Finite Group Databasebeta

← #1866×D71 #31998498

Subgroups — #1866×D71 #31998498

Order 18176.

1398 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#131×D71C211yesmaximal, characteristic
2C2×#108×D71C211yesmaximal, characteristic, complemented
3#424×D71C211yesmaximal, characteristic, complemented
4C2×#104×D71C211yesmaximal, characteristic
5#416×D71C211yesmaximal, characteristic
6#22588618C211yesmaximal, characteristic, complemented
7#22588617C211yesmaximal, characteristic, complemented
8#22588616C211yesmaximal, characteristic, complemented
9#22588615C211yesmaximal, characteristic, complemented
10#22588614C211yesmaximal, characteristic, complemented
11#22588613C211yesmaximal, characteristic, complemented
12#22588612C211yesmaximal, characteristic, complemented
13#339×D71C211yesmaximal, characteristic, complemented
14#336×D71C211yesmaximal, characteristic, complemented
15C71×#1866C211yesmaximal, characteristic, complemented
16C2×#41×D71C2211yescharacteristic
17C2×#14556136—21no—
18C2×#14556136C2211yescharacteristic
19C2×#14556135C2211yescharacteristic
20C2×#14556134—21no—
21C2×#14556134C2211yescharacteristic
22#131×D71—24no—
23#131×D71—24no—
24C2×M16×D71—21no—
25C2×M16×D71C2211yescharacteristic
26C2×M16×D71C2211yescharacteristic
27C22×C8×D71—21no—
28C22×C8×D71C2211yescharacteristic
29C22×C8×D71C2211yescharacteristic
30#117×D71C2211yescharacteristic
31C2×C42×D71C2211yescharacteristic
32C2×#14556064C2211yescharacteristic, complemented
33C2×#14556063C2211yescharacteristic, complemented
34C2×#14556063C2211yescharacteristic, complemented
35#108×D71—24no—
36#17986027C2211yescharacteristic, complemented
37#17986026C2211yescharacteristic, complemented
38#17986025C2211yescharacteristic, complemented
39#17986024—21no—
40#17986024—21no—
41C4⋊C8×D71—21no—
42C4⋊C8×D71—21no—
43C2×#14556056C2211yescharacteristic
44C2×#14556055C2211yescharacteristic
45C2×#14556054C2211yescharacteristic
46#104×D71—24no—
47#17985996C2211yescharacteristic
48#17985995C2211yescharacteristic
49#17985994C411yescharacteristic, complemented
50#17985994C411yescharacteristic, complemented
51#17985993C2211yescharacteristic
52#17985992C411yescharacteristic, complemented
53#17985992C411yescharacteristic, complemented
54#103×D71C411yescharacteristic, complemented
55#103×D71C411yescharacteristic, complemented
56#102×D71C411yescharacteristic, complemented
57#102×D71C411yescharacteristic, complemented
58#17985760C2211yescharacteristic, complemented
59#17985759C2211yescharacteristic, complemented
60#17985758C2211yescharacteristic, complemented
61#17985754C2211yescharacteristic, complemented
62#17985753C2211yescharacteristic, complemented
63#17985753C2211yescharacteristic, complemented
