Finite Group Databasebeta

← C2×C4×#6495 #14217858

Subgroups — C2×C4×#6495 #14217858

Order 1792.

3242 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C7×D4C211yesmaximal, characteristic, complemented
2C22×#6495C211yesmaximal, characteristic
3C2×C4×#1157C211yesmaximal, characteristic, complemented
4C2×#89987C211yesmaximal, characteristic, complemented
5C2×C4×#1142C212yesmaximal, complemented
6C4×#6495C2116yesmaximal, direct product factor
7C2×#89786C212yesmaximal, complemented
8C2×#89790C212yesmaximal, complemented
9C2×C4×#1141C212yesmaximal, complemented
10C2×#89738C211yesmaximal, characteristic, complemented
11C2×#89736C211yesmaximal, characteristic, complemented
12C2×C4×#1136C211yesmaximal, characteristic, complemented
13C23×C7×D4C2211yescharacteristic
14C24×C4×C7—21no—
15C22×#1157C2211yescharacteristic
16C2×C4×C7×D4—21no—
17C2×C4×C7×D4—21no—
18C2×C4×C7×D4—24no—
19C2×C4×C7×D4C2212yes—
20C2×C4×C7×D4C2212yes—
21C2×C4×C7×D4C2218yescomplemented
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4—21no—
24C22×C42×C7C2211yescharacteristic
25C22×#1142C2212yes—
26C2×#6495C4116yesdirect product factor
27C2×#6495C2218yes—
28C22×#1141C2212yes—
29C2×C4×C22⋊D7—21no—
30C2×C4×C22⋊D7—21no—
31C2×#6489C2211yescharacteristic
32C22×#1136C2211yescharacteristic
33C22×#1136C2211yescharacteristic
34C4×#1157—24no—
35C4×#1157C2218yescomplemented
36C2×C4×D28C2211yescharacteristic, complemented
37C2×C4×D28C2211yescharacteristic, complemented
38C2×#6435—21no—
39C2×C42×D7—21no—
40C2×C4×Dic14C2211yescharacteristic, complemented
41C2×C4×Dic14C2211yescharacteristic, complemented
42#89987C2218yescomplemented
43C2×#6406C2212yes—
44C2×#6406C2212yes—
45#89790C22116yescomplemented
46C4×#1142C22116yescomplemented
47#89786C22116yescomplemented
48C4×#1141C22116yescomplemented
49C2×#6384C2212yescomplemented
50#89738C2218yescomplemented
51C2×#6383C2212yescomplemented
52#89736C2218yescomplemented
53C2×#6382C2212yescomplemented
54C2×#6381C2212yescomplemented
55C4×#1136C2218yescomplemented
56C2×#6377C2212yescomplemented
57C2×C4×C7⋊C8C2212yescomplemented
58C2×C4×AGL(1,ℤ/8)—71nomaximal, Sylow
59C25×C7—21no—
60C22×C7×D4—21no—
61C22×C7×D4—22no—
62C22×C7×D4—24no—
63C22×C7×D4C2×C418yescomplemented
64C22×C7×D4C2312yes—
65C22×C7×D4C2314yes—
66C23×C4×C7—21no—
67C23×C4×C7—22no—
68C23×C4×C7—22no—
69C23×C4×C7—28no—
70C23×C4×C7—48no—
71C23×C4×C7D411yescharacteristic
