Finite Group Databasebeta

← #31918987

Subgroups — #31918987

Order 18176.

1906 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17985889C212yesmaximal
2C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic
3C2×#17985846C211yesmaximal, characteristic
4C2×#17985844C211yesmaximal, characteristic, complemented
5#22586576C212yesmaximal
6#22586572C212yesmaximal, complemented
7#22586564C211yesmaximal, characteristic, complemented
8(C2×D71)⋊#95C211yesmaximal, characteristic
9C4×C71⋊#95C211yesmaximal, characteristic, complemented
10#95×Dic71C212yesmaximal, complemented
11C71×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D71C2211yescharacteristic
13C22×(C2×D71)⋊C4C2212yes—
14C22×(C2×D71)⋊C4C2211yescharacteristic
15C22×(C2×D71)⋊C4C2212yes—
16C22×(C2×D71)⋊C4C2211yescharacteristic
17C22×C4×Dic71C2212yes—
18C22×C4×Dic71C2212yes—
19C22×C4×Dic71C2211yescharacteristic
20C22×C4×Dic71C2212yes—
21#17985889C4116yescomplemented
22C4×(C2×D71)⋊C4C418yescomplemented
23#17985846—24no—
24#17985844—24no—
25C2×C71⋊#95C2212yes—
26C2×C71⋊#95C2211yescharacteristic
27C2×C71⋊#95C2212yes—
28C2×C71⋊#95C2212yes—
29C2×C71⋊#95C2211yescharacteristic
30C2×C71⋊#95C2211yescharacteristic
31C2×C71⋊#95C2212yes—
32C2×C71⋊#95C2212yes—
33C2×C71⋊#95C2211yescharacteristic
34C22×C4⋊C4×C71C2212yes—
35C22×C42×C71C2211yescharacteristic
36C2×#95×C71C2212yes—
37C2×#95×C71C2211yescharacteristic
38C2×#95×C71C2211yescharacteristic
39C24×D71C2311yescharacteristic
40C23×Dic71C2311yescharacteristic
41C23×Dic71C2312yes—
42C23×Dic71C2311yescharacteristic
43C23×Dic71C2312yes—
44C23×Dic71C2311yescharacteristic
45C22×C4×D71—24no—
46C22×C4×D71—22no—
47C22×C4×D71—22no—
48C22×C4×D71—42no—
49C22×C4×D71C2×C414yes—
50C2×(C2×D71)⋊C4—24no—
51C2×(C2×D71)⋊C4—24no—
52C2×(C2×D71)⋊C4—22no—
53C2×(C2×D71)⋊C4—22no—
54C2×(C2×D71)⋊C4—42no—
55C2×(C2×D71)⋊C4—42no—
56C2×(C2×D71)⋊C4C2×C414yes—
57C2×(C2×D71)⋊C4C2×C418yes—
58C2×(C2×D71)⋊C4C2×C418yes—
59C2×(C2×D71)⋊C4C2×C414yes—
60C2×(C2×D71)⋊C4C2×C418yes—
61C2×C4×Dic71—24no—
62C2×C4×Dic71—24no—
63C2×C4×Dic71—24no—
64C2×C4×Dic71—24no—
65C2×C4×Dic71—24no—
66C2×C4×Dic71—22no—
67C2×C4×Dic71—22no—
68C2×C4×Dic71—24no—
69C2×C4×Dic71—42no—
70C2×C4×Dic71—42no—
71C2×C4×Dic71C2×C414yes—
72C2×C4×Dic71C2×C418yescomplemented
73C71⋊#95—24no—
74C71⋊#95—24no—
75C71⋊#95—22no—
76C71⋊#95—42no—
77C71⋊#95C2×C414yes—
78C71⋊#95C2×C414yes—
79C71⋊#95C2×C418yescomplemented
80C71⋊#95C2×C418yescomplemented
81C71⋊#95D414yes—
82C23×C4×C71C2312yes—
83C23×C4×C71C2312yes—
84C23×C4×C71C2311yescharacteristic
85C23×C4×C71C2311yescharacteristic
86C23×C4×C71C2311yescharacteristic
87C2×C4⋊C4×C71—42no—
88C2×C4⋊C4×C71—42no—
89C2×C4⋊C4×C71C2×C418yescomplemented
90C2×C42×C71—42no—
91C2×C42×C71C2×C414yes—
92#95×C71—22no—
93#95×C71—22no—
94#95×C71—24no—
95C23×D71—21no—
96C23×D71—22no—
97C23×D71—21no—
98C23×D71—22no—
99C23×D71—21no—
100C23×D71—21no—
101C23×D71—22no—
102C23×D71—21no—
103C23×D71—21no—
