Finite Group Databasebeta

← #32882469

Subgroups — #32882469

Order 18176.

2258 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986645C211yesmaximal, characteristic, complemented
2#22600550C214yesmaximal, complemented
3#22600535C214yesmaximal, complemented
4#22599972C214yesmaximal, complemented
5#22599947C214yesmaximal, complemented
6#22599301C212yesmaximal, complemented
7#22599166C212yesmaximal, complemented
8#22599142C211yesmaximal, characteristic, complemented
9#22599137C211yesmaximal, characteristic, complemented
10#22598383C212yesmaximal, complemented
11#22597598C211yesmaximal, characteristic, complemented
12#22597590C211yesmaximal, characteristic, complemented
13#22597566C212yesmaximal, complemented
14#22597381C211yesmaximal, characteristic, complemented
15C71×#3505C211yesmaximal, characteristic, complemented
16C22×#11765865C2211yescharacteristic
17C23×D284C2211yescharacteristic, complemented
18C2×#14556159C2212yescomplemented
19C2×#14556154C2212yescomplemented
20C2×#14556153C2214yescomplemented
21#17986645—22no—
22#17986645—22no—
23#17986645C2214yes—
24#17986645C2214yescomplemented
25C2×#14556116C2211yescharacteristic, complemented
26C2×#14556113—21no—
27C2×#14556107C2211yescharacteristic, complemented
28C2×#14556102C2211yescharacteristic
29C2×#14556101—21no—
30C2×#14556096—21no—
31C2×C4×D284C2211yescharacteristic, complemented
32C2×C22⋊C4×D71—21no—
33#17986381C2214yescomplemented
34#17986356C2214yescomplemented
35#17986340C2214yescomplemented
36#17986332C2212yescomplemented
37#17986317C2212yescomplemented
38#17986315C2212yescomplemented
39#17986312C2212yescomplemented
40#17986296C2214yescomplemented
41#17986255C2214yescomplemented
42#17986250C2214yescomplemented
43#17986247C2214yescomplemented
44#17986243C2214yescomplemented
45#17986221C2214yescomplemented
46#17986214C2214yescomplemented
47#17986211C2214yescomplemented
48#17986161C2214yescomplemented
49#17986159C2214yescomplemented
50#17986154C2212yescomplemented
51#17986149C2214yescomplemented
52#17986149C2212yescomplemented
53#17986149C2212yescomplemented
54#17986142C2214yescomplemented
55#17986138C2212yescomplemented
56#17986137C2212yescomplemented
57#17986133C2212yescomplemented
58#17986132C2212yes—
59#17986132C2212yes—
60#17986132C2214yescomplemented
61C4×#11765852C2214yescomplemented
62C4×#11765850C2214yescomplemented
63#17986077C2214yescomplemented
64#17986077C2214yescomplemented
65#17986052C2212yescomplemented
66#17986003C2214yescomplemented
67#17985998C2212yescomplemented
68#17985998C2212yescomplemented
69#17985963C2212yescomplemented
70#17985963C2211yescharacteristic, complemented
71#17985963C2211yescharacteristic, complemented
72#553×C71—22no—
73#553×C71C2212yescomplemented
74#552×C71C2212yescomplemented
75#551×C71—22no—
76#548×C71C2212yescomplemented
77#546×C71C2212yescomplemented
78#539×C71—21no—
79#538×C71—21no—
80#534×C71—21no—
81#529×C71C2212yescomplemented
82#525×C71C2212yes—
83C2×C22⋊Q8×C71C2211yescharacteristic, complemented
