Finite Group Databasebeta

← C71×#13995 #31834867

Subgroups — C71×#13995 #31834867

Order 18176.

4210 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C71C211yesmaximal, characteristic
2C23×C22⋊C4×C71C211yesmaximal, characteristic, complemented
3C2×#390×C71C212yesmaximal, complemented
4C2×#386×C71C211yesmaximal, characteristic, complemented
5C2×#386×C71C211yesmaximal, characteristic, complemented
6C2×#385×C71C211yesmaximal, characteristic, complemented
7C2×#379×C71C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊C4×C71C211yesmaximal, characteristic, complemented
9C71×#1439C212yesmaximal, complemented
10C71×#1438C212yesmaximal, complemented
11C71×#1437C212yesmaximal, complemented
12C26×C71C2211yescharacteristic
13C23×D4×C71C2211yescharacteristic
14C23×D4×C71C2212yes—
15C24×C4×C71C2211yescharacteristic
16C24×C4×C71C2211yescharacteristic
17C2×#120×C71—24no—
18C2×#120×C71—24no—
19C2×#120×C71C418yescomplemented
20C22×C4⋊C4×C71C2212yescomplemented
21C22×C22⋊C4×C71—24no—
22C22×C22⋊C4×C71—28no—
23C22×C22⋊C4×C71C2211yescharacteristic
24C22×C22⋊C4×C71C2212yes—
25C22×C22⋊C4×C71C2212yes—
26C22×C22⋊C4×C71C2212yes—
27C22×C22⋊C4×C71C2212yes—
28C22×C22⋊C4×C71C2211yescharacteristic
29C22×C22⋊C4×C71C2212yes—
30C22×C22⋊C4×C71C2211yescharacteristic
31C22×C22⋊C4×C71C2211yescharacteristic, complemented
32C22×C22⋊C4×C71C2212yescomplemented
33C22×C22⋊C4×C71C2211yescharacteristic, complemented
34C22×C42×C71C2212yescomplemented
35#390×C71—28no—
36#386×C71—24no—
37#386×C71—24no—
38#385×C71—24no—
39#379×C71—24no—
40C4×C22⋊C4×C71—24no—
41C2×#95×C71C2212yescomplemented
42C2×#95×C71C2211yescharacteristic, complemented
43C2×#95×C71C2212yescomplemented
44C2×#95×C71C2211yescharacteristic, complemented
45C2×#95×C71C2212yescomplemented
46C25×C71—24no—
47C25×C71—22no—
48C25×C71—24no—
49C25×C71—22no—
50C25×C71—22no—
51C25×C71—22no—
52C25×C71—22no—
53C25×C71—22no—
54C25×C71—42no—
55C25×C71—42no—
56C25×C71C2×C414yes—
57C25×C71C2311yescharacteristic
58C25×C71C2312yes—
59C25×C71C2311yescharacteristic
60C22×D4×C71—22no—
61C22×D4×C71—22no—
62C22×D4×C71—22no—
63C22×D4×C71—22no—
64C22×D4×C71—24no—
65C22×D4×C71—24no—
66C22×D4×C71—22no—
67C22×D4×C71—22no—
68C22×D4×C71—24no—
69C22×D4×C71—24no—
70C22×D4×C71—42no—
71C22×D4×C71—42no—
72C22×D4×C71C2×C414yes—
73C22×D4×C71C2×C418yescomplemented
74C23×C4×C71—22no—
75C23×C4×C71—22no—
76C23×C4×C71—22no—
77C23×C4×C71—24no—
78C23×C4×C71—24no—
79C23×C4×C71—22no—
80C23×C4×C71—22no—
81C23×C4×C71—42no—
82C23×C4×C71—42no—
83C23×C4×C71D414yescomplemented
84C23×C4×C71C2311yescharacteristic
85C23×C4×C71C2311yescharacteristic
86C23×C4×C71C2311yescharacteristic
87C23×C4×C71C2312yes—
88C23×C4×C71C2312yes—
89C23×C4×C71C2311yescharacteristic
