Finite Group Databasebeta

← C71×#13996 #31834868

Subgroups — C71×#13996 #31834868

Order 18176.

2474 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C71C211yesmaximal, characteristic
2C2×#386×C71C211yesmaximal, characteristic
3C2×#386×C71C211yesmaximal, characteristic
4C2×#385×C71C211yesmaximal, characteristic, complemented
5C2×#381×C71C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C71C211yesmaximal, characteristic, complemented
7C22×#95×C71C211yesmaximal, characteristic, complemented
8C71×#1445C212yesmaximal, complemented
9C71×#1439C212yesmaximal, complemented
10C71×#1437C212yesmaximal, complemented
11C71×C4⋊#95C212yesmaximal, complemented
12C23×D4×C71C2211yescharacteristic
13C24×C4×C71C2211yescharacteristic
14C24×C4×C71C2211yescharacteristic
15C24×C4×C71C2211yescharacteristic
16C2×#123×C71—24no—
17C2×#123×C71—24no—
18C2×#123×C71C418yescomplemented
19C22×C4⋊C4×C71C2212yes—
20C22×C4⋊C4×C71C2212yes—
21C22×C22⋊C4×C71C2211yescharacteristic
22C22×C22⋊C4×C71C2211yescharacteristic
23C22×C22⋊C4×C71C2212yes—
24C22×C22⋊C4×C71C2212yes—
25C22×C22⋊C4×C71C2211yescharacteristic
26C22×C22⋊C4×C71C2211yescharacteristic
27C22×C22⋊C4×C71C2211yescharacteristic
28C22×C42×C71C2212yes—
29#386×C71—24no—
30#386×C71—24no—
31#385×C71—24no—
32#381×C71—24no—
33C4×C22⋊C4×C71—24no—
34C2×#95×C71—24no—
35C2×#95×C71C2212yes—
36C2×#95×C71C2212yes—
37C2×#95×C71C2212yes—
38C2×#95×C71C2211yescharacteristic
39C2×#95×C71C2212yes—
40C2×#95×C71C2211yescharacteristic
41C2×#95×C71C2212yes—
42C2×#95×C71C2212yes—
43C2×#95×C71C2212yes—
44C25×C71C2311yescharacteristic
45C25×C71C2311yescharacteristic
46C22×D4×C71—22no—
47C22×D4×C71—22no—
48C22×D4×C71—22no—
49C22×D4×C71—22no—
50C22×D4×C71—22no—
51C22×D4×C71—22no—
52C22×D4×C71C2×C414yes—
53C23×C4×C71—22no—
54C23×C4×C71—22no—
55C23×C4×C71—22no—
56C23×C4×C71—22no—
57C23×C4×C71—22no—
58C23×C4×C71—22no—
59C23×C4×C71—22no—
60C23×C4×C71—22no—
61C23×C4×C71—22no—
62C23×C4×C71—24no—
63C23×C4×C71—24no—
64C23×C4×C71—22no—
65C23×C4×C71—22no—
66C23×C4×C71—42no—
67C23×C4×C71—42no—
68C23×C4×C71C2×C414yes—
69C23×C4×C71D414yes—
70C23×C4×C71C2311yescharacteristic
71C23×C4×C71C2311yescharacteristic
72C23×C4×C71C2312yes—
73C23×C4×C71C2311yescharacteristic
74C23×C4×C71C2312yes—
75C23×C4×C71C2311yescharacteristic
76C23×C4×C71C2312yes—
77C23×C4×C71C2312yes—
78C23×C4×C71C2311yescharacteristic
79#123×C71—232no—
80C2×C4⋊C4×C71—24no—
81C2×C4⋊C4×C71—24no—
82C2×C4⋊C4×C71—24no—
83C2×C4⋊C4×C71—24no—
84C2×C4⋊C4×C71—42no—
85C2×C4⋊C4×C71C2×C418yescomplemented
86C2×C22⋊C4×C71—22no—
87C2×C22⋊C4×C71—22no—
88C2×C22⋊C4×C71—24no—
89C2×C22⋊C4×C71—24no—
90C2×C22⋊C4×C71—22no—
91C2×C22⋊C4×C71—22no—
92C2×C22⋊C4×C71—22no—
93C2×C22⋊C4×C71—24no—
94C2×C22⋊C4×C71—22no—
95C2×C22⋊C4×C71—22no—
