Finite Group Databasebeta

← #32865839

Subgroups — #32865839

Order 18176.

2570 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22601636C211yesmaximal, characteristic, complemented
2#22598478C214yesmaximal, complemented
3#22598439C212yesmaximal, complemented
4#22598431C212yesmaximal, complemented
5#22598387C214yesmaximal, complemented
6#22598348C212yesmaximal, complemented
7#22598340C212yesmaximal, complemented
8#22598263C212yesmaximal, complemented
9#22598137C212yesmaximal, complemented
10#22597804C212yesmaximal, complemented
11#22597567C212yesmaximal, complemented
12C4×#14556154C214yesmaximal, complemented
13#22596973C211yesmaximal, characteristic, complemented
14C22×C4×D4×C71C211yesmaximal, characteristic, complemented
15C2×#14556154C2214yes—
16#17986556C2211yescharacteristic, complemented
17#17986556C2211yescharacteristic, complemented
18#17986556C2211yescharacteristic, complemented
19#17986549C2211yescharacteristic, complemented
20#17986549C2211yescharacteristic, complemented
21#17986549C2211yescharacteristic, complemented
22#17986533—21no—
23#17986533—21no—
24#17986533—21no—
25#17986533—21no—
26#17986533C2212yescomplemented
27#17986533C2212yescomplemented
28#17986510—21no—
29#17986510—21no—
30#17986510C2212yes—
31C4×#11765865—21no—
32C4×#11765865—21no—
33C4×#11765865C2212yescomplemented
34#17986334C2214yescomplemented
35#17986329C2214yescomplemented
36#17986317C2214yescomplemented
37#17986312C2214yescomplemented
38#17986299C2218yescomplemented
39#17986289C2214yescomplemented
40#17986279C2214yescomplemented
41#17986214C2218yescomplemented
42#17986204C2214yescomplemented
43#17986194C2214yescomplemented
44#17986150C2214yes—
45#17986150C2214yes—
46#17986133C2214yes—
47#17986133C2214yes—
48#17986109C2218yescomplemented
49#17986099C2218yescomplemented
50C4×#11765853C2218yescomplemented
51C4×#11765850C2218yescomplemented
52#17986056C2212yescomplemented
53#17986056C2212yescomplemented
54#17986052C2212yescomplemented
55#17986052C2212yescomplemented
56#17986039C2214yescomplemented
57#17986023C2212yescomplemented
58#17986004C2214yes—
59#17985998C2214yescomplemented
60#17985963C2212yes—
61C4×#11765849C2212yescomplemented
62C23×D4×C71C2211yescharacteristic
63C24×C4×C71—21no—
64C2×C4×D4×C71—21no—
65C2×C4×D4×C71—21no—
66C2×C4×D4×C71—21no—
67C2×C4×D4×C71—21no—
68C2×C4×D4×C71—21no—
69C2×C4×D4×C71—21no—
70C2×C4×D4×C71C2212yes—
71C2×C4×D4×C71C2212yes—
72C2×C4×D4×C71C2212yes—
73C2×C4×D4×C71C2212yes—
74C2×C4×D4×C71C2212yes—
75C2×C4×D4×C71C2212yes—
76C22×C4⋊C4×C71C2211yescharacteristic
77C22×C22⋊C4×C71—21no—
78C22×C42×C71C2211yescharacteristic
79C2×#11765865—21no—
80C2×#11765865—21no—
81C2×#11765865C2312yes—
82#14556154—216no—
83C2×#11765853C2318yes—
84C2×#11765850C2318yes—
85C2×#11765849C2314yes—
