Finite Group Databasebeta

← C71×#11195 #31832067

Subgroups — C71×#11195 #31832067

Order 18176.

962 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#104×C71C211yesmaximal, characteristic
2C2×#417×C71C211yesmaximal, characteristic
3C71×#2311C211yesmaximal, characteristic
4C2×#343×C71C211yesmaximal, characteristic, complemented
5C71×#1736C211yesmaximal, characteristic, complemented
6C2×#339×C71C211yesmaximal, characteristic, complemented
7C71×C4⋊#95C211yesmaximal, characteristic, complemented
8C22×#41×C71C2211yescharacteristic
9C22×M16×C71C2211yescharacteristic
10C22×M16×C71C2211yescharacteristic
11C2×#117×C71C2211yescharacteristic
12C22×C4⋊C4×C71C2211yescharacteristic
13C22×C4⋊C4×C71C2211yescharacteristic
14C22×C42×C71C2211yescharacteristic
15C2×#104×C71—22no—
16C2×#104×C71—22no—
17C2×#104×C71—22no—
18#417×C71—22no—
19#417×C71C414yescomplemented
20C2×#103×C71—21no—
21C2×#102×C71—21no—
22#391×C71—21no—
23#390×C71—21no—
24#386×C71—22no—
25#380×C71—21no—
26#380×C71—21no—
27C2×#95×C71—22no—
28#343×C71—22no—
29#340×C71—21no—
30#340×C71—21no—
31#339×C71—22no—
32C2×#41×C71—21no—
33C2×#41×C71—21no—
34C2×#41×C71—21no—
35C2×#41×C71—21no—
36C2×#41×C71—21no—
37C2×#41×C71—21no—
38C2×#41×C71—21no—
39C2×#41×C71—21no—
40C2×#41×C71—21no—
41C2×#41×C71—21no—
42C2×#41×C71C2×C412yes—
43C2×#41×C71D412yes—
44C22×Q8×C71D411yescharacteristic
45C22×D4×C71—21no—
46C22×D4×C71D411yescharacteristic
47C23×C4×C71—21no—
48C23×C4×C71—21no—
49C23×C4×C71—21no—
50C23×C4×C71D412yes—
51C23×C4×C71C2311yescharacteristic
52C2×M16×C71—21no—
53C2×M16×C71—21no—
54C2×M16×C71—21no—
55C2×M16×C71—21no—
56C2×M16×C71—21no—
57C2×M16×C71—21no—
58C2×M16×C71—21no—
59C2×M16×C71—21no—
60C2×M16×C71—21no—
61C2×M16×C71—21no—
62C2×M16×C71C2×C412yes—
63C2×M16×C71D412yes—
64C22×C8×C71—21no—
65C22×C8×C71—21no—
66#117×C71—21no—
67#117×C71—21no—
68#117×C71—21no—
69#117×C71—21no—
70C2×C4⋊C4×C71—21no—
71C2×C4⋊C4×C71—21no—
72C2×C4⋊C4×C71—21no—
73C2×C4⋊C4×C71—21no—
74C2×C4⋊C4×C71—21no—
75C2×C4⋊C4×C71—21no—
76C2×C4⋊C4×C71—21no—
77C2×C4⋊C4×C71—21no—
78C2×C4⋊C4×C71—21no—
79C2×C4⋊C4×C71—21no—
80C2×C4⋊C4×C71—21no—
81C2×C4⋊C4×C71C2×C412yes—
82C2×C4⋊C4×C71D411yescharacteristic
83C2×C4⋊C4×C71D411yescharacteristic
84C2×C22⋊C4×C71—21no—
85C2×C22⋊C4×C71—22no—
86C2×C22⋊C4×C71—22no—
87C2×C42×C71—21no—
88C2×C42×C71—21no—
89C2×C42×C71—21no—
90C2×C42×C71—21no—
91C2×C42×C71—21no—
92C2×C42×C71—21no—
93C2×C42×C71D412yes—
94#104×C71—28no—
95#103×C71—24no—
96#102×C71—24no—
97#95×C71—22no—
98#95×C71—22no—
99#95×C71—44no—
100C24×C71—21no—
101C24×C71C2×D411yescharacteristic
102#41×C71—22no—
103#41×C71—22no—
104#41×C71—22no—
105#41×C71—22no—
106#41×C71—22no—
107#41×C71—22no—
108#41×C71—22no—
109#41×C71—22no—
110#41×C71—41no—
111#41×C71—41no—
112#41×C71—41no—
113#41×C71—41no—
114#41×C71—41no—
115#41×C71—41no—
116#41×C71—41no—
117#41×C71—41no—
118C2×Q8×C71—21no—
119C2×Q8×C71—21no—
120C2×Q8×C71—21no—
121C2×Q8×C71—21no—
122C2×Q8×C71—21no—
123C2×Q8×C71C22⋊C412yes—
124C2×D4×C71—22no—
125C2×D4×C71—22no—
126C2×D4×C71—21no—
127C2×D4×C71—21no—
128C2×D4×C71—21no—
129C2×D4×C71—21no—
130C2×D4×C71—21no—
131C2×D4×C71—41no—
132C2×D4×C71—41no—
133C2×D4×C71—41no—