90C23×C4×C71C2312yes—
91C23×C4×C71C2311yescharacteristic
92#120×C71—232no—
93C2×C4⋊C4×C71—24no—
94C2×C4⋊C4×C71—24no—
95C2×C4⋊C4×C71—42no—
96C2×C22⋊C4×C71—232no—
97C2×C22⋊C4×C71—24no—
98C2×C22⋊C4×C71—22no—
99C2×C22⋊C4×C71—22no—
100C2×C22⋊C4×C71—24no—
101C2×C22⋊C4×C71—24no—
102C2×C22⋊C4×C71—24no—
103C2×C22⋊C4×C71—24no—
104C2×C22⋊C4×C71—24no—
105C2×C22⋊C4×C71—24no—
106C2×C22⋊C4×C71—22no—
107C2×C22⋊C4×C71—22no—
108C2×C22⋊C4×C71—22no—
109C2×C22⋊C4×C71—24no—
110C2×C22⋊C4×C71—24no—
111C2×C22⋊C4×C71—24no—
112C2×C22⋊C4×C71—24no—
113C2×C22⋊C4×C71—24no—
114C2×C22⋊C4×C71—22no—
115C2×C22⋊C4×C71—22no—
116C2×C22⋊C4×C71—24no—
117C2×C22⋊C4×C71—24no—
118C2×C22⋊C4×C71—42no—
119C2×C22⋊C4×C71—42no—
120C2×C22⋊C4×C71—42no—
121C2×C22⋊C4×C71—42no—
122C2×C22⋊C4×C71C2×C414yes—
123C2×C22⋊C4×C71C2×C418yescomplemented
124C2×C22⋊C4×C71D414yes—
125C2×C22⋊C4×C71D414yes—
126C2×C22⋊C4×C71D418yescomplemented
127C2×C22⋊C4×C71D414yescomplemented
128C2×C42×C71—24no—
129C2×C42×C71—24no—
130C2×C42×C71—42no—
131#95×C71—24no—
132#95×C71—24no—
133#95×C71—24no—
134#95×C71—22no—
135#95×C71—22no—
136C24×C71—22no—
137C24×C71—22no—
138C24×C71—22no—
139C24×C71—22no—
140C24×C71—28no—
141C24×C71—28no—
142C24×C71—216no—
143C24×C71—216no—
144C24×C71—28no—
145C24×C71—22no—
146C24×C71—22no—
147C24×C71—22no—
148C24×C71—22no—
149C24×C71—22no—
150C24×C71—22no—
151C24×C71—22no—
152C24×C71—22no—
153C24×C71—22no—
154C24×C71—22no—
155C24×C71—22no—
156C24×C71—22no—
157C24×C71—28no—
158C24×C71—28no—
159C24×C71—21no—
160C24×C71—22no—
161C24×C71—21no—
162C24×C71—21no—
163C24×C71—21no—
164C24×C71—21no—
165C24×C71—21no—
166C24×C71—22no—
167C24×C71—22no—
168C24×C71—22no—
169C24×C71—48no—
170C24×C71—48no—
171C24×C71—48no—
172C24×C71—48no—
173C24×C71—48no—
174C24×C71—48no—
175C24×C71—48no—
176C24×C71—48no—
177C24×C71—48no—
178C24×C71—44no—
179C24×C71—44no—
180C24×C71—48no—
181C24×C71—44no—
182C24×C71—44no—
183C24×C71—44no—
184C24×C71—44no—
185C24×C71C22×C412yes—
186C24×C71C22×C414yes—
187C24×C71C22×C412yes—
188C24×C71C2×D414yes—
189C24×C71C2×D412yes—
190C24×C71C2×D412yes—
191C24×C71C2×D412yes—
192C24×C71C2×D412yes—
193C24×C71#4114yes—
194C24×C71#4112yes—
195C24×C71#4112yes—
196C24×C71C2411yescharacteristic
197C2×D4×C71—28no—
198C2×D4×C71—28no—
199C2×D4×C71—28no—
200C2×D4×C71—216no—
201C2×D4×C71—216no—
202C2×D4×C71—48no—
203C2×D4×C71—48no—
204C2×D4×C71—48no—
205C2×D4×C71—48no—
206C2×D4×C71—48no—
207C2×D4×C71—44no—
208C2×D4×C71—44no—
209C2×D4×C71—44no—
210C2×D4×C71—44no—
211C22×C4×C71—21no—
212C22×C4×C71—22no—
213C22×C4×C71—21no—
214C22×C4×C71—22no—
215C22×C4×C71—22no—
216C22×C4×C71—22no—
217C22×C4×C71—22no—
218C22×C4×C71—28no—
219C22×C4×C71—28no—
220C22×C4×C71—21no—
221C22×C4×C71—21no—
222C22×C4×C71—21no—
