Finite Group Databasebeta

← C71×#23857 #31844729

Subgroups — C71×#23857 #31844729

Order 18176.

1852 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C71C211yesmaximal, characteristic, complemented
2C2×#550×C71C211yesmaximal, characteristic, complemented
3C2×#452×C71C211yesmaximal, characteristic, complemented
4C2×#449×C71C211yesmaximal, characteristic, complemented
5C2×#449×C71C211yesmaximal, characteristic, complemented
6C71×#2407C211yesmaximal, characteristic, complemented
7C71×#2014C211yesmaximal, characteristic, complemented
8C71×#2011C211yesmaximal, characteristic, complemented
9C71×#2000C211yesmaximal, characteristic, complemented
10C71×#1999C211yesmaximal, characteristic, complemented
11C71×#1893C211yesmaximal, characteristic, complemented
12C71×#1880C211yesmaximal, characteristic, complemented
13C71×#1878C211yesmaximal, characteristic, complemented
14C71×#1869C211yesmaximal, characteristic, complemented
15C71×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C71C2211yescharacteristic
17C22×#41×C71C2211yescharacteristic
18C22×#41×C71C2211yescharacteristic
19C2×#135×C71—24no—
20C2×#135×C71—24no—
21C2×#135×C71—24no—
22C22×Q16×C71C2211yescharacteristic
23C22×SD16×C71C2211yescharacteristic
24C22×SD16×C71C2211yescharacteristic
25C22×SD16×C71C2211yescharacteristic
26C22×D8×C71C2211yescharacteristic
27C22×D8×C71C2211yescharacteristic
28C23×C8×C71C2211yescharacteristic
29#550×C71—24no—
30#550×C71—24no—
31C2×#127×C71—21no—
32C2×#127×C71C2211yescharacteristic
33C2×C22⋊Q8×C71C2211yescharacteristic
34C2×#121×C71—21no—
35C2×#121×C71—21no—
36C2×#121×C71C2211yescharacteristic
37C2×#121×C71C2211yescharacteristic
38C2×#121×C71C2211yescharacteristic
39C2×C4×Q8×C71C2211yescharacteristic
40C2×C4×D4×C71—21no—
41C2×C4×D4×C71C2211yescharacteristic
42#452×C71—24no—
43#449×C71—24no—
44#449×C71—24no—
45C2×#103×C71C2211yescharacteristic
46C2×#103×C71C2211yescharacteristic
47C2×#103×C71C2211yescharacteristic
48C2×#102×C71C2211yescharacteristic
49C2×#102×C71C2211yescharacteristic
50C2×#102×C71C2211yescharacteristic
51C2×#102×C71C2211yescharacteristic
52C2×#102×C71C2211yescharacteristic
53C2×C22⋊C8×C71C2211yescharacteristic
54C2×C22⋊C8×C71C2211yescharacteristic
55C2×C22⋊C8×C71C2211yescharacteristic
56#394×C71—21no—
57#392×C71—21no—
58#391×C71C2211yescharacteristic
59#390×C71C2211yescharacteristic
60#386×C71—21no—
61#385×C71—21no—
62#380×C71C2211yescharacteristic
63#340×C71C2211yescharacteristic
64#340×C71C2211yescharacteristic
65#336×C71C2211yescharacteristic
66#336×C71C2211yescharacteristic
67C2×#41×C71—22no—
68C2×#41×C71—22no—
69C2×#41×C71—22no—
70C2×#41×C71—22no—
71C2×#41×C71—22no—
72C2×#41×C71—22no—
73C2×#41×C71—22no—
74C2×#41×C71—22no—
75C2×#41×C71—22no—
76C2×#41×C71—22no—
77C2×#41×C71—22no—
78C2×#41×C71—41no—
79C2×#41×C71—41no—
80C2×#41×C71—41no—
81C2×#41×C71—41no—
82C2×#41×C71—41no—
83C2×#41×C71—41no—
84C2×#41×C71D414yescomplemented
85C22×Q8×C71C2311yescharacteristic
86C22×Q8×C71C2311yescharacteristic
87C22×D4×C71—21no—
88C22×D4×C71—21no—
89C22×D4×C71—21no—
90C22×D4×C71—21no—
91C22×D4×C71—21no—
