Finite Group Databasebeta

← #32016934

Subgroups — #32016934

Order 18176.

960 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×(C22⋊D71)⋊C4C211yesmaximal, characteristic
2#22588946C211yesmaximal, characteristic, complemented
3#22588944C211yesmaximal, characteristic, complemented
4#22588897C211yesmaximal, characteristic, complemented
5#22588895C211yesmaximal, characteristic, complemented
6#22588632C211yesmaximal, characteristic
7#22588630C211yesmaximal, characteristic
8#22588482C211yesmaximal, characteristic, complemented
9#22588407C211yesmaximal, characteristic, complemented
10#22588318C211yesmaximal, characteristic, complemented
11C22⋊C4×C71⋊C8C211yesmaximal, characteristic, complemented
12C4×(C2×D71)⋊C8C211yesmaximal, characteristic, complemented
13#22588085C211yesmaximal, characteristic, complemented
14C2×#17985753C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C71C211yesmaximal, characteristic, complemented
16C23×C71⋊C8C2211yescharacteristic
17C2×C4×C22⋊D71C2211yescharacteristic
18C2×(C22⋊D71)⋊C4C411yescharacteristic
19C2×(C22⋊D71)⋊C4C411yescharacteristic
20C22×C4×Dic71C2211yescharacteristic
21C2×C42×D71C2211yescharacteristic
22C2×Dic71⋊C8C2211yescharacteristic
23C2×Dic71⋊C8C2211yescharacteristic
24C2×C22⋊(C71⋊C8)C2211yescharacteristic
25C2×(C2×D71)⋊C8C2211yescharacteristic
26C2×(C2×D71)⋊C8C2211yescharacteristic
27C2×(C2×D71)⋊C8C2211yescharacteristic
28C2×(C2×D71)⋊C8C2211yescharacteristic
29C2×C4×C71⋊C8C2211yescharacteristic
30C2×C4×C71⋊C8C2211yescharacteristic
31C4×Dic71⋊C4C2211yescharacteristic
32#17985850C411yescharacteristic
33#17985850C411yescharacteristic
34C22⋊C4×Dic71C411yescharacteristic
35C22⋊C4×Dic71C411yescharacteristic
36C4×(C2×D71)⋊C4C2211yescharacteristic
37#17985846C411yescharacteristic
38#17985846C411yescharacteristic
39C42×Dic71C2211yescharacteristic
40#17985754C2211yescharacteristic
41#17985754C2211yescharacteristic
42#17985753C2211yescharacteristic
43#17985753C2211yescharacteristic
44#17985753C2211yescharacteristic
45#17985753C2211yescharacteristic
46#17985753C2211yescharacteristic
47#17985753C2211yescharacteristic
48#17985753C2211yescharacteristic
49#17985753C2211yescharacteristic
50#17985753C2211yescharacteristic
51#17985753C2211yescharacteristic
52C23×C8×C71C2211yescharacteristic
53C2×C22⋊C8×C71C2211yescharacteristic
54C2×C4×C8×C71C2211yescharacteristic
55C2×C4×C8×C71C2211yescharacteristic
56C4×C22⋊C4×C71C2211yescharacteristic
57#336×C71C2211yescharacteristic
58#336×C71C2211yescharacteristic
59C22×C22⋊D71C2×C411yescharacteristic
60C23×Dic71C2×C411yescharacteristic
61C23×Dic71C2×C411yescharacteristic
62C22×C4×D71C2×C411yescharacteristic
63C22×C4×D71C2×C411yescharacteristic
64C22×C4×D71C2311yescharacteristic
65C22×C71⋊C8—22no—
66C22×C71⋊C8—22no—
67C22×C71⋊C8—41no—
68C22×C71⋊C8C2311yescharacteristic
69C22×C71⋊C8C2311yescharacteristic
