Finite Group Databasebeta

← C2×#22600302 #32873963

Subgroups — C2×#22600302 #32873963

Order 18176.

2514 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986650C211yesmaximal, characteristic, complemented
2C2×#17986637C211yesmaximal, characteristic, complemented
3#22600302C2116yesmaximal, direct product factor
4C2×#17986360C211yesmaximal, characteristic, complemented
5C2×#17986317C211yesmaximal, characteristic, complemented
6C2×#17986328C211yesmaximal, characteristic, complemented
7C2×#17986287C211yesmaximal, characteristic, complemented
8C2×#17986252C211yesmaximal, characteristic, complemented
9C2×#17986231C211yesmaximal, characteristic, complemented
10C2×#17986217C211yesmaximal, characteristic, complemented
11C2×#17986144C211yesmaximal, characteristic, complemented
12C2×#17986134C211yesmaximal, characteristic, complemented
13C2×#17986108C211yesmaximal, characteristic, complemented
14C2×#17986068C211yesmaximal, characteristic, complemented
15C2×#102×D71C211yesmaximal, characteristic, complemented
16C2×#417×C71C211yesmaximal, characteristic, complemented
17C22×#11765865—21no—
18C22×D4×D71C2211yescharacteristic
19C22×#11765852C2211yescharacteristic, complemented
20C22×D568C2211yescharacteristic
21C22×#11765850C2211yescharacteristic
22C22×C8×D71C2211yescharacteristic
23#17986650—24no—
24#17986650C2218yescomplemented
25#17986637—24no—
26#17986637C2218yescomplemented
27C2×#14556127C2211yescharacteristic, complemented
28C2×#14556117C2211yescharacteristic
29C2×#14556113—21no—
30C2×#14556111—21no—
31C2×#14556111—21no—
32C2×#14556106—21no—
33C2×#14556104C2211yescharacteristic
34C2×#14556103C2211yescharacteristic
35C2×#14556102C2211yescharacteristic
36C2×#14556102C2211yescharacteristic, complemented
37C2×#14556100—21no—
38C2×#14556096—21no—
39C2×D4×Dic71C2211yescharacteristic
40C2×#14556090C2211yescharacteristic, complemented
41C2×C4×C22⋊D71C2211yescharacteristic
42C2×C4⋊C4×D71C2211yescharacteristic
43C22×(C2×D71)⋊C4—21no—
44#17986360C2218yescomplemented
45#17986328C2218yescomplemented
46#17986317C2218yescomplemented
47#17986287C2218yescomplemented
48#17986252C2218yescomplemented
49#17986231C2218yescomplemented
50#17986217C2218yescomplemented
51#17986144C2218yescomplemented
52#17986134C2218yescomplemented
53#17986108C2218yescomplemented
54#17986068C2218yescomplemented
55C2×#14556060C2211yescharacteristic, complemented
56C2×#14556059C2211yescharacteristic, complemented
57C2×#14556059C2211yescharacteristic, complemented
58C2×Dic71⋊C8C2211yescharacteristic, complemented
59C2×#14556052C2211yescharacteristic, complemented
60C2×#14556050C2211yescharacteristic
61C2×#14556050C2211yescharacteristic, complemented
