Finite Group Databasebeta

← #1872×D71 #31998642

Subgroups — #1872×D71 #31998642

Order 18176.

2270 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D71C211yesmaximal, characteristic
2C22×C4⋊C4×D71C211yesmaximal, characteristic
3C2×#103×D71C212yesmaximal, complemented
4C2×C22⋊C8×D71C211yesmaximal, characteristic
5#22588648C211yesmaximal, characteristic, complemented
6#22588647C211yesmaximal, characteristic, complemented
7#22588646C212yesmaximal, complemented
8#22588645C211yesmaximal, characteristic, complemented
9#22588644C212yesmaximal, complemented
10#340×D71C212yesmaximal, complemented
11C71×#1872C211yesmaximal, characteristic, complemented
12C22×Q8×D71C2211yescharacteristic
13C23×C4×D71—21no—
14C23×C4×D71C2211yescharacteristic
15C22×C8×D71C2212yes—
16C2×#14556108C2211yescharacteristic
17C2×#14556107C2211yescharacteristic
18C2×#14556106—21no—
19C2×#14556105—21no—
20C2×#14556104C2211yescharacteristic
21C22⋊Q8×D71—24no—
22C22⋊Q8×D71C418yescomplemented
23C22×C4⋊Dic71C2211yescharacteristic
24C22×Dic71⋊C4—21no—
25C2×C4⋊C4×D71—28no—
26C2×C4⋊C4×D71—21no—
27C2×C4⋊C4×D71—21no—
28C2×C4⋊C4×D71—21no—
29C2×C4⋊C4×D71C2212yes—
30C2×C4⋊C4×D71C2211yescharacteristic
31C2×C4⋊C4×D71C2212yes—
32C2×C22⋊C4×D71—21no—
33C2×#14556053C2212yescomplemented
34C2×#14556052C2212yescomplemented
35C2×#14556051C2212yescomplemented
36#103×D71—28no—
37C2×C22⋊(C71⋊C8)C2211yescharacteristic
38C2×(C2×D71)⋊C8C2212yes—
39C22⋊C8×D71—24no—
40#17985762C2212yescomplemented
41#17985761C2212yescomplemented
42#17985761C2212yescomplemented
43C2×C22⋊Q8×C71C2211yescharacteristic
44C22×C4⋊C4×C71C2211yescharacteristic
45C2×#103×C71C2212yescomplemented
46C2×C22⋊C8×C71C2211yescharacteristic
47#340×C71C2212yescomplemented
48C24×D71D411yescharacteristic
49C22×Dic142—21no—
50C22×Dic142C2311yescharacteristic
51C2×Q8×D71—22no—
52C2×Q8×D71—24no—
53C2×Q8×D71—24no—
54C2×Q8×D71C2×C414yescomplemented
55C23×Dic71—21no—
56C23×Dic71D411yescharacteristic
57C22×C4×D71—24no—
58C22×C4×D71—24no—
59C22×C4×D71—28no—
60C22×C4×D71—22no—
61C22×C4×D71—22no—
62C22×C4×D71—21no—
63C22×C4×D71—21no—
64C22×C4×D71—44no—
65C22×C4×D71—44no—
66C22×C4×D71C2×C414yes—
67C22×C4×D71D411yescharacteristic
68C22×C4×D71D411yescharacteristic
69C22×C4×D71D414yes—
70C22×C4×D71C2311yescharacteristic
71C22×C4×D71C2311yescharacteristic
72C22×C71⋊C8C2312yes—
73C2×C8×D71—24no—
74C2×C8×D71—24no—
75C2×C8×D71—24no—
76#14556108—22no—
77#14556108C2×C414yescomplemented
78#14556107—22no—
79#14556107C2×C414yescomplemented
80#14556106—28no—
81#14556105—28no—
82#14556104—22no—
83#14556104C2×C414yescomplemented
84C2×C4⋊Dic71—21no—
85C2×C4⋊Dic71—24no—
86C2×C4⋊Dic71—21no—
87C2×C4⋊Dic71C2311yescharacteristic
88C2×C4⋊Dic71C2312yes—
89C2×Dic71⋊C4—28no—
90C2×Dic71⋊C4—22no—
91C2×Dic71⋊C4—22no—
92C2×Dic71⋊C4—21no—
93C2×Dic71⋊C4—21no—
94C2×Dic71⋊C4—21no—
