Finite Group Databasebeta

← #3548×D71 #32905241

Subgroups — #3548×D71 #32905241

Order 18176.

7810 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602740C211yesmaximal, characteristic, complemented
2#22602739C214yesmaximal, complemented
3#22602738C212yesmaximal, complemented
4#22602737C214yesmaximal, complemented
5#22602736C214yesmaximal, complemented
6#22602735C218yesmaximal, complemented
7#22602734C214yesmaximal, complemented
8#22602733C214yesmaximal, complemented
9#562×D71C214yesmaximal, complemented
10#554×D71C214yesmaximal, complemented
11#550×D71C214yesmaximal, complemented
12#547×D71C214yesmaximal, complemented
13#540×D71C214yesmaximal, complemented
14#537×D71C218yesmaximal, complemented
15#533×D71C211yesmaximal, characteristic, complemented
16#532×D71C212yesmaximal, complemented
17C71×#3548C211yesmaximal, characteristic, complemented
18C2×#41×D71C2218yes—
19C2×#41×D71C2214yes—
20#17986747C2214yescomplemented
21#17986746C22116yescomplemented
22#17986745C22116yescomplemented
23#17986744C22116yescomplemented
24#17986743C2218yescomplemented
25#17986710C2214yescomplemented
26#17986709C2214yescomplemented
27#17986708C2218yescomplemented
28#17986707C2218yescomplemented
29#17986706C2214yescomplemented
30#17986705C2218yescomplemented
31#17986704C2218yescomplemented
32#17986703C22116yescomplemented
33#17986671C2214yescomplemented
34#17986670C2218yescomplemented
35#17986670C2214yescomplemented
36#17986669C2218yescomplemented
37#17986669C2214yescomplemented
38#17986668C2218yescomplemented
39#17986667C22116yescomplemented
40#17986667C2218yescomplemented
41#17986654C2214yescomplemented
42#17986653C2214yescomplemented
43#17986652C2214yescomplemented
44#17986651C2218yescomplemented
45#17986650C2218yescomplemented
46#17986649C2218yescomplemented
47#17986648C2218yescomplemented
48#17986647C22116yescomplemented
49#17986605C2214yescomplemented
50#17986604C2214yescomplemented
51#17986603C2214yescomplemented
52#17986602C2218yescomplemented
53#17986601C22116yescomplemented
54#17986600C2218yescomplemented
55#17986599C22116yescomplemented
56#17986580C2218yescomplemented
57#17986579C2218yescomplemented
58#17986579C22116yescomplemented
59#17986579C2218yescomplemented
60#17986578C2218yescomplemented
61#17986578C22116yescomplemented
62#17986578C2218yescomplemented
63#17986577C2218yescomplemented
64#17986577C2218yescomplemented
65#17986576C22116yescomplemented
66#17986576C22116yescomplemented
67#17986556C2211yescharacteristic, complemented
68#17986555C2212yescomplemented
69#17986554C2212yescomplemented
70#17986553C2214yescomplemented
71#17986552C2212yescomplemented
72#17986551C2214yescomplemented
73#17986550C2212yescomplemented
74#17986549C2212yescomplemented
75#17986548C2214yescomplemented
76#17986547C2212yescomplemented
77#17986546C2214yescomplemented
78#17986546C2214yescomplemented
79#17986545C2214yescomplemented
80#17986544C2214yescomplemented
81#17986544C2214yescomplemented
82C4⋊Q8×D71C2212yes—
83C4⋊Q8×D71C2212yes—
84#127×D71C2212yes—
85#127×D71C2214yes—
86#125×D71C2214yes—
87#125×D71C2212yes—
88#124×D71C2214yes—
