Finite Group Databasebeta

← #3487×D71 #32905692

Subgroups — #3487×D71 #32905692

Order 18176.

11510 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D71C211yesmaximal, characteristic, complemented
2C22×#41×D71C211yesmaximal, characteristic, complemented
3#22601999C211yesmaximal, characteristic, complemented
4#22601998C211yesmaximal, characteristic, complemented
5#22601997C218yesmaximal, complemented
6#22601996C216yesmaximal, complemented
7#22601995C211yesmaximal, characteristic, complemented
8#22601994C216yesmaximal, complemented
9#22601993C218yesmaximal, complemented
10#550×D71C218yesmaximal, complemented
11#548×D71C218yesmaximal, complemented
12#535×D71C216yesmaximal, complemented
13#525×D71C216yesmaximal, complemented
14#519×D71C211yesmaximal, characteristic, complemented
15C71×#3487C211yesmaximal, characteristic, complemented
16C2×#14556176C2214yescomplemented
17C2×#14556176C2211yescharacteristic, complemented
18C2×#14556175C2214yescomplemented
19C2×#14556175C2216yescomplemented
202−1+4×D71—216no—
21C22×#11765866C2211yescharacteristic, complemented
22C22×#11765865C2213yescomplemented
23C22×#11765864C2213yescomplemented
24C2×#41×D71—216no—
25C2×#41×D71C2218yes—
26C2×#41×D71C2216yes—
27C2×#41×D71C2218yescomplemented
28C2×#41×D71C2214yescomplemented
29C22×Q8×D71C2211yescharacteristic
30C22×Q8×D71C2214yescomplemented
31C22×D4×D71C2213yes—
32C23×C4×D71C2213yes—
33#17986671C2218yescomplemented
34#17986670C22124yescomplemented
35#17986669C22124yescomplemented
36#17986668C2218yescomplemented
37#17986668C2218yescomplemented
38#17986667C22124yescomplemented
39#17986667C22124yescomplemented
40#17986661C2218yescomplemented
41#17986660C2218yescomplemented
42#17986659C22124yescomplemented
43#17986658C22124yescomplemented
44#17986657C22124yescomplemented
45#17986656C2218yescomplemented
46#17986655C22124yescomplemented
47#17986568C2216yescomplemented
48#17986567C22112yescomplemented
49#17986566C2216yescomplemented
50#17986565C22124yescomplemented
51#17986564C22124yescomplemented
52#17986563C2216yescomplemented
53#17986562C22112yescomplemented
54#127×D71C22112yescomplemented
55#124×D71C22112yescomplemented
56#17986512C22112yescomplemented
57#17986511C2216yescomplemented
58#17986510C2216yescomplemented
59#17986509C22112yescomplemented
60#17986508C22124yescomplemented
61#17986507C22112yescomplemented
62#17986506C2216yescomplemented
63#17986505C22112yescomplemented
64#123×D71C2214yes—
65C22⋊Q8×D71C22112yescomplemented
66#121×D71C22124yescomplemented
67#121×D71C22112yescomplemented
68#120×D71C22112yes—
69#17986477C2211yescharacteristic, complemented
70#17986476C2216yescomplemented
71#17986475C2218yescomplemented
72C4×Q8×D71C2218yescomplemented
73C4×D4×D71C22124yescomplemented
74#117×D71C2216yes—
75C2×2−1+4×C71C2211yescharacteristic, complemented
