Finite Group Databasebeta

← C2×#22591703 #32165397

Subgroups — C2×#22591703 #32165397

Order 18176.

5566 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Q8×D71C211yesmaximal, characteristic, complemented
2C22×#14556108C211yesmaximal, characteristic, complemented
3C22×#14556104C211yesmaximal, characteristic, complemented
4C22×C4×D284C211yesmaximal, characteristic
5#22591703C2116yesmaximal, direct product factor
6C2×#17985920C212yesmaximal, complemented
7C2×#17985912C212yesmaximal, complemented
8C2×#17985905C211yesmaximal, characteristic, complemented
9C2×#17985877C212yesmaximal
10C2×#17985873C212yesmaximal, complemented
11C2×#17985856C211yesmaximal, characteristic, complemented
12C2×#391×C71C211yesmaximal, characteristic, complemented
13C23×Dic142C2212yes—
14C23×Dic142C2211yescharacteristic
15C22×Q8×D71—28no—
16C22×Q8×D71—28no—
17C22×Q8×D71—28no—
18C22×Q8×D71C2218yescomplemented
19C23×D284C2211yescharacteristic
20C23×C4×D71C2212yes—
21C23×C4×D71C2211yescharacteristic
22C23×C4×D71C2211yescharacteristic
23C2×#14556108—28no—
24C2×#14556108C2218yescomplemented
25C2×#14556104—28no—
26C2×#14556104C2218yescomplemented
27C2×C4×D284—28no—
28C2×C4×D284C2218yes—
29C22×C4⋊Dic71C2212yes—
30C22×C4⋊Dic71C2211yescharacteristic
31C22×C4⋊Dic71C2211yescharacteristic
32C22×Dic71⋊C4C2212yes—
33C22×(C2×D71)⋊C4C2211yescharacteristic
34C22×(C2×D71)⋊C4C2212yes—
35C22×(C2×D71)⋊C4C2212yes—
36C22×(C2×D71)⋊C4C2212yes—
37C22×(C2×D71)⋊C4C2211yescharacteristic
38#17985920C22116yescomplemented
39#17985912C22116yescomplemented
40#17985905C2218yescomplemented
41#17985877C22116yes—
42#17985873C22116yescomplemented
43#17985856C2218yescomplemented
44C2×C71⋊#95C2212yes—
45C2×C71⋊#95C2212yes—
46C2×C71⋊#95C2212yes—
47C23×Q8×C71C2211yescharacteristic
48C22×C4⋊C4×C71C2211yescharacteristic
49C22×C42×C71C2211yescharacteristic
50#391×C71C2218yescomplemented
51C2×#95×C71C2212yes—
52C2×#95×C71C2212yes—
53C24×D71C2311yescharacteristic
54C24×D71C2311yescharacteristic
55C22×Dic142—28no—
56C22×Dic142—28no—
57C22×Dic142—24no—
58C22×Dic142—28no—
59C22×Dic142—24no—
60C22×Dic142D418yescomplemented
61C22×Dic142C2318yes—
62C22×Dic142C2314yes—
63C2×Q8×D71—2128no—
64C2×Q8×D71—232no—
65C2×Q8×D71—232no—
66C2×Q8×D71—232no—
67C22×D284—24no—
68C22×D284—24no—
69C22×D284Q818yescomplemented
70C22×D284C2314yes—
71C23×Dic71C2311yescharacteristic
72C23×Dic71C2312yes—
73C23×Dic71C2312yes—
74C23×Dic71C2311yescharacteristic
75C22×C4×D71—28no—
76C22×C4×D71—28no—
77C22×C4×D71—24no—
78C22×C4×D71—28no—
79C22×C4×D71—24no—
80C22×C4×D71—24no—
81C22×C4×D71—24no—
82C22×C4×D71—24no—
83C22×C4×D71D418yes—
84C22×C4×D71C2318yes—
85C22×C4×D71C2314yes—
86C22×C4×D71C2314yes—
87#14556108—232no—
88#14556104—232no—
89C4×D284—232no—
90C2×C4⋊Dic71—24no—
