Finite Group Databasebeta

← C2×#22598261 #32865228

Subgroups — C2×#22598261 #32865228

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×#17986506C211yesmaximal, characteristic
2C22×C4⋊C4×D71C211yesmaximal, characteristic, complemented
3#22598261C2116yesmaximal, direct product factor
4C2×#17986333C212yesmaximal, complemented
5C2×#17986316C212yesmaximal, complemented
6C2×#17986328C212yesmaximal, complemented
7C2×#17986311C212yesmaximal, complemented
8C2×#17986041C211yesmaximal, characteristic, complemented
9C2×#17986039C211yesmaximal, characteristic, complemented
10C2×#17986000C211yesmaximal, characteristic, complemented
11C2×#17985962C211yesmaximal, characteristic, complemented
12C2×#417×C71C211yesmaximal, characteristic, complemented
13C23×C4×D71—21no—
14C23×C4×D71C2211yescharacteristic
15C22×#11765849C2211yescharacteristic
16#17986506—24no—
17#17986506C2218yes—
18C2×#14556109—21no—
19C2×#14556104C2211yescharacteristic
20C2×#14556104C2211yescharacteristic
21C2×#14556099C2211yescharacteristic
22C2×#14556099C2211yescharacteristic
23C2×#14556096—21no—
24C2×C4×C22⋊D71—21no—
25C2×C4×C22⋊D71—21no—
26C2×#14556087C2211yescharacteristic
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#17986333C22116yescomplemented
36#17986328C22116yescomplemented
37#17986316C22116yescomplemented
38#17986311C22116yescomplemented
39#17986041C2218yescomplemented
40#17986039C2218yescomplemented
41C2×#14556062C2212yescomplemented
42C2×#14556061C2212yescomplemented
43C2×#14556060C2212yescomplemented
44C2×#14556059C2212yescomplemented
45#17986000C2218yescomplemented
46C2×#14556052C2212yescomplemented
47C2×#14556049C2212yescomplemented
48#17985962C2218yescomplemented
49C2×(C2×D71)⋊C8C2212yes—
50C2×(C2×D71)⋊C8C2212yes—
51C22×#41×C71C2211yescharacteristic
52C22×M16×C71C2211yescharacteristic
53C22×C4⋊C4×C71C2211yescharacteristic
54#417×C71C2218yescomplemented
55C2×#103×C71C2212yescomplemented
56C2×#102×C71C2212yescomplemented
57C24×D71D411yescharacteristic
58C22×C22⋊D71—21no—
59C22×C22⋊D71—21no—
60C23×Dic71—21no—
61C23×Dic71D411yescharacteristic
62C22×C4×D71—22no—
63C22×C4×D71—22no—
64C22×C4×D71—28no—
65C22×C4×D71—24no—
66C22×C4×D71—24no—
67C22×C4×D71—48no—
68C22×C4×D71D411yescharacteristic
69C22×C4×D71D411yescharacteristic
70C22×C4×D71D414yes—
71C22×C4×D71C2311yescharacteristic
72C22×C4×D71C2311yescharacteristic
73C22×C4×D71C2314yes—
74C2×#11765849—24no—
75C2×#11765849C2314yes—
76C22×C71⋊C8C2312yes—
77#14556109—28no—
78#14556104—22no—
79#14556104—22no—
80#14556104C2314yes—
81#14556104C2314yes—
82#14556099—22no—
83#14556099—22no—
84#14556099C2314yes—
85#14556099C2314yes—
86#14556096—28no—
87C4×C22⋊D71—28no—
88C4×C22⋊D71—28no—
89#14556087—22no—
90#14556087C2314yes—
91C2×C4⋊Dic71—21no—
92C2×C4⋊Dic71—22no—
93C2×C4⋊Dic71C2312yes—
94C2×C4⋊Dic71C2314yes—
95C2×C4⋊Dic71C2311yescharacteristic
96C2×C4⋊Dic71C2311yescharacteristic
97C2×Dic71⋊C4—22no—
98C2×Dic71⋊C4—22no—
99C2×Dic71⋊C4—28no—
