Finite Group Databasebeta

← #32865841

Subgroups — #32865841

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
2C22×C4×D284C211yesmaximal, characteristic, complemented
3#22598480C214yesmaximal, complemented
4#22598440C212yesmaximal, complemented
5#22598432C212yesmaximal, complemented
6#22598389C214yesmaximal, complemented
7#22598349C212yesmaximal, complemented
8#22598341C212yesmaximal, complemented
9#22598265C212yesmaximal, complemented
10#22598139C212yesmaximal, complemented
11#22597806C212yesmaximal, complemented
12#22597570C212yesmaximal, complemented
13C4×#14556156C214yesmaximal, complemented
14C71×#2920C211yesmaximal, characteristic, complemented
15C23×D284C2211yescharacteristic
16C23×C4×D71—21no—
17C2×#14556156C2214yes—
18#17986556C2211yescharacteristic, complemented
19#17986556C2211yescharacteristic, complemented
20#17986556C2211yescharacteristic, complemented
21#17986549C2211yescharacteristic, complemented
22#17986549C2211yescharacteristic, complemented
23#17986549C2211yescharacteristic, complemented
24#17986533—21no—
25#17986533—21no—
26#17986533—21no—
27#17986533—21no—
28#17986533C2212yescomplemented
29#17986533C2212yescomplemented
30#17986510—21no—
31#17986510—21no—
32#17986510C2212yes—
33C4×#11765865—21no—
34C4×#11765865—21no—
35C4×#11765865C2212yescomplemented
36C2×C4×D284—21no—
37C2×C4×D284—21no—
38C2×C4×D284—21no—
39C2×C4×D284—21no—
40C2×C4×D284—21no—
41C2×C4×D284—21no—
42C2×C4×D284C2212yes—
43C2×C4×D284C2212yes—
44C2×C4×D284C2212yes—
45C2×C4×D284C2212yes—
46C2×C4×D284C2212yes—
47C2×C4×D284C2212yes—
48C22×C4⋊Dic71C2211yescharacteristic
49C22×(C2×D71)⋊C4—21no—
50#17986335C2214yescomplemented
51#17986330C2214yescomplemented
52#17986318C2214yescomplemented
53#17986313C2214yescomplemented
54#17986300C2218yescomplemented
55#17986290C2214yescomplemented
56#17986280C2214yescomplemented
57#17986215C2218yescomplemented
58#17986205C2214yescomplemented
59#17986195C2214yescomplemented
60#17986152C2214yes—
61#17986152C2214yes—
62#17986135C2214yes—
63#17986135C2214yes—
64#17986112C2218yescomplemented
65#17986101C2218yescomplemented
66C4×#11765854C2218yescomplemented
67C4×D568C2218yescomplemented
68#17986041C2214yescomplemented
69#17986005C2214yes—
70#17986001C2214yescomplemented
71C22×C42×C71C2211yescharacteristic
72#432×C71C2212yescomplemented
73#432×C71C2212yescomplemented
74#431×C71C2212yescomplemented
75#431×C71C2212yescomplemented
76#423×C71C2212yescomplemented
77#407×C71C2212yes—
78C4×M16×C71C2212yescomplemented
79C24×D71—21no—
80C2×#11765865—21no—
81C2×#11765865—21no—
82C2×#11765865C2312yes—
83C22×D284—28no—
84C22×D284—21no—
85C22×D284—21no—
86C22×D284—21no—
87C22×D284C2312yes—
88C22×D284C2312yes—
89C22×D284C2312yes—
90C23×Dic71—21no—
91C22×C4×D71—22no—
92C22×C4×D71—22no—
93C22×C4×D71—22no—
94C22×C4×D71—22no—
95C22×C4×D71—22no—
