Finite Group Databasebeta

← C2×#22591356 #32156981

Subgroups — C2×#22591356 #32156981

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×#14556102C211yesmaximal, characteristic
2C22×#14556090C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D71C212yesmaximal, complemented
4#22591356C2116yesmaximal, direct product factor
5C2×#17985900C211yesmaximal, characteristic, complemented
6C2×#17985895C211yesmaximal, characteristic, complemented
7C2×#17985889C212yesmaximal, complemented
8C2×#17985878C212yesmaximal, complemented
9C2×#17985870C212yesmaximal, complemented
10C2×C4⋊C4×Dic71C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊Dic71C211yesmaximal, characteristic, complemented
12C23×C4⋊C4×C71C211yesmaximal, characteristic, complemented
13C23×D284C2211yescharacteristic
14C23×C22⋊D71C2212yes—
15C23×C4×D71C2212yes—
16C2×#14556102C4116yescomplemented
17C2×#14556102C2218yes—
18C2×#14556090—28no—
19C2×#14556090C2218yescomplemented
20C2×C4×C22⋊D71—216no—
21C2×C4×C22⋊D71C22116yescomplemented
22C22×C4⋊Dic71C2211yescharacteristic
23C22×Dic71⋊C4C2212yes—
24C22×C22⋊Dic71C2211yescharacteristic
25C22×C22⋊Dic71C2211yescharacteristic
26C22×(C2×D71)⋊C4C2212yes—
27C22×(C2×D71)⋊C4C2212yes—
28C22×(C2×D71)⋊C4C2212yes—
29C22×(C2×D71)⋊C4C2212yes—
30C22×C4×Dic71C2212yes—
31C22×C4×Dic71C2211yescharacteristic
32C22×C4×Dic71C2211yescharacteristic
33#17985900C2218yescomplemented
34#17985895C2218yescomplemented
35#17985889C22116yescomplemented
36#17985878C22116yescomplemented
37#17985870C22116yescomplemented
38C4⋊C4×Dic71C2218yescomplemented
39C4×C22⋊Dic71C2218yescomplemented
40C2×C71⋊#95C2211yescharacteristic
41C2×C71⋊#95C2212yes—
42C2×C71⋊#95C2212yes—
43C2×C71⋊#95C2211yescharacteristic
44C24×C4×C71C2212yes—
45C24×C4×C71C2211yescharacteristic
46C22×C4⋊C4×C71—28no—
47C22×C4⋊C4×C71C2212yes—
48C22×C4⋊C4×C71C2211yescharacteristic
49C22×C4⋊C4×C71C2211yescharacteristic
50C22×C4⋊C4×C71C2218yescomplemented
51C24×D71C2312yes—
52C22×D284—24no—
53C22×D284—24no—
54C22×D284C2×C418yescomplemented
55C22×D284C2314yes—
56C22×C22⋊D71—28no—
57C22×C22⋊D71—28no—
58C22×C22⋊D71C2×C4116yescomplemented
59C22×C22⋊D71C2318yes—
60C23×Dic71C2311yescharacteristic
61C23×Dic71C2311yescharacteristic
62C23×Dic71C2312yes—
63C23×Dic71C2311yescharacteristic
64C23×Dic71C2311yescharacteristic
65C22×C4×D71—28no—
66C22×C4×D71—28no—
67C22×C4×D71—44no—
68C22×C4×D71C2318yes—
69#14556102C2×C4164yescomplemented
70#14556090—232no—
71C4×C22⋊D71—264no—
72C2×C4⋊Dic71C2×C418yescomplemented
73C2×C4⋊Dic71C2314yes—
74C2×Dic71⋊C4—28no—
75C2×Dic71⋊C4C2318yes—
76C2×C22⋊Dic71—24no—
77C2×C22⋊Dic71D418yescomplemented
78C2×C22⋊Dic71C2314yes—
