Finite Group Databasebeta

← C71×#14751 #31835623

Subgroups — C71×#14751 #31835623

Order 18176.

2302 conjugacy classes of subgroups.

The subgroup lattice has 1334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#394×C71C211yesmaximal, characteristic, complemented
2C2×#394×C71C211yesmaximal, characteristic, complemented
3C2×#392×C71C211yesmaximal, characteristic
4C2×#390×C71C211yesmaximal, characteristic, complemented
5C2×#388×C71C211yesmaximal, characteristic, complemented
6C2×#386×C71C211yesmaximal, characteristic, complemented
7C2×#386×C71C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊C4×C71C211yesmaximal, characteristic, complemented
9C71×#1441C211yesmaximal, characteristic, complemented
10C71×#1440C211yesmaximal, characteristic, complemented
11C71×#1439C211yesmaximal, characteristic, complemented
12C71×#1439C211yesmaximal, characteristic, complemented
13C71×#1438C211yesmaximal, characteristic, complemented
14C71×#1437C211yesmaximal, characteristic, complemented
15C71×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C71C2211yescharacteristic
17C23×D4×C71C2211yescharacteristic
18C23×D4×C71C2211yescharacteristic
19C24×C4×C71C2211yescharacteristic
20C22×C4⋊C4×C71C2211yescharacteristic
21C22×C4⋊C4×C71C2211yescharacteristic
22C22×C4⋊C4×C71C2211yescharacteristic
23C22×C22⋊C4×C71C2211yescharacteristic
24C22×C22⋊C4×C71C2211yescharacteristic
25C22×C22⋊C4×C71C2211yescharacteristic
26C22×C22⋊C4×C71C2211yescharacteristic
27C22×C22⋊C4×C71C2211yescharacteristic
28C22×C22⋊C4×C71C2211yescharacteristic
29C22×C22⋊C4×C71C2211yescharacteristic
30C22×C22⋊C4×C71C2211yescharacteristic
31C22×C22⋊C4×C71C2211yescharacteristic
32C22×C22⋊C4×C71C2211yescharacteristic
33C22×C22⋊C4×C71C2211yescharacteristic
34C22×C22⋊C4×C71C2211yescharacteristic
35C22×C22⋊C4×C71C2211yescharacteristic
36C22×C22⋊C4×C71C2211yescharacteristic
37C22×C42×C71C2211yescharacteristic
38C22×C42×C71C2211yescharacteristic
39#394×C71—24no—
40#394×C71—24no—
41#392×C71—24no—
42#390×C71—24no—
43#388×C71—24no—
44#386×C71—24no—
45#386×C71—24no—
46C4×C22⋊C4×C71—24no—
47C2×#95×C71C2211yescharacteristic
48C2×#95×C71C2211yescharacteristic
49C2×#95×C71C2211yescharacteristic
50C2×#95×C71C2211yescharacteristic
51C2×#95×C71C2211yescharacteristic
52C2×#95×C71C2211yescharacteristic
53C2×#95×C71C2211yescharacteristic
54C2×#95×C71C2211yescharacteristic
55C2×#95×C71C2211yescharacteristic
56C2×#95×C71C2211yescharacteristic
57C2×#95×C71C2211yescharacteristic
58C2×#95×C71C2211yescharacteristic
59C25×C71C2311yescharacteristic
60C25×C71C2311yescharacteristic
61C25×C71C2311yescharacteristic
62C22×D4×C71—22no—
63C22×D4×C71—22no—
64C22×D4×C71—22no—
65C22×D4×C71—22no—
66C22×D4×C71—22no—
67C22×D4×C71—22no—
68C22×D4×C71—22no—
69C22×D4×C71—22no—
70C22×D4×C71—22no—
71C22×D4×C71—22no—
72C22×D4×C71—22no—
73C22×D4×C71—22no—
74C22×D4×C71—22no—
75C22×D4×C71—22no—
76C22×D4×C71—22no—
77C22×D4×C71—41no—
78C22×D4×C71—41no—
79C22×D4×C71—41no—
80C22×D4×C71—41no—
81C22×D4×C71—41no—
82C22×D4×C71—41no—
83C23×C4×C71—22no—
84C23×C4×C71—22no—
