Finite Group Databasebeta

← C71×#23688 #31844560

Subgroups — C71×#23688 #31844560

Order 18176.

956 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#442×C71C211yesmaximal, characteristic, complemented
2C2×C4×D8×C71C211yesmaximal, characteristic, complemented
3C71×#2328C211yesmaximal, characteristic, complemented
4C71×#2319C211yesmaximal, characteristic, complemented
5C71×#2085C211yesmaximal, characteristic, complemented
6C71×#2073C211yesmaximal, characteristic, complemented
7C71×#2067C211yesmaximal, characteristic, complemented
8C71×#2065C211yesmaximal, characteristic, complemented
9C71×#2054C211yesmaximal, characteristic, complemented
10C71×#2054C211yesmaximal, characteristic, complemented
11C71×#2041C211yesmaximal, characteristic, complemented
12C71×#2011C211yesmaximal, characteristic
13C71×#1768C211yesmaximal, characteristic, complemented
14C71×#1762C211yesmaximal, characteristic, complemented
15C4×#102×C71C211yesmaximal, characteristic, complemented
16C22×D8×C71C2211yescharacteristic
17C22×D8×C71C2211yescharacteristic
18C2×#127×C71C2211yescharacteristic
19C2×C4×D4×C71C2211yescharacteristic
20C2×C4×D4×C71C2211yescharacteristic
21C2×C4×D4×C71C2211yescharacteristic
22#442×C71—24no—
23C4×D8×C71—24no—
24C2×#107×C71C2211yescharacteristic
25C2×#106×C71C2211yescharacteristic
26C2×C4⋊C8×C71C2211yescharacteristic
27C2×C4⋊C8×C71C2211yescharacteristic
28C2×#102×C71C2211yescharacteristic
29C2×#102×C71C2211yescharacteristic
30C2×#102×C71C2211yescharacteristic
31C2×#102×C71C2211yescharacteristic
32C2×#102×C71C2211yescharacteristic
33C2×#102×C71C2211yescharacteristic
34C2×#102×C71C2211yescharacteristic
35C2×#102×C71C2211yescharacteristic
36C2×#97×C71C2211yescharacteristic
37C2×C4×C8×C71C2211yescharacteristic
38#390×C71C2211yescharacteristic
39#390×C71C2211yescharacteristic
40#390×C71C2211yescharacteristic
41#390×C71C2211yescharacteristic
42#389×C71C2211yescharacteristic
43#389×C71C2211yescharacteristic
44#388×C71—21no—
45#388×C71—21no—
46#386×C71—21no—
47#386×C71—21no—
48#386×C71—21no—
49#386×C71—21no—
50#382×C71C2211yescharacteristic
51#381×C71—21no—
52#380×C71—21no—
53C4×C4⋊C4×C71C2211yescharacteristic
54#376×C71C2211yescharacteristic
55#340×C71C2211yescharacteristic
56#340×C71C2211yescharacteristic
57#340×C71C2211yescharacteristic
58#340×C71C2211yescharacteristic
59#336×C71C2211yescharacteristic
60#336×C71C2211yescharacteristic
61C22×D4×C71—21no—
62C22×D4×C71—21no—
63C22×D4×C71C2311yescharacteristic
64C22×D4×C71C2311yescharacteristic
65C22×D4×C71C2311yescharacteristic
66C23×C4×C71—21no—
67C23×C4×C71—21no—
68C23×C4×C71—21no—
69C2×D8×C71—22no—
70C2×D8×C71—22no—
71C2×D8×C71—22no—
72C2×D8×C71—22no—
73C2×D8×C71—22no—
74C2×D8×C71—22no—
75C22×C8×C71C2311yescharacteristic
