Finite Group Databasebeta

← C71×#16290 #31837162

Subgroups — C71×#16290 #31837162

Order 18176.

2090 conjugacy classes of subgroups.

The subgroup lattice has 1324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#396×C71C211yesmaximal, characteristic, complemented
2C2×#396×C71C211yesmaximal, characteristic, complemented
3C2×#394×C71C211yesmaximal, characteristic, complemented
4C2×#394×C71C211yesmaximal, characteristic, complemented
5C2×#394×C71C211yesmaximal, characteristic, complemented
6C2×#392×C71C211yesmaximal, characteristic
7C2×#390×C71C211yesmaximal, characteristic, complemented
8C2×#388×C71C211yesmaximal, characteristic, complemented
9C71×#1444C211yesmaximal, characteristic, complemented
10C71×#1439C211yesmaximal, characteristic, complemented
11C71×#1439C211yesmaximal, characteristic, complemented
12C71×#1439C211yesmaximal, characteristic, complemented
13C71×#1438C211yesmaximal, characteristic, complemented
14C71×#1438C211yesmaximal, characteristic, complemented
15C71×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C71C2211yescharacteristic
17C23×D4×C71C2211yescharacteristic
18C23×D4×C71C2211yescharacteristic
19C22×C4⋊C4×C71C2211yescharacteristic
20C22×C4⋊C4×C71C2211yescharacteristic
21C22×C4⋊C4×C71C2211yescharacteristic
22C22×C4⋊C4×C71C2211yescharacteristic
23C22×C4⋊C4×C71C2211yescharacteristic
24C22×C4⋊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×C22⋊C4×C71C2211yescharacteristic
38C22×C22⋊C4×C71C2211yescharacteristic
39C22×C22⋊C4×C71C2211yescharacteristic
40C22×C42×C71C2211yescharacteristic
41#396×C71—24no—
42#396×C71—24no—
43#394×C71—24no—
44#394×C71—24no—
45#394×C71—24no—
46#392×C71—24no—
47#390×C71—24no—
48#388×C71—24no—
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—41no—
74C22×D4×C71—41no—
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×C71—41no—
82C22×D4×C71—41no—
83C23×C4×C71C2311yescharacteristic
84C23×C4×C71C2311yescharacteristic
85C23×C4×C71C2311yescharacteristic
86C23×C4×C71C2311yescharacteristic
87C23×C4×C71C2311yescharacteristic
88C23×C4×C71C2311yescharacteristic
89C23×C4×C71C2311yescharacteristic
90C23×C4×C71C2311yescharacteristic
91C23×C4×C71C2311yescharacteristic
92C23×C4×C71C2311yescharacteristic
93C23×C4×C71C2311yescharacteristic
94C23×C4×C71C2311yescharacteristic
95C2×C4⋊C4×C71—22no—
96C2×C4⋊C4×C71—22no—
97C2×C4⋊C4×C71—22no—
98C2×C4⋊C4×C71—22no—
99C2×C4⋊C4×C71—22no—
100C2×C4⋊C4×C71—22no—
101C2×C4⋊C4×C71—22no—
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—41no—
108C2×C4⋊C4×C71—41no—
109C2×C4⋊C4×C71—41no—
110C2×C4⋊C4×C71—41no—
111C2×C4⋊C4×C71—41no—
112C2×C4⋊C4×C71—41no—
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×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×C71D414yes—
157C2×C22⋊C4×C71D414yescomplemented
158C2×C42×C71—22no—
159C2×C42×C71—22no—
160C2×C42×C71—41no—
161#95×C71—22no—
162#95×C71—22no—
163#95×C71—22no—
164#95×C71—22no—
165#95×C71—22no—
166#95×C71—41no—
167#95×C71—41no—
168#95×C71—41no—
169#95×C71D414yescomplemented
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×C71—21no—
212C24×C71—21no—
213C24×C71C2×D412yes—
214C24×C71C2×D412yes—
215C24×C71#4112yes—
216C24×C71C2411yescharacteristic
217C2×D4×C71—28no—
218C2×D4×C71—44no—
219C2×D4×C71—44no—