92C22×D4×C71—21no—
93C22×D4×C71—21no—
94C22×D4×C71—21no—
95C22×D4×C71D411yescharacteristic
96C22×D4×C71C2311yescharacteristic
97C22×D4×C71C2311yescharacteristic
98C22×D4×C71C2311yescharacteristic
99C23×C4×C71—21no—
100C23×C4×C71—21no—
101C23×C4×C71—21no—
102C23×C4×C71C2311yescharacteristic
103C23×C4×C71C2311yescharacteristic
104#135×C71—232no—
105C2×Q16×C71—22no—
106C2×Q16×C71—22no—
107C2×Q16×C71D414yescomplemented
108C2×SD16×C71—22no—
109C2×SD16×C71—22no—
110C2×SD16×C71—22no—
111C2×SD16×C71—22no—
112C2×SD16×C71—22no—
113C2×SD16×C71—22no—
114C2×SD16×C71—22no—
115C2×SD16×C71—41no—
116C2×SD16×C71D414yescomplemented
117C2×D8×C71—22no—
118C2×D8×C71—22no—
119C2×D8×C71—22no—
120C2×D8×C71—22no—
121C2×D8×C71—22no—
122C2×D8×C71—41no—
123C22×C8×C71—22no—
124C22×C8×C71—22no—
125C22×C8×C71—22no—
126C22×C8×C71C2311yescharacteristic
127C22×C8×C71C2311yescharacteristic
128C22×C8×C71C2311yescharacteristic
129C22×C8×C71C2311yescharacteristic
130#127×C71—28no—
131#127×C71—22no—
132#127×C71—22no—
133C22⋊Q8×C71—22no—
134C22⋊Q8×C71—41no—
135#121×C71—28no—
136#121×C71—28no—
137#121×C71—22no—
138#121×C71—22no—
139#121×C71—22no—
140#121×C71—22no—
141#121×C71—41no—
142#121×C71D414yescomplemented
143C4×Q8×C71—22no—
144C4×Q8×C71—22no—
145C4×D4×C71—28no—
146C4×D4×C71—22no—
147C4×D4×C71—22no—
148C2×C4⋊C4×C71—21no—
149C2×C4⋊C4×C71—21no—
150C2×C4⋊C4×C71D411yescharacteristic
151C2×C4⋊C4×C71C2311yescharacteristic
152C2×C4⋊C4×C71C2311yescharacteristic
153C2×C4⋊C4×C71C2311yescharacteristic
154C2×C22⋊C4×C71—21no—
155C2×C22⋊C4×C71—21no—
156C2×C22⋊C4×C71—21no—
157C2×C22⋊C4×C71—21no—
158C2×C22⋊C4×C71—21no—
159C2×C22⋊C4×C71—21no—
160C2×C22⋊C4×C71—21no—
161C2×C22⋊C4×C71D411yescharacteristic
162C2×C22⋊C4×C71D411yescharacteristic
163C2×C42×C71—21no—
164C2×C42×C71C2311yescharacteristic
165#103×C71—22no—
166#103×C71—22no—
167#103×C71—22no—
168#102×C71—22no—
169#102×C71—22no—
170#102×C71—22no—
171#102×C71—41no—
172#102×C71—41no—
173C22⋊C8×C71—22no—
174C22⋊C8×C71—22no—
175C22⋊C8×C71—22no—
176#95×C71—21no—
177#95×C71—21no—
178#95×C71—21no—
179C24×C71—21no—
180C24×C71—21no—
181C24×C71—21no—
182C24×C71C2×D411yescharacteristic
183C24×C71C2×D411yescharacteristic
184#41×C71—28no—
185#41×C71—28no—
186#41×C71—44no—
187#41×C71—44no—
188#41×C71—44no—
189#41×C71—44no—
190#41×C71—44no—
191#41×C71—44no—
192#41×C71—44no—
193#41×C71—44no—
194#41×C71—44no—
195#41×C71—44no—
196C2×Q8×C71—21no—
197C2×Q8×C71—21no—
198C2×Q8×C71—21no—
199C2×Q8×C71—21no—
200C2×Q8×C71—21no—
201C2×Q8×C71—21no—
202C2×Q8×C71—21no—
203C2×Q8×C71—21no—
204C2×Q8×C71C2×D412yes—
205C2×Q8×C71C2×D412yes—
206C2×Q8×C71C2×D412yes—
207C2×Q8×C71C2×D412yes—
208C2×D4×C71—24no—
209C2×D4×C71—24no—
210C2×D4×C71—22no—
211C2×D4×C71—24no—
212C2×D4×C71—24no—
213C2×D4×C71—24no—
214C2×D4×C71—24no—
215C2×D4×C71—22no—
216C2×D4×C71—21no—
217C2×D4×C71—21no—
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—21no—
228C2×D4×C71—21no—
229C2×D4×C71—21no—
230C2×D4×C71—21no—
231C2×D4×C71—41no—
232C2×D4×C71—42no—
233C2×D4×C71—42no—
234C2×D4×C71—42no—
235C2×D4×C71—42no—
236C2×D4×C71—42no—
237C2×D4×C71—42no—
