Finite Group Databasebeta

← #32868951

Subgroups — #32868951

Order 18176.

2196 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986549C211yesmaximal, characteristic, complemented
2#22599373C214yesmaximal, complemented
3#22599364C212yesmaximal, complemented
4#22599355C212yesmaximal, complemented
5#22599312C214yesmaximal, complemented
6#22599301C214yesmaximal, complemented
7#22598804C212yesmaximal, complemented
8#22598743C212yesmaximal, complemented
9#22597812C212yesmaximal, complemented
10#22597804C212yesmaximal, complemented
11#22597598C212yesmaximal, complemented
12#22597590C212yesmaximal, complemented
13#22596973C211yesmaximal, characteristic, complemented
14C2×#529×C71C211yesmaximal, characteristic, complemented
15C22×#11765865C2212yes—
16C2×#14556159C2214yescomplemented
17C2×#14556154C2214yescomplemented
18#17986549—21no—
19#17986549—21no—
20#17986549—21no—
21#17986549—21no—
22#17986549C2212yes—
23#17986549C2212yes—
24#17986549C2212yescomplemented
25#17986549C2212yescomplemented
26C2×#14556128C2211yescharacteristic, complemented
27C2×#14556125C2211yescharacteristic, complemented
28C2×#14556116C2212yescomplemented
29C2×#14556102—21no—
30C2×#14556102—21no—
31C2×C4×D284—21no—
32C2×C4×D284—21no—
33#17986394C2214yescomplemented
34#17986389C2214yescomplemented
35#17986381C2218yescomplemented
36#17986369C2214yescomplemented
37#17986365C2214yescomplemented
38#17986356C2218yescomplemented
39#17986221C2218yescomplemented
40#17986214C2218yescomplemented
41#17986209C2214yescomplemented
42#17986204C2214yescomplemented
43#17986199C2214yescomplemented
44#17986194C2214yescomplemented
45#17986159C2218yescomplemented
46#17986154C2214yescomplemented
47#17986149C2214yescomplemented
48#17986142C2218yescomplemented
49#17986137C2214yes—
50#17986132C2214yes—
51#17986056C2212yescomplemented
52#17986056C2212yescomplemented
53#17986052C2212yescomplemented
54#17986052C2212yescomplemented
55#17986023C2212yescomplemented
56#17985998C2214yescomplemented
57#17985998C2214yescomplemented
58#17985963C2212yes—
59C4×#11765849C2212yescomplemented
60#529×C71—21no—
61#529×C71—21no—
62#529×C71—21no—
63#529×C71—21no—
64#529×C71C2212yes—
65#529×C71C2212yes—
66#529×C71C2212yescomplemented
67#529×C71C2212yescomplemented
68C2×#126×C71—21no—
69C2×#125×C71C2211yescharacteristic, complemented
70C2×#124×C71C2211yescharacteristic, complemented
71C2×#123×C71—21no—
72C2×C22⋊Q8×C71C2211yescharacteristic
73C2×#121×C71C2211yescharacteristic
74C2×C4×Q8×C71C2211yescharacteristic, complemented
75C2×C4×D4×C71—21no—
76C2×C4×D4×C71C2211yescharacteristic, complemented
77C2×#117×C71—21no—
78C22×C42×C71C2211yescharacteristic
79C2×#11765865—22no—
80C2×#11765865—22no—
81C2×#11765865—48no—
82C2×#11765865C2314yes—
83C2×#11765865C2314yes—
84C22×Dic142C2312yes—
85C22×D284—21no—
86C22×D284—21no—
87C22×D284C2312yes—
88C22×C22⋊D71—22no—