86#14556128C2311yescharacteristic, complemented
87#14556128C2311yescharacteristic, complemented
88#14556128C2311yescharacteristic, complemented
89#14556125C2311yescharacteristic, complemented
90#14556122—22no—
91#14556122—22no—
92#14556120—21no—
93#14556120—21no—
94#14556120C2312yescomplemented
95#14556116—21no—
96#14556116—21no—
97#14556116C2312yescomplemented
98#14556111—22no—
99#14556111—22no—
100#14556111—22no—
101#14556107—21no—
102#14556107—21no—
103#14556107—21no—
104#14556107—21no—
105#14556107C2312yes—
106#14556107C2312yes—
107#14556102—21no—
108#14556102—21no—
109#14556102—21no—
110#14556102—21no—
111#14556102C2312yes—
112#14556102C2312yes—
113#14556097—22no—
114C4×Dic142—21no—
115C4×Dic142—21no—
116C4×Dic142—21no—
117C4×Dic142—21no—
118C4×Dic142C2312yescomplemented
119C4×Dic142C2312yescomplemented
120C4×D284—21no—
121C4×D284—21no—
122C4×D284—21no—
123C4×D284—21no—
124C4×D284C2312yescomplemented
125C4×D284C2312yescomplemented
126C4×C22⋊D71—22no—
127C4×C22⋊D71—22no—
128C4×C22⋊D71—22no—
129C4×C22⋊D71—22no—
130C4×C22⋊D71—22no—
131C4×C22⋊D71—22no—
132#14556087—21no—
133#14556087—21no—
134#14556087C2312yes—
135#14556085—22no—
136#14556085—22no—
137#14556085—22no—
138C42×D71—22no—
139#14556061C2318yescomplemented
140#14556059C2318yescomplemented
141C4⋊(C71⋊C8)C2314yescomplemented
142C4⋊(C71⋊C8)C2314yescomplemented
143#14556051C2318yescomplemented
144#14556049C2318yes—
145#14556049C2318yes—
146#14556048C2318yescomplemented
147C22⋊(C71⋊C8)C2314yes—
148C22⋊(C71⋊C8)C2314yes—
149#14556039C2314yescomplemented
150C4×C71⋊C8C2314yescomplemented
151C25×C71—21no—
152C22×D4×C71—28no—
153C22×D4×C71—21no—
154C22×D4×C71—21no—
155C22×D4×C71—21no—
156C22×D4×C71C2312yes—
157C22×D4×C71C2312yes—
158C22×D4×C71C2312yes—
159C23×C4×C71—21no—
160C23×C4×C71—22no—
161C23×C4×C71—22no—
162C23×C4×C71—22no—
163C23×C4×C71—22no—
164C23×C4×C71—22no—
165C23×C4×C71—22no—
166C23×C4×C71—48no—
167C23×C4×C71D411yescharacteristic
168C23×C4×C71D411yescharacteristic
169C23×C4×C71C2311yescharacteristic
170C4×D4×C71—22no—
171C4×D4×C71—22no—
172C4×D4×C71—22no—
173C4×D4×C71—22no—
174C4×D4×C71—22no—
175C4×D4×C71—22no—
176C4×D4×C71—22no—
177C4×D4×C71—22no—
178C4×D4×C71—22no—
179C4×D4×C71—22no—
180C4×D4×C71—22no—
181C4×D4×C71—22no—
182C4×D4×C71C2314yes—
183C4×D4×C71C2314yes—
184C4×D4×C71C2314yes—
185C4×D4×C71C2314yes—
186C2×C4⋊C4×C71—21no—
187C2×C4⋊C4×C71—21no—
188C2×C4⋊C4×C71—21no—
189C2×C4⋊C4×C71C2312yes—
190C2×C4⋊C4×C71C2312yes—
191C2×C4⋊C4×C71C2312yes—
192C2×C22⋊C4×C71—22no—
193C2×C22⋊C4×C71—22no—
194C2×C22⋊C4×C71—22no—
195C2×C22⋊C4×C71—22no—
196C2×C22⋊C4×C71—22no—
197C2×C22⋊C4×C71—22no—
198C2×C42×C71D411yescharacteristic
199C2×C42×C71D411yescharacteristic
200C2×C42×C71D411yescharacteristic
201C2×C42×C71D411yescharacteristic
202C2×C42×C71D411yescharacteristic
