Finite Group Databasebeta

← #31919395

Subgroups — #31919395

Order 18176.

1702 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17985856C211yesmaximal, characteristic
2C2×#17985856C211yesmaximal, characteristic
3C2×C4⋊C4×Dic71C211yesmaximal, characteristic, complemented
4C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic
5#22586601C212yesmaximal, complemented
6#22586588C212yesmaximal
7#22586576C212yesmaximal
8#22586570C211yesmaximal, characteristic, complemented
9#22586569C211yesmaximal, characteristic, complemented
10#22586566C212yesmaximal, complemented
11C2×#382×C71C211yesmaximal, characteristic, complemented
12C23×C4×D71C2211yescharacteristic
13C22×C4⋊Dic71C2211yescharacteristic
14C22×C4⋊Dic71C2211yescharacteristic
15C22×(C2×D71)⋊C4C2212yes—
16C22×(C2×D71)⋊C4C2212yes—
17C22×(C2×D71)⋊C4C2211yescharacteristic
18C22×(C2×D71)⋊C4C2211yescharacteristic
19C22×C4×Dic71C2212yes—
20C22×C4×Dic71C2211yescharacteristic
21#17985856—24no—
22#17985856—24no—
23C4⋊C4×Dic71—24no—
24C4×(C2×D71)⋊C4C418yescomplemented
25C2×C71⋊#95C2212yes—
26C2×C71⋊#95C2212yes—
27C2×C71⋊#95C2212yes—
28C2×C71⋊#95C2212yes—
29C2×C71⋊#95C2212yes—
30C2×C71⋊#95C2212yes—
31C2×C71⋊#95C2212yes—
32C2×C71⋊#95C2211yescharacteristic
33C2×C71⋊#95C2211yescharacteristic
34C22×C4⋊C4×C71C2211yescharacteristic
35C22×C4⋊C4×C71C2211yescharacteristic
36C22×C42×C71C2211yescharacteristic
37#382×C71—24no—
38C2×#95×C71C2212yes—
39C2×#95×C71C2212yes—
40C24×D71C2311yescharacteristic
41C23×Dic71C2312yes—
42C23×Dic71C2311yescharacteristic
43C23×Dic71C2311yescharacteristic
44C23×Dic71C2312yes—
45C23×Dic71C2311yescharacteristic
46C22×C4×D71—22no—
47C22×C4×D71—22no—
48C22×C4×D71—22no—
49C22×C4×D71—22no—
50C22×C4×D71—22no—
51C22×C4×D71—22no—
52C22×C4×D71C2×C414yes—
53C2×C4⋊Dic71—22no—
54C2×C4⋊Dic71—22no—
55C2×C4⋊Dic71—22no—
56C2×C4⋊Dic71—22no—
57C2×C4⋊Dic71—22no—
58C2×C4⋊Dic71D414yes—
59C2×(C2×D71)⋊C4—22no—
60C2×(C2×D71)⋊C4—22no—
61C2×(C2×D71)⋊C4—22no—
62C2×(C2×D71)⋊C4—22no—
63C2×(C2×D71)⋊C4—24no—
64C2×(C2×D71)⋊C4—24no—
65C2×(C2×D71)⋊C4—24no—
66C2×(C2×D71)⋊C4—24no—
67C2×(C2×D71)⋊C4—42no—
68C2×(C2×D71)⋊C4—42no—
69C2×(C2×D71)⋊C4C2×C414yes—
70C2×(C2×D71)⋊C4C2×C414yes—
71C2×C4×Dic71—24no—
72C2×C4×Dic71—24no—
73C2×C4×Dic71—22no—
74C2×C4×Dic71—22no—
75C2×C4×Dic71—42no—
76C2×C4×Dic71C2×C414yes—
77C71⋊#95—24no—
78C71⋊#95—24no—
79C71⋊#95—24no—
80C71⋊#95—24no—
81C71⋊#95—42no—
82C71⋊#95—42no—
83C71⋊#95—42no—
84C71⋊#95C2×C414yes—
85C71⋊#95C2×C414yes—
86C23×C4×C71C2312yes—
87C23×C4×C71C2311yescharacteristic
88C23×C4×C71C2311yescharacteristic
