Finite Group Databasebeta

← #32016543

Subgroups — #32016543

Order 18176.

894 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986059C211yesmaximal, characteristic, complemented
2#22590783C211yesmaximal, characteristic
3#22588952C211yesmaximal, characteristic, complemented
4#22588945C211yesmaximal, characteristic, complemented
5#22588901C211yesmaximal, characteristic, complemented
6#22588894C211yesmaximal, characteristic, complemented
7#22588632C211yesmaximal, characteristic
8#22588632C211yesmaximal, characteristic
9#22588459C211yesmaximal, characteristic, complemented
10#22588321C211yesmaximal, characteristic, complemented
11#22588320C211yesmaximal, characteristic, complemented
12#22588199C211yesmaximal, characteristic, complemented
13#22588116C211yesmaximal, characteristic, complemented
14C8×C22⋊Dic71C211yesmaximal, characteristic, complemented
15C22×C4⋊C8×C71C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊D71C2211yescharacteristic
17C2×#14556085C2211yescharacteristic
18#17986059—24no—
19C2×C4⋊(C71⋊C8)C2211yescharacteristic
20C2×C4⋊(C71⋊C8)C2211yescharacteristic
21C2×C22⋊(C71⋊C8)C2211yescharacteristic
22C2×C22⋊(C71⋊C8)C2211yescharacteristic
23C2×(C2×D71)⋊C8C2211yescharacteristic
24C2×(C2×D71)⋊C8C2211yescharacteristic
25C2×(C2×D71)⋊C8C2211yescharacteristic
26C2×(C2×D71)⋊C8C2211yescharacteristic
27C2×#14556038C2211yescharacteristic
28C2×#14556038C2211yescharacteristic
29C2×C8×Dic71C2211yescharacteristic
30C2×C8×Dic71C2211yescharacteristic
31#17985890C411yescharacteristic
32#17985890C411yescharacteristic
33#17985883C411yescharacteristic
34#17985883C411yescharacteristic
35#17985878C411yescharacteristic
36#17985878C411yescharacteristic
37#17985872C411yescharacteristic
38#17985872C411yescharacteristic
39C4×Dic71⋊C4C2211yescharacteristic
40C4×(C2×D71)⋊C4C2211yescharacteristic
41C4×C22⋊Dic71C2211yescharacteristic
42#17985845C2211yescharacteristic
43#17985754C2211yescharacteristic
44#17985754C2211yescharacteristic
45#17985753C2211yescharacteristic
46#17985753C2211yescharacteristic
47#17985753C2211yescharacteristic
48#17985753C2211yescharacteristic
49#17985753C2211yescharacteristic
50#17985753C2211yescharacteristic
51#17985753C2211yescharacteristic
52#17985753C2211yescharacteristic
53C23×C8×C71C2211yescharacteristic
54C23×C8×C71C2211yescharacteristic
55C22×C42×C71C2211yescharacteristic
56C2×C4⋊C8×C71—24no—
57C2×C4⋊C8×C71C2211yescharacteristic
58C2×C4⋊C8×C71C2211yescharacteristic
59C2×C4⋊C8×C71C2211yescharacteristic
60C2×C4⋊C8×C71C2211yescharacteristic
61C22×C22⋊D71C2×C411yescharacteristic
62C22×C4×D71C2311yescharacteristic
63C22×C71⋊C8C2311yescharacteristic
64C22×C71⋊C8C2311yescharacteristic
