Finite Group Databasebeta

← C2×#22598266 #32865233

Subgroups — C2×#22598266 #32865233

Order 18176.

2650 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986511C211yesmaximal, characteristic
2C22×C4⋊C4×D71C211yesmaximal, characteristic, complemented
3#22598266C2116yesmaximal, direct product factor
4C2×#17986336C212yesmaximal, complemented
5C2×#17986319C212yesmaximal, complemented
6C2×#17986331C212yesmaximal, complemented
7C2×#17986314C212yesmaximal, complemented
8C2×#17986042C211yesmaximal, characteristic, complemented
9C2×#17986001C211yesmaximal, characteristic, complemented
10C2×#17985998C211yesmaximal, characteristic, complemented
11C2×#17985962C211yesmaximal, characteristic, complemented
12C2×#428×C71C211yesmaximal, characteristic, complemented
13C22×#11765865C2211yescharacteristic
14C23×C4×D71—21no—
15C23×C4×D71C2211yescharacteristic
16C22×#11765849C2211yescharacteristic
17#17986511—24no—
18#17986511C2218yes—
19C2×#14556112—21no—
20C2×#14556108C2211yescharacteristic
21C2×#14556108C2211yescharacteristic
22C2×#14556103C2211yescharacteristic
23C2×#14556103C2211yescharacteristic
24C2×#14556098—21no—
25C2×C4×D284—21no—
26C2×C4×D284—21no—
27C22×C4⋊Dic71C2211yescharacteristic
28C22×Dic71⋊C4—21no—
29C2×C4⋊C4×D71—21no—
30C2×C4⋊C4×D71—21no—
31C2×C4⋊C4×D71—24no—
32C2×C4⋊C4×D71C2212yes—
33C2×C4⋊C4×D71C2212yes—
34C2×C4⋊C4×D71C2218yescomplemented
35#17986336C22116yescomplemented
36#17986331C22116yescomplemented
37#17986319C22116yescomplemented
38#17986314C22116yescomplemented
39#17986042C2218yescomplemented
40C2×#14556061C2212yescomplemented
41C2×#14556059C2212yescomplemented
42#17986001C2218yescomplemented
43#17985998C2218yescomplemented
44C2×#14556053C2212yescomplemented
45C2×#14556051C2212yescomplemented
46C2×#14556050C2212yescomplemented
47C2×#14556048C2212yescomplemented
48#17985962C2218yescomplemented
49C2×(C2×D71)⋊C8C2212yes—
50C2×(C2×D71)⋊C8C2212yes—
51C22×M16×C71C2211yescharacteristic
52C2×#117×C71C2211yescharacteristic
53C22×C4⋊C4×C71C2211yescharacteristic
54#428×C71C2218yescomplemented
55C2×#107×C71C2212yescomplemented
56C2×#106×C71C2212yescomplemented
57C24×D71D411yescharacteristic
58C2×#11765865—22no—
59C2×#11765865—24no—
60C2×#11765865—24no—
61C2×#11765865C2314yes—
62C22×Dic142C2311yescharacteristic
63C22×D284—21no—
64C22×D284—21no—
65C22×D284C2311yescharacteristic
66C22×C22⋊D71—21no—
67C23×Dic71—21no—
68C23×Dic71D411yescharacteristic
69C22×C4×D71—22no—
70C22×C4×D71—22no—
71C22×C4×D71—28no—
72C22×C4×D71—21no—
73C22×C4×D71—24no—
74C22×C4×D71—24no—
75C22×C4×D71—48no—
76C22×C4×D71D411yescharacteristic
77C22×C4×D71D411yescharacteristic
78C22×C4×D71D414yes—
79C22×C4×D71C2311yescharacteristic
80C22×C4×D71C2311yescharacteristic
81C22×C4×D71C2314yes—
82C2×#11765849—24no—