72C23×C4×C7D411yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C22×C22⋊D7—21no—
75C2×#1157—22no—
76C2×#1157—24no—
77C2×#1157C2×C418yescomplemented
78C2×#1157C2314yes—
79C22×D28C2311yescharacteristic
80C22×C4×D7—21no—
81C22×C4×D7—21no—
82C22×C4×D7—21no—
83C22×Dic14C2311yescharacteristic
84C4×C7×D4—24no—
85C4×C7×D4—24no—
86C4×C7×D4—28no—
87C4×C7×D4—28no—
88C4×C7×D4C2318yes—
89C4×C7×D4C2318yes—
90C2×C7×C4⋊C4—21no—
91C2×C7×C4⋊C4—22no—
92C2×C7×C4⋊C4C2312yes—
93C2×C7×C4⋊C4C2314yes—
94C2×C7×C22⋊C4—22no—
95C2×C7×C22⋊C4—22no—
96C2×C7×C22⋊C4—28no—
97C2×C42×C7D411yescharacteristic
98C2×C42×C7D411yescharacteristic
99C2×C42×C7D414yes—
100C2×C42×C7C2311yescharacteristic
101C2×C42×C7C2311yescharacteristic
102C2×C42×C7C2314yes—
103C2×C22⋊Dic7—21no—
104C2×#1142C2×C4116yescomplemented
105C2×#1142C2318yes—
106#6495C2×C4164yesdirect product factor
107C2×#1141C2×C4116yescomplemented
108C2×#1141C2318yes—
109C4×C22⋊D7—28no—
110C4×C22⋊D7—28no—
111C2×(C2×D7)⋊C4—21no—
112C2×(C2×D7)⋊C4—21no—
113#6489—22no—
114#6489C2314yes—
115C2×C4⋊Dic7C2311yescharacteristic
116C2×C4⋊Dic7C2311yescharacteristic
117C2×Dic7⋊C4—21no—
118C2×Dic7⋊C4—21no—
119C2×C4×Dic7—21no—
120C2×C4×Dic7—21no—
121C2×C4×Dic7—21no—
122C2×#1136—24no—
123C2×#1136C2×C418yescomplemented
124C2×#1136C2314yes—
125C2×#1136C2314yes—
126C22×C7⋊C8C2312yes—
127C22×C7⋊C8C2312yes—
128C4×D28—22no—
129C4×D28—22no—
130C4×D28C2314yescomplemented
131C4×D28C2314yescomplemented
132#6435—28no—
133C42×D7—28no—
134C4×Dic14—22no—
135C4×Dic14—22no—
136C4×Dic14C2314yescomplemented
137C4×Dic14C2314yescomplemented
138#6406C2318yes—
139#6406C2318yes—
140#6384C2318yescomplemented
141#6383C2318yescomplemented
142#6382C2318yescomplemented
143#6381C2318yescomplemented
144#6377C2318yescomplemented
145C4×C7⋊C8C2318yescomplemented
146C22×AGL(1,ℤ/8)—71no—
147C2×C4×#41—71no—
148C22×C4×D4D711yescharacteristic, complemented
149C4×AGL(1,ℤ/8)—716no—
150C2×#442—72no—
151C2×#440—72no—
152C2×C4×SD16—72no—
153C2×C4×D8—72no—
154C2×#428—71no—
155C2×#417—71no—
156C2×#418—71no—
157C2×C4×M16—71no—
158C24×C7—28no—
159C24×C7—22no—
160C24×C7—24no—
161C24×C7—44no—
162C24×C7—44no—
163C24×C7C2×D411yescharacteristic
164C23×D7—21no—
165C2×C7×D4—28no—
166C2×C7×D4—216no—
167C2×C7×D4—24no—
168C2×C7×D4—22no—
169C2×C7×D4—24no—
170C2×C7×D4—28no—
171C2×C7×D4C22×C418yes—
172C2×C7×D4C22×C4116yescomplemented
173C2×C7×D4C2414yes—
174C22×C4×C7—24no—
175C22×C4×C7—24no—
176C22×C4×C7—22no—
177C22×C4×C7—28no—
178C22×C4×C7—28no—
