Finite Group Databasebeta

← #32016082

Subgroups — #32016082

Order 18176.

1054 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×(C22⋊D71)⋊C8C211yesmaximal, characteristic
2C4⋊C4×C22⋊D71C211yesmaximal, characteristic
3#22591236C211yesmaximal, characteristic
4#22589097C211yesmaximal, characteristic, complemented
5#22589095C211yesmaximal, characteristic, complemented
6#22588530C211yesmaximal, characteristic, complemented
7#22588529C211yesmaximal, characteristic, complemented
8#22588526C211yesmaximal, characteristic, complemented
9#22588466C211yesmaximal, characteristic, complemented
10#22588367C211yesmaximal, characteristic, complemented
11#22588366C211yesmaximal, characteristic, complemented
12#107×Dic71C211yesmaximal, characteristic, complemented
13C2×#17985761C211yesmaximal, characteristic, complemented
14#340×D71C211yesmaximal, characteristic, complemented
15C71×#1852C211yesmaximal, characteristic, complemented
16C23×C71⋊C8C2211yescharacteristic
17C22×C8×D71C2211yescharacteristic
18C2×C4×C22⋊D71—21no—
19C2×C4×C22⋊D71C2211yescharacteristic
20C2×(C22⋊D71)⋊C4—21no—
21C22×C4⋊Dic71C2211yescharacteristic
22C2×C4⋊C4×D71C2211yescharacteristic
23C2×C4⋊C4×D71C2211yescharacteristic
24(C22⋊D71)⋊C8C418yescomplemented
25C2×#14556062C2211yescharacteristic
26C2×#14556062C2211yescharacteristic
27C2×#14556061C2211yescharacteristic
28C2×#14556061C2211yescharacteristic
29C2×Dic71⋊C8C2211yescharacteristic
30C2×(C2×D71)⋊C8C2211yescharacteristic
31C2×C8×Dic71C2211yescharacteristic
32#17985896—21no—
33#17985894—21no—
34#17985873—21no—
35#17985872—21no—
36#17985871—21no—
37#17985870—21no—
38#17985868C2211yescharacteristic
39#17985868C2211yescharacteristic
40#17985859C2211yescharacteristic
41#17985856C2211yescharacteristic
42#17985856C2211yescharacteristic
43C4⋊C4×Dic71C2211yescharacteristic
44C4⋊C4×Dic71C2211yescharacteristic
45#17985762C2211yescharacteristic
46#17985762C2211yescharacteristic
47#17985761C2211yescharacteristic
48#17985761C2211yescharacteristic
49#17985761C2211yescharacteristic
50#17985761C2211yescharacteristic
51#17985761C2211yescharacteristic
52#17985761C2211yescharacteristic
53C22×C4⋊C4×C71C2211yescharacteristic
54C2×#107×C71C2211yescharacteristic
55C2×#107×C71C2211yescharacteristic
56C2×C22⋊C8×C71C2211yescharacteristic
57#380×C71C2211yescharacteristic
58#340×C71C2211yescharacteristic
59#340×C71C2211yescharacteristic
60C22×C22⋊D71D411yescharacteristic
61C23×Dic71—21no—
62C22×C4×D71—21no—
63C22×C4×D71—21no—
64C22×C4×D71C2311yescharacteristic
65C22×C71⋊C8—41no—
66C22×C71⋊C8—41no—
67C22×C71⋊C8C2×C414yescomplemented
68C22×C71⋊C8C2311yescharacteristic
69C22×C71⋊C8C2311yescharacteristic