89#123×D71C22116yes—
90C22⋊Q8×D71C2218yes—
91C22⋊Q8×D71C22116yes—
92C22⋊Q8×D71C2214yes—
93#121×D71C2218yes—
94#121×D71C22116yes—
95#121×D71C2214yes—
96#121×D71C2214yes—
97#121×D71C22116yes—
98C4×Q8×D71C2214yes—
99C4×D4×D71C2214yes—
100C4×D4×D71C2214yes—
101C4×D4×D71C2218yes—
102#117×D71C2212yes—
103C2×C4⋊C4×D71C2218yes—
104C2×C42×D71C2211yescharacteristic
105#562×C71C2214yescomplemented
106#554×C71C2214yescomplemented
107#550×C71C2214yescomplemented
108#547×C71C2214yescomplemented
109#540×C71C2214yescomplemented
110#537×C71C2218yescomplemented
111#533×C71C2211yescharacteristic, complemented
112#532×C71C2212yescomplemented
113C2×#11765866C2314yes—
114C2×#11765866C2318yes—
115C2×#11765865C2318yes—
116C2×#11765865C2318yes—
117C2×#11765865C2314yes—
118C2×#11765865C23116yes—
119C2×#11765864C2314yes—
120C2×#11765864C2318yes—
121C2×#11765864C23116yes—
122C2×#11765864C2318yes—
123#41×D71—416no—
124#41×D71—432no—
125C2×Q8×D71C2314yes—
126C2×Q8×D71C2314yes—
127C2×D4×D71C2314yes—
128C2×D4×D71C2314yes—
129C2×D4×D71C2318yes—
130C2×D4×D71C23116yes—
131C2×D4×D71C2314yes—
132C22×C4×D71C2312yes—
133C22×C4×D71C2318yes—
134C22×C4×D71C2311yescharacteristic
135C22×C4×D71C23116yes—
136#14556128C2312yes—
137#14556128C2312yes—
138#14556127C2314yes—
139#14556127C2314yes—
140#14556127C2314yes—
141#14556127C2314yes—
142#14556126C2314yes—
143#14556126C2314yes—
144#14556125C2314yes—
145#14556125C2312yes—
146#14556124C23116yes—
147#14556124C2318yes—
148#14556124C2314yes—
149#14556124C2314yes—
150#14556124C2314yes—
151#14556120C2314yes—
152#14556120C2312yes—
153#14556119C2318yes—
154#14556119C2314yes—
155#14556118C23116yes—
156#14556118C2318yes—
157#14556117C2314yes—
158#14556116C2314yes—
159#14556115C2314yes—
160#14556114C2318yes—
161#14556114C2318yes—
162#14556113C23116yes—
163#14556113C23116yes—
164#14556112C23116yes—
165#14556111C23116yes—
166#14556110C23116yes—
167#14556110C23116yes—
168#14556109C23116yes—
169#14556108C2314yes—
170#14556108C2318yes—
171#14556108C23116yes—
172#14556107C2314yes—
173#14556107C2318yes—
174#14556107C23116yes—
175#14556106C2318yes—
176#14556106C23116yes—
177#14556106C23116yes—
178#14556106C23116yes—
179#14556105C2318yes—
180#14556105C23116yes—
181#14556105C23116yes—
182#14556105C23116yes—
183#14556104C2314yes—
184#14556104C2318yes—
185#14556104C23116yes—
186#14556103C23116yes—
187#14556103C2314yes—
188#14556103C23116yes—
189#14556103C2318yes—
190#14556103C2314yes—
191#14556102C23116yes—
192#14556102C23116yes—
193#14556102C2314yes—
194#14556102C2318yes—
195#14556102C2314yes—
196#14556101C2318yes—
197#14556101C23116yes—
198#14556101C23116yes—
199#14556101C23116yes—
200#14556101C23116yes—
201#14556101C23116yes—
202#14556101C2318yes—
203#14556100C23116yes—
204#14556100C23116yes—
205#14556100C2318yes—
206#14556100C23116yes—
207#14556100C23116yes—
208#14556100C23116yes—
209#14556100C2318yes—
210#14556099C2314yes—
211#14556099C23116yes—
212#14556099C2318yes—
213#14556099C23116yes—
214#14556099C2314yes—
215Q8×Dic71C2314yes—
216C4×Dic142C2318yes—
217C4×Dic142C2314yes—
218#14556093C2318yes—