134C2×D4×C71—41no—
135C2×D4×C71C22⋊C412yes—
136C22×C4×C71—22no—
137C22×C4×C71—22no—
138C22×C4×C71—21no—
139C22×C4×C71—22no—
140C22×C4×C71—22no—
141C22×C4×C71—22no—
142C22×C4×C71—22no—
143C22×C4×C71—21no—
144C22×C4×C71—21no—
145C22×C4×C71—22no—
146C22×C4×C71—22no—
147C22×C4×C71—22no—
148C22×C4×C71—41no—
149C22×C4×C71—41no—
150C22×C4×C71—41no—
151C22×C4×C71—41no—
152C22×C4×C71—41no—
153C22×C4×C71—41no—
154C22×C4×C71—41no—
155C22×C4×C71—41no—
156C22×C4×C71—42no—
157C22×C4×C71—42no—
158C22×C4×C71—42no—
159C22×C4×C71—42no—
160C22×C4×C71—41no—
161C22×C4×C71—41no—
162C22×C4×C71C22×C411yescharacteristic
163C22×C4×C71C2×D411yescharacteristic
164C22×C4×C71C2×D411yescharacteristic
165C22×C4×C71C2×D411yescharacteristic
166C22×C4×C71C2×D411yescharacteristic
167C22×C4×C71C2×D411yescharacteristic
168C22×C4×C71#4111yescharacteristic
169C22×C4×C71#4111yescharacteristic
170C22×C4×C71#4111yescharacteristic
171C22×C4×C71#4111yescharacteristic
172C22×C4×C71#4111yescharacteristic
173C22×C4×C71#4111yescharacteristic
174C22×C4×C71#4111yescharacteristic
175C22×C4×C71#4111yescharacteristic
176M16×C71—22no—
177M16×C71—22no—
178M16×C71—22no—
179M16×C71—22no—
180M16×C71—41no—
181M16×C71—41no—
182M16×C71—41no—
183M16×C71—41no—
184C2×C8×C71—22no—
185C2×C8×C71—22no—
186C2×C8×C71—41no—
187C2×C8×C71—41no—
188C2×C8×C71—41no—
189C2×C8×C71—41no—
190C4⋊C4×C71—22no—
191C4⋊C4×C71—22no—
192C4⋊C4×C71—21no—
193C4⋊C4×C71—21no—
194C4⋊C4×C71—21no—
195C4⋊C4×C71—21no—
196C4⋊C4×C71—41no—
197C4⋊C4×C71—41no—
198C4⋊C4×C71—41no—
199C4⋊C4×C71—41no—
200C4⋊C4×C71—41no—
201C4⋊C4×C71—41no—
202C22⋊C4×C71—41no—
203C22⋊C4×C71—41no—
204C22⋊C4×C71—82no—
205C22⋊C4×C71—82no—
206C42×C71—22no—
207C42×C71—22no—
208C42×C71—41no—
209C42×C71—41no—
210C42×C71—41no—
211C42×C71—41no—
212C23×C71—21no—
213C23×C71—21no—
214C23×C71—21no—
215C23×C71—21no—
216C23×C71—22no—
217C23×C71—41no—
218C23×C71—41no—
219C23×C71—41no—
220C23×C71—41no—
221C23×C71—41no—
222C23×C71—41no—
223C23×C71C4×D411yescharacteristic
224C23×C71#12011yescharacteristic
225C23×C71#12111yescharacteristic
226C23×C71#12111yescharacteristic
227C23×C71#12111yescharacteristic
228C23×C71#12311yescharacteristic
229C23×C71#12411yescharacteristic
230Q8×C71—22no—
231Q8×C71—22no—
232Q8×C71—41no—
233Q8×C71—41no—
234D4×C71—22no—
235D4×C71—22no—
236D4×C71—42no—
237D4×C71—42no—
238D4×C71—42no—
239D4×C71—42no—
240D4×C71—41no—
241D4×C71—41no—
242C2×C4×C71—24no—
243C2×C4×C71—22no—
244C2×C4×C71—42no—
245C2×C4×C71—42no—
246C2×C4×C71—42no—
247C2×C4×C71—42no—
248C2×C4×C71—42no—
249C2×C4×C71—42no—
250C2×C4×C71—41no—
251C2×C4×C71—41no—
252C2×C4×C71—42no—
253C2×C4×C71—42no—
254C2×C4×C71—42no—
255C2×C4×C71—42no—
256C2×C4×C71—44no—
257C2×C4×C71—44no—
258C2×C4×C71—42no—
259C2×C4×C71—41no—
260C2×C4×C71—41no—
261C2×C4×C71—42no—
262C2×C4×C71—41no—
263C2×C4×C71—42no—
264C2×C4×C71—41no—
265C2×C4×C71—41no—
266C2×C4×C71—42no—
267C2×C4×C71—41no—
268C2×C4×C71—82no—
269C2×C4×C71—81no—
270C2×C4×C71—81no—
271C2×C4×C71—82no—
272C2×C4×C71C2×C22⋊C411yescharacteristic
273C2×C4×C71#11711yescharacteristic
274C2×C4×C71#11711yescharacteristic
275C2×C4×C71C4×D411yescharacteristic
276C2×C4×C71C4×D411yescharacteristic