223C22×C4×C71—22no—
224C22×C4×C71—22no—
225C22×C4×C71—22no—
226C22×C4×C71—22no—
227C22×C4×C71—22no—
228C22×C4×C71—22no—
229C22×C4×C71—22no—
230C22×C4×C71—21no—
231C22×C4×C71—21no—
232C22×C4×C71—22no—
233C22×C4×C71—22no—
234C22×C4×C71—21no—
235C22×C4×C71—21no—
236C22×C4×C71—21no—
237C22×C4×C71—22no—
238C22×C4×C71—22no—
239C22×C4×C71—22no—
240C22×C4×C71—22no—
241C22×C4×C71—22no—
242C22×C4×C71—28no—
243C22×C4×C71—21no—
244C22×C4×C71—21no—
245C22×C4×C71—21no—
246C22×C4×C71—21no—
247C22×C4×C71—21no—
248C22×C4×C71—22no—
249C22×C4×C71—21no—
250C22×C4×C71—22no—
251C22×C4×C71—22no—
252C22×C4×C71—22no—
253C22×C4×C71—44no—
254C22×C4×C71—48no—
255C22×C4×C71—48no—
256C22×C4×C71—48no—
257C22×C4×C71—48no—
258C22×C4×C71—44no—
259C22×C4×C71—44no—
260C22×C4×C71C22×C412yes—
261C22×C4×C71C22×C414yes—
262C22×C4×C71C2×D414yes—
263C22×C4×C71C2×D412yes—
264C22×C4×C71C2×D414yes—
265C22×C4×C71C2×D414yes—
266C22×C4×C71C2×D414yes—
267C22×C4×C71C2×D412yes—
268C22×C4×C71C2×D414yes—
269C4⋊C4×C71—48no—
270C22⋊C4×C71—216no—
271C22⋊C4×C71—28no—
272C22⋊C4×C71—216no—
273C22⋊C4×C71—216no—
274C22⋊C4×C71—48no—
275C22⋊C4×C71—48no—
276C22⋊C4×C71—48no—
277C22⋊C4×C71—44no—
278C22⋊C4×C71—44no—
279C22⋊C4×C71—44no—
280C22⋊C4×C71C22⋊C4116yescomplemented
281C42×C71—48no—
282C23×C71—24no—
283C23×C71—24no—
284C23×C71—22no—
285C23×C71—22no—
286C23×C71—24no—
287C23×C71—22no—
288C23×C71—22no—
289C23×C71—24no—
290C23×C71—24no—
291C23×C71—24no—
292C23×C71—24no—
293C23×C71—24no—
294C23×C71—24no—
295C23×C71—24no—
296C23×C71—24no—
297C23×C71—24no—
298C23×C71—232no—
299C23×C71—24no—
300C23×C71—24no—
301C23×C71—24no—
302C23×C71—24no—
303C23×C71—24no—
304C23×C71—24no—
305C23×C71—24no—
306C23×C71—24no—
307C23×C71—24no—
308C23×C71—24no—
309C23×C71—24no—
310C23×C71—24no—
311C23×C71—24no—
312C23×C71—24no—
313C23×C71—24no—
314C23×C71—24no—
315C23×C71—24no—
316C23×C71—24no—
317C23×C71—22no—
318C23×C71—22no—
319C23×C71—24no—
320C23×C71—22no—
321C23×C71—24no—
322C23×C71—432no—
323C23×C71—432no—
324C23×C71—416no—
325C23×C71—416no—
326C23×C71—416no—
327C23×C71—432no—
328C23×C71—416no—
329C23×C71—432no—
330C23×C71—416no—
331C23×C71—42no—
332C23×C71—42no—
333C23×C71—42no—
334C23×C71—42no—
335C23×C71—42no—
336C23×C71—42no—
337C23×C71—42no—
338C23×C71—42no—
339C23×C71—42no—
340C23×C71—42no—
341C23×C71—42no—
342C23×C71—42no—
343C23×C71—42no—
344C23×C71—42no—
345C23×C71—42no—
346C23×C71—42no—
347C23×C71—416no—
348C23×C71—41no—
349C23×C71—41no—
350C23×C71—41no—
351C23×C71—41no—
352C23×C71—42no—
353C23×C71—41no—
354C23×C71—41no—
355C23×C71—41no—
356C23×C71—41no—
357C23×C71—42no—
358C23×C71—42no—
359C23×C71—42no—
360C23×C71—42no—
361C23×C71—42no—
362C23×C71—42no—
363C23×C71—42no—
364C23×C71—42no—
365C23×C71—42no—
