Finite Group Databasebeta

← C2×#22600784 #32875987

Subgroups — C2×#22600784 #32875987

Order 18176.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986684C211yesmaximal, characteristic, complemented
2C2×#17986649C211yesmaximal, characteristic
3#22600784C2116yesmaximal, direct product factor
4C2×#17986407C211yesmaximal, characteristic, complemented
5C2×#17986336C211yesmaximal, characteristic, complemented
6C2×#17986322C211yesmaximal, characteristic, complemented
7C2×#17986330C211yesmaximal, characteristic, complemented
8C2×#17986293C211yesmaximal, characteristic, complemented
9C2×#17986301C211yesmaximal, characteristic, complemented
10C2×#17986244C211yesmaximal, characteristic, complemented
11C2×#17986226C211yesmaximal, characteristic, complemented
12C2×#17986096C211yesmaximal, characteristic, complemented
13C2×#17986067C211yesmaximal, characteristic, complemented
14C2×#17986040C211yesmaximal, characteristic, complemented
15C22×#14556061C211yesmaximal, characteristic, complemented
16C2×#480×C71C211yesmaximal, characteristic, complemented
17C22×#11765864—21no—
18C22×#11765853C2211yescharacteristic
19C22×#11765848C2211yescharacteristic
20C23×C71⋊C8C2211yescharacteristic
21#17986684—24no—
22#17986684C2218yescomplemented
23#17986649—24no—
24#17986649C2218yes—
25C2×#14556127C2211yescharacteristic
26C2×#14556123—21no—
27C2×#14556119C2211yescharacteristic
28C2×#14556118—21no—
29C2×#14556111—21no—
30C2×#14556110—21no—
31C2×#14556109—21no—
32C2×#14556108C2211yescharacteristic
33C2×#14556107C2211yescharacteristic
34C2×#14556105—21no—
35C2×#14556099C2211yescharacteristic
36C2×#14556093C2211yescharacteristic
37C2×D4×Dic71C2211yescharacteristic
38C2×C4×C22⋊D71C2211yescharacteristic
39C2×#14556087—21no—
40C2×#14556086C2211yescharacteristic
41C22×C4⋊Dic71C2211yescharacteristic
42C2×C4⋊C4×D71C2211yescharacteristic
43#17986407C2218yescomplemented
44#17986336C2218yescomplemented
45#17986330C2218yescomplemented
46#17986322C2218yescomplemented
47#17986301C2218yescomplemented
48#17986293C2218yescomplemented
49#17986244C2218yescomplemented
50#17986226C2218yescomplemented
51#17986096C2218yescomplemented
52#17986067C2218yescomplemented
53#17986040C2218yescomplemented
54C2×#14556061C2211yescharacteristic
55C2×#14556061C2211yescharacteristic
56C2×#14556061C2211yescharacteristic
57C2×#14556061C2211yescharacteristic
58C2×#14556061C2218yescomplemented
59C2×#14556060C2211yescharacteristic
60C2×#14556060C2211yescharacteristic
61C2×#14556059C2211yescharacteristic
62C2×Dic71⋊C8C2211yescharacteristic
63C2×#14556053C2211yescharacteristic
64C2×#14556053C2211yescharacteristic
65C2×#14556051C2211yescharacteristic
66C2×#14556049C2211yescharacteristic
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×#14556038C2211yescharacteristic
69C2×#121×C71C2211yescharacteristic
70C22×C4⋊C4×C71C2211yescharacteristic
71#480×C71C2218yescomplemented
72C2×#107×C71C2211yescharacteristic
73C2×#107×C71C2211yescharacteristic
74C2×#102×C71C2211yescharacteristic
