Finite Group Databasebeta

← C4×#17985890 #31918610

Subgroups — C4×#17985890 #31918610

Order 18176.

2134 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17985890C212yesmaximal
2C2×C4×Dic71⋊C4C211yesmaximal, characteristic, complemented
3C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic
4C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic
5C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic
6#22586578C212yesmaximal
7#22586573C212yesmaximal, complemented
8#22586567C212yesmaximal, complemented
9C4×C71⋊#95C211yesmaximal, characteristic, complemented
10C4×C71⋊#95C211yesmaximal, characteristic, complemented
11C2×C43×C71C211yesmaximal, characteristic, complemented
12C23×C4×D71C2211yescharacteristic
13C22×Dic71⋊C4C2212yes—
14C22×(C2×D71)⋊C4C2212yes—
15C22×(C2×D71)⋊C4C2212yes—
16C22×(C2×D71)⋊C4C2211yescharacteristic
17C22×(C2×D71)⋊C4C2211yescharacteristic
18C22×C4×Dic71C2211yescharacteristic
19C22×C4×Dic71C2211yescharacteristic
20C22×C4×Dic71C2211yescharacteristic
21#17985890C4116yesdirect product factor
22C4×Dic71⋊C4—24no—
23C4×(C2×D71)⋊C4—24no—
24C4×(C2×D71)⋊C4—24no—
25C4×(C2×D71)⋊C4C418yescomplemented
26C2×C71⋊#95C2212yes—
27C2×C71⋊#95C2212yes—
28C2×C71⋊#95C2212yes—
29C2×C71⋊#95C2212yes—
30C2×C71⋊#95C2212yes—
31C2×C71⋊#95C2211yescharacteristic
32C2×C71⋊#95C2211yescharacteristic
33C2×C71⋊#95C2212yes—
34C2×C71⋊#95C2212yes—
35C22×C42×C71C2212yes—
36C22×C42×C71C2211yescharacteristic
37C22×C42×C71C2212yes—
38C22×C42×C71C2211yescharacteristic
39C22×C42×C71C2211yescharacteristic
40C43×C71—24no—
41C24×D71C2311yescharacteristic
42C23×Dic71C2311yescharacteristic
43C23×Dic71C2311yescharacteristic
44C23×Dic71C2312yes—
45C23×Dic71C2312yes—
46C23×Dic71C2311yescharacteristic
47C22×C4×D71—22no—
48C22×C4×D71—22no—
49C22×C4×D71—22no—
50C22×C4×D71—22no—
51C22×C4×D71—22no—
52C22×C4×D71—22no—
53C22×C4×D71C2×C414yes—
54C2×Dic71⋊C4—24no—
55C2×Dic71⋊C4—24no—
56C2×Dic71⋊C4C2×C418yescomplemented
57C2×(C2×D71)⋊C4—24no—
58C2×(C2×D71)⋊C4—24no—
59C2×(C2×D71)⋊C4—24no—
60C2×(C2×D71)⋊C4—24no—
61C2×(C2×D71)⋊C4—24no—
62C2×(C2×D71)⋊C4C2×C414yes—
63C2×(C2×D71)⋊C4C2×C418yes—
64C2×(C2×D71)⋊C4C2×C418yes—
65C2×(C2×D71)⋊C4C2×C414yes—
66C2×(C2×D71)⋊C4C2×C418yes—
67C2×C4×Dic71—22no—
68C2×C4×Dic71—22no—
69C2×C4×Dic71—22no—
70C2×C4×Dic71—22no—
71C2×C4×Dic71—22no—
72C2×C4×Dic71—22no—
73C2×C4×Dic71—22no—
74C2×C4×Dic71—22no—
75C2×C4×Dic71C2×C414yes—
76C71⋊#95—24no—
77C71⋊#95—24no—
78C71⋊#95—24no—
79C71⋊#95—24no—
80C71⋊#95—24no—
81C71⋊#95C2×C414yes—
82C71⋊#95C2×C414yes—
83C71⋊#95C2×C418yescomplemented
84C71⋊#95C2×C418yescomplemented
85C23×C4×C71C2311yescharacteristic
86C23×C4×C71C2312yes—
87C23×C4×C71C2312yes—
88C23×C4×C71C2311yescharacteristic
