Finite Group Databasebeta

← C2×#22600786 #32875989

Subgroups — C2×#22600786 #32875989

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×#17986691C211yesmaximal, characteristic, complemented
2C2×#17986649C211yesmaximal, characteristic
3#22600786C2116yesmaximal, direct product factor
4C2×#17986406C211yesmaximal, characteristic, complemented
5C2×#17986333C211yesmaximal, characteristic, complemented
6C2×#17986321C211yesmaximal, characteristic, complemented
7C2×#17986327C211yesmaximal, characteristic, complemented
8C2×#17986310C211yesmaximal, characteristic, complemented
9C2×#17986292C211yesmaximal, characteristic, complemented
10C2×#17986297C211yesmaximal, characteristic, complemented
11C2×#17986242C211yesmaximal, characteristic, complemented
12C2×#17986100C211yesmaximal, characteristic, complemented
13C2×#17986070C211yesmaximal, characteristic, complemented
14C2×#17986038C211yesmaximal, characteristic, complemented
15C22×#14556062C211yesmaximal, characteristic, complemented
16C2×#465×C71C211yesmaximal, characteristic, complemented
17C22×#11765864—21no—
18C22×#11765848C2211yescharacteristic
19#17986691—24no—
20#17986691C2218yescomplemented
21#17986649—24no—
22#17986649C2218yes—
23C2×#14556127C2211yescharacteristic
24C2×#14556123—21no—
25C2×#14556119—21no—
26C2×#14556119C2211yescharacteristic
27C2×#14556112—21no—
28C2×#14556110—21no—
29C2×#14556109—21no—
30C2×#14556105—21no—
31C2×#14556104C2211yescharacteristic
32C2×#14556099C2211yescharacteristic
33C2×Q8×Dic71C2211yescharacteristic
34C2×D4×Dic71C2211yescharacteristic
35C2×C4×C22⋊D71C2211yescharacteristic
36C2×#14556086C2211yescharacteristic
37C2×#14556084—21no—
38C22×C4⋊Dic71C2211yescharacteristic
39C22×C4⋊Dic71C2211yescharacteristic
40C2×C4⋊C4×D71C2211yescharacteristic
41#17986406C2218yescomplemented
42#17986333C2218yescomplemented
43#17986327C2218yescomplemented
44#17986321C2218yescomplemented
45#17986310C2218yescomplemented
46#17986297C2218yescomplemented
47#17986292C2218yescomplemented
48#17986242C2218yescomplemented
49#17986100C2218yescomplemented
50#17986070C2218yescomplemented
51#17986038C2218yescomplemented
52C2×#14556062C2211yescharacteristic
53C2×#14556062C2211yescharacteristic
54C2×#14556062C2211yescharacteristic
55C2×#14556062C2211yescharacteristic
56C2×#14556062C2218yescomplemented
57C2×#14556061C2211yescharacteristic
58C2×#14556061C2211yescharacteristic
59C2×#14556059C2211yescharacteristic
60C2×#14556059C2211yescharacteristic
61C2×Dic71⋊C8C2211yescharacteristic
62C2×#14556052C2211yescharacteristic
63C2×#14556052C2211yescharacteristic
64C2×#14556049C2211yescharacteristic
65C2×#14556049C2211yescharacteristic
66C2×C22⋊(C71⋊C8)C2211yescharacteristic
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×#14556038C2211yescharacteristic
69C22×SD16×C71C2211yescharacteristic
70C23×C8×C71C2211yescharacteristic
71C2×C22⋊Q8×C71C2211yescharacteristic
72C2×#121×C71C2211yescharacteristic
73#465×C71C2218yescomplemented