79C2×C22⋊Dic71C2314yes—
80C2×(C2×D71)⋊C4—28no—
81C2×(C2×D71)⋊C4—28no—
82C2×(C2×D71)⋊C4—44no—
83C2×(C2×D71)⋊C4C2×C4116yescomplemented
84C2×(C2×D71)⋊C4C2318yes—
85C2×(C2×D71)⋊C4C2318yes—
86C2×(C2×D71)⋊C4C2318yes—
87C2×(C2×D71)⋊C4C2318yes—
88C2×C4×Dic71—28no—
89C2×C4×Dic71—24no—
90C2×C4×Dic71—24no—
91C2×C4×Dic71C2314yes—
92C2×C4×Dic71C2314yes—
93C2×C4×Dic71C2318yes—
94C71⋊#95C2314yes—
95C71⋊#95C2314yes—
96C71⋊#95C2318yes—
97C71⋊#95C2318yes—
98C25×C71C2311yescharacteristic
99C23×C4×C71—24no—
100C23×C4×C71—24no—
101C23×C4×C71—28no—
102C23×C4×C71—28no—
103C23×C4×C71—44no—
104C23×C4×C71C2×C418yescomplemented
105C23×C4×C71C2312yes—
106C23×C4×C71C2318yes—
107C23×C4×C71C2311yescharacteristic
108C23×C4×C71C2314yes—
109C23×C4×C71C2312yes—
110C23×C4×C71C2311yescharacteristic
111C2×C4⋊C4×C71—28no—
112C2×C4⋊C4×C71—24no—
113C2×C4⋊C4×C71—232no—
114C2×C4⋊C4×C71D418yescomplemented
115C2×C4⋊C4×C71C2318yes—
116C2×C4⋊C4×C71C2314yes—
117C2×C4⋊C4×C71C2314yes—
118C23×D71—24no—
119C23×D71—24no—
120C23×D71—24no—
121C23×D71—24no—
122C23×D71—24no—
123C23×D71—24no—
124C23×D71C22×C418yes—
125C23×D71C2414yes—
126C2×D284—232no—
127C2×D284—28no—
128C2×D284—28no—
129C2×D284C22×C4116yescomplemented
130C2×C22⋊D71—264no—
131C2×C22⋊D71—216no—
132C2×C22⋊D71—216no—
133C2×C22⋊D71C22×C4132yescomplemented
134C22×Dic71—22no—
135C22×Dic71—24no—
136C22×Dic71—24no—
137C22×Dic71—22no—
138C22×Dic71—22no—
139C22×Dic71—22no—
140C22×Dic71—22no—
141C22×Dic71—22no—
142C22×Dic71—22no—
143C22×Dic71—22no—
144C22×Dic71—22no—
145C22×Dic71—22no—
146C22×Dic71C22×C418yes—
147C22×Dic71C2×D414yes—
148C22×Dic71C2×D414yes—
149C22×Dic71C2412yes—
150C22×Dic71C2412yes—
151C22×Dic71C2414yes—
152C22×Dic71C2412yes—
153C22×Dic71C2412yes—
154C2×C4×D71—216no—
155C2×C4×D71—216no—
156C2×C4×D71—48no—
157C2×C4×D71—432no—
158C4⋊Dic71C22×C4116yescomplemented
159Dic71⋊C4—216no—
160C22⋊Dic71—28no—
161C22⋊Dic71C2×D4116yescomplemented
162(C2×D71)⋊C4—216no—
163(C2×D71)⋊C4—216no—
164(C2×D71)⋊C4—48no—
165(C2×D71)⋊C4C22×C4132yescomplemented
166C4×Dic71—28no—
167C4×Dic71—28no—
168C4×Dic71—216no—
169C24×C71—22no—
170C24×C71—22no—
171C24×C71—22no—
172C24×C71—22no—
173C24×C71C22×C414yes—
174C24×C71C2×D414yes—
175C24×C71#4114yes—
176C24×C71C2412yes—
177C24×C71C2411yescharacteristic
178C22×C4×C71—24no—
179C22×C4×C71—22no—
180C22×C4×C71—22no—
181C22×C4×C71—24no—
182C22×C4×C71—232no—
183C22×C4×C71—28no—
184C22×C4×C71—28no—
185C22×C4×C71—24no—
186C22×C4×C71—24no—
187C22×C4×C71—216no—
188C22×C4×C71—24no—
189C22×C4×C71—216no—
190C22×C4×C71—48no—
191C22×C4×C71—432no—
192C22×C4×C71C22×C414yes—
193C22×C4×C71C22×C414yes—
194C22×C4×C71C22×C4116yescomplemented
195C22×C4×C71C2×D418yes—