91C2×C4⋊Dic71—28no—
92C2×C4⋊Dic71—24no—
93C2×C4⋊Dic71C2314yes—
94C2×C4⋊Dic71C2318yes—
95C2×C4⋊Dic71C2314yes—
96C2×Dic71⋊C4—28no—
97C2×Dic71⋊C4C2318yes—
98C2×(C2×D71)⋊C4—24no—
99C2×(C2×D71)⋊C4—28no—
100C2×(C2×D71)⋊C4—24no—
101C2×(C2×D71)⋊C4—28no—
102C2×(C2×D71)⋊C4—28no—
103C2×(C2×D71)⋊C4C2318yes—
104C2×(C2×D71)⋊C4C2314yes—
105C2×(C2×D71)⋊C4C2318yes—
106C2×(C2×D71)⋊C4C2318yes—
107C2×(C2×D71)⋊C4C2314yes—
108C71⋊#95C2318yes—
109C71⋊#95C2318yes—
110C71⋊#95C2318yes—
111C22×Q8×C71—24no—
112C22×Q8×C71—24no—
113C22×Q8×C71D418yescomplemented
114C22×Q8×C71C2314yes—
115C23×C4×C71C2311yescharacteristic
116C23×C4×C71C2312yes—
117C23×C4×C71C2312yes—
118C23×C4×C71C2311yescharacteristic
119C23×C4×C71C2311yescharacteristic
120C2×C4⋊C4×C71—24no—
121C2×C4⋊C4×C71C2314yes—
122C2×C42×C71—24no—
123C2×C42×C71C2314yes—
124#95×C71C2318yes—
125#95×C71C2318yes—
126C23×D71—22no—
127C23×D71—22no—
128C23×D71—22no—
129C23×D71—22no—
130C23×D71—22no—
131C23×D71—22no—
132C23×D71—22no—
133C23×D71—22no—
134C23×D71—22no—
135C23×D71—22no—
136C23×D71C2×D414yes—
137C23×D71C2×Q814yes—
138C23×D71C2×Q814yescomplemented
139C23×D71#4114yes—
140C23×D71C2412yes—
141C23×D71C2412yes—
142C2×Dic142—264no—
143C2×Dic142—232no—
144C2×Dic142—28no—
145C2×Dic142—216no—
146C2×Dic142—28no—
147C2×Dic142—216no—
148C2×Dic142—216no—
149C2×Dic142C2×D4116yescomplemented
150Q8×D71—2256no—
151C2×D284—232no—
152C2×D284—28no—
153C2×D284—28no—
154C2×D284C2×Q8116yescomplemented
155C22×Dic71—24no—
156C22×Dic71—22no—
157C22×Dic71—24no—
158C22×Dic71—22no—
159C22×Dic71—22no—
160C22×Dic71—22no—
161C22×Dic71—22no—
162C22×Dic71—24no—
163C22×Dic71—24no—
164C22×Dic71—24no—
165C22×Dic71C2×D418yes—
166C22×Dic71C2×D414yes—
167C22×Dic71C2412yes—
168C22×Dic71C2414yes—
169C22×Dic71C2414yes—
170C22×Dic71C2412yes—
171C2×C4×D71—264no—
172C2×C4×D71—216no—
173C2×C4×D71—232no—
174C2×C4×D71—28no—
175C2×C4×D71—216no—
176C2×C4×D71—28no—
177C2×C4×D71—216no—
178C2×C4×D71—28no—
179C2×C4×D71—28no—
180C2×C4×D71—28no—
181C2×C4×D71—416no—
182C2×C4×D71C2×D4116yes—
183C4⋊Dic71—28no—
184C4⋊Dic71—28no—
185C4⋊Dic71—216no—
186Dic71⋊C4—216no—
187(C2×D71)⋊C4—28no—
188(C2×D71)⋊C4—216no—
189(C2×D71)⋊C4—216no—
190(C2×D71)⋊C4—28no—
191(C2×D71)⋊C4—216no—
192C24×C71C2411yescharacteristic
193C2×Q8×C71—232no—
194C2×Q8×C71—28no—
195C2×Q8×C71—28no—
196C2×Q8×C71C2×D4116yescomplemented
197C22×C4×C71—24no—
198C22×C4×C71—24no—
199C22×C4×C71—22no—
200C22×C4×C71—22no—
201C22×C4×C71—22no—
202C22×C4×C71—24no—
203C22×C4×C71—24no—
204C22×C4×C71—22no—
205C22×C4×C71—24no—
206C22×C4×C71—22no—
207C22×C4×C71C2×D414yes—
208C22×C4×C71C2×D414yes—
209C22×C4×C71C2×D418yes—
210C22×C4×C71C2×D414yes—
211C22×C4×C71C2×Q814yescomplemented
212C22×C4×C71C2412yes—
213C22×C4×C71C2414yes—
214C22×C4×C71C2414yes—
215C22×C4×C71C2412yes—
