Finite Group Databasebeta

← #32009791

Subgroups — #32009791

Order 18176.

1010 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×(C22⋊D71)⋊C8C211yesmaximal, characteristic, complemented
2C2×#17986051C211yesmaximal, characteristic, complemented
3C4×#14556101C211yesmaximal, characteristic
4#22589134C211yesmaximal, characteristic, complemented
5#22589132C211yesmaximal, characteristic, complemented
6#22589132C211yesmaximal, characteristic, complemented
7#22589057C211yesmaximal, characteristic, complemented
8#22588945C211yesmaximal, characteristic, complemented
9#22588631C211yesmaximal, characteristic, complemented
10#22588630C211yesmaximal, characteristic, complemented
11#22588520C211yesmaximal, characteristic, complemented
12#22588519C211yesmaximal, characteristic, complemented
13#22588319C211yesmaximal, characteristic, complemented
14C8×Dic71⋊C4C211yesmaximal, characteristic, complemented
15C71×#1923C211yesmaximal, characteristic, complemented
16C23×C71⋊C8C2211yescharacteristic
17C22×C8×D71C2211yescharacteristic
18C2×#14556101C411yescharacteristic
19C2×C4×D284C2211yescharacteristic
20C2×C4×C22⋊D71C2211yescharacteristic
21C2×C4×C22⋊D71C2211yescharacteristic
22C2×C42×D71C2211yescharacteristic
23(C22⋊D71)⋊C8—24no—
24#17986051—24no—
25C2×C4⋊(C71⋊C8)C2211yescharacteristic
26C2×C4⋊(C71⋊C8)C2211yescharacteristic
27C2×Dic71⋊C8C2211yescharacteristic
28C2×Dic71⋊C8C2211yescharacteristic
29C2×Dic71⋊C8C2211yescharacteristic
30C2×C22⋊(C71⋊C8)C2211yescharacteristic
31C2×(C2×D71)⋊C8C2211yescharacteristic
32C2×(C2×D71)⋊C8C2211yescharacteristic
33C2×(C2×D71)⋊C8C2211yescharacteristic
34C2×(C2×D71)⋊C8C2211yescharacteristic
35C2×(C2×D71)⋊C8C2211yescharacteristic
36C2×(C2×D71)⋊C8C2211yescharacteristic
37C2×(C2×D71)⋊C8C2211yescharacteristic
38C2×C8×Dic71C2211yescharacteristic
39C2×C8×Dic71C2211yescharacteristic
40C2×C8×Dic71C2211yescharacteristic
41#17985899C411yescharacteristic
42#17985896C411yescharacteristic
43#17985892C411yescharacteristic
44#17985888C411yescharacteristic
45#17985877C411yescharacteristic
46#17985875C411yescharacteristic
47#17985858C411yescharacteristic
48C4×Dic71⋊C4C2211yescharacteristic
49C4×(C2×D71)⋊C4C2211yescharacteristic
50#17985754C2211yescharacteristic
51#17985754C2211yescharacteristic
52#17985753C2211yescharacteristic
53#17985753C2211yescharacteristic
54C2×C4⋊C8×C71C2211yescharacteristic
55C2×C22⋊C8×C71C2211yescharacteristic
56C2×C22⋊C8×C71C2211yescharacteristic
57C2×C4×C8×C71C2211yescharacteristic
58C4×C22⋊C4×C71C2211yescharacteristic
59#336×C71C2211yescharacteristic
60#336×C71C2211yescharacteristic
