Finite Group Databasebeta

← #31919399

Subgroups — #31919399

Order 18176.

1846 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17985887C212yesmaximal
2C2×#17985868C211yesmaximal, characteristic, complemented
3C2×#17985859C211yesmaximal, characteristic
4C2×C4⋊C4×Dic71C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊Dic71C211yesmaximal, characteristic
6#22586595C212yesmaximal, complemented
7#22586583C212yesmaximal
8#22586571C212yesmaximal, complemented
9#22586569C211yesmaximal, characteristic, complemented
10#22586569C211yesmaximal, characteristic, complemented
11C2×#380×C71C211yesmaximal, characteristic
12C22×C4⋊Dic71C2211yescharacteristic
13C22×C4⋊Dic71C2211yescharacteristic
14C22×Dic71⋊C4C2212yes—
15C22×Dic71⋊C4C2212yes—
16C22×C22⋊Dic71C2212yes—
17C22×C22⋊Dic71C2211yescharacteristic
18C22×C22⋊Dic71C2211yescharacteristic
19C22×C4×Dic71C2212yes—
20C22×C4×Dic71C2211yescharacteristic
21C22×C4×Dic71C2211yescharacteristic
22#17985887—28no—
23#17985868—24no—
24#17985859—24no—
25C4⋊C4×Dic71—24no—
26C4×C22⋊Dic71C418yescomplemented
27C2×C71⋊#95C2212yes—
28C2×C71⋊#95C2212yes—
29C2×C71⋊#95C2212yes—
30C2×C71⋊#95C2212yes—
31C2×C71⋊#95C2212yes—
32C2×C71⋊#95C2212yes—
33C2×C71⋊#95C2211yescharacteristic
34C2×C71⋊#95C2211yescharacteristic
35C24×C4×C71C2211yescharacteristic
36C22×C4⋊C4×C71C2211yescharacteristic
37C22×C4⋊C4×C71C2211yescharacteristic
38C22×C22⋊C4×C71C2212yes—
39#380×C71—24no—
40C2×#95×C71C2212yes—
41C23×Dic71C2312yes—
42C23×Dic71C2311yescharacteristic
43C23×Dic71C2312yes—
44C23×Dic71C2311yescharacteristic
45C23×Dic71C2311yescharacteristic
46C23×Dic71C2311yescharacteristic
47C2×C4⋊Dic71—22no—
48C2×C4⋊Dic71—22no—
49C2×C4⋊Dic71—22no—
50C2×C4⋊Dic71—22no—
51C2×C4⋊Dic71—22no—
52C2×C4⋊Dic71D414yes—
53C2×Dic71⋊C4—24no—
54C2×Dic71⋊C4—24no—
55C2×Dic71⋊C4—24no—
56C2×Dic71⋊C4—24no—
57C2×Dic71⋊C4—42no—
58C2×Dic71⋊C4—42no—
59C2×C22⋊Dic71—22no—
60C2×C22⋊Dic71—22no—
61C2×C22⋊Dic71—24no—
62C2×C22⋊Dic71—24no—
63C2×C22⋊Dic71—42no—
64C2×C22⋊Dic71C2×C414yes—
65C2×C22⋊Dic71C2×C414yes—
66C2×C22⋊Dic71D414yes—
67C2×C22⋊Dic71Q814yes—
68C2×C4×Dic71—24no—
69C2×C4×Dic71—22no—
70C2×C4×Dic71—22no—
71C2×C4×Dic71—24no—
72C2×C4×Dic71—22no—
73C2×C4×Dic71—22no—
74C2×C4×Dic71—42no—
75C2×C4×Dic71C2×C414yes—
76C2×C4×Dic71C2×C414yes—
77C71⋊#95—24no—
78C71⋊#95—24no—
79C71⋊#95—24no—
80C71⋊#95—24no—
81C71⋊#95—24no—
82C71⋊#95—42no—
83C71⋊#95C2×C414yes—
84C71⋊#95C2×C414yes—
85C25×C71C2311yescharacteristic
86C23×C4×C71—22no—
87C23×C4×C71—22no—
88C23×C4×C71—22no—
89C23×C4×C71—22no—
90C23×C4×C71—22no—
91C23×C4×C71—22no—
92C23×C4×C71C2×C414yes—
93C23×C4×C71C2312yes—
94C23×C4×C71C2311yescharacteristic
95C23×C4×C71C2312yes—
96C23×C4×C71C2311yescharacteristic
97C2×C4⋊C4×C71—22no—
98C2×C4⋊C4×C71—22no—
99C2×C4⋊C4×C71—22no—
100C2×C4⋊C4×C71—22no—
101C2×C4⋊C4×C71—22no—
102C2×C4⋊C4×C71D414yes—
103C2×C22⋊C4×C71—24no—
104C2×C22⋊C4×C71—24no—
105C2×C22⋊C4×C71—42no—
106#95×C71—24no—
