Finite Group Databasebeta

← #32906002

Subgroups — #32906002

Order 18176.

11346 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986835C212yesmaximal, complemented
2#22602132C214yesmaximal, complemented
3#22602129C214yesmaximal, complemented
4#22602122C214yesmaximal, complemented
5#22602115C214yesmaximal, complemented
6#22602109C214yesmaximal, complemented
7#22602103C214yesmaximal, complemented
8#22602101C218yesmaximal, complemented
9#22601823C2116yesmaximal, complemented
10#22601673C211yesmaximal, characteristic, complemented
11#22601667C214yesmaximal, complemented
12C2×#17986545C212yesmaximal, complemented
13#532×D71C214yesmaximal, complemented
14C2×#17986467C211yesmaximal, characteristic, complemented
15C71×#3449C211yesmaximal, characteristic, complemented
16#17986835—232no—
17C2×#14556176C2214yescomplemented
18C2×#14556175C2214yescomplemented
19C2×#14556175C2214yescomplemented
20C2×#14556174C2214yescomplemented
21C2×#14556174C2214yescomplemented
22C2×#14556173C2218yescomplemented
23C2×#14556173C2214yescomplemented
24C22×#11765865C2211yescharacteristic
25C22×#11765865C2218yescomplemented
26C22×#11765865C2212yescomplemented
27C2×#41×D71C2218yescomplemented
28C2×#41×D71C2218yescomplemented
29#17986667C22116yescomplemented
30#17986662C22116yescomplemented
31#17986659C22116yescomplemented
32#17986655C22116yescomplemented
33#17986651C22116yescomplemented
34#17986647C22132yescomplemented
35#17986646C22116yescomplemented
36#17986641C22132yescomplemented
37#17986640C22116yescomplemented
38#17986636C22132yescomplemented
39#17986633C22116yescomplemented
40#17986631C22132yescomplemented
41#17986580C2214yescomplemented
42#17986576C22116yescomplemented
43#17986575C2214yescomplemented
44#17986574C2218yescomplemented
45#17986569C2218yescomplemented
46#17986568C2214yescomplemented
47#17986567C2218yescomplemented
48#17986562C2218yescomplemented
49#17986561C2214yescomplemented
50#17986557C22116yescomplemented
51#17986550C2214yescomplemented
52#17986549C2214yescomplemented
53#17986548C2218yescomplemented
54#17986547C2214yescomplemented
55#17986546C22116yescomplemented
56#17986545C2218yescomplemented
57#17986545C2218yescomplemented
58#17986545C2214yescomplemented
59#17986545C2214yescomplemented
60#17986545C2214yescomplemented
61#17986545C2214yescomplemented
62#17986544C22116yescomplemented
63C2×#14556126C2212yescomplemented
64C4⋊Q8×D71C2214yescomplemented
65C2×#14556124C2212yescomplemented
66#127×D71C2214yescomplemented
67C2×#14556117C2212yescomplemented
68C2×#14556115C2212yescomplemented
69#124×D71C2218yescomplemented
70#17986511C2218yescomplemented
71#17986508C22132yescomplemented
72C2×#14556100C2218yescomplemented
73#121×D71C22116yescomplemented
74#17986467C2218yescomplemented
75#17986467C2214yescomplemented
76#17986467C2214yescomplemented
77C2×#14556093C2212yescomplemented
78C2×#14556090C2212yescomplemented
79C2×C4×C22⋊D71C2218yescomplemented
80C2×(C22⋊D71)⋊C4C2214yescomplemented