100C2×Dic71⋊C4—21no—
101C2×Dic71⋊C4—21no—
102C4⋊C4×D71—24no—
103C4⋊C4×D71—24no—
104C4⋊C4×D71—28no—
105C4⋊C4×D71—28no—
106C4⋊C4×D71C2318yes—
107C4⋊C4×D71C2318yes—
108C2×C22⋊Dic71—21no—
109C2×C22⋊Dic71—21no—
110C2×C22⋊Dic71—21no—
111C2×(C2×D71)⋊C4—21no—
112C2×(C2×D71)⋊C4—21no—
113C2×C4×Dic71—21no—
114#14556062C2318yescomplemented
115#14556061C2318yescomplemented
116#14556060C2318yescomplemented
117#14556059C2318yescomplemented
118#14556052C2318yescomplemented
119#14556049C2318yescomplemented
120(C2×D71)⋊C8C2318yes—
121(C2×D71)⋊C8C2318yes—
122C2×#41×C71—22no—
123C2×#41×C71—24no—
124C2×#41×C71—24no—
125C2×#41×C71C2314yes—
126C22×Q8×C71C2311yescharacteristic
127C22×D4×C71—21no—
128C22×D4×C71C2311yescharacteristic
129C23×C4×C71—21no—
130C23×C4×C71—21no—
131C23×C4×C71C2311yescharacteristic
132C2×M16×C71—24no—
133C2×M16×C71C2314yes—
134C22×C8×C71C2312yes—
135C2×C4⋊C4×C71—21no—
136C2×C4⋊C4×C71—22no—
137C2×C4⋊C4×C71C2312yes—
138C2×C4⋊C4×C71C2314yes—
139#103×C71C2318yescomplemented
140#102×C71C2318yescomplemented
141C23×D71—24no—
142C23×D71—24no—
143C23×D71—24no—
144C23×D71C2×D414yes—
145C23×D71C2×D411yescharacteristic
146C23×D71C2×D411yescharacteristic
147C2×C22⋊D71—24no—
148C2×C22⋊D71—24no—
149C2×C22⋊D71—44no—
150C2×C22⋊D71—44no—
151C22×Dic71—24no—
152C22×Dic71—24no—
153C22×Dic71—22no—
154C22×Dic71—21no—
155C22×Dic71—21no—
156C22×Dic71—44no—
157C22×Dic71C2×D411yescharacteristic
158C22×Dic71C2×D411yescharacteristic
159C22×Dic71C2×D414yes—
160C2×C4×D71—24no—
161C2×C4×D71—24no—
162C2×C4×D71—216no—
163C2×C4×D71—22no—
164C2×C4×D71—22no—
165C2×C4×D71—28no—
166C2×C4×D71—22no—
167C2×C4×D71—22no—
168C2×C4×D71—28no—
169C2×C4×D71—28no—
170C2×C4×D71—28no—
171C2×C4×D71—48no—
172C2×C4×D71—432no—
173C2×C4×D71—48no—
174C2×C4×D71C2×D414yes—
175C2×C4×D71C2×D414yes—
176C2×C4×D71C2×D412yes—
177C2×C4×D71C2×D412yes—
178C2×C4×D71C2412yes—
179C2×C4×D71C2412yes—
180#11765849—28no—
181C2×C71⋊C8—24no—
182C2×C71⋊C8C2414yes—
183C4⋊Dic71—24no—
184C4⋊Dic71—22no—
185C4⋊Dic71—21no—
186C4⋊Dic71—21no—
187C4⋊Dic71C2414yes—
188C4⋊Dic71C2412yes—
189C4⋊Dic71C2412yes—
190Dic71⋊C4—28no—
191Dic71⋊C4—28no—
192Dic71⋊C4—24no—
193Dic71⋊C4—24no—
194C22⋊Dic71—24no—
195C22⋊Dic71—24no—
196C22⋊Dic71—24no—
197(C2×D71)⋊C4—24no—
198(C2×D71)⋊C4—24no—
199C4×Dic71—24no—
200C24×C71—21no—
201C24×C71C2×D411yescharacteristic
202#41×C71—28no—
203#41×C71—28no—
204#41×C71—48no—
205C2×Q8×C71—21no—
206C2×Q8×C71—22no—
207C2×Q8×C71—22no—
208C2×Q8×C71C2412yes—
209C2×D4×C71—24no—
210C2×D4×C71—21no—
211C2×D4×C71—22no—
212C2×D4×C71—22no—
213C2×D4×C71—44no—
214C2×D4×C71C2412yes—
215C22×C4×C71—24no—
216C22×C4×C71—22no—
217C22×C4×C71—21no—
218C22×C4×C71—24no—
219C22×C4×C71—44no—
220C22×C4×C71—44no—
221C22×C4×C71C2×D411yescharacteristic
222C22×C4×C71C2×D412yes—
223C22×C4×C71#4114yes—
224C22×C4×C71#4114yes—
225C22×C4×C71C2411yescharacteristic
226C22×C4×C71C2412yes—
227M16×C71—28no—
228C2×C8×C71—24no—
229C2×C8×C71C2414yes—
230C4⋊C4×C71—24no—