65C22×C71⋊C8C2311yescharacteristic
66C22×C71⋊C8C2311yescharacteristic
67C4×C22⋊D71—22no—
68C4×C22⋊D71—22no—
69#14556085—22no—
70#14556085—22no—
71C2×Dic71⋊C4C2×C411yescharacteristic
72C2×Dic71⋊C4C2×C411yescharacteristic
73C2×Dic71⋊C4C2×C411yescharacteristic
74C2×Dic71⋊C4C2×C411yescharacteristic
75C2×Dic71⋊C4C2×C411yescharacteristic
76C2×C22⋊Dic71C2×C411yescharacteristic
77C2×C22⋊Dic71C2×C411yescharacteristic
78C2×C22⋊Dic71C2×C411yescharacteristic
79C2×(C2×D71)⋊C4C2×C411yescharacteristic
80C2×(C2×D71)⋊C4C2×C411yescharacteristic
81C2×(C2×D71)⋊C4C2×C411yescharacteristic
82C2×(C2×D71)⋊C4C2×C411yescharacteristic
83C2×(C2×D71)⋊C4C2×C411yescharacteristic
84C2×C4×Dic71C2311yescharacteristic
85C2×C4×Dic71C2311yescharacteristic
86C2×C4×Dic71C2311yescharacteristic
87C4⋊(C71⋊C8)—22no—
88C4⋊(C71⋊C8)—22no—
89C22⋊(C71⋊C8)—22no—
90C22⋊(C71⋊C8)—22no—
91(C2×D71)⋊C8—22no—
92(C2×D71)⋊C8—22no—
93(C2×D71)⋊C8—41no—
94(C2×D71)⋊C8—41no—
95#14556038—22no—
96#14556038—41no—
97C8×Dic71—22no—
98C8×Dic71—41no—
99C71⋊#95C2×C411yescharacteristic
100C71⋊#95C2×C411yescharacteristic
101C71⋊#95C2×C411yescharacteristic
102C71⋊#95C2×C411yescharacteristic
103C71⋊#95C2×C411yescharacteristic
104C71⋊#95C2×C411yescharacteristic
105C71⋊#95C2×C411yescharacteristic
106C71⋊#95C2×C411yescharacteristic
107C71⋊#95C2×C411yescharacteristic
108C71⋊#95C2×C411yescharacteristic
109C23×C4×C71C2×C411yescharacteristic
110C23×C4×C71C2×C411yescharacteristic
111C23×C4×C71C2311yescharacteristic
112C22×C8×C71—22no—
113C22×C8×C71—22no—
114C22×C8×C71—22no—
115C22×C8×C71—22no—
116C22×C8×C71—41no—
117C22×C8×C71—41no—
118C22×C8×C71C2311yescharacteristic
119C22×C8×C71C2311yescharacteristic
120C22×C8×C71C2311yescharacteristic
121C22×C8×C71C2311yescharacteristic
122C2×C42×C71—22no—
123C2×C42×C71—22no—
124C2×C42×C71C2×C411yescharacteristic
125C2×C42×C71C2×C411yescharacteristic
126C2×C42×C71C2311yescharacteristic
127C2×C42×C71C2311yescharacteristic
128C4⋊C8×C71—22no—
129C4⋊C8×C71—22no—
130C4⋊C8×C71—22no—
131C4⋊C8×C71D414yescomplemented
132C23×D71C22×C411yescharacteristic
133C2×C22⋊D71—22no—
134C2×C22⋊D71—22no—
135C2×C22⋊D71—22no—
136C22×Dic71C22×C411yescharacteristic
137C22×Dic71C22×C411yescharacteristic
138C22×Dic71C22×C411yescharacteristic
139C22×Dic71C22×C411yescharacteristic
140C22×Dic71C22×C411yescharacteristic
141C22×Dic71C22×C411yescharacteristic
142C22×Dic71C22×C411yescharacteristic
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×C71⋊C8—21no—
150C2×C71⋊C8—21no—
151C2×C71⋊C8—21no—
152C2×C71⋊C8—21no—
153C2×C71⋊C8—21no—
154C2×C71⋊C8—21no—
155C2×C71⋊C8—21no—
156C2×C71⋊C8—21no—
157C2×C71⋊C8—21no—
158C2×C71⋊C8—21no—
159C2×C71⋊C8—21no—
160C2×C71⋊C8—21no—
