Finite Group Databasebeta

← #31919864

Subgroups — #31919864

Order 18176.

1854 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic142C211yesmaximal, characteristic
2C2×#17985903C212yesmaximal
3C2×#17985868C211yesmaximal, characteristic
4C2×C4⋊C4×Dic71C211yesmaximal, characteristic
5#22586592C212yesmaximal
6#22586591C212yesmaximal
7#22586570C211yesmaximal, characteristic
8#22586569C211yesmaximal, characteristic
9#22586569C211yesmaximal, characteristic
10Dic71⋊#95C212yesmaximal
11C71×C4⋊#95C211yesmaximal, characteristic
12C23×Dic142C2211yescharacteristic
13C2×C4×Dic142—24no—
14C2×C4×Dic142—24no—
15C2×C4×Dic142C418yescomplemented
16C22×C4⋊Dic71C2211yescharacteristic
17C22×C4⋊Dic71C2211yescharacteristic
18C22×C4⋊Dic71C2211yescharacteristic
19C22×Dic71⋊C4C2212yes—
20C22×Dic71⋊C4C2211yescharacteristic
21C22×Dic71⋊C4C2211yescharacteristic
22C22×Dic71⋊C4C2212yes—
23C22×C4×Dic71C2212yes—
24C22×C4×Dic71C2211yescharacteristic
25C22×C4×Dic71C2211yescharacteristic
26#17985903—28no—
27#17985868—24no—
28C4⋊C4×Dic71—24no—
29C2×C71⋊#95C2212yes—
30C2×C71⋊#95C2212yes—
31C2×C71⋊#95C2212yes—
32C2×C71⋊#95C2212yes—
33C2×C71⋊#95C2212yes—
34C2×C71⋊#95C2212yes—
35C2×C71⋊#95C2212yes—
36C22×C4⋊C4×C71C2211yescharacteristic
37C22×C4⋊C4×C71C2211yescharacteristic
38C22×C42×C71C2211yescharacteristic
39C2×#95×C71C2212yes—
40C2×#95×C71C2212yes—
41C22×Dic142—22no—
42C22×Dic142—22no—
43C22×Dic142—22no—
44C22×Dic142—22no—
45C22×Dic142C2×C414yes—
46C22×Dic142D414yes—
47C22×Dic142Q814yes—
48C23×Dic71C2312yes—
49C23×Dic71C2311yescharacteristic
50C23×Dic71C2312yes—
51C23×Dic71C2311yescharacteristic
52C23×Dic71C2311yescharacteristic
53C23×Dic71C2311yescharacteristic
54C4×Dic142—232no—
55C2×C4⋊Dic71—22no—
56C2×C4⋊Dic71—22no—
57C2×C4⋊Dic71—22no—
58C2×C4⋊Dic71—22no—
59C2×C4⋊Dic71—22no—
60C2×C4⋊Dic71—22no—
61C2×C4⋊Dic71—22no—
62C2×C4⋊Dic71C2×C414yes—
63C2×C4⋊Dic71Q814yescomplemented
64C2×Dic71⋊C4—22no—
65C2×Dic71⋊C4—22no—
66C2×Dic71⋊C4—22no—
67C2×Dic71⋊C4—22no—
68C2×Dic71⋊C4—24no—
69C2×Dic71⋊C4—24no—
70C2×Dic71⋊C4—24no—
71C2×Dic71⋊C4—24no—
72C2×Dic71⋊C4—42no—
73C2×Dic71⋊C4—42no—
74C2×Dic71⋊C4C2×C414yes—
75C2×Dic71⋊C4C2×C414yes—
76C2×C4×Dic71—24no—
77C2×C4×Dic71—24no—
78C2×C4×Dic71—24no—
79C2×C4×Dic71—22no—
80C2×C4×Dic71—22no—
81C2×C4×Dic71C2×C414yes—
82C2×C4×Dic71C2×C414yes—
83C2×C4×Dic71D414yes—
84C2×C4×Dic71D414yes—
85C71⋊#95—24no—
86C71⋊#95—24no—
87C71⋊#95—24no—
88C71⋊#95—24no—
89C71⋊#95—42no—
90C71⋊#95—42no—
91C71⋊#95—42no—
92C23×C4×C71C2312yes—
93C23×C4×C71C2311yescharacteristic
94C23×C4×C71C2312yes—
95C23×C4×C71C2311yescharacteristic
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×C71Q814yescomplemented
103C2×C42×C71—22no—