81C4×D4×D71C22116yescomplemented
82C2×#14556085C2212yescomplemented
83C22×C4×Dic71C2211yescharacteristic, complemented
84C2×C42×D71C2212yescomplemented
85C22×#41×C71C2212yescomplemented
86#537×C71C2214yescomplemented
87#536×C71C2214yescomplemented
88#535×C71C2214yescomplemented
89#534×C71C2214yescomplemented
90#532×C71C2214yescomplemented
91#525×C71C2218yescomplemented
92C2×#117×C71C2211yescharacteristic, complemented
93#14556176—232no—
94#14556175—232no—
95#14556175—232no—
96#14556174—232no—
97#14556174—232no—
98#14556173—232no—
99#14556173—264no—
100C2×#11765866C2318yes—
101C2×#11765866C2318yes—
102C2×#11765865—264no—
103C2×#11765865—216no—
104C2×#11765865D4116yescomplemented
105C2×#11765865C2314yes—
106C2×#11765865C23116yes—
107C2×#11765865C2314yes—
108C2×#11765865C2314yes—
109C2×#11765865C23116yes—
110C2×#11765865C2314yes—
111C2×#11765865C2318yes—
112C2×#11765865C2318yes—
113C2×#11765865C2314yes—
114C2×#11765865C2314yes—
115C2×#11765864C2318yes—
116C2×#11765864C23116yes—
117C2×#11765864C23116yes—
118C2×#11765864C2318yes—
119#41×D71—264no—
120#41×D71—264no—
121C22×Dic142C2312yes—
122C22×Dic142C2318yes—
123C22×Dic142C2311yescharacteristic
124C2×Q8×D71C2318yes—
125C2×Q8×D71C2318yes—
126C22×D284C2312yes—
127C22×D284C2318yes—
128C22×D284C2311yescharacteristic
129C22×C22⋊D71C2314yes—
130C22×C22⋊D71C23116yes—
131C22×C22⋊D71C2318yes—
132C22×C22⋊D71C2312yes—
133C2×D4×D71C2318yes—
134C2×D4×D71C23116yes—
135C2×D4×D71C2318yes—
136C2×D4×D71C23116yes—
137C2×D4×D71C23116yes—
138C23×Dic71C2312yes—
139C22×C4×D71C23116yes—
140C22×C4×D71C2314yes—
141C22×C4×D71C2314yes—
142C22×C4×D71C2312yes—
143#14556128C2314yes—
144#14556127C23116yes—
145#14556126C2314yes—
146#14556126C2318yes—
147#14556126C2314yes—
148#14556125C2314yes—
149#14556124C2314yes—
150#14556124C23116yes—
151#14556124C2318yes—
152#14556124C2314yes—
153#14556117C2314yes—
154#14556117C2318yes—
155#14556117C2314yes—
156#14556116C2318yes—
157#14556115C2314yes—
158#14556115C2318yes—
159#14556115C2314yes—
160#14556114C23132yes—
161#14556113C23132yes—
162#14556112C23116yes—
163#14556110C23132yes—
164#14556108C23116yes—
165#14556106C23132yes—
166#14556105C23132yes—
167#14556103C23116yes—
168#14556103C23116yes—
169#14556102C23116yes—
170#14556101C23132yes—
171#14556101C23132yes—
172#14556100C23132yes—
173#14556100C23116yes—
174#14556100C23116yes—
175#14556100C23116yes—
176#14556100C23116yes—
177#14556099C23116yes—
178#14556098C23116yes—
179#14556098C23132yes—
180#14556096C23132yes—
181#14556093C2318yes—
182#14556093C2318yes—
183C4×D284C23116yes—
184D4×Dic71C23116yes—
185#14556090C2318yes—
186#14556090C2318yes—
187#14556090C23116yes—
188C4×C22⋊D71C23116yes—
189C4×C22⋊D71C23116yes—
190C4×C22⋊D71C23116yes—
191C4×C22⋊D71C23116yes—
192(C22⋊D71)⋊C4C23116yes—
193(C22⋊D71)⋊C4C23132yes—
194(C22⋊D71)⋊C4C23116yes—
195#14556085C2318yes—
196#14556085C2318yes—
197C2×Dic71⋊C4C2314yes—
198C2×Dic71⋊C4C2318yes—
199C4⋊C4×D71C23116yes—
