Finite Group Databasebeta

← C71×#14722 #31835594

Subgroups — C71×#14722 #31835594

Order 18176.

3246 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C71C211yesmaximal, characteristic, complemented
2C22×C4×D4×C71C211yesmaximal, characteristic, complemented
3C2×#394×C71C211yesmaximal, characteristic, complemented
4C2×#392×C71C212yesmaximal, complemented
5C2×#392×C71C211yesmaximal, characteristic, complemented
6C2×#386×C71C212yesmaximal, complemented
7C71×#1441C211yesmaximal, characteristic, complemented
8C71×#1439C211yesmaximal, characteristic, complemented
9C71×#1438C212yesmaximal, complemented
10C71×#1437C212yesmaximal, complemented
11C71×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C71C2211yescharacteristic
13C23×D4×C71C2212yes—
14C23×D4×C71C2211yescharacteristic
15C23×D4×C71C2212yes—
16C24×C4×C71C2211yescharacteristic
17C24×C4×C71C2211yescharacteristic
18C2×#121×C71—24no—
19C2×#121×C71—28no—
20C2×C4×D4×C71—24no—
21C2×C4×D4×C71—24no—
22C2×C4×D4×C71—24no—
23C22×C4⋊C4×C71C2211yescharacteristic
24C22×C4⋊C4×C71C2211yescharacteristic
25C22×C22⋊C4×C71C2212yes—
26C22×C22⋊C4×C71C2211yescharacteristic
27C22×C22⋊C4×C71C2212yes—
28C22×C22⋊C4×C71C2212yes—
29C22×C22⋊C4×C71C2212yes—
30C22×C22⋊C4×C71C2212yes—
31C22×C22⋊C4×C71C2212yes—
32C22×C22⋊C4×C71C2211yescharacteristic
33C22×C42×C71C2211yescharacteristic
34#394×C71—24no—
35#392×C71—28no—
36#392×C71—24no—
37#386×C71—28no—
38C2×#95×C71C2212yes—
39C2×#95×C71C2212yes—
40C2×#95×C71C2211yescharacteristic
41C2×#95×C71C2212yes—
42C2×#95×C71C2211yescharacteristic
43C2×#95×C71C2212yes—
44C25×C71C2312yes—
45C25×C71C2311yescharacteristic
46C25×C71C2311yescharacteristic
47C22×D4×C71—22no—
48C22×D4×C71—22no—
49C22×D4×C71—22no—
50C22×D4×C71—22no—
51C22×D4×C71—24no—
52C22×D4×C71—24no—
53C22×D4×C71—24no—
54C22×D4×C71—24no—
55C22×D4×C71—24no—
56C22×D4×C71—24no—
57C22×D4×C71—24no—
58C22×D4×C71—24no—
59C22×D4×C71—24no—
60C22×D4×C71—22no—
61C22×D4×C71—24no—
62C22×D4×C71—22no—
63C22×D4×C71—22no—
64C22×D4×C71—22no—
65C22×D4×C71—22no—
66C22×D4×C71—24no—
67C22×D4×C71—42no—
68C22×D4×C71—42no—
69C22×D4×C71—42no—
70C22×D4×C71—42no—
71C22×D4×C71—42no—
72C22×D4×C71D414yescomplemented
73C23×C4×C71—22no—
74C23×C4×C71—22no—
75C23×C4×C71—22no—
76C23×C4×C71—22no—
77C23×C4×C71—22no—
78C23×C4×C71—24no—
79C23×C4×C71—24no—
80C23×C4×C71—42no—
81C23×C4×C71—42no—
82C23×C4×C71D414yescomplemented
83C23×C4×C71C2312yes—
84C23×C4×C71C2311yescharacteristic
85C23×C4×C71C2311yescharacteristic
86C23×C4×C71C2312yes—
87C23×C4×C71C2312yes—
88C23×C4×C71C2311yescharacteristic
89C23×C4×C71C2311yescharacteristic
90C23×C4×C71C2311yescharacteristic
91#121×C71—232no—
92C4×D4×C71—232no—