61C22×D284C2×C411yescharacteristic
62C22×C22⋊D71C2×C411yescharacteristic
63C22×C22⋊D71C2×C411yescharacteristic
64C22×C4×D71C2×C411yescharacteristic
65C22×C4×D71C2×C411yescharacteristic
66C22×C4×D71C2311yescharacteristic
67C22×C4×D71C2311yescharacteristic
68C22×C71⋊C8—22no—
69C22×C71⋊C8—41no—
70C22×C71⋊C8—41no—
71C22×C71⋊C8C2311yescharacteristic
72C22×C71⋊C8C2311yescharacteristic
73C22×C71⋊C8C2311yescharacteristic
74C22×C71⋊C8C2311yescharacteristic
75C2×C8×D71—22no—
76C2×C8×D71—41no—
77C2×C8×D71—41no—
78#14556101C818yescomplemented
79C4×D284—41no—
80C4×D284—41no—
81C4×C22⋊D71—22no—
82C4×C22⋊D71—22no—
83C4×C22⋊D71—41no—
84C4×C22⋊D71—41no—
85C2×C4⋊Dic71C2×C411yescharacteristic
86C2×Dic71⋊C4C2×C411yescharacteristic
87C2×Dic71⋊C4C2×C411yescharacteristic
88C2×Dic71⋊C4C2×C411yescharacteristic
89C2×Dic71⋊C4C2×C411yescharacteristic
90C2×C22⋊Dic71C2×C411yescharacteristic
91C2×C22⋊Dic71C2×C411yescharacteristic
92C2×(C2×D71)⋊C4C2×C411yescharacteristic
93C2×(C2×D71)⋊C4C2×C411yescharacteristic
94C2×(C2×D71)⋊C4C2×C411yescharacteristic
95C2×(C2×D71)⋊C4C2×C411yescharacteristic
96C2×(C2×D71)⋊C4C2×C411yescharacteristic
97C2×(C2×D71)⋊C4C2×C411yescharacteristic
98C2×C4×Dic71C2×C411yescharacteristic
99C2×C4×Dic71C2×C411yescharacteristic
100C2×C4×Dic71C2311yescharacteristic
101C2×C4×Dic71C2311yescharacteristic
102C42×D71—22no—
103C42×D71—22no—
104C4⋊(C71⋊C8)—22no—
105C4⋊(C71⋊C8)—41no—
106Dic71⋊C8—22no—
107Dic71⋊C8—22no—
108Dic71⋊C8—41no—
109C22⋊(C71⋊C8)—41no—
110(C2×D71)⋊C8—22no—
111(C2×D71)⋊C8—22no—
112(C2×D71)⋊C8—22no—
113(C2×D71)⋊C8—41no—
114(C2×D71)⋊C8—41no—
115(C2×D71)⋊C8—41no—
116(C2×D71)⋊C8—41no—
117C8×Dic71—22no—
118C8×Dic71—41no—
119C8×Dic71D414yescomplemented
120C71⋊#95C2×C411yescharacteristic
121C71⋊#95C2×C411yescharacteristic
122C71⋊#95C2×C411yescharacteristic
123C71⋊#95C2×C411yescharacteristic
124C23×C4×C71C2311yescharacteristic
125C22×C8×C71C2311yescharacteristic
126C22×C8×C71C2311yescharacteristic
127C22×C8×C71C2311yescharacteristic
128C22×C8×C71C2311yescharacteristic
129C2×C22⋊C4×C71C2×C411yescharacteristic
130C2×C22⋊C4×C71C2×C411yescharacteristic
131C2×C42×C71C2311yescharacteristic
132C2×C42×C71C2311yescharacteristic
133C4⋊C8×C71—22no—
134C22⋊C8×C71—22no—
135C22⋊C8×C71—41no—
136C4×C8×C71—41no—
137#95×C71C2×C411yescharacteristic
138#95×C71C2×C411yescharacteristic
139C23×D71C22×C411yescharacteristic
140C23×D71C22×C411yescharacteristic
141C2×D284—41no—
142C2×D284—41no—
143C2×D284C2×C814yescomplemented
144C2×C22⋊D71—22no—
145C2×C22⋊D71—22no—
146C2×C22⋊D71—41no—
147C2×C22⋊D71—41no—
148C2×C22⋊D71C2×C814yes—