83C2×#11765849C2314yes—
84C22×C71⋊C8C2312yes—
85#14556112—28no—
86#14556108—22no—
87#14556108—22no—
88#14556108C2314yes—
89#14556108C2314yes—
90#14556103—22no—
91#14556103—22no—
92#14556103C2314yes—
93#14556103C2314yes—
94#14556098—28no—
95C4×D284—28no—
96C4×D284—28no—
97C2×C4⋊Dic71—21no—
98C2×C4⋊Dic71—21no—
99C2×C4⋊Dic71—21no—
100C2×C4⋊Dic71—22no—
101C2×C4⋊Dic71C2312yes—
102C2×C4⋊Dic71C2314yes—
103C2×Dic71⋊C4—22no—
104C2×Dic71⋊C4—22no—
105C2×Dic71⋊C4—28no—
106C4⋊C4×D71—24no—
107C4⋊C4×D71—24no—
108C4⋊C4×D71—28no—
109C4⋊C4×D71—28no—
110C4⋊C4×D71C2318yes—
111C4⋊C4×D71C2318yes—
112C2×(C2×D71)⋊C4—21no—
113C2×(C2×D71)⋊C4—21no—
114C2×(C2×D71)⋊C4—21no—
115C2×(C2×D71)⋊C4—21no—
116#14556061C2318yescomplemented
117#14556059C2318yescomplemented
118#14556053C2318yescomplemented
119#14556051C2318yescomplemented
120#14556050C2318yescomplemented
121#14556048C2318yescomplemented
122(C2×D71)⋊C8C2318yes—
123(C2×D71)⋊C8C2318yes—
124C23×C4×C71—21no—
125C23×C4×C71C2311yescharacteristic
126C2×M16×C71—24no—
127C2×M16×C71C2314yes—
128C22×C8×C71C2312yes—
129#117×C71—22no—
130#117×C71C2314yes—
131C2×C4⋊C4×C71—21no—
132C2×C4⋊C4×C71—22no—
133C2×C4⋊C4×C71C2311yescharacteristic
134C2×C4⋊C4×C71C2312yes—
135C2×C4⋊C4×C71C2311yescharacteristic
136C2×C4⋊C4×C71C2314yes—
137C2×C22⋊C4×C71—21no—
138C2×C42×C71—21no—
139#107×C71C2318yescomplemented
140#106×C71C2318yescomplemented
141C23×D71—24no—
142C23×D71—24no—
143C23×D71—24no—
144C23×D71—21no—
145C23×D71C2×D414yes—
146C23×D71C2×D411yescharacteristic
147C23×D71C2×D411yescharacteristic
148#11765865—28no—
149#11765865—28no—
150#11765865—48no—
151C2×Dic142—22no—
152C2×Dic142—22no—
153C2×Dic142—21no—
154C2×Dic142C2412yes—
155C2×D284—22no—
156C2×D284—22no—
157C2×D284—24no—
158C2×D284—24no—
159C2×D284—21no—
160C2×D284—44no—
161C2×D284—44no—
162C2×D284C2412yes—
163C2×C22⋊D71—24no—
164C2×C22⋊D71—44no—
165C22×Dic71—24no—
166C22×Dic71—24no—
167C22×Dic71—22no—
168C22×Dic71—21no—
169C22×Dic71—44no—
170C22×Dic71C2×D411yescharacteristic
171C22×Dic71C2×D411yescharacteristic
172C22×Dic71C2×D414yes—
173C2×C4×D71—24no—
174C2×C4×D71—24no—
175C2×C4×D71—216no—
176C2×C4×D71—22no—
177C2×C4×D71—22no—
178C2×C4×D71—28no—
179C2×C4×D71—22no—
180C2×C4×D71—22no—
181C2×C4×D71—28no—
182C2×C4×D71—28no—
183C2×C4×D71—28no—
184C2×C4×D71—24no—
185C2×C4×D71—48no—
186C2×C4×D71—432no—
187C2×C4×D71—48no—
188C2×C4×D71—44no—
189C2×C4×D71C2×D414yes—
190C2×C4×D71C2×D414yes—
191C2×C4×D71C2×D412yes—
192C2×C4×D71C2×D412yes—
193C2×C4×D71C2412yes—
194C2×C4×D71C2412yes—
195#11765849—28no—
196C2×C71⋊C8—24no—
197C2×C71⋊C8C2414yes—
198C4⋊Dic71—24no—
199C4⋊Dic71—22no—
200C4⋊Dic71—24no—
201C4⋊Dic71—24no—
202C4⋊Dic71C2414yes—
203Dic71⋊C4—28no—
204Dic71⋊C4—28no—
205(C2×D71)⋊C4—24no—
206(C2×D71)⋊C4—24no—
207(C2×D71)⋊C4—24no—
208(C2×D71)⋊C4—24no—