89C23×C4×C71C2311yescharacteristic
90C2×C42×C71—24no—
91C2×C42×C71—22no—
92C2×C42×C71—24no—
93C2×C42×C71—22no—
94C2×C42×C71—24no—
95C2×C42×C71—24no—
96C2×C42×C71—22no—
97C2×C42×C71—24no—
98C2×C42×C71—22no—
99C2×C42×C71—22no—
100C2×C42×C71—22no—
101C2×C42×C71C2×C414yes—
102C2×C42×C71C2×C418yescomplemented
103C2×C42×C71D414yes—
104C2×C42×C71D414yes—
105C23×D71—21no—
106C23×D71—21no—
107C23×D71—21no—
108C23×D71—21no—
109C23×D71—21no—
110C23×D71—21no—
111C23×D71—22no—
112C23×D71—22no—
113C23×D71—22no—
114C23×D71C22×C412yes—
115C23×D71C22×C414yes—
116C22×Dic71—21no—
117C22×Dic71—21no—
118C22×Dic71—22no—
119C22×Dic71—21no—
120C22×Dic71—21no—
121C22×Dic71—21no—
122C22×Dic71—22no—
123C22×Dic71—22no—
124C22×Dic71—22no—
125C22×Dic71—21no—
126C22×Dic71—21no—
127C22×Dic71—21no—
128C22×Dic71—21no—
129C22×Dic71—22no—
130C22×Dic71—22no—
131C22×Dic71—22no—
132C22×Dic71—22no—
133C22×Dic71—21no—
134C22×Dic71—22no—
135C22×Dic71—22no—
136C22×Dic71—22no—
137C22×Dic71—22no—
138C22×Dic71—22no—
139C22×Dic71—22no—
140C22×Dic71—22no—
141C22×Dic71C22×C412yes—
142C22×Dic71C22×C412yes—
143C22×Dic71C22×C414yes—
144C22×Dic71C22×C414yes—
145C22×Dic71C22×C412yes—
146C22×Dic71C22×C414yes—
147C2×C4×D71—28no—
148C2×C4×D71—28no—
149C2×C4×D71—28no—
150C2×C4×D71—44no—
151C2×C4×D71—44no—
152C2×C4×D71—44no—
153C2×C4×D71—44no—
154Dic71⋊C4—216no—
155(C2×D71)⋊C4—28no—
156(C2×D71)⋊C4—216no—
157(C2×D71)⋊C4—216no—
158(C2×D71)⋊C4C42116yescomplemented
159C4×Dic71—28no—
160C4×Dic71—44no—
161C4×Dic71—44no—
162C24×C71C2411yescharacteristic
163C22×C4×C71—21no—
164C22×C4×C71—22no—
165C22×C4×C71—21no—
166C22×C4×C71—21no—
167C22×C4×C71—22no—
168C22×C4×C71—21no—
169C22×C4×C71—22no—
170C22×C4×C71—22no—
171C22×C4×C71—22no—
172C22×C4×C71—22no—
173C22×C4×C71—22no—
174C22×C4×C71—22no—
175C22×C4×C71—22no—
176C22×C4×C71—22no—
177C22×C4×C71C22×C412yes—
178C22×C4×C71C22×C414yes—
179C22×C4×C71C22×C412yes—
180C22×C4×C71C22×C414yes—
181C22×C4×C71C22×C414yes—
182C22×C4×C71C22×C412yes—
183C22×C4×C71C2×D414yes—
184C22×C4×C71C2×D412yes—
185C22×C4×C71C2×D414yes—
186C22×C4×C71C2×D412yes—
187C22×C4×C71#4114yes—
188C22×C4×C71#4114yes—
189C22×C4×C71#4114yes—
190C22×C4×C71#4112yes—
191C22×C4×C71#4112yes—
192C22×C4×C71#4112yes—
193C22×C4×C71#4112yes—
194C42×C71—216no—
195C42×C71—28no—
196C42×C71—216no—
197C42×C71—28no—
198C42×C71—28no—
199C23×C71C23×C411yescharacteristic
200C23×C71C23×C412yes—
201C23×C71C22×D411yescharacteristic
202C23×C71C22×D411yescharacteristic
203C23×C71C2×#4111yescharacteristic
204C23×C71C2×#4111yescharacteristic
205C23×C71C2×#4112yes—
206C23×C71C2×#4111yescharacteristic
207C23×C71C2×#4112yes—
208C23×C71C2×#4111yescharacteristic
209C23×C71C2×#4112yes—