85C23×C4×C71—22no—
86C23×C4×C71—22no—
87C23×C4×C71—22no—
88C23×C4×C71—41no—
89C23×C4×C71—41no—
90C23×C4×C71C2311yescharacteristic
91C23×C4×C71C2311yescharacteristic
92C23×C4×C71C2311yescharacteristic
93C23×C4×C71C2311yescharacteristic
94C23×C4×C71C2311yescharacteristic
95C23×C4×C71C2311yescharacteristic
96C23×C4×C71C2311yescharacteristic
97C23×C4×C71C2311yescharacteristic
98C23×C4×C71C2311yescharacteristic
99C23×C4×C71C2311yescharacteristic
100C23×C4×C71C2311yescharacteristic
101C23×C4×C71C2311yescharacteristic
102C2×C4⋊C4×C71—22no—
103C2×C4⋊C4×C71—22no—
104C2×C4⋊C4×C71—22no—
105C2×C4⋊C4×C71—22no—
106C2×C4⋊C4×C71—22no—
107C2×C4⋊C4×C71—22no—
108C2×C4⋊C4×C71—41no—
109C2×C4⋊C4×C71—41no—
110C2×C4⋊C4×C71—41no—
111C2×C22⋊C4×C71—22no—
112C2×C22⋊C4×C71—22no—
113C2×C22⋊C4×C71—22no—
114C2×C22⋊C4×C71—22no—
115C2×C22⋊C4×C71—22no—
116C2×C22⋊C4×C71—22no—
117C2×C22⋊C4×C71—22no—
118C2×C22⋊C4×C71—22no—
119C2×C22⋊C4×C71—22no—
120C2×C22⋊C4×C71—22no—
121C2×C22⋊C4×C71—22no—
122C2×C22⋊C4×C71—22no—
123C2×C22⋊C4×C71—22no—
124C2×C22⋊C4×C71—22no—
125C2×C22⋊C4×C71—22no—
126C2×C22⋊C4×C71—22no—
127C2×C22⋊C4×C71—22no—
128C2×C22⋊C4×C71—22no—
129C2×C22⋊C4×C71—22no—
130C2×C22⋊C4×C71—22no—
131C2×C22⋊C4×C71—22no—
132C2×C22⋊C4×C71—22no—
133C2×C22⋊C4×C71—22no—
134C2×C22⋊C4×C71—22no—
135C2×C22⋊C4×C71—22no—
136C2×C22⋊C4×C71—22no—
137C2×C22⋊C4×C71—22no—
138C2×C22⋊C4×C71—22no—
139C2×C22⋊C4×C71—22no—
140C2×C22⋊C4×C71—41no—
141C2×C22⋊C4×C71—41no—
142C2×C22⋊C4×C71—41no—
143C2×C22⋊C4×C71—41no—
144C2×C22⋊C4×C71—41no—
145C2×C22⋊C4×C71—41no—
146C2×C22⋊C4×C71—41no—
147C2×C22⋊C4×C71—41no—
148C2×C22⋊C4×C71—41no—
149C2×C22⋊C4×C71—41no—
150C2×C22⋊C4×C71D414yes—
151C2×C22⋊C4×C71D414yescomplemented
152C2×C22⋊C4×C71D414yescomplemented
153C2×C42×C71—22no—
154C2×C42×C71—22no—
155C2×C42×C71—22no—
156C2×C42×C71—22no—
157C2×C42×C71—41no—
158C2×C42×C71—41no—
159#95×C71—22no—
160#95×C71—22no—
161#95×C71—22no—
162#95×C71—22no—
163#95×C71—22no—
164#95×C71—22no—
165#95×C71—22no—
166#95×C71—22no—
167#95×C71—22no—
168#95×C71—22no—
169#95×C71—41no—
170#95×C71D414yescomplemented
171C24×C71—21no—
172C24×C71—21no—
173C24×C71—21no—
174C24×C71—21no—
175C24×C71—21no—
176C24×C71—21no—
177C24×C71—21no—
178C24×C71—21no—
179C24×C71—21no—
180C24×C71—21no—
181C24×C71—21no—
182C24×C71—21no—
183C24×C71—21no—
184C24×C71—21no—
185C24×C71—21no—
186C24×C71—21no—
187C24×C71—21no—
188C24×C71—21no—
189C24×C71—21no—
190C24×C71—21no—
191C24×C71—21no—
192C24×C71—21no—
193C24×C71—21no—
194C24×C71—21no—
195C24×C71—21no—
196C24×C71—21no—
197C24×C71—21no—
198C24×C71—21no—
199C24×C71—21no—
200C24×C71—21no—
201C24×C71—21no—
202C24×C71—21no—
203C24×C71—21no—
204C24×C71—21no—
205C24×C71—21no—
206C24×C71—21no—
207C24×C71—21no—
208C24×C71—21no—
209C24×C71—21no—
210C24×C71—21no—
211C24×C71C2×D412yes—
212C24×C71C2×D412yes—
213C24×C71C2×D412yes—
214C24×C71#4112yes—
215C24×C71#4112yes—
216C24×C71C2411yescharacteristic
217C2×D4×C71—28no—
218C2×D4×C71—28no—
219C2×D4×C71—28no—
220C2×D4×C71—44no—
221C2×D4×C71—44no—
222C2×D4×C71—44no—
223C2×D4×C71—44no—