74C2×#106×C71C2211yescharacteristic
75C2×#103×C71C2211yescharacteristic
76C2×#102×C71C2211yescharacteristic
77C2×#11765864—28no—
78C2×#11765864—48no—
79C22×Dic142—21no—
80C22×C22⋊D71—21no—
81C22×C22⋊D71D411yescharacteristic
82C23×Dic71—21no—
83C23×Dic71—21no—
84C23×Dic71—21no—
85C22×C4×D71—21no—
86C22×C4×D71C2311yescharacteristic
87C2×#11765848—24no—
88C2×#11765848C2314yes—
89C22×C71⋊C8C2311yescharacteristic
90C22×C71⋊C8C2311yescharacteristic
91#14556127—22no—
92#14556127C2314yes—
93#14556123—28no—
94#14556119—28no—
95#14556119—22no—
96#14556119C2314yes—
97#14556112—28no—
98#14556110—28no—
99#14556109—28no—
100#14556105—28no—
101#14556104—22no—
102#14556104C2314yes—
103#14556099—22no—
104#14556099C2314yes—
105Q8×Dic71—22no—
106Q8×Dic71C2314yes—
107D4×Dic71—22no—
108D4×Dic71C2314yes—
109C4×C22⋊D71D414yes—
110C4×C22⋊D71C2314yes—
111#14556086—22no—
112#14556086C2314yes—
113#14556084—28no—
114C2×C4⋊Dic71—21no—
115C2×C4⋊Dic71—21no—
116C2×C4⋊Dic71—22no—
117C2×C4⋊Dic71—22no—
118C2×C4⋊Dic71—21no—
119C2×C4⋊Dic71—21no—
120C2×C4⋊Dic71C2314yes—
121C2×C4⋊Dic71C2314yes—
122C2×C4⋊Dic71C2311yescharacteristic
123C2×C4⋊Dic71C2311yescharacteristic
124C2×C4⋊Dic71C2311yescharacteristic
125C2×C4⋊Dic71C2311yescharacteristic
126C2×Dic71⋊C4—21no—
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—21no—
129C2×Dic71⋊C4—21no—
130C2×Dic71⋊C4D411yescharacteristic
131C4⋊C4×D71—22no—
132C4⋊C4×D71C2314yes—
133C2×C22⋊Dic71—21no—
134C2×C22⋊Dic71—21no—
135C2×C22⋊Dic71D411yescharacteristic
136C2×(C2×D71)⋊C4—21no—
137C2×(C2×D71)⋊C4—21no—
138C2×(C2×D71)⋊C4D411yescharacteristic
139C2×C4×Dic71—21no—
140C2×C4×Dic71—21no—
141C2×C4×Dic71C2311yescharacteristic
142#14556062C2314yes—
143#14556062C2314yes—
144#14556062C2314yes—
145#14556062C2314yes—
146#14556061C2314yes—
147#14556061C2314yes—
148#14556059C2314yes—
149#14556059C2314yes—
150Dic71⋊C8C2314yes—
151#14556052C2314yes—
152#14556052C2314yes—
153#14556049C2314yes—
154#14556049C2314yes—
155C22⋊(C71⋊C8)C2314yes—
156(C2×D71)⋊C8C2314yes—
157#14556038C2314yes—
158C22×Q8×C71C2311yescharacteristic
159C22×D4×C71—21no—
160C22×D4×C71C2311yescharacteristic
161C23×C4×C71C2311yescharacteristic
162C2×SD16×C71—24no—
163C2×SD16×C71C2314yes—
164C22×C8×C71—24no—
165C22×C8×C71C2311yescharacteristic
166C22×C8×C71C2314yes—
167C22×C8×C71C2311yescharacteristic
168C22⋊Q8×C71—22no—
169C22⋊Q8×C71C2314yes—
170#121×C71—22no—
171#121×C71C2314yes—
172C2×C4⋊C4×C71—21no—
173C2×C4⋊C4×C71C2311yescharacteristic
174C2×C4⋊C4×C71C2311yescharacteristic
175C2×C22⋊C4×C71—21no—
176C2×C22⋊C4×C71—21no—
177#106×C71C2314yes—
178#103×C71C2314yes—
179#102×C71C2314yes—
180C23×D71C2×D411yescharacteristic
181#11765864—432no—
182C2×Dic142—24no—
183C2×Dic142—44no—
184C2×C22⋊D71—24no—
185C2×C22⋊D71—24no—
186C2×C22⋊D71—44no—
187C2×C22⋊D71C2×D414yes—
188C22×Dic71—21no—
189C22×Dic71—21no—
190C22×Dic71—24no—
191C22×Dic71—21no—
192C22×Dic71—21no—
193C22×Dic71—24no—
194C22×Dic71—24no—
195C22×Dic71—44no—
196C22×Dic71—44no—
197C22×Dic71—44no—
