Finite Group Databasebeta

← #31920554

Subgroups — #31920554

Order 18176.

1802 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17985898C211yesmaximal, characteristic, complemented
2C2×#17985891C212yesmaximal
3C2×#17985856C211yesmaximal, characteristic
4C2×#17985856C211yesmaximal, characteristic
5C2×C4×C4⋊Dic71C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic
7#22586596C212yesmaximal, complemented
8#22586588C212yesmaximal
9#22586569C211yesmaximal, characteristic, complemented
10#22586564C212yesmaximal, complemented
11C71×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D71C2211yescharacteristic
13C22×C4⋊Dic71C2212yes—
14C22×C4⋊Dic71C2211yescharacteristic
15C22×C4⋊Dic71C2211yescharacteristic
16C22×(C2×D71)⋊C4C2211yescharacteristic
17C22×(C2×D71)⋊C4C2212yes—
18C22×(C2×D71)⋊C4C2212yes—
19C22×(C2×D71)⋊C4C2211yescharacteristic
20C22×C4×Dic71C2212yes—
21C22×C4×Dic71C2211yescharacteristic
22#17985898—24no—
23#17985891—28no—
24#17985856—24no—
25#17985856C418yescomplemented
26C4×C4⋊Dic71—24no—
27C4×(C2×D71)⋊C4—24no—
28C2×C71⋊#95C2212yes—
29C2×C71⋊#95C2212yes—
30C2×C71⋊#95C2211yescharacteristic
31C2×C71⋊#95C2212yes—
32C2×C71⋊#95C2212yes—
33C2×C71⋊#95C2211yescharacteristic
34C2×C71⋊#95C2212yes—
35C2×C71⋊#95C2212yes—
36C22×C4⋊C4×C71C2211yescharacteristic
37C22×C4⋊C4×C71C2211yescharacteristic
38C22×C42×C71C2211yescharacteristic
39C2×#95×C71C2212yes—
40C2×#95×C71C2212yes—
41C24×D71C2311yescharacteristic
42C23×Dic71C2311yescharacteristic
43C23×Dic71C2312yes—
44C23×Dic71C2311yescharacteristic
45C23×Dic71C2312yes—
46C23×Dic71C2311yescharacteristic
47C22×C4×D71—22no—
48C22×C4×D71—22no—
49C22×C4×D71—22no—
50C22×C4×D71—22no—
51C22×C4×D71—22no—
52C22×C4×D71—22no—
53C22×C4×D71C2×C414yes—
54C2×C4⋊Dic71—24no—
55C2×C4⋊Dic71—24no—
56C2×C4⋊Dic71—22no—
57C2×C4⋊Dic71—22no—
58C2×C4⋊Dic71—22no—
59C2×C4⋊Dic71—22no—
60C2×C4⋊Dic71—42no—
61C2×C4⋊Dic71C2×C414yes—
62C2×C4⋊Dic71D414yes—
63C2×(C2×D71)⋊C4—24no—
64C2×(C2×D71)⋊C4—22no—
65C2×(C2×D71)⋊C4—24no—
66C2×(C2×D71)⋊C4—22no—
67C2×(C2×D71)⋊C4—24no—
68C2×(C2×D71)⋊C4—24no—
69C2×(C2×D71)⋊C4—22no—
70C2×(C2×D71)⋊C4—22no—
71C2×(C2×D71)⋊C4—22no—
72C2×(C2×D71)⋊C4—42no—
73C2×(C2×D71)⋊C4C2×C418yes—
74C2×(C2×D71)⋊C4D414yes—
75C2×C4×Dic71—22no—
76C2×C4×Dic71—24no—
77C2×C4×Dic71—24no—
78C2×C4×Dic71—22no—
79C2×C4×Dic71—24no—
80C2×C4×Dic71—22no—
81C71⋊#95—24no—
82C71⋊#95—24no—
83C71⋊#95—24no—
84C71⋊#95—24no—
85C71⋊#95—22no—
86C71⋊#95—22no—
87C71⋊#95—24no—
88C71⋊#95C2×C418yes—
89C23×C4×C71C2312yes—
90C23×C4×C71C2312yes—
91C23×C4×C71C2311yescharacteristic
92C23×C4×C71C2311yescharacteristic
93C23×C4×C71C2311yescharacteristic