224C2×D4×C71—44no—
225C2×D4×C71—44no—
226C2×D4×C71—44no—
227C2×D4×C71—44no—
228C2×D4×C71—44no—
229C2×D4×C71—44no—
230C2×D4×C71—44no—
231C2×D4×C71—44no—
232C2×D4×C71—44no—
233C2×D4×C71—44no—
234C2×D4×C71—44no—
235C2×D4×C71—44no—
236C2×D4×C71—44no—
237C2×D4×C71—44no—
238C22×C4×C71—21no—
239C22×C4×C71—21no—
240C22×C4×C71—21no—
241C22×C4×C71—21no—
242C22×C4×C71—21no—
243C22×C4×C71—21no—
244C22×C4×C71—21no—
245C22×C4×C71—21no—
246C22×C4×C71—28no—
247C22×C4×C71—21no—
248C22×C4×C71—21no—
249C22×C4×C71—21no—
250C22×C4×C71—21no—
251C22×C4×C71—21no—
252C22×C4×C71—21no—
253C22×C4×C71—21no—
254C22×C4×C71—21no—
255C22×C4×C71—21no—
256C22×C4×C71—21no—
257C22×C4×C71—21no—
258C22×C4×C71—21no—
259C22×C4×C71—21no—
260C22×C4×C71—21no—
261C22×C4×C71—21no—
262C22×C4×C71—21no—
263C22×C4×C71—21no—
264C22×C4×C71—21no—
265C22×C4×C71—21no—
266C22×C4×C71—21no—
267C22×C4×C71—21no—
268C22×C4×C71—21no—
269C22×C4×C71—21no—
270C22×C4×C71—21no—
271C22×C4×C71—21no—
272C22×C4×C71—21no—
273C22×C4×C71—21no—
274C22×C4×C71—21no—
275C22×C4×C71—21no—
276C22×C4×C71—21no—
277C22×C4×C71—21no—
278C22×C4×C71—21no—
279C22×C4×C71—21no—
280C22×C4×C71—21no—
281C22×C4×C71—21no—
282C22×C4×C71—21no—
283C22×C4×C71—21no—
284C22×C4×C71—21no—
285C22×C4×C71—21no—
286C22×C4×C71—21no—
287C22×C4×C71—21no—
288C22×C4×C71—21no—
289C22×C4×C71—21no—
290C22×C4×C71—21no—
291C22×C4×C71—21no—
292C22×C4×C71—21no—
293C22×C4×C71—21no—
294C22×C4×C71—21no—
295C22×C4×C71—21no—
296C22×C4×C71—21no—
297C22×C4×C71—21no—
298C22×C4×C71—21no—
299C22×C4×C71—21no—
300C22×C4×C71—21no—
301C22×C4×C71—21no—
302C22×C4×C71—21no—
303C22×C4×C71—21no—
304C22×C4×C71—21no—
305C22×C4×C71—21no—
306C22×C4×C71—21no—
307C22×C4×C71—21no—
308C22×C4×C71—21no—
309C22×C4×C71—44no—
310C22×C4×C71—44no—
311C22×C4×C71—44no—
312C22×C4×C71—44no—
313C22×C4×C71—44no—
314C22×C4×C71—44no—
315C22×C4×C71C2×D412yes—
316C22×C4×C71C2×D412yes—
317C22×C4×C71C2×D412yes—
318C22×C4×C71C2×D412yes—
319C22×C4×C71C2×D412yes—
320C22×C4×C71C2×D412yes—
321C22×C4×C71C2×D412yes—
322C22×C4×C71C2×D412yes—
323C22×C4×C71C2×D412yes—
324C22×C4×C71#4112yes—
325C22×C4×C71#4112yes—
326C22×C4×C71#4112yes—
327C22×C4×C71#4112yes—
328C22×C4×C71#4112yes—
329C4⋊C4×C71—44no—
330C4⋊C4×C71—44no—
331C4⋊C4×C71—44no—
332C22⋊C4×C71—28no—
333C22⋊C4×C71—28no—
334C22⋊C4×C71—28no—
335C22⋊C4×C71—44no—
336C22⋊C4×C71—44no—
337C22⋊C4×C71—44no—
338C22⋊C4×C71—44no—
339C22⋊C4×C71—44no—
340C22⋊C4×C71—44no—
341C22⋊C4×C71—44no—
342C22⋊C4×C71—44no—
343C22⋊C4×C71—44no—
344C22⋊C4×C71—44no—
345C22⋊C4×C71—44no—
346C42×C71—44no—
347C42×C71—44no—
348C23×C71—22no—
349C23×C71—22no—
350C23×C71—22no—
351C23×C71—22no—
352C23×C71—22no—
353C23×C71—22no—
354C23×C71—22no—
355C23×C71—22no—
356C23×C71—22no—
357C23×C71—22no—
358C23×C71—22no—
359C23×C71—22no—
360C23×C71—22no—
361C23×C71—22no—
362C23×C71—22no—
363C23×C71—22no—
364C23×C71—22no—
365C23×C71—22no—
366C23×C71—22no—
367C23×C71—22no—
368C23×C71—22no—
369C23×C71—22no—
370C23×C71—22no—
371C23×C71—22no—
372C23×C71—22no—
373C23×C71—22no—
374C23×C71—22no—
375C23×C71—22no—