198C22×Dic71C2×D411yescharacteristic
199C22×Dic71C2×D411yescharacteristic
200C22×Dic71C2×D411yescharacteristic
201C2×C4×D71—22no—
202C2×C4×D71—22no—
203C2×C4×D71—24no—
204C2×C4×D71—44no—
205C2×C4×D71C2×D412yes—
206C2×C4×D71C2412yes—
207#11765848—28no—
208C2×C71⋊C8—22no—
209C2×C71⋊C8—22no—
210C2×C71⋊C8C2412yes—
211C2×C71⋊C8C2412yes—
212C4⋊Dic71—21no—
213C4⋊Dic71—21no—
214C4⋊Dic71—21no—
215C4⋊Dic71—21no—
216C4⋊Dic71—24no—
217C4⋊Dic71—24no—
218C4⋊Dic71—24no—
219C4⋊Dic71—24no—
220C4⋊Dic71C2412yes—
221C4⋊Dic71C2412yes—
222C4⋊Dic71C2412yes—
223C4⋊Dic71C2412yes—
224Dic71⋊C4—24no—
225Dic71⋊C4—24no—
226Dic71⋊C4—24no—
227Dic71⋊C4—24no—
228Dic71⋊C4C2×D414yes—
229C22⋊Dic71—24no—
230C22⋊Dic71—24no—
231C22⋊Dic71C2×D414yes—
232(C2×D71)⋊C4—24no—
233(C2×D71)⋊C4—24no—
234(C2×D71)⋊C4C2×D414yes—
235C4×Dic71—24no—
236C4×Dic71—24no—
237C4×Dic71C2×D412yes—
238C4×Dic71C2412yes—
239C24×C71—21no—
240C24×C71C2×D411yescharacteristic
241C2×Q8×C71—21no—
242C2×Q8×C71—22no—
243C2×Q8×C71—22no—
244C2×Q8×C71C2412yes—
245C2×D4×C71—24no—
246C2×D4×C71—21no—
247C2×D4×C71—22no—
248C2×D4×C71—22no—
249C2×D4×C71—44no—
250C2×D4×C71C2412yes—
251C22×C4×C71—22no—
252C22×C4×C71—22no—
253C22×C4×C71—21no—
254C22×C4×C71—21no—
255C22×C4×C71—21no—
256C22×C4×C71C2×D411yescharacteristic
257C22×C4×C71C2×D412yes—
258C22×C4×C71C2412yes—
259C22×C4×C71C2411yescharacteristic
260SD16×C71—28no—
261C2×C8×C71—22no—
262C2×C8×C71—28no—
263C2×C8×C71#4114yescomplemented
264C2×C8×C71C2412yes—
265C2×C8×C71C2412yes—
266C4⋊C4×C71—24no—
267C4⋊C4×C71—21no—
268C4⋊C4×C71—21no—
269C4⋊C4×C71C2412yes—
270C4⋊C4×C71C2412yes—
271C22⋊C4×C71—24no—
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—
286Q8×C71—22no—
287Q8×C71—22no—
288Q8×C71—42no—
289D4×C71—22no—
290D4×C71—22no—
291D4×C71—48no—
292D4×C71—42no—
293C2×C4×C71—22no—
294C2×C4×C71—24no—
295C2×C4×C71—22no—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—42no—
301C2×C4×C71—42no—
302C2×C4×C71—42no—
303C2×C4×C71C22×D412yes—
304C2×C4×C71C22×D411yescharacteristic
305C2×C4×C71C2×#4112yes—
306C2×C4×C712−1+412yes—
307C2×C4×C71C2511yescharacteristic
308C22⋊D71—28no—
309C22⋊D71—48no—
310C2×Dic71—22no—
311C2×Dic71—22no—
312C2×Dic71—22no—
313C2×Dic71—22no—
314C2×Dic71—22no—
315C2×Dic71—22no—
316C2×Dic71—22no—
317C2×Dic71—48no—
318C2×Dic71—42no—
319C2×Dic71—48no—
320C2×Dic71—42no—
321C2×Dic71—42no—
322C2×Dic71—42no—
323C2×Dic71—48no—
324C2×Dic71C22×D412yes—
325C2×Dic71C22×D412yes—
326C2×Dic71C22×D412yes—
327C4×D71—24no—
328C4×D71—22no—
329C4×D71—22no—
330C4×D71—48no—
331Dic142—48no—
332C8×C71—22no—
333C8×C71C2×#4114yescomplemented
334C71⋊C8—22no—
335C71⋊C8—22no—
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×#480—711no—
382C2×#477—711no—
383C2×#478—711no—
384C2×#468—711no—
385C2×#465D7111yescharacteristic, complemented
386C2×#440—711no—
387C2×#435—711no—
388C2×#428—711no—
389C22×#107—711no—
390C71C2×#334311yescharacteristic, complemented, Sylow
391C22×#41—1421no—
392C22×SD16C2×D7111yescharacteristic