238C2×D4×C71—42no—
239C2×D4×C71—42no—
240C2×D4×C71—42no—
241C2×D4×C71—42no—
242C2×D4×C71—42no—
243C2×D4×C71—81no—
244C2×D4×C71—81no—
245C2×D4×C71—81no—
246C2×D4×C71—81no—
247C2×D4×C71—81no—
248C2×D4×C71—81no—
249C2×D4×C71—81no—
250C2×D4×C71C2×D412yes—
251C2×D4×C71C2×D412yes—
252C2×D4×C71C2×D412yes—
253C22×C4×C71—21no—
254C22×C4×C71—21no—
255C22×C4×C71—21no—
256C22×C4×C71—21no—
257C22×C4×C71—21no—
258C22×C4×C71—24no—
259C22×C4×C71—21no—
260C22×C4×C71—21no—
261C22×C4×C71—24no—
262C22×C4×C71—21no—
263C22×C4×C71—21no—
264C22×C4×C71—21no—
265C22×C4×C71—21no—
266C22×C4×C71—21no—
267C22×C4×C71—21no—
268C22×C4×C71—21no—
269C22×C4×C71—21no—
270C22×C4×C71—42no—
271C22×C4×C71—42no—
272C22×C4×C71—42no—
273C22×C4×C71—42no—
274C22×C4×C71—42no—
275C22×C4×C71—42no—
276C22×C4×C71—42no—
277C22×C4×C71C2×D411yescharacteristic
278C22×C4×C71C2×D411yescharacteristic
279C22×C4×C71C2×D411yescharacteristic
280C22×C4×C71C2×D412yes—
281C22×C4×C71C2×D412yes—
282C22×C4×C71C2×D411yescharacteristic
283C22×C4×C71C2411yescharacteristic
284Q16×C71—28no—
285SD16×C71—28no—
286SD16×C71—28no—
287SD16×C71—44no—
288D8×C71—28no—
289D8×C71—44no—
290C2×C8×C71—28no—
291C2×C8×C71—21no—
292C2×C8×C71—21no—
293C2×C8×C71—21no—
294C2×C8×C71—21no—
295C2×C8×C71—21no—
296C2×C8×C71—21no—
297C2×C8×C71—21no—
298C2×C8×C71—21no—
299C2×C8×C71—21no—
300C2×C8×C71—21no—
301C2×C8×C71C2×D412yes—
302C2×C8×C71C2×D412yes—
303C4⋊C4×C71—24no—
304C4⋊C4×C71—22no—
305C4⋊C4×C71—21no—
306C4⋊C4×C71—21no—
307C4⋊C4×C71—21no—
308C4⋊C4×C71—21no—
309C4⋊C4×C71—21no—
310C4⋊C4×C71—42no—
311C4⋊C4×C71C2×D412yes—
312C22⋊C4×C71—24no—
313C22⋊C4×C71—22no—
314C22⋊C4×C71—24no—
315C22⋊C4×C71—22no—
316C22⋊C4×C71—42no—
317C22⋊C4×C71—42no—
318C22⋊C4×C71—42no—
319C22⋊C4×C71—81no—
320C22⋊C4×C71—81no—
321C42×C71—24no—
322C42×C71—21no—
323C42×C71—21no—
324C23×C71—21no—
325C23×C71—21no—
326C23×C71—21no—
327C23×C71—21no—
328C23×C71—21no—
329C23×C71—21no—
330C23×C71—21no—
331C23×C71—22no—
332C23×C71—22no—
333C23×C71—21no—
334C23×C71—22no—
335C23×C71—21no—
336C23×C71—21no—
337C23×C71—21no—
338C23×C71—21no—
339C23×C71—21no—
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—41no—
351C23×C71—41no—
352C23×C71—41no—
353C23×C71—41no—
354C23×C71—41no—
355C23×C71—41no—
356C23×C71—41no—
357C23×C71—41no—
358C23×C71#12012yes—
359C23×C71C22×D411yescharacteristic
360Q8×C71—22no—
361Q8×C71—22no—
362Q8×C71—22no—
363Q8×C71—22no—
364Q8×C71—22no—
365Q8×C71—41no—
366Q8×C71—41no—
367Q8×C71#12014yes—
368D4×C71—22no—
369D4×C71—22no—
370D4×C71—22no—
371D4×C71—22no—
372D4×C71—22no—
373D4×C71—22no—
374D4×C71—44no—
375D4×C71—48no—
376D4×C71—48no—
377D4×C71—48no—
378D4×C71—48no—
379D4×C71—41no—
380D4×C71—41no—
381D4×C71—41no—
382D4×C71—41no—
383D4×C71—41no—
384D4×C71—41no—
385D4×C71—84no—
386D4×C71—84no—
387D4×C71—84no—
388D4×C71—84no—
389C2×C4×C71—21no—
390C2×C4×C71—22no—
391C2×C4×C71—21no—
392C2×C4×C71—21no—
393C2×C4×C71—22no—
394C2×C4×C71—22no—
395C2×C4×C71—21no—
396C2×C4×C71—22no—
397C2×C4×C71—22no—
398C2×C4×C71—22no—
399C2×C4×C71—22no—
400C2×C4×C71—21no—
401C2×C4×C71—22no—
402C2×C4×C71—21no—
403C2×C4×C71—21no—