179C22×C4×C7—42no—
180C22×C4×C7—48no—
181C22×C4×C7—432no—
182C22×C4×C7—44no—
183C22×C4×C7—48no—
184C22×C4×C7C22×C414yes—
185C22×C4×C7C2×D411yescharacteristic
186C22×C4×C7C2×D411yescharacteristic
187C22×C4×C7C2×D411yescharacteristic
188C22×C4×C7C2×D414yes—
189C22×C4×C7C2×D414yes—
190C22×C4×C7C2×D411yescharacteristic
191C22×C4×C7C2×D412yes—
192C22×C4×C7C2×D411yescharacteristic
193C22×C4×C7#4114yes—
194C22×C4×C7C2411yescharacteristic
195C22×C4×C7C2412yes—
196C2×C22⋊D7—28no—
197C2×C22⋊D7—24no—
198C22×Dic7—21no—
199C22×Dic7—21no—
200C22×Dic7—21no—
201#1157—216no—
202#1157—28no—
203#1157C22×C4116yescomplemented
204C2×D28—21no—
205C2×D28—22no—
206C2×D28C22×C414yescomplemented
207C2×D28C2412yes—
208C2×C4×D7—28no—
209C2×C4×D7—24no—
210C2×C4×D7—24no—
211C2×C4×D7—24no—
212C2×C4×D7—44no—
213C2×C4×D7—44no—
214C2×Dic14—21no—
215C2×Dic14—22no—
216C2×Dic14C22×C414yescomplemented
217C2×Dic14C2412yes—
218C7×C4⋊C4—24no—
219C7×C4⋊C4—22no—
220C7×C4⋊C4C2414yes—
221C7×C22⋊C4—28no—
222C7×C22⋊C4—28no—
223C42×C7C2×D412yes—
224C42×C7C2×D412yes—
225C42×C7C2×D414yes—
226C42×C7C2×D414yes—
227C42×C7C2412yes—
228C42×C7C2412yes—
229C22⋊Dic7—24no—
230#1142C22×C4132yescomplemented
231#1141C22×C4132yescomplemented
232(C2×D7)⋊C4—24no—
233(C2×D7)⋊C4—24no—
234C4⋊Dic7—21no—
235C4⋊Dic7—21no—
236C4⋊Dic7C2412yes—
237C4⋊Dic7C2412yes—
238Dic7⋊C4—24no—
239Dic7⋊C4—24no—
240C4×Dic7—24no—
241C4×Dic7—24no—
242C4×Dic7—24no—
243#1136—28no—
244#1136C22×C4116yescomplemented
245C2×C7⋊C8—24no—
246C2×C7⋊C8C22×C418yescomplemented
247C2×C7⋊C8C2414yes—
248C2×C7⋊C8C2414yes—
249C22×#41—71no—
250C23×D4C2×D711yescharacteristic
251C24×C4—21no—
252C2×AGL(1,ℤ/8)—716no—
253C2×AGL(1,ℤ/8)—78no—
254C22×SD16—72no—
255C22×D8—72no—
256C22×M16—71no—
257C22×M16—71no—
258C4×#41—78no—
259C4×#41—144no—
260C2×C4×Q8—71no—
261C2×C4×Q8—71no—
262C2×C4×D4—21no—
263C2×C4×D4—24no—
264C2×C4×D4—21no—
265C2×C4×D4—71no—
266C2×C4×D4—71no—
267C2×C4×D4—141no—
268C2×C4×D4—141no—
269C2×C4×D4C2×D712yes—
270C2×C4×D4C2×D712yes—
271C2×C4×D4C2×D718yescomplemented
272C2×#117—71no—
273C2×#117—141no—
274C22×C4⋊C4C2×D711yescharacteristic
275C22×C22⋊C4—21no—
276C22×C42—141no—
277C22×C42C2×D711yescharacteristic
278#442—716no—
279#440—716no—
280C4×SD16—716no—
281C4×D8—716no—
282#428—78no—
283C2×#107—72no—
284C2×#106—72no—
285#418—78no—
286#417—78no—
287C2×#103—72no—
288C2×#102—72no—
289C2×#102—72no—
290C2×#102—72no—
291C4×M16—78no—
292C2×#97—72no—