62C2×#14556049C2211yescharacteristic
63C2×#14556048C2211yescharacteristic
64C2×#14556048C2211yescharacteristic
65#102×D71C2218yescomplemented
66C2×C22⋊(C71⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×#14556038C2211yescharacteristic, complemented
69C22×#41×C71C2211yescharacteristic
70C22×M16×C71C2211yescharacteristic, complemented
71C22×C4⋊C4×C71C2211yescharacteristic, complemented
72#417×C71C2218yescomplemented
73C2×#103×C71C2211yescharacteristic, complemented
74C2×#103×C71C2211yescharacteristic, complemented
75C2×#102×C71C2211yescharacteristic
76C2×#102×C71C2211yescharacteristic
77C24×D71—21no—
78C2×#11765865—28no—
79C2×#11765865—48no—
80C22×Dic142—21no—
81C22×D284—21no—
82C22×D284C2311yescharacteristic
83C22×D284C2311yescharacteristic
84C22×C22⋊D71—21no—
85C22×C22⋊D71—21no—
86C22×C22⋊D71—21no—
87C22×C22⋊D71D411yescharacteristic
88C2×D4×D71—22no—
89C2×D4×D71—24no—
90C2×D4×D71—42no—
91C2×D4×D71C2314yes—
92C23×Dic71—21no—
93C22×C4×D71—21no—
94C22×C4×D71—21no—
95C22×C4×D71C2311yescharacteristic
96C2×#11765852—42no—
97C2×#11765852C2314yescomplemented
98C2×D568—42no—
99C2×D568C2314yes—
100C2×#11765850—24no—
101C2×#11765850C2314yes—
102C22×C71⋊C8C2311yescharacteristic
103C22×C71⋊C8C2311yescharacteristic
104C2×C8×D71—42no—
105C2×C8×D71C2314yes—
106#14556127—22no—
107#14556127C2314yescomplemented
108#14556117—22no—
109#14556117C2314yes—
110#14556113—28no—
111#14556111—28no—
112#14556111—28no—
113#14556106—28no—
114#14556104—22no—
115#14556104C2314yes—
116#14556103—22no—
117#14556103C2314yes—
118#14556102—22no—
119#14556102—22no—
120#14556102C2314yes—
121#14556102C2314yescomplemented
122#14556100—28no—
123#14556096—28no—
124D4×Dic71—22no—
125D4×Dic71C2314yes—
126#14556090—22no—
127#14556090C2314yescomplemented
128C4×C22⋊D71D414yes—
129C4×C22⋊D71C2314yes—
130C2×C4⋊Dic71C2311yescharacteristic
131C2×C4⋊Dic71C2311yescharacteristic
132C2×Dic71⋊C4—21no—
133C2×Dic71⋊C4—21no—
134C2×Dic71⋊C4—21no—
135C2×Dic71⋊C4D411yescharacteristic
136C4⋊C4×D71—22no—
137C4⋊C4×D71C2314yes—
138C2×C22⋊Dic71—21no—
139C2×C22⋊Dic71D411yescharacteristic
140C2×(C2×D71)⋊C4—21no—
141C2×(C2×D71)⋊C4—21no—
142C2×(C2×D71)⋊C4—21no—
143C2×(C2×D71)⋊C4—21no—
144C2×(C2×D71)⋊C4—21no—
145C2×(C2×D71)⋊C4—28no—
146C2×(C2×D71)⋊C4—21no—
147C2×(C2×D71)⋊C4—21no—
148C2×(C2×D71)⋊C4D411yescharacteristic
149C2×C4×Dic71C2311yescharacteristic
150#14556060C2314yescomplemented
151#14556059C2314yescomplemented
152#14556059C2314yescomplemented
153Dic71⋊C8C2314yescomplemented
154#14556052C2314yescomplemented
155#14556050C2314yes—
156#14556050C2314yescomplemented
157#14556049C2314yes—
158#14556048C2314yes—
159#14556048C2314yes—
160C22⋊(C71⋊C8)C2314yescomplemented
161(C2×D71)⋊C8C2314yes—