89C23×C4×C71C2312yes—
90C23×C4×C71C2311yescharacteristic
91C2×C4⋊C4×C71—22no—
92C2×C4⋊C4×C71—22no—
93C2×C4⋊C4×C71—22no—
94C2×C4⋊C4×C71—22no—
95C2×C4⋊C4×C71—22no—
96C2×C4⋊C4×C71D414yes—
97C2×C42×C71—22no—
98C2×C42×C71—22no—
99C2×C42×C71C2×C414yes—
100#95×C71—24no—
101#95×C71—24no—
102C23×D71—21no—
103C23×D71—21no—
104C23×D71—21no—
105C23×D71—21no—
106C23×D71—21no—
107C23×D71—21no—
108C23×D71—21no—
109C23×D71—21no—
110C23×D71—21no—
111C23×D71—21no—
112C23×D71—21no—
113C23×D71—21no—
114C23×D71C22×C412yes—
115C23×D71#4112yes—
116C23×D71#4112yes—
117C22×Dic71—21no—
118C22×Dic71—21no—
119C22×Dic71—21no—
120C22×Dic71—21no—
121C22×Dic71—21no—
122C22×Dic71—21no—
123C22×Dic71—21no—
124C22×Dic71—21no—
125C22×Dic71—21no—
126C22×Dic71—21no—
127C22×Dic71—21no—
128C22×Dic71—22no—
129C22×Dic71—21no—
130C22×Dic71—21no—
131C22×Dic71—21no—
132C22×Dic71—22no—
133C22×Dic71—22no—
134C22×Dic71—22no—
135C22×Dic71—21no—
136C22×Dic71—22no—
137C22×Dic71—22no—
138C22×Dic71—21no—
139C22×Dic71—22no—
140C22×Dic71—22no—
141C22×Dic71—22no—
142C22×Dic71—22no—
143C22×Dic71—22no—
144C22×Dic71—22no—
145C22×Dic71—22no—
146C22×Dic71C22×C412yes—
147C22×Dic71C22×C412yes—
148C22×Dic71C22×C412yes—
149C22×Dic71C2×D414yes—
150C22×Dic71#4112yes—
151C22×Dic71#4112yes—
152C2×C4×D71—28no—
153C2×C4×D71—28no—
154C2×C4×D71—28no—
155C2×C4×D71—44no—
156C2×C4×D71—44no—
157C2×C4×D71—44no—
158C2×C4×D71—44no—
159C4⋊Dic71—28no—
160C4⋊Dic71—44no—
161(C2×D71)⋊C4—28no—
162(C2×D71)⋊C4—28no—
163(C2×D71)⋊C4—48no—
164(C2×D71)⋊C4—48no—
165C4×Dic71—28no—
166C4×Dic71—48no—
167C24×C71C2411yescharacteristic
168C22×C4×C71—21no—
169C22×C4×C71—21no—
170C22×C4×C71—22no—
171C22×C4×C71—21no—
172C22×C4×C71—21no—
173C22×C4×C71—22no—
174C22×C4×C71—22no—
175C22×C4×C71—21no—
176C22×C4×C71—21no—
177C22×C4×C71—21no—
178C22×C4×C71—21no—
179C22×C4×C71—22no—
180C22×C4×C71—21no—
181C22×C4×C71—21no—
182C22×C4×C71—22no—
183C22×C4×C71—21no—
184C22×C4×C71—21no—
185C22×C4×C71—22no—
186C22×C4×C71—22no—
187C22×C4×C71—22no—
188C22×C4×C71—22no—
189C22×C4×C71—22no—
190C22×C4×C71—22no—
191C22×C4×C71—22no—
192C22×C4×C71—22no—
193C22×C4×C71C22×C412yes—
194C22×C4×C71C22×C412yes—
195C22×C4×C71C22×C412yes—
196C22×C4×C71C2×D412yes—
197C22×C4×C71C2×D414yes—
198C22×C4×C71C2×D412yes—
199C22×C4×C71#4112yes—
200C22×C4×C71#4112yes—
201C22×C4×C71#4112yes—
202C22×C4×C71#4112yes—
203C4⋊C4×C71—28no—
204C4⋊C4×C71—44no—
205C42×C71—28no—
206C23×C71C23×C411yescharacteristic
207C23×C71C22×D411yescharacteristic
208C23×C71C22×D411yescharacteristic
209C23×C71C2×#4111yescharacteristic
210C23×C71C2×#4111yescharacteristic