209C24×C71C2×D411yescharacteristic
210C22×C4×C71—24no—
211C22×C4×C71—22no—
212C22×C4×C71—21no—
213C22×C4×C71—21no—
214C22×C4×C71—44no—
215C22×C4×C71C2×D411yescharacteristic
216C22×C4×C71C2×D412yes—
217C22×C4×C71#4114yes—
218C22×C4×C71#4114yes—
219C22×C4×C71C2411yescharacteristic
220C22×C4×C71C2412yes—
221M16×C71—28no—
222C2×C8×C71—24no—
223C2×C8×C71C2414yes—
224C4⋊C4×C71—24no—
225C4⋊C4×C71—22no—
226C4⋊C4×C71—21no—
227C4⋊C4×C71—21no—
228C4⋊C4×C71C2412yes—
229C4⋊C4×C71C2414yes—
230C4⋊C4×C71C2412yes—
231C22⋊C4×C71—24no—
232C42×C71—24no—
233C23×C71—22no—
234C23×C71—22no—
235C23×C71#12314yes—
236C23×C71C22×D412yes—
237C23×C71C22×D411yescharacteristic
238C22×D71—232no—
239C22×D71—28no—
240C22×D71—22no—
241C22×D71—22no—
242C22×D71—22no—
243C22×D71—22no—
244C22×D71—28no—
245C22×D71—28no—
246C22×D71—22no—
247C22×D71—42no—
248C22×D71—42no—
249C22×D71—42no—
250C22×D71AGL(1,ℤ/8)14yes—
251C22×D71#13714yes—
252C22×D71C22×D412yes—
253C22×D71C22×D412yes—
254C2×C4×C71—22no—
255C2×C4×C71—22no—
256C2×C4×C71—24no—
257C2×C4×C71—48no—
258C2×C4×C71—44no—
259C2×C4×C71—42no—
260C2×C4×C71—42no—
261C2×C4×C71#12314yes—
262C2×C4×C71#12318yes—
263C2×C4×C71C22×D412yes—
264C2×C4×C71C22×D411yescharacteristic
265C2×C4×C71C2×#4112yes—
266C2×C4×C71C2×#4114yes—
267C2×C4×C71C2×#4112yes—
268C2×C4×C71C2×#4114yes—
269C2×C4×C71C2511yescharacteristic
270C22⋊D71—48no—
271C2×Dic71—28no—
272C2×Dic71—22no—
273C2×Dic71—22no—
274C2×Dic71—22no—
275C2×Dic71—24no—
276C2×Dic71—48no—
277C2×Dic71—42no—
278C2×Dic71—44no—
279C2×Dic71C22×D412yes—
280C2×Dic71C22×D412yes—
281D284—22no—
282D284—22no—
283D284—48no—
284D284—48no—
285D284—42no—
286C4×D71—24no—
287C4×D71—24no—
288C4×D71—28no—
289C4×D71—28no—
290C4×D71—22no—
291C4×D71—22no—
292C4×D71—22no—
293C4×D71—22no—
294C4×D71—416no—
295C4×D71—416no—
296C4×D71—48no—
297Dic142—22no—
298Dic142—22no—
299Dic142—42no—
300C8×C71—24no—
301C71⋊C8—24no—
302C22×C71—28no—
303C22×C71—22no—
304C22×C71—22no—
305C22×C71C2×#12314yes—
306C22×C71C2×#12312yes—
307C22×C71C2×AGL(1,ℤ/8)12yes—
308C22×C71C2×#13712yes—
309C22×C71C23×D411yescharacteristic
310C2×D71—232no—
311C2×D71—28no—
312C2×D71—28no—
313C2×D71—22no—
314C2×D71—22no—
315C2×D71—22no—
316C2×D71—22no—
317C2×D71—42no—
318C2×D71—42no—
319C2×D71—42no—
320C2×D71—84no—
321C2×D71C2×AGL(1,ℤ/8)14yes—
322C2×D71C2×#13714yes—
323C4×C71—44no—
324C4×C71—42no—
325C4×C71—42no—
326C4×C71C2×#12312yes—
327C4×C71C2×#12314yes—
328C4×C71C22×#4111yescharacteristic
329C4×C71C22×#4111yescharacteristic
330Dic71—22no—
331Dic71—22no—
332Dic71—42no—
333Dic71—44no—
334C2×#3092—711nomaximal, Sylow
335C2×C71—24no—
336C2×C71#309214yescomplemented
337C2×C71C22×#12311yescharacteristic
338C2×C71C22×AGL(1,ℤ/8)11yescharacteristic
339C2×C71C22×#13711yescharacteristic
340D71—24no—