70C22×C71⋊C8C2311yescharacteristic
71C22×C71⋊C8C2311yescharacteristic
72C4×C22⋊D71—22no—
73C4×C22⋊D71—22no—
74(C22⋊D71)⋊C4—24no—
75(C22⋊D71)⋊C4C818yescomplemented
76C2×Dic71⋊C4C2×C411yescharacteristic
77C2×Dic71⋊C4C2×C411yescharacteristic
78C2×Dic71⋊C4C2×C411yescharacteristic
79C2×C22⋊Dic71C2×C411yescharacteristic
80C2×(C2×D71)⋊C4C2×C411yescharacteristic
81C2×(C2×D71)⋊C4C2×C411yescharacteristic
82C2×(C2×D71)⋊C4C2×C411yescharacteristic
83C2×C4×Dic71—41no—
84C2×C4×Dic71—41no—
85C2×C4×Dic71C2×C411yescharacteristic
86C2×C4×Dic71C2×C411yescharacteristic
87C2×C4×Dic71C2×C411yescharacteristic
88C2×C4×Dic71C2×C411yescharacteristic
89C2×C4×Dic71C2×C411yescharacteristic
90C2×C4×Dic71C2×C411yescharacteristic
91C2×C4×Dic71C2×C411yescharacteristic
92C2×C4×Dic71C2×C411yescharacteristic
93C2×C4×Dic71C2311yescharacteristic
94C2×C4×Dic71C2311yescharacteristic
95C2×C4×Dic71C2311yescharacteristic
96C42×D71—41no—
97C42×D71—41no—
98Dic71⋊C8—41no—
99Dic71⋊C8—41no—
100C22⋊(C71⋊C8)—22no—
101(C2×D71)⋊C8—22no—
102(C2×D71)⋊C8—22no—
103(C2×D71)⋊C8—41no—
104(C2×D71)⋊C8—41no—
105C4×C71⋊C8—22no—
106C4×C71⋊C8—41no—
107C71⋊#95C2×C411yescharacteristic
108C71⋊#95C2×C411yescharacteristic
109C71⋊#95C2×C411yescharacteristic
110C71⋊#95C2×C411yescharacteristic
111C23×C4×C71C2311yescharacteristic
112C22×C8×C71—22no—
113C22×C8×C71—22no—
114C22×C8×C71—41no—
115C22×C8×C71C2311yescharacteristic
116C22×C8×C71C2311yescharacteristic
117C22×C8×C71C2311yescharacteristic
118C22×C8×C71C2311yescharacteristic
119C2×C22⋊C4×C71C2×C411yescharacteristic
120C2×C22⋊C4×C71C2×C411yescharacteristic
121C2×C42×C71C2311yescharacteristic
122C2×C42×C71C2311yescharacteristic
123C22⋊C8×C71—22no—
124C4×C8×C71—22no—
125C4×C8×C71—41no—
126#95×C71C2×C411yescharacteristic
127#95×C71C2×C411yescharacteristic
128C23×D71C22×C411yescharacteristic
129C2×C22⋊D71—22no—
130C2×C22⋊D71—22no—
131C2×C22⋊D71C2×C814yes—
132C22×Dic71—22no—
133C22×Dic71—22no—
134C22×Dic71—41no—
135C22×Dic71—41no—
136C22×Dic71—41no—
137C22×Dic71C2×C814yes—
138C22×Dic71C22×C411yescharacteristic
139C22×Dic71C22×C411yescharacteristic
140C22×Dic71C22×C411yescharacteristic
141C22×Dic71C22×C411yescharacteristic
142C22×Dic71C22×C411yescharacteristic
143C22×Dic71C22×C411yescharacteristic
144C22×Dic71C22×C411yescharacteristic
145C2×C4×D71—22no—
146C2×C4×D71—21no—
147C2×C4×D71—21no—
148C2×C4×D71—21no—
149C2×C4×D71—21no—
150C2×C4×D71—21no—
151C2×C4×D71—21no—
152C2×C4×D71—22no—
153C2×C4×D71—41no—
154C2×C4×D71—41no—
155C2×C4×D71—41no—
156C2×C4×D71C2×C814yescomplemented
157C2×C71⋊C8—21no—
158C2×C71⋊C8—21no—
159C2×C71⋊C8—21no—
160C2×C71⋊C8—21no—
161C2×C71⋊C8—21no—
162C2×C71⋊C8—21no—
163C2×C71⋊C8—21no—
164C2×C71⋊C8—21no—
165C2×C71⋊C8—21no—
166C2×C71⋊C8—21no—
167C2×C71⋊C8—21no—
168C2×C71⋊C8—44no—
169C2×C71⋊C8#4112yes—
170Dic71⋊C4—22no—
171Dic71⋊C4—22no—
172Dic71⋊C4C2×C814yescomplemented
173C22⋊Dic71—22no—