104C23×D71C22×C412yes—
105C23×D71C22×C414yes—
106C22×Dic71—21no—
107C22×Dic71—21no—
108C22×Dic71—21no—
109C22×Dic71—22no—
110C22×Dic71—22no—
111C22×Dic71—21no—
112C22×Dic71—22no—
113C22×Dic71—22no—
114C22×Dic71—22no—
115C22×Dic71—22no—
116C22×Dic71—21no—
117C22×Dic71—22no—
118C22×Dic71—22no—
119C22×Dic71—22no—
120C22×Dic71—21no—
121C22×Dic71—22no—
122C22×Dic71—21no—
123C22×Dic71—21no—
124C22×Dic71—21no—
125C22×Dic71—22no—
126C22×Dic71—22no—
127C22×Dic71—21no—
128C22×Dic71C22×C412yes—
129C22×Dic71C22×C414yes—
130C22×Dic71C22×C412yes—
131C22×Dic71C22×C414yes—
132C22×Dic71C22×C412yes—
133C22×Dic71C22×C414yes—
134C22×Dic71C2×D414yes—
135C22×Dic71#4114yes—
136C22×Dic71#4114yes—
137C2×C4×D71—28no—
138C2×C4×D71—28no—
139C2×C4×D71—44no—
140C2×C4×D71—48no—
141C2×C4×D71—48no—
142(C2×D71)⋊C4—28no—
143(C2×D71)⋊C4—216no—
144(C2×D71)⋊C4—48no—
145(C2×D71)⋊C4C42116yescomplemented
146C4×Dic71—28no—
147C4×Dic71—216no—
148C4×Dic71—48no—
149C4×Dic71—48no—
150C24×C71C2411yescharacteristic
151C22×C4×C71—22no—
152C22×C4×C71—22no—
153C22×C4×C71—22no—
154C22×C4×C71—22no—
155C22×C4×C71—22no—
156C22×C4×C71—21no—
157C22×C4×C71—21no—
158C22×C4×C71—22no—
159C22×C4×C71—22no—
160C22×C4×C71—22no—
161C22×C4×C71—22no—
162C22×C4×C71—22no—
163C22×C4×C71—22no—
164C22×C4×C71—22no—
165C22×C4×C71—22no—
166C22×C4×C71—22no—
167C22×C4×C71—22no—
168C22×C4×C71—22no—
169C22×C4×C71—22no—
170C22×C4×C71C22×C414yes—
171C22×C4×C71C22×C414yes—
172C22×C4×C71C22×C412yes—
173C22×C4×C71C22×C414yes—
174C22×C4×C71C22×C412yes—
175C22×C4×C71C22×C412yes—
176C22×C4×C71C2×D412yes—
177C22×C4×C71#4112yes—
178C22×C4×C71#4112yes—
179C22×C4×C71#4112yes—
180C4⋊C4×C71—48no—
181C42×C71—44no—
182C23×C71C23×C411yescharacteristic
183C23×C71C23×C412yes—
184C23×C71C22×D411yescharacteristic
185C23×C71C2×#4112yes—
186C23×C71C2×#4112yes—
187C23×C71C2×#4111yescharacteristic
188C23×C71C2×#4111yescharacteristic
189C23×C71C2×#4111yescharacteristic
190C23×C71H(5,𝔽2)12yes—
191C23×C71H(5,𝔽2)11yescharacteristic
192C23×C712−1+411yescharacteristic
193C22×D71—22no—
194C22×D71—22no—
195C22×D71—24no—
196C22×D71—22no—
197C22×D71—24no—
198C22×D71—22no—
199C22×D71—24no—
200C22×D71—24no—
201C22×D71—24no—
202C22×D71—22no—
203C22×D71—22no—
204C22×D71—24no—
205C22×D71—42no—
206C22×D71—41no—
207C22×D71—41no—
208C22×D71—42no—
209C22×D71—42no—
210C22×D71—42no—
211C22×D71—42no—
212C22×D71—42no—
213C22×D71—41no—
214C22×D71—41no—
215C22×D71C2×C4214yes—
216C2×C4×C71—22no—
217C2×C4×C71—22no—
218C2×C4×C71—22no—
219C2×C4×C71—22no—
220C2×C4×C71—22no—
221C2×C4×C71—24no—
222C2×C4×C71—22no—
223C2×C4×C71—24no—
224C2×C4×C71—24no—
225C2×C4×C71—24no—
226C2×C4×C71—24no—
227C2×C4×C71—24no—
228C2×C4×C71—24no—
229C2×C4×C71—24no—
230C2×C4×C71—24no—
231C2×C4×C71—24no—
232C2×C4×C71—24no—
233C2×C4×C71—24no—
234C2×C4×C71—42no—
235C2×C4×C71—42no—
236C2×C4×C71—42no—
237C2×C4×C71—42no—
238C2×C4×C71—42no—
239C2×C4×C71—42no—
240C2×C4×C71—42no—
241C2×C4×C71—42no—
242C2×C4×C71C2×C4214yes—