162#14556038C2314yescomplemented
163C2×#41×C71—22no—
164C2×#41×C71—24no—
165C2×#41×C71—42no—
166C2×#41×C71C2314yes—
167C22×Q8×C71C2311yescharacteristic
168C22×D4×C71—21no—
169C22×D4×C71C2311yescharacteristic
170C23×C4×C71—21no—
171C23×C4×C71—21no—
172C23×C4×C71C2311yescharacteristic
173C2×M16×C71—42no—
174C2×M16×C71C2314yescomplemented
175C22×C8×C71C2311yescharacteristic
176C22×C8×C71C2311yescharacteristic
177C2×C4⋊C4×C71—22no—
178C2×C4⋊C4×C71—21no—
179C2×C4⋊C4×C71C2311yescharacteristic
180C2×C4⋊C4×C71C2311yescharacteristic
181C2×C4⋊C4×C71C2314yescomplemented
182#103×C71C2314yescomplemented
183#103×C71C2314yescomplemented
184#102×C71C2314yes—
185#102×C71C2314yes—
186C23×D71—21no—
187C23×D71—21no—
188C23×D71—24no—
189C23×D71—44no—
190C23×D71—44no—
191C23×D71—82no—
192C23×D71C2×D411yescharacteristic
193#11765865—432no—
194C2×Dic142—24no—
195C2×Dic142—44no—
196C2×D284—22no—
197C2×D284—22no—
198C2×D284—22no—
199C2×D284—22no—
200C2×D284—24no—
201C2×D284—21no—
202C2×D284—21no—
203C2×D284—44no—
204C2×D284C2412yes—
205C2×D284C2412yes—
206C2×C22⋊D71—24no—
207C2×C22⋊D71—24no—
208C2×C22⋊D71—24no—
209C2×C22⋊D71—24no—
210C2×C22⋊D71—44no—
211C2×C22⋊D71—44no—
212C2×C22⋊D71—82no—
213C2×C22⋊D71C2×D414yes—
214D4×D71—28no—
215D4×D71—44no—
216D4×D71—48no—
217C22×Dic71—21no—
218C22×Dic71—21no—
219C22×Dic71—24no—
220C22×Dic71—82no—
221C22×Dic71C2×D411yescharacteristic
222C22×Dic71C2×D411yescharacteristic
223C22×Dic71C2×D411yescharacteristic
224C2×C4×D71—22no—
225C2×C4×D71—22no—
226C2×C4×D71—24no—
227C2×C4×D71—24no—
228C2×C4×D71—44no—
229C2×C4×D71—44no—
230C2×C4×D71C2×D412yes—
231C2×C4×D71C2412yes—
232#11765852—44no—
233D568—44no—
234#11765850—28no—
235C2×C71⋊C8—22no—
236C2×C71⋊C8—22no—
237C2×C71⋊C8C2412yes—
238C2×C71⋊C8C2412yes—
239C8×D71—44no—
240C4⋊Dic71—21no—
241C4⋊Dic71—21no—
242C4⋊Dic71C2412yes—
243C4⋊Dic71C2412yes—
244Dic71⋊C4—24no—
245Dic71⋊C4—24no—
246Dic71⋊C4—24no—
247Dic71⋊C4C2×D414yes—
248C22⋊Dic71—24no—
249C22⋊Dic71C2×D414yes—
250(C2×D71)⋊C4—24no—
251(C2×D71)⋊C4—24no—
252(C2×D71)⋊C4—24no—
253(C2×D71)⋊C4—24no—
254(C2×D71)⋊C4—24no—
255(C2×D71)⋊C4—24no—
256(C2×D71)⋊C4—24no—
257(C2×D71)⋊C4C2×D414yes—
258C4×Dic71C2×D412yes—
259C4×Dic71C2412yes—
260C24×C71—21no—
261C24×C71C2×D411yescharacteristic
262#41×C71—28no—
263#41×C71—44no—
264#41×C71—48no—
265C2×Q8×C71—21no—
266C2×Q8×C71—22no—
267C2×Q8×C71—22no—
268C2×Q8×C71C2412yes—
269C2×D4×C71—24no—
270C2×D4×C71—21no—
271C2×D4×C71—22no—
272C2×D4×C71—44no—
273C2×D4×C71#4114yescomplemented
274C2×D4×C71C2412yes—
275C22×C4×C71—22no—
276C22×C4×C71—22no—
277C22×C4×C71—21no—
278C22×C4×C71—21no—
279C22×C4×C71—24no—
280C22×C4×C71—21no—
281C22×C4×C71—24no—
282C22×C4×C71—44no—
283C22×C4×C71—44no—