84C2×#121×C71C2211yescharacteristic, complemented
85#518×C71—21no—
86C2×C4×D4×C71C2211yescharacteristic
87C24×D71—21no—
88C2×#11765865—21no—
89C2×#11765865—21no—
90C2×#11765865—44no—
91C2×#11765865C2312yes—
92C2×#11765865C2312yes—
93C22×Dic142C2311yescharacteristic
94C22×D284—22no—
95C22×D284—21no—
96C22×D284—44no—
97C22×D284C2311yescharacteristic
98C22×D284C2314yes—
99C22×D284C2311yescharacteristic
100C22×C22⋊D71—21no—
101C22×C22⋊D71—21no—
102C22×C4×D71—21no—
103C22×C4×D71—21no—
104#14556159—44no—
105#14556154—44no—
106#14556153—48no—
107C2×#11765855C2314yescomplemented
108C2×#11765853C2314yescomplemented
109C2×#11765852C2314yes—
110C2×#11765852C2314yes—
111C2×#11765850C2314yes—
112C2×#11765850C2314yes—
113C2×#11765849C2314yes—
114C2×#11765849C2312yescomplemented
115C2×#11765849C2312yescomplemented
116#14556116—22no—
117#14556116C2314yes—
118#14556113—24no—
119#14556113—24no—
120#14556107—22no—
121#14556107C2314yes—
122#14556102—21no—
123#14556102—21no—
124#14556102C2312yes—
125#14556102C2312yes—
126#14556101—24no—
127#14556101—24no—
128#14556096—24no—
129#14556096—24no—
130C4×D284—22no—
131C4×D284C2314yes—
132C2×C4⋊Dic71C2311yescharacteristic
133C2×Dic71⋊C4—21no—
134C2×C22⋊Dic71—21no—
135C2×(C2×D71)⋊C4—21no—
136C2×(C2×D71)⋊C4—21no—
137C2×(C2×D71)⋊C4—21no—
138C2×(C2×D71)⋊C4—21no—
139C22⋊C4×D71—24no—
140C22⋊C4×D71—24no—
141#14556061C2314yescomplemented
142#14556059C2314yescomplemented
143C4⋊(C71⋊C8)C2314yescomplemented
144#14556052C2314yescomplemented
145#14556051C2314yescomplemented
146#14556051C2314yescomplemented
147#14556049C2314yescomplemented
148#14556048C2314yes—
149#14556048C2314yes—
150#14556048C2314yes—
151#14556048C2314yes—
152C22⋊(C71⋊C8)C2312yes—
153C22⋊(C71⋊C8)C2312yes—
154C22⋊(C71⋊C8)C2314yes—
155C22⋊(C71⋊C8)C2312yescomplemented
156C22⋊(C71⋊C8)C2312yescomplemented
157C4×C71⋊C8C2314yescomplemented
158C2×#41×C71C2312yes—
159C22×Q8×C71C2311yescharacteristic, complemented
160C22×D4×C71—21no—
161C22×D4×C71D411yescharacteristic
162C22×D4×C71C2311yescharacteristic, complemented
163C23×C4×C71C2311yescharacteristic
164C23×C4×C71C2311yescharacteristic
165#126×C71—22no—
166#126×C71—22no—
167#126×C71—22no—
168#125×C71—22no—
169#125×C71C2312yescomplemented
170#124×C71—22no—
171#124×C71C2312yescomplemented
172#123×C71—22no—
173#123×C71—22no—
174#123×C71—22no—
175#123×C71—22no—
176#123×C71—22no—
177C22⋊Q8×C71—21no—
178C22⋊Q8×C71—21no—
179C22⋊Q8×C71—22no—
180C22⋊Q8×C71C2312yes—
181C22⋊Q8×C71C2312yes—
182C22⋊Q8×C71C2312yescomplemented
183#121×C71—22no—
184#121×C71—22no—
185#121×C71—21no—
186#121×C71—21no—
187#121×C71—22no—
188#121×C71C2312yes—
189#121×C71C2312yes—
190#121×C71C2312yescomplemented
191#120×C71—22no—
192#120×C71—22no—
193C4×Q8×C71C2312yescomplemented
194C4×D4×C71—22no—
195C4×D4×C71—22no—
196C4×D4×C71—22no—
197C4×D4×C71—22no—
198C4×D4×C71—22no—
199C4×D4×C71D412yes—
200C4×D4×C71D412yes—
201C4×D4×C71C2312yes—
202C4×D4×C71C2312yes—
203C4×D4×C71C2312yescomplemented
204#117×C71—22no—
