Finite Group Databasebeta

← C2×#22591361 #32156986

Subgroups — C2×#22591361 #32156986

Order 18176.

4782 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556099C211yesmaximal, characteristic
2C22×D4×Dic71C211yesmaximal, characteristic, complemented
3C22×(C22⋊D71)⋊C4C212yesmaximal, complemented
4C22×C4⋊C4×D71C211yesmaximal, characteristic, complemented
5#22591361C2116yesmaximal, direct product factor
6C2×#17985895C211yesmaximal, characteristic, complemented
7C2×#17985887C212yesmaximal, complemented
8C2×#17985875C212yesmaximal, complemented
9C2×#17985871C212yesmaximal, complemented
10C2×C4×C4⋊Dic71C211yesmaximal, characteristic, complemented
11C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
12C2×#390×C71C211yesmaximal, characteristic, complemented
13C23×C22⋊D71C2212yes—
14C24×Dic71C2212yes—
15C23×C4×D71C2212yes—
16C23×C4×D71C2211yescharacteristic
17C2×#14556099C4116yescomplemented
18C2×#14556099C2218yes—
19C2×D4×Dic71—28no—
20C2×D4×Dic71C2218yescomplemented
21C2×(C22⋊D71)⋊C4—216no—
22C2×(C22⋊D71)⋊C4C22116yescomplemented
23C22×C4⋊Dic71C2211yescharacteristic
24C22×C4⋊Dic71C2211yescharacteristic
25C22×Dic71⋊C4C2212yes—
26C22×Dic71⋊C4C2212yes—
27C2×C4⋊C4×D71—28no—
28C2×C4⋊C4×D71C2218yescomplemented
29C22×C22⋊Dic71C2212yes—
30C22×C22⋊Dic71C2212yes—
31C22×(C2×D71)⋊C4C2211yescharacteristic
32C22×(C2×D71)⋊C4C2211yescharacteristic
33C22×C4×Dic71C2212yes—
34C22×C4×Dic71C2211yescharacteristic
35#17985895C2218yescomplemented
36#17985887C22116yescomplemented
37#17985875C22116yescomplemented
38#17985871C22116yescomplemented
39C4×C4⋊Dic71C2218yescomplemented
40C4×(C2×D71)⋊C4C2218yescomplemented
41C2×C71⋊#95C2211yescharacteristic
42C2×C71⋊#95C2212yes—
43C2×C71⋊#95C2212yes—
44C2×C71⋊#95C2211yescharacteristic
45C23×D4×C71C2211yescharacteristic
46C22×C4⋊C4×C71C2211yescharacteristic
47C22×C22⋊C4×C71C2212yes—
48C22×C22⋊C4×C71C2212yes—
49C22×C42×C71C2211yescharacteristic
50#390×C71C2218yescomplemented
51C24×D71C2311yescharacteristic
52C22×C22⋊D71—28no—
53C22×C22⋊D71—28no—
54C22×C22⋊D71C2×C4116yescomplemented
55C22×C22⋊D71C2318yes—
56C23×Dic71—28no—
57C23×Dic71—28no—
58C23×Dic71—44no—
59C23×Dic71C2311yescharacteristic
60C23×Dic71C2318yes—
61C23×Dic71C2311yescharacteristic
62C23×Dic71C2312yes—
63C23×Dic71C2312yes—
64C23×Dic71C2311yescharacteristic
65C22×C4×D71—28no—
66C22×C4×D71—28no—
67C22×C4×D71—24no—
68C22×C4×D71—24no—
69C22×C4×D71—44no—
70C22×C4×D71C2×C418yescomplemented
71C22×C4×D71C2318yes—
72C22×C4×D71C2314yes—
73#14556099C2×C4164yescomplemented
74D4×Dic71—232no—
75(C22⋊D71)⋊C4—264no—
76C2×C4⋊Dic71C2×C418yescomplemented
77C2×C4⋊Dic71D418yescomplemented
78C2×C4⋊Dic71C2314yes—
79C2×C4⋊Dic71C2314yes—
80C2×Dic71⋊C4—28no—
81C2×Dic71⋊C4—28no—
82C2×Dic71⋊C4C2318yes—