149C2×C22⋊D71C2×C814yescomplemented
150C22×Dic71C22×C411yescharacteristic
151C22×Dic71C22×C411yescharacteristic
152C22×Dic71C22×C411yescharacteristic
153C22×Dic71C22×C411yescharacteristic
154C22×Dic71C22×C411yescharacteristic
155C22×Dic71C22×C411yescharacteristic
156C2×C4×D71—22no—
157C2×C4×D71—22no—
158C2×C4×D71—21no—
159C2×C4×D71—21no—
160C2×C4×D71—21no—
161C2×C4×D71—21no—
162C2×C4×D71—21no—
163C2×C4×D71—21no—
164C2×C4×D71—21no—
165C2×C4×D71—21no—
166C2×C4×D71—21no—
167C2×C4×D71—21no—
168C2×C4×D71—21no—
169C2×C4×D71—21no—
170C2×C4×D71—22no—
171C2×C4×D71—41no—
172C2×C4×D71—41no—
173C2×C4×D71C2×C814yescomplemented
174C2×C71⋊C8—21no—
175C2×C71⋊C8—21no—
176C2×C71⋊C8—21no—
177C2×C71⋊C8—21no—
178C2×C71⋊C8—21no—
179C2×C71⋊C8—21no—
180C2×C71⋊C8—21no—
181C2×C71⋊C8—21no—
182C2×C71⋊C8—21no—
183C2×C71⋊C8—21no—
184C2×C71⋊C8—21no—
185C2×C71⋊C8—44no—
186C2×C71⋊C8C2×D412yes—
187C8×D71—44no—
188C4⋊Dic71—41no—
189Dic71⋊C4—22no—
190Dic71⋊C4—22no—
191Dic71⋊C4—41no—
192Dic71⋊C4C2×C814yescomplemented
193C22⋊Dic71—22no—
194C22⋊Dic71—41no—
195(C2×D71)⋊C4—22no—
196(C2×D71)⋊C4—41no—
197(C2×D71)⋊C4—41no—
198(C2×D71)⋊C4—41no—
199(C2×D71)⋊C4—41no—
200(C2×D71)⋊C4C2×C814yescomplemented
201C4×Dic71—21no—
202C4×Dic71—21no—
203C4×Dic71—22no—
204C4×Dic71—22no—
205C4×Dic71C2×D412yes—
206C4×Dic71#4112yes—
207C24×C71C22×C411yescharacteristic
208C22×C4×C71—21no—
209C22×C4×C71—21no—
210C22×C4×C71—21no—
211C22×C4×C71—21no—
212C22×C4×C71—21no—
213C22×C4×C71—21no—
214C22×C4×C71C22×C411yescharacteristic
215C22×C4×C71C22×C411yescharacteristic
216C22×C4×C71C22×C411yescharacteristic
217C22×C4×C71C22×C411yescharacteristic
218C22×C4×C71C22×C411yescharacteristic
219C22×C4×C71C2411yescharacteristic
220C2×C8×C71—21no—
221C2×C8×C71—21no—
222C2×C8×C71—21no—
223C2×C8×C71—21no—
224C2×C8×C71—21no—
225C2×C8×C71—21no—
226C2×C8×C71—21no—
227C2×C8×C71—21no—
228C2×C8×C71—21no—
229C2×C8×C71—21no—
230C2×C8×C71—21no—
231C2×C8×C71C2×D412yes—
232C22⋊C4×C71—41no—
233C22⋊C4×C71C2×C814yescomplemented
234C42×C71—21no—
235C42×C71—21no—
236C42×C71—21no—
237C42×C71—21no—
238C23×C71—21no—
239C23×C71—21no—
240C23×C71—21no—
241C23×C71—21no—
242C23×C71—21no—
243C23×C71—21no—
244C23×C71C22×C812yes—
245C23×C71C23×C411yescharacteristic
246C22×D71—21no—
247C22×D71—21no—
248C22×D71—21no—
249C22×D71—21no—
250C22×D71—21no—
251C22×D71—21no—
252C22×D71—21no—
253C22×D71—21no—
254C22×D71—21no—
255C22×D71—21no—
256C22×D71—21no—
257C22×D71—21no—
258C22×D71C22×C812yes—
259C22×D71C22×C812yes—
260C2×C4×C71—21no—
261C2×C4×C71—21no—
262C2×C4×C71—21no—
263C2×C4×C71—21no—
264C2×C4×C71—21no—