205#117×C71—22no—
206#117×C71C2312yes—
207C2×C4⋊C4×C71—21no—
208C2×C4⋊C4×C71D411yescharacteristic
209C2×C4⋊C4×C71C2311yescharacteristic, complemented
210C2×C4⋊C4×C71C2311yescharacteristic, complemented
211C2×C22⋊C4×C71—21no—
212C2×C22⋊C4×C71—21no—
213C2×C22⋊C4×C71—22no—
214C2×C22⋊C4×C71D411yescharacteristic
215C2×C22⋊C4×C71D411yescharacteristic
216C2×C42×C71C2311yescharacteristic
217C23×D71—21no—
218C23×D71—21no—
219C23×D71—24no—
220C23×D71—44no—
221C23×D71—44no—
222C23×D71—82no—
223#11765865—24no—
224#11765865—24no—
225#11765865—42no—
226#11765865—42no—
227#11765865—44no—
228#11765865—44no—
229C2×Dic142—21no—
230C2×Dic142—42no—
231C2×Dic142C2412yes—
232C2×D284—21no—
233C2×D284—24no—
234C2×D284—28no—
235C2×D284—24no—
236C2×D284—21no—
237C2×D284—44no—
238C2×D284—42no—
239C2×D284—48no—
240C2×D284—44no—
241C2×D284C2412yes—
242C2×D284C2412yes—
243C2×C22⋊D71—22no—
244C2×C22⋊D71—22no—
245C2×C22⋊D71—22no—
246C2×C22⋊D71—22no—
247C2×C22⋊D71—44no—
248C2×C22⋊D71—82no—
249C22×Dic71—21no—
250C22×Dic71—21no—
251C2×C4×D71—22no—
252C2×C4×D71—22no—
253C2×C4×D71—24no—
254C2×C4×D71—44no—
255C2×C4×D71—82no—
256#11765855—44no—
257#11765853—44no—
258#11765852—28no—
259#11765852—44no—
260#11765850—28no—
261#11765850—44no—
262#11765849—44no—
263#11765849—42no—
264#11765849—42no—
265C2×C71⋊C8C2414yes—
266C2×C71⋊C8C2414yes—
267C4⋊Dic71—21no—
268C4⋊Dic71C2412yes—
269Dic71⋊C4—24no—
270C22⋊Dic71—24no—
271(C2×D71)⋊C4—24no—
272(C2×D71)⋊C4—22no—
273(C2×D71)⋊C4—22no—
274(C2×D71)⋊C4—24no—
275(C2×D71)⋊C4—24no—
276C24×C71—21no—
277C24×C71C2×D411yescharacteristic
278C24×C71C2×D411yescharacteristic
279#41×C71—44no—
280C2×Q8×C71—21no—
281C2×Q8×C71—42no—
282C2×Q8×C71C2412yes—
283C2×D4×C71—22no—
284C2×D4×C71—22no—
285C2×D4×C71—22no—
286C2×D4×C71—22no—
287C2×D4×C71—21no—
288C2×D4×C71—42no—
289C2×D4×C71—42no—
290C2×D4×C71—44no—
291C2×D4×C71C2×D412yes—
292C2×D4×C71C2×D412yes—
293C2×D4×C71C2412yes—
294C22×C4×C71—21no—
295C22×C4×C71—21no—
296C22×C4×C71—21no—
297C22×C4×C71—22no—
298C22×C4×C71—22no—
299C22×C4×C71—42no—
300C22×C4×C71—42no—
301C22×C4×C71C2×D411yescharacteristic
302C22×C4×C71C2×D411yescharacteristic
303C22×C4×C71C2×D411yescharacteristic
304C22×C4×C71C2×D411yescharacteristic
305C22×C4×C71C2×D412yes—
306C22×C4×C71C2×D411yescharacteristic
307C22×C4×C71C2×D411yescharacteristic
308C22×C4×C71C2411yescharacteristic
309C22×C4×C71C2412yes—
310C22×C4×C71C2411yescharacteristic
311C22×C4×C71C2411yescharacteristic
312C4⋊C4×C71—22no—
313C4⋊C4×C71—22no—
314C4⋊C4×C71—21no—
315C4⋊C4×C71—21no—
316C4⋊C4×C71—22no—
317C4⋊C4×C71—22no—
318C4⋊C4×C71—22no—
319C4⋊C4×C71—22no—
320C4⋊C4×C71C2×D412yes—
321C4⋊C4×C71C2×D412yes—
322C4⋊C4×C71C2412yes—
323C4⋊C4×C71C2412yes—
324C22⋊C4×C71—22no—
325C22⋊C4×C71—22no—
326C22⋊C4×C71—22no—
327C22⋊C4×C71—22no—
328C22⋊C4×C71—22no—
329C22⋊C4×C71—22no—
330C22⋊C4×C71—22no—
331C22⋊C4×C71—22no—
332C22⋊C4×C71—22no—
333C22⋊C4×C71—22no—
334C22⋊C4×C71C2×D412yes—
335C22⋊C4×C71C2×D412yes—
336C22⋊C4×C71C2×D412yes—
337C22⋊C4×C71C2×D412yes—