293C2×C4×C8—72no—
294C23×C7—22no—
295C23×C7—22no—
296C23×C7—28no—
297C23×C7—216no—
298C23×C7—24no—
299C23×C7—48no—
300C23×C7—432no—
301C23×C7—48no—
302C23×C7—44no—
303C23×C7—44no—
304C23×C7C4×D414yes—
305C23×C7C22×D412yes—
306C23×C7C22×D411yescharacteristic
307C22×D7—24no—
308C22×D7—22no—
309C22×D7—42no—
310C22×D7—42no—
311C7×D4—28no—
312C7×D4—216no—
313C7×D4—24no—
314C7×D4C23×C418yes—
315C2×C4×C7—22no—
316C2×C4×C7—22no—
317C2×C4×C7—22no—
318C2×C4×C7—28no—
319C2×C4×C7—24no—
320C2×C4×C7—44no—
321C2×C4×C7—416no—
322C2×C4×C7—48no—
323C2×C4×C7—44no—
324C2×C4×C7—416no—
325C2×C4×C7C4×D414yes—
326C2×C4×C7C4×D418yes—
327C2×C4×C7AGL(1,ℤ/8)14yescomplemented
328C2×C4×C7C23×C412yes—
329C2×C4×C7C23×C414yes—
330C2×C4×C7C22×D412yes—
331C2×C4×C7C22×D412yes—
332C2×C4×C7C22×D412yes—
333C2×C4×C7C22×D412yes—
334C2×C4×C7C22×D411yescharacteristic
335C2×C4×C7C22×D412yes—
336C2×C4×C7C2×#4112yes—
337C2×C4×C7C2×#4114yes—
338C2×C4×C7C2511yescharacteristic
339C22⋊D7—216no—
340C2×Dic7—24no—
341C2×Dic7—22no—
342C2×Dic7—22no—
343C2×Dic7—22no—
344C2×Dic7—42no—
345C2×Dic7—42no—
346D28—24no—
347D28—22no—
348D28C23×C414yescomplemented
349C4×D7—216no—
350C4×D7—48no—
351C4×D7—48no—
352Dic14—24no—
353Dic14—22no—
354Dic14C23×C414yescomplemented
355C7⋊C8—24no—
356C7⋊C8C23×C418yescomplemented
357C25—21no—
358C2×#41—78no—
359C2×#41—74no—
360C2×#41—144no—
361C2×#41—142no—
362C22×Q8—71no—
363C22×D4—24no—
364C22×D4—21no—
365C22×D4—22no—
366C22×D4—71no—
367C22×D4—141no—
368C22×D4C4×D718yescomplemented
369C22×D4C22×D712yes—
370C22×D4C22×D714yes—
371C23×C4—21no—
372C23×C4—22no—
373C23×C4—28no—
374C23×C4—22no—
375C23×C4—48no—
376C23×C4—141no—
377C23×C4—141no—
378C23×C4—141no—
379C23×C4C22⋊D711yescharacteristic
380C23×C4C22⋊D711yescharacteristic
381C23×C4C22×D711yescharacteristic
382AGL(1,ℤ/8)—764no—
383C2×SD16—716no—
384C2×SD16—78no—
385C2×D8—716no—
386C2×D8—78no—
387C2×M16—78no—
388C2×M16—74no—
389C2×M16—74no—
390C2×M16—144no—
391C22×C8—72no—
392C22×C8—72no—
393C4×Q8—74no—
394C4×Q8—74no—
395C4×Q8—142no—
396C4×Q8—142no—
397C4×D4—24no—
398C4×D4—24no—
399C4×D4—28no—
400C4×D4—28no—
401C4×D4—74no—
402C4×D4—74no—
403C4×D4—148no—
404C4×D4—148no—
405C4×D4—142no—
406C4×D4—142no—
407C4×D4C22×D718yes—
408C4×D4C22×D718yes—
409#117—74no—
410#117—142no—
411#117—148no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—71no—
415C2×C4⋊C4—71no—
416C2×C4⋊C4—141no—
417C2×C4⋊C4—141no—
418C2×C4⋊C4C22×D712yes—