366C23×C71C2×C22⋊C414yes—
367C23×C71C4×D418yes—
368C23×C71C4×D414yes—
369C23×C71C4×D414yes—
370C23×C71#12114yes—
371C23×C71#12114yes—
372C23×C71#12414yes—
373C23×C71#12714yes—
374C23×C71C23×C411yescharacteristic
375C23×C71C22×D411yescharacteristic
376C23×C71C22×D411yescharacteristic
377C23×C71C22×D411yescharacteristic
378C23×C71C22×D412yes—
379C23×C71C22×D411yescharacteristic
380C23×C71C2×#4111yescharacteristic
381C23×C71C2×#4111yescharacteristic
382C23×C71C2×#4112yes—
383C23×C71H(5,𝔽2)12yes—
384C23×C71H(5,𝔽2)12yes—
385D4×C71—432no—
386D4×C71—416no—
387C2×C4×C71—24no—
388C2×C4×C71—24no—
389C2×C4×C71—22no—
390C2×C4×C71—22no—
391C2×C4×C71—24no—
392C2×C4×C71—24no—
393C2×C4×C71—24no—
394C2×C4×C71—24no—
395C2×C4×C71—24no—
396C2×C4×C71—24no—
397C2×C4×C71—22no—
398C2×C4×C71—22no—
399C2×C4×C71—22no—
400C2×C4×C71—22no—
401C2×C4×C71—24no—
402C2×C4×C71—24no—
403C2×C4×C71—22no—
404C2×C4×C71—22no—
405C2×C4×C71—24no—
406C2×C4×C71—24no—
407C2×C4×C71—24no—
408C2×C4×C71—24no—
409C2×C4×C71—416no—
410C2×C4×C71—416no—
411C2×C4×C71—41no—
412C2×C4×C71—41no—
413C2×C4×C71—42no—
414C2×C4×C71—41no—
415C2×C4×C71—42no—
416C2×C4×C71—41no—
417C2×C4×C71—42no—
418C2×C4×C71—42no—
419C2×C4×C71—42no—
420C2×C4×C71—42no—
421C2×C4×C71—42no—
422C2×C4×C71—42no—
423C2×C4×C71—42no—
424C2×C4×C71—42no—
425C2×C4×C71—41no—
426C2×C4×C71—41no—
427C2×C4×C71—41no—
428C2×C4×C71—41no—
429C2×C4×C71—41no—
430C2×C4×C71—41no—
431C2×C4×C71—42no—
432C2×C4×C71—42no—
433C2×C4×C71—42no—
434C2×C4×C71—42no—
435C2×C4×C71C2×C22⋊C418yescomplemented
436C2×C4×C71#12014yescomplemented
437C22×C71—24no—
438C22×C71—28no—
439C22×C71—28no—
440C22×C71—24no—
441C22×C71—24no—
442C22×C71—28no—
443C22×C71—24no—
444C22×C71—28no—
445C22×C71—24no—
446C22×C71—24no—
447C22×C71—28no—
448C22×C71—28no—
449C22×C71—28no—
450C22×C71—464no—
451C22×C71—44no—
452C22×C71—44no—
453C22×C71—44no—
454C22×C71—44no—
455C22×C71—44no—
456C22×C71—44no—
457C22×C71—44no—
458C22×C71—44no—
459C22×C71—44no—
460C22×C71—44no—
461C22×C71—44no—
462C22×C71—44no—
463C22×C71—42no—
464C22×C71—44no—
465C22×C71—44no—
466C22×C71—42no—
467C22×C71—42no—
468C22×C71—81no—
469C22×C71—81no—
470C22×C71—82no—
471C22×C71—81no—
472C22×C71—82no—
473C22×C71—81no—
474C22×C71#39018yescomplemented
475C22×C71C22×C22⋊C411yescharacteristic
476C22×C71C2×C4×D411yescharacteristic
477C22×C71C2×C4×D412yes—
478C22×C71C2×C4×D411yescharacteristic
479C22×C71#51812yes—
480C22×C71C2×#12011yescharacteristic
481C22×C71C2×#12111yescharacteristic
482C22×C71C2×#12111yescharacteristic
483C22×C71#52511yescharacteristic
484C22×C71#52512yes—
485C22×C71C2×#12411yescharacteristic
486C22×C71C2×#12711yescharacteristic
487C22×C71#53411yescharacteristic
488C22×C71#53511yescharacteristic