64C2×#131×C71C2211yescharacteristic
65C2×#108×C71C2211yescharacteristic, complemented
66#424×C71C2211yescharacteristic, complemented
67C2×#104×C71C2211yescharacteristic
68#416×C71C2211yescharacteristic
69#339×C71C2211yescharacteristic, complemented
70#336×C71C2211yescharacteristic, complemented
71C2×#11765866C2×C411yescharacteristic
72C2×#11765865—21no—
73C2×#11765865C2311yescharacteristic
74C2×#11765864—21no—
75C2×#11765864C2×C411yescharacteristic
76#41×D71—22no—
77#41×D71—22no—
78#41×D71D414yes—
79#41×D71Q814yes—
80C2×Q8×D71C2×C411yescharacteristic
81C2×D4×D71—21no—
82C2×D4×D71C2×C411yescharacteristic
83C22×C4×D71—21no—
84C22×C4×D71—21no—
85C22×C4×D71C2311yescharacteristic
86#14556136—28no—
87#14556136—22no—
88#14556136—22no—
89#14556135—22no—
90#14556135—22no—
91#14556134—28no—
92#14556134—22no—
93#14556134—22no—
94C2×#11765849—21no—
95C2×#11765849C2311yescharacteristic
96C2×#11765849C2311yescharacteristic
97C2×#11765848—21no—
98C2×#11765848—21no—
99C2×#11765848—21no—
100C2×#11765848—21no—
101M16×D71—28no—
102M16×D71—22no—
103M16×D71—22no—
104M16×D71—22no—
105M16×D71D414yes—
106C22×C71⋊C8—21no—
107C22×C71⋊C8C2311yescharacteristic
108C22×C71⋊C8C2311yescharacteristic
109C2×C8×D71—28no—
110C2×C8×D71—21no—
111C2×C8×D71—22no—
112C2×C8×D71—22no—
113C2×C8×D71—22no—
114C2×C8×D71—22no—
115C2×C8×D71—21no—
116C2×C8×D71—21no—
117C2×C8×D71—21no—
118C2×C8×D71C2×C411yescharacteristic
119C2×C8×D71C2×C411yescharacteristic
120C2×C8×D71C2×C411yescharacteristic
121C2×C8×D71C2×C411yescharacteristic
122C2×C8×D71D411yescharacteristic
123C2×C8×D71D411yescharacteristic
124C2×C8×D71D411yescharacteristic
125C2×C8×D71D411yescharacteristic
126#14556087C2311yescharacteristic
127#14556086C2×C411yescharacteristic
128#14556086C2×C411yescharacteristic
129#14556085—21no—
130#14556084—21no—
131C4⋊C4×D71C2×C411yescharacteristic
132C4⋊C4×D71C2×C411yescharacteristic
133C22⋊C4×D71—21no—
134C2×C4×Dic71—21no—
135C2×C4×Dic71C2311yescharacteristic
136C42×D71—21no—
137C42×D71—22no—
138C42×D71—22no—
139#14556064—22no—
140#14556063—22no—
141#14556063—22no—
142C4⋊(C71⋊C8)—21no—
143C4⋊(C71⋊C8)—21no—
144Dic71⋊C8—21no—
145Dic71⋊C8—21no—
146Dic71⋊C8—21no—
147Dic71⋊C8—21no—
148#14556056—22no—
149#14556055—22no—
150#14556054—22no—
151#14556053C2×C411yescharacteristic, complemented
152#14556053C2×C411yescharacteristic, complemented
153#14556052C2×C411yescharacteristic, complemented
154#14556052C2×C411yescharacteristic, complemented
155#14556051C2×C411yescharacteristic, complemented
156#14556051C2×C411yescharacteristic, complemented
157#14556050C2×C411yescharacteristic, complemented
158#14556050C2×C411yescharacteristic, complemented
159#14556049C2×C411yescharacteristic, complemented