75C2×#102×C71C2211yescharacteristic
76C2×C22⋊C8×C71C2211yescharacteristic
77C2×#11765864—28no—
78C2×#11765864—48no—
79C22×Dic142—21no—
80C22×Dic142C2311yescharacteristic
81C22×C22⋊D71—21no—
82C22×C22⋊D71D411yescharacteristic
83C23×Dic71—21no—
84C23×Dic71—21no—
85C22×C4×D71—21no—
86C22×C4×D71C2311yescharacteristic
87C2×#11765853—24no—
88C2×#11765853C2314yes—
89C2×#11765848—24no—
90C2×#11765848C2314yes—
91C22×C71⋊C8—24no—
92C22×C71⋊C8C2314yes—
93C22×C71⋊C8C2311yescharacteristic
94C22×C71⋊C8C2311yescharacteristic
95#14556127—22no—
96#14556127C2314yes—
97#14556123—28no—
98#14556119—22no—
99#14556119C2314yes—
100#14556118—28no—
101#14556111—28no—
102#14556110—28no—
103#14556109—28no—
104#14556108—22no—
105#14556108C2314yes—
106#14556107—22no—
107#14556107C2314yes—
108#14556105—28no—
109#14556099—22no—
110#14556099C2314yes—
111#14556093—22no—
112#14556093C2314yes—
113D4×Dic71—22no—
114D4×Dic71C2314yes—
115C4×C22⋊D71D414yes—
116C4×C22⋊D71C2314yes—
117#14556087—28no—
118#14556086—22no—
119#14556086C2314yes—
120C2×C4⋊Dic71—21no—
121C2×C4⋊Dic71—21no—
122C2×C4⋊Dic71—22no—
123C2×C4⋊Dic71—21no—
124C2×C4⋊Dic71C2314yes—
125C2×C4⋊Dic71C2311yescharacteristic
126C2×C4⋊Dic71C2311yescharacteristic
127C2×C4⋊Dic71C2311yescharacteristic
128C2×Dic71⋊C4—21no—
129C2×Dic71⋊C4—21no—
130C2×Dic71⋊C4—21no—
131C2×Dic71⋊C4—21no—
132C2×Dic71⋊C4—21no—
133C2×Dic71⋊C4D411yescharacteristic
134C4⋊C4×D71—22no—
135C4⋊C4×D71C2314yes—
136C2×C22⋊Dic71—21no—
137C2×C22⋊Dic71—21no—
138C2×C22⋊Dic71—21no—
139C2×C22⋊Dic71D411yescharacteristic
140C2×(C2×D71)⋊C4—21no—
141C2×(C2×D71)⋊C4—21no—
142C2×(C2×D71)⋊C4D411yescharacteristic
143C2×C4×Dic71—21no—
144C2×C4×Dic71—21no—
145C2×C4×Dic71C2311yescharacteristic
146#14556061C2314yes—
147#14556061C2314yes—
148#14556061C2314yes—
149#14556061C2314yes—
150#14556060C2314yes—
151#14556060C2314yes—
152#14556059C2314yes—
153Dic71⋊C8C2314yes—
154#14556053C2314yes—
155#14556053C2314yes—
156#14556051C2314yes—
157#14556049C2314yes—
158(C2×D71)⋊C8C2314yes—
159#14556038C2314yes—
160C22×D4×C71—21no—
161C22×D4×C71C2311yescharacteristic
162C23×C4×C71—21no—
163C23×C4×C71C2311yescharacteristic
164C22×C8×C71C2311yescharacteristic
165C22×C8×C71C2311yescharacteristic
166#121×C71—22no—
167#121×C71C2314yes—
168C2×C4⋊C4×C71—22no—
169C2×C4⋊C4×C71—21no—
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C4⋊C4×C71C2314yes—
174C2×C22⋊C4×C71—21no—
175#107×C71C2314yes—
176#107×C71C2314yes—
177#102×C71C2314yes—
178#102×C71C2314yes—
179C22⋊C8×C71C2314yes—
180C23×D71C2×D411yescharacteristic
181#11765864—432no—
182C2×Dic142—22no—
183C2×Dic142—22no—
184C2×Dic142—21no—
185C2×Dic142—24no—
186C2×Dic142—44no—
187C2×Dic142C2412yes—
188C2×C22⋊D71—24no—
189C2×C22⋊D71—24no—
190C2×C22⋊D71—44no—
191C2×C22⋊D71C2×D414yes—
192C22×Dic71—21no—
193C22×Dic71—21no—
194C22×Dic71—24no—
195C22×Dic71—21no—
196C22×Dic71—21no—
197C22×Dic71—24no—
198C22×Dic71—44no—
199C22×Dic71—44no—
200C22×Dic71C2×D411yescharacteristic
201C22×Dic71C2×D411yescharacteristic
