Finite Group Databasebeta

← C71×#14361 #31835233

Subgroups — C71×#14361 #31835233

Order 18176.

2594 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C71C211yesmaximal, characteristic
2C2×#390×C71C211yesmaximal, characteristic, complemented
3C2×#388×C71C211yesmaximal, characteristic, complemented
4C2×#386×C71C211yesmaximal, characteristic, complemented
5C2×#386×C71C211yesmaximal, characteristic, complemented
6C2×#385×C71C211yesmaximal, characteristic, complemented
7C2×#380×C71C211yesmaximal, characteristic, complemented
8C71×#1441C211yesmaximal, characteristic, complemented
9C71×#1439C211yesmaximal, characteristic, complemented
10C71×#1439C211yesmaximal, characteristic, complemented
11C71×#1438C211yesmaximal, characteristic, complemented
12C71×#1438C211yesmaximal, characteristic, complemented
13C71×#1438C211yesmaximal, characteristic, complemented
14C71×#1436C211yesmaximal, characteristic, complemented
15C71×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C71C2211yescharacteristic
17C23×D4×C71C2211yescharacteristic
18C23×D4×C71C2211yescharacteristic
19C24×C4×C71C2211yescharacteristic
20C24×C4×C71C2211yescharacteristic
21C2×#121×C71—24no—
22C2×#121×C71—24no—
23C2×#121×C71C418yescomplemented
24C22×C4⋊C4×C71C2211yescharacteristic
25C22×C4⋊C4×C71C2211yescharacteristic
26C22×C4⋊C4×C71C2211yescharacteristic
27C22×C4⋊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×C22⋊C4×C71C2211yescharacteristic
41C22×C42×C71C2211yescharacteristic
42#390×C71—24no—
43#388×C71—24no—
44#386×C71—24no—
45#386×C71—24no—
46#385×C71—24no—
47#380×C71—24no—
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
59C2×#95×C71C2211yescharacteristic
60C25×C71C2311yescharacteristic
61C25×C71C2311yescharacteristic
62C25×C71C2311yescharacteristic
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—41no—
76C22×D4×C71—41no—
77C22×D4×C71—41no—
78C22×D4×C71—41no—
79C22×D4×C71—41no—
80C22×D4×C71—41no—
81C22×D4×C71C2×C414yes—
82C22×D4×C71C2×C414yes—
83C22×D4×C71C2×C414yescomplemented
84C23×C4×C71—22no—
85C23×C4×C71—22no—
86C23×C4×C71—22no—
87C23×C4×C71—22no—
88C23×C4×C71—22no—
89C23×C4×C71—22no—
90C23×C4×C71—22no—
91C23×C4×C71—41no—
92C23×C4×C71—41no—
93C23×C4×C71—41no—
94C23×C4×C71—41no—
95C23×C4×C71—41no—
96C23×C4×C71—41no—
97C23×C4×C71C2×C414yescomplemented
98C23×C4×C71C2311yescharacteristic
99C23×C4×C71C2311yescharacteristic
100C23×C4×C71C2311yescharacteristic
101C23×C4×C71C2311yescharacteristic
102C23×C4×C71C2311yescharacteristic
103C23×C4×C71C2311yescharacteristic
104C23×C4×C71C2311yescharacteristic
105C23×C4×C71C2311yescharacteristic
106C23×C4×C71C2311yescharacteristic
107C23×C4×C71C2311yescharacteristic
108C23×C4×C71C2311yescharacteristic
109C23×C4×C71C2311yescharacteristic
110#121×C71—232no—
111C2×C4⋊C4×C71—22no—
112C2×C4⋊C4×C71—22no—
113C2×C4⋊C4×C71—22no—
114C2×C4⋊C4×C71—22no—
115C2×C4⋊C4×C71—22no—
116C2×C4⋊C4×C71—22no—
117C2×C4⋊C4×C71—22no—
118C2×C4⋊C4×C71—22no—
119C2×C4⋊C4×C71—41no—
120C2×C4⋊C4×C71—41no—
