Finite Group Databasebeta

← C71×#14725 #31835597

Subgroups — C71×#14725 #31835597

Order 18176.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C71C211yesmaximal, characteristic
2C23×C22⋊C4×C71C211yesmaximal, characteristic, complemented
3C2×#394×C71C212yesmaximal, complemented
4C2×#386×C71C211yesmaximal, characteristic, complemented
5C2×#386×C71C211yesmaximal, characteristic, complemented
6C2×#380×C71C211yesmaximal, characteristic, complemented
7C2×#379×C71C211yesmaximal, characteristic, complemented
8C71×#1440C212yesmaximal, complemented
9C71×#1439C212yesmaximal, complemented
10C71×#1438C212yesmaximal, complemented
11C71×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C71C2211yescharacteristic
13C23×D4×C71C2211yescharacteristic
14C23×D4×C71C2212yes—
15C24×C4×C71C2211yescharacteristic
16C24×C4×C71C2211yescharacteristic
17C2×#120×C71—24no—
18C2×#120×C71—24no—
19C2×#120×C71—24no—
20C22×C4⋊C4×C71C2212yescomplemented
21C22×C22⋊C4×C71—24no—
22C22×C22⋊C4×C71—28no—
23C22×C22⋊C4×C71C2211yescharacteristic
24C22×C22⋊C4×C71C2211yescharacteristic
25C22×C22⋊C4×C71C2212yes—
26C22×C22⋊C4×C71C2212yes—
27C22×C22⋊C4×C71C2212yes—
28C22×C22⋊C4×C71C2211yescharacteristic
29C22×C22⋊C4×C71C2212yes—
30C22×C22⋊C4×C71C2212yes—
31C22×C22⋊C4×C71C2211yescharacteristic, complemented
32C22×C22⋊C4×C71C2212yescomplemented
33C22×C22⋊C4×C71C2211yescharacteristic, complemented
34#394×C71—28no—
35#386×C71—24no—
36#386×C71—24no—
37#380×C71—24no—
38#379×C71—24no—
39C2×#95×C71C2212yescomplemented
40C2×#95×C71C2211yescharacteristic, complemented
41C2×#95×C71C2212yescomplemented
42C2×#95×C71C2211yescharacteristic, complemented
43C2×#95×C71C2212yescomplemented
44C2×#95×C71C2212yescomplemented
45C25×C71—24no—
46C25×C71—22no—
47C25×C71—24no—
48C25×C71—22no—
49C25×C71—22no—
50C25×C71—22no—
51C25×C71—22no—
52C25×C71—22no—
53C25×C71—42no—
54C25×C71—42no—
55C25×C71D414yes—
56C25×C71C2311yescharacteristic
57C25×C71C2312yes—
58C25×C71C2311yescharacteristic
59C22×D4×C71—24no—
60C22×D4×C71—24no—
61C22×D4×C71—22no—
62C22×D4×C71—22no—
63C22×D4×C71—22no—
64C22×D4×C71—22no—
65C22×D4×C71—22no—
66C22×D4×C71—22no—
67C22×D4×C71—24no—
68C22×D4×C71—24no—
69C22×D4×C71—24no—
70C22×D4×C71—42no—
71C22×D4×C71—42no—
72C22×D4×C71D414yes—
73C23×C4×C71—22no—
74C23×C4×C71—22no—
75C23×C4×C71—22no—
76C23×C4×C71—24no—
77C23×C4×C71—24no—
78C23×C4×C71—22no—
79C23×C4×C71—22no—
80C23×C4×C71—42no—
81C23×C4×C71—42no—
82C23×C4×C71D414yescomplemented
83C23×C4×C71C2312yes—
84C23×C4×C71C2311yescharacteristic
85C23×C4×C71C2311yescharacteristic
86C23×C4×C71C2311yescharacteristic
87C23×C4×C71C2312yes—
88C23×C4×C71C2312yes—
89C23×C4×C71C2311yescharacteristic
90C23×C4×C71C2311yescharacteristic
91#120×C71—232no—
92C2×C4⋊C4×C71—24no—
93C2×C4⋊C4×C71—24no—
94C2×C4⋊C4×C71—42no—
95C2×C22⋊C4×C71—232no—
96C2×C22⋊C4×C71—24no—
97C2×C22⋊C4×C71—24no—
98C2×C22⋊C4×C71—22no—
99C2×C22⋊C4×C71—22no—
100C2×C22⋊C4×C71—24no—