93C2×C4⋊C4×C71—22no—
94C2×C4⋊C4×C71—22no—
95C2×C4⋊C4×C71—24no—
96C2×C4⋊C4×C71—22no—
97C2×C4⋊C4×C71D414yescomplemented
98C2×C22⋊C4×C71—22no—
99C2×C22⋊C4×C71—22no—
100C2×C22⋊C4×C71—22no—
101C2×C22⋊C4×C71—22no—
102C2×C22⋊C4×C71—22no—
103C2×C22⋊C4×C71—24no—
104C2×C22⋊C4×C71—24no—
105C2×C22⋊C4×C71—24no—
106C2×C22⋊C4×C71—24no—
107C2×C22⋊C4×C71—24no—
108C2×C22⋊C4×C71—24no—
109C2×C22⋊C4×C71—24no—
110C2×C22⋊C4×C71—24no—
111C2×C22⋊C4×C71—24no—
112C2×C22⋊C4×C71—24no—
113C2×C22⋊C4×C71—24no—
114C2×C22⋊C4×C71—24no—
115C2×C22⋊C4×C71—24no—
116C2×C22⋊C4×C71—42no—
117C2×C22⋊C4×C71—42no—
118C2×C22⋊C4×C71—42no—
119C2×C22⋊C4×C71—42no—
120C2×C22⋊C4×C71D414yescomplemented
121C2×C22⋊C4×C71D418yescomplemented
122C2×C42×C71—22no—
123C2×C42×C71—22no—
124C2×C42×C71—22no—
125#95×C71—24no—
126#95×C71—24no—
127#95×C71—22no—
128#95×C71—24no—
129#95×C71—22no—
130#95×C71—42no—
131C24×C71—21no—
132C24×C71—21no—
133C24×C71—21no—
134C24×C71—21no—
135C24×C71—22no—
136C24×C71—22no—
137C24×C71—22no—
138C24×C71—21no—
139C24×C71—21no—
140C24×C71—21no—
141C24×C71—21no—
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—22no—
155C24×C71—22no—
156C24×C71—22no—
157C24×C71—22no—
158C24×C71—22no—
159C24×C71—22no—
160C24×C71—22no—
161C24×C71C2×D414yes—
162C24×C71C2×D412yes—
163C24×C71C2×D412yes—
164C24×C71C2×D412yes—
165C24×C71C2×D412yes—
166C24×C71#4112yes—
167C24×C71#4112yes—
168C24×C71C2411yescharacteristic
169C2×D4×C71—28no—
170C2×D4×C71—28no—
171C2×D4×C71—28no—
172C2×D4×C71—28no—
173C2×D4×C71—28no—
174C2×D4×C71—28no—
175C2×D4×C71—28no—
176C2×D4×C71—216no—
177C2×D4×C71—216no—
178C2×D4×C71—28no—
179C2×D4×C71—48no—
180C2×D4×C71—48no—
181C2×D4×C71—48no—
182C2×D4×C71—48no—
183C2×D4×C71—48no—
184C2×D4×C71—48no—
185C2×D4×C71—44no—
186C2×D4×C71—48no—
187C2×D4×C71—48no—
188C2×D4×C71—48no—
189C2×D4×C71—48no—
190C2×D4×C71—48no—
191C2×D4×C71—48no—
192C2×D4×C71—48no—
193C2×D4×C71—48no—
194C2×D4×C71—44no—
195C22×C4×C71—21no—
196C22×C4×C71—21no—
197C22×C4×C71—21no—
198C22×C4×C71—21no—
199C22×C4×C71—22no—
200C22×C4×C71—21no—
201C22×C4×C71—21no—
202C22×C4×C71—22no—
203C22×C4×C71—22no—
204C22×C4×C71—28no—
205C22×C4×C71—22no—
206C22×C4×C71—22no—
207C22×C4×C71—22no—
208C22×C4×C71—22no—
209C22×C4×C71—22no—
210C22×C4×C71—21no—
211C22×C4×C71—21no—
212C22×C4×C71—21no—
213C22×C4×C71—21no—
214C22×C4×C71—22no—
215C22×C4×C71—22no—
216C22×C4×C71—22no—
217C22×C4×C71—22no—
218C22×C4×C71—22no—
219C22×C4×C71—22no—
220C22×C4×C71—22no—
221C22×C4×C71—22no—
222C22×C4×C71—22no—
223C22×C4×C71—22no—
224C22×C4×C71—22no—
225C22×C4×C71—28no—
226C22×C4×C71—28no—
227C22×C4×C71—22no—
228C22×C4×C71—22no—
229C22×C4×C71—22no—
230C22×C4×C71—22no—
231C22×C4×C71—22no—
232C22×C4×C71—22no—