96C2×C22⋊C4×C71—24no—
97C2×C22⋊C4×C71—24no—
98C2×C22⋊C4×C71—42no—
99C2×C22⋊C4×C71—42no—
100C2×C22⋊C4×C71C2×C414yes—
101C2×C22⋊C4×C71C2×C418yescomplemented
102C2×C22⋊C4×C71D414yes—
103C2×C22⋊C4×C71D414yes—
104C2×C22⋊C4×C71D414yes—
105C2×C42×C71—24no—
106C2×C42×C71—24no—
107C2×C42×C71—42no—
108#95×C71—24no—
109#95×C71—24no—
110#95×C71—24no—
111#95×C71—24no—
112#95×C71—24no—
113#95×C71—24no—
114#95×C71—24no—
115#95×C71—22no—
116#95×C71—22no—
117C24×C71—22no—
118C24×C71—22no—
119C24×C71—22no—
120C24×C71—22no—
121C24×C71—21no—
122C24×C71—21no—
123C24×C71—21no—
124C24×C71—21no—
125C24×C71—22no—
126C24×C71—22no—
127C24×C71—21no—
128C24×C71—21no—
129C24×C71—22no—
130C24×C71—22no—
131C24×C71C22×C412yes—
132C24×C71C22×C412yes—
133C24×C71C2×D412yes—
134C24×C71C2×D412yes—
135C24×C71C2×D412yes—
136C24×C71C2×D412yes—
137C24×C71#4112yes—
138C24×C71#4112yes—
139C24×C71C2411yescharacteristic
140C2×D4×C71—28no—
141C2×D4×C71—28no—
142C2×D4×C71—28no—
143C2×D4×C71—44no—
144C2×D4×C71—44no—
145C2×D4×C71—44no—
146C2×D4×C71—44no—
147C22×C4×C71—21no—
148C22×C4×C71—22no—
149C22×C4×C71—22no—
150C22×C4×C71—21no—
151C22×C4×C71—22no—
152C22×C4×C71—22no—
153C22×C4×C71—22no—
154C22×C4×C71—28no—
155C22×C4×C71—28no—
156C22×C4×C71—28no—
157C22×C4×C71—28no—
158C22×C4×C71—28no—
159C22×C4×C71—22no—
160C22×C4×C71—22no—
161C22×C4×C71—21no—
162C22×C4×C71—22no—
163C22×C4×C71—21no—
164C22×C4×C71—21no—
165C22×C4×C71—22no—
166C22×C4×C71—22no—
167C22×C4×C71—22no—
168C22×C4×C71—22no—
169C22×C4×C71—22no—
170C22×C4×C71—21no—
171C22×C4×C71—21no—
172C22×C4×C71—22no—
173C22×C4×C71—22no—
174C22×C4×C71—22no—
175C22×C4×C71—22no—
176C22×C4×C71—22no—
177C22×C4×C71—21no—
178C22×C4×C71—22no—
179C22×C4×C71—22no—
180C22×C4×C71—21no—
181C22×C4×C71—21no—
182C22×C4×C71—22no—
183C22×C4×C71—22no—
184C22×C4×C71—22no—
185C22×C4×C71—22no—
186C22×C4×C71—22no—
187C22×C4×C71—28no—
188C22×C4×C71—21no—
189C22×C4×C71—21no—
190C22×C4×C71—21no—
191C22×C4×C71—21no—
192C22×C4×C71—21no—
193C22×C4×C71—21no—
194C22×C4×C71—22no—
195C22×C4×C71—22no—
196C22×C4×C71—22no—
197C22×C4×C71—22no—
198C22×C4×C71—44no—
199C22×C4×C71—48no—
200C22×C4×C71—48no—
201C22×C4×C71—48no—
202C22×C4×C71—48no—
203C22×C4×C71—44no—
204C22×C4×C71—44no—
205C22×C4×C71—44no—
206C22×C4×C71—44no—
207C22×C4×C71—44no—
208C22×C4×C71—44no—
209C22×C4×C71C22×C414yes—
210C22×C4×C71C22×C412yes—
211C22×C4×C71C22×C414yes—
212C22×C4×C71C2×D414yes—
213C22×C4×C71C2×D412yes—
214C22×C4×C71C2×D414yes—
215C22×C4×C71C2×D414yes—
216C22×C4×C71C2×D412yes—
217C22×C4×C71#4114yes—
218C22×C4×C71#4114yes—
219C4⋊C4×C71—216no—
220C4⋊C4×C71—48no—
221C22⋊C4×C71—28no—
222C22⋊C4×C71—216no—
223C22⋊C4×C71—48no—
224C22⋊C4×C71—44no—
225C22⋊C4×C71—44no—
226C22⋊C4×C71—44no—
227C22⋊C4×C71C22⋊C4116yescomplemented
228C42×C71—48no—
