Finite Group Databasebeta

← #31998598

Subgroups — #31998598

Order 18176.

2230 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D71C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D71C211yesmaximal, characteristic
3C2×#17985963C211yesmaximal, characteristic, complemented
4C2×#17985962C211yesmaximal, characteristic, complemented
5#22588634C214yesmaximal, complemented
6#22588629C214yesmaximal, complemented
7#22588033C211yesmaximal, characteristic, complemented
8#22588033C211yesmaximal, characteristic, complemented
9C2×#407×C71C211yesmaximal, characteristic, complemented
10C23×C22⋊D71C411yescharacteristic
11C23×C4×D71C2211yescharacteristic
12C22×#11765849C2211yescharacteristic
13C22×#11765849C2211yescharacteristic
14C22×#11765848C2212yescomplemented
15C2×M16×D71—24no—
16C2×M16×D71—24no—
17C2×M16×D71—24no—
18C22×C8×D71C2212yescomplemented
19C2×C4×C22⋊D71—24no—
20C2×C4×C22⋊D71—24no—
21C2×C4×C22⋊D71C412yes—
22C2×C4×C22⋊D71C412yes—
23C2×C4×C22⋊D71C2212yes—
24C2×C4×C22⋊D71C2212yes—
25C22×Dic71⋊C4C411yescharacteristic
26C22×C22⋊Dic71C411yescharacteristic
27C22×(C2×D71)⋊C4C411yescharacteristic
28C22×C4×Dic71C2211yescharacteristic
29#17985963—24no—
30#17985962—24no—
31C2×C22⋊(C71⋊C8)C2214yescomplemented
32C2×(C2×D71)⋊C8C2212yescomplemented
33C2×(C2×D71)⋊C8C2212yescomplemented
34#17985753C2214yescomplemented
35#17985753C2214yescomplemented
36C24×C4×C71C2211yescharacteristic
37C22×M16×C71C2211yescharacteristic
38C22×M16×C71C2211yescharacteristic
39#407×C71—24no—
40C2×C22⋊C8×C71C2214yescomplemented
41C24×D71C2×C411yescharacteristic
42C22×C22⋊D71—24no—
43C22×C22⋊D71—28no—
44C22×C22⋊D71C2×C412yes—
45C22×C22⋊D71C2×C412yes—
46C23×Dic71C2×C411yescharacteristic
47C23×Dic71C2×C411yescharacteristic
48C23×Dic71C2×C411yescharacteristic
49C22×C4×D71—22no—
50C22×C4×D71—22no—
51C22×C4×D71—22no—
52C22×C4×D71—22no—
53C22×C4×D71C2×C411yescharacteristic
54C22×C4×D71C2×C411yescharacteristic
55C22×C4×D71D414yes—
56C22×C4×D71D414yes—
57C22×C4×D71C2311yescharacteristic
58C22×C4×D71C2311yescharacteristic
59C2×#11765849—22no—
60C2×#11765849—22no—
61C2×#11765849—22no—
62C2×#11765849—22no—
63C2×#11765849—22no—
64C2×#11765849D414yescomplemented
65C2×#11765848—24no—
66C2×#11765848—24no—
67C2×#11765848—24no—
68M16×D71—232no—
69C22×C71⋊C8C2312yes—
70C22×C71⋊C8C2312yes—
71C2×C8×D71—24no—
72C2×C8×D71—24no—
73C2×C8×D71—24no—
74C4×C22⋊D71—28no—
75C4×C22⋊D71—28no—
76C4×C22⋊D71—24no—
77C4×C22⋊D71—24no—
78C4×C22⋊D71—24no—
79C4×C22⋊D71—24no—
80C2×Dic71⋊C4—24no—
81C2×Dic71⋊C4C2×C412yes—
82C2×Dic71⋊C4C2×C412yes—
83C2×C22⋊Dic71—24no—
84C2×C22⋊Dic71C2×C412yes—
85C2×C22⋊Dic71C2×C412yes—
86C2×(C2×D71)⋊C4—24no—
87C2×(C2×D71)⋊C4C2×C412yes—
