Finite Group Databasebeta

← #32017513

Subgroups — #32017513

Order 18176.

876 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14556090C211yesmaximal, characteristic
2#22589138C211yesmaximal, characteristic
3#22589137C211yesmaximal, characteristic
4#22588953C211yesmaximal, characteristic, complemented
5#22588951C211yesmaximal, characteristic, complemented
6#22588946C211yesmaximal, characteristic, complemented
7#22588944C211yesmaximal, characteristic, complemented
8#22588456C211yesmaximal, characteristic, complemented
9#22588407C211yesmaximal, characteristic, complemented
10#22588407C211yesmaximal, characteristic, complemented
11#22588215C211yesmaximal, characteristic, complemented
12#22588194C211yesmaximal, characteristic, complemented
13#22588103C211yesmaximal, characteristic, complemented
14C4×(C2×D71)⋊C8C211yesmaximal, characteristic, complemented
15C71×#1771C211yesmaximal, characteristic, complemented
16C2×C4×D284C2211yescharacteristic
17C2×#14556090C411yescharacteristic
18C2×#14556090C411yescharacteristic
19C2×C42×D71C2211yescharacteristic
20C2×C42×D71C2211yescharacteristic
21C2×C4⋊(C71⋊C8)C2211yescharacteristic
22C2×Dic71⋊C8C2211yescharacteristic
23C2×Dic71⋊C8C2211yescharacteristic
24C2×(C2×D71)⋊C8C2211yescharacteristic
25C2×(C2×D71)⋊C8C2211yescharacteristic
26C2×(C2×D71)⋊C8C2211yescharacteristic
27C2×(C2×D71)⋊C8C2211yescharacteristic
28C2×(C2×D71)⋊C8C2211yescharacteristic
29C2×(C2×D71)⋊C8C2211yescharacteristic
30C2×(C2×D71)⋊C8C2211yescharacteristic
31C2×(C2×D71)⋊C8C2211yescharacteristic
32C2×#14556039C2211yescharacteristic
33C2×#14556039C2211yescharacteristic
34C2×C4×C71⋊C8C2211yescharacteristic
35C4⋊C4×Dic71C411yescharacteristic
36C4⋊C4×Dic71C411yescharacteristic
37C4×(C2×D71)⋊C4C2211yescharacteristic
38C4×(C2×D71)⋊C4C2211yescharacteristic
39#17985846C411yescharacteristic
40#17985846C411yescharacteristic
41#17985846C411yescharacteristic
42#17985846C411yescharacteristic
43C42×Dic71C2211yescharacteristic
44#17985754C2211yescharacteristic
45#17985754C2211yescharacteristic
46#17985753C2211yescharacteristic
47#17985753C2211yescharacteristic
48#17985753C2211yescharacteristic
49#17985753C2211yescharacteristic
50#17985753C2211yescharacteristic
51#17985753C2211yescharacteristic
52C2×C4⋊C8×C71C2211yescharacteristic
53C2×#97×C71C2211yescharacteristic
54C2×#97×C71C2211yescharacteristic
55C2×C4×C8×C71C2211yescharacteristic
56C4×C4⋊C4×C71C2211yescharacteristic
57#336×C71C2211yescharacteristic
58#336×C71C2211yescharacteristic
59C22×D284C2×C411yescharacteristic
60C22×C4×D71C2×C411yescharacteristic
61C22×C4×D71C2×C411yescharacteristic
62C22×C4×D71C2×C411yescharacteristic
63C22×C4×D71C2×C411yescharacteristic