121C2×C4⋊C4×C71—41no—
122C2×C4⋊C4×C71C2×C414yescomplemented
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—41no—
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×C71—41no—
151C2×C22⋊C4×C71—41no—
152C2×C22⋊C4×C71—41no—
153C2×C22⋊C4×C71—41no—
154C2×C22⋊C4×C71—41no—
155C2×C22⋊C4×C71—41no—
156C2×C22⋊C4×C71—41no—
157C2×C22⋊C4×C71C2×C414yes—
158C2×C22⋊C4×C71C2×C414yescomplemented
159C2×C22⋊C4×C71D414yes—
160C2×C22⋊C4×C71D414yes—
161C2×C22⋊C4×C71D414yescomplemented
162C2×C42×C71—22no—
163C2×C42×C71—22no—
164C2×C42×C71—41no—
165#95×C71—22no—
166#95×C71—22no—
167#95×C71—22no—
168#95×C71—22no—
169#95×C71—22no—
170#95×C71—22no—
171#95×C71—22no—
172#95×C71—22no—
173#95×C71—22no—
174#95×C71—41no—
175#95×C71—41no—
176#95×C71D414yescomplemented
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×C71—21no—
213C24×C71—21no—
214C24×C71—21no—
215C24×C71C22×C412yes—
216C24×C71C22×C412yes—
217C24×C71C22×C412yes—
218C24×C71C2×D412yes—
219C24×C71C2×D412yes—
220C24×C71C2×D412yes—
221C24×C71#4112yes—
222C24×C71C2411yescharacteristic
223C2×D4×C71—28no—
224C2×D4×C71—28no—
225C2×D4×C71—28no—
226C2×D4×C71—28no—
227C2×D4×C71—28no—
228C2×D4×C71—28no—
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—
239C2×D4×C71—44no—
240C2×D4×C71—44no—
241C2×D4×C71—44no—
242C2×D4×C71—44no—
243C2×D4×C71—44no—
244C22×C4×C71—21no—
245C22×C4×C71—21no—
246C22×C4×C71—21no—
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—28no—
287C22×C4×C71—28no—
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—21no—
310C22×C4×C71—21no—
311C22×C4×C71—21no—
312C22×C4×C71—21no—
313C22×C4×C71—21no—
314C22×C4×C71—21no—
315C22×C4×C71—21no—
316C22×C4×C71—44no—
317C22×C4×C71—44no—
318C22×C4×C71—44no—
319C22×C4×C71—44no—
320C22×C4×C71—44no—
321C22×C4×C71—44no—
322C22×C4×C71—44no—
323C22×C4×C71—44no—
324C22×C4×C71—44no—
325C22×C4×C71—44no—
326C22×C4×C71—44no—
327C22×C4×C71—44no—
328C22×C4×C71C22×C412yes—
329C22×C4×C71C22×C412yes—
330C22×C4×C71C22×C412yes—
331C22×C4×C71C22×C412yes—
332C22×C4×C71C2×D412yes—
333C22×C4×C71C2×D412yes—
334C22×C4×C71C2×D412yes—
335C22×C4×C71C2×D412yes—
336C22×C4×C71C2×D412yes—
337C22×C4×C71C2×D412yes—
338C22×C4×C71C2×D412yes—
339C22×C4×C71C2×D412yes—
340C22×C4×C71C2×D412yes—
341C22×C4×C71#4112yes—
342C4⋊C4×C71—28no—
343C4⋊C4×C71—44no—
344C4⋊C4×C71—44no—
345C4⋊C4×C71—44no—
346C22⋊C4×C71—28no—
347C22⋊C4×C71—44no—
348C22⋊C4×C71—44no—
349C22⋊C4×C71—44no—
350C22⋊C4×C71—44no—
351C22⋊C4×C71—44no—
352C22⋊C4×C71—44no—
353C22⋊C4×C71—44no—
354C22⋊C4×C71—44no—
355C22⋊C4×C71—44no—
356C22⋊C4×C71—44no—
357C22⋊C4×C71—44no—
358C22⋊C4×C71C22⋊C4116yescomplemented
359C42×C71—44no—
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—22no—
382C23×C71—22no—
383C23×C71—22no—
384C23×C71—22no—
385C23×C71—22no—
386C23×C71—22no—
387C23×C71—22no—
388C23×C71—22no—
389C23×C71—22no—
390C23×C71—22no—
391C23×C71—22no—
392C23×C71—22no—
393C23×C71—22no—
394C23×C71—22no—
395C23×C71—22no—
396C23×C71—22no—
397C23×C71—22no—
398C23×C71—22no—
399C23×C71—22no—
