Finite Group Databasebeta

← C71×#14760 #31835632

Subgroups — C71×#14760 #31835632

Order 18176.

2414 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C71C211yesmaximal, characteristic, complemented
2C2×#392×C71C211yesmaximal, characteristic
3C2×#390×C71C211yesmaximal, characteristic, complemented
4C2×#388×C71C211yesmaximal, characteristic, complemented
5C2×#386×C71C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C71C211yesmaximal, characteristic, complemented
7C71×#1441C211yesmaximal, characteristic, complemented
8C71×#1440C211yesmaximal, characteristic, complemented
9C71×#1439C211yesmaximal, characteristic, complemented
10C71×#1439C211yesmaximal, characteristic, complemented
11C71×#1438C211yesmaximal, characteristic, complemented
12C71×#1438C211yesmaximal, 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
20C2×#123×C71—24no—
21C2×#123×C71—24no—
22C2×#123×C71—24no—
23C22×C4⋊C4×C71C2211yescharacteristic
24C22×C4⋊C4×C71C2211yescharacteristic
25C22×C4⋊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×C22⋊C4×C71C2211yescharacteristic
38C22×C22⋊C4×C71C2211yescharacteristic
39C22×C22⋊C4×C71C2211yescharacteristic
40C22×C42×C71C2211yescharacteristic
41C22×C42×C71C2211yescharacteristic
42#392×C71—24no—
43#390×C71—24no—
44#388×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—41no—
88C23×C4×C71—41no—
89C23×C4×C71D414yescomplemented
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
102#123×C71—232no—
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—22no—
109C2×C4⋊C4×C71—22no—
110C2×C4⋊C4×C71—41no—
111C2×C4⋊C4×C71D414yescomplemented
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—22no—
141C2×C22⋊C4×C71—22no—
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×C71—41no—
151C2×C22⋊C4×C71—41no—
152C2×C22⋊C4×C71D414yes—
153C2×C22⋊C4×C71D414yescomplemented
154C2×C42×C71—22no—
155C2×C42×C71—22no—
156C2×C42×C71—22no—
157C2×C42×C71—22no—
158C2×C42×C71—41no—
159C2×C42×C71—41no—
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×C71—41no—
171#95×C71—41no—
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×C71—21no—
212C24×C71C2×D412yes—
213C24×C71C2×D412yes—
214C24×C71C2×D412yes—
215C24×C71#4112yes—
216C24×C71#4112yes—
217C24×C71C2411yescharacteristic
218C2×D4×C71—28no—
219C2×D4×C71—28no—
220C2×D4×C71—28no—
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—
238C2×D4×C71—44no—
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—21no—
247C22×C4×C71—28no—
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—28no—
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—21no—
310C22×C4×C71—21no—
311C22×C4×C71—44no—
312C22×C4×C71—44no—
313C22×C4×C71—44no—
314C22×C4×C71—44no—
315C22×C4×C71—44no—
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×C71C2×D412yes—
325C22×C4×C71#4112yes—
326C22×C4×C71#4112yes—
327C22×C4×C71#4112yes—
328C22×C4×C71#4112yes—
329C22×C4×C71#4112yes—
330C4⋊C4×C71—28no—
331C4⋊C4×C71—28no—
332C4⋊C4×C71—44no—
333C22⋊C4×C71—28no—
334C22⋊C4×C71—28no—
335C22⋊C4×C71—28no—
336C22⋊C4×C71—28no—
337C22⋊C4×C71—28no—
338C22⋊C4×C71—28no—
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—
346C22⋊C4×C71—44no—
347C42×C71—44no—
348C42×C71—44no—
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—22no—
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—41no—
453C23×C71#12114yes—
454C23×C71C22×D411yescharacteristic
455C23×C71C22×D411yescharacteristic
456C23×C71C22×D411yescharacteristic
457C23×C71C22×D411yescharacteristic
458C23×C71C2×#4111yescharacteristic
459C23×C71C2×#4111yescharacteristic
460C23×C71C2×#4111yescharacteristic
461C23×C71C2×#4111yescharacteristic