64C22×C4×D71C2311yescharacteristic
65C22×C4×D71C2311yescharacteristic
66C22×C71⋊C8C2311yescharacteristic
67C22×C71⋊C8C2311yescharacteristic
68C22×C71⋊C8C2311yescharacteristic
69C22×C71⋊C8C2311yescharacteristic
70C4×D284—22no—
71C4×D284—22no—
72#14556090—24no—
73#14556090—24no—
74C2×C4⋊Dic71C2×C411yescharacteristic
75C2×(C2×D71)⋊C4C2×C411yescharacteristic
76C2×(C2×D71)⋊C4C2×C411yescharacteristic
77C2×(C2×D71)⋊C4C2×C411yescharacteristic
78C2×(C2×D71)⋊C4C2×C411yescharacteristic
79C2×(C2×D71)⋊C4C2×C411yescharacteristic
80C2×(C2×D71)⋊C4C2×C411yescharacteristic
81C2×C4×Dic71C2×C411yescharacteristic
82C2×C4×Dic71C2×C411yescharacteristic
83C2×C4×Dic71C2×C411yescharacteristic
84C2×C4×Dic71C2×C411yescharacteristic
85C2×C4×Dic71C2×C411yescharacteristic
86C2×C4×Dic71C2×C411yescharacteristic
87C2×C4×Dic71C2×C411yescharacteristic
88C2×C4×Dic71C2×C411yescharacteristic
89C2×C4×Dic71C2311yescharacteristic
90C2×C4×Dic71C2311yescharacteristic
91C42×D71—41no—
92C42×D71—41no—
93C42×D71—41no—
94C42×D71—41no—
95C4⋊(C71⋊C8)—22no—
96Dic71⋊C8—22no—
97Dic71⋊C8—22no—
98(C2×D71)⋊C8—22no—
99(C2×D71)⋊C8—22no—
100(C2×D71)⋊C8—22no—
101(C2×D71)⋊C8—22no—
102(C2×D71)⋊C8—41no—
103(C2×D71)⋊C8—41no—
104(C2×D71)⋊C8—41no—
105(C2×D71)⋊C8—41no—
106#14556039—22no—
107#14556039—41no—
108C4×C71⋊C8—41no—
109C71⋊#95C2×C411yescharacteristic
110C71⋊#95C2×C411yescharacteristic
111C71⋊#95C2×C411yescharacteristic
112C71⋊#95C2×C411yescharacteristic
113C22×C8×C71C2311yescharacteristic
114C22×C8×C71C2311yescharacteristic
115C22×C8×C71C2311yescharacteristic
116C22×C8×C71C2311yescharacteristic
117C2×C4⋊C4×C71C2×C411yescharacteristic
118C2×C4⋊C4×C71C2×C411yescharacteristic
119C2×C42×C71C2311yescharacteristic
120C2×C42×C71C2311yescharacteristic
121C2×C42×C71C2311yescharacteristic
122C4⋊C8×C71—22no—
123#97×C71—22no—
124#97×C71—41no—
125C4×C8×C71—41no—
126#95×C71C2×C411yescharacteristic
127#95×C71C2×C411yescharacteristic
128C23×D71C22×C411yescharacteristic
129C23×D71C22×C411yescharacteristic
130C2×D284—22no—
131C2×D284—22no—
132C2×D284—22no—
133C22×Dic71C22×C411yescharacteristic
134C22×Dic71C22×C411yescharacteristic
135C22×Dic71C22×C411yescharacteristic
136C22×Dic71C22×C411yescharacteristic
137C22×Dic71C22×C411yescharacteristic
138C22×Dic71C22×C411yescharacteristic
139C2×C4×D71—22no—
140C2×C4×D71—22no—
141C2×C4×D71—21no—
142C2×C4×D71—21no—
143C2×C4×D71—21no—
144C2×C4×D71—21no—
145C2×C4×D71—21no—
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—21no—
153C2×C4×D71—22no—
154C2×C4×D71—22no—
155C2×C4×D71—22no—
156C2×C4×D71—41no—
157C2×C4×D71—41no—
158C2×C4×D71—41no—
159C2×C4×D71—41no—
160C2×C4×D71—41no—
161C2×C4×D71—41no—
162C2×C4×D71M1614yes—