104C2×C42×C71—22no—
105C2×C42×C71C2×C414yes—
106#95×C71—24no—
107#95×C71—42no—
108C2×Dic142—28no—
109C2×Dic142—28no—
110C2×Dic142—28no—
111C2×Dic142—28no—
112C2×Dic142—28no—
113C2×Dic142—28no—
114C2×Dic142C4⋊C4116yescomplemented
115C22×Dic71—21no—
116C22×Dic71—21no—
117C22×Dic71—21no—
118C22×Dic71—21no—
119C22×Dic71—21no—
120C22×Dic71—21no—
121C22×Dic71—21no—
122C22×Dic71—21no—
123C22×Dic71—22no—
124C22×Dic71—22no—
125C22×Dic71—21no—
126C22×Dic71—21no—
127C22×Dic71—22no—
128C22×Dic71—22no—
129C22×Dic71—21no—
130C22×Dic71—21no—
131C22×Dic71—22no—
132C22×Dic71—21no—
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×Dic71—22no—
142C22×Dic71C22×C412yes—
143C22×Dic71C22×C412yes—
144C22×Dic71C22×C412yes—
145C22×Dic71C22×C412yes—
146C22×Dic71C2×D412yes—
147C22×Dic71C2×D412yes—
148C22×Dic71C2×D412yes—
149C22×Dic71C2×D412yes—
150C22×Dic71C2×D412yes—
151C22×Dic71C2×D412yes—
152C22×Dic71C2×Q814yes—
153C22×Dic71C2×Q812yes—
154C22×Dic71C2×Q812yes—
155C22×Dic71#4112yes—
156C22×Dic71#4112yes—
157C4⋊Dic71—28no—
158C4⋊Dic71—28no—
159C4⋊Dic71—44no—
160Dic71⋊C4—28no—
161Dic71⋊C4—28no—
162Dic71⋊C4—48no—
163Dic71⋊C4—48no—
164C4×Dic71—28no—
165C4×Dic71—48no—
166C4×Dic71C22⋊C4116yes—
167C24×C71C2411yescharacteristic
168C22×C4×C71—21no—
169C22×C4×C71—21no—
170C22×C4×C71—21no—
171C22×C4×C71—21no—
172C22×C4×C71—22no—
173C22×C4×C71—21no—
174C22×C4×C71—21no—
175C22×C4×C71—22no—
176C22×C4×C71—22no—
177C22×C4×C71—22no—
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—22no—
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×C71C22×C412yes—
192C22×C4×C71C22×C412yes—
193C22×C4×C71C22×C412yes—
194C22×C4×C71C2×D412yes—
195C22×C4×C71C2×D412yes—
196C22×C4×C71C2×D412yes—
197C22×C4×C71C2×Q812yes—
198C22×C4×C71C2×Q812yes—
199C22×C4×C71C2×Q814yes—
200C22×C4×C71C2×Q812yes—
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×C71C22×D411yescharacteristic
210C23×C71C22×Q811yescharacteristic
211C23×C71C22×Q811yescharacteristic
212C23×C71C22×Q811yescharacteristic
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
221C2×C4×C71—22no—
222C2×C4×C71—22no—
223C2×C4×C71—22no—
224C2×C4×C71—22no—
225C2×C4×C71—22no—
226C2×C4×C71—22no—
227C2×C4×C71—22no—
228C2×C4×C71—22no—
229C2×C4×C71—22no—
230C2×C4×C71—24no—
231C2×C4×C71—24no—
232C2×C4×C71—24no—
233C2×C4×C71—42no—
234C2×C4×C71—41no—
235C2×C4×C71—41no—
236C2×C4×C71—41no—
237C2×C4×C71—42no—
238C2×C4×C71—41no—
239C2×C4×C71—42no—
240C2×C4×C71—42no—
241C2×C4×C71—42no—
242C2×C4×C71—42no—
243C2×C4×C71—42no—
244C2×C4×C71—42no—
245C2×C4×C71—42no—
246C2×C4×C71—42no—
247C2×C4×C71—42no—
248C2×C4×C71C2×C22⋊C414yes—
249C2×C4×C71C2×C4⋊C414yes—
250C2×C4×C71C4×Q814yes—
251C2×C4×C71C4×Q814yes—