233C22×C4×C71—22no—
234C22×C4×C71—44no—
235C22×C4×C71—48no—
236C22×C4×C71—48no—
237C22×C4×C71—48no—
238C22×C4×C71—48no—
239C22×C4×C71—44no—
240C22×C4×C71—44no—
241C22×C4×C71C2×D414yes—
242C22×C4×C71C2×D412yes—
243C22×C4×C71C2×D412yes—
244C22×C4×C71C2×D414yes—
245C22×C4×C71C2×D412yes—
246C22×C4×C71C2×D412yes—
247C22×C4×C71C2×D412yes—
248C22×C4×C71C2×D412yes—
249C22×C4×C71C2×D412yes—
250C22×C4×C71C2×D412yes—
251C22×C4×C71#4114yes—
252C22×C4×C71#4112yes—
253C4⋊C4×C71—28no—
254C4⋊C4×C71—28no—
255C22⋊C4×C71—28no—
256C22⋊C4×C71—28no—
257C22⋊C4×C71—216no—
258C22⋊C4×C71—48no—
259C22⋊C4×C71—48no—
260C22⋊C4×C71—48no—
261C22⋊C4×C71—48no—
262C22⋊C4×C71—48no—
263C42×C71—28no—
264C23×C71—22no—
265C23×C71—22no—
266C23×C71—22no—
267C23×C71—22no—
268C23×C71—22no—
269C23×C71—22no—
270C23×C71—22no—
271C23×C71—22no—
272C23×C71—22no—
273C23×C71—22no—
274C23×C71—22no—
275C23×C71—22no—
276C23×C71—22no—
277C23×C71—24no—
278C23×C71—22no—
279C23×C71—22no—
280C23×C71—22no—
281C23×C71—24no—
282C23×C71—24no—
283C23×C71—24no—
284C23×C71—24no—
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—24no—
295C23×C71—24no—
296C23×C71—24no—
297C23×C71—41no—
298C23×C71—42no—
299C23×C71—42no—
300C23×C71—42no—
301C23×C71—41no—
302C23×C71—41no—
303C23×C71—41no—
304C23×C71—42no—
305C23×C71—42no—
306C23×C71—42no—
307C23×C71—42no—
308C23×C71—42no—
309C23×C71—42no—
310C23×C71—42no—
311C23×C71—42no—
312C23×C71—42no—
313C23×C71—42no—
314C23×C71—42no—
315C23×C71—42no—
316C23×C71—42no—
317C23×C71—42no—
318C23×C71—42no—
319C23×C71—42no—
320C23×C71—42no—
321C23×C71—42no—
322C23×C71—42no—
323C23×C71—42no—
324C23×C71—42no—
325C23×C71—42no—
326C23×C71—42no—
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#12114yes—
344C23×C71#12114yescomplemented
345C23×C71C22×D411yescharacteristic
346C23×C71C22×D411yescharacteristic
347C23×C71C22×D411yescharacteristic
348C23×C71C22×D412yes—
349C23×C71C22×D411yescharacteristic
350C23×C71C2×#4111yescharacteristic
351C23×C71C2×#4111yescharacteristic
352C23×C71C2×#4111yescharacteristic
353C23×C71C2×#4112yes—
354C23×C71H(5,𝔽2)12yes—
355C23×C71H(5,𝔽2)12yes—
356D4×C71—232no—
357D4×C71—416no—
358D4×C71—432no—
359D4×C71—432no—
360C2×C4×C71—22no—
361C2×C4×C71—22no—
362C2×C4×C71—22no—
363C2×C4×C71—22no—
364C2×C4×C71—22no—
365C2×C4×C71—22no—
366C2×C4×C71—22no—
367C2×C4×C71—22no—
368C2×C4×C71—22no—
369C2×C4×C71—22no—
370C2×C4×C71—24no—
371C2×C4×C71—24no—
372C2×C4×C71—24no—
373C2×C4×C71—24no—
374C2×C4×C71—22no—
375C2×C4×C71—22no—
376C2×C4×C71—24no—
377C2×C4×C71—24no—
378C2×C4×C71—24no—
379C2×C4×C71—24no—
380C2×C4×C71—24no—
381C2×C4×C71—24no—
382C2×C4×C71—24no—
383C2×C4×C71—24no—
384C2×C4×C71—416no—
385C2×C4×C71—416no—