89C22×C4×D71—22no—
90#14556159—48no—
91#14556154—48no—
92C2×#11765855C2318yes—
93C2×#11765853C2318yes—
94C2×#11765852C2318yes—
95C2×#11765850C2318yes—
96C2×#11765849C2314yes—
97#14556128—21no—
98#14556128—21no—
99#14556128C2312yes—
100#14556128C2312yes—
101#14556125—21no—
102#14556125—21no—
103#14556125C2312yes—
104#14556125C2312yes—
105#14556116—22no—
106#14556116—22no—
107#14556116C2314yes—
108#14556116C2314yes—
109#14556102—22no—
110#14556102—22no—
111#14556102—22no—
112#14556102—22no—
113#14556102—22no—
114#14556102—22no—
115#14556102—22no—
116#14556102—22no—
117C4×D284—22no—
118C4×D284—22no—
119C4×D284—22no—
120C4×D284—22no—
121C4×D284—22no—
122C4×D284—22no—
123C4×D284—22no—
124C4×D284—22no—
125C2×C4⋊Dic71—21no—
126C2×C4⋊Dic71—21no—
127C2×(C2×D71)⋊C4—22no—
128C2×(C2×D71)⋊C4—22no—
129C4⋊(C71⋊C8)C2314yes—
130C4⋊(C71⋊C8)C2314yes—
131#14556051C2318yes—
132#14556051C2318yes—
133#14556048C2318yes—
134#14556048C2318yes—
135C22⋊(C71⋊C8)C2314yes—
136C22⋊(C71⋊C8)C2314yes—
137#14556039C2314yes—
138C4×C71⋊C8C2314yes—
139C22×Q8×C71C2311yescharacteristic
140C22×D4×C71—21no—
141C22×D4×C71C2311yescharacteristic
142C23×C4×C71—21no—
143C23×C4×C71D411yescharacteristic
144C23×C4×C71D411yescharacteristic
145C23×C4×C71C2311yescharacteristic
146#126×C71—22no—
147#126×C71—22no—
148#126×C71—22no—
149#126×C71—22no—
150#125×C71—21no—
151#125×C71—21no—
152#125×C71C2312yes—
153#125×C71C2312yes—
154#124×C71—21no—
155#124×C71—21no—
156#124×C71C2312yes—
157#124×C71C2312yes—
158#123×C71—22no—
159#123×C71—22no—
160#123×C71—22no—
161#123×C71—22no—
162C22⋊Q8×C71—21no—
163C22⋊Q8×C71—21no—
164C22⋊Q8×C71C2312yes—
165C22⋊Q8×C71C2312yes—
166#121×C71—21no—
167#121×C71—21no—
168#121×C71C2312yes—
169#121×C71C2312yes—
170C4×Q8×C71—21no—
171C4×Q8×C71—21no—
172C4×Q8×C71C2312yes—
173C4×Q8×C71C2312yes—
174C4×D4×C71—22no—
175C4×D4×C71—22no—
176C4×D4×C71—22no—
177C4×D4×C71—22no—
178C4×D4×C71—21no—
179C4×D4×C71—21no—
180C4×D4×C71C2312yes—
181C4×D4×C71C2312yes—
182#117×C71—22no—
183#117×C71—22no—
184#117×C71—22no—
185#117×C71—22no—
186C2×C4⋊C4×C71—21no—
187C2×C4⋊C4×C71—21no—
188C2×C4⋊C4×C71—21no—
189C2×C4⋊C4×C71—21no—
190C2×C4⋊C4×C71C2311yescharacteristic
191C2×C4⋊C4×C71C2311yescharacteristic
192C2×C22⋊C4×C71—21no—
193C2×C22⋊C4×C71—21no—
194C2×C22⋊C4×C71—21no—
195C2×C22⋊C4×C71—21no—
196C2×C22⋊C4×C71—21no—
197C2×C42×C71—21no—
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
210C23×D71—22no—
211#11765865—28no—
212#11765865—28no—
213#11765865—44no—
214#11765865—44no—
215#11765865—48no—
216#11765865—48no—
217C2×Dic142—22no—
218C2×Dic142—44no—
219C2×Dic142C2414yes—
220C2×D284—22no—
221C2×D284—22no—
222C2×D284—22no—
223C2×D284—22no—
224C2×D284—22no—
225C2×D284—44no—
226C2×D284—44no—
227C2×D284—44no—
228C2×D284C2414yes—
229C2×C22⋊D71—24no—
230C2×C22⋊D71—24no—
231C2×C22⋊D71—48no—
232C22×Dic71—22no—
233C2×C4×D71—24no—
234C2×C4×D71—24no—