76C22×#41×C71C2211yescharacteristic, complemented
77#550×C71C2218yescomplemented
78#548×C71C2218yescomplemented
79#535×C71C2216yescomplemented
80#525×C71C2216yescomplemented
81#519×C71C2211yescharacteristic, complemented
82C24×D71C2313yes—
83#14556176—232no—
84#14556176—28no—
85#14556175—248no—
86#14556175—232no—
87C2×#11765866—28no—
88C2×#11765866C2316yes—
89C2×#11765866C2318yes—
90C2×#11765866C2314yescomplemented
91C2×#11765865—224no—
92C2×#11765865C23112yes—
93C2×#11765865C2316yes—
94C2×#11765865C23124yes—
95C2×#11765865C23112yescomplemented
96C2×#11765864—224no—
97C2×#11765864C2316yes—
98C2×#11765864C23112yes—
99C2×#11765864C23124yes—
100C2×#11765864C23112yescomplemented
101#41×D71—264no—
102#41×D71—232no—
103#41×D71—264no—
104#41×D71—248no—
105C22×Dic142C2313yes—
106C22×Dic142C23112yescomplemented
107C2×Q8×D71—232no—
108C2×Q8×D71D4116yescomplemented
109C2×Q8×D71C2316yes—
110C2×Q8×D71C2314yes—
111C2×Q8×D71C2314yes—
112C2×Q8×D71C2314yescomplemented
113C2×Q8×D71C23112yescomplemented
114C22×D284C2313yes—
115C22×C22⋊D71C2316yes—
116C2×D4×D71—224no—
117C2×D4×D71C23112yes—
118C2×D4×D71C23112yes—
119C2×D4×D71C2314yes—
120C2×D4×D71C2316yes—
121C2×D4×D71C23124yes—
122C23×Dic71C2313yes—
123C22×C4×D71—224no—
124C22×C4×D71C2311yescharacteristic
125C22×C4×D71C23112yes—
126C22×C4×D71C23112yes—
127C22×C4×D71C2313yes—
128C22×C4×D71C2313yes—
129C22×C4×D71C23112yes—
130C22×C4×D71C2313yes—
131#14556125C23112yescomplemented
132#14556124C23112yescomplemented
133#14556124C23148yescomplemented
134#14556124C23112yescomplemented
135#14556117C23112yescomplemented
136#14556116C23112yescomplemented
137#14556115C23112yescomplemented
138#14556114C23148yescomplemented
139#14556113C2318yes—
140#14556112C2314yes—
141#14556111C2314yes—
142#14556110C2318yes—
143#14556109C2314yes—
144#14556108C23112yescomplemented
145#14556107C23112yescomplemented
146#14556106C23124yescomplemented
147#14556105C23124yescomplemented
148#14556104C23112yescomplemented
149#14556103C23124yescomplemented
150#14556103C23112yescomplemented
151#14556102C23124yescomplemented
152#14556102C23112yescomplemented
153#14556101C23148yescomplemented
154#14556101C23124yescomplemented
155#14556100C23148yescomplemented
156#14556100C23124yescomplemented
157#14556099C23124yescomplemented
158#14556099C23112yescomplemented
159#14556098C23112yes—
160#14556098C23124yes—
161#14556097C23112yes—
162#14556096C23124yes—
163#14556096C23112yes—
164Q8×Dic71C2318yescomplemented
165C4×Dic142C23124yescomplemented
166#14556093C23124yescomplemented
167C4×D284C23124yescomplemented
168D4×Dic71C23124yescomplemented
169#14556090C23124yescomplemented
170C4×C22⋊D71C23124yescomplemented
171C4×C22⋊D71C23124yescomplemented
172(C22⋊D71)⋊C4C23124yescomplemented
173(C22⋊D71)⋊C4C23124yescomplemented
174#14556087C2316yes—
175#14556086C23112yes—
176#14556085C23112yes—
177#14556084C23112yes—