219#14556093C2314yes—
220C4×D284C2318yes—
221C4×D284C2314yes—
222C4×D284C2314yes—
223D4×Dic71C2318yes—
224D4×Dic71C2314yes—
225D4×Dic71C2314yes—
226#14556090C2318yes—
227#14556090C2314yes—
228#14556090C2314yes—
229C4×C22⋊D71C23116yes—
230C4×C22⋊D71C2318yes—
231C4×C22⋊D71C2318yes—
232(C22⋊D71)⋊C4C23116yes—
233(C22⋊D71)⋊C4C2318yes—
234(C22⋊D71)⋊C4C2318yes—
235#14556087C2312yes—
236#14556086C2314yes—
237#14556085C2314yes—
238#14556084C2314yes—
239C2×C4⋊Dic71C2318yes—
240C2×Dic71⋊C4C23116yes—
241C4⋊C4×D71C23116yes—
242C4⋊C4×D71C2318yes—
243C4⋊C4×D71C2318yes—
244C4⋊C4×D71C2314yes—
245C4⋊C4×D71C2314yes—
246C4⋊C4×D71C23116yes—
247C4⋊C4×D71C2314yes—
248C4⋊C4×D71C2314yes—
249C4⋊C4×D71C2318yes—
250C22⋊C4×D71C2314yes—
251C22⋊C4×D71C23116yes—
252C22⋊C4×D71C2318yes—
253C22⋊C4×D71C2318yes—
254C2×C4×Dic71C2311yescharacteristic
255C2×C4×Dic71C2312yes—
256C42×D71C2311yescharacteristic
257C42×D71C2312yes—
258C42×D71C2311yescharacteristic
259C42×D71C2311yescharacteristic
260C42×D71C2312yes—
261C42×D71C2311yescharacteristic
262C42×D71C2314yes—
263C2×#41×C71C2314yes—
264C2×#41×C71C2318yes—
265C4⋊Q8×C71C2312yes—
266C4⋊Q8×C71C2312yes—
267#127×C71C2314yes—
268#127×C71C2312yes—
269#125×C71C2314yes—
270#125×C71C2312yes—
271#124×C71C2314yes—
272#123×C71C23116yes—
273C22⋊Q8×C71C2314yes—
274C22⋊Q8×C71C2318yes—
275C22⋊Q8×C71C23116yes—
276#121×C71C23116yes—
277#121×C71C23116yes—
278#121×C71C2314yes—
279#121×C71C2318yes—
280#121×C71C2314yes—
281C4×Q8×C71C2314yes—
282C4×D4×C71C2318yes—
283C4×D4×C71C2314yes—
284C4×D4×C71C2314yes—
285#117×C71C2312yes—
286C2×C4⋊C4×C71C2318yes—
287C2×C42×C71C2311yescharacteristic
288C23×D71C2411yescharacteristic
289C23×D71C2418yes—
290#11765866—48no—
291#11765866—416no—
292#11765865—432no—
293#11765865—416no—
294#11765865—48no—
295#11765865—416no—
296#11765864—416no—
297#11765864—432no—
298#11765864—48no—
299#11765864—416no—
300C2×Dic142C2418yes—
301C2×Dic142C2414yes—
302C2×Dic142C2414yes—
303C2×Dic142C2418yes—
304Q8×D71—216no—
305Q8×D71—48no—
306C2×D284C2414yes—
307C2×D284C2414yes—
308C2×D284C2418yes—
309C2×D284C2414yes—
310C2×D284C24116yes—
311C2×C22⋊D71C2418yes—
312C2×C22⋊D71C2418yes—
313C2×C22⋊D71C2418yes—
314C2×C22⋊D71C2418yes—
315C2×C22⋊D71C24116yes—
316C2×C22⋊D71C2418yes—
317C2×C22⋊D71C24116yes—
318D4×D71—216no—
319D4×D71—216no—
320D4×D71—416no—
321D4×D71—48no—
322D4×D71—432no—
323C22×Dic71C2412yes—
324C22×Dic71C2418yes—
325C22×Dic71C2411yescharacteristic
326C22×Dic71C24116yes—
327C2×C4×D71—232no—
328C2×C4×D71—28no—
329C2×C4×D71—24no—
330C2×C4×D71—432no—
331C2×C4×D71C2418yes—
332C2×C4×D71C2418yes—
333C2×C4×D71C2412yes—
334C2×C4×D71C2412yes—
335C2×C4×D71C2418yes—
336C2×C4×D71C2418yes—
337C2×C4×D71C2412yes—
338C2×C4×D71C2411yescharacteristic
339C2×C4×D71C2411yescharacteristic
340C2×C4×D71C2411yescharacteristic
341C2×C4×D71C24116yes—
342C2×C4×D71C24116yes—
343C2×C4×D71C2412yes—
344C2×C4×D71C2411yescharacteristic
345C4⋊Dic71C2414yes—
346C4⋊Dic71C2414yes—
347C4⋊Dic71C24116yes—
348C4⋊Dic71C2414yes—
349C4⋊Dic71C2414yes—
350C4⋊Dic71C2418yes—
351Dic71⋊C4C2418yes—
352Dic71⋊C4C2418yes—
353Dic71⋊C4C24116yes—