96C22×C4×D71—22no—
97C22×C4×D71—48no—
98#14556156—216no—
99C2×#11765854C2318yes—
100C2×D568C2318yes—
101#14556128C2311yescharacteristic, complemented
102#14556128C2311yescharacteristic, complemented
103#14556128C2311yescharacteristic, complemented
104#14556125C2311yescharacteristic, complemented
105#14556122—22no—
106#14556122—22no—
107#14556120—21no—
108#14556120—21no—
109#14556120C2312yescomplemented
110#14556116—21no—
111#14556116—21no—
112#14556116C2312yescomplemented
113#14556111—22no—
114#14556111—22no—
115#14556111—22no—
116#14556107—21no—
117#14556107—21no—
118#14556107—21no—
119#14556107—21no—
120#14556107C2312yes—
121#14556107C2312yes—
122#14556102—21no—
123#14556102—21no—
124#14556102—21no—
125#14556102—21no—
126#14556102C2312yes—
127#14556102C2312yes—
128#14556097—22no—
129C4×Dic142—21no—
130C4×Dic142—21no—
131C4×Dic142—21no—
132C4×Dic142—21no—
133C4×Dic142C2312yescomplemented
134C4×Dic142C2312yescomplemented
135C4×D284—22no—
136C4×D284—22no—
137C4×D284—22no—
138C4×D284—22no—
139C4×D284—22no—
140C4×D284—22no—
141C4×D284—22no—
142C4×D284—22no—
143C4×D284—22no—
144C4×D284—22no—
145C4×D284—22no—
146C4×D284—22no—
147C4×D284—21no—
148C4×D284—21no—
149C4×D284—21no—
150C4×D284—21no—
151C4×D284C2314yes—
152C4×D284C2314yes—
153C4×D284C2314yes—
154C4×D284C2314yes—
155C4×D284C2312yescomplemented
156C4×D284C2312yescomplemented
157C4×C22⋊D71—22no—
158C4×C22⋊D71—22no—
159C4×C22⋊D71—22no—
160C4×C22⋊D71—22no—
161C4×C22⋊D71—22no—
162C4×C22⋊D71—22no—
163#14556087—21no—
164#14556087—21no—
165#14556087C2312yes—
166#14556085—22no—
167#14556085—22no—
168#14556085—22no—
169C2×C4⋊Dic71—21no—
170C2×C4⋊Dic71—21no—
171C2×C4⋊Dic71—21no—
172C2×C4⋊Dic71C2312yes—
173C2×C4⋊Dic71C2312yes—
174C2×C4⋊Dic71C2312yes—
175C2×(C2×D71)⋊C4—22no—
176C2×(C2×D71)⋊C4—22no—
177C2×(C2×D71)⋊C4—22no—
178C2×(C2×D71)⋊C4—22no—
179C2×(C2×D71)⋊C4—22no—
180C2×(C2×D71)⋊C4—22no—
181C42×D71—22no—
182#14556062C2318yescomplemented
183#14556060C2318yescomplemented
184#14556053C2318yescomplemented
185#14556050C2318yes—
186#14556050C2318yes—
187#14556050C2318yescomplemented
188C23×C4×C71D411yescharacteristic
189C23×C4×C71D411yescharacteristic
190C23×C4×C71C2311yescharacteristic
191C2×M16×C71C2314yes—
192C2×C42×C71D411yescharacteristic
193C2×C42×C71D411yescharacteristic
194C2×C42×C71D411yescharacteristic
195C2×C42×C71D411yescharacteristic
196C2×C42×C71D411yescharacteristic
197C2×C42×C71D411yescharacteristic
198C2×C42×C71C2311yescharacteristic
199C2×C42×C71C2311yescharacteristic
200C2×C42×C71C2311yescharacteristic
201C2×C42×C71C2311yescharacteristic
202C2×C42×C71C2311yescharacteristic
203C2×C42×C71C2311yescharacteristic
204C4⋊C8×C71C2314yescomplemented
205C4⋊C8×C71C2314yescomplemented
206C22⋊C8×C71C2314yes—
207C22⋊C8×C71C2314yes—
208#97×C71C2314yescomplemented
209C4×C8×C71C2314yescomplemented
210C23×D71—28no—