229C23×C71—24no—
230C23×C71—24no—
231C23×C71—22no—
232C23×C71—22no—
233C23×C71—24no—
234C23×C71—22no—
235C23×C71—22no—
236C23×C71—24no—
237C23×C71—24no—
238C23×C71—24no—
239C23×C71—24no—
240C23×C71—24no—
241C23×C71—24no—
242C23×C71—24no—
243C23×C71—24no—
244C23×C71—24no—
245C23×C71—22no—
246C23×C71—22no—
247C23×C71—22no—
248C23×C71—24no—
249C23×C71—24no—
250C23×C71—41no—
251C23×C71—41no—
252C23×C71—41no—
253C23×C71—41no—
254C23×C71—41no—
255C23×C71—42no—
256C23×C71—41no—
257C23×C71—41no—
258C23×C71—41no—
259C23×C71—42no—
260C23×C71—42no—
261C23×C71—42no—
262C23×C71—42no—
263C23×C71—42no—
264C23×C71—42no—
265C23×C71—42no—
266C23×C71—42no—
267C23×C71—42no—
268C23×C71C2×C22⋊C414yes—
269C23×C71C4×D414yes—
270C23×C71C4×D414yes—
271C23×C71#12114yes—
272C23×C71#12114yes—
273C23×C71#12414yes—
274C23×C71#12714yes—
275C23×C71C23×C411yescharacteristic
276C23×C71C22×D411yescharacteristic
277C23×C71C22×D411yescharacteristic
278C23×C71C22×D411yescharacteristic
279C23×C71C22×D411yescharacteristic
280C23×C71C2×#4111yescharacteristic
281C23×C71C2×#4111yescharacteristic
282C23×C71C2×#4112yes—
283C23×C71C2×#4112yes—
284C23×C71H(5,𝔽2)12yes—
285C23×C712−1+412yes—
286D4×C71—416no—
287C2×C4×C71—24no—
288C2×C4×C71—24no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—24no—
292C2×C4×C71—24no—
293C2×C4×C71—24no—
294C2×C4×C71—24no—
295C2×C4×C71—24no—
296C2×C4×C71—24no—
297C2×C4×C71—24no—
298C2×C4×C71—22no—
299C2×C4×C71—24no—
300C2×C4×C71—24no—
301C2×C4×C71—22no—
302C2×C4×C71—22no—
303C2×C4×C71—24no—
304C2×C4×C71—22no—
305C2×C4×C71—22no—
306C2×C4×C71—24no—
307C2×C4×C71—22no—
308C2×C4×C71—24no—
309C2×C4×C71—24no—
310C2×C4×C71—24no—
311C2×C4×C71—24no—
312C2×C4×C71—416no—
313C2×C4×C71—416no—
314C2×C4×C71—42no—
315C2×C4×C71—42no—
316C2×C4×C71—41no—
317C2×C4×C71—41no—
318C2×C4×C71—42no—
319C2×C4×C71—41no—
320C2×C4×C71—42no—
321C2×C4×C71—42no—
322C2×C4×C71—42no—
323C2×C4×C71—41no—
324C2×C4×C71—42no—
325C2×C4×C71—42no—
326C2×C4×C71—42no—
327C2×C4×C71—42no—
328C2×C4×C71—42no—
329C2×C4×C71—42no—
330C2×C4×C71—42no—
331C2×C4×C71—42no—
332C2×C4×C71—416no—
333C2×C4×C71—41no—
334C2×C4×C71—41no—
335C2×C4×C71—41no—
336C2×C4×C71—41no—
337C2×C4×C71—41no—
338C2×C4×C71—41no—
339C2×C4×C71—42no—
340C2×C4×C71—42no—
341C2×C4×C71—42no—
342C2×C4×C71—42no—
343C2×C4×C71C2×C22⋊C418yes—
344C2×C4×C71#12314yescomplemented
345C22×C71—24no—
346C22×C71—28no—
347C22×C71—28no—
348C22×C71—24no—
349C22×C71—24no—
350C22×C71—28no—
351C22×C71—28no—
352C22×C71—24no—
353C22×C71—24no—
354C22×C71—24no—
355C22×C71—42no—
356C22×C71—44no—
357C22×C71—44no—
358C22×C71—42no—
359C22×C71—42no—
360C22×C71—81no—
361C22×C71—81no—
362C22×C71—82no—
363C22×C71—82no—
364C22×C71—81no—
365C22×C71—81no—
366C22×C71#39018yes—
367C22×C71C22×C22⋊C411yescharacteristic