161Dic71⋊C4—22no—
162Dic71⋊C4—22no—
163Dic71⋊C4—22no—
164Dic71⋊C4—22no—
165Dic71⋊C4—41no—
166C22⋊Dic71—22no—
167C22⋊Dic71—22no—
168C22⋊Dic71—22no—
169(C2×D71)⋊C4—22no—
170(C2×D71)⋊C4—22no—
171(C2×D71)⋊C4—22no—
172(C2×D71)⋊C4—22no—
173(C2×D71)⋊C4—41no—
174C4×Dic71—21no—
175C4×Dic71—21no—
176C4×Dic71—21no—
177C4×Dic71—21no—
178C4×Dic71—21no—
179C4×Dic71—21no—
180C24×C71C22×C411yescharacteristic
181C22×C4×C71—22no—
182C22×C4×C71—22no—
183C22×C4×C71—22no—
184C22×C4×C71—21no—
185C22×C4×C71—21no—
186C22×C4×C71—21no—
187C22×C4×C71—21no—
188C22×C4×C71—22no—
189C22×C4×C71—22no—
190C22×C4×C71—41no—
191C22×C4×C71C22×C411yescharacteristic
192C22×C4×C71C22×C411yescharacteristic
193C22×C4×C71C22×C411yescharacteristic
194C22×C4×C71C22×C411yescharacteristic
195C22×C4×C71C22×C411yescharacteristic
196C22×C4×C71#4112yes—
197C22×C4×C71#4112yes—
198C22×C4×C71C2411yescharacteristic
199C2×C8×C71—21no—
200C2×C8×C71—21no—
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—44no—
210C2×C8×C71—44no—
211C2×C8×C71C2×D412yes—
212C2×C8×C71C2×D412yes—
213C42×C71—22no—
214C42×C71—22no—
215C42×C71—21no—
216C42×C71—21no—
217C42×C71C2×D412yes—
218C42×C71#4112yes—
219C23×C71—21no—
220C23×C71—21no—
221C23×C71—21no—
222C23×C71—21no—
223C23×C71#11712yes—
224C23×C71#13112yes—
225C23×C71#13112yes—
226C23×C71C23×C411yescharacteristic
227C22×D71—21no—
228C22×D71—21no—
229C22×D71—21no—
230C22×D71—21no—
231C22×D71—21no—
232C22×D71—21no—
233C22×D71—21no—
234C2×C4×C71—28no—
235C2×C4×C71—21no—
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—22no—
244C2×C4×C71—22no—
245C2×C4×C71—22no—
246C2×C4×C71—22no—
247C2×C4×C71—21no—
248C2×C4×C71—21no—
249C2×C4×C71—21no—
250C2×C4×C71—44no—
251C2×C4×C71#11712yes—
252C2×C4×C71C4×D412yes—
253C2×C4×C71C4×D412yes—
254C2×C4×C71#13112yes—
255C2×C4×C71C22×D411yescharacteristic
256C2×C4×C71C2×#4111yescharacteristic
257C2×C4×C71C2×#4111yescharacteristic
258C2×C4×C71C2×#4111yescharacteristic
259C2×C4×C71H(5,𝔽2)11yescharacteristic
260C2×C4×C712−1+411yescharacteristic
261C22⋊D71—44no—
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×Dic71—21no—
276C2×Dic71—21no—
277C2×Dic71—21no—
278C2×Dic71—21no—
279C2×Dic71—21no—
280C2×Dic71—21no—
281C2×Dic71—21no—
282C2×Dic71—21no—
283C4×D71—41no—
284C4×D71—41no—
285C4×D71—41no—
286C4×D71—41no—
287C8×C71—22no—
288C8×C71—22no—
289C8×C71—41no—
290C8×C71—41no—
291C71⋊C8—41no—
292C71⋊C8—41no—
293C71⋊C8—41no—
294C71⋊C8—41no—
295C22×C71—22no—
296C22×C71—22no—
297C22×C71—22no—
298C22×C71—22no—
299C22×C71—22no—
300C22×C71—22no—
301C22×C71#43314yescomplemented
302C22×C71C2×#11711yescharacteristic
303C22×C71C2×C4×D411yescharacteristic
304C22×C71#52011yescharacteristic
305C22×C71C2×#13111yescharacteristic
