011C22semidirect
21. #10583198C22semidirect
22. C2×#62328C22semidirect
23. C2×#62270C22semidirect
24. C2×#61661C22semidirect
25. C2×#61630C22semidirect
28. C2×#60399C22semidirect
29. C2×#60388C22semidirect
30. C2×#60305C22semidirect
31. C2×#33570C22semidirect
32. #7622880C22semidirect
33. C2×#33559C22semidirect
34. C2×#33559C22semidirect
35. C2×#33553C22semidirect
36. C2×#33553C22semidirect
37. C2×#33553C22semidirect
39. C2×#33546C22semidirect
40. C2×#33359C22semidirect
41. C2×#33348C22semidirect
42. C2×#32951C22semidirect
43. C2×#32948C22semidirect
44. C2×#32894C22semidirect
45. C2×#32894C22semidirect
46. #6573729C22semidirect
47. #6573705C22semidirect
48. C2×#25799C22semidirect
49. C2×#25799C22semidirect
50. C2×#24285C22semidirect
51. C2×#24287C22semidirect
52. C2×#24408C22semidirect
53. C2×#24420C22semidirect
54. C2×#23872C22semidirect
55. C2×#23882C22semidirect
56. C2×#22458C22semidirect
57. C2×#22455C22semidirect
58. C2×#21483C22semidirect
59. C2×#21477C22semidirect
60. #511930C22semidirect
61. #511819C22semidirect
62. #503232C22semidirect
63. #503225C22semidirect
64. #501188C22semidirect
65. #501108C22semidirect
66. #500810C22semidirect
67. #500801C22semidirect
68. #499886C22semidirect
69. #499819C22semidirect
70. C2×#13432C22semidirect
71. C2×#13436C22semidirect
72. C2×#13353C22semidirect
73. C2×#13353C22semidirect
74. C2×#13360C22semidirect
75. C2×#13350C22semidirect
76. C2×#13350C22semidirect
77. #497333C22semidirect
78. #497323C22semidirect
79. #495753C22semidirect
80. C2×#13234C22semidirect
81. C2×#13231C22semidirect
82. C2×#13231C22semidirect
83. C2×#13102C22semidirect
84. C2×#13102C22semidirect
85. C2×#13099C22semidirect
86. C2×#13054C22semidirect
87. C2×#13051C22semidirect
88. C2×#13045C22semidirect
89. C2×#13045C22semidirect
90. C2×#12968C22semidirect
91. C2×#12962C22semidirect
92. C2×#12807C22semidirect
93. C2×#12805C22semidirect
94. C2×#12778C22semidirect
95. C2×#12765C22semidirect
96. C2×#12755C22semidirect
97. C2×#12718C22semidirect
98. C2×#12711C22semidirect
99. C2×#12633C22semidirect
100. C2×#12623C22semidirect
101. C2×H(7,𝔽2)C23semidirect
102. #63091C23semidirect
103. C2×#3585C23semidirect
104. C2×#3584C23semidirect
105. C22×#576D4semidirect
107. C24×D8D4semidirect
108. C2×#3573C23semidirect
109. #63011C23semidirect
115. #62328C23semidirect
116. #62270C23semidirect
117. #61661C23semidirect
118. #61630C23semidirect
119. #61089D4semidirect
121. #61049D4semidirect
125. C2×#3155D4semidirect
126. C22×#493D4semidirect
127. C2×#3058D4semidirect
130. C2×#3050D4semidirect
131. C2×#3041D4semidirect
132. C2×#3038D4semidirect
133. #60399C23semidirect
134. C2×#3027C23semidirect
135. C2×#3027C23semidirect
136. C2×#3027C23semidirect
139. #60388C23semidirect
140. C2×#3021C23semidirect
141. C2×#3021C23semidirect
142. C2×#3021C23semidirect
145. C2×#3008D4semidirect
148. C2×#3003D4semidirect