462C23×C71C2×#4111yescharacteristic
463C23×C71C2×#4111yescharacteristic
464C23×C71C2×#4111yescharacteristic
465C23×C71H(5,𝔽2)11yescharacteristic
466C23×C71H(5,𝔽2)11yescharacteristic
467C23×C71H(5,𝔽2)11yescharacteristic
468C23×C71H(5,𝔽2)11yescharacteristic
469D4×C71—416no—
470D4×C71—416no—
471D4×C71—416no—
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—22no—
508C2×C4×C71—416no—
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—41no—
555C2×C4×C71#12014yes—
556C2×C4×C71#12314yescomplemented
557C22×C71—24no—
558C22×C71—24no—
559C22×C71—24no—
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—42no—
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×C71—81no—
602C22×C71C2×#12011yescharacteristic
603C22×C71C2×#12111yescharacteristic
604C22×C71C2×#12311yescharacteristic
605C22×C71#52511yescharacteristic
606C22×C71#52511yescharacteristic
607C22×C71#52511yescharacteristic
608C22×C71#52511yescharacteristic
609C22×C71#52911yescharacteristic
610C22×C71#52911yescharacteristic
611C22×C71#53211yescharacteristic
612C22×C71#53211yescharacteristic
613C22×C71#53211yescharacteristic
614C22×C71#53211yescharacteristic
615C22×C71#53411yescharacteristic
616C22×C71#53511yescharacteristic
617C22×C71#53811yescharacteristic
618C22×C71#53811yescharacteristic
619C22×C71#54011yescharacteristic
620C22×C71#54011yescharacteristic
621C22×C71D4211yescharacteristic
622C22×C71D4211yescharacteristic
623C22×C71#54611yescharacteristic
624C22×C71#54611yescharacteristic
625C22×C71#54611yescharacteristic
626C22×C71#54611yescharacteristic
627C22×C71#54611yescharacteristic
628C22×C71#54611yescharacteristic
629C22×C71#55011yescharacteristic
630C22×C71#55011yescharacteristic
631C22×C71#55111yescharacteristic
632C22×C71#55111yescharacteristic
633C22×C71#55111yescharacteristic
634C22×C71#55311yescharacteristic
635C22×C71#55311yescharacteristic
636C22×C71#55911yescharacteristic
637C4×C71—24no—
638C4×C71—24no—
639C4×C71—42no—
640C4×C71—42no—
641C4×C71—42no—
642C4×C71—42no—
643C4×C71—42no—
644C4×C71—42no—
645C4×C71—42no—
646C4×C71—42no—
647C4×C71—81no—
648C4×C71—81no—
649#14760C7111yesmaximal, characteristic, direct product factor, Sylow
650C2×C71—44no—
651C2×C71—82no—
652C2×C71—82no—
653C2×C71#238811yescharacteristic
654C2×C71#241011yescharacteristic
655C2×C71#241111yescharacteristic
656C2×C71#241811yescharacteristic
657C2×C71#243111yescharacteristic
658C2×C71#244511yescharacteristic
659C2×C71#245611yescharacteristic
660C2×C71#245711yescharacteristic
661C2×C71#246411yescharacteristic
662C2×C71#247111yescharacteristic
663C2×C71#255411yescharacteristic
664C2×C71#255711yescharacteristic
665C2×C71#260211yescharacteristic
666C2×C71#266111yescharacteristic
667C2×C71#285411yescharacteristic
668C22×#123C2×C7111yescharacteristic, complemented
669C2×#392C2×C7111yescharacteristic
670C2×#390C2×C7111yescharacteristic, complemented
671C2×#388C2×C7111yescharacteristic, complemented
672C2×#386C2×C7111yescharacteristic, complemented
673C2×C4×C22⋊C4C2×C7111yescharacteristic, complemented
674#1441C2×C7111yescharacteristic, complemented
675#1440C2×C7111yescharacteristic, complemented
676#1439C2×C7111yescharacteristic, complemented
677#1439C2×C7111yescharacteristic, complemented
678#1438C2×C7111yescharacteristic, complemented
679#1438C2×C7111yescharacteristic, complemented
680#1438C2×C7111yescharacteristic, complemented
681#1437C2×C7111yescharacteristic, complemented
682#1436C2×C7111yescharacteristic, complemented
683C71#1476011yescharacteristic, direct product factor, Sylow
684C23×D4C22×C7111yescharacteristic
685C23×D4C22×C7111yescharacteristic