277C2×C4×C71C4×D411yescharacteristic
278C2×C4×C71#12011yescharacteristic
279C2×C4×C71#12111yescharacteristic
280C2×C4×C71#12111yescharacteristic
281C2×C4×C71#12111yescharacteristic
282C2×C4×C71#12111yescharacteristic
283C2×C4×C71#12111yescharacteristic
284C2×C4×C71#12311yescharacteristic
285C2×C4×C71#12311yescharacteristic
286C2×C4×C71#12311yescharacteristic
287C2×C4×C71#12311yescharacteristic
288C2×C4×C71#12311yescharacteristic
289C2×C4×C71#12311yescharacteristic
290C2×C4×C71#12311yescharacteristic
291C2×C4×C71#12311yescharacteristic
292C2×C4×C71#12311yescharacteristic
293C2×C4×C71#12411yescharacteristic
294C2×C4×C71#12411yescharacteristic
295C2×C4×C71#12411yescharacteristic
296C2×C4×C71#12611yescharacteristic
297C2×C4×C71#12611yescharacteristic
298C2×C4×C71#12611yescharacteristic
299C2×C4×C71#12611yescharacteristic
300C8×C71—42no—
301C8×C71—42no—
302C22×C71—21no—
303C22×C71—21no—
304C22×C71—21no—
305C22×C71—21no—
306C22×C71—21no—
307C22×C71—21no—
308C22×C71—21no—
309C22×C71—21no—
310C22×C71—21no—
311C22×C71—21no—
312C22×C71—21no—
313C22×C71—21no—
314C22×C71—42no—
315C22×C71—42no—
316C22×C71—42no—
317C22×C71—81no—
318C22×C71—81no—
319C22×C71—81no—
320C22×C71—81no—
321C22×C71#38611yescharacteristic
322C22×C71#38811yescharacteristic
323C22×C71#38811yescharacteristic
324C22×C71#39411yescharacteristic
325C22×C71#39411yescharacteristic
326C22×C71#39411yescharacteristic
327C22×C71#39711yescharacteristic
328C22×C71#45311yescharacteristic
329C22×C71#45411yescharacteristic
330C22×C71#45511yescharacteristic
331C22×C71#45611yescharacteristic
332C4×C71—44no—
333C4×C71—42no—
334C4×C71—82no—
335C4×C71—82no—
336C4×C71—81no—
337C4×C71—81no—
338C4×C71#38111yescharacteristic
339C4×C71#38611yescharacteristic
340C4×C71#38811yescharacteristic
341C4×C71#38811yescharacteristic
342C4×C71#39411yescharacteristic
343C4×C71#39711yescharacteristic
344C4×C71#39711yescharacteristic
345C4×C71#39711yescharacteristic
346#11195C7111yesmaximal, characteristic, direct product factor, Sylow
347C2×C71—21no—
348C2×C71—21no—
349C2×C71—21no—
350C2×C71—21no—
351C2×C71—82no—
352C2×C71#144011yescharacteristic
353C2×C71#188211yescharacteristic
354C2×C71#188311yescharacteristic
355C2×C71#203711yescharacteristic
356C2×C71#203811yescharacteristic
357C2×C71#203911yescharacteristic
358C2×C71#204011yescharacteristic
359C22×#104C2×C7111yescharacteristic
360C2×#417C2×C7111yescharacteristic
361#2311C2×C7111yescharacteristic
362C2×#343C2×C7111yescharacteristic, complemented
363#1736C2×C7111yescharacteristic, complemented
364C2×#339C2×C7111yescharacteristic, complemented
365C4⋊#95C2×C7111yescharacteristic, complemented
366C71#1119511yescharacteristic, direct product factor, Sylow
367C22×#41C22×C7111yescharacteristic
368C22×M16C22×C7111yescharacteristic
369C22×M16C22×C7111yescharacteristic
370C2×#117C22×C7111yescharacteristic
371C22×C4⋊C4C22×C7111yescharacteristic
372C22×C4⋊C4C22×C7111yescharacteristic
373C22×C42C22×C7111yescharacteristic
374C2×#104—22no—
375C2×#104—22no—
376C2×#104—22no—
377#417—22no—
378#417C4×C7114yescomplemented
379C2×#103—21no—
380C2×#102—21no—
381#391—21no—
382#390—21no—
383#386—22no—
384#380—21no—