76C22×C8×C71C2311yescharacteristic
77C22×C8×C71C2311yescharacteristic
78C22×C8×C71C2311yescharacteristic
79#127×C71—22no—
80#127×C71—22no—
81C4×D4×C71—22no—
82C4×D4×C71—22no—
83C4×D4×C71—22no—
84C4×D4×C71—22no—
85C4×D4×C71—22no—
86C4×D4×C71D414yescomplemented
87C2×C4⋊C4×C71—21no—
88C2×C4⋊C4×C71—21no—
89C2×C4⋊C4×C71C2311yescharacteristic
90C2×C4⋊C4×C71C2311yescharacteristic
91C2×C4⋊C4×C71C2311yescharacteristic
92C2×C4⋊C4×C71C2311yescharacteristic
93C2×C4⋊C4×C71C2311yescharacteristic
94C2×C22⋊C4×C71—21no—
95C2×C22⋊C4×C71—21no—
96C2×C22⋊C4×C71—21no—
97C2×C22⋊C4×C71—21no—
98C2×C22⋊C4×C71—21no—
99C2×C22⋊C4×C71—21no—
100C2×C22⋊C4×C71—21no—
101C2×C22⋊C4×C71—21no—
102C2×C22⋊C4×C71—21no—
103C2×C22⋊C4×C71—21no—
104C2×C22⋊C4×C71—21no—
105C2×C42×C71—21no—
106C2×C42×C71C2311yescharacteristic
107C2×C42×C71C2311yescharacteristic
108C2×C42×C71C2311yescharacteristic
109#107×C71—22no—
110#106×C71—22no—
111C4⋊C8×C71—22no—
112C4⋊C8×C71—22no—
113#102×C71—22no—
114#102×C71—22no—
115#102×C71—22no—
116#102×C71—22no—
117#102×C71—22no—
118#102×C71—22no—
119#102×C71—22no—
120#102×C71—22no—
121#97×C71—22no—
122C4×C8×C71—22no—
123#95×C71—21no—
124#95×C71—21no—
125#95×C71—21no—
126#95×C71—21no—
127#95×C71—21no—
128#95×C71D411yescharacteristic
129#95×C71D411yescharacteristic
130#95×C71D411yescharacteristic
131#95×C71D411yescharacteristic
132C24×C71—21no—
133C24×C71—21no—
134C24×C71—21no—
135C2×D4×C71—24no—
136C2×D4×C71—24no—
137C2×D4×C71—21no—
138C2×D4×C71—21no—
139C2×D4×C71—21no—
140C2×D4×C71—21no—
141C2×D4×C71—21no—
142C2×D4×C71—21no—
143C2×D4×C71—21no—
144C2×D4×C71—21no—
145C2×D4×C71—21no—
146C2×D4×C71—21no—
147C2×D4×C71—21no—
148C2×D4×C71—21no—
149C2×D4×C71—21no—
150C2×D4×C71—21no—
151C2×D4×C71—21no—
152C2×D4×C71—81no—
153C2×D4×C71—81no—
154C2×D4×C71—81no—
155C2×D4×C71—81no—
156C2×D4×C71C2×D412yes—
157C2×D4×C71#4112yes—
158C2×D4×C71#4112yes—
159C22×C4×C71—21no—
160C22×C4×C71—24no—
161C22×C4×C71—21no—
162C22×C4×C71—21no—
163C22×C4×C71—21no—
164C22×C4×C71—21no—
165C22×C4×C71—42no—
166C22×C4×C71—42no—
167C22×C4×C71—81no—
168C22×C4×C71—81no—
169C22×C4×C71—81no—
170C22×C4×C71—81no—
171C22×C4×C71—81no—
172C22×C4×C71—81no—
173C22×C4×C71C2×D411yescharacteristic
174C22×C4×C71C2×D411yescharacteristic
175C22×C4×C71C2×D411yescharacteristic
176C22×C4×C71C2×D411yescharacteristic
177C22×C4×C71C2×D411yescharacteristic
178C22×C4×C71C2×D411yescharacteristic
179C22×C4×C71C2411yescharacteristic
180D8×C71—28no—
181D8×C71—28no—
182C2×C8×C71—21no—
183C2×C8×C71—21no—
184C2×C8×C71—21no—
185C2×C8×C71—21no—
186C2×C8×C71—21no—
187C2×C8×C71—21no—
188C2×C8×C71—21no—
189C2×C8×C71—21no—
190C2×C8×C71—21no—
191C2×C8×C71—21no—
192C2×C8×C71#4112yes—
193C2×C8×C71#4112yes—
194C4⋊C4×C71—21no—
195C4⋊C4×C71—21no—
196C4⋊C4×C71—21no—