163C2×C71⋊C8—21no—
164C2×C71⋊C8—21no—
165C2×C71⋊C8—21no—
166C2×C71⋊C8—21no—
167C2×C71⋊C8—21no—
168C2×C71⋊C8—21no—
169C2×C71⋊C8—21no—
170C2×C71⋊C8—21no—
171C2×C71⋊C8—21no—
172C2×C71⋊C8—21no—
173C2×C71⋊C8—21no—
174C2×C71⋊C8#4112yes—
175C4⋊Dic71—22no—
176(C2×D71)⋊C4—22no—
177(C2×D71)⋊C4—22no—
178(C2×D71)⋊C4—22no—
179(C2×D71)⋊C4—22no—
180(C2×D71)⋊C4—22no—
181(C2×D71)⋊C4M1614yes—
182C4×Dic71—21no—
183C4×Dic71—21no—
184C4×Dic71—21no—
185C4×Dic71—21no—
186C4×Dic71—22no—
187C4×Dic71—22no—
188C4×Dic71—22no—
189C4×Dic71—41no—
190C4×Dic71—41no—
191C4×Dic71—41no—
192C4×Dic71—41no—
193C4×Dic71—41no—
194C22×C4×C71C22×C411yescharacteristic
195C22×C4×C71C22×C411yescharacteristic
196C22×C4×C71C22×C411yescharacteristic
197C22×C4×C71C22×C411yescharacteristic
198C22×C4×C71C22×C411yescharacteristic
199C22×C4×C71C22×C411yescharacteristic
200C22×C4×C71C2411yescharacteristic
201C2×C8×C71—21no—
202C2×C8×C71—21no—
203C2×C8×C71—21no—
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#4112yes—
213C4⋊C4×C71—22no—
214C4⋊C4×C71—22no—
215C42×C71—21no—
216C42×C71—21no—
217C42×C71—21no—
218C42×C71—21no—
219C42×C71#4112yes—
220C42×C71#4112yes—
221C23×C71C23×C411yescharacteristic
222C22×D71—21no—
223C22×D71—21no—
224C22×D71—21no—
225C22×D71—21no—
226C22×D71—21no—
227C22×D71—21no—
228C22×D71—21no—
229C22×D71—21no—
230C22×D71—21no—
231C22×D71—21no—
232C22×D71—21no—
233C22×D71—21no—
234C22×D71C2×M1612yes—
235C22×D71C2×M1612yes—
236C2×C4×C71—21no—
237C2×C4×C71—21no—
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—21no—
249C2×C4×C71—21no—
250C2×C4×C71#11712yes—
251C2×C4×C71#11712yes—
252C2×C4×C71C2×M1612yes—
253C2×C4×C71C2×M1612yes—
254C2×C4×C71C2×#4111yescharacteristic
255C2×C4×C71C2×#4111yescharacteristic
256C2×C4×C71C2×#4111yescharacteristic
257C2×C4×C71C2×#4111yescharacteristic
258C2×C4×C71H(5,𝔽2)11yescharacteristic
259C2×C4×C71H(5,𝔽2)11yescharacteristic
260C2×Dic71—21no—
261C2×Dic71—21no—
262C2×Dic71—21no—
263C2×Dic71—21no—
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×Dic71C2×M1612yes—
276C2×Dic71C2×M1612yes—
277C2×Dic71#13112yes—
278D284—28no—
279C4×D71—44no—
280C4×D71—44no—
281C4×D71—44no—
282C4×D71—44no—
283C4×D71—41no—
284C4×D71—41no—
285C4×D71—41no—
286C4×D71—41no—
287C4×D71—41no—
288C4×D71—41no—
289C4×D71—41no—
290C4×D71—41no—
291C8×C71—22no—
292C8×C71—41no—
293C8×C71—41no—
294C8×C71—41no—
295C71⋊C8—22no—
296C71⋊C8—41no—
297C71⋊C8—41no—
298C71⋊C8—41no—
299C22×C71C2×#11711yescharacteristic
300C22×C71C4×#4111yescharacteristic
301C22×C71#51811yescharacteristic
302C22×C71C22×M1611yescharacteristic
303C22×C71C22×M1611yescharacteristic
304C22×C71C2×#13111yescharacteristic
305C22×C71#56811yescharacteristic
306C2×D71—22no—
