Finite Group Databasebeta

← C71×#18434 #31839306

Subgroups — C71×#18434 #31839306

Order 18176.

982 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C71×#3560C211yesmaximal, characteristic, complemented
2C71×#3213C211yesmaximal, characteristic, complemented
3C71×#3211C211yesmaximal, characteristic, complemented
4C71×#2662C211yesmaximal, characteristic, complemented
5C71×#1606C211yesmaximal, characteristic, complemented
6C71×#1604C211yesmaximal, characteristic, complemented
7C71×#1603C211yesmaximal, characteristic, complemented
8C71×#1601C211yesmaximal, characteristic, complemented
9C71×#1600C211yesmaximal, characteristic, complemented
10C71×#1598C211yesmaximal, characteristic, complemented
11C71×#1597C211yesmaximal, characteristic, complemented
12C71×#1595C211yesmaximal, characteristic, complemented
13C71×#1509C211yesmaximal, characteristic, complemented
14C71×#1502C211yesmaximal, characteristic, complemented
15C71×#1473C211yesmaximal, characteristic, complemented
16#563×C71—21no—
17#560×C71—21no—
18#553×C71—21no—
19#553×C71—21no—
20#551×C71—21no—
21#547×C71—21no—
22#546×C71—21no—
23#546×C71—21no—
24#542×C71—21no—
25#539×C71—21no—
26#539×C71C2211yescharacteristic
27#538×C71—21no—
28#538×C71—21no—
29#538×C71C2211yescharacteristic
30#537×C71C2211yescharacteristic
31#534×C71C2211yescharacteristic
32#532×C71C2211yescharacteristic
33#529×C71C2211yescharacteristic
34C2×#126×C71C2211yescharacteristic
35C2×#124×C71C2211yescharacteristic, complemented
36#496×C71—21no—
37#495×C71—21no—
38#489×C71—21no—
39#488×C71—21no—
40#464×C71—21no—
41#463×C71—21no—
42#463×C71—21no—
43#463×C71—21no—
44#451×C71C2211yescharacteristic, complemented
45#450×C71C2211yescharacteristic, complemented
46#448×C71C2211yescharacteristic
47#448×C71C2211yescharacteristic
48#448×C71C2211yescharacteristic, complemented
49#447×C71C2211yescharacteristic
50#447×C71C2211yescharacteristic
51#447×C71C2211yescharacteristic, complemented
52#432×C71C2211yescharacteristic, complemented
53#431×C71C2211yescharacteristic, complemented
54#396×C71—21no—
55#395×C71C2211yescharacteristic, complemented
56#394×C71—21no—
57#394×C71C2211yescharacteristic, complemented
58#393×C71C2211yescharacteristic
59#392×C71C2211yescharacteristic
60#390×C71—21no—
61#388×C71—21no—
62C4×C4⋊C4×C71C2211yescharacteristic, complemented
63#328×C71C2211yescharacteristic, complemented
64#328×C71C2211yescharacteristic, complemented
65#327×C71C2211yescharacteristic
66#327×C71C2211yescharacteristic
67#327×C71C2211yescharacteristic
68#327×C71C2211yescharacteristic
69#327×C71C2211yescharacteristic, complemented
70#327×C71C2211yescharacteristic, complemented
71#324×C71C2211yescharacteristic, complemented
72#324×C71C2211yescharacteristic, complemented
73#323×C71C2211yescharacteristic
74#323×C71C2211yescharacteristic
75C2×#41×C71—21no—
76C2×#41×C71—21no—
77C22×Q8×C71C2311yescharacteristic
78C22×D4×C71—21no—
79C22×D4×C71—21no—
80C22×D4×C71C2311yescharacteristic
81C2×Q16×C71—21no—
82C2×SD16×C71—21no—
83C2×SD16×C71—21no—