149. #60305C23semidirect
152. C2×#2948D4semidirect
153. C2×C4×#135D4semidirect
156. C2×#2888C23semidirect
157. C2×#2883C23semidirect
158. #33570C23semidirect
159. #33559C23semidirect
160. #33559C23semidirect
161. #33553C23semidirect
162. #33553C23semidirect
163. #33553C23semidirect
164. #33546D4semidirect
166. #33546C23semidirect
167. C2×#2198D4semidirect
168. C2×#2197D4semidirect
169. C2×#2196D4semidirect
170. C2×#2134C23semidirect
172. #33359C23semidirect
173. C2×#2128C23semidirect
174. C2×#2128C23semidirect
177. #33348C23semidirect
178. C2×#2122C23semidirect
179. C2×#2122C23semidirect
180. C2×#2122C23semidirect
184. #32951C23semidirect
185. #32948C23semidirect
186. #32894C23semidirect
187. #32894C23semidirect
188. #25799C23semidirect
189. #25799C23semidirect
190. #24420C23semidirect
191. #24408C23semidirect
192. #24287C23semidirect
193. #24285C23semidirect
194. #23882C23semidirect
195. #23872C23semidirect
196. #22458C23semidirect
197. #22455C23semidirect
198. #21483C23semidirect
199. #21477C23semidirect
200. C2×#1914C23semidirect
201. C2×#1910C23semidirect
204. C2×#1868C23semidirect
205. C2×#1858C23semidirect
206. C2×#1813C23semidirect
207. C2×#1812C23semidirect
208. C2×#1795C23semidirect
209. C2×#1795C23semidirect
210. C2×#1794C23semidirect
211. C2×#1794C23semidirect
212. C2×#1791C23semidirect
213. C2×#1791C23semidirect
214. C2×#1757C23semidirect
215. C2×#1757C23semidirect
216. #13436C23semidirect
217. #13432C23semidirect
218. #13360C23semidirect
219. #13353C23semidirect
220. #13353C23semidirect
221. #13350C23semidirect
222. #13350C23semidirect
223. #13234C23semidirect
224. #13231C23semidirect
225. #13231C23semidirect
226. #13102C23semidirect
227. #13102C23semidirect
228. #13099C23semidirect
229. #13054C23semidirect
230. #13051C23semidirect
231. #13045C23semidirect
232. #13045C23semidirect
233. #12968C23semidirect
234. #12962C23semidirect
235. #12807C23semidirect
236. #12805C23semidirect
237. #12778C23semidirect
238. #12765C23semidirect
239. #12755C23semidirect
240. #12718C23semidirect
241. #12711C23semidirect
242. #12633C23semidirect
243. #12623C23semidirect
244. C2×#1395C23semidirect
245. C2×#1395C23semidirect
246. C2×#1392C23semidirect
247. C2×#1391C23semidirect
248. C2×#1391C23semidirect
249. H(7,𝔽2)C24semidirect
252. C22×H(5,𝔽2)C2×D4semidirect
254. C24×D4C2×D4semidirect
255. #3585C24semidirect
256. #3584C24semidirect
259. C2×#576C2×D4semidirect
263. C22×AGL(1,ℤ/8)C2×D4semidirect
264. C22×AGL(1,ℤ/8)C2×D4semidirect
269. C23×D8C2×D4semidirect
270. C23×D8C2×D4semidirect
271. C23×D8C2×D4semidirect
272. C23×D8C2×D4semidirect
273. C23×D8C2×D4semidirect
274. #3573C24semidirect
276. C22×#131C2×D4semidirect
278. C24×C8C2×D4semidirect
281. #3498C2×D4semidirect
283. #3484C2×D4semidirect
290. C2×#535C2×D4semidirect
291. C2×#535C2×D4semidirect
295. C22×#127C2×D4semidirect
296. C2×#525C2×D4semidirect