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—41no—
274C2×C4×C71—41no—
275C2×C4×C71—41no—
276C2×C4×C71—41no—
277C2×C4×C71C22×C812yes—
278C2×C4×C71C22×C812yes—
279C2×C4×C71C22×D411yescharacteristic
280C2×C4×C71C2×#4111yescharacteristic
281C2×C4×C71H(5,𝔽2)11yescharacteristic
282C2×C4×C71H(5,𝔽2)11yescharacteristic
283C2×C4×C71H(5,𝔽2)11yescharacteristic
284C2×C4×C712−1+411yescharacteristic
285C22⋊D71—28no—
286C22⋊D71—44no—
287C2×Dic71—21no—
288C2×Dic71—21no—
289C2×Dic71—21no—
290C2×Dic71—21no—
291C2×Dic71—21no—
292C2×Dic71—21no—
293C2×Dic71—21no—
294C2×Dic71—21no—
295C2×Dic71—21no—
296C2×Dic71—21no—
297C2×Dic71—21no—
298C2×Dic71—21no—
299C2×Dic71—21no—
300C2×Dic71C4×D412yes—
301C2×Dic71C4×D412yes—
302C2×Dic71C22×C812yes—
303C2×Dic71C22×C812yes—
304C2×Dic71#13112yes—
305D284—44no—
306C4×D71—28no—
307C4×D71—44no—
308C4×D71—41no—
309C4×D71—41no—
310C4×D71—41no—
311C4×D71—41no—
312C4×D71—41no—
313C4×D71—41no—
314C4×D71—41no—
315C4×D71—41no—
316C8×C71—22no—
317C8×C71—41no—
318C8×C71—41no—
319C8×C71—41no—
320C71⋊C8—22no—
321C71⋊C8—41no—
322C71⋊C8—41no—
323C71⋊C8—41no—
324C22×C71—22no—
325C22×C71—22no—
326C22×C71—22no—
327C22×C71—41no—
328C22×C71—41no—
329C22×C71—41no—
330C22×C71—41no—
331C22×C71C2×C4×D411yescharacteristic
332C22×C71#51811yescharacteristic
333C22×C71#52011yescharacteristic
334C22×C71C23×C811yescharacteristic
335C22×C71C2×#13111yescharacteristic
336C22×C71#56811yescharacteristic
337C22×C71#56811yescharacteristic
338C2×D71—22no—
339C2×D71—22no—
340C2×D71—22no—
341C2×D71—22no—
342C2×D71—22no—
343C2×D71—22no—
344C2×D71—41no—
345C2×D71—41no—
346C2×D71—41no—
347C2×D71—41no—
348C2×D71—41no—
349C2×D71—41no—
350C2×D71—41no—
351C2×D71—41no—
352C4×C71—22no—
353C4×C71—22no—
354C4×C71—41no—
355C4×C71—41no—
356C4×C71—41no—
357C4×C71#53511yescharacteristic
358C4×C71#53711yescharacteristic
359C4×C71#54011yescharacteristic
360C4×C71#54211yescharacteristic
361Dic71—22no—
362Dic71—22no—
363Dic71—41no—
364Dic71—41no—
365Dic71—41no—
366Dic71C8×D414yes—
367#22133—711nomaximal, Sylow
368C2×C71—42no—
369C2×C71#232411yescharacteristic
370C2×C71C2×C8×D411yescharacteristic
371C2×C71#293011yescharacteristic
372C2×C71#297211yescharacteristic
373C2×C71#298111yescharacteristic
374C2×C71#298811yescharacteristic
375C2×C71#299311yescharacteristic
376D71—42no—
377D71—42no—
378C2×C8×D4—711no—
379C2×#431—711no—
380C4×#121—711no—
381#1954—711no—
382#1954—711no—
383#1954—711no—
384#1939—711no—
385#1923—711no—
386#1923D7111yescharacteristic, complemented
387#1869—711no—
388#1869—711no—
389#1850—711no—
390#1850—711no—
