Finite Group Databasebeta

← C71×#13873 #31834745

Subgroups — C71×#13873 #31834745

Order 18176.

3526 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C71C211yesmaximal, characteristic
2C2×#388×C71C212yesmaximal, complemented
3C2×#380×C71C211yesmaximal, characteristic, complemented
4C2×#379×C71C211yesmaximal, characteristic
5C2×#379×C71C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C71C211yesmaximal, characteristic, complemented
7C71×#1440C212yesmaximal, complemented
8C71×#1439C212yesmaximal, complemented
9C71×#1437C212yesmaximal, complemented
10C71×C22⋊#95C211yesmaximal, characteristic, complemented
11C71×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C71C2211yescharacteristic
13C24×C4×C71C2211yescharacteristic
14C24×C4×C71C2211yescharacteristic
15C22×C4⋊C4×C71C2212yescomplemented
16C22×C22⋊C4×C71—28no—
17C22×C22⋊C4×C71C418yescomplemented
18C22×C22⋊C4×C71C2211yescharacteristic
19C22×C22⋊C4×C71C2211yescharacteristic
20C22×C22⋊C4×C71C2212yes—
21C22×C22⋊C4×C71C2212yes—
22C22×C22⋊C4×C71C2212yes—
23C22×C22⋊C4×C71C2212yes—
24C22×C22⋊C4×C71C2211yescharacteristic
25C22×C22⋊C4×C71C2211yescharacteristic
26C22×C22⋊C4×C71C2211yescharacteristic
27C22×C22⋊C4×C71C2211yescharacteristic
28C22×C22⋊C4×C71C2211yescharacteristic
29C22×C22⋊C4×C71C2211yescharacteristic
30C22×C42×C71C2212yescomplemented
31#388×C71—28no—
32#380×C71—24no—
33#379×C71—24no—
34#379×C71—24no—
35C4×C22⋊C4×C71—24no—
36C2×#95×C71C2212yescomplemented
37C2×#95×C71C2212yescomplemented
38C2×#95×C71C2212yescomplemented
39C2×#95×C71C2212yescomplemented
40C2×#95×C71C2212yescomplemented
41C2×#95×C71C2212yescomplemented
42C25×C71—24no—
43C25×C71—24no—
44C25×C71—22no—
45C25×C71—22no—
46C25×C71—22no—
47C25×C71—22no—
48C25×C71—22no—
49C25×C71—22no—
50C25×C71—42no—
51C25×C71—42no—
52C25×C71C2×C414yes—
53C25×C71C2311yescharacteristic
54C25×C71C2311yescharacteristic
55C25×C71C2311yescharacteristic
56C23×C4×C71—22no—
57C23×C4×C71—22no—
58C23×C4×C71—22no—
59C23×C4×C71—22no—
60C23×C4×C71—24no—
61C23×C4×C71—24no—
62C23×C4×C71—42no—
63C23×C4×C71—42no—
64C23×C4×C71C2×C414yes—
65C23×C4×C71C2×C414yes—
66C23×C4×C71C2312yes—
67C23×C4×C71C2312yes—
68C23×C4×C71C2311yescharacteristic
69C23×C4×C71C2311yescharacteristic
70C23×C4×C71C2312yes—
71C23×C4×C71C2312yes—
72C23×C4×C71C2311yescharacteristic
73C23×C4×C71C2311yescharacteristic
74C2×C4⋊C4×C71—24no—
75C2×C4⋊C4×C71—24no—
76C2×C4⋊C4×C71—42no—
77C2×C22⋊C4×C71—24no—
78C2×C22⋊C4×C71—22no—
79C2×C22⋊C4×C71—22no—
80C2×C22⋊C4×C71—22no—
81C2×C22⋊C4×C71—22no—
82C2×C22⋊C4×C71—24no—
83C2×C22⋊C4×C71—24no—
84C2×C22⋊C4×C71—232no—
85C2×C22⋊C4×C71—22no—
86C2×C22⋊C4×C71—22no—
87C2×C22⋊C4×C71—22no—
88C2×C22⋊C4×C71—24no—