386C2×C4×C71—41no—
387C2×C4×C71—42no—
388C2×C4×C71—42no—
389C2×C4×C71—41no—
390C2×C4×C71—41no—
391C2×C4×C71—41no—
392C2×C4×C71—42no—
393C2×C4×C71—42no—
394C2×C4×C71—42no—
395C2×C4×C71—42no—
396C2×C4×C71—42no—
397C2×C4×C71—42no—
398C2×C4×C71—42no—
399C2×C4×C71—42no—
400C2×C4×C71—42no—
401C2×C4×C71—42no—
402C2×C4×C71—42no—
403C2×C4×C71—42no—
404C2×C4×C71—42no—
405C2×C4×C71—42no—
406C2×C4×C71—42no—
407C2×C4×C71#12014yes—
408C2×C4×C71#12014yes—
409C2×C4×C71#12114yescomplemented
410C22×C71—24no—
411C22×C71—24no—
412C22×C71—24no—
413C22×C71—28no—
414C22×C71—24no—
415C22×C71—42no—
416C22×C71—42no—
417C22×C71—42no—
418C22×C71—42no—
419C22×C71—42no—
420C22×C71—42no—
421C22×C71—42no—
422C22×C71—44no—
423C22×C71—44no—
424C22×C71—44no—
425C22×C71—42no—
426C22×C71—42no—
427C22×C71—44no—
428C22×C71—44no—
429C22×C71—44no—
430C22×C71—44no—
431C22×C71—42no—
432C22×C71—44no—
433C22×C71—44no—
434C22×C71—44no—
435C22×C71—44no—
436C22×C71—44no—
437C22×C71—44no—
438C22×C71—44no—
439C22×C71—82no—
440C22×C71—82no—
441C22×C71—82no—
442C22×C71—82no—
443C22×C71—82no—
444C22×C71—82no—
445C22×C71—82no—
446C22×C71—82no—
447C22×C71C2×#12011yescharacteristic
448C22×C71C2×#12011yescharacteristic
449C22×C71C2×#12111yescharacteristic
450C22×C71C2×#12111yescharacteristic
451C22×C71C2×#12111yescharacteristic
452C22×C71#52511yescharacteristic
453C22×C71#52511yescharacteristic
454C22×C71#52511yescharacteristic
455C22×C71#52512yes—
456C22×C71#53212yes—
457C22×C71#53211yescharacteristic
458C22×C71#53411yescharacteristic
459C22×C71#53511yescharacteristic
460C22×C71#53812yes—
461C22×C71#54012yes—
462C22×C71D4212yes—
463C22×C71D4212yes—
464C22×C71D4212yes—
465C22×C71#54612yes—
466C22×C71#54612yes—
467C22×C71#54612yes—
468C22×C71#55012yes—
469C22×C71#55312yes—
470C4×C71—24no—
471C4×C71—24no—
472C4×C71—24no—
473C4×C71—42no—
474C4×C71—44no—
475C4×C71—44no—
476C4×C71—42no—
477C4×C71—82no—
478#14722C7111yesmaximal, characteristic, direct product factor, Sylow
479C2×C71—44no—
480C2×C71—44no—
481C2×C71—84no—
482C2×C71#238811yescharacteristic
483C2×C71#240311yescharacteristic
484C2×C71#240811yescharacteristic
485C2×C71#242412yes—
486C2×C71#242812yes—
487C2×C71#243111yescharacteristic
488C2×C71#245612yes—
489C2×C71#246412yes—
490C2×C71#254311yescharacteristic
491C2×C71#263511yescharacteristic
492C2×C71#284711yescharacteristic
493C22×#121C2×C7111yescharacteristic, complemented
494C22×C4×D4C2×C7111yescharacteristic, complemented
495C2×#394C2×C7111yescharacteristic, complemented
496C2×#392C2×C7112yescomplemented
497C2×#392C2×C7111yescharacteristic, complemented
498C2×#386C2×C7112yescomplemented
499#1441C2×C7111yescharacteristic, complemented