341D71—24no—
342D71—82no—
343C2×#525—711no—
344C23×C4⋊C4—711no—
345#3092—7116no—
346C2×#484—712no—
347C2×#481—712no—
348C2×#483—712no—
349C2×#480—712no—
350C2×#428—711no—
351C2×#428D7111yescharacteristic, complemented
352C2×#417—711no—
353C2×#417—711no—
354C2×#407—711no—
355C71C2×#309211yescharacteristic, complemented, Sylow
356C22×#41—711no—
357C24×C4—711no—
358C24×C4—1421no—
359C22×M16—711no—
360C22×M16C2×D7111yescharacteristic
361#525—718no—
362#525—1424no—
363C2×#123—1421no—
364C2×C22⋊Q8—711no—
365C2×C22⋊Q8—711no—
366C2×#121—711no—
367C2×#121—711no—
368C2×#120—1421no—
369C2×C4×D4—1421no—
370C2×C4×D4—1421no—
371C2×#117C2×D7111yescharacteristic
372C22×C4⋊C4—711no—
373C22×C4⋊C4—712no—
374C22×C4⋊C4—712no—
375C22×C4⋊C4—718no—
376C22×C4⋊C4—1421no—
377C22×C4⋊C4—1421no—
378C22×C4⋊C4—1424no—
379C22×C4⋊C4—1421no—
380C22×C4⋊C4C2×D7111yescharacteristic
381#484—7116no—
382#483—7116no—
383#481—7116no—
384#480—7116no—
385#428—718no—
386#428C2×D7118yescomplemented
387C2×#107—712no—
388C2×#107C2×D7112yescomplemented
389C2×#106—712no—
390C2×#106C2×D7112yescomplemented
391#417—718no—
392#417—718no—
393C2×#103—712no—
394C2×#103—712no—
395C2×#102—712no—
396C2×#102—712no—
397#407—718no—
398C2×C22⋊C8—712no—
399C2×C22⋊C8—712no—
400C25—711no—
401C2×#41—714no—
402C2×#41—1424no—
403C2×#41—1424no—
404C2×#41—1422no—
405C22×Q8—711no—
406C22×D4—711no—
407C22×D4—1421no—
408C22×D4—1421no—
409C22×D4—1421no—
410C23×C4—21no—
411C23×C4—2848no—
412C23×C4—711no—
413C23×C4—711no—
414C23×C4—711no—
415C23×C4—714no—
416C23×C4—711no—
417C23×C4—711no—
418C23×C4—714no—
419C23×C4—1428no—
420C23×C4—1422no—
421C23×C4—1422no—
422C23×C4—1421no—
423C23×C4—1421no—
424C23×C4—1424no—
425C23×C4—1424no—
426C23×C4C22×D7111yescharacteristic
427C2×M16—24no—
428C2×M16—714no—
429C2×M16—1424no—
430C2×M16C22×D7114yes—
431C22×C8—712no—
432C22×C8C22×D7112yes—
433#123—1428no—
434C22⋊Q8—714no—
435C22⋊Q8—714no—
436C22⋊Q8—1422no—
437C22⋊Q8—1422no—
438#121—714no—
439#121—714no—
440#121—1422no—
441#121—1422no—
442#120—1428no—
443C4×D4—1428no—
444C4×D4—1428no—
445#117—22no—
446#117C22×D7114yes—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—712no—
450C2×C4⋊C4—714no—
451C2×C4⋊C4—718no—
452C2×C4⋊C4—718no—
453C2×C4⋊C4—1428no—
454C2×C4⋊C4—1428no—
455C2×C4⋊C4—1424no—
456C2×C4⋊C4—1424no—
457C2×C4⋊C4—1428no—
458C2×C4⋊C4—1422no—
459C2×C4⋊C4—1422no—
460C2×C4⋊C4—1421no—
461C2×C4⋊C4—1421no—
462C2×C4⋊C4—1422no—
463C2×C4⋊C4—1421no—
464C2×C4⋊C4C22×D7112yes—
465C2×C4⋊C4C22×D7114yes—
466C2×C4⋊C4C22×D7111yescharacteristic
467C2×C4⋊C4C22×D7111yescharacteristic
468C2×C22⋊C4—21no—
469C2×C22⋊C4—1421no—
470C2×C22⋊C4—1421no—
471C2×C22⋊C4—1421no—
472C2×C22⋊C4—1421no—
473C2×C42—21no—
474#107—718no—
475#107C22×D7118yescomplemented
476#106—718no—
477#106C22×D7118yescomplemented