210C22×D71—22no—
211C22×D71—22no—
212C22×D71—24no—
213C22×D71—24no—
214C22×D71—22no—
215C22×D71—22no—
216C22×D71—24no—
217C22×D71—24no—
218C22×D71—24no—
219C22×D71—24no—
220C22×D71—22no—
221C22×D71—22no—
222C22×D71—41no—
223C22×D71—41no—
224C22×D71—42no—
225C22×D71—41no—
226C22×D71—41no—
227C22×D71—42no—
228C22×D71—42no—
229C22×D71—42no—
230C22×D71—42no—
231C22×D71—42no—
232C22×D71C2×C4214yes—
233C2×C4×C71—22no—
234C2×C4×C71—24no—
235C2×C4×C71—22no—
236C2×C4×C71—24no—
237C2×C4×C71—24no—
238C2×C4×C71—22no—
239C2×C4×C71—22no—
240C2×C4×C71—24no—
241C2×C4×C71—24no—
242C2×C4×C71—24no—
243C2×C4×C71—24no—
244C2×C4×C71—24no—
245C2×C4×C71—24no—
246C2×C4×C71—24no—
247C2×C4×C71—24no—
248C2×C4×C71—24no—
249C2×C4×C71—24no—
250C2×C4×C71—24no—
251C2×C4×C71—24no—
252C2×C4×C71—24no—
253C2×C4×C71C2×C4214yes—
254C2×C4×C71#11714yes—
255C2×C4×C71#11714yes—
256C2×C4×C71C4×D418yes—
257C2×C4×C71C4×D414yes—
258C2×C4×C71C4×D418yes—
259C2×C4×C71C4×D414yes—
260C2×C4×C71#12114yes—
261C2×C4×C71#12314yes—
262C2×C4×C71#12414yes—
263C2×C4×C71#12614yes—
264C2×Dic71—22no—
265C2×Dic71—24no—
266C2×Dic71—24no—
267C2×Dic71—22no—
268C2×Dic71—22no—
269C2×Dic71—22no—
270C2×Dic71—22no—
271C2×Dic71—24no—
272C2×Dic71—24no—
273C2×Dic71—24no—
274C2×Dic71—22no—
275C2×Dic71—22no—
276C2×Dic71—22no—
277C2×Dic71—24no—
278C2×Dic71—24no—
279C2×Dic71—24no—
280C2×Dic71—42no—
281C2×Dic71—41no—
282C2×Dic71—41no—
283C2×Dic71—42no—
284C2×Dic71—42no—
285C2×Dic71—41no—
286C2×Dic71—41no—
287C2×Dic71—42no—
288C2×Dic71—42no—
289C2×Dic71—42no—
290C2×Dic71—42no—
291C2×Dic71—42no—
292C2×Dic71—42no—
293C2×Dic71—42no—
294C2×Dic71C2×C4214yes—
295C4×D71—416no—
296C22×C71C22×C4211yescharacteristic
297C22×C71C2×#11711yescharacteristic
298C22×C71C2×#11711yescharacteristic
299C22×C71C2×C4×D411yescharacteristic
300C22×C71C2×C4×D412yes—
301C22×C71C2×C4×D411yescharacteristic
302C22×C71C2×C4×D412yes—
303C22×C71C4×#4112yes—
304C22×C71C4×#4112yes—
305C22×C71C4×#4112yes—
306C22×C71C4×#4112yes—
307C22×C71C4×#4111yescharacteristic
308C22×C71C4×#4111yescharacteristic
309C22×C71C2×#12111yescharacteristic
310C22×C71C2×#12311yescharacteristic
311C22×C71#52512yes—
312C22×C71C2×#12411yescharacteristic
313C22×C71C2×#12611yescharacteristic
314C22×C71#52912yes—
315C22×C71#52912yes—
316C22×C71#52912yes—
317C22×C71#52912yes—
318C22×C71#53212yes—
319C2×D71—24no—
320C2×D71—24no—
321C2×D71—24no—
322C2×D71—44no—
323C2×D71—42no—
324C2×D71—42no—
325C2×D71—42no—
326C2×D71—42no—
327C2×D71—44no—
328C2×D71—44no—
329C2×D71—44no—
330C4×C71—24no—
331C4×C71—24no—
332C4×C71—28no—
333C4×C71—28no—
334C4×C71#38818yescomplemented
335Dic71—24no—
336Dic71—42no—
337Dic71—42no—
338Dic71—44no—
339Dic71—44no—
340C4×#388—711nomaximal, Sylow
