Finite Group Databasebeta

← C2×#22591358 #32156983

Subgroups — C2×#22591358 #32156983

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×#14556103C211yesmaximal, characteristic
2C22×C4×D284C212yesmaximal, complemented
3C22×#14556090C211yesmaximal, characteristic, complemented
4C22×C4⋊C4×D71C211yesmaximal, characteristic, complemented
5#22591358C2116yesmaximal, direct product factor
6C2×#17985901C211yesmaximal, characteristic, complemented
7C2×#17985898C211yesmaximal, characteristic, complemented
8C2×#17985890C212yesmaximal, complemented
9C2×#17985877C212yesmaximal, complemented
10C2×#17985873C212yesmaximal, complemented
11C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
12C2×C4×C4⋊C4×C71C211yesmaximal, characteristic, complemented
13C23×D284C2212yes—
14C23×D284C2211yescharacteristic
15C23×C4×D71C2212yes—
16C23×C4×D71C2212yes—
17C23×C4×D71C2211yescharacteristic
18C2×#14556103C4116yescomplemented
19C2×#14556103C2218yes—
20C2×C4×D284—216no—
21C2×C4×D284C22116yescomplemented
22C2×#14556090—28no—
23C2×#14556090C2218yescomplemented
24C22×C4⋊Dic71C2211yescharacteristic
25C22×C4⋊Dic71C2212yes—
26C22×Dic71⋊C4C2212yes—
27C2×C4⋊C4×D71—28no—
28C2×C4⋊C4×D71C2218yescomplemented
29C22×(C2×D71)⋊C4C2211yescharacteristic
30C22×(C2×D71)⋊C4C2212yes—
31C22×(C2×D71)⋊C4C2212yes—
32C22×(C2×D71)⋊C4C2212yes—
33C22×(C2×D71)⋊C4C2212yes—
34C22×(C2×D71)⋊C4C2211yescharacteristic
35C22×C4×Dic71C2211yescharacteristic
36#17985901C2218yescomplemented
37#17985898C2218yescomplemented
38#17985890C22116yescomplemented
39#17985877C22116yescomplemented
40#17985873C22116yescomplemented
41C4×(C2×D71)⋊C4C2218yescomplemented
42C2×C71⋊#95C2211yescharacteristic
43C2×C71⋊#95C2212yes—
44C2×C71⋊#95C2211yescharacteristic
45C22×C4⋊C4×C71C2211yescharacteristic
46C22×C4⋊C4×C71C2211yescharacteristic
47C22×C42×C71C2212yes—
48C22×C42×C71C2211yescharacteristic
49C4×C4⋊C4×C71C2218yescomplemented
50C2×#95×C71C2212yes—
51C24×D71C2312yes—
52C24×D71C2311yescharacteristic
53C22×D284—28no—
54C22×D284—28no—
55C22×D284—24no—
56C22×D284—24no—
57C22×D284C2×C4116yescomplemented
58C22×D284C2×C418yescomplemented
59C22×D284C2318yes—
60C22×D284C2314yes—
61C23×Dic71C2312yes—
62C23×Dic71C2311yescharacteristic
63C23×Dic71C2311yescharacteristic
64C23×Dic71C2311yescharacteristic
65C22×C4×D71—28no—
66C22×C4×D71—28no—
67C22×C4×D71—24no—
68C22×C4×D71—28no—
69C22×C4×D71—28no—
70C22×C4×D71—24no—
71C22×C4×D71—44no—
72C22×C4×D71—44no—
73C22×C4×D71C2×C418yescomplemented
74C22×C4×D71C2318yes—
75C22×C4×D71C2318yes—
76C22×C4×D71C2314yes—
77#14556103C2×C4164yescomplemented
78C4×D284—264no—
79#14556090—232no—
80C2×C4⋊Dic71—28no—
81C2×C4⋊Dic71—24no—
82C2×C4⋊Dic71C2318yes—
83C2×C4⋊Dic71C2314yes—
84C2×Dic71⋊C4—28no—
85C2×Dic71⋊C4C2318yes—
86C4⋊C4×D71—232no—