88C2×(C2×D71)⋊C4C2×C412yes—
89C2×C4×Dic71—22no—
90C2×C4×Dic71—22no—
91C2×C4×Dic71C2×C412yes—
92C2×C4×Dic71C2312yes—
93C22⋊(C71⋊C8)—28no—
94(C2×D71)⋊C8—24no—
95(C2×D71)⋊C8—24no—
96C25×C71C2×C411yescharacteristic
97C23×C4×C71—22no—
98C23×C4×C71—22no—
99C23×C4×C71—22no—
100C23×C4×C71—22no—
101C23×C4×C71—22no—
102C23×C4×C71—22no—
103C23×C4×C71C2×C411yescharacteristic
104C23×C4×C71C2×C412yes—
105C23×C4×C71C2312yes—
106C23×C4×C71C2311yescharacteristic
107C2×M16×C71—22no—
108C2×M16×C71—22no—
109C2×M16×C71—22no—
110C2×M16×C71—22no—
111C2×M16×C71—22no—
112C2×M16×C71D414yescomplemented
113C22×C8×C71C2312yes—
114C22×C8×C71C2312yes—
115C22⋊C8×C71—28no—
116C23×D71—22no—
117C23×D71—22no—
118C23×D71—24no—
119C23×D71—42no—
120C23×D71C22⋊C414yes—
121C23×D71C22×C411yescharacteristic
122C23×D71C22×C411yescharacteristic
123C2×C22⋊D71—232no—
124C2×C22⋊D71—24no—
125C2×C22⋊D71—24no—
126C2×C22⋊D71—24no—
127C2×C22⋊D71—24no—
128C2×C22⋊D71—24no—
129C2×C22⋊D71M1618yescomplemented
130C22×Dic71—22no—
131C22×Dic71—22no—
132C22×Dic71—22no—
133C22×Dic71—24no—
134C22×Dic71—22no—
135C22×Dic71—42no—
136C22×Dic71C22⋊C414yes—
137C22×Dic71C22×C412yes—
138C22×Dic71C22×C411yescharacteristic
139C22×Dic71C22×C411yescharacteristic
140C22×Dic71C22×C412yes—
141C2×C4×D71—22no—
142C2×C4×D71—22no—
143C2×C4×D71—22no—
144C2×C4×D71—22no—
145C2×C4×D71—28no—
146C2×C4×D71—28no—
147C2×C4×D71—28no—
148C2×C4×D71—28no—
149C2×C4×D71—21no—
150C2×C4×D71—21no—
151C2×C4×D71—21no—
152C2×C4×D71—21no—
153C2×C4×D71—21no—
154C2×C4×D71—21no—
155C2×C4×D71—21no—
156C2×C4×D71—21no—
157C2×C4×D71C22⋊C414yes—
158C2×C4×D71C22⋊C414yes—
159C2×C4×D71C2×D412yes—
160C2×C4×D71C2×D412yes—
161C2×C4×D71C2×D412yes—
162C2×C4×D71C2×D412yes—
163#11765849—28no—
164#11765849—44no—
165#11765848—216no—
166C2×C71⋊C8—22no—
167C2×C71⋊C8—22no—
168C2×C71⋊C8—22no—
169C2×C71⋊C8—22no—
170C2×C71⋊C8—22no—
171C2×C71⋊C8C2×D414yescomplemented
172C8×D71—216no—
173Dic71⋊C4—24no—
174Dic71⋊C4—24no—
175C22⋊Dic71—24no—
176C22⋊Dic71—24no—
177(C2×D71)⋊C4—24no—
178(C2×D71)⋊C4—24no—
179C4×Dic71—24no—
180C4×Dic71—22no—
181C4×Dic71—22no—
182C24×C71—22no—
183C24×C71—24no—
184C24×C71—22no—
185C24×C71—22no—
186C24×C71—42no—
187C24×C71C22×C412yes—
188C24×C71C22×C411yescharacteristic
189C22×C4×C71—22no—
190C22×C4×C71—22no—
191C22×C4×C71—22no—
192C22×C4×C71—24no—
193C22×C4×C71—24no—
194C22×C4×C71—24no—
195C22×C4×C71—22no—
196C22×C4×C71—22no—
197C22×C4×C71—22no—
198C22×C4×C71—22no—
199C22×C4×C71—22no—
200C22×C4×C71—22no—
201C22×C4×C71—44no—
202C22×C4×C71—44no—
203C22×C4×C71—44no—
204C22×C4×C71—44no—
205C22×C4×C71C22×C412yes—
206C22×C4×C71C22×C411yescharacteristic
207C22×C4×C71C2×D412yes—
208C22×C4×C71C2×D412yes—
209C22×C4×C71C2×D412yes—