95C4⋊C4×D71—28no—
96C4⋊C4×D71—28no—
97C4⋊C4×D71—28no—
98C4⋊C4×D71—24no—
99C4⋊C4×D71—22no—
100C4⋊C4×D71—24no—
101C4⋊C4×D71—24no—
102C4⋊C4×D71C2×C414yescomplemented
103C4⋊C4×D71D418yes—
104C2×C22⋊Dic71—21no—
105C2×(C2×D71)⋊C4—21no—
106C2×(C2×D71)⋊C4—21no—
107C22⋊C4×D71—28no—
108#14556053—24no—
109#14556052—24no—
110#14556051—24no—
111C22⋊(C71⋊C8)—22no—
112(C2×D71)⋊C8—24no—
113C22×Q8×C71C2311yescharacteristic
114C23×C4×C71—21no—
115C23×C4×C71C2311yescharacteristic
116C22×C8×C71C2312yes—
117C22⋊Q8×C71—22no—
118C22⋊Q8×C71C2×C414yescomplemented
119C2×C4⋊C4×C71—21no—
120C2×C4⋊C4×C71—21no—
121C2×C4⋊C4×C71—24no—
122C2×C4⋊C4×C71C2311yescharacteristic
123C2×C4⋊C4×C71C2312yes—
124C2×C22⋊C4×C71—21no—
125#103×C71—24no—
126C22⋊C8×C71—22no—
127C23×D71—22no—
128C23×D71—22no—
129C23×D71—22no—
130C23×D71—22no—
131C23×D71C22⋊C414yes—
132C23×D71SD1614yes—
133C23×D71Q1614yes—
134C23×D71C2×D411yescharacteristic
135C23×D71C2×D411yescharacteristic
136C2×Dic142—22no—
137C2×Dic142—22no—
138C2×Dic142—21no—
139C2×Dic142—24no—
140C2×Dic142—42no—
141C2×Dic142—42no—
142C2×Dic142C22×C412yescomplemented
143Q8×D71—216no—
144Q8×D71—48no—
145C22×Dic71—22no—
146C22×Dic71—22no—
147C22×Dic71—24no—
148C22×Dic71—22no—
149C22×Dic71—21no—
150C22×Dic71—21no—
151C22×Dic71—42no—
152C22×Dic71—42no—
153C22×Dic71C22⋊C414yes—
154C22×Dic71C2×D411yescharacteristic
155C22×Dic71C2×D411yescharacteristic
156C2×C4×D71—22no—
157C2×C4×D71—22no—
158C2×C4×D71—22no—
159C2×C4×D71—22no—
160C2×C4×D71—22no—
161C2×C4×D71—22no—
162C2×C4×D71—216no—
163C2×C4×D71—216no—
164C2×C4×D71—28no—
165C2×C4×D71—24no—
166C2×C4×D71—24no—
167C2×C4×D71—28no—
168C2×C4×D71—44no—
169C2×C4×D71—432no—
170C2×C4×D71—42no—
171C2×C4×D71—42no—
172C2×C4×D71—44no—
173C2×C4×D71—44no—
174C2×C4×D71—42no—
175C2×C4×D71—44no—
176C2×C4×D71—42no—
177C2×C4×D71C22⋊C414yes—
178C2×C4×D71C22⋊C414yes—
179C2×C4×D71C22×C412yes—
180C2×C4×D71C22×C412yes—
181C2×C4×D71C2×D412yes—
182C2×C4×D71C2×D414yes—
183C2×C4×D71C2×D412yes—
184C2×C4×D71#4114yes—
185C2×C71⋊C8—22no—
186C2×C71⋊C8—22no—
187C2×C71⋊C8—22no—
188C8×D71—48no—
189C4⋊Dic71—24no—
190C4⋊Dic71—22no—
191C4⋊Dic71—21no—
192C4⋊Dic71—24no—
193C4⋊Dic71C22×C412yescomplemented
194C4⋊Dic71C2×D414yes—
195Dic71⋊C4—28no—
196Dic71⋊C4—24no—
197Dic71⋊C4—24no—
198Dic71⋊C4—24no—
199Dic71⋊C4—28no—
200C22⋊Dic71—24no—
201(C2×D71)⋊C4—24no—
202(C2×D71)⋊C4—24no—
203C24×C71C2×D411yescharacteristic
204C2×Q8×C71—21no—
205C2×Q8×C71—22no—
206C2×Q8×C71—22no—
207C2×Q8×C71C22×C412yescomplemented
208C22×C4×C71—22no—
209C22×C4×C71—22no—
210C22×C4×C71—24no—
211C22×C4×C71—22no—
212C22×C4×C71—21no—
213C22×C4×C71—21no—
214C22×C4×C71—42no—
215C22×C4×C71—42no—
216C22×C4×C71C22×C412yes—
217C22×C4×C71C2×D411yescharacteristic
218C22×C4×C71C2×D412yes—
219C22×C4×C71C2411yescharacteristic
220C2×C8×C71—22no—
221C2×C8×C71—22no—
