Finite Group Databasebeta

← #31995106

Subgroups — #31995106

Order 18176.

1834 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986471C211yesmaximal, characteristic
2C2×#99×D71C212yesmaximal
3#22590692C212yesmaximal, complemented
4#99×Dic71C212yesmaximal, complemented
5C4×#14556042C212yesmaximal, complemented
6C4×#14556043C211yesmaximal, characteristic, complemented
7#22588127C212yesmaximal, complemented
8#342×D71C212yesmaximal, complemented
9C4×#99×C71C211yesmaximal, characteristic, complemented
10C22×D4×D71C2211yescharacteristic
11#17986471—24no—
12#17986471—24no—
13C2×C4×D284C411yescharacteristic, complemented
14C2×D4×Dic71C2211yescharacteristic
15C2×#14556090C411yescharacteristic, complemented
16C2×C4×C22⋊D71C411yescharacteristic, complemented
17C2×C4×C22⋊D71C2211yescharacteristic
18C2×(C22⋊D71)⋊C4C411yescharacteristic, complemented
19C2×(C22⋊D71)⋊C4C2211yescharacteristic
20C2×#14556086C411yescharacteristic, complemented
21C2×#14556085C411yescharacteristic, complemented
22C22×(C2×D71)⋊C4C411yescharacteristic, complemented
23C22×(C2×D71)⋊C4C2211yescharacteristic
24C2×C22⋊C4×D71C411yescharacteristic, complemented
25C2×C22⋊C4×D71C2214yes—
26C2×C22⋊C4×D71C2211yescharacteristic
27C2×#14556043C2212yes—
28C2×#14556042C2214yes—
29#99×D71C4116yescomplemented
30C22⋊C4×Dic71C2214yescomplemented
31C4×(C2×D71)⋊C4—24no—
32C4×C22⋊Dic71C2212yescomplemented
33#17985846—24no—
34#17985766C2212yescomplemented
35#17985765C2214yescomplemented
36C2×C4×D4×C71C2211yescharacteristic
37C2×#99×C71C2212yes—
38C4×C22⋊C4×C71C2212yescomplemented
39#342×C71C2212yescomplemented
40C24×D71C2×C411yescharacteristic
41C24×D71C2311yescharacteristic
42C22×D284C2×C411yescharacteristic
43C22×C22⋊D71C2×C411yescharacteristic
44C22×C22⋊D71C2311yescharacteristic
45C2×D4×D71—24no—
46C2×D4×D71—24no—
47C2×D4×D71C2×C418yes—
48C23×Dic71C2×C411yescharacteristic, complemented
49C23×Dic71C2311yescharacteristic
50C22×C4×D71—24no—
51C22×C4×D71C2×C411yescharacteristic
52C22×C4×D71C2×C411yescharacteristic
53C22×C4×D71C2×C411yescharacteristic
54C22×C4×D71C2×C411yescharacteristic, complemented
55C22×C4×D71C2×C411yescharacteristic, complemented
56C4×D284—22no—
57C4×D284—22no—
58D4×Dic71—24no—
59#14556090—24no—
60C4×C22⋊D71—22no—
61C4×C22⋊D71—22no—
62C4×C22⋊D71—22no—
63C4×C22⋊D71—22no—
64(C22⋊D71)⋊C4—24no—
65(C22⋊D71)⋊C4—24no—
66#14556086—24no—
67#14556085—22no—
68#14556085—22no—
69C2×C4⋊Dic71C2×C411yescharacteristic, complemented
70C2×Dic71⋊C4C2×C411yescharacteristic, complemented