216C22×C4×C71C2412yes—
217C4⋊C4×C71—28no—
218C42×C71—28no—
219C23×C71C22×D412yes—
220C23×C71C22×D412yes—
221C23×C71C22×D412yes—
222C23×C71C22×Q812yes—
223C23×C71C2×#4112yes—
224C23×C712−1+412yes—
225C23×C712−1+412yes—
226C23×C71C2511yescharacteristic
227C22×D71—28no—
228C22×D71—28no—
229C22×D71—28no—
230C22×D71—28no—
231C22×D71—28no—
232C22×D71—28no—
233C22×D71—22no—
234C22×D71—22no—
235C22×D71—22no—
236C22×D71—22no—
237C22×D71—28no—
238C22×D71—28no—
239C22×D71—28no—
240C22×D71—22no—
241C22×D71—22no—
242C22×D71—22no—
243C22×D71—22no—
244C22×D71—22no—
245C22×D71—22no—
246C22×D71—44no—
247C22×D71—44no—
248C22×D71—44no—
249C22×D71—44no—
250C22×D71C22⋊Q8116yescomplemented
251C22×D71C22×D414yes—
252C22×D71C22×Q814yes—
253C22×D71C22×Q814yescomplemented
254C22×D71C2×#4114yes—
255Q8×C71—232no—
256C2×C4×C71—216no—
257C2×C4×C71—28no—
258C2×C4×C71—22no—
259C2×C4×C71—24no—
260C2×C4×C71—24no—
261C2×C4×C71—22no—
262C2×C4×C71—22no—
263C2×C4×C71—24no—
264C2×C4×C71—24no—
265C2×C4×C71—22no—
266C2×C4×C71—24no—
267C2×C4×C71—22no—
268C2×C4×C71—44no—
269C2×C4×C71—48no—
270C2×C4×C71#120116yes—
271C2×C4×C71C22×D414yes—
272C2×C4×C71C22×D414yes—
273C2×C4×C71C22×D418yes—
274C2×C4×C71C22×D414yes—
275C2×C4×C71C22×Q814yescomplemented
276C2×Dic71—216no—
277C2×Dic71—28no—
278C2×Dic71—24no—
279C2×Dic71—22no—
280C2×Dic71—22no—
281C2×Dic71—24no—
282C2×Dic71—24no—
283C2×Dic71—22no—
284C2×Dic71—22no—
285C2×Dic71—22no—
286C2×Dic71—24no—
287C2×Dic71—24no—
288C2×Dic71—44no—
289C2×Dic71—48no—
290C2×Dic71C22×D418yes—
291C2×Dic71C22×D414yes—
292D284—232no—
293C4×D71—264no—
294C4×D71—232no—
295C4×D71—416no—
296Dic142—264no—
297Dic142—232no—
298C22×C71C2×#12014yes—
299C22×C71C2×C22⋊Q814yes—
300C22×C71#53614yes—
301C22×C71#54814yes—
302C22×C71#54814yes—
303C22×C71D4×Q814yes—
304C22×C71D4×Q814yes—
305C22×C71C23×D411yescharacteristic
306C22×C71C23×D411yescharacteristic
307C22×C71C23×D411yescharacteristic
308C22×C71C23×Q811yescharacteristic
309C22×C71C22×#4111yescharacteristic
310C22×C71C2×2−1+411yescharacteristic
311C22×C71C2×2−1+411yescharacteristic
312C2×D71—24no—
313C2×D71—232no—
314C2×D71—24no—
315C2×D71—24no—
316C2×D71—24no—
317C2×D71—24no—
318C2×D71—24no—
319C2×D71—24no—
320C2×D71—24no—
321C2×D71—24no—
322C2×D71—42no—
323C2×D71—416no—
324C2×D71—42no—
325C2×D71—42no—
326C2×D71—42no—
327C2×D71C2×C22⋊Q818yescomplemented
328C4×C71—28no—
329C4×C71—24no—
330C4×C71—42no—
331C4×C71—44no—
332C4×C71C2×#12018yes—
333Dic71—24no—
334Dic71—28no—
335Dic71—42no—
336Dic71—44no—
337C2×#2409—711nomaximal, Sylow
338C2×C71#240918yescomplemented
339C2×C71C22×#12011yescharacteristic
340C2×C71C22×C22⋊Q811yescharacteristic
341C2×C71C2×#53611yescharacteristic
342C2×C71C2×#54811yescharacteristic
343C2×C71C2×#54811yescharacteristic