94C2×C4⋊C4×C71—22no—
95C2×C4⋊C4×C71—22no—
96C2×C4⋊C4×C71—22no—
97C2×C4⋊C4×C71—22no—
98C2×C4⋊C4×C71—22no—
99C2×C4⋊C4×C71C2×C414yes—
100C2×C42×C71—22no—
101C2×C42×C71—22no—
102C2×C42×C71D414yes—
103#95×C71—24no—
104#95×C71—42no—
105C23×D71—21no—
106C23×D71—21no—
107C23×D71—21no—
108C23×D71—21no—
109C23×D71—21no—
110C23×D71—21no—
111C23×D71—21no—
112C23×D71—21no—
113C23×D71—21no—
114C23×D71—21no—
115C23×D71—21no—
116C23×D71—21no—
117C23×D71C22×C412yes—
118C23×D71C2×D412yes—
119C23×D71#4112yes—
120C22×Dic71—21no—
121C22×Dic71—21no—
122C22×Dic71—21no—
123C22×Dic71—22no—
124C22×Dic71—21no—
125C22×Dic71—21no—
126C22×Dic71—22no—
127C22×Dic71—22no—
128C22×Dic71—22no—
129C22×Dic71—21no—
130C22×Dic71—21no—
131C22×Dic71—21no—
132C22×Dic71—21no—
133C22×Dic71—21no—
134C22×Dic71—22no—
135C22×Dic71—22no—
136C22×Dic71—21no—
137C22×Dic71—22no—
138C22×Dic71—21no—
139C22×Dic71—22no—
140C22×Dic71—21no—
141C22×Dic71—21no—
142C22×Dic71—22no—
143C22×Dic71—22no—
144C22×Dic71—22no—
145C22×Dic71—21no—
146C22×Dic71—21no—
147C22×Dic71—21no—
148C22×Dic71—21no—
149C22×Dic71—22no—
150C22×Dic71C22×C412yes—
151C22×Dic71C22×C414yes—
152C22×Dic71C2×D414yes—
153C22×Dic71C2×D412yes—
154C22×Dic71#4112yes—
155C2×C4×D71—28no—
156C2×C4×D71—28no—
157C2×C4×D71—28no—
158C2×C4×D71—44no—
159C2×C4×D71—44no—
160C2×C4×D71—44no—
161C2×C4×D71—44no—
162C4⋊Dic71—28no—
163C4⋊Dic71—28no—
164C4⋊Dic71—48no—
165(C2×D71)⋊C4—28no—
166(C2×D71)⋊C4—216no—
167(C2×D71)⋊C4—28no—
168(C2×D71)⋊C4—48no—
169C4×Dic71—48no—
170C4×Dic71—44no—
171C24×C71C2411yescharacteristic
172C22×C4×C71—21no—
173C22×C4×C71—21no—
174C22×C4×C71—21no—
175C22×C4×C71—21no—
176C22×C4×C71—22no—
177C22×C4×C71—22no—
178C22×C4×C71—21no—
179C22×C4×C71—21no—
180C22×C4×C71—22no—
181C22×C4×C71—22no—
182C22×C4×C71—21no—
183C22×C4×C71—21no—
184C22×C4×C71—21no—
185C22×C4×C71—22no—
186C22×C4×C71—22no—
187C22×C4×C71—21no—
188C22×C4×C71—22no—
189C22×C4×C71—22no—
190C22×C4×C71—22no—
191C22×C4×C71—22no—
192C22×C4×C71—22no—
193C22×C4×C71—22no—
194C22×C4×C71—22no—
195C22×C4×C71C22×C414yes—
196C22×C4×C71C22×C412yes—
197C22×C4×C71C2×D412yes—
198C22×C4×C71C2×D412yes—
199C22×C4×C71C2×D412yes—
200C22×C4×C71C2×D412yes—
201C22×C4×C71C2×D412yes—
202C22×C4×C71#4112yes—
203C22×C4×C71#4112yes—
204C22×C4×C71#4112yes—
205C22×C4×C71#4112yes—
206C22×C4×C71#4112yes—
207C4⋊C4×C71—28no—
208C4⋊C4×C71—44no—
209C42×C71—28no—
210C23×C71C23×C411yescharacteristic
211C23×C71C22×D411yescharacteristic
212C23×C71C22×D411yescharacteristic
213C23×C71C22×D411yescharacteristic
214C23×C71C2×#4111yescharacteristic
215C23×C71C2×#4111yescharacteristic
