Finite Group Databasebeta

← C71×#18416 #31839288

Subgroups — C71×#18416 #31839288

Order 18176.

978 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C71×#3535C211yesmaximal, characteristic, complemented
2C71×#3194C211yesmaximal, characteristic, complemented
3C71×#3187C211yesmaximal, characteristic, complemented
4C71×#2661C211yesmaximal, characteristic, complemented
5C71×#1612C211yesmaximal, characteristic, complemented
6C71×#1611C211yesmaximal, characteristic, complemented
7C71×#1609C211yesmaximal, characteristic, complemented
8C71×#1608C211yesmaximal, characteristic, complemented
9C71×#1600C211yesmaximal, characteristic, complemented
10C71×#1599C211yesmaximal, characteristic, complemented
11C71×#1597C211yesmaximal, characteristic, complemented
12C71×#1596C211yesmaximal, characteristic, complemented
13C71×#1508C211yesmaximal, characteristic, complemented
14C71×#1501C211yesmaximal, characteristic, complemented
15C71×#1468C211yesmaximal, characteristic, complemented
16#563×C71—21no—
17#562×C71—21no—
18#554×C71—21no—
19#552×C71—21no—
20#551×C71—21no—
21#551×C71—21no—
22#547×C71—21no—
23#546×C71—21no—
24#544×C71C2211yescharacteristic
25#543×C71C2211yescharacteristic
26#542×C71—21no—
27#539×C71—21no—
28#539×C71—21no—
29#539×C71C2211yescharacteristic
30#538×C71C2211yescharacteristic
31#536×C71—21no—
32#525×C71C2211yescharacteristic
33C2×#123×C71C2211yescharacteristic
34C2×C22⋊Q8×C71C2211yescharacteristic
35C2×#121×C71C2211yescharacteristic
36#483×C71C2211yescharacteristic
37#483×C71C2211yescharacteristic
38#483×C71C2211yescharacteristic
39#482×C71—21no—
40#481×C71—21no—
41#480×C71C2211yescharacteristic
42#469×C71—21no—
43#468×C71—21no—
44#465×C71—21no—
45#465×C71—21no—
46#450×C71C2211yescharacteristic
47#450×C71C2211yescharacteristic
48#450×C71C2211yescharacteristic
49#449×C71—21no—
50#448×C71—21no—
51#447×C71C2211yescharacteristic
52#407×C71C2211yescharacteristic
53C2×C22⋊C8×C71C2211yescharacteristic
54#398×C71C2211yescharacteristic
55#397×C71C2211yescharacteristic
56#394×C71—21no—
57#394×C71C2211yescharacteristic
58#392×C71—21no—
59#392×C71C2211yescharacteristic
60#390×C71—21no—
61#388×C71—21no—
62C4×C22⋊C4×C71C2211yescharacteristic
63#328×C71C2211yescharacteristic
64#328×C71C2211yescharacteristic
65#328×C71C2211yescharacteristic
66#328×C71C2211yescharacteristic
67#328×C71C2211yescharacteristic
68#328×C71C2211yescharacteristic
69#327×C71C2211yescharacteristic
70#327×C71C2211yescharacteristic
71#324×C71C2211yescharacteristic
72#324×C71C2211yescharacteristic
73#323×C71C2211yescharacteristic
74#323×C71C2211yescharacteristic
75C2×#41×C71—21no—
76C2×#41×C71D411yescharacteristic, complemented
77C22×Q8×C71D411yescharacteristic, complemented
78C22×D4×C71—21no—
79C22×D4×C71—21no—
80C22×D4×C71D411yescharacteristic
81C22×D4×C71C2311yescharacteristic
82C23×C4×C71C2311yescharacteristic
83C2×SD16×C71—21no—
84C2×SD16×C71—21no—
85C2×SD16×C71—21no—
86C2×D8×C71—21no—
87C2×M16×C71—21no—
88C22×C8×C71—21no—
89C4⋊Q8×C71—21no—
90C4⋊Q8×C71—21no—