160#14556049C2×C411yescharacteristic, complemented
161#14556048C2×C411yescharacteristic, complemented
162#14556048C2×C411yescharacteristic, complemented
163C2×#41×C71C2311yescharacteristic
164#131×C71—22no—
165#131×C71—22no—
166C2×M16×C71—21no—
167C2×M16×C71C2311yescharacteristic
168C2×M16×C71C2311yescharacteristic
169C22×C8×C71—21no—
170C22×C8×C71C2311yescharacteristic
171C22×C8×C71C2311yescharacteristic
172#117×C71C2311yescharacteristic
173C2×C42×C71C2311yescharacteristic
174#108×C71—22no—
175C4⋊C8×C71—21no—
176C4⋊C8×C71—21no—
177#104×C71—22no—
178#103×C71C2×C411yescharacteristic, complemented
179#103×C71C2×C411yescharacteristic, complemented
180#102×C71C2×C411yescharacteristic, complemented
181#102×C71C2×C411yescharacteristic, complemented
182C23×D71—21no—
183C23×D71#4111yescharacteristic
184#11765866—22no—
185#11765866C4⋊C414yes—
186#11765865—21no—
187#11765865—21no—
188#11765865—24no—
189#11765865—24no—
190#11765865C2×D412yes—
191#11765865C2×Q812yes—
192#11765864—24no—
193#11765864—24no—
194#11765864—22no—
195#11765864C4⋊C414yes—
196C2×Dic142—21no—
197C2×Dic142C22×C411yescharacteristic
198Q8×D71—22no—
199Q8×D71C4⋊C414yes—
200C2×D284—21no—
201C2×D284C22×C411yescharacteristic
202C2×C22⋊D71—21no—
203C2×C22⋊D71—21no—
204C2×C22⋊D71—21no—
205D4×D71—24no—
206D4×D71—24no—
207D4×D71—22no—
208D4×D71C4⋊C414yes—
209C22×Dic71—21no—
210C22×Dic71—21no—
211C22×Dic71#4111yescharacteristic
212C2×C4×D71—21no—
213C2×C4×D71—21no—
214C2×C4×D71—21no—
215C2×C4×D71—24no—
216C2×C4×D71—24no—
217C2×C4×D71—24no—
218C2×C4×D71—21no—
219C2×C4×D71—21no—
220C2×C4×D71—42no—
221C2×C4×D71—42no—
222C2×C4×D71C22×C411yescharacteristic
223C2×C4×D71C22×C411yescharacteristic
224C2×C4×D71C2×D412yes—
225C2×C4×D71C2×D412yes—
226C2×C4×D71C2×D411yescharacteristic
227C2×C4×D71C2×D411yescharacteristic
228C2×C4×D71C2×Q812yes—
229C2×C4×D71#4112yes—
230#11765849—24no—
231#11765849—21no—
232#11765849—21no—
233#11765849—21no—
234#11765849C2×D412yes—
235#11765848—24no—
236#11765848—24no—
237#11765848—24no—
238#11765848—42no—
239C2×C71⋊C8—24no—
240C2×C71⋊C8—21no—
241C2×C71⋊C8—21no—
242C2×C71⋊C8—21no—
243C2×C71⋊C8—21no—
244C2×C71⋊C8—21no—
245C2×C71⋊C8—21no—
246C2×C71⋊C8C22×C411yescharacteristic
247C2×C71⋊C8C22×C411yescharacteristic
248C2×C71⋊C8C2×D411yescharacteristic
249C2×C71⋊C8C2×D411yescharacteristic
250C8×D71—24no—
251C8×D71—24no—
252C8×D71—22no—
253C8×D71—22no—
254C8×D71—22no—
255C8×D71—22no—
256C8×D71—22no—
257C8×D71—24no—
258C8×D71—22no—
259C8×D71—22no—
260C8×D71—22no—
261C8×D71—42no—
262C4⋊Dic71C22×C411yescharacteristic
263C4⋊Dic71C22×C411yescharacteristic
264Dic71⋊C4—21no—
265Dic71⋊C4—21no—
266C22⋊Dic71—21no—
267(C2×D71)⋊C4—21no—
268(C2×D71)⋊C4—21no—
269C4×Dic71—21no—
270C4×Dic71—21no—