101C2×C22⋊C4×C71—24no—
102C2×C22⋊C4×C71—24no—
103C2×C22⋊C4×C71—24no—
104C2×C22⋊C4×C71—24no—
105C2×C22⋊C4×C71—24no—
106C2×C22⋊C4×C71—24no—
107C2×C22⋊C4×C71—22no—
108C2×C22⋊C4×C71—24no—
109C2×C22⋊C4×C71—22no—
110C2×C22⋊C4×C71—22no—
111C2×C22⋊C4×C71—22no—
112C2×C22⋊C4×C71—22no—
113C2×C22⋊C4×C71—24no—
114C2×C22⋊C4×C71—24no—
115C2×C22⋊C4×C71—24no—
116C2×C22⋊C4×C71—22no—
117C2×C22⋊C4×C71—22no—
118C2×C22⋊C4×C71—22no—
119C2×C22⋊C4×C71—24no—
120C2×C22⋊C4×C71—24no—
121C2×C22⋊C4×C71—42no—
122C2×C22⋊C4×C71—42no—
123C2×C22⋊C4×C71—42no—
124C2×C22⋊C4×C71—42no—
125C2×C22⋊C4×C71D414yes—
126C2×C22⋊C4×C71D418yescomplemented
127#95×C71—24no—
128#95×C71—22no—
129#95×C71—22no—
130#95×C71—24no—
131#95×C71—24no—
132#95×C71—42no—
133C24×C71—22no—
134C24×C71—22no—
135C24×C71—22no—
136C24×C71—22no—
137C24×C71—28no—
138C24×C71—28no—
139C24×C71—216no—
140C24×C71—216no—
141C24×C71—28no—
142C24×C71—22no—
143C24×C71—22no—
144C24×C71—22no—
145C24×C71—22no—
146C24×C71—22no—
147C24×C71—22no—
148C24×C71—22no—
149C24×C71—22no—
150C24×C71—22no—
151C24×C71—22no—
152C24×C71—22no—
153C24×C71—22no—
154C24×C71—28no—
155C24×C71—28no—
156C24×C71—21no—
157C24×C71—22no—
158C24×C71—21no—
159C24×C71—21no—
160C24×C71—21no—
161C24×C71—21no—
162C24×C71—21no—
163C24×C71—22no—
164C24×C71—22no—
165C24×C71—22no—
166C24×C71—48no—
167C24×C71—48no—
168C24×C71—48no—
169C24×C71—48no—
170C24×C71—48no—
171C24×C71—48no—
172C24×C71—48no—
173C24×C71—48no—
174C24×C71—48no—
175C24×C71—44no—
176C24×C71—44no—
177C24×C71—48no—
178C24×C71—44no—
179C24×C71—44no—
180C24×C71—44no—
181C24×C71—44no—
182C24×C71C2×D412yes—
183C24×C71C2×D414yes—
184C24×C71C2×D414yes—
185C24×C71C2×D412yes—
186C24×C71C2×D412yes—
187C24×C71C2×D412yes—
188C24×C71C2×D412yes—
189C24×C71#4114yes—
190C24×C71#4112yes—
191C24×C71#4112yes—
192C24×C71#4112yes—
193C24×C71C2411yescharacteristic
194C2×D4×C71—216no—
195C2×D4×C71—28no—
196C2×D4×C71—28no—
197C2×D4×C71—28no—
198C2×D4×C71—48no—
199C2×D4×C71—48no—
200C2×D4×C71—48no—
201C2×D4×C71—48no—
202C2×D4×C71—48no—
203C2×D4×C71—48no—
204C2×D4×C71—44no—
205C2×D4×C71—44no—
206C2×D4×C71—44no—
207C2×D4×C71—44no—
208C22×C4×C71—21no—
209C22×C4×C71—21no—
210C22×C4×C71—22no—
211C22×C4×C71—28no—
212C22×C4×C71—28no—
213C22×C4×C71—21no—
214C22×C4×C71—21no—
215C22×C4×C71—22no—
216C22×C4×C71—22no—
217C22×C4×C71—22no—
218C22×C4×C71—22no—
219C22×C4×C71—22no—
220C22×C4×C71—21no—
221C22×C4×C71—21no—
222C22×C4×C71—22no—
223C22×C4×C71—22no—
224C22×C4×C71—21no—
225C22×C4×C71—22no—
226C22×C4×C71—21no—
227C22×C4×C71—21no—
228C22×C4×C71—21no—
229C22×C4×C71—22no—
230C22×C4×C71—22no—
231C22×C4×C71—22no—
232C22×C4×C71—22no—
233C22×C4×C71—22no—
234C22×C4×C71—22no—
235C22×C4×C71—28no—
236C22×C4×C71—21no—
237C22×C4×C71—22no—
238C22×C4×C71—22no—
239C22×C4×C71—21no—
240C22×C4×C71—22no—
241C22×C4×C71—22no—
242C22×C4×C71—21no—
243C22×C4×C71—21no—
244C22×C4×C71—22no—
245C22×C4×C71—21no—
246C22×C4×C71—22no—
247C22×C4×C71—21no—