341C2×C71C4×#11711yescharacteristic
342C2×C71C42×D411yescharacteristic
343C2×C71C42×D411yescharacteristic
344C2×C71C2×#38811yescharacteristic
345C2×C71#229011yescharacteristic
346C2×C71#229311yescharacteristic
347C2×C71#229811yescharacteristic
348C2×C71C4×#12112yes—
349C2×C71C4×#12312yes—
350C2×C71C4×#12412yes—
351C2×C71C4×#12612yes—
352D71—44no—
353C2×#388—712no—
354C2×C4×C4⋊C4—711no—
355C2×C4×C22⋊C4—711no—
356C2×C4×C22⋊C4—711no—
357C2×C4×C22⋊C4—711no—
358C2×C43D7111yescharacteristic, complemented
359#1437—712no—
360#1436—712no—
361#1434—712no—
362C4×#95—711no—
363C4×#95—711no—
364C71C4×#38811yescharacteristic, complemented, Sylow
365C24×C4—711no—
366C22×C4⋊C4—712no—
367C22×C22⋊C4—711no—
368C22×C22⋊C4—711no—
369C22×C22⋊C4—712no—
370C22×C22⋊C4—712no—
371C22×C42—711no—
372C22×C42—711no—
373C22×C42—711no—
374C22×C42C2×D7112yes—
375C22×C42C2×D7111yescharacteristic
376C22×C42C2×D7112yes—
377C22×C42C2×D7111yescharacteristic
378C22×C42C2×D7111yescharacteristic
379#388—7116no—
380C4×C4⋊C4—1424no—
381C4×C22⋊C4—718no—
382C4×C22⋊C4—1424no—
383C4×C22⋊C4—1424no—
384C2×#95—712no—
385C2×#95—712no—
386C2×#95—711no—
387C2×#95—711no—
388C2×#95—712no—
389C2×#95—712no—
390C2×#95—712no—
391C2×#95—712no—
392C2×#95—712no—
393C43—24no—
394C25—711no—
395C23×C4—711no—
396C23×C4—712no—
397C23×C4—712no—
398C23×C4—711no—
399C23×C4—711no—
400C23×C4—714no—
401C23×C4—1422no—
402C23×C4—1422no—
403C23×C4—1422no—
404C23×C4—1422no—
405C23×C4—1422no—
406C23×C4—1422no—
407C23×C4C22×D7111yescharacteristic
408C23×C4C22×D7112yes—
409C23×C4C22×D7112yes—
410C23×C4C22×D7111yescharacteristic
411C23×C4C22×D7111yescharacteristic
412C2×C4⋊C4—718no—
413C2×C4⋊C4—1424no—
414C2×C4⋊C4—1424no—
415C2×C22⋊C4—714no—
416C2×C22⋊C4—718no—
417C2×C22⋊C4—714no—
418C2×C22⋊C4—718no—
419C2×C22⋊C4—718no—
420C2×C22⋊C4—1424no—
421C2×C22⋊C4—1424no—
422C2×C22⋊C4—1424no—
423C2×C22⋊C4—1424no—
424C2×C22⋊C4—1424no—
425C2×C42—24no—
426C2×C42—22no—
427C2×C42—24no—
428C2×C42—22no—
429C2×C42—24no—
430C2×C42—24no—
431C2×C42—22no—
432C2×C42—24no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—714no—
437C2×C42—1422no—
438C2×C42—1422no—
439C2×C42—1422no—
440C2×C42—1422no—
441C2×C42—1422no—
442C2×C42—1422no—
443C2×C42—1422no—
444C2×C42—1422no—
445C2×C42C4×D7114yes—
446C2×C42C4×D7118yescomplemented
447C2×C42D28414yes—
448C2×C42C22⋊D7114yes—
449#95—714no—
450#95—714no—
451#95—718no—
452#95—718no—
453#95—1424no—
454#95—1424no—
455#95—1424no—
456#95—1424no—
457#95—1424no—
458C24—714no—
459C24—712no—
460C24—1421no—
461C24—1421no—
462C24—1422no—
463C24—1422no—
464C24—1422no—
465C24—1421no—
466C24—1421no—
467C24—1421no—
468C24—1421no—
469C24C23×D7111yescharacteristic