338C42×C71—22no—
339C42×C71—22no—
340C42×C71C2×D412yes—
341C42×C71C2412yes—
342C23×C71—22no—
343C23×C71—22no—
344C23×C71—22no—
345C23×C71—41no—
346C23×C71—41no—
347C23×C71—41no—
348C23×C71—41no—
349C23×C71—42no—
350C23×C71—81no—
351C23×C71—81no—
352C23×C71C22×D411yescharacteristic
353C23×C71C22×D412yes—
354C23×C71C22×D411yescharacteristic
355C23×C71C22×D411yescharacteristic
356C22×D71—24no—
357C22×D71—22no—
358C22×D71—22no—
359C22×D71—48no—
360C22×D71—42no—
361C22×D71—42no—
362C22×D71—42no—
363C22×D71—42no—
364C22×D71—48no—
365C22×D71—42no—
366C22×D71—84no—
367C22×D71—816no—
368Q8×C71—24no—
369Q8×C71—81no—
370D4×C71—24no—
371D4×C71—42no—
372D4×C71—42no—
373D4×C71—44no—
374D4×C71—44no—
375D4×C71—81no—
376D4×C71—82no—
377D4×C71—82no—
378C2×C4×C71—22no—
379C2×C4×C71—22no—
380C2×C4×C71—22no—
381C2×C4×C71—22no—
382C2×C4×C71—24no—
383C2×C4×C71—22no—
384C2×C4×C71—22no—
385C2×C4×C71—22no—
386C2×C4×C71—41no—
387C2×C4×C71—42no—
388C2×C4×C71—41no—
389C2×C4×C71—41no—
390C2×C4×C71—41no—
391C2×C4×C71—41no—
392C2×C4×C71—42no—
393C2×C4×C71—82no—
394C2×C4×C71—82no—
395C2×C4×C71—81no—
396C2×C4×C71—81no—
397C2×C4×C71C22×D412yes—
398C2×C4×C71C22×D412yes—
399C2×C4×C71C22×D411yescharacteristic
400C2×C4×C71C22×D412yes—
401C2×C4×C71C22×D411yescharacteristic
402C2×C4×C71C22×D411yescharacteristic
403C2×C4×C71C2511yescharacteristic
404C22⋊D71—44no—
405C22⋊D71—44no—
406C22⋊D71—82no—
407C22⋊D71—82no—
408C2×Dic71—22no—
409C2×Dic71—22no—
410C2×Dic71—42no—
411C2×Dic71—42no—
412D284—24no—
413D284—22no—
414D284—24no—
415D284—48no—
416D284—42no—
417D284H(5,𝔽2)14yes—
418C4×D71—44no—
419C4×D71—44no—
420C4×D71—84no—
421Dic142—22no—
422Dic142—22no—
423Dic142—42no—
424C71⋊C8—24no—
425C71⋊C8—24no—
426C22×C71—21no—
427C22×C71—21no—
428C22×C71—21no—
429C22×C71—21no—
430C22×C71—22no—
431C22×C71—21no—
432C22×C71—21no—
433C22×C71—22no—
434C22×C71—21no—
435C22×C71—21no—
436C22×C71—22no—
437C22×C71—44no—
438C22×C71—42no—
439C22×C71—42no—
440C22×C71—42no—
441C22×C71—82no—
442C22×C71—162no—
443C22×C71#57512yes—
444C22×C71C23×D411yescharacteristic
445C2×D71—24no—
446C2×D71—48no—
447C2×D71—42no—
448C2×D71—42no—
449C2×D71—42no—
450C2×D71—42no—
451C2×D71—42no—
452C2×D71—816no—
453C2×D71—84no—
454C4×C71—22no—
455C4×C71—21no—
456C4×C71—21no—
457C4×C71—21no—
458C4×C71—22no—
459C4×C71—22no—
460C4×C71—42no—
461C4×C71—42no—
462C4×C71—42no—
463C4×C71C2×H(5,𝔽2)12yes—
464Dic71—42no—
465Dic71—42no—
466#61581—711nomaximal, Sylow
467C2×C71—22no—
468C2×C71—42no—
469C2×C71—41no—
470C2×C71—41no—
471C2×C71—82no—
472C2×C71#348411yescharacteristic
473C2×C71C2×#57511yescharacteristic
474C2×C71#358511yescharacteristic
475D71—44no—
476D71—82no—
477#3505D7111yescharacteristic, complemented
478C2×#546—711no—
479#3323—714no—
480#3322—714no—
481#3275—714no—
482#3273—714no—
483#3211—712no—
484#3196—712no—
485#3193—711no—
486#3192—711no—
487#3105—712no—
488#3007—711no—
489#3006—711no—
490#3003—712no—
491#2975—711no—
492C71#6158111yescharacteristic, complemented, Sylow
493C22×#41—711no—