87C2×(C2×D71)⋊C4—24no—
88C2×(C2×D71)⋊C4—28no—
89C2×(C2×D71)⋊C4—28no—
90C2×(C2×D71)⋊C4—44no—
91C2×(C2×D71)⋊C4C2×C4116yescomplemented
92C2×(C2×D71)⋊C4D418yescomplemented
93C2×(C2×D71)⋊C4C2314yes—
94C2×(C2×D71)⋊C4C2318yes—
95C2×(C2×D71)⋊C4C2318yes—
96C2×(C2×D71)⋊C4C2318yes—
97C2×(C2×D71)⋊C4C2318yes—
98C2×(C2×D71)⋊C4C2314yes—
99C2×C4×Dic71—24no—
100C2×C4×Dic71C2314yes—
101C71⋊#95C2314yes—
102C71⋊#95C2314yes—
103C71⋊#95C2318yes—
104C23×C4×C71C2311yescharacteristic
105C23×C4×C71C2312yes—
106C23×C4×C71C2312yes—
107C23×C4×C71C2311yescharacteristic
108C23×C4×C71C2311yescharacteristic
109C2×C4⋊C4×C71C2×C418yescomplemented
110C2×C4⋊C4×C71D418yescomplemented
111C2×C4⋊C4×C71C2314yes—
112C2×C4⋊C4×C71C2314yes—
113C2×C42×C71—28no—
114C2×C42×C71—24no—
115C2×C42×C71C2314yes—
116C2×C42×C71C2318yes—
117#95×C71C2318yes—
118C23×D71—22no—
119C23×D71—22no—
120C23×D71—22no—
121C23×D71—22no—
122C23×D71—24no—
123C23×D71—24no—
124C23×D71—24no—
125C23×D71—24no—
126C23×D71—24no—
127C23×D71—24no—
128C23×D71C22×C418yes—
129C23×D71C22×C414yes—
130C23×D71C2×D414yes—
131C23×D71#4114yes—
132C23×D71C2414yes—
133C23×D71C2412yes—
134C2×D284—264no—
135C2×D284—216no—
136C2×D284—216no—
137C2×D284—232no—
138C2×D284—28no—
139C2×D284—28no—
140C2×D284C22×C4132yescomplemented
141C2×D284C22×C4116yescomplemented
142C22×Dic71—22no—
143C22×Dic71—22no—
144C22×Dic71—22no—
145C22×Dic71—22no—
146C22×Dic71—24no—
147C22×Dic71—24no—
148C22×Dic71—22no—
149C22×Dic71—22no—
150C22×Dic71—24no—
151C22×Dic71—22no—
152C22×Dic71C22×C414yes—
153C22×Dic71C2×D414yes—
154C22×Dic71C2414yes—
155C22×Dic71C2412yes—
156C22×Dic71C2412yes—
157C22×Dic71C2412yes—
158C2×C4×D71—232no—
159C2×C4×D71—28no—
160C2×C4×D71—28no—
161C2×C4×D71—216no—
162C2×C4×D71—216no—
163C2×C4×D71—216no—
164C2×C4×D71—216no—
165C2×C4×D71—48no—
166C2×C4×D71—48no—
167C2×C4×D71—432no—
168C2×C4×D71—432no—
169C2×C4×D71C22×C4116yescomplemented
170C4⋊Dic71—28no—
171C4⋊Dic71—216no—
172Dic71⋊C4—216no—
173(C2×D71)⋊C4—28no—
174(C2×D71)⋊C4—216no—
175(C2×D71)⋊C4—216no—
176(C2×D71)⋊C4—48no—
177(C2×D71)⋊C4C22×C4132yescomplemented
178(C2×D71)⋊C4C2×D4116yescomplemented
179C4×Dic71—28no—
180C24×C71C2411yescharacteristic
181C22×C4×C71—24no—
182C22×C4×C71—24no—
183C22×C4×C71—24no—
184C22×C4×C71—22no—
185C22×C4×C71—24no—
186C22×C4×C71—22no—
187C22×C4×C71—22no—
188C22×C4×C71—22no—
189C22×C4×C71—22no—
190C22×C4×C71C22×C418yes—
191C22×C4×C71C22×C414yes—
192C22×C4×C71C2×D414yes—
193C22×C4×C71C2×D418yes—
194C22×C4×C71C2×D414yes—
195C22×C4×C71#4114yes—
196C22×C4×C71C2412yes—
197C22×C4×C71C2414yes—
198C22×C4×C71C2414yes—
199C22×C4×C71C2412yes—
200C22×C4×C71C2412yes—
201C4⋊C4×C71C22×C4116yescomplemented
202C4⋊C4×C71C2×D4116yescomplemented
203C42×C71—216no—
204C42×C71—28no—
205C23×C71C23×C412yes—