211C23×C71C2×#4111yescharacteristic
212C23×C71C2×#4111yescharacteristic
213C23×C71C2×#4111yescharacteristic
214C23×C71C2×#4111yescharacteristic
215C23×C71C2×#4111yescharacteristic
216C23×C71C2×#4111yescharacteristic
217C23×C71H(5,𝔽2)11yescharacteristic
218C23×C71H(5,𝔽2)11yescharacteristic
219C23×C712−1+411yescharacteristic
220C23×C712−1+411yescharacteristic
221C22×D71—22no—
222C22×D71—22no—
223C22×D71—22no—
224C22×D71—22no—
225C22×D71—22no—
226C22×D71—22no—
227C22×D71—22no—
228C22×D71—22no—
229C22×D71—22no—
230C22×D71—22no—
231C22×D71—22no—
232C22×D71—22no—
233C22×D71—22no—
234C22×D71—22no—
235C22×D71—22no—
236C22×D71—22no—
237C22×D71—22no—
238C22×D71—22no—
239C22×D71—41no—
240C22×D71—41no—
241C22×D71—41no—
242C22×D71—41no—
243C22×D71—41no—
244C22×D71—41no—
245C22×D71—41no—
246C22×D71—41no—
247C22×D71—41no—
248C22×D71—41no—
249C22×D71—41no—
250C22×D71—41no—
251C22×D71—41no—
252C22×D71—41no—
253C22×D71—41no—
254C22×D71—41no—
255C22×D71#11714yes—
256C2×C4×C71—22no—
257C2×C4×C71—22no—
258C2×C4×C71—22no—
259C2×C4×C71—22no—
260C2×C4×C71—22no—
261C2×C4×C71—22no—
262C2×C4×C71—24no—
263C2×C4×C71—24no—
264C2×C4×C71—24no—
265C2×C4×C71—42no—
266C2×C4×C71—42no—
267C2×C4×C71—41no—
268C2×C4×C71—42no—
269C2×C4×C71—41no—
270C2×C4×C71—41no—
271C2×C4×C71—42no—
272C2×C4×C71—41no—
273C2×C4×C71—41no—
274C2×C4×C71—41no—
275C2×C4×C71—41no—
276C2×C4×C71—41no—
277C2×C4×C71—42no—
278C2×C4×C71—42no—
279C2×C4×C71—42no—
280C2×C4×C71—42no—
281C2×C4×C71—42no—
282C2×C4×C71—42no—
283C2×C4×C71—42no—
284C2×C4×C71#11714yes—
285C2×C4×C71C4×D414yes—
286C2×C4×C71C4×D414yes—
287C2×C4×C71#12114yes—
288C2×C4×C71#12314yes—
289C2×C4×C71#12414yes—
290C2×C4×C71#12614yes—
291C2×Dic71—22no—
292C2×Dic71—22no—
293C2×Dic71—22no—
294C2×Dic71—22no—
295C2×Dic71—22no—
296C2×Dic71—22no—
297C2×Dic71—22no—
298C2×Dic71—22no—
299C2×Dic71—22no—
300C2×Dic71—22no—
301C2×Dic71—22no—
302C2×Dic71—22no—
303C2×Dic71—24no—
304C2×Dic71—24no—
305C2×Dic71—24no—
306C2×Dic71—41no—
307C2×Dic71—41no—
308C2×Dic71—41no—
309C2×Dic71—41no—
310C2×Dic71—42no—
311C2×Dic71—42no—
312C2×Dic71—41no—
313C2×Dic71—41no—
314C2×Dic71—41no—
315C2×Dic71—42no—
316C2×Dic71—41no—
317C2×Dic71—42no—
318C2×Dic71—42no—
319C2×Dic71—42no—
320C2×Dic71—42no—
321C2×Dic71—42no—
322C2×Dic71—42no—
323C2×Dic71—42no—
324C2×Dic71—42no—
325C2×Dic71#11714yes—
326C4×D71—416no—
327C22×C71C2×#11711yescharacteristic
328C22×C71C2×#11711yescharacteristic
329C22×C71C2×#11711yescharacteristic
330C22×C71C2×C4×D411yescharacteristic
331C22×C71C2×C4×D411yescharacteristic
332C22×C71#52011yescharacteristic