200C2×C22⋊Dic71C2318yes—
201C2×(C2×D71)⋊C4C2318yes—
202C2×(C2×D71)⋊C4C2314yes—
203C22⋊C4×D71C23132yes—
204C2×C4×Dic71C2311yescharacteristic
205C2×C4×Dic71C2314yes—
206C2×C4×Dic71C2311yescharacteristic
207C2×C4×Dic71C2314yes—
208C2×C4×Dic71C2312yes—
209C2×C4×Dic71C2312yes—
210C2×C4×Dic71C2312yes—
211C42×D71C2318yes—
212C42×D71C2314yes—
213C42×D71C2314yes—
214C2×#41×C71—216no—
215C2×#41×C71C2314yes—
216C2×#41×C71C2314yes—
217C2×#41×C71C2314yes—
218C2×#41×C71C2314yes—
219C22×Q8×C71C2312yes—
220C22×D4×C71C2314yes—
221C22×D4×C71C2312yes—
222C23×C4×C71C2314yes—
223C23×C4×C71C2311yescharacteristic
224C4⋊Q8×C71C2314yes—
225#127×C71C2314yes—
226#124×C71C2318yes—
227#123×C71C23116yes—
228C22⋊Q8×C71C23116yes—
229#121×C71C23116yes—
230#121×C71C23116yes—
231#120×C71C23116yes—
232C4×D4×C71C23116yes—
233#117×C71C2314yes—
234#117×C71C2314yes—
235C2×C4⋊C4×C71C2312yes—
236C2×C22⋊C4×C71C2312yes—
237C2×C42×C71C2312yes—
238C23×D71C24116yes—
239C23×D71C2414yes—
240C23×D71C2412yes—
241#11765866—232no—
242#11765866—232no—
243#11765865—216no—
244#11765865—216no—
245#11765865—216no—
246#11765865—216no—
247#11765865—264no—
248#11765865—232no—
249#11765865—264no—
250#11765865—232no—
251#11765865C2×D4132yescomplemented
252#11765865C2×D4132yescomplemented
253#11765864—264no—
254#11765864—264no—
255#11765864—232no—
256#11765864—232no—
257C2×Dic142—28no—
258C2×Dic142—232no—
259C2×Dic142C2×D418yescomplemented
260C2×Dic142C24116yes—
261C2×Dic142C2414yes—
262C2×Dic142C2414yes—
263C2×Dic142C2414yes—
264Q8×D71—232no—
265Q8×D71—232no—
266C2×D284—28no—
267C2×D284—232no—
268C2×D284C2×D418yescomplemented
269C2×D284C24116yes—
270C2×D284C2414yes—
271C2×D284C2414yes—
272C2×D284C24116yes—
273C2×D284C2414yes—
274C2×C22⋊D71—216no—
275C2×C22⋊D71—264no—
276C2×C22⋊D71—416no—
277C2×C22⋊D71C2×D4116yescomplemented
278C2×C22⋊D71C24116yes—
279C2×C22⋊D71C2418yes—
280C2×C22⋊D71C24116yes—
281C2×C22⋊D71C24116yes—
282C2×C22⋊D71C2418yes—
283C2×C22⋊D71C24116yes—
284C2×C22⋊D71C2418yes—
285D4×D71—264no—
286D4×D71—264no—
287D4×D71—232no—
288D4×D71—232no—
289D4×D71—432no—
290C22×Dic71—44no—
291C22×Dic71C2412yes—
292C22×Dic71C2414yes—
293C22×Dic71C24116yes—
294C22×Dic71C2414yes—
295C22×Dic71C2414yes—
296C22×Dic71C2412yes—
297C22×Dic71C2412yes—
298C2×C4×D71—216no—
299C2×C4×D71—264no—
300C2×C4×D71—48no—
301C2×C4×D71C2×D4116yescomplemented
302C2×C4×D71C2418yes—
303C2×C4×D71C2418yes—
304C2×C4×D71C24116yes—
305C2×C4×D71C24116yes—
306C2×C4×D71C2418yes—
307C2×C4×D71C2418yes—
308C2×C4×D71C2414yes—
309C2×C4×D71C2414yes—
310C4⋊Dic71C24116yes—
311Dic71⋊C4C24116yes—
312Dic71⋊C4C24116yes—
313Dic71⋊C4C24116yes—
314C22⋊Dic71C24116yes—
315C22⋊Dic71C24116yes—
316(C2×D71)⋊C4C24116yes—
317(C2×D71)⋊C4C24132yes—
318(C2×D71)⋊C4C24116yes—
319(C2×D71)⋊C4C24116yes—
320C4×Dic71C2412yes—
321C4×Dic71C2411yescharacteristic
322C4×Dic71C2411yescharacteristic
323C4×Dic71C2418yes—
324C4×Dic71C2418yes—
325C4×Dic71C2412yes—
326C4×Dic71C2412yes—
327C4×Dic71C2414yes—