271C4×Dic71—21no—
272C4×Dic71—21no—
273C4×Dic71—21no—
274C4×Dic71—42no—
275#41×C71—21no—
276#41×C71—21no—
277#41×C71C2×D412yes—
278#41×C71C2×Q812yes—
279C2×Q8×C71C22×C411yescharacteristic
280C2×D4×C71—21no—
281C2×D4×C71C22×C411yescharacteristic
282C22×C4×C71—21no—
283C22×C4×C71—21no—
284C22×C4×C71C2411yescharacteristic
285M16×C71—24no—
286M16×C71—21no—
287M16×C71—21no—
288M16×C71—21no—
289M16×C71C2×D412yes—
290C2×C8×C71—24no—
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×C71C22×C411yescharacteristic
298C2×C8×C71C22×C411yescharacteristic
299C2×C8×C71C2×D411yescharacteristic
300C2×C8×C71C2×D411yescharacteristic
301C4⋊C4×C71C22×C411yescharacteristic
302C4⋊C4×C71C22×C411yescharacteristic
303C22⋊C4×C71—21no—
304C42×C71—21no—
305C42×C71—21no—
306C42×C71—21no—
307C23×C71—21no—
308C23×C71C2×#4111yescharacteristic
309C22×D71—22no—
310C22×D71—22no—
311C22×D71—21no—
312C22×D71—24no—
313C22×D71—42no—
314C22×D71—42no—
315C22×D71C4×D411yescharacteristic
316C22×D71C4×D411yescharacteristic
317C22×D71C22⋊Q812yes—
318C22×D71#12312yes—
319Q8×C71—21no—
320Q8×C71C2×C4⋊C412yes—
321D4×C71—22no—
322D4×C71—22no—
323D4×C71—21no—
324D4×C71C2×C4⋊C412yes—
325C2×C4×C71—21no—
326C2×C4×C71—22no—
327C2×C4×C71—22no—
328C2×C4×C71—22no—
329C2×C4×C71—21no—
330C2×C4×C71—21no—
331C2×C4×C71—41no—
332C2×C4×C71—41no—
333C2×C4×C71C23×C411yescharacteristic
334C2×C4×C71C22×D411yescharacteristic
335C2×C4×C71C22×D411yescharacteristic
336C2×C4×C71C22×D411yescharacteristic
337C2×C4×C71C22×Q811yescharacteristic
338C2×C4×C71C2×#4111yescharacteristic
339C22⋊D71—22no—
340C22⋊D71—22no—
341C22⋊D71—24no—
342C22⋊D71—24no—
343C2×Dic71—21no—
344C2×Dic71—24no—
345C2×Dic71—22no—
346C2×Dic71—21no—
347C2×Dic71—21no—
348C2×Dic71—41no—
349C2×Dic71—41no—
350C2×Dic71C4×D411yescharacteristic
351C2×Dic71C4×D411yescharacteristic
352C2×Dic71C22⋊Q812yes—
353C2×Dic71#12312yes—
354D284—24no—
355D284—21no—
356D284C2×C4⋊C412yes—
357C4×D71—24no—
358C4×D71—22no—
359C4×D71—22no—
360C4×D71—24no—
361C4×D71—48no—
362C4×D71—42no—
363C4×D71—42no—
364C4×D71C2×C4⋊C412yes—
365C4×D71C2×C4⋊C412yes—
366C4×D71C4×D412yes—
367C4×D71C4×D412yes—
368C4×D71#12012yes—
369C4×D71#12012yes—
370C4×D71C22⋊Q812yes—
371C4×D71C22⋊Q812yes—
372Dic142—21no—
373Dic142—24no—
374Dic142C2×C4⋊C412yes—
375C8×C71—21no—
376C8×C71—21no—
377C8×C71—21no—
378C8×C71—22no—
379C8×C71—21no—
380C8×C71—41no—
381C71⋊C8—21no—
382C71⋊C8—21no—
383C71⋊C8—21no—
384C71⋊C8—22no—
385C71⋊C8—21no—
386C71⋊C8—41no—
387C22×C71—21no—
388C22×C71—21no—
389C22×C71—22no—
390C22×C71—41no—
391C22×C71—41no—
392C22×C71C2×C4×D411yescharacteristic
393C22×C71C2×C22⋊Q811yescharacteristic
394C22×C71C2×#12311yescharacteristic
395C2×D71—21no—
396C2×D71—21no—
397C2×D71—24no—
398C2×D71—24no—