252C2×C4×C71C22⋊Q814yes—
253C2×C4×C71C22⋊Q814yes—
254C2×C4×C71#12414yes—
255C2×C4×C71C4⋊Q814yes—
256C2×Dic71—22no—
257C2×Dic71—22no—
258C2×Dic71—22no—
259C2×Dic71—22no—
260C2×Dic71—22no—
261C2×Dic71—22no—
262C2×Dic71—22no—
263C2×Dic71—22no—
264C2×Dic71—22no—
265C2×Dic71—22no—
266C2×Dic71—22no—
267C2×Dic71—22no—
268C2×Dic71—22no—
269C2×Dic71—22no—
270C2×Dic71—22no—
271C2×Dic71—24no—
272C2×Dic71—24no—
273C2×Dic71—24no—
274C2×Dic71—42no—
275C2×Dic71—41no—
276C2×Dic71—41no—
277C2×Dic71—41no—
278C2×Dic71—41no—
279C2×Dic71—42no—
280C2×Dic71—42no—
281C2×Dic71—42no—
282C2×Dic71—42no—
283C2×Dic71—42no—
284C2×Dic71—42no—
285C2×Dic71—42no—
286C2×Dic71—42no—
287C2×Dic71—42no—
288C2×Dic71—42no—
289C2×Dic71C2×C22⋊C414yes—
290C2×Dic71C2×C22⋊C414yes—
291C2×Dic71C2×C4⋊C414yes—
292C2×Dic71C2×C4⋊C414yes—
293C2×Dic71#11714yes—
294C2×Dic71#12114yes—
295C2×Dic71#12114yes—
296C2×Dic71C22⋊Q814yes—
297C2×Dic71C22⋊Q814yes—
298Dic142—232no—
299C22×C71C22×C22⋊C411yescharacteristic
300C22×C71C22×C4⋊C411yescharacteristic
301C22×C71C2×#11711yescharacteristic
302C22×C71C2×C4×Q811yescharacteristic
303C22×C71C2×C4×Q811yescharacteristic
304C22×C71#52011yescharacteristic
305C22×C71#52011yescharacteristic
306C22×C71C2×#12111yescharacteristic
307C22×C71C2×#12111yescharacteristic
308C22×C71C2×C22⋊Q811yescharacteristic
309C22×C71C2×C22⋊Q811yescharacteristic
310C22×C71C2×C22⋊Q811yescharacteristic
311C22×C71C2×C22⋊Q811yescharacteristic
312C22×C71C2×#12411yescharacteristic
313C22×C71C2×C4⋊Q811yescharacteristic
314C22×C71#53511yescharacteristic
315C22×C71#53611yescharacteristic
316C22×C71#53711yescharacteristic
317C22×C71#53711yescharacteristic
318C22×C71D4×Q811yescharacteristic
319C22×C71D4×Q811yescharacteristic
320C22×C71#55011yescharacteristic
321C22×C71#55011yescharacteristic
322C22×C71#55411yescharacteristic
323C22×C71#55411yescharacteristic
324C22×C71#55611yescharacteristic
325C22×C71#55611yescharacteristic
326C22×C71#55711yescharacteristic
327C22×C71#55711yescharacteristic
328C22×C71#55711yescharacteristic
329C22×C71#55711yescharacteristic
330C22×C71Q8211yescharacteristic
331C22×C71Q8211yescharacteristic
332C22×C71#55911yescharacteristic
333C22×C71#55911yescharacteristic
334C4×C71—24no—
335C4×C71—42no—
336C4×C71—44no—
337C4×C71—82no—
338C4×C71#39118yescomplemented
339Dic71—24no—
340Dic71—24no—
341Dic71—42no—
342Dic71—44no—
343Dic71—82no—
344Dic71#38018yes—
345#13926—711nomaximal, Sylow
346C2×C71C2×#38011yescharacteristic
347C2×C71C2×#39111yescharacteristic
348C2×C71#231111yescharacteristic
349C2×C71Q8×C4⋊C411yescharacteristic
350C2×C71Q8×C4⋊C411yescharacteristic
351C2×C71#235511yescharacteristic
352C2×C71#235511yescharacteristic