174(C2×D71)⋊C4—22no—
175(C2×D71)⋊C4—22no—
176(C2×D71)⋊C4C2×C814yescomplemented
177C4×Dic71—22no—
178C4×Dic71—21no—
179C4×Dic71—21no—
180C4×Dic71—21no—
181C4×Dic71—21no—
182C4×Dic71—21no—
183C4×Dic71—21no—
184C4×Dic71—22no—
185C4×Dic71—41no—
186C4×Dic71—41no—
187C4×Dic71—41no—
188C4×Dic71—41no—
189C4×Dic71—41no—
190C4×Dic71C2×C814yescomplemented
191C24×C71C22×C411yescharacteristic
192C22×C4×C71—21no—
193C22×C4×C71—21no—
194C22×C4×C71—21no—
195C22×C4×C71—21no—
196C22×C4×C71C22×C411yescharacteristic
197C22×C4×C71C22×C411yescharacteristic
198C22×C4×C71C22×C411yescharacteristic
199C22×C4×C71C22×C411yescharacteristic
200C22×C4×C71C22×C411yescharacteristic
201C22×C4×C71#4112yes—
202C22×C4×C71#4112yes—
203C22×C4×C71C2411yescharacteristic
204C2×C8×C71—21no—
205C2×C8×C71—21no—
206C2×C8×C71—21no—
207C2×C8×C71—21no—
208C2×C8×C71—21no—
209C2×C8×C71—21no—
210C2×C8×C71—21no—
211C2×C8×C71—21no—
212C2×C8×C71—21no—
213C2×C8×C71—21no—
214C2×C8×C71—21no—
215C2×C8×C71—44no—
216C2×C8×C71#4112yes—
217C22⋊C4×C71C2×C814yes—
218C22⋊C4×C71M1614yes—
219C42×C71—21no—
220C42×C71—21no—
221C42×C71—21no—
222C42×C71—21no—
223C23×C71—21no—
224C23×C71—21no—
225C23×C71—21no—
226C23×C71—21no—
227C23×C71#11712yes—
228C23×C71C22×C812yes—
229C23×C71C2×M1612yes—
230C23×C71C23×C411yescharacteristic
231C22×D71—21no—
232C22×D71—21no—
233C22×D71—21no—
234C22×D71—21no—
235C22×D71—21no—
236C22×D71—21no—
237C22×D71C22×C812yes—
238C2×C4×C71—21no—
239C2×C4×C71—21no—
240C2×C4×C71—21no—
241C2×C4×C71—21no—
242C2×C4×C71—21no—
243C2×C4×C71—21no—
244C2×C4×C71—21no—
245C2×C4×C71—21no—
246C2×C4×C71—21no—
247C2×C4×C71—21no—
248C2×C4×C71—22no—
249C2×C4×C71—22no—
250C2×C4×C71—22no—
251C2×C4×C71—22no—
252C2×C4×C71#11712yes—
253C2×C4×C71C22×C812yes—
254C2×C4×C71C22×C812yes—
255C2×C4×C71C2×M1612yes—
256C2×C4×C71C2×M1612yes—
257C2×C4×C71C2×#4111yescharacteristic
258C2×C4×C71C2×#4111yescharacteristic
259C2×C4×C71C2×#4111yescharacteristic
260C2×C4×C71C2×#4111yescharacteristic
261C2×C4×C71H(5,𝔽2)11yescharacteristic
262C2×C4×C71H(5,𝔽2)11yescharacteristic
263C22⋊D71—28no—
264C2×Dic71—21no—
265C2×Dic71—21no—
266C2×Dic71—21no—
267C2×Dic71—21no—
268C2×Dic71—21no—
269C2×Dic71—21no—
270C2×Dic71—21no—
271C2×Dic71—21no—
272C2×Dic71—21no—
273C2×Dic71—21no—
274C2×Dic71—21no—
275C2×Dic71—21no—
276C2×Dic71—21no—
277C2×Dic71—21no—
278C2×Dic71—21no—
279C2×Dic71—21no—
280C2×Dic71—21no—
281C2×Dic71—44no—
282C2×Dic71—44no—
283C2×Dic71C22×C812yes—
284C2×Dic71C22×C812yes—
285C2×Dic71C22×C812yes—
286C2×Dic71#13112yes—
287C4×D71—44no—
288C4×D71—44no—
289C4×D71—41no—
290C4×D71—41no—
291C4×D71—41no—
292C4×D71—41no—
293C8×C71—22no—
294C8×C71—41no—
295C8×C71—41no—
296C8×C71—41no—
297C71⋊C8—22no—
298C71⋊C8—41no—
299C71⋊C8—41no—
300C71⋊C8—41no—
301C22×C71—22no—
302C22×C71—22no—
303C22×C71—22no—
304C22×C71—22no—
305C22×C71—22no—
306C22×C71—22no—
307C22×C71#43114yes—