91C4⋊Q8×C71—21no—
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#125×C71—21no—
99#125×C71—21no—
100#125×C71—21no—
101#125×C71—21no—
102#125×C71—21no—
103#124×C71—21no—
104#124×C71—21no—
105#124×C71—21no—
106#124×C71—21no—
107#123×C71—21no—
108#123×C71—21no—
109#123×C71—21no—
110#123×C71—21no—
111#123×C71—21no—
112#123×C71—21no—
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—
121C22⋊Q8×C71—21no—
122C22⋊Q8×C71—21no—
123C22⋊Q8×C71—21no—
124C22⋊Q8×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×C71—21no—
133C22⋊Q8×C71—21no—
134C22⋊Q8×C71—21no—
135C22⋊Q8×C71D411yescharacteristic, complemented
136C22⋊Q8×C71D411yescharacteristic, complemented
137C22⋊Q8×C71D411yescharacteristic, complemented
138C22⋊Q8×C71C2311yescharacteristic
139C22⋊Q8×C71C2311yescharacteristic
140C22⋊Q8×C71C2311yescharacteristic
141#121×C71—21no—
142#121×C71—21no—
143#121×C71—21no—
144#121×C71—21no—
145#121×C71—21no—
146#121×C71—21no—
147#121×C71—21no—
148#121×C71—21no—
149#121×C71D411yescharacteristic, complemented
150#121×C71C2311yescharacteristic
151#120×C71—21no—
152#120×C71—21no—
153C4×Q8×C71—21no—
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—
161#117×C71—21no—
162#117×C71—21no—
163#117×C71—21no—
164#117×C71D411yescharacteristic, complemented
165C2×C4⋊C4×C71—21no—
166C2×C4⋊C4×C71—21no—
167C2×C4⋊C4×C71—21no—
168C2×C4⋊C4×C71D411yescharacteristic
169C2×C4⋊C4×C71D411yescharacteristic, complemented
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C22⋊C4×C71—21no—
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×C71D411yescharacteristic
181C2×C22⋊C4×C71D411yescharacteristic
182C2×C22⋊C4×C71C2311yescharacteristic
183C2×C42×C71—21no—
184#107×C71—21no—
185#106×C71—21no—
186#106×C71—21no—
187#106×C71—21no—
188#103×C71—21no—
189#103×C71—21no—
190#103×C71—21no—
191#102×C71—21no—
192#102×C71—21no—
193#102×C71—21no—
194#102×C71—21no—
195#102×C71—21no—
196C22⋊C8×C71—21no—
197C22⋊C8×C71—21no—
198C22⋊C8×C71C2311yescharacteristic
199C22⋊C8×C71C2311yescharacteristic
200C22⋊C8×C71C2311yescharacteristic
201C22⋊C8×C71C2311yescharacteristic
202#95×C71—21no—
203#95×C71—21no—
204#95×C71C2311yescharacteristic
205#95×C71C2311yescharacteristic
206C24×C71—21no—
207C24×C71C2×D411yescharacteristic
208C24×C71C2×D411yescharacteristic
209#41×C71—82no—
210#41×C71—81no—
211C2×Q8×C71—21no—
212C2×Q8×C71—21no—
213C2×Q8×C71—21no—
214C2×Q8×C71—81no—
215C2×Q8×C71C2×D411yescharacteristic
216C2×Q8×C71C2×D411yescharacteristic
217C2×Q8×C71C2×D411yescharacteristic
218C2×D4×C71—21no—
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—42no—
228C2×D4×C71—41no—
229C2×D4×C71—41no—
230C2×D4×C71—81no—
231C2×D4×C71—81no—
232C2×D4×C71—81no—
233C2×D4×C71—81no—
234C2×D4×C71—81no—
235C2×D4×C71—81no—
236C2×D4×C71C2×D411yescharacteristic
237C22×C4×C71—21no—
238C22×C4×C71—21no—
239C22×C4×C71—21no—
240C22×C4×C71—21no—
241C22×C4×C71—21no—
242C22×C4×C71—21no—
243C22×C4×C71—21no—
244C22×C4×C71—21no—
245C22×C4×C71—21no—
246C22×C4×C71—21no—
247C22×C4×C71—81no—
248C22×C4×C71C2×D411yescharacteristic