83C2×Dic71⋊C4C2318yes—
84C4⋊C4×D71—232no—
85C2×C22⋊Dic71—28no—
86C2×C22⋊Dic71C2×C4116yescomplemented
87C2×C22⋊Dic71C2318yes—
88C2×C22⋊Dic71C2318yes—
89C2×(C2×D71)⋊C4—24no—
90C2×(C2×D71)⋊C4D418yescomplemented
91C2×(C2×D71)⋊C4C2314yes—
92C2×(C2×D71)⋊C4C2314yes—
93C2×C4×Dic71—28no—
94C2×C4×Dic71—24no—
95C2×C4×Dic71C2314yes—
96C2×C4×Dic71C2318yes—
97C71⋊#95C2314yes—
98C71⋊#95C2314yes—
99C71⋊#95C2318yes—
100C71⋊#95C2318yes—
101C25×C71C2312yes—
102C22×D4×C71—24no—
103C22×D4×C71—24no—
104C22×D4×C71C2×C418yescomplemented
105C22×D4×C71C2314yes—
106C23×C4×C71C2312yes—
107C23×C4×C71C2311yescharacteristic
108C23×C4×C71C2311yescharacteristic
109C23×C4×C71C2311yescharacteristic
110C2×C4⋊C4×C71—24no—
111C2×C4⋊C4×C71C2314yes—
112C2×C22⋊C4×C71—28no—
113C2×C22⋊C4×C71—44no—
114C2×C22⋊C4×C71C2318yes—
115C2×C22⋊C4×C71C2318yes—
116C2×C42×C71—24no—
117C2×C42×C71C2314yes—
118C23×D71—22no—
119C23×D71—22no—
120C23×D71—22no—
121C23×D71—22no—
122C23×D71C22×C414yes—
123C23×D71C2×D414yes—
124C23×D71#4114yes—
125C23×D71C2412yes—
126C2×C22⋊D71—264no—
127C2×C22⋊D71—216no—
128C2×C22⋊D71—216no—
129C2×C22⋊D71C22×C4132yescomplemented
130C22×Dic71—24no—
131C22×Dic71—22no—
132C22×Dic71—22no—
133C22×Dic71—24no—
134C22×Dic71—22no—
135C22×Dic71—24no—
136C22×Dic71—24no—
137C22×Dic71—22no—
138C22×Dic71—22no—
139C22×Dic71—22no—
140C22×Dic71—22no—
141C22×Dic71—216no—
142C22×Dic71—216no—
143C22×Dic71—48no—
144C22×Dic71—432no—
145C22×Dic71C22×C414yes—
146C22×Dic71C22×C418yes—
147C22×Dic71C2×D418yes—
148C22×Dic71C2×D414yes—
149C22×Dic71C2412yes—
150C22×Dic71C2412yes—
151C22×Dic71C2414yes—
152C22×Dic71C2414yes—
153C22×Dic71C2412yes—
154C2×C4×D71—232no—
155C2×C4×D71—28no—
156C2×C4×D71—28no—
157C2×C4×D71—216no—
158C2×C4×D71—216no—
159C2×C4×D71—48no—
160C2×C4×D71—432no—
161C2×C4×D71C22×C4116yescomplemented
162C4⋊Dic71C22×C4116yescomplemented
163C4⋊Dic71C2×D4116yescomplemented
164Dic71⋊C4—216no—
165Dic71⋊C4—216no—
166C22⋊Dic71—216no—
167C22⋊Dic71C22×C4132yescomplemented
168(C2×D71)⋊C4—28no—
169(C2×D71)⋊C4C2×D4116yescomplemented
170C4×Dic71—216no—
171C4×Dic71—28no—
172C24×C71—24no—
173C24×C71—24no—
174C24×C71—24no—
175C24×C71—24no—
176C24×C71—24no—
177C24×C71—24no—
178C24×C71C22×C418yes—
179C24×C71C2414yes—
180C24×C71C2411yescharacteristic
181C2×D4×C71—232no—
182C2×D4×C71—28no—
183C2×D4×C71—28no—
184C2×D4×C71C22×C4116yescomplemented
185C22×C4×C71—22no—
186C22×C4×C71—22no—
187C22×C4×C71—24no—
188C22×C4×C71—24no—
189C22×C4×C71—22no—
190C22×C4×C71—22no—
191C22×C4×C71—24no—
192C22×C4×C71—22no—
193C22×C4×C71C22×C414yes—
194C22×C4×C71C2×D414yes—
195C22×C4×C71C2×D414yes—
196C22×C4×C71#4114yes—
197C22×C4×C71C2414yes—
198C22×C4×C71C2412yes—
199C22×C4×C71C2412yes—
200C22×C4×C71C2412yes—
201C4⋊C4×C71—28no—
202C22⋊C4×C71—216no—