107C22×Dic71—21no—
108C22×Dic71—21no—
109C22×Dic71—21no—
110C22×Dic71—21no—
111C22×Dic71—21no—
112C22×Dic71—21no—
113C22×Dic71—21no—
114C22×Dic71—21no—
115C22×Dic71—21no—
116C22×Dic71—21no—
117C22×Dic71—21no—
118C22×Dic71—21no—
119C22×Dic71—21no—
120C22×Dic71—22no—
121C22×Dic71—22no—
122C22×Dic71—21no—
123C22×Dic71—21no—
124C22×Dic71—21no—
125C22×Dic71—22no—
126C22×Dic71—22no—
127C22×Dic71—21no—
128C22×Dic71—22no—
129C22×Dic71—22no—
130C22×Dic71—21no—
131C22×Dic71—22no—
132C22×Dic71—22no—
133C22×Dic71—22no—
134C22×Dic71—22no—
135C22×Dic71—22no—
136C22×Dic71—22no—
137C22×Dic71—22no—
138C22×Dic71C22×C412yes—
139C22×Dic71C22×C412yes—
140C22×Dic71C22×C412yes—
141C22×Dic71C22×C412yes—
142C22×Dic71C2×D414yes—
143C22×Dic71C2×D412yes—
144C22×Dic71C2×D412yes—
145C22×Dic71C2×Q812yes—
146C22×Dic71C2×Q812yes—
147C22×Dic71#4112yes—
148C22×Dic71#4112yes—
149C4⋊Dic71—28no—
150C4⋊Dic71—44no—
151Dic71⋊C4—48no—
152Dic71⋊C4—48no—
153C22⋊Dic71—28no—
154C22⋊Dic71—48no—
155C22⋊Dic71C4⋊C4116yescomplemented
156C4×Dic71—28no—
157C4×Dic71—28no—
158C4×Dic71—48no—
159C24×C71—21no—
160C24×C71—21no—
161C24×C71—21no—
162C24×C71—21no—
163C24×C71—21no—
164C24×C71—21no—
165C24×C71—21no—
166C24×C71—21no—
167C24×C71—21no—
168C24×C71—21no—
169C24×C71—21no—
170C24×C71—21no—
171C24×C71C22×C412yes—
172C24×C71C2×D412yes—
173C24×C71C2×Q812yes—
174C24×C71C2411yescharacteristic
175C22×C4×C71—21no—
176C22×C4×C71—22no—
177C22×C4×C71—21no—
178C22×C4×C71—22no—
179C22×C4×C71—22no—
180C22×C4×C71—21no—
181C22×C4×C71—21no—
182C22×C4×C71—21no—
183C22×C4×C71—21no—
184C22×C4×C71—22no—
185C22×C4×C71—22no—
186C22×C4×C71—22no—
187C22×C4×C71—28no—
188C22×C4×C71—28no—
189C22×C4×C71—28no—
190C22×C4×C71—22no—
191C22×C4×C71—22no—
192C22×C4×C71—22no—
193C22×C4×C71—22no—
194C22×C4×C71—22no—
195C22×C4×C71—22no—
196C22×C4×C71—22no—
197C22×C4×C71—44no—
198C22×C4×C71—44no—
199C22×C4×C71—44no—
200C22×C4×C71—44no—
201C22×C4×C71C22×C412yes—
202C22×C4×C71C22×C412yes—
203C22×C4×C71C2×D412yes—
204C22×C4×C71C2×D414yes—
205C22×C4×C71C2×D412yes—
206C22×C4×C71#4112yes—
207C22×C4×C71#4112yes—
208C22×C4×C71#4112yes—
209C22×C4×C71#4112yes—
210C4⋊C4×C71—28no—
211C4⋊C4×C71—44no—
212C22⋊C4×C71—48no—
213C23×C71—22no—
214C23×C71—22no—
215C23×C71—22no—
216C23×C71—22no—
217C23×C71—22no—
218C23×C71—22no—
219C23×C71—22no—
220C23×C71—22no—
221C23×C71—22no—
222C23×C71—22no—
223C23×C71—22no—
224C23×C71—22no—
225C23×C71—22no—
226C23×C71—22no—
227C23×C71—22no—
228C23×C71—22no—
229C23×C71—22no—
230C23×C71—22no—
231C23×C71—41no—
232C23×C71—41no—
233C23×C71—41no—
234C23×C71—41no—
235C23×C71—41no—
236C23×C71—41no—
237C23×C71—41no—
238C23×C71—41no—
239C23×C71—41no—
240C23×C71—41no—
241C23×C71—41no—
242C23×C71—41no—
243C23×C71—41no—
244C23×C71—41no—
245C23×C71—41no—
246C23×C71—41no—
247C23×C71C2×C4⋊C414yes—
248C23×C71C23×C411yescharacteristic
249C23×C71C22×D411yescharacteristic
250C23×C71C22×D411yescharacteristic
251C23×C71C22×D411yescharacteristic