71C2×Dic71⋊C4C2×C411yescharacteristic, complemented
72C2×C22⋊Dic71C2×C411yescharacteristic, complemented
73C2×C22⋊Dic71C2311yescharacteristic
74C2×C22⋊Dic71C2314yes—
75C2×(C2×D71)⋊C4—24no—
76C2×(C2×D71)⋊C4—22no—
77C2×(C2×D71)⋊C4—22no—
78C2×(C2×D71)⋊C4C2×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×(C2×D71)⋊C4C2×C411yescharacteristic, complemented
85C2×(C2×D71)⋊C4C2×C411yescharacteristic, complemented
86C2×(C2×D71)⋊C4D414yes—
87C2×(C2×D71)⋊C4D414yes—
88C22⋊C4×D71—24no—
89C22⋊C4×D71—28no—
90C22⋊C4×D71—24no—
91C22⋊C4×D71C2×C4116yescomplemented
92C2×C4×Dic71—24no—
93C2×C4×Dic71—22no—
94C2×C4×Dic71C2×C411yescharacteristic, complemented
95C2×C4×Dic71C2×C411yescharacteristic, complemented
96C2×C4×Dic71C2×C411yescharacteristic, complemented
97#14556043C2×C418yescomplemented
98#14556042C2×C4116yescomplemented
99C71⋊#95—24no—
100C71⋊#95—22no—
101C22×D4×C71C2311yescharacteristic
102C23×C4×C71C2×C411yescharacteristic, complemented
103C23×C4×C71C2311yescharacteristic
104C4×D4×C71—22no—
105C4×D4×C71—22no—
106C2×C4⋊C4×C71C2×C411yescharacteristic, complemented
107C2×C22⋊C4×C71C2×C411yescharacteristic, complemented
108C2×C22⋊C4×C71C2311yescharacteristic
109C2×C22⋊C4×C71C2314yes—
110C2×C42×C71—22no—
111C2×C42×C71C2×C411yescharacteristic, complemented
112#99×C71C2×C418yescomplemented
113#95×C71—22no—
114C23×D71—22no—
115C23×D71—22no—
116C23×D71—81no—
117C23×D71—81no—
118C23×D71—81no—
119C23×D71—81no—
120C23×D71C4214yescomplemented
121C23×D71C22×C411yescharacteristic
122C23×D71C22×C411yescharacteristic
123C23×D71C22×C411yescharacteristic
124C23×D71C22×C414yes—
125C23×D71C2×D414yes—
126C23×D71#4114yes—
127C2×D284—22no—
128C2×D284—22no—
129C2×D284C4214yescomplemented
130C2×C22⋊D71—22no—
131C2×C22⋊D71—22no—
132C2×C22⋊D71—22no—
133C2×C22⋊D71—22no—
134C2×C22⋊D71C4214yescomplemented
135C2×C22⋊D71C22×C414yes—
136D4×D71—216no—
137D4×D71—216no—
138C22×Dic71—24no—
139C22×Dic71—22no—
140C22×Dic71—81no—
141C22×Dic71—81no—
142C22×Dic71C22×C411yescharacteristic
143C22×Dic71C22×C411yescharacteristic
144C22×Dic71C22×C411yescharacteristic
145C22×Dic71C22×C411yescharacteristic
146C22×Dic71C22×C411yescharacteristic
147C22×Dic71C2×D414yes—
148C2×C4×D71—22no—
149C2×C4×D71—22no—
150C2×C4×D71—22no—
151C2×C4×D71—22no—
152C2×C4×D71—216no—
153C2×C4×D71—22no—
154C2×C4×D71—22no—
155C2×C4×D71—84no—
156C2×C4×D71—84no—
157C2×C4×D71—81no—
158C2×C4×D71—81no—
159C2×C4×D71—81no—
160C2×C4×D71—81no—
161C2×C4×D71C4214yescomplemented
162C4⋊Dic71—22no—