333C22×C71#52011yescharacteristic
334C22×C71C2×#12111yescharacteristic
335C22×C71C2×#12311yescharacteristic
336C22×C71C2×#12411yescharacteristic
337C22×C71C2×#12611yescharacteristic
338C22×C71#52911yescharacteristic
339C22×C71#52911yescharacteristic
340C22×C71#52911yescharacteristic
341C22×C71#52911yescharacteristic
342C22×C71#54011yescharacteristic
343C22×C71#54111yescharacteristic
344C22×C71#54211yescharacteristic
345C22×C71#54211yescharacteristic
346C22×C71#54611yescharacteristic
347C22×C71#54611yescharacteristic
348C22×C71#54611yescharacteristic
349C22×C71#54711yescharacteristic
350C22×C71#54811yescharacteristic
351C22×C71#54811yescharacteristic
352C22×C71#54811yescharacteristic
353C22×C71#55011yescharacteristic
354C22×C71#55211yescharacteristic
355C22×C71#55211yescharacteristic
356C22×C71#55211yescharacteristic
357C22×C71#55311yescharacteristic
358C22×C71#55311yescharacteristic
359C22×C71#55311yescharacteristic
360C22×C71#55511yescharacteristic
361C22×C71#55611yescharacteristic
362C2×D71—24no—
363C2×D71—24no—
364C2×D71—24no—
365C2×D71—42no—
366C2×D71—42no—
367C2×D71—42no—
368C2×D71—42no—
369C2×D71—42no—
370C2×D71—42no—
371C2×D71—42no—
372C2×D71—42no—
373C2×D71—42no—
374C2×D71—42no—
375C2×D71—42no—
376C2×D71—42no—
377C4×C71—42no—
378C4×C71—42no—
379C4×C71—44no—
380C4×C71—82no—
381C4×C71#38818yes—
382Dic71—24no—
383Dic71—42no—
384Dic71—44no—
385Dic71—42no—
386Dic71—82no—
387#13875—711nomaximal, Sylow
388C2×C71#228311yescharacteristic
389C2×C71C2×#38811yescharacteristic
390C2×C71#231411yescharacteristic
391C2×C71#235211yescharacteristic
392C2×C71#235211yescharacteristic
393C2×C71#235211yescharacteristic
394C2×C71#235411yescharacteristic
395C2×C71#242011yescharacteristic
396C2×C71#242111yescharacteristic
397C2×C71#242611yescharacteristic
398C2×C71#242711yescharacteristic
399C2×C71#248911yescharacteristic
400C2×C71#249011yescharacteristic
401C2×C71#249411yescharacteristic
402C2×C71#249511yescharacteristic
403D71—44no—
404C2×#382D7111yescharacteristic, complemented
405C2×#380—711no—
406C2×#380—711no—
407C2×C4×C4⋊C4—711no—
408C2×C4×C22⋊C4—711no—
409#1443—712no—
410#1440—712no—
411#1437—712no—
412C4⋊#95—711no—
413C4⋊#95—711no—
414#1434—712no—
415C71#1387511yescharacteristic, complemented, Sylow
416C24×C4—711no—
417C22×C4⋊C4—711no—
418C22×C4⋊C4—711no—
419C22×C4⋊C4C2×D7111yescharacteristic
420C22×C4⋊C4C2×D7111yescharacteristic
421C22×C22⋊C4—712no—
422C22×C22⋊C4—712no—
423C22×C22⋊C4—711no—
424C22×C22⋊C4—711no—
425C22×C42—712no—
426C22×C42—711no—
427C22×C42C2×D7111yescharacteristic