284C22×C4×C71C2×D411yescharacteristic
285C22×C4×C71C2×D412yes—
286C22×C4×C71C2412yes—
287C22×C4×C71C2411yescharacteristic
288M16×C71—44no—
289C2×C8×C71—22no—
290C2×C8×C71—22no—
291C2×C8×C71C2412yes—
292C2×C8×C71C2412yes—
293C4⋊C4×C71—21no—
294C4⋊C4×C71—21no—
295C4⋊C4×C71—24no—
296C4⋊C4×C71C2412yes—
297C4⋊C4×C71C2412yes—
298C23×C71—22no—
299C23×C71—24no—
300C23×C71—22no—
301C23×C71—22no—
302C23×C71—22no—
303C23×C71—42no—
304C23×C71—42no—
305C23×C71C22×D412yes—
306C23×C71C22×D411yescharacteristic
307C22×D71—22no—
308C22×D71—22no—
309C22×D71—22no—
310C22×D71—22no—
311C22×D71—48no—
312C22×D71—42no—
313C22×D71—42no—
314C22×D71—42no—
315C22×D71—42no—
316C22×D71—42no—
317C22×D71—42no—
318C22×D71—48no—
319C22×D71—84no—
320C22×D71—816no—
321C22×D71AGL(1,ℤ/8)14yes—
322C22×D71C22×D412yes—
323Q8×C71—22no—
324Q8×C71—22no—
325Q8×C71—42no—
326D4×C71—24no—
327D4×C71—22no—
328D4×C71—48no—
329D4×C71C2×#4114yescomplemented
330C2×C4×C71—22no—
331C2×C4×C71—24no—
332C2×C4×C71—22no—
333C2×C4×C71—22no—
334C2×C4×C71—22no—
335C2×C4×C71—22no—
336C2×C4×C71—22no—
337C2×C4×C71—48no—
338C2×C4×C71—48no—
339C2×C4×C71—42no—
340C2×C4×C71—42no—
341C2×C4×C71—42no—
342C2×C4×C71C22×D412yes—
343C2×C4×C71C22×D411yescharacteristic
344C2×C4×C71C2×#4112yes—
345C2×C4×C71H(5,𝔽2)12yes—
346C2×C4×C71C2511yescharacteristic
347C22⋊D71—28no—
348C22⋊D71—48no—
349C22⋊D71—48no—
350C22⋊D71—84no—
351C2×Dic71—22no—
352C2×Dic71—22no—
353C2×Dic71—22no—
354C2×Dic71—22no—
355C2×Dic71—22no—
356C2×Dic71—42no—
357C2×Dic71—42no—
358C2×Dic71—84no—
359C2×Dic71C22×D412yes—
360C2×Dic71C22×D412yes—
361C2×Dic71C22×D412yes—
362D284—22no—
363D284—22no—
364D284—22no—
365D284—22no—
366D284—48no—
367D284—42no—
368D284—42no—
369C4×D71—24no—
370C4×D71—22no—
371C4×D71—22no—
372C4×D71—48no—
373C4×D71—48no—
374Dic142—48no—
375C8×C71—22no—
376C8×C71—22no—
377C71⋊C8—22no—
378C71⋊C8—22no—
379C22×C71—24no—
380C22×C71—22no—
381C22×C71—22no—
382C22×C71—22no—
383C22×C71—48no—
384C22×C71—44no—
385C22×C71—42no—
386C22×C71—42no—
387C22×C71#54612yes—
388C22×C71C2×AGL(1,ℤ/8)12yes—
389C22×C71#57712yes—
390C22×C71C23×D411yescharacteristic
391C2×D71—22no—
392C2×D71—28no—
393C2×D71—22no—
394C2×D71—42no—
395C2×D71—42no—
396C2×D71—42no—
397C2×D71—42no—
398C2×D71—42no—
399C2×D71—42no—
400C2×D71—816no—
401C2×D71—84no—
402C2×D71—84no—
403C2×D71C2×AGL(1,ℤ/8)14yes—
404C4×C71—22no—
405C4×C71—42no—
406C4×C71—42no—
407C4×C71—42no—
408C4×C71#54612yes—
409C4×C71C22×#4111yescharacteristic
410C4×C71C2×H(5,𝔽2)11yescharacteristic
411Dic71—22no—
412Dic71—22no—
413Dic71—22no—
414Dic71—42no—
415Dic71—42no—
416C2×#3306—711nomaximal, Sylow
417C2×C71—44no—
418C2×C71—42no—
419C2×C71#330614yescomplemented
420C2×C71C2×#54611yescharacteristic