385#380—21no—
386C2×#95—22no—
387#343—22no—
388#340—21no—
389#340—21no—
390#339—22no—
391C2×#41—21no—
392C2×#41—21no—
393C2×#41—21no—
394C2×#41—21no—
395C2×#41—21no—
396C2×#41—21no—
397C2×#41—21no—
398C2×#41—21no—
399C2×#41—21no—
400C2×#41—21no—
401C2×#41C2×C4×C7112yes—
402C2×#41D4×C7112yes—
403C22×Q8D4×C7111yescharacteristic
404C22×D4—21no—
405C22×D4D4×C7111yescharacteristic
406C23×C4—21no—
407C23×C4—21no—
408C23×C4—21no—
409C23×C4D4×C7112yes—
410C23×C4C23×C7111yescharacteristic
411C2×M16—21no—
412C2×M16—21no—
413C2×M16—21no—
414C2×M16—21no—
415C2×M16—21no—
416C2×M16—21no—
417C2×M16—21no—
418C2×M16—21no—
419C2×M16—21no—
420C2×M16—21no—
421C2×M16C2×C4×C7112yes—
422C2×M16D4×C7112yes—
423C22×C8—21no—
424C22×C8—21no—
425#117—21no—
426#117—21no—
427#117—21no—
428#117—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4C2×C4×C7112yes—
441C2×C4⋊C4D4×C7111yescharacteristic
442C2×C4⋊C4D4×C7111yescharacteristic
443C2×C22⋊C4—21no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42D4×C7112yes—
453#104—28no—
454#103—24no—
455#102—24no—
456#95—22no—
457#95—22no—
458#95—44no—
459C24—21no—
460C24C2×D4×C7111yescharacteristic
461#41—22no—
462#41—22no—
463#41—22no—
464#41—22no—
465#41—22no—
466#41—22no—
467#41—22no—
468#41—22no—
469#41—41no—
470#41—41no—
471#41—41no—
472#41—41no—
473#41—41no—
474#41—41no—
475#41—41no—
476#41—41no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8C22⋊C4×C7112yes—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—41no—
491C2×D4—41no—
492C2×D4—41no—
493C2×D4—41no—
494C2×D4C22⋊C4×C7112yes—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4C22×C4×C7111yescharacteristic
522C22×C4C2×D4×C7111yescharacteristic
523C22×C4C2×D4×C7111yescharacteristic
524C22×C4C2×D4×C7111yescharacteristic
525C22×C4C2×D4×C7111yescharacteristic
526C22×C4C2×D4×C7111yescharacteristic
527C22×C4#41×C7111yescharacteristic
528C22×C4#41×C7111yescharacteristic
529C22×C4#41×C7111yescharacteristic
530C22×C4#41×C7111yescharacteristic
531C22×C4#41×C7111yescharacteristic
532C22×C4#41×C7111yescharacteristic
533C22×C4#41×C7111yescharacteristic
534C22×C4#41×C7111yescharacteristic
535M16—22no—
536M16—22no—
537M16—22no—
538M16—22no—
539M16—41no—
540M16—41no—
541M16—41no—
542M16—41no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8—41no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4—41no—
558C4⋊C4—41no—
559C4⋊C4—41no—
560C4⋊C4—41no—
561C22⋊C4—41no—
562C22⋊C4—41no—
563C22⋊C4—82no—
564C22⋊C4—82no—
565C42—22no—
566C42—22no—
567C42—41no—
568C42—41no—
569C42—41no—
570C42—41no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—22no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23C4×D4×C7111yescharacteristic
583C23#120×C7111yescharacteristic
584C23#121×C7111yescharacteristic
585C23#121×C7111yescharacteristic
586C23#121×C7111yescharacteristic
587C23#123×C7111yescharacteristic
588C23#124×C7111yescharacteristic
589Q8—22no—
590Q8—22no—
591Q8—41no—
592Q8—41no—
593D4—22no—
594D4—22no—
595D4—42no—
596D4—42no—
597D4—42no—
598D4—42no—
599D4—41no—
600D4—41no—
601C2×C4—24no—
602C2×C4—22no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—44no—
616C2×C4—44no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—42no—