404C2×C4×C71—22no—
405C2×C4×C71—21no—
406C2×C4×C71—21no—
407C2×C4×C71—21no—
408C2×C4×C71—48no—
409C2×C4×C71—48no—
410C2×C4×C71—48no—
411C2×C4×C71—41no—
412C2×C4×C71—41no—
413C2×C4×C71—41no—
414C2×C4×C71—41no—
415C2×C4×C71—41no—
416C2×C4×C71—41no—
417C2×C4×C71—41no—
418C2×C4×C71—41no—
419C2×C4×C71—41no—
420C2×C4×C71—41no—
421C2×C4×C71—41no—
422C2×C4×C71—41no—
423C2×C4×C71—41no—
424C2×C4×C71—41no—
425C2×C4×C71#12012yes—
426C2×C4×C71#13512yescomplemented
427C2×C4×C71C22×D411yescharacteristic
428C2×C4×C71C22×D411yescharacteristic
429C2×C4×C71C22×D411yescharacteristic
430C2×C4×C71C22×D411yescharacteristic
431C2×C4×C71H(5,𝔽2)11yescharacteristic
432C2×C4×C71H(5,𝔽2)11yescharacteristic
433C8×C71—22no—
434C8×C71—22no—
435C8×C71—41no—
436C8×C71—41no—
437C22×C71—22no—
438C22×C71—22no—
439C22×C71—22no—
440C22×C71—41no—
441C22×C71—41no—
442C22×C71—41no—
443C22×C71—41no—
444C22×C71—42no—
445C22×C71—42no—
446C22×C71—42no—
447C22×C71—41no—
448C22×C71—41no—
449C22×C71—42no—
450C22×C71—42no—
451C22×C71—41no—
452C22×C71—42no—
453C22×C71—42no—
454C22×C71—41no—
455C22×C71—42no—
456C22×C71—41no—
457C22×C71—41no—
458C22×C71—42no—
459C22×C71—41no—
460C22×C71—81no—
461C22×C71—81no—
462C22×C71—81no—
463C22×C71—81no—
464C22×C71—81no—
465C22×C71—81no—
466C22×C71—81no—
467C22×C71—81no—
468C22×C71—81no—
469C22×C71—81no—
470C22×C71—81no—
471C22×C71—81no—
472C22×C71C2×#12011yescharacteristic
473C22×C71D4211yescharacteristic
474C22×C71D4211yescharacteristic
475C22×C71C2×#13511yescharacteristic
476C22×C71#57511yescharacteristic
477C22×C71#57611yescharacteristic
478C22×C71#57711yescharacteristic
479C4×C71—22no—
480C4×C71—24no—
481C4×C71—22no—
482C4×C71—41no—
483C4×C71—42no—
484C4×C71—41no—
485C4×C71—42no—
486C4×C71—81no—
487C4×C71—81no—
488C4×C71C2×#12011yescharacteristic
489C4×C71#53411yescharacteristic
490C4×C71D4211yescharacteristic
491C4×C71D4211yescharacteristic
492#23857C7111yesmaximal, characteristic, direct product factor, Sylow
493C2×C71—42no—
494C2×C71—81no—
495C2×C71—82no—
496C2×C71—82no—
497C2×C71—82no—
498C2×C71#240311yescharacteristic
499C2×C71#300211yescharacteristic
500C2×C71#301211yescharacteristic
501C2×C71#326811yescharacteristic
502C2×C71#327111yescharacteristic
503C2×C71#328411yescharacteristic
504C2×C71#328711yescharacteristic
505C22×#135C2×C7111yescharacteristic, complemented
506C2×#550C2×C7111yescharacteristic, complemented
507C2×#452C2×C7111yescharacteristic, complemented
508C2×#449C2×C7111yescharacteristic, complemented
509C2×#449C2×C7111yescharacteristic, complemented
510#2407C2×C7111yescharacteristic, complemented
511#2014C2×C7111yescharacteristic, complemented
512#2011C2×C7111yescharacteristic, complemented
513#2000C2×C7111yescharacteristic, complemented
514#1999C2×C7111yescharacteristic, complemented
515#1893C2×C7111yescharacteristic, complemented
516#1880C2×C7111yescharacteristic, complemented
517#1878C2×C7111yescharacteristic, complemented
518#1869C2×C7111yescharacteristic, complemented
519#1788C2×C7111yescharacteristic, complemented
520C71#2385711yescharacteristic, direct product factor, Sylow