84C2×SD16×C71—21no—
85C2×SD16×C71—21no—
86C2×D8×C71—21no—
87C2×D8×C71—21no—
88C2×D8×C71—21no—
89C4⋊Q8×C71—21no—
90C4⋊Q8×C71D411yescharacteristic, complemented
91#127×C71D411yescharacteristic, complemented
92#126×C71—21no—
93#126×C71—21no—
94#126×C71—21no—
95#126×C71—21no—
96#126×C71—21no—
97#126×C71—21no—
98#126×C71—21no—
99#126×C71—21no—
100#126×C71—21no—
101#125×C71—21no—
102#125×C71—21no—
103#125×C71D411yescharacteristic, complemented
104#124×C71—21no—
105#124×C71—21no—
106#124×C71—21no—
107#124×C71—21no—
108#124×C71—21no—
109#124×C71—21no—
110#124×C71—21no—
111#124×C71—21no—
112#124×C71D411yescharacteristic, complemented
113#123×C71—21no—
114#123×C71—21no—
115#123×C71—21no—
116#123×C71—21no—
117#123×C71—21no—
118#123×C71—21no—
119#123×C71—21no—
120#123×C71—21no—
121#123×C71—21no—
122#123×C71—21no—
123#123×C71—21no—
124#123×C71—21no—
125C22⋊Q8×C71—21no—
126C22⋊Q8×C71—21no—
127C22⋊Q8×C71—21no—
128C22⋊Q8×C71—21no—
129C22⋊Q8×C71—21no—
130C22⋊Q8×C71—21no—
131C22⋊Q8×C71—21no—
132C22⋊Q8×C71C2311yescharacteristic
133#121×C71—21no—
134#121×C71—21no—
135#121×C71—21no—
136#121×C71—21no—
137#121×C71—21no—
138#121×C71—21no—
139#121×C71—21no—
140#121×C71—21no—
141#121×C71—21no—
142#121×C71—21no—
143#121×C71—21no—
144#121×C71—21no—
145#121×C71C2311yescharacteristic
146#121×C71C2311yescharacteristic
147#121×C71C2311yescharacteristic
148#120×C71—21no—
149#120×C71—21no—
150#120×C71—21no—
151#120×C71—21no—
152#120×C71—21no—
153C4×Q8×C71D411yescharacteristic, complemented
154C4×D4×C71—21no—
155C4×D4×C71—21no—
156C4×D4×C71—21no—
157C4×D4×C71—21no—
158C4×D4×C71—21no—
159C4×D4×C71—21no—
160C4×D4×C71—21no—
161C4×D4×C71—21no—
162C4×D4×C71D411yescharacteristic, complemented
163C4×D4×C71D411yescharacteristic, complemented
164C4×D4×C71D411yescharacteristic, complemented
165#117×C71—21no—
166#117×C71—21no—
167C2×C4⋊C4×C71—21no—
168C2×C4⋊C4×C71—21no—
169C2×C4⋊C4×C71—21no—
170C2×C4⋊C4×C71D411yescharacteristic
171C2×C4⋊C4×C71D411yescharacteristic
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C22⋊C4×C71—21no—
174C2×C22⋊C4×C71—21no—
175C2×C22⋊C4×C71—21no—
176C2×C22⋊C4×C71—21no—
177C2×C22⋊C4×C71—21no—
178C2×C22⋊C4×C71—21no—
179C2×C22⋊C4×C71—21no—
180C2×C22⋊C4×C71—21no—
181C2×C22⋊C4×C71D411yescharacteristic
182C2×C22⋊C4×C71D411yescharacteristic
183C2×C22⋊C4×C71C2311yescharacteristic
184C2×C42×C71—21no—
185C2×C42×C71C2311yescharacteristic
186C4⋊C8×C71—21no—
187C4⋊C8×C71—21no—
188#103×C71—21no—
189#103×C71—21no—
190#103×C71—21no—
191#103×C71—21no—
192#102×C71—21no—
193#102×C71—21no—
194#102×C71—21no—
195#102×C71—21no—
196C22⋊C8×C71C2311yescharacteristic
197C22⋊C8×C71C2311yescharacteristic
198C22⋊C8×C71C2311yescharacteristic
199C22⋊C8×C71C2311yescharacteristic
200#97×C71—21no—
201C4×C8×C71—21no—
202#95×C71—21no—
203#95×C71—21no—
204#95×C71C2311yescharacteristic
205#95×C71C2311yescharacteristic
206C24×C71—21no—
207C24×C71—21no—
208C24×C71C2×D411yescharacteristic
209#41×C71—81no—
210#41×C71—81no—
211#41×C71—81no—
212#41×C71—81no—
213C2×Q8×C71—21no—
214C2×Q8×C71—21no—
215C2×Q8×C71—21no—