249C22×C4×C71C2×D411yescharacteristic
250C22×C4×C71C2×D411yescharacteristic
251C22×C4×C71C2×D411yescharacteristic
252C22×C4×C71C2×D411yescharacteristic
253C22×C4×C71C2×D411yescharacteristic
254C22×C4×C71C2×D411yescharacteristic
255C22×C4×C71C2×D411yescharacteristic
256C22×C4×C71C2411yescharacteristic
257SD16×C71—81no—
258SD16×C71—81no—
259SD16×C71—81no—
260D8×C71—81no—
261M16×C71—81no—
262C2×C8×C71—21no—
263C2×C8×C71—21no—
264C2×C8×C71—21no—
265C2×C8×C71—21no—
266C2×C8×C71—81no—
267C4⋊C4×C71—21no—
268C4⋊C4×C71—21no—
269C4⋊C4×C71—21no—
270C4⋊C4×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—21no—
289C4⋊C4×C71—21no—
290C4⋊C4×C71—21no—
291C4⋊C4×C71—21no—
292C4⋊C4×C71—81no—
293C4⋊C4×C71C2×D411yescharacteristic
294C4⋊C4×C71C2×D411yescharacteristic
295C4⋊C4×C71C2×D411yescharacteristic
296C4⋊C4×C71C2×D411yescharacteristic
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—21no—
320C22⋊C4×C71—42no—
321C22⋊C4×C71—42no—
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—21no—
331C42×C71—21no—
332C42×C71—81no—
333C23×C71—21no—
334C23×C71—21no—
335C23×C71—21no—
336C23×C71—21no—
337C23×C71—21no—
338C23×C71—21no—
339C23×C71—41no—
340C23×C71—41no—
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#12011yescharacteristic
351C23×C71#12011yescharacteristic
352C23×C71C22×D411yescharacteristic
353Q8×C71—41no—
354Q8×C71—41no—
355Q8×C71—41no—
356Q8×C71—81no—
357Q8×C71—81no—
358Q8×C71—81no—
359D4×C71—41no—
360D4×C71—41no—
361D4×C71—41no—
362D4×C71—41no—
363D4×C71—41no—
364D4×C71—42no—
365D4×C71—42no—
366D4×C71—41no—
367D4×C71—41no—
368D4×C71—81no—
369D4×C71—81no—
370D4×C71—81no—
371D4×C71—81no—
372D4×C71—84no—
373D4×C71—82no—
374D4×C71—82no—
375C2×C4×C71—22no—
376C2×C4×C71—21no—
377C2×C4×C71—21no—
378C2×C4×C71—21no—
379C2×C4×C71—21no—
380C2×C4×C71—21no—
381C2×C4×C71—21no—
382C2×C4×C71—21no—
383C2×C4×C71—21no—
384C2×C4×C71—21no—
385C2×C4×C71—21no—
386C2×C4×C71—21no—
387C2×C4×C71—21no—
388C2×C4×C71—41no—
389C2×C4×C71—41no—
390C2×C4×C71—41no—
391C2×C4×C71—41no—
392C2×C4×C71—41no—
393C2×C4×C71—41no—
394C2×C4×C71—41no—
395C2×C4×C71—42no—
396C2×C4×C71—41no—
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—81no—
406C2×C4×C71—81no—
407C2×C4×C71—81no—
408C2×C4×C71—81no—
409C2×C4×C71—81no—
410C2×C4×C71—81no—
411C2×C4×C71#12011yescharacteristic
412C2×C4×C71#12011yescharacteristic
413C2×C4×C71C22×D411yescharacteristic
414C2×C4×C71C22×D411yescharacteristic
415C8×C71—41no—
416C8×C71—41no—
417C8×C71—41no—
418C8×C71—41no—
419C22×C71—21no—
420C22×C71—21no—
421C22×C71—21no—
422C22×C71—21no—
423C22×C71—21no—
424C22×C71—21no—
425C22×C71—21no—
426C22×C71—21no—
427C22×C71—41no—
428C22×C71—41no—
429C22×C71—41no—
430C22×C71—41no—
431C22×C71—41no—
432C22×C71—41no—
433C22×C71—81no—
434C22×C71—81no—
435C22×C71—81no—
436C22×C71—81no—
437C22×C71—81no—
438C22×C71—81no—
439C22×C71—81no—
440C22×C71—81no—
441C22×C71—81no—
442C22×C71—81no—
443C22×C71—81no—
444C22×C71C2×#12011yescharacteristic
445C22×C71#57711yescharacteristic
446C22×C71#57711yescharacteristic