197C4⋊C4×C71—21no—
198C4⋊C4×C71—21no—
199C4⋊C4×C71—21no—
200C4⋊C4×C71—21no—
201C4⋊C4×C71—21no—
202C4⋊C4×C71—21no—
203C4⋊C4×C71—81no—
204C4⋊C4×C71—81no—
205C4⋊C4×C71C2×D412yes—
206C22⋊C4×C71—24no—
207C22⋊C4×C71—42no—
208C22⋊C4×C71—42no—
209C22⋊C4×C71—81no—
210C22⋊C4×C71—81no—
211C22⋊C4×C71—81no—
212C22⋊C4×C71—81no—
213C22⋊C4×C71—81no—
214C22⋊C4×C71—81no—
215C22⋊C4×C71—81no—
216C22⋊C4×C71—81no—
217C42×C71—21no—
218C42×C71—21no—
219C42×C71—21no—
220C42×C71—21no—
221C42×C71—81no—
222C42×C71C2×D412yes—
223C42×C71#4112yes—
224C23×C71—22no—
225C23×C71—22no—
226C23×C71—22no—
227C23×C71—41no—
228C23×C71—41no—
229C23×C71—41no—
230C23×C71—41no—
231C23×C71—41no—
232C23×C71—41no—
233C23×C71—41no—
234C23×C71—41no—
235C23×C71—41no—
236C23×C71—41no—
237C23×C71—41no—
238C23×C71—41no—
239C23×C71—41no—
240C23×C71—41no—
241C23×C71—41no—
242C23×C71—41no—
243C23×C71—41no—
244C23×C71—41no—
245C23×C71C22×D411yescharacteristic
246D4×C71—22no—
247D4×C71—22no—
248D4×C71—22no—
249D4×C71—22no—
250D4×C71—22no—
251D4×C71—22no—
252D4×C71—41no—
253D4×C71—41no—
254D4×C71—41no—
255D4×C71—41no—
256D4×C71—41no—
257D4×C71—41no—
258D4×C71—84no—
259D4×C71—84no—
260C2×C4×C71—21no—
261C2×C4×C71—21no—
262C2×C4×C71—21no—
263C2×C4×C71—21no—
264C2×C4×C71—22no—
265C2×C4×C71—21no—
266C2×C4×C71—21no—
267C2×C4×C71—21no—
268C2×C4×C71—21no—
269C2×C4×C71—21no—
270C2×C4×C71—21no—
271C2×C4×C71—21no—
272C2×C4×C71—21no—
273C2×C4×C71—21no—
274C2×C4×C71—21no—
275C2×C4×C71—21no—
276C2×C4×C71—21no—
277C2×C4×C71—41no—
278C2×C4×C71—41no—
279C2×C4×C71—41no—
280C2×C4×C71—41no—
281C2×C4×C71—41no—
282C2×C4×C71—41no—
283C2×C4×C71—41no—
284C2×C4×C71—41no—
285C2×C4×C71—41no—
286C2×C4×C71—41no—
287C2×C4×C71—41no—
288C2×C4×C71—41no—
289C2×C4×C71—41no—
290C2×C4×C71—41no—
291C2×C4×C71—84no—
292C2×C4×C71—84no—
293C2×C4×C71—84no—
294C2×C4×C71#12112yes—
295C2×C4×C71#12112yes—
296C2×C4×C71C22×D411yescharacteristic
297C2×C4×C71C2×#4111yescharacteristic
298C2×C4×C71C2×#4111yescharacteristic
299C2×C4×C71C2×#4111yescharacteristic
300C2×C4×C71C2×#4111yescharacteristic
301C2×C4×C71C2×#4111yescharacteristic
302C8×C71—22no—
303C8×C71—22no—
304C8×C71—41no—
305C8×C71—41no—
306C22×C71—42no—
307C22×C71—42no—
308C22×C71—42no—
309C22×C71—42no—
310C22×C71—42no—
311C22×C71—42no—
312C22×C71—42no—
313C22×C71—42no—
314C22×C71—42no—
315C22×C71—81no—
316C22×C71—81no—
317C22×C71—81no—
318C22×C71—81no—
319C22×C71—81no—
320C22×C71—81no—
321C22×C71—81no—
322C22×C71—81no—
323C22×C71—81no—
324C22×C71—81no—
325C22×C71—81no—
326C22×C71—81no—
327C22×C71C2×#12111yescharacteristic
328C22×C71#52511yescharacteristic
329C22×C71#53211yescharacteristic
330C22×C71#57611yescharacteristic
331C22×C71#57611yescharacteristic
332C22×C71#57611yescharacteristic
333C22×C71#57711yescharacteristic