203C22⋊C4×C71—48no—
204C42×C71—28no—
205C23×C71—216no—
206C23×C71—216no—
207C23×C71—216no—
208C23×C71—24no—
209C23×C71—24no—
210C23×C71—24no—
211C23×C71—24no—
212C23×C71—24no—
213C23×C71—24no—
214C23×C71—48no—
215C23×C71—48no—
216C23×C71—48no—
217C23×C71—48no—
218C23×C71C23×C418yes—
219C23×C71C23×C412yes—
220C23×C71C22×D412yes—
221C23×C71C22×D412yes—
222C23×C71C2×#4112yes—
223C23×C71C2×#4112yes—
224C23×C71H(5,𝔽2)12yes—
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×D71C4×D4116yescomplemented
238C22×D71C23×C414yes—
239C22×D71C22×D414yes—
240C22×D71C2×#4114yes—
241D4×C71—232no—
242C2×C4×C71—28no—
243C2×C4×C71—22no—
244C2×C4×C71—22no—
245C2×C4×C71—24no—
246C2×C4×C71—24no—
247C2×C4×C71—22no—
248C2×C4×C71—22no—
249C2×C4×C71—22no—
250C2×C4×C71—24no—
251C2×C4×C71—48no—
252C2×C4×C71—44no—
253C2×C4×C71C4×D4116yescomplemented
254C2×C4×C71C23×C414yes—
255C2×C4×C71C22×D414yes—
256C2×C4×C71C22×D414yes—
257C2×C4×C71C2×#4114yes—
258C22⋊D71—264no—
259C2×Dic71—28no—
260C2×Dic71—216no—
261C2×Dic71—216no—
262C2×Dic71—28no—
263C2×Dic71—24no—
264C2×Dic71—24no—
265C2×Dic71—22no—
266C2×Dic71—22no—
267C2×Dic71—22no—
268C2×Dic71—24no—
269C2×Dic71—24no—
270C2×Dic71—22no—
271C2×Dic71—22no—
272C2×Dic71—22no—
273C2×Dic71—22no—
274C2×Dic71—432no—
275C2×Dic71—44no—
276C2×Dic71C23×C414yes—
277C2×Dic71C23×C418yes—
278C2×Dic71C22×D414yes—
279C2×Dic71C22×D418yes—
280C4×D71—232no—
281C4×D71—432no—
282C22×C71—28no—
283C22×C71—28no—
284C22×C71—28no—
285C22×C71—432no—
286C22×C71—44no—
287C22×C71—44no—
288C22×C71—44no—
289C22×C71—44no—
290C22×C71C2×C4×D414yes—
291C22×C71C2×C4×D414yes—
292C22×C71#52014yes—
293C22×C71D4214yes—
294C22×C71#54714yes—
295C22×C71#54814yes—
296C22×C71#55314yes—
297C22×C71C24×C411yescharacteristic
298C22×C71C23×D411yescharacteristic
299C22×C71C23×D411yescharacteristic
300C22×C71C22×#4111yescharacteristic
301C22×C71C22×#4111yescharacteristic
302C22×C71C2×H(5,𝔽2)11yescharacteristic
303C22×C71C2×2−1+411yescharacteristic
304C2×D71—232no—
305C2×D71—24no—
306C2×D71—24no—
307C2×D71—24no—
308C2×D71—24no—
309C2×D71—24no—
310C2×D71—24no—
311C2×D71C2×C4×D418yescomplemented
312C4×C71—24no—
313C4×C71—44no—
314C4×C71—42no—
315C4×C71C2×C4×D418yescomplemented
316Dic71—24no—
317Dic71—28no—
318Dic71—28no—
319Dic71—24no—
320Dic71—42no—
321C2×#2361—711nomaximal, Sylow
322C2×C71—48no—
323C2×C71#236118yescomplemented
324C2×C71C22×C4×D411yescharacteristic
325C2×C71C22×C4×D411yescharacteristic
326C2×C71C2×#52011yescharacteristic
327C2×C71C2×D4211yescharacteristic
328C2×C71C2×#54711yescharacteristic
329C2×C71C2×#54811yescharacteristic
330C2×C71C2×#55311yescharacteristic
331D71—28no—
332C22×#121—711no—
333C22×C4×D4—711no—
334C22×C4×D4—712no—
335C23×C4⋊C4—711no—
336#2361—7116no—