307C2×D71—22no—
308C2×D71—22no—
309C2×D71—22no—
310C2×D71—22no—
311C2×D71—22no—
312C2×D71—41no—
313C2×D71—41no—
314C2×D71—41no—
315C2×D71—41no—
316C2×D71—41no—
317C2×D71—41no—
318C2×D71—41no—
319C2×D71—41no—
320C4×C71—22no—
321C4×C71—22no—
322C4×C71—22no—
323C4×C71—22no—
324C4×C71—41no—
325C4×C71—41no—
326C4×C71#55311yescharacteristic
327C4×C71#55311yescharacteristic
328C4×C71#55911yescharacteristic
329C4×C71#55911yescharacteristic
330Dic71—22no—
331Dic71—22no—
332Dic71—22no—
333Dic71—41no—
334Dic71—41no—
335Dic71—41no—
336#22837—711nomaximal, Sylow
337C2×C71#235711yescharacteristic
338C2×C71#292011yescharacteristic
339C2×C71#292511yescharacteristic
340C2×C71#296511yescharacteristic
341C2×C71#297011yescharacteristic
342C2×C71#297311yescharacteristic
343C2×C71#297411yescharacteristic
344D71—42no—
345D71—42no—
346C42×D4—711no—
347#1955—711no—
348#1955—711no—
349#1924—711no—
350#1924—711no—
351#1923—711no—
352#1923—711no—
353#1831—711no—
354#1817—711no—
355#1817—711no—
356#1771—711no—
357#1771D7111yescharacteristic, complemented
358#1767—711no—
359#1749—711no—
360C4×C22⋊C8—711no—
361C71#2283711yescharacteristic, complemented, Sylow
362C2×C4×D4—711no—
363C2×C4×D4—711no—
364C2×C4×D4—711no—
365C22×C42—711no—
366C22×C42—711no—
367C2×C4⋊C8—711no—
368C2×C4⋊C8—711no—
369C2×C4⋊C8—711no—
370C2×C4⋊C8C2×D7111yescharacteristic
371C2×C22⋊C8—711no—
372C2×C22⋊C8—711no—
373C2×C22⋊C8—711no—
374C2×C22⋊C8—711no—
375C2×C22⋊C8—711no—
376C2×C22⋊C8—711no—
377C2×C22⋊C8—711no—
378C2×C22⋊C8—711no—
379C2×#97—711no—
380C2×#97—711no—
381C2×#97C2×D7111yescharacteristic
382C2×#97C2×D7111yescharacteristic
383C2×C4×C8—711no—
384C2×C4×C8C2×D7111yescharacteristic
385C4×C4⋊C4—711no—
386C4×C4⋊C4—711no—
387C4×C4⋊C4C2×D7111yescharacteristic
388C4×C22⋊C4—711no—
389C4×C22⋊C4—711no—
390C4×C22⋊C4—711no—
391C4×C22⋊C4—711no—
392C4×C22⋊C4—711no—
393C4×C22⋊C4—711no—
394C43—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#336C2×D7111yescharacteristic
404#336C2×D7111yescharacteristic
405C22×D4—711no—
406C23×C4—711no—
407C23×C4—711no—
408C23×C4—711no—
409C23×C4—711no—
410C23×C4—711no—
411C23×C4—711no—
412C22×C8—711no—
413C22×C8—711no—
414C22×C8—711no—
415C22×C8—711no—
416C22×C8C22×D7111yescharacteristic
417C22×C8C22×D7111yescharacteristic
418C22×C8C22×D7111yescharacteristic
419C22×C8C22×D7111yescharacteristic
420C4×D4—1424no—
421C4×D4—1424no—
422C4×D4—1422no—
423C4×D4—1422no—
424C2×C4⋊C4—711no—
425C2×C4⋊C4C4×D7111yescharacteristic
426C2×C4⋊C4C4×D7111yescharacteristic
427C2×C22⋊C4—711no—
428C2×C22⋊C4—711no—
429C2×C22⋊C4—711no—
430C2×C22⋊C4—711no—
431C2×C22⋊C4—711no—
432C2×C22⋊C4—711no—
433C2×C42—2841no—
434C2×C42—2841no—
435C2×C42—2841no—