248C22×C4×C71—22no—
249C22×C4×C71—22no—
250C22×C4×C71—22no—
251C22×C4×C71—22no—
252C22×C4×C71—22no—
253C22×C4×C71—44no—
254C22×C4×C71—48no—
255C22×C4×C71—48no—
256C22×C4×C71—48no—
257C22×C4×C71—48no—
258C22×C4×C71—44no—
259C22×C4×C71—44no—
260C22×C4×C71C2×D412yes—
261C22×C4×C71C2×D412yes—
262C22×C4×C71C2×D414yes—
263C22×C4×C71C2×D414yes—
264C22×C4×C71C2×D412yes—
265C22×C4×C71C2×D414yes—
266C4⋊C4×C71—48no—
267C22⋊C4×C71—216no—
268C22⋊C4×C71—216no—
269C22⋊C4×C71—28no—
270C22⋊C4×C71—216no—
271C22⋊C4×C71—48no—
272C22⋊C4×C71—44no—
273C22⋊C4×C71—48no—
274C22⋊C4×C71—44no—
275C22⋊C4×C71—48no—
276C22⋊C4×C71—44no—
277C22⋊C4×C71—44no—
278C23×C71—22no—
279C23×C71—24no—
280C23×C71—22no—
281C23×C71—24no—
282C23×C71—22no—
283C23×C71—24no—
284C23×C71—22no—
285C23×C71—24no—
286C23×C71—24no—
287C23×C71—24no—
288C23×C71—24no—
289C23×C71—24no—
290C23×C71—24no—
291C23×C71—24no—
292C23×C71—24no—
293C23×C71—24no—
294C23×C71—232no—
295C23×C71—24no—
296C23×C71—24no—
297C23×C71—24no—
298C23×C71—24no—
299C23×C71—24no—
300C23×C71—24no—
301C23×C71—24no—
302C23×C71—24no—
303C23×C71—24no—
304C23×C71—24no—
305C23×C71—24no—
306C23×C71—24no—
307C23×C71—24no—
308C23×C71—24no—
309C23×C71—24no—
310C23×C71—24no—
311C23×C71—24no—
312C23×C71—24no—
313C23×C71—22no—
314C23×C71—22no—
315C23×C71—22no—
316C23×C71—24no—
317C23×C71—24no—
318C23×C71—432no—
319C23×C71—432no—
320C23×C71—416no—
321C23×C71—416no—
322C23×C71—416no—
323C23×C71—416no—
324C23×C71—432no—
325C23×C71—432no—
326C23×C71—416no—
327C23×C71—42no—
328C23×C71—42no—
329C23×C71—42no—
330C23×C71—42no—
331C23×C71—42no—
332C23×C71—42no—
333C23×C71—42no—
334C23×C71—42no—
335C23×C71—42no—
336C23×C71—42no—
337C23×C71—42no—
338C23×C71—42no—
339C23×C71—42no—
340C23×C71—42no—
341C23×C71—42no—
342C23×C71—42no—
343C23×C71—416no—
344C23×C71—41no—
345C23×C71—41no—
346C23×C71—41no—
347C23×C71—42no—
348C23×C71—41no—
349C23×C71—42no—
350C23×C71—41no—
351C23×C71—41no—
352C23×C71—41no—
353C23×C71—42no—
354C23×C71—41no—
355C23×C71—42no—
356C23×C71—42no—
357C23×C71—42no—
358C23×C71—42no—
359C23×C71—42no—
360C23×C71—42no—
361C23×C71—42no—
362C23×C71#12014yes—
363C23×C71#12118yes—
364C23×C71#12114yes—
365C23×C71#12114yes—
366C23×C71#12114yes—
367C23×C71#12314yes—
368C23×C71#12314yes—
369C23×C71#12414yes—
370C23×C71C22×D411yescharacteristic
371C23×C71C22×D411yescharacteristic
372C23×C71C22×D411yescharacteristic
373C23×C71C22×D412yes—
374C23×C71C22×D411yescharacteristic
375C23×C71C2×#4111yescharacteristic
376C23×C71C2×#4111yescharacteristic
377C23×C71C2×#4111yescharacteristic
378C23×C71C2×#4112yes—
379C23×C71H(5,𝔽2)12yes—
380C23×C71H(5,𝔽2)12yes—
381D4×C71—432no—
382D4×C71—416no—
383C2×C4×C71—22no—
384C2×C4×C71—22no—
385C2×C4×C71—24no—
386C2×C4×C71—24no—
387C2×C4×C71—24no—
388C2×C4×C71—22no—
389C2×C4×C71—22no—
390C2×C4×C71—24no—
391C2×C4×C71—22no—
392C2×C4×C71—22no—
393C2×C4×C71—22no—
394C2×C4×C71—22no—
395C2×C4×C71—24no—