163Dic71⋊C4—21no—
164Dic71⋊C4—21no—
165Dic71⋊C4—22no—
166C22⋊Dic71—22no—
167C22⋊Dic71—24no—
168C22⋊Dic71—22no—
169C22⋊Dic71C22×C418yes—
170(C2×D71)⋊C4—22no—
171(C2×D71)⋊C4—22no—
172(C2×D71)⋊C4—216no—
173(C2×D71)⋊C4—21no—
174(C2×D71)⋊C4—21no—
175(C2×D71)⋊C4—22no—
176(C2×D71)⋊C4C22⋊C414yes—
177(C2×D71)⋊C4C22⋊C412yes—
178(C2×D71)⋊C4C22⋊C412yes—
179(C2×D71)⋊C4C22⋊C414yes—
180(C2×D71)⋊C4C22⋊C412yes—
181(C2×D71)⋊C4C22⋊C412yes—
182C4×Dic71—22no—
183C4×Dic71—22no—
184C4×Dic71—22no—
185C4×Dic71—84no—
186C4×Dic71—82no—
187C24×C71C22×C411yescharacteristic
188C24×C71C2411yescharacteristic
189C2×D4×C71—22no—
190C2×D4×C71—22no—
191C2×D4×C71C22×C414yes—
192C22×C4×C71—24no—
193C22×C4×C71—21no—
194C22×C4×C71—21no—
195C22×C4×C71—81no—
196C22×C4×C71—81no—
197C22×C4×C71C22×C411yescharacteristic
198C22×C4×C71C22×C411yescharacteristic
199C22×C4×C71C22×C411yescharacteristic
200C22×C4×C71C22×C411yescharacteristic
201C22×C4×C71C22×C411yescharacteristic
202C22×C4×C71C2×D412yes—
203C22×C4×C71C2×D412yes—
204C4⋊C4×C71—22no—
205C22⋊C4×C71—22no—
206C22⋊C4×C71—24no—
207C22⋊C4×C71—22no—
208C22⋊C4×C71C22×C418yes—
209C42×C71—21no—
210C42×C71—21no—
211C42×C71—82no—
212C23×C71—21no—
213C23×C71—21no—
214C23×C71—41no—
215C23×C71—41no—
216C23×C71—41no—
217C23×C71—41no—
218C23×C71C2×C4212yes—
219C23×C71C23×C411yescharacteristic
220C23×C71C23×C412yes—
221C23×C71C22×D412yes—
222C23×C71C2×#4112yes—
223C22×D71—21no—
224C22×D71—21no—
225C22×D71—28no—
226C22×D71—41no—
227C22×D71—41no—
228C22×D71—44no—
229C22×D71—44no—
230C22×D71—41no—
231C22×D71—41no—
232C22×D71—41no—
233C22×D71—41no—
234C22×D71—82no—
235C22×D71—82no—
236C22×D71—84no—
237C22×D71—84no—
238C22×D71—84no—
239C22×D71—84no—
240C22×D71C2×C4212yes—
241C22×D71C2×C4212yes—
242C22×D71C2×C4212yes—
243C22×D71C2×C22⋊C412yes—
244C22×D71C2×C22⋊C412yes—
245C22×D71#11712yes—
246C22×D71#11712yes—
247C22×D71C4×D418yes—
248C22×D71C4×D418yes—
249D4×C71—28no—
250C2×C4×C71—21no—
251C2×C4×C71—21no—
252C2×C4×C71—21no—
253C2×C4×C71—21no—
254C2×C4×C71—28no—
255C2×C4×C71—42no—
256C2×C4×C71—41no—
257C2×C4×C71—41no—
258C2×C4×C71—42no—
259C2×C4×C71—44no—
260C2×C4×C71—44no—
261C2×C4×C71—41no—
262C2×C4×C71—41no—
263C2×C4×C71—81no—
264C2×C4×C71—81no—
265C2×C4×C71C2×C4212yes—
266C2×C4×C71C2×C22⋊C411yescharacteristic
267C2×C4×C71C2×C22⋊C411yescharacteristic
268C2×C4×C71C2×C22⋊C412yes—
269C22⋊D71—28no—
270C22⋊D71—28no—
271C2×Dic71—21no—
272C2×Dic71—21no—
273C2×Dic71—21no—
274C2×Dic71—21no—
275C2×Dic71—28no—
276C2×Dic71—44no—