368C22×C71C2×C4×D411yescharacteristic
369C22×C71C2×C4×D411yescharacteristic
370C22×C71C4×#4112yes—
371C22×C71#52012yes—
372C22×C71C2×#12111yescharacteristic
373C22×C71C2×#12111yescharacteristic
374C22×C71C2×#12311yescharacteristic
375C22×C71#52511yescharacteristic
376C22×C71C2×#12411yescharacteristic
377C22×C71#52912yes—
378C22×C71C2×#12711yescharacteristic
379C22×C71#53411yescharacteristic
380C22×C71#53611yescharacteristic
381C22×C71#53912yes—
382C22×C71#54612yes—
383C22×C71#54612yes—
384C22×C71#54612yes—
385C22×C71#54712yes—
386C22×C71#54712yes—
387C22×C71#54712yes—
388C22×C71#55112yes—
389C22×C71#55212yes—
390C4×C71—28no—
391C4×C71—24no—
392C4×C71—42no—
393C4×C71—44no—
394C4×C71—44no—
395C4×C71—44no—
396C4×C71—42no—
397C4×C71—81no—
398C4×C71—81no—
399#13996C7111yesmaximal, characteristic, direct product factor, Sylow
400C2×C71—28no—
401C2×C71—82no—
402C2×C71C2×#39011yescharacteristic
403C2×C71C4×#12311yescharacteristic
404C2×C71#232211yescharacteristic
405C2×C71#233912yes—
406C2×C71#235912yes—
407C2×C71#241211yescharacteristic
408C2×C71#241311yescharacteristic
409C2×C71#242512yes—
410C2×C71#248812yes—
411C2×C71#250111yescharacteristic
412C2×C71#253911yescharacteristic
413C22×#123C2×C7111yescharacteristic
414C2×#386C2×C7111yescharacteristic
415C2×#386C2×C7111yescharacteristic
416C2×#385C2×C7111yescharacteristic, complemented
417C2×#381C2×C7111yescharacteristic, complemented
418C2×C4×C22⋊C4C2×C7111yescharacteristic, complemented
419C22×#95C2×C7111yescharacteristic, complemented
420#1445C2×C7112yescomplemented
421#1439C2×C7112yescomplemented
422#1437C2×C7112yescomplemented
423C4⋊#95C2×C7112yescomplemented
424C71#1399611yescharacteristic, direct product factor, Sylow
425C23×D4C22×C7111yescharacteristic
426C24×C4C22×C7111yescharacteristic
427C24×C4C22×C7111yescharacteristic
428C24×C4C22×C7111yescharacteristic
429C2×#123—24no—
430C2×#123—24no—
431C2×#123C4×C7118yescomplemented
432C22×C4⋊C4C22×C7112yes—
433C22×C4⋊C4C22×C7112yes—
434C22×C22⋊C4C22×C7111yescharacteristic
435C22×C22⋊C4C22×C7111yescharacteristic
436C22×C22⋊C4C22×C7112yes—
437C22×C22⋊C4C22×C7112yes—
438C22×C22⋊C4C22×C7111yescharacteristic
439C22×C22⋊C4C22×C7111yescharacteristic
440C22×C22⋊C4C22×C7111yescharacteristic
441C22×C42C22×C7112yes—
442#386—24no—
443#386—24no—
444#385—24no—
445#381—24no—
446C4×C22⋊C4—24no—
447C2×#95—24no—
448C2×#95C22×C7111yescharacteristic
449C2×#95C22×C7112yes—
450C2×#95C22×C7112yes—
451C2×#95C22×C7112yes—
452C2×#95C22×C7112yes—
453C2×#95C22×C7112yes—
454C2×#95C22×C7112yes—
455C2×#95C22×C7112yes—
456C2×#95C22×C7111yescharacteristic
457C25C23×C7111yescharacteristic
458C25C23×C7111yescharacteristic
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4C2×C4×C7114yes—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—24no—