306C22×C71C2×#13111yescharacteristic
307C22×C71C2×#13111yescharacteristic
308C22×C71#56811yescharacteristic
309C2×D71—41no—
310C2×D71—41no—
311C2×D71—41no—
312C2×D71—41no—
313C2×D71—41no—
314C2×D71—41no—
315C2×D71—41no—
316C4×C71—22no—
317C4×C71—22no—
318C4×C71—22no—
319C4×C71—22no—
320C4×C71—41no—
321C4×C71#54611yescharacteristic
322C4×C71#54811yescharacteristic
323C4×C71#55211yescharacteristic
324C4×C71#55311yescharacteristic
325Dic71—41no—
326Dic71—41no—
327Dic71—41no—
328Dic71—41no—
329Dic71—41no—
330Dic71—41no—
331Dic71—41no—
332#22754—711nomaximal, Sylow
333C2×C71—24no—
334C2×C71#235211yescharacteristic
335C2×C71C2×#43311yescharacteristic
336C2×C71#292511yescharacteristic
337C2×C71#292911yescharacteristic
338C2×C71#293311yescharacteristic
339C2×C71#299211yescharacteristic
340C2×C71#299411yescharacteristic
341D71—81no—
342C2×#433—711no—
343C22×C4⋊C8D7111yescharacteristic, complemented
344#2290—711no—
345#1924—711no—
346#1923—711no—
347#1917—711no—
348#1916—711no—
349#1869—711no—
350#1869—711no—
351#1832—711no—
352#1798—711no—
353#1797—711no—
354#1768—711no—
355#1752—711no—
356C8×C22⋊C4—711no—
357C71#2275411yescharacteristic, complemented, Sylow
358C23×C8C2×D7111yescharacteristic
359C23×C8C2×D7111yescharacteristic
360C2×C4×D4—711no—
361C2×#117—711no—
362C22×C42C2×D7111yescharacteristic
363#433—1424no—
364C2×C4⋊C8—24no—
365C2×C4⋊C8—711no—
366C2×C4⋊C8—711no—
367C2×C4⋊C8C2×D7111yescharacteristic
368C2×C4⋊C8C2×D7111yescharacteristic
369C2×C4⋊C8C2×D7111yescharacteristic
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×#97—711no—
378C2×#97—711no—
379C2×C4×C8—711no—
380C2×C4×C8—711no—
381#388—711no—
382#388—711no—
383#387—711no—
384#387—711no—
385#386—711no—
386#386—711no—
387#385—711no—
388#385—711no—
389C4×C4⋊C4—711no—
390C4×C22⋊C4—711no—
391C4×C22⋊C4—711no—
392#376—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—
403C22×D4—711no—
404C23×C4—711no—
405C23×C4C4×D7111yescharacteristic
406C23×C4C4×D7111yescharacteristic
407C23×C4C22×D7111yescharacteristic
408C22×C8—22no—
409C22×C8—22no—
410C22×C8—22no—
411C22×C8—22no—
412C22×C8—41no—
413C22×C8—41no—
414C22×C8—711no—
415C22×C8—711no—
416C22×C8—711no—
417C22×C8—711no—
418C22×C8C22×D7111yescharacteristic
419C22×C8C22×D7111yescharacteristic
420C22×C8C22×D7111yescharacteristic
421C22×C8C22×D7111yescharacteristic
422C4×D4—1422no—
423C4×D4—1422no—
424#117—1422no—
425#117—1422no—
426C2×C4⋊C4—711no—
427C2×C4⋊C4—711no—
428C2×C4⋊C4—711no—
429C2×C4⋊C4—711no—
430C2×C4⋊C4—711no—
431C2×C22⋊C4—711no—
432C2×C22⋊C4—711no—
433C2×C22⋊C4—711no—
434C2×C22⋊C4—711no—
435C2×C22⋊C4—711no—
436C2×C22⋊C4—711no—
437C2×C22⋊C4—711no—