89C2×C22⋊C4×C71—24no—
90C2×C22⋊C4×C71—24no—
91C2×C22⋊C4×C71—24no—
92C2×C22⋊C4×C71—22no—
93C2×C22⋊C4×C71—22no—
94C2×C22⋊C4×C71—22no—
95C2×C22⋊C4×C71—24no—
96C2×C22⋊C4×C71—24no—
97C2×C22⋊C4×C71—24no—
98C2×C22⋊C4×C71—24no—
99C2×C22⋊C4×C71—42no—
100C2×C22⋊C4×C71—42no—
101C2×C22⋊C4×C71—42no—
102C2×C22⋊C4×C71—42no—
103C2×C22⋊C4×C71C2×C414yes—
104C2×C22⋊C4×C71C2×C414yes—
105C2×C22⋊C4×C71C2×C414yes—
106C2×C22⋊C4×C71C2×C414yes—
107C2×C22⋊C4×C71D414yes—
108C2×C22⋊C4×C71D414yes—
109C2×C22⋊C4×C71D418yes—
110C2×C42×C71—24no—
111C2×C42×C71—24no—
112C2×C42×C71—42no—
113#95×C71—24no—
114#95×C71—24no—
115#95×C71—24no—
116#95×C71—24no—
117#95×C71—42no—
118#95×C71—42no—
119C24×C71—22no—
120C24×C71—22no—
121C24×C71—22no—
122C24×C71—22no—
123C24×C71—216no—
124C24×C71—216no—
125C24×C71—28no—
126C24×C71—28no—
127C24×C71—28no—
128C24×C71—22no—
129C24×C71—21no—
130C24×C71—21no—
131C24×C71—21no—
132C24×C71—21no—
133C24×C71—21no—
134C24×C71—21no—
135C24×C71—22no—
136C24×C71—21no—
137C24×C71—21no—
138C24×C71—21no—
139C24×C71—21no—
140C24×C71—21no—
141C24×C71—21no—
142C24×C71—22no—
143C24×C71—22no—
144C24×C71—22no—
145C24×C71—22no—
146C24×C71—28no—
147C24×C71—28no—
148C24×C71—44no—
149C24×C71—44no—
150C24×C71—48no—
151C24×C71—48no—
152C24×C71—48no—
153C24×C71—48no—
154C24×C71—48no—
155C24×C71—48no—
156C24×C71—48no—
157C24×C71—48no—
158C24×C71—48no—
159C24×C71—48no—
160C24×C71—44no—
161C24×C71—44no—
162C24×C71—44no—
163C24×C71—44no—
164C24×C71C22×C412yes—
165C24×C71C22×C412yes—
166C24×C71C22×C412yes—
167C24×C71C2×D414yes—
168C24×C71C2×D412yes—
169C24×C71C2×D412yes—
170C24×C71#4114yes—
171C24×C71#4112yes—
172C24×C71#4112yes—
173C24×C71#4112yes—
174C24×C71#4112yes—
175C24×C71C2411yescharacteristic
176C22×C4×C71—21no—
177C22×C4×C71—21no—
178C22×C4×C71—21no—
179C22×C4×C71—21no—
180C22×C4×C71—22no—
181C22×C4×C71—22no—
182C22×C4×C71—28no—
183C22×C4×C71—28no—
184C22×C4×C71—21no—
185C22×C4×C71—21no—
186C22×C4×C71—22no—
187C22×C4×C71—22no—
188C22×C4×C71—22no—
189C22×C4×C71—22no—
190C22×C4×C71—22no—
191C22×C4×C71—22no—
192C22×C4×C71—22no—
193C22×C4×C71—22no—
194C22×C4×C71—22no—
195C22×C4×C71—22no—
196C22×C4×C71—21no—
197C22×C4×C71—21no—
198C22×C4×C71—22no—
199C22×C4×C71—22no—
200C22×C4×C71—22no—
201C22×C4×C71—22no—
202C22×C4×C71—22no—
203C22×C4×C71—22no—
204C22×C4×C71—28no—
205C22×C4×C71—28no—
206C22×C4×C71—22no—
207C22×C4×C71—22no—
208C22×C4×C71—22no—
209C22×C4×C71—22no—
210C22×C4×C71—22no—
211C22×C4×C71—22no—
212C22×C4×C71—22no—
213C22×C4×C71—22no—
214C22×C4×C71—22no—
215C22×C4×C71—22no—
216C22×C4×C71—22no—
217C22×C4×C71—22no—
218C22×C4×C71—22no—
219C22×C4×C71—22no—
220C22×C4×C71—44no—
221C22×C4×C71—44no—