70C2×C8×D71—41no—
71C2×C8×D71—41no—
72C2×C8×D71C2×C414yescomplemented
73C4×C22⋊D71—44no—
74C4×C22⋊D71C2×C414yes—
75C4×C22⋊D71Q814yes—
76(C22⋊D71)⋊C4—44no—
77C2×C4⋊Dic71—22no—
78C2×C4⋊Dic71—21no—
79C2×C4⋊Dic71—41no—
80C2×C4⋊Dic71C2311yescharacteristic
81C2×C4⋊Dic71C2311yescharacteristic
82C2×C4⋊Dic71C2311yescharacteristic
83C2×C4⋊Dic71C2311yescharacteristic
84C2×Dic71⋊C4—21no—
85C2×Dic71⋊C4—21no—
86C2×Dic71⋊C4—21no—
87C2×Dic71⋊C4—21no—
88C2×Dic71⋊C4—21no—
89C2×Dic71⋊C4—21no—
90C2×Dic71⋊C4D411yescharacteristic
91C4⋊C4×D71—22no—
92C4⋊C4×D71—22no—
93C4⋊C4×D71—41no—
94C4⋊C4×D71—41no—
95C2×C22⋊Dic71—21no—
96C2×C22⋊Dic71D411yescharacteristic
97C2×(C2×D71)⋊C4—21no—
98C2×(C2×D71)⋊C4—21no—
99C2×(C2×D71)⋊C4D411yescharacteristic
100C2×C4×Dic71—21no—
101C2×C4×Dic71—21no—
102C2×C4×Dic71C2311yescharacteristic
103#14556062—22no—
104#14556062—41no—
105#14556061—41no—
106#14556061—41no—
107Dic71⋊C8C2×C414yescomplemented
108(C2×D71)⋊C8C2×C414yescomplemented
109C8×Dic71C2×C414yescomplemented
110C71⋊#95—21no—
111C71⋊#95—21no—
112C71⋊#95—21no—
113C71⋊#95—21no—
114C71⋊#95—21no—
115C23×C4×C71—21no—
116C23×C4×C71C2311yescharacteristic
117C22×C8×C71C2311yescharacteristic
118C22×C8×C71C2311yescharacteristic
119C2×C4⋊C4×C71—22no—
120C2×C4⋊C4×C71—21no—
121C2×C4⋊C4×C71—41no—
122C2×C4⋊C4×C71C2311yescharacteristic
123C2×C4⋊C4×C71C2311yescharacteristic
124C2×C4⋊C4×C71C2311yescharacteristic
125C2×C4⋊C4×C71C2311yescharacteristic
126C2×C22⋊C4×C71—21no—
127#107×C71—22no—
128#107×C71—41no—
129C22⋊C8×C71C2×C414yescomplemented
130#95×C71—21no—
131C23×D71C2×D411yescharacteristic
132C2×C22⋊D71C4⋊C414yes—
133C2×C22⋊D71D814yes—
134C2×C22⋊D71Q1614yes—
135C22×Dic71—21no—
136C22×Dic71—21no—
137C22×Dic71—21no—
138C22×Dic71—21no—
139C22×Dic71—42no—
140C22×Dic71—42no—
141C22×Dic71—81no—
142C22×Dic71C2×D411yescharacteristic
143C22×Dic71C2×D411yescharacteristic
144C22×Dic71C2×D411yescharacteristic
145C2×C4×D71—21no—
146C2×C4×D71—21no—
147C2×C4×D71—21no—
148C2×C4×D71—21no—
149C2×C4×D71—42no—
150C2×C4×D71—42no—
151C2×C4×D71—42no—
152C2×C4×D71—42no—
153C2×C4×D71—81no—
154C2×C4×D71—81no—
155C2×C4×D71C22×C412yes—
156C2×C4×D71C2×Q812yes—
157C2×C71⋊C8—21no—
158C2×C71⋊C8—21no—
159C2×C71⋊C8—21no—
160C2×C71⋊C8—21no—
161C2×C71⋊C8—44no—
162C2×C71⋊C8C22×C412yes—
163C2×C71⋊C8C22×C412yes—
164C8×D71—44no—
165C4⋊Dic71—21no—
166C4⋊Dic71—21no—
167C4⋊Dic71—21no—
168C4⋊Dic71—21no—
169C4⋊Dic71—21no—
170C4⋊Dic71—21no—
171C4⋊Dic71—21no—
172C4⋊Dic71—42no—
173C4⋊Dic71#4112yes—
174Dic71⋊C4—42no—
175Dic71⋊C4—42no—
176Dic71⋊C4—42no—
177Dic71⋊C4—42no—
178Dic71⋊C4—81no—
179Dic71⋊C4—81no—
180Dic71⋊C4C4⋊C414yes—
181C22⋊Dic71—42no—
182C22⋊Dic71C4⋊C414yes—
183(C2×D71)⋊C4—42no—