334C4×C71—22no—
335C4×C71—22no—
336C4×C71—41no—
337C4×C71—41no—
338C4×C71—41no—
339C4×C71—41no—
340C4×C71—42no—
341C4×C71—81no—
342C4×C71—81no—
343C4×C71—81no—
344C4×C71—81no—
345C4×C71#52511yescharacteristic
346C4×C71#52511yescharacteristic
347C4×C71#52911yescharacteristic
348C4×C71#52911yescharacteristic
349#23688C7111yesmaximal, characteristic, direct product factor, Sylow
350C2×C71—82no—
351C2×C71—82no—
352C2×C71—82no—
353C2×C71#239211yescharacteristic
354C2×C71#304111yescharacteristic
355C2×C71#304511yescharacteristic
356C2×C71#311811yescharacteristic
357C2×C71#312211yescharacteristic
358C2×C71#317611yescharacteristic
359C2×C71#317911yescharacteristic
360C2×#442C2×C7111yescharacteristic, complemented
361C2×C4×D8C2×C7111yescharacteristic, complemented
362#2328C2×C7111yescharacteristic, complemented
363#2319C2×C7111yescharacteristic, complemented
364#2085C2×C7111yescharacteristic, complemented
365#2073C2×C7111yescharacteristic, complemented
366#2067C2×C7111yescharacteristic, complemented
367#2065C2×C7111yescharacteristic, complemented
368#2054C2×C7111yescharacteristic, complemented
369#2054C2×C7111yescharacteristic, complemented
370#2041C2×C7111yescharacteristic, complemented
371#2011C2×C7111yescharacteristic
372#1768C2×C7111yescharacteristic, complemented
373#1762C2×C7111yescharacteristic, complemented
374C4×#102C2×C7111yescharacteristic, complemented
375C71#2368811yescharacteristic, direct product factor, Sylow
376C22×D8C22×C7111yescharacteristic
377C22×D8C22×C7111yescharacteristic
378C2×#127C22×C7111yescharacteristic
379C2×C4×D4C22×C7111yescharacteristic
380C2×C4×D4C22×C7111yescharacteristic
381C2×C4×D4C22×C7111yescharacteristic
382#442—24no—
383C4×D8—24no—
384C2×#107C22×C7111yescharacteristic
385C2×#106C22×C7111yescharacteristic
386C2×C4⋊C8C22×C7111yescharacteristic
387C2×C4⋊C8C22×C7111yescharacteristic
388C2×#102C22×C7111yescharacteristic
389C2×#102C22×C7111yescharacteristic
390C2×#102C22×C7111yescharacteristic
391C2×#102C22×C7111yescharacteristic
392C2×#102C22×C7111yescharacteristic
393C2×#102C22×C7111yescharacteristic
394C2×#102C22×C7111yescharacteristic
395C2×#102C22×C7111yescharacteristic
396C2×#97C22×C7111yescharacteristic
397C2×C4×C8C22×C7111yescharacteristic
398#390C22×C7111yescharacteristic
399#390C22×C7111yescharacteristic
400#390C22×C7111yescharacteristic
401#390C22×C7111yescharacteristic
402#389C22×C7111yescharacteristic
403#389C22×C7111yescharacteristic
404#388—21no—
405#388—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#382C22×C7111yescharacteristic
411#381—21no—
412#380—21no—
413C4×C4⋊C4C22×C7111yescharacteristic
414#376C22×C7111yescharacteristic
415#340C22×C7111yescharacteristic
416#340C22×C7111yescharacteristic