216C23×C71C2×#4111yescharacteristic
217C23×C71C2×#4111yescharacteristic
218C23×C71C2×#4111yescharacteristic
219C23×C71C2×#4111yescharacteristic
220C23×C71C2×#4111yescharacteristic
221C23×C71H(5,𝔽2)11yescharacteristic
222C23×C712−1+411yescharacteristic
223C23×C712−1+411yescharacteristic
224C23×C712−1+411yescharacteristic
225C22×D71—22no—
226C22×D71—22no—
227C22×D71—22no—
228C22×D71—22no—
229C22×D71—22no—
230C22×D71—22no—
231C22×D71—22no—
232C22×D71—22no—
233C22×D71—22no—
234C22×D71—22no—
235C22×D71—22no—
236C22×D71—22no—
237C22×D71—22no—
238C22×D71—22no—
239C22×D71—22no—
240C22×D71—22no—
241C22×D71—22no—
242C22×D71—22no—
243C22×D71—41no—
244C22×D71—41no—
245C22×D71—41no—
246C22×D71—41no—
247C22×D71—41no—
248C22×D71—41no—
249C22×D71—41no—
250C22×D71—41no—
251C22×D71—41no—
252C22×D71—41no—
253C22×D71—41no—
254C22×D71—41no—
255C22×D71—41no—
256C22×D71—41no—
257C22×D71—41no—
258C22×D71—41no—
259C22×D71C4×D414yes—
260C2×C4×C71—22no—
261C2×C4×C71—22no—
262C2×C4×C71—22no—
263C2×C4×C71—22no—
264C2×C4×C71—22no—
265C2×C4×C71—22no—
266C2×C4×C71—24no—
267C2×C4×C71—24no—
268C2×C4×C71—24no—
269C2×C4×C71—22no—
270C2×C4×C71—22no—
271C2×C4×C71—22no—
272C2×C4×C71—42no—
273C2×C4×C71—42no—
274C2×C4×C71—42no—
275C2×C4×C71—41no—
276C2×C4×C71—42no—
277C2×C4×C71—41no—
278C2×C4×C71—41no—
279C2×C4×C71—41no—
280C2×C4×C71—42no—
281C2×C4×C71—42no—
282C2×C4×C71—42no—
283C2×C4×C71—42no—
284C2×C4×C71—42no—
285C2×C4×C71—42no—
286C2×C4×C71—42no—
287C2×C4×C71#11714yes—
288C2×C4×C71C4×D414yes—
289C2×C4×C71C4×D414yes—
290C2×C4×C71#12114yes—
291C2×C4×C71#12114yes—
292C2×C4×C71#12314yes—
293C2×C4×C71#12414yes—
294C2×C4×C71#12614yes—
295C2×Dic71—22no—
296C2×Dic71—24no—
297C2×Dic71—24no—
298C2×Dic71—22no—
299C2×Dic71—22no—
300C2×Dic71—24no—
301C2×Dic71—22no—
302C2×Dic71—24no—
303C2×Dic71—22no—
304C2×Dic71—24no—
305C2×Dic71—22no—
306C2×Dic71—22no—
307C2×Dic71—24no—
308C2×Dic71—22no—
309C2×Dic71—22no—
310C2×Dic71—41no—
311C2×Dic71—42no—
312C2×Dic71—41no—
313C2×Dic71—42no—
314C2×Dic71—41no—
315C2×Dic71—41no—
316C2×Dic71—42no—
317C2×Dic71—41no—
318C2×Dic71—41no—
319C2×Dic71—42no—
320C2×Dic71—42no—
321C2×Dic71—41no—
322C2×Dic71—41no—
323C2×Dic71—42no—
324C2×Dic71—42no—
325C2×Dic71—41no—
326C2×Dic71—41no—
327C2×Dic71—41no—
328C2×Dic71—41no—
329C2×Dic71—42no—
330C4×D71—416no—
331C22×C71C2×#11711yescharacteristic
332C22×C71C2×C4×D411yescharacteristic
333C22×C71C2×C4×D411yescharacteristic
334C22×C71C2×C4×D411yescharacteristic
335C22×C71C4×#4111yescharacteristic
336C22×C71#51911yescharacteristic
337C22×C71#52011yescharacteristic
338C22×C71C2×#12111yescharacteristic