184(C2×D71)⋊C4—42no—
185(C2×D71)⋊C4C4⋊C414yes—
186C4×Dic71—42no—
187C4×Dic71—42no—
188C4×Dic71C22×C412yes—
189C4×Dic71C2×Q812yes—
190C24×C71C2×D411yescharacteristic
191C22×C4×C71—21no—
192C22×C4×C71—21no—
193C22×C4×C71—21no—
194C22×C4×C71—21no—
195C22×C4×C71—21no—
196C22×C4×C71—21no—
197C22×C4×C71—21no—
198C22×C4×C71—21no—
199C22×C4×C71—42no—
200C22×C4×C71—42no—
201C22×C4×C71—81no—
202C22×C4×C71C22×C412yes—
203C22×C4×C71C2×D411yescharacteristic
204C22×C4×C71C2×Q812yes—
205C22×C4×C71C2411yescharacteristic
206C2×C8×C71—21no—
207C2×C8×C71—21no—
208C2×C8×C71—21no—
209C2×C8×C71—21no—
210C2×C8×C71C22×C412yes—
211C2×C8×C71C22×C412yes—
212C4⋊C4×C71—21no—
213C4⋊C4×C71—21no—
214C4⋊C4×C71—21no—
215C4⋊C4×C71—21no—
216C4⋊C4×C71—21no—
217C4⋊C4×C71—21no—
218C4⋊C4×C71—21no—
219C4⋊C4×C71—42no—
220C4⋊C4×C71#4112yes—
221C22⋊C4×C71—42no—
222C23×C71—21no—
223C23×C71—21no—
224C23×C71—21no—
225C23×C71—21no—
226C23×C71C2×C4⋊C412yes—
227C23×C71C2×D812yes—
228C23×C71C2×Q1612yes—
229C23×C71C22×D411yescharacteristic
230C22×D71—21no—
231C22×D71—21no—
232C22×D71—21no—
233C22×D71—21no—
234C22×D71C2×C4⋊C412yes—
235C22×D71C2×D812yes—
236C22×D71C2×Q1612yes—
237C2×C4×C71—21no—
238C2×C4×C71—21no—
239C2×C4×C71—22no—
240C2×C4×C71—22no—
241C2×C4×C71—22no—
242C2×C4×C71—22no—
243C2×C4×C71—22no—
244C2×C4×C71—41no—
245C2×C4×C71—41no—
246C2×C4×C71—41no—
247C2×C4×C71—41no—
248C2×C4×C71—41no—
249C2×C4×C71—41no—
250C2×C4×C71—41no—
251C2×C4×C71—41no—
252C2×C4×C71—41no—
253C2×C4×C71—41no—
254C2×C4×C71—41no—
255C2×C4×C71—84no—
256C2×C4×C71C2×C4⋊C412yes—
257C2×C4×C71C23×C411yescharacteristic
258C2×C4×C71C22×Q811yescharacteristic
259C2×C4×C71C2×#4111yescharacteristic
260C2×C4×C71C2×#4111yescharacteristic
261C2×C4×C71H(5,𝔽2)11yescharacteristic
262C2×C4×C71H(5,𝔽2)11yescharacteristic
263C22⋊D71#107116yescomplemented
264C2×Dic71—21no—
265C2×Dic71—21no—
266C2×Dic71—21no—
267C2×Dic71—21no—
268C2×Dic71—22no—
269C2×Dic71—41no—
270C2×Dic71—41no—
271C2×Dic71—41no—
272C2×Dic71—41no—
273C2×Dic71—41no—
274C2×Dic71—41no—
275C2×Dic71—41no—
276C2×Dic71—41no—
277C2×Dic71—41no—
278C2×Dic71—41no—
279C2×Dic71—41no—
280C2×Dic71—84no—
281C2×Dic71C2×C4⋊C412yes—
282C2×Dic71C2×C4⋊C412yes—
283C2×Dic71C2×C4⋊C412yes—
284C2×Dic71C2×D812yes—
285C2×Dic71C2×Q1612yes—
286C4×D71—22no—
287C4×D71—22no—
288C4×D71—22no—
289C4×D71—22no—
290C4×D71—84no—
291C4×D71—84no—
292C8×C71—22no—
293C8×C71—22no—
294C71⋊C8—22no—
295C71⋊C8—22no—
296C22×C71—22no—
297C22×C71—22no—
298C22×C71—22no—
299C22×C71—22no—
300C22×C71—22no—
301C22×C71—22no—
302C22×C71C2×#10714yes—
303C22×C71C22×C4⋊C411yescharacteristic
304C22×C71#54611yescharacteristic
305C22×C71#54611yescharacteristic
306C22×C71C22×D811yescharacteristic