447C4×C71—21no—
448C4×C71—21no—
449C4×C71—21no—
450C4×C71—21no—
451C4×C71—42no—
452C4×C71—41no—
453C4×C71—41no—
454C4×C71—41no—
455C4×C71—41no—
456C4×C71—41no—
457C4×C71—41no—
458C4×C71—41no—
459C4×C71—41no—
460C4×C71—41no—
461C4×C71—41no—
462C4×C71—81no—
463C4×C71—81no—
464#18416C7111yesmaximal, characteristic, direct product factor, Sylow
465C2×C71—21no—
466C2×C71—21no—
467C2×C71—41no—
468C2×C71—41no—
469C2×C71—81no—
470C2×C71—81no—
471C2×C71—161no—
472C2×C71#301011yescharacteristic
473C2×C71#301811yescharacteristic
474C2×C71#302611yescharacteristic
475#3535C2×C7111yescharacteristic, complemented
476#3194C2×C7111yescharacteristic, complemented
477#3187C2×C7111yescharacteristic, complemented
478#2661C2×C7111yescharacteristic, complemented
479#1612C2×C7111yescharacteristic, complemented
480#1611C2×C7111yescharacteristic, complemented
481#1609C2×C7111yescharacteristic, complemented
482#1608C2×C7111yescharacteristic, complemented
483#1600C2×C7111yescharacteristic, complemented
484#1599C2×C7111yescharacteristic, complemented
485#1597C2×C7111yescharacteristic, complemented
486#1596C2×C7111yescharacteristic, complemented
487#1508C2×C7111yescharacteristic, complemented
488#1501C2×C7111yescharacteristic, complemented
489#1468C2×C7111yescharacteristic, complemented
490C71#1841611yescharacteristic, direct product factor, Sylow
491#563—21no—
492#562—21no—
493#554—21no—
494#552—21no—
495#551—21no—
496#551—21no—
497#547—21no—
498#546—21no—
499#544C22×C7111yescharacteristic
500#543C22×C7111yescharacteristic
501#542—21no—
502#539—21no—
503#539—21no—
504#539C22×C7111yescharacteristic
505#538C22×C7111yescharacteristic
506#536—21no—
507#525C22×C7111yescharacteristic
508C2×#123C22×C7111yescharacteristic
509C2×C22⋊Q8C22×C7111yescharacteristic
510C2×#121C22×C7111yescharacteristic
511#483C22×C7111yescharacteristic
512#483C22×C7111yescharacteristic
513#483C22×C7111yescharacteristic
514#482—21no—
515#481—21no—
516#480C22×C7111yescharacteristic
517#469—21no—
518#468—21no—
519#465—21no—
520#465—21no—
521#450C22×C7111yescharacteristic
522#450C22×C7111yescharacteristic
523#450C22×C7111yescharacteristic
524#449—21no—
525#448—21no—
526#447C22×C7111yescharacteristic
527#407C22×C7111yescharacteristic
528C2×C22⋊C8C22×C7111yescharacteristic
529#398C22×C7111yescharacteristic
530#397C22×C7111yescharacteristic
531#394—21no—
532#394C22×C7111yescharacteristic
533#392—21no—
534#392C22×C7111yescharacteristic
535#390—21no—
536#388—21no—
537C4×C22⋊C4C22×C7111yescharacteristic
538#328C22×C7111yescharacteristic
539#328C22×C7111yescharacteristic
540#328C22×C7111yescharacteristic
541#328C22×C7111yescharacteristic
542#328C22×C7111yescharacteristic
543#328C22×C7111yescharacteristic
544#327C22×C7111yescharacteristic
545#327C22×C7111yescharacteristic
546#324C22×C7111yescharacteristic
547#324C22×C7111yescharacteristic
548#323C22×C7111yescharacteristic
549#323C22×C7111yescharacteristic
550C2×#41—21no—
551C2×#41D4×C7111yescharacteristic, complemented
552C22×Q8D4×C7111yescharacteristic, complemented