196C22×C4×C71C2×D414yes—
197C22×C4×C71#4114yes—
198C22×C4×C71C2414yes—
199C22×C4×C71C2412yes—
200C22×C4×C71C2414yes—
201C22×C4×C71C2412yes—
202C4⋊C4×C71—216no—
203C4⋊C4×C71—28no—
204C4⋊C4×C71C2×D4116yescomplemented
205C23×C71—28no—
206C23×C71—28no—
207C23×C71—28no—
208C23×C71—28no—
209C23×C71—28no—
210C23×C71—28no—
211C23×C71—22no—
212C23×C71—22no—
213C23×C71—22no—
214C23×C71—22no—
215C23×C71C4×D4116yescomplemented
216C23×C71C23×C414yes—
217C23×C71C23×C412yes—
218C23×C71C22×D414yes—
219C23×C71C22×D412yes—
220C23×C71C22×D412yes—
221C23×C71C2×#4112yes—
222C23×C71C2×#4114yes—
223C23×C71C2×#4112yes—
224C23×C71H(5,𝔽2)12yes—
225C23×C712−1+412yes—
226C23×C71C2511yescharacteristic
227C22×D71—216no—
228C22×D71—216no—
229C22×D71—216no—
230C22×D71—24no—
231C22×D71—24no—
232C22×D71—24no—
233C22×D71—24no—
234C22×D71—24no—
235C22×D71—24no—
236C22×D71—48no—
237C22×D71—48no—
238C22×D71—48no—
239C22×D71—48no—
240C22×D71C23×C418yes—
241C2×C4×C71—28no—
242C2×C4×C71—216no—
243C2×C4×C71—22no—
244C2×C4×C71—24no—
245C2×C4×C71—22no—
246C2×C4×C71—24no—
247C2×C4×C71—232no—
248C2×C4×C71—24no—
249C2×C4×C71—24no—
250C2×C4×C71—24no—
251C2×C4×C71—432no—
252C2×C4×C71—48no—
253C2×C4×C71C4×D4116yescomplemented
254C2×C4×C71C23×C414yes—
255C2×C4×C71C23×C414yes—
256C2×C4×C71C22×D418yes—
257C2×C4×C71C22×D414yes—
258C2×C4×C71C2×#4114yes—
259C22⋊D71—264no—
260C2×Dic71—216no—
261C2×Dic71—28no—
262C2×Dic71—28no—
263C2×Dic71—24no—
264C2×Dic71—22no—
265C2×Dic71—22no—
266C2×Dic71—24no—
267C2×Dic71—22no—
268C2×Dic71—22no—
269C2×Dic71—22no—
270C2×Dic71—22no—
271C2×Dic71—22no—
272C2×Dic71—22no—
273C2×Dic71—22no—
274C2×Dic71—22no—
275C2×Dic71—44no—
276C2×Dic71—44no—
277C2×Dic71C23×C418yes—
278C2×Dic71C22×D414yes—
279C2×Dic71C22×D414yes—
280D284—232no—
281C4×D71—432no—
282C22×C71—232no—
283C22×C71—24no—
284C22×C71—24no—
285C22×C71—24no—
286C22×C71—24no—
287C22×C71—24no—
288C22×C71—24no—
289C22×C71C2×C4×D414yes—
290C22×C71C2×C4×D414yes—
291C22×C71C2×C4×D418yescomplemented
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—28no—
305C2×D71—28no—
306C2×D71—28no—
307C2×D71—432no—
308C2×D71—44no—
309C2×D71—44no—
310C2×D71—44no—
311C2×D71—44no—
312C4×C71—24no—
313C4×C71—28no—
314C4×C71—44no—
315C4×C71C2×C4×D418yescomplemented
316Dic71—28no—
317Dic71—24no—
318Dic71—24no—
319Dic71—42no—
320Dic71—42no—
321C2×#2361—711nomaximal, Sylow
322C2×C71—28no—
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—48no—
332C22×#121—711no—
333C22×C4×D4—712no—
334C22×C4×D4—711no—
335C23×C4⋊C4D7111yescharacteristic, complemented
336#2361—7116no—
337C2×#390—711no—
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×D4—711no—
347C24×C4—712no—