243C2×C4×C71#11714yes—
244C2×C4×C71C4×D414yes—
245C2×Dic71—24no—
246C2×Dic71—22no—
247C2×Dic71—22no—
248C2×Dic71—22no—
249C2×Dic71—24no—
250C2×Dic71—24no—
251C2×Dic71—22no—
252C2×Dic71—24no—
253C2×Dic71—24no—
254C2×Dic71—24no—
255C2×Dic71—24no—
256C2×Dic71—24no—
257C2×Dic71—24no—
258C2×Dic71—24no—
259C2×Dic71—22no—
260C2×Dic71—22no—
261C2×Dic71—24no—
262C2×Dic71—24no—
263C2×Dic71—24no—
264C2×Dic71—22no—
265C2×Dic71—41no—
266C2×Dic71—41no—
267C2×Dic71—42no—
268C2×Dic71—42no—
269C2×Dic71—42no—
270C2×Dic71—41no—
271C2×Dic71—42no—
272C2×Dic71—41no—
273C2×Dic71C2×C4214yes—
274C2×Dic71#11714yes—
275C2×Dic71C4×D418yes—
276C4×D71—416no—
277C22×C71C22×C4211yescharacteristic
278C22×C71C2×#11711yescharacteristic
279C22×C71C2×#11711yescharacteristic
280C22×C71C2×C4×D412yes—
281C22×C71C2×C4×D411yescharacteristic
282C22×C71C4×#4112yes—
283C22×C71C4×#4111yescharacteristic
284C22×C71C4×#4112yes—
285C22×C71C4×#4112yes—
286C22×C71#51811yescharacteristic
287C22×C71#51812yes—
288C22×C71#52011yescharacteristic
289C22×C71#52012yes—
290C22×C71#54612yes—
291C22×C71#54711yescharacteristic
292C22×C71#55011yescharacteristic
293C22×C71#55112yes—
294C22×C71#55112yes—
295C22×C71#55212yes—
296C22×C71#55312yes—
297C22×C71#55512yes—
298C22×C71#55511yescharacteristic
299C22×C71#55611yescharacteristic
300C2×D71—24no—
301C2×D71—24no—
302C2×D71—24no—
303C2×D71—42no—
304C2×D71—42no—
305C2×D71—42no—
306C2×D71—42no—
307C2×D71—44no—
308C2×D71—44no—
309C2×D71—44no—
310C2×D71—44no—
311C4×C71—24no—
312C4×C71—24no—
313C4×C71—24no—
314C4×C71—44no—
315C4×C71—44no—
316Dic71—24no—
317Dic71—28no—
318Dic71—24no—
319Dic71—42no—
320Dic71—44no—
321#13816—711nomaximal, Sylow
322C2×C71C4×#11711yescharacteristic
323C2×C71C42×D411yescharacteristic
324C2×C71#227511yescharacteristic
325C2×C71#234211yescharacteristic
326C2×C71#234611yescharacteristic
327C2×C71#235311yescharacteristic
328C2×C71#235411yescharacteristic
329C2×C71#235912yes—
330C2×C71#236312yes—
331C2×C71#237212yes—
332C2×C71#237312yes—
333D71—44no—
334C2×#388—712no—
335C2×C4×C22⋊C4—711no—
336C2×C4×C22⋊C4—711no—
337C2×#376—711no—
338#1437—712no—
339#1436—712no—
340C4⋊#95D7111yescharacteristic, complemented
341#1434—711no—
342C22⋊#95—711no—
343C4×#95—711no—
344C4×#95—712no—
345C71#1381611yescharacteristic, complemented, Sylow
346C24×C4—711no—
347C22×C4⋊C4C2×D7112yes—
348C22×C22⋊C4—712no—
349C22×C22⋊C4—711no—
350C22×C22⋊C4—711no—
351C22×C22⋊C4—712no—
352C22×C42—712no—
353C22×C42—712no—
354C22×C42—712no—
355C22×C42—711no—
356C22×C42C2×D7111yescharacteristic
357#388—7116no—
358C4×C22⋊C4—718no—
359C4×C22⋊C4—1424no—
360#376—1424no—
361C2×#95—712no—
362C2×#95—711no—
363C2×#95—712no—
364C2×#95—712no—
365C2×#95—711no—
366C2×#95—711no—
367C2×#95—711no—
368C2×#95—712no—
369C2×#95—712no—
370C2×#95C2×D7112yes—
371C2×#95C2×D7111yescharacteristic
372C2×#95C2×D7111yescharacteristic
373C25—711no—
374C23×C4—2842no—
375C23×C4—714no—
376C23×C4—711no—