353C2×C71#253811yescharacteristic
354C2×C71#253811yescharacteristic
355C2×C71#254611yescharacteristic
356C2×C71#254811yescharacteristic
357C2×C71#256711yescharacteristic
358C2×C71#256811yescharacteristic
359C2×C71#258211yescharacteristic
360C2×C71#258211yescharacteristic
361C22×C4×Q8—711no—
362C2×#391—712no—
363C2×#384—711no—
364C2×C4×C4⋊C4—711no—
365#1441—712no—
366#1441—712no—
367C4⋊#95—711no—
368C4⋊#95—712no—
369C4⋊#95—711no—
370C4⋊#95—711no—
371C4⋊#95D7111yescharacteristic
372C71#1392611yescharacteristic, complemented, Sylow
373C23×Q8—711no—
374C2×C4×Q8—718no—
375C2×C4×Q8—1424no—
376C2×C4×Q8—1424no—
377C22×C4⋊C4—712no—
378C22×C4⋊C4—711no—
379C22×C4⋊C4—711no—
380C22×C4⋊C4—711no—
381C22×C4⋊C4—711no—
382C22×C4⋊C4—712no—
383C22×C4⋊C4—711no—
384C22×C4⋊C4C2×D7111yescharacteristic
385C22×C4⋊C4C2×D7111yescharacteristic
386C22×C42—711no—
387C22×C42—711no—
388C22×C42—712no—
389C22×C42C2×D7111yescharacteristic
390#391—1428no—
391#384—1424no—
392C4×C4⋊C4—1424no—
393C2×#95—712no—
394C2×#95—712no—
395C2×#95—712no—
396C2×#95—712no—
397C2×#95—712no—
398C2×#95—712no—
399C2×#95—712no—
400C2×#95C2×D7112yes—
401C2×#95C2×D7112yes—
402C22×Q8—714no—
403C22×Q8—714no—
404C22×Q8—714no—
405C22×Q8—1422no—
406C22×Q8—1422no—
407C22×Q8—1422no—
408C22×Q8—1422no—
409C23×C4—711no—
410C23×C4—711no—
411C23×C4—711no—
412C23×C4—711no—
413C23×C4—712no—
414C23×C4—712no—
415C23×C4C22×D7112yes—
416C23×C4C22×D7111yescharacteristic
417C23×C4C22×D7112yes—
418C23×C4C22×D7111yescharacteristic
419C23×C4C22×D7111yescharacteristic
420C4×Q8—14232no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—2842no—
427C2×C4⋊C4—2842no—
428C2×C4⋊C4—714no—
429C2×C4⋊C4—714no—
430C2×C4⋊C4—714no—
431C2×C4⋊C4—714no—
432C2×C4⋊C4—1424no—
433C2×C4⋊C4—1424no—
434C2×C4⋊C4—1424no—
435C2×C4⋊C4—1424no—
436C2×C4⋊C4—1422no—
437C2×C4⋊C4—1422no—
438C2×C4⋊C4—1422no—
439C2×C4⋊C4—1422no—
440C2×C4⋊C4—1422no—
441C2×C4⋊C4—1422no—
442C2×C4⋊C4—1422no—
443C2×C4⋊C4—1422no—
444C2×C4⋊C4—1422no—
445C2×C4⋊C4—1422no—
446C2×C4⋊C4—1422no—
447C2×C4⋊C4Dic14214yescomplemented
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—714no—
451C2×C42—714no—
452C2×C42—714no—
453C2×C42—714no—
454C2×C42—1424no—
455C2×C42—1424no—
456C2×C42—1424no—
457C2×C42—1422no—
458C2×C42—1422no—
459C2×C42C4×D7114yes—
460#95—24no—
461#95—42no—
462#95—2842no—
463#95—2842no—
464#95—2842no—
465#95—1424no—
466#95—1424no—
467#95—1424no—
468#95—1424no—
469C24C23×D7111yescharacteristic
470C2×Q8—7116no—
471C2×Q8—1428no—
472C2×Q8—1428no—
473C2×Q8—1428no—
474C2×Q8—1428no—
475C2×Q8—1428no—
476C2×Q8—1428no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—712no—
501C22×C4—712no—
502C22×C4—712no—
503C22×C4—712no—
504C22×C4—712no—