222C2×C8×C71—22no—
223C4⋊C4×C71—24no—
224C4⋊C4×C71—24no—
225C4⋊C4×C71—22no—
226C4⋊C4×C71—21no—
227C4⋊C4×C71C22×C412yescomplemented
228C4⋊C4×C71C2×D414yes—
229C22⋊C4×C71—24no—
230C23×C71—21no—
231C23×C71—21no—
232C23×C71—21no—
233C23×C71—21no—
234C23×C71C2×C22⋊C412yes—
235C23×C71C2×SD1612yes—
236C23×C71C2×Q1612yes—
237C23×C71C22×D411yescharacteristic
238C22×D71—21no—
239C22×D71—21no—
240C22×D71—21no—
241C22×D71—21no—
242C22×D71—28no—
243C22×D71—28no—
244C22×D71—28no—
245C22×D71—28no—
246C22×D71—28no—
247C22×D71—28no—
248C22×D71#103116yescomplemented
249C22×D71C2×C22⋊C412yes—
250C22×D71C2×C22⋊C412yes—
251C22×D71#12012yes—
252C22×D71#12312yes—
253C22×D71C2×SD1612yes—
254C22×D71C2×SD1612yes—
255C22×D71C2×Q1612yes—
256C22×D71C2×Q1612yes—
257C22×D71AGL(1,ℤ/8)12yes—
258C22×D71#13712yes—
259Q8×C71—24no—
260Q8×C71—42no—
261C2×C4×C71—21no—
262C2×C4×C71—21no—
263C2×C4×C71—24no—
264C2×C4×C71—24no—
265C2×C4×C71—22no—
266C2×C4×C71—22no—
267C2×C4×C71—24no—
268C2×C4×C71—48no—
269C2×C4×C71—41no—
270C2×C4×C71—41no—
271C2×C4×C71—42no—
272C2×C4×C71—42no—
273C2×C4×C71—41no—
274C2×C4×C71—41no—
275C2×C4×C71C2×C22⋊C412yes—
276C2×C4×C71C23×C411yescharacteristic
277C2×C4×C71C22×D412yes—
278C2×C4×C71C22×D411yescharacteristic
279C2×C4×C71C2×#4112yes—
280C2×Dic71—21no—
281C2×Dic71—21no—
282C2×Dic71—28no—
283C2×Dic71—22no—
284C2×Dic71—22no—
285C2×Dic71—24no—
286C2×Dic71—48no—
287C2×Dic71—41no—
288C2×Dic71—41no—
289C2×Dic71—42no—
290C2×Dic71—42no—
291C2×Dic71—41no—
292C2×Dic71—41no—
293C2×Dic71C2×C22⋊C412yes—
294C2×Dic71C2×C22⋊C412yes—
295C2×Dic71#12012yes—
296C2×Dic71#12312yes—
297C4×D71—28no—
298C4×D71—24no—
299C4×D71—24no—
300C4×D71—28no—
301C4×D71—416no—
302C4×D71—48no—
303C4×D71—48no—
304C4×D71—416no—
305C4×D71C4×D418yes—
306C4×D71#12118yes—
307Dic142—24no—
308Dic142—42no—
309Dic142—48no—
310C8×C71—42no—
311C71⋊C8—42no—
312C22×C71—22no—
313C22×C71—22no—
314C22×C71—22no—
315C22×C71—22no—
316C22×C71—22no—
317C22×C71—22no—
318C22×C71C2×#10314yescomplemented
319C22×C71C22×C22⋊C411yescharacteristic
320C22×C71C2×#12011yescharacteristic
321C22×C71C2×#12311yescharacteristic
322C22×C71C22×SD1611yescharacteristic
323C22×C71C22×Q1611yescharacteristic
324C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C71C2×#13711yescharacteristic
326C2×D71—22no—
327C2×D71—22no—
328C2×D71—22no—
329C2×D71—22no—
330C2×D71—22no—
331C2×D71—22no—
332C2×D71—232no—
333C2×D71#38614yes—
334C2×D71C2×#10314yes—
335C2×D71C2×#10314yescomplemented
336C2×D71#41714yes—
337C2×D71#45014yes—
338C2×D71#45114yes—
339C2×D71#48314yes—
340C2×D71#48414yes—
341C4×C71—22no—
342C4×C71—42no—
343C4×C71—44no—
344C4×C71—42no—
345C4×C71C2×C4×D412yes—
346C4×C71C2×#12112yes—
347Dic71—22no—
348Dic71—42no—
349Dic71—44no—
350Dic71—42no—
351Dic71#38614yes—
352C2×#1872—711nomaximal, Sylow
353C2×C71—24no—
354C2×C71C2×#38611yescharacteristic