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—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—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—21no—
310C22×C4×C71C2×D412yes—
311C22×C4×C71C2×D412yes—
312C22×C4×C71C2×D412yes—
313C22×C4×C71C2×D412yes—
314C22×C4×C71C2×D412yes—
315C22×C4×C71C2×D412yes—
316C22×C4×C71C2×D412yes—
317C22×C4×C71C2×D412yes—
318C22×C4×C71C2×D412yes—
319C22×C4×C71C2×D412yes—
320C22×C4×C71#4112yes—
321C22×C4×C71#4112yes—
322C4⋊C4×C71—44no—
323C4⋊C4×C71—44no—
324C4⋊C4×C71—44no—
325C4⋊C4×C71—44no—
326C4⋊C4×C71—44no—
327C4⋊C4×C71—44no—
328C22⋊C4×C71—28no—
329C22⋊C4×C71—44no—
330C22⋊C4×C71—44no—
331C22⋊C4×C71—44no—
332C22⋊C4×C71—44no—
333C22⋊C4×C71—44no—
334C22⋊C4×C71—44no—
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—
343C42×C71—44no—
344C23×C71—22no—
345C23×C71—22no—
346C23×C71—22no—
347C23×C71—22no—
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—41no—
366C23×C71—41no—
367C23×C71—41no—
368C23×C71—41no—
369C23×C71—41no—
370C23×C71—41no—
371C23×C71—41no—
372C23×C71—41no—
373C23×C71—41no—
374C23×C71—41no—
375C23×C71—41no—
376C23×C71—41no—
377C23×C71—41no—
378C23×C71—41no—
379C23×C71—41no—
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×C71C22×D411yescharacteristic
450C23×C71C22×D411yescharacteristic
451C23×C71C22×D411yescharacteristic
452C23×C71C22×D411yescharacteristic
453C23×C71C2×#4111yescharacteristic
454C23×C71C2×#4111yescharacteristic
455C23×C71C2×#4111yescharacteristic
456C23×C71H(5,𝔽2)11yescharacteristic
457C23×C71H(5,𝔽2)11yescharacteristic
458C23×C71H(5,𝔽2)11yescharacteristic
459C23×C71H(5,𝔽2)11yescharacteristic
460C23×C71H(5,𝔽2)11yescharacteristic
461C23×C71H(5,𝔽2)11yescharacteristic
462C23×C712−1+411yescharacteristic
463C23×C712−1+411yescharacteristic
464D4×C71—416no—
465D4×C71—416no—
466D4×C71—416no—
467C2×C4×C71—22no—
468C2×C4×C71—22no—
469C2×C4×C71—22no—
470C2×C4×C71—22no—
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—41no—
501C2×C4×C71—41no—
502C2×C4×C71—41no—
503C2×C4×C71—41no—
504C2×C4×C71—41no—
505C2×C4×C71—41no—
506C2×C4×C71—41no—
507C2×C4×C71—41no—
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#12114yes—
551C22×C71—42no—
552C22×C71—42no—
553C22×C71—42no—
554C22×C71—42no—
555C22×C71—42no—
556C22×C71—42no—
557C22×C71—42no—
558C22×C71—42no—
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—81no—
573C22×C71—81no—
574C22×C71—81no—
575C22×C71—81no—
576C22×C71—81no—
577C22×C71—81no—
578C22×C71—81no—
579C22×C71—81no—
580C22×C71—81no—
581C22×C71—81no—
582C22×C71—81no—
583C22×C71—81no—
584C22×C71—81no—
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×C71C2×#12111yescharacteristic
597C22×C71#52511yescharacteristic
598C22×C71#53211yescharacteristic
599C22×C71#53411yescharacteristic
600C22×C71#53511yescharacteristic
601C22×C71#53511yescharacteristic
602C22×C71#53611yescharacteristic
603C22×C71#53711yescharacteristic
604C22×C71#53711yescharacteristic
605C22×C71#53711yescharacteristic
606C22×C71#53711yescharacteristic
607C22×C71#53811yescharacteristic
608C22×C71#53811yescharacteristic
609C22×C71#53811yescharacteristic
610C22×C71#53911yescharacteristic
611C22×C71#54011yescharacteristic
612C22×C71#54211yescharacteristic
613C22×C71#54211yescharacteristic
614C22×C71#54211yescharacteristic
615C22×C71D4211yescharacteristic
616C22×C71D4211yescharacteristic
617C22×C71D4211yescharacteristic
618C22×C71D4211yescharacteristic