419C2×C4⋊C4C22×D714yes—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—28no—
423C2×C22⋊C4—141no—
424C2×C22⋊C4—141no—
425C2×C22⋊C4—141no—
426C2×C42—141no—
427C2×C42—141no—
428C2×C42—141no—
429C2×C42—148no—
430C2×C42C22⋊D711yescharacteristic
431C2×C42C22⋊D714yes—
432C2×C42C22⋊D711yescharacteristic
433C2×C42C22×D711yescharacteristic
434C2×C42C22×D714yes—
435C2×C42C22×D711yescharacteristic
436#107—78no—
437#106—78no—
438#103—78no—
439#102—78no—
440#102—78no—
441#102—78no—
442#97—78no—
443C4×C8—78no—
444C22×C7—28no—
445C22×C7—22no—
446C22×C7—22no—
447C22×C7—28no—
448C22×C7—432no—
449C22×C7—416no—
450C22×C7—44no—
451C22×C7—44no—
452C22×C7C2×C4×D414yes—
453C22×C7C2×C4×D412yes—
454C22×C7C2×AGL(1,ℤ/8)12yes—
455C22×C7#57512yes—
456C22×C7C23×D411yescharacteristic
457C2×D7—24no—
458C2×D7—48no—
459C2×D7—42no—
460C2×D7—42no—
461C4×C7—22no—
462C4×C7—22no—
463C4×C7—22no—
464C4×C7—44no—
465C4×C7C2×C4×D412yes—
466C4×C7C2×C4×D414yes—
467C4×C7C2×AGL(1,ℤ/8)14yescomplemented
468C4×C7C24×C411yescharacteristic
469C4×C7C22×#4111yescharacteristic
470Dic7—24no—
471Dic7—42no—
472Dic7—42no—
473C24—28no—
474C24—22no—
475C24—24no—
476C24—44no—
477C24—44no—
478C24—141no—
479C24C2×C22⋊D711yescharacteristic
480#41—716no—
481#41—1416no—
482#41—148no—
483C2×Q8—74no—
484C2×Q8—72no—
485C2×Q8—142no—
486C2×Q8—141no—
487C2×D4—28no—
488C2×D4—216no—
489C2×D4—24no—
490C2×D4—28no—
491C2×D4—24no—
492C2×D4—22no—
493C2×D4—74no—
494C2×D4—72no—
495C2×D4—148no—
496C2×D4—144no—
497C2×D4—142no—
498C2×D4—141no—
499C2×D4C2×C4×D718yes—
500C2×D4C2×C4×D7116yescomplemented
501C2×D4C23×D714yes—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—42no—
508C22×C4—48no—
509C22×C4—432no—
510C22×C4—44no—
511C22×C4—48no—
512C22×C4—141no—
513C22×C4—148no—
514C22×C4—144no—
515C22×C4—141no—
516C22×C4—141no—
517C22×C4—144no—
518C22×C4—144no—
519C22×C4—284no—
520C22×C4—284no—
521C22×C4C2×C4×D714yes—
522C22×C4#115714yes—
523C22×C4C2×C22⋊D711yescharacteristic
524C22×C4C2×C22⋊D711yescharacteristic
525C22×C4C2×C22⋊D711yescharacteristic
526C22×C4C2×C22⋊D714yes—
527C22×C4C2×C22⋊D714yes—
528C22×C4C2×C22⋊D711yescharacteristic
529C22×C4C2×C22⋊D712yes—
530C22×C4C2×C22⋊D711yescharacteristic
531C22×C4C23×D711yescharacteristic
532C22×C4C23×D712yes—
533SD16—732no—
534D8—732no—
535M16—716no—
536M16—148no—
537C2×C8—78no—
538C2×C8—74no—
539C2×C8—74no—
540C2×C8—144no—
541C4⋊C4—24no—
542C4⋊C4—22no—
543C4⋊C4—72no—
544C4⋊C4—72no—
545C4⋊C4—144no—
