Finite Group Databasebeta

← #31918924

Subgroups — #31918924

Order 18176.

2154 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic
2C2×#17985846C212yesmaximal
3C2×#17985845C211yesmaximal, characteristic, complemented
4C2×#95×D71C211yesmaximal, characteristic
5#22586566C211yesmaximal, characteristic, complemented
6#22586565C212yesmaximal, complemented
7#22586564C212yesmaximal, complemented
8(C2×D71)⋊#95C212yesmaximal
9(C2×D71)⋊#95C211yesmaximal, characteristic
10#95×Dic71C211yesmaximal, characteristic, complemented
11C71×#1434C211yesmaximal, characteristic, complemented
12C23×C4×D71C2212yes—
13C23×C4×D71C2211yescharacteristic
14C22×(C2×D71)⋊C4C2212yes—
15C22×(C2×D71)⋊C4C2211yescharacteristic
16C22×(C2×D71)⋊C4C2211yescharacteristic
17C22×C4×Dic71C2212yes—
18C22×C4×Dic71C2212yes—
19C22×C4×Dic71C2211yescharacteristic
20C4×(C2×D71)⋊C4C418yescomplemented
21#17985846C4116yescomplemented
22#17985845—24no—
23C2×C71⋊#95C2212yes—
24C2×C71⋊#95C2212yes—
25C2×C71⋊#95C2211yescharacteristic
26C2×C71⋊#95C2212yes—
27C2×C71⋊#95C2212yes—
28C2×C71⋊#95C2212yes—
29C2×C71⋊#95C2211yescharacteristic
30C2×C71⋊#95C2212yes—
31C2×C71⋊#95C2211yescharacteristic
32C2×C71⋊#95C2211yescharacteristic
33#95×D71—24no—
34C22×C42×C71C2211yescharacteristic
35C2×#95×C71C2211yescharacteristic
36C2×#95×C71C2211yescharacteristic
37C2×#95×C71C2212yes—
38C2×#95×C71C2212yes—
39C24×D71C2311yescharacteristic
40C23×Dic71C2311yescharacteristic
41C23×Dic71C2312yes—
42C23×Dic71C2311yescharacteristic
43C23×Dic71C2311yescharacteristic
44C23×Dic71C2312yes—
45C22×C4×D71—24no—
46C22×C4×D71—24no—
47C22×C4×D71—24no—
48C22×C4×D71—24no—
49C22×C4×D71—24no—
50C22×C4×D71—22no—
51C22×C4×D71—22no—
52C22×C4×D71—42no—
53C22×C4×D71—42no—
54C22×C4×D71—42no—
55C22×C4×D71C2×C418yes—
56C22×C4×D71C2×C414yes—
57C2×(C2×D71)⋊C4—24no—
58C2×(C2×D71)⋊C4—22no—
59C2×(C2×D71)⋊C4—24no—
60C2×(C2×D71)⋊C4—22no—
61C2×(C2×D71)⋊C4C2×C418yes—
62C2×(C2×D71)⋊C4C2×C414yes—
63C2×(C2×D71)⋊C4C2×C418yes—
64C2×(C2×D71)⋊C4C2×C414yes—
65C2×C4×Dic71—24no—
66C2×C4×Dic71—24no—
67C2×C4×Dic71—42no—
68C2×C4×Dic71—42no—
69C2×C4×Dic71—42no—
70C2×C4×Dic71C2×C418yescomplemented
71C2×C4×Dic71C2×C418yescomplemented
72C2×C4×Dic71C2×C414yescomplemented
73C71⋊#95—24no—
74C71⋊#95—24no—
75C71⋊#95—24no—
76C71⋊#95—22no—
77C71⋊#95—42no—
78C71⋊#95—42no—
79C71⋊#95C2×C418yescomplemented
80C71⋊#95C2×C414yescomplemented
81C71⋊#95C2×C414yescomplemented
82C71⋊#95D414yes—
83C23×C4×C71C2312yes—
84C23×C4×C71C2311yescharacteristic