308C22×C71C2×#11711yescharacteristic
309C22×C71C4×#4111yescharacteristic
310C22×C71#51811yescharacteristic
311C22×C71C23×C811yescharacteristic
312C22×C71C22×M1611yescharacteristic
313C22×C71C2×#13111yescharacteristic
314C22×C71#56811yescharacteristic
315C2×D71—22no—
316C2×D71—22no—
317C2×D71—22no—
318C2×D71—41no—
319C2×D71—41no—
320C2×D71—41no—
321C2×D71—41no—
322C4×C71—22no—
323C4×C71—22no—
324C4×C71—22no—
325C4×C71—22no—
326C4×C71—22no—
327C4×C71#55111yescharacteristic
328C4×C71#55111yescharacteristic
329C4×C71#55311yescharacteristic
330C4×C71#55311yescharacteristic
331Dic71—22no—
332Dic71—22no—
333Dic71—22no—
334Dic71—22no—
335Dic71—41no—
336Dic71—41no—
337Dic71—41no—
338#22785—711nomaximal, Sylow
339C2×C71—24no—
340C2×C71#235311yescharacteristic
341C2×C71C2×#43111yescharacteristic
342C2×C71#292511yescharacteristic
343C2×C71C8×#4111yescharacteristic
344C2×C71#297011yescharacteristic
345C2×C71#297211yescharacteristic
346C2×C71#297411yescharacteristic
347D71—42no—
348C42×D4—711no—
349#1923—711no—
350#1923—711no—
351#1916—711no—
352#1916—711no—
353#1869—711no—
354#1869—711no—
355#1839—711no—
356#1817—711no—
357#1797—711no—
358C8×C22⋊C4—711no—
359C8×C22⋊C4D7111yescharacteristic, complemented
360C4×C22⋊C8—711no—
361#1744—711no—
362C2×#336—711no—
363C71#2278511yescharacteristic, complemented, Sylow
364C23×C8—711no—
365C23×C8C2×D7111yescharacteristic
366C2×C4×D4—711no—
367C2×C4×D4—711no—
368C2×C4×D4—711no—
369C22×C42—711no—
370C22×C42—711no—
371C2×C4⋊C8—711no—
372C2×C4⋊C8—711no—
373C2×C22⋊C8—711no—
374C2×C22⋊C8—711no—
375C2×C22⋊C8—711no—
376C2×C22⋊C8—711no—
377C2×C22⋊C8—711no—
378C2×C22⋊C8C2×D7111yescharacteristic
379C2×C4×C8—711no—
380C2×C4×C8—711no—
381C2×C4×C8C2×D7111yescharacteristic
382C2×C4×C8C2×D7111yescharacteristic
383C4×C4⋊C4—711no—
384C4×C4⋊C4—711no—
385C4×C4⋊C4—711no—
386C4×C22⋊C4—711no—
387C4×C22⋊C4—711no—
388C4×C22⋊C4—711no—
389C4×C22⋊C4—711no—
390C4×C22⋊C4—711no—
391C4×C22⋊C4C2×D7111yescharacteristic
392C43—711no—
393#336—711no—
394#336—711no—
395#336—711no—
396#336—711no—
397#336—711no—
398#336—711no—
399#336—711no—
400#336—711no—
401#336—711no—
402#336—711no—
403#336—711no—
404#336—711no—
405#336C2×D7111yescharacteristic
406#336C2×D7111yescharacteristic
407C22×D4—711no—
408C23×C4—711no—
409C23×C4—711no—
410C23×C4—711no—
411C23×C4—711no—
412C23×C4—711no—
413C23×C4C22×D7111yescharacteristic
414C22×C8—22no—
415C22×C8—22no—
416C22×C8—41no—
417C22×C8—2841no—
418C22×C8—711no—
419C22×C8—711no—
420C22×C8—711no—
421C22×C8—711no—
422C22×C8—1422no—
423C22×C8—1422no—
424C22×C8C22×D7111yescharacteristic
425C22×C8C22×D7111yescharacteristic
426C22×C8C22×D7111yescharacteristic
427C22×C8C22×D7111yescharacteristic
428C4×D4—718no—
429C4×D4—1422no—
430C4×D4—1422no—
431C4×D4—1424no—
432C2×C4⋊C4—711no—
433C2×C4⋊C4—711no—
434C2×C4⋊C4—711no—
435C2×C22⋊C4—711no—
436C2×C22⋊C4—711no—