339C22×C71C2×#12111yescharacteristic
340C22×C71C2×#12311yescharacteristic
341C22×C71#52511yescharacteristic
342C22×C71C2×#12411yescharacteristic
343C22×C71C2×#12611yescharacteristic
344C22×C71#52911yescharacteristic
345C22×C71#53211yescharacteristic
346C22×C71#53611yescharacteristic
347C22×C71#53711yescharacteristic
348C22×C71#54111yescharacteristic
349C22×C71#54211yescharacteristic
350C22×C71D4211yescharacteristic
351C22×C71#54711yescharacteristic
352C22×C71#54711yescharacteristic
353C22×C71#54711yescharacteristic
354C22×C71#54711yescharacteristic
355C22×C71#54811yescharacteristic
356C22×C71#54811yescharacteristic
357C22×C71#55211yescharacteristic
358C22×C71#55211yescharacteristic
359C22×C71#55211yescharacteristic
360C22×C71#55211yescharacteristic
361C22×C71#55211yescharacteristic
362C22×C71#55311yescharacteristic
363C22×C71#55511yescharacteristic
364C22×C71#55511yescharacteristic
365C22×C71#55611yescharacteristic
366C2×D71—24no—
367C2×D71—24no—
368C2×D71—24no—
369C2×D71—42no—
370C2×D71—42no—
371C2×D71—42no—
372C2×D71—42no—
373C2×D71—42no—
374C2×D71—42no—
375C2×D71—42no—
376C2×D71—42no—
377C2×D71—42no—
378C2×D71—42no—
379C2×D71—42no—
380C2×D71—42no—
381C4×C71—24no—
382C4×C71—44no—
383C4×C71—42no—
384C4×C71—82no—
385C4×C71#38818yescomplemented
386Dic71—42no—
387Dic71—42no—
388Dic71—44no—
389Dic71—42no—
390Dic71—44no—
391#13994—711nomaximal, Sylow
392C2×C71C2×#38811yescharacteristic
393C2×C71C4×#12111yescharacteristic
394C2×C71#232311yescharacteristic
395C2×C71#234411yescharacteristic
396C2×C71#234611yescharacteristic
397C2×C71#236111yescharacteristic
398C2×C71#236211yescharacteristic
399C2×C71#248511yescharacteristic
400C2×C71#248611yescharacteristic
401C2×C71#248911yescharacteristic
402C2×C71#249111yescharacteristic
403C2×C71#249511yescharacteristic
404C2×C71#249611yescharacteristic
405C2×C71#253611yescharacteristic
406C2×C71#253711yescharacteristic
407D71—44no—
408C2×#389—711no—
409C2×#388—712no—
410C2×#380—711no—
411C2×#380—711no—
412C2×C4×C4⋊C4—711no—
413C2×C4×C22⋊C4—711no—
414#1442—712no—
415#1440—712no—
416C4⋊#95—711no—
417C4⋊#95D7111yescharacteristic, complemented
418#1434—712no—
419C71#1399411yescharacteristic, complemented, Sylow
420C24×C4—711no—
421C22×C4⋊C4—712no—
422C22×C4⋊C4—711no—
423C22×C4⋊C4—711no—
424C22×C4⋊C4C2×D7111yescharacteristic
425C22×C4⋊C4C2×D7111yescharacteristic
426C22×C22⋊C4—712no—
427C22×C22⋊C4—712no—
428C22×C22⋊C4—711no—
429C22×C22⋊C4—711no—
430C22×C42—712no—
431C22×C42—711no—
432C22×C42C2×D7111yescharacteristic
433#389—1424no—
434#388—1428no—
435#380—718no—
436#380—1424no—
437C4×C4⋊C4—1424no—