438C2×C22⋊C4—711no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—711no—
442C2×C42—711no—
443C2×C42—711no—
444C2×C42C4×D7111yescharacteristic
445C2×C42C4×D7111yescharacteristic
446C2×C42C22×D7111yescharacteristic
447C2×C42C22×D7111yescharacteristic
448C4⋊C8—22no—
449C4⋊C8—22no—
450C4⋊C8—22no—
451C4⋊C8—1422no—
452C4⋊C8—1422no—
453C4⋊C8C22⋊D7114yescomplemented
454C22⋊C8—2841no—
455C22⋊C8—2841no—
456C22⋊C8—1422no—
457C22⋊C8—1422no—
458C22⋊C8—1422no—
459C22⋊C8—1422no—
460#97—2841no—
461#97—1422no—
462C4×C8—2841no—
463C4×C8—1422no—
464#95—711no—
465#95—711no—
466#95—711no—
467#95—711no—
468#95—711no—
469#95—711no—
470#95—711no—
471#95—711no—
472#95—711no—
473#95—711no—
474C24—711no—
475C24C2×C4×D7111yescharacteristic
476C2×D4—1422no—
477C2×D4—1422no—
478C2×D4—1422no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—41no—
489C22×C4—711no—
490C22×C4—711no—
491C22×C4—711no—
492C22×C4—711no—
493C22×C4—711no—
494C22×C4—711no—
495C22×C4—711no—
496C22×C4—1421no—
497C22×C4—1421no—
498C22×C4—1421no—
499C22×C4—1421no—
500C22×C4—1421no—
501C22×C4—1421no—
502C22×C4C2×C4×D7111yescharacteristic
503C22×C4C2×C4×D7111yescharacteristic
504C22×C4C2×C4×D7111yescharacteristic
505C22×C4C2×C4×D7111yescharacteristic
506C22×C4C2×C4×D7111yescharacteristic
507C22×C4#1176586412yes—
508C22×C4#1176586612yes—
509C22×C4C23×D7111yescharacteristic
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—44no—
521C2×C8—44no—
522C2×C8—1421no—
523C2×C8—1421no—
524C2×C8—1421no—
525C2×C8—1421no—
526C2×C8—1421no—
527C2×C8—1421no—
528C2×C8—1421no—
529C2×C8—1421no—
530C2×C8—1421no—
531C2×C8—1421no—
532C2×C8—1421no—
533C2×C8—1421no—
534C2×C8C2×C22⋊D7112yes—
535C2×C8C2×C22⋊D7112yes—
536C4⋊C4—2841no—
537C4⋊C4—1422no—
538C4⋊C4—1422no—
539C4⋊C4—1422no—
540C4⋊C4—1422no—
541C22⋊C4—2841no—
542C22⋊C4—1422no—
543C22⋊C4—1422no—
544C22⋊C4—1422no—
545C22⋊C4—1422no—
546C22⋊C4—1422no—
547C22⋊C4—1422no—
548C22⋊C4—1422no—
549C42—21no—
550C42—21no—
551C42—22no—
552C42—22no—
553C42—1421no—
554C42—1421no—
555C42—1421no—
556C42—1421no—
557C42—1421no—
558C42—1421no—
559C42C2×C22⋊D7112yes—
560C42#1176586512yes—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—1421no—
566C23—1421no—
567C23—1421no—
568C23—1421no—
569C23—1421no—
570C23—1421no—
571C23—1421no—
572C23#1455608612yes—
573C23#1455613412yes—
574C23#1455613612yes—
575C23C22×C4×D7111yescharacteristic
576D4—2844no—
577C2×C4—28no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—44no—
594C2×C4—2841no—
595C2×C4—2841no—
596C2×C4—2841no—
597C2×C4—2841no—
598C2×C4—1421no—
599C2×C4—1421no—
600C2×C4—1421no—
601C2×C4—1421no—
602C2×C4—1421no—
603C2×C4—1421no—
604C2×C4—1421no—
605C2×C4—1421no—
606C2×C4—1421no—
607C2×C4—1421no—