376C23×C71—22no—
377C23×C71—22no—
378C23×C71—22no—
379C23×C71—22no—
380C23×C71—41no—
381C23×C71—41no—
382C23×C71—41no—
383C23×C71—41no—
384C23×C71—41no—
385C23×C71—41no—
386C23×C71—41no—
387C23×C71—41no—
388C23×C71—41no—
389C23×C71—41no—
390C23×C71—41no—
391C23×C71—41no—
392C23×C71—41no—
393C23×C71—41no—
394C23×C71—41no—
395C23×C71—41no—
396C23×C71—41no—
397C23×C71—41no—
398C23×C71—41no—
399C23×C71—41no—
400C23×C71—41no—
401C23×C71—41no—
402C23×C71—41no—
403C23×C71—41no—
404C23×C71—41no—
405C23×C71—41no—
406C23×C71—41no—
407C23×C71—41no—
408C23×C71—41no—
409C23×C71—41no—
410C23×C71—41no—
411C23×C71—41no—
412C23×C71—41no—
413C23×C71—41no—
414C23×C71—41no—
415C23×C71—41no—
416C23×C71—41no—
417C23×C71—41no—
418C23×C71—41no—
419C23×C71—41no—
420C23×C71—41no—
421C23×C71—41no—
422C23×C71—41no—
423C23×C71—41no—
424C23×C71—41no—
425C23×C71—41no—
426C23×C71—41no—
427C23×C71—41no—
428C23×C71—41no—
429C23×C71—41no—
430C23×C71—41no—
431C23×C71—41no—
432C23×C71—41no—
433C23×C71—41no—
434C23×C71—41no—
435C23×C71—41no—
436C23×C71—41no—
437C23×C71—41no—
438C23×C71—41no—
439C23×C71—41no—
440C23×C71—41no—
441C23×C71—41no—
442C23×C71—41no—
443C23×C71—41no—
444C23×C71—41no—
445C23×C71—41no—
446C23×C71—41no—
447C23×C71—41no—
448C23×C71—41no—
449C23×C71—41no—
450C23×C71—41no—
451C23×C71—41no—
452C23×C71#12114yes—
453C23×C71C22×D411yescharacteristic
454C23×C71C22×D411yescharacteristic
455C23×C71C22×D411yescharacteristic
456C23×C71C22×D411yescharacteristic
457C23×C71C2×#4111yescharacteristic
458C23×C71C2×#4111yescharacteristic
459C23×C71C2×#4111yescharacteristic
460C23×C71C2×#4111yescharacteristic
461C23×C71C2×#4111yescharacteristic
462C23×C71C2×#4111yescharacteristic
463C23×C71C2×#4111yescharacteristic
464C23×C71H(5,𝔽2)11yescharacteristic
465C23×C71H(5,𝔽2)11yescharacteristic
466C23×C71H(5,𝔽2)11yescharacteristic
467C23×C71H(5,𝔽2)11yescharacteristic
468D4×C71—416no—
469D4×C71—416no—
470D4×C71—416no—
471C2×C4×C71—22no—
472C2×C4×C71—22no—
473C2×C4×C71—22no—
474C2×C4×C71—22no—
475C2×C4×C71—22no—
476C2×C4×C71—22no—
477C2×C4×C71—22no—
478C2×C4×C71—22no—
479C2×C4×C71—22no—
480C2×C4×C71—22no—
481C2×C4×C71—22no—
482C2×C4×C71—22no—
483C2×C4×C71—22no—
484C2×C4×C71—22no—
485C2×C4×C71—22no—
486C2×C4×C71—22no—
487C2×C4×C71—22no—
488C2×C4×C71—22no—
489C2×C4×C71—22no—
490C2×C4×C71—22no—
491C2×C4×C71—22no—
492C2×C4×C71—22no—
493C2×C4×C71—22no—
494C2×C4×C71—22no—
495C2×C4×C71—22no—
496C2×C4×C71—22no—
497C2×C4×C71—22no—
498C2×C4×C71—22no—
499C2×C4×C71—22no—
500C2×C4×C71—22no—
501C2×C4×C71—22no—
502C2×C4×C71—22no—
503C2×C4×C71—22no—
504C2×C4×C71—22no—
505C2×C4×C71—22no—
506C2×C4×C71—22no—
507C2×C4×C71—416no—
508C2×C4×C71—41no—
509C2×C4×C71—41no—
510C2×C4×C71—41no—
511C2×C4×C71—41no—
512C2×C4×C71—41no—
513C2×C4×C71—41no—
514C2×C4×C71—41no—
515C2×C4×C71—41no—
516C2×C4×C71—41no—
517C2×C4×C71—41no—
518C2×C4×C71—41no—
519C2×C4×C71—41no—
520C2×C4×C71—41no—
521C2×C4×C71—41no—
522C2×C4×C71—41no—
523C2×C4×C71—41no—
524C2×C4×C71—41no—
525C2×C4×C71—41no—
526C2×C4×C71—41no—
527C2×C4×C71—41no—
528C2×C4×C71—41no—