396C2×C4×C71—24no—
397C2×C4×C71—24no—
398C2×C4×C71—24no—
399C2×C4×C71—416no—
400C2×C4×C71—416no—
401C2×C4×C71—42no—
402C2×C4×C71—41no—
403C2×C4×C71—41no—
404C2×C4×C71—42no—
405C2×C4×C71—41no—
406C2×C4×C71—41no—
407C2×C4×C71—42no—
408C2×C4×C71—42no—
409C2×C4×C71—42no—
410C2×C4×C71—42no—
411C2×C4×C71—42no—
412C2×C4×C71—42no—
413C2×C4×C71—42no—
414C2×C4×C71—42no—
415C2×C4×C71—41no—
416C2×C4×C71—42no—
417C2×C4×C71—41no—
418C2×C4×C71—42no—
419C2×C4×C71—41no—
420C2×C4×C71—42no—
421C2×C4×C71—41no—
422C2×C4×C71—42no—
423C2×C4×C71—42no—
424C2×C4×C71—41no—
425C2×C4×C71—42no—
426C2×C4×C71—41no—
427C2×C4×C71—42no—
428C2×C4×C71—42no—
429C2×C4×C71—42no—
430C2×C4×C71—42no—
431C2×C4×C71—42no—
432C2×C4×C71#12014yescomplemented
433C22×C71—24no—
434C22×C71—24no—
435C22×C71—24no—
436C22×C71—24no—
437C22×C71—28no—
438C22×C71—24no—
439C22×C71—28no—
440C22×C71—28no—
441C22×C71—28no—
442C22×C71—24no—
443C22×C71—28no—
444C22×C71—28no—
445C22×C71—28no—
446C22×C71—464no—
447C22×C71—44no—
448C22×C71—44no—
449C22×C71—44no—
450C22×C71—44no—
451C22×C71—44no—
452C22×C71—44no—
453C22×C71—44no—
454C22×C71—44no—
455C22×C71—44no—
456C22×C71—44no—
457C22×C71—44no—
458C22×C71—44no—
459C22×C71—42no—
460C22×C71—42no—
461C22×C71—44no—
462C22×C71—44no—
463C22×C71—42no—
464C22×C71—81no—
465C22×C71—81no—
466C22×C71—81no—
467C22×C71—81no—
468C22×C71—82no—
469C22×C71—82no—
470C22×C71#39418yescomplemented
471C22×C71C2×#12011yescharacteristic
472C22×C71C2×#12011yescharacteristic
473C22×C71C2×#12111yescharacteristic
474C22×C71C2×#12112yes—
475C22×C71C2×#12111yescharacteristic
476C22×C71C2×#12111yescharacteristic
477C22×C71C2×#12311yescharacteristic
478C22×C71C2×#12311yescharacteristic
479C22×C71#52511yescharacteristic
480C22×C71#52512yes—
481C22×C71C2×#12411yescharacteristic
482C22×C71#53412yes—
483C22×C71#53411yescharacteristic
484C22×C71#53511yescharacteristic
485C22×C71#53812yes—
486C22×C71D4212yes—
487C22×C71D4212yes—
488C22×C71#54612yes—
489C22×C71#54612yes—
490C22×C71#54612yes—
491C22×C71#54612yes—
492C22×C71#55112yes—
493C22×C71#55112yes—
494C4×C71—24no—
495C4×C71—42no—
496C4×C71—44no—
497C4×C71—42no—
498C4×C71—44no—
499C4×C71—81no—
500C4×C71—81no—
501C4×C71—82no—
502#14725C7111yesmaximal, characteristic, direct product factor, Sylow
503C2×C71—28no—
504C2×C71—48no—
505C2×C71—82no—
506C2×C71C2×#39411yescharacteristic
507C2×C71#240811yescharacteristic
508C2×C71#241011yescharacteristic
509C2×C71#241012yes—
510C2×C71#241111yescharacteristic
511C2×C71#241212yes—
512C2×C71#241812yes—
513C2×C71#247212yes—
514C2×C71#253411yescharacteristic
515C2×C71#261711yescharacteristic
516C2×C71#284711yescharacteristic
517C22×#120C2×C7111yescharacteristic
518C23×C22⋊C4C2×C7111yescharacteristic, complemented
519C2×#394C2×C7112yescomplemented
520C2×#386C2×C7111yescharacteristic, complemented
521C2×#386C2×C7111yescharacteristic, complemented
522C2×#380C2×C7111yescharacteristic, complemented