235C2×C4×D71—48no—
236#11765855—48no—
237#11765853—48no—
238#11765852—48no—
239#11765850—48no—
240#11765849—28no—
241C2×C71⋊C8C2418yes—
242C4⋊Dic71—22no—
243C4⋊Dic71—22no—
244C4⋊Dic71—22no—
245C4⋊Dic71—22no—
246(C2×D71)⋊C4—24no—
247(C2×D71)⋊C4—24no—
248(C2×D71)⋊C4—24no—
249(C2×D71)⋊C4—24no—
250C24×C71—21no—
251C24×C71C2×D411yescharacteristic
252C2×Q8×C71—21no—
253C2×Q8×C71—24no—
254C2×Q8×C71C2412yes—
255C2×D4×C71—22no—
256C2×D4×C71—22no—
257C2×D4×C71—21no—
258C2×D4×C71—24no—
259C2×D4×C71—44no—
260C2×D4×C71C2412yes—
261C22×C4×C71—24no—
262C22×C4×C71—21no—
263C22×C4×C71—21no—
264C22×C4×C71—21no—
265C22×C4×C71—22no—
266C22×C4×C71—22no—
267C22×C4×C71—42no—
268C22×C4×C71—42no—
269C22×C4×C71—44no—
270C22×C4×C71C2×D411yescharacteristic
271C22×C4×C71C2×D411yescharacteristic
272C22×C4×C71C2×D411yescharacteristic
273C22×C4×C71C2×D411yescharacteristic
274C22×C4×C71C2×D411yescharacteristic
275C22×C4×C71C2×D411yescharacteristic
276C22×C4×C71C2×D411yescharacteristic
277C22×C4×C71C2×D411yescharacteristic
278C22×C4×C71C2×D411yescharacteristic
279C22×C4×C71C2×D411yescharacteristic
280C22×C4×C71C2×D411yescharacteristic
281C22×C4×C71C2×D411yescharacteristic
282C22×C4×C71C2×D411yescharacteristic
283C22×C4×C71C2×D411yescharacteristic
284C22×C4×C71C2×D411yescharacteristic
285C22×C4×C71C2411yescharacteristic
286C22×C4×C71C2411yescharacteristic
287C22×C4×C71C2411yescharacteristic
288C4⋊C4×C71—22no—
289C4⋊C4×C71—22no—
290C4⋊C4×C71—22no—
291C4⋊C4×C71—22no—
292C4⋊C4×C71—22no—
293C4⋊C4×C71—22no—
294C4⋊C4×C71—22no—
295C4⋊C4×C71—22no—
296C4⋊C4×C71—21no—
297C4⋊C4×C71—21no—
298C4⋊C4×C71C2412yes—
299C4⋊C4×C71C2412yes—
300C22⋊C4×C71—22no—
301C22⋊C4×C71—22no—
302C22⋊C4×C71—22no—
303C22⋊C4×C71—22no—
304C22⋊C4×C71—22no—
305C22⋊C4×C71—22no—
306C22⋊C4×C71—22no—
307C22⋊C4×C71—22no—
308C22⋊C4×C71—22no—
309C22⋊C4×C71—22no—
310C42×C71—22no—
311C42×C71—22no—
312C42×C71C2×D411yescharacteristic
313C42×C71C2×D411yescharacteristic
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×C71C2411yescharacteristic
325C42×C71C2411yescharacteristic
326C42×C71C2411yescharacteristic
327C42×C71C2411yescharacteristic
328C23×C71—22no—
329C23×C71—22no—
330C23×C71—22no—
331C23×C71—41no—
332C23×C71—42no—
333C23×C71—42no—
334C23×C71—42no—
335C23×C71C22×D411yescharacteristic
336C23×C71C22×D411yescharacteristic
337C23×C71C22×D411yescharacteristic
338C22×D71—24no—
339C22×D71—44no—
340C22×D71—44no—
341C22×D71—44no—
342Q8×C71—24no—
343Q8×C71—42no—
344D4×C71—24no—
345D4×C71—44no—
346D4×C71—44no—
347D4×C71—42no—
348C2×C4×C71—22no—
349C2×C4×C71—22no—
350C2×C4×C71—22no—
351C2×C4×C71—22no—
352C2×C4×C71—22no—
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—41no—
362C2×C4×C71—41no—
363C2×C4×C71—41no—
364C2×C4×C71—41no—
365C2×C4×C71—41no—
366C2×C4×C71—41no—
367C2×C4×C71—41no—
368C2×C4×C71—44no—
369C2×C4×C71—42no—
370C2×C4×C71—42no—