252C23×C71C22×Q811yescharacteristic
253C23×C71C2×#4111yescharacteristic
254C23×C71C2×#4111yescharacteristic
255C23×C71C2×#4111yescharacteristic
256C23×C71C2×#4111yescharacteristic
257C23×C71C2×#4111yescharacteristic
258C23×C71C2×#4111yescharacteristic
259C23×C71H(5,𝔽2)11yescharacteristic
260C23×C71H(5,𝔽2)11yescharacteristic
261C23×C712−1+411yescharacteristic
262C23×C712−1+411yescharacteristic
263C2×C4×C71—22no—
264C2×C4×C71—22no—
265C2×C4×C71—22no—
266C2×C4×C71—24no—
267C2×C4×C71—24no—
268C2×C4×C71—24no—
269C2×C4×C71—41no—
270C2×C4×C71—41no—
271C2×C4×C71—41no—
272C2×C4×C71—41no—
273C2×C4×C71—42no—
274C2×C4×C71—42no—
275C2×C4×C71—42no—
276C2×C4×C71—42no—
277C2×C4×C71—416no—
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—42no—
285C2×C4×C71#11714yes—
286C2×C4×C71C4×D414yes—
287C2×C4×C71C4×D414yes—
288C2×C4×C71#12114yes—
289C2×C4×C71#12314yes—
290C2×C4×C71#12414yes—
291C2×C4×C71#12614yes—
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—22no—
304C2×Dic71—22no—
305C2×Dic71—22no—
306C2×Dic71—22no—
307C2×Dic71—22no—
308C2×Dic71—22no—
309C2×Dic71—22no—
310C2×Dic71—22no—
311C2×Dic71—22no—
312C2×Dic71—22no—
313C2×Dic71—24no—
314C2×Dic71—24no—
315C2×Dic71—24no—
316C2×Dic71—42no—
317C2×Dic71—42no—
318C2×Dic71—42no—
319C2×Dic71—41no—
320C2×Dic71—41no—
321C2×Dic71—42no—
322C2×Dic71—41no—
323C2×Dic71—41no—
324C2×Dic71—42no—
325C2×Dic71—42no—
326C2×Dic71—42no—
327C2×Dic71—42no—
328C2×Dic71—42no—
329C2×Dic71—42no—
330C2×Dic71—42no—
331C2×Dic71C2×C4⋊C414yes—
332C2×Dic71C2×C4⋊C414yes—
333C2×Dic71#11714yes—
334C22×C71—24no—
335C22×C71—24no—
336C22×C71—24no—
337C22×C71—42no—
338C22×C71—42no—
339C22×C71—42no—
340C22×C71—42no—
341C22×C71—42no—
342C22×C71—42no—
343C22×C71—42no—
344C22×C71—42no—
345C22×C71—42no—
346C22×C71—42no—
347C22×C71—42no—
348C22×C71—42no—
349C22×C71C22×C4⋊C411yescharacteristic
350C22×C71C2×#11711yescharacteristic
351C22×C71C2×#11711yescharacteristic
352C22×C71C2×C4×D411yescharacteristic
353C22×C71C2×C4×D411yescharacteristic
354C22×C71#52011yescharacteristic
355C22×C71#52011yescharacteristic
356C22×C71C2×#12111yescharacteristic
357C22×C71C2×#12311yescharacteristic
358C22×C71C2×#12411yescharacteristic
359C22×C71C2×#12611yescharacteristic
360C22×C71#53211yescharacteristic
361C22×C71#53211yescharacteristic
362C22×C71#53311yescharacteristic
363C22×C71#53311yescharacteristic
364C22×C71#54011yescharacteristic
365C22×C71#54111yescharacteristic
366C22×C71#54211yescharacteristic
367C22×C71#54211yescharacteristic
368C22×C71D4211yescharacteristic
369C22×C71D4211yescharacteristic
370C22×C71#54611yescharacteristic
371C22×C71#54711yescharacteristic
372C22×C71#54711yescharacteristic
373C22×C71#54711yescharacteristic
374C22×C71#54811yescharacteristic
375C22×C71D4×Q811yescharacteristic
376C22×C71D4×Q811yescharacteristic
377C22×C71#55011yescharacteristic
378C22×C71#55211yescharacteristic
379C22×C71#55311yescharacteristic