85C23×C4×C71C2312yes—
86C23×C4×C71C2311yescharacteristic
87C23×C4×C71C2311yescharacteristic
88C2×C42×C71—22no—
89C2×C42×C71—22no—
90C2×C42×C71C2×C414yescomplemented
91#95×C71—22no—
92#95×C71—22no—
93#95×C71—42no—
94#95×C71C2×C418yescomplemented
95C23×D71—21no—
96C23×D71—22no—
97C23×D71—21no—
98C23×D71—21no—
99C23×D71—22no—
100C23×D71—21no—
101C23×D71C22×C414yes—
102C23×D71C22×C412yes—
103C23×D71#4114yes—
104C23×D71#4112yes—
105C23×D71#4112yes—
106C22×Dic71—22no—
107C22×Dic71—22no—
108C22×Dic71—22no—
109C22×Dic71—22no—
110C22×Dic71—21no—
111C22×Dic71—22no—
112C22×Dic71—21no—
113C22×Dic71—21no—
114C22×Dic71—22no—
115C22×Dic71—22no—
116C22×Dic71—21no—
117C22×Dic71—22no—
118C22×Dic71—22no—
119C22×Dic71—22no—
120C22×Dic71—22no—
121C22×Dic71—21no—
122C22×Dic71—21no—
123C22×Dic71—22no—
124C22×Dic71—22no—
125C22×Dic71—22no—
126C22×Dic71—22no—
127C22×Dic71C22×C412yes—
128C22×Dic71C22×C414yes—
129C22×Dic71C22×C412yes—
130C22×Dic71C22×C414yes—
131C22×Dic71C22×C412yes—
132C22×Dic71C22×C414yes—
133C22×Dic71C2×D414yes—
134C22×Dic71#4114yes—
135C2×C4×D71—216no—
136C2×C4×D71—28no—
137C2×C4×D71—28no—
138C2×C4×D71—216no—
139C2×C4×D71—48no—
140C2×C4×D71—44no—
141C2×C4×D71—48no—
142C2×C4×D71—48no—
143C2×C4×D71—48no—
144C2×C4×D71—48no—
145C2×C4×D71—48no—
146C2×C4×D71—48no—
147(C2×D71)⋊C4—216no—
148(C2×D71)⋊C4—28no—
149(C2×D71)⋊C4C42116yes—
150C4×Dic71—216no—
151C4×Dic71—48no—
152C4×Dic71—44no—
153C24×C71C2411yescharacteristic
154C22×C4×C71—21no—
155C22×C4×C71—22no—
156C22×C4×C71—21no—
157C22×C4×C71—22no—
158C22×C4×C71—22no—
159C22×C4×C71—22no—
160C22×C4×C71—21no—
161C22×C4×C71—22no—
162C22×C4×C71—22no—
163C22×C4×C71—22no—
164C22×C4×C71—22no—
165C22×C4×C71—21no—
166C22×C4×C71—22no—
167C22×C4×C71—21no—
168C22×C4×C71—21no—
169C22×C4×C71—22no—
170C22×C4×C71—22no—
171C22×C4×C71—22no—
172C22×C4×C71—22no—
173C22×C4×C71—21no—
174C22×C4×C71—22no—
175C22×C4×C71—22no—
176C22×C4×C71—21no—
177C22×C4×C71C22×C414yes—
178C22×C4×C71C22×C414yes—
179C22×C4×C71C22×C412yes—
180C22×C4×C71C22×C414yes—
181C22×C4×C71C22×C412yes—
182C22×C4×C71C22×C412yes—
183C22×C4×C71C2×D412yes—
184C22×C4×C71#4112yes—
185C42×C71—28no—
186C23×C71C23×C412yes—
187C23×C71C23×C411yescharacteristic
188C23×C71C22×D411yescharacteristic
189C23×C71C2×#4112yes—
190C23×C71C2×#4111yescharacteristic
191C23×C71C2×#4111yescharacteristic
192C23×C71C2×#4112yes—
193C23×C71C2×#4111yescharacteristic
194C23×C71H(5,𝔽2)11yescharacteristic
195C23×C71H(5,𝔽2)12yes—