505C22×C4—712no—
506C22×C4—712no—
507C22×C4—712no—
508C22×C4—712no—
509C22×C4—712no—
510C22×C4—712no—
511C22×C4—712no—
512C22×C4—712no—
513C22×C4—712no—
514C22×C4—714no—
515C22×C4—1422no—
516C22×C4—1422no—
517C22×C4—1422no—
518C22×C4—1422no—
519C22×C4—1422no—
520C22×C4—1422no—
521C22×C4—1422no—
522C22×C4—1422no—
523C22×C4—1422no—
524C22×C4—1421no—
525C22×C4—1421no—
526C22×C4—1422no—
527C22×C4—1422no—
528C22×C4—1421no—
529C22×C4—1421no—
530C22×C4—1422no—
531C22×C4—1421no—
532C22×C4—1421no—
533C22×C4—1422no—
534C22×C4—1421no—
535C22×C4—1421no—
536C22×C4—1421no—
537C22×C4—1421no—
538C22×C4—1421no—
539C22×C4—1421no—
540C22×C4—1421no—
541C22×C4—1421no—
542C22×C4C2×C4×D7112yes—
543C22×C4C2×C4×D7112yes—
544C22×C4C2×C4×D7112yes—
545C22×C4D4×D7112yes—
546C22×C4D4×D7112yes—
547C22×C4D4×D7112yes—
548C22×C4Q8×D7112yes—
549C22×C4Q8×D7112yes—
550C22×C4C2×Dic14214yes—
551C22×C4C2×Dic14212yes—
552C22×C4#1176586412yes—
553C22×C4#1176586512yes—
554C4⋊C4—28no—
555C4⋊C4—44no—
556C4⋊C4—2848no—
557C4⋊C4—2848no—
558C4⋊C4—2844no—
559C4⋊C4—1428no—
560C4⋊C4—1428no—
561C4⋊C4—1428no—
562C4⋊C4—1428no—
563C42—28no—
564C42—2848no—
565C42—7116no—
566C42—1428no—
567C23C22×C4×D7111yescharacteristic
568C23C2×D4×D7111yescharacteristic
569C23C2×D4×D7111yescharacteristic
570C23C2×D4×D7111yescharacteristic
571C23C2×Q8×D7111yescharacteristic
572C23C2×Q8×D7111yescharacteristic
573C23C22×Dic14211yescharacteristic
574C23#41×D7111yescharacteristic
575C23#41×D7111yescharacteristic
576C23C2×#1176586411yescharacteristic
577C23C2×#1176586511yescharacteristic
578C23#1455617311yescharacteristic
579C23#1455617411yescharacteristic
580C23#1455617511yescharacteristic
581C23#1455617611yescharacteristic
582Q8—14232no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—24no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—42no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—2841no—
611C2×C4—2841no—
612C2×C4—2841no—
613C2×C4—2841no—
614C2×C4—2842no—
615C2×C4—2842no—
616C2×C4—2842no—
617C2×C4—2842no—
618C2×C4—2842no—
619C2×C4—2842no—
620C2×C4—2842no—
621C2×C4—2842no—
622C2×C4—2842no—
623C2×C4—2842no—
624C2×C4—2842no—
625C2×C4—714no—
626C2×C4—714no—
627C2×C4—714no—
628C2×C4—714no—
629C2×C4—714no—
630C2×C4—714no—
631C2×C4—714no—
632C2×C4—714no—
633C2×C4—714no—
634C2×C4—1424no—
635C2×C4—1422no—
636C2×C4—1424no—
637C2×C4—1422no—
638C2×C4—1422no—
639C2×C4—1424no—
640C2×C4—1422no—
641C2×C4—1422no—
642C2×C4—1422no—
643C2×C4—1422no—
644C2×C4—1422no—
645C2×C4—1422no—
646C2×C4—1422no—
647C2×C4—1422no—
648C2×C4—1422no—
649C2×C4—1422no—
650C2×C4—1422no—
651C2×C4—1422no—
652C2×C4C22⋊C4×D7114yes—
653C2×C4C4⋊C4×D7114yes—
654C2×C4#1455609314yes—