211C23×D71—22no—
212C23×D71—22no—
213C23×D71—22no—
214C23×D71—44no—
215C23×D71—44no—
216#11765865—28no—
217#11765865—44no—
218#11765865—44no—
219C2×Dic142—21no—
220C2×Dic142—21no—
221C2×Dic142C2412yes—
222C2×D284—28no—
223C2×D284—28no—
224C2×D284—28no—
225C2×D284—22no—
226C2×D284—22no—
227C2×D284—22no—
228C2×D284—24no—
229C2×D284—28no—
230C2×D284—28no—
231C2×D284—21no—
232C2×D284—21no—
233C2×D284#4118yescomplemented
234C2×D284C2412yes—
235C2×D284C2414yes—
236C2×C22⋊D71—22no—
237C2×C22⋊D71—22no—
238C2×C22⋊D71—22no—
239C22×Dic71—22no—
240C22×Dic71—22no—
241C22×Dic71—22no—
242C22×Dic71—44no—
243C2×C4×D71—24no—
244C2×C4×D71—24no—
245C2×C4×D71—24no—
246C2×C4×D71—24no—
247C2×C4×D71—22no—
248C2×C4×D71—22no—
249C2×C4×D71—22no—
250C2×C4×D71—48no—
251C2×C4×D71—48no—
252C2×C4×D71—48no—
253C2×C4×D71—48no—
254C2×C4×D71—48no—
255C2×C4×D71—48no—
256#11765854—216no—
257D568—216no—
258C4⋊Dic71—22no—
259C4⋊Dic71—22no—
260C4⋊Dic71—22no—
261C4⋊Dic71—21no—
262C4⋊Dic71—21no—
263C4⋊Dic71—21no—
264C4⋊Dic71—21no—
265C4⋊Dic71C2412yes—
266C4⋊Dic71C2412yes—
267C4⋊Dic71C2414yes—
268Dic71⋊C4—22no—
269Dic71⋊C4—22no—
270Dic71⋊C4—22no—
271Dic71⋊C4—22no—
272Dic71⋊C4—22no—
273Dic71⋊C4—22no—
274C22⋊Dic71—22no—
275C22⋊Dic71—22no—
276C22⋊Dic71—22no—
277(C2×D71)⋊C4—24no—
278(C2×D71)⋊C4—24no—
279(C2×D71)⋊C4—24no—
280(C2×D71)⋊C4—24no—
281(C2×D71)⋊C4—22no—
282(C2×D71)⋊C4—22no—
283(C2×D71)⋊C4—22no—
284(C2×D71)⋊C4—22no—
285(C2×D71)⋊C4—22no—
286(C2×D71)⋊C4—22no—
287C4×Dic71—22no—
288C4×Dic71—22no—
289C4×Dic71—22no—
290C24×C71C2×D411yescharacteristic
291C22×C4×C71—24no—
292C22×C4×C71—24no—
293C22×C4×C71—42no—
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×C71C2×D411yescharacteristic
304C22×C4×C71C2×D411yescharacteristic
305C22×C4×C71C2×D411yescharacteristic
306C22×C4×C71C2×D411yescharacteristic
307C22×C4×C71C2×D411yescharacteristic
308C22×C4×C71C2×D411yescharacteristic
309C22×C4×C71C2411yescharacteristic
310C22×C4×C71C2411yescharacteristic
311C22×C4×C71C2411yescharacteristic
312M16×C71—28no—
313C2×C8×C71C2418yes—
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×C71C22×D411yescharacteristic
334C23×C71C22×D411yescharacteristic
335C23×C71C22×D411yescharacteristic
336C22×D71—28no—
337C22×D71—28no—
338C22×D71—28no—
339C22×D71—24no—
340C22×D71—22no—
341C22×D71—44no—
342C22×D71—44no—
343C22×D71—432no—
344C22×D71—44no—
345C22×D71—44no—
346C22×D71—44no—
347C22×D71—44no—
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—41no—
361C2×C4×C71—41no—
362C2×C4×C71—41no—
363C2×C4×C71—41no—
364C2×C4×C71AGL(1,ℤ/8)14yescomplemented
365C2×C4×C71C22×D411yescharacteristic
366C2×C4×C71C22×D411yescharacteristic
367C2×C4×C71C22×D411yescharacteristic
368C2×C4×C71C22×D411yescharacteristic
369C2×C4×C71C22×D411yescharacteristic
370C2×C4×C71C22×D411yescharacteristic
371C2×C4×C71C22×D411yescharacteristic