400C23×C71—22no—
401C23×C71—22no—
402C23×C71—22no—
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—41no—
454C23×C71—41no—
455C23×C71—41no—
456C23×C71—41no—
457C23×C71—41no—
458C23×C71—41no—
459C23×C71—41no—
460C23×C71—41no—
461C23×C71—41no—
462C23×C71—41no—
463C23×C71C2×C22⋊C414yes—
464C23×C71C4×D414yes—
465C23×C71C23×C411yescharacteristic
466C23×C71C22×D411yescharacteristic
467C23×C71C22×D411yescharacteristic
468C23×C71C22×D411yescharacteristic
469C23×C71C22×D411yescharacteristic
470C23×C71C2×#4111yescharacteristic
471C23×C71C2×#4111yescharacteristic
472C23×C71H(5,𝔽2)11yescharacteristic
473C23×C71H(5,𝔽2)11yescharacteristic
474C23×C71H(5,𝔽2)11yescharacteristic
475C23×C71H(5,𝔽2)11yescharacteristic
476C23×C71H(5,𝔽2)11yescharacteristic
477C23×C71H(5,𝔽2)11yescharacteristic
478C23×C712−1+411yescharacteristic
479C23×C712−1+411yescharacteristic
480D4×C71—416no—
481D4×C71—416no—
482D4×C71—416no—
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—22no—
509C2×C4×C71—22no—
510C2×C4×C71—22no—
511C2×C4×C71—22no—
512C2×C4×C71—22no—
513C2×C4×C71—22no—
514C2×C4×C71—22no—
515C2×C4×C71—22no—
516C2×C4×C71—416no—
517C2×C4×C71—416no—
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—41no—
556C2×C4×C71—41no—
557C2×C4×C71—41no—
558C2×C4×C71—41no—
559C2×C4×C71—41no—
560C2×C4×C71—41no—
561C2×C4×C71—41no—
562C2×C4×C71—41no—
563C2×C4×C71—41no—
564C2×C4×C71—41no—
565C2×C4×C71—41no—
566C2×C4×C71C2×C22⋊C414yes—
567C2×C4×C71C2×C22⋊C414yes—
568C2×C4×C71C4×D414yes—
569C22×C71—24no—
570C22×C71—24no—
571C22×C71—24no—
572C22×C71—24no—
573C22×C71—24no—
574C22×C71—24no—
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—42no—
587C22×C71—42no—
588C22×C71—42no—
589C22×C71—42no—
590C22×C71—42no—
591C22×C71—42no—
592C22×C71—42no—
593C22×C71—42no—
594C22×C71—42no—
595C22×C71—42no—
596C22×C71—42no—
597C22×C71—42no—
598C22×C71—42no—
599C22×C71—42no—
600C22×C71—42no—
601C22×C71—42no—
602C22×C71—42no—
603C22×C71—42no—
604C22×C71—42no—
605C22×C71—42no—
606C22×C71—81no—
607C22×C71—81no—
608C22×C71—81no—
609C22×C71—81no—
610C22×C71—81no—
611C22×C71—81no—
612C22×C71—81no—
613C22×C71—81no—
614C22×C71C22×C22⋊C411yescharacteristic
615C22×C71C2×C4×D411yescharacteristic
616C22×C71C2×C4×D411yescharacteristic
617C22×C71#51811yescharacteristic
618C22×C71#51811yescharacteristic
619C22×C71#52011yescharacteristic
620C22×C71#52011yescharacteristic
621C22×C71#53411yescharacteristic
622C22×C71#53511yescharacteristic
623C22×C71#53511yescharacteristic
624C22×C71#53611yescharacteristic
625C22×C71#53711yescharacteristic
626C22×C71#53711yescharacteristic
627C22×C71#53711yescharacteristic
628C22×C71#53711yescharacteristic
629C22×C71#53811yescharacteristic
630C22×C71#53911yescharacteristic
631C22×C71#54011yescharacteristic
632C22×C71#54211yescharacteristic
633C22×C71D4211yescharacteristic
634C22×C71D4211yescharacteristic
635C22×C71D4211yescharacteristic
636C22×C71D4211yescharacteristic
637C22×C71D4211yescharacteristic
638C22×C71#54611yescharacteristic