529C2×C4×C71—41no—
530C2×C4×C71—41no—
531C2×C4×C71—41no—
532C2×C4×C71—41no—
533C2×C4×C71—41no—
534C2×C4×C71—41no—
535C2×C4×C71—41no—
536C2×C4×C71—41no—
537C2×C4×C71—41no—
538C2×C4×C71—41no—
539C2×C4×C71—41no—
540C2×C4×C71—41no—
541C2×C4×C71—41no—
542C2×C4×C71—41no—
543C2×C4×C71—41no—
544C2×C4×C71—41no—
545C2×C4×C71—41no—
546C2×C4×C71—41no—
547C2×C4×C71—41no—
548C2×C4×C71—41no—
549C2×C4×C71—41no—
550C2×C4×C71—41no—
551C2×C4×C71—41no—
552C2×C4×C71—41no—
553C2×C4×C71—41no—
554C2×C4×C71#12114yes—
555C2×C4×C71#12314yes—
556C22×C71—24no—
557C22×C71—24no—
558C22×C71—24no—
559C22×C71—42no—
560C22×C71—42no—
561C22×C71—42no—
562C22×C71—42no—
563C22×C71—42no—
564C22×C71—42no—
565C22×C71—42no—
566C22×C71—42no—
567C22×C71—42no—
568C22×C71—42no—
569C22×C71—42no—
570C22×C71—42no—
571C22×C71—42no—
572C22×C71—42no—
573C22×C71—42no—
574C22×C71—42no—
575C22×C71—42no—
576C22×C71—42no—
577C22×C71—42no—
578C22×C71—42no—
579C22×C71—42no—
580C22×C71—42no—
581C22×C71—42no—
582C22×C71—42no—
583C22×C71—42no—
584C22×C71—42no—
585C22×C71—81no—
586C22×C71—81no—
587C22×C71—81no—
588C22×C71—81no—
589C22×C71—81no—
590C22×C71—81no—
591C22×C71—81no—
592C22×C71—81no—
593C22×C71—81no—
594C22×C71—81no—
595C22×C71—81no—
596C22×C71—81no—
597C22×C71—81no—
598C22×C71—81no—
599C22×C71—81no—
600C22×C71—81no—
601C22×C71C2×#12111yescharacteristic
602C22×C71C2×#12111yescharacteristic
603C22×C71C2×#12311yescharacteristic
604C22×C71#52511yescharacteristic
605C22×C71#52511yescharacteristic
606C22×C71#52511yescharacteristic
607C22×C71#52511yescharacteristic
608C22×C71#52911yescharacteristic
609C22×C71#52911yescharacteristic
610C22×C71#52911yescharacteristic
611C22×C71#53211yescharacteristic
612C22×C71#53211yescharacteristic
613C22×C71#53211yescharacteristic
614C22×C71#53811yescharacteristic
615C22×C71#53811yescharacteristic
616C22×C71#53811yescharacteristic
617C22×C71#53811yescharacteristic
618C22×C71#54011yescharacteristic
619C22×C71#54011yescharacteristic
620C22×C71D4211yescharacteristic
621C22×C71D4211yescharacteristic
622C22×C71D4211yescharacteristic
623C22×C71D4211yescharacteristic
624C22×C71#54611yescharacteristic
625C22×C71#54611yescharacteristic
626C22×C71#54611yescharacteristic
627C22×C71#54611yescharacteristic
628C22×C71#54611yescharacteristic
629C22×C71#54611yescharacteristic
630C22×C71#54611yescharacteristic
631C22×C71#55011yescharacteristic
632C22×C71#55111yescharacteristic
633C22×C71#55311yescharacteristic
634C22×C71#55511yescharacteristic
635C22×C71#55911yescharacteristic
636C4×C71—24no—
637C4×C71—24no—
638C4×C71—42no—
639C4×C71—42no—
640C4×C71—42no—
641C4×C71—42no—
642C4×C71—42no—
643C4×C71—42no—
644C4×C71—42no—
645C4×C71—42no—
646C4×C71—81no—
647C4×C71—81no—
648#14751C7111yesmaximal, characteristic, direct product factor, Sylow
649C2×C71—44no—
650C2×C71—82no—
651C2×C71—82no—
652C2×C71#239211yescharacteristic
653C2×C71#241811yescharacteristic
654C2×C71#242411yescharacteristic
655C2×C71#242411yescharacteristic
656C2×C71#242411yescharacteristic
657C2×C71#242811yescharacteristic