437C2×C22⋊C4—711no—
438C2×C22⋊C4—711no—
439C2×C22⋊C4C4×D7111yescharacteristic
440C2×C22⋊C4C4×D7111yescharacteristic
441C2×C42—2841no—
442C2×C42—2841no—
443C2×C42—2841no—
444C2×C42—2841no—
445C2×C42—711no—
446C2×C42—711no—
447C2×C42—711no—
448C2×C42—711no—
449C2×C42—711no—
450C2×C42—711no—
451C2×C42—711no—
452C2×C42—711no—
453C2×C42—711no—
454C2×C42—711no—
455C2×C42—711no—
456C2×C42C22×D7111yescharacteristic
457C2×C42C22×D7111yescharacteristic
458C4⋊C8—2841no—
459C4⋊C8—2841no—
460C22⋊C8—22no—
461C22⋊C8—2841no—
462C22⋊C8—2841no—
463C22⋊C8—1422no—
464C22⋊C8—1422no—
465C22⋊C8—1422no—
466C4×C8—22no—
467C4×C8—41no—
468C4×C8—2841no—
469C4×C8—1422no—
470#95—711no—
471#95—711no—
472#95—711no—
473#95—711no—
474#95C4×D7111yescharacteristic
475#95C4×D7111yescharacteristic
476C24—711no—
477C24C2×C4×D7111yescharacteristic
478C2×D4—714no—
479C2×D4—1422no—
480C2×D4—1422no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—2841no—
486C22×C4—2841no—
487C22×C4—2841no—
488C22×C4—2841no—
489C22×C4—2841no—
490C22×C4—2841no—
491C22×C4—714no—
492C22×C4—714no—
493C22×C4—711no—
494C22×C4—711no—
495C22×C4—711no—
496C22×C4—711no—
497C22×C4—711no—
498C22×C4—711no—
499C22×C4—711no—
500C22×C4—1422no—
501C22×C4—1422no—
502C22×C4—1422no—
503C22×C4—1421no—
504C22×C4—1421no—
505C22×C4—1421no—
506C22×C4—1421no—
507C22×C4—1421no—
508C22×C4—1421no—
509C22×C4—1422no—
510C22×C4C2×C4×D7111yescharacteristic
511C22×C4C2×C4×D7111yescharacteristic
512C22×C4C2×C4×D7111yescharacteristic
513C22×C4C2×C4×D7111yescharacteristic
514C22×C4C2×C4×D7111yescharacteristic
515C22×C4#1176586512yes—
516C22×C4#1176586512yes—
517C22×C4C23×D7111yescharacteristic
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—44no—
530C2×C8—2844no—
531C2×C8—712no—
532C2×C8—1421no—
533C2×C8—1421no—
534C2×C8—1421no—
535C2×C8—1421no—
536C2×C8—1421no—
537C2×C8—1421no—
538C2×C8—1421no—
539C2×C8—1421no—
540C2×C8—1421no—
541C2×C8—1421no—
542C2×C8—1421no—
543C2×C8#1176586412yes—
544C4⋊C4—714no—
545C4⋊C4—1422no—
546C4⋊C4—1422no—
547C22⋊C4—714no—
548C22⋊C4—1422no—
549C22⋊C4—1422no—
550C22⋊C4—1422no—
551C22⋊C4C8×D7114yes—
552C22⋊C4#1176584814yes—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—2841no—
558C42—2841no—
559C42—2841no—
560C42—2841no—
561C42—2841no—
562C42—714no—
563C42—1422no—
564C42—1421no—
565C42—1421no—
566C42—1421no—
567C42—1421no—
568C42—1421no—
569C42—1421no—
570C42—1422no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—712no—
576C23—1421no—
577C23—1421no—
578C23—1421no—
579C23—1421no—
580C23—1421no—
581C23—1421no—
582C23#1455608512yes—
583C23C2×C8×D7112yes—
584C23C2×#1176584812yes—
585C23C22×C4×D7111yescharacteristic
586D4—1428no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—2844no—
602C2×C4—2844no—
603C2×C4—2844no—
604C2×C4—2841no—
605C2×C4—2841no—
606C2×C4—2841no—
607C2×C4—2841no—
608C2×C4—2844no—
609C2×C4—712no—
610C2×C4—712no—