639C22×C71#54611yescharacteristic
640C22×C71#54611yescharacteristic
641C22×C71#54611yescharacteristic
642C22×C71#54711yescharacteristic
643C22×C71#54811yescharacteristic
644C22×C71#55311yescharacteristic
645C22×C71#56011yescharacteristic
646C22×C71#56011yescharacteristic
647C22×C71#56211yescharacteristic
648C22×C71#56211yescharacteristic
649C4×C71—24no—
650C4×C71—24no—
651C4×C71—24no—
652C4×C71—42no—
653C4×C71—42no—
654C4×C71—42no—
655C4×C71—42no—
656C4×C71—42no—
657C4×C71—81no—
658C4×C71—81no—
659C4×C71—81no—
660C4×C71—81no—
661#14361C7111yesmaximal, characteristic, direct product factor, Sylow
662C2×C71—44no—
663C2×C71—44no—
664C2×C71—82no—
665C2×C71#231111yescharacteristic
666C2×C71#232411yescharacteristic
667C2×C71#232511yescharacteristic
668C2×C71D4×C22⋊C411yescharacteristic
669C2×C71D4×C22⋊C411yescharacteristic
670C2×C71#236111yescharacteristic
671C2×C71#237711yescharacteristic
672C2×C71#266911yescharacteristic
673C2×C71#267111yescharacteristic
674C2×C71#267211yescharacteristic
675C2×C71#267511yescharacteristic
676C2×C71#267611yescharacteristic
677C2×C71#268111yescharacteristic
678C2×C71#269111yescharacteristic
679C2×C71#270311yescharacteristic
680C22×#121C2×C7111yescharacteristic
681C2×#390C2×C7111yescharacteristic, complemented
682C2×#388C2×C7111yescharacteristic, complemented
683C2×#386C2×C7111yescharacteristic, complemented
684C2×#386C2×C7111yescharacteristic, complemented
685C2×#385C2×C7111yescharacteristic, complemented
686C2×#380C2×C7111yescharacteristic, complemented
687#1441C2×C7111yescharacteristic, complemented
688#1439C2×C7111yescharacteristic, complemented
689#1439C2×C7111yescharacteristic, complemented
690#1438C2×C7111yescharacteristic, complemented
691#1438C2×C7111yescharacteristic, complemented
692#1438C2×C7111yescharacteristic, complemented
693#1436C2×C7111yescharacteristic, complemented
694C22⋊#95C2×C7111yescharacteristic, complemented
695C71#1436111yescharacteristic, direct product factor, Sylow
696C23×D4C22×C7111yescharacteristic
697C23×D4C22×C7111yescharacteristic
698C23×D4C22×C7111yescharacteristic
699C24×C4C22×C7111yescharacteristic
700C24×C4C22×C7111yescharacteristic
701C2×#121—24no—
702C2×#121—24no—
703C2×#121C4×C7118yescomplemented
704C22×C4⋊C4C22×C7111yescharacteristic
705C22×C4⋊C4C22×C7111yescharacteristic
706C22×C4⋊C4C22×C7111yescharacteristic
707C22×C4⋊C4C22×C7111yescharacteristic
708C22×C22⋊C4C22×C7111yescharacteristic
709C22×C22⋊C4C22×C7111yescharacteristic
710C22×C22⋊C4C22×C7111yescharacteristic
711C22×C22⋊C4C22×C7111yescharacteristic
712C22×C22⋊C4C22×C7111yescharacteristic
713C22×C22⋊C4C22×C7111yescharacteristic
714C22×C22⋊C4C22×C7111yescharacteristic
715C22×C22⋊C4C22×C7111yescharacteristic
716C22×C22⋊C4C22×C7111yescharacteristic
717C22×C22⋊C4C22×C7111yescharacteristic
718C22×C22⋊C4C22×C7111yescharacteristic
719C22×C22⋊C4C22×C7111yescharacteristic
720C22×C22⋊C4C22×C7111yescharacteristic
721C22×C42C22×C7111yescharacteristic
722#390—24no—
723#388—24no—
724#386—24no—