658C2×C71#244511yescharacteristic
659C2×C71#245911yescharacteristic
660C2×C71#246411yescharacteristic
661C2×C71#246711yescharacteristic
662C2×C71#247611yescharacteristic
663C2×C71#255511yescharacteristic
664C2×C71#255711yescharacteristic
665C2×C71#264811yescharacteristic
666C2×C71#285411yescharacteristic
667C2×#394C2×C7111yescharacteristic, complemented
668C2×#394C2×C7111yescharacteristic, complemented
669C2×#392C2×C7111yescharacteristic
670C2×#390C2×C7111yescharacteristic, complemented
671C2×#388C2×C7111yescharacteristic, complemented
672C2×#386C2×C7111yescharacteristic, complemented
673C2×#386C2×C7111yescharacteristic, complemented
674C2×C4×C22⋊C4C2×C7111yescharacteristic, complemented
675#1441C2×C7111yescharacteristic, complemented
676#1440C2×C7111yescharacteristic, complemented
677#1439C2×C7111yescharacteristic, complemented
678#1439C2×C7111yescharacteristic, complemented
679#1438C2×C7111yescharacteristic, complemented
680#1437C2×C7111yescharacteristic, complemented
681#1436C2×C7111yescharacteristic, complemented
682C71#1475111yescharacteristic, direct product factor, Sylow
683C23×D4C22×C7111yescharacteristic
684C23×D4C22×C7111yescharacteristic
685C23×D4C22×C7111yescharacteristic
686C24×C4C22×C7111yescharacteristic
687C22×C4⋊C4C22×C7111yescharacteristic
688C22×C4⋊C4C22×C7111yescharacteristic
689C22×C4⋊C4C22×C7111yescharacteristic
690C22×C22⋊C4C22×C7111yescharacteristic
691C22×C22⋊C4C22×C7111yescharacteristic
692C22×C22⋊C4C22×C7111yescharacteristic
693C22×C22⋊C4C22×C7111yescharacteristic
694C22×C22⋊C4C22×C7111yescharacteristic
695C22×C22⋊C4C22×C7111yescharacteristic
696C22×C22⋊C4C22×C7111yescharacteristic
697C22×C22⋊C4C22×C7111yescharacteristic
698C22×C22⋊C4C22×C7111yescharacteristic
699C22×C22⋊C4C22×C7111yescharacteristic
700C22×C22⋊C4C22×C7111yescharacteristic
701C22×C22⋊C4C22×C7111yescharacteristic
702C22×C22⋊C4C22×C7111yescharacteristic
703C22×C22⋊C4C22×C7111yescharacteristic
704C22×C42C22×C7111yescharacteristic
705C22×C42C22×C7111yescharacteristic
706#394—24no—
707#394—24no—
708#392—24no—
709#390—24no—
710#388—24no—
711#386—24no—
712#386—24no—
713C4×C22⋊C4—24no—
714C2×#95C22×C7111yescharacteristic
715C2×#95C22×C7111yescharacteristic
716C2×#95C22×C7111yescharacteristic
717C2×#95C22×C7111yescharacteristic
718C2×#95C22×C7111yescharacteristic
719C2×#95C22×C7111yescharacteristic
720C2×#95C22×C7111yescharacteristic
721C2×#95C22×C7111yescharacteristic
722C2×#95C22×C7111yescharacteristic
723C2×#95C22×C7111yescharacteristic
724C2×#95C22×C7111yescharacteristic
725C2×#95C22×C7111yescharacteristic
726C25C23×C7111yescharacteristic
727C25C23×C7111yescharacteristic
728C25C23×C7111yescharacteristic
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—22no—
740C22×D4—22no—
741C22×D4—22no—
742C22×D4—22no—
743C22×D4—22no—
744C22×D4—41no—
745C22×D4—41no—
746C22×D4—41no—
747C22×D4—41no—
748C22×D4—41no—
749C22×D4—41no—
750C23×C4—22no—
751C23×C4—22no—
752C23×C4—22no—
753C23×C4—22no—
754C23×C4—22no—
755C23×C4—41no—
756C23×C4—41no—
757C23×C4C23×C7111yescharacteristic