500#1439C2×C7111yescharacteristic, complemented
501#1438C2×C7112yescomplemented
502#1437C2×C7112yescomplemented
503C22⋊#95C2×C7111yescharacteristic, complemented
504C71#1472211yescharacteristic, direct product factor, Sylow
505C23×D4C22×C7111yescharacteristic
506C23×D4C22×C7112yes—
507C23×D4C22×C7111yescharacteristic
508C23×D4C22×C7112yes—
509C24×C4C22×C7111yescharacteristic
510C24×C4C22×C7111yescharacteristic
511C2×#121—24no—
512C2×#121—28no—
513C2×C4×D4—24no—
514C2×C4×D4—24no—
515C2×C4×D4—24no—
516C22×C4⋊C4C22×C7111yescharacteristic
517C22×C4⋊C4C22×C7111yescharacteristic
518C22×C22⋊C4C22×C7112yes—
519C22×C22⋊C4C22×C7111yescharacteristic
520C22×C22⋊C4C22×C7112yes—
521C22×C22⋊C4C22×C7112yes—
522C22×C22⋊C4C22×C7112yes—
523C22×C22⋊C4C22×C7112yes—
524C22×C22⋊C4C22×C7111yescharacteristic
525C22×C22⋊C4C22×C7112yes—
526C22×C42C22×C7111yescharacteristic
527#394—24no—
528#392—28no—
529#392—24no—
530#386—28no—
531C2×#95C22×C7111yescharacteristic
532C2×#95C22×C7112yes—
533C2×#95C22×C7111yescharacteristic
534C2×#95C22×C7112yes—
535C2×#95C22×C7112yes—
536C2×#95C22×C7112yes—
537C25C23×C7112yes—
538C25C23×C7111yescharacteristic
539C25C23×C7111yescharacteristic
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—24no—
545C22×D4—24no—
546C22×D4—24no—
547C22×D4—24no—
548C22×D4—24no—
549C22×D4—24no—
550C22×D4—24no—
551C22×D4—24no—
552C22×D4—24no—
553C22×D4—22no—
554C22×D4—24no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—24no—
560C22×D4—42no—
561C22×D4—42no—
562C22×D4—42no—
563C22×D4—42no—
564C22×D4—42no—
565C22×D4D4×C7114yescomplemented
566C23×C4—22no—
567C23×C4—22no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—24no—
572C23×C4—24no—
573C23×C4—42no—
574C23×C4—42no—
575C23×C4D4×C7114yescomplemented
576C23×C4C23×C7112yes—
577C23×C4C23×C7111yescharacteristic
578C23×C4C23×C7111yescharacteristic
579C23×C4C23×C7112yes—
580C23×C4C23×C7112yes—
581C23×C4C23×C7111yescharacteristic
582C23×C4C23×C7111yescharacteristic
583C23×C4C23×C7111yescharacteristic
584#121—232no—
585C4×D4—232no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—24no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4D4×C7114yescomplemented
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—24no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4—24no—
600C2×C22⋊C4—24no—
601C2×C22⋊C4—24no—
602C2×C22⋊C4—24no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—24no—
605C2×C22⋊C4—24no—
606C2×C22⋊C4—24no—
607C2×C22⋊C4—24no—
608C2×C22⋊C4—24no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4—42no—
611C2×C22⋊C4—42no—
612C2×C22⋊C4—42no—
613C2×C22⋊C4D4×C7114yescomplemented
614C2×C22⋊C4D4×C7118yescomplemented