203C2×C42×C71D411yescharacteristic
204C2×C42×C71C2311yescharacteristic
205C2×C42×C71C2311yescharacteristic
206C2×C42×C71C2311yescharacteristic
207C2×C42×C71C2311yescharacteristic
208C2×C42×C71C2311yescharacteristic
209C2×C42×C71C2311yescharacteristic
210#11765865—28no—
211#11765865—44no—
212#11765865—44no—
213C2×Dic142—21no—
214C2×Dic142—21no—
215C2×Dic142C2412yes—
216C2×D284—21no—
217C2×D284—21no—
218C2×D284C2412yes—
219C2×C22⋊D71—22no—
220C2×C22⋊D71—22no—
221C2×C22⋊D71—22no—
222C2×C4×D71—22no—
223C2×C4×D71—22no—
224C2×C4×D71—22no—
225#11765853—216no—
226#11765850—216no—
227#11765849—28no—
228C2×C71⋊C8C2418yes—
229C4⋊Dic71—21no—
230C4⋊Dic71—21no—
231C4⋊Dic71—21no—
232C4⋊Dic71—21no—
233C4⋊Dic71C2412yes—
234C4⋊Dic71C2412yes—
235Dic71⋊C4—22no—
236Dic71⋊C4—22no—
237Dic71⋊C4—22no—
238Dic71⋊C4—22no—
239Dic71⋊C4—22no—
240Dic71⋊C4—22no—
241C22⋊Dic71—22no—
242C22⋊Dic71—22no—
243C22⋊Dic71—22no—
244(C2×D71)⋊C4—22no—
245(C2×D71)⋊C4—22no—
246(C2×D71)⋊C4—22no—
247(C2×D71)⋊C4—22no—
248(C2×D71)⋊C4—22no—
249(C2×D71)⋊C4—22no—
250C4×Dic71—22no—
251C4×Dic71—22no—
252C4×Dic71—22no—
253C24×C71—28no—
254C24×C71—22no—
255C24×C71—22no—
256C24×C71—22no—
257C24×C71—44no—
258C24×C71—44no—
259C24×C71C2×D411yescharacteristic
260C2×D4×C71—28no—
261C2×D4×C71—28no—
262C2×D4×C71—28no—
263C2×D4×C71—28no—
264C2×D4×C71—28no—
265C2×D4×C71—22no—
266C2×D4×C71—22no—
267C2×D4×C71—22no—
268C2×D4×C71—24no—
269C2×D4×C71#4118yescomplemented
270C2×D4×C71C2414yes—
271C22×C4×C71—24no—
272C22×C4×C71—24no—
273C22×C4×C71—22no—
274C22×C4×C71—22no—
275C22×C4×C71—22no—
276C22×C4×C71—24no—
277C22×C4×C71—24no—
278C22×C4×C71—24no—
279C22×C4×C71—24no—
280C22×C4×C71—42no—
281C22×C4×C71—48no—
282C22×C4×C71—48no—
283C22×C4×C71—48no—
284C22×C4×C71—48no—
285C22×C4×C71—48no—
286C22×C4×C71—44no—
287C22×C4×C71—48no—
288C22×C4×C71C2×D411yescharacteristic
289C22×C4×C71C2×D411yescharacteristic
290C22×C4×C71C2×D411yescharacteristic
291C22×C4×C71C2×D411yescharacteristic
292C22×C4×C71C2×D411yescharacteristic
293C22×C4×C71C2×D411yescharacteristic
294C22×C4×C71C2×D411yescharacteristic
295C22×C4×C71C2×D411yescharacteristic
296C22×C4×C71C2×D411yescharacteristic
297C22×C4×C71C2×D411yescharacteristic
298C22×C4×C71C2×D411yescharacteristic
299C22×C4×C71C2×D411yescharacteristic
300C22×C4×C71C2×D411yescharacteristic
301C22×C4×C71C2×D411yescharacteristic
302C22×C4×C71C2×D411yescharacteristic
303C22×C4×C71C2411yescharacteristic
304C22×C4×C71C2411yescharacteristic
305C22×C4×C71C2411yescharacteristic
306C4⋊C4×C71—22no—
307C4⋊C4×C71—22no—
308C4⋊C4×C71—22no—
309C4⋊C4×C71C2414yes—
310C22⋊C4×C71—24no—
311C22⋊C4×C71—24no—
312C22⋊C4×C71—24no—
313C22⋊C4×C71—24no—
314C42×C71C2×D411yescharacteristic
315C42×C71C2×D411yescharacteristic
316C42×C71C2×D411yescharacteristic
317C42×C71C2×D411yescharacteristic