377C23×C4—712no—
378C23×C4—711no—
379C23×C4—712no—
380C23×C4—711no—
381C23×C4—1424no—
382C23×C4—1422no—
383C23×C4—1422no—
384C23×C4C22×D7112yes—
385C23×C4C22×D7112yes—
386C23×C4C22×D7111yescharacteristic
387C23×C4C22×D7111yescharacteristic
388C23×C4C22×D7111yescharacteristic
389C2×C4⋊C4—42no—
390C2×C4⋊C4—42no—
391C2×C4⋊C4C4×D7118yescomplemented
392C2×C22⋊C4—2842no—
393C2×C22⋊C4—2842no—
394C2×C22⋊C4—718no—
395C2×C22⋊C4—714no—
396C2×C22⋊C4—718no—
397C2×C22⋊C4—714no—
398C2×C22⋊C4—718no—
399C2×C22⋊C4—1424no—
400C2×C22⋊C4—1424no—
401C2×C22⋊C4—1422no—
402C2×C22⋊C4—1422no—
403C2×C42—42no—
404C2×C42—2842no—
405C2×C42—2842no—
406C2×C42—714no—
407C2×C42—718no—
408C2×C42—1424no—
409C2×C42—1424no—
410C2×C42—1424no—
411C2×C42—1424no—
412C2×C42—1424no—
413C2×C42—1424no—
414C2×C42—1422no—
415C2×C42—1422no—
416C2×C42C4×D7114yes—
417#95—22no—
418#95—22no—
419#95—24no—
420#95—2842no—
421#95—714no—
422#95—714no—
423#95—718no—
424#95—718no—
425#95—714no—
426#95—1424no—
427#95—1424no—
428#95—1422no—
429C24—714no—
430C24—712no—
431C24—1421no—
432C24—1422no—
433C24—1422no—
434C24—1421no—
435C24—1421no—
436C24—1421no—
437C24—1421no—
438C24—1422no—
439C24—1421no—
440C24C23×D7111yescharacteristic
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—2848no—
461C22×C4—2848no—
462C22×C4—2844no—
463C22×C4—712no—
464C22×C4—714no—
465C22×C4—712no—
466C22×C4—714no—
467C22×C4—714no—
468C22×C4—714no—
469C22×C4—714no—
470C22×C4—714no—
471C22×C4—712no—
472C22×C4—1428no—
473C22×C4—1421no—
474C22×C4—1422no—
475C22×C4—1422no—
476C22×C4—1421no—
477C22×C4—1422no—
478C22×C4—1422no—
479C22×C4—1421no—
480C22×C4—1421no—
481C22×C4—1421no—
482C22×C4—1422no—
483C22×C4—1422no—
484C22×C4—1421no—
485C22×C4—1428no—
486C22×C4—1421no—
487C22×C4—1421no—
488C22×C4—1422no—
489C22×C4—1422no—
490C22×C4—1422no—
491C22×C4—1421no—
492C22×C4—1421no—
493C22×C4—1422no—
494C22×C4—1422no—
495C22×C4—1422no—
496C22×C4C2×C4×D7114yes—
497C22×C4C2×C4×D7114yes—
498C22×C4C2×C4×D7112yes—
499C22×C4C2×C4×D7114yes—
500C22×C4C2×C4×D7112yes—
501C22×C4C2×C4×D7112yes—
502C22×C4D4×D7112yes—
503C22×C4#1176586412yes—
504C22×C4#1176586612yes—
505C22×C4#1176586612yes—
506C4⋊C4—48no—
507C22⋊C4—2848no—
508C22⋊C4—7116no—
509C22⋊C4—14216no—
510C22⋊C4—1428no—
511C42—44no—
512C42—2848no—
513C42—2848no—
514C42—14216no—
515C42—1428no—
516C23—2842no—
517C23—2841no—
518C23—2841no—
519C23—2842no—
520C23—2842no—
521C23—2842no—
522C23—2842no—
523C23—2842no—
524C23—2841no—
525C23—2841no—
526C23—714no—
527C23—1422no—
528C23—1422no—
529C23—1424no—
530C23—1422no—
531C23—1424no—
532C23—1422no—
533C23—1424no—
534C23—1424no—
535C23—1424no—
536C23—1422no—
537C23—1422no—
538C23—1424no—
539C23C22×C4×D7111yescharacteristic
540C23C22×C4×D7112yes—
541C23C2×D4×D7111yescharacteristic
542C23#41×D7112yes—
543C23#41×D7112yes—
544C23C2×#1176586411yescharacteristic
545C23C2×#1176586611yescharacteristic
546C23C2×#1176586611yescharacteristic