725#386—24no—
726#385—24no—
727#380—24no—
728C2×#95C22×C7111yescharacteristic
729C2×#95C22×C7111yescharacteristic
730C2×#95C22×C7111yescharacteristic
731C2×#95C22×C7111yescharacteristic
732C2×#95C22×C7111yescharacteristic
733C2×#95C22×C7111yescharacteristic
734C2×#95C22×C7111yescharacteristic
735C2×#95C22×C7111yescharacteristic
736C2×#95C22×C7111yescharacteristic
737C2×#95C22×C7111yescharacteristic
738C2×#95C22×C7111yescharacteristic
739C2×#95C22×C7111yescharacteristic
740C25C23×C7111yescharacteristic
741C25C23×C7111yescharacteristic
742C25C23×C7111yescharacteristic
743C22×D4—22no—
744C22×D4—22no—
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—22no—
753C22×D4—22no—
754C22×D4—22no—
755C22×D4—41no—
756C22×D4—41no—
757C22×D4—41no—
758C22×D4—41no—
759C22×D4—41no—
760C22×D4—41no—
761C22×D4C2×C4×C7114yes—
762C22×D4C2×C4×C7114yes—
763C22×D4C2×C4×C7114yescomplemented
764C23×C4—22no—
765C23×C4—22no—
766C23×C4—22no—
767C23×C4—22no—
768C23×C4—22no—
769C23×C4—22no—
770C23×C4—22no—
771C23×C4—41no—
772C23×C4—41no—
773C23×C4—41no—
774C23×C4—41no—
775C23×C4—41no—
776C23×C4—41no—
777C23×C4C2×C4×C7114yescomplemented
778C23×C4C23×C7111yescharacteristic
779C23×C4C23×C7111yescharacteristic
780C23×C4C23×C7111yescharacteristic
781C23×C4C23×C7111yescharacteristic
782C23×C4C23×C7111yescharacteristic
783C23×C4C23×C7111yescharacteristic
784C23×C4C23×C7111yescharacteristic
785C23×C4C23×C7111yescharacteristic
786C23×C4C23×C7111yescharacteristic
787C23×C4C23×C7111yescharacteristic
788C23×C4C23×C7111yescharacteristic
789C23×C4C23×C7111yescharacteristic
790#121—232no—
791C2×C4⋊C4—22no—
792C2×C4⋊C4—22no—
793C2×C4⋊C4—22no—
794C2×C4⋊C4—22no—
795C2×C4⋊C4—22no—
796C2×C4⋊C4—22no—
797C2×C4⋊C4—22no—
798C2×C4⋊C4—22no—
799C2×C4⋊C4—41no—
800C2×C4⋊C4—41no—
801C2×C4⋊C4—41no—
802C2×C4⋊C4C2×C4×C7114yescomplemented
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—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—22no—
813C2×C22⋊C4—22no—
814C2×C22⋊C4—22no—
815C2×C22⋊C4—22no—
816C2×C22⋊C4—22no—
817C2×C22⋊C4—22no—
818C2×C22⋊C4—22no—
819C2×C22⋊C4—41no—
820C2×C22⋊C4—41no—
821C2×C22⋊C4—41no—
822C2×C22⋊C4—41no—
823C2×C22⋊C4—41no—
824C2×C22⋊C4—41no—
825C2×C22⋊C4—41no—
826C2×C22⋊C4—41no—
827C2×C22⋊C4—41no—
828C2×C22⋊C4—41no—
829C2×C22⋊C4—41no—
830C2×C22⋊C4—41no—
831C2×C22⋊C4—41no—
832C2×C22⋊C4—41no—
833C2×C22⋊C4—41no—
834C2×C22⋊C4—41no—
835C2×C22⋊C4—41no—
836C2×C22⋊C4—41no—
837C2×C22⋊C4C2×C4×C7114yes—
838C2×C22⋊C4C2×C4×C7114yescomplemented
839C2×C22⋊C4D4×C7114yes—
840C2×C22⋊C4D4×C7114yes—
841C2×C22⋊C4D4×C7114yescomplemented
842C2×C42—22no—
843C2×C42—22no—
844C2×C42—41no—
845#95—22no—
846#95—22no—
847#95—22no—
848#95—22no—
849#95—22no—
850#95—22no—
851#95—22no—
852#95—22no—
853#95—22no—
854#95—41no—
855#95—41no—
856#95D4×C7114yescomplemented
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—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24C22×C4×C7112yes—
896C24C22×C4×C7112yes—
897C24C22×C4×C7112yes—
898C24C2×D4×C7112yes—