318C42×C71C2×D411yescharacteristic
319C42×C71C2×D411yescharacteristic
320C42×C71C2×D411yescharacteristic
321C42×C71C2×D411yescharacteristic
322C42×C71C2×D411yescharacteristic
323C42×C71C2×D411yescharacteristic
324C42×C71C2×D411yescharacteristic
325C42×C71C2×D411yescharacteristic
326C42×C71C2411yescharacteristic
327C42×C71C2411yescharacteristic
328C42×C71C2411yescharacteristic
329C42×C71C2411yescharacteristic
330C23×C71—22no—
331C23×C71—22no—
332C23×C71—22no—
333C23×C71—28no—
334C23×C71—28no—
335C23×C71—28no—
336C23×C71—24no—
337C23×C71—44no—
338C23×C71—44no—
339C23×C71—432no—
340C23×C71—44no—
341C23×C71—44no—
342C23×C71—44no—
343C23×C71—44no—
344C23×C71C22×D411yescharacteristic
345C23×C71C22×D411yescharacteristic
346C23×C71C22×D411yescharacteristic
347C22×D71—22no—
348D4×C71—28no—
349D4×C71—28no—
350D4×C71—28no—
351D4×C71—24no—
352D4×C71C2×#4118yes—
353C2×C4×C71—22no—
354C2×C4×C71—22no—
355C2×C4×C71—22no—
356C2×C4×C71—22no—
357C2×C4×C71—22no—
358C2×C4×C71—22no—
359C2×C4×C71—22no—
360C2×C4×C71—22no—
361C2×C4×C71—22no—
362C2×C4×C71—22no—
363C2×C4×C71—22no—
364C2×C4×C71—22no—
365C2×C4×C71—24no—
366C2×C4×C71—41no—
367C2×C4×C71—41no—
368C2×C4×C71—41no—
369C2×C4×C71—41no—
370C2×C4×C71—48no—
371C2×C4×C71—48no—
372C2×C4×C71—44no—
373C2×C4×C71—44no—
374C2×C4×C71—44no—
375C2×C4×C71—48no—
376C2×C4×C71—48no—
377C2×C4×C71AGL(1,ℤ/8)14yescomplemented
378C2×C4×C71C22×D411yescharacteristic
379C2×C4×C71C22×D411yescharacteristic
380C2×C4×C71C22×D411yescharacteristic
381C2×C4×C71C22×D411yescharacteristic
382C2×C4×C71C22×D411yescharacteristic
383C2×C4×C71C22×D411yescharacteristic
384C2×C4×C71C22×D411yescharacteristic
385C2×C4×C71C22×D411yescharacteristic
386C2×C4×C71C22×D411yescharacteristic
387C2×C4×C71C22×D411yescharacteristic
388C2×C4×C71C22×D411yescharacteristic
389C2×C4×C71C2×#4114yes—
390C2×C4×C71C2511yescharacteristic
391C22⋊D71—44no—
392C22⋊D71—44no—
393C22⋊D71—44no—
394C2×Dic71—22no—
395C2×Dic71—22no—
396C2×Dic71—22no—
397D284—24no—
398D284—42no—
399D284—42no—
400C4×D71—44no—
401C4×D71—44no—
402C4×D71—44no—
403Dic142—24no—
404Dic142—42no—
405Dic142—42no—
406C71⋊C8—28no—
407C22×C71—28no—
408C22×C71—21no—
409C22×C71—21no—
410C22×C71—21no—
411C22×C71—21no—
412C22×C71—21no—
413C22×C71—21no—
414C22×C71—28no—
415C22×C71—416no—
416C22×C71—416no—
417C22×C71—416no—
418C22×C71—44no—
419C22×C71—44no—
420C22×C71#52512yes—
421C22×C71C2×AGL(1,ℤ/8)12yes—
422C22×C71#57512yes—
423C22×C71C23×D411yescharacteristic
424C2×D71—42no—
425C2×D71—42no—
426C2×D71—42no—
427C4×C71—21no—
428C4×C71—21no—
429C4×C71—21no—
430C4×C71—21no—
431C4×C71—21no—
432C4×C71—21no—
433C4×C71—21no—
434C4×C71—21no—
435C4×C71—44no—
436C4×C71#52512yes—
437C4×C71C2×AGL(1,ℤ/8)12yes—
438C4×C71C2×AGL(1,ℤ/8)12yes—
439C4×C71C22×#4112yes—
440Dic71—42no—
441Dic71—42no—