421C2×C71C22×AGL(1,ℤ/8)11yescharacteristic
422C2×C71C2×#57711yescharacteristic
423D71—24no—
424D71—82no—
425D71—82no—
426C2×#547—711no—
427C2×#546—711no—
428#3306—7116no—
429C2×#489—711no—
430C2×#481—711no—
431C2×#483—711no—
432C2×#476—711no—
433C2×#469—711no—
434C2×#465—711no—
435C2×#463—711no—
436C2×#449—711no—
437C2×#447—711no—
438C2×#442—711no—
439C2×#435—711no—
440C2×#417D7111yescharacteristic, complemented
441C22×#102—711no—
442C71C2×#330611yescharacteristic, complemented, Sylow
443C22×#41—1421no—
444C22×#41C2×D7111yescharacteristic
445C23×D4—711no—
446C22×SD16—711no—
447C22×D8—711no—
448C22×D8—711no—
449C22×M16C2×D7111yescharacteristic, complemented
450C23×C8—711no—
451#547—718no—
452#547—1424no—
453#546—718no—
454#546—1424no—
455C2×C4⋊Q8—711no—
456C2×#124—711no—
457C2×#123—1421no—
458C2×#123—1421no—
459C2×#123—1421no—
460C2×C22⋊Q8—711no—
461C2×C22⋊Q8—1421no—
462C2×#121—711no—
463C2×#121—711no—
464C2×#121—711no—
465C2×#121—1421no—
466C2×#120—1421no—
467C2×C4×D4—711no—
468C2×C4×D4—711no—
469C2×C4×D4—711no—
470C22×C4⋊C4—711no—
471C22×C4⋊C4C2×D7111yescharacteristic, complemented
472C22×C22⋊C4—1421no—
473#489—718no—
474#483—718no—
475#481—718no—
476#476—718no—
477#469—718no—
478#465—718no—
479#463—718no—
480#449—718no—
481#447—718no—
482#442—718no—
483#435—718no—
484C2×#106—711no—
485C2×#106—711no—
486C2×#106—711no—
487C2×C4⋊C8—711no—
488#417C2×D7118yescomplemented
489C2×#103—711no—
490C2×#103C2×D7111yescharacteristic, complemented
491C2×#103C2×D7111yescharacteristic, complemented
492C2×#102—711no—
493C2×#102—711no—
494C2×#102—711no—
495C2×#102—711no—
496C2×#102—711no—
497C2×#102—718no—
498C2×#102C2×D7111yescharacteristic
499C2×#102C2×D7111yescharacteristic
500C2×C22⋊C8—711no—
501C2×C22⋊C8—711no—
502C2×#97—711no—
503C25—1421no—
504C2×#41—22no—
505C2×#41—24no—
506C2×#41—42no—
507C2×#41—2848no—
508C2×#41—1428no—
509C2×#41C22×D7114yes—
510C22×Q8—1421no—
511C22×Q8C22×D7111yescharacteristic
512C22×D4—21no—
513C22×D4—2842no—
514C22×D4—714no—
515C22×D4—711no—
516C22×D4—711no—
517C22×D4—711no—
518C22×D4—1421no—
519C22×D4—1422no—
520C22×D4—1421no—
521C22×D4—1421no—
522C22×D4—1424no—
523C22×D4—1421no—
524C22×D4C22×D7111yescharacteristic
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—711no—
528C23×C4—1421no—
529C23×C4—1421no—
530C23×C4—1421no—
531C23×C4C22×D7111yescharacteristic
532C2×SD16—2842no—
533C2×SD16—714no—
534C2×D8—2842no—
535C2×D8—714no—
536C2×D8—714no—
537C2×D8—1424no—
538C2×M16—42no—
539C2×M16C22×D7114yescomplemented
540C22×C8—2842no—
541C22×C8—714no—
542C22×C8—711no—
543C22×C8—711no—
544C22×C8C22×D7111yescharacteristic
545C22×C8C22×D7111yescharacteristic
546C4⋊Q8—714no—
547C4⋊Q8—1422no—