611C2×C4—712no—
612C2×C4—712no—
613C2×C4—1421no—
614C2×C4—1421no—
615C2×C4—1421no—
616C2×C4—1421no—
617C2×C4—1421no—
618C2×C4—1421no—
619C2×C4—1421no—
620C2×C4—1421no—
621C2×C4—1421no—
622C2×C4—1421no—
623C2×C4—1421no—
624C2×C4—1421no—
625C2×C4—1421no—
626C2×C4—1421no—
627C2×C4—1421no—
628C2×C4—1421no—
629C2×C4—1421no—
630C2×C4#1455608512yes—
631C2×C4C2×C8×D7112yes—
632C2×C4C2×C8×D7112yes—
633C2×C4C2×#1176584812yes—
634C2×C4C2×#1176584812yes—
635C2×C4#41×D7111yescharacteristic
636C2×C4C2×#1176586411yescharacteristic
637C2×C4C2×#1176586511yescharacteristic
638C2×C4C2×#1176586511yescharacteristic
639C2×C4#1455617311yescharacteristic
640C2×C4#1455617411yescharacteristic
641C8—22no—
642C8—41no—
643C8—41no—
644C8—41no—
645C8—2841no—
646C8—2841no—
647C8—2841no—
648C8—1422no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—2841no—
656C22—2841no—
657C22—2841no—
658C22—2841no—
659C22—1422no—
660C22—1422no—
661C22—1422no—
662C22#1798605014yes—
663C22C2×#1455608511yescharacteristic
664C22C4×#1176586411yescharacteristic
665C22#1798647111yescharacteristic
666C22C22×C8×D7111yescharacteristic
667C22C22×#1176584811yescharacteristic
668C22#131×D7111yescharacteristic
669C22#1798676411yescharacteristic
670C4—22no—
671C4—22no—
672C4—22no—
673C4—22no—
674C4—22no—
675C4—2841no—
676C4—2841no—
677C4—2841no—
678C4—1422no—
679C4—1422no—
680C4—1422no—
681C4—1422no—
682C4#1798667311yescharacteristic
683C4#1798667511yescharacteristic
684C4#1798669511yescharacteristic
685C4#1798669811yescharacteristic
686C2—24no—
687C2—2842no—
688C2#2259127411yescharacteristic
689C2C2×#1798605011yescharacteristic
690C2#2259700411yescharacteristic
691C2C8×#1176586411yescharacteristic
692C2#2259734811yescharacteristic
693C2#2259736111yescharacteristic
694C2#2259737311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutatorC22×C71C23×C8
FittingC8×C22⋊C4×C71C2
socleC23×C71C23×C4
prime radicalC22×C22⋊D71C2×C4
cosocleC22×C4×C71C24
hypercenterC8×C22⋊C4D71
hypocenterC71#22785
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #22588946C2semidirect
3. #22588944C2semidirect
4. #22588897C2semidirect
5. #22588895C2semidirect
8. #22588482C2semidirect
9. #22588407C2semidirect
10. #22588318C2semidirect
11. C22⋊C4×C71⋊C8C2semidirect
12. C4×(C2×D71)⋊C8C2semidirect
13. #22588085C2semidirect
14. C2×#17985753C2semidirect
15. C8×C22⋊C4×C71C2semidirect
75. (C22⋊D71)⋊C4C8semidirect
156. C2×C4×D71C2×C8semidirect
172. Dic71⋊C4C2×C8semidirect
176. (C2×D71)⋊C4C2×C8semidirect
190. C4×Dic71C2×C8semidirect
359. C8×C22⋊C4D71semidirect
363. C71#22785semidirect

Maximal subgroups

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

subgroupindex
C4×(C22⋊D71)⋊C42
#225889462
#225889442
#225888972
#225888952
#225886322
#225886302
#225884822
#225884072
#225883182
C22⋊C4×C71⋊C82
C4×(C2×D71)⋊C82
#225880852
C2×#179857532
C8×C22⋊C4×C712
#2278571