619C22×C71D4211yescharacteristic
620C22×C71#54611yescharacteristic
621C22×C71#54611yescharacteristic
622C22×C71#54611yescharacteristic
623C22×C71#54711yescharacteristic
624C22×C71#54811yescharacteristic
625C22×C71#55011yescharacteristic
626C22×C71#55111yescharacteristic
627C22×C71#56011yescharacteristic
628C22×C71#56011yescharacteristic
629C22×C71#56211yescharacteristic
630C22×C71#56211yescharacteristic
631C4×C71—24no—
632C4×C71—42no—
633C4×C71—42no—
634C4×C71—42no—
635C4×C71—42no—
636C4×C71—42no—
637C4×C71—42no—
638C4×C71—42no—
639C4×C71—42no—
640C4×C71—42no—
641C4×C71—81no—
642C4×C71—81no—
643#16290C7111yesmaximal, characteristic, direct product factor, Sylow
644C2×C71—82no—
645C2×C71—82no—
646C2×C71—82no—
647C2×C71#242411yescharacteristic
648C2×C71#242811yescharacteristic
649C2×C71#246111yescharacteristic
650C2×C71#262011yescharacteristic
651C2×C71#263011yescharacteristic
652C2×C71#266211yescharacteristic
653C2×C71#266911yescharacteristic
654C2×C71#267211yescharacteristic
655C2×C71#267511yescharacteristic
656C2×C71#267611yescharacteristic
657C2×C71#268111yescharacteristic
658C2×C71#268211yescharacteristic
659C2×C71#268511yescharacteristic
660C2×C71#270511yescharacteristic
661C2×C71#282911yescharacteristic
662C2×#396C2×C7111yescharacteristic, complemented
663C2×#396C2×C7111yescharacteristic, complemented
664C2×#394C2×C7111yescharacteristic, complemented
665C2×#394C2×C7111yescharacteristic, complemented
666C2×#394C2×C7111yescharacteristic, complemented
667C2×#392C2×C7111yescharacteristic
668C2×#390C2×C7111yescharacteristic, complemented
669C2×#388C2×C7111yescharacteristic, complemented
670#1444C2×C7111yescharacteristic, complemented
671#1439C2×C7111yescharacteristic, complemented
672#1439C2×C7111yescharacteristic, complemented
673#1439C2×C7111yescharacteristic, complemented
674#1438C2×C7111yescharacteristic, complemented
675#1438C2×C7111yescharacteristic, complemented
676#1436C2×C7111yescharacteristic, complemented
677C71#1629011yescharacteristic, direct product factor, Sylow
678C23×D4C22×C7111yescharacteristic
679C23×D4C22×C7111yescharacteristic
680C23×D4C22×C7111yescharacteristic
681C22×C4⋊C4C22×C7111yescharacteristic
682C22×C4⋊C4C22×C7111yescharacteristic
683C22×C4⋊C4C22×C7111yescharacteristic
684C22×C4⋊C4C22×C7111yescharacteristic
685C22×C4⋊C4C22×C7111yescharacteristic
686C22×C4⋊C4C22×C7111yescharacteristic
687C22×C22⋊C4C22×C7111yescharacteristic
688C22×C22⋊C4C22×C7111yescharacteristic
689C22×C22⋊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×C42C22×C7111yescharacteristic
703#396—24no—
704#396—24no—
705#394—24no—
706#394—24no—
707#394—24no—
708#392—24no—
709#390—24no—
710#388—24no—
711C2×#95C22×C7111yescharacteristic
712C2×#95C22×C7111yescharacteristic
713C2×#95C22×C7111yescharacteristic
714C2×#95C22×C7111yescharacteristic
715C2×#95C22×C7111yescharacteristic
716C2×#95C22×C7111yescharacteristic
717C2×#95C22×C7111yescharacteristic
718C2×#95C22×C7111yescharacteristic
719C2×#95C22×C7111yescharacteristic
720C2×#95C22×C7111yescharacteristic
721C25C23×C7111yescharacteristic
722C25C23×C7111yescharacteristic
723C25C23×C7111yescharacteristic
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—41no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4—41no—
739C22×D4—41no—
740C22×D4—41no—