307C22×C71C22×Q1611yescharacteristic
308C22×C71#57711yescharacteristic
309C22×C71#57711yescharacteristic
310C2×D71—22no—
311C2×D71—22no—
312C2×D71—22no—
313C2×D71—22no—
314C2×D71—22no—
315C2×D71—22no—
316C2×D71C2×#10714yes—
317C4×C71—22no—
318C4×C71—42no—
319C4×C71—81no—
320C4×C71—81no—
321C4×C71—81no—
322C4×C71C4×#4111yescharacteristic
323C4×C71#51811yescharacteristic
324C4×C71#55411yescharacteristic
325C4×C71#55411yescharacteristic
326Dic71—22no—
327Dic71—22no—
328Dic71—42no—
329Dic71—81no—
330Dic71—81no—
331Dic71—81no—
332Dic71C2×#10714yes—
333#22705—711nomaximal, Sylow
334C2×C71—24no—
335C2×C71#234911yescharacteristic
336C2×C71C22×#10711yescharacteristic
337C2×C71#291211yescharacteristic
338C2×C71#329411yescharacteristic
339C2×C71#329411yescharacteristic
340C2×C71#329911yescharacteristic
341C2×C71#329911yescharacteristic
342D71—24no—
343C2×C8×D4—711no—
344D4×C4⋊C4—711no—
345D4×C4⋊C4—711no—
346#1947—711no—
347#1947—711no—
348#1852—711no—
349#1852—711no—
350#1852—711no—
351#1852D7111yescharacteristic, complemented
352#1834—711no—
353#1808—711no—
354#1808—711no—
355C4×#107—711no—
356C2×#340—711no—
357C2×#340—711no—
358C71#2270511yescharacteristic, complemented, Sylow
359C23×C8—711no—
360C23×C8—711no—
361C2×C4×D4—711no—
362C2×C4×D4—1421no—
363C2×C4×D4—1421no—
364C22×C4⋊C4—711no—
365C22×C4⋊C4—711no—
366C22×C4⋊C4—711no—
367C22×C4⋊C4C2×D7111yescharacteristic
368C8×D4—718no—
369C2×#107—711no—
370C2×#107—711no—
371C2×#107—711no—
372C2×#107—711no—
373C2×#107C2×D7111yescharacteristic
374C2×#107C2×D7111yescharacteristic
375C2×C4⋊C8—711no—
376C2×C22⋊C8—711no—
377C2×C22⋊C8C2×D7111yescharacteristic
378C2×C4×C8—711no—
379#389—1421no—
380#389—1421no—
381#385—1421no—
382#385—1421no—
383#385—1421no—
384#385—1421no—
385#384—711no—
386#384—711no—
387#380—711no—
388#380—711no—
389#380—711no—
390#380C2×D7111yescharacteristic
391C4×C4⋊C4—711no—
392C4×C4⋊C4—711no—
393#340—711no—
394#340—711no—
395#340—711no—
396#340—711no—
397#340—711no—
398#340—711no—
399#340—711no—
400#340—711no—
401#340C2×D7111yescharacteristic
402#340C2×D7111yescharacteristic
403C22×D4—711no—
404C23×C4—21no—
405C23×C4—711no—
406C23×C4—1421no—
407C23×C4—1421no—
408C23×C4—1421no—
409C23×C4C22×D7111yescharacteristic
410C22×C8—2841no—
411C22×C8—2841no—
412C22×C8—2841no—
413C22×C8—2841no—
414C22×C8—714no—
415C22×C8—714no—
416C22×C8—711no—
417C22×C8—711no—
418C22×C8C22×D7111yescharacteristic
419C22×C8C22×D7111yescharacteristic
420C4×D4—2844no—
421C4×D4—2844no—
422C4×D4—714no—
423C4×D4—714no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—41no—
427C2×C4⋊C4—2841no—
428C2×C4⋊C4—2841no—
429C2×C4⋊C4—2841no—
430C2×C4⋊C4—711no—
431C2×C4⋊C4—711no—