489C22×C71#53812yes—
490C22×C71D4212yes—
491C22×C71D4212yes—
492C22×C71D4212yes—
493C22×C71#54612yes—
494C22×C71#54612yes—
495C22×C71#54612yes—
496C22×C71#54612yes—
497C22×C71#55112yes—
498C4×C71—28no—
499C4×C71—24no—
500C4×C71—42no—
501C4×C71—44no—
502C4×C71—44no—
503C4×C71—42no—
504C4×C71—81no—
505C4×C71—81no—
506#13995C7111yesmaximal, characteristic, direct product factor, Sylow
507C2×C71—28no—
508C2×C71—48no—
509C2×C71—82no—
510C2×C71C2×#39011yescharacteristic
511C2×C71C4×#12011yescharacteristic
512C2×C71#232111yescharacteristic
513C2×C71D4×C22⋊C412yes—
514C2×C71#235812yes—
515C2×C71#241011yescharacteristic
516C2×C71#241111yescharacteristic
517C2×C71#242412yes—
518C2×C71#243311yescharacteristic
519C2×C71#247212yes—
520C2×C71#253911yescharacteristic
521C22×#120C2×C7111yescharacteristic
522C23×C22⋊C4C2×C7111yescharacteristic, complemented
523C2×#390C2×C7112yescomplemented
524C2×#386C2×C7111yescharacteristic, complemented
525C2×#386C2×C7111yescharacteristic, complemented
526C2×#385C2×C7111yescharacteristic, complemented
527C2×#379C2×C7111yescharacteristic, complemented
528C2×C4×C22⋊C4C2×C7111yescharacteristic, complemented
529#1439C2×C7112yescomplemented
530#1438C2×C7112yescomplemented
531#1437C2×C7112yescomplemented
532C71#1399511yescharacteristic, direct product factor, Sylow
533C26C22×C7111yescharacteristic
534C23×D4C22×C7111yescharacteristic
535C23×D4C22×C7112yes—
536C24×C4C22×C7111yescharacteristic
537C24×C4C22×C7111yescharacteristic
538C2×#120—24no—
539C2×#120—24no—
540C2×#120C4×C7118yescomplemented
541C22×C4⋊C4C22×C7112yescomplemented
542C22×C22⋊C4—24no—
543C22×C22⋊C4—28no—
544C22×C22⋊C4C22×C7112yes—
545C22×C22⋊C4C22×C7111yescharacteristic
546C22×C22⋊C4C22×C7112yes—
547C22×C22⋊C4C22×C7112yes—
548C22×C22⋊C4C22×C7112yes—
549C22×C22⋊C4C22×C7112yes—
550C22×C22⋊C4C22×C7111yescharacteristic
551C22×C22⋊C4C22×C7111yescharacteristic
552C22×C22⋊C4C22×C7111yescharacteristic, complemented
553C22×C22⋊C4C22×C7112yescomplemented
554C22×C22⋊C4C22×C7111yescharacteristic, complemented
555C22×C42C22×C7112yescomplemented
556#390—28no—
557#386—24no—
558#386—24no—
559#385—24no—
560#379—24no—
561C4×C22⋊C4—24no—
562C2×#95C22×C7111yescharacteristic, complemented
563C2×#95C22×C7112yescomplemented
564C2×#95C22×C7112yescomplemented
565C2×#95C22×C7112yescomplemented
566C2×#95C22×C7111yescharacteristic, complemented
567C25—24no—
568C25—22no—
569C25—24no—
570C25—22no—
571C25—22no—
572C25—22no—
573C25—22no—
574C25—22no—
575C25—42no—
576C25—42no—
577C25C2×C4×C7114yes—
578C25C23×C7111yescharacteristic
579C25C23×C7112yes—
580C25C23×C7111yescharacteristic
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—22no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—24no—