391#1797—711no—
392C8×C4⋊C4—711no—
393C71#2213311yescharacteristic, complemented, Sylow
394C23×C8—711no—
395C23×C8—711no—
396C2×#121—711no—
397C2×C4×D4—711no—
398C2×C4×D4—711no—
399C2×C4×D4—711no—
400C22×C42—711no—
401C8×D4—1424no—
402#431—1424no—
403C2×C4⋊C8—711no—
404C2×C4⋊C8—711no—
405C2×C4⋊C8—711no—
406C2×C4⋊C8—711no—
407C2×C4⋊C8—711no—
408C2×C4⋊C8C2×D7111yescharacteristic
409C2×C22⋊C8—711no—
410C2×C22⋊C8—711no—
411C2×C22⋊C8—711no—
412C2×C22⋊C8—711no—
413C2×C22⋊C8—711no—
414C2×C22⋊C8—711no—
415C2×C22⋊C8—711no—
416C2×C22⋊C8—711no—
417C2×C22⋊C8C2×D7111yescharacteristic
418C2×C22⋊C8C2×D7111yescharacteristic
419C2×C4×C8—711no—
420C2×C4×C8—711no—
421C2×C4×C8—711no—
422C2×C4×C8C2×D7111yescharacteristic
423#390—711no—
424#389—711no—
425#388—711no—
426#388—711no—
427#386—711no—
428#386—711no—
429#380—711no—
430C4×C4⋊C4—711no—
431C4×C22⋊C4—711no—
432C4×C22⋊C4C2×D7111yescharacteristic
433#336—711no—
434#336—711no—
435#336—711no—
436#336—711no—
437#336C2×D7111yescharacteristic
438#336C2×D7111yescharacteristic
439C22×D4—711no—
440C22×D4—711no—
441C22×D4—711no—
442C23×C4—711no—
443C23×C4—711no—
444C23×C4—711no—
445C23×C4—711no—
446C23×C4C22×D7111yescharacteristic
447C22×C8—2841no—
448C22×C8—2841no—
449C22×C8—2841no—
450C22×C8—2841no—
451C22×C8—711no—
452C22×C8—711no—
453C22×C8—711no—
454C22×C8—711no—
455C22×C8—1422no—
456C22×C8—1422no—
457C22×C8C22×D7111yescharacteristic
458C22×C8C22×D7111yescharacteristic
459C22×C8C22×D7111yescharacteristic
460C22×C8C22×D7111yescharacteristic
461#121—718no—
462C4×D4—2841no—
463C4×D4—2841no—
464C4×D4—2841no—
465C4×D4—2841no—
466C4×D4—1422no—
467C4×D4—1422no—
468C2×C4⋊C4—711no—
469C2×C4⋊C4—711no—
470C2×C4⋊C4—711no—
471C2×C4⋊C4—711no—
472C2×C4⋊C4—711no—
473C2×C22⋊C4—711no—
474C2×C22⋊C4—711no—
475C2×C22⋊C4—711no—
476C2×C22⋊C4—711no—
477C2×C22⋊C4—711no—
478C2×C22⋊C4—711no—
479C2×C22⋊C4—711no—
480C2×C22⋊C4—711no—
481C2×C22⋊C4C4×D7111yescharacteristic
482C2×C22⋊C4C4×D7111yescharacteristic
483C2×C42—711no—
484C2×C42—711no—
485C2×C42—711no—
486C2×C42—711no—
487C2×C42—1422no—
488C2×C42—1422no—
489C2×C42C22×D7111yescharacteristic
490C2×C42C22×D7111yescharacteristic
491C4⋊C8—22no—
492C4⋊C8—2841no—
493C4⋊C8—2841no—
494C4⋊C8—1422no—
495C4⋊C8—1422no—
496C4⋊C8—1422no—
497C22⋊C8—22no—
498C22⋊C8—41no—
499C22⋊C8—2841no—
500C22⋊C8—2841no—
501C22⋊C8—2841no—
502C22⋊C8—2841no—
503C22⋊C8—2841no—
504C22⋊C8—1422no—
505C22⋊C8—1422no—
506C22⋊C8—1422no—
507C4×C8—41no—
508C4×C8—2841no—
509C4×C8—714no—
510C4×C8—1422no—
511#95—711no—
512#95—711no—
513#95—711no—
514#95—711no—
515#95C4×D7111yescharacteristic
