Finite Group Databasebeta

← #1441×D71 #31919121

Subgroups — #1441×D71 #31919121

Order 18176.

3246 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D71C211yesmaximal, characteristic
2C22×C4⋊C4×D71C211yesmaximal, characteristic
3C2×#95×D71C212yesmaximal
4C2×#95×D71C212yesmaximal
5C2×#95×D71C211yesmaximal, characteristic
6#22586594C211yesmaximal, characteristic, complemented
7#22586593C211yesmaximal, characteristic, complemented
8#22586592C212yesmaximal, complemented
9#22586591C212yesmaximal, complemented
10#22586590C211yesmaximal, characteristic, complemented
11C71×#1441C211yesmaximal, characteristic, complemented
12C23×C4×D71C2211yescharacteristic
13C23×C4×D71C2212yes—
14C23×C4×D71C2212yes—
15C23×C4×D71C2211yescharacteristic
16C23×C4×D71C2211yescharacteristic
17C22×C4⋊Dic71C2211yescharacteristic
18C22×C4⋊Dic71C2211yescharacteristic
19C22×Dic71⋊C4C2212yes—
20C22×Dic71⋊C4C2211yescharacteristic
21C22×Dic71⋊C4C2211yescharacteristic
22C2×C4⋊C4×D71—28no—
23C2×C4⋊C4×D71—24no—
24C2×C4⋊C4×D71—24no—
25C2×C4⋊C4×D71—24no—
26C2×C4⋊C4×D71C418yescomplemented
27C2×C71⋊#95C2212yes—
28C2×C71⋊#95C2212yes—
29C2×C71⋊#95C2211yescharacteristic
30C2×C71⋊#95C2212yes—
31C2×C71⋊#95C2212yes—
32C2×C71⋊#95C2212yes—
33C2×C71⋊#95C2212yes—
34C2×C71⋊#95C2212yes—
35#95×D71—28no—
36#95×D71—24no—
37#95×D71—28no—
38C22×C4⋊C4×C71C2211yescharacteristic
39C22×C4⋊C4×C71C2211yescharacteristic
40C2×#95×C71C2212yes—
41C2×#95×C71C2212yes—
42C2×#95×C71C2211yescharacteristic
43C24×D71C2311yescharacteristic
44C23×Dic71C2311yescharacteristic
45C23×Dic71C2312yes—
46C23×Dic71C2312yes—
47C23×Dic71C2311yescharacteristic
48C23×Dic71C2311yescharacteristic
49C22×C4×D71—22no—
50C22×C4×D71—22no—
51C22×C4×D71—24no—
52C22×C4×D71—22no—
53C22×C4×D71—22no—
54C22×C4×D71—24no—
55C22×C4×D71—24no—
56C22×C4×D71—24no—
57C22×C4×D71—24no—
58C22×C4×D71—24no—
59C22×C4×D71—24no—
60C22×C4×D71—22no—
61C22×C4×D71—22no—
62C22×C4×D71—24no—
63C22×C4×D71—24no—
64C22×C4×D71—24no—
65C22×C4×D71—24no—
66C22×C4×D71—24no—
67C22×C4×D71—24no—
68C22×C4×D71—24no—
69C22×C4×D71—24no—
70C22×C4×D71—24no—
71C22×C4×D71C2×C414yes—
72C22×C4×D71C2×C414yes—
73C22×C4×D71C2×C414yes—
74C22×C4×D71D418yes—
75C22×C4×D71D414yes—
76C22×C4×D71D414yes—
77C22×C4×D71D414yes—
78C22×C4×D71Q818yes—
79C22×C4×D71Q814yes—
80C2×C4⋊Dic71—24no—
81C2×C4⋊Dic71—22no—
82C2×C4⋊Dic71—22no—
83C2×C4⋊Dic71—22no—
84C2×C4⋊Dic71C2×C414yescomplemented