348C24×C4C2×D7112yes—
349C24×C4C2×D7111yescharacteristic
350C2×#121—7116no—
351C2×#121—718no—
352C2×C4×D4—7116no—
353C2×C4×D4—718no—
354C2×C4×D4—14216no—
355C2×C4×D4—1428no—
356C22×C4⋊C4—28no—
357C22×C4⋊C4—711no—
358C22×C4⋊C4—712no—
359C22×C4⋊C4C2×D7112yes—
360C22×C4⋊C4C2×D7111yescharacteristic
361C22×C4⋊C4C2×D7111yescharacteristic
362C22×C4⋊C4C2×D7118yescomplemented
363C22×C22⋊C4—712no—
364C22×C22⋊C4—711no—
365C22×C22⋊C4—712no—
366C22×C22⋊C4—711no—
367C22×C22⋊C4—712no—
368C22×C22⋊C4—712no—
369C22×C42—711no—
370C22×C42—712no—
371C22×C42—711no—
372#390—718no—
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—712no—
384C25C22×D7111yescharacteristic
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—24no—
394C23×C4—24no—
395C23×C4—28no—
396C23×C4—28no—
397C23×C4—44no—
398C23×C4—2844no—
399C23×C4—718no—
400C23×C4—711no—
401C23×C4—711no—
402C23×C4—712no—
403C23×C4—711no—
404C23×C4—711no—
405C23×C4—1428no—
406C23×C4—1428no—
407C23×C4C4×D7118yescomplemented
408C23×C4C22×D7112yes—
409C23×C4C22×D7118yes—
410C23×C4C22×D7111yescharacteristic
411C23×C4C22×D7114yes—
412C23×C4C22×D7112yes—
413C23×C4C22×D7111yescharacteristic
414#121—7164no—
415C4×D4—14264no—
416C4×D4—14232no—
417C2×C4⋊C4—28no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—232no—
420C2×C4⋊C4—718no—
421C2×C4⋊C4—714no—
422C2×C4⋊C4—718no—
423C2×C4⋊C4—1428no—
424C2×C4⋊C4C22⋊D7118yescomplemented
425C2×C4⋊C4C22×D7118yes—
426C2×C4⋊C4C22×D7114yes—
427C2×C4⋊C4C22×D7114yes—
428C2×C22⋊C4—2844no—
429C2×C22⋊C4—718no—
430C2×C22⋊C4—718no—
431C2×C22⋊C4—714no—
432C2×C22⋊C4—7116no—
433C2×C22⋊C4—718no—
434C2×C22⋊C4—714no—
435C2×C22⋊C4—718no—
436C2×C22⋊C4—718no—
437C2×C22⋊C4—1428no—
438C2×C22⋊C4—1424no—
439C2×C22⋊C4—1428no—
440C2×C42—714no—
441C2×C42—718no—
442C2×C42—714no—
443C2×C42—1428no—
444C2×C42—1424no—
445C2×C42—1424no—
446#95—714no—
447#95—714no—
448#95—718no—
449#95—718no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—718no—
455C24—714no—
456C24—1424no—
457C24—1424no—
458C24—1424no—
459C24—1424no—
460C24—1424no—
461C24—1424no—
462C24C2×C4×D7114yes—
463C24D4×D7114yes—
464C24#1176586614yes—
465C24C23×D7112yes—
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—22no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—232no—
482C22×C4—24no—
483C22×C4—216no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—216no—
487C22×C4—48no—
488C22×C4—432no—
489C22×C4—28432no—
490C22×C4—2848no—
491C22×C4—718no—
492C22×C4—714no—
493C22×C4—714no—
494C22×C4—714no—
495C22×C4—712no—
496C22×C4—712no—
497C22×C4—712no—
498C22×C4—712no—
499C22×C4—14216no—
500C22×C4—1422no—
501C22×C4—1422no—
502C22×C4—1422no—
503C22×C4—1422no—