899C24C2×D4×C7112yes—
900C24C2×D4×C7112yes—
901C24#41×C7112yes—
902C24C24×C7111yescharacteristic
903C2×D4—28no—
904C2×D4—28no—
905C2×D4—28no—
906C2×D4—28no—
907C2×D4—28no—
908C2×D4—28no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—44no—
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—28no—
967C22×C4—28no—
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—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—21no—
993C22×C4—21no—
994C22×C4—21no—
995C22×C4—21no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4C22×C4×C7112yes—
1009C22×C4C22×C4×C7112yes—
1010C22×C4C22×C4×C7112yes—
1011C22×C4C22×C4×C7112yes—
1012C22×C4C2×D4×C7112yes—
1013C22×C4C2×D4×C7112yes—
1014C22×C4C2×D4×C7112yes—
1015C22×C4C2×D4×C7112yes—
1016C22×C4C2×D4×C7112yes—
1017C22×C4C2×D4×C7112yes—
1018C22×C4C2×D4×C7112yes—
1019C22×C4C2×D4×C7112yes—
1020C22×C4C2×D4×C7112yes—
1021C22×C4#41×C7112yes—
1022C4⋊C4—28no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C22⋊C4—28no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C22⋊C4—44no—
1035C22⋊C4—44no—
1036C22⋊C4—44no—
1037C22⋊C4—44no—
1038C22⋊C4C22⋊C4×C71116yescomplemented
1039C42—44no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
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—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23C2×C22⋊C4×C7114yes—
1144C23C4×D4×C7114yes—
1145C23C23×C4×C7111yescharacteristic
1146C23C22×D4×C7111yescharacteristic
1147C23C22×D4×C7111yescharacteristic
1148C23C22×D4×C7111yescharacteristic
1149C23C22×D4×C7111yescharacteristic
1150C23C2×#41×C7111yescharacteristic
1151C23C2×#41×C7111yescharacteristic
1152C23H(5,𝔽2)×C7111yescharacteristic
1153C23H(5,𝔽2)×C7111yescharacteristic
1154C23H(5,𝔽2)×C7111yescharacteristic
1155C23H(5,𝔽2)×C7111yescharacteristic
1156C23H(5,𝔽2)×C7111yescharacteristic
1157C23H(5,𝔽2)×C7111yescharacteristic
1158C232−1+4×C7111yescharacteristic
1159C232−1+4×C7111yescharacteristic
1160D4—416no—
1161D4—416no—
1162D4—416no—
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—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—416no—
1197C2×C4—416no—
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—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4C2×C22⋊C4×C7114yes—
1247C2×C4C2×C22⋊C4×C7114yes—
1248C2×C4C4×D4×C7114yes—
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22C22×C22⋊C4×C7111yescharacteristic
1295C22C2×C4×D4×C7111yescharacteristic
1296C22C2×C4×D4×C7111yescharacteristic
1297C22#518×C7111yescharacteristic
1298C22#518×C7111yescharacteristic
1299C22#520×C7111yescharacteristic
1300C22#520×C7111yescharacteristic
1301C22#534×C7111yescharacteristic
1302C22#535×C7111yescharacteristic
1303C22#535×C7111yescharacteristic
1304C22#536×C7111yescharacteristic
1305C22#537×C7111yescharacteristic
1306C22#537×C7111yescharacteristic
1307C22#537×C7111yescharacteristic
1308C22#537×C7111yescharacteristic
1309C22#538×C7111yescharacteristic
1310C22#539×C7111yescharacteristic
1311C22#540×C7111yescharacteristic