478#103—718no—
479#103—718no—
480#102—718no—
481#102—718no—
482C22⋊C8—718no—
483C22⋊C8—718no—
484C24—711no—
485C24—711no—
486C24—714no—
487C24—1424no—
488C24—1424no—
489C24—1421no—
490C24—1424no—
491C24D4×D7111yescharacteristic
492#41—2848no—
493#41—1428no—
494#41—1428no—
495C2×Q8—712no—
496C2×Q8—1422no—
497C2×Q8—1422no—
498C2×Q8—1421no—
499C2×D4—2844no—
500C2×D4—2844no—
501C2×D4—2844no—
502C2×D4—712no—
503C2×D4—1424no—
504C2×D4—1424no—
505C2×D4—1424no—
506C2×D4—1421no—
507C2×D4—1422no—
508C2×D4—1422no—
509C22×C4—24no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—44no—
514C22×C4—2848no—
515C22×C4—28432no—
516C22×C4—2848no—
517C22×C4—2844no—
518C22×C4—2844no—
519C22×C4—714no—
520C22×C4—711no—
521C22×C4—711no—
522C22×C4—714no—
523C22×C4—714no—
524C22×C4—712no—
525C22×C4—712no—
526C22×C4—712no—
527C22×C4—712no—
528C22×C4—1428no—
529C22×C4—1428no—
530C22×C4—1424no—
531C22×C4—1421no—
532C22×C4—1422no—
533C22×C4—1424no—
534C22×C4—1424no—
535C22×C4—1422no—
536C22×C4—1422no—
537C22×C4—1428no—
538C22×C4—1422no—
539C22×C4—1422no—
540C22×C4—1428no—
541C22×C4—1424no—
542C22×C4—1424no—
543C22×C4—14216no—
544C22×C4D4×D7112yes—
545C22×C4D4×D7111yescharacteristic
546C22×C4#1176586514yes—
547C22×C4#1176586614yes—
548C22×C4C23×D7112yes—
549C22×C4C23×D7111yescharacteristic
550M16—28no—
551M16—1428no—
552C2×C8—24no—
553C2×C8—714no—
554C2×C8—1424no—
555C2×C8C23×D7114yes—
556C4⋊C4—24no—
557C4⋊C4—22no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—714no—
561C4⋊C4—1428no—
562C4⋊C4—1428no—
563C4⋊C4—1424no—
564C4⋊C4—1424no—
565C4⋊C4—1424no—
566C4⋊C4—1422no—
567C4⋊C4C23×D7114yes—
568C4⋊C4C23×D7112yes—
569C4⋊C4C23×D7112yes—
570C22⋊C4—24no—
571C22⋊C4—1424no—
572C22⋊C4—1424no—
573C22⋊C4—1424no—
574C22⋊C4—1424no—
575C42—24no—
576C23—22no—
577C23—22no—
578C23—2842no—
579C23—2842no—
580C23—2842no—
581C23—712no—
582C23—712no—
583C23—714no—
584C23—714no—
585C23—1428no—
586C23—1428no—
587C23—14232no—
588C23—1422no—
589C23—1428no—
590C23—1422no—
591C23—1422no—
592C23—1422no—
593C23—1422no—
594C23#1455611314yes—
595C23C2×D4×D7112yes—
596C23C2×D4×D7111yescharacteristic
597Q8—2842no—
598Q8—1422no—
599Q8—1422no—
600D4—2848no—
601D4—2848no—
602D4—2848no—
603D4—2842no—
604D4—1422no—
605D4—1422no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—24no—
609C2×C4—48no—
610C2×C4—44no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—28416no—
614C2×C4—28416no—
615C2×C4—2848no—
616C2×C4—2842no—
617C2×C4—2844no—
618C2×C4—2848no—
619C2×C4—712no—
620C2×C4—712no—
621C2×C4—1422no—
622C2×C4—1424no—
623C2×C4—1428no—
624C2×C4—1422no—
625C2×C4—1422no—
626C2×C4—1422no—
627C2×C4—1422no—
628C2×C4—1422no—
629C2×C4—1422no—
630C2×C4—1428no—
631C2×C4—1428no—
632C2×C4—1424no—
633C2×C4—1424no—
634C2×C4#1455611314yes—