196C23×C712−1+411yescharacteristic
197C22×D71—24no—
198C22×D71—22no—
199C22×D71—24no—
200C22×D71—22no—
201C22×D71—24no—
202C22×D71—22no—
203C22×D71—22no—
204C22×D71—24no—
205C22×D71—24no—
206C22×D71—22no—
207C22×D71—22no—
208C22×D71—24no—
209C22×D71—24no—
210C22×D71—24no—
211C22×D71—24no—
212C22×D71—22no—
213C22×D71—22no—
214C22×D71—24no—
215C22×D71C2×C4214yes—
216C22×D71#11714yes—
217C22×D71#11718yes—
218C22×D71#11714yes—
219C22×D71#11718yes—
220C2×C4×C71—22no—
221C2×C4×C71—22no—
222C2×C4×C71—24no—
223C2×C4×C71—24no—
224C2×C4×C71—22no—
225C2×C4×C71—22no—
226C2×C4×C71—24no—
227C2×C4×C71—24no—
228C2×C4×C71—22no—
229C2×C4×C71—24no—
230C2×C4×C71—24no—
231C2×C4×C71—22no—
232C2×C4×C71—24no—
233C2×C4×C71—24no—
234C2×C4×C71—24no—
235C2×C4×C71—24no—
236C2×C4×C71—22no—
237C2×C4×C71—41no—
238C2×C4×C71—42no—
239C2×C4×C71—42no—
240C2×C4×C71—41no—
241C2×C4×C71—42no—
242C2×C4×C71—42no—
243C2×C4×C71—42no—
244C2×C4×C71—42no—
245C2×C4×C71—41no—
246C2×C4×C71—41no—
247C2×C4×C71—42no—
248C2×C4×C71—42no—
249C2×C4×C71C2×C4214yes—
250C2×C4×C71C4×D414yes—
251C2×Dic71—24no—
252C2×Dic71—24no—
253C2×Dic71—24no—
254C2×Dic71—22no—
255C2×Dic71—22no—
256C2×Dic71—24no—
257C2×Dic71—24no—
258C2×Dic71—24no—
259C2×Dic71—24no—
260C2×Dic71—24no—
261C2×Dic71—24no—
262C2×Dic71—22no—
263C2×Dic71—22no—
264C2×Dic71—24no—
265C2×Dic71—22no—
266C2×Dic71—22no—
267C2×Dic71—22no—
268C2×Dic71—22no—
269C2×Dic71—24no—
270C2×Dic71—42no—
271C2×Dic71—42no—
272C2×Dic71—42no—
273C2×Dic71—42no—
274C2×Dic71—42no—
275C2×Dic71—42no—
276C2×Dic71—42no—
277C2×Dic71—42no—
278C2×Dic71C2×C4214yes—
279C2×Dic71C4×D418yes—
280C4×D71—432no—
281C4×D71—416no—
282C22×C71C22×C4211yescharacteristic
283C22×C71C2×#11711yescharacteristic
284C22×C71C2×#11712yes—
285C22×C71C2×#11711yescharacteristic
286C22×C71C2×#11712yes—
287C22×C71C2×C4×D412yes—
288C22×C71C2×C4×D411yescharacteristic
289C22×C71C4×#4112yes—
290C22×C71C4×#4111yescharacteristic
291C22×C71#51812yes—
292C22×C71#51811yescharacteristic
293C22×C71#52011yescharacteristic
294C22×C71#52012yes—
295C22×C71#54612yes—
296C22×C71#54611yescharacteristic
297C22×C71#54811yescharacteristic
298C22×C71#55112yes—
299C22×C71#55112yes—
300C22×C71#55112yes—
301C22×C71#55212yes—
302C22×C71#55211yescharacteristic
303C22×C71#55311yescharacteristic
304C22×C71#55312yes—
305C2×D71—24no—
306C2×D71—28no—
307C2×D71—24no—
308C2×D71—28no—
309C2×D71—24no—
310C2×D71—28no—
311C2×D71—24no—
312C2×D71—28no—
313C2×D71—24no—
314C2×D71—24no—