328C4×Dic71C2414yes—
329C24×C71C2414yes—
330C24×C71C2411yescharacteristic
331#41×C71—216no—
332#41×C71—216no—
333#41×C71—216no—
334#41×C71—216no—
335C2×Q8×C71—28no—
336C2×Q8×C71C2414yes—
337C2×Q8×C71C2414yes—
338C2×D4×C71—216no—
339C2×D4×C71—28no—
340C2×D4×C71C2418yes—
341C2×D4×C71C2418yes—
342C2×D4×C71C2414yes—
343C2×D4×C71C2414yes—
344C2×D4×C71C24116yes—
345C22×C4×C71—216no—
346C22×C4×C71C2×D418yescomplemented
347C22×C4×C71C2418yes—
348C22×C4×C71C2418yes—
349C22×C4×C71C2414yes—
350C22×C4×C71C2414yes—
351C22×C4×C71C2411yescharacteristic
352C22×C4×C71C2412yes—
353C22×C4×C71C2411yescharacteristic
354C22×C4×C71C2412yes—
355C4⋊C4×C71C2418yes—
356C4⋊C4×C71C24116yes—
357C22⋊C4×C71C2418yes—
358C22⋊C4×C71C24132yes—
359C42×C71C2414yes—
360C42×C71C2414yes—
361C23×C71—28no—
362C23×C71—42no—
363C23×C71—48no—
364C23×C71C22×D414yes—
365C23×C71C2518yes—
366C23×C71C2512yes—
367C23×C71C2511yescharacteristic
368C22×D71—28no—
369C22×D71—232no—
370C22×D71—44no—
371C22×D71—432no—
372C22×D71—48no—
373C22×D71C22×D418yes—
374C22×D71C2518yes—
375C22×D71C2514yes—
376Q8×C71—28no—
377Q8×C71—28no—
378D4×C71—216no—
379D4×C71—216no—
380D4×C71—28no—
381D4×C71—28no—
382D4×C71—416no—
383C2×C4×C71—28no—
384C2×C4×C71—216no—
385C2×C4×C71—216no—
386C2×C4×C71—44no—
387C2×C4×C71C22×D418yes—
388C2×C4×C71C22×D418yes—
389C2×C4×C71C22×D414yes—
390C2×C4×C71C22×D414yes—
391C2×C4×C71C2518yes—
392C2×C4×C71C2518yes—
393C2×C4×C71C2511yescharacteristic
394C2×C4×C71C2512yes—
395C2×C4×C71C2511yescharacteristic
396C22⋊D71—216no—
397C22⋊D71—216no—
398C22⋊D71—232no—
399C22⋊D71—232no—
400C22⋊D71—232no—
401C22⋊D71—416no—
402C22⋊D71C22×D4132yes—
403C2×Dic71—28no—
404C2×Dic71—232no—
405C2×Dic71—24no—
406C2×Dic71—28no—
407C2×Dic71—44no—
408C2×Dic71—42no—
409C2×Dic71C22×D418yes—
410C2×Dic71C2512yes—
411C2×Dic71C2514yes—
412C2×Dic71C2518yes—
413C2×Dic71C2514yes—
414C2×Dic71C2512yes—
415D284—232no—
416D284—28no—
417D284—28no—
418D284—416no—
419D284C22×D4116yes—
420C4×D71—232no—
421C4×D71—216no—
422C4×D71—216no—
423C4×D71—232no—
424C4×D71—216no—
425C4×D71—48no—
426C4×D71C22×D4116yes—
427C4×D71C22×D4116yes—
428Dic142—28no—
429Dic142—28no—
430Dic142—232no—
431Dic142C22×D4116yes—
432C22×C71—22no—
433C22×C71—24no—
434C22×C71—28no—
435C22×C71—216no—
436C22×C71—44no—
437C22×C71—88no—
438C22×C71C23×D414yes—
439C22×C71C23×D412yes—
440C22×C71C2611yescharacteristic
441C2×D71—28no—
442C2×D71—28no—
443C2×D71—216no—
444C2×D71—48no—
445C2×D71—832no—
446C2×D71—88no—
447C2×D71C23×D418yes—
448C4×C71—28no—
449C4×C71—28no—
450C4×C71C23×D412yes—
451C4×C71C23×D414yes—
452C4×C71C23×D412yes—
453Dic71—28no—
454Dic71—22no—
455Dic71—24no—
456Dic71C23×D418yes—
457Dic71#58514yescomplemented
458#62812—711nomaximal, Sylow
459C2×C71—22no—
460C2×C71—24no—
461C2×C71—48no—
462C2×C71C24×D411yescharacteristic
463C2×C71C2×#58512yes—
464D71—28no—
465D71—48no—
466C2×#585—712no—
467#3500—714no—
468#3500—714no—
469#3499—714no—
470#3498—714no—
471#3497—714no—
472#3496—714no—