590C22×D4—24no—
591C22×D4—42no—
592C22×D4—42no—
593C22×D4C2×C4×C7114yes—
594C22×D4C2×C4×C7118yescomplemented
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—24no—
599C23×C4—24no—
600C23×C4—22no—
601C23×C4—22no—
602C23×C4—42no—
603C23×C4—42no—
604C23×C4D4×C7114yescomplemented
605C23×C4C23×C7111yescharacteristic
606C23×C4C23×C7111yescharacteristic
607C23×C4C23×C7111yescharacteristic
608C23×C4C23×C7112yes—
609C23×C4C23×C7112yes—
610C23×C4C23×C7111yescharacteristic
611C23×C4C23×C7112yes—
612C23×C4C23×C7111yescharacteristic
613#120—232no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4—24no—
616C2×C4⋊C4—42no—
617C2×C22⋊C4—232no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—24no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—24no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—24no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4—42no—
643C2×C22⋊C4C2×C4×C7114yes—
644C2×C22⋊C4C2×C4×C7118yescomplemented
645C2×C22⋊C4D4×C7114yes—
646C2×C22⋊C4D4×C7114yes—
647C2×C22⋊C4D4×C7118yescomplemented
648C2×C22⋊C4D4×C7114yescomplemented
649C2×C42—24no—
650C2×C42—24no—
651C2×C42—42no—
652#95—24no—
653#95—24no—
654#95—24no—
655#95—22no—
656#95—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—28no—
662C24—28no—
663C24—216no—
664C24—216no—
665C24—28no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—28no—
679C24—28no—
680C24—21no—
681C24—22no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—48no—
691C24—48no—
692C24—48no—
693C24—48no—
694C24—48no—
695C24—48no—
696C24—48no—
697C24—48no—
698C24—48no—
699C24—44no—
700C24—44no—
701C24—48no—
702C24—44no—
703C24—44no—
704C24—44no—
705C24—44no—
706C24C22×C4×C7112yes—
707C24C22×C4×C7114yes—
708C24C22×C4×C7112yes—
709C24C2×D4×C7114yes—
710C24C2×D4×C7112yes—
711C24C2×D4×C7112yes—
712C24C2×D4×C7112yes—
713C24C2×D4×C7112yes—
714C24#41×C7114yes—
715C24#41×C7112yes—
716C24#41×C7112yes—
717C24C24×C7111yescharacteristic
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—216no—
722C2×D4—216no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—44no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—21no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—28no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—44no—
775C22×C4—48no—
776C22×C4—48no—
777C22×C4—48no—
778C22×C4—48no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4C22×C4×C7112yes—
782C22×C4C22×C4×C7114yes—
783C22×C4C2×D4×C7114yes—
784C22×C4C2×D4×C7112yes—
785C22×C4C2×D4×C7114yes—
786C22×C4C2×D4×C7114yes—
787C22×C4C2×D4×C7114yes—
788C22×C4C2×D4×C7112yes—
789C22×C4C2×D4×C7114yes—
790C4⋊C4—48no—
791C22⋊C4—216no—
792C22⋊C4—28no—
793C22⋊C4—216no—
794C22⋊C4—216no—
795C22⋊C4—48no—
796C22⋊C4—48no—