476C23×C4—24no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—42no—
480C23×C4—42no—
481C23×C4C2×C4×C7114yes—
482C23×C4D4×C7114yes—
483C23×C4C23×C7111yescharacteristic
484C23×C4C23×C7111yescharacteristic
485C23×C4C23×C7112yes—
486C23×C4C23×C7111yescharacteristic
487C23×C4C23×C7112yes—
488C23×C4C23×C7111yescharacteristic
489C23×C4C23×C7112yes—
490C23×C4C23×C7112yes—
491C23×C4C23×C7111yescharacteristic
492#123—232no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—42no—
498C2×C4⋊C4C2×C4×C7118yescomplemented
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4C2×C4×C7114yes—
514C2×C22⋊C4C2×C4×C7118yescomplemented
515C2×C22⋊C4D4×C7114yes—
516C2×C22⋊C4D4×C7114yes—
517C2×C22⋊C4D4×C7114yes—
518C2×C42—24no—
519C2×C42—24no—
520C2×C42—42no—
521#95—24no—
522#95—24no—
523#95—24no—
524#95—24no—
525#95—24no—
526#95—24no—
527#95—24no—
528#95—22no—
529#95—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24—21no—
541C24—21no—
542C24—22no—
543C24—22no—
544C24C22×C4×C7112yes—
545C24C22×C4×C7112yes—
546C24C2×D4×C7112yes—
547C24C2×D4×C7112yes—
548C24C2×D4×C7112yes—
549C24C2×D4×C7112yes—
550C24#41×C7112yes—
551C24#41×C7112yes—
552C24C24×C7111yescharacteristic
553C2×D4—28no—
554C2×D4—28no—
555C2×D4—28no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—44no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—28no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—44no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4C22×C4×C7114yes—
623C22×C4C22×C4×C7112yes—
624C22×C4C22×C4×C7114yes—
625C22×C4C2×D4×C7114yes—
626C22×C4C2×D4×C7112yes—
627C22×C4C2×D4×C7114yes—
628C22×C4C2×D4×C7114yes—
629C22×C4C2×D4×C7112yes—
630C22×C4#41×C7114yes—
631C22×C4#41×C7114yes—
632C4⋊C4—216no—
633C4⋊C4—48no—
634C22⋊C4—28no—
635C22⋊C4—216no—
636C22⋊C4—48no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4C22⋊C4×C71116yescomplemented
641C42—48no—
642C23—24no—
643C23—24no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—42no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23C2×C22⋊C4×C7114yes—
682C23C4×D4×C7114yes—
683C23C4×D4×C7114yes—
684C23#121×C7114yes—
685C23#121×C7114yes—
686C23#124×C7114yes—
687C23#127×C7114yes—
688C23C23×C4×C7111yescharacteristic
689C23C22×D4×C7111yescharacteristic
690C23C22×D4×C7111yescharacteristic
691C23C22×D4×C7111yescharacteristic
692C23C22×D4×C7111yescharacteristic
693C23C2×#41×C7111yescharacteristic
694C23C2×#41×C7111yescharacteristic
695C23C2×#41×C7112yes—
696C23C2×#41×C7112yes—
697C23H(5,𝔽2)×C7112yes—
698C232−1+4×C7112yes—
699D4—416no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—416no—
726C2×C4—416no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—416no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4C2×C22⋊C4×C7118yes—