277C2×Dic71—41no—
278C2×Dic71—41no—
279C2×Dic71—44no—
280C2×Dic71—44no—
281C2×Dic71—41no—
282C2×Dic71—41no—
283C2×Dic71—82no—
284C2×Dic71C2×C4212yes—
285C2×Dic71C2×C22⋊C412yes—
286C2×Dic71C2×C22⋊C412yes—
287D284—28no—
288C4×D71—28no—
289C4×D71—82no—
290C4×D71—82no—
291C4×D71—82no—
292C4×D71—82no—
293C4×D71—816no—
294C22×C71—22no—
295C22×C71—21no—
296C22×C71—22no—
297C22×C71—21no—
298C22×C71—22no—
299C22×C71—42no—
300C22×C71—42no—
301C22×C71—42no—
302C22×C71—42no—
303C22×C71—41no—
304C22×C71—41no—
305C22×C71C22×C4211yescharacteristic
306C22×C71C22×C22⋊C411yescharacteristic
307C22×C71C2×#11711yescharacteristic
308C22×C71C2×C4×D414yes—
309C2×D71—22no—
310C2×D71—22no—
311C2×D71—22no—
312C2×D71—22no—
313C2×D71—22no—
314C2×D71—48no—
315C2×D71—42no—
316C2×D71—42no—
317C2×D71—42no—
318C2×D71—42no—
319C2×D71—48no—
320C2×D71—42no—
321C2×D71—41no—
322C2×D71—41no—
323C2×D71—42no—
324C2×D71—88no—
325C2×D71C4×C22⋊C414yes—
326C2×D71C4×C22⋊C414yes—
327C4×C71—22no—
328C4×C71—21no—
329C4×C71—21no—
330C4×C71—22no—
331C4×C71—48no—
332C4×C71—41no—
333C4×C71—41no—
334Dic71—22no—
335Dic71—22no—
336Dic71—22no—
337Dic71—48no—
338Dic71—41no—
339Dic71—41no—
340#20392—711nomaximal, Sylow
341C2×C71—24no—
342C2×C71—21no—
343C2×C71—21no—
344C2×C71—42no—
345C2×C71C2×C4×C22⋊C411yescharacteristic
346C2×C71#288311yescharacteristic
347C2×C71#288311yescharacteristic
348D71—24no—
349D71—24no—
350D71—42no—
351C2×#518—711no—
352C22×#99—712no—
353#2273—712no—
354C4×#99—712no—
355C4×#99—712no—
356C4×#99—712no—
357C4×#99—711no—
358C4×#99D7111yescharacteristic, complemented
359C2×#342—712no—
360C71#2039211yescharacteristic, complemented, Sylow
361C23×D4—711no—
362#518—1424no—
363#518—1424no—
364C2×C4×D4—711no—
365C2×C4×D4—711no—
366C2×C4×D4—711no—
367C2×C4×D4—711no—
368C2×C4×D4—711no—
369C2×C4×D4—711no—
370C2×C4×D4—711no—
371C2×C4×D4C2×D7111yescharacteristic
372C2×#117—711no—
373C2×#117—711no—
374C22×C22⋊C4—711no—
375C22×C22⋊C4—714no—
376C22×C22⋊C4—711no—
377C22×C22⋊C4—711no—
378C22×C22⋊C4—711no—
379C2×#99—712no—
380C2×#99—714no—
381C2×#99—7116no—
382C2×#99C2×D7112yes—
383C4×C22⋊C4—712no—
384C4×C22⋊C4—714no—
385C4×C22⋊C4—1424no—
386C4×C22⋊C4—1424no—
387C4×C22⋊C4C2×D7112yescomplemented
388#342—714no—
389#342—712no—
390#342C2×D7112yescomplemented
391C25—711no—
392C25—711no—
393C22×D4—711no—
394C22×D4—711no—
395C22×D4—718no—
396C22×D4—711no—
397C22×D4—1424no—
398C22×D4—1424no—
399C22×D4C22×D7111yescharacteristic
400C23×C4—711no—
401C23×C4—711no—
402C23×C4—711no—