85C2×Dic71⋊C4—24no—
86C2×Dic71⋊C4—24no—
87C2×Dic71⋊C4—22no—
88C2×Dic71⋊C4—22no—
89C2×Dic71⋊C4—24no—
90C2×Dic71⋊C4—22no—
91C2×Dic71⋊C4—22no—
92C2×Dic71⋊C4C2×C414yescomplemented
93C2×Dic71⋊C4C2×C414yescomplemented
94C4⋊C4×D71—232no—
95C4⋊C4×D71—232no—
96C71⋊#95—24no—
97C71⋊#95—24no—
98C71⋊#95—24no—
99C71⋊#95—24no—
100C71⋊#95—24no—
101C71⋊#95—24no—
102C71⋊#95—22no—
103C71⋊#95—24no—
104C23×C4×C71C2311yescharacteristic
105C23×C4×C71C2312yes—
106C23×C4×C71C2312yes—
107C23×C4×C71C2311yescharacteristic
108C23×C4×C71C2311yescharacteristic
109C2×C4⋊C4×C71—24no—
110C2×C4⋊C4×C71—22no—
111C2×C4⋊C4×C71—22no—
112C2×C4⋊C4×C71—22no—
113C2×C4⋊C4×C71C2×C414yescomplemented
114#95×C71—24no—
115#95×C71—22no—
116#95×C71—24no—
117C23×D71C22×C412yes—
118C23×D71C2×D412yes—
119C23×D71C2×D412yes—
120C23×D71C2×D412yes—
121C23×D71C2×D414yes—
122C23×D71C2×Q812yes—
123C23×D71C2×Q814yes—
124C23×D71#4112yes—
125C23×D71#4112yes—
126C23×D71#4114yes—
127C23×D71#4114yes—
128C22×Dic71—21no—
129C22×Dic71—21no—
130C22×Dic71—22no—
131C22×Dic71—21no—
132C22×Dic71—21no—
133C22×Dic71—22no—
134C22×Dic71—22no—
135C22×Dic71—22no—
136C22×Dic71—22no—
137C22×Dic71—22no—
138C22×Dic71—22no—
139C22×Dic71—21no—
140C22×Dic71—21no—
141C22×Dic71—22no—
142C22×Dic71—22no—
143C22×Dic71—22no—
144C22×Dic71—22no—
145C22×Dic71—22no—
146C22×Dic71—22no—
147C22×Dic71—22no—
148C22×Dic71—22no—
149C22×Dic71—22no—
150C22×Dic71C22×C412yes—
151C22×Dic71C22×C412yes—
152C22×Dic71C22×C412yes—
153C22×Dic71C2×D414yes—
154C22×Dic71C2×D412yes—
155C22×Dic71C2×D412yes—
156C22×Dic71C2×D412yes—
157C22×Dic71C2×Q814yes—
158C22×Dic71C2×Q812yes—
159C2×C4×D71—28no—
160C2×C4×D71—28no—
161C2×C4×D71—216no—
162C2×C4×D71—28no—
163C2×C4×D71—28no—
164C2×C4×D71—28no—
165C2×C4×D71—216no—
166C2×C4×D71—28no—
167C2×C4×D71—28no—
168C2×C4×D71—28no—
169C2×C4×D71—28no—
170C2×C4×D71—216no—
171C2×C4×D71—216no—
172C2×C4×D71—216no—
173C2×C4×D71—216no—
174C2×C4×D71—216no—
175C2×C4×D71—216no—
176C2×C4×D71—216no—
177C2×C4×D71—44no—
178C2×C4×D71—48no—
179C2×C4×D71—48no—
180C2×C4×D71—48no—
181C2×C4×D71—48no—
182C2×C4×D71—48no—
183C2×C4×D71—48no—
184C2×C4×D71—44no—
185C2×C4×D71—48no—
186C2×C4×D71—48no—
187C2×C4×D71—48no—
188C2×C4×D71C22⋊C4116yes—
189C2×C4×D71C4⋊C4116yescomplemented
190C4⋊Dic71—28no—
191C4⋊Dic71—28no—
192Dic71⋊C4—216no—
193Dic71⋊C4—28no—
194Dic71⋊C4—28no—
195C24×C71C2411yescharacteristic
196C22×C4×C71—21no—