438C4×C22⋊C4—1424no—
439C2×#95—712no—
440C2×#95—711no—
441C2×#95—712no—
442C2×#95—712no—
443C2×#95—712no—
444C2×#95—712no—
445C2×#95—712no—
446C2×#95—711no—
447C2×#95C2×D7112yes—
448C2×#95C2×D7112yes—
449C25—711no—
450C23×C4—711no—
451C23×C4—712no—
452C23×C4—712no—
453C23×C4—711no—
454C23×C4—711no—
455C23×C4—714no—
456C23×C4—1422no—
457C23×C4—1422no—
458C23×C4—1422no—
459C23×C4—1422no—
460C23×C4—1422no—
461C23×C4—1422no—
462C23×C4C22×D7112yes—
463C23×C4C22×D7112yes—
464C23×C4C22×D7111yescharacteristic
465C23×C4C22×D7111yescharacteristic
466C23×C4C22×D7111yescharacteristic
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—2842no—
473C2×C4⋊C4—714no—
474C2×C4⋊C4—714no—
475C2×C4⋊C4—1424no—
476C2×C4⋊C4—1424no—
477C2×C4⋊C4—1422no—
478C2×C4⋊C4—1422no—
479C2×C4⋊C4—1422no—
480C2×C4⋊C4—1422no—
481C2×C4⋊C4C4×D7114yes—
482C2×C22⋊C4—2842no—
483C2×C22⋊C4—718no—
484C2×C22⋊C4—714no—
485C2×C22⋊C4—1424no—
486C2×C22⋊C4—1424no—
487C2×C22⋊C4—1422no—
488C2×C22⋊C4—1424no—
489C2×C22⋊C4—1424no—
490C2×C22⋊C4—1422no—
491C2×C22⋊C4—1422no—
492C2×C22⋊C4—1422no—
493C2×C22⋊C4—1422no—
494C2×C42—22no—
495C2×C42—22no—
496C2×C42—1424no—
497C2×C42—1422no—
498C2×C42—1422no—
499C2×C42—1424no—
500C2×C42—1424no—
501C2×C42—1422no—
502C2×C42D28414yes—
503#95—24no—
504#95—42no—
505#95—718no—
506#95—1424no—
507#95—1424no—
508#95—1424no—
509#95—1424no—
510#95—1422no—
511#95—1422no—
512#95—1424no—
513C24—712no—
514C24—712no—
515C24—712no—
516C24—1421no—
517C24—1421no—
518C24—1421no—
519C24—1421no—
520C24—1421no—
521C24—1421no—
522C24—1421no—
523C24—1421no—
524C24—1421no—
525C24—1421no—
526C24—1421no—
527C24—1421no—
528C24C23×D7111yescharacteristic
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—2844no—
553C22×C4—2844no—
554C22×C4—2844no—
555C22×C4—2844no—
556C22×C4—712no—
557C22×C4—714no—
558C22×C4—712no—
559C22×C4—714no—
560C22×C4—712no—
561C22×C4—1421no—
562C22×C4—1421no—
563C22×C4—1422no—
564C22×C4—1422no—
565C22×C4—1421no—
566C22×C4—1421no—
567C22×C4—1421no—
568C22×C4—1421no—
569C22×C4—1422no—
570C22×C4—1422no—
571C22×C4—1422no—
572C22×C4—1421no—
573C22×C4—1422no—
574C22×C4—1421no—
575C22×C4—1421no—
576C22×C4—1422no—
577C22×C4—1421no—
578C22×C4—1421no—
579C22×C4—1421no—
580C22×C4—1422no—
581C22×C4—1422no—
582C22×C4—1421no—
583C22×C4—1422no—
584C22×C4—1421no—
585C22×C4—1422no—
586C22×C4—1421no—
587C22×C4—1421no—
588C22×C4—1421no—
589C22×C4—1421no—
590C22×C4—1422no—
591C22×C4—1428no—
592C22×C4—1428no—
593C22×C4—1428no—
594C22×C4C2×C4×D7114yes—
595C22×C4C2×C4×D7112yes—
596C22×C4D4×D7112yes—
597C22×C4D4×D7112yes—
598C22×C4C2×D28412yes—
599C22×C4C2×D28412yes—