216C2×Q8×C71—21no—
217C2×Q8×C71—81no—
218C2×Q8×C71C2×D411yescharacteristic
219C2×D4×C71—21no—
220C2×D4×C71—21no—
221C2×D4×C71—21no—
222C2×D4×C71—21no—
223C2×D4×C71—21no—
224C2×D4×C71—21no—
225C2×D4×C71—21no—
226C2×D4×C71—21no—
227C2×D4×C71—21no—
228C2×D4×C71—21no—
229C2×D4×C71—21no—
230C2×D4×C71—21no—
231C2×D4×C71—21no—
232C2×D4×C71—21no—
233C2×D4×C71—42no—
234C2×D4×C71—81no—
235C2×D4×C71—81no—
236C2×D4×C71—81no—
237C2×D4×C71—81no—
238C2×D4×C71—81no—
239C2×D4×C71C2×D411yescharacteristic
240C2×D4×C71C2×D411yescharacteristic
241C2×D4×C71C2×D411yescharacteristic
242C22×C4×C71—21no—
243C22×C4×C71—21no—
244C22×C4×C71—21no—
245C22×C4×C71—21no—
246C22×C4×C71—21no—
247C22×C4×C71—21no—
248C22×C4×C71—21no—
249C22×C4×C71—21no—
250C22×C4×C71—21no—
251C22×C4×C71—21no—
252C22×C4×C71—21no—
253C22×C4×C71C2×D411yescharacteristic
254C22×C4×C71C2×D411yescharacteristic
255C22×C4×C71C2×D411yescharacteristic
256C22×C4×C71C2×D411yescharacteristic
257C22×C4×C71C2×D411yescharacteristic
258C22×C4×C71C2411yescharacteristic
259Q16×C71—81no—
260SD16×C71—81no—
261SD16×C71—81no—
262SD16×C71—81no—
263SD16×C71—81no—
264D8×C71—81no—
265D8×C71—81no—
266D8×C71—81no—
267C2×C8×C71—21no—
268C2×C8×C71—21no—
269C2×C8×C71—21no—
270C2×C8×C71—21no—
271C4⋊C4×C71—21no—
272C4⋊C4×C71—21no—
273C4⋊C4×C71—21no—
274C4⋊C4×C71—21no—
275C4⋊C4×C71—21no—
276C4⋊C4×C71—21no—
277C4⋊C4×C71—21no—
278C4⋊C4×C71—21no—
279C4⋊C4×C71—21no—
280C4⋊C4×C71—21no—
281C4⋊C4×C71—21no—
282C4⋊C4×C71—21no—
283C4⋊C4×C71—21no—
284C4⋊C4×C71—21no—
285C4⋊C4×C71—21no—
286C4⋊C4×C71—21no—
287C4⋊C4×C71—21no—
288C4⋊C4×C71—42no—
289C4⋊C4×C71—81no—
290C4⋊C4×C71C2×D411yescharacteristic
291C4⋊C4×C71C2×D411yescharacteristic
292C4⋊C4×C71C2×D411yescharacteristic
293C4⋊C4×C71C2×D411yescharacteristic
294C22⋊C4×C71—21no—
295C22⋊C4×C71—21no—
296C22⋊C4×C71—21no—
297C22⋊C4×C71—21no—
298C22⋊C4×C71—21no—
299C22⋊C4×C71—21no—
300C22⋊C4×C71—21no—
301C22⋊C4×C71—21no—
302C22⋊C4×C71—21no—
303C22⋊C4×C71—21no—
304C22⋊C4×C71—21no—
305C22⋊C4×C71—21no—
306C22⋊C4×C71—21no—
307C22⋊C4×C71—21no—
308C22⋊C4×C71—21no—
309C22⋊C4×C71—21no—
310C22⋊C4×C71—21no—
311C22⋊C4×C71—21no—
312C22⋊C4×C71—21no—
313C22⋊C4×C71—21no—
314C22⋊C4×C71—21no—
315C22⋊C4×C71—21no—
316C22⋊C4×C71—21no—
317C22⋊C4×C71—21no—
318C22⋊C4×C71—21no—
319C22⋊C4×C71—42no—
320C22⋊C4×C71—41no—
321C22⋊C4×C71—41no—
322C22⋊C4×C71—41no—
323C22⋊C4×C71—41no—
324C22⋊C4×C71—81no—
325C22⋊C4×C71—81no—
326C22⋊C4×C71—81no—
327C42×C71—21no—
328C42×C71—21no—
329C42×C71—21no—
330C42×C71—81no—
331C42×C71C2×D411yescharacteristic
332C42×C71C2×D411yescharacteristic
333C42×C71C2×D411yescharacteristic
334C42×C71C2×D411yescharacteristic
335C23×C71—21no—
336C23×C71—21no—
337C23×C71—21no—
338C23×C71—21no—
339C23×C71—21no—
340C23×C71—21no—
341C23×C71—41no—
342C23×C71—41no—
343C23×C71—41no—
344C23×C71—41no—
345C23×C71—41no—
346C23×C71—41no—
347C23×C71—41no—
348C23×C71—41no—
349C23×C71—41no—
350C23×C71—81no—
351C23×C71—81no—
352C23×C71—81no—
353C23×C71C22×D411yescharacteristic
354Q8×C71—41no—
355Q8×C71—41no—
356Q8×C71—41no—