202C22×Dic71C2×D411yescharacteristic
203C2×C4×D71—22no—
204C2×C4×D71—22no—
205C2×C4×D71—24no—
206C2×C4×D71—44no—
207C2×C4×D71C2×D412yes—
208C2×C4×D71C2412yes—
209#11765853—28no—
210#11765848—28no—
211C2×C71⋊C8—22no—
212C2×C71⋊C8—28no—
213C2×C71⋊C8#4114yescomplemented
214C2×C71⋊C8C2412yes—
215C2×C71⋊C8C2412yes—
216C4⋊Dic71—21no—
217C4⋊Dic71—21no—
218C4⋊Dic71—24no—
219C4⋊Dic71—21no—
220C4⋊Dic71—24no—
221C4⋊Dic71—24no—
222C4⋊Dic71C2412yes—
223C4⋊Dic71C2412yes—
224C4⋊Dic71C2412yes—
225Dic71⋊C4—24no—
226Dic71⋊C4—24no—
227Dic71⋊C4—24no—
228Dic71⋊C4—24no—
229Dic71⋊C4—24no—
230Dic71⋊C4C2×D414yes—
231C22⋊Dic71—24no—
232C22⋊Dic71—24no—
233C22⋊Dic71—24no—
234C22⋊Dic71C2×D414yes—
235(C2×D71)⋊C4—24no—
236(C2×D71)⋊C4—24no—
237(C2×D71)⋊C4C2×D414yes—
238C4×Dic71—24no—
239C4×Dic71—24no—
240C4×Dic71C2×D412yes—
241C4×Dic71C2412yes—
242C24×C71—21no—
243C24×C71C2×D411yescharacteristic
244C2×D4×C71—24no—
245C2×D4×C71—21no—
246C2×D4×C71—22no—
247C2×D4×C71—22no—
248C2×D4×C71—44no—
249C2×D4×C71C2412yes—
250C22×C4×C71—22no—
251C22×C4×C71—22no—
252C22×C4×C71—21no—
253C22×C4×C71—21no—
254C22×C4×C71—21no—
255C22×C4×C71—24no—
256C22×C4×C71—44no—
257C22×C4×C71C2×D411yescharacteristic
258C22×C4×C71C2×D412yes—
259C22×C4×C71C2412yes—
260C22×C4×C71C2411yescharacteristic
261C2×C8×C71—22no—
262C2×C8×C71—22no—
263C2×C8×C71C2412yes—
264C2×C8×C71C2412yes—
265C4⋊C4×C71—21no—
266C4⋊C4×C71—21no—
267C4⋊C4×C71—24no—
268C4⋊C4×C71—21no—
269C4⋊C4×C71C2412yes—
270C4⋊C4×C71C2412yes—
271C4⋊C4×C71C2412yes—
272C22⋊C4×C71—24no—
273C23×C71—22no—
274C23×C71—22no—
275C23×C71—22no—
276C23×C71—42no—
277C23×C71—42no—
278C23×C71—42no—
279C23×C71AGL(1,ℤ/8)14yes—
280C23×C71C22×D412yes—
281C23×C71C22×D411yescharacteristic
282C22×D71—22no—
283C22×D71—22no—
284C22×D71—22no—
285C22×D71C22×D412yes—
286D4×C71—22no—
287D4×C71—22no—
288D4×C71—48no—
289D4×C71—42no—
290C2×C4×C71—22no—
291C2×C4×C71—24no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71—22no—
295C2×C4×C71—22no—
296C2×C4×C71—22no—
297C2×C4×C71—48no—
298C2×C4×C71—42no—
299C2×C4×C71—42no—
300C2×C4×C71—42no—
301C2×C4×C71C22×D412yes—
302C2×C4×C71C22×D411yescharacteristic
303C2×C4×C71C2×#4112yes—
304C2×C4×C712−1+412yes—
305C2×C4×C71C2511yescharacteristic
306C22⋊D71—28no—
307C22⋊D71—48no—
308C2×Dic71—22no—
309C2×Dic71—22no—
310C2×Dic71—22no—
311C2×Dic71—22no—
312C2×Dic71—22no—
313C2×Dic71—22no—
314C2×Dic71—22no—
315C2×Dic71—48no—
316C2×Dic71—42no—
317C2×Dic71—42no—
318C2×Dic71—42no—
319C2×Dic71—48no—
320C2×Dic71—42no—
321C2×Dic71C22×D412yes—
322C2×Dic71C22×D412yes—
323C2×Dic71C22×D412yes—
324C4×D71—24no—
325C4×D71—22no—
326C4×D71—22no—
327C4×D71—48no—
328Dic142—22no—
329Dic142—22no—
330Dic142—48no—
331Dic142—42no—
332C8×C71—22no—
333C8×C71—22no—
334C71⋊C8—22no—
335C71⋊C8C2×#4114yescomplemented
336C22×C71—28no—
337C22×C71—22no—
338C22×C71—22no—
339C22×C71—42no—
340C22×C71—42no—
341C22×C71—42no—
342C22×C71—84no—
343C22×C71#54712yes—
344C22×C71C2×AGL(1,ℤ/8)14yes—
345C22×C71C2×AGL(1,ℤ/8)12yes—