523C2×#379C2×C7111yescharacteristic, complemented
524#1440C2×C7112yescomplemented
525#1439C2×C7112yescomplemented
526#1438C2×C7112yescomplemented
527C22⋊#95C2×C7111yescharacteristic, complemented
528C71#1472511yescharacteristic, direct product factor, Sylow
529C26C22×C7111yescharacteristic
530C23×D4C22×C7111yescharacteristic
531C23×D4C22×C7112yes—
532C24×C4C22×C7111yescharacteristic
533C24×C4C22×C7111yescharacteristic
534C2×#120—24no—
535C2×#120—24no—
536C2×#120—24no—
537C22×C4⋊C4C22×C7112yescomplemented
538C22×C22⋊C4—24no—
539C22×C22⋊C4—28no—
540C22×C22⋊C4C22×C7112yes—
541C22×C22⋊C4C22×C7112yes—
542C22×C22⋊C4C22×C7112yes—
543C22×C22⋊C4C22×C7111yescharacteristic
544C22×C22⋊C4C22×C7111yescharacteristic
545C22×C22⋊C4C22×C7111yescharacteristic
546C22×C22⋊C4C22×C7112yes—
547C22×C22⋊C4C22×C7112yes—
548C22×C22⋊C4C22×C7111yescharacteristic, complemented
549C22×C22⋊C4C22×C7112yescomplemented
550C22×C22⋊C4C22×C7111yescharacteristic, complemented
551#394—28no—
552#386—24no—
553#386—24no—
554#380—24no—
555#379—24no—
556C2×#95C22×C7112yescomplemented
557C2×#95C22×C7112yescomplemented
558C2×#95C22×C7111yescharacteristic, complemented
559C2×#95C22×C7112yescomplemented
560C2×#95C22×C7111yescharacteristic, complemented
561C2×#95C22×C7112yescomplemented
562C25—24no—
563C25—22no—
564C25—24no—
565C25—22no—
566C25—22no—
567C25—22no—
568C25—22no—
569C25—22no—
570C25—42no—
571C25—42no—
572C25D4×C7114yes—
573C25C23×C7111yescharacteristic
574C25C23×C7112yes—
575C25C23×C7111yescharacteristic
576C22×D4—24no—
577C22×D4—24no—
578C22×D4—22no—
579C22×D4—22no—
580C22×D4—22no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—42no—
588C22×D4—42no—
589C22×D4D4×C7114yes—
590C23×C4—22no—
591C23×C4—22no—
592C23×C4—22no—
593C23×C4—24no—
594C23×C4—24no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—42no—
598C23×C4—42no—
599C23×C4D4×C7114yescomplemented
600C23×C4C23×C7112yes—
601C23×C4C23×C7111yescharacteristic
602C23×C4C23×C7111yescharacteristic
603C23×C4C23×C7111yescharacteristic
604C23×C4C23×C7112yes—
605C23×C4C23×C7112yes—
606C23×C4C23×C7111yescharacteristic
607C23×C4C23×C7111yescharacteristic
608#120—232no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—42no—
612C2×C22⋊C4—232no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—24no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—24no—
620C2×C22⋊C4—24no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—42no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4D4×C7114yes—
643C2×C22⋊C4D4×C7118yescomplemented
644#95—24no—
645#95—22no—
646#95—22no—
647#95—24no—
648#95—24no—
649#95—42no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—28no—
655C24—28no—
656C24—216no—
657C24—216no—
658C24—28no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—28no—
672C24—28no—
673C24—21no—
674C24—22no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—44no—
693C24—44no—