371C2×C4×C71—42no—
372C2×C4×C71—44no—
373C2×C4×C71C22×D411yescharacteristic
374C2×C4×C71C22×D411yescharacteristic
375C2×C4×C71C22×D411yescharacteristic
376C2×C4×C71C22×D411yescharacteristic
377C2×C4×C71C22×D411yescharacteristic
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×C71H(5,𝔽2)14yes—
385C2×C4×C71C2511yescharacteristic
386C22⋊D71—48no—
387C22⋊D71—48no—
388C2×Dic71—24no—
389C2×Dic71—44no—
390D284—24no—
391D284—24no—
392D284—44no—
393D284—44no—
394D284—44no—
395D284—44no—
396D284—44no—
397C4×D71—48no—
398C4×D71—48no—
399Dic142—24no—
400Dic142—24no—
401Dic142—44no—
402C71⋊C8—28no—
403C22×C71—21no—
404C22×C71—21no—
405C22×C71—21no—
406C22×C71—21no—
407C22×C71—21no—
408C22×C71—21no—
409C22×C71—21no—
410C22×C71—44no—
411C22×C71—42no—
412C22×C71—42no—
413C22×C71—42no—
414C22×C71—84no—
415C22×C71#53512yes—
416C22×C71#57512yes—
417C22×C71C23×D411yescharacteristic
418C2×D71—44no—
419C2×D71—44no—
420C2×D71—44no—
421C2×D71—88no—
422C4×C71—21no—
423C4×C71—21no—
424C4×C71—21no—
425C4×C71—21no—
426C4×C71—21no—
427C4×C71—21no—
428C4×C71—21no—
429C4×C71—21no—
430C4×C71—21no—
431C4×C71—42no—
432C4×C71—42no—
433C4×C71—42no—
434C4×C71#53512yes—
435C4×C71#57512yes—
436C4×C71C2×H(5,𝔽2)12yes—
437Dic71—44no—
438#60805—711nomaximal, Sylow
439C2×C71—22no—
440C2×C71—22no—
441C2×C71—41no—
442C2×C71—82no—
443C2×C71C2×#53511yescharacteristic
444C2×C71C2×#57511yescharacteristic
445C2×C71C2×#57511yescharacteristic
446D71—84no—
447C2×#532—711no—
448C2×#529D7111yescharacteristic, complemented
449#3219—714no—
450#3218—712no—
451#3217—712no—
452#3212—714no—
453#3211—714no—
454#3153—712no—
455#3142—712no—
456#3037—712no—
457#3036—712no—
458#3007—712no—
459#3006—712no—
460#2920—711no—
461C71#6080511yescharacteristic, complemented, Sylow
462C22×#41—712no—
463C2×#137—714no—
464C2×AGL(1,ℤ/8)—714no—
465#532—712no—
466#532—712no—
467#532—712no—
468#532—712no—
469#532—1421no—
470#532—1421no—
471#532—1421no—
472#532—1421no—
473C2×C4⋊Q8—711no—
474C2×#127—711no—
475#529—21no—
476#529—21no—
477#529—21no—
478#529—21no—
479#529C2×D7112yes—
480#529C2×D7112yes—
481#529C2×D7112yescomplemented
482#529C2×D7112yescomplemented
483C2×#126—21no—
484C2×#125C2×D7111yescharacteristic, complemented
485C2×#124—712no—
486C2×#124C2×D7111yescharacteristic, complemented
487C2×#123—21no—
488C2×C22⋊Q8C2×D7111yescharacteristic
489C2×#121—1421no—
490C2×#121—1421no—
491C2×#121C2×D7111yescharacteristic
492C2×C4×Q8C2×D7111yescharacteristic, complemented
493C2×C4×D4—21no—
494C2×C4×D4—1421no—
495C2×C4×D4—1421no—
496C2×C4×D4C2×D7111yescharacteristic, complemented
497C2×#117—21no—
498C22×C42C2×D7111yescharacteristic
499#497—714no—
500#496—714no—
501#495—718no—
502#491—714no—
503#490—714no—
504#488—718no—
505#464—718no—
506#463—718no—
507#462—714no—
508#461—714no—
509#460—714no—
510#459—714no—
511#452—718no—
512#451—714no—
513#450—714no—
514#449—718no—