494C23×D4—711no—
495C2×#137—712no—
496C2×AGL(1,ℤ/8)—714no—
497C2×AGL(1,ℤ/8)—712no—
498#553—22no—
499#553C2×D7112yescomplemented
500#552C2×D7112yescomplemented
501#551—22no—
502#548C2×D7112yescomplemented
503#546—714no—
504#546—714no—
505#546—1422no—
506#546—1422no—
507#546C2×D7112yescomplemented
508#539—21no—
509#538—21no—
510#534—21no—
511#529C2×D7112yescomplemented
512C2×#124—711no—
513#525C2×D7112yes—
514C2×#123—1421no—
515C2×C22⋊Q8—711no—
516C2×C22⋊Q8C2×D7111yescharacteristic, complemented
517C2×#121—711no—
518C2×#121—1421no—
519C2×#121C2×D7111yescharacteristic, complemented
520C2×#120—1421no—
521#518—21no—
522C2×C4×D4—711no—
523C2×C4×D4C2×D7111yescharacteristic
524C22×C22⋊C4—1421no—
525#495—714no—
526#488—714no—
527#485—714no—
528#484—712no—
529#481—712no—
530#481—712no—
531#480—712no—
532#478—714no—
533#470—714no—
534#469—714no—
535#468—714no—
536#468—714no—
537#464—714no—
538#463—714no—
539#463—714no—
540#452—714no—
541#452—714no—
542#451—712no—
543#450—712no—
544#450—712no—
545#450—714no—
546#449—714no—
547#448—712no—
548#448—712no—
549#447—712no—
550#447—712no—
551#447—712no—
552#447—714no—
553C4×SD16—714no—
554C4×D8—714no—
555#436—714no—
556#436—714no—
557#431—712no—
558#418—714no—
559#417—712no—
560#417—712no—
561#407—711no—
562#407—711no—
563#407—712no—
564C25—1421no—
565C2×#41—2844no—
566C2×#41—712no—
567C2×#41—712no—
568C2×#41—1421no—
569C2×#41—1421no—
570C2×#41C22×D7112yes—
571C22×Q8—711no—
572C22×Q8C22×D7111yescharacteristic, complemented
573C22×D4—21no—
574C22×D4—2844no—
575C22×D4—711no—
576C22×D4—714no—
577C22×D4—711no—
578C22×D4—1421no—
579C22×D4—1421no—
580C22×D4—1421no—
581C22×D4—1422no—
582C22×D4C22⋊D7111yescharacteristic
583C22×D4C22×D7111yescharacteristic, complemented
584C23×C4—1421no—
585C23×C4—1421no—
586C23×C4C22×D7111yescharacteristic
587C23×C4C22×D7111yescharacteristic
588#137—2844no—
589AGL(1,ℤ/8)—2848no—
590AGL(1,ℤ/8)—2844no—
591C2×Q16—714no—
592C2×SD16—714no—
593C2×SD16—714no—
594C2×SD16—714no—
595C2×D8—714no—
596C2×D8—714no—
597C2×M16—712no—
598C2×M16—714no—
599C2×M16—712no—
600#126—22no—
601#126—22no—
602#126—22no—
603#125—22no—
604#125C22×D7112yescomplemented
605#124—22no—
606#124—714no—
607#124—1422no—
608#124C22×D7112yescomplemented
609#123—22no—
610#123—22no—
611#123—22no—
612#123—22no—
613#123—22no—
614#123—1424no—
615#123—1424no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618C22⋊Q8—22no—
619C22⋊Q8—714no—
620C22⋊Q8—1422no—
621C22⋊Q8C22×D7112yes—
622C22⋊Q8C22×D7112yes—
623C22⋊Q8C22×D7112yescomplemented
624#121—22no—
625#121—22no—
626#121—21no—
627#121—21no—
628#121—22no—
629#121—712no—
630#121—712no—
631#121—1421no—
632#121—1421no—
633#121—1424no—
634#121—1424no—
635#121C22×D7112yes—
636#121C22×D7112yes—
637#121C22×D7112yescomplemented
638#120—22no—
639#120—22no—
640#120—1424no—
641#120—1424no—
642C4×Q8C22×D7112yescomplemented
643C4×D4—22no—
644C4×D4—22no—
645C4×D4—22no—
646C4×D4—22no—
647C4×D4—22no—
648C4×D4—714no—
649C4×D4—1422no—
650C4×D4C22⋊D7112yes—