758C23×C4C23×C7111yescharacteristic
759C23×C4C23×C7111yescharacteristic
760C23×C4C23×C7111yescharacteristic
761C23×C4C23×C7111yescharacteristic
762C23×C4C23×C7111yescharacteristic
763C23×C4C23×C7111yescharacteristic
764C23×C4C23×C7111yescharacteristic
765C23×C4C23×C7111yescharacteristic
766C23×C4C23×C7111yescharacteristic
767C23×C4C23×C7111yescharacteristic
768C23×C4C23×C7111yescharacteristic
769C2×C4⋊C4—22no—
770C2×C4⋊C4—22no—
771C2×C4⋊C4—22no—
772C2×C4⋊C4—22no—
773C2×C4⋊C4—22no—
774C2×C4⋊C4—22no—
775C2×C4⋊C4—41no—
776C2×C4⋊C4—41no—
777C2×C4⋊C4—41no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4D4×C7114yes—
818C2×C22⋊C4D4×C7114yescomplemented
819C2×C22⋊C4D4×C7114yescomplemented
820C2×C42—22no—
821C2×C42—22no—
822C2×C42—22no—
823C2×C42—22no—
824C2×C42—41no—
825C2×C42—41no—
826#95—22no—
827#95—22no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—41no—
837#95D4×C7114yescomplemented
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24C2×D4×C7112yes—
879C24C2×D4×C7112yes—
880C24C2×D4×C7112yes—
881C24#41×C7112yes—
882C24#41×C7112yes—
883C24C24×C7111yescharacteristic
884C2×D4—28no—
885C2×D4—28no—
886C2×D4—28no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—28no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4C2×D4×C7112yes—
983C22×C4C2×D4×C7112yes—
984C22×C4C2×D4×C7112yes—
985C22×C4C2×D4×C7112yes—
986C22×C4C2×D4×C7112yes—
987C22×C4C2×D4×C7112yes—
988C22×C4C2×D4×C7112yes—
989C22×C4C2×D4×C7112yes—
990C22×C4C2×D4×C7112yes—
991C22×C4#41×C7112yes—
992C22×C4#41×C7112yes—
993C22×C4#41×C7112yes—
994C22×C4#41×C7112yes—
995C22×C4#41×C7112yes—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C22⋊C4—28no—
1000C22⋊C4—28no—
1001C22⋊C4—28no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C42—44no—
1014C42—44no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23#121×C7114yes—
1120C23C22×D4×C7111yescharacteristic
1121C23C22×D4×C7111yescharacteristic
1122C23C22×D4×C7111yescharacteristic
1123C23C22×D4×C7111yescharacteristic
1124C23C2×#41×C7111yescharacteristic
1125C23C2×#41×C7111yescharacteristic
1126C23C2×#41×C7111yescharacteristic
1127C23C2×#41×C7111yescharacteristic
1128C23C2×#41×C7111yescharacteristic
1129C23C2×#41×C7111yescharacteristic
1130C23C2×#41×C7111yescharacteristic
1131C23H(5,𝔽2)×C7111yescharacteristic
1132C23H(5,𝔽2)×C7111yescharacteristic
1133C23H(5,𝔽2)×C7111yescharacteristic
1134C23H(5,𝔽2)×C7111yescharacteristic
1135D4—416no—
1136D4—416no—
1137D4—416no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—416no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4#121×C7114yes—
1222C2×C4#123×C7114yes—
1223C22—24no—
1224C22—24no—
1225C22—24no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22C2×#121×C7111yescharacteristic
1269C22C2×#121×C7111yescharacteristic
1270C22C2×#123×C7111yescharacteristic
1271C22#525×C7111yescharacteristic
1272C22#525×C7111yescharacteristic
1273C22#525×C7111yescharacteristic
1274C22#525×C7111yescharacteristic
1275C22#529×C7111yescharacteristic
1276C22#529×C7111yescharacteristic
1277C22#529×C7111yescharacteristic