432C2×C4⋊C4—711no—
433C2×C4⋊C4—711no—
434C2×C4⋊C4—711no—
435C2×C4⋊C4—1422no—
436C2×C4⋊C4—1421no—
437C2×C4⋊C4—1421no—
438C2×C4⋊C4—1421no—
439C2×C4⋊C4—1421no—
440C2×C4⋊C4—1421no—
441C2×C4⋊C4—1422no—
442C2×C4⋊C4—1422no—
443C2×C4⋊C4—1421no—
444C2×C4⋊C4—1421no—
445C2×C4⋊C4C22×D7111yescharacteristic
446C2×C4⋊C4C22×D7111yescharacteristic
447C2×C4⋊C4C22×D7111yescharacteristic
448C2×C4⋊C4C22×D7111yescharacteristic
449C2×C22⋊C4—21no—
450C2×C22⋊C4—711no—
451C2×C22⋊C4—711no—
452C2×C22⋊C4—1421no—
453C2×C22⋊C4—1421no—
454C2×C22⋊C4—1421no—
455C2×C42—711no—
456C2×C42—1421no—
457C2×C42—1421no—
458#107—22no—
459#107—41no—
460#107—2841no—
461#107—2841no—
462#107—2841no—
463#107—1422no—
464C4⋊C8—714no—
465C22⋊C8—714no—
466C22⋊C8C4×D7114yescomplemented
467C4×C8—714no—
468#95—21no—
469#95—1421no—
470#95—1421no—
471#95—1421no—
472#95—1421no—
473#95—1421no—
474C24—711no—
475C24D4×D7111yescharacteristic
476C2×D4—714no—
477C2×D4—714no—
478C2×D4—714no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—81no—
490C22×C4—2842no—
491C22×C4—2842no—
492C22×C4—2842no—
493C22×C4—2842no—
494C22×C4—2842no—
495C22×C4—2842no—
496C22×C4—5681no—
497C22×C4—5681no—
498C22×C4—5681no—
499C22×C4—711no—
500C22×C4—711no—
501C22×C4—711no—
502C22×C4—712no—
503C22×C4—712no—
504C22×C4—1421no—
505C22×C4—1421no—
506C22×C4—1421no—
507C22×C4—1421no—
508C22×C4—1421no—
509C22×C4—1421no—
510C22×C4—1421no—
511C22×C4—1421no—
512C22×C4C2×C4×D7112yes—
513C22×C4D4×D7111yescharacteristic
514C22×C4Q8×D7112yes—
515C22×C4C23×D7111yescharacteristic
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—2844no—
521C2×C8—2844no—
522C2×C8—712no—
523C2×C8—712no—
524C2×C8—1421no—
525C2×C8—1421no—
526C2×C8—1421no—
527C2×C8—1421no—
528C2×C8C2×C4×D7112yes—
529C2×C8C2×C4×D7112yes—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—42no—
538C4⋊C4—2842no—
539C4⋊C4—2842no—
540C4⋊C4—2842no—
541C4⋊C4—2842no—
542C4⋊C4—2842no—
543C4⋊C4—5681no—
544C4⋊C4—5681no—
545C4⋊C4—714no—
546C4⋊C4—712no—
547C4⋊C4—1421no—
548C4⋊C4—1421no—
549C4⋊C4—1421no—
550C4⋊C4—1421no—
551C4⋊C4—1421no—
552C4⋊C4—1421no—
553C4⋊C4—1421no—
554C4⋊C4#1176586412yes—
555C22⋊C4—42no—
556C22⋊C4—2842no—
557C22⋊C4—2842no—
558C22⋊C4—2842no—
559C22⋊C4—714no—
560C22⋊C4—714no—
561C42—2842no—
562C42—2842no—
563C42—712no—
564C42—712no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—712no—
570C23—712no—
571C23—712no—
572C23—1421no—
573C23—1421no—
574C23—1421no—
575C23—1421no—
576C23C4⋊C4×D7112yes—
577C23D8×D7112yes—
578C23Q16×D7112yes—
579C23C2×D4×D7111yescharacteristic
580D4—7116no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—84no—
600C2×C4—2841no—
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—2841no—