393C22×M16—711no—
394C23×C8C2×D7111yescharacteristic
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—1421no—
408C2×C22⋊Q8C2×D7111yescharacteristic
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⋊C4—711no—
419#501—718no—
420#484—718no—
421#483—718no—
422#482—718no—
423#480—718no—
424#478—718no—
425#477—718no—
426#468—718no—
427#465C2×D7118yescomplemented
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×#107—711no—
437C2×#107—711no—
438C2×#106—711no—
439C2×#106—711no—
440C2×#106C2×D7111yescharacteristic
441C2×C4⋊C8—711no—
442C2×#103—711no—
443C2×#103—711no—
444C2×#103C2×D7111yescharacteristic
445C2×#102—711no—
446C2×#102—711no—
447C2×#102C2×D7111yescharacteristic
448C2×C22⋊C8—711no—
449C2×C22⋊C8—711no—
450C2×#97—711no—
451C2×#41—2848no—
452C2×#41—1428no—
453C22×Q8—1421no—
454C22×Q8C22×D7111yescharacteristic
455C22×D4—21no—
456C22×D4—711no—
457C22×D4—1421no—
458C22×D4C22×D7111yescharacteristic
459C23×C4—711no—
460C23×C4—1421no—
461C23×C4—1421no—
462C23×C4—1421no—
463C23×C4—1421no—
464C23×C4C22×D7111yescharacteristic
465C2×SD16—24no—
466C2×SD16C22×D7114yes—
467C2×M16—714no—
468C2×M16—1424no—
469C22×C8—24no—
470C22×C8—711no—
471C22×C8—711no—
472C22×C8C22×D7111yescharacteristic
473C22×C8C22×D7114yes—
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—22no—
485C22⋊Q8—714no—
486C22⋊Q8—1428no—
487C22⋊Q8—1422no—
488C22⋊Q8C22×D7114yes—
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—711no—
504C2×C4⋊C4—711no—
505C2×C4⋊C4—711no—
506C2×C4⋊C4—711no—
507C2×C4⋊C4—711no—
508C2×C4⋊C4—714no—
509C2×C4⋊C4—714no—
510C2×C4⋊C4—714no—
511C2×C4⋊C4—1422no—
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—1421no—
519C2×C4⋊C4—1421no—
520C2×C4⋊C4—1422no—
521C2×C4⋊C4—1422no—
522C2×C4⋊C4C22×D7111yescharacteristic
523C2×C4⋊C4C22×D7111yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—711no—
527C2×C22⋊C4—711no—
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#107—714no—
540#107—714no—
541#106—714no—
542#106—714no—
543#106C22×D7114yes—
544C4⋊C8—714no—
545#103—714no—
546#103—714no—
547#103C22×D7114yes—
548#102—714no—
549#102—714no—
550#102C22×D7114yes—
551C22⋊C8—714no—
552C22⋊C8—714no—
553#97—714no—
554C24—21no—
555C24—711no—
556C24D4×D7111yescharacteristic
557#41—28432no—
558C2×Q8—21no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—2844no—
562C2×Q8—1424no—
563C2×Q8C23×D7112yes—
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—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—2844no—
580C22×C4—2844no—
581C22×C4—2844no—
582C22×C4—2844no—
583C22×C4—711no—
584C22×C4—711no—
585C22×C4—711no—
586C22×C4—712no—
587C22×C4—712no—
588C22×C4—1424no—
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—28no—
603M16—1428no—
604C2×C8—22no—
605C2×C8—28no—
606C2×C8—712no—
607C2×C8—712no—
608C2×C8—1422no—
609C2×C8—1422no—
610C2×C8#1176586414yescomplemented
611C2×C8C23×D7112yes—
612C2×C8C23×D7112yes—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—714no—
617C4⋊C4—712no—