504C22×C4—1422no—
505C22×C4—1422no—
506C22×C4—14216no—
507C22×C4—1424no—
508C22×C4—1422no—
509C22×C4—1422no—
510C22×C4—1424no—
511C22×C4—1422no—
512C22×C4—1422no—
513C22×C4C2×C4×D7114yes—
514C22×C4C2×C4×D7114yes—
515C22×C4C2×C4×D71116yescomplemented
516C22×C4C2×C22⋊D7118yes—
517C22×C4C2×C22⋊D7114yes—
518C22×C4#1176586514yes—
519C22×C4C23×D7114yes—
520C22×C4C23×D7112yes—
521C22×C4C23×D7114yes—
522C22×C4C23×D7112yes—
523C4⋊C4—216no—
524C4⋊C4—28no—
525C4⋊C4—7116no—
526C4⋊C4—14216no—
527C4⋊C4C2×C22⋊D71116yescomplemented
528C22⋊C4—2848no—
529C22⋊C4—7116no—
530C22⋊C4—7132no—
531C22⋊C4—14216no—
532C22⋊C4—1428no—
533C22⋊C4—14216no—
534C42—14216no—
535C42—1428no—
536C42—1428no—
537C23—22no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—28no—
542C23—28no—
543C23—28no—
544C23—28no—
545C23—28no—
546C23—28no—
547C23—2848no—
548C23—2848no—
549C23—2848no—
550C23—2848no—
551C23—718no—
552C23—1424no—
553C23—1424no—
554C23—1424no—
555C23—1424no—
556C23—1424no—
557C23—1424no—
558C23—14216no—
559C23—14216no—
560C23—14216no—
561C23#14556090116yescomplemented
562C23C22×C4×D7114yes—
563C23C22×C4×D7112yes—
564C23C2×D4×D7114yes—
565C23C2×D4×D7112yes—
566C23C22×C22⋊D7112yes—
567C23C2×#1176586512yes—
568C23C2×#1176586614yes—
569C23C2×#1176586612yes—
570C23#1455617312yes—
571C23#1455617612yes—
572C23C24×D7111yescharacteristic
573D4—14264no—
574D4—14232no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—216no—
580C2×C4—28no—
581C2×C4—232no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—432no—
586C2×C4—48no—
587C2×C4—28432no—
588C2×C4—2844no—
589C2×C4—2844no—
590C2×C4—718no—
591C2×C4—714no—
592C2×C4—714no—
593C2×C4—1422no—
594C2×C4—1422no—
595C2×C4—1422no—
596C2×C4—1422no—
597C2×C4—1422no—
598C2×C4—1422no—
599C2×C4—1424no—
600C2×C4—1422no—
601C2×C4—1422no—
602C2×C4—1424no—
603C2×C4—1422no—
604C2×C4—1422no—
605C2×C4—1428no—
606C2×C4—1428no—
607C2×C4—14216no—
608C2×C4C4×C22⋊D71116yescomplemented
609C2×C4C22×C4×D7114yes—
610C2×C4C22×C4×D7114yes—
611C2×C4C22×C22⋊D7118yes—
612C2×C4C22×C22⋊D7114yes—
613C2×C4C2×#1176586514yes—
614C22—24no—
615C22—24no—
616C22—24no—
617C22—24no—
618C22—24no—
619C22—232no—
620C22—24no—
621C22—2844no—
622C22—2844no—
623C22—2844no—
624C22—28432no—
625C22—2844no—
626C22—1428no—
627C22—1428no—
628C22—1428no—
629C22C2×C4×C22⋊D7114yes—
630C22C2×#1455609014yes—
631C22C2×#1455609018yescomplemented
632C22#1798648014yes—
633C22D4×C22⋊D7114yes—
634C22#1798665014yes—
635C22#1798666014yes—
636C22#1798669714yes—
637C22C23×C4×D7111yescharacteristic
638C22C22×D4×D7111yescharacteristic
639C22C23×C22⋊D7111yescharacteristic
640C22C22×#1176586511yescharacteristic