355C2×C71C22×#10311yescharacteristic
356C2×C71C2×#41711yescharacteristic
357C2×C71C2×#45011yescharacteristic
358C2×C71C2×#45111yescharacteristic
359C2×C71C2×#48311yescharacteristic
360C2×C71C2×#48411yescharacteristic
361D71—24no—
362D71#187218yesdirect product factor
363C22×C22⋊Q8—711no—
364C23×C4⋊C4—711no—
365C22×#103—712no—
366C22×C22⋊C8—711no—
367#1872—712no—
368#1872—711no—
369#1872—712no—
370#1872—711no—
371#1872—711no—
372#1872D7111yescharacteristic, direct product factor
373C2×#340—712no—
374C71C2×#187211yescharacteristic, complemented, Sylow
375C23×Q8—711no—
376C24×C4—711no—
377C24×C4—1421no—
378C23×C8—712no—
379C2×C22⋊Q8—711no—
380C2×C22⋊Q8—711no—
381C2×C22⋊Q8—718no—
382C2×C22⋊Q8—711no—
383C2×C22⋊Q8—1421no—
384C2×C22⋊Q8—1421no—
385C2×C22⋊Q8—1424no—
386C2×C22⋊Q8C2×D7111yescharacteristic
387C22×C4⋊C4—712no—
388C22×C4⋊C4—711no—
389C22×C4⋊C4—711no—
390C22×C4⋊C4—712no—
391C22×C4⋊C4—1428no—
392C22×C4⋊C4—1421no—
393C22×C4⋊C4—1421no—
394C22×C4⋊C4—1421no—
395C22×C4⋊C4—1421no—
396C22×C4⋊C4C2×D7111yescharacteristic
397C22×C22⋊C4—1421no—
398C2×#103—712no—
399C2×#103—712no—
400C2×#103—712no—
401C2×#103—1428no—
402C2×#103C2×D7112yescomplemented
403C2×C22⋊C8—711no—
404C2×C22⋊C8—712no—
405C2×C22⋊C8—1424no—
406C2×C22⋊C8C2×D7111yescharacteristic
407#340—712no—
408#340—712no—
409#340—712no—
410#340C2×D7112yescomplemented
411C25—711no—
412C22×Q8—714no—
413C22×Q8—711no—
414C22×Q8—1421no—
415C22×Q8—1424no—
416C22×Q8—1424no—
417C22×Q8—1422no—
418C22×Q8C22×D7111yescharacteristic
419C23×C4—21no—
420C23×C4—2844no—
421C23×C4—2844no—
422C23×C4—711no—
423C23×C4—711no—
424C23×C4—714no—
425C23×C4—711no—
426C23×C4—711no—
427C23×C4—714no—
428C23×C4—711no—
429C23×C4—1421no—
430C23×C4—1421no—
431C23×C4—1422no—
432C23×C4—1422no—
433C23×C4—1428no—
434C23×C4—1424no—
435C23×C4—1424no—
436C23×C4—1421no—
437C23×C4C22×D7111yescharacteristic
438C22×C8—712no—
439C22×C8—1424no—
440C22×C8—1424no—
441C22×C8—1424no—
442C22×C8C22×D7112yes—
443C22⋊Q8—22no—
444C22⋊Q8—714no—
445C22⋊Q8—714no—
446C22⋊Q8—714no—
447C22⋊Q8—1428no—
448C22⋊Q8—1428no—
449C22⋊Q8—1422no—
450C22⋊Q8—1422no—
451C22⋊Q8—1422no—
452C22⋊Q8C4×D7114yescomplemented
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—712no—
457C2×C4⋊C4—711no—
458C2×C4⋊C4—714no—
459C2×C4⋊C4—718no—
460C2×C4⋊C4—1424no—
461C2×C4⋊C4—1424no—
462C2×C4⋊C4—1422no—
463C2×C4⋊C4—1428no—
464C2×C4⋊C4—1428no—
465C2×C4⋊C4—1428no—
466C2×C4⋊C4—1424no—
467C2×C4⋊C4—1422no—
468C2×C4⋊C4—1422no—
469C2×C4⋊C4—1421no—
470C2×C4⋊C4—1421no—
471C2×C4⋊C4—1421no—
472C2×C4⋊C4—1428no—
473C2×C4⋊C4—1421no—
474C2×C4⋊C4—1421no—
475C2×C4⋊C4—1424no—
476C2×C4⋊C4C22×D7111yescharacteristic
477C2×C4⋊C4C22×D7112yes—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—1428no—
480C2×C22⋊C4—1421no—
481C2×C22⋊C4—1421no—
482C2×C22⋊C4—1421no—
483#103—24no—