206C23×C71C22×D412yes—
207C23×C71C22×D412yes—
208C23×C71C2×#4112yes—
209C23×C71C2×#4112yes—
210C23×C71H(5,𝔽2)12yes—
211C23×C712−1+412yes—
212C23×C71C2511yescharacteristic
213C22×D71—28no—
214C22×D71—28no—
215C22×D71—28no—
216C22×D71—28no—
217C22×D71—28no—
218C22×D71—28no—
219C22×D71—22no—
220C22×D71—22no—
221C22×D71—22no—
222C22×D71—22no—
223C22×D71—216no—
224C22×D71—216no—
225C22×D71—216no—
226C22×D71—24no—
227C22×D71—24no—
228C22×D71—24no—
229C22×D71—24no—
230C22×D71—24no—
231C22×D71—24no—
232C22×D71—48no—
233C22×D71—48no—
234C22×D71—48no—
235C22×D71—48no—
236C22×D71C4×D4116yescomplemented
237C22×D71C23×C418yes—
238C22×D71C23×C414yes—
239C22×D71C22×D414yes—
240C22×D71C2×#4114yes—
241C2×C4×C71—216no—
242C2×C4×C71—216no—
243C2×C4×C71—28no—
244C2×C4×C71—24no—
245C2×C4×C71—24no—
246C2×C4×C71—22no—
247C2×C4×C71—24no—
248C2×C4×C71—24no—
249C2×C4×C71—22no—
250C2×C4×C71—22no—
251C2×C4×C71—22no—
252C2×C4×C71—22no—
253C2×C4×C71—44no—
254C2×C4×C71C4×D4116yescomplemented
255C2×C4×C71C23×C418yes—
256C2×C4×C71C23×C414yes—
257C2×C4×C71C22×D414yes—
258C2×C4×C71C22×D418yes—
259C2×C4×C71C22×D414yes—
260C2×C4×C71C2×#4114yes—
261C2×Dic71—28no—
262C2×Dic71—28no—
263C2×Dic71—22no—
264C2×Dic71—22no—
265C2×Dic71—22no—
266C2×Dic71—22no—
267C2×Dic71—22no—
268C2×Dic71—24no—
269C2×Dic71—24no—
270C2×Dic71—22no—
271C2×Dic71—24no—
272C2×Dic71—22no—
273C2×Dic71—48no—
274C2×Dic71—44no—
275C2×Dic71C23×C414yes—
276C2×Dic71C22×D414yes—
277D284—264no—
278D284—232no—
279C4×D71—232no—
280C4×D71—432no—
281C4×D71—432no—
282C22×C71C2×C4×D414yes—
283C22×C71C2×C4×D414yes—
284C22×C71#52014yes—
285C22×C71D4214yes—
286C22×C71#54714yes—
287C22×C71#54814yes—
288C22×C71#55314yes—
289C22×C71C24×C411yescharacteristic
290C22×C71C23×D411yescharacteristic
291C22×C71C23×D411yescharacteristic
292C22×C71C22×#4111yescharacteristic
293C22×C71C22×#4111yescharacteristic
294C22×C71C2×H(5,𝔽2)11yescharacteristic
295C22×C71C2×2−1+411yescharacteristic
296C2×D71—232no—
297C2×D71—24no—
298C2×D71—24no—
299C2×D71—24no—
300C2×D71—24no—
301C2×D71—24no—
302C2×D71—24no—
303C2×D71—28no—
304C2×D71—28no—
305C2×D71—28no—
306C2×D71—432no—
307C2×D71—44no—
308C2×D71—44no—
309C2×D71—44no—
310C2×D71—44no—
311C2×D71C2×C4×D418yescomplemented
312C4×C71—28no—
313C4×C71—28no—
314C4×C71—24no—
315C4×C71—42no—
316C4×C71C2×C4×D418yescomplemented
317Dic71—24no—
318Dic71—24no—
319Dic71—44no—
320Dic71—42no—
321C2×#2361—711nomaximal, Sylow
322C2×C71#236118yescomplemented
323C2×C71C22×C4×D411yescharacteristic
324C2×C71C22×C4×D411yescharacteristic
325C2×C71C2×#52011yescharacteristic
326C2×C71C2×D4211yescharacteristic
327C2×C71C2×#54711yescharacteristic
328C2×C71C2×#54811yescharacteristic
329C2×C71C2×#55311yescharacteristic
330D71—28no—
331D71—48no—
332C22×#121—711no—