757C2×C4#123×C7114yescomplemented
758C22—24no—
759C22—24no—
760C22—24no—
761C22—28no—
762C22—28no—
763C22—24no—
764C22—24no—
765C22—28no—
766C22—28no—
767C22—24no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—44no—
772C22—44no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—82no—
777C22—82no—
778C22—81no—
779C22#390×C7118yes—
780C22C22×C22⋊C4×C7111yescharacteristic
781C22C2×C4×D4×C7111yescharacteristic
782C22C2×C4×D4×C7111yescharacteristic
783C22C4×#41×C7112yes—
784C22#520×C7112yes—
785C22C2×#121×C7111yescharacteristic
786C22C2×#121×C7111yescharacteristic
787C22C2×#123×C7111yescharacteristic
788C22#525×C7111yescharacteristic
789C22C2×#124×C7111yescharacteristic
790C22#529×C7112yes—
791C22C2×#127×C7111yescharacteristic
792C22#534×C7111yescharacteristic
793C22#536×C7111yescharacteristic
794C22#539×C7112yes—
795C22#546×C7112yes—
796C22#546×C7112yes—
797C22#546×C7112yes—
798C22#547×C7112yes—
799C22#547×C7112yes—
800C22#547×C7112yes—
801C22#551×C7112yes—
802C22#552×C7112yes—
803C4—28no—
804C4—24no—
805C4—44no—
806C4—44no—
807C4—42no—
808C4—42no—
809C4—44no—
810C4—81no—
811C4—81no—
812C2—28no—
813C2—82no—
814C2C2×#390×C7111yescharacteristic
815C2C4×#123×C7111yescharacteristic
816C2C71×#232211yescharacteristic
817C2C71×#233912yes—
818C2C71×#235912yes—
819C2C71×#241211yescharacteristic
820C2C71×#241311yescharacteristic
821C2C71×#242512yes—
822C2C71×#248812yes—
823C2C71×#250111yescharacteristic
824C2C71×#253911yescharacteristic
subgroupG/H
center, socleC24×C71C24
commutatorC23C23×C4×C71
Frattini, cosocleC24C24×C71
prime radicalC23×D4×C71C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C71 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#385×C71C2semidirect
5. C2×#381×C71C2semidirect
6. C2×C4×C22⋊C4×C71C2semidirect
7. C22×#95×C71C2semidirect
8. C71×#1445C2semidirect
9. C71×#1439C2semidirect
10. C71×#1437C2semidirect
11. C71×C4⋊#95C2semidirect
18. C2×#123×C71C4semidirect
85. C2×C4⋊C4×C71C2×C4semidirect
101. C2×C22⋊C4×C71C2×C4semidirect
227. C22⋊C4×C71C22⋊C4semidirect
344. C2×C4×C71#123semidirect
399. #13996C71direct (N × H)
416. C2×#385C2×C71semidirect
417. C2×#381C2×C71semidirect
418. C2×C4×C22⋊C4C2×C71semidirect
419. C22×#95C2×C71semidirect
420. #1445C2×C71semidirect
421. #1439C2×C71semidirect
422. #1437C2×C71semidirect
423. C4⋊#95C2×C71semidirect
424. C71#13996direct (N × H)
431. C2×#123C4×C71semidirect
498. C2×C4⋊C4C2×C4×C71semidirect
514. C2×C22⋊C4C2×C4×C71semidirect
640. C22⋊C4C22⋊C4×C71semidirect
757. C2×C4#123×C71semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C712
C2×#386×C712
C2×#385×C712
C2×#381×C712
C2×C4×C22⋊C4×C712
C22×#95×C712
C71×#14452
C71×#14392
C71×#14372
C71×C4⋊#952
#1399671