473#3496—718no—
474D4×#41—7116no—
475#3449—714no—
476#3449—711no—
477#3449D7111yescharacteristic, complemented
478C2×#532—712no—
479C2×#532—714no—
480C2×C4×#41—711no—
481C71#6281211yescharacteristic, complemented, Sylow
482#585—14232no—
483C2×2−1+4—714no—
484C2×2−1+4—714no—
485C2×2−1+4—714no—
486C2×H(5,𝔽2)—714no—
487C2×H(5,𝔽2)—714no—
488C2×H(5,𝔽2)—718no—
489C2×H(5,𝔽2)—714no—
490C22×#41—718no—
491C22×#41—718no—
492C22×#41—711no—
493C22×#41—712no—
494C22×#41—718no—
495C22×#41C2×D7112yescomplemented
496#550—7116no—
497D4×Q8—7116no—
498#548—7116no—
499#548—7116no—
500#547—7132no—
501#547—7116no—
502#546—7132no—
503#546—7116no—
504#546—7116no—
505#546—7132no—
506D42—7116no—
507D42—7132no—
508#537—7116no—
509#537—714no—
510#537C2×D7114yescomplemented
511#536—718no—
512#536—718no—
513#536—714no—
514#536C2×D7114yescomplemented
515#535—718no—
516#535—718no—
517#535—714no—
518#535C2×D7114yescomplemented
519#534—7116no—
520#534—714no—
521#534C2×D7114yescomplemented
522#532—714no—
523#532—714no—
524#532—718no—
525#532—718no—
526#532—714no—
527#532—714no—
528#532—714no—
529#532—714no—
530#532—718no—
531#532—7116no—
532#532—7116no—
533#532—714no—
534#532C2×D7114yescomplemented
535C2×C4⋊Q8—712no—
536C2×C4⋊Q8—714no—
537C2×#127—712no—
538C2×#127—714no—
539C2×#124—712no—
540C2×#124—712no—
541C2×#124—718no—
542#525—7132no—
543#525—718no—
544#525C2×D7118yescomplemented
545C2×#121—718no—
546C2×#121—7116no—
547C4×#41—718no—
548C4×#41—714no—
549C4×#41—714no—
550C2×C4×Q8—712no—
551C2×C4×D4—718no—
552C2×C4×D4—7116no—
553C2×C4×D4—712no—
554C2×C4×D4—714no—
555C2×#117—712no—
556C2×#117C2×D7111yescharacteristic, complemented
557C22×C42—711no—
558C22×C42—712no—
5592−1+4—14232no—
5602−1+4—14232no—
5612−1+4—14232no—
562H(5,𝔽2)—14264no—
563H(5,𝔽2)—14232no—
564H(5,𝔽2)—14232no—
565H(5,𝔽2)—14232no—
566C2×#41—216no—
567C2×#41—718no—
568C2×#41—718no—
569C2×#41—718no—
570C2×#41—7116no—
571C2×#41—7116no—
572C2×#41—718no—
573C2×#41—7116no—
574C2×#41—714no—
575C2×#41—714no—
576C2×#41—7116no—
577C2×#41—714no—
578C2×#41—714no—
579C2×#41—714no—
580C2×#41—714no—
581C2×#41—718no—
582C2×#41—7116no—
583C2×#41—718no—
584C2×#41—14264no—
585C2×#41—14264no—
586C2×#41—14264no—
587C2×#41—14216no—
588C2×#41C22×D7114yes—
589C2×#41C22×D7114yes—
590C2×#41C22×D7114yes—
591C2×#41C22×D7114yes—
592C22×Q8—718no—
593C22×Q8—718no—
594C22×Q8—711no—
595C22×Q8—712no—
596C22×Q8—718no—
597C22×Q8C22×D7112yes—
598C22×D4—718no—
599C22×D4—7116no—
600C22×D4—712no—
601C22×D4—714no—
602C22×D4—7116no—
603C22×D4—7116no—
604C22×D4—718no—
605C22×D4—7116no—
606C22×D4—718no—
607C22×D4—711no—
608C22×D4—712no—
609C22×D4—718no—
610C22×D4C22×D7114yes—
611C22×D4C22×D7112yes—
612C23×C4—712no—
613C23×C4—714no—
614C23×C4—712no—
615C23×C4—7116no—
616C23×C4—714no—
617C23×C4C22×D7114yes—
618C23×C4C22×D7111yescharacteristic
619C4⋊Q8—714no—
620C4⋊Q8—714no—
621C4⋊Q8—718no—
622C4⋊Q8—7116no—
623C4⋊Q8—714no—
624C4⋊Q8C22×D7114yes—
625#127—714no—
626#127—714no—
627#127—718no—