635C2×C4#1455611318yes—
636C2×C4C2×D4×D7112yes—
637C2×C4C2×D4×D7111yescharacteristic
638C2×C4C2×#1176586512yes—
639C2×C4C2×#1176586514yes—
640C2×C4C2×#1176586612yes—
641C2×C4C2×#1176586614yes—
642C2×C4C24×D7111yescharacteristic
643C8—24no—
644C8—1424no—
645C22—22no—
646C22—22no—
647C22—28no—
648C22—2842no—
649C22—2842no—
650C22—2842no—
651C22—5684no—
652C22—714no—
653C22—714no—
654C22—14232no—
655C22—1422no—
656C22—1422no—
657C22—1422no—
658C22—1422no—
659C22—1428no—
660C22—1428no—
661C22C2×#1455611314yes—
662C22C2×#1455611312yes—
663C22AGL(1,ℤ/8)×D7112yes—
664C22#137×D7112yes—
665C22C22×D4×D7111yescharacteristic
666C4—44no—
667C4—42no—
668C4—42no—
669C4—2844no—
670C4—2842no—
671C4—1422no—
672C4—1422no—
673C4C2×#1455611314yes—
674C4C2×#1455611312yes—
675C4C22×#1176586511yescharacteristic
676C4C22×#1176586611yescharacteristic
677C2—24no—
678C2—5682no—
679C2—1424no—
680C2—1424no—
681C2#2259826614yesdirect product factor
682C2C22×#1455611311yescharacteristic
683C2C2×AGL(1,ℤ/8)×D7111yescharacteristic
684C2C2×#137×D7111yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#428×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986511C2
hypercenterC2×#428D71
hypocenterC71C2×#3092
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D71C2semidirect
3. #22598266C2direct (N × H)
4. C2×#17986336C2semidirect
5. C2×#17986319C2semidirect
6. C2×#17986331C2semidirect
7. C2×#17986314C2semidirect
8. C2×#17986042C2semidirect
9. C2×#17986001C2semidirect
10. C2×#17985998C2semidirect
11. C2×#17985962C2semidirect
12. C2×#428×C71C2semidirect
34. C2×C4⋊C4×D71C22semidirect
35. #17986336C22semidirect
36. #17986331C22semidirect
37. #17986319C22semidirect
38. #17986314C22semidirect
39. #17986042C22semidirect
40. C2×#14556061C22semidirect
41. C2×#14556059C22semidirect
42. #17986001C22semidirect
43. #17985998C22semidirect
44. C2×#14556053C22semidirect
45. C2×#14556051C22semidirect
46. C2×#14556050C22semidirect
47. C2×#14556048C22semidirect
48. #17985962C22semidirect
54. #428×C71C22semidirect
55. C2×#107×C71C22semidirect
56. C2×#106×C71C22semidirect
116. #14556061C23semidirect
117. #14556059C23semidirect
118. #14556053C23semidirect
119. #14556051C23semidirect
120. #14556050C23semidirect
121. #14556048C23semidirect
139. #107×C71C23semidirect
140. #106×C71C23semidirect
336. C2×C71#3092semidirect
351. C2×#428D71semidirect
355. C71C2×#3092semidirect
386. #428C2×D71semidirect
388. C2×#107C2×D71semidirect
390. C2×#106C2×D71semidirect
475. #107C22×D71semidirect
477. #106C22×D71semidirect
681. C2#22598266direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179865112
C22×C4⋊C4×D712
#225982662
C2×#179863362
C2×#179863192
C2×#179863312
C2×#179863142
C2×#179860422
C2×#179860012
C2×#179859982
C2×#179859622
C2×#428×C712
C2×#309271