333C22×C4×D4—712no—
334C22×C4×D4—711no—
335C23×C4⋊C4—711no—
336#2361—7116no—
337C2×#390—711no—
338C2×#389—711no—
339C2×#388—712no—
340C2×#386—712no—
341C2×#385—712no—
342C2×C4×C4⋊C4D7111yescharacteristic, complemented
343C2×C4×C22⋊C4—711no—
344C71C2×#236111yescharacteristic, complemented, Sylow
345C23×D4—712no—
346C23×D4—711no—
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—712no—
357C22×C4⋊C4—711no—
358C22×C4⋊C4—712no—
359C22×C4⋊C4—718no—
360C22×C4⋊C4—1428no—
361C22×C4⋊C4C2×D7111yescharacteristic
362C22×C4⋊C4C2×D7111yescharacteristic
363C22×C22⋊C4—712no—
364C22×C22⋊C4—711no—
365C22×C22⋊C4—712no—
366C22×C22⋊C4—712no—
367C22×C22⋊C4—712no—
368C22×C22⋊C4—711no—
369C22×C42—711no—
370C22×C42C2×D7112yes—
371C22×C42C2×D7111yescharacteristic
372#390—718no—
373#389—718no—
374#388—7116no—
375#386—7116no—
376#385—7116no—
377C4×C4⋊C4C2×D7118yescomplemented
378C4×C22⋊C4—718no—
379C2×#95—711no—
380C2×#95—711no—
381C2×#95—712no—
382C2×#95C2×D7112yes—
383C25—711no—
384C25—712no—
385C22×D4—7116no—
386C22×D4—718no—
387C22×D4—718no—
388C22×D4—714no—
389C22×D4—1428no—
390C22×D4—1428no—
391C22×D4—1424no—
392C22×D4—1424no—
393C23×C4—2844no—
394C23×C4—2844no—
395C23×C4—718no—
396C23×C4—718no—
397C23×C4—711no—
398C23×C4—711no—
399C23×C4—718no—
400C23×C4—714no—
401C23×C4—711no—
402C23×C4—712no—
403C23×C4—1428no—
404C23×C4—1428no—
405C23×C4—1428no—
406C23×C4—1428no—
407C23×C4—1424no—
408C23×C4—1424no—
409C23×C4C22×D7111yescharacteristic
410C23×C4C22×D7112yes—
411C23×C4C22×D7111yescharacteristic
412C23×C4C22×D7112yes—
413C23×C4C22×D7111yescharacteristic
414#121—7164no—
415C4×D4—14264no—
416C4×D4—14232no—
417C2×C4⋊C4—718no—
418C2×C4⋊C4—714no—
419C2×C4⋊C4—718no—
420C2×C4⋊C4—1428no—
421C2×C4⋊C4—1428no—
422C2×C4⋊C4—1424no—
423C2×C4⋊C4—14232no—
424C2×C4⋊C4C4×D7118yescomplemented
425C2×C4⋊C4D28418yescomplemented
426C2×C4⋊C4C22×D7114yes—
427C2×C4⋊C4C22×D7114yes—
428C2×C22⋊C4—2844no—
429C2×C22⋊C4—718no—
430C2×C22⋊C4—7116no—
431C2×C22⋊C4—718no—
432C2×C22⋊C4—714no—
433C2×C22⋊C4—718no—
434C2×C22⋊C4—718no—
435C2×C22⋊C4—718no—
436C2×C22⋊C4—714no—
437C2×C22⋊C4—1424no—
438C2×C22⋊C4—1428no—
439C2×C22⋊C4—1428no—
440C2×C42—28no—
441C2×C42—24no—
442C2×C42—714no—
443C2×C42—1424no—
444C2×C42C22×D7118yes—
445C2×C42C22×D7114yes—
446#95—714no—
447#95—714no—
448#95—718no—
449#95C22×D7118yes—
450C24—714no—
451C24—714no—
452C24—714no—
453C24—712no—
454C24—718no—
455C24—714no—
456C24—1424no—
457C24—1424no—
458C24—1424no—
459C24—1424no—
460C24—1424no—
461C24—1424no—
462C24—1422no—
463C24—1422no—
464C24—1422no—
465C24—1422no—
466C24C23×D7111yescharacteristic
467C2×D4—7132no—
468C2×D4—7116no—
469C2×D4—14216no—
470C2×D4—14216no—
471C2×D4—14264no—
472C2×D4—1428no—
473C2×D4—1428no—
474C2×D4—14232no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—28432no—