442Dic71—42no—
443#60558—711nomaximal, Sylow
444C2×C71—22no—
445C2×C71—22no—
446C2×C71—22no—
447C2×C71—48no—
448C2×C71C2×#52511yescharacteristic
449C2×C71C22×AGL(1,ℤ/8)11yescharacteristic
450C2×C71C2×#57511yescharacteristic
451D71—82no—
452#3444—711no—
453C22×C4×D4D7111yescharacteristic, complemented
454#3114—714no—
455#3110—712no—
456#3109—712no—
457#3105—714no—
458#3101—712no—
459#3100—712no—
460#3092—712no—
461#3077—712no—
462#3036—712no—
463#3003—712no—
464C4×AGL(1,ℤ/8)—714no—
465#2920—711no—
466C71#6055811yescharacteristic, complemented, Sylow
467C23×D4C2×D7111yescharacteristic
468C24×C4—21no—
469C2×AGL(1,ℤ/8)—714no—
470#533—711no—
471#533—711no—
472#533—711no—
473#532—711no—
474#532—711no—
475#532—711no—
476#529—712no—
477#529—712no—
478#529—1421no—
479#529—1421no—
480#529—1421no—
481#529—1421no—
482#525—712no—
483#525—1421no—
484#525—1421no—
485C4×#41—712no—
486C4×#41—1421no—
487C4×#41—1421no—
488C2×C4×D4—21no—
489C2×C4×D4—21no—
490C2×C4×D4—21no—
491C2×C4×D4—21no—
492C2×C4×D4—21no—
493C2×C4×D4—21no—
494C2×C4×D4C2×D7112yes—
495C2×C4×D4C2×D7112yes—
496C2×C4×D4C2×D7112yes—
497C2×C4×D4C2×D7112yes—
498C2×C4×D4C2×D7112yes—
499C2×C4×D4C2×D7112yes—
500C22×C4⋊C4C2×D7111yescharacteristic
501C22×C22⋊C4—21no—
502C22×C42C2×D7111yescharacteristic
503#484—714no—
504#483—714no—
505#481—714no—
506#480—714no—
507#478—718no—
508#476—714no—
509#474—714no—
510#463—718no—
511#461—714no—
512#459—714no—
513#450—714no—
514#450—714no—
515#447—714no—
516#447—714no—
517#442—718no—
518#440—718no—
519C4×SD16—718no—
520C4×D8—718no—
521#432—712no—
522#432—712no—
523#431—712no—
524#431—712no—
525#428—714no—
526#423—712no—
527#418—714no—
528#417—714no—
529#407—712no—
530C4×M16—712no—
531C25—21no—
532C2×#41—712no—
533C2×#41—1421no—
534C2×#41—1421no—
535C22×D4—28no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4C22×D7112yes—
540C22×D4C22×D7112yes—
541C22×D4C22×D7112yes—
542C23×C4—21no—
543C23×C4—22no—
544C23×C4—22no—
545C23×C4—22no—
546C23×C4—22no—
547C23×C4—22no—
548C23×C4—22no—
549C23×C4—48no—
550C23×C4C22⋊D7111yescharacteristic
551C23×C4C22⋊D7111yescharacteristic
552C23×C4C22×D7111yescharacteristic
553AGL(1,ℤ/8)—14216no—
554C2×SD16—718no—
555C2×D8—718no—
556C2×M16—714no—
557C4⋊Q8—711no—
558C4⋊Q8—711no—
559C4⋊Q8—711no—
560#127—711no—
561#126—1422no—
562#126—1422no—
563#125—712no—
564#125—1421no—
565#125—1421no—
566#124—712no—
567#124—1421no—
568#124—1421no—
569#123—1422no—
570#123—1422no—
571#123—1422no—
572C22⋊Q8—712no—
573C22⋊Q8—712no—
574C22⋊Q8—1421no—
575C22⋊Q8—1421no—
576C22⋊Q8—1421no—
577C22⋊Q8—1421no—
578#121—712no—
579#121—712no—
580#121—1421no—
581#121—1421no—
582#121—1421no—
583#121—1421no—
584#120—1422no—
585C4×Q8—712no—
586C4×Q8—712no—
587C4×Q8—1421no—
588C4×Q8—1421no—
589C4×Q8—1421no—