298. C2×#518C2×D4semidirect
299. C2×C4×#41C2×D4semidirect
302. #3155C2×D4semidirect
303. C2×#493C2×D4semidirect
304. #3058C2×D4semidirect
305. #3058C2×D4semidirect
306. #3058C2×D4semidirect
309. #3050C2×D4semidirect
310. #3041C2×D4semidirect
311. #3038C2×D4semidirect
312. #3027C24semidirect
313. #3027C24semidirect
314. #3027C24semidirect
320. #3021C24semidirect
321. #3021C24semidirect
322. #3021C24semidirect
328. #3008C2×D4semidirect
329. #3008C2×D4semidirect
330. #3008C2×D4semidirect
333. #3003C2×D4semidirect
336. #2948C2×D4semidirect
337. C4×#135C2×D4semidirect
338. #2931C2×D4semidirect
340. #2929C2×D4semidirect
342. C2×#427C2×D4semidirect
343. C2×#427C2×D4semidirect
344. C2×#424C2×D4semidirect
345. C2×#423C2×D4semidirect
346. C2×#418C2×D4semidirect
347. C2×#418C2×D4semidirect
348. C2×#418C2×D4semidirect
349. C2×#418C2×D4semidirect
350. C2×#416C2×D4semidirect
351. C2×#416C2×D4semidirect
352. #2888C24semidirect
356. #2883C24semidirect
360. C2×#408C2×D4semidirect
363. C2×#407C2×D4semidirect
364. C2×#405C2×D4semidirect
365. C22×C4×C8C2×D4semidirect
366. #2198C2×D4semidirect
367. #2197C2×D4semidirect
368. #2196C2×D4semidirect
369. #2134C24semidirect
371. #2128C24semidirect
372. #2128C24semidirect
378. #2122C24semidirect
379. #2122C24semidirect
380. #2122C24semidirect
387. #1914C24semidirect
388. #1910C24semidirect
391. #1868C24semidirect
392. #1858C24semidirect
393. #1813C24semidirect
394. #1812C24semidirect
395. #1795C24semidirect
396. #1795C24semidirect
397. #1794C24semidirect
398. #1794C24semidirect
399. #1791C24semidirect
400. #1791C24semidirect
401. #1757C24semidirect
402. #1757C24semidirect
403. #1395C24semidirect
404. #1395C24semidirect
405. #1392C24semidirect
406. #1391C24semidirect
407. #1391C24semidirect
414. C2×H(5,𝔽2)C22×D4semidirect
424. C23×D4C22×D4semidirect
430. C2×AGL(1,ℤ/8)C22×D4semidirect
431. C2×AGL(1,ℤ/8)C22×D4semidirect
447. C22×D8C22×D4semidirect
448. C22×D8C22×D4semidirect
449. C22×D8C22×D4semidirect
450. C22×D8C22×D4semidirect
454. C2×#131C22×D4semidirect
464. C23×C8C22×D4semidirect
470. #535C22×D4semidirect
471. #535C22×D4semidirect
480. C2×#127C22×D4semidirect
485. #525C22×D4semidirect
492. #518C22×D4semidirect
493. C4×#41C22×D4semidirect
502. #427C22×D4semidirect
503. #427C22×D4semidirect
504. #424C22×D4semidirect
505. #423C22×D4semidirect
506. #418C22×D4semidirect
507. #418C22×D4semidirect
508. #418C22×D4semidirect
509. #418C22×D4semidirect
510. #416C22×D4semidirect
511. #416C22×D4semidirect
524. #408C22×D4semidirect
527. #407C22×D4semidirect
528. #405C22×D4semidirect
529. C2×C4×C8C22×D4semidirect
689. C2#72237526direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#4957532
C2×#5032322
C2×#4998862
C2×#5008012
C2×#5011882
C2×#4973232
C2×#5032252
C2×#4973332
C2×#65737052
C2×#5011082
C2×#5008102
C2×#105831982
C2×#5119302
C2×#4998192
C2×#65737292
#722375262
C2×#76228802
C2×#5118192