372C2×C4×C71C22×D411yescharacteristic
373C2×C4×C71C22×D411yescharacteristic
374C2×C4×C71C22×D411yescharacteristic
375C2×C4×C71C22×D411yescharacteristic
376C2×C4×C71C2×#4114yes—
377C2×C4×C71C2511yescharacteristic
378C22⋊D71—44no—
379C22⋊D71—44no—
380C22⋊D71—44no—
381C2×Dic71—22no—
382C2×Dic71—22no—
383C2×Dic71—22no—
384C2×Dic71—24no—
385C2×Dic71—44no—
386C2×Dic71—44no—
387C2×Dic71—44no—
388D284—28no—
389D284—28no—
390D284—28no—
391D284—24no—
392D284—24no—
393D284—42no—
394D284—42no—
395D284C2×#4118yes—
396C4×D71—48no—
397C4×D71—48no—
398C4×D71—44no—
399C4×D71—44no—
400C4×D71—48no—
401C4×D71—48no—
402C4×D71—44no—
403Dic142—24no—
404Dic142—42no—
405Dic142—42no—
406C8×C71—28no—
407C22×C71—28no—
408C22×C71—21no—
409C22×C71—21no—
410C22×C71—21no—
411C22×C71—21no—
412C22×C71—21no—
413C22×C71—21no—
414C22×C71#52512yes—
415C22×C71C2×AGL(1,ℤ/8)12yes—
416C22×C71#57512yes—
417C22×C71C23×D411yescharacteristic
418C2×D71—28no—
419C2×D71—416no—
420C2×D71—416no—
421C2×D71—416no—
422C2×D71—44no—
423C2×D71—44no—
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#52512yes—
436C4×C71C2×AGL(1,ℤ/8)12yes—
437C4×C71C2×AGL(1,ℤ/8)12yes—
438C4×C71C22×#4112yes—
439Dic71—42no—
440Dic71—42no—
441Dic71—44no—
442Dic71—42no—
443#60558—711nomaximal, Sylow
444C2×C71—22no—
445C2×C71—22no—
446C2×C71—22no—
447C2×C71C2×#52511yescharacteristic
448C2×C71C22×AGL(1,ℤ/8)11yescharacteristic
449C2×C71C2×#57511yescharacteristic
450D71—48no—
451D71—82no—
452#3444—711no—
453C22×C4×D4—711no—
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#2920D7111yescharacteristic, complemented
466C71#6055811yescharacteristic, complemented, Sylow
467C23×D4—711no—
468C24×C4—1421no—
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—712no—
489C2×C4×D4—712no—
490C2×C4×D4—712no—
491C2×C4×D4—712no—
492C2×C4×D4—712no—
493C2×C4×D4—712no—
494C2×C4×D4—1421no—
495C2×C4×D4—1421no—
496C2×C4×D4—1421no—
497C2×C4×D4—1421no—
498C2×C4×D4—1421no—
499C2×C4×D4—1421no—
500C22×C4⋊C4—711no—
501C22×C22⋊C4—1421no—
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#432C2×D7112yescomplemented
522#432C2×D7112yescomplemented
523#431C2×D7112yescomplemented
524#431C2×D7112yescomplemented
525#428—714no—
526#423C2×D7112yescomplemented
527#418—714no—
528#417—714no—
529#407C2×D7112yes—
530C4×M16C2×D7112yescomplemented
531C25—1421no—
532C2×#41—712no—
533C2×#41—1421no—
534C2×#41—1421no—
535C22×D4—712no—
536C22×D4—712no—
537C22×D4—712no—
538C22×D4—1428no—
539C22×D4—1421no—
540C22×D4—1421no—
541C22×D4—1421no—
542C23×C4—2848no—
543C23×C4—1421no—
544C23×C4—1422no—
545C23×C4—1422no—
546C23×C4—1422no—
547C23×C4—1422no—
548C23×C4—1422no—
549C23×C4—1422no—
550C23×C4D28411yescharacteristic
551C23×C4D28411yescharacteristic
552C23×C4C22×D7111yescharacteristic
553AGL(1,ℤ/8)—14216no—
554C2×SD16—718no—
555C2×D8—718no—
556C2×M16C22×D7114yes—