337C2×#390D7111yescharacteristic, complemented
338C2×#389—711no—
339C2×#388—712no—
340C2×#386—712no—
341C2×#385—712no—
342C2×C4×C4⋊C4—711no—
343C2×C4×C22⋊C4—711no—
344C71C2×#236111yescharacteristic, complemented, Sylow
345C23×D4—712no—
346C23×D4C2×D7111yescharacteristic
347C24×C4—712no—
348C24×C4—712no—
349C24×C4—711no—
350C2×#121—7116no—
351C2×#121—718no—
352C2×C4×D4—718no—
353C2×C4×D4—7116no—
354C2×C4×D4—14216no—
355C2×C4×D4—1428no—
356C22×C4⋊C4—711no—
357C22×C4⋊C4—711no—
358C22×C4⋊C4—712no—
359C22×C4⋊C4—712no—
360C22×C4⋊C4—718no—
361C22×C4⋊C4—1428no—
362C22×C4⋊C4C2×D7111yescharacteristic
363C22×C22⋊C4—712no—
364C22×C22⋊C4—711no—
365C22×C22⋊C4—712no—
366C22×C22⋊C4—711no—
367C22×C22⋊C4C2×D7112yes—
368C22×C22⋊C4C2×D7112yes—
369C22×C42—711no—
370C22×C42—712no—
371C22×C42C2×D7111yescharacteristic
372#390C2×D7118yescomplemented
373#389—718no—
374#388—7116no—
375#386—7116no—
376#385—7116no—
377C4×C4⋊C4—718no—
378C4×C22⋊C4—718no—
379C2×#95—711no—
380C2×#95—711no—
381C2×#95—712no—
382C2×#95—712no—
383C25—711no—
384C25C22×D7112yes—
385C22×D4—24no—
386C22×D4—24no—
387C22×D4—7116no—
388C22×D4—718no—
389C22×D4—1428no—
390C22×D4—1428no—
391C22×D4C4×D7118yescomplemented
392C22×D4C22×D7114yes—
393C23×C4—2844no—
394C23×C4—2844no—
395C23×C4—718no—
396C23×C4—718no—
397C23×C4—711no—
398C23×C4—711no—
399C23×C4—712no—
400C23×C4—712no—
401C23×C4—718no—
402C23×C4—714no—
403C23×C4—711no—
404C23×C4—1428no—
405C23×C4—1428no—
406C23×C4—1428no—
407C23×C4—1428no—
408C23×C4—1424no—
409C23×C4—1424no—
410C23×C4C22×D7111yescharacteristic
411C23×C4C22×D7112yes—
412C23×C4C22×D7111yescharacteristic
413C23×C4C22×D7111yescharacteristic
414#121—7164no—
415C4×D4—14264no—
416C4×D4—14232no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—718no—
419C2×C4⋊C4—718no—
420C2×C4⋊C4—714no—
421C2×C4⋊C4—714no—
422C2×C4⋊C4—718no—
423C2×C4⋊C4—718no—
424C2×C4⋊C4—14232no—
425C2×C4⋊C4—1428no—
426C2×C4⋊C4—1428no—
427C2×C4⋊C4C22×D7114yes—
428C2×C22⋊C4—28no—
429C2×C22⋊C4—44no—
430C2×C22⋊C4—7116no—
431C2×C22⋊C4—718no—
432C2×C22⋊C4—718no—
433C2×C22⋊C4—714no—
434C2×C22⋊C4—718no—
435C2×C22⋊C4—714no—
436C2×C22⋊C4—1424no—
437C2×C22⋊C4—1428no—
438C2×C22⋊C4C22×D7118yes—
439C2×C22⋊C4C22×D7118yes—
440C2×C42—24no—
441C2×C42—714no—
442C2×C42—718no—
443C2×C42—1424no—
444C2×C42—1428no—
445C2×C42C22×D7114yes—
446#95—714no—
447#95—714no—
448#95—718no—
449#95—718no—
450C24—24no—
451C24—24no—
452C24—24no—
453C24—24no—
454C24—24no—
455C24—24no—
456C24—714no—
457C24—714no—
458C24—714no—
459C24—712no—
460C24—1422no—
461C24—1422no—
462C24—1422no—
463C24—1422no—
464C24C2×C4×D7118yes—
465C24C23×D7114yes—
466C24C23×D7111yescharacteristic
467C2×D4—28no—
468C2×D4—28no—
469C2×D4—232no—
470C2×D4—7132no—
471C2×D4—14216no—
472C2×D4—14216no—