797C22⋊C4—48no—
798C22⋊C4—44no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4C22⋊C4×C71116yescomplemented
802C42—48no—
803C23—24no—
804C23—24no—
805C23—22no—
806C23—22no—
807C23—24no—
808C23—22no—
809C23—22no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—232no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—24no—
842C23—24no—
843C23—432no—
844C23—432no—
845C23—416no—
846C23—416no—
847C23—416no—
848C23—416no—
849C23—432no—
850C23—416no—
851C23—432no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—416no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—42no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—42no—
887C23C2×C22⋊C4×C7114yes—
888C23C4×D4×C7118yes—
889C23C4×D4×C7114yes—
890C23C4×D4×C7114yes—
891C23#121×C7114yes—
892C23#121×C7114yes—
893C23#124×C7114yes—
894C23#127×C7114yes—
895C23C23×C4×C7111yescharacteristic
896C23C22×D4×C7111yescharacteristic
897C23C22×D4×C7111yescharacteristic
898C23C22×D4×C7111yescharacteristic
899C23C22×D4×C7112yes—
900C23C22×D4×C7111yescharacteristic
901C23C2×#41×C7111yescharacteristic
902C23C2×#41×C7111yescharacteristic
903C23C2×#41×C7112yes—
904C23H(5,𝔽2)×C7112yes—
905C23H(5,𝔽2)×C7112yes—
906D4—432no—
907D4—416no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—416no—
931C2×C4—416no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—42no—
937C2×C4—41no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4C2×C22⋊C4×C7118yescomplemented
957C2×C4#120×C7114yescomplemented
958C22—24no—
959C22—24no—
960C22—24no—
961C22—28no—
962C22—28no—
963C22—24no—
964C22—24no—
965C22—28no—
966C22—24no—
967C22—28no—
968C22—28no—
969C22—28no—
970C22—28no—
971C22—464no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—44no—
977C22—44no—
978C22—44no—
979C22—44no—
980C22—44no—
981C22—44no—
982C22—44no—
983C22—44no—
984C22—42no—
985C22—42no—
986C22—42no—
987C22—44no—
988C22—44no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—82no—
993C22—81no—
994C22—82no—
995C22#390×C7118yescomplemented
996C22C22×C22⋊C4×C7111yescharacteristic
997C22C2×C4×D4×C7111yescharacteristic
998C22C2×C4×D4×C7111yescharacteristic
999C22C2×C4×D4×C7112yes—
1000C22#518×C7112yes—
1001C22C2×#120×C7111yescharacteristic
1002C22C2×#121×C7111yescharacteristic
1003C22C2×#121×C7111yescharacteristic
1004C22#525×C7111yescharacteristic
1005C22#525×C7112yes—
1006C22C2×#124×C7111yescharacteristic
1007C22C2×#127×C7111yescharacteristic
1008C22#534×C7111yescharacteristic
1009C22#535×C7111yescharacteristic
1010C22#538×C7112yes—
1011C22D42×C7112yes—
1012C22D42×C7112yes—
1013C22D42×C7112yes—
1014C22#546×C7112yes—
1015C22#546×C7112yes—
1016C22#546×C7112yes—
1017C22#546×C7112yes—
1018C22#551×C7112yes—
1019C4—28no—
1020C4—24no—