548#124—714no—
549#124—1422no—
550#123—1428no—
551#123—1428no—
552#123—1428no—
553C22⋊Q8—714no—
554C22⋊Q8—1428no—
555C22⋊Q8—1422no—
556#121—714no—
557#121—714no—
558#121—714no—
559#121—1428no—
560#121—1422no—
561#121—1422no—
562#121—1422no—
563#120—1428no—
564C4×D4—714no—
565C4×D4—714no—
566C4×D4—714no—
567C4×D4—714no—
568C4×D4—1422no—
569C4×D4—1422no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—711no—
573C2×C4⋊C4—711no—
574C2×C4⋊C4—711no—
575C2×C4⋊C4—714no—
576C2×C4⋊C4—1422no—
577C2×C4⋊C4—1421no—
578C2×C4⋊C4—1421no—
579C2×C4⋊C4—1421no—
580C2×C4⋊C4C22×D7111yescharacteristic
581C2×C4⋊C4C22×D7111yescharacteristic
582C2×C4⋊C4C22×D7114yescomplemented
583C2×C22⋊C4—711no—
584C2×C22⋊C4—711no—
585C2×C22⋊C4—1428no—
586C2×C22⋊C4—1421no—
587C2×C22⋊C4—1421no—
588C2×C22⋊C4—1421no—
589C2×C22⋊C4—1421no—
590C2×C22⋊C4—1421no—
591C2×C22⋊C4—1421no—
592C2×C22⋊C4—1421no—
593C2×C22⋊C4—1421no—
594C2×C42—711no—
595#106—714no—
596#106—714no—
597#106—714no—
598C4⋊C8—714no—
599#103—714no—
600#103C22×D7114yescomplemented
601#103C22×D7114yescomplemented
602#102—714no—
603#102—714no—
604#102—714no—
605#102—714no—
606#102—714no—
607#102C22×D7114yes—
608#102C22×D7114yes—
609C22⋊C8—714no—
610C22⋊C8—714no—
611#97—714no—
612C24—21no—
613C24—2844no—
614C24—2844no—
615C24—5682no—
616C24—711no—
617C24—1424no—
618C24—1421no—
619C24—1421no—
620C24D4×D7111yescharacteristic
621#41—28no—
622#41—44no—
623#41—48no—
624#41—28432no—
625C2×Q8—21no—
626C2×Q8—22no—
627C2×Q8—22no—
628C2×Q8—2844no—
629C2×Q8—1424no—
630C2×Q8C23×D7112yes—
631C2×D4—24no—
632C2×D4—21no—
633C2×D4—22no—
634C2×D4—44no—
635C2×D4—2844no—
636C2×D4—2844no—
637C2×D4—2848no—
638C2×D4—2844no—
639C2×D4—2844no—
640C2×D4—5682no—
641C2×D4—714no—
642C2×D4—712no—
643C2×D4—712no—
644C2×D4—1424no—
645C2×D4—1424no—
646C2×D4—1424no—
647C2×D4—1428no—
648C2×D4—1424no—
649C2×D4—1424no—
650C2×D4—1421no—
651C2×D4—1421no—
652C2×D4—1422no—
653C2×D4—1422no—
654C2×D4—1422no—
655C2×D4—1422no—
656C2×D4#1176586514yescomplemented
657C2×D4C23×D7112yes—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—24no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—24no—
665C22×C4—44no—
666C22×C4—44no—
667C22×C4—2844no—
668C22×C4—2844no—
669C22×C4—5682no—
670C22×C4—711no—
671C22×C4—711no—
672C22×C4—711no—
673C22×C4—712no—
674C22×C4—712no—
675C22×C4—1424no—
676C22×C4—1424no—
677C22×C4—1421no—
678C22×C4—1421no—
679C22×C4—1424no—
680C22×C4—1422no—
681C22×C4—1422no—
682C22×C4D4×D7112yes—
683C22×C4D4×D7111yescharacteristic
684C22×C4C23×D7112yes—
685C22×C4C23×D7111yescharacteristic
686SD16—2844no—
687D8—2844no—
688D8—1428no—
689M16—44no—
690C2×C8—22no—
691C2×C8—22no—
692C2×C8—2844no—
693C2×C8—712no—
694C2×C8—712no—