546C4⋊C4—144no—
547C4⋊C4—141no—
548C4⋊C4—141no—
549C4⋊C4C23×D714yes—
550C22⋊C4—28no—
551C22⋊C4—28no—
552C22⋊C4—144no—
553C22⋊C4—144no—
554C22⋊C4—144no—
555C42—144no—
556C42—144no—
557C42—144no—
558C42C2×C22⋊D714yes—
559C42C2×C22⋊D714yes—
560C42C2×C22⋊D712yes—
561C42C2×C22⋊D712yes—
562C42C23×D712yes—
563C42C23×D712yes—
564C2×C7—24no—
565C2×C7—48no—
566C2×C7C4×AGL(1,ℤ/8)14yescomplemented
567C2×C7C22×C4×D411yescharacteristic
568C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
569C2×C7C2×#57511yescharacteristic
570D7—44no—
571C23—22no—
572C23—22no—
573C23—28no—
574C23—216no—
575C23—24no—
576C23—48no—
577C23—48no—
578C23—432no—
579C23—44no—
580C23—44no—
581C23—144no—
582C23—142no—
583C23—282no—
584C23—282no—
585C23C4×C22⋊D714yes—
586C23C22×C22⋊D712yes—
587C23C22×C22⋊D711yescharacteristic
588Q8—74no—
589Q8—144no—
590Q8—142no—
591D4—28no—
592D4—216no—
593D4—24no—
594D4—74no—
595D4—1416no—
596D4—144no—
597D4—142no—
598D4C22×C4×D718yes—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—28no—
603C2×C4—24no—
604C2×C4—44no—
605C2×C4—416no—
606C2×C4—48no—
607C2×C4—44no—
608C2×C4—416no—
609C2×C4—144no—
610C2×C4—142no—
611C2×C4—1416no—
612C2×C4—142no—
613C2×C4—142no—
614C2×C4—288no—
615C2×C4—282no—
616C2×C4—282no—
617C2×C4—288no—
618C2×C4C4×C22⋊D714yes—
619C2×C4C4×C22⋊D718yes—
620C2×C4#649514yesdirect product factor
621C2×C4C22×C4×D712yes—
622C2×C4C22×C4×D714yes—
623C2×C4C2×#115712yes—
624C2×C4C2×#115714yes—
625C2×C4C22×C22⋊D712yes—
626C2×C4C22×C22⋊D712yes—
627C2×C4C22×C22⋊D712yes—
628C2×C4C22×C22⋊D712yes—
629C2×C4C22×C22⋊D711yescharacteristic
630C2×C4C22×C22⋊D712yes—
631C2×C4C24×D711yescharacteristic
632C8—78no—
633C8—144no—
634C7C2×C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
635C22—22no—
636C22—22no—
637C22—28no—
638C22—28no—
639C22—432no—
640C22—44no—
641C22—44no—
642C22—416no—
643C22—144no—
644C22—282no—
645C22—282no—
646C22—288no—
647C22C2×C4×C22⋊D714yes—
648C22C2×C4×C22⋊D712yes—
649C22C2×#649512yes—
650C22#9051312yes—
651C22C23×C22⋊D711yescharacteristic
652C4—22no—
653C4—22no—
654C4—22no—
655C4—44no—
656C4—144no—
657C4—282no—
658C4—282no—
659C4C2×C4×C22⋊D714yes—
660C4C2×C4×C22⋊D712yes—
661C4C2×#649514yesdirect product factor
662C4C23×C4×D711yescharacteristic
663C4C22×#115711yescharacteristic
664C2—24no—
665C2—48no—
666C2—284no—
667C2C4×#649514yesdirect product factor
668C2C22×C4×C22⋊D711yescharacteristic
669C2C22×#649511yescharacteristic