354Dic71⋊C4C24116yes—
355Dic71⋊C4C2418yes—
356Dic71⋊C4C2418yes—
357Dic71⋊C4C2418yes—
358Dic71⋊C4C2418yes—
359C22⋊Dic71C2414yes—
360C22⋊Dic71C24116yes—
361C22⋊Dic71C2418yes—
362C22⋊Dic71C2418yes—
363(C2×D71)⋊C4C2418yes—
364(C2×D71)⋊C4C2418yes—
365(C2×D71)⋊C4C24116yes—
366(C2×D71)⋊C4C2418yes—
367(C2×D71)⋊C4C24116yes—
368(C2×D71)⋊C4C2418yes—
369(C2×D71)⋊C4C2418yes—
370C4×Dic71C2411yescharacteristic
371C4×Dic71C2412yes—
372C4×Dic71C2412yes—
373C4×Dic71C2412yes—
374C4×Dic71C2412yes—
375C4×Dic71C2411yescharacteristic
376C4×Dic71C2412yes—
377C4×Dic71C2418yes—
378C4×Dic71C2414yes—
379#41×C71—48no—
380#41×C71—416no—
381C2×Q8×C71C2414yes—
382C2×Q8×C71C2414yes—
383C2×D4×C71C2414yes—
384C2×D4×C71C2414yes—
385C2×D4×C71C2418yes—
386C2×D4×C71C24116yes—
387C2×D4×C71C2414yes—
388C22×C4×C71C2412yes—
389C22×C4×C71C2418yes—
390C22×C4×C71C2411yescharacteristic
391C22×C4×C71C24116yes—
392C4⋊C4×C71C2414yes—
393C4⋊C4×C71C2414yes—
394C4⋊C4×C71C24116yes—
395C4⋊C4×C71C2414yes—
396C4⋊C4×C71C2414yes—
397C4⋊C4×C71C2418yes—
398C22⋊C4×C71C2414yes—
399C22⋊C4×C71C24116yes—
400C22⋊C4×C71C2418yes—
401C22⋊C4×C71C2418yes—
402C42×C71C2411yescharacteristic
403C42×C71C2412yes—
404C42×C71C2411yescharacteristic
405C42×C71C2414yes—
406C23×C71C2511yescharacteristic
407C23×C71C2518yes—
408C22×D71—216no—
409C22×D71—24no—
410C22×D71—216no—
411C22×D71—22no—
412C22×D71—216no—
413C22×D71C2511yescharacteristic
414C22×D71C2518yes—
415C22×D71C2511yescharacteristic
416Q8×C71—28no—
417Q8×C71—44no—
418D4×C71—28no—
419D4×C71—28no—
420D4×C71—416no—
421D4×C71—44no—
422D4×C71—48no—
423C2×C4×C71—24no—
424C2×C4×C71—216no—
425C2×C4×C71—22no—
426C2×C4×C71—416no—
427C2×C4×C71C2511yescharacteristic
428C2×C4×C71C2512yes—
429C2×C4×C71C2518yes—
430C2×C4×C71C2518yes—
431C2×C4×C71C2512yes—
432C2×C4×C71C2511yescharacteristic
433C22⋊D71—216no—
434C22⋊D71—216no—
435C22⋊D71—416no—
436C22⋊D71—416no—
437C22⋊D71—48no—
438C22⋊D71—48no—
439C22⋊D71—48no—
440C2×Dic71—24no—
441C2×Dic71—216no—
442C2×Dic71—22no—
443C2×Dic71—416no—
444C2×Dic71C2511yescharacteristic
445C2×Dic71C2512yes—
446C2×Dic71C2518yes—
447C2×Dic71C2518yes—
448C2×Dic71C2512yes—
449C2×Dic71C2511yescharacteristic
450D284—28no—
451D284—28no—
452D284—416no—
453D284—44no—
454D284—48no—
455C4×D71—216no—
456C4×D71—24no—
457C4×D71—216no—
458C4×D71—22no—
459C4×D71—216no—
460C4×D71—24no—
461C4×D71—22no—
462C4×D71—24no—
463C4×D71—216no—
464C4×D71—22no—
465C4×D71—416no—
466C4×D71—416no—
467C4×D71H(5,𝔽2)18yes—
468C4×D712−1+414yes—
469Dic142—28no—
470Dic142—216no—
471Dic142—48no—
472Dic142—44no—
473C22×C71—22no—
474C22×C71—28no—
475C22×C71—28no—
476C22×C71—21no—
477C22×C71—28no—
478C22×C71C2611yescharacteristic
479C2×D71—28no—
480C2×D71—22no—
481C2×D71—28no—
482C2×D71—21no—
483C2×D71—28no—
484C2×D71—44no—
485C2×D71—432no—
486C2×D71C2×H(5,𝔽2)14yes—
487C2×D71C2×2−1+412yes—
488C4×C71—28no—
489C4×C71—22no—
490C4×C71—28no—
491C4×C71—21no—
492C4×C71C2×H(5,𝔽2)14yes—
493C4×C71C2×2−1+412yes—
494Dic71—28no—
495Dic71—22no—
496Dic71—28no—
497Dic71—21no—
498Dic71C2×H(5,𝔽2)14yes—
499Dic71C2×2−1+412yes—
500C2×#3548—711nomaximal, Sylow
501C2×C71—41no—