485C22×C4—28432no—
486C22×C4—2848no—
487C22×C4—2848no—
488C22×C4—714no—
489C22×C4—714no—
490C22×C4—712no—
491C22×C4—712no—
492C22×C4—7116no—
493C22×C4—712no—
494C22×C4—714no—
495C22×C4—14216no—
496C22×C4—14216no—
497C22×C4—1424no—
498C22×C4—1422no—
499C22×C4—1424no—
500C22×C4—1422no—
501C22×C4—1424no—
502C22×C4—1422no—
503C22×C4—14216no—
504C22×C4—14216no—
505C22×C4—1422no—
506C22×C4—1422no—
507C22×C4—1422no—
508C22×C4—1422no—
509C22×C4—1428no—
510C22×C4—1428no—
511C22×C4—14232no—
512C22×C4C2×C4×D7118yes—
513C22×C4C2×C4×D7114yes—
514C22×C4D4×D7114yes—
515C22×C4C2×D28418yes—
516C22×C4C2×D28414yes—
517C22×C4#1176586514yes—
518C22×C4C23×D7112yes—
519C22×C4C23×D7114yes—
520C22×C4C23×D7112yes—
521C22×C4C23×D7114yes—
522C22×C4C23×D7112yes—
523C4⋊C4—14216no—
524C4⋊C4—14216no—
525C4⋊C4—1428no—
526C4⋊C4C2×C4×D71116yescomplemented
527C4⋊C4C2×D284116yescomplemented
528C22⋊C4—2848no—
529C22⋊C4—7132no—
530C22⋊C4—7116no—
531C22⋊C4—1428no—
532C22⋊C4—14216no—
533C22⋊C4—14216no—
534C42—216no—
535C42—28no—
536C42—1428no—
537C23—2848no—
538C23—2848no—
539C23—2848no—
540C23—2848no—
541C23—714no—
542C23—714no—
543C23—714no—
544C23—7116no—
545C23—718no—
546C23—1424no—
547C23—1424no—
548C23—1424no—
549C23—1424no—
550C23—1424no—
551C23—1424no—
552C23—14216no—
553C23—14216no—
554C23—14216no—
555C23—1422no—
556C23—1422no—
557C23—1422no—
558C23—1422no—
559C23—1428no—
560C23—1428no—
561C23—1428no—
562C23—1428no—
563C23—1428no—
564C23—1428no—
565C23C22×C4×D7112yes—
566C23C2×D4×D7112yes—
567C23C22×D28412yes—
568C23#41×D7112yes—
569C23C2×#1176586512yes—
570C23#1455617412yes—
571C23#1455617612yes—
572C23C24×D7111yescharacteristic
573D4—14264no—
574D4—14232no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—216no—
582C2×C4—28no—
583C2×C4—216no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—44no—
588C2×C4—28432no—
589C2×C4—28432no—
590C2×C4—2848no—
591C2×C4—2844no—
592C2×C4—714no—
593C2×C4—714no—
594C2×C4—1424no—
595C2×C4—1422no—
596C2×C4—1424no—
597C2×C4—1422no—
598C2×C4—1424no—
599C2×C4—1422no—
600C2×C4—1422no—
601C2×C4—1422no—
602C2×C4—1422no—
603C2×C4—1422no—
604C2×C4—1428no—
605C2×C4—1428no—
606C2×C4—14232no—
607C2×C4C4×D284116yescomplemented
608C2×C4C22×C4×D7118yes—
609C2×C4C22×C4×D7114yes—
610C2×C4C2×D4×D7114yes—
611C2×C4C22×D28418yes—
612C2×C4C22×D28414yes—
613C2×C4C2×#1176586514yes—
614C22—2844no—
615C22—2844no—
616C22—2844no—
617C22—28432no—
618C22—2844no—
619C22—718no—
620C22—1428no—
621C22—1428no—
622C22—1428no—
623C22—1424no—
624C22—1424no—
625C22—1424no—
626C22—1424no—
627C22—1424no—
628C22—14232no—
629C22—1424no—
630C22C4×D4×D7114yes—
631C22C2×C4×D28414yes—
632C22#1798648114yes—
633C22D4×D28414yes—
634C22#1798665014yes—
635C22#1798666114yes—