344C2×C71C2×D4×Q811yescharacteristic
345C2×C71C2×D4×Q811yescharacteristic
346D71—28no—
347D71—44no—
348C24×Q8—711no—
349C22×C22⋊Q8—711no—
350C22×C22⋊Q8—711no—
351C22×C4×D4—711no—
352#2409—7116no—
353C2×#395—712no—
354C2×#393—712no—
355C2×#391—711no—
356C2×#391D7111yescharacteristic, complemented
357C2×#386—712no—
358C2×#385—712no—
359C2×#380—711no—
360C71C2×#240911yescharacteristic, complemented, Sylow
361C23×Q8—718no—
362C23×Q8—711no—
363C23×Q8—712no—
364C23×Q8—1428no—
365C23×Q8—1428no—
366C23×Q8—1428no—
367C23×Q8C2×D7111yescharacteristic
368C23×D4—711no—
369C24×C4—711no—
370C24×C4—712no—
371C24×C4—711no—
372C2×C22⋊Q8—718no—
373C2×C22⋊Q8—718no—
374C2×C22⋊Q8—1428no—
375C2×C22⋊Q8—1428no—
376C2×C4×D4—718no—
377C2×C4×D4—1428no—
378C22×C4⋊C4—711no—
379C22×C4⋊C4—712no—
380C22×C4⋊C4—712no—
381C22×C4⋊C4—711no—
382C22×C4⋊C4C2×D7111yescharacteristic
383C22×C22⋊C4—711no—
384C22×C22⋊C4—712no—
385C22×C22⋊C4—712no—
386C22×C22⋊C4—711no—
387C22×C22⋊C4—712no—
388C22×C42C2×D7111yescharacteristic
389#395—7116no—
390#393—7116no—
391#391—718no—
392#391C2×D7118yescomplemented
393#386—7116no—
394#385—7116no—
395#380—718no—
396C2×#95—712no—
397C2×#95—712no—
398C2×#95—712no—
399C2×#95C2×D7112yes—
400C2×#95C2×D7112yes—
401C25—711no—
402C25—711no—
403C22×Q8—24no—
404C22×Q8—24no—
405C22×Q8—718no—
406C22×Q8—714no—
407C22×Q8—718no—
408C22×Q8—1428no—
409C22×Q8—1428no—
410C22×Q8—14232no—
411C22×Q8—14232no—
412C22×Q8—142128no—
413C22×Q8—14232no—
414C22×Q8—1424no—
415C22×Q8—1428no—
416C22×Q8—1424no—
417C22×Q8D28418yescomplemented
418C22×Q8C22×D7114yes—
419C22×D4—718no—
420C22×D4—714no—
421C22×D4—1424no—
422C22×D4—1424no—
423C23×C4—711no—
424C23×C4—712no—
425C23×C4—718no—
426C23×C4—714no—
427C23×C4—712no—
428C23×C4—711no—
429C23×C4—714no—
430C23×C4—718no—
431C23×C4—1428no—
432C23×C4—1428no—
433C23×C4—1424no—
434C23×C4—1424no—
435C23×C4—1424no—
436C23×C4—1424no—
437C23×C4—1428no—
438C23×C4—1424no—
439C23×C4C22×D7112yes—
440C23×C4C22×D7111yescharacteristic
441C23×C4C22×D7112yes—
442C23×C4C22×D7111yescharacteristic
443C23×C4C22×D7111yescharacteristic
444C22⋊Q8—14232no—
445C22⋊Q8—14232no—
446C4×D4—14232no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—714no—
449C2×C4⋊C4—714no—
450C2×C4⋊C4—718no—
451C2×C4⋊C4—718no—
452C2×C4⋊C4—1424no—
453C2×C4⋊C4—1428no—
454C2×C4⋊C4—1428no—
455C2×C4⋊C4—1424no—
456C2×C4⋊C4C22×D7114yes—
457C2×C22⋊C4—714no—
458C2×C22⋊C4—714no—
459C2×C22⋊C4—718no—
460C2×C22⋊C4—718no—
461C2×C22⋊C4—718no—
462C2×C22⋊C4—1424no—
463C2×C22⋊C4—1428no—
464C2×C22⋊C4—1424no—
465C2×C22⋊C4—1428no—
466C2×C22⋊C4—1428no—
467C2×C42—24no—
468C2×C42C22×D7114yes—
469#95—718no—
470#95—718no—
471#95—718no—
472#95C22×D7118yes—
473#95C22×D7118yes—
474C24—714no—
475C24—714no—
476C24—714no—
477C24—712no—
478C24—714no—