210C22×C4×C71C2×D412yes—
211C22×C4×C71#4112yes—
212C22×C4×C71#4112yes—
213C22×C4×C71C2411yescharacteristic
214M16×C71—28no—
215M16×C71—44no—
216C2×C8×C71—22no—
217C2×C8×C71—22no—
218C2×C8×C71—22no—
219C2×C8×C71—22no—
220C2×C8×C71—22no—
221C2×C8×C71C2×D414yescomplemented
222C23×C71—22no—
223C23×C71—22no—
224C23×C71—28no—
225C23×C71—22no—
226C23×C71—22no—
227C23×C71—22no—
228C23×C71—22no—
229C23×C71—22no—
230C23×C71—22no—
231C23×C71—48no—
232C23×C71—48no—
233C23×C71—44no—
234C23×C71—44no—
235C23×C71C2×C22⋊C412yes—
236C23×C71C4×D412yes—
237C23×C71C4×D412yes—
238C23×C71C2×M1614yescomplemented
239C23×C71C23×C411yescharacteristic
240C22×D71—21no—
241C22×D71—21no—
242C22×D71—22no—
243C22×D71—21no—
244C22×D71—21no—
245C22×D71—22no—
246C22×D71—22no—
247C22×D71—28no—
248C22×D71—28no—
249C22×D71—44no—
250C22×D71—48no—
251C22×D71—48no—
252C22×D71C2×C22⋊C412yes—
253C22×D71C2×C22⋊C412yes—
254C22×D71C2×M1614yes—
255C2×C4×C71—22no—
256C2×C4×C71—22no—
257C2×C4×C71—22no—
258C2×C4×C71—44no—
259C2×C4×C71—42no—
260C2×C4×C71—42no—
261C2×C4×C71—42no—
262C2×C4×C71—42no—
263C2×C4×C71—48no—
264C2×C4×C71C2×C22⋊C412yes—
265C2×C4×C71C4×D412yes—
266C2×C4×C71C4×D412yes—
267C2×C4×C71#12014yes—
268C2×C4×C71#12114yes—
269C2×C4×C71#12114yes—
270C2×C4×C71#12314yes—
271C2×C4×C71C22×D411yescharacteristic
272C2×C4×C71C22×D411yescharacteristic
273C2×C4×C71C22×D411yescharacteristic
274C2×C4×C71C22×D411yescharacteristic
275C2×C4×C71C2×#4111yescharacteristic
276C2×C4×C71C2×#4111yescharacteristic
277C22⋊D71—216no—
278C22⋊D71—216no—
279C2×Dic71—28no—
280C2×Dic71—22no—
281C2×Dic71—21no—
282C2×Dic71—21no—
283C2×Dic71—21no—
284C2×Dic71—21no—
285C2×Dic71—22no—
286C2×Dic71—28no—
287C2×Dic71—22no—
288C2×Dic71—24no—
289C2×Dic71—44no—
290C2×Dic71C2×C22⋊C412yes—
291C2×Dic71C2×C22⋊C412yes—
292C2×Dic71C2×M1614yescomplemented
293C4×D71—22no—
294C4×D71—22no—
295C4×D71—22no—
296C4×D71—22no—
297C4×D71—22no—
298C4×D71—22no—
299C4×D71—22no—
300C4×D71—22no—
301C4×D71—28no—
302C4×D71—28no—
303C8×C71—24no—
304C8×C71—42no—
305C71⋊C8—24no—
306C71⋊C8—42no—
307C22×C71—22no—
308C22×C71—22no—
309C22×C71—24no—
310C22×C71—24no—
311C22×C71—24no—
312C22×C71—24no—
313C22×C71—24no—
314C22×C71—416no—
315C22×C71—42no—
316C22×C71—42no—
317C22×C71—42no—
318C22×C71—42no—
319C22×C71#38614yes—
320C22×C71C22×C22⋊C411yescharacteristic
321C22×C71C2×C4×D411yescharacteristic
322C22×C71C2×C4×D411yescharacteristic
323C22×C71C22×M1612yes—
324C22×C71#56812yes—
325C2×D71—22no—
326C2×D71—24no—
327C2×D71—24no—
328C2×D71—22no—
329C2×D71—22no—
330C2×D71—22no—
331C2×D71—22no—
332C2×D71—416no—
333C2×D71—42no—
334C2×D71—42no—
335C2×D71#40714yescomplemented
336C4×C71—42no—
337C4×C71#38614yes—