484#103—1424no—
485#103—1424no—
486#103—1424no—
487C22⋊C8—22no—
488C22⋊C8—1424no—
489C22⋊C8—1422no—
490C24—711no—
491C24—711no—
492C24—714no—
493C24—714no—
494C24—714no—
495C24—1422no—
496C24—1422no—
497C24—1422no—
498C24—1422no—
499C24D4×D7111yescharacteristic
500C2×Q8—21no—
501C2×Q8—22no—
502C2×Q8—22no—
503C2×Q8—2842no—
504C2×Q8—2842no—
505C2×Q8—2848no—
506C2×Q8—712no—
507C2×Q8—1424no—
508C2×Q8—14216no—
509C2×Q8—1422no—
510C2×Q8—1422no—
511C2×Q8—1421no—
512C2×Q8C2×C4×D7112yescomplemented
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—2844no—
522C22×C4—2844no—
523C22×C4—2844no—
524C22×C4—2842no—
525C22×C4—2842no—
526C22×C4—2842no—
527C22×C4—2842no—
528C22×C4—28432no—
529C22×C4—2844no—
530C22×C4—2842no—
531C22×C4—2842no—
532C22×C4—711no—
533C22×C4—712no—
534C22×C4—714no—
535C22×C4—712no—
536C22×C4—714no—
537C22×C4—711no—
538C22×C4—714no—
539C22×C4—712no—
540C22×C4—712no—
541C22×C4—714no—
542C22×C4—714no—
543C22×C4—1424no—
544C22×C4—1424no—
545C22×C4—1428no—
546C22×C4—1428no—
547C22×C4—1422no—
548C22×C4—1422no—
549C22×C4—14216no—
550C22×C4—14216no—
551C22×C4—1422no—
552C22×C4—1422no—
553C22×C4—1424no—
554C22×C4—1421no—
555C22×C4—1421no—
556C22×C4—1422no—
557C22×C4—1422no—
558C22×C4—1422no—
559C22×C4—1422no—
560C22×C4—1422no—
561C22×C4C2×C4×D7112yes—
562C22×C4D4×D7112yes—
563C22×C4D4×D7111yescharacteristic
564C22×C4C23×D7111yescharacteristic
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—2848no—
569C2×C8—1422no—
570C2×C8—1422no—
571C2×C8—1422no—
572C4⋊C4—24no—
573C4⋊C4—22no—
574C4⋊C4—21no—
575C4⋊C4—24no—
576C4⋊C4—712no—
577C4⋊C4—714no—
578C4⋊C4—1428no—
579C4⋊C4—1424no—
580C4⋊C4—1424no—
581C4⋊C4—1424no—
582C4⋊C4—1428no—
583C4⋊C4—1424no—
584C4⋊C4—1422no—
585C4⋊C4—1421no—
586C4⋊C4—1424no—
587C4⋊C4C2×C4×D7112yescomplemented
588C4⋊C4D4×D7114yes—
589C22⋊C4—24no—
590C22⋊C4—1424no—
591C22⋊C4—1424no—
592C22⋊C4—1424no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—712no—
598C23—712no—
599C23—712no—
600C23—712no—
601C23—712no—
602C23—712no—
603C23—712no—
604C23—712no—
605C23—7116no—
606C23—712no—
607C23—712no—
608C23—1428no—
609C23—1428no—
610C23—1428no—
611C23—1428no—
612C23—1428no—
613C23—1428no—
614C23—1421no—
615C23—1421no—
616C23—1421no—
617C23—1421no—
618C23C22⋊C4×D7112yes—
619C23SD16×D7112yes—
620C23Q16×D7112yes—
621C23C2×D4×D7111yescharacteristic
622Q8—24no—
623Q8—42no—
624Q8—2848no—
625Q8—2842no—
626Q8—1424no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—24no—
634C2×C4—48no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—28416no—
642C2×C4—2848no—
643C2×C4—2848no—
644C2×C4—28416no—
645C2×C4—2848no—
646C2×C4—2841no—
647C2×C4—2841no—
648C2×C4—2842no—
649C2×C4—2842no—
650C2×C4—2841no—
651C2×C4—2841no—
652C2×C4—712no—
653C2×C4—712no—
654C2×C4—712no—
655C2×C4—718no—
656C2×C4—718no—
657C2×C4—712no—
658C2×C4—1428no—