178C4⋊C4×D71C23112yes—
179C4⋊C4×D71C2318yes—
180C22⋊C4×D71C2314yes—
181C22⋊C4×D71C2318yes—
182C22⋊C4×D71C23124yes—
183C42×D71C23112yes—
1842−1+4×C71—28no—
185C2×#41×C71—28no—
186C2×#41×C71C2316yes—
187C2×#41×C71C2318yes—
188C2×#41×C71C2314yescomplemented
189C22×Q8×C71C2311yescharacteristic
190C22×Q8×C71C2314yescomplemented
191C22×D4×C71C2313yes—
192C23×C4×C71C2313yes—
193#127×C71C23112yescomplemented
194#124×C71C23112yescomplemented
195#123×C71C2314yes—
196C22⋊Q8×C71C23112yescomplemented
197#121×C71C23124yescomplemented
198#121×C71C23112yescomplemented
199#120×C71C23112yes—
200C4×Q8×C71C2318yescomplemented
201C4×D4×C71C23124yescomplemented
202#117×C71C2316yes—
203C23×D71—212no—
204C23×D71—412no—
205C23×D71C2414yes—
206C23×D71C2416yes—
207C23×D71C2411yescharacteristic
208C23×D71C2416yes—
209C23×D71C2413yes—
210#11765866—232no—
211#11765866—216no—
212#11765866—224no—
213#11765865—224no—
214#11765865—248no—
215#11765865—296no—
216#11765865—248no—
217#11765864—248no—
218#11765864—224no—
219#11765864—296no—
220#11765864—248no—
221C2×Dic142—248no—
222C2×Dic142C2×D4124yescomplemented
223C2×Dic142C24112yes—
224C2×Dic142C2416yes—
225C2×Dic142C24112yes—
226Q8×D71—216no—
227Q8×D71—224no—
228Q8×D71—248no—
229Q8×D71C2×D4132yes—
230Q8×D71C2×D4132yescomplemented
231C2×D284—212no—
232C2×D284C24112yes—
233C2×D284C2414yes—
234C2×D284C2416yes—
235C2×D284C24124yes—
236C2×C22⋊D71—224no—
237C2×C22⋊D71C24124yes—
238C2×C22⋊D71C2414yes—
239C2×C22⋊D71C2414yes—
240C2×C22⋊D71C24112yes—
241C2×C22⋊D71C24124yes—
242C2×C22⋊D71C24124yes—
243D4×D71—216no—
244D4×D71—248no—
245D4×D71—248no—
246D4×D71—224no—
247D4×D71—448no—
248C22×Dic71—212no—
249C22×Dic71C2411yescharacteristic
250C22×Dic71C24112yes—
251C22×Dic71C24112yes—
252C22×Dic71C2413yes—
253C2×C4×D71—24no—
254C2×C4×D71—212no—
255C2×C4×D71—212no—
256C2×C4×D71—248no—
257C2×C4×D71—248no—
258C2×C4×D71—248no—
259C2×C4×D71C2×D4124yes—
260C2×C4×D71C2412yes—
261C2×C4×D71C2412yes—
262C2×C4×D71C2414yes—
263C2×C4×D71C24112yes—
264C2×C4×D71C24112yes—
265C2×C4×D71C24112yes—
266C2×C4×D71C24112yes—
267C2×C4×D71C2418yes—
268C2×C4×D71C2416yes—
269C2×C4×D71C2416yes—
270C4⋊Dic71C24112yes—
271C4⋊Dic71C2418yes—
272Dic71⋊C4C24124yes—
273Dic71⋊C4C2418yes—
274Dic71⋊C4C2418yes—
275C22⋊Dic71C2414yes—
276C22⋊Dic71C2418yes—
277C22⋊Dic71C24124yes—
278(C2×D71)⋊C4C2418yes—
279(C2×D71)⋊C4C2418yes—
280(C2×D71)⋊C4C24124yes—
281(C2×D71)⋊C4C2418yes—
282(C2×D71)⋊C4C24124yes—
283C4×Dic71C24124yes—
284C4×Dic71C24112yes—
285C24×C71C2413yes—
286#41×C71—232no—
287#41×C71—216no—
288#41×C71—224no—
289C2×Q8×C71—216no—
290C2×Q8×C71C2×D418yescomplemented
291C2×Q8×C71C2416yes—
292C2×Q8×C71C2414yes—
293C2×D4×C71—212no—
294C2×D4×C71C24112yes—
295C2×D4×C71C2414yes—
296C2×D4×C71C2416yes—
297C2×D4×C71C24124yes—
298C22×C4×C71—212no—
299C22×C4×C71C2411yescharacteristic
300C22×C4×C71C24112yes—