547C23#1455617312yes—
548C23#1455617311yescharacteristic
549C23#1455617611yescharacteristic
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—28416no—
577C2×C4—2841no—
578C2×C4—2841no—
579C2×C4—2842no—
580C2×C4—2842no—
581C2×C4—2842no—
582C2×C4—2841no—
583C2×C4—2842no—
584C2×C4—2841no—
585C2×C4—714no—
586C2×C4—714no—
587C2×C4—718no—
588C2×C4—1422no—
589C2×C4—1422no—
590C2×C4—1424no—
591C2×C4—1424no—
592C2×C4—1424no—
593C2×C4—1422no—
594C2×C4—1424no—
595C2×C4—1424no—
596C2×C4—1424no—
597C2×C4—1424no—
598C2×C4—1424no—
599C2×C4—1424no—
600C2×C4—1424no—
601C2×C4—1422no—
602C2×C4—1422no—
603C2×C4—1422no—
604C2×C4—1424no—
605C2×C4—1424no—
606C2×C4—1422no—
607C2×C4—1424no—
608C2×C4C42×D7114yes—
609C2×C4#1455608614yes—
610C2×C4#1455609014yes—
611C22—2842no—
612C22—2842no—
613C22—2844no—
614C22—2844no—
615C22—2842no—
616C22—2844no—
617C22—2844no—
618C22—2842no—
619C22—1424no—
620C22—1424no—
621C22—1424no—
622C22C2×C42×D7111yescharacteristic
623C22#117×D7111yescharacteristic
624C22C2×#1455608611yescharacteristic
625C22C4×D4×D7112yes—
626C22C2×#1455609011yescharacteristic
627C22C4×#1176586412yes—
628C22#1798646711yescharacteristic
629C22C4×#1176586612yes—
630C22C4×#1176586612yes—
631C22#1798647211yescharacteristic
632C22#1798647212yes—
633C22#1798648011yescharacteristic
634C22#1798648012yes—
635C22#1798663812yes—
636C22#1798665211yescharacteristic
637C22#1798666911yescharacteristic
638C22#1798667612yes—
639C22#1798667612yes—
640C22#1798668112yes—
641C22#1798669212yes—
642C22#1798671112yes—
643C22#1798671511yescharacteristic
644C22#1798672311yescharacteristic
645C4—24no—
646C4—24no—
647C4—24no—
648C4—44no—
649C4—44no—
650C4—2842no—
651C4—2844no—
652C4—1428no—
653C4—1424no—
654C4—1424no—
655C2—2844no—
656C2C4×#1455608611yescharacteristic
657C2C4×#1455609011yescharacteristic
658C2#2259069811yescharacteristic
659C2#2259118611yescharacteristic
660C2#2259122011yescharacteristic
661C2#2259128211yescharacteristic
662C2#2259129111yescharacteristic
663C2#2259132712yes—
664C2#2259137512yes—
665C2#2259145112yes—
666C2#2259146312yes—
subgroupG/H
center, FrattiniC24C23×D71
commutatorC22×C71C22×C42
FittingC71×C4⋊#95C2
socle, cosocleC24×C71C24
prime radicalC24×D71C23
hypercenterC4⋊#95D71
hypocenterC71#13816
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#17985844C2semidirect
6. #22586572C2semidirect
7. #22586564C2semidirect
9. C4×C71⋊#95C2semidirect
10. #95×Dic71C2semidirect
11. C71×C4⋊#95C2semidirect
21. #17985889C4semidirect
22. C4×(C2×D71)⋊C4C4semidirect
72. C2×C4×Dic71C2×C4semidirect
79. C71⋊#95C2×C4semidirect
80. C71⋊#95C2×C4semidirect
89. C2×C4⋊C4×C71C2×C4semidirect
145. (C2×D71)⋊C4C42semidirect
340. C4⋊#95D71semidirect
345. C71#13816semidirect
391. C2×C4⋊C4C4×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179858892
C2×C4×(C2×D71)⋊C42
C2×#179858462
C2×#179858442
#225865762
#225865722
#225865642
(C2×D71)⋊#952
C4×C71⋊#952
#95×Dic712
C71×C4⋊#952
#1381671