417#340C22×C7111yescharacteristic
418#340C22×C7111yescharacteristic
419#336C22×C7111yescharacteristic
420#336C22×C7111yescharacteristic
421C22×D4—21no—
422C22×D4—21no—
423C22×D4C23×C7111yescharacteristic
424C22×D4C23×C7111yescharacteristic
425C22×D4C23×C7111yescharacteristic
426C23×C4—21no—
427C23×C4—21no—
428C23×C4—21no—
429C2×D8—22no—
430C2×D8—22no—
431C2×D8—22no—
432C2×D8—22no—
433C2×D8—22no—
434C2×D8—22no—
435C22×C8C23×C7111yescharacteristic
436C22×C8C23×C7111yescharacteristic
437C22×C8C23×C7111yescharacteristic
438C22×C8C23×C7111yescharacteristic
439#127—22no—
440#127—22no—
441C4×D4—22no—
442C4×D4—22no—
443C4×D4—22no—
444C4×D4—22no—
445C4×D4—22no—
446C4×D4D4×C7114yescomplemented
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4C23×C7111yescharacteristic
450C2×C4⋊C4C23×C7111yescharacteristic
451C2×C4⋊C4C23×C7111yescharacteristic
452C2×C4⋊C4C23×C7111yescharacteristic
453C2×C4⋊C4C23×C7111yescharacteristic
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C42—21no—
466C2×C42C23×C7111yescharacteristic
467C2×C42C23×C7111yescharacteristic
468C2×C42C23×C7111yescharacteristic
469#107—22no—
470#106—22no—
471C4⋊C8—22no—
472C4⋊C8—22no—
473#102—22no—
474#102—22no—
475#102—22no—
476#102—22no—
477#102—22no—
478#102—22no—
479#102—22no—
480#102—22no—
481#97—22no—
482C4×C8—22no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95D4×C7111yescharacteristic
489#95D4×C7111yescharacteristic
490#95D4×C7111yescharacteristic
491#95D4×C7111yescharacteristic
492C24—21no—
493C24—21no—
494C24—21no—
495C2×D4—24no—
496C2×D4—24no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—81no—
513C2×D4—81no—
514C2×D4—81no—
515C2×D4—81no—
516C2×D4C2×D4×C7112yes—
517C2×D4#41×C7112yes—
518C2×D4#41×C7112yes—
519C22×C4—21no—
520C22×C4—24no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—81no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4C2×D4×C7111yescharacteristic
534C22×C4C2×D4×C7111yescharacteristic
535C22×C4C2×D4×C7111yescharacteristic
536C22×C4C2×D4×C7111yescharacteristic
537C22×C4C2×D4×C7111yescharacteristic
538C22×C4C2×D4×C7111yescharacteristic
539C22×C4C24×C7111yescharacteristic
540D8—28no—
541D8—28no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8#41×C7112yes—
553C2×C8#41×C7112yes—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—81no—
564C4⋊C4—81no—
565C4⋊C4C2×D4×C7112yes—
566C22⋊C4—24no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—81no—
570C22⋊C4—81no—
571C22⋊C4—81no—
572C22⋊C4—81no—
573C22⋊C4—81no—
574C22⋊C4—81no—
575C22⋊C4—81no—
576C22⋊C4—81no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—81no—
582C42C2×D4×C7112yes—
583C42#41×C7112yes—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23C22×D4×C7111yescharacteristic
606D4—22no—
607D4—22no—
608D4—22no—