515#448—714no—
516#447—714no—
517#432—712no—
518#432—712no—
519#431—712no—
520#431—712no—
521#423—712no—
522#417—714no—
523#417—714no—
524#407—712no—
525C4×M16—712no—
526C2×#41—2848no—
527C2×#41—714no—
528C2×#41—714no—
529C2×#41—1422no—
530C2×#41—1422no—
531C22×Q8—712no—
532C22×Q8C22×D7111yescharacteristic
533C22×D4—21no—
534C22×D4—712no—
535C22×D4—1422no—
536C22×D4—1421no—
537C22×D4—1421no—
538C22×D4C22×D7111yescharacteristic
539C23×C4—21no—
540C23×C4—1422no—
541C23×C4C22⋊D7111yescharacteristic
542C23×C4C22⋊D7111yescharacteristic
543C23×C4C22×D7111yescharacteristic
544#137—2848no—
545AGL(1,ℤ/8)—2848no—
546C2×Q16—718no—
547C2×SD16—718no—
548C2×SD16—718no—
549C2×D8—718no—
550C2×M16—714no—
551C4⋊Q8—712no—
552C4⋊Q8—712no—
553C4⋊Q8—1421no—
554C4⋊Q8—1421no—
555#127—712no—
556#127—712no—
557#127—1421no—
558#127—1421no—
559#126—22no—
560#126—22no—
561#126—22no—
562#126—22no—
563#125—21no—
564#125—21no—
565#125C22×D7112yes—
566#125C22×D7112yes—
567#124—21no—
568#124—21no—
569#124—714no—
570#124—714no—
571#124—1422no—
572#124—1422no—
573#124C22×D7112yes—
574#124C22×D7112yes—
575#123—22no—
576#123—22no—
577#123—22no—
578#123—22no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8C22×D7112yes—
582C22⋊Q8C22×D7112yes—
583#121—21no—
584#121—21no—
585#121—1422no—
586#121—1422no—
587#121—1422no—
588#121—1422no—
589#121—1422no—
590#121—1422no—
591#121—1422no—
592#121—1422no—
593#121C22×D7112yes—
594#121C22×D7112yes—
595C4×Q8—21no—
596C4×Q8—21no—
597C4×Q8C22×D7112yes—
598C4×Q8C22×D7112yes—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—21no—
604C4×D4—21no—
605C4×D4—1422no—
606C4×D4—1422no—
607C4×D4—1422no—
608C4×D4—1422no—
609C4×D4—1422no—
610C4×D4—1422no—
611C4×D4—1422no—
612C4×D4—1422no—
613C4×D4C22×D7112yes—
614C4×D4C22×D7112yes—
615#117—22no—
616#117—22no—
617#117—22no—
618#117—22no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—1421no—
624C2×C4⋊C4—1421no—
625C2×C4⋊C4C22×D7111yescharacteristic
626C2×C4⋊C4C22×D7111yescharacteristic
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—1422no—
633C2×C22⋊C4—1422no—
634C2×C42—21no—
635C2×C42C22⋊D7111yescharacteristic
636C2×C42C22⋊D7111yescharacteristic
637C2×C42C22⋊D7111yescharacteristic
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
647C4⋊C8—714no—
648C4⋊C8—714no—
649#103—718no—
650#103—718no—
651#102—718no—
652#102—718no—
653C22⋊C8—714no—
654C22⋊C8—714no—
655#97—714no—
656C4×C8—714no—
657C24—21no—
658C24—1422no—
659C24C2×C22⋊D7111yescharacteristic
660#41—2848no—
661#41—2848no—
662#41—2844no—
663#41—2844no—
664#41—1428no—
665#41—1428no—
666C2×Q8—21no—
667C2×Q8—24no—
668C2×Q8—2844no—
669C2×Q8—714no—
670C2×Q8—1422no—
671C2×Q8C23×D7112yes—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—21no—
675C2×D4—24no—
676C2×D4—44no—
677C2×D4—2844no—
678C2×D4—2844no—
679C2×D4—2844no—
680C2×D4—2848no—
681C2×D4—714no—
682C2×D4—1424no—