380C22×C71#55411yescharacteristic
381C22×C71#55411yescharacteristic
382C22×C71#55511yescharacteristic
383C22×C71#55611yescharacteristic
384C4×C71—44no—
385C4×C71—42no—
386C4×C71—82no—
387C4×C71#38818yescomplemented
388Dic71—24no—
389Dic71—24no—
390Dic71—24no—
391Dic71—42no—
392Dic71—44no—
393Dic71—82no—
394#13876—711nomaximal, Sylow
395C2×C71—44no—
396C2×C71#228511yescharacteristic
397C2×C71C2×#38811yescharacteristic
398C2×C71#231411yescharacteristic
399C2×C71D4×C4⋊C411yescharacteristic
400C2×C71D4×C4⋊C411yescharacteristic
401C2×C71#235211yescharacteristic
402C2×C71#235411yescharacteristic
403C2×C71#242211yescharacteristic
404C2×C71#242311yescharacteristic
405C2×C71#242811yescharacteristic
406C2×C71#242911yescharacteristic
407C2×C71#249111yescharacteristic
408C2×C71#249211yescharacteristic
409C2×C71#249611yescharacteristic
410C2×C71#249711yescharacteristic
411C2×#388—712no—
412C2×#384—711no—
413C2×#380—711no—
414C2×#380D7111yescharacteristic
415C2×C4×C4⋊C4—711no—
416C2×C4×C22⋊C4—711no—
417#1442—712no—
418#1439—712no—
419#1436—712no—
420C4⋊#95—711no—
421C4⋊#95—711no—
422C71#1387611yescharacteristic, complemented, Sylow
423C24×C4C2×D7111yescharacteristic
424C22×C4⋊C4—712no—
425C22×C4⋊C4—712no—
426C22×C4⋊C4—711no—
427C22×C4⋊C4—711no—
428C22×C4⋊C4C2×D7111yescharacteristic
429C22×C4⋊C4C2×D7111yescharacteristic
430C22×C22⋊C4—712no—
431C22×C22⋊C4—711no—
432C22×C22⋊C4—711no—
433C22×C22⋊C4C2×D7112yes—
434C22×C42—712no—
435C22×C42—711no—
436C22×C42—711no—
437#388—1428no—
438#384—1424no—
439#380—24no—
440#380—1424no—
441C4×C4⋊C4—1424no—
442C4×C22⋊C4—718no—
443C2×#95—712no—
444C2×#95—711no—
445C2×#95—711no—
446C2×#95—712no—
447C2×#95—712no—
448C2×#95—712no—
449C2×#95—712no—
450C2×#95—712no—
451C2×#95C2×D7112yes—
452C25C22×D7111yescharacteristic
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—22no—
456C23×C4—22no—
457C23×C4—22no—
458C23×C4—22no—
459C23×C4—711no—
460C23×C4—711no—
461C23×C4—711no—
462C23×C4—712no—
463C23×C4—711no—
464C23×C4—712no—
465C23×C4C4×D7114yes—
466C23×C4C22×D7112yes—
467C23×C4C22×D7111yescharacteristic
468C23×C4C22×D7112yes—
469C23×C4C22×D7111yescharacteristic
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—2842no—
476C2×C4⋊C4—2842no—
477C2×C4⋊C4—714no—
478C2×C4⋊C4—1424no—
479C2×C4⋊C4—1424no—
480C2×C4⋊C4—1424no—
481C2×C4⋊C4—1424no—
482C2×C4⋊C4—1422no—
483C2×C4⋊C4—1422no—
484C2×C4⋊C4—1422no—
485C2×C4⋊C4—1422no—
486C2×C4⋊C4—1422no—
487C2×C4⋊C4C22⋊D7114yes—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—2842no—
492C2×C22⋊C4—714no—
493C2×C22⋊C4—714no—
494C2×C22⋊C4—714no—
495C2×C22⋊C4—714no—
496C2×C22⋊C4—1424no—
497C2×C22⋊C4—1424no—
498C2×C22⋊C4—1422no—
499C2×C22⋊C4—1422no—
500C2×C42—2842no—
501C2×C42—714no—
502C2×C42—714no—
503C2×C42—1424no—
504C2×C42—1424no—
505C2×C42—1422no—
506C2×C42—1422no—
507C2×C42—1422no—
508C2×C42—1422no—
509#95—24no—
510#95—2842no—
511#95—714no—
512#95—714no—
513#95—1424no—
514#95—1424no—