1021C4—42no—
1022C4—42no—
1023C4—44no—
1024C4—44no—
1025C4—81no—
1026C4—81no—
1027C2—28no—
1028C2—48no—
1029C2—82no—
1030C2C2×#390×C7111yescharacteristic
1031C2C4×#120×C7111yescharacteristic
1032C2C71×#232111yescharacteristic
1033C2D4×C22⋊C4×C7112yes—
1034C2C71×#235812yes—
1035C2C71×#241011yescharacteristic
1036C2C71×#241111yescharacteristic
1037C2C71×#242412yes—
1038C2C71×#243311yescharacteristic
1039C2C71×#247212yes—
1040C2C71×#253911yescharacteristic
subgroupG/H
center, socleC24×C71C24
commutatorC23C23×C4×C71
Frattini, cosocleC24C24×C71
prime radicalC22×#120×C71C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C71 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C71C2semidirect
3. C2×#390×C71C2semidirect
4. C2×#386×C71C2semidirect
5. C2×#386×C71C2semidirect
6. C2×#385×C71C2semidirect
7. C2×#379×C71C2semidirect
8. C2×C4×C22⋊C4×C71C2semidirect
9. C71×#1439C2semidirect
10. C71×#1438C2semidirect
11. C71×#1437C2semidirect
19. C2×#120×C71C4semidirect
20. C22×C4⋊C4×C71C22semidirect
31. C22×C22⋊C4×C71C22semidirect
32. C22×C22⋊C4×C71C22semidirect
33. C22×C22⋊C4×C71C22semidirect
34. C22×C42×C71C22semidirect
41. C2×#95×C71C22semidirect
42. C2×#95×C71C22semidirect
43. C2×#95×C71C22semidirect
44. C2×#95×C71C22semidirect
45. C2×#95×C71C22semidirect
73. C22×D4×C71C2×C4semidirect
83. C23×C4×C71D4semidirect
123. C2×C22⋊C4×C71C2×C4semidirect
126. C2×C22⋊C4×C71D4semidirect
127. C2×C22⋊C4×C71D4semidirect
280. C22⋊C4×C71C22⋊C4semidirect
435. C2×C4×C71C2×C22⋊C4semidirect
436. C2×C4×C71#120semidirect
474. C22×C71#390semidirect
506. #13995C71direct (N × H)
522. C23×C22⋊C4C2×C71semidirect
523. C2×#390C2×C71semidirect
524. C2×#386C2×C71semidirect
525. C2×#386C2×C71semidirect
526. C2×#385C2×C71semidirect
527. C2×#379C2×C71semidirect
528. C2×C4×C22⋊C4C2×C71semidirect
529. #1439C2×C71semidirect
530. #1438C2×C71semidirect
531. #1437C2×C71semidirect
532. C71#13995direct (N × H)
540. C2×#120C4×C71semidirect
541. C22×C4⋊C4C22×C71semidirect
552. C22×C22⋊C4C22×C71semidirect
553. C22×C22⋊C4C22×C71semidirect
554. C22×C22⋊C4C22×C71semidirect
555. C22×C42C22×C71semidirect
562. C2×#95C22×C71semidirect
563. C2×#95C22×C71semidirect
564. C2×#95C22×C71semidirect
565. C2×#95C22×C71semidirect
566. C2×#95C22×C71semidirect
594. C22×D4C2×C4×C71semidirect
604. C23×C4D4×C71semidirect
644. C2×C22⋊C4C2×C4×C71semidirect
647. C2×C22⋊C4D4×C71semidirect
648. C2×C22⋊C4D4×C71semidirect
801. C22⋊C4C22⋊C4×C71semidirect
956. C2×C4C2×C22⋊C4×C71semidirect
957. C2×C4#120×C71semidirect
995. C22#390×C71semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C712
C23×C22⋊C4×C712
C2×#390×C712
C2×#386×C712
C2×#385×C712
C2×#379×C712
C2×C4×C22⋊C4×C712
C71×#14392
C71×#14382
C71×#14372
#1399571