357Q8×C71—41no—
358Q8×C71—41no—
359Q8×C71—81no—
360Q8×C71—81no—
361D4×C71—41no—
362D4×C71—41no—
363D4×C71—41no—
364D4×C71—41no—
365D4×C71—41no—
366D4×C71—41no—
367D4×C71—41no—
368D4×C71—41no—
369D4×C71—41no—
370D4×C71—41no—
371D4×C71—41no—
372D4×C71—41no—
373D4×C71—41no—
374D4×C71—81no—
375D4×C71—81no—
376D4×C71—81no—
377D4×C71—81no—
378D4×C71—81no—
379D4×C71—81no—
380D4×C71—81no—
381D4×C71—81no—
382D4×C71—81no—
383D4×C71—84no—
384C2×C4×C71—21no—
385C2×C4×C71—21no—
386C2×C4×C71—22no—
387C2×C4×C71—21no—
388C2×C4×C71—21no—
389C2×C4×C71—21no—
390C2×C4×C71—21no—
391C2×C4×C71—21no—
392C2×C4×C71—21no—
393C2×C4×C71—21no—
394C2×C4×C71—21no—
395C2×C4×C71—21no—
396C2×C4×C71—21no—
397C2×C4×C71—41no—
398C2×C4×C71—41no—
399C2×C4×C71—41no—
400C2×C4×C71—41no—
401C2×C4×C71—41no—
402C2×C4×C71—41no—
403C2×C4×C71—41no—
404C2×C4×C71—41no—
405C2×C4×C71—41no—
406C2×C4×C71—41no—
407C2×C4×C71—41no—
408C2×C4×C71—41no—
409C2×C4×C71—81no—
410C2×C4×C71—81no—
411C2×C4×C71—81no—
412C2×C4×C71—81no—
413C2×C4×C71—81no—
414C2×C4×C71—81no—
415C2×C4×C71—81no—
416C2×C4×C71—81no—
417C2×C4×C71#12011yescharacteristic
418C2×C4×C71#12011yescharacteristic
419C2×C4×C71#12011yescharacteristic
420C2×C4×C71#12011yescharacteristic
421C2×C4×C71C22×D411yescharacteristic
422C2×C4×C71C22×D411yescharacteristic
423C8×C71—41no—
424C8×C71—41no—
425C8×C71—41no—
426C8×C71—41no—
427C22×C71—21no—
428C22×C71—21no—
429C22×C71—41no—
430C22×C71—41no—
431C22×C71—41no—
432C22×C71—41no—
433C22×C71—41no—
434C22×C71—41no—
435C22×C71—41no—
436C22×C71—41no—
437C22×C71—41no—
438C22×C71—41no—
439C22×C71—41no—
440C22×C71—41no—
441C22×C71—81no—
442C22×C71—81no—
443C22×C71—81no—
444C22×C71—81no—
445C22×C71—81no—
446C22×C71—81no—
447C22×C71—81no—
448C22×C71—81no—
449C22×C71—81no—
450C22×C71—162no—
451C22×C71C2×#12011yescharacteristic
452C22×C71#57611yescharacteristic
453C22×C71#57711yescharacteristic
454C4×C71—21no—
455C4×C71—21no—
456C4×C71—21no—
457C4×C71—21no—
458C4×C71—21no—
459C4×C71—21no—
460C4×C71—42no—
461C4×C71—41no—
462C4×C71—41no—
463C4×C71—41no—
464C4×C71—41no—
465C4×C71—41no—
466C4×C71—41no—
467C4×C71—41no—
468C4×C71—41no—
469C4×C71—81no—
470C4×C71—81no—
471#18434C7111yesmaximal, characteristic, direct product factor, Sylow
472C2×C71—21no—
473C2×C71—21no—
474C2×C71—81no—
475C2×C71—81no—
476C2×C71—81no—
477C2×C71—81no—
478C2×C71—161no—
479C2×C71#301211yescharacteristic
480C2×C71#301811yescharacteristic
481C2×C71#302711yescharacteristic
482#3560C2×C7111yescharacteristic, complemented
483#3213C2×C7111yescharacteristic, complemented
484#3211C2×C7111yescharacteristic, complemented
485#2662C2×C7111yescharacteristic, complemented
486#1606C2×C7111yescharacteristic, complemented
487#1604C2×C7111yescharacteristic, complemented
488#1603C2×C7111yescharacteristic, complemented
489#1601C2×C7111yescharacteristic, complemented
490#1600C2×C7111yescharacteristic, complemented
491#1598C2×C7111yescharacteristic, complemented
492#1597C2×C7111yescharacteristic, complemented
493#1595C2×C7111yescharacteristic, complemented