301C22×C4×C71C24112yes—
302C22×C4×C71C2413yes—
303C4⋊C4×C71C24112yes—
304C4⋊C4×C71C2418yes—
305C22⋊C4×C71C2414yes—
306C22⋊C4×C71C2418yes—
307C22⋊C4×C71C24124yes—
308C42×C71C24112yes—
309C23×C71—26no—
310C23×C71—46no—
311C23×C71C2516yes—
312C23×C71C2514yes—
313C23×C71C2511yescharacteristic
314C22×D71—24no—
315C22×D71—26no—
316C22×D71—28no—
317C22×D71—212no—
318C22×D71—212no—
319C22×D71—216no—
320C22×D71—224no—
321C22×D71—412no—
322C22×D71—46no—
323C22×D71—448no—
324C22×D71C22×D414yes—
325C22×D71C2516yes—
326C22×D71C2514yes—
327C22×D71C2511yescharacteristic
328C22×D71C2511yescharacteristic
329Q8×C71—212no—
330Q8×C71C22×D4116yes—
331D4×C71—28no—
332D4×C71—224no—
333D4×C71—212no—
334D4×C71—424no—
335C2×C4×C71—22no—
336C2×C4×C71—224no—
337C2×C4×C71—224no—
338C2×C4×C71C22×D4112yes—
339C2×C4×C71C2518yes—
340C2×C4×C71C2514yes—
341C2×C4×C71C2512yes—
342C2×C4×C71C2516yes—
343C22⋊D71—28no—
344C22⋊D71—28no—
345C22⋊D71—248no—
346C22⋊D71—224no—
347C22⋊D71—424no—
348C22⋊D71—424no—
349C2×Dic71—22no—
350C2×Dic71—224no—
351C2×Dic71—224no—
352C2×Dic71C22×D4112yes—
353C2×Dic71C2518yes—
354C2×Dic71C2514yes—
355C2×Dic71C2512yes—
356C2×Dic71C2516yes—
357D284—28no—
358D284—224no—
359D284—212no—
360D284—424no—
361C4×D71—24no—
362C4×D71—24no—
363C4×D71—28no—
364C4×D71—216no—
365C4×D71—224no—
366C4×D71—224no—
367C4×D71—224no—
368C4×D71—224no—
369C4×D71C22×D4124yes—
370C4×D71C22×D4124yes—
371Dic142—212no—
372Dic142—224no—
373Dic142C22×D4148yes—
374C22×C71—22no—
375C22×C71—24no—
376C22×C71—26no—
377C22×C71—28no—
378C22×C71—212no—
379C22×C71—412no—
380C22×C71C23×D412yes—
381C22×C71C2611yescharacteristic
382C2×D71—22no—
383C2×D71—28no—
384C2×D71—24no—
385C2×D71—26no—
386C2×D71—28no—
387C2×D71—212no—
388C2×D71—424no—
389C2×D71—412no—
390C2×D71—416no—
391C2×D71—424no—
392C2×D71C23×D412yes—
393C2×D71C23×D412yes—
394C2×D71#58514yes—
395C4×C71—24no—
396C4×C71—22no—
397C4×C71—28no—
398C4×C71C23×D4112yes—
399Dic71—24no—
400Dic71—22no—
401Dic71—28no—
402Dic71C23×D4112yes—
403C2×#3487—711nomaximal, Sylow
404C2×C71—22no—
405C2×C71—46no—
406C2×C71—44no—
407C2×C71C24×D411yescharacteristic
408C2×C71C2×#58512yes—
409D71—22no—
410D71—44no—
411D71—46no—
412D71#348714yesdirect product factor
413C22×2−1+4—711no—
414C23×#41—711no—
415#3487—711no—
416#3487—711no—
417#3487—718no—
418#3487—718no—
419#3487—716no—
420#3487—716no—
421#3487—711no—
422#3487D7111yescharacteristic, direct product factor
423C2×#550—718no—
424C2×#548—718no—
425C2×#535—716no—
426C2×#525—716no—
427C2×#519—711no—
428C71C2×#348711yescharacteristic, complemented, Sylow
429C2×2−1+4—716no—
430C2×2−1+4—714no—
431C2×2−1+4—711no—
432C2×2−1+4—714no—
433C2×2−1+4—14216no—
434C2×2−1+4C2×D7111yescharacteristic, complemented
435C22×#41—718no—
436C22×#41—718no—
437C22×#41—716no—
438C22×#41—714no—
439C22×#41—711no—
440C22×#41—713no—
441C22×#41—713no—