651C4×D4C22⋊D7112yes—
652C4×D4C22×D7112yes—
653C4×D4C22×D7112yes—
654C4×D4C22×D7112yescomplemented
655#117—22no—
656#117—22no—
657#117C22×D7112yes—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—711no—
660C2×C4⋊C4—1421no—
661C2×C4⋊C4C22⋊D7111yescharacteristic
662C2×C4⋊C4C22×D7111yescharacteristic, complemented
663C2×C4⋊C4C22×D7111yescharacteristic, complemented
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—1421no—
668C2×C22⋊C4—1421no—
669C2×C22⋊C4—1421no—
670C2×C22⋊C4—1421no—
671C2×C22⋊C4—1421no—
672C2×C22⋊C4—1424no—
673C2×C22⋊C4—1424no—
674C2×C22⋊C4C22⋊D7111yescharacteristic
675C2×C22⋊C4C22⋊D7111yescharacteristic
676C2×C42C22×D7111yescharacteristic
677#107—714no—
678#106—714no—
679C4⋊C8—714no—
680#103—714no—
681#103—714no—
682#103—714no—
683#102—714no—
684#102—714no—
685#102—714no—
686#102—714no—
687#102—714no—
688C22⋊C8—712no—
689C22⋊C8—712no—
690C22⋊C8—714no—
691C22⋊C8—712no—
692C22⋊C8—712no—
693C4×C8—714no—
694C24—21no—
695C24—2844no—
696C24—2844no—
697C24—5682no—
698C24—1421no—
699C24—1424no—
700C24—1421no—
701C24C2×C22⋊D7111yescharacteristic
702C24C2×C22⋊D7111yescharacteristic
703#41—44no—
704#41—2842no—
705#41—2842no—
706#41—2844no—
707#41—2844no—
708#41—1424no—
709#41—1424no—
710C2×Q8—21no—
711C2×Q8—42no—
712C2×Q8—2842no—
713C2×Q8—712no—
714C2×Q8—1421no—
715C2×Q8C23×D7112yes—
716C2×D4—22no—
717C2×D4—22no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—21no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—44no—
724C2×D4—2844no—
725C2×D4—2842no—
726C2×D4—2844no—
727C2×D4—2848no—
728C2×D4—2844no—
729C2×D4—5682no—
730C2×D4—712no—
731C2×D4—712no—
732C2×D4—1428no—
733C2×D4—1424no—
734C2×D4—1422no—
735C2×D4—1422no—
736C2×D4—1422no—
737C2×D4—1422no—
738C2×D4—1424no—
739C2×D4—1421no—
740C2×D4—1421no—
741C2×D4C2×C22⋊D7112yes—
742C2×D4C2×C22⋊D7112yes—
743C2×D4C23×D7112yes—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—2844no—
752C22×C4—5682no—
753C22×C4—1421no—
754C22×C4—1421no—
755C22×C4—1422no—
756C22×C4—1422no—
757C22×C4—1424no—
758C22×C4C2×C22⋊D7111yescharacteristic
759C22×C4C2×C22⋊D7111yescharacteristic
760C22×C4C2×C22⋊D7111yescharacteristic
761C22×C4C2×C22⋊D7111yescharacteristic
762C22×C4C2×C22⋊D7111yescharacteristic
763C22×C4C2×C22⋊D7111yescharacteristic
764C22×C4C2×C22⋊D7112yes—
765C22×C4C23×D7111yescharacteristic
766C22×C4C23×D7111yescharacteristic
767C22×C4C23×D7111yescharacteristic
768C22×C4C23×D7112yes—
769Q16—2844no—
770SD16—2844no—
771SD16—2844no—
772SD16—1428no—
773D8—2844no—
774D8—1428no—
775M16—2844no—
776M16—2842no—
777M16—2842no—
778C2×C8—714no—
779C2×C8—714no—
780C4⋊C4—22no—
781C4⋊C4—22no—
782C4⋊C4—21no—
783C4⋊C4—21no—
784C4⋊C4—22no—
785C4⋊C4—22no—
786C4⋊C4—22no—
787C4⋊C4—22no—
788C4⋊C4—712no—
789C4⋊C4—1424no—
790C4⋊C4—1421no—
791C4⋊C4C2×C22⋊D7112yes—
792C4⋊C4C2×C22⋊D7112yes—
793C4⋊C4C23×D7112yes—
794C4⋊C4C23×D7112yes—
795C22⋊C4—22no—
796C22⋊C4—22no—
797C22⋊C4—22no—
798C22⋊C4—22no—
799C22⋊C4—22no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—1424no—