636C22#1798669314yes—
637C22C23×C4×D7111yescharacteristic
638C22C22×D4×D7111yescharacteristic
639C22C23×D28411yescharacteristic
640C22C2×#41×D7111yescharacteristic
641C22C22×#1176586511yescharacteristic
642C22C2×#1455617411yescharacteristic
643C22C2×#1455617611yescharacteristic
644C4—28no—
645C4—28no—
646C4—24no—
647C4—42no—
648C4—2844no—
649C4—2842no—
650C4—1424no—
651C4—1424no—
652C4C2×C4×D28418yescomplemented
653C2—2848no—
654C2—1428no—
655C2#2259135818yesdirect product factor
656C2C2×C4×D4×D7111yescharacteristic
657C2C22×C4×D28411yescharacteristic
658C2C2×#1798648111yescharacteristic
659C2C2×D4×D28411yescharacteristic
660C2C2×#1798665011yescharacteristic
661C2C2×#1798666111yescharacteristic
662C2C2×#1798669311yescharacteristic
subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC2×C4×C4⋊C4×C71C2
socleC24×C71C24
prime radicalC22×#14556103C2
cosocleC23×C71C25
hypercenterC2×C4×C4⋊C4D71
hypocenterC71C2×#2361
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×D284C2semidirect
3. C22×#14556090C2semidirect
4. C22×C4⋊C4×D71C2semidirect
5. #22591358C2direct (N × H)
6. C2×#17985901C2semidirect
7. C2×#17985898C2semidirect
8. C2×#17985890C2semidirect
9. C2×#17985877C2semidirect
10. C2×#17985873C2semidirect
11. C2×C4×(C2×D71)⋊C4C2semidirect
12. C2×C4×C4⋊C4×C71C2semidirect
18. C2×#14556103C4semidirect
21. C2×C4×D284C22semidirect
23. C2×#14556090C22semidirect
28. C2×C4⋊C4×D71C22semidirect
36. #17985901C22semidirect
37. #17985898C22semidirect
38. #17985890C22semidirect
39. #17985877C22semidirect
40. #17985873C22semidirect
41. C4×(C2×D71)⋊C4C22semidirect
49. C4×C4⋊C4×C71C22semidirect
57. C22×D284C2×C4semidirect
58. C22×D284C2×C4semidirect
73. C22×C4×D71C2×C4semidirect
77. #14556103C2×C4semidirect
91. C2×(C2×D71)⋊C4C2×C4semidirect
92. C2×(C2×D71)⋊C4D4semidirect
109. C2×C4⋊C4×C71C2×C4semidirect
110. C2×C4⋊C4×C71D4semidirect
140. C2×D284C22×C4semidirect
141. C2×D284C22×C4semidirect
169. C2×C4×D71C22×C4semidirect
177. (C2×D71)⋊C4C22×C4semidirect
178. (C2×D71)⋊C4C2×D4semidirect
201. C4⋊C4×C71C22×C4semidirect
202. C4⋊C4×C71C2×D4semidirect
236. C22×D71C4×D4semidirect
254. C2×C4×C71C4×D4semidirect
311. C2×D71C2×C4×D4semidirect
316. C4×C71C2×C4×D4semidirect
322. C2×C71#2361semidirect
342. C2×C4×C4⋊C4D71semidirect
344. C71C2×#2361semidirect
377. C4×C4⋊C4C2×D71semidirect
424. C2×C4⋊C4C4×D71semidirect
425. C2×C4⋊C4D284semidirect
526. C4⋊C4C2×C4×D71semidirect
527. C4⋊C4C2×D284semidirect
607. C2×C4C4×D284semidirect
652. C4C2×C4×D284semidirect
655. C2#22591358direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561032
C22×C4×D2842
C22×#145560902
C22×C4⋊C4×D712
#225913582
C2×#179859012
C2×#179858982
C2×#179858902
C2×#179858772
C2×#179858732
C2×C4×(C2×D71)⋊C42
C2×C4×C4⋊C4×C712
C2×#236171