197C22×C4×C71—21no—
198C22×C4×C71—22no—
199C22×C4×C71—21no—
200C22×C4×C71—21no—
201C22×C4×C71—22no—
202C22×C4×C71—22no—
203C22×C4×C71—22no—
204C22×C4×C71—22no—
205C22×C4×C71—22no—
206C22×C4×C71—22no—
207C22×C4×C71—21no—
208C22×C4×C71—21no—
209C22×C4×C71—22no—
210C22×C4×C71—22no—
211C22×C4×C71—22no—
212C22×C4×C71—22no—
213C22×C4×C71—22no—
214C22×C4×C71—22no—
215C22×C4×C71—22no—
216C22×C4×C71—22no—
217C22×C4×C71—22no—
218C22×C4×C71C22×C412yes—
219C22×C4×C71C22×C412yes—
220C22×C4×C71C22×C412yes—
221C22×C4×C71C2×D414yes—
222C22×C4×C71C2×D412yes—
223C22×C4×C71C2×D412yes—
224C22×C4×C71C2×D412yes—
225C22×C4×C71C2×Q814yes—
226C22×C4×C71C2×Q812yes—
227C4⋊C4×C71—28no—
228C4⋊C4×C71—28no—
229C23×C71C23×C411yescharacteristic
230C23×C71C22×D411yescharacteristic
231C23×C71C22×D411yescharacteristic
232C23×C71C22×D411yescharacteristic
233C23×C71C22×D412yes—
234C23×C71C22×Q811yescharacteristic
235C23×C71C22×Q812yes—
236C23×C71C2×#4111yescharacteristic
237C23×C71C2×#4111yescharacteristic
238C23×C71C2×#4112yes—
239C23×C71C2×#4112yes—
240C22×D71C2×C22⋊C414yes—
241C22×D71C2×C4⋊C414yes—
242C22×D71#11714yes—
243C22×D71C4×D418yes—
244C22×D71C4×Q818yes—
245C22×D71#12014yes—
246C22×D71#12114yes—
247C22×D71#12114yes—
248C22×D71#12118yes—
249C22×D71#12118yes—
250C22×D71C22⋊Q814yes—
251C22×D71C22⋊Q814yes—
252C22×D71C22⋊Q818yes—
253C22×D71C22⋊Q818yes—
254C22×D71C22⋊Q818yes—
255C22×D71#12314yes—
256C22×D71#12318yes—
257C22×D71#12414yes—
258C22×D71#12518yes—
259C22×D71#12518yes—
260C22×D71#12618yes—
261C22×D71C4⋊Q818yes—
262C22×D71C4⋊Q814yes—
263C2×C4×C71—22no—
264C2×C4×C71—22no—
265C2×C4×C71—24no—
266C2×C4×C71—22no—
267C2×C4×C71—22no—
268C2×C4×C71—22no—
269C2×C4×C71—24no—
270C2×C4×C71—22no—
271C2×C4×C71—22no—
272C2×C4×C71—22no—
273C2×C4×C71—22no—
274C2×C4×C71—24no—
275C2×C4×C71—24no—
276C2×C4×C71—24no—
277C2×C4×C71—24no—
278C2×C4×C71—24no—
279C2×C4×C71—24no—
280C2×C4×C71—24no—
281C2×C4×C71—41no—
282C2×C4×C71—42no—
283C2×C4×C71—42no—
284C2×C4×C71—42no—
285C2×C4×C71—42no—
286C2×C4×C71—42no—
287C2×C4×C71—42no—
288C2×C4×C71—42no—
289C2×C4×C71—41no—
290C2×C4×C71—42no—
291C2×C4×C71—42no—
292C2×C4×C71C2×C22⋊C414yes—
293C2×C4×C71C2×C4⋊C414yescomplemented
294C2×Dic71—22no—
295C2×Dic71—22no—
296C2×Dic71—24no—
297C2×Dic71—22no—
298C2×Dic71—22no—
299C2×Dic71—22no—
300C2×Dic71—24no—
301C2×Dic71—22no—
302C2×Dic71—22no—
303C2×Dic71—22no—
304C2×Dic71—22no—
305C2×Dic71—24no—