222C22×C4×C71—48no—
223C22×C4×C71—48no—
224C22×C4×C71—48no—
225C22×C4×C71—48no—
226C22×C4×C71C22×C412yes—
227C22×C4×C71C22×C412yes—
228C22×C4×C71C22×C412yes—
229C22×C4×C71C22×C412yes—
230C22×C4×C71C2×D414yes—
231C22×C4×C71C2×D414yes—
232C22×C4×C71C2×D414yes—
233C22×C4×C71C2×D414yes—
234C4⋊C4×C71—48no—
235C22⋊C4×C71—28no—
236C22⋊C4×C71—28no—
237C22⋊C4×C71—28no—
238C22⋊C4×C71—28no—
239C22⋊C4×C71—28no—
240C22⋊C4×C71—48no—
241C22⋊C4×C71—48no—
242C22⋊C4×C71—48no—
243C22⋊C4×C71—48no—
244C22⋊C4×C71—44no—
245C22⋊C4×C71—44no—
246C22⋊C4×C71C22⋊C4116yescomplemented
247C42×C71—48no—
248C23×C71—22no—
249C23×C71—22no—
250C23×C71—22no—
251C23×C71—22no—
252C23×C71—24no—
253C23×C71—24no—
254C23×C71—24no—
255C23×C71—24no—
256C23×C71—24no—
257C23×C71—24no—
258C23×C71—24no—
259C23×C71—24no—
260C23×C71—24no—
261C23×C71—24no—
262C23×C71—24no—
263C23×C71—24no—
264C23×C71—232no—
265C23×C71—22no—
266C23×C71—22no—
267C23×C71—22no—
268C23×C71—22no—
269C23×C71—22no—
270C23×C71—22no—
271C23×C71—22no—
272C23×C71—22no—
273C23×C71—22no—
274C23×C71—22no—
275C23×C71—22no—
276C23×C71—22no—
277C23×C71—24no—
278C23×C71—24no—
279C23×C71—24no—
280C23×C71—24no—
281C23×C71—24no—
282C23×C71—24no—
283C23×C71—24no—
284C23×C71—24no—
285C23×C71—24no—
286C23×C71—24no—
287C23×C71—24no—
288C23×C71—24no—
289C23×C71—416no—
290C23×C71—416no—
291C23×C71—416no—
292C23×C71—416no—
293C23×C71—416no—
294C23×C71—432no—
295C23×C71—432no—
296C23×C71—432no—
297C23×C71—432no—
298C23×C71—41no—
299C23×C71—41no—
300C23×C71—41no—
301C23×C71—41no—
302C23×C71—41no—
303C23×C71—41no—
304C23×C71—41no—
305C23×C71—41no—
306C23×C71—42no—
307C23×C71—42no—
308C23×C71—42no—
309C23×C71—42no—
310C23×C71—42no—
311C23×C71—42no—
312C23×C71—42no—
313C23×C71—42no—
314C23×C71—42no—
315C23×C71—42no—
316C23×C71—42no—
317C23×C71—42no—
318C23×C71—416no—
319C23×C71C2×C22⋊C414yes—
320C23×C71#11714yes—
321C23×C71#11714yes—
322C23×C71C4×D414yes—
323C23×C71C4×D414yes—
324C23×C71#12114yes—
325C23×C71#12314yes—
326C23×C71#12414yes—
327C23×C71#12614yes—
328C23×C71C23×C411yescharacteristic
329C23×C71C22×D412yes—
330C23×C71C22×D411yescharacteristic
331C23×C71C22×D411yescharacteristic
332C23×C71C2×#4111yescharacteristic
333C23×C71C2×#4111yescharacteristic
334C23×C71C2×#4112yes—
335C23×C71C2×#4111yescharacteristic
336C23×C71C2×#4111yescharacteristic
337C23×C71H(5,𝔽2)12yes—
338C23×C71H(5,𝔽2)12yes—
339C2×C4×C71—22no—
340C2×C4×C71—22no—
341C2×C4×C71—22no—
342C2×C4×C71—22no—
343C2×C4×C71—24no—
344C2×C4×C71—24no—
345C2×C4×C71—24no—
346C2×C4×C71—24no—
347C2×C4×C71—22no—
348C2×C4×C71—22no—
349C2×C4×C71—22no—
350C2×C4×C71—22no—
351C2×C4×C71—22no—
352C2×C4×C71—22no—
353C2×C4×C71—24no—
354C2×C4×C71—24no—