502C2×C71—48no—
503C2×C71C22×H(5,𝔽2)12yes—
504C2×C71C22×2−1+411yescharacteristic
505D71—41no—
506D71—48no—
507D71#354814yesdirect product factor
508#3548—714no—
509#3548—714no—
510#3548—714no—
511#3548—714no—
512#3548—714no—
513#3548—718no—
514#3548—711no—
515#3548—712no—
516#3548D7111yescharacteristic, direct product factor
517C2×#562—714no—
518C2×#554—714no—
519C2×#550—714no—
520C2×#547—714no—
521C2×#540—714no—
522C2×#537—718no—
523C2×#533—711no—
524C2×#532—712no—
525C71C2×#354811yescharacteristic, complemented, Sylow
526C22×#41—714no—
527C22×#41—718no—
528#562—714no—
529#562—718no—
530#562—7116no—
531#562—7116no—
532#562—7116no—
533#562C2×D7114yescomplemented
534#554—714no—
535#554—718no—
536#554—7116no—
537#554—718no—
538#554—714no—
539#554—714no—
540#554—718no—
541#554—718no—
542#554C2×D7114yescomplemented
543#550—718no—
544#550—718no—
545#550—714no—
546#550—718no—
547#550—7116no—
548#550—714no—
549#550—718no—
550#550—714no—
551#550C2×D7114yescomplemented
552#547—718no—
553#547—714no—
554#547—7116no—
555#547—718no—
556#547—718no—
557#547—714no—
558#547—714no—
559#547—718no—
560#547C2×D7114yescomplemented
561#540—714no—
562#540—714no—
563#540—7116no—
564#540—7116no—
565#540—718no—
566#540—718no—
567#540—714no—
568#540C2×D7114yescomplemented
569#537—718no—
570#537—718no—
571#537—718no—
572#537—7116no—
573#537—718no—
574#537—7116no—
575#537—7116no—
576#537—718no—
577#537—7116no—
578#537—718no—
579#537—718no—
580#537C2×D7118yescomplemented
581#533—712no—
582#533—712no—
583#533—714no—
584#533—714no—
585#533—712no—
586#533—711no—
587#533C2×D7111yescharacteristic, complemented
588#532—714no—
589#532—712no—
590#532—712no—
591#532—714no—
592#532—714no—
593#532—714no—
594#532—714no—
595#532—714no—
596#532—712no—
597#532C2×D7112yescomplemented
598C2×C4⋊Q8—712no—
599C2×C4⋊Q8—712no—
600C2×#127—712no—
601C2×#127—714no—
602C2×#125—712no—
603C2×#125—714no—
604C2×#124—714no—
605C2×#123—7116no—
606C2×C22⋊Q8—714no—
607C2×C22⋊Q8—718no—
608C2×C22⋊Q8—7116no—
609C2×#121—714no—
610C2×#121—714no—
611C2×#121—7116no—
612C2×#121—718no—
613C2×#121—7116no—
614C2×C4×Q8—714no—
615C2×C4×D4—714no—
616C2×C4×D4—714no—
617C2×C4×D4—718no—
618C2×#117—712no—
619C22×C4⋊C4—718no—
620C22×C42—711no—
621C2×#41—28432no—
622C2×#41—28416no—
623C2×#41—714no—
624C2×#41—718no—
625C2×#41—718no—
626C2×#41—714no—
627C2×#41—718no—
628C2×#41—7116no—
629C2×#41—718no—
630C2×#41—714no—
631C2×#41—718no—
632C2×#41—7116no—
633C2×#41C22×D7114yes—
634C2×#41C22×D7118yes—
635C22×Q8—714no—
636C22×Q8—714no—
637C22×D4—718no—
638C22×D4—7116no—
639C22×D4—714no—
640C22×D4—714no—
641C22×D4—714no—
642C23×C4—7116no—
643C23×C4—718no—
644C23×C4—711no—
645C23×C4—712no—
646C4⋊Q8—714no—
647C4⋊Q8—714no—
648C4⋊Q8—714no—
649C4⋊Q8—714no—
650C4⋊Q8—714no—
651C4⋊Q8—714no—
652C4⋊Q8—712no—
653C4⋊Q8—712no—
654C4⋊Q8C22×D7112yes—
655C4⋊Q8C22×D7112yes—
656#127—714no—
657#127—714no—
658#127—714no—
659#127—718no—
660#127—7116no—
661#127—712no—
662#127—714no—
663#127C22×D7112yes—
664#127C22×D7114yes—
665#125—718no—
666#125—714no—
667#125—7116no—
668#125—718no—
669#125—712no—