442C22×#41—14216no—
443C22×#41C2×D7111yescharacteristic, complemented
444C23×Q8—711no—
445C23×Q8—714no—
446C23×D4—713no—
447C24×C4—713no—
448#550—718no—
449#550—718no—
450#550—7124no—
451#550—7124no—
452#550—7124no—
453#550—718no—
454#550—7124no—
455#550C2×D7118yescomplemented
456#548—718no—
457#548—718no—
458#548—7124no—
459#548—7124no—
460#548—7124no—
461#548—718no—
462#548—7124no—
463#548C2×D7118yescomplemented
464#535—716no—
465#535—716no—
466#535—7112no—
467#535—7112no—
468#535—7124no—
469#535—7124no—
470#535—716no—
471#535C2×D7116yescomplemented
472C2×#127—7112no—
473C2×#124—7112no—
474#525—716no—
475#525—716no—
476#525—7112no—
477#525—7112no—
478#525—7112no—
479#525—7112no—
480#525—7124no—
481#525—716no—
482#525C2×D7116yescomplemented
483C2×#123—714no—
484C2×C22⋊Q8—7112no—
485C2×#121—7112no—
486C2×#121—7124no—
487C2×#120—7112no—
488#519—711no—
489#519—718no—
490#519—716no—
491#519C2×D7111yescharacteristic, complemented
492C2×C4×Q8—718no—
493C2×C4×D4—7124no—
494C2×#117—716no—
495C25—713no—
4962−1+4—28no—
4972−1+4—14232no—
4982−1+4—14232no—
4992−1+4—14248no—
5002−1+4—1428no—
501C2×#41—28no—
502C2×#41—716no—
503C2×#41—718no—
504C2×#41—714no—
505C2×#41—7112no—
506C2×#41—716no—
507C2×#41—7124no—
508C2×#41—7112no—
509C2×#41—7112no—
510C2×#41—716no—
511C2×#41—7124no—
512C2×#41—7112no—
513C2×#41—14224no—
514C2×#41—14248no—
515C2×#41—14224no—
516C2×#41—14264no—
517C2×#41—14264no—
518C2×#41—14232no—
519C2×#41—1428no—
520C2×#41C22×D7116yes—
521C2×#41C22×D7118yes—
522C2×#41C22×D7114yescomplemented
523C22×Q8—7116no—
524C22×Q8—714no—
525C22×Q8—714no—
526C22×Q8—716no—
527C22×Q8—7112no—
528C22×Q8—714no—
529C22×Q8—713no—
530C22×Q8—7112no—
531C22×Q8—14232no—
532C22×Q8C22×D7111yescharacteristic
533C22×Q8C22×D7114yescomplemented
534C22×D4—7124no—
535C22×D4—716no—
536C22×D4—714no—
537C22×D4—7112no—
538C22×D4—716no—
539C22×D4—7112no—
540C22×D4—713no—
541C22×D4—14224no—
542C22×D4C22×D7113yes—
543C23×C4—713no—
544C23×C4—713no—
545C23×C4—7112no—
546C23×C4—7112no—
547C23×C4—711no—
548C23×C4—713no—
549C23×C4—7112no—
550C23×C4—713no—
551C23×C4—14224no—
552C23×C4C22×D7113yes—
553#127—7112no—
554#127—7112no—
555#127—7148no—
556#127—7112no—
557#127C22×D71112yescomplemented
558#124—7112no—
559#124—7112no—
560#124—7148no—
561#124—7112no—
562#124C22×D71112yescomplemented
563#123—714no—
564#123—714no—
565#123—718no—
566#123—718no—
567#123—714no—
568#123C22×D7114yes—
569C22⋊Q8—7112no—
570C22⋊Q8—7112no—
571C22⋊Q8—7124no—
572C22⋊Q8—7112no—
573C22⋊Q8—7124no—
574C22⋊Q8C22×D71112yescomplemented
575#121—7112no—
576#121—7124no—
577#121—7124no—
578#121—7148no—
579#121—7112no—
580#121—7124no—
581#121—7112no—
582#121—7124no—
583#121—7124no—
584#121—7148no—
585#121C22×D71112yescomplemented
586#121C22×D71124yescomplemented
587#120—7112no—
588#120—7112no—
589#120—7124no—
590#120—7124no—
591#120—7112no—