628#127—7116no—
629#127—714no—
630#127C22×D7114yes—
631#124—714no—
632#124—714no—
633#124—718no—
634#124—714no—
635#124—714no—
636#124—718no—
637#124—7132no—
638#124—718no—
639#124C22×D7118yes—
640#123—7132no—
641#123—7132no—
642#123—7116no—
643#123C22×D71116yes—
644C22⋊Q8—7132no—
645C22⋊Q8—7116no—
646C22⋊Q8—7132no—
647C22⋊Q8C22×D71116yes—
648#121—7116no—
649#121—7116no—
650#121—7116no—
651#121—7116no—
652#121—7116no—
653#121—7132no—
654#121—7116no—
655#121—7116no—
656#121—7116no—
657#121—7132no—
658#121—7132no—
659#121C22×D71116yes—
660#121C22×D71116yes—
661#120—7132no—
662#120—7132no—
663#120—7116no—
664#120C22×D71116yes—
665C4×Q8—718no—
666C4×Q8—718no—
667C4×D4—7116no—
668C4×D4—7116no—
669C4×D4—7116no—
670C4×D4—7116no—
671C4×D4—7116no—
672C4×D4—718no—
673C4×D4—718no—
674C4×D4—7116no—
675C4×D4—7116no—
676C4×D4—7116no—
677C4×D4—7132no—
678C4×D4—7116no—
679C4×D4C22×D71116yes—
680#117—718no—
681#117—718no—
682#117C22×D7114yes—
683#117C22×D7114yes—
684C2×C4⋊C4—714no—
685C2×C4⋊C4—718no—
686C2×C4⋊C4—7116no—
687C2×C4⋊C4C22×D7112yes—
688C2×C22⋊C4—718no—
689C2×C22⋊C4—714no—
690C2×C22⋊C4—718no—
691C2×C22⋊C4—7132no—
692C2×C22⋊C4C22×D7112yes—
693C2×C42—711no—
694C2×C42—714no—
695C2×C42—712no—
696C2×C42—714no—
697C2×C42—712no—
698C2×C42—712no—
699C2×C42—711no—
700C2×C42—718no—
701C2×C42—714no—
702C2×C42—714no—
703C2×C42C22×D7112yes—
704C24—712no—
705C24—7116no—
706C24—714no—
707C24C23×D7114yes—
708C24C23×D7111yescharacteristic
709#41—216no—
710#41—216no—
711#41—216no—
712#41—216no—
713#41—7132no—
714#41—7132no—
715#41—14264no—
716#41—14264no—
717#41—14232no—
718#41—14232no—
719#41—14264no—
720#41—14232no—
721#41—14232no—
722#41—14264no—
723#41—14232no—
724#41—14232no—
725#41—14216no—
726#41—14216no—
727#41—14216no—
728#41—14216no—
729C2×Q8—28no—
730C2×Q8—718no—
731C2×Q8—714no—
732C2×Q8—7116no—
733C2×Q8—714no—
734C2×Q8—714no—
735C2×Q8—14232no—
736C2×Q8—14232no—
737C2×Q8—14232no—
738C2×Q8—1428no—
739C2×Q8C23×D7114yes—
740C2×Q8C23×D7114yes—
741C2×D4—216no—
742C2×D4—28no—
743C2×D4—28432no—
744C2×D4—28416no—
745C2×D4—7116no—
746C2×D4—7116no—
747C2×D4—718no—
748C2×D4—7116no—
749C2×D4—7116no—
750C2×D4—718no—
751C2×D4—718no—
752C2×D4—7116no—
753C2×D4—718no—
754C2×D4—7116no—
755C2×D4—714no—
756C2×D4—7116no—
757C2×D4—714no—
758C2×D4—714no—
759C2×D4—14232no—
760C2×D4—14232no—
761C2×D4—14264no—
762C2×D4—14232no—
763C2×D4—14264no—
764C2×D4—14264no—
765C2×D4—14216no—
766C2×D4—1428no—
767C2×D4C23×D7118yes—
768C2×D4C23×D7118yes—
769C2×D4C23×D7114yes—
770C2×D4C23×D7114yes—
771C2×D4C23×D71116yes—
772C22×C4—216no—
773C22×C4—2848no—
774C22×C4—2844no—
775C22×C4—714no—
776C22×C4—712no—
777C22×C4—718no—
778C22×C4—712no—
779C22×C4—7116no—
780C22×C4—714no—
781C22×C4—714no—
782C22×C4—712no—
783C22×C4—714no—
784C22×C4—714no—
785C22×C4—7116no—
786C22×C4—718no—
787C22×C4—7116no—
788C22×C4—7116no—
789C22×C4—718no—
790C22×C4—718no—
791C22×C4—14264no—
792C22×C4—14216no—
793C22×C4D4×D7118yescomplemented