346C22×C71#57812yes—
347C22×C71C23×D411yescharacteristic
348C2×D71—22no—
349C2×D71—22no—
350C2×D71—22no—
351C2×D71—44no—
352C4×C71—22no—
353C4×C71—42no—
354C4×C71—42no—
355C4×C71—42no—
356C4×C71#54712yes—
357C4×C71C22×#4111yescharacteristic
358C4×C71C2×2−1+411yescharacteristic
359Dic71—22no—
360Dic71—22no—
361Dic71—22no—
362Dic71—42no—
363Dic71—42no—
364Dic71—42no—
365Dic71—42no—
366C2×#3343—711nomaximal, Sylow
367C2×C71—24no—
368C2×C71—82no—
369C2×C71#334314yescomplemented
370C2×C71C2×#54711yescharacteristic
371C2×C71C22×AGL(1,ℤ/8)11yescharacteristic
372C2×C71C2×#57811yescharacteristic
373D71—42no—
374C2×#552—711no—
375C2×#547—711no—
376#3343—7116no—
377C2×#501—711no—
378C2×#484—711no—
379C2×#482—711no—
380C2×#483—711no—
381C2×#480D7111yescharacteristic, complemented
382C2×#477—711no—
383C2×#478—711no—
384C2×#468—711no—
385C2×#465—711no—
386C2×#440—711no—
387C2×#435—711no—
388C2×#428—711no—
389C22×#107—711no—
390C71C2×#334311yescharacteristic, complemented, Sylow
391C22×#41—1421no—
392C22×SD16—711no—
393C22×M16—711no—
394C23×C8—711no—
395#552—718no—
396#552—1424no—
397#547—718no—
398#547—1424no—
399C2×C4⋊Q8—711no—
400C2×#126—1421no—
401C2×#125—711no—
402C2×#125—1421no—
403C2×#123—1421no—
404C2×#123—1421no—
405C2×#123—1421no—
406C2×C22⋊Q8—711no—
407C2×C22⋊Q8—711no—
408C2×C22⋊Q8—1421no—
409C2×#121—711no—
410C2×#121C2×D7111yescharacteristic
411C2×C4×Q8—711no—
412C2×C4×D4—711no—
413C2×C4×D4—711no—
414C2×#117—711no—
415C2×#117—1421no—
416C22×C4⋊C4—711no—
417C22×C4⋊C4—711no—
418C22×C4⋊C4C2×D7111yescharacteristic
419#501—718no—
420#484—718no—
421#483—718no—
422#482—718no—
423#480C2×D7118yescomplemented
424#478—718no—
425#477—718no—
426#468—718no—
427#465—718no—
428#440—718no—
429#435—718no—
430#428—718no—
431C2×#107—711no—
432C2×#107—711no—
433C2×#107—718no—
434C2×#107—711no—
435C2×#107—711no—
436C2×#107C2×D7111yescharacteristic
437C2×#107C2×D7111yescharacteristic
438C2×#106—711no—
439C2×#106—711no—
440C2×#106—711no—
441C2×C4⋊C8—711no—
442C2×#103—711no—
443C2×#103—711no—
444C2×#103—711no—
445C2×#102—711no—
446C2×#102C2×D7111yescharacteristic
447C2×#102C2×D7111yescharacteristic
448C2×C22⋊C8—711no—
449C2×C22⋊C8C2×D7111yescharacteristic
450C2×#97—711no—
451C2×#41—2848no—
452C2×#41—1428no—
453C22×Q8—711no—
454C22×Q8—1421no—
455C22×D4—21no—
456C22×D4—711no—
457C22×D4—1421no—
458C22×D4C22×D7111yescharacteristic
459C23×C4—21no—
460C23×C4—711no—
461C23×C4—1421no—
462C23×C4—1421no—
463C23×C4—1421no—
464C23×C4C22×D7111yescharacteristic
465C2×SD16—714no—
466C2×SD16—1424no—
467C2×M16—714no—
468C2×M16—1424no—
469C22×C8—711no—
470C22×C8—711no—
471C22×C8—714no—
472C22×C8—1424no—
473C22×C8C22×D7111yescharacteristic
474C22×C8C22×D7111yescharacteristic
475C4⋊Q8—714no—
476C4⋊Q8—1422no—
477#126—1428no—
478#125—714no—
479#125—1422no—
480#125—1428no—
481#123—1428no—
482#123—1428no—
483#123—1428no—
484C22⋊Q8—714no—
485C22⋊Q8—714no—
486C22⋊Q8—1428no—
487C22⋊Q8—1422no—
488C22⋊Q8—1422no—
489#121—22no—
490#121—714no—
491#121—1422no—