683C2×D4—1424no—
684C2×D4—1422no—
685C2×D4—1422no—
686C2×D4—1422no—
687C2×D4—1422no—
688C2×D4—1422no—
689C2×D4C23×D7112yes—
690C22×C4—24no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—44no—
699C22×C4—2848no—
700C22×C4—1422no—
701C22×C4—1424no—
702C22×C4—1424no—
703C22×C4C2×C22⋊D7111yescharacteristic
704C22×C4C2×C22⋊D7111yescharacteristic
705C22×C4C2×C22⋊D7111yescharacteristic
706C22×C4C2×C22⋊D7111yescharacteristic
707C22×C4C2×C22⋊D7111yescharacteristic
708C22×C4C2×C22⋊D7111yescharacteristic
709C22×C4C2×C22⋊D7111yescharacteristic
710C22×C4C2×C22⋊D7111yescharacteristic
711C22×C4C2×C22⋊D7111yescharacteristic
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×C4C23×D7111yescharacteristic
719C22×C4C23×D7111yescharacteristic
720C22×C4C23×D7111yescharacteristic
721Q16—2848no—
722SD16—2848no—
723SD16—2848no—
724D8—2848no—
725M16—1428no—
726C2×C8—718no—
727C4⋊C4—22no—
728C4⋊C4—22no—
729C4⋊C4—22no—
730C4⋊C4—22no—
731C4⋊C4—22no—
732C4⋊C4—22no—
733C4⋊C4—22no—
734C4⋊C4—22no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—1422no—
738C4⋊C4—1422no—
739C4⋊C4—1422no—
740C4⋊C4—1422no—
741C4⋊C4C23×D7112yes—
742C4⋊C4C23×D7112yes—
743C22⋊C4—22no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—22no—
748C22⋊C4—22no—
749C22⋊C4—22no—
750C22⋊C4—22no—
751C22⋊C4—22no—
752C22⋊C4—22no—
753C22⋊C4—1424no—
754C22⋊C4—1424no—
755C22⋊C4—1424no—
756C22⋊C4—1424no—
757C42—22no—
758C42—22no—
759C42C2×C22⋊D7111yescharacteristic
760C42C2×C22⋊D7111yescharacteristic
761C42C2×C22⋊D7111yescharacteristic
762C42C2×C22⋊D7111yescharacteristic
763C42C2×C22⋊D7111yescharacteristic
764C42C2×C22⋊D7111yescharacteristic
765C42C2×C22⋊D7111yescharacteristic
766C42C2×C22⋊D7111yescharacteristic
767C42C2×C22⋊D7111yescharacteristic
768C42C2×C22⋊D7111yescharacteristic
769C42C2×C22⋊D7111yescharacteristic
770C42C2×C22⋊D7111yescharacteristic
771C42C23×D7111yescharacteristic
772C42C23×D7111yescharacteristic
773C42C23×D7111yescharacteristic
774C42C23×D7111yescharacteristic
775C23—22no—
776C23—22no—
777C23—22no—
778C23—41no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—2844no—
783C23—2844no—
784C23—2844no—
785C23—1424no—
786C23C22×C22⋊D7111yescharacteristic
787C23C22×C22⋊D7111yescharacteristic
788C23C22×C22⋊D7111yescharacteristic
789Q8—24no—
790Q8—42no—
791Q8—2844no—
792Q8—1424no—
793Q8—1424no—
794D4—24no—
795D4—44no—
796D4—44no—
797D4—42no—
798D4—2844no—
799D4—2844no—
800D4—2844no—
801D4—2844no—
802D4—2848no—
803D4—2848no—
804D4—2844no—
805D4—1424no—
806D4—1424no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—44no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—44no—
832C2×C4—2848no—
833C2×C4—2844no—
834C2×C4—2848no—
835C2×C4—1424no—
836C2×C4C22×C22⋊D7111yescharacteristic
837C2×C4C22×C22⋊D7111yescharacteristic
838C2×C4C22×C22⋊D7111yescharacteristic
839C2×C4C22×C22⋊D7111yescharacteristic
840C2×C4C22×C22⋊D7111yescharacteristic