592#120C22×D71112yes—
593C4×Q8—718no—
594C4×Q8—7124no—
595C4×Q8—7124no—
596C4×Q8C22×D7118yescomplemented
597C4×D4—7124no—
598C4×D4—7124no—
599C4×D4—7124no—
600C4×D4—7124no—
601C4×D4—7124no—
602C4×D4—7124no—
603C4×D4—7124no—
604C4×D4C22×D71124yescomplemented
605#117—716no—
606#117—7112no—
607#117—7112no—
608#117—7112no—
609#117C22×D7116yes—
610C2×C4⋊C4—7112no—
611C2×C4⋊C4—718no—
612C2×C22⋊C4—714no—
613C2×C22⋊C4—718no—
614C2×C22⋊C4—7124no—
615C2×C42—7112no—
616C24—28412no—
617C24—716no—
618C24—713no—
619C24—711no—
620C24—716no—
621C24—714no—
622C24—14212no—
623C24C23×D7113yes—
624#41—232no—
625#41—216no—
626#41—224no—
627#41—14248no—
628#41—14296no—
629#41—14248no—
630#41—14248no—
631#41—14224no—
632#41—14224no—
633#41—14296no—
634#41—14248no—
635#41—14232no—
636#41—14216no—
637#41—14224no—
638C2×Q8—216no—
639C2×Q8—7132no—
640C2×Q8—7132no—
641C2×Q8—7124no—
642C2×Q8—7112no—
643C2×Q8—7112no—
644C2×Q8—716no—
645C2×Q8—14248no—
646C2×Q8—14224no—
647C2×Q8—14248no—
648C2×Q8—14216no—
649C2×Q8D4×D7118yescomplemented
650C2×Q8C23×D7116yes—
651C2×Q8C23×D7114yes—
652C2×D4—212no—
653C2×D4—28448no—
654C2×D4—7124no—
655C2×D4—7124no—
656C2×D4—714no—
657C2×D4—714no—
658C2×D4—7124no—
659C2×D4—7112no—
660C2×D4—7124no—
661C2×D4—714no—
662C2×D4—7112no—
663C2×D4—716no—
664C2×D4—14248no—
665C2×D4—14248no—
666C2×D4—14224no—
667C2×D4—14224no—
668C2×D4—14216no—
669C2×D4—14212no—
670C2×D4C23×D7114yes—
671C2×D4C23×D71112yes—
672C2×D4C23×D7116yes—
673C2×D4C23×D71124yes—
674C22×C4—212no—
675C22×C4—713no—
676C22×C4—7124no—
677C22×C4—716no—
678C22×C4—716no—
679C22×C4—7112no—
680C22×C4—7112no—
681C22×C4—711no—
682C22×C4—718no—
683C22×C4—714no—
684C22×C4—712no—
685C22×C4—7112no—
686C22×C4—7112no—
687C22×C4—7112no—
688C22×C4—7112no—
689C22×C4—712no—
690C22×C4—14212no—
691C22×C4—14248no—
692C22×C4—14248no—
693C22×C4—14248no—
694C22×C4—1424no—
695C22×C4—14212no—
696C22×C4—14212no—
697C22×C4C23×D71112yes—
698C22×C4C23×D71112yes—
699C22×C4C23×D7111yescharacteristic
700C22×C4C23×D7113yes—
701C4⋊C4—7124no—
702C4⋊C4—718no—
703C4⋊C4—718no—
704C4⋊C4—7112no—
705C4⋊C4—718no—
706C4⋊C4C23×D71112yes—
707C4⋊C4C23×D7118yes—
708C22⋊C4—714no—
709C22⋊C4—718no—
710C22⋊C4—7124no—
711C22⋊C4—718no—
712C22⋊C4—718no—
713C22⋊C4—718no—
714C22⋊C4—7124no—
715C22⋊C4—7124no—
716C22⋊C4C23×D7114yes—
717C22⋊C4C23×D7118yes—
718C22⋊C4C23×D71124yes—
719C42—7124no—
720C42—7112no—
721C42C23×D71112yes—
722C23—26no—
723C23—46no—
724C23—2846no—
725C23—28412no—
726C23—28448no—
727C23—711no—
728C23—714no—
729C23—711no—
730C23—716no—
731C23—714no—
732C23—1428no—
733C23—14212no—
734C23—14212no—
735C23—14216no—
736C23—14224no—
737C23—1424no—
738C23—1426no—
739C23C24×D7116yes—
740C23C24×D7114yes—
741C23C24×D7111yescharacteristic
742Q8—212no—
743Q8—7148no—
744Q8—14224no—
745Q8—14212no—
746Q8C2×D4×D71116yes—
747D4—28no—
748D4—224no—
749D4—212no—