428#382—24no—
429#380—1424no—
430#380—1424no—
431C4×C4⋊C4—1424no—
432C4×C22⋊C4—718no—
433C2×#95—712no—
434C2×#95—712no—
435C2×#95—712no—
436C2×#95—711no—
437C2×#95—711no—
438C2×#95—712no—
439C2×#95—712no—
440C2×#95—712no—
441C2×#95—712no—
442C2×#95C2×D7112yes—
443C2×#95C2×D7112yes—
444C25—711no—
445C23×C4—711no—
446C23×C4—712no—
447C23×C4—711no—
448C23×C4—711no—
449C23×C4—714no—
450C23×C4—712no—
451C23×C4—1422no—
452C23×C4—1422no—
453C23×C4—1422no—
454C23×C4—1422no—
455C23×C4—1422no—
456C23×C4—1422no—
457C23×C4C22×D7112yes—
458C23×C4C22×D7111yescharacteristic
459C23×C4C22×D7111yescharacteristic
460C23×C4C22×D7112yes—
461C23×C4C22×D7111yescharacteristic
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—714no—
468C2×C4⋊C4—1422no—
469C2×C4⋊C4—1422no—
470C2×C4⋊C4—1422no—
471C2×C4⋊C4—1422no—
472C2×C4⋊C4—1422no—
473C2×C4⋊C4C22⋊D7114yes—
474C2×C22⋊C4—2842no—
475C2×C22⋊C4—2842no—
476C2×C22⋊C4—714no—
477C2×C22⋊C4—714no—
478C2×C22⋊C4—1424no—
479C2×C22⋊C4—1424no—
480C2×C22⋊C4—1424no—
481C2×C22⋊C4—1424no—
482C2×C22⋊C4—1422no—
483C2×C22⋊C4—1422no—
484C2×C22⋊C4—1422no—
485C2×C22⋊C4—1422no—
486C2×C42—22no—
487C2×C42—22no—
488C2×C42—2842no—
489C2×C42—714no—
490C2×C42—1424no—
491C2×C42—1424no—
492C2×C42—1422no—
493C2×C42—1422no—
494C2×C42C4×D7114yes—
495#95—24no—
496#95—24no—
497#95—2842no—
498#95—2842no—
499#95—2842no—
500#95—714no—
501#95—714no—
502#95—1424no—
503#95—1424no—
504#95—1424no—
505#95—1424no—
506C24—712no—
507C24—712no—
508C24—712no—
509C24—1421no—
510C24—1421no—
511C24—1421no—
512C24—1421no—
513C24—1421no—
514C24—1421no—
515C24—1421no—
516C24—1421no—
517C24—1421no—
518C24—1421no—
519C24—1421no—
520C24—1421no—
521C24C23×D7111yescharacteristic
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—2844no—
548C22×C4—2844no—
549C22×C4—2844no—
550C22×C4—2844no—
551C22×C4—712no—
552C22×C4—712no—
553C22×C4—712no—
554C22×C4—712no—
555C22×C4—712no—
556C22×C4—714no—
557C22×C4—1422no—
558C22×C4—1422no—
559C22×C4—1422no—
560C22×C4—1422no—
561C22×C4—1422no—
562C22×C4—1422no—
563C22×C4—1422no—
564C22×C4—1421no—
565C22×C4—1421no—
566C22×C4—1421no—
567C22×C4—1422no—
568C22×C4—1421no—
569C22×C4—1421no—
570C22×C4—1422no—
571C22×C4—1421no—
572C22×C4—1422no—
573C22×C4—1421no—
574C22×C4—1421no—
575C22×C4—1422no—
576C22×C4—1421no—
577C22×C4—1421no—
578C22×C4—1421no—
579C22×C4—1422no—
580C22×C4—1422no—
581C22×C4—1421no—
582C22×C4—1428no—
583C22×C4—1428no—
584C22×C4—1428no—
585C22×C4—1421no—
586C22×C4—1421no—
587C22×C4—1421no—
588C22×C4—1421no—
589C22×C4C2×C4×D7112yes—
590C22×C4C2×C4×D7112yes—