338C4×C71C2×#12011yescharacteristic
339C4×C71C2×#12111yescharacteristic
340C4×C71C2×#12111yescharacteristic
341C4×C71C2×#12311yescharacteristic
342Dic71—24no—
343Dic71—22no—
344Dic71—22no—
345Dic71—42no—
346#20898—711nomaximal, Sylow
347C2×C71—24no—
348C2×C71—44no—
349C2×C71C2×#38611yescharacteristic
350C2×C71C2×#40711yescharacteristic
351C2×C71#287911yescharacteristic
352C2×C71D4×M1612yes—
353C2×C71D4×M1612yes—
354D71—24no—
355D71—42no—
356C23×M16—711no—
357C22×C4×D4—711no—
358C2×#407—711no—
359C2×#407—711no—
360C2×#407D7111yescharacteristic, complemented
361#1870—714no—
362#1869—714no—
363#1728—711no—
364#1728—711no—
365C71#2089811yescharacteristic, complemented, Sylow
366C23×D4—711no—
367C24×C4—711no—
368C24×C4C2×D7111yescharacteristic
369C22×M16—711no—
370C22×M16—711no—
371C22×M16—712no—
372C22×M16—1424no—
373C22×M16—1424no—
374C22×M16—1424no—
375C22×M16C2×D7111yescharacteristic
376C22×M16C2×D7111yescharacteristic
377C23×C8—712no—
378C2×C4×D4—712no—
379C2×C4×D4—712no—
380C2×C4×D4—712no—
381C2×C4×D4—712no—
382C2×C4×D4—1424no—
383C2×C4×D4—1424no—
384C22×C4⋊C4—711no—
385C22×C22⋊C4—711no—
386C22×C22⋊C4—711no—
387C22×C42—711no—
388#407—24no—
389#407—1424no—
390#407—1424no—
391C2×C22⋊C8—714no—
392C2×C22⋊C8—712no—
393C2×C22⋊C8—712no—
394C2×C22⋊C8C2×D7114yescomplemented
395#336—714no—
396#336—714no—
397C25—711no—
398C25C4×D7111yescharacteristic
399C22×D4—712no—
400C22×D4—712no—
401C22×D4—1428no—
402C22×D4—1424no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—711no—
410C23×C4—711no—
411C23×C4—711no—
412C23×C4—711no—
413C23×C4—714no—
414C23×C4—714no—
415C23×C4—711no—
416C23×C4—711no—
417C23×C4—711no—
418C23×C4—1422no—
419C23×C4—1422no—
420C23×C4—1422no—
421C23×C4—1422no—
422C23×C4C4×D7111yescharacteristic
423C23×C4C4×D7112yes—
424C23×C4C22×D7112yes—
425C23×C4C22×D7111yescharacteristic
426C2×M16—22no—
427C2×M16—22no—
428C2×M16—22no—
429C2×M16—22no—
430C2×M16—22no—
431C2×M16—714no—
432C2×M16—1424no—
433C2×M16—1424no—
434C2×M16—14232no—
435C2×M16—1422no—
436C2×M16—1422no—
437C2×M16—1422no—
438C2×M16—1422no—
439C2×M16—1422no—
440C2×M16—1424no—
441C2×M16C22⋊D7114yescomplemented
442C22×C8—712no—
443C22×C8—712no—
444C22×C8—1424no—
445C22×C8—1424no—
446C22×C8—1424no—
447C22×C8C22×D7112yes—
448C22×C8C22×D7112yes—
449C4×D4—1424no—
450C4×D4—1424no—
451C4×D4—1424no—
452C4×D4—1424no—
453C4×D4—1428no—
454C4×D4—1428no—
455C2×C4⋊C4—712no—
456C2×C4⋊C4—712no—
457C2×C4⋊C4—1424no—
458C2×C22⋊C4—712no—
459C2×C22⋊C4—712no—
460C2×C22⋊C4—712no—
461C2×C22⋊C4—712no—
462C2×C22⋊C4—1424no—
463C2×C22⋊C4—1424no—
464C2×C42—712no—
465C2×C42—712no—
466C2×C42—1422no—
467C2×C42—1422no—
468C22⋊C8—28no—
469C22⋊C8—1424no—
470C22⋊C8—1424no—
471C22⋊C8—1428no—