670#125—714no—
671#125C22×D7112yes—
672#125C22×D7114yes—
673#124—714no—
674#124—714no—
675#124—718no—
676#124—718no—
677#124—714no—
678#124C22×D7114yes—
679#123—7116no—
680#123—7116no—
681#123—7116no—
682#123—7116no—
683#123—7116no—
684#123—7116no—
685#123—7116no—
686#123C22×D71116yes—
687C22⋊Q8—714no—
688C22⋊Q8—718no—
689C22⋊Q8—7116no—
690C22⋊Q8—714no—
691C22⋊Q8—718no—
692C22⋊Q8—7116no—
693C22⋊Q8—718no—
694C22⋊Q8—714no—
695C22⋊Q8—7116no—
696C22⋊Q8—718no—
697C22⋊Q8—7116no—
698C22⋊Q8—7116no—
699C22⋊Q8—7116no—
700C22⋊Q8—718no—
701C22⋊Q8—7116no—
702C22⋊Q8—7116no—
703C22⋊Q8—7116no—
704C22⋊Q8C22×D7114yes—
705C22⋊Q8C22×D7118yes—
706C22⋊Q8C22×D71116yes—
707#121—714no—
708#121—718no—
709#121—714no—
710#121—718no—
711#121—7116no—
712#121—7116no—
713#121—7116no—
714#121—718no—
715#121—7116no—
716#121—7116no—
717#121—7116no—
718#121—7116no—
719#121—714no—
720#121—714no—
721#121—7116no—
722#121—718no—
723#121—7116no—
724#121—714no—
725#121—714no—
726#121—7116no—
727#121—718no—
728#121—7116no—
729#121—718no—
730#121—718no—
731#121—7116no—
732#121—7116no—
733#121—7116no—
734#121—7116no—
735#121—7116no—
736#121C22×D7114yes—
737#121C22×D7114yes—
738#121C22×D71116yes—
739#121C22×D7118yes—
740#121C22×D71116yes—
741C4×Q8—714no—
742C4×Q8—718no—
743C4×Q8—714no—
744C4×Q8—718no—
745C4×Q8—714no—
746C4×Q8C22×D7114yes—
747C4×D4—714no—
748C4×D4—714no—
749C4×D4—718no—
750C4×D4—718no—
751C4×D4—718no—
752C4×D4—7116no—
753C4×D4—714no—
754C4×D4—714no—
755C4×D4—718no—
756C4×D4—718no—
757C4×D4—718no—
758C4×D4—7116no—
759C4×D4—714no—
760C4×D4—714no—
761C4×D4—718no—
762C4×D4C22×D7114yes—
763C4×D4C22×D7114yes—
764C4×D4C22×D7118yes—
765#117—712no—
766#117—714no—
767#117—714no—
768#117—714no—
769#117C22×D7112yes—
770C2×C4⋊C4—7116no—
771C2×C4⋊C4—718no—
772C2×C4⋊C4—714no—
773C2×C4⋊C4—714no—
774C2×C4⋊C4—7116no—
775C2×C4⋊C4—7116no—
776C2×C4⋊C4—718no—
777C2×C4⋊C4—718no—
778C2×C4⋊C4—714no—
779C2×C4⋊C4—714no—
780C2×C4⋊C4—718no—
781C2×C4⋊C4C22×D7118yes—
782C2×C22⋊C4—714no—
783C2×C22⋊C4—7116no—
784C2×C22⋊C4—718no—
785C2×C22⋊C4—718no—
786C2×C42—712no—
787C2×C42—711no—
788C2×C42—714no—
789C2×C42—711no—
790C2×C42—712no—
791C2×C42—711no—
792C2×C42—711no—
793C2×C42—712no—
794C2×C42—711no—
795C2×C42C22×D7111yescharacteristic
796C24—718no—
797C24—711no—
798#41—48no—
799#41—416no—
800#41—28416no—
801#41—28416no—
802#41—2848no—
803#41—28432no—
804#41—28416no—
805#41—28432no—
806#41—28416no—
807#41—28416no—
808#41—2848no—
809#41—2848no—
810C2×Q8—2848no—
811C2×Q8—718no—
812C2×Q8—714no—
813C2×Q8—718no—
814C2×Q8—714no—
815C2×Q8—14216no—
816C2×Q8C23×D7114yes—
817C2×Q8C23×D7114yes—
818C2×D4—28416no—
819C2×D4—28432no—
820C2×D4—2848no—
821C2×D4—718no—
822C2×D4—718no—
823C2×D4—7116no—
824C2×D4—7116no—
825C2×D4—718no—
826C2×D4—718no—
827C2×D4—718no—
828C2×D4—718no—
829C2×D4—7116no—
830C2×D4—714no—
831C2×D4—714no—
832C2×D4—714no—
833C2×D4—14216no—
834C2×D4—14216no—
835C2×D4C23×D7114yes—
836C2×D4C23×D7114yes—
837C2×D4C23×D7118yes—
838C2×D4C23×D71116yes—
839C2×D4C23×D7114yes—
840C22×C4—28432no—
841C22×C4—7116no—
842C22×C4—7116no—
843C22×C4—7116no—
844C22×C4—711no—
845C22×C4—712no—