306C2×Dic71—24no—
307C2×Dic71—24no—
308C2×Dic71—24no—
309C2×Dic71—24no—
310C2×Dic71—24no—
311C2×Dic71—24no—
312C2×Dic71—41no—
313C2×Dic71—42no—
314C2×Dic71—42no—
315C2×Dic71—42no—
316C2×Dic71—42no—
317C2×Dic71—42no—
318C2×Dic71—42no—
319C2×Dic71—42no—
320C2×Dic71—41no—
321C2×Dic71—42no—
322C2×Dic71—42no—
323C2×Dic71C2×C22⋊C414yes—
324C2×Dic71C2×C4⋊C414yescomplemented
325C4×D71—232no—
326C4×D71—232no—
327C4×D71—416no—
328C4×D71—432no—
329C4×D71—432no—
330C22×C71C22×C22⋊C411yescharacteristic
331C22×C71C22×C4⋊C411yescharacteristic
332C22×C71C2×#11711yescharacteristic
333C22×C71C2×C4×D412yes—
334C22×C71C2×C4×Q812yes—
335C22×C71C2×#12011yescharacteristic
336C22×C71C2×#12112yes—
337C22×C71C2×#12111yescharacteristic
338C22×C71C2×#12111yescharacteristic
339C22×C71C2×#12112yes—
340C22×C71C2×C22⋊Q812yes—
341C22×C71C2×C22⋊Q811yescharacteristic
342C22×C71C2×C22⋊Q812yes—
343C22×C71C2×C22⋊Q812yes—
344C22×C71C2×C22⋊Q811yescharacteristic
345C22×C71C2×#12312yes—
346C22×C71C2×#12311yescharacteristic
347C22×C71C2×#12411yescharacteristic
348C22×C71C2×#12512yes—
349C22×C71C2×#12512yes—
350C22×C71C2×#12612yes—
351C22×C71C2×C4⋊Q812yes—
352C22×C71C2×C4⋊Q811yescharacteristic
353C2×D71#38018yes—
354C2×D71#38618yes—
355C2×D71#387116yes—
356C2×D71#389116yes—
357C2×D71#39118yes—
358C2×D71#39418yes—
359C2×D71#39518yes—
360C2×D71#396116yes—
361C2×D71#39818yes—
362C2×D71#398116yes—
363C2×D71#40018yes—
364C4×C71—24no—
365C4×C71—24no—
366C4×C71—44no—
367C4×C71—44no—
368C4×C71—42no—
369Dic71—24no—
370Dic71—24no—
371Dic71—44no—
372Dic71—44no—
373Dic71—42no—
374C2×#1441—711nomaximal, Sylow
375C2×C71C2×#38011yescharacteristic
376C2×C71C2×#38611yescharacteristic
377C2×C71C2×#38712yes—
378C2×C71C2×#38912yes—
379C2×C71C2×#39111yescharacteristic
380C2×C71C2×#39411yescharacteristic
381C2×C71C2×#39511yescharacteristic
382C2×C71C2×#39612yes—
383C2×C71C2×#39811yescharacteristic
384C2×C71C2×#39812yes—
385C2×C71C2×#40011yescharacteristic
386D71#1441116yesdirect product factor
387C23×C4⋊C4—711no—
388C23×C4⋊C4—711no—
389C22×#95—711no—
390C22×#95—712no—
391C22×#95—712no—
392#1441—712no—
393#1441—712no—
394#1441—711no—
395#1441—711no—
396#1441—711no—
397#1441D7111yescharacteristic, direct product factor
398C71C2×#144111yescharacteristic, complemented, Sylow
399C24×C4—711no—
400C24×C4—711no—
401C24×C4—711no—
402C24×C4—712no—
403C24×C4—712no—
404C22×C4⋊C4—711no—
405C22×C4⋊C4—711no—