590C4×Q8—1421no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—712no—
604C4×D4—712no—
605C4×D4—1422no—
606C4×D4—1422no—
607C4×D4—1422no—
608C4×D4—1422no—
609C4×D4—1422no—
610C4×D4—1422no—
611C4×D4—1421no—
612C4×D4—1421no—
613C4×D4—1421no—
614C4×D4—1421no—
615C4×D4C22×D7114yes—
616C4×D4C22×D7114yes—
617C4×D4C22×D7114yes—
618C4×D4C22×D7114yes—
619#117—712no—
620#117—1421no—
621#117—1421no—
622#117—1422no—
623#117—1422no—
624#117—1422no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4C22×D7112yes—
629C2×C4⋊C4C22×D7112yes—
630C2×C4⋊C4C22×D7112yes—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C42—1422no—
638C2×C42C22⋊D7111yescharacteristic
639C2×C42C22⋊D7111yescharacteristic
640C2×C42C22⋊D7111yescharacteristic
641C2×C42C22⋊D7111yescharacteristic
642C2×C42C22⋊D7111yescharacteristic
643C2×C42C22⋊D7111yescharacteristic
644C2×C42C22×D7111yescharacteristic
645C2×C42C22×D7111yescharacteristic
646C2×C42C22×D7111yescharacteristic
647C2×C42C22×D7111yescharacteristic
648C2×C42C22×D7111yescharacteristic
649C2×C42C22×D7111yescharacteristic
650#107—718no—
651#106—718no—
652C4⋊C8—714no—
653C4⋊C8—714no—
654#103—718no—
655#102—718no—
656#102—718no—
657#102—718no—
658C22⋊C8—714no—
659C22⋊C8—714no—
660#97—714no—
661C4×C8—714no—
662C24—28no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—44no—
667C24—44no—
668C24C2×C22⋊D7111yescharacteristic
669#41—2844no—
670#41—2844no—
671#41—1428no—
672C2×Q8—712no—
673C2×Q8—1421no—
674C2×Q8—1421no—
675C2×D4—28no—
676C2×D4—28no—
677C2×D4—28no—
678C2×D4—28no—
679C2×D4—28no—
680C2×D4—22no—
681C2×D4—22no—
682C2×D4—22no—
683C2×D4—24no—
684C2×D4—712no—
685C2×D4—1422no—
686C2×D4—1422no—
687C2×D4—1422no—
688C2×D4—1421no—
689C2×D4—1421no—
690C2×D4#1176586518yescomplemented
691C2×D4C23×D7114yes—
692C22×C4—24no—
693C22×C4—24no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—24no—
698C22×C4—24no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—42no—
702C22×C4—48no—
703C22×C4—48no—
704C22×C4—48no—
705C22×C4—48no—
706C22×C4—48no—
707C22×C4—44no—
708C22×C4—48no—
709C22×C4—1422no—
710C22×C4—1422no—
711C22×C4—1422no—
712C22×C4C2×C22⋊D7111yescharacteristic
713C22×C4C2×C22⋊D7111yescharacteristic
714C22×C4C2×C22⋊D7111yescharacteristic
715C22×C4C2×C22⋊D7111yescharacteristic
716C22×C4C2×C22⋊D7111yescharacteristic
717C22×C4C2×C22⋊D7111yescharacteristic
718C22×C4C2×C22⋊D7111yescharacteristic
719C22×C4C2×C22⋊D7111yescharacteristic
720C22×C4C2×C22⋊D7111yescharacteristic
721C22×C4C2×C22⋊D7111yescharacteristic
722C22×C4C2×C22⋊D7111yescharacteristic
723C22×C4C2×C22⋊D7111yescharacteristic
724C22×C4C2×C22⋊D7111yescharacteristic
725C22×C4C2×C22⋊D7111yescharacteristic
726C22×C4C2×C22⋊D7111yescharacteristic
727C22×C4C23×D7111yescharacteristic
728C22×C4C23×D7111yescharacteristic
729C22×C4C23×D7111yescharacteristic