622C2×C4—41no—
623C2×C4—42no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—42no—
627C2×C4—82no—
628C2×C4—81no—
629C2×C4—81no—
630C2×C4—82no—
631C2×C4C2×C22⋊C4×C7111yescharacteristic
632C2×C4#117×C7111yescharacteristic
633C2×C4#117×C7111yescharacteristic
634C2×C4C4×D4×C7111yescharacteristic
635C2×C4C4×D4×C7111yescharacteristic
636C2×C4C4×D4×C7111yescharacteristic
637C2×C4#120×C7111yescharacteristic
638C2×C4#121×C7111yescharacteristic
639C2×C4#121×C7111yescharacteristic
640C2×C4#121×C7111yescharacteristic
641C2×C4#121×C7111yescharacteristic
642C2×C4#121×C7111yescharacteristic
643C2×C4#123×C7111yescharacteristic
644C2×C4#123×C7111yescharacteristic
645C2×C4#123×C7111yescharacteristic
646C2×C4#123×C7111yescharacteristic
647C2×C4#123×C7111yescharacteristic
648C2×C4#123×C7111yescharacteristic
649C2×C4#123×C7111yescharacteristic
650C2×C4#123×C7111yescharacteristic
651C2×C4#123×C7111yescharacteristic
652C2×C4#124×C7111yescharacteristic
653C2×C4#124×C7111yescharacteristic
654C2×C4#124×C7111yescharacteristic
655C2×C4#126×C7111yescharacteristic
656C2×C4#126×C7111yescharacteristic
657C2×C4#126×C7111yescharacteristic
658C2×C4#126×C7111yescharacteristic
659C8—42no—
660C8—42no—
661C22—21no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—42no—
674C22—42no—
675C22—42no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22#386×C7111yescharacteristic
681C22#388×C7111yescharacteristic
682C22#388×C7111yescharacteristic
683C22#394×C7111yescharacteristic
684C22#394×C7111yescharacteristic
685C22#394×C7111yescharacteristic
686C22#397×C7111yescharacteristic
687C22#453×C7111yescharacteristic
688C22#454×C7111yescharacteristic
689C22#455×C7111yescharacteristic
690C22#456×C7111yescharacteristic
691C4—44no—
692C4—42no—
693C4—82no—
694C4—81no—
695C4—81no—
696C4—82no—
697C4#381×C7111yescharacteristic
698C4#386×C7111yescharacteristic
699C4#388×C7111yescharacteristic
700C4#388×C7111yescharacteristic
701C4#394×C7111yescharacteristic
702C4#397×C7111yescharacteristic
703C4#397×C7111yescharacteristic
704C4#397×C7111yescharacteristic
705C2—21no—
706C2—21no—
707C2—21no—
708C2—21no—
709C2—82no—
710C2C71×#144011yescharacteristic
711C2C71×#188211yescharacteristic
712C2C71×#188311yescharacteristic
713C2C71×#203711yescharacteristic
714C2C71×#203811yescharacteristic
715C2C71×#203911yescharacteristic
716C2C71×#204011yescharacteristic
subgroupG/H
center, socleC23×C71#120
commutatorC22×C4C22×C4×C71
Frattini, cosocleC23×C4C23×C71
prime radicalC22×#41×C71C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C71 ◁ C23×C4×C71 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#343×C71C2semidirect
5. C71×#1736C2semidirect
6. C2×#339×C71C2semidirect
7. C71×C4⋊#95C2semidirect
19. #417×C71C4semidirect
346. #11195C71direct (N × H)
362. C2×#343C2×C71semidirect
363. #1736C2×C71semidirect
364. C2×#339C2×C71semidirect
365. C4⋊#95C2×C71semidirect
366. C71#11195direct (N × H)
378. #417C4×C71semidirect

Maximal subgroups

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

subgroupindex
C22×#104×C712
C2×#417×C712
C71×#23112
C2×#343×C712
C71×#17362
C2×#339×C712
C71×C4⋊#952
#1119571