806C22⋊C4—1422no—
807C22⋊C4—1422no—
808C22⋊C4—1424no—
809C22⋊C4—1424no—
810C22⋊C4—1424no—
811C22⋊C4C2×C22⋊D7112yes—
812C22⋊C4C2×C22⋊D7112yes—
813C22⋊C4C2×C22⋊D7112yes—
814C22⋊C4C2×C22⋊D7112yes—
815C42—22no—
816C42—22no—
817C42C2×C22⋊D7112yes—
818C42C23×D7112yes—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—42no—
827C23—81no—
828C23—81no—
829C23—2842no—
830C23—2842no—
831C23—2842no—
832C23—2848no—
833C23—2848no—
834C23—2842no—
835C23—2842no—
836C23—5684no—
837C23—56816no—
838C23—1424no—
839C23—1422no—
840C23—1422no—
841C23C22×C22⋊D7112yes—
842C23C22×C22⋊D7111yescharacteristic
843C23C22×C22⋊D7111yescharacteristic
844C23C22×C22⋊D7111yescharacteristic
845Q8—24no—
846Q8—81no—
847Q8—2842no—
848Q8—1422no—
849Q8—1422no—
850D4—24no—
851D4—42no—
852D4—42no—
853D4—44no—
854D4—44no—
855D4—81no—
856D4—82no—
857D4—82no—
858D4—2842no—
859D4—2848no—
860D4—2844no—
861D4—2844no—
862D4—5682no—
863D4—5682no—
864D4—714no—
865D4—1424no—
866D4—1424no—
867D4—1422no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—24no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—41no—
877C2×C4—42no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—42no—
883C2×C4—82no—
884C2×C4—82no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—2844no—
888C2×C4—2844no—
889C2×C4—2842no—
890C2×C4—2842no—
891C2×C4—5684no—
892C2×C4—1422no—
893C2×C4—1422no—
894C2×C4C22×C22⋊D7112yes—
895C2×C4C22×C22⋊D7112yes—
896C2×C4C22×C22⋊D7111yescharacteristic
897C2×C4C22×C22⋊D7112yes—
898C2×C4C22×C22⋊D7111yescharacteristic
899C2×C4C22×C22⋊D7111yescharacteristic
900C2×C4C24×D7111yescharacteristic
901C8—1424no—
902C8—1424no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—22no—
908C22—21no—
909C22—22no—
910C22—21no—
911C22—21no—
912C22—22no—
913C22—21no—
914C22—44no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—82no—
919C22—162no—
920C22—2848no—
921C22—2842no—
922C22—2842no—
923C22—2842no—
924C22—2842no—
925C22—2842no—
926C22—5684no—
927C22—56816no—
928C22—1424no—
929C22#1798679712yes—
930C22C23×C22⋊D7111yescharacteristic
931C4—22no—
932C4—22no—
933C4—21no—
934C4—22no—
935C4—21no—
936C4—21no—
937C4—42no—
938C4—42no—
939C4—42no—
940C4—2842no—
941C4—2842no—
942C4H(5,𝔽2)×D7112yes—
943C2—22no—
944C2—42no—
945C2—41no—
946C2—41no—
947C2—82no—
948C2—2844no—
949C2—5682no—
950C2#2260197111yescharacteristic
951C2C2×#1798679711yescharacteristic
952C2#2260311911yescharacteristic
subgroupG/H
centerC22C23×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC71×#3505C2
socleC22×C71C23×D4
hypercenter#3505D71
hypocenterC71#61581
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3505

Complements

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

NH ≅ G/Ntype
1. C2×#17986645C2semidirect
2. #22600550C2semidirect
3. #22600535C2semidirect
4. #22599972C2semidirect
5. #22599947C2semidirect
6. #22599301C2semidirect
7. #22599166C2semidirect
8. #22599142C2semidirect
9. #22599137C2semidirect
10. #22598383C2semidirect
11. #22597598C2semidirect