406C22×C4⋊C4—711no—
407C22×C4⋊C4—718no—
408C22×C4⋊C4—712no—
409C22×C4⋊C4—711no—
410C22×C4⋊C4—1424no—
411C22×C4⋊C4—1424no—
412C22×C4⋊C4—1424no—
413C22×C4⋊C4—1428no—
414C22×C4⋊C4C2×D7111yescharacteristic
415C22×C4⋊C4C2×D7111yescharacteristic
416C2×#95—712no—
417C2×#95—712no—
418C2×#95—712no—
419C2×#95—712no—
420C2×#95—712no—
421C2×#95—712no—
422C2×#95—712no—
423C2×#95—711no—
424C2×#95—1424no—
425C2×#95—1428no—
426C2×#95—1428no—
427C2×#95C2×D7112yes—
428C2×#95C2×D7112yes—
429C2×#95C2×D7111yescharacteristic
430C25—711no—
431C23×C4—711no—
432C23×C4—711no—
433C23×C4—714no—
434C23×C4—714no—
435C23×C4—714no—
436C23×C4—714no—
437C23×C4—714no—
438C23×C4—714no—
439C23×C4—711no—
440C23×C4—712no—
441C23×C4—712no—
442C23×C4—714no—
443C23×C4—718no—
444C23×C4—718no—
445C23×C4—1422no—
446C23×C4—1422no—
447C23×C4—1424no—
448C23×C4—1424no—
449C23×C4—1424no—
450C23×C4—1424no—
451C23×C4—1424no—
452C23×C4—1424no—
453C23×C4—1424no—
454C23×C4—1424no—
455C23×C4—1424no—
456C23×C4—1424no—
457C23×C4—1424no—
458C23×C4—1424no—
459C23×C4—1424no—
460C23×C4—1424no—
461C23×C4—1424no—
462C23×C4—1422no—
463C23×C4—1422no—
464C23×C4—1424no—
465C23×C4—1422no—
466C23×C4—1422no—
467C23×C4C22×D7111yescharacteristic
468C23×C4C22×D7112yes—
469C23×C4C22×D7112yes—
470C23×C4C22×D7111yescharacteristic
471C23×C4C22×D7111yescharacteristic
472C2×C4⋊C4—24no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—714no—
477C2×C4⋊C4—714no—
478C2×C4⋊C4—714no—
479C2×C4⋊C4—14232no—
480C2×C4⋊C4—14232no—
481C2×C4⋊C4—1422no—
482C2×C4⋊C4—1422no—
483C2×C4⋊C4—1424no—
484C2×C4⋊C4—1424no—
485C2×C4⋊C4—1422no—
486C2×C4⋊C4—1422no—
487C2×C4⋊C4—1424no—
488C2×C4⋊C4—1424no—
489C2×C4⋊C4—1422no—
490C2×C4⋊C4—1422no—
491C2×C4⋊C4—1422no—
492C2×C4⋊C4C4×D7114yescomplemented
493#95—24no—
494#95—22no—
495#95—24no—
496#95—1424no—
497#95—1424no—
498#95—1424no—
499#95—1424no—
500#95—1424no—
501#95—1424no—
502#95—1422no—
503#95—1424no—
504C24—712no—
505C24—712no—
506C24—712no—
507C24—712no—
508C24—714no—
509C24—712no—
510C24—714no—
511C24—712no—
512C24—712no—
513C24—714no—
514C24—714no—
515C24C23×D7111yescharacteristic
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—2844no—
539C22×C4—2848no—
540C22×C4—2848no—
541C22×C4—2848no—
542C22×C4—2848no—
543C22×C4—2848no—
544C22×C4—2848no—
545C22×C4—2844no—
546C22×C4—2848no—
547C22×C4—2848no—
548C22×C4—2848no—
549C22×C4—712no—
550C22×C4—712no—