695C2×C8—1422no—
696C2×C8—1422no—
697C2×C8C23×D7112yes—
698C2×C8C23×D7112yes—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—24no—
702C4⋊C4—714no—
703C4⋊C4—712no—
704C4⋊C4—712no—
705C4⋊C4—1424no—
706C4⋊C4—1424no—
707C4⋊C4—1424no—
708C4⋊C4—1421no—
709C4⋊C4—1421no—
710C4⋊C4C23×D7112yes—
711C4⋊C4C23×D7112yes—
712C22⋊C4—714no—
713C22⋊C4—714no—
714C22⋊C4—1424no—
715C22⋊C4—1424no—
716C22⋊C4—1424no—
717C22⋊C4—1424no—
718C22⋊C4—1424no—
719C22⋊C4—1424no—
720C22⋊C4—1424no—
721C22⋊C4—1424no—
722C42—712no—
723C42—712no—
724C23—22no—
725C23—22no—
726C23—24no—
727C23—22no—
728C23—22no—
729C23—42no—
730C23—42no—
731C23—2848no—
732C23—2848no—
733C23—2842no—
734C23—2842no—
735C23—2842no—
736C23—2842no—
737C23—2842no—
738C23—2842no—
739C23—5684no—
740C23—56816no—
741C23—712no—
742C23—714no—
743C23—1422no—
744C23—1422no—
745C23—1422no—
746C23—1422no—
747C23C2×D4×D7112yes—
748C23C2×D4×D7111yescharacteristic
749Q8—22no—
750Q8—22no—
751Q8—42no—
752Q8—2848no—
753D4—22no—
754D4—24no—
755D4—48no—
756D4—2848no—
757D4—2848no—
758D4—2848no—
759D4—2842no—
760D4—2842no—
761D4—5684no—
762D4—1428no—
763D4—1422no—
764D4—1422no—
765D4—1422no—
766D4—1422no—
767D4C2×#1176586514yescomplemented
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—48no—
776C2×C4—48no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—2848no—
781C2×C4—2848no—
782C2×C4—2842no—
783C2×C4—2842no—
784C2×C4—5684no—
785C2×C4—712no—
786C2×C4—712no—
787C2×C4—712no—
788C2×C4—1422no—
789C2×C4—1422no—
790C2×C4—1422no—
791C2×C4—1422no—
792C2×C4—1422no—
793C2×C4—1422no—
794C2×C4—1422no—
795C2×C4—1424no—
796C2×C4C2×D4×D7112yes—
797C2×C4C2×D4×D7111yescharacteristic
798C2×C4C2×#1176586512yes—
799C2×C4#1455617312yes—
800C2×C4C24×D7111yescharacteristic
801C8—22no—
802C8—22no—
803C8—1422no—
804C8—1422no—
805C22—22no—
806C22—24no—
807C22—22no—
808C22—22no—
809C22—42no—
810C22—42no—
811C22—44no—
812C22—48no—
813C22—2842no—
814C22—2842no—
815C22—2842no—
816C22—2842no—
817C22—2842no—
818C22—2842no—
819C22—56816no—
820C22—5684no—
821C22—5684no—
822C22—714no—
823C22—1422no—
824C22—1422no—
825C22—1428no—
826C22#1798663912yes—
827C22AGL(1,ℤ/8)×D7112yes—
828C22#1798680812yes—
829C22C22×D4×D7111yescharacteristic
830C4—22no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—2842no—
835C4—2842no—
836C4—1422no—
837C4—1422no—
838C4—1422no—
839C4#1798663912yes—
840C4C22×#1176586511yescharacteristic
841C4C2×#1455617311yescharacteristic
842C2—42no—
843C2—44no—
844C2—5682no—
845C2—5682no—
846C2—1424no—
847C2#2260030214yesdirect product factor
848C2C2×#1798663911yescharacteristic
849C2C2×AGL(1,ℤ/8)×D7111yescharacteristic
850C2C2×#1798680811yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#417×C71C2