231C4⋊C4×C71—22no—
232C4⋊C4×C71C2414yes—
233C23×C71—22no—
234C23×C71—22no—
235C23×C71—22no—
236C23×C71—42no—
237C23×C71—42no—
238C23×C71—42no—
239C23×C71#12314yes—
240C23×C71C22×D412yes—
241C23×C71C22×D411yescharacteristic
242C22×D71—232no—
243C22×D71—28no—
244C22×D71—22no—
245C22×D71—22no—
246C22×D71—22no—
247C22×D71—22no—
248C22×D71—28no—
249C22×D71—28no—
250C22×D71AGL(1,ℤ/8)14yes—
251C22×D71#13714yes—
252C22×D71C22×D412yes—
253C22×D71C22×D412yes—
254Q8×C71—22no—
255Q8×C71—22no—
256Q8×C71—42no—
257D4×C71—22no—
258D4×C71—22no—
259D4×C71—48no—
260D4×C71—42no—
261C2×C4×C71—24no—
262C2×C4×C71—22no—
263C2×C4×C71—48no—
264C2×C4×C71—42no—
265C2×C4×C71—44no—
266C2×C4×C71—48no—
267C2×C4×C71#12314yes—
268C2×C4×C71#12318yes—
269C2×C4×C71C22×D412yes—
270C2×C4×C71C22×D411yescharacteristic
271C2×C4×C71C2×#4112yes—
272C2×C4×C71C2×#4114yes—
273C2×C4×C71C2×#4112yes—
274C2×C4×C71C2×#4114yes—
275C2×C4×C71C2511yescharacteristic
276C22⋊D71—48no—
277C22⋊D71—48no—
278C2×Dic71—28no—
279C2×Dic71—22no—
280C2×Dic71—22no—
281C2×Dic71—22no—
282C2×Dic71—22no—
283C2×Dic71—24no—
284C2×Dic71—48no—
285C2×Dic71—44no—
286C2×Dic71—42no—
287C2×Dic71—42no—
288C2×Dic71C22×D412yes—
289C2×Dic71C22×D412yes—
290C4×D71—28no—
291C4×D71—28no—
292C4×D71—24no—
293C4×D71—24no—
294C4×D71—22no—
295C4×D71—22no—
296C4×D71—22no—
297C4×D71—22no—
298C4×D71—416no—
299C4×D71—416no—
300C8×C71—24no—
301C71⋊C8—24no—
302C22×C71—28no—
303C22×C71—22no—
304C22×C71—22no—
305C22×C71—42no—
306C22×C71—42no—
307C22×C71—42no—
308C22×C71—84no—
309C22×C71C2×#12314yes—
310C22×C71C2×#12312yes—
311C22×C71C2×AGL(1,ℤ/8)12yes—
312C22×C71C2×#13712yes—
313C22×C71C23×D411yescharacteristic
314C2×D71—232no—
315C2×D71—28no—
316C2×D71—28no—
317C2×D71—22no—
318C2×D71—22no—
319C2×D71—22no—
320C2×D71—22no—
321C2×D71C2×AGL(1,ℤ/8)14yes—
322C2×D71C2×#13714yes—
323C4×C71—42no—
324C4×C71—44no—
325C4×C71C2×#12314yes—
326C4×C71C2×#12312yes—
327C4×C71C22×#4111yescharacteristic
328C4×C71C22×#4111yescharacteristic
329Dic71—22no—
330Dic71—22no—
331Dic71—44no—
332Dic71—42no—
333Dic71—42no—
334C2×#3092—711nomaximal, Sylow
335C2×C71—24no—
336C2×C71—82no—
337C2×C71#309214yescomplemented
338C2×C71C22×#12311yescharacteristic
339C2×C71C22×AGL(1,ℤ/8)11yescharacteristic
340C2×C71C22×#13711yescharacteristic
341D71—24no—
342D71—24no—
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×#428—711no—
352C2×#417—711no—
353C2×#417D7111yescharacteristic, complemented
354C2×#407—711no—
355C71C2×#309211yescharacteristic, complemented, Sylow
356C22×#41C2×D7111yescharacteristic
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×#117—711no—
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#428—718no—
387C2×#107—712no—
388C2×#107—712no—
389C2×#106—712no—
390C2×#106—712no—
391#417—718no—
392#417C2×D7118yescomplemented
393C2×#103—712no—
394C2×#103C2×D7112yescomplemented
395C2×#102—712no—
396C2×#102C2×D7112yescomplemented
397#407—718no—
398C2×C22⋊C8—712no—