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—2844no—
485C22×C4—2844no—
486C22×C4—2844no—
487C22×C4—2844no—
488C22×C4—712no—
489C22×C4—714no—
490C22×C4—714no—
491C22×C4—712no—
492C22×C4—712no—
493C22×C4—714no—
494C22×C4—1421no—
495C22×C4—1422no—
496C22×C4—1421no—
497C22×C4—1421no—
498C22×C4—1422no—
499C22×C4—1422no—
500C22×C4—1422no—
501C22×C4—1422no—
502C22×C4—1422no—
503C22×C4—1422no—
504C22×C4—1422no—
505C22×C4—1422no—
506C22×C4—1422no—
507C22×C4—1421no—
508C22×C4—1422no—
509C22×C4—1422no—
510C22×C4—1422no—
511C22×C4—1422no—
512C22×C4—1421no—
513C22×C4—1421no—
514C22×C4—1421no—
515C22×C4—1421no—
516C22×C4—1428no—
517C22×C4—1428no—
518C22×C4—1428no—
519C22×C4—1421no—
520C22×C4—1421no—
521C22×C4—1422no—
522C22×C4C2×C4×D7112yes—
523C22×C4C2×C4×D7114yes—
524C22×C4C2×C4×D7112yes—
525C22×C4C2×C4×D7114yes—
526C22×C4C2×C4×D7114yes—
527C22×C4C2×C4×D7112yes—
528C22×C4C2×C22⋊D7114yes—
529C22×C4C2×C22⋊D7112yes—
530C22×C4C2×D28414yes—
531C22×C4C2×D28412yes—
532C22×C4#1176586514yes—
533C22×C4#1176586514yes—
534C22×C4#1176586514yes—
535C22×C4#1176586512yes—
536C22×C4#1176586512yes—
537C22×C4#1176586512yes—
538C22×C4#1176586512yes—
539C4⋊C4—14216no—
540C22⋊C4—7116no—
541C22⋊C4—1428no—
542C22⋊C4—14216no—
543C22⋊C4—14216no—
544C42—216no—
545C42—28no—
546C42—216no—
547C42—28no—
548C42—28no—
549C42—2844no—
550C42—2844no—
551C42—1428no—
552C23—2841no—
553C23—2841no—
554C23—2842no—
555C23—2841no—
556C23—2841no—
557C23—2842no—
558C23—2842no—
559C23—2842no—
560C23—2842no—
561C23—2842no—
562C23—714no—
563C23—1422no—
564C23—1422no—
565C23—1424no—
566C23—1422no—
567C23—1424no—
568C23—1422no—
569C23—1422no—
570C23—1422no—
571C23—1424no—
572C23—1424no—
573C23—1424no—
574C23—1424no—
575C23C22×C4×D7111yescharacteristic
576C23C22×C4×D7112yes—
577C23C22×C22⋊D7111yescharacteristic
578C23C22×D28411yescharacteristic
579C23C2×#1176586511yescharacteristic
580C23C2×#1176586511yescharacteristic
581C23C2×#1176586512yes—
582C23C2×#1176586511yescharacteristic
583C23C2×#1176586512yes—
584C23C2×#1176586511yescharacteristic
585C23C2×#1176586512yes—
586C2×C4—22no—
587C2×C4—24no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—22no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—2842no—
607C2×C4—2841no—
608C2×C4—2841no—
609C2×C4—2842no—
610C2×C4—2842no—
611C2×C4—2841no—
612C2×C4—2841no—
613C2×C4—2842no—
614C2×C4—2842no—
615C2×C4—2842no—
616C2×C4—2842no—
617C2×C4—2842no—
618C2×C4—2842no—
619C2×C4—2842no—
620C2×C4—28416no—
621C2×C4—714no—
622C2×C4—1422no—
623C2×C4—1422no—
624C2×C4—1424no—
625C2×C4—1422no—
626C2×C4—1422no—
627C2×C4—1424no—
628C2×C4—1424no—
629C2×C4—1422no—
630C2×C4—1422no—
631C2×C4—1424no—
632C2×C4—1424no—
633C2×C4—1424no—