355C2×C4×C71—24no—
356C2×C4×C71—24no—
357C2×C4×C71—24no—
358C2×C4×C71—24no—
359C2×C4×C71—416no—
360C2×C4×C71—416no—
361C2×C4×C71—42no—
362C2×C4×C71—42no—
363C2×C4×C71—42no—
364C2×C4×C71—42no—
365C2×C4×C71—42no—
366C2×C4×C71—42no—
367C2×C4×C71—42no—
368C2×C4×C71—42no—
369C2×C4×C71—42no—
370C2×C4×C71—42no—
371C2×C4×C71—42no—
372C2×C4×C71—42no—
373C2×C4×C71—42no—
374C2×C4×C71—42no—
375C2×C4×C71—42no—
376C2×C4×C71—42no—
377C2×C4×C71—42no—
378C2×C4×C71—42no—
379C2×C4×C71—42no—
380C2×C4×C71—42no—
381C2×C4×C71—42no—
382C2×C4×C71—42no—
383C2×C4×C71—42no—
384C2×C4×C71—42no—
385C2×C4×C71—42no—
386C2×C4×C71—42no—
387C2×C4×C71C2×C22⋊C414yes—
388C2×C4×C71C2×C22⋊C414yes—
389C22×C71—24no—
390C22×C71—24no—
391C22×C71—24no—
392C22×C71—24no—
393C22×C71—24no—
394C22×C71—28no—
395C22×C71—28no—
396C22×C71—28no—
397C22×C71—28no—
398C22×C71—24no—
399C22×C71—24no—
400C22×C71—24no—
401C22×C71—24no—
402C22×C71—24no—
403C22×C71—24no—
404C22×C71—24no—
405C22×C71—464no—
406C22×C71—42no—
407C22×C71—42no—
408C22×C71—42no—
409C22×C71—42no—
410C22×C71—42no—
411C22×C71—42no—
412C22×C71—44no—
413C22×C71—44no—
414C22×C71—44no—
415C22×C71—44no—
416C22×C71—44no—
417C22×C71—44no—
418C22×C71—44no—
419C22×C71—44no—
420C22×C71—42no—
421C22×C71—42no—
422C22×C71#38818yescomplemented
423C22×C71C22×C22⋊C411yescharacteristic
424C22×C71C2×#11711yescharacteristic
425C22×C71C2×#11711yescharacteristic
426C22×C71C2×C4×D411yescharacteristic
427C22×C71C2×C4×D411yescharacteristic
428C22×C71#51811yescharacteristic
429C22×C71#51811yescharacteristic
430C22×C71C2×#12111yescharacteristic
431C22×C71C2×#12311yescharacteristic
432C22×C71#52512yes—
433C22×C71#52512yes—
434C22×C71C2×#12411yescharacteristic
435C22×C71C2×#12611yescharacteristic
436C22×C71#53812yes—
437C22×C71#53812yes—
438C22×C71D4212yes—
439C22×C71D4212yes—
440C22×C71#54612yes—
441C22×C71#54612yes—
442C22×C71#54612yes—
443C22×C71#54612yes—
444C22×C71#55112yes—
445C22×C71#55112yes—
446C4×C71—24no—
447C4×C71—24no—
448C4×C71—42no—
449C4×C71—42no—
450C4×C71—44no—
451C4×C71—44no—
452C4×C71—82no—
453C4×C71—82no—
454#13873C7111yesmaximal, characteristic, direct product factor, Sylow
455C2×C71—28no—
456C2×C71—44no—
457C2×C71—44no—
458C2×C71#228011yescharacteristic
459C2×C71C2×#38811yescharacteristic
460C2×C71#231211yescharacteristic
461C2×C71D4×C22⋊C411yescharacteristic
462C2×C71D4×C22⋊C411yescharacteristic
463C2×C71#234211yescharacteristic
464C2×C71#234211yescharacteristic
465C2×C71#241812yes—
466C2×C71#242412yes—
467C2×C71#247212yes—
468C2×C71#248012yes—
469C23×C22⋊C4C2×C7111yescharacteristic
470C2×#388C2×C7112yescomplemented
471C2×#380C2×C7111yescharacteristic, complemented