551C22×C4—712no—
552C22×C4—712no—
553C22×C4—712no—
554C22×C4—712no—
555C22×C4—7116no—
556C22×C4—7116no—
557C22×C4—712no—
558C22×C4—714no—
559C22×C4—714no—
560C22×C4—1428no—
561C22×C4—14216no—
562C22×C4—14216no—
563C22×C4—14216no—
564C22×C4—14216no—
565C22×C4—14216no—
566C22×C4—14216no—
567C22×C4—14216no—
568C22×C4—1428no—
569C22×C4—1428no—
570C22×C4—1428no—
571C22×C4—14216no—
572C22×C4—14216no—
573C22×C4—1428no—
574C22×C4—1428no—
575C22×C4—1428no—
576C22×C4—1428no—
577C22×C4—1428no—
578C22×C4—1422no—
579C22×C4—1422no—
580C22×C4—1422no—
581C22×C4—1422no—
582C22×C4—1422no—
583C22×C4—1421no—
584C22×C4—1421no—
585C22×C4—1422no—
586C22×C4—1422no—
587C22×C4—1422no—
588C22×C4—1422no—
589C22×C4—1422no—
590C22×C4—1422no—
591C22×C4—1422no—
592C22×C4—1422no—
593C22×C4—1422no—
594C22×C4—1421no—
595C22×C4—1421no—
596C22×C4—1422no—
597C22×C4—1421no—
598C22×C4—1421no—
599C22×C4—1422no—
600C22×C4C2×C4×D7112yes—
601C22×C4C2×C4×D7112yes—
602C22×C4C2×C4×D7112yes—
603C22×C4D4×D7114yes—
604C22×C4D4×D7112yes—
605C22×C4D4×D7112yes—
606C22×C4D4×D7112yes—
607C22×C4Q8×D7114yes—
608C22×C4Q8×D7112yes—
609C4⋊C4—28no—
610C4⋊C4—28no—
611C4⋊C4—1428no—
612C4⋊C4—1428no—
613C4⋊C4—14216no—
614C4⋊C4—1428no—
615C4⋊C4—1428no—
616C23—714no—
617C23—714no—
618C23—714no—
619C23—718no—
620C23—718no—
621C23—714no—
622C23—718no—
623C23—718no—
624C23—714no—
625C23—714no—
626C23—718no—
627C23—714no—
628C23—718no—
629C23—718no—
630C23—714no—
631C23—714no—
632C23—718no—
633C23—714no—
634C23—718no—
635C23—718no—
636C23—718no—
637C23—718no—
638C23—714no—
639C23C22×C4×D7111yescharacteristic
640C23C2×D4×D7111yescharacteristic
641C23C2×D4×D7111yescharacteristic
642C23C2×D4×D7111yescharacteristic
643C23C2×D4×D7112yes—
644C23C2×Q8×D7111yescharacteristic
645C23C2×Q8×D7112yes—
646C23#41×D7111yescharacteristic
647C23#41×D7111yescharacteristic
648C23#41×D7112yes—
649C23#41×D7112yes—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—28416no—
680C2×C4—28432no—
681C2×C4—28432no—
682C2×C4—2841no—
683C2×C4—2842no—
684C2×C4—2842no—
685C2×C4—2842no—
686C2×C4—2842no—
687C2×C4—2842no—
688C2×C4—2842no—
689C2×C4—2841no—
690C2×C4—2842no—
691C2×C4—2842no—
692C2×C4—2842no—
693C2×C4—714no—
694C2×C4—714no—
695C2×C4—14232no—
696C2×C4—14232no—
697C2×C4—1422no—
698C2×C4—1424no—
699C2×C4—1424no—
700C2×C4—1424no—
701C2×C4—1424no—
702C2×C4—1424no—
703C2×C4—1424no—
704C2×C4—1424no—
705C2×C4—1422no—
706C2×C4—1422no—