750D4—424no—
751D4—28424no—
752D4—28424no—
753D4—28424no—
754D4—1428no—
755D4—14248no—
756D4—14224no—
757D4—1428no—
758D4—1428no—
759D4—14224no—
760D4—14212no—
761C2×C4—22no—
762C2×C4—224no—
763C2×C4—224no—
764C2×C4—7112no—
765C2×C4—716no—
766C2×C4—7124no—
767C2×C4—7124no—
768C2×C4—718no—
769C2×C4—714no—
770C2×C4—712no—
771C2×C4—14224no—
772C2×C4—14224no—
773C2×C4—1424no—
774C2×C4—1424no—
775C2×C4—1428no—
776C2×C4—14216no—
777C2×C4—14224no—
778C2×C4—14224no—
779C2×C4—1422no—
780C2×C4—14224no—
781C2×C4—14224no—
782C2×C4C2×D4×D71112yes—
783C2×C4C24×D7118yes—
784C2×C4C24×D7114yes—
785C2×C4C24×D7112yes—
786C2×C4C24×D7116yes—
787C22—22no—
788C22—24no—
789C22—26no—
790C22—28no—
791C22—212no—
792C22—412no—
793C22—28412no—
794C22—28424no—
795C22—28416no—
796C22—28424no—
797C22—712no—
798C22—714no—
799C22—712no—
800C22—1428no—
801C22—1424no—
802C22—1426no—
803C22—1428no—
804C22—14212no—
805C22—1422no—
806C22C22×D4×D7112yes—
807C22C25×D7111yescharacteristic
808C4—22no—
809C4—24no—
810C4—28no—
811C4—7112no—
812C4—1422no—
813C4—1424no—
814C4—1428no—
815C4C22×D4×D71112yes—
816C2—22no—
817C2—46no—
818C2—44no—
819C2—2846no—
820C2—2844no—
821C2—714no—
822C2—1422no—
823C2C23×D4×D7111yescharacteristic
824C2#585×D7112yes—
subgroupG/H
center, FrattiniC22C25×D71
commutator, socle, cosocleC22×C71C26
FittingC71×#3487C2
hypercenter#3487D71
hypocenterC71C2×#3487
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ #3487

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4×D71C2semidirect
2. C22×#41×D71C2semidirect
3. #22601999C2semidirect
4. #22601998C2semidirect
5. #22601997C2semidirect
6. #22601996C2semidirect
7. #22601995C2semidirect
8. #22601994C2semidirect
9. #22601993C2semidirect
10. #550×D71C2semidirect
11. #548×D71C2semidirect
12. #535×D71C2semidirect
13. #525×D71C2semidirect
14. #519×D71C2semidirect
15. C71×#3487C2semidirect
16. C2×#14556176C22semidirect
17. C2×#14556176C22semidirect
18. C2×#14556175C22semidirect
19. C2×#14556175C22semidirect
21. C22×#11765866C22semidirect
22. C22×#11765865C22semidirect
23. C22×#11765864C22semidirect
27. C2×#41×D71C22semidirect
28. C2×#41×D71C22semidirect
30. C22×Q8×D71C22semidirect
33. #17986671C22semidirect
34. #17986670C22semidirect
35. #17986669C22semidirect
36. #17986668C22semidirect
37. #17986668C22semidirect
38. #17986667C22semidirect
39. #17986667C22semidirect
40. #17986661C22semidirect
41. #17986660C22semidirect
42. #17986659C22semidirect
43. #17986658C22semidirect
44. #17986657C22semidirect
45. #17986656C22semidirect
46. #17986655C22semidirect
47. #17986568C22semidirect
48. #17986567C22semidirect
49. #17986566C22semidirect
50. #17986565C22semidirect
51. #17986564C22semidirect
52. #17986563C22semidirect
53. #17986562C22semidirect
54. #127×D71C22semidirect
55. #124×D71C22semidirect
56. #17986512C22semidirect
57. #17986511C22semidirect