694C24—48no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24C2×D4×C7112yes—
700C24C2×D4×C7114yes—
701C24C2×D4×C7114yes—
702C24C2×D4×C7112yes—
703C24C2×D4×C7112yes—
704C24C2×D4×C7112yes—
705C24C2×D4×C7112yes—
706C24#41×C7114yes—
707C24#41×C7112yes—
708C24#41×C7112yes—
709C24#41×C7112yes—
710C24C24×C7111yescharacteristic
711C2×D4—216no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—28no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—44no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—48no—
774C22×C4—48no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4C2×D4×C7112yes—
778C22×C4C2×D4×C7112yes—
779C22×C4C2×D4×C7114yes—
780C22×C4C2×D4×C7114yes—
781C22×C4C2×D4×C7112yes—
782C22×C4C2×D4×C7114yes—
783C4⋊C4—48no—
784C22⋊C4—216no—
785C22⋊C4—216no—
786C22⋊C4—28no—
787C22⋊C4—216no—
788C22⋊C4—48no—
789C22⋊C4—44no—
790C22⋊C4—48no—
791C22⋊C4—44no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C23—22no—
796C23—24no—
797C23—22no—
798C23—24no—
799C23—22no—
800C23—24no—
801C23—22no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—232no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—24no—
834C23—24no—
835C23—432no—
836C23—432no—
837C23—416no—
838C23—416no—
839C23—416no—
840C23—416no—
841C23—416no—
842C23—432no—
843C23—432no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—416no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—41no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—41no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23#120×C7114yes—
880C23#121×C7118yes—
881C23#121×C7114yes—
882C23#121×C7114yes—
883C23#121×C7114yes—
884C23#123×C7114yes—
885C23#123×C7114yes—
886C23#124×C7114yes—
887C23C22×D4×C7111yescharacteristic
888C23C22×D4×C7111yescharacteristic
889C23C22×D4×C7111yescharacteristic
890C23C22×D4×C7112yes—
891C23C22×D4×C7111yescharacteristic
892C23C2×#41×C7111yescharacteristic
893C23C2×#41×C7111yescharacteristic
894C23C2×#41×C7111yescharacteristic
895C23C2×#41×C7112yes—
896C23H(5,𝔽2)×C7112yes—
897C23H(5,𝔽2)×C7112yes—
898D4—432no—
899D4—416no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—416no—
917C2×C4—416no—
918C2×C4—42no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—42no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—41no—
933C2×C4—42no—
934C2×C4—41no—
935C2×C4—42no—
936C2×C4—41no—
937C2×C4—42no—
938C2×C4—41no—
939C2×C4—42no—
940C2×C4—41no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—41no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4#120×C7114yescomplemented
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—28no—
956C22—24no—
957C22—28no—
958C22—28no—
959C22—28no—
960C22—28no—
961C22—28no—
962C22—28no—
963C22—464no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—44no—
980C22—44no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—82no—
986C22—82no—
987C22#394×C7118yescomplemented
988C22C2×#120×C7111yescharacteristic
989C22C2×#120×C7111yescharacteristic