472C2×#379C2×C7111yescharacteristic
473C2×#379C2×C7111yescharacteristic
474C2×C4×C22⋊C4C2×C7111yescharacteristic, complemented
475#1440C2×C7112yescomplemented
476#1439C2×C7112yescomplemented
477#1437C2×C7112yescomplemented
478C22⋊#95C2×C7111yescharacteristic, complemented
479C22⋊#95C2×C7111yescharacteristic, complemented
480C71#1387311yescharacteristic, direct product factor, Sylow
481C26C22×C7111yescharacteristic
482C24×C4C22×C7111yescharacteristic
483C24×C4C22×C7111yescharacteristic
484C22×C4⋊C4C22×C7112yescomplemented
485C22×C22⋊C4—28no—
486C22×C22⋊C4C4×C7118yescomplemented
487C22×C22⋊C4C22×C7111yescharacteristic
488C22×C22⋊C4C22×C7111yescharacteristic
489C22×C22⋊C4C22×C7112yes—
490C22×C22⋊C4C22×C7112yes—
491C22×C22⋊C4C22×C7112yes—
492C22×C22⋊C4C22×C7112yes—
493C22×C22⋊C4C22×C7111yescharacteristic
494C22×C22⋊C4C22×C7111yescharacteristic
495C22×C22⋊C4C22×C7111yescharacteristic
496C22×C22⋊C4C22×C7111yescharacteristic
497C22×C22⋊C4C22×C7111yescharacteristic
498C22×C22⋊C4C22×C7111yescharacteristic
499C22×C42C22×C7112yescomplemented
500#388—28no—
501#380—24no—
502#379—24no—
503#379—24no—
504C4×C22⋊C4—24no—
505C2×#95C22×C7112yescomplemented
506C2×#95C22×C7112yescomplemented
507C2×#95C22×C7112yescomplemented
508C2×#95C22×C7112yescomplemented
509C2×#95C22×C7112yescomplemented
510C2×#95C22×C7112yescomplemented
511C25—24no—
512C25—24no—
513C25—22no—
514C25—22no—
515C25—22no—
516C25—22no—
517C25—22no—
518C25—22no—
519C25—42no—
520C25—42no—
521C25C2×C4×C7114yes—
522C25C23×C7111yescharacteristic
523C25C23×C7111yescharacteristic
524C25C23×C7111yescharacteristic
525C23×C4—22no—
526C23×C4—22no—
527C23×C4—22no—
528C23×C4—22no—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—42no—
532C23×C4—42no—
533C23×C4C2×C4×C7114yes—
534C23×C4C2×C4×C7114yes—
535C23×C4C23×C7112yes—
536C23×C4C23×C7112yes—
537C23×C4C23×C7111yescharacteristic
538C23×C4C23×C7111yescharacteristic
539C23×C4C23×C7112yes—
540C23×C4C23×C7112yes—
541C23×C4C23×C7111yescharacteristic
542C23×C4C23×C7111yescharacteristic
543C2×C4⋊C4—24no—
544C2×C4⋊C4—24no—
545C2×C4⋊C4—42no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—232no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4C2×C4×C7114yes—
573C2×C22⋊C4C2×C4×C7114yes—
574C2×C22⋊C4C2×C4×C7114yes—
575C2×C22⋊C4C2×C4×C7114yes—
576C2×C22⋊C4D4×C7114yes—
577C2×C22⋊C4D4×C7114yes—
578C2×C22⋊C4D4×C7118yes—
579C2×C42—24no—
580C2×C42—24no—
581C2×C42—42no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—42no—
587#95—42no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—216no—
593C24—216no—
594C24—28no—
595C24—28no—
596C24—28no—
597C24—22no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—22no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—28no—