399C2×D71—22no—
400C2×D71—41no—
401C2×D71—41no—
402C2×D71—48no—
403C2×D71#38512yes—
404C2×D71#38512yes—
405C2×D71#44312yes—
406C2×D71#44412yes—
407C4×C71—22no—
408C4×C71—42no—
409C4×C71—41no—
410C4×C71—41no—
411C4×C71C22×C4⋊C411yescharacteristic
412C4×C71C2×C4×D411yescharacteristic
413C4×C71C2×#12011yescharacteristic
414C4×C71C2×C22⋊Q811yescharacteristic
415Dic71—22no—
416Dic71—42no—
417Dic71—41no—
418Dic71—41no—
419Dic71#38512yes—
420Dic71#38512yes—
421C2×#1866—711nomaximal, Sylow
422C2×C71—21no—
423C2×C71—21no—
424C2×C71—42no—
425C2×C71C2×#38511yescharacteristic
426C2×C71C2×#44311yescharacteristic
427C2×C71C2×#44411yescharacteristic
428D71—22no—
429D71—42no—
430D71#186614yesdirect product factor
431C22×#131—711no—
432C22×#108—711no—
433C2×#424—711no—
434C22×#104—711no—
435C2×#416—711no—
436#1866—711no—
437#1866—711no—
438#1866—711no—
439#1866—711no—
440#1866—711no—
441#1866—711no—
442#1866—711no—
443#1866D7111yescharacteristic, direct product factor
444C2×#339—711no—
445C2×#336—711no—
446C71C2×#186611yescharacteristic, complemented, Sylow
447C22×#41—711no—
448C2×#131—711no—
449C2×#131—711no—
450C2×#131—711no—
451C2×#131—1421no—
452C2×#131—1421no—
453C2×#131—1424no—
454C2×#131—1424no—
455C2×#131C2×D7111yescharacteristic
456C22×M16—711no—
457C22×M16—711no—
458C22×M16—1421no—
459C23×C8—711no—
460C23×C8—711no—
461C23×C8—1421no—
462C2×#117—711no—
463C22×C42—711no—
464C2×#108—711no—
465C2×#108—711no—
466C2×#108—711no—
467C2×#108—1424no—
468C2×#108C2×D7111yescharacteristic, complemented
469#424—711no—
470#424—711no—
471#424—711no—
472#424—1421no—
473#424—1421no—
474#424C2×D7111yescharacteristic, complemented
475C2×C4⋊C8—1421no—
476C2×C4⋊C8—1421no—
477C2×#104—711no—
478C2×#104—711no—
479C2×#104—711no—
480C2×#104—1424no—
481C2×#104C2×D7111yescharacteristic
482#416—711no—
483#416—711no—
484#416—711no—
485#416—711no—
486#416—711no—
487#416—711no—
488#416—711no—
489#416C2×D7111yescharacteristic
490C2×#103—711no—
491C2×#103—711no—
492C2×#102—711no—
493C2×#102—711no—
494#339—711no—
495#339—711no—
496#339—711no—
497#339C2×D7111yescharacteristic, complemented
498#336—711no—
499#336—711no—
500#336—711no—
501#336C2×D7111yescharacteristic, complemented
502C2×#41—714no—
503C2×#41—714no—
504C2×#41—711no—
505C2×#41—711no—
506C2×#41—711no—
507C2×#41—1421no—
508C2×#41—1421no—
509C2×#41—1422no—
510C2×#41—1422no—
511C2×#41C22×D7111yescharacteristic
512C22×Q8—711no—
513C22×D4—711no—
514C22×D4—1421no—
515C23×C4—711no—
516C23×C4—1421no—
517C23×C4—1421no—
518#131—22no—
519#131—22no—
520#131—1422no—
521#131—1422no—
522#131—1428no—
523#131—1422no—
524#131—1428no—
525#131—1422no—
526#131—1422no—
527#131—1422no—
528C2×M16—21no—
529C2×M16—711no—
530C2×M16—714no—