707C2×C4—1424no—
708C2×C4—1422no—
709C2×C4—1424no—
710C2×C4—1422no—
711C2×C4—1422no—
712C2×C4—1422no—
713C2×C4—1422no—
714C2×C4—1422no—
715C2×C4C22⋊C4×D7114yes—
716C2×C4C4⋊C4×D7114yescomplemented
717C22—718no—
718C22—7116no—
719C22—718no—
720C22—718no—
721C22—7116no—
722C22—7116no—
723C22—7116no—
724C22—718no—
725C22—718no—
726C22—718no—
727C22—718no—
728C22C2×C22⋊C4×D7111yescharacteristic
729C22C2×C4⋊C4×D7111yescharacteristic
730C22#117×D7111yescharacteristic
731C22C4×D4×D7112yes—
732C22C4×Q8×D7112yes—
733C22#120×D7111yescharacteristic
734C22#121×D7112yes—
735C22#121×D7112yes—
736C22#121×D7111yescharacteristic
737C22#121×D7111yescharacteristic
738C22C22⋊Q8×D7112yes—
739C22C22⋊Q8×D7111yescharacteristic
740C22C22⋊Q8×D7112yes—
741C22C22⋊Q8×D7112yes—
742C22C22⋊Q8×D7111yescharacteristic
743C22#123×D7111yescharacteristic
744C22#123×D7112yes—
745C22#124×D7111yescharacteristic
746C22#125×D7112yes—
747C22#125×D7112yes—
748C22#126×D7112yes—
749C22C4⋊Q8×D7112yes—
750C22C4⋊Q8×D7111yescharacteristic
751C4—24no—
752C4—24no—
753C4—42no—
754C4—44no—
755C4—44no—
756C4—2842no—
757C4—2844no—
758C4—2844no—
759C4—1424no—
760C4—1424no—
761C2—7116no—
762C2#380×D7111yescharacteristic
763C2#386×D7111yescharacteristic
764C2#387×D7112yes—
765C2#389×D7112yes—
766C2#391×D7111yescharacteristic
767C2#394×D7111yescharacteristic
768C2#395×D7111yescharacteristic
769C2#396×D7112yes—
770C2#398×D7112yes—
771C2#398×D7111yescharacteristic
772C2#400×D7111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC23×C71C23×C4
FittingC71×#1441C2
socle, cosocleC24×C71C24
prime radicalC24×D71C23
hypercenter#1441D71
hypocenterC71C2×#1441
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
6. #22586594C2semidirect
7. #22586593C2semidirect
8. #22586592C2semidirect
9. #22586591C2semidirect
10. #22586590C2semidirect
11. C71×#1441C2semidirect
26. C2×C4⋊C4×D71C4semidirect
84. C2×C4⋊Dic71C2×C4semidirect
92. C2×Dic71⋊C4C2×C4semidirect
93. C2×Dic71⋊C4C2×C4semidirect
113. C2×C4⋊C4×C71C2×C4semidirect
189. C2×C4×D71C4⋊C4semidirect
293. C2×C4×C71C2×C4⋊C4semidirect
324. C2×Dic71C2×C4⋊C4semidirect
386. D71#1441direct (N × H)
397. #1441D71direct (N × H)
398. C71C2×#1441semidirect
492. C2×C4⋊C4C4×D71semidirect
716. C2×C4C4⋊C4×D71semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D712
C2×#95×D712
#225865942
#225865932
#225865922
#225865912
#225865902
C71×#14412
C2×#144171