473C2×D4—14264no—
474C2×D4C2×C4×D71116yescomplemented
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—2848no—
484C22×C4—28432no—
485C22×C4—2848no—
486C22×C4—28432no—
487C22×C4—714no—
488C22×C4—718no—
489C22×C4—714no—
490C22×C4—718no—
491C22×C4—714no—
492C22×C4—712no—
493C22×C4—712no—
494C22×C4—714no—
495C22×C4—7116no—
496C22×C4—712no—
497C22×C4—14216no—
498C22×C4—14216no—
499C22×C4—14216no—
500C22×C4—14216no—
501C22×C4—1422no—
502C22×C4—1422no—
503C22×C4—1422no—
504C22×C4—1424no—
505C22×C4—1424no—
506C22×C4—1422no—
507C22×C4—1422no—
508C22×C4—1424no—
509C22×C4—1422no—
510C22×C4—1424no—
511C22×C4—1422no—
512C22×C4—1428no—
513C22×C4—1428no—
514C22×C4—14232no—
515C22×C4C2×C4×D7114yes—
516C22×C4D4×D7114yes—
517C22×C4D4×D7114yes—
518C22×C4#1176586414yes—
519C22×C4C23×D7112yes—
520C22×C4C23×D7114yes—
521C22×C4C23×D7112yes—
522C22×C4C23×D7112yes—
523C4⋊C4—28no—
524C4⋊C4—7116no—
525C4⋊C4—7116no—
526C4⋊C4—14216no—
527C4⋊C4—14216no—
528C22⋊C4—216no—
529C22⋊C4—48no—
530C22⋊C4—7132no—
531C22⋊C4—7116no—
532C22⋊C4—1428no—
533C22⋊C4—14216no—
534C42—28no—
535C42—1428no—
536C42—14216no—
537C23—24no—
538C23—24no—
539C23—24no—
540C23—24no—
541C23—24no—
542C23—24no—
543C23—216no—
544C23—216no—
545C23—216no—
546C23—48no—
547C23—48no—
548C23—48no—
549C23—48no—
550C23—714no—
551C23—714no—
552C23—714no—
553C23—7116no—
554C23—1422no—
555C23—1422no—
556C23—1422no—
557C23—1422no—
558C23—1428no—
559C23—1428no—
560C23—1428no—
561C23—1428no—
562C23—1428no—
563C23—1428no—
564C23C22×C4×D7118yes—
565C23C22×C4×D7112yes—
566C23C2×D4×D7112yes—
567C23C2×D4×D7112yes—
568C23#41×D7112yes—
569C23C2×#1176586412yes—
570C23#1455617312yes—
571C23#1455617512yes—
572C23C24×D7111yescharacteristic
573D4—232no—
574D4—14264no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—28no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—48no—
585C2×C4—44no—
586C2×C4—28432no—
587C2×C4—2844no—
588C2×C4—28432no—
589C2×C4—714no—
590C2×C4—718no—
591C2×C4—714no—
592C2×C4—718no—
593C2×C4—1422no—
594C2×C4—1422no—
595C2×C4—1422no—
596C2×C4—1424no—
597C2×C4—1424no—
598C2×C4—1422no—
599C2×C4—1422no—
600C2×C4—1424no—
601C2×C4—1422no—
602C2×C4—1424no—
603C2×C4—1422no—
604C2×C4—14216no—
605C2×C4—1428no—
606C2×C4—14216no—
607C2×C4—1428no—
608C2×C4—14232no—
609C2×C4(C22⋊D71)⋊C4116yescomplemented
610C2×C4C22×C4×D7114yes—
611C2×C4C2×D4×D7114yes—
612C2×C4C2×D4×D7114yes—
613C2×C4C2×#1176586414yes—
614C22—28no—
615C22—28no—
616C22—28no—
617C22—44no—
618C22—44no—
619C22—44no—
620C22—432no—
621C22—44no—
622C22—718no—
623C22—1424no—
624C22—1424no—
625C22—1424no—
626C22—1424no—
627C22—1424no—
628C22—14232no—
629C22—1424no—
630C22C4×D4×D7114yes—
631C22C2×(C22⋊D71)⋊C414yes—
632C22#1798647814yes—
633C22#1798663414yes—
634C22#1798664914yes—