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—22no—
618#95—24no—
619#95—24no—
620#95—22no—
621#95—24no—
622#95—22no—
623#95—42no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24C2×D4×C7114yes—
655C24C2×D4×C7112yes—
656C24C2×D4×C7112yes—
657C24C2×D4×C7112yes—
658C24C2×D4×C7112yes—
659C24#41×C7112yes—
660C24#41×C7112yes—
661C24C24×C7111yescharacteristic
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—216no—
670C2×D4—216no—
671C2×D4—28no—
672C2×D4—48no—
673C2×D4—48no—
674C2×D4—48no—
675C2×D4—48no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—44no—
679C2×D4—48no—
680C2×D4—48no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—48no—
687C2×D4—44no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—28no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—28no—
719C22×C4—28no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—44no—
728C22×C4—48no—
729C22×C4—48no—
730C22×C4—48no—
731C22×C4—48no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4C2×D4×C7114yes—
735C22×C4C2×D4×C7112yes—
736C22×C4C2×D4×C7112yes—
737C22×C4C2×D4×C7114yes—
738C22×C4C2×D4×C7112yes—
739C22×C4C2×D4×C7112yes—
740C22×C4C2×D4×C7112yes—
741C22×C4C2×D4×C7112yes—
742C22×C4C2×D4×C7112yes—
743C22×C4C2×D4×C7112yes—
744C22×C4#41×C7114yes—
745C22×C4#41×C7112yes—
746C4⋊C4—28no—
747C4⋊C4—28no—
748C22⋊C4—28no—
749C22⋊C4—28no—
750C22⋊C4—216no—
751C22⋊C4—48no—
752C22⋊C4—48no—
753C22⋊C4—48no—
754C22⋊C4—48no—
755C22⋊C4—48no—
756C42—28no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—24no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—41no—
791C23—42no—
792C23—41no—
793C23—42no—
794C23—42no—
795C23—41no—
796C23—41no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23#121×C7114yes—
837C23#121×C7114yescomplemented
838C23C22×D4×C7111yescharacteristic
839C23C22×D4×C7111yescharacteristic
840C23C22×D4×C7111yescharacteristic
841C23C22×D4×C7112yes—
842C23C22×D4×C7111yescharacteristic
843C23C2×#41×C7111yescharacteristic
844C23C2×#41×C7111yescharacteristic
845C23C2×#41×C7111yescharacteristic
846C23C2×#41×C7112yes—
847C23H(5,𝔽2)×C7112yes—
848C23H(5,𝔽2)×C7112yes—
849D4—232no—
850D4—416no—
851D4—432no—
852D4—432no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—416no—
878C2×C4—416no—
879C2×C4—41no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—42no—
885C2×C4—41no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4#120×C7114yes—
901C2×C4#120×C7114yes—
902C2×C4#121×C7114yescomplemented
903C22—24no—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—28no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—44no—
917C22—44no—
918C22—44no—
919C22—42no—