436C2×C42—2841no—
437C2×C42—711no—
438C2×C42—711no—
439C2×C42—711no—
440C2×C42—711no—
441C2×C42—711no—
442C2×C42—711no—
443C2×C42—711no—
444C2×C42—711no—
445C2×C42—711no—
446C2×C42—711no—
447C2×C42C22×D7111yescharacteristic
448C2×C42C22×D7111yescharacteristic
449C2×C42C22×D7111yescharacteristic
450C4⋊C8—22no—
451C4⋊C8—1422no—
452C4⋊C8—1422no—
453C4⋊C8—1422no—
454C22⋊C8—2841no—
455C22⋊C8—2841no—
456C22⋊C8—2841no—
457C22⋊C8—2841no—
458C22⋊C8—1422no—
459C22⋊C8—1422no—
460C22⋊C8—1422no—
461C22⋊C8—1422no—
462#97—22no—
463#97—41no—
464#97—2841no—
465#97—1422no—
466C4×C8—41no—
467C4×C8—2841no—
468#95—711no—
469#95—711no—
470#95—711no—
471#95—711no—
472#95C4×D7111yescharacteristic
473#95C4×D7111yescharacteristic
474C24—711no—
475C24—711no—
476C2×D4—1422no—
477C2×D4—1422no—
478C2×D4—1422no—
479C22×C4—2841no—
480C22×C4—2841no—
481C22×C4—2841no—
482C22×C4—2841no—
483C22×C4—2841no—
484C22×C4—2841no—
485C22×C4—714no—
486C22×C4—711no—
487C22×C4—711no—
488C22×C4—711no—
489C22×C4—711no—
490C22×C4—711no—
491C22×C4—711no—
492C22×C4—1422no—
493C22×C4—1422no—
494C22×C4—1422no—
495C22×C4—1422no—
496C22×C4—1421no—
497C22×C4—1421no—
498C22×C4—1421no—
499C22×C4—1421no—
500C22×C4—1421no—
501C22×C4—1421no—
502C22×C4—1421no—
503C22×C4—1421no—
504C22×C4—1421no—
505C22×C4—1421no—
506C22×C4—1421no—
507C22×C4—1421no—
508C22×C4—1422no—
509C22×C4C2×C4×D7111yescharacteristic
510C22×C4C2×C4×D7111yescharacteristic
511C22×C4C2×C4×D7111yescharacteristic
512C22×C4C2×C4×D7111yescharacteristic
513C22×C4C2×C4×D7111yescharacteristic
514C22×C4C2×C4×D7111yescharacteristic
515C22×C4C23×D7111yescharacteristic
516C2×C8—21no—
517C2×C8—21no—
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—712no—
528C2×C8—1421no—
529C2×C8—1421no—
530C2×C8—1421no—
531C2×C8—1421no—
532C2×C8—1421no—
533C2×C8—1421no—
534C2×C8—1421no—
535C2×C8—1421no—
536C2×C8—1421no—
537C2×C8—1421no—
538C2×C8—1421no—
539C2×C8#1176586612yes—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—1422no—
543C22⋊C4—714no—
544C22⋊C4—1422no—
545C22⋊C4—1422no—
546C22⋊C4—1422no—
547C22⋊C4—1422no—
548C22⋊C4—1422no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—2841no—
554C42—2841no—
555C42—2841no—
556C42—2841no—
557C42—2841no—
558C42—1422no—
559C42—1422no—
560C42—1422no—
561C42—1421no—
562C42—1421no—
563C42—1421no—
564C42—1421no—
565C42#1176586512yes—
566C42#1176586512yes—
567C23—712no—
568C23—712no—
569C23—1421no—
570C23—1421no—
571C23—1421no—
572C23—1421no—
573C23—1421no—
574C23—1421no—
575C23—1421no—
576C23—1421no—
577C23—1421no—
578C23—1421no—
579C23—1421no—
580C23—1421no—
581C23C22×C4×D7111yescharacteristic
582D4—1428no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