841C2×C4C22×C22⋊D7111yescharacteristic
842C2×C4C22×C22⋊D7111yescharacteristic
843C2×C4C22×C22⋊D7111yescharacteristic
844C2×C4C22×C22⋊D7111yescharacteristic
845C2×C4C22×C22⋊D7111yescharacteristic
846C2×C4C22×C22⋊D7111yescharacteristic
847C2×C4#1455617414yes—
848C2×C4C24×D7111yescharacteristic
849C8—1428no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—44no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—84no—
862C22—2844no—
863C22—2844no—
864C22—2844no—
865C22—5688no—
866C22#1798656312yes—
867C22#1798679712yes—
868C22C23×C22⋊D7111yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—2844no—
882C4#1798656312yes—
883C4#1798679712yes—
884C4C2×#1455617412yes—
885C2—22no—
886C2—22no—
887C2—41no—
888C2—82no—
889C2—5684no—
890C2C2×#1798656311yescharacteristic
891C2C2×#1798679711yescharacteristic
892C2C2×#1798679711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#529×C71C2
socleC22×C71C23×D4
hypercenterC2×#529D71
hypocenterC71#60805
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#17986549C2semidirect
2. #22599373C2semidirect
3. #22599364C2semidirect
4. #22599355C2semidirect
5. #22599312C2semidirect
6. #22599301C2semidirect
7. #22598804C2semidirect
8. #22598743C2semidirect
9. #22597812C2semidirect
10. #22597804C2semidirect
11. #22597598C2semidirect
12. #22597590C2semidirect
13. #22596973C2semidirect
14. C2×#529×C71C2semidirect
16. C2×#14556159C22semidirect
17. C2×#14556154C22semidirect
24. #17986549C22semidirect
25. #17986549C22semidirect
26. C2×#14556128C22semidirect
27. C2×#14556125C22semidirect
28. C2×#14556116C22semidirect
33. #17986394C22semidirect
34. #17986389C22semidirect
35. #17986381C22semidirect
36. #17986369C22semidirect
37. #17986365C22semidirect
38. #17986356C22semidirect
39. #17986221C22semidirect
40. #17986214C22semidirect
41. #17986209C22semidirect
42. #17986204C22semidirect
43. #17986199C22semidirect
44. #17986194C22semidirect
45. #17986159C22semidirect
46. #17986154C22semidirect
47. #17986149C22semidirect
48. #17986142C22semidirect
51. #17986056C22semidirect
52. #17986056C22semidirect
53. #17986052C22semidirect
54. #17986052C22semidirect
55. #17986023C22semidirect
56. #17985998C22semidirect
57. #17985998C22semidirect
59. C4×#11765849C22semidirect
66. #529×C71C22semidirect
67. #529×C71C22semidirect
69. C2×#125×C71C22semidirect
70. C2×#124×C71C22semidirect
74. C2×C4×Q8×C71C22semidirect
76. C2×C4×D4×C71C22semidirect
448. C2×#529D71semidirect
461. C71#60805semidirect
481. #529C2×D71semidirect
482. #529C2×D71semidirect
484. C2×#125C2×D71semidirect
486. C2×#124C2×D71semidirect
492. C2×C4×Q8C2×D71semidirect
496. C2×C4×D4C2×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179865492
#225993732
#225993642
#225993552
#225993122
#225993012
#225988042
#225987432
#225978122
#225978042
#225975982
#225975902
#225969732
C2×#529×C712
#6080571