990C22C2×#121×C7111yescharacteristic
991C22C2×#121×C7111yescharacteristic
992C22C2×#121×C7112yes—
993C22C2×#121×C7111yescharacteristic
994C22C2×#123×C7111yescharacteristic
995C22C2×#123×C7111yescharacteristic
996C22#525×C7111yescharacteristic
997C22#525×C7112yes—
998C22C2×#124×C7111yescharacteristic
999C22#534×C7111yescharacteristic
1000C22#534×C7112yes—
1001C22#535×C7111yescharacteristic
1002C22#538×C7112yes—
1003C22D42×C7112yes—
1004C22D42×C7112yes—
1005C22#546×C7112yes—
1006C22#546×C7112yes—
1007C22#546×C7112yes—
1008C22#546×C7112yes—
1009C22#551×C7112yes—
1010C22#551×C7112yes—
1011C4—24no—
1012C4—42no—
1013C4—44no—
1014C4—42no—
1015C4—44no—
1016C4—81no—
1017C4—81no—
1018C4—82no—
1019C2—28no—
1020C2—48no—
1021C2—82no—
1022C2C2×#394×C7111yescharacteristic
1023C2C71×#240811yescharacteristic
1024C2C71×#241011yescharacteristic
1025C2C71×#241012yes—
1026C2C71×#241111yescharacteristic
1027C2C71×#241212yes—
1028C2C71×#241812yes—
1029C2C71×#247212yes—
1030C2C71×#253411yescharacteristic
1031C2C71×#261711yescharacteristic
1032C2C71×#284711yescharacteristic
subgroupG/H
center, socleC24×C71C24
commutator, Frattini, cosocleC24C24×C71
prime radicalC22×#120×C71C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C71 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C71C2semidirect
3. C2×#394×C71C2semidirect
4. C2×#386×C71C2semidirect
5. C2×#386×C71C2semidirect
6. C2×#380×C71C2semidirect
7. C2×#379×C71C2semidirect
8. C71×#1440C2semidirect
9. C71×#1439C2semidirect
10. C71×#1438C2semidirect
11. C71×C22⋊#95C2semidirect
20. C22×C4⋊C4×C71C22semidirect
31. C22×C22⋊C4×C71C22semidirect
32. C22×C22⋊C4×C71C22semidirect
33. C22×C22⋊C4×C71C22semidirect
39. C2×#95×C71C22semidirect
40. C2×#95×C71C22semidirect
41. C2×#95×C71C22semidirect
42. C2×#95×C71C22semidirect
43. C2×#95×C71C22semidirect
44. C2×#95×C71C22semidirect
82. C23×C4×C71D4semidirect
126. C2×C22⋊C4×C71D4semidirect
432. C2×C4×C71#120semidirect
470. C22×C71#394semidirect
502. #14725C71direct (N × H)
518. C23×C22⋊C4C2×C71semidirect
519. C2×#394C2×C71semidirect
520. C2×#386C2×C71semidirect
521. C2×#386C2×C71semidirect
522. C2×#380C2×C71semidirect
523. C2×#379C2×C71semidirect
524. #1440C2×C71semidirect
525. #1439C2×C71semidirect
526. #1438C2×C71semidirect
527. C22⋊#95C2×C71semidirect
528. C71#14725direct (N × H)
537. C22×C4⋊C4C22×C71semidirect
548. C22×C22⋊C4C22×C71semidirect
549. C22×C22⋊C4C22×C71semidirect
550. C22×C22⋊C4C22×C71semidirect
556. C2×#95C22×C71semidirect
557. C2×#95C22×C71semidirect
558. C2×#95C22×C71semidirect
559. C2×#95C22×C71semidirect
560. C2×#95C22×C71semidirect
561. C2×#95C22×C71semidirect
599. C23×C4D4×C71semidirect
643. C2×C22⋊C4D4×C71semidirect
949. C2×C4#120×C71semidirect
987. C22#394×C71semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C712
C23×C22⋊C4×C712
C2×#394×C712
C2×#386×C712
C2×#380×C712
C2×#379×C712
C71×#14402
C71×#14392
C71×#14382
C71×C22⋊#952
#1472571