741C22×D4—41no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C23×C4C23×C7111yescharacteristic
746C23×C4C23×C7111yescharacteristic
747C23×C4C23×C7111yescharacteristic
748C23×C4C23×C7111yescharacteristic
749C23×C4C23×C7111yescharacteristic
750C23×C4C23×C7111yescharacteristic
751C23×C4C23×C7111yescharacteristic
752C23×C4C23×C7111yescharacteristic
753C23×C4C23×C7111yescharacteristic
754C23×C4C23×C7111yescharacteristic
755C23×C4C23×C7111yescharacteristic
756C23×C4C23×C7111yescharacteristic
757C2×C4⋊C4—22no—
758C2×C4⋊C4—22no—
759C2×C4⋊C4—22no—
760C2×C4⋊C4—22no—
761C2×C4⋊C4—22no—
762C2×C4⋊C4—22no—
763C2×C4⋊C4—22no—
764C2×C4⋊C4—22no—
765C2×C4⋊C4—22no—
766C2×C4⋊C4—22no—
767C2×C4⋊C4—22no—
768C2×C4⋊C4—22no—
769C2×C4⋊C4—41no—
770C2×C4⋊C4—41no—
771C2×C4⋊C4—41no—
772C2×C4⋊C4—41no—
773C2×C4⋊C4—41no—
774C2×C4⋊C4—41no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
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—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
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⋊C4—41no—
818C2×C22⋊C4D4×C7114yes—
819C2×C22⋊C4D4×C7114yescomplemented
820C2×C42—22no—
821C2×C42—22no—
822C2×C42—41no—
823#95—22no—
824#95—22no—
825#95—22no—
826#95—22no—
827#95—22no—
828#95—41no—
829#95—41no—
830#95—41no—
831#95D4×C7114yescomplemented
832#95D4×C7114yescomplemented
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
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—
875C24C2×D4×C7112yes—
876C24C2×D4×C7112yes—
877C24#41×C7112yes—
878C24C24×C7111yescharacteristic
879C2×D4—28no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
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—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
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—21no—
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×C4C2×D4×C7112yes—
973C22×C4C2×D4×C7112yes—
974C22×C4C2×D4×C7112yes—
975C22×C4C2×D4×C7112yes—
976C22×C4C2×D4×C7112yes—
977C22×C4C2×D4×C7112yes—
978C22×C4C2×D4×C7112yes—
979C22×C4C2×D4×C7112yes—
980C22×C4C2×D4×C7112yes—
981C22×C4C2×D4×C7112yes—
982C22×C4#41×C7112yes—
983C22×C4#41×C7112yes—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C22⋊C4—28no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
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—
1005C42—44no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
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—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
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—
1111C23C22×D4×C7111yescharacteristic
1112C23C22×D4×C7111yescharacteristic
1113C23C22×D4×C7111yescharacteristic
1114C23C22×D4×C7111yescharacteristic
1115C23C2×#41×C7111yescharacteristic
1116C23C2×#41×C7111yescharacteristic
1117C23C2×#41×C7111yescharacteristic
1118C23H(5,𝔽2)×C7111yescharacteristic
1119C23H(5,𝔽2)×C7111yescharacteristic
1120C23H(5,𝔽2)×C7111yescharacteristic
1121C23H(5,𝔽2)×C7111yescharacteristic
1122C23H(5,𝔽2)×C7111yescharacteristic
1123C23H(5,𝔽2)×C7111yescharacteristic
1124C232−1+4×C7111yescharacteristic
1125C232−1+4×C7111yescharacteristic
1126D4—416no—
1127D4—416no—
1128D4—416no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
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—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