472C24—22no—
473C24—24no—
474C24—22no—
475C24—22no—
476C24—42no—
477C24—2842no—
478C24—714no—
479C24—711no—
480C24—711no—
481C24—1424no—
482C24—1422no—
483C24—1422no—
484C24C2×C4×D7112yes—
485C24C2×C4×D7111yescharacteristic
486C2×D4—718no—
487C2×D4—1424no—
488C2×D4—1424no—
489C2×D4—1424no—
490C2×D4—1424no—
491C2×D4—14232no—
492C2×D4—1424no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—2842no—
510C22×C4—712no—
511C22×C4—711no—
512C22×C4—711no—
513C22×C4—714no—
514C22×C4—712no—
515C22×C4—712no—
516C22×C4—712no—
517C22×C4—712no—
518C22×C4—714no—
519C22×C4—714no—
520C22×C4—712no—
521C22×C4—1422no—
522C22×C4—1424no—
523C22×C4—1422no—
524C22×C4—1422no—
525C22×C4—1422no—
526C22×C4—1421no—
527C22×C4—1421no—
528C22×C4—1421no—
529C22×C4—1421no—
530C22×C4—1421no—
531C22×C4—1421no—
532C22×C4—1421no—
533C22×C4—1421no—
534C22×C4—1422no—
535C22×C4—1422no—
536C22×C4—1422no—
537C22×C4—1422no—
538C22×C4—1428no—
539C22×C4—1428no—
540C22×C4—1428no—
541C22×C4—1428no—
542C22×C4C2×C4×D7112yes—
543C22×C4C2×C4×D7111yescharacteristic
544C22×C4D4×D7112yes—
545C22×C4D4×D7112yes—
546C22×C4D4×D7112yes—
547C22×C4C2×C22⋊D7112yes—
548C22×C4#1176586412yes—
549C22×C4#1176586512yes—
550C22×C4C23×D7111yescharacteristic
551M16—28no—
552M16—44no—
553M16—2844no—
554M16—14216no—
555M16—1428no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—714no—
562C2×C8—14216no—
563C2×C8—1422no—
564C2×C8—1422no—
565C2×C8—1422no—
566C2×C8—1422no—
567C2×C8—1422no—
568C2×C8C2×C22⋊D7114yescomplemented
569C4⋊C4—1424no—
570C4⋊C4—1424no—
571C22⋊C4—1424no—
572C22⋊C4—1424no—
573C22⋊C4—1424no—
574C22⋊C4—1424no—
575C42—1422no—
576C42—1422no—
577C42—1424no—
578C23—22no—
579C23—22no—
580C23—28no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—48no—
588C23—48no—
589C23—44no—
590C23—44no—
591C23—2848no—
592C23—2848no—
593C23—2844no—
594C23—712no—
595C23—714no—
596C23—712no—
597C23—1428no—
598C23—1428no—
599C23—1421no—
600C23—1421no—
601C23—1422no—
602C23—1422no—
603C23—1421no—
604C23—1421no—
605C23—1422no—
606C23C22⋊C4×D7112yes—
607C23(C22⋊D71)⋊C412yes—
608C23C4×C22⋊D7112yes—
609C23M16×D7114yescomplemented
610C23C22×C4×D7111yescharacteristic
611D4—14216no—
612D4—14216no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—44no—
617C2×C4—48no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—2844no—
623C2×C4—712no—
624C2×C4—712no—
625C2×C4—714no—
626C2×C4—1422no—
627C2×C4—1424no—
628C2×C4—1428no—
629C2×C4—1428no—
630C2×C4—1422no—
631C2×C4—1421no—
632C2×C4—1421no—
633C2×C4—1421no—
634C2×C4—1421no—
635C2×C4—1422no—
636C2×C4—1428no—
637C2×C4—1428no—
638C2×C4—1422no—
639C2×C4—1422no—
640C2×C4—1422no—
641C2×C4—1422no—
642C2×C4—1422no—
643C2×C4—1422no—