794C22×C4C23×D7114yes—
795C22×C4C23×D7118yes—
796C22×C4C23×D7118yes—
797C22×C4C23×D7114yes—
798C22×C4C23×D7111yescharacteristic
799C22×C4C23×D7112yes—
800C22×C4C23×D7111yescharacteristic
801C22×C4C23×D7112yes—
802C4⋊C4—7116no—
803C4⋊C4—7116no—
804C4⋊C4—7116no—
805C4⋊C4—7116no—
806C4⋊C4C23×D71116yes—
807C4⋊C4C23×D7118yes—
808C22⋊C4—7116no—
809C22⋊C4—7116no—
810C22⋊C4—7116no—
811C22⋊C4—7116no—
812C22⋊C4—7116no—
813C22⋊C4—7132no—
814C22⋊C4C23×D71132yes—
815C22⋊C4C23×D7118yes—
816C42—711no—
817C42—711no—
818C42—712no—
819C42—718no—
820C42—714no—
821C42—718no—
822C42—714no—
823C42—712no—
824C42—712no—
825C42C23×D7114yes—
826C42C23×D7114yes—
827C23—28no—
828C23—42no—
829C23—48no—
830C23—2844no—
831C23—2848no—
832C23—28432no—
833C23—718no—
834C23—714no—
835C23—718no—
836C23—14232no—
837C23—1428no—
838C23C2×D4×D7114yes—
839C23C24×D7118yes—
840C23C24×D7112yes—
841C23C24×D7111yescharacteristic
842Q8—28no—
843Q8—28no—
844Q8—7116no—
845Q8—14232no—
846Q8—1428no—
847Q8—1428no—
848D4—216no—
849D4—216no—
850D4—28no—
851D4—28no—
852D4—416no—
853D4—28416no—
854D4—28416no—
855D4—7132no—
856D4—7116no—
857D4—14232no—
858D4—14232no—
859D4—14232no—
860D4—14232no—
861D4—14216no—
862D4—14216no—
863D4—1428no—
864D4—1428no—
865C2×C4—28no—
866C2×C4—216no—
867C2×C4—216no—
868C2×C4—44no—
869C2×C4—2848no—
870C2×C4—2844no—
871C2×C4—2842no—
872C2×C4—718no—
873C2×C4—712no—
874C2×C4—714no—
875C2×C4—7116no—
876C2×C4—7116no—
877C2×C4—712no—
878C2×C4—714no—
879C2×C4—718no—
880C2×C4—14216no—
881C2×C4—14232no—
882C2×C4—14232no—
883C2×C4—1424no—
884C2×C4—1428no—
885C2×C4—14232no—
886C2×C4—1428no—
887C2×C4—14216no—
888C2×C4—14216no—
889C2×C4C2×D4×D7118yes—
890C2×C4C2×D4×D7114yes—
891C2×C4C2×D4×D7118yes—
892C2×C4C2×D4×D7114yes—
893C2×C4C24×D7118yes—
894C2×C4C24×D7118yes—
895C2×C4C24×D7111yescharacteristic
896C2×C4C24×D7112yes—
897C2×C4C24×D7111yescharacteristic
898C22—22no—
899C22—24no—
900C22—28no—
901C22—216no—
902C22—44no—
903C22—88no—
904C22—2848no—
905C22—5688no—
906C22—56832no—
907C22—718no—
908C22—1428no—
909C22—14216no—
910C22—1428no—
911C22C22×D4×D7114yes—
912C22C22×D4×D7112yes—
913C22C25×D7111yescharacteristic
914C4—28no—
915C4—28no—
916C4—718no—
917C4—714no—
918C4—1428no—
919C4—1422no—
920C4—1424no—
921C4C22×D4×D7112yes—
922C4C22×D4×D7114yes—
923C4C22×D4×D7112yes—
924C2—24no—
925C2—22no—
926C2—48no—
927C2—2848no—
928C2—1428no—
929C2C23×D4×D7111yescharacteristic
930C2#585×D7112yes—
subgroupG/H
centerC2×C4C24×D71
commutator, socle, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC71×#3449C2
hypercenter#3449D71
hypocenterC71#62812
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#17986835C2semidirect
2. #22602132C2semidirect
3. #22602129C2semidirect
4. #22602122C2semidirect
5. #22602115C2semidirect
6. #22602109C2semidirect
7. #22602103C2semidirect
8. #22602101C2semidirect
9. #22601823C2semidirect
10. #22601673C2semidirect
11. #22601667C2semidirect
12. C2×#17986545C2semidirect
13. #532×D71C2semidirect