521C22×#41C22×C7111yescharacteristic
522C22×#41C22×C7111yescharacteristic
523C22×#41C22×C7111yescharacteristic
524C2×#135—24no—
525C2×#135—24no—
526C2×#135—24no—
527C22×Q16C22×C7111yescharacteristic
528C22×SD16C22×C7111yescharacteristic
529C22×SD16C22×C7111yescharacteristic
530C22×SD16C22×C7111yescharacteristic
531C22×D8C22×C7111yescharacteristic
532C22×D8C22×C7111yescharacteristic
533C23×C8C22×C7111yescharacteristic
534#550—24no—
535#550—24no—
536C2×#127—21no—
537C2×#127C22×C7111yescharacteristic
538C2×C22⋊Q8C22×C7111yescharacteristic
539C2×#121—21no—
540C2×#121—21no—
541C2×#121C22×C7111yescharacteristic
542C2×#121C22×C7111yescharacteristic
543C2×#121C22×C7111yescharacteristic
544C2×C4×Q8C22×C7111yescharacteristic
545C2×C4×D4—21no—
546C2×C4×D4C22×C7111yescharacteristic
547#452—24no—
548#449—24no—
549#449—24no—
550C2×#103C22×C7111yescharacteristic
551C2×#103C22×C7111yescharacteristic
552C2×#103C22×C7111yescharacteristic
553C2×#102C22×C7111yescharacteristic
554C2×#102C22×C7111yescharacteristic
555C2×#102C22×C7111yescharacteristic
556C2×#102C22×C7111yescharacteristic
557C2×#102C22×C7111yescharacteristic
558C2×C22⋊C8C22×C7111yescharacteristic
559C2×C22⋊C8C22×C7111yescharacteristic
560C2×C22⋊C8C22×C7111yescharacteristic
561#394—21no—
562#392—21no—
563#391C22×C7111yescharacteristic
564#390C22×C7111yescharacteristic
565#386—21no—
566#385—21no—
567#380C22×C7111yescharacteristic
568#340C22×C7111yescharacteristic
569#340C22×C7111yescharacteristic
570#336C22×C7111yescharacteristic
571#336C22×C7111yescharacteristic
572C2×#41—22no—
573C2×#41—22no—
574C2×#41—22no—
575C2×#41—22no—
576C2×#41—22no—
577C2×#41—22no—
578C2×#41—22no—
579C2×#41—22no—
580C2×#41—22no—
581C2×#41—22no—
582C2×#41—22no—
583C2×#41—41no—
584C2×#41—41no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41—41no—
588C2×#41—41no—
589C2×#41D4×C7114yescomplemented
590C22×Q8C23×C7111yescharacteristic
591C22×Q8C23×C7111yescharacteristic
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—21no—
600C22×D4D4×C7111yescharacteristic
601C22×D4C23×C7111yescharacteristic
602C22×D4C23×C7111yescharacteristic
603C22×D4C23×C7111yescharacteristic
604C23×C4—21no—
605C23×C4—21no—
606C23×C4—21no—
607C23×C4C23×C7111yescharacteristic
608C23×C4C23×C7111yescharacteristic
609#135—232no—
610C2×Q16—22no—
611C2×Q16—22no—
612C2×Q16D4×C7114yescomplemented
613C2×SD16—22no—
614C2×SD16—22no—
615C2×SD16—22no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—41no—
621C2×SD16D4×C7114yescomplemented
622C2×D8—22no—
623C2×D8—22no—
624C2×D8—22no—
625C2×D8—22no—
626C2×D8—22no—
627C2×D8—41no—
628C22×C8—22no—
629C22×C8—22no—
630C22×C8—22no—
631C22×C8C23×C7111yescharacteristic
632C22×C8C23×C7111yescharacteristic
633C22×C8C23×C7111yescharacteristic
634C22×C8C23×C7111yescharacteristic
635#127—28no—
636#127—22no—
637#127—22no—
638C22⋊Q8—22no—
639C22⋊Q8—41no—
640#121—28no—
641#121—28no—
642#121—22no—
643#121—22no—
644#121—22no—
645#121—22no—
646#121—41no—
647#121D4×C7114yescomplemented
648C4×Q8—22no—
649C4×Q8—22no—
650C4×D4—28no—
651C4×D4—22no—