591C22×C4C2×C4×D7112yes—
592C22×C4D4×D7112yes—
593C22×C4C2×C22⋊D7114yes—
594C22×C4C2×C22⋊D7112yes—
595C22×C4#1176586412yes—
596C22×C4#1176586512yes—
597C22×C4#1176586612yes—
598C22×C4#1176586612yes—
599C4⋊C4—28no—
600C4⋊C4—44no—
601C4⋊C4—2844no—
602C4⋊C4—1428no—
603C22⋊C4—2848no—
604C22⋊C4—2848no—
605C22⋊C4—1428no—
606C22⋊C4—1428no—
607C42—28no—
608C42—2848no—
609C42—1428no—
610C23—2841no—
611C23—2841no—
612C23—2841no—
613C23—2841no—
614C23—2841no—
615C23—2841no—
616C23—2841no—
617C23—2841no—
618C23—2841no—
619C23—2841no—
620C23—2841no—
621C23—2841no—
622C23—2841no—
623C23—2841no—
624C23—2841no—
625C23—2841no—
626C23—714no—
627C23—1422no—
628C23—1422no—
629C23—1422no—
630C23—1422no—
631C23—1422no—
632C23—1422no—
633C23—1422no—
634C23—1422no—
635C23—1422no—
636C23—1422no—
637C23—1422no—
638C23—1422no—
639C23—1422no—
640C23—1422no—
641C23—1422no—
642C23—1422no—
643C23—1422no—
644C23—1422no—
645C23C22×C4×D7111yescharacteristic
646C23C2×D4×D7111yescharacteristic
647C23C22×C22⋊D7111yescharacteristic
648C23#41×D7111yescharacteristic
649C23#41×D7111yescharacteristic
650C23#41×D7111yescharacteristic
651C23#41×D7111yescharacteristic
652C23C2×#1176586411yescharacteristic
653C23C2×#1176586511yescharacteristic
654C23C2×#1176586611yescharacteristic
655C23C2×#1176586611yescharacteristic
656C23#1455617411yescharacteristic
657C23#1455617411yescharacteristic
658C23#1455617511yescharacteristic
659C23#1455617511yescharacteristic
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—2842no—
689C2×C4—2841no—
690C2×C4—2841no—
691C2×C4—2841no—
692C2×C4—2842no—
693C2×C4—2841no—
694C2×C4—2842no—
695C2×C4—2841no—
696C2×C4—2841no—
697C2×C4—2841no—
698C2×C4—2841no—
699C2×C4—2842no—
700C2×C4—28416no—
701C2×C4—2842no—
702C2×C4—2842no—
703C2×C4—2842no—
704C2×C4—2842no—
705C2×C4—2842no—
706C2×C4—2842no—
707C2×C4—2842no—
708C2×C4—714no—
709C2×C4—1424no—
710C2×C4—1424no—
711C2×C4—1422no—
712C2×C4—1422no—
713C2×C4—1422no—
714C2×C4—1422no—
715C2×C4—1422no—
716C2×C4—1422no—
717C2×C4—1424no—
718C2×C4—1422no—
719C2×C4—1422no—
720C2×C4—1422no—
721C2×C4—1422no—
722C2×C4—1422no—
723C2×C4—1422no—
724C2×C4#1455608614yes—
725C2×C4C4×C22⋊D7114yes—
726C2×C4#1455609014yes—
727C2×C4#1455610014yes—
728C2×C4#1455611314yes—
729C2×C4#1455611714yes—
730C2×C4#1455612314yes—
731C22—2842no—
732C22—2842no—
733C22—2842no—
734C22—2842no—
735C22—2842no—
736C22—2842no—
737C22—2842no—
738C22—2842no—
739C22—2842no—
740C22—2842no—
741C22—2842no—
742C22—2842no—
743C22—1424no—
744C22—1424no—
745C22—1424no—
746C22#117×D7111yescharacteristic
747C22#117×D7111yescharacteristic