403C23×C4—711no—
404C23×C4—711no—
405C23×C4—711no—
406C23×C4—711no—
407C23×C4—1424no—
408C23×C4C4×D7111yescharacteristic, complemented
409C23×C4C22×D7111yescharacteristic
410C4×D4—22no—
411C4×D4—22no—
412C4×D4—1422no—
413C4×D4—1422no—
414C4×D4—1424no—
415C4×D4—1424no—
416C4×D4—1424no—
417C4×D4—1422no—
418C4×D4—1422no—
419C4×D4—1424no—
420C4×D4—1422no—
421C4×D4—1422no—
422#117—1422no—
423#117—1422no—
424#117—1424no—
425C2×C4⋊C4—711no—
426C2×C4⋊C4—711no—
427C2×C4⋊C4—711no—
428C2×C4⋊C4C4×D7111yescharacteristic, complemented
429C2×C22⋊C4—711no—
430C2×C22⋊C4—711no—
431C2×C22⋊C4—711no—
432C2×C22⋊C4—711no—
433C2×C22⋊C4—714no—
434C2×C22⋊C4—714no—
435C2×C22⋊C4—714no—
436C2×C22⋊C4—7116no—
437C2×C22⋊C4—711no—
438C2×C22⋊C4—711no—
439C2×C22⋊C4—711no—
440C2×C22⋊C4—711no—
441C2×C22⋊C4—711no—
442C2×C22⋊C4—711no—
443C2×C22⋊C4—1424no—
444C2×C22⋊C4—1424no—
445C2×C22⋊C4—1428no—
446C2×C22⋊C4—1422no—
447C2×C22⋊C4—1422no—
448C2×C22⋊C4—1424no—
449C2×C22⋊C4C4×D7111yescharacteristic, complemented
450C2×C22⋊C4C22×D7111yescharacteristic
451C2×C22⋊C4C22×D7114yes—
452C2×C42—22no—
453C2×C42—711no—
454C2×C42—711no—
455C2×C42—711no—
456C2×C42—1424no—
457C2×C42—1422no—
458C2×C42C4×D7111yescharacteristic, complemented
459#99—718no—
460#99—7116no—
461#99C4×D7118yescomplemented
462#95—22no—
463#95—1424no—
464#95—1422no—
465C24—5681no—
466C24—5681no—
467C24—5681no—
468C24—5681no—
469C24—711no—
470C24—711no—
471C24—714no—
472C24—711no—
473C24—714no—
474C24—714no—
475C24—714no—
476C24—1422no—
477C24—1422no—
478C24C2×C4×D7111yescharacteristic
479C24C23×D7111yescharacteristic
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—714no—
483C2×D4—714no—
484C2×D4—714no—
485C2×D4—1422no—
486C2×D4—1422no—
487C2×D4—14216no—
488C2×D4—14216no—
489C2×D4—1422no—
490C2×D4—1422no—
491C2×D4—1422no—
492C2×D4—1422no—
493C2×D4C2×C4×D7114yes—
494C22×C4—24no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—81no—
498C22×C4—81no—
499C22×C4—5684no—
500C22×C4—5684no—
501C22×C4—5681no—
502C22×C4—5681no—
503C22×C4—5681no—
504C22×C4—5681no—
505C22×C4—5681no—
506C22×C4—5681no—
507C22×C4—711no—
508C22×C4—711no—
509C22×C4—714no—
510C22×C4—711no—
511C22×C4—711no—
512C22×C4—711no—
513C22×C4—714no—
514C22×C4—1422no—
515C22×C4—14216no—
516C22×C4—1422no—
517C22×C4—1422no—
518C22×C4—1422no—
519C22×C4—1422no—
520C22×C4—1424no—
521C22×C4—1422no—
522C22×C4—1422no—
523C22×C4C2×C4×D7111yescharacteristic
524C22×C4C2×C4×D7111yescharacteristic
525C22×C4C2×C4×D7111yescharacteristic