12. #22597590C2semidirect
13. #22597566C2semidirect
14. #22597381C2semidirect
15. C71×#3505C2semidirect
17. C23×D284C22semidirect
18. C2×#14556159C22semidirect
19. C2×#14556154C22semidirect
20. C2×#14556153C22semidirect
24. #17986645C22semidirect
25. C2×#14556116C22semidirect
27. C2×#14556107C22semidirect
31. C2×C4×D284C22semidirect
33. #17986381C22semidirect
34. #17986356C22semidirect
35. #17986340C22semidirect
36. #17986332C22semidirect
37. #17986317C22semidirect
38. #17986315C22semidirect
39. #17986312C22semidirect
40. #17986296C22semidirect
41. #17986255C22semidirect
42. #17986250C22semidirect
43. #17986247C22semidirect
44. #17986243C22semidirect
45. #17986221C22semidirect
46. #17986214C22semidirect
47. #17986211C22semidirect
48. #17986161C22semidirect
49. #17986159C22semidirect
50. #17986154C22semidirect
51. #17986149C22semidirect
52. #17986149C22semidirect
53. #17986149C22semidirect
54. #17986142C22semidirect
55. #17986138C22semidirect
56. #17986137C22semidirect
57. #17986133C22semidirect
60. #17986132C22semidirect
61. C4×#11765852C22semidirect
62. C4×#11765850C22semidirect
63. #17986077C22semidirect
64. #17986077C22semidirect
65. #17986052C22semidirect
66. #17986003C22semidirect
67. #17985998C22semidirect
68. #17985998C22semidirect
69. #17985963C22semidirect
70. #17985963C22semidirect
71. #17985963C22semidirect
73. #553×C71C22semidirect
74. #552×C71C22semidirect
76. #548×C71C22semidirect
77. #546×C71C22semidirect
81. #529×C71C22semidirect
83. C2×C22⋊Q8×C71C22semidirect
84. C2×#121×C71C22semidirect
107. C2×#11765855C23semidirect
108. C2×#11765853C23semidirect
114. C2×#11765849C23semidirect
115. C2×#11765849C23semidirect
141. #14556061C23semidirect
142. #14556059C23semidirect
143. C4⋊(C71⋊C8)C23semidirect
144. #14556052C23semidirect
145. #14556051C23semidirect
146. #14556051C23semidirect
147. #14556049C23semidirect
155. C22⋊(C71⋊C8)C23semidirect
156. C22⋊(C71⋊C8)C23semidirect
157. C4×C71⋊C8C23semidirect
159. C22×Q8×C71C23semidirect
162. C22×D4×C71C23semidirect
169. #125×C71C23semidirect
171. #124×C71C23semidirect
182. C22⋊Q8×C71C23semidirect
190. #121×C71C23semidirect
193. C4×Q8×C71C23semidirect
203. C4×D4×C71C23semidirect
209. C2×C4⋊C4×C71C23semidirect
210. C2×C4⋊C4×C71C23semidirect
477. #3505D71semidirect
492. C71#61581semidirect
499. #553C2×D71semidirect
500. #552C2×D71semidirect
502. #548C2×D71semidirect
507. #546C2×D71semidirect
511. #529C2×D71semidirect
516. C2×C22⋊Q8C2×D71semidirect
519. C2×#121C2×D71semidirect
572. C22×Q8C22×D71semidirect
583. C22×D4C22×D71semidirect
604. #125C22×D71semidirect
608. #124C22×D71semidirect
623. C22⋊Q8C22×D71semidirect
637. #121C22×D71semidirect
642. C4×Q8C22×D71semidirect
654. C4×D4C22×D71semidirect
662. C2×C4⋊C4C22×D71semidirect
663. C2×C4⋊C4C22×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179866452
#226005502
#226005352
#225999722
#225999472
#225993012
#225991662
#225991422
#225991372
#225983832
#225975982
#225975902
#225975662
#225973812
C71×#35052
#6158171