600C22×C4C2×D28412yes—
601C22×C4#1176586412yes—
602C22×C4#1176586412yes—
603C22×C4#1176586512yes—
604C22×C4#1176586612yes—
605C22×C4#1176586612yes—
606C4⋊C4—28no—
607C4⋊C4—44no—
608C4⋊C4—2848no—
609C4⋊C4—1428no—
610C4⋊C4—1428no—
611C22⋊C4—2848no—
612C22⋊C4—14216no—
613C22⋊C4—1428no—
614C22⋊C4—1428no—
615C42—28no—
616C42—2848no—
617C42—2844no—
618C23—2841no—
619C23—2841no—
620C23—2841no—
621C23—2841no—
622C23—2841no—
623C23—2841no—
624C23—2841no—
625C23—2841no—
626C23—2841no—
627C23—2841no—
628C23—2841no—
629C23—2841no—
630C23—2841no—
631C23—2841no—
632C23—2841no—
633C23—2841no—
634C23—714no—
635C23—1422no—
636C23—1422no—
637C23—1422no—
638C23—1422no—
639C23—1422no—
640C23—1422no—
641C23—1422no—
642C23—1422no—
643C23—1422no—
644C23—1422no—
645C23—1422no—
646C23—1422no—
647C23—1422no—
648C23—1422no—
649C23—1422no—
650C23—1422no—
651C23—1422no—
652C23—1422no—
653C23C22×C4×D7111yescharacteristic
654C23C2×D4×D7111yescharacteristic
655C23C2×D4×D7111yescharacteristic
656C23C22×D28411yescharacteristic
657C23#41×D7111yescharacteristic
658C23#41×D7111yescharacteristic
659C23C2×#1176586411yescharacteristic
660C23C2×#1176586411yescharacteristic
661C23C2×#1176586511yescharacteristic
662C23C2×#1176586611yescharacteristic
663C23C2×#1176586611yescharacteristic
664C23#1455617311yescharacteristic
665C23#1455617511yescharacteristic
666C23#1455617511yescharacteristic
667C23#1455617611yescharacteristic
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—2841no—
696C2×C4—2841no—
697C2×C4—2842no—
698C2×C4—2841no—
699C2×C4—2842no—
700C2×C4—2841no—
701C2×C4—2841no—
702C2×C4—2841no—
703C2×C4—2842no—
704C2×C4—2842no—
705C2×C4—2841no—
706C2×C4—2841no—
707C2×C4—2842no—
708C2×C4—2841no—
709C2×C4—2841no—
710C2×C4—2842no—
711C2×C4—2841no—
712C2×C4—2841no—
713C2×C4—2842no—
714C2×C4—2842no—
715C2×C4—28416no—
716C2×C4—1424no—
717C2×C4—1422no—
718C2×C4—1424no—
719C2×C4—1422no—
720C2×C4—1422no—
721C2×C4—1422no—
722C2×C4—1422no—
723C2×C4—1424no—
724C2×C4—1422no—
725C2×C4—1424no—
726C2×C4—1422no—
727C2×C4—1424no—
728C2×C4—1422no—
729C2×C4—1424no—
730C2×C4—1422no—
731C2×C4#1455608614yes—
732C2×C4(C22⋊D71)⋊C414yes—
733C2×C4C4×D28414yes—
734C2×C4#1455610314yes—
735C2×C4#1455610314yes—
736C2×C4#1455611214yes—
737C2×C4#1455611414yes—
738C2×C4#1455612314yes—
739C22—2842no—
740C22—2842no—
741C22—2842no—
742C22—2842no—
743C22—2842no—
744C22—2842no—
745C22—2842no—
746C22—2842no—
747C22—2842no—
748C22—2842no—
749C22—2842no—
750C22—2842no—
751C22—1424no—
752C22—1424no—
753C22—1424no—
754C22C2×#1455608611yescharacteristic
755C22C4×D4×D7111yescharacteristic
756C22C2×(C22⋊D71)⋊C411yescharacteristic