609D4—22no—
610D4—22no—
611D4—22no—
612D4—41no—
613D4—41no—
614D4—41no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—84no—
619D4—84no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—84no—
652C2×C4—84no—
653C2×C4—84no—
654C2×C4#121×C7112yes—
655C2×C4#121×C7112yes—
656C2×C4C22×D4×C7111yescharacteristic
657C2×C4C2×#41×C7111yescharacteristic
658C2×C4C2×#41×C7111yescharacteristic
659C2×C4C2×#41×C7111yescharacteristic
660C2×C4C2×#41×C7111yescharacteristic
661C2×C4C2×#41×C7111yescharacteristic
662C8—22no—
663C8—22no—
664C8—41no—
665C8—41no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22C2×#121×C7111yescharacteristic
688C22#525×C7111yescharacteristic
689C22#532×C7111yescharacteristic
690C22#576×C7111yescharacteristic
691C22#576×C7111yescharacteristic
692C22#576×C7111yescharacteristic
693C22#577×C7111yescharacteristic
694C4—22no—
695C4—22no—
696C4—42no—
697C4—41no—
698C4—41no—
699C4—41no—
700C4—41no—
701C4—81no—
702C4—81no—
703C4—81no—
704C4—81no—
705C4#525×C7111yescharacteristic
706C4#525×C7111yescharacteristic
707C4#529×C7111yescharacteristic
708C4#529×C7111yescharacteristic
709C2—82no—
710C2—82no—
711C2—82no—
712C2C71×#239211yescharacteristic
713C2C71×#304111yescharacteristic
714C2C71×#304511yescharacteristic
715C2C71×#311811yescharacteristic
716C2C71×#312211yescharacteristic
717C2C71×#317611yescharacteristic
718C2C71×#317911yescharacteristic
subgroupG/H
center, socleC23×C71C22×D4
commutator, Frattini, cosocleC22×C4C24×C71
prime radicalC71×#2011C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C71 ◁ #376×C71 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#442×C71C2semidirect
2. C2×C4×D8×C71C2semidirect
3. C71×#2328C2semidirect
4. C71×#2319C2semidirect
5. C71×#2085C2semidirect
6. C71×#2073C2semidirect
7. C71×#2067C2semidirect
8. C71×#2065C2semidirect
9. C71×#2054C2semidirect
10. C71×#2054C2semidirect
11. C71×#2041C2semidirect
13. C71×#1768C2semidirect
14. C71×#1762C2semidirect
15. C4×#102×C71C2semidirect
86. C4×D4×C71D4semidirect
349. #23688C71direct (N × H)
360. C2×#442C2×C71semidirect
361. C2×C4×D8C2×C71semidirect
362. #2328C2×C71semidirect
363. #2319C2×C71semidirect
364. #2085C2×C71semidirect
365. #2073C2×C71semidirect
366. #2067C2×C71semidirect
367. #2065C2×C71semidirect
368. #2054C2×C71semidirect
369. #2054C2×C71semidirect
370. #2041C2×C71semidirect
372. #1768C2×C71semidirect
373. #1762C2×C71semidirect
374. C4×#102C2×C71semidirect
375. C71#23688direct (N × H)
446. C4×D4D4×C71semidirect

Maximal subgroups

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

subgroupindex
C2×#442×C712
C2×C4×D8×C712
C71×#23282
C71×#23192
C71×#20852
C71×#20732
C71×#20672
C71×#20652
C71×#20542
C71×#20412
C71×#20112
C71×#17682
C71×#17622
C4×#102×C712
#2368871