315C2×D71#37618yescomplemented
316C4×C71—24no—
317C4×C71—24no—
318C4×C71—44no—
319C4×C71—42no—
320C4×C71—44no—
321Dic71—28no—
322Dic71—24no—
323Dic71—42no—
324Dic71—44no—
325Dic71—42no—
326#13809—711nomaximal, Sylow
327C2×C71C2×#37611yescharacteristic
328C2×C71C42×D411yescharacteristic
329C2×C71#227511yescharacteristic
330C2×C71#234211yescharacteristic
331C2×C71#234212yes—
332C2×C71#234311yescharacteristic
333C2×C71#234312yes—
334C2×C71#235211yescharacteristic
335C2×C71#235212yes—
336C2×C71#235311yescharacteristic
337C2×C71#235312yes—
338D71—28no—
339C2×C4×C22⋊C4—711no—
340C2×C4×C22⋊C4—712no—
341C2×#376—711no—
342C22×#95—711no—
343#1434—712no—
344#1434—712no—
345#1434—711no—
346#1434D7111yescharacteristic, complemented
347C22⋊#95—711no—
348C22⋊#95—712no—
349C4×#95—711no—
350C71#1380911yescharacteristic, complemented, Sylow
351C24×C4—712no—
352C24×C4—711no—
353C22×C22⋊C4—711no—
354C22×C22⋊C4—711no—
355C22×C22⋊C4—712no—
356C22×C42—712no—
357C22×C42—711no—
358C22×C42—712no—
359C22×C42C2×D7111yescharacteristic
360C4×C22⋊C4—718no—
361C4×C22⋊C4—7116no—
362#376—1424no—
363C2×#95—712no—
364C2×#95—712no—
365C2×#95—711no—
366C2×#95—712no—
367C2×#95—711no—
368C2×#95—711no—
369C2×#95—712no—
370C2×#95—712no—
371C2×#95—711no—
372C2×#95—712no—
373C2×#95—1424no—
374C2×#95C2×D7111yescharacteristic
375C2×#95C2×D7111yescharacteristic
376C2×#95C2×D7112yes—
377C2×#95C2×D7112yes—
378C25—711no—
379C23×C4—2842no—
380C23×C4—2842no—
381C23×C4—2842no—
382C23×C4—718no—
383C23×C4—714no—
384C23×C4—711no—
385C23×C4—712no—
386C23×C4—712no—
387C23×C4—711no—
388C23×C4—711no—
389C23×C4—1424no—
390C23×C4—1424no—
391C23×C4—1424no—
392C23×C4—1424no—
393C23×C4—1424no—
394C23×C4—1422no—
395C23×C4—1422no—
396C23×C4C22×D7111yescharacteristic
397C23×C4C22×D7112yes—
398C23×C4C22×D7112yes—
399C23×C4C22×D7111yescharacteristic
400C23×C4C22×D7111yescharacteristic
401C2×C22⋊C4—714no—
402C2×C22⋊C4—718no—
403C2×C22⋊C4—714no—
404C2×C22⋊C4—718no—
405C2×C22⋊C4—1422no—
406C2×C22⋊C4—1424no—
407C2×C22⋊C4—1422no—
408C2×C22⋊C4—1424no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—2842no—
412C2×C42—2842no—
413C2×C42—2842no—
414C2×C42—718no—
415C2×C42—714no—
416C2×C42—718no—
417C2×C42—1424no—
418C2×C42—1424no—
419C2×C42C4×D7114yescomplemented
420#95—22no—
421#95—22no—
422#95—42no—
423#95—2842no—
424#95—2842no—
425#95—714no—
426#95—718no—
427#95—714no—
428#95—714no—
429#95—1424no—
430#95—1424no—
431#95—1424no—
432#95—1422no—
433#95C4×D7118yescomplemented
434C24—714no—