531C2×M16—711no—
532C2×M16—1421no—
533C2×M16—1421no—
534C2×M16—1421no—
535C2×M16—1422no—
536C2×M16—1422no—
537C2×M16—1421no—
538C2×M16—1422no—
539C2×M16—1428no—
540C2×M16—1421no—
541C2×M16C22×D7111yescharacteristic
542C2×M16C22×D7111yescharacteristic
543C22×C8—21no—
544C22×C8—711no—
545C22×C8—711no—
546C22×C8—711no—
547C22×C8—711no—
548C22×C8—711no—
549C22×C8—711no—
550C22×C8—711no—
551C22×C8—711no—
552C22×C8—711no—
553C22×C8—711no—
554C22×C8—1421no—
555C22×C8—1421no—
556C22×C8—1422no—
557C22×C8—1422no—
558C22×C8—1422no—
559C22×C8—1422no—
560C22×C8—1421no—
561C22×C8—1428no—
562C22×C8—1421no—
563C22×C8—1421no—
564C22×C8C22×D7111yescharacteristic
565C22×C8C22×D7111yescharacteristic
566#117—711no—
567#117—711no—
568#117—711no—
569#117—1421no—
570#117—1421no—
571#117C22×D7111yescharacteristic
572C2×C4⋊C4—711no—
573C2×C4⋊C4—711no—
574C2×C22⋊C4—1421no—
575C2×C42—711no—
576C2×C42—1422no—
577C2×C42—1422no—
578C2×C42—1421no—
579C2×C42—1421no—
580C2×C42C22×D7111yescharacteristic
581#108—22no—
582#108—1422no—
583#108—1422no—
584#108—1422no—
585C4⋊C8—21no—
586C4⋊C8—21no—
587C4⋊C8—1421no—
588C4⋊C8—1421no—
589C4⋊C8—1421no—
590C4⋊C8—1421no—
591C4⋊C8—1421no—
592C4⋊C8—1421no—
593#104—22no—
594#104—1422no—
595#104—1422no—
596#104—1422no—
597#103—711no—
598#103—711no—
599#103—711no—
600#103—711no—
601#103—711no—
602#103—711no—
603#103C4×D7111yescharacteristic, complemented
604#103C4×D7111yescharacteristic, complemented
605#102—711no—
606#102—711no—
607#102—711no—
608#102—711no—
609#102—711no—
610#102—711no—
611#102C4×D7111yescharacteristic, complemented
612#102C4×D7111yescharacteristic, complemented
613C24—711no—
614C24—1421no—
615#41—21no—
616#41—21no—
617#41—714no—
618#41—714no—
619#41—712no—
620#41—712no—
621#41—1424no—
622#41—1424no—
623#41—1424no—
624#41—1424no—
625#41—1422no—
626#41—1422no—
627#41—1421no—
628#41—1421no—
629#41D4×D7112yes—
630#41Q8×D7112yes—
631C2×Q8—714no—
632C2×Q8—711no—
633C2×Q8—1421no—
634C2×Q8—1422no—
635C2×Q8C2×C4×D7111yescharacteristic
636C2×D4—21no—
637C2×D4—714no—
638C2×D4—711no—
639C2×D4—1421no—
640C2×D4—1422no—
641C2×D4—1421no—
642C2×D4—1424no—
643C2×D4—1424no—
644C2×D4—1421no—
645C2×D4—1421no—
646C2×D4C2×C4×D7111yescharacteristic
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—2842no—
650C22×C4—2842no—
651C22×C4—711no—
652C22×C4—711no—
653C22×C4—711no—
654C22×C4—712no—
655C22×C4—712no—
656C22×C4—711no—
657C22×C4—711no—
658C22×C4—712no—
659C22×C4—712no—
660C22×C4—1421no—
661C22×C4—1421no—
662C22×C4—1424no—
663C22×C4—1424no—
664C22×C4—1421no—
665C22×C4—1424no—
666C22×C4—1421no—
667C22×C4—1421no—
668C22×C4—1421no—
669C22×C4—1421no—
670C22×C4C23×D7111yescharacteristic
671M16—24no—
672M16—21no—
673M16—21no—
674M16—21no—