652C4×D4—22no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4D4×C7111yescharacteristic
656C2×C4⋊C4C23×C7111yescharacteristic
657C2×C4⋊C4C23×C7111yescharacteristic
658C2×C4⋊C4C23×C7111yescharacteristic
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4D4×C7111yescharacteristic
667C2×C22⋊C4D4×C7111yescharacteristic
668C2×C42—21no—
669C2×C42C23×C7111yescharacteristic
670#103—22no—
671#103—22no—
672#103—22no—
673#102—22no—
674#102—22no—
675#102—22no—
676#102—41no—
677#102—41no—
678C22⋊C8—22no—
679C22⋊C8—22no—
680C22⋊C8—22no—
681#95—21no—
682#95—21no—
683#95—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24C2×D4×C7111yescharacteristic
688C24C2×D4×C7111yescharacteristic
689#41—28no—
690#41—28no—
691#41—44no—
692#41—44no—
693#41—44no—
694#41—44no—
695#41—44no—
696#41—44no—
697#41—44no—
698#41—44no—
699#41—44no—
700#41—44no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—21no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8—21no—
709C2×Q8C2×D4×C7112yes—
710C2×Q8C2×D4×C7112yes—
711C2×Q8C2×D4×C7112yes—
712C2×Q8C2×D4×C7112yes—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—22no—
716C2×D4—24no—
717C2×D4—24no—
718C2×D4—24no—
719C2×D4—24no—
720C2×D4—22no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—41no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—42no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4C2×D4×C7112yes—
756C2×D4C2×D4×C7112yes—
757C2×D4C2×D4×C7112yes—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—24no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—24no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4C2×D4×C7111yescharacteristic
783C22×C4C2×D4×C7111yescharacteristic
784C22×C4C2×D4×C7111yescharacteristic
785C22×C4C2×D4×C7112yes—
786C22×C4C2×D4×C7112yes—
787C22×C4C2×D4×C7111yescharacteristic
788C22×C4C24×C7111yescharacteristic
789Q16—28no—
790SD16—28no—
791SD16—28no—
792SD16—44no—
793D8—28no—
794D8—44no—
795C2×C8—28no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8C2×D4×C7112yes—
807C2×C8C2×D4×C7112yes—
808C4⋊C4—24no—
809C4⋊C4—22no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—42no—
816C4⋊C4C2×D4×C7112yes—
817C22⋊C4—24no—
818C22⋊C4—22no—
819C22⋊C4—24no—
820C22⋊C4—22no—
821C22⋊C4—42no—
822C22⋊C4—42no—
823C22⋊C4—42no—
824C22⋊C4—81no—
825C22⋊C4—81no—
826C42—24no—
827C42—21no—
828C42—21no—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—22no—
837C23—22no—
838C23—21no—
839C23—22no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23#120×C7112yes—
864C23C22×D4×C7111yescharacteristic
865Q8—22no—
866Q8—22no—
867Q8—22no—
868Q8—22no—
869Q8—22no—
870Q8—41no—
871Q8—41no—
872Q8#120×C7114yes—
873D4—22no—
874D4—22no—
875D4—22no—
876D4—22no—
877D4—22no—
878D4—22no—
879D4—44no—
880D4—48no—
881D4—48no—
882D4—48no—
883D4—48no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—84no—
891D4—84no—
892D4—84no—
893D4—84no—
894C2×C4—21no—
895C2×C4—22no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—21no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—22no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—22no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—48no—