846C22×C4—711no—
847C22×C4—712no—
848C22×C4—718no—
849C22×C4—711no—
850C22×C4—712no—
851C22×C4—711no—
852C22×C4—711no—
853C22×C4—712no—
854C22×C4—712no—
855C22×C4—718no—
856C22×C4—718no—
857C22×C4—718no—
858C22×C4—718no—
859C22×C4—1424no—
860C22×C4—14232no—
861C22×C4—1428no—
862C22×C4C23×D7111yescharacteristic
863C22×C4C23×D7112yes—
864C22×C4C23×D7118yes—
865C22×C4C23×D71116yes—
866C4⋊C4—718no—
867C4⋊C4—718no—
868C4⋊C4—7116no—
869C4⋊C4—7116no—
870C4⋊C4—718no—
871C4⋊C4—718no—
872C4⋊C4—718no—
873C4⋊C4—718no—
874C4⋊C4—714no—
875C4⋊C4—714no—
876C4⋊C4—7116no—
877C4⋊C4—714no—
878C4⋊C4—714no—
879C4⋊C4—718no—
880C4⋊C4C23×D7114yes—
881C4⋊C4C23×D7114yes—
882C4⋊C4C23×D71116yes—
883C4⋊C4C23×D7114yes—
884C4⋊C4C23×D7114yes—
885C4⋊C4C23×D7118yes—
886C22⋊C4—714no—
887C22⋊C4—7116no—
888C22⋊C4—718no—
889C22⋊C4—718no—
890C22⋊C4—718no—
891C22⋊C4—7116no—
892C22⋊C4—7116no—
893C22⋊C4—718no—
894C22⋊C4—718no—
895C22⋊C4—718no—
896C22⋊C4—718no—
897C22⋊C4C23×D7114yes—
898C22⋊C4C23×D71116yes—
899C22⋊C4C23×D7118yes—
900C22⋊C4C23×D7118yes—
901C42—711no—
902C42—712no—
903C42—712no—
904C42—712no—
905C42—712no—
906C42—712no—
907C42—711no—
908C42—718no—
909C42—714no—
910C42C23×D7111yescharacteristic
911C42C23×D7112yes—
912C42C23×D7111yescharacteristic
913C42C23×D7114yes—
914C23—711no—
915C23—718no—
916C23—711no—
917C23—14216no—
918C23—14216no—
919C23—1424no—
920C23—1422no—
921C23—14216no—
922C23C24×D7111yescharacteristic
923C23C24×D7118yes—
924Q8—28no—
925Q8—44no—
926Q8—2848no—
927Q8—2844no—
928Q8—14216no—
929Q8—1428no—
930D4—28no—
931D4—28no—
932D4—48no—
933D4—44no—
934D4—416no—
935D4—2848no—
936D4—2844no—
937D4—28416no—
938D4—2848no—
939D4—2848no—
940D4—28416no—
941D4—28416no—
942D4—2848no—
943D4—14216no—
944D4—14216no—
945D4—1428no—
946D4—1428no—
947C2×C4—216no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—416no—
951C2×C4—28416no—
952C2×C4—28416no—
953C2×C4—28416no—
954C2×C4—711no—
955C2×C4—712no—
956C2×C4—718no—
957C2×C4—714no—
958C2×C4—711no—
959C2×C4—712no—
960C2×C4—718no—
961C2×C4—718no—
962C2×C4—14216no—
963C2×C4—1424no—
964C2×C4—1422no—
965C2×C4—14216no—
966C2×C4—14216no—
967C2×C4—1424no—
968C2×C4—1422no—
969C2×C4—14216no—
970C2×C4—1424no—
971C2×C4—1422no—
972C2×C4—14216no—
973C2×C4—1424no—
974C2×C4—1422no—
975C2×C4C24×D7111yescharacteristic
976C2×C4C24×D7112yes—
977C2×C4C24×D7118yes—
978C2×C4C24×D7118yes—
979C2×C4C24×D7112yes—
980C2×C4C24×D7111yescharacteristic
981C22—22no—
982C22—28no—
983C22—28no—
984C22—21no—
985C22—28no—
986C22—28432no—
987C22—2844no—
988C22—714no—
989C22—712no—
990C22—1428no—
991C22—1428no—
992C22—1422no—
993C22—1421no—
994C22—1428no—
995C22C25×D7111yescharacteristic
996C4—28no—
997C4—22no—
998C4—28no—
999C4—21no—
1000C4—714no—
1001C4—712no—
1002C4—1428no—
1003C4—1428no—
1004C4—1422no—
1005C4—1421no—
1006C4H(5,𝔽2)×D7114yes—
1007C42−1+4×D7112yes—
1008C2—41no—
1009C2—48no—
1010C2—2848no—
1011C2—2841no—
1012C2—714no—
1013C2C2×H(5,𝔽2)×D7112yes—
1014C2C2×2−1+4×D7111yescharacteristic
subgroupG/H
center, FrattiniC22C25×D71
commutator, socle, cosocleC22×C71C26
FittingC71×#3548C2
hypercenter#3548D71