526C22×C4C2×C4×D7111yescharacteristic
527C22×C4C2×C4×D7111yescharacteristic
528C22×C4D4×D7112yes—
529C22×C4D4×D7112yes—
530C4⋊C4—22no—
531C4⋊C4—1422no—
532C4⋊C4—1422no—
533C4⋊C4—1421no—
534C4⋊C4—1421no—
535C22⋊C4—22no—
536C22⋊C4—24no—
537C22⋊C4—22no—
538C22⋊C4—712no—
539C22⋊C4—712no—
540C22⋊C4—714no—
541C22⋊C4—712no—
542C22⋊C4—712no—
543C22⋊C4—714no—
544C22⋊C4—718no—
545C22⋊C4—1422no—
546C22⋊C4—14216no—
547C22⋊C4—1422no—
548C22⋊C4—1422no—
549C22⋊C4—1422no—
550C22⋊C4—1422no—
551C22⋊C4—1424no—
552C22⋊C4—1421no—
553C22⋊C4—1421no—
554C22⋊C4C2×C4×D7118yes—
555C42—21no—
556C42—21no—
557C42—82no—
558C42—5682no—
559C42—5684no—
560C42—1422no—
561C42—1422no—
562C42—1422no—
563C23—21no—
564C23—21no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—2841no—
570C23—2841no—
571C23—2844no—
572C23—2841no—
573C23—2844no—
574C23—2841no—
575C23—2841no—
576C23—2841no—
577C23—5684no—
578C23—5684no—
579C23—5684no—
580C23—5684no—
581C23—5682no—
582C23—5682no—
583C23—712no—
584C23—712no—
585C23—712no—
586C23—712no—
587C23—718no—
588C23—718no—
589C23—712no—
590C23—712no—
591C23—712no—
592C23—1428no—
593C23—1421no—
594C23—1421no—
595C23C42×D7112yes—
596C23C22×C4×D7111yescharacteristic
597C23C22×C4×D7112yes—
598C23C2×D4×D7112yes—
599C23#41×D7112yes—
600D4—28no—
601D4—1428no—
602D4—1428no—
603D4—1428no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—28no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—44no—
614C2×C4—44no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—81no—
618C2×C4—81no—
619C2×C4—2844no—
620C2×C4—2844no—
621C2×C4—2841no—
622C2×C4—2841no—
623C2×C4—2844no—
624C2×C4—2841no—
625C2×C4—2841no—
626C2×C4—5682no—
627C2×C4—56816no—
628C2×C4—5682no—
629C2×C4—5682no—
630C2×C4—5682no—
631C2×C4—5682no—
632C2×C4—712no—
633C2×C4—712no—
634C2×C4—712no—
635C2×C4—1428no—
636C2×C4—1421no—
637C2×C4—1421no—
638C2×C4—1428no—
639C2×C4—1421no—
640C2×C4—1421no—
641C2×C4C42×D7112yes—
642C2×C4C22⋊C4×D7111yescharacteristic
643C2×C4C22⋊C4×D7111yescharacteristic
644C2×C4C22⋊C4×D7112yes—
645C22—22no—
646C22—21no—
647C22—22no—
648C22—21no—
649C22—22no—
650C22—42no—
651C22—42no—
652C22—42no—
653C22—42no—
654C22—41no—
655C22—41no—
656C22—2842no—
657C22—2842no—
658C22—2848no—
659C22—2842no—
660C22—2842no—
661C22—2848no—
662C22—2842no—
663C22—2842no—
664C22—2841no—
665C22—2841no—
666C22—5688no—
667C22—714no—
668C22—714no—
669C22—1422no—
670C22—1422no—
671C22—1422no—
672C22—1422no—
673C22—1422no—
674C22C2×C42×D7111yescharacteristic
675C22C2×C22⋊C4×D7111yescharacteristic