670C2C2×#9051311yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D7
commutatorC4×C7C24×C4
FrattiniC2×C4C24×D7
FittingC22×C4×C7×D4C2
socleC23×C7C22×D4
prime radicalC22×#6495C2
cosocleC2×C4×C7C25
hypercenterC22×C4×D4D7
hypocenterC7C2×C4×AGL(1,ℤ/8)
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C7×D4C2semidirect
3. C2×C4×#1157C2semidirect
4. C2×#89987C2semidirect
5. C2×C4×#1142C2semidirect
6. C4×#6495C2direct (N × H)
7. C2×#89786C2semidirect
8. C2×#89790C2semidirect
9. C2×C4×#1141C2semidirect
10. C2×#89738C2semidirect
11. C2×#89736C2semidirect
12. C2×C4×#1136C2semidirect
21. C2×C4×C7×D4C22semidirect
26. C2×#6495C4direct (N × H)
35. C4×#1157C22semidirect
36. C2×C4×D28C22semidirect
37. C2×C4×D28C22semidirect
40. C2×C4×Dic14C22semidirect
41. C2×C4×Dic14C22semidirect
42. #89987C22semidirect
45. #89790C22semidirect
46. C4×#1142C22semidirect
47. #89786C22semidirect
48. C4×#1141C22semidirect
49. C2×#6384C22semidirect
50. #89738C22semidirect
51. C2×#6383C22semidirect
52. #89736C22semidirect
53. C2×#6382C22semidirect
54. C2×#6381C22semidirect
55. C4×#1136C22semidirect
56. C2×#6377C22semidirect
57. C2×C4×C7⋊C8C22semidirect
63. C22×C7×D4C2×C4semidirect
77. C2×#1157C2×C4semidirect
104. C2×#1142C2×C4semidirect
106. #6495C2×C4direct (N × H)
107. C2×#1141C2×C4semidirect
123. C2×#1136C2×C4semidirect
130. C4×D28C23semidirect
131. C4×D28C23semidirect
136. C4×Dic14C23semidirect
137. C4×Dic14C23semidirect
140. #6384C23semidirect
141. #6383C23semidirect
142. #6382C23semidirect
143. #6381C23semidirect
144. #6377C23semidirect
145. C4×C7⋊C8C23semidirect
148. C22×C4×D4D7semidirect
172. C2×C7×D4C22×C4semidirect
203. #1157C22×C4semidirect
206. C2×D28C22×C4semidirect
216. C2×Dic14C22×C4semidirect
230. #1142C22×C4semidirect
231. #1141C22×C4semidirect
244. #1136C22×C4semidirect
246. C2×C7⋊C8C22×C4semidirect
271. C2×C4×D4C2×D7semidirect
327. C2×C4×C7AGL(1,ℤ/8)semidirect
348. D28C23×C4semidirect
354. Dic14C23×C4semidirect
356. C7⋊C8C23×C4semidirect
368. C22×D4C4×D7semidirect
467. C4×C7C2×AGL(1,ℤ/8)semidirect
500. C2×D4C2×C4×D7semidirect
566. C2×C7C4×AGL(1,ℤ/8)semidirect
620. C2×C4#6495direct (N × H)
634. C7C2×C4×AGL(1,ℤ/8)semidirect
661. C4C2×#6495direct (N × H)
667. C2C4×#6495direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C7×D42
C22×#64952
C2×C4×#11572
C2×#899872
C2×C4×#11422
C4×#64952
C2×#897862
C2×#897902
C2×C4×#11412
C2×#897382
C2×#897362
C2×C4×#11362
C2×C4×AGL(1,ℤ/8)7