515#95—1424no—
516#95—1424no—
517#95—1424no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24C2×C4×D7112yes—
531C24D4×D7112yes—
532C24Q8×D7112yes—
533C24C23×D7111yescharacteristic
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—28no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—712no—
561C22×C4—712no—
562C22×C4—712no—
563C22×C4—712no—
564C22×C4—712no—
565C22×C4—712no—
566C22×C4—712no—
567C22×C4—712no—
568C22×C4—712no—
569C22×C4—712no—
570C22×C4—714no—
571C22×C4—1422no—
572C22×C4—1422no—
573C22×C4—1422no—
574C22×C4—1422no—
575C22×C4—1422no—
576C22×C4—1422no—
577C22×C4—1422no—
578C22×C4—1422no—
579C22×C4—1421no—
580C22×C4—1422no—
581C22×C4—1421no—
582C22×C4—1421no—
583C22×C4—1422no—
584C22×C4—1422no—
585C22×C4—1421no—
586C22×C4—1422no—
587C22×C4—1421no—
588C22×C4—1422no—
589C22×C4—1421no—
590C22×C4—1421no—
591C22×C4—1421no—
592C22×C4—1421no—
593C22×C4—1421no—
594C22×C4—1421no—
595C22×C4—1421no—
596C22×C4—1421no—
597C22×C4—1421no—
598C22×C4—1421no—
599C22×C4—1421no—
600C22×C4—1421no—
601C22×C4—1421no—
602C22×C4C2×C4×D7112yes—
603C22×C4C2×C4×D7112yes—
604C22×C4D4×D7112yes—
605C22×C4C2×C22⋊D7114yes—
606C22×C4C2×C22⋊D7112yes—
607C22×C4#1176586412yes—
608C22×C4#1176586412yes—
609C22×C4#1176586412yes—
610C22×C4#1176586512yes—
611C4⋊C4—28no—
612C4⋊C4—44no—
613C4⋊C4—2848no—
614C4⋊C4—2848no—
615C4⋊C4—2844no—
616C4⋊C4—1428no—
617C22⋊C4—48no—
618C22⋊C4—2848no—
619C22⋊C4—7116no—
620C22⋊C4—1428no—
621C42—2848no—
622C42—1428no—
623C42—1428no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23C4⋊C4×D7114yes—
659C23C22×C4×D7111yescharacteristic
660C23C2×D4×D7111yescharacteristic
661C23C2×D4×D7111yescharacteristic
662C23C22×C22⋊D7111yescharacteristic
663C23C2×Q8×D7111yescharacteristic
664C23#41×D7111yescharacteristic
665C23#41×D7111yescharacteristic
666C23C2×#1176586411yescharacteristic
667C23C2×#1176586411yescharacteristic
668C23C2×#1176586411yescharacteristic
669C23C2×#1176586511yescharacteristic
670C23#1455617311yescharacteristic
671C23#1455617411yescharacteristic
672C23#1455617511yescharacteristic
673C23#1455617611yescharacteristic
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—416no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—2842no—
697C2×C4—2842no—
698C2×C4—2841no—
699C2×C4—2841no—
700C2×C4—2842no—
701C2×C4—2841no—
702C2×C4—2841no—
703C2×C4—2842no—
704C2×C4—2842no—
705C2×C4—2842no—
706C2×C4—2842no—
707C2×C4—2842no—
708C2×C4—2842no—
709C2×C4—2842no—
710C2×C4—2842no—
711C2×C4—714no—
712C2×C4—714no—
713C2×C4—714no—
714C2×C4—1424no—
715C2×C4—1424no—
716C2×C4—1422no—
717C2×C4—1422no—
718C2×C4—1422no—
719C2×C4—1424no—
720C2×C4—1422no—
721C2×C4—1422no—
722C2×C4—1422no—
723C2×C4—1422no—
724C2×C4—1422no—
725C2×C4—1422no—
726C2×C4—1422no—
727C2×C4—1422no—
728C2×C4—1422no—
729C2×C4—1422no—
730C2×C4—1422no—
731C2×C4—1422no—
732C2×C4—1422no—
733C2×C4—1422no—
734C2×C4—1422no—
735C2×C4—1422no—
736C2×C4—1422no—
737C2×C4—1422no—