920C22—42no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—44no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22—82no—
936C22—82no—
937C22—82no—
938C22—82no—
939C22—82no—
940C22C2×#120×C7111yescharacteristic
941C22C2×#120×C7111yescharacteristic
942C22C2×#121×C7111yescharacteristic
943C22C2×#121×C7111yescharacteristic
944C22C2×#121×C7111yescharacteristic
945C22#525×C7111yescharacteristic
946C22#525×C7111yescharacteristic
947C22#525×C7111yescharacteristic
948C22#525×C7112yes—
949C22#532×C7111yescharacteristic
950C22#532×C7112yes—
951C22#534×C7111yescharacteristic
952C22#535×C7111yescharacteristic
953C22#538×C7112yes—
954C22#540×C7112yes—
955C22D42×C7112yes—
956C22D42×C7112yes—
957C22D42×C7112yes—
958C22#546×C7112yes—
959C22#546×C7112yes—
960C22#546×C7112yes—
961C22#550×C7112yes—
962C22#553×C7112yes—
963C4—24no—
964C4—24no—
965C4—24no—
966C4—42no—
967C4—44no—
968C4—44no—
969C4—42no—
970C4—82no—
971C2—44no—
972C2—44no—
973C2—84no—
974C2C71×#238811yescharacteristic
975C2C71×#240311yescharacteristic
976C2C71×#240811yescharacteristic
977C2C71×#242412yes—
978C2C71×#242812yes—
979C2C71×#243111yescharacteristic
980C2C71×#245612yes—
981C2C71×#246412yes—
982C2C71×#254311yescharacteristic
983C2C71×#263511yescharacteristic
984C2C71×#284711yescharacteristic
subgroupG/H
center, socleC24×C71C24
commutator, Frattini, cosocleC24C24×C71
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C71 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#121×C71C2semidirect
2. C22×C4×D4×C71C2semidirect
3. C2×#394×C71C2semidirect
4. C2×#392×C71C2semidirect
5. C2×#392×C71C2semidirect
6. C2×#386×C71C2semidirect
7. C71×#1441C2semidirect
8. C71×#1439C2semidirect
9. C71×#1438C2semidirect
10. C71×#1437C2semidirect
11. C71×C22⋊#95C2semidirect
72. C22×D4×C71D4semidirect
82. C23×C4×C71D4semidirect
97. C2×C4⋊C4×C71D4semidirect
120. C2×C22⋊C4×C71D4semidirect
121. C2×C22⋊C4×C71D4semidirect
344. C23×C71#121semidirect
409. C2×C4×C71#121semidirect
478. #14722C71direct (N × H)
493. C22×#121C2×C71semidirect
494. C22×C4×D4C2×C71semidirect
495. C2×#394C2×C71semidirect
496. C2×#392C2×C71semidirect
497. C2×#392C2×C71semidirect
498. C2×#386C2×C71semidirect
499. #1441C2×C71semidirect
500. #1439C2×C71semidirect
501. #1438C2×C71semidirect
502. #1437C2×C71semidirect
503. C22⋊#95C2×C71semidirect
504. C71#14722direct (N × H)
565. C22×D4D4×C71semidirect
575. C23×C4D4×C71semidirect
590. C2×C4⋊C4D4×C71semidirect
613. C2×C22⋊C4D4×C71semidirect
614. C2×C22⋊C4D4×C71semidirect
837. C23#121×C71semidirect
902. C2×C4#121×C71semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C712
C22×C4×D4×C712
C2×#394×C712
C2×#392×C712
C2×#386×C712
C71×#14412
C71×#14392
C71×#14382
C71×#14372
C71×C22⋊#952
#1472271