516#95C4×D7111yescharacteristic
517C24—711no—
518C24—711no—
519C24C2×C4×D7111yescharacteristic
520C2×D4—2841no—
521C2×D4—2841no—
522C2×D4—2841no—
523C2×D4—2841no—
524C2×D4—714no—
525C2×D4—714no—
526C2×D4—714no—
527C2×D4—1422no—
528C2×D4—1422no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—2841no—
536C22×C4—2841no—
537C22×C4—711no—
538C22×C4—711no—
539C22×C4—711no—
540C22×C4—714no—
541C22×C4—711no—
542C22×C4—711no—
543C22×C4—711no—
544C22×C4—1422no—
545C22×C4—1422no—
546C22×C4—1422no—
547C22×C4—1421no—
548C22×C4—1421no—
549C22×C4—1421no—
550C22×C4—1421no—
551C22×C4—1421no—
552C22×C4—1421no—
553C22×C4—1421no—
554C22×C4—1421no—
555C22×C4—1421no—
556C22×C4—1421no—
557C22×C4—1421no—
558C22×C4—1421no—
559C22×C4C2×C4×D7111yescharacteristic
560C22×C4C2×C4×D7111yescharacteristic
561C22×C4C2×C4×D7111yescharacteristic
562C22×C4C2×C4×D7111yescharacteristic
563C22×C4C2×C4×D7111yescharacteristic
564C22×C4C23×D7111yescharacteristic
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—2844no—
577C2×C8—2844no—
578C2×C8—712no—
579C2×C8—1421no—
580C2×C8—1421no—
581C2×C8—1421no—
582C2×C8—1421no—
583C2×C8—1421no—
584C2×C8—1421no—
585C2×C8—1421no—
586C2×C8—1421no—
587C2×C8—1421no—
588C2×C8—1421no—
589C2×C8—1421no—
590C2×C8D4×D7112yes—
591C4⋊C4—2841no—
592C4⋊C4—2841no—
593C4⋊C4—714no—
594C4⋊C4—1422no—
595C4⋊C4—1422no—
596C22⋊C4—41no—
597C22⋊C4—2841no—
598C22⋊C4—2841no—
599C22⋊C4—2841no—
600C22⋊C4—2841no—
601C22⋊C4—2841no—
602C22⋊C4—714no—
603C22⋊C4—1422no—
604C22⋊C4—1422no—
605C22⋊C4C8×D7114yescomplemented
606C42—21no—
607C42—21no—
608C42—21no—
609C42—21no—
610C42—712no—
611C42—712no—
612C42—1422no—
613C42—1422no—
614C42—1421no—
615C42—1421no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—712no—
623C23—712no—
624C23—1421no—
625C23—1421no—
626C23—1421no—
627C23—1421no—
628C23—1421no—
629C23—1421no—
630C23—1421no—
631C23—1421no—
632C23—1421no—
633C23—1421no—
634C23—1421no—
635C23—1421no—
636C23C2×C8×D7112yes—
637C23C22×C4×D7111yescharacteristic
638D4—2844no—
639D4—2844no—
640D4—1428no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—2844no—
659C2×C4—2841no—
660C2×C4—2841no—
661C2×C4—2841no—
662C2×C4—2841no—
663C2×C4—2841no—
664C2×C4—2841no—
665C2×C4—2841no—
666C2×C4—2841no—
667C2×C4—712no—
668C2×C4—712no—
669C2×C4—712no—
670C2×C4—712no—
671C2×C4—712no—
672C2×C4—1428no—
673C2×C4—1421no—
674C2×C4—1421no—
675C2×C4—1421no—
676C2×C4—1421no—
677C2×C4—1421no—
678C2×C4—1421no—
679C2×C4—1421no—
680C2×C4—1421no—
681C2×C4—1421no—
682C2×C4—1421no—
683C2×C4—1421no—
684C2×C4—1421no—
685C2×C4—1421no—
686C2×C4C2×C8×D7112yes—