738C2×C4#1455608414yes—
739C2×C4(C22⋊D71)⋊C414yes—
740C2×C4C4×C22⋊D7114yes—
741C2×C4#1455609914yes—
742C2×C4#1455610914yes—
743C2×C4#1455611414yes—
744C2×C4#1455612114yes—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22C2×C4⋊C4×D7111yescharacteristic
761C22#117×D7111yescharacteristic
762C22C2×#1455608411yescharacteristic
763C22C2×(C22⋊D71)⋊C411yescharacteristic
764C22C2×C4×C22⋊D7111yescharacteristic
765C22#1798647911yescharacteristic
766C22#1798648011yescharacteristic
767C22C2×#1455609911yescharacteristic
768C22C2×#1455610911yescharacteristic
769C22C2×#1455611411yescharacteristic
770C22C2×#1455612111yescharacteristic
771C22#1798654411yescharacteristic
772C22#1798654411yescharacteristic
773C22#1798655111yescharacteristic
774C22#1798655111yescharacteristic
775C22#1798660211yescharacteristic
776C22#1798660911yescharacteristic
777C22#1798661611yescharacteristic
778C22#1798662211yescharacteristic
779C22D4×C22⋊D7111yescharacteristic
780C22#1798663311yescharacteristic
781C22#1798664611yescharacteristic
782C22#1798664811yescharacteristic
783C22#1798664911yescharacteristic
784C22#1798665011yescharacteristic
785C22#1798665911yescharacteristic
786C22#1798666211yescharacteristic
787C22Q8×C22⋊D7111yescharacteristic
788C22#1798666811yescharacteristic
789C22#1798668311yescharacteristic
790C22#1798669611yescharacteristic
791C22#1798670411yescharacteristic
792C22#1798670711yescharacteristic
793C22#1798671211yescharacteristic
794C22#1798671711yescharacteristic
795C4—42no—
796C4—44no—
797C4—82no—
798C4—2842no—
799C4—2844no—
800C4—5682no—
801C4—1424no—
802C4—1424no—
803C4—1424no—
804C4#1798588718yescomplemented
805C2—44no—
806C2#2259074211yescharacteristic
807C2C2×#1798588711yescharacteristic
808C2#2259094711yescharacteristic
809C2#2259123611yescharacteristic
810C2C4⋊C4×C22⋊D7111yescharacteristic
811C2#2259126211yescharacteristic
812C2#2259129011yescharacteristic
813C2#2259185011yescharacteristic
814C2#2259186111yescharacteristic
815C2#2259192411yescharacteristic
816C2#2259193511yescharacteristic
817C2#2259269911yescharacteristic
818C2#2259271011yescharacteristic
819C2#2259275811yescharacteristic
820C2#2259276911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC23×C71C23×C4
FittingC2×#380×C71C2
socle, cosocleC24×C71C24
prime radicalC25×C71C23
hypercenterC2×#380D71
hypocenterC71#13876
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#17985868C2semidirect
4. C2×C4⋊C4×Dic71C2semidirect
6. #22586595C2semidirect
8. #22586571C2semidirect
9. #22586569C2semidirect
10. #22586569C2semidirect
26. C4×C22⋊Dic71C4semidirect
155. C22⋊Dic71C4⋊C4semidirect
387. C4×C71#388semidirect
422. C71#13876semidirect
804. C4#17985887semidirect

Maximal subgroups

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

subgroupindex
C2×#179858872
C2×#179858682
C2×#179858592
C2×C4⋊C4×Dic712
C2×C4×C22⋊Dic712
#225865952
#225865832
#225865712
#225865692
C2×#380×C712
#1387671