610C2×C4—2841no—
611C2×C4—5684no—
612C2×C4—5684no—
613C2×C4—5684no—
614C2×C4—712no—
615C2×C4—712no—
616C2×C4—712no—
617C2×C4—712no—
618C2×C4—712no—
619C2×C4—1422no—
620C2×C4—1421no—
621C2×C4—1421no—
622C2×C4—1421no—
623C2×C4—1421no—
624C2×C4—1422no—
625C2×C4—1422no—
626C2×C4—1422no—
627C2×C4—1422no—
628C2×C4C4⋊C4×D7112yes—
629C2×C4C22×C4×D7111yescharacteristic
630C2×C4C2×Q8×D7111yescharacteristic
631C2×C4#41×D7111yescharacteristic
632C2×C4C2×#1176586411yescharacteristic
633C2×C4#1455617311yescharacteristic
634C2×C4#1455617411yescharacteristic
635C8—22no—
636C8—22no—
637C8—1422no—
638C8—1422no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—714no—
646C22—1422no—
647C22—1422no—
648C22—1422no—
649C22—1422no—
650C22—1422no—
651C22—1422no—
652C22#107×D7114yes—
653C22C2×C4⋊C4×D7111yescharacteristic
654C22#1798663611yescharacteristic
655C22#1798664111yescharacteristic
656C22C2×D8×D7111yescharacteristic
657C22C2×Q16×D7111yescharacteristic
658C22#1798680811yescharacteristic
659C22#1798680911yescharacteristic
660C4—22no—
661C4—42no—
662C4—81no—
663C4—81no—
664C4—81no—
665C4—2842no—
666C4—5681no—
667C4—5681no—
668C4—5681no—
669C4—714no—
670C4—1422no—
671C4—1422no—
672C4C4×#1176586411yescharacteristic
673C4#1798647111yescharacteristic
674C4#1798670311yescharacteristic
675C4#1798670711yescharacteristic
676C2—24no—
677C2—1424no—
678C2#2259124611yescharacteristic
679C2C2×#107×D7111yescharacteristic
680C2#2259693411yescharacteristic
681C2#2260014611yescharacteristic
682C2#2260015111yescharacteristic
683C2#2260020911yescharacteristic
684C2#2260021411yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC71×#1852C2
socleC23×C71C22×D4
prime radicalC22×C22⋊D71D4
cosocleC22×C4×C71C24
hypercenter#1852D71
hypocenterC71#22705
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
4. #22589097C2semidirect
5. #22589095C2semidirect
6. #22588530C2semidirect
7. #22588529C2semidirect
8. #22588526C2semidirect
9. #22588466C2semidirect
10. #22588367C2semidirect
11. #22588366C2semidirect
12. #107×Dic71C2semidirect
13. C2×#17985761C2semidirect
14. #340×D71C2semidirect
15. C71×#1852C2semidirect
24. (C22⋊D71)⋊C8C4semidirect
67. C22×C71⋊C8C2×C4semidirect
72. C2×C8×D71C2×C4semidirect
107. Dic71⋊C8C2×C4semidirect
108. (C2×D71)⋊C8C2×C4semidirect
109. C8×Dic71C2×C4semidirect
129. C22⋊C8×C71C2×C4semidirect
263. C22⋊D71#107semidirect
351. #1852D71semidirect
358. C71#22705semidirect
466. C22⋊C8C4×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
C4⋊C4×C22⋊D712
#225912362
#225890972
#225890952
#225885302
#225885292
#225885262
#225884662
#225883672
#225883662
#107×Dic712
C2×#179857612
#340×D712
C71×#18522
#2270571