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—1421no—
628C4⋊C4—1421no—
629C4⋊C4—1421no—
630C4⋊C4—1424no—
631C4⋊C4—1421no—
632C4⋊C4—1424no—
633C4⋊C4C23×D7112yes—
634C4⋊C4C23×D7112yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—714no—
638C22⋊C4—714no—
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#1455615514yes—
658C23C2×D4×D7112yes—
659C23C2×D4×D7111yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—2848no—
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—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—2848no—
681C2×C4—2842no—
682C2×C4—2842no—
683C2×C4—2848no—
684C2×C4—2848no—
685C2×C4—2842no—
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×C4C2×#1176586412yes—
704C2×C4#1455617512yes—
705C2×C4C24×D7111yescharacteristic
706C8—22no—
707C8—1422no—
708C8—1422no—
709C8C2×#1176586414yescomplemented
710C22—22no—
711C22—28no—
712C22—22no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—84no—
717C22—2844no—
718C22—1422no—
719C22—1422no—
720C22—1422no—
721C22#1798664912yes—
722C22C2×#1455615514yes—
723C22C2×#1455615512yes—
724C22#1798681312yes—
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#1798664912yes—
738C4C22×#1176586411yescharacteristic
739C4C2×#1455617511yescharacteristic
740C2—24no—
741C2—82no—
742C2—2842no—
743C2#2260078614yesdirect product factor
744C2C2×#1798664911yescharacteristic
745C2C22×#1455615511yescharacteristic
746C2C2×#1798681311yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#465×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986649C2
hypercenterC2×#465D71
hypocenterC71C2×#3343
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#17986691C2semidirect
3. #22600786C2direct (N × H)
4. C2×#17986406C2semidirect
5. C2×#17986333C2semidirect
6. C2×#17986321C2semidirect
7. C2×#17986327C2semidirect
8. C2×#17986310C2semidirect
9. C2×#17986292C2semidirect
10. C2×#17986297C2semidirect
11. C2×#17986242C2semidirect
12. C2×#17986100C2semidirect
13. C2×#17986070C2semidirect
14. C2×#17986038C2semidirect
15. C22×#14556062C2semidirect
16. C2×#465×C71C2semidirect
20. #17986691C22semidirect
41. #17986406C22semidirect
42. #17986333C22semidirect
43. #17986327C22semidirect
44. #17986321C22semidirect
45. #17986310C22semidirect
46. #17986297C22semidirect
47. #17986292C22semidirect
48. #17986242C22semidirect
49. #17986100C22semidirect
50. #17986070C22semidirect
51. #17986038C22semidirect
56. C2×#14556062C22semidirect
73. #465×C71C22semidirect
263. C2×C8×C71#41semidirect
333. C8×C71C2×#41semidirect
369. C2×C71#3343semidirect
385. C2×#465D71semidirect
390. C71C2×#3343semidirect
427. #465C2×D71semidirect
610. C2×C8#11765864semidirect
709. C8C2×#11765864semidirect
743. C2#22600786direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866912
C2×#179866492
#226007862
C2×#179864062
C2×#179863332
C2×#179863212
C2×#179863272
C2×#179863102
C2×#179862922
C2×#179862972
C2×#179862422
C2×#179861002
C2×#179860702
C2×#179860382
C22×#145560622
C2×#465×C712
C2×#334371