687C2×C4C2×C8×D7112yes—
688C2×C4C2×D4×D7111yescharacteristic
689C2×C4#41×D7111yescharacteristic
690C2×C4#1455617311yescharacteristic
691C2×C4#1455617411yescharacteristic
692C2×C4#1455617411yescharacteristic
693C2×C4#1455617511yescharacteristic
694C8—22no—
695C8—41no—
696C8—41no—
697C8—41no—
698C8—2841no—
699C8—2841no—
700C8—2841no—
701C8—1422no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—2841no—
710C22—2841no—
711C22—2841no—
712C22—2841no—
713C22—2841no—
714C22—2841no—
715C22—2841no—
716C22—2841no—
717C22—1422no—
718C22—1422no—
719C22—1422no—
720C22—1422no—
721C22—1422no—
722C22—1422no—
723C22C4×D4×D7111yescharacteristic
724C22#1798647111yescharacteristic
725C22#1798647911yescharacteristic
726C22C22×C8×D7111yescharacteristic
727C22#131×D7111yescharacteristic
728C22#1798676411yescharacteristic
729C22#1798676511yescharacteristic
730C4—22no—
731C4—22no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—2841no—
736C4—2841no—
737C4—2841no—
738C4—714no—
739C4—1422no—
740C4—1422no—
741C4#1798656711yescharacteristic
742C4#1798657611yescharacteristic
743C4#1798660111yescharacteristic
744C4#1798661511yescharacteristic
745C2—42no—
746C2—2842no—
747C2—2842no—
748C2#2259102811yescharacteristic
749C2C8×D4×D7111yescharacteristic
750C2#2259704011yescharacteristic
751C2#2259736111yescharacteristic
752C2#2259741211yescharacteristic
753C2#2259744811yescharacteristic
754C2#2259748311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutatorC22×C71C23×C8
FittingC71×#1923C2
socleC23×C71C23×C4
prime radicalC2×#14556101C4
cosocleC22×C4×C71C24
hypercenter#1923D71
hypocenterC71#22133
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. C2×(C22⋊D71)⋊C8C2semidirect
2. C2×#17986051C2semidirect
4. #22589134C2semidirect
5. #22589132C2semidirect
6. #22589132C2semidirect
7. #22589057C2semidirect
8. #22588945C2semidirect
9. #22588631C2semidirect
10. #22588630C2semidirect
11. #22588520C2semidirect
12. #22588519C2semidirect
13. #22588319C2semidirect
14. C8×Dic71⋊C4C2semidirect
15. C71×#1923C2semidirect
78. #14556101C8semidirect
119. C8×Dic71D4semidirect
143. C2×D284C2×C8semidirect
149. C2×C22⋊D71C2×C8semidirect
173. C2×C4×D71C2×C8semidirect
192. Dic71⋊C4C2×C8semidirect
200. (C2×D71)⋊C4C2×C8semidirect
233. C22⋊C4×C71C2×C8semidirect
386. #1923D71semidirect
393. C71#22133semidirect
605. C22⋊C4C8×D71semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D71)⋊C82
C2×#179860512
C4×#145561012
#225891342
#225891322
#225890572
#225889452
#225886312
#225886302
#225885202
#225885192
#225883192
C8×Dic71⋊C42
C71×#19232
#2213371