399C2×C22⋊C8—712no—
400C25—711no—
401C2×#41—22no—
402C2×#41—24no—
403C2×#41—24no—
404C2×#41C22×D7114yes—
405C22×Q8C22×D7111yescharacteristic
406C22×D4—21no—
407C22×D4—1421no—
408C22×D4—1421no—
409C22×D4C22×D7111yescharacteristic
410C23×C4—21no—
411C23×C4—21no—
412C23×C4—2848no—
413C23×C4—711no—
414C23×C4—711no—
415C23×C4—711no—
416C23×C4—714no—
417C23×C4—711no—
418C23×C4—711no—
419C23×C4—714no—
420C23×C4—1428no—
421C23×C4—1422no—
422C23×C4—1422no—
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—714no—
446#117—1422no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—712no—
450C2×C4⋊C4—714no—
451C2×C4⋊C4—711no—
452C2×C4⋊C4—711no—
453C2×C4⋊C4—718no—
454C2×C4⋊C4—718no—
455C2×C4⋊C4—1428no—
456C2×C4⋊C4—1428no—
457C2×C4⋊C4—1424no—
458C2×C4⋊C4—1424no—
459C2×C4⋊C4—1428no—
460C2×C4⋊C4—1422no—
461C2×C4⋊C4—1422no—
462C2×C4⋊C4—1421no—
463C2×C4⋊C4—1421no—
464C2×C4⋊C4—1422no—
465C2×C4⋊C4—1421no—
466C2×C4⋊C4C22×D7112yes—
467C2×C4⋊C4C22×D7114yes—
468C2×C22⋊C4—1421no—
469C2×C22⋊C4—1421no—
470C2×C22⋊C4—1421no—
471C2×C22⋊C4—1421no—
472C2×C22⋊C4—1421no—
473C2×C42—1421no—
474#107—718no—
475#107—718no—
476#106—718no—
477#106—718no—
478#103—718no—
479#103C22×D7118yescomplemented
480#102—718no—
481#102C22×D7118yescomplemented
482C22⋊C8—718no—
483C22⋊C8—718no—
484C24—21no—
485C24—711no—
486C24—711no—
487C24—714no—
488C24—1424no—
489C24—1424no—
490C24—1424no—
491C24D4×D7111yescharacteristic
492#41—28no—
493#41—28no—
494#41—48no—
495C2×Q8—21no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8C23×D7112yes—
499C2×D4—24no—
500C2×D4—21no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—44no—
504C2×D4—2844no—
505C2×D4—2844no—
506C2×D4—1424no—
507C2×D4—1424no—
508C2×D4C23×D7112yes—
509C22×C4—24no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—2848no—
516C22×C4—28432no—
517C22×C4—2848no—
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—1421no—
533C22×C4—1422no—
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#1176586414yes—
547C22×C4#1176586514yes—
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—714no—
559C4⋊C4—712no—
560C4⋊C4—712no—
561C4⋊C4—1428no—
562C4⋊C4—1428no—
563C4⋊C4—1424no—
564C4⋊C4—1424no—
565C4⋊C4—1424no—
566C4⋊C4—1422no—
567C4⋊C4—1421no—
568C4⋊C4—1421no—
569C4⋊C4C23×D7114yes—
570C22⋊C4—1424no—
571C22⋊C4—1424no—
572C22⋊C4—1424no—
573C22⋊C4—1424no—
574C22⋊C4—1424no—
575C42—1424no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—712no—
583C23—712no—
584C23—714no—
585C23—714no—
586C23—1428no—
587C23—1428no—
588C23—14232no—
589C23—1428no—
590C23—1422no—
591C23—1422no—
592C23—1422no—
593C23—1422no—
594C23#1455611014yes—
595C23C2×D4×D7112yes—
596C23C2×D4×D7111yescharacteristic
597Q8—22no—
598Q8—22no—
599Q8—42no—
600D4—22no—
601D4—22no—
602D4—48no—
603D4—42no—
604D4—2848no—
605D4—2848no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—48no—
609C2×C4—42no—
610C2×C4—44no—
611C2×C4—48no—
612C2×C4—28416no—
613C2×C4—28416no—
614C2×C4—2848no—