14. C2×#17986467C2semidirect
15. C71×#3449C2semidirect
17. C2×#14556176C22semidirect
18. C2×#14556175C22semidirect
19. C2×#14556175C22semidirect
20. C2×#14556174C22semidirect
21. C2×#14556174C22semidirect
22. C2×#14556173C22semidirect
23. C2×#14556173C22semidirect
25. C22×#11765865C22semidirect
26. C22×#11765865C22semidirect
27. C2×#41×D71C22semidirect
28. C2×#41×D71C22semidirect
29. #17986667C22semidirect
30. #17986662C22semidirect
31. #17986659C22semidirect
32. #17986655C22semidirect
33. #17986651C22semidirect
34. #17986647C22semidirect
35. #17986646C22semidirect
36. #17986641C22semidirect
37. #17986640C22semidirect
38. #17986636C22semidirect
39. #17986633C22semidirect
40. #17986631C22semidirect
41. #17986580C22semidirect
42. #17986576C22semidirect
43. #17986575C22semidirect
44. #17986574C22semidirect
45. #17986569C22semidirect
46. #17986568C22semidirect
47. #17986567C22semidirect
48. #17986562C22semidirect
49. #17986561C22semidirect
50. #17986557C22semidirect
51. #17986550C22semidirect
52. #17986549C22semidirect
53. #17986548C22semidirect
54. #17986547C22semidirect
55. #17986546C22semidirect
56. #17986545C22semidirect
57. #17986545C22semidirect
58. #17986545C22semidirect
59. #17986545C22semidirect
60. #17986545C22semidirect
61. #17986545C22semidirect
62. #17986544C22semidirect
63. C2×#14556126C22semidirect
64. C4⋊Q8×D71C22semidirect
65. C2×#14556124C22semidirect
66. #127×D71C22semidirect
67. C2×#14556117C22semidirect
68. C2×#14556115C22semidirect
69. #124×D71C22semidirect
70. #17986511C22semidirect
71. #17986508C22semidirect
72. C2×#14556100C22semidirect
73. #121×D71C22semidirect
74. #17986467C22semidirect
75. #17986467C22semidirect
76. #17986467C22semidirect
77. C2×#14556093C22semidirect
78. C2×#14556090C22semidirect
79. C2×C4×C22⋊D71C22semidirect
80. C2×(C22⋊D71)⋊C4C22semidirect
81. C4×D4×D71C22semidirect
82. C2×#14556085C22semidirect
83. C22×C4×Dic71C22semidirect
84. C2×C42×D71C22semidirect
85. C22×#41×C71C22semidirect
86. #537×C71C22semidirect
87. #536×C71C22semidirect
88. #535×C71C22semidirect
89. #534×C71C22semidirect
90. #532×C71C22semidirect
91. #525×C71C22semidirect
92. C2×#117×C71C22semidirect
104. C2×#11765865D4semidirect
251. #11765865C2×D4semidirect
252. #11765865C2×D4semidirect
259. C2×Dic142C2×D4semidirect
268. C2×D284C2×D4semidirect
277. C2×C22⋊D71C2×D4semidirect
301. C2×C4×D71C2×D4semidirect
346. C22×C4×C71C2×D4semidirect
457. Dic71#585semidirect
477. #3449D71semidirect
481. C71#62812semidirect
495. C22×#41C2×D71semidirect
510. #537C2×D71semidirect
514. #536C2×D71semidirect
518. #535C2×D71semidirect
521. #534C2×D71semidirect
534. #532C2×D71semidirect
544. #525C2×D71semidirect
556. C2×#117C2×D71semidirect
793. C22×C4D4×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179868352
#226021322
#226021292
#226021222
#226021152
#226021092
#226021032
#226021012
#226018232
#226016732
#226016672
C2×#179865452
#532×D712
C2×#179864672
C71×#34492
#6281271