730SD16—14216no—
731D8—14216no—
732M16—1428no—
733C2×C8—718no—
734C4⋊C4—22no—
735C4⋊C4—22no—
736C4⋊C4—22no—
737C4⋊C4—712no—
738C4⋊C4—712no—
739C4⋊C4—1422no—
740C4⋊C4—1422no—
741C4⋊C4—1422no—
742C4⋊C4—1422no—
743C4⋊C4—1422no—
744C4⋊C4—1422no—
745C4⋊C4—1421no—
746C4⋊C4—1421no—
747C4⋊C4—1421no—
748C4⋊C4—1421no—
749C4⋊C4C23×D7114yes—
750C22⋊C4—24no—
751C22⋊C4—24no—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—1422no—
755C22⋊C4—1422no—
756C22⋊C4—1422no—
757C22⋊C4—1422no—
758C22⋊C4—1422no—
759C22⋊C4—1422no—
760C22⋊C4—1422no—
761C22⋊C4—1422no—
762C22⋊C4—1422no—
763C42—1422no—
764C42—1422no—
765C42—1422no—
766C42C2×C22⋊D7111yescharacteristic
767C42C2×C22⋊D7111yescharacteristic
768C42C2×C22⋊D7111yescharacteristic
769C42C2×C22⋊D7111yescharacteristic
770C42C2×C22⋊D7111yescharacteristic
771C42C2×C22⋊D7111yescharacteristic
772C42C2×C22⋊D7111yescharacteristic
773C42C2×C22⋊D7111yescharacteristic
774C42C2×C22⋊D7111yescharacteristic
775C42C2×C22⋊D7111yescharacteristic
776C42C2×C22⋊D7111yescharacteristic
777C42C2×C22⋊D7111yescharacteristic
778C42C23×D7111yescharacteristic
779C42C23×D7111yescharacteristic
780C42C23×D7111yescharacteristic
781C42C23×D7111yescharacteristic
782C23—22no—
783C23—22no—
784C23—22no—
785C23—28no—
786C23—28no—
787C23—24no—
788C23—28no—
789C23—44no—
790C23—44no—
791C23—432no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—1422no—
797C23C22×C22⋊D7111yescharacteristic
798C23C22×C22⋊D7111yescharacteristic
799C23C22×C22⋊D7111yescharacteristic
800Q8—2842no—
801Q8—2842no—
802Q8—1424no—
803D4—28no—
804D4—28no—
805D4—24no—
806D4—28no—
807D4—2842no—
808D4—2844no—
809D4—2844no—
810D4—2844no—
811D4—2842no—
812D4—1424no—
813D4C2×#1176586518yes—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—24no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—48no—
832C2×C4—48no—
833C2×C4—44no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4—48no—
837C2×C4—48no—
838C2×C4—2844no—
839C2×C4—2844no—
840C2×C4—2844no—
841C2×C4—1422no—
842C2×C4—1422no—
843C2×C4—1422no—
844C2×C4#1455615414yescomplemented
845C2×C4C22×C22⋊D7111yescharacteristic
846C2×C4C22×C22⋊D7111yescharacteristic
847C2×C4C22×C22⋊D7111yescharacteristic
848C2×C4C22×C22⋊D7111yescharacteristic
849C2×C4C22×C22⋊D7111yescharacteristic
850C2×C4C22×C22⋊D7111yescharacteristic
851C2×C4C22×C22⋊D7111yescharacteristic
852C2×C4C22×C22⋊D7111yescharacteristic
853C2×C4C22×C22⋊D7111yescharacteristic
854C2×C4C22×C22⋊D7111yescharacteristic
855C2×C4C22×C22⋊D7111yescharacteristic
856C2×C4C2×#1176586514yes—
857C2×C4C24×D7111yescharacteristic
858C8—1428no—
859C22—28no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—28no—
867C22—416no—
868C22—416no—
869C22—416no—
870C22—44no—
871C22—44no—
872C22—2842no—
873C22—2842no—
874C22—2842no—
875C22#1798651012yes—