676C22#117×D7111yescharacteristic
677C22C4×D4×D7114yes—
678C4—21no—
679C4—21no—
680C4—22no—
681C4—22no—
682C4—48no—
683C4—41no—
684C4—41no—
685C4—2848no—
686C4—2841no—
687C4—2841no—
688C4—1422no—
689C4—1422no—
690C4—1422no—
691C2—24no—
692C2—21no—
693C2—21no—
694C2—42no—
695C2—2842no—
696C2—1424no—
697C2—1424no—
698C2C4×C22⋊C4×D7111yescharacteristic
699C2#2259679811yescharacteristic
700C2#2259679911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D71
commutatorC22×C71C22×C42
FrattiniC24C23×D71
FittingC4×#99×C71C2
socleC22×C71C22×C22⋊C4
prime radicalC22×D4×D71C22
cosocleC24×C71C24
hypercenterC4×#99D71
hypocenterC71#20392
LCSG ▷ C22×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. #22590692C2semidirect
4. #99×Dic71C2semidirect
5. C4×#14556042C2semidirect
6. C4×#14556043C2semidirect
7. #22588127C2semidirect
8. #342×D71C2semidirect
9. C4×#99×C71C2semidirect
13. C2×C4×D284C4semidirect
15. C2×#14556090C4semidirect
16. C2×C4×C22⋊D71C4semidirect
18. C2×(C22⋊D71)⋊C4C4semidirect
20. C2×#14556086C4semidirect
21. C2×#14556085C4semidirect
22. C22×(C2×D71)⋊C4C4semidirect
24. C2×C22⋊C4×D71C4semidirect
29. #99×D71C4semidirect
30. C22⋊C4×Dic71C22semidirect
32. C4×C22⋊Dic71C22semidirect
34. #17985766C22semidirect
35. #17985765C22semidirect
38. C4×C22⋊C4×C71C22semidirect
39. #342×C71C22semidirect
48. C23×Dic71C2×C4semidirect
54. C22×C4×D71C2×C4semidirect
55. C22×C4×D71C2×C4semidirect
69. C2×C4⋊Dic71C2×C4semidirect
70. C2×Dic71⋊C4C2×C4semidirect
71. C2×Dic71⋊C4C2×C4semidirect
72. C2×C22⋊Dic71C2×C4semidirect
84. C2×(C2×D71)⋊C4C2×C4semidirect
85. C2×(C2×D71)⋊C4C2×C4semidirect
91. C22⋊C4×D71C2×C4semidirect
94. C2×C4×Dic71C2×C4semidirect
95. C2×C4×Dic71C2×C4semidirect
96. C2×C4×Dic71C2×C4semidirect
97. #14556043C2×C4semidirect
98. #14556042C2×C4semidirect
102. C23×C4×C71C2×C4semidirect
106. C2×C4⋊C4×C71C2×C4semidirect
107. C2×C22⋊C4×C71C2×C4semidirect
111. C2×C42×C71C2×C4semidirect
112. #99×C71C2×C4semidirect
120. C23×D71C42semidirect
129. C2×D284C42semidirect
134. C2×C22⋊D71C42semidirect
161. C2×C4×D71C42semidirect
358. C4×#99D71semidirect
360. C71#20392semidirect
387. C4×C22⋊C4C2×D71semidirect
390. #342C2×D71semidirect
408. C23×C4C4×D71semidirect
428. C2×C4⋊C4C4×D71semidirect
449. C2×C22⋊C4C4×D71semidirect
458. C2×C42C4×D71semidirect
461. #99C4×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179864712
C2×#99×D712
#225906922
#99×Dic712
C4×#145560422
C4×#145560432
#225881272
#342×D712
C4×#99×C712
#2039271