1312C22#542×C7111yescharacteristic
1313C22D42×C7111yescharacteristic
1314C22D42×C7111yescharacteristic
1315C22D42×C7111yescharacteristic
1316C22D42×C7111yescharacteristic
1317C22D42×C7111yescharacteristic
1318C22#546×C7111yescharacteristic
1319C22#546×C7111yescharacteristic
1320C22#546×C7111yescharacteristic
1321C22#546×C7111yescharacteristic
1322C22#547×C7111yescharacteristic
1323C22#548×C7111yescharacteristic
1324C22#553×C7111yescharacteristic
1325C22#560×C7111yescharacteristic
1326C22#560×C7111yescharacteristic
1327C22#562×C7111yescharacteristic
1328C22#562×C7111yescharacteristic
1329C4—24no—
1330C4—24no—
1331C4—24no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C2—44no—
1342C2—44no—
1343C2—82no—
1344C2C71×#231111yescharacteristic
1345C2C71×#232411yescharacteristic
1346C2C71×#232511yescharacteristic
1347C2D4×C22⋊C4×C7111yescharacteristic
1348C2D4×C22⋊C4×C7111yescharacteristic
1349C2C71×#236111yescharacteristic
1350C2C71×#237711yescharacteristic
1351C2C71×#266911yescharacteristic
1352C2C71×#267111yescharacteristic
1353C2C71×#267211yescharacteristic
1354C2C71×#267511yescharacteristic
1355C2C71×#267611yescharacteristic
1356C2C71×#268111yescharacteristic
1357C2C71×#269111yescharacteristic
1358C2C71×#270311yescharacteristic
subgroupG/H
center, socleC24×C71C24
commutatorC23C23×C4×C71
Frattini, cosocleC24C24×C71
prime radicalC22×#121×C71C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C71 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#390×C71C2semidirect
3. C2×#388×C71C2semidirect
4. C2×#386×C71C2semidirect
5. C2×#386×C71C2semidirect
6. C2×#385×C71C2semidirect
7. C2×#380×C71C2semidirect
8. C71×#1441C2semidirect
9. C71×#1439C2semidirect
10. C71×#1439C2semidirect
11. C71×#1438C2semidirect
12. C71×#1438C2semidirect
13. C71×#1438C2semidirect
14. C71×#1436C2semidirect
15. C71×C22⋊#95C2semidirect
23. C2×#121×C71C4semidirect
83. C22×D4×C71C2×C4semidirect
97. C23×C4×C71C2×C4semidirect
122. C2×C4⋊C4×C71C2×C4semidirect
158. C2×C22⋊C4×C71C2×C4semidirect
161. C2×C22⋊C4×C71D4semidirect
176. #95×C71D4semidirect
358. C22⋊C4×C71C22⋊C4semidirect
661. #14361C71direct (N × H)
681. C2×#390C2×C71semidirect
682. C2×#388C2×C71semidirect
683. C2×#386C2×C71semidirect
684. C2×#386C2×C71semidirect
685. C2×#385C2×C71semidirect
686. C2×#380C2×C71semidirect
687. #1441C2×C71semidirect
688. #1439C2×C71semidirect
689. #1439C2×C71semidirect
690. #1438C2×C71semidirect
691. #1438C2×C71semidirect
692. #1438C2×C71semidirect
693. #1436C2×C71semidirect
694. C22⋊#95C2×C71semidirect
695. C71#14361direct (N × H)
703. C2×#121C4×C71semidirect
763. C22×D4C2×C4×C71semidirect
777. C23×C4C2×C4×C71semidirect
802. C2×C4⋊C4C2×C4×C71semidirect
838. C2×C22⋊C4C2×C4×C71semidirect
841. C2×C22⋊C4D4×C71semidirect
856. #95D4×C71semidirect
1038. C22⋊C4C22⋊C4×C71semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C712
C2×#390×C712
C2×#388×C712
C2×#386×C712
C2×#385×C712
C2×#380×C712
C71×#14412
C71×#14392
C71×#14382
C71×#14362
C71×C22⋊#952
#1436171