494#1509C2×C7111yescharacteristic, complemented
495#1502C2×C7111yescharacteristic, complemented
496#1473C2×C7111yescharacteristic, complemented
497C71#1843411yescharacteristic, direct product factor, Sylow
498#563—21no—
499#560—21no—
500#553—21no—
501#553—21no—
502#551—21no—
503#547—21no—
504#546—21no—
505#546—21no—
506#542—21no—
507#539—21no—
508#539C22×C7111yescharacteristic
509#538—21no—
510#538—21no—
511#538C22×C7111yescharacteristic
512#537C22×C7111yescharacteristic
513#534C22×C7111yescharacteristic
514#532C22×C7111yescharacteristic
515#529C22×C7111yescharacteristic
516C2×#126C22×C7111yescharacteristic
517C2×#124C22×C7111yescharacteristic, complemented
518#496—21no—
519#495—21no—
520#489—21no—
521#488—21no—
522#464—21no—
523#463—21no—
524#463—21no—
525#463—21no—
526#451C22×C7111yescharacteristic, complemented
527#450C22×C7111yescharacteristic, complemented
528#448C22×C7111yescharacteristic
529#448C22×C7111yescharacteristic
530#448C22×C7111yescharacteristic, complemented
531#447C22×C7111yescharacteristic
532#447C22×C7111yescharacteristic
533#447C22×C7111yescharacteristic, complemented
534#432C22×C7111yescharacteristic, complemented
535#431C22×C7111yescharacteristic, complemented
536#396—21no—
537#395C22×C7111yescharacteristic, complemented
538#394—21no—
539#394C22×C7111yescharacteristic, complemented
540#393C22×C7111yescharacteristic
541#392C22×C7111yescharacteristic
542#390—21no—
543#388—21no—
544C4×C4⋊C4C22×C7111yescharacteristic, complemented
545#328C22×C7111yescharacteristic, complemented
546#328C22×C7111yescharacteristic, complemented
547#327C22×C7111yescharacteristic
548#327C22×C7111yescharacteristic
549#327C22×C7111yescharacteristic
550#327C22×C7111yescharacteristic
551#327C22×C7111yescharacteristic, complemented
552#327C22×C7111yescharacteristic, complemented
553#324C22×C7111yescharacteristic, complemented
554#324C22×C7111yescharacteristic, complemented
555#323C22×C7111yescharacteristic
556#323C22×C7111yescharacteristic
557C2×#41—21no—
558C2×#41—21no—
559C22×Q8C23×C7111yescharacteristic
560C22×D4—21no—
561C22×D4—21no—
562C22×D4C23×C7111yescharacteristic
563C2×Q16—21no—
564C2×SD16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×D8—21no—
569C2×D8—21no—
570C2×D8—21no—
571C4⋊Q8—21no—
572C4⋊Q8D4×C7111yescharacteristic, complemented
573#127D4×C7111yescharacteristic, complemented
574#126—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#126—21no—
581#126—21no—
582#126—21no—
583#125—21no—
584#125—21no—
585#125D4×C7111yescharacteristic, complemented
586#124—21no—
587#124—21no—
588#124—21no—
589#124—21no—
590#124—21no—
591#124—21no—
592#124—21no—
593#124—21no—
594#124D4×C7111yescharacteristic, complemented
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—21no—
603#123—21no—
604#123—21no—
605#123—21no—
606#123—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8—21no—
614C22⋊Q8C23×C7111yescharacteristic
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121C23×C7111yescharacteristic
628#121C23×C7111yescharacteristic