58. #17986510C22semidirect
59. #17986509C22semidirect
60. #17986508C22semidirect
61. #17986507C22semidirect
62. #17986506C22semidirect
63. #17986505C22semidirect
65. C22⋊Q8×D71C22semidirect
66. #121×D71C22semidirect
67. #121×D71C22semidirect
69. #17986477C22semidirect
70. #17986476C22semidirect
71. #17986475C22semidirect
72. C4×Q8×D71C22semidirect
73. C4×D4×D71C22semidirect
75. C2×2−1+4×C71C22semidirect
76. C22×#41×C71C22semidirect
77. #550×C71C22semidirect
78. #548×C71C22semidirect
79. #535×C71C22semidirect
80. #525×C71C22semidirect
81. #519×C71C22semidirect
90. C2×#11765866C23semidirect
95. C2×#11765865C23semidirect
100. C2×#11765864C23semidirect
106. C22×Dic142C23semidirect
108. C2×Q8×D71D4semidirect
112. C2×Q8×D71C23semidirect
113. C2×Q8×D71C23semidirect
131. #14556125C23semidirect
132. #14556124C23semidirect
133. #14556124C23semidirect
134. #14556124C23semidirect
135. #14556117C23semidirect
136. #14556116C23semidirect
137. #14556115C23semidirect
138. #14556114C23semidirect
144. #14556108C23semidirect
145. #14556107C23semidirect
146. #14556106C23semidirect
147. #14556105C23semidirect
148. #14556104C23semidirect
149. #14556103C23semidirect
150. #14556103C23semidirect
151. #14556102C23semidirect
152. #14556102C23semidirect
153. #14556101C23semidirect
154. #14556101C23semidirect
155. #14556100C23semidirect
156. #14556100C23semidirect
157. #14556099C23semidirect
158. #14556099C23semidirect
164. Q8×Dic71C23semidirect
165. C4×Dic142C23semidirect
166. #14556093C23semidirect
167. C4×D284C23semidirect
168. D4×Dic71C23semidirect
169. #14556090C23semidirect
170. C4×C22⋊D71C23semidirect
171. C4×C22⋊D71C23semidirect
172. (C22⋊D71)⋊C4C23semidirect
173. (C22⋊D71)⋊C4C23semidirect
188. C2×#41×C71C23semidirect
190. C22×Q8×C71C23semidirect
193. #127×C71C23semidirect
194. #124×C71C23semidirect
196. C22⋊Q8×C71C23semidirect
197. #121×C71C23semidirect
198. #121×C71C23semidirect
200. C4×Q8×C71C23semidirect
201. C4×D4×C71C23semidirect
222. C2×Dic142C2×D4semidirect
230. Q8×D71C2×D4semidirect
290. C2×Q8×C71C2×D4semidirect
412. D71#3487direct (N × H)
422. #3487D71direct (N × H)
428. C71C2×#3487semidirect
434. C2×2−1+4C2×D71semidirect
443. C22×#41C2×D71semidirect
455. #550C2×D71semidirect
463. #548C2×D71semidirect
471. #535C2×D71semidirect
482. #525C2×D71semidirect
491. #519C2×D71semidirect
522. C2×#41C22×D71semidirect
533. C22×Q8C22×D71semidirect
557. #127C22×D71semidirect
562. #124C22×D71semidirect
574. C22⋊Q8C22×D71semidirect
585. #121C22×D71semidirect
586. #121C22×D71semidirect
596. C4×Q8C22×D71semidirect
604. C4×D4C22×D71semidirect
649. C2×Q8D4×D71semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4×D712
C22×#41×D712
#226019992
#226019982
#226019972
#226019962
#226019952
#226019942
#226019932
#550×D712
#548×D712
#535×D712
#525×D712
#519×D712
C71×#34872
C2×#348771