675M16—2842no—
676M16—712no—
677M16—1424no—
678M16—1424no—
679M16—1424no—
680M16—1421no—
681M16—1421no—
682M16—1424no—
683M16—1421no—
684M16D4×D7112yes—
685C2×C8—24no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—2842no—
693C2×C8—711no—
694C2×C8—711no—
695C2×C8—711no—
696C2×C8—711no—
697C2×C8—1422no—
698C2×C8—1422no—
699C2×C8—1422no—
700C2×C8—1422no—
701C2×C8—1422no—
702C2×C8—1422no—
703C2×C8—1422no—
704C2×C8—1422no—
705C2×C8—1424no—
706C2×C8—1424no—
707C2×C8—1424no—
708C2×C8—1421no—
709C2×C8—1424no—
710C2×C8—1421no—
711C2×C8—1421no—
712C2×C8—1421no—
713C2×C8—1421no—
714C2×C8—1421no—
715C2×C8C2×C4×D7111yescharacteristic
716C2×C8C2×C4×D7111yescharacteristic
717C2×C8D4×D7111yescharacteristic
718C2×C8D4×D7111yescharacteristic
719C4⋊C4—711no—
720C4⋊C4—711no—
721C4⋊C4—1421no—
722C4⋊C4—1421no—
723C4⋊C4C2×C4×D7111yescharacteristic
724C4⋊C4C2×C4×D7111yescharacteristic
725C22⋊C4—21no—
726C22⋊C4—1421no—
727C22⋊C4—1421no—
728C22⋊C4—1421no—
729C42—21no—
730C42—21no—
731C42—21no—
732C42—2842no—
733C42—1421no—
734C42—1421no—
735C42—1421no—
736C42—1421no—
737C42—1421no—
738C23—21no—
739C23—2842no—
740C23—2842no—
741C23—711no—
742C23—711no—
743C23—712no—
744C23—712no—
745C23—1424no—
746C23—1422no—
747C23—1422no—
748C23—1421no—
749C23#41×D7111yescharacteristic
750Q8—21no—
751Q8—712no—
752Q8—1424no—
753Q8—1421no—
754Q8C4⋊C4×D7112yes—
755D4—22no—
756D4—22no—
757D4—21no—
758D4—712no—
759D4—1424no—
760D4—1424no—
761D4—1424no—
762D4—1422no—
763D4—1422no—
764D4—1421no—
765D4C4⋊C4×D7112yes—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—2842no—
775C2×C4—2842no—
776C2×C4—2848no—
777C2×C4—2841no—
778C2×C4—2841no—
779C2×C4—711no—
780C2×C4—711no—
781C2×C4—712no—
782C2×C4—712no—
783C2×C4—712no—
784C2×C4—712no—
785C2×C4—712no—
786C2×C4—712no—
787C2×C4—712no—
788C2×C4—712no—
789C2×C4—712no—
790C2×C4—712no—
791C2×C4—1424no—
792C2×C4—1424no—
793C2×C4—1422no—
794C2×C4—1421no—
795C2×C4—1421no—
796C2×C4—1424no—
797C2×C4—1421no—
798C2×C4—1422no—
799C2×C4—1422no—
800C2×C4C22×C4×D7111yescharacteristic
801C2×C4C2×D4×D7111yescharacteristic
802C2×C4C2×D4×D7111yescharacteristic
803C2×C4C2×D4×D7111yescharacteristic
804C2×C4C2×Q8×D7111yescharacteristic
805C2×C4#41×D7111yescharacteristic
806C8—21no—
807C8—21no—
808C8—21no—
809C8—22no—
810C8—21no—
811C8—41no—
812C8—2841no—
813C8—1421no—
814C8—1421no—
815C8—1421no—
816C8—1421no—
817C8—1422no—
818C22—21no—
819C22—21no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—2848no—
824C22—2841no—
825C22—2841no—
826C22—712no—
827C22—712no—
828C22—712no—
829C22—712no—
830C22—1424no—
831C22—1424no—
832C22—1422no—
833C22—1421no—
834C22—1421no—
835C22C4×D4×D7111yescharacteristic
836C22C22⋊Q8×D7111yescharacteristic
837C22#123×D7111yescharacteristic