644C2×C4—1422no—
645C2×C4—1422no—
646C2×C4C22⋊C4×D7112yes—
647C2×C4(C22⋊D71)⋊C412yes—
648C2×C4C4×C22⋊D7112yes—
649C2×C4#1455609614yes—
650C2×C4#1455609914yes—
651C2×C4#1455610114yes—
652C2×C4#1455611014yes—
653C2×C4C2×D4×D7111yescharacteristic
654C2×C4C2×D4×D7111yescharacteristic
655C2×C4C2×D4×D7111yescharacteristic
656C2×C4C22×C22⋊D7111yescharacteristic
657C2×C4C2×#1176586411yescharacteristic
658C2×C4C2×#1176586511yescharacteristic
659C8—24no—
660C8—42no—
661C8—2842no—
662C8—1424no—
663C22—22no—
664C22—22no—
665C22—24no—
666C22—24no—
667C22—24no—
668C22—24no—
669C22—24no—
670C22—416no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—28416no—
676C22—2842no—
677C22—2842no—
678C22—714no—
679C22—1422no—
680C22—1422no—
681C22—1422no—
682C22—1422no—
683C22—1422no—
684C22—1424no—
685C22—1424no—
686C22#1798587514yes—
687C22C2×C22⋊C4×D7111yescharacteristic
688C22C2×(C22⋊D71)⋊C411yescharacteristic
689C22C2×C4×C22⋊D7111yescharacteristic
690C22C2×M16×D7112yes—
691C22#1798676512yes—
692C4—42no—
693C4—2842no—
694C4—1422no—
695C4—1422no—
696C4—1424no—
697C4#1798587514yes—
698C4C2×#1455609611yescharacteristic
699C4C2×#1455609911yescharacteristic
700C4C2×#1455610111yescharacteristic
701C4C2×#1455611011yescharacteristic
702C2—24no—
703C2—44no—
704C2—2842no—
705C2—1424no—
706C2C2×#1798587511yescharacteristic
707C2#407×D7111yescharacteristic
708C2#2259678311yescharacteristic
709C2#2259707212yes—
710C2M16×C22⋊D7112yes—
subgroupG/H
center, FrattiniC22×C4C23×D71
commutator, socleC23×C71C23×C4
FittingC2×#407×C71C2
prime radicalC23×C22⋊D71C4
cosocleC22×C4×C71C24
hypercenterC2×#407D71
hypocenterC71#20898
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C22×M16×D71C2semidirect
3. C2×#17985963C2semidirect
4. C2×#17985962C2semidirect
5. #22588634C2semidirect
6. #22588629C2semidirect
7. #22588033C2semidirect
8. #22588033C2semidirect
9. C2×#407×C71C2semidirect
14. C22×#11765848C22semidirect
18. C22×C8×D71C22semidirect
31. C2×C22⋊(C71⋊C8)C22semidirect
32. C2×(C2×D71)⋊C8C22semidirect
33. C2×(C2×D71)⋊C8C22semidirect
34. #17985753C22semidirect
35. #17985753C22semidirect
40. C2×C22⋊C8×C71C22semidirect
64. C2×#11765849D4semidirect
112. C2×M16×C71D4semidirect
129. C2×C22⋊D71M16semidirect
171. C2×C71⋊C8C2×D4semidirect
221. C2×C8×C71C2×D4semidirect
238. C23×C71C2×M16semidirect
292. C2×Dic71C2×M16semidirect
335. C2×D71#407semidirect
360. C2×#407D71semidirect
365. C71#20898semidirect
394. C2×C22⋊C8C2×D71semidirect
441. C2×M16C22⋊D71semidirect
568. C2×C8C2×C22⋊D71semidirect
609. C23M16×D71semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D712
C22×C4×C22⋊D712
C2×#179859632
C2×#179859622
#225886342
#225886292
#225880332
C2×#407×C712
#2089871