659C2×C4—1428no—
660C2×C4—1422no—
661C2×C4—1422no—
662C2×C4—1424no—
663C2×C4—1428no—
664C2×C4—1421no—
665C2×C4—1421no—
666C2×C4—1424no—
667C2×C4—1424no—
668C2×C4C22⋊C4×D7112yes—
669C2×C4C22×C4×D7111yescharacteristic
670C2×C4C2×D4×D7112yes—
671C2×C4C2×D4×D7111yescharacteristic
672C2×C4#41×D7112yes—
673C8—42no—
674C8—2842no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—714no—
682C22—714no—
683C22—714no—
684C22—714no—
685C22—714no—
686C22—714no—
687C22—714no—
688C22—714no—
689C22—14232no—
690C22—1422no—
691C22—1422no—
692C22—1422no—
693C22—1422no—
694C22—1422no—
695C22—1422no—
696C22#103×D7114yescomplemented
697C22C2×C22⋊C4×D7111yescharacteristic
698C22#120×D7111yescharacteristic
699C22#123×D7111yescharacteristic
700C22C2×SD16×D7111yescharacteristic
701C22C2×Q16×D7111yescharacteristic
702C22AGL(1,ℤ/8)×D7111yescharacteristic
703C22#137×D7111yescharacteristic
704C4—22no—
705C4—42no—
706C4—44no—
707C4—42no—
708C4—2842no—
709C4—2844no—
710C4—2842no—
711C4—714no—
712C4—1422no—
713C4C4×D4×D7112yes—
714C4#121×D7112yes—
715C2—24no—
716C2—718no—
717C2—1424no—
718C2#386×D7111yescharacteristic
719C2C2×#103×D7111yescharacteristic
720C2#417×D7111yescharacteristic
721C2#450×D7111yescharacteristic
722C2#451×D7111yescharacteristic
723C2#483×D7111yescharacteristic
724C2#484×D7111yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC71×#1872C2
socleC23×C71C22×D4
prime radicalC24×D71D4
cosocleC22×C4×C71C24
hypercenter#1872D71
hypocenterC71C2×#1872
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
3. C2×#103×D71C2semidirect
5. #22588648C2semidirect
6. #22588647C2semidirect
7. #22588646C2semidirect
8. #22588645C2semidirect
9. #22588644C2semidirect
10. #340×D71C2semidirect
11. C71×#1872C2semidirect
22. C22⋊Q8×D71C4semidirect
33. C2×#14556053C22semidirect
34. C2×#14556052C22semidirect
35. C2×#14556051C22semidirect
40. #17985762C22semidirect
41. #17985761C22semidirect
42. #17985761C22semidirect
45. C2×#103×C71C22semidirect
47. #340×C71C22semidirect
54. C2×Q8×D71C2×C4semidirect
77. #14556108C2×C4semidirect
79. #14556107C2×C4semidirect
83. #14556104C2×C4semidirect
102. C4⋊C4×D71C2×C4semidirect
118. C22⋊Q8×C71C2×C4semidirect
142. C2×Dic142C22×C4semidirect
193. C4⋊Dic71C22×C4semidirect
207. C2×Q8×C71C22×C4semidirect
227. C4⋊C4×C71C22×C4semidirect
248. C22×D71#103semidirect
318. C22×C71C2×#103semidirect
335. C2×D71C2×#103semidirect
362. D71#1872direct (N × H)
372. #1872D71direct (N × H)
374. C71C2×#1872semidirect
402. C2×#103C2×D71semidirect
410. #340C2×D71semidirect
452. C22⋊Q8C4×D71semidirect
512. C2×Q8C2×C4×D71semidirect
587. C4⋊C4C2×C4×D71semidirect
696. C22#103×D71semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D712
C22×C4⋊C4×D712
C2×#103×D712
C2×C22⋊C8×D712
#225886482
#225886472
#225886462
#225886452
#225886442
#340×D712
C71×#18722
C2×#187271