655C2×C4C4×Dic14214yes—
656C2×C4#1455610514yes—
657C2×C4#1455610614yes—
658C2×C4#1455611414yes—
659C2×C4#1455612714yes—
660C22C2×C22⋊C4×D7111yescharacteristic
661C22C2×C4⋊C4×D7111yescharacteristic
662C22#117×D7111yescharacteristic
663C22C2×#1455609311yescharacteristic
664C22C2×C4×Dic14211yescharacteristic
665C22#1798647911yescharacteristic
666C22#1798648011yescharacteristic
667C22#121×D7111yescharacteristic
668C22#121×D7111yescharacteristic
669C22C22⋊Q8×D7111yescharacteristic
670C22C22⋊Q8×D7111yescharacteristic
671C22C2×#1455610511yescharacteristic
672C22C2×#1455610611yescharacteristic
673C22C2×#1455611411yescharacteristic
674C22C2×#1455612711yescharacteristic
675C22#1798656511yescharacteristic
676C22#1798657211yescharacteristic
677C22#1798657811yescharacteristic
678C22#1798657911yescharacteristic
679C22#1798666411yescharacteristic
680C22D4×Dic14211yescharacteristic
681C22#1798666911yescharacteristic
682C22#1798667011yescharacteristic
683C22#1798670511yescharacteristic
684C22#1798670811yescharacteristic
685C22#1798671811yescharacteristic
686C22#1798672111yescharacteristic
687C22#1798672411yescharacteristic
688C22#1798672511yescharacteristic
689C22#1798672611yescharacteristic
690C22#1798672711yescharacteristic
691C22#1798672911yescharacteristic
692C22Q8×Dic14211yescharacteristic
693C22#1798673111yescharacteristic
694C22#1798673211yescharacteristic
695C4—24no—
696C4—42no—
697C4—44no—
698C4—82no—
699C4—2842no—
700C4—2844no—
701C4—5682no—
702C4—718no—
703C4—1424no—
704C4—1424no—
705C4#1798590318yescomplemented
706C2#380×D7111yescharacteristic
707C2C2×#1798590311yescharacteristic
708C2#2259092911yescharacteristic
709C2#2259125211yescharacteristic
710C2C4⋊C4×Dic14211yescharacteristic
711C2#2259129211yescharacteristic
712C2#2259129811yescharacteristic
713C2#2259326011yescharacteristic
714C2#2259326111yescharacteristic
715C2#2259332711yescharacteristic
716C2#2259334111yescharacteristic
717C2#2259354711yescharacteristic
718C2#2259355411yescharacteristic
719C2#2259371111yescharacteristic
720C2#2259371211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC23×C71C23×C4
FittingC71×C4⋊#95C2
socle, prime radical, cosocleC24×C71C24
hypercenterC4⋊#95D71
hypocenterC71#13926
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
15. C2×C4×Dic142C4semidirect
63. C2×C4⋊Dic71Q8semidirect
102. C2×C4⋊C4×C71Q8semidirect
114. C2×Dic142C4⋊C4semidirect
338. C4×C71#391semidirect
372. C71#13926semidirect
447. C2×C4⋊C4Dic142semidirect
705. C4#17985903semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic1422
C2×#179859032
C2×#179858682
C2×C4⋊C4×Dic712
#225865922
#225865912
#225865702
#225865692
Dic71⋊#952
C71×C4⋊#952
#1392671