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—714no—
592C4×D4—714no—
593C4×D4—714no—
594C4×D4—714no—
595C4×D4—712no—
596C4×D4—712no—
597C4×D4—1422no—
598C4×D4—1422no—
599C4×D4—1422no—
600C4×D4—1422no—
601C4×D4—1422no—
602C4×D4—1422no—
603C4×D4—1422no—
604C4×D4—1422no—
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×D4—1422no—
614C4×D4—1422no—
615C4×D4—1421no—
616C4×D4—1421no—
617C4×D4—1421no—
618C4×D4—1421no—
619#117—712no—
620#117—1421no—
621#117—1421no—
622#117—1422no—
623#117—1422no—
624#117—1422no—
625C2×C4⋊C4—712no—
626C2×C4⋊C4—712no—
627C2×C4⋊C4—712no—
628C2×C4⋊C4—1421no—
629C2×C4⋊C4—1421no—
630C2×C4⋊C4—1421no—
631C2×C22⋊C4—1422no—
632C2×C22⋊C4—1422no—
633C2×C22⋊C4—1422no—
634C2×C22⋊C4—1422no—
635C2×C22⋊C4—1422no—
636C2×C22⋊C4—1422no—
637C2×C42—1422no—
638C2×C42D28411yescharacteristic
639C2×C42D28411yescharacteristic
640C2×C42D28411yescharacteristic
641C2×C42D28411yescharacteristic
642C2×C42D28411yescharacteristic
643C2×C42D28411yescharacteristic
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⋊C8C22×D7114yescomplemented
653C4⋊C8C22×D7114yescomplemented
654#103—718no—
655#102—718no—
656#102—718no—
657#102—718no—
658C22⋊C8C22×D7114yes—
659C22⋊C8C22×D7114yes—
660#97C22×D7114yescomplemented
661C4×C8C22×D7114yescomplemented
662C24—2844no—
663C24—2844no—
664C24—1428no—
665C24—1422no—
666C24—1422no—
667C24—1422no—
668C24C2×D28411yescharacteristic
669#41—2844no—
670#41—2844no—
671#41—1428no—
672C2×Q8—712no—
673C2×Q8—1421no—
674C2×Q8—1421no—
675C2×D4—718no—
676C2×D4—714no—
677C2×D4—712no—
678C2×D4—1428no—
679C2×D4—1428no—
680C2×D4—1428no—
681C2×D4—1428no—
682C2×D4—1428no—
683C2×D4—1422no—
684C2×D4—1422no—
685C2×D4—1422no—
686C2×D4—1421no—
687C2×D4—1421no—
688C2×D4—1422no—
689C2×D4—1422no—
690C2×D4—1422no—
691C2×D4—1424no—
692C22×C4—24no—
693C22×C4—24no—
694C22×C4—42no—
695C22×C4—2848no—
696C22×C4—2848no—
697C22×C4—2848no—
698C22×C4—2848no—
699C22×C4—2848no—
700C22×C4—2844no—
701C22×C4—2848no—
702C22×C4—1422no—
703C22×C4—1422no—
704C22×C4—1422no—
705C22×C4—1422no—
706C22×C4—1422no—
707C22×C4—1424no—
708C22×C4—1424no—
709C22×C4—1424no—
710C22×C4—1422no—
711C22×C4—1424no—
712C22×C4C2×D28411yescharacteristic
713C22×C4C2×D28411yescharacteristic
714C22×C4C2×D28411yescharacteristic
715C22×C4C2×D28411yescharacteristic
716C22×C4C2×D28411yescharacteristic
717C22×C4C2×D28411yescharacteristic
718C22×C4C2×D28411yescharacteristic
719C22×C4C2×D28411yescharacteristic
720C22×C4C2×D28411yescharacteristic
721C22×C4C2×D28411yescharacteristic
722C22×C4C2×D28411yescharacteristic
723C22×C4C2×D28411yescharacteristic
724C22×C4C2×D28411yescharacteristic
725C22×C4C2×D28411yescharacteristic
726C22×C4C2×D28411yescharacteristic
727C22×C4C23×D7111yescharacteristic
728C22×C4C23×D7111yescharacteristic
729C22×C4C23×D7111yescharacteristic
730SD16—14216no—
731D8—14216no—