hypocenterC71C2×#3548
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ #3548

Complements

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

NH ≅ G/Ntype
1. #22602740C2semidirect
2. #22602739C2semidirect
3. #22602738C2semidirect
4. #22602737C2semidirect
5. #22602736C2semidirect
6. #22602735C2semidirect
7. #22602734C2semidirect
8. #22602733C2semidirect
9. #562×D71C2semidirect
10. #554×D71C2semidirect
11. #550×D71C2semidirect
12. #547×D71C2semidirect
13. #540×D71C2semidirect
14. #537×D71C2semidirect
15. #533×D71C2semidirect
16. #532×D71C2semidirect
17. C71×#3548C2semidirect
20. #17986747C22semidirect
21. #17986746C22semidirect
22. #17986745C22semidirect
23. #17986744C22semidirect
24. #17986743C22semidirect
25. #17986710C22semidirect
26. #17986709C22semidirect
27. #17986708C22semidirect
28. #17986707C22semidirect
29. #17986706C22semidirect
30. #17986705C22semidirect
31. #17986704C22semidirect
32. #17986703C22semidirect
33. #17986671C22semidirect
34. #17986670C22semidirect
35. #17986670C22semidirect
36. #17986669C22semidirect
37. #17986669C22semidirect
38. #17986668C22semidirect
39. #17986667C22semidirect
40. #17986667C22semidirect
41. #17986654C22semidirect
42. #17986653C22semidirect
43. #17986652C22semidirect
44. #17986651C22semidirect
45. #17986650C22semidirect
46. #17986649C22semidirect
47. #17986648C22semidirect
48. #17986647C22semidirect
49. #17986605C22semidirect
50. #17986604C22semidirect
51. #17986603C22semidirect
52. #17986602C22semidirect
53. #17986601C22semidirect
54. #17986600C22semidirect
55. #17986599C22semidirect
56. #17986580C22semidirect
57. #17986579C22semidirect
58. #17986579C22semidirect
59. #17986579C22semidirect
60. #17986578C22semidirect
61. #17986578C22semidirect
62. #17986578C22semidirect
63. #17986577C22semidirect
64. #17986577C22semidirect
65. #17986576C22semidirect
66. #17986576C22semidirect
67. #17986556C22semidirect
68. #17986555C22semidirect
69. #17986554C22semidirect
70. #17986553C22semidirect
71. #17986552C22semidirect
72. #17986551C22semidirect
73. #17986550C22semidirect
74. #17986549C22semidirect
75. #17986548C22semidirect
76. #17986547C22semidirect
77. #17986546C22semidirect
78. #17986546C22semidirect
79. #17986545C22semidirect
80. #17986544C22semidirect
81. #17986544C22semidirect
105. #562×C71C22semidirect
106. #554×C71C22semidirect
107. #550×C71C22semidirect
108. #547×C71C22semidirect
109. #540×C71C22semidirect
110. #537×C71C22semidirect
111. #533×C71C22semidirect
112. #532×C71C22semidirect
507. D71#3548direct (N × H)
516. #3548D71direct (N × H)
525. C71C2×#3548semidirect
533. #562C2×D71semidirect
542. #554C2×D71semidirect
551. #550C2×D71semidirect
560. #547C2×D71semidirect
568. #540C2×D71semidirect
580. #537C2×D71semidirect
587. #533C2×D71semidirect
597. #532C2×D71semidirect

Maximal subgroups

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

subgroupindex
#226027402
#226027392
#226027382
#226027372
#226027362
#226027352
#226027342
#226027332
#562×D712
#554×D712
#550×D712
#547×D712
#540×D712
#537×D712
#533×D712
#532×D712
C71×#35482
C2×#354871