553C22×D4—21no—
554C22×D4—21no—
555C22×D4D4×C7111yescharacteristic
556C22×D4C23×C7111yescharacteristic
557C23×C4C23×C7111yescharacteristic
558C2×SD16—21no—
559C2×SD16—21no—
560C2×SD16—21no—
561C2×D8—21no—
562C2×M16—21no—
563C22×C8—21no—
564C4⋊Q8—21no—
565C4⋊Q8—21no—
566C4⋊Q8—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#126—21no—
573#125—21no—
574#125—21no—
575#125—21no—
576#125—21no—
577#125—21no—
578#124—21no—
579#124—21no—
580#124—21no—
581#124—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8D4×C7111yescharacteristic, complemented
611C22⋊Q8D4×C7111yescharacteristic, complemented
612C22⋊Q8D4×C7111yescharacteristic, complemented
613C22⋊Q8C23×C7111yescharacteristic
614C22⋊Q8C23×C7111yescharacteristic
615C22⋊Q8C23×C7111yescharacteristic
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#121D4×C7111yescharacteristic, complemented
625#121C23×C7111yescharacteristic
626#120—21no—
627#120—21no—
628C4×Q8—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—21no—
635C4×D4—21no—
636#117—21no—
637#117—21no—
638#117—21no—
639#117D4×C7111yescharacteristic, complemented
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4D4×C7111yescharacteristic
644C2×C4⋊C4D4×C7111yescharacteristic, complemented
645C2×C4⋊C4C23×C7111yescharacteristic
646C2×C4⋊C4C23×C7111yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4D4×C7111yescharacteristic
656C2×C22⋊C4D4×C7111yescharacteristic
657C2×C22⋊C4C23×C7111yescharacteristic
658C2×C42—21no—
659#107—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#103—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C7111yescharacteristic
674C22⋊C8C23×C7111yescharacteristic
675C22⋊C8C23×C7111yescharacteristic
676C22⋊C8C23×C7111yescharacteristic
677#95—21no—
678#95—21no—
679#95C23×C7111yescharacteristic
680#95C23×C7111yescharacteristic
681C24—21no—
682C24C2×D4×C7111yescharacteristic
683C24C2×D4×C7111yescharacteristic
684#41—82no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—81no—
690C2×Q8C2×D4×C7111yescharacteristic
691C2×Q8C2×D4×C7111yescharacteristic
692C2×Q8C2×D4×C7111yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—42no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C7111yescharacteristic
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—81no—
723C22×C4C2×D4×C7111yescharacteristic
724C22×C4C2×D4×C7111yescharacteristic
725C22×C4C2×D4×C7111yescharacteristic
726C22×C4C2×D4×C7111yescharacteristic
727C22×C4C2×D4×C7111yescharacteristic
728C22×C4C2×D4×C7111yescharacteristic
729C22×C4C2×D4×C7111yescharacteristic
730C22×C4C2×D4×C7111yescharacteristic
731C22×C4C24×C7111yescharacteristic
732SD16—81no—
733SD16—81no—
734SD16—81no—
735D8—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—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—81no—
768C4⋊C4C2×D4×C7111yescharacteristic
769C4⋊C4C2×D4×C7111yescharacteristic
770C4⋊C4C2×D4×C7111yescharacteristic
771C4⋊C4C2×D4×C7111yescharacteristic
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