616C24—28no—
617C24—44no—
618C24—44no—
619C24—48no—
620C24—48no—
621C24—48no—
622C24—48no—
623C24—48no—
624C24—48no—
625C24—48no—
626C24—48no—
627C24—48no—
628C24—48no—
629C24—44no—
630C24—44no—
631C24—44no—
632C24—44no—
633C24C22×C4×C7112yes—
634C24C22×C4×C7112yes—
635C24C22×C4×C7112yes—
636C24C2×D4×C7114yes—
637C24C2×D4×C7112yes—
638C24C2×D4×C7112yes—
639C24#41×C7114yes—
640C24#41×C7112yes—
641C24#41×C7112yes—
642C24#41×C7112yes—
643C24#41×C7112yes—
644C24C24×C7111yescharacteristic
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—28no—
652C22×C4—28no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—28no—
674C22×C4—28no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—48no—
692C22×C4—48no—
693C22×C4—48no—
694C22×C4—48no—
695C22×C4C22×C4×C7112yes—
696C22×C4C22×C4×C7112yes—
697C22×C4C22×C4×C7112yes—
698C22×C4C22×C4×C7112yes—
699C22×C4C2×D4×C7114yes—
700C22×C4C2×D4×C7114yes—
701C22×C4C2×D4×C7114yes—
702C22×C4C2×D4×C7114yes—
703C4⋊C4—48no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—48no—
710C22⋊C4—48no—
711C22⋊C4—48no—
712C22⋊C4—48no—
713C22⋊C4—44no—
714C22⋊C4—44no—
715C22⋊C4C22⋊C4×C71116yescomplemented
716C42—48no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—232no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—416no—
759C23—416no—
760C23—416no—
761C23—416no—
762C23—416no—
763C23—432no—
764C23—432no—
765C23—432no—
766C23—432no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—416no—
788C23C2×C22⋊C4×C7114yes—
789C23#117×C7114yes—
790C23#117×C7114yes—
791C23C4×D4×C7114yes—
792C23C4×D4×C7114yes—
793C23#121×C7114yes—
794C23#123×C7114yes—
795C23#124×C7114yes—
796C23#126×C7114yes—
797C23C23×C4×C7111yescharacteristic
798C23C22×D4×C7112yes—
799C23C22×D4×C7111yescharacteristic
800C23C22×D4×C7111yescharacteristic
801C23C2×#41×C7111yescharacteristic
802C23C2×#41×C7111yescharacteristic
803C23C2×#41×C7112yes—
804C23C2×#41×C7111yescharacteristic
805C23C2×#41×C7111yescharacteristic
806C23H(5,𝔽2)×C7112yes—
807C23H(5,𝔽2)×C7112yes—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—416no—
829C2×C4—416no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4C2×C22⋊C4×C7114yes—
857C2×C4C2×C22⋊C4×C7114yes—
858C22—24no—
859C22—24no—
860C22—24no—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—28no—
865C22—28no—
866C22—28no—
867C22—28no—
868C22—24no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—24no—
874C22—464no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—44no—
884C22—44no—
885C22—44no—
886C22—44no—
887C22—44no—
888C22—44no—
889C22—44no—
890C22—44no—
891C22#388×C7118yescomplemented