615C2×C4—2844no—
616C2×C4—2842no—
617C2×C4—2842no—
618C2×C4—712no—
619C2×C4—712no—
620C2×C4—1422no—
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#1455611014yes—
635C2×C4#1455611018yes—
636C2×C4C2×D4×D7112yes—
637C2×C4C2×D4×D7111yescharacteristic
638C2×C4C2×#1176586412yes—
639C2×C4C2×#1176586414yes—
640C2×C4C2×#1176586512yes—
641C2×C4C2×#1176586514yes—
642C2×C4C24×D7111yescharacteristic
643C8—24no—
644C8—1424no—
645C22—22no—
646C22—22no—
647C22—28no—
648C22—42no—
649C22—42no—
650C22—42no—
651C22—84no—
652C22—714no—
653C22—714no—
654C22—14232no—
655C22—1422no—
656C22—1422no—
657C22—1422no—
658C22—1422no—
659C22—1428no—
660C22—1428no—
661C22C2×#1455611014yes—
662C22C2×#1455611012yes—
663C22AGL(1,ℤ/8)×D7112yes—
664C22#137×D7112yes—
665C22C22×D4×D7111yescharacteristic
666C4—44no—
667C4—42no—
668C4—2844no—
669C4—2842no—
670C4—2842no—
671C4—1422no—
672C4—1422no—
673C4C2×#1455611014yes—
674C4C2×#1455611012yes—
675C4C22×#1176586411yescharacteristic
676C4C22×#1176586511yescharacteristic
677C2—24no—
678C2—82no—
679C2—1424no—
680C2—1424no—
681C2#2259826114yesdirect product factor
682C2C22×#1455611011yescharacteristic
683C2C2×AGL(1,ℤ/8)×D7111yescharacteristic
684C2C2×#137×D7111yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#417×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986506C2
hypercenterC2×#417D71
hypocenterC71C2×#3092
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D71C2semidirect
3. #22598261C2direct (N × H)
4. C2×#17986333C2semidirect
5. C2×#17986316C2semidirect
6. C2×#17986328C2semidirect
7. C2×#17986311C2semidirect
8. C2×#17986041C2semidirect
9. C2×#17986039C2semidirect
10. C2×#17986000C2semidirect
11. C2×#17985962C2semidirect
12. C2×#417×C71C2semidirect
34. C2×C4⋊C4×D71C22semidirect
35. #17986333C22semidirect
36. #17986328C22semidirect
37. #17986316C22semidirect
38. #17986311C22semidirect
39. #17986041C22semidirect
40. #17986039C22semidirect
41. C2×#14556062C22semidirect
42. C2×#14556061C22semidirect
43. C2×#14556060C22semidirect
44. C2×#14556059C22semidirect
45. #17986000C22semidirect
46. C2×#14556052C22semidirect
47. C2×#14556049C22semidirect
48. #17985962C22semidirect
54. #417×C71C22semidirect
55. C2×#103×C71C22semidirect
56. C2×#102×C71C22semidirect
114. #14556062C23semidirect
115. #14556061C23semidirect
116. #14556060C23semidirect
117. #14556059C23semidirect
118. #14556052C23semidirect
119. #14556049C23semidirect
139. #103×C71C23semidirect
140. #102×C71C23semidirect
337. C2×C71#3092semidirect
353. C2×#417D71semidirect
355. C71C2×#3092semidirect
392. #417C2×D71semidirect
394. C2×#103C2×D71semidirect
396. C2×#102C2×D71semidirect
479. #103C22×D71semidirect
481. #102C22×D71semidirect
681. C2#22598261direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179865062
C22×C4⋊C4×D712
#225982612
C2×#179863332
C2×#179863162
C2×#179863282
C2×#179863112
C2×#179860412
C2×#179860392
C2×#179860002
C2×#179859622
C2×#417×C712
C2×#309271