492#121C22×D7114yes—
493C4×Q8—714no—
494C4×Q8—1422no—
495C4×D4—714no—
496C4×D4—714no—
497C4×D4—714no—
498C4×D4—1422no—
499#117—714no—
500#117—1428no—
501#117—1422no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—711no—
505C2×C4⋊C4—711no—
506C2×C4⋊C4—711no—
507C2×C4⋊C4—714no—
508C2×C4⋊C4—711no—
509C2×C4⋊C4—714no—
510C2×C4⋊C4—1422no—
511C2×C4⋊C4—1421no—
512C2×C4⋊C4—1421no—
513C2×C4⋊C4—1421no—
514C2×C4⋊C4—1421no—
515C2×C4⋊C4—1421no—
516C2×C4⋊C4—1421no—
517C2×C4⋊C4—1421no—
518C2×C4⋊C4—1422no—
519C2×C4⋊C4—1421no—
520C2×C4⋊C4C22×D7111yescharacteristic
521C2×C4⋊C4C22×D7111yescharacteristic
522C2×C4⋊C4C22×D7111yescharacteristic
523C2×C4⋊C4C22×D7114yes—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—711no—
526C2×C22⋊C4—711no—
527C2×C22⋊C4—1421no—
528C2×C22⋊C4—1421no—
529C2×C22⋊C4—1421no—
530C2×C22⋊C4—1421no—
531C2×C22⋊C4—1421no—
532C2×C42—711no—
533C2×C42—1421no—
534C2×C42—1421no—
535#107—714no—
536#107—714no—
537#107—714no—
538#107—714no—
539#107C22×D7114yes—
540#107C22×D7114yes—
541#106—714no—
542#106—714no—
543#106—714no—
544C4⋊C8—714no—
545#103—714no—
546#103—714no—
547#103—714no—
548#102—714no—
549#102C22×D7114yes—
550#102C22×D7114yes—
551C22⋊C8—714no—
552C22⋊C8C22×D7114yes—
553#97—714no—
554C24—21no—
555C24—711no—
556C24D4×D7111yescharacteristic
557#41—28432no—
558C2×Q8—2844no—
559C2×Q8—712no—
560C2×Q8—1424no—
561C2×Q8—1422no—
562C2×Q8—1422no—
563C2×Q8—1421no—
564C2×D4—24no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—44no—
569C2×D4—2844no—
570C2×D4—714no—
571C2×D4—1424no—
572C2×D4—1424no—
573C2×D4C23×D7112yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—44no—
581C22×C4—2844no—
582C22×C4—2844no—
583C22×C4—2844no—
584C22×C4—711no—
585C22×C4—711no—
586C22×C4—711no—
587C22×C4—712no—
588C22×C4—712no—
589C22×C4—1424no—
590C22×C4—1424no—
591C22×C4—1424no—
592C22×C4—1421no—
593C22×C4—1421no—
594C22×C4—1421no—
595C22×C4—1421no—
596C22×C4—1422no—
597C22×C4—1422no—
598C22×C4D4×D7112yes—
599C22×C4D4×D7111yescharacteristic
600C22×C4C23×D7112yes—
601C22×C4C23×D7111yescharacteristic
602SD16—1428no—
603M16—1428no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—714no—
607C2×C8—712no—
608C2×C8—712no—
609C2×C8—1428no—
610C2×C8—1422no—
611C2×C8C23×D7112yes—
612C2×C8C23×D7112yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—714no—
618C4⋊C4—712no—
619C4⋊C4—712no—
620C4⋊C4—712no—
621C4⋊C4—1424no—
622C4⋊C4—1424no—
623C4⋊C4—1424no—
624C4⋊C4—1424no—
625C4⋊C4—1424no—
626C4⋊C4—1424no—
627C4⋊C4—1424no—
628C4⋊C4—1421no—
629C4⋊C4—1421no—
630C4⋊C4—1424no—
631C4⋊C4—1421no—
632C4⋊C4C23×D7112yes—
633C4⋊C4C23×D7112yes—
634C4⋊C4C23×D7112yes—
635C22⋊C4—24no—
636C22⋊C4—714no—
637C22⋊C4—714no—
638C22⋊C4—1424no—
639C22⋊C4—1424no—
640C22⋊C4—1424no—
641C22⋊C4—1424no—
642C22⋊C4—1424no—
643C42—712no—
644C42—712no—
645C42—1424no—
646C42—1424no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—712no—
654C23—1422no—
655C23—1422no—
656C23—1422no—
657C23#1455615214yes—
658C23C2×D4×D7112yes—