435C24—712no—
436C24—712no—
437C24—714no—
438C24—712no—
439C24—1421no—
440C24—1422no—
441C24—1421no—
442C24—1421no—
443C24—1422no—
444C24—1421no—
445C24C23×D7111yescharacteristic
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—2848no—
470C22×C4—2848no—
471C22×C4—2844no—
472C22×C4—2848no—
473C22×C4—2848no—
474C22×C4—2848no—
475C22×C4—2848no—
476C22×C4—2848no—
477C22×C4—714no—
478C22×C4—712no—
479C22×C4—714no—
480C22×C4—714no—
481C22×C4—714no—
482C22×C4—712no—
483C22×C4—714no—
484C22×C4—712no—
485C22×C4—14216no—
486C22×C4—1428no—
487C22×C4—14216no—
488C22×C4—1422no—
489C22×C4—1421no—
490C22×C4—1422no—
491C22×C4—1422no—
492C22×C4—1422no—
493C22×C4—1422no—
494C22×C4—1421no—
495C22×C4—1421no—
496C22×C4—1422no—
497C22×C4—1421no—
498C22×C4—1422no—
499C22×C4—1422no—
500C22×C4—1422no—
501C22×C4—1422no—
502C22×C4—1428no—
503C22×C4—1422no—
504C22×C4—1422no—
505C22×C4—1421no—
506C22×C4—1422no—
507C22×C4—1422no—
508C22×C4—1422no—
509C22×C4—1421no—
510C22×C4C2×C4×D7114yes—
511C22×C4C2×C4×D7112yes—
512C22×C4C2×C4×D7114yes—
513C22×C4C2×C4×D7112yes—
514C22×C4C2×C4×D7114yes—
515C22×C4C2×C4×D7112yes—
516C22×C4D4×D7112yes—
517C22×C4#1176586412yes—
518C22⋊C4—7116no—
519C22⋊C4—1428no—
520C22⋊C4—14216no—
521C42—28no—
522C42—2844no—
523C42—2848no—
524C42—14216no—
525C23—714no—
526C23—714no—
527C23—718no—
528C23—714no—
529C23—718no—
530C23—1424no—
531C23—1422no—
532C23—1422no—
533C23—1424no—
534C23—1424no—
535C23—1424no—
536C23—1424no—
537C23—1422no—
538C23—1422no—
539C23—1424no—
540C23—1424no—
541C23—1422no—
542C23—1424no—
543C23—1422no—
544C23—1424no—
545C23—1422no—
546C23—1422no—
547C23—1424no—
548C23C22×C4×D7112yes—
549C23C22×C4×D7111yescharacteristic
550C23C2×D4×D7111yescharacteristic
551C23#41×D7112yes—
552C23#41×D7111yescharacteristic
553C23#41×D7111yescharacteristic
554C23#41×D7112yes—
555C23C2×#1176586411yescharacteristic
556C23#1455617311yescharacteristic
557C23#1455617412yes—
558C23#1455617611yescharacteristic
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—28416no—
589C2×C4—28432no—
590C2×C4—2842no—
591C2×C4—2842no—
592C2×C4—2842no—
593C2×C4—2842no—
594C2×C4—2842no—
595C2×C4—2842no—
596C2×C4—2842no—
597C2×C4—2842no—
598C2×C4—714no—
599C2×C4—718no—
600C2×C4—1424no—
601C2×C4—1422no—
602C2×C4—1422no—
603C2×C4—1424no—
604C2×C4—1422no—
605C2×C4—1422no—
606C2×C4—1422no—
607C2×C4—1422no—
608C2×C4—1424no—
609C2×C4—1424no—
610C2×C4—1424no—
611C2×C4—1424no—
612C2×C4—1424no—
613C2×C4—1424no—