479C24—712no—
480C24—1422no—
481C24—1422no—
482C24—1422no—
483C24—1422no—
484C24—1422no—
485C24—1422no—
486C24—1422no—
487C24—1422no—
488C24—1422no—
489C24—1422no—
490C24C23×D7111yescharacteristic
491C2×Q8—28no—
492C2×Q8—28no—
493C2×Q8—232no—
494C2×Q8—7116no—
495C2×Q8—14216no—
496C2×Q8—14216no—
497C2×Q8—14264no—
498C2×Q8—142256no—
499C2×Q8—1428no—
500C2×Q8—14216no—
501C2×Q8—1428no—
502C2×Q8—14232no—
503C2×Q8C2×D284116yescomplemented
504C2×D4—7116no—
505C2×D4—1428no—
506C2×D4—1428no—
507C2×D4—14232no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—28416no—
519C22×C4—714no—
520C22×C4—718no—
521C22×C4—712no—
522C22×C4—714no—
523C22×C4—7116no—
524C22×C4—714no—
525C22×C4—712no—
526C22×C4—14216no—
527C22×C4—14216no—
528C22×C4—14264no—
529C22×C4—1422no—
530C22×C4—1422no—
531C22×C4—1424no—
532C22×C4—1422no—
533C22×C4—1424no—
534C22×C4—1424no—
535C22×C4—1428no—
536C22×C4—1428no—
537C22×C4—1428no—
538C22×C4—1424no—
539C22×C4—1422no—
540C22×C4—1422no—
541C22×C4—1424no—
542C22×C4—1428no—
543C22×C4—14216no—
544C22×C4—1428no—
545C22×C4—14232no—
546C22×C4D4×D7114yes—
547C22×C4D4×D7114yes—
548C22×C4C2×D28418yes—
549C22×C4C2×D28414yes—
550C22×C4Q8×D7114yescomplemented
551C22×C4C23×D7112yes—
552C22×C4C23×D7114yes—
553C22×C4C23×D7114yes—
554C22×C4C23×D7112yes—
555C22×C4C23×D7112yes—
556C4⋊C4—28no—
557C4⋊C4—1428no—
558C4⋊C4—14216no—
559C4⋊C4—14216no—
560C4⋊C4—1428no—
561C22⋊C4—1428no—
562C22⋊C4—14216no—
563C22⋊C4—14216no—
564C22⋊C4—1428no—
565C22⋊C4—14216no—
566C42—28no—
567C23—2844no—
568C23—2844no—
569C23—2844no—
570C23—2844no—
571C23—714no—
572C23—714no—
573C23—714no—
574C23—7116no—
575C23—714no—
576C23—1422no—
577C23—1422no—
578C23—1422no—
579C23—1422no—
580C23—1422no—
581C23—1422no—
582C23—1428no—
583C23—1428no—
584C23—1428no—
585C23—1422no—
586C23—1422no—
587C23—1428no—
588C23—1422no—
589C23—1422no—
590C23—1428no—
591C23—1428no—
592C23—1428no—
593C23—1428no—
594C23—1428no—
595C23C2×D4×D7112yes—
596C23C2×D4×D7112yes—
597C23C22×D28412yes—
598C23C2×Q8×D7112yes—
599C23#41×D7112yes—
600C23#1455617512yes—
601C23#1455617612yes—
602C23C24×D7111yescharacteristic
603Q8—232no—
604Q8—14264no—
605Q8—14232no—
606D4—14232no—
607C2×C4—22no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—22no—
611C2×C4—216no—
612C2×C4—28no—
613C2×C4—22no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—44no—
620C2×C4—48no—
621C2×C4—2848no—
622C2×C4—2844no—
623C2×C4—28416no—
624C2×C4—714no—
625C2×C4—718no—
626C2×C4—14264no—
627C2×C4—1422no—
628C2×C4—1422no—
629C2×C4—1424no—
630C2×C4—1422no—
631C2×C4—1424no—
632C2×C4—1424no—
633C2×C4—1422no—
634C2×C4—1424no—
635C2×C4—1422no—
636C2×C4—1424no—
637C2×C4—1428no—
638C2×C4—14216no—
639C2×C4—14232no—
640C2×C4#14556098116yes—
641C2×C4C2×D4×D7114yes—
642C2×C4C2×D4×D7114yes—