876C22C2×#1455615412yes—
877C22#1798679712yes—
878C22C23×C22⋊D7111yescharacteristic
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—44no—
888C4—2842no—
889C4—2842no—
890C4—2842no—
891C4#1798651012yes—
892C4C2×#1455615412yes—
893C4C2×#1455615412yes—
894C4C22×#1176586512yes—
895C2—22no—
896C2—22no—
897C2—22no—
898C2—48no—
899C2—5682no—
900C2C2×#1798651011yescharacteristic
901C2C22×#1455615411yescharacteristic
902C2C2×#1798679711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC22×C4×D4×C71C2
socleC22×C71C23×D4
hypercenterC22×C4×D4D71
hypocenterC71#60558
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. #22601636C2semidirect
2. #22598478C2semidirect
3. #22598439C2semidirect
4. #22598431C2semidirect
5. #22598387C2semidirect
6. #22598348C2semidirect
7. #22598340C2semidirect
8. #22598263C2semidirect
9. #22598137C2semidirect
10. #22597804C2semidirect
11. #22597567C2semidirect
12. C4×#14556154C2semidirect
13. #22596973C2semidirect
14. C22×C4×D4×C71C2semidirect
16. #17986556C22semidirect
17. #17986556C22semidirect
18. #17986556C22semidirect
19. #17986549C22semidirect
20. #17986549C22semidirect
21. #17986549C22semidirect
26. #17986533C22semidirect
27. #17986533C22semidirect
33. C4×#11765865C22semidirect
34. #17986334C22semidirect
35. #17986329C22semidirect
36. #17986317C22semidirect
37. #17986312C22semidirect
38. #17986299C22semidirect
39. #17986289C22semidirect
40. #17986279C22semidirect
41. #17986214C22semidirect
42. #17986204C22semidirect
43. #17986194C22semidirect
48. #17986109C22semidirect
49. #17986099C22semidirect
50. C4×#11765853C22semidirect
51. C4×#11765850C22semidirect
52. #17986056C22semidirect
53. #17986056C22semidirect
54. #17986052C22semidirect
55. #17986052C22semidirect
56. #17986039C22semidirect
57. #17986023C22semidirect
59. #17985998C22semidirect
61. C4×#11765849C22semidirect
86. #14556128C23semidirect
87. #14556128C23semidirect
88. #14556128C23semidirect
89. #14556125C23semidirect
94. #14556120C23semidirect
97. #14556116C23semidirect
118. C4×Dic142C23semidirect
119. C4×Dic142C23semidirect
124. C4×D284C23semidirect
125. C4×D284C23semidirect
139. #14556061C23semidirect
140. #14556059C23semidirect
141. C4⋊(C71⋊C8)C23semidirect
142. C4⋊(C71⋊C8)C23semidirect
143. #14556051C23semidirect
146. #14556048C23semidirect
149. #14556039C23semidirect
150. C4×C71⋊C8C23semidirect
269. C2×D4×C71#41semidirect
377. C2×C4×C71AGL(1,ℤ/8)semidirect
453. C22×C4×D4D71semidirect
466. C71#60558semidirect
690. C2×D4#11765865semidirect
844. C2×C4#14556154semidirect

Maximal subgroups

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

subgroupindex
#226016362
#225984782
#225984392
#225984312
#225983872
#225983482
#225983402
#225982632
#225981372
#225978042
#225975672
C4×#145561542
#225969732
C22×C4×D4×C712
#6055871