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—42no—
796C22⋊C4—42no—
797C22⋊C4—41no—
798C22⋊C4—41no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—21no—
806C42—21no—
807C42—81no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23#120×C7111yescharacteristic
826C23#120×C7111yescharacteristic
827C23C22×D4×C7111yescharacteristic
828Q8—41no—
829Q8—41no—
830Q8—41no—
831Q8—81no—
832Q8—81no—
833Q8—81no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—41no—
842D4—41no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—84no—
848D4—82no—
849D4—82no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4#120×C7111yescharacteristic
887C2×C4#120×C7111yescharacteristic
888C2×C4C22×D4×C7111yescharacteristic
889C2×C4C22×D4×C7111yescharacteristic
890C8—41no—
891C8—41no—
892C8—41no—
893C8—41no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22C2×#120×C7111yescharacteristic
920C22#577×C7111yescharacteristic
921C22#577×C7111yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—42no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—41no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—161no—
946C2C71×#301011yescharacteristic
947C2C71×#301811yescharacteristic
948C2C71×#302611yescharacteristic
subgroupG/H
center, socleC22×C71C2×#120
commutator, Frattini, cosocleC22×C4C24×C71
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C71 ◁ C23×C4×C71 ◁ G

Complements

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

NH ≅ G/Ntype
1. C71×#3535C2semidirect
2. C71×#3194C2semidirect
3. C71×#3187C2semidirect
4. C71×#2661C2semidirect
5. C71×#1612C2semidirect
6. C71×#1611C2semidirect
7. C71×#1609C2semidirect
8. C71×#1608C2semidirect
9. C71×#1600C2semidirect
10. C71×#1599C2semidirect
11. C71×#1597C2semidirect
12. C71×#1596C2semidirect
13. C71×#1508C2semidirect
14. C71×#1501C2semidirect
15. C71×#1468C2semidirect
76. C2×#41×C71D4semidirect
77. C22×Q8×C71D4semidirect
135. C22⋊Q8×C71D4semidirect
136. C22⋊Q8×C71D4semidirect
137. C22⋊Q8×C71D4semidirect
149. #121×C71D4semidirect
164. #117×C71D4semidirect
169. C2×C4⋊C4×C71D4semidirect
464. #18416C71direct (N × H)
475. #3535C2×C71semidirect
476. #3194C2×C71semidirect
477. #3187C2×C71semidirect
478. #2661C2×C71semidirect
479. #1612C2×C71semidirect
480. #1611C2×C71semidirect
481. #1609C2×C71semidirect
482. #1608C2×C71semidirect
483. #1600C2×C71semidirect
484. #1599C2×C71semidirect
485. #1597C2×C71semidirect
486. #1596C2×C71semidirect
487. #1508C2×C71semidirect
488. #1501C2×C71semidirect
489. #1468C2×C71semidirect
490. C71#18416direct (N × H)
551. C2×#41D4×C71semidirect
552. C22×Q8D4×C71semidirect
610. C22⋊Q8D4×C71semidirect
611. C22⋊Q8D4×C71semidirect
612. C22⋊Q8D4×C71semidirect
624. #121D4×C71semidirect
639. #117D4×C71semidirect
644. C2×C4⋊C4D4×C71semidirect

Maximal subgroups

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

subgroupindex
C71×#35352
C71×#31942
C71×#31872
C71×#26612
C71×#16122
C71×#16112
C71×#16092
C71×#16082
C71×#16002
C71×#15992
C71×#15972
C71×#15962
C71×#15082
C71×#15012
C71×#14682
#1841671