659C23C2×D4×D7111yescharacteristic
660Q8—2848no—
661Q8—2842no—
662Q8—1422no—
663Q8—1422no—
664D4—22no—
665D4—22no—
666D4—48no—
667D4—42no—
668D4—2848no—
669D4—1428no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—48no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—2848no—
682C2×C4—2842no—
683C2×C4—2842no—
684C2×C4—2842no—
685C2×C4—2848no—
686C2×C4—2842no—
687C2×C4—2848no—
688C2×C4—712no—
689C2×C4—712no—
690C2×C4—712no—
691C2×C4—1422no—
692C2×C4—1422no—
693C2×C4—1422no—
694C2×C4—1422no—
695C2×C4—1422no—
696C2×C4—1422no—
697C2×C4—1422no—
698C2×C4—1422no—
699C2×C4—1422no—
700C2×C4—1424no—
701C2×C4C2×D4×D7112yes—
702C2×C4C2×D4×D7111yescharacteristic
703C2×C4#41×D7112yes—
704C2×C4#1455617512yes—
705C2×C4C24×D7111yescharacteristic
706C8—22no—
707C8—22no—
708C8—714no—
709C8—1422no—
710C22—22no—
711C22—28no—
712C22—22no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—84no—
717C22—2844no—
718C22—1422no—
719C22—1422no—
720C22—1422no—
721C22#1798664712yes—
722C22C2×#1455615214yes—
723C22C2×#1455615212yes—
724C22#1798681512yes—
725C22C22×D4×D7111yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—2842no—
731C4—2842no—
732C4—2842no—
733C4—2842no—
734C4—1422no—
735C4—1422no—
736C4—1422no—
737C4#1798664712yes—
738C4C2×#41×D7111yescharacteristic
739C4C2×#1455617511yescharacteristic
740C2—24no—
741C2—82no—
742C2—2842no—
743C2#2260078414yesdirect product factor
744C2C2×#1798664711yescharacteristic
745C2C22×#1455615211yescharacteristic
746C2C2×#1798681511yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#480×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986649C2
hypercenterC2×#480D71
hypocenterC71C2×#3343
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#17986684C2semidirect
3. #22600784C2direct (N × H)
4. C2×#17986407C2semidirect
5. C2×#17986336C2semidirect
6. C2×#17986322C2semidirect
7. C2×#17986330C2semidirect
8. C2×#17986293C2semidirect
9. C2×#17986301C2semidirect
10. C2×#17986244C2semidirect
11. C2×#17986226C2semidirect
12. C2×#17986096C2semidirect
13. C2×#17986067C2semidirect
14. C2×#17986040C2semidirect
15. C22×#14556061C2semidirect
16. C2×#480×C71C2semidirect
22. #17986684C22semidirect
43. #17986407C22semidirect
44. #17986336C22semidirect
45. #17986330C22semidirect
46. #17986322C22semidirect
47. #17986301C22semidirect
48. #17986293C22semidirect
49. #17986244C22semidirect
50. #17986226C22semidirect
51. #17986096C22semidirect
52. #17986067C22semidirect
53. #17986040C22semidirect
58. C2×#14556061C22semidirect
71. #480×C71C22semidirect
213. C2×C71⋊C8#41semidirect
335. C71⋊C8C2×#41semidirect
369. C2×C71#3343semidirect
381. C2×#480D71semidirect
390. C71C2×#3343semidirect
423. #480C2×D71semidirect
743. C2#22600784direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866842
C2×#179866492
#226007842
C2×#179864072
C2×#179863362
C2×#179863222
C2×#179863302
C2×#179862932
C2×#179863012
C2×#179862442
C2×#179862262
C2×#179860962
C2×#179860672
C2×#179860402
C22×#145560612
C2×#480×C712
C2×#334371