641C22C22×#1176586611yescharacteristic
642C22C2×#1455617311yescharacteristic
643C22C2×#1455617611yescharacteristic
644C4—24no—
645C4—28no—
646C4—44no—
647C4—2842no—
648C4—2842no—
649C4—1428no—
650C4—1424no—
651C4—1424no—
652C4C2×C4×C22⋊D7118yescomplemented
653C2—28no—
654C2—2848no—
655C2#2259135618yesdirect product factor
656C2C22×C4×C22⋊D7111yescharacteristic
657C2C22×#1455609011yescharacteristic
658C2C2×#1798648011yescharacteristic
659C2C2×D4×C22⋊D7111yescharacteristic
660C2C2×#1798665011yescharacteristic
661C2C2×#1798666011yescharacteristic
662C2C2×#1798669711yescharacteristic
subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC23×C4⋊C4×C71C2
socleC24×C71C24
prime radicalC22×#14556102C2
cosocleC23×C71C25
hypercenterC23×C4⋊C4D71
hypocenterC71C2×#2361
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#14556090C2semidirect
3. C22×C4×C22⋊D71C2semidirect
4. #22591356C2direct (N × H)
5. C2×#17985900C2semidirect
6. C2×#17985895C2semidirect
7. C2×#17985889C2semidirect
8. C2×#17985878C2semidirect
9. C2×#17985870C2semidirect
10. C2×C4⋊C4×Dic71C2semidirect
11. C2×C4×C22⋊Dic71C2semidirect
12. C23×C4⋊C4×C71C2semidirect
16. C2×#14556102C4semidirect
19. C2×#14556090C22semidirect
21. C2×C4×C22⋊D71C22semidirect
33. #17985900C22semidirect
34. #17985895C22semidirect
35. #17985889C22semidirect
36. #17985878C22semidirect
37. #17985870C22semidirect
38. C4⋊C4×Dic71C22semidirect
39. C4×C22⋊Dic71C22semidirect
50. C22×C4⋊C4×C71C22semidirect
54. C22×D284C2×C4semidirect
58. C22×C22⋊D71C2×C4semidirect
69. #14556102C2×C4semidirect
72. C2×C4⋊Dic71C2×C4semidirect
77. C2×C22⋊Dic71D4semidirect
83. C2×(C2×D71)⋊C4C2×C4semidirect
104. C23×C4×C71C2×C4semidirect
114. C2×C4⋊C4×C71D4semidirect
129. C2×D284C22×C4semidirect
133. C2×C22⋊D71C22×C4semidirect
158. C4⋊Dic71C22×C4semidirect
161. C22⋊Dic71C2×D4semidirect
165. (C2×D71)⋊C4C22×C4semidirect
194. C22×C4×C71C22×C4semidirect
204. C4⋊C4×C71C2×D4semidirect
215. C23×C71C4×D4semidirect
253. C2×C4×C71C4×D4semidirect
291. C22×C71C2×C4×D4semidirect
315. C4×C71C2×C4×D4semidirect
323. C2×C71#2361semidirect
335. C23×C4⋊C4D71semidirect
344. C71C2×#2361semidirect
362. C22×C4⋊C4C2×D71semidirect
407. C23×C4C4×D71semidirect
424. C2×C4⋊C4C22⋊D71semidirect
515. C22×C4C2×C4×D71semidirect
527. C4⋊C4C2×C22⋊D71semidirect
561. C23#14556090semidirect
608. C2×C4C4×C22⋊D71semidirect
631. C22C2×#14556090semidirect
652. C4C2×C4×C22⋊D71semidirect
655. C2#22591356direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561022
C22×#145560902
C22×C4×C22⋊D712
#225913562
C2×#179859002
C2×#179858952
C2×#179858892
C2×#179858782
C2×#179858702
C2×C4⋊C4×Dic712
C2×C4×C22⋊Dic712
C23×C4⋊C4×C712
C2×#236171