838C4—22no—
839C4—42no—
840C4—41no—
841C4—41no—
842C4—2842no—
843C4—2841no—
844C4—2841no—
845C4—712no—
846C4—712no—
847C4—1422no—
848C4C2×C4⋊C4×D7111yescharacteristic
849C4C4×D4×D7111yescharacteristic
850C4#120×D7111yescharacteristic
851C4C22⋊Q8×D7111yescharacteristic
852C2—21no—
853C2—21no—
854C2—42no—
855C2—2842no—
856C2—714no—
857C2—1422no—
858C2#385×D7111yescharacteristic
859C2#443×D7111yescharacteristic
860C2#444×D7111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC71×#1866C2
socleC22×C71C2×C4×D4
prime radicalC2×#41×D71C22
cosocleC22×C4×C71C24
hypercenter#1866D71
hypocenterC71C2×#1866
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1866

Complements

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

NH ≅ G/Ntype
2. C2×#108×D71C2semidirect
3. #424×D71C2semidirect
6. #22588618C2semidirect
7. #22588617C2semidirect
8. #22588616C2semidirect
9. #22588615C2semidirect
10. #22588614C2semidirect
11. #22588613C2semidirect
12. #22588612C2semidirect
13. #339×D71C2semidirect
14. #336×D71C2semidirect
15. C71×#1866C2semidirect
32. C2×#14556064C22semidirect
33. C2×#14556063C22semidirect
34. C2×#14556063C22semidirect
36. #17986027C22semidirect
37. #17986026C22semidirect
38. #17986025C22semidirect
49. #17985994C4semidirect
50. #17985994C4semidirect
52. #17985992C4semidirect
53. #17985992C4semidirect
54. #103×D71C4semidirect
55. #103×D71C4semidirect
56. #102×D71C4semidirect
57. #102×D71C4semidirect
58. #17985760C22semidirect
59. #17985759C22semidirect
60. #17985758C22semidirect
61. #17985754C22semidirect
62. #17985753C22semidirect
63. #17985753C22semidirect
65. C2×#108×C71C22semidirect
66. #424×C71C22semidirect
69. #339×C71C22semidirect
70. #336×C71C22semidirect
151. #14556053C2×C4semidirect
152. #14556053C2×C4semidirect
153. #14556052C2×C4semidirect
154. #14556052C2×C4semidirect
155. #14556051C2×C4semidirect
156. #14556051C2×C4semidirect
157. #14556050C2×C4semidirect
158. #14556050C2×C4semidirect
159. #14556049C2×C4semidirect
160. #14556049C2×C4semidirect
161. #14556048C2×C4semidirect
162. #14556048C2×C4semidirect
178. #103×C71C2×C4semidirect
179. #103×C71C2×C4semidirect
180. #102×C71C2×C4semidirect
181. #102×C71C2×C4semidirect
430. D71#1866direct (N × H)
443. #1866D71direct (N × H)
446. C71C2×#1866semidirect
468. C2×#108C2×D71semidirect
474. #424C2×D71semidirect
497. #339C2×D71semidirect
501. #336C2×D71semidirect
603. #103C4×D71semidirect
604. #103C4×D71semidirect
611. #102C4×D71semidirect
612. #102C4×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#131×D712
C2×#108×D712
#424×D712
C2×#104×D712
#416×D712
#225886182
#225886172
#225886162
#225886152
#225886142
#225886132
#225886122
#339×D712
#336×D712
C71×#18662
C2×#186671