914C2×C4—48no—
915C2×C4—48no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4#120×C7112yes—
931C2×C4#135×C7112yescomplemented
932C2×C4C22×D4×C7111yescharacteristic
933C2×C4C22×D4×C7111yescharacteristic
934C2×C4C22×D4×C7111yescharacteristic
935C2×C4C22×D4×C7111yescharacteristic
936C2×C4H(5,𝔽2)×C7111yescharacteristic
937C2×C4H(5,𝔽2)×C7111yescharacteristic
938C8—22no—
939C8—22no—
940C8—41no—
941C8—41no—
942C22—22no—
943C22—22no—
944C22—22no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—41no—
953C22—41no—
954C22—42no—
955C22—42no—
956C22—41no—
957C22—42no—
958C22—42no—
959C22—41no—
960C22—42no—
961C22—41no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22C2×#120×C7111yescharacteristic
978C22D42×C7111yescharacteristic
979C22D42×C7111yescharacteristic
980C22C2×#135×C7111yescharacteristic
981C22#575×C7111yescharacteristic
982C22#576×C7111yescharacteristic
983C22#577×C7111yescharacteristic
984C4—22no—
985C4—24no—
986C4—22no—
987C4—41no—
988C4—42no—
989C4—41no—
990C4—42no—
991C4—81no—
992C4—81no—
993C4C2×#120×C7111yescharacteristic
994C4#534×C7111yescharacteristic
995C4D42×C7111yescharacteristic
996C4D42×C7111yescharacteristic
997C2—42no—
998C2—81no—
999C2—82no—
1000C2—82no—
1001C2—82no—
1002C2C71×#240311yescharacteristic
1003C2C71×#300211yescharacteristic
1004C2C71×#301211yescharacteristic
1005C2C71×#326811yescharacteristic
1006C2C71×#327111yescharacteristic
1007C2C71×#328411yescharacteristic
1008C2C71×#328711yescharacteristic
subgroupG/H
center, socleC23×C71C22×D4
commutator, Frattini, cosocleC22×C4C24×C71
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C71 ◁ C2×C4×D4×C71 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#135×C71C2semidirect
2. C2×#550×C71C2semidirect
3. C2×#452×C71C2semidirect
4. C2×#449×C71C2semidirect
5. C2×#449×C71C2semidirect
6. C71×#2407C2semidirect
7. C71×#2014C2semidirect
8. C71×#2011C2semidirect
9. C71×#2000C2semidirect
10. C71×#1999C2semidirect
11. C71×#1893C2semidirect
12. C71×#1880C2semidirect
13. C71×#1878C2semidirect
14. C71×#1869C2semidirect
15. C71×#1788C2semidirect
84. C2×#41×C71D4semidirect
107. C2×Q16×C71D4semidirect
116. C2×SD16×C71D4semidirect
142. #121×C71D4semidirect
426. C2×C4×C71#135semidirect
492. #23857C71direct (N × H)
505. C22×#135C2×C71semidirect
506. C2×#550C2×C71semidirect
507. C2×#452C2×C71semidirect
508. C2×#449C2×C71semidirect
509. C2×#449C2×C71semidirect
510. #2407C2×C71semidirect
511. #2014C2×C71semidirect
512. #2011C2×C71semidirect
513. #2000C2×C71semidirect
514. #1999C2×C71semidirect
515. #1893C2×C71semidirect
516. #1880C2×C71semidirect
517. #1878C2×C71semidirect
518. #1869C2×C71semidirect
519. #1788C2×C71semidirect
520. C71#23857direct (N × H)
589. C2×#41D4×C71semidirect
612. C2×Q16D4×C71semidirect
621. C2×SD16D4×C71semidirect
647. #121D4×C71semidirect
931. C2×C4#135×C71semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C712
C2×#550×C712
C2×#452×C712
C2×#449×C712
C71×#24072
C71×#20142
C71×#20112
C71×#20002
C71×#19992
C71×#18932
C71×#18802
C71×#18782
C71×#18692
C71×#17882
#2385771