614C2×C4—1424no—
615C2×C4—1424no—
616C2×C4—1422no—
617C2×C4—1422no—
618C2×C4—1424no—
619C2×C4C42×D7114yes—
620C2×C4(C22⋊D71)⋊C414yes—
621C22—718no—
622C22—1424no—
623C22—1428no—
624C22—1424no—
625C22—1428no—
626C22—1424no—
627C22—1428no—
628C22—1424no—
629C22—1428no—
630C22—1424no—
631C22—1424no—
632C22C2×C42×D7111yescharacteristic
633C22#117×D7111yescharacteristic
634C22#117×D7112yes—
635C22#117×D7111yescharacteristic
636C22#117×D7112yes—
637C22C4×D4×D7112yes—
638C22C2×(C22⋊D71)⋊C411yescharacteristic
639C22C4×#1176586412yes—
640C22#1798646711yescharacteristic
641C22#1798647112yes—
642C22#1798647311yescharacteristic
643C22#1798648011yescharacteristic
644C22#1798648112yes—
645C22#1798664112yes—
646C22#1798664611yescharacteristic
647C22#1798665911yescharacteristic
648C22#1798667212yes—
649C22#1798667412yes—
650C22#1798667912yes—
651C22#1798668112yes—
652C22#1798668311yescharacteristic
653C22#1798669611yescharacteristic
654C22#1798670012yes—
655C4—24no—
656C4—24no—
657C4—42no—
658C4—44no—
659C4—44no—
660C4—2844no—
661C4—2842no—
662C4—2842no—
663C4—1428no—
664C4—1424no—
665C2—1428no—
666C2#376×D7111yescharacteristic
667C2C4×(C22⋊D71)⋊C411yescharacteristic
668C2#2259070011yescharacteristic
669C2#2259118211yescharacteristic
670C2#2259118412yes—
671C2#2259119311yescharacteristic
672C2#2259119512yes—
673C2#2259126211yescharacteristic
674C2#2259126412yes—
675C2#2259127311yescharacteristic
676C2#2259127512yes—
subgroupG/H
center, FrattiniC24C23×D71
commutatorC22×C71C22×C42
FittingC71×#1434C2
socle, cosocleC24×C71C24
prime radicalC24×D71C23
hypercenter#1434D71
hypocenterC71#13809
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. C2×#17985845C2semidirect
5. #22586566C2semidirect
6. #22586565C2semidirect
7. #22586564C2semidirect
10. #95×Dic71C2semidirect
11. C71×#1434C2semidirect
20. C4×(C2×D71)⋊C4C4semidirect
21. #17985846C4semidirect
70. C2×C4×Dic71C2×C4semidirect
71. C2×C4×Dic71C2×C4semidirect
72. C2×C4×Dic71C2×C4semidirect
79. C71⋊#95C2×C4semidirect
80. C71⋊#95C2×C4semidirect
81. C71⋊#95C2×C4semidirect
90. C2×C42×C71C2×C4semidirect
94. #95×C71C2×C4semidirect
315. C2×D71#376semidirect
346. #1434D71semidirect
350. C71#13809semidirect
419. C2×C42C4×D71semidirect
433. #95C4×D71semidirect

Maximal subgroups

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

subgroupindex
C2×C4×(C2×D71)⋊C42
C2×#179858462
C2×#179858452
C2×#95×D712
#225865662
#225865652
#225865642
(C2×D71)⋊#952
#95×Dic712
C71×#14342
#1380971