608C2×C4—1421no—
609C2×C4—1421no—
610C2×C4—1421no—
611C2×C4—1421no—
612C2×C4—1421no—
613C2×C4—1421no—
614C2×C4—1421no—
615C2×C4—1421no—
616C2×C4—1421no—
617C2×C4—1421no—
618C2×C4—1421no—
619C2×C4#1455608612yes—
620C2×C4C4×C22⋊D7112yes—
621C2×C4C4×C22⋊D7112yes—
622C2×C4#1455613412yes—
623C2×C4C22×C22⋊D7111yescharacteristic
624C2×C4C2×#1176586411yescharacteristic
625C2×C4C2×#1176586511yescharacteristic
626C2×C4C2×#1176586611yescharacteristic
627C2×C4#1455617311yescharacteristic
628C2×C4#1455617611yescharacteristic
629C8—22no—
630C8—22no—
631C8—41no—
632C8—41no—
633C8—2841no—
634C8—2841no—
635C8—2841no—
636C8—2841no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—2841no—
644C22—2841no—
645C22—2841no—
646C22—2841no—
647C22—2841no—
648C22—2841no—
649C22—2841no—
650C22#1798605914yescomplemented
651C22C2×#1455608611yescharacteristic
652C22C2×C4×C22⋊D7111yescharacteristic
653C22#1798648011yescharacteristic
654C22C2×#1455613411yescharacteristic
655C22C2×#1455613411yescharacteristic
656C22C2×#1455613611yescharacteristic
657C22#1798676511yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—22no—
662C4—41no—
663C4—2841no—
664C4—2841no—
665C4—2841no—
666C4—2841no—
667C4—2841no—
668C4—2841no—
669C4—2841no—
670C4#1798664311yescharacteristic
671C4#1798666011yescharacteristic
672C4#1798668411yescharacteristic
673C4#1798669711yescharacteristic
674C2—24no—
675C2—5681no—
676C2#2259126511yescharacteristic
677C2C2×#1798605911yescharacteristic
678C2#2259700511yescharacteristic
679C2#2259703411yescharacteristic
680C2#2259706511yescharacteristic
681C2#2259747611yescharacteristic
682C2#2259749611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutator, socleC23×C71C23×C4
FittingC22×C4⋊C8×C71C2
prime radicalC22×C22⋊D71C2×C4
cosocleC22×C4×C71C24
hypercenterC22×C4⋊C8D71
hypocenterC71#22754
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C22×C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#17986059C2semidirect
3. #22588952C2semidirect
4. #22588945C2semidirect
5. #22588901C2semidirect
6. #22588894C2semidirect
9. #22588459C2semidirect
10. #22588321C2semidirect
11. #22588320C2semidirect
12. #22588199C2semidirect
13. #22588116C2semidirect
14. C8×C22⋊Dic71C2semidirect
15. C22×C4⋊C8×C71C2semidirect
131. C4⋊C8×C71D4semidirect
301. C22×C71#433semidirect
343. C22×C4⋊C8D71semidirect
357. C71#22754semidirect
453. C4⋊C8C22⋊D71semidirect
650. C22#17986059semidirect

Maximal subgroups

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

subgroupindex
C2×#179860592
#225907832
#225889522
#225889452
#225889012
#225888942
#225886322
#225884592
#225883212
#225883202
#225881992
#225881162
C8×C22⋊Dic712
C22×C4⋊C8×C712
#2275471