686C23×D4C22×C7111yescharacteristic
687C24×C4C22×C7111yescharacteristic
688C2×#123—24no—
689C2×#123—24no—
690C2×#123—24no—
691C22×C4⋊C4C22×C7111yescharacteristic
692C22×C4⋊C4C22×C7111yescharacteristic
693C22×C4⋊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×C22⋊C4C22×C7111yescharacteristic
705C22×C22⋊C4C22×C7111yescharacteristic
706C22×C22⋊C4C22×C7111yescharacteristic
707C22×C22⋊C4C22×C7111yescharacteristic
708C22×C42C22×C7111yescharacteristic
709C22×C42C22×C7111yescharacteristic
710#392—24no—
711#390—24no—
712#388—24no—
713#386—24no—
714C4×C22⋊C4—24no—
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
726C2×#95C22×C7111yescharacteristic
727C25C23×C7111yescharacteristic
728C25C23×C7111yescharacteristic
729C25C23×C7111yescharacteristic
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—22no—
745C22×D4—41no—
746C22×D4—41no—
747C22×D4—41no—
748C22×D4—41no—
749C22×D4—41no—
750C22×D4—41no—
751C23×C4—22no—
752C23×C4—22no—
753C23×C4—22no—
754C23×C4—22no—
755C23×C4—41no—
756C23×C4—41no—
757C23×C4D4×C7114yescomplemented
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
769C23×C4C23×C7111yescharacteristic
770#123—232no—
771C2×C4⋊C4—22no—
772C2×C4⋊C4—22no—
773C2×C4⋊C4—22no—
774C2×C4⋊C4—22no—
775C2×C4⋊C4—22no—
776C2×C4⋊C4—22no—
777C2×C4⋊C4—22no—
778C2×C4⋊C4—41no—
779C2×C4⋊C4D4×C7114yescomplemented
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—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
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⋊C4—41no—
818C2×C22⋊C4—41no—
819C2×C22⋊C4—41no—
820C2×C22⋊C4D4×C7114yes—
821C2×C22⋊C4D4×C7114yescomplemented
822C2×C42—22no—
823C2×C42—22no—
824C2×C42—22no—
825C2×C42—22no—
826C2×C42—41no—
827C2×C42—41no—
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—22no—
837#95—41no—
838#95—41no—
839#95—41no—
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—
878C24—21no—
879C24—21no—
880C24C2×D4×C7112yes—
881C24C2×D4×C7112yes—
882C24C2×D4×C7112yes—
883C24#41×C7112yes—
884C24#41×C7112yes—
885C24C24×C7111yescharacteristic
886C2×D4—28no—
887C2×D4—28no—
888C2×D4—28no—
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—
905C2×D4—44no—
906C2×D4—44no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—28no—
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—28no—
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—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
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×C4C2×D4×C7112yes—
992C22×C4C2×D4×C7112yes—
993C22×C4#41×C7112yes—
994C22×C4#41×C7112yes—
995C22×C4#41×C7112yes—
996C22×C4#41×C7112yes—
997C22×C4#41×C7112yes—
998C4⋊C4—28no—
999C4⋊C4—28no—
1000C4⋊C4—44no—
1001C22⋊C4—28no—
1002C22⋊C4—28no—
1003C22⋊C4—28no—
1004C22⋊C4—28no—
1005C22⋊C4—28no—
1006C22⋊C4—28no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C42—44no—
1016C42—44no—
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—22no—
1048C23—22no—
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—41no—
1120C23—41no—
1121C23#121×C7114yes—
1122C23C22×D4×C7111yescharacteristic
1123C23C22×D4×C7111yescharacteristic
1124C23C22×D4×C7111yescharacteristic
1125C23C22×D4×C7111yescharacteristic
1126C23C2×#41×C7111yescharacteristic
1127C23C2×#41×C7111yescharacteristic
1128C23C2×#41×C7111yescharacteristic
1129C23C2×#41×C7111yescharacteristic
1130C23C2×#41×C7111yescharacteristic
1131C23C2×#41×C7111yescharacteristic
1132C23C2×#41×C7111yescharacteristic
1133C23H(5,𝔽2)×C7111yescharacteristic
1134C23H(5,𝔽2)×C7111yescharacteristic
1135C23H(5,𝔽2)×C7111yescharacteristic
1136C23H(5,𝔽2)×C7111yescharacteristic
1137D4—416no—
1138D4—416no—
1139D4—416no—