732M16—28no—
733C2×C8C23×D7118yes—
734C4⋊C4—712no—
735C4⋊C4—712no—
736C4⋊C4—714no—
737C4⋊C4—1422no—
738C4⋊C4—1422no—
739C4⋊C4—1422no—
740C4⋊C4—1422no—
741C4⋊C4—1422no—
742C4⋊C4—1422no—
743C4⋊C4—1422no—
744C4⋊C4—1422no—
745C4⋊C4—1422no—
746C4⋊C4—1421no—
747C4⋊C4—1421no—
748C4⋊C4—1421no—
749C4⋊C4—1421no—
750C22⋊C4—1422no—
751C22⋊C4—1422no—
752C22⋊C4—1422no—
753C22⋊C4—1424no—
754C22⋊C4—1424no—
755C22⋊C4—1424no—
756C22⋊C4—1424no—
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×D28411yescharacteristic
767C42C2×D28411yescharacteristic
768C42C2×D28411yescharacteristic
769C42C2×D28411yescharacteristic
770C42C2×D28411yescharacteristic
771C42C2×D28411yescharacteristic
772C42C2×D28411yescharacteristic
773C42C2×D28411yescharacteristic
774C42C2×D28411yescharacteristic
775C42C2×D28411yescharacteristic
776C42C2×D28411yescharacteristic
777C42C2×D28411yescharacteristic
778C42C23×D7111yescharacteristic
779C42C23×D7111yescharacteristic
780C42C23×D7111yescharacteristic
781C42C23×D7111yescharacteristic
782C23—22no—
783C23—22no—
784C23—22no—
785C23—2844no—
786C23—2844no—
787C23—28432no—
788C23—2844no—
789C23—2844no—
790C23—2844no—
791C23—2844no—
792C23—1428no—
793C23—1428no—
794C23—1422no—
795C23—1424no—
796C23—1428no—
797C23C22×D28411yescharacteristic
798C23C22×D28411yescharacteristic
799C23C22×D28411yescharacteristic
800Q8—2842no—
801Q8—2842no—
802Q8—1424no—
803D4—2842no—
804D4—2844no—
805D4—2844no—
806D4—2844no—
807D4—2842no—
808D4—718no—
809D4—1428no—
810D4—1428no—
811D4—1424no—
812D4—1424no—
813D4—1428no—
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—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—2848no—
831C2×C4—2848no—
832C2×C4—2844no—
833C2×C4—2844no—
834C2×C4—2844no—
835C2×C4—2844no—
836C2×C4—2844no—
837C2×C4—2848no—
838C2×C4—2848no—
839C2×C4—2844no—
840C2×C4—1422no—
841C2×C4—1422no—
842C2×C4—1422no—
843C2×C4—1424no—
844C2×C4#1455615614yescomplemented
845C2×C4C22×D28411yescharacteristic
846C2×C4C22×D28411yescharacteristic
847C2×C4C22×D28411yescharacteristic
848C2×C4C22×D28411yescharacteristic
849C2×C4C22×D28411yescharacteristic
850C2×C4C22×D28411yescharacteristic
851C2×C4C22×D28411yescharacteristic
852C2×C4C22×D28411yescharacteristic
853C2×C4C22×D28411yescharacteristic
854C2×C4C22×D28411yescharacteristic
855C2×C4C22×D28411yescharacteristic
856C2×C4#41×D7114yes—
857C2×C4C24×D7111yescharacteristic
858C8—28no—
859C22—28no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—28416no—
867C22—28416no—
868C22—28416no—
869C22—2844no—
870C22—2844no—
871C22—2842no—
872C22—2842no—
873C22—2842no—
874C22—1428no—
875C22#1798651112yes—
876C22C2×#1455615612yes—
877C22#1798679912yes—
878C22C23×D28411yescharacteristic
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—2844no—
888C4—2842no—
889C4—2842no—
890C4—2842no—
891C4#1798651112yes—
892C4C2×#1455615612yes—