634C2×C4—1422no—
635C2×C4—1424no—
636C2×C4—1422no—
637C2×C4—1424no—
638C2×C4C42×D7114yes—
639C2×C4#1455608514yes—
640C2×C4#1455608514yes—
641C2×C4C4×C22⋊D7118yes—
642C2×C4C4×C22⋊D7114yes—
643C2×C4C4×D28418yes—
644C2×C4C4×D28414yes—
645C2×C4#1455610214yes—
646C2×C4#1455611114yes—
647C2×C4#1455611614yes—
648C2×C4#1455612214yes—
649C22—2842no—
650C22—2842no—
651C22—2842no—
652C22—2842no—
653C22—2844no—
654C22—2844no—
655C22—2844no—
656C22—2844no—
657C22—1424no—
658C22—1424no—
659C22—1424no—
660C22C2×C42×D7111yescharacteristic
661C22C2×#1455608511yescharacteristic
662C22C2×#1455608511yescharacteristic
663C22C2×C4×C22⋊D7111yescharacteristic
664C22C2×C4×C22⋊D7112yes—
665C22C2×C4×D28411yescharacteristic
666C22C2×C4×D28412yes—
667C22C4×#1176586511yescharacteristic
668C22C4×#1176586511yescharacteristic
669C22C4×#1176586512yes—
670C22C4×#1176586512yes—
671C22C4×#1176586512yes—
672C22C4×#1176586512yes—
673C22C2×#1455610211yescharacteristic
674C22C2×#1455611111yescharacteristic
675C22#1798651012yes—
676C22C2×#1455611611yescharacteristic
677C22C2×#1455612211yescharacteristic
678C22#1798653312yes—
679C22#1798653312yes—
680C22#1798653312yes—
681C22#1798653312yes—
682C22#1798654912yes—
683C4—24no—
684C4—28no—
685C4—28no—
686C4—24no—
687C4—2842no—
688C4—2842no—
689C4—2844no—
690C4—2844no—
691C4—1424no—
692C4#1798589018yesdirect product factor
693C2—2844no—
694C2C4×#1455608511yescharacteristic
695C2C42×C22⋊D7111yescharacteristic
696C2C42×D28411yescharacteristic
697C2C2×#1798589011yescharacteristic
698C2#2259078311yescharacteristic
699C2#2259080411yescharacteristic
700C2#2259083711yescharacteristic
701C2C4×#1455610212yes—
702C2C4×#1455611112yes—
703C2C4×#1455611612yes—
704C2C4×#1455612212yes—
subgroupG/H
centerC23×C4C22×D71
commutatorC22×C71C22×C42
FrattiniC24C23×D71
FittingC2×C43×C71C2
socle, cosocleC24×C71C24
prime radicalC24×D71C23
hypercenterC2×C43D71
hypocenterC71C4×#388
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23×C4 ◁ C2×C43

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic71⋊C4C2semidirect
7. #22586573C2semidirect
8. #22586567C2semidirect
9. C4×C71⋊#95C2semidirect
10. C4×C71⋊#95C2semidirect
11. C2×C43×C71C2semidirect
21. #17985890C4direct (N × H)
25. C4×(C2×D71)⋊C4C4semidirect
56. C2×Dic71⋊C4C2×C4semidirect
83. C71⋊#95C2×C4semidirect
84. C71⋊#95C2×C4semidirect
102. C2×C42×C71C2×C4semidirect
158. (C2×D71)⋊C4C42semidirect
334. C4×C71#388semidirect
358. C2×C43D71semidirect
364. C71C4×#388semidirect
446. C2×C42C4×D71semidirect
692. C4#17985890direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179858902
C2×C4×Dic71⋊C42
C2×C4×(C2×D71)⋊C42
#225865782
#225865732
#225865672
C4×C71⋊#952
C2×C43×C712
C4×#38871