629#121C23×C7111yescharacteristic
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635C4×Q8D4×C7111yescharacteristic, complemented
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4D4×C7111yescharacteristic, complemented
645C4×D4D4×C7111yescharacteristic, complemented
646C4×D4D4×C7111yescharacteristic, complemented
647#117—21no—
648#117—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C7111yescharacteristic
653C2×C4⋊C4D4×C7111yescharacteristic
654C2×C4⋊C4C23×C7111yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C7111yescharacteristic
664C2×C22⋊C4D4×C7111yescharacteristic
665C2×C22⋊C4C23×C7111yescharacteristic
666C2×C42—21no—
667C2×C42C23×C7111yescharacteristic
668C4⋊C8—21no—
669C4⋊C8—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#102—21no—
675#102—21no—
676#102—21no—
677#102—21no—
678C22⋊C8C23×C7111yescharacteristic
679C22⋊C8C23×C7111yescharacteristic
680C22⋊C8C23×C7111yescharacteristic
681C22⋊C8C23×C7111yescharacteristic
682#97—21no—
683C4×C8—21no—
684#95—21no—
685#95—21no—
686#95C23×C7111yescharacteristic
687#95C23×C7111yescharacteristic
688C24—21no—
689C24—21no—
690C24C2×D4×C7111yescharacteristic
691#41—81no—
692#41—81no—
693#41—81no—
694#41—81no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—81no—
700C2×Q8C2×D4×C7111yescharacteristic
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—42no—
716C2×D4—81no—
717C2×D4—81no—
718C2×D4—81no—
719C2×D4—81no—
720C2×D4—81no—
721C2×D4C2×D4×C7111yescharacteristic
722C2×D4C2×D4×C7111yescharacteristic
723C2×D4C2×D4×C7111yescharacteristic
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4C2×D4×C7111yescharacteristic
736C22×C4C2×D4×C7111yescharacteristic
737C22×C4C2×D4×C7111yescharacteristic
738C22×C4C2×D4×C7111yescharacteristic
739C22×C4C2×D4×C7111yescharacteristic
740C22×C4C24×C7111yescharacteristic
741Q16—81no—
742SD16—81no—
743SD16—81no—
744SD16—81no—
745SD16—81no—
746D8—81no—
747D8—81no—
748D8—81no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—42no—
771C4⋊C4—81no—
772C4⋊C4C2×D4×C7111yescharacteristic
773C4⋊C4C2×D4×C7111yescharacteristic
774C4⋊C4C2×D4×C7111yescharacteristic
775C4⋊C4C2×D4×C7111yescharacteristic
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—81no—
807C22⋊C4—81no—
808C22⋊C4—81no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—81no—
813C42C2×D4×C7111yescharacteristic
814C42C2×D4×C7111yescharacteristic
815C42C2×D4×C7111yescharacteristic
816C42C2×D4×C7111yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23C22×D4×C7111yescharacteristic
836Q8—41no—
837Q8—41no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—81no—
842Q8—81no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—84no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4#120×C7111yescharacteristic
900C2×C4#120×C7111yescharacteristic
901C2×C4#120×C7111yescharacteristic
902C2×C4#120×C7111yescharacteristic
903C2×C4C22×D4×C7111yescharacteristic
904C2×C4C22×D4×C7111yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C22—21no—
910C22—21no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—162no—