893C4C2×#1455615612yes—
894C4C2×#41×D7112yes—
895C2—22no—
896C2—22no—
897C2—22no—
898C2—2848no—
899C2—5682no—
900C2C2×#1798651111yescharacteristic
901C2C22×#1455615611yescharacteristic
902C2C2×#1798679911yescharacteristic
subgroupG/H
centerC2×C4C22×D284
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC71×#2920C2
socleC22×C71C23×D4
hypercenter#2920D71
hypocenterC71#60558
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
1. #22601636C2semidirect
2. C22×C4×D284C2semidirect
3. #22598480C2semidirect
4. #22598440C2semidirect
5. #22598432C2semidirect
6. #22598389C2semidirect
7. #22598349C2semidirect
8. #22598341C2semidirect
9. #22598265C2semidirect
10. #22598139C2semidirect
11. #22597806C2semidirect
12. #22597570C2semidirect
13. C4×#14556156C2semidirect
14. C71×#2920C2semidirect
18. #17986556C22semidirect
19. #17986556C22semidirect
20. #17986556C22semidirect
21. #17986549C22semidirect
22. #17986549C22semidirect
23. #17986549C22semidirect
28. #17986533C22semidirect
29. #17986533C22semidirect
35. C4×#11765865C22semidirect
50. #17986335C22semidirect
51. #17986330C22semidirect
52. #17986318C22semidirect
53. #17986313C22semidirect
54. #17986300C22semidirect
55. #17986290C22semidirect
56. #17986280C22semidirect
57. #17986215C22semidirect
58. #17986205C22semidirect
59. #17986195C22semidirect
64. #17986112C22semidirect
65. #17986101C22semidirect
66. C4×#11765854C22semidirect
67. C4×D568C22semidirect
68. #17986041C22semidirect
70. #17986001C22semidirect
72. #432×C71C22semidirect
73. #432×C71C22semidirect
74. #431×C71C22semidirect
75. #431×C71C22semidirect
76. #423×C71C22semidirect
78. C4×M16×C71C22semidirect
101. #14556128C23semidirect
102. #14556128C23semidirect
103. #14556128C23semidirect
104. #14556125C23semidirect
109. #14556120C23semidirect
112. #14556116C23semidirect
133. C4×Dic142C23semidirect
134. C4×Dic142C23semidirect
155. C4×D284C23semidirect
156. C4×D284C23semidirect
182. #14556062C23semidirect
183. #14556060C23semidirect
184. #14556053C23semidirect
187. #14556050C23semidirect
204. C4⋊C8×C71C23semidirect
205. C4⋊C8×C71C23semidirect
208. #97×C71C23semidirect
209. C4×C8×C71C23semidirect
233. C2×D284#41semidirect
364. C2×C4×C71AGL(1,ℤ/8)semidirect
465. #2920D71semidirect
466. C71#60558semidirect
521. #432C2×D71semidirect
522. #432C2×D71semidirect
523. #431C2×D71semidirect
524. #431C2×D71semidirect
526. #423C2×D71semidirect
530. C4×M16C2×D71semidirect
652. C4⋊C8C22×D71semidirect
653. C4⋊C8C22×D71semidirect
660. #97C22×D71semidirect
661. C4×C8C22×D71semidirect
844. C2×C4#14556156semidirect

Maximal subgroups

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

subgroupindex
#226016362
C22×C4×D2842
#225984802
#225984402
#225984322
#225983892
#225983492
#225983412
#225982652
#225981392
#225978062
#225975702
C4×#145561562
C71×#29202
#6055871