892C22C22×C22⋊C4×C7111yescharacteristic
893C22C2×#117×C7111yescharacteristic
894C22C2×#117×C7111yescharacteristic
895C22C2×C4×D4×C7111yescharacteristic
896C22C2×C4×D4×C7111yescharacteristic
897C22#518×C7111yescharacteristic
898C22#518×C7111yescharacteristic
899C22C2×#121×C7111yescharacteristic
900C22C2×#123×C7111yescharacteristic
901C22#525×C7112yes—
902C22#525×C7112yes—
903C22C2×#124×C7111yescharacteristic
904C22C2×#126×C7111yescharacteristic
905C22#538×C7112yes—
906C22#538×C7112yes—
907C22D42×C7112yes—
908C22D42×C7112yes—
909C22#546×C7112yes—
910C22#546×C7112yes—
911C22#546×C7112yes—
912C22#546×C7112yes—
913C22#551×C7112yes—
914C22#551×C7112yes—
915C4—24no—
916C4—24no—
917C4—42no—
918C4—42no—
919C4—44no—
920C4—44no—
921C4—82no—
922C4—82no—
923C2—28no—
924C2—44no—
925C2—44no—
926C2C71×#228011yescharacteristic
927C2C2×#388×C7111yescharacteristic
928C2C71×#231211yescharacteristic
929C2D4×C22⋊C4×C7111yescharacteristic
930C2D4×C22⋊C4×C7111yescharacteristic
931C2C71×#234211yescharacteristic
932C2C71×#234211yescharacteristic
933C2C71×#241812yes—
934C2C71×#242412yes—
935C2C71×#247212yes—
936C2C71×#248012yes—
subgroupG/H
center, socleC24×C71C24
commutatorC23C23×C4×C71
Frattini, cosocleC24C24×C71
prime radicalC26×C71C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C71 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#388×C71C2semidirect
3. C2×#380×C71C2semidirect
6. C2×C4×C22⋊C4×C71C2semidirect
7. C71×#1440C2semidirect
8. C71×#1439C2semidirect
9. C71×#1437C2semidirect
10. C71×C22⋊#95C2semidirect
11. C71×C22⋊#95C2semidirect
15. C22×C4⋊C4×C71C22semidirect
17. C22×C22⋊C4×C71C4semidirect
30. C22×C42×C71C22semidirect
36. C2×#95×C71C22semidirect
37. C2×#95×C71C22semidirect
38. C2×#95×C71C22semidirect
39. C2×#95×C71C22semidirect
40. C2×#95×C71C22semidirect
41. C2×#95×C71C22semidirect
246. C22⋊C4×C71C22⋊C4semidirect
422. C22×C71#388semidirect
454. #13873C71direct (N × H)
470. C2×#388C2×C71semidirect
471. C2×#380C2×C71semidirect
474. C2×C4×C22⋊C4C2×C71semidirect
475. #1440C2×C71semidirect
476. #1439C2×C71semidirect
477. #1437C2×C71semidirect
478. C22⋊#95C2×C71semidirect
479. C22⋊#95C2×C71semidirect
480. C71#13873direct (N × H)
484. C22×C4⋊C4C22×C71semidirect
486. C22×C22⋊C4C4×C71semidirect
499. C22×C42C22×C71semidirect
505. C2×#95C22×C71semidirect
506. C2×#95C22×C71semidirect
507. C2×#95C22×C71semidirect
508. C2×#95C22×C71semidirect
509. C2×#95C22×C71semidirect
510. C2×#95C22×C71semidirect
715. C22⋊C4C22⋊C4×C71semidirect
891. C22#388×C71semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C712
C2×#388×C712
C2×#380×C712
C2×#379×C712
C2×C4×C22⋊C4×C712
C71×#14402
C71×#14392
C71×#14372
C71×C22⋊#952
#1387371