933C22C2×#120×C7111yescharacteristic
934C22#576×C7111yescharacteristic
935C22#577×C7111yescharacteristic
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C2—21no—
954C2—21no—
955C2—81no—
956C2—81no—
957C2—81no—
958C2—81no—
959C2—161no—
960C2C71×#301211yescharacteristic
961C2C71×#301811yescharacteristic
962C2C71×#302711yescharacteristic
subgroupG/H
center, socleC22×C71C2×#120
commutator, Frattini, cosocleC22×C4C24×C71
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C71 ◁ C2×C42×C71 ◁ G

Complements

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

NH ≅ G/Ntype
1. C71×#3560C2semidirect
2. C71×#3213C2semidirect
3. C71×#3211C2semidirect
4. C71×#2662C2semidirect
5. C71×#1606C2semidirect
6. C71×#1604C2semidirect
7. C71×#1603C2semidirect
8. C71×#1601C2semidirect
9. C71×#1600C2semidirect
10. C71×#1598C2semidirect
11. C71×#1597C2semidirect
12. C71×#1595C2semidirect
13. C71×#1509C2semidirect
14. C71×#1502C2semidirect
15. C71×#1473C2semidirect
35. C2×#124×C71C22semidirect
44. #451×C71C22semidirect
45. #450×C71C22semidirect
48. #448×C71C22semidirect
51. #447×C71C22semidirect
52. #432×C71C22semidirect
53. #431×C71C22semidirect
55. #395×C71C22semidirect
57. #394×C71C22semidirect
62. C4×C4⋊C4×C71C22semidirect
63. #328×C71C22semidirect
64. #328×C71C22semidirect
69. #327×C71C22semidirect
70. #327×C71C22semidirect
71. #324×C71C22semidirect
72. #324×C71C22semidirect
90. C4⋊Q8×C71D4semidirect
91. #127×C71D4semidirect
103. #125×C71D4semidirect
112. #124×C71D4semidirect
153. C4×Q8×C71D4semidirect
162. C4×D4×C71D4semidirect
163. C4×D4×C71D4semidirect
164. C4×D4×C71D4semidirect
471. #18434C71direct (N × H)
482. #3560C2×C71semidirect
483. #3213C2×C71semidirect
484. #3211C2×C71semidirect
485. #2662C2×C71semidirect
486. #1606C2×C71semidirect
487. #1604C2×C71semidirect
488. #1603C2×C71semidirect
489. #1601C2×C71semidirect
490. #1600C2×C71semidirect
491. #1598C2×C71semidirect
492. #1597C2×C71semidirect
493. #1595C2×C71semidirect
494. #1509C2×C71semidirect
495. #1502C2×C71semidirect
496. #1473C2×C71semidirect
497. C71#18434direct (N × H)
517. C2×#124C22×C71semidirect
526. #451C22×C71semidirect
527. #450C22×C71semidirect
530. #448C22×C71semidirect
533. #447C22×C71semidirect
534. #432C22×C71semidirect
535. #431C22×C71semidirect
537. #395C22×C71semidirect
539. #394C22×C71semidirect
544. C4×C4⋊C4C22×C71semidirect
545. #328C22×C71semidirect
546. #328C22×C71semidirect
551. #327C22×C71semidirect
552. #327C22×C71semidirect
553. #324C22×C71semidirect
554. #324C22×C71semidirect
572. C4⋊Q8D4×C71semidirect
573. #127D4×C71semidirect
585. #125D4×C71semidirect
594. #124D4×C71semidirect
635. C4×Q8D4×C71semidirect
644. C4×D4D4×C71semidirect
645. C4×D4D4×C71semidirect
646. C4×D4D4×C71semidirect

Maximal subgroups

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

subgroupindex
C71×#35602
C71×#32132
C71×#32112
C71×#26622
C71×#16062
C71×#16042
C71×#16032
C71×#16012
C71×#16002
C71×#15982
C71×#15972
C71×#15952
C71×#15092
C71×#15022
C71×#14732
#1843471