1278C22#532×C7111yescharacteristic
1279C22#532×C7111yescharacteristic
1280C22#532×C7111yescharacteristic
1281C22#538×C7111yescharacteristic
1282C22#538×C7111yescharacteristic
1283C22#538×C7111yescharacteristic
1284C22#538×C7111yescharacteristic
1285C22#540×C7111yescharacteristic
1286C22#540×C7111yescharacteristic
1287C22D42×C7111yescharacteristic
1288C22D42×C7111yescharacteristic
1289C22D42×C7111yescharacteristic
1290C22D42×C7111yescharacteristic
1291C22#546×C7111yescharacteristic
1292C22#546×C7111yescharacteristic
1293C22#546×C7111yescharacteristic
1294C22#546×C7111yescharacteristic
1295C22#546×C7111yescharacteristic
1296C22#546×C7111yescharacteristic
1297C22#546×C7111yescharacteristic
1298C22#550×C7111yescharacteristic
1299C22#551×C7111yescharacteristic
1300C22#553×C7111yescharacteristic
1301C22#555×C7111yescharacteristic
1302C22#559×C7111yescharacteristic
1303C4—24no—
1304C4—24no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—81no—
1314C4—81no—
1315C2—44no—
1316C2—82no—
1317C2—82no—
1318C2C71×#239211yescharacteristic
1319C2C71×#241811yescharacteristic
1320C2C71×#242411yescharacteristic
1321C2C71×#242411yescharacteristic
1322C2C71×#242411yescharacteristic
1323C2C71×#242811yescharacteristic
1324C2C71×#244511yescharacteristic
1325C2C71×#245911yescharacteristic
1326C2C71×#246411yescharacteristic
1327C2C71×#246711yescharacteristic
1328C2C71×#247611yescharacteristic
1329C2C71×#255511yescharacteristic
1330C2C71×#255711yescharacteristic
1331C2C71×#264811yescharacteristic
1332C2C71×#285411yescharacteristic
subgroupG/H
center, socleC24×C71C24
commutator, Frattini, cosocleC24C24×C71
prime radicalC2×#392×C71C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C71 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#394×C71C2semidirect
2. C2×#394×C71C2semidirect
4. C2×#390×C71C2semidirect
5. C2×#388×C71C2semidirect
6. C2×#386×C71C2semidirect
7. C2×#386×C71C2semidirect
8. C2×C4×C22⋊C4×C71C2semidirect
9. C71×#1441C2semidirect
10. C71×#1440C2semidirect
11. C71×#1439C2semidirect
12. C71×#1439C2semidirect
13. C71×#1438C2semidirect
14. C71×#1437C2semidirect
15. C71×#1436C2semidirect
151. C2×C22⋊C4×C71D4semidirect
152. C2×C22⋊C4×C71D4semidirect
170. #95×C71D4semidirect
648. #14751C71direct (N × H)
667. C2×#394C2×C71semidirect
668. C2×#394C2×C71semidirect
670. C2×#390C2×C71semidirect
671. C2×#388C2×C71semidirect
672. C2×#386C2×C71semidirect
673. C2×#386C2×C71semidirect
674. C2×C4×C22⋊C4C2×C71semidirect
675. #1441C2×C71semidirect
676. #1440C2×C71semidirect
677. #1439C2×C71semidirect
678. #1439C2×C71semidirect
679. #1438C2×C71semidirect
680. #1437C2×C71semidirect
681. #1436C2×C71semidirect
682. C71#14751direct (N × H)
818. C2×C22⋊C4D4×C71semidirect
819. C2×C22⋊C4D4×C71semidirect
837. #95D4×C71semidirect

Maximal subgroups

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

subgroupindex
C2×#394×C712
C2×#392×C712
C2×#390×C712
C2×#388×C712
C2×#386×C712
C2×C4×C22⋊C4×C712
C71×#14412
C71×#14402
C71×#14392
C71×#14382
C71×#14372
C71×#14362
#1475171