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#121×C7114yes—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22C2×#121×C7111yescharacteristic
1259C22#525×C7111yescharacteristic
1260C22#532×C7111yescharacteristic
1261C22#534×C7111yescharacteristic
1262C22#535×C7111yescharacteristic
1263C22#535×C7111yescharacteristic
1264C22#536×C7111yescharacteristic
1265C22#537×C7111yescharacteristic
1266C22#537×C7111yescharacteristic
1267C22#537×C7111yescharacteristic
1268C22#537×C7111yescharacteristic
1269C22#538×C7111yescharacteristic
1270C22#538×C7111yescharacteristic
1271C22#538×C7111yescharacteristic
1272C22#539×C7111yescharacteristic
1273C22#540×C7111yescharacteristic
1274C22#542×C7111yescharacteristic
1275C22#542×C7111yescharacteristic
1276C22#542×C7111yescharacteristic
1277C22D42×C7111yescharacteristic
1278C22D42×C7111yescharacteristic
1279C22D42×C7111yescharacteristic
1280C22D42×C7111yescharacteristic
1281C22D42×C7111yescharacteristic
1282C22#546×C7111yescharacteristic
1283C22#546×C7111yescharacteristic
1284C22#546×C7111yescharacteristic
1285C22#547×C7111yescharacteristic
1286C22#548×C7111yescharacteristic
1287C22#550×C7111yescharacteristic
1288C22#551×C7111yescharacteristic
1289C22#560×C7111yescharacteristic
1290C22#560×C7111yescharacteristic
1291C22#562×C7111yescharacteristic
1292C22#562×C7111yescharacteristic
1293C4—24no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—42no—
1299C4—42no—
1300C4—42no—
1301C4—42no—
1302C4—42no—
1303C4—81no—
1304C4—81no—
1305C2—82no—
1306C2—82no—
1307C2—82no—
1308C2C71×#242411yescharacteristic
1309C2C71×#242811yescharacteristic
1310C2C71×#246111yescharacteristic
1311C2C71×#262011yescharacteristic
1312C2C71×#263011yescharacteristic
1313C2C71×#266211yescharacteristic
1314C2C71×#266911yescharacteristic
1315C2C71×#267211yescharacteristic
1316C2C71×#267511yescharacteristic
1317C2C71×#267611yescharacteristic
1318C2C71×#268111yescharacteristic
1319C2C71×#268211yescharacteristic
1320C2C71×#268511yescharacteristic
1321C2C71×#270511yescharacteristic
1322C2C71×#282911yescharacteristic
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×#396×C71C2semidirect
2. C2×#396×C71C2semidirect
3. C2×#394×C71C2semidirect
4. C2×#394×C71C2semidirect
5. C2×#394×C71C2semidirect
7. C2×#390×C71C2semidirect
8. C2×#388×C71C2semidirect
9. C71×#1444C2semidirect
10. C71×#1439C2semidirect
11. C71×#1439C2semidirect
12. C71×#1439C2semidirect
13. C71×#1438C2semidirect
14. C71×#1438C2semidirect
15. C71×#1436C2semidirect
157. C2×C22⋊C4×C71D4semidirect
169. #95×C71D4semidirect
170. #95×C71D4semidirect
643. #16290C71direct (N × H)
662. C2×#396C2×C71semidirect
663. C2×#396C2×C71semidirect
664. C2×#394C2×C71semidirect
665. C2×#394C2×C71semidirect
666. C2×#394C2×C71semidirect
668. C2×#390C2×C71semidirect
669. C2×#388C2×C71semidirect
670. #1444C2×C71semidirect
671. #1439C2×C71semidirect
672. #1439C2×C71semidirect
673. #1439C2×C71semidirect
674. #1438C2×C71semidirect
675. #1438C2×C71semidirect
676. #1436C2×C71semidirect
677. C71#16290direct (N × H)
819. C2×C22⋊C4D4×C71semidirect
831. #95D4×C71semidirect
832. #95D4×C71semidirect

Maximal subgroups

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

subgroupindex
C2×#396×C712
C2×#394×C712
C2×#392×C712
C2×#390×C712
C2×#388×C712
C71×#14442
C71×#14392
C71×#14382
C71×#14362
#1629071