748C22C2×#1455608611yescharacteristic
749C22C2×C4×C22⋊D7111yescharacteristic
750C22C2×#1455609011yescharacteristic
751C22#1798647911yescharacteristic
752C22#1798647911yescharacteristic
753C22C2×#1455610011yescharacteristic
754C22C2×#1455611311yescharacteristic
755C22C2×#1455611711yescharacteristic
756C22C2×#1455612311yescharacteristic
757C22#1798652811yescharacteristic
758C22#1798652811yescharacteristic
759C22#1798653411yescharacteristic
760C22#1798653411yescharacteristic
761C22#1798660511yescharacteristic
762C22#1798661211yescharacteristic
763C22#1798661811yescharacteristic
764C22#1798661811yescharacteristic
765C22#1798663711yescharacteristic
766C22#1798664211yescharacteristic
767C22#1798664211yescharacteristic
768C22#1798664811yescharacteristic
769C22#1798665611yescharacteristic
770C22#1798665711yescharacteristic
771C22#1798665711yescharacteristic
772C22#1798666811yescharacteristic
773C22#1798668711yescharacteristic
774C22#1798668711yescharacteristic
775C22#1798668811yescharacteristic
776C22#1798669311yescharacteristic
777C22#1798670211yescharacteristic
778C22#1798670211yescharacteristic
779C22#1798671211yescharacteristic
780C22#1798671711yescharacteristic
781C4—42no—
782C4—42no—
783C4—44no—
784C4—82no—
785C4—2842no—
786C4—2842no—
787C4—2844no—
788C4—5682no—
789C4—1424no—
790C4#1798588918yes—
791C2—2844no—
792C2#2259073311yescharacteristic
793C2C2×#1798588911yescharacteristic
794C2#2259095011yescharacteristic
795C2#2259126611yescharacteristic
796C2#2259126611yescharacteristic
797C2#2259127011yescharacteristic
798C2#2259129011yescharacteristic
799C2#2259183511yescharacteristic
800C2#2259184611yescharacteristic
801C2#2259190911yescharacteristic
802C2#2259192011yescharacteristic
803C2#2259268411yescharacteristic
804C2#2259269511yescharacteristic
805C2#2259274311yescharacteristic
806C2#2259275411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC23×C71C23×C4
FittingC2×#382×C71C2
socle, cosocleC24×C71C24
prime radicalC24×D71C23
hypercenterC2×#382D71
hypocenterC71#13875
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic71C2semidirect
5. #22586601C2semidirect
8. #22586570C2semidirect
9. #22586569C2semidirect
10. #22586566C2semidirect
11. C2×#382×C71C2semidirect
24. C4×(C2×D71)⋊C4C4semidirect
404. C2×#382D71semidirect
415. C71#13875semidirect

Maximal subgroups

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

subgroupindex
C2×#179858562
C2×C4⋊C4×Dic712
C2×C4×(C2×D71)⋊C42
#225866012
#225865882
#225865762
#225865702
#225865692
#225865662
C2×#382×C712
#1387571