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—22no—
1175C2×C4—22no—
1176C2×C4—416no—
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—41no—
1222C2×C4—41no—
1223C2×C4#120×C7114yes—
1224C2×C4#123×C7114yescomplemented
1225C22—24no—
1226C22—24no—
1227C22—24no—
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—42no—
1253C22—42no—
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—
1268C22—81no—
1269C22—81no—
1270C22C2×#120×C7111yescharacteristic
1271C22C2×#121×C7111yescharacteristic
1272C22C2×#123×C7111yescharacteristic
1273C22#525×C7111yescharacteristic
1274C22#525×C7111yescharacteristic
1275C22#525×C7111yescharacteristic
1276C22#525×C7111yescharacteristic
1277C22#529×C7111yescharacteristic
1278C22#529×C7111yescharacteristic
1279C22#532×C7111yescharacteristic
1280C22#532×C7111yescharacteristic
1281C22#532×C7111yescharacteristic
1282C22#532×C7111yescharacteristic
1283C22#534×C7111yescharacteristic
1284C22#535×C7111yescharacteristic
1285C22#538×C7111yescharacteristic
1286C22#538×C7111yescharacteristic
1287C22#540×C7111yescharacteristic
1288C22#540×C7111yescharacteristic
1289C22D42×C7111yescharacteristic
1290C22D42×C7111yescharacteristic
1291C22#546×C7111yescharacteristic
1292C22#546×C7111yescharacteristic
1293C22#546×C7111yescharacteristic
1294C22#546×C7111yescharacteristic
1295C22#546×C7111yescharacteristic
1296C22#546×C7111yescharacteristic
1297C22#550×C7111yescharacteristic
1298C22#550×C7111yescharacteristic
1299C22#551×C7111yescharacteristic
1300C22#551×C7111yescharacteristic
1301C22#551×C7111yescharacteristic
1302C22#553×C7111yescharacteristic
1303C22#553×C7111yescharacteristic
1304C22#559×C7111yescharacteristic
1305C4—24no—
1306C4—24no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—81no—
1316C4—81no—
1317C2—44no—
1318C2—82no—
1319C2—82no—
1320C2C71×#238811yescharacteristic
1321C2C71×#241011yescharacteristic
1322C2C71×#241111yescharacteristic
1323C2C71×#241811yescharacteristic
1324C2C71×#243111yescharacteristic
1325C2C71×#244511yescharacteristic
1326C2C71×#245611yescharacteristic
1327C2C71×#245711yescharacteristic
1328C2C71×#246411yescharacteristic
1329C2C71×#247111yescharacteristic
1330C2C71×#255411yescharacteristic
1331C2C71×#255711yescharacteristic
1332C2C71×#260211yescharacteristic
1333C2C71×#266111yescharacteristic
1334C2C71×#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. C22×#123×C71C2semidirect
3. C2×#390×C71C2semidirect
4. C2×#388×C71C2semidirect
5. C2×#386×C71C2semidirect
6. C2×C4×C22⋊C4×C71C2semidirect
7. C71×#1441C2semidirect
8. C71×#1440C2semidirect
9. C71×#1439C2semidirect
10. C71×#1439C2semidirect
11. C71×#1438C2semidirect
12. C71×#1438C2semidirect
13. C71×#1438C2semidirect
14. C71×#1437C2semidirect
15. C71×#1436C2semidirect
89. C23×C4×C71D4semidirect
111. C2×C4⋊C4×C71D4semidirect
153. C2×C22⋊C4×C71D4semidirect
556. C2×C4×C71#123semidirect
649. #14760C71direct (N × H)
668. C22×#123C2×C71semidirect
670. C2×#390C2×C71semidirect
671. C2×#388C2×C71semidirect
672. C2×#386C2×C71semidirect
673. C2×C4×C22⋊C4C2×C71semidirect
674. #1441C2×C71semidirect
675. #1440C2×C71semidirect
676. #1439C2×C71semidirect
677. #1439C2×C71semidirect
678. #1438C2×C71semidirect
679. #1438C2×C71semidirect
680. #1438C2×C71semidirect
681. #1437C2×C71semidirect
682. #1436C2×C71semidirect
683. C71#14760direct (N × H)
757. C23×C4D4×C71semidirect
779. C2×C4⋊C4D4×C71semidirect
821. C2×C22⋊C4D4×C71semidirect
1224. C2×C4#123×C71semidirect

Maximal subgroups

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

subgroupindex
C22×#123×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
#1476071