643C2×C4C22×D28418yes—
644C2×C4C22×D28414yes—
645C2×C4C2×Q8×D7114yescomplemented
646C22—2842no—
647C22—2842no—
648C22—2842no—
649C22—2842no—
650C22—28416no—
651C22—718no—
652C22—1424no—
653C22—1424no—
654C22—1424no—
655C22—1424no—
656C22—1424no—
657C22—1424no—
658C22—1424no—
659C22—1424no—
660C22—1424no—
661C22—14232no—
662C22C2×#1455609814yes—
663C22C22⋊Q8×D7114yes—
664C22#1798657214yes—
665C22#1798665714yes—
666C22#1798666114yes—
667C22#1798666414yes—
668C22Q8×D28414yes—
669C22C22×D4×D7111yescharacteristic
670C22C22×D4×D7111yescharacteristic
671C22C23×D28411yescharacteristic
672C22C22×Q8×D7111yescharacteristic
673C22C2×#41×D7111yescharacteristic
674C22C2×#1455617511yescharacteristic
675C22C2×#1455617611yescharacteristic
676C4—28no—
677C4—24no—
678C4—44no—
679C4—42no—
680C4—2844no—
681C4—2842no—
682C4—1424no—
683C4—1428no—
684C4C2×#1455609818yes—
685C2—2844no—
686C2—1428no—
687C2#2259170318yesdirect product factor
688C2C22×#1455609811yescharacteristic
689C2C2×C22⋊Q8×D7111yescharacteristic
690C2C2×#1798657211yescharacteristic
691C2C2×#1798665711yescharacteristic
692C2C2×#1798666111yescharacteristic
693C2C2×#1798666411yescharacteristic
694C2C2×Q8×D28411yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#391×C71C2
socleC24×C71C24
prime radicalC23×D284C22
hypercenterC2×#391D71
hypocenterC71C2×#2409
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
1. C23×Q8×D71C2semidirect
2. C22×#14556108C2semidirect
3. C22×#14556104C2semidirect
5. #22591703C2direct (N × H)
6. C2×#17985920C2semidirect
7. C2×#17985912C2semidirect
8. C2×#17985905C2semidirect
10. C2×#17985873C2semidirect
11. C2×#17985856C2semidirect
12. C2×#391×C71C2semidirect
18. C22×Q8×D71C22semidirect
24. C2×#14556108C22semidirect
26. C2×#14556104C22semidirect
38. #17985920C22semidirect
39. #17985912C22semidirect
40. #17985905C22semidirect
42. #17985873C22semidirect
43. #17985856C22semidirect
50. #391×C71C22semidirect
60. C22×Dic142D4semidirect
69. C22×D284Q8semidirect
113. C22×Q8×C71D4semidirect
138. C23×D71C2×Q8semidirect
149. C2×Dic142C2×D4semidirect
154. C2×D284C2×Q8semidirect
196. C2×Q8×C71C2×D4semidirect
211. C22×C4×C71C2×Q8semidirect
250. C22×D71C22⋊Q8semidirect
253. C22×D71C22×Q8semidirect
275. C2×C4×C71C22×Q8semidirect
327. C2×D71C2×C22⋊Q8semidirect
338. C2×C71#2409semidirect
356. C2×#391D71semidirect
360. C71C2×#2409semidirect
392. #391C2×D71semidirect
417. C22×Q8D284semidirect
503. C2×Q8C2×D284semidirect
550. C22×C4Q8×D71semidirect
645. C2×C4C2×Q8×D71semidirect
687. C2#22591703direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Q8×D712
C22×#145561082
C22×#145561042
C22×C4×D2842
#225917032
C2×#179859202
C2×#179859122
C2×#179859052
C2×#179858772
C2×#179858732
C2×#179858562
C2×#391×C712
C2×#240971