socleC23×C71C22×D4
hypercenterC2×#417D71
hypocenterC71C2×#3306
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#17986650C2semidirect
2. C2×#17986637C2semidirect
3. #22600302C2direct (N × H)
4. C2×#17986360C2semidirect
5. C2×#17986317C2semidirect
6. C2×#17986328C2semidirect
7. C2×#17986287C2semidirect
8. C2×#17986252C2semidirect
9. C2×#17986231C2semidirect
10. C2×#17986217C2semidirect
11. C2×#17986144C2semidirect
12. C2×#17986134C2semidirect
13. C2×#17986108C2semidirect
14. C2×#17986068C2semidirect
15. C2×#102×D71C2semidirect
16. C2×#417×C71C2semidirect
19. C22×#11765852C22semidirect
24. #17986650C22semidirect
26. #17986637C22semidirect
27. C2×#14556127C22semidirect
36. C2×#14556102C22semidirect
40. C2×#14556090C22semidirect
44. #17986360C22semidirect
45. #17986328C22semidirect
46. #17986317C22semidirect
47. #17986287C22semidirect
48. #17986252C22semidirect
49. #17986231C22semidirect
50. #17986217C22semidirect
51. #17986144C22semidirect
52. #17986134C22semidirect
53. #17986108C22semidirect
54. #17986068C22semidirect
55. C2×#14556060C22semidirect
56. C2×#14556059C22semidirect
57. C2×#14556059C22semidirect
58. C2×Dic71⋊C8C22semidirect
59. C2×#14556052C22semidirect
61. C2×#14556050C22semidirect
65. #102×D71C22semidirect
66. C2×C22⋊(C71⋊C8)C22semidirect
68. C2×#14556038C22semidirect
70. C22×M16×C71C22semidirect
71. C22×C4⋊C4×C71C22semidirect
72. #417×C71C22semidirect
73. C2×#103×C71C22semidirect
74. C2×#103×C71C22semidirect
97. C2×#11765852C23semidirect
107. #14556127C23semidirect
121. #14556102C23semidirect
127. #14556090C23semidirect
150. #14556060C23semidirect
151. #14556059C23semidirect
152. #14556059C23semidirect
153. Dic71⋊C8C23semidirect
154. #14556052C23semidirect
156. #14556050C23semidirect
160. C22⋊(C71⋊C8)C23semidirect
162. #14556038C23semidirect
174. C2×M16×C71C23semidirect
181. C2×C4⋊C4×C71C23semidirect
182. #103×C71C23semidirect
183. #103×C71C23semidirect
273. C2×D4×C71#41semidirect
329. D4×C71C2×#41semidirect
419. C2×C71#3306semidirect
440. C2×#417D71semidirect
442. C71C2×#3306semidirect
449. C22×M16C2×D71semidirect
471. C22×C4⋊C4C2×D71semidirect
488. #417C2×D71semidirect
490. C2×#103C2×D71semidirect
491. C2×#103C2×D71semidirect
539. C2×M16C22×D71semidirect
582. C2×C4⋊C4C22×D71semidirect
600. #103C22×D71semidirect
601. #103C22×D71semidirect
656. C2×D4#11765865semidirect
767. D4C2×#11765865semidirect
847. C2#22600302direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866502
C2×#179866372
#226003022
C2×#179863602
C2×#179863172
C2×#179863282
C2×#179862872
C2×#179862522
C2×#179862312
C2×#179862172
C2×#179861442
C2×#179861342
C2×#179861082
C2×#179860682
C2×#102×D712
C2×#417×C712
C2×#330671