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—2844no—
598C2×C4—2844no—
599C2×C4—2844no—
600C2×C4—2844no—
601C2×C4—2841no—
602C2×C4—2841no—
603C2×C4—2841no—
604C2×C4—2841no—
605C2×C4—2841no—
606C2×C4—2841no—
607C2×C4—2841no—
608C2×C4—2841no—
609C2×C4—712no—
610C2×C4—712no—
611C2×C4—712no—
612C2×C4—1421no—
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#1455608512yes—
628C2×C4#1455608512yes—
629C2×C4M16×D7112yes—
630C2×C4M16×D7112yes—
631C2×C4#41×D7111yescharacteristic
632C2×C4C2×#1176586511yescharacteristic
633C2×C4C2×#1176586511yescharacteristic
634C2×C4C2×#1176586611yescharacteristic
635C2×C4#1455617311yescharacteristic
636C2×C4#1455617411yescharacteristic
637C8—22no—
638C8—41no—
639C8—41no—
640C8—41no—
641C8—2841no—
642C8—2841no—
643C8—2841no—
644C8—1422no—
645C22—2841no—
646C22—2841no—
647C22—2841no—
648C22—2841no—
649C22—2841no—
650C22—2841no—
651C22—2841no—
652C22—2841no—
653C22—1422no—
654C22—1422no—
655C22—1422no—
656C22—1422no—
657C22—1422no—
658C22—1422no—
659C22C2×#1455608511yescharacteristic
660C22C4×#1176586611yescharacteristic
661C22#1798647111yescharacteristic
662C22C2×M16×D7111yescharacteristic
663C22C2×M16×D7111yescharacteristic
664C22#131×D7111yescharacteristic
665C22#1798676411yescharacteristic
666C4—22no—
667C4—22no—
668C4—22no—
669C4—22no—
670C4—41no—
671C4—41no—
672C4—2841no—
673C4—2841no—
674C4—2841no—
675C4—1422no—
676C4—1422no—
677C4—1422no—
678C4#1798669311yescharacteristic
679C4#1798669711yescharacteristic
680C4#1798673211yescharacteristic
681C4#1798673411yescharacteristic
682C2—2842no—
683C2—2842no—
684C2#2259130911yescharacteristic
685C2#2259697111yescharacteristic
686C2#2259700411yescharacteristic
687C2#2259730511yescharacteristic
688C2#2259735311yescharacteristic
689C2#2259736511yescharacteristic
690C2#2259737011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutator, socleC23×C71C23×C4
FittingC71×#1771C2
prime radicalC22×D284C2×C4
cosocleC22×C4×C71C24
hypercenter#1771D71
hypocenterC71#22837
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
4. #22588953C2semidirect
5. #22588951C2semidirect
6. #22588946C2semidirect
7. #22588944C2semidirect
8. #22588456C2semidirect
9. #22588407C2semidirect
10. #22588407C2semidirect
11. #22588215C2semidirect
12. #22588194C2semidirect
13. #22588103C2semidirect
14. C4×(C2×D71)⋊C8C2semidirect
15. C71×#1771C2semidirect
357. #1771D71semidirect
361. C71#22837semidirect

Maximal subgroups

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

subgroupindex
C4×#145560902
#225891382
#225891372
#225889532
#225889512
#225889462
#225889442
#225884562
#225884072
#225882152
#225881942
#225881032
C4×(C2×D71)⋊C82
C71×#17712
#2283771