757C22C2×C4×D28411yescharacteristic
758C22C4×#1176586611yescharacteristic
759C22#1798647511yescharacteristic
760C22#1798647811yescharacteristic
761C22C2×#1455610311yescharacteristic
762C22C2×#1455610311yescharacteristic
763C22C2×#1455611211yescharacteristic
764C22#1798651111yescharacteristic
765C22C2×#1455611411yescharacteristic
766C22C2×#1455612311yescharacteristic
767C22#1798653611yescharacteristic
768C22#1798654611yescharacteristic
769C22#1798657511yescharacteristic
770C22#1798658011yescharacteristic
771C22#1798660711yescharacteristic
772C22#1798661411yescharacteristic
773C22#1798663411yescharacteristic
774C22#1798664911yescharacteristic
775C22#1798664911yescharacteristic
776C22#1798665211yescharacteristic
777C22#1798665211yescharacteristic
778C22#1798665711yescharacteristic
779C22#1798665711yescharacteristic
780C22#1798668311yescharacteristic
781C22#1798668711yescharacteristic
782C22#1798668711yescharacteristic
783C22#1798669111yescharacteristic
784C22#1798669111yescharacteristic
785C22#1798669611yescharacteristic
786C22#1798671311yescharacteristic
787C22#1798671511yescharacteristic
788C22#1798672011yescharacteristic
789C4—24no—
790C4—42no—
791C4—44no—
792C4—82no—
793C4—2842no—
794C4—2844no—
795C4—2842no—
796C4—2844no—
797C4—2842no—
798C4#1798589118yescomplemented
799C2—2844no—
800C2C2×#1798589111yescharacteristic
801C2C4×#1455610311yescharacteristic
802C2#2259102311yescharacteristic
803C2#2259120811yescharacteristic
804C2#2259122411yescharacteristic
805C2#2259136111yescharacteristic
806C2#2259137211yescharacteristic
807C2#2259263811yescharacteristic
808C2#2259264911yescharacteristic
809C2#2259268211yescharacteristic
810C2#2259270411yescharacteristic
811C2#2259275211yescharacteristic
812C2#2259276311yescharacteristic
813C2#2259325011yescharacteristic
814C2#2259325611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC23×C71C23×C4
FittingC71×C4⋊#95C2
socle, cosocleC24×C71C24
prime radicalC24×D71C23
hypercenterC4⋊#95D71
hypocenterC71#13994
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
1. C2×#17985898C2semidirect
5. C2×C4×C4⋊Dic71C2semidirect
7. #22586596C2semidirect
9. #22586569C2semidirect
10. #22586564C2semidirect
11. C71×C4⋊#95C2semidirect
25. #17985856C4semidirect
385. C4×C71#388semidirect
417. C4⋊#95D71semidirect
419. C71#13994semidirect
798. C4#17985891semidirect

Maximal subgroups

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

subgroupindex
C2×#179858982
C2×#179858912
C2×#179858562
C2×C4×C4⋊Dic712
C2×C4×(C2×D71)⋊C42
#225865962
#225865882
#225865692
#225865642
C71×C4⋊#952
#1399471