635C22#1798665714yes—
636C22#1798669614yes—
637C22C23×C4×D7111yescharacteristic
638C22C22×D4×D7111yescharacteristic
639C22C22×D4×D7111yescharacteristic
640C22C2×#41×D7111yescharacteristic
641C22C22×#1176586411yescharacteristic
642C22C2×#1455617311yescharacteristic
643C22C2×#1455617511yescharacteristic
644C4—24no—
645C4—44no—
646C4—42no—
647C4—2842no—
648C4—1428no—
649C4—1424no—
650C4—1428no—
651C4—1424no—
652C4C2×(C22⋊D71)⋊C418yescomplemented
653C2—48no—
654C2—1428no—
655C2#2259136118yesdirect product factor
656C2C2×C4×D4×D7111yescharacteristic
657C2C22×(C22⋊D71)⋊C411yescharacteristic
658C2C2×#1798647811yescharacteristic
659C2C2×#1798663411yescharacteristic
660C2C2×#1798664911yescharacteristic
661C2C2×#1798665711yescharacteristic
662C2C2×#1798669611yescharacteristic
subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC2×#390×C71C2
socleC24×C71C24
prime radicalC22×#14556099C2
cosocleC23×C71C25
hypercenterC2×#390D71
hypocenterC71C2×#2361
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C22×D4×Dic71C2semidirect
3. C22×(C22⋊D71)⋊C4C2semidirect
4. C22×C4⋊C4×D71C2semidirect
5. #22591361C2direct (N × H)
6. C2×#17985895C2semidirect
7. C2×#17985887C2semidirect
8. C2×#17985875C2semidirect
9. C2×#17985871C2semidirect
10. C2×C4×C4⋊Dic71C2semidirect
11. C2×C4×(C2×D71)⋊C4C2semidirect
12. C2×#390×C71C2semidirect
17. C2×#14556099C4semidirect
20. C2×D4×Dic71C22semidirect
22. C2×(C22⋊D71)⋊C4C22semidirect
28. C2×C4⋊C4×D71C22semidirect
35. #17985895C22semidirect
36. #17985887C22semidirect
37. #17985875C22semidirect
38. #17985871C22semidirect
39. C4×C4⋊Dic71C22semidirect
40. C4×(C2×D71)⋊C4C22semidirect
50. #390×C71C22semidirect
54. C22×C22⋊D71C2×C4semidirect
70. C22×C4×D71C2×C4semidirect
73. #14556099C2×C4semidirect
76. C2×C4⋊Dic71C2×C4semidirect
77. C2×C4⋊Dic71D4semidirect
86. C2×C22⋊Dic71C2×C4semidirect
90. C2×(C2×D71)⋊C4D4semidirect
104. C22×D4×C71C2×C4semidirect
129. C2×C22⋊D71C22×C4semidirect
161. C2×C4×D71C22×C4semidirect
162. C4⋊Dic71C22×C4semidirect
163. C4⋊Dic71C2×D4semidirect
167. C22⋊Dic71C22×C4semidirect
169. (C2×D71)⋊C4C2×D4semidirect
184. C2×D4×C71C22×C4semidirect
237. C22×D71C4×D4semidirect
253. C2×C4×C71C4×D4semidirect
311. C2×D71C2×C4×D4semidirect
315. C4×C71C2×C4×D4semidirect
323. C2×C71#2361semidirect
337. C2×#390D71semidirect
344. C71C2×#2361semidirect
372. #390C2×D71semidirect
391. C22×D4C4×D71semidirect
474. C2×D4C2×C4×D71semidirect
609. C2×C4(C22⋊D71)⋊C4semidirect
652. C4C2×(C22⋊D71)⋊C4semidirect
655. C2#22591361direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145560992
C22×D4×Dic712
C22×(C22⋊D71)⋊C42
C22×C4⋊C4×D712
#225913612
C2×#179858952
C2×#179858872
C2×#179858752
C2×#179858712
C2×C4×C4⋊Dic712
C2×C4×(C2×D71)⋊C42
C2×#390×C712
C2×#236171