Finite Group Databasebeta

← C2×#22600812 #32876017

Subgroups — C2×#22600812 #32876017

Order 18176.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986695C211yesmaximal, characteristic, complemented
2C2×#17986653C211yesmaximal, characteristic, complemented
3#22600812C2116yesmaximal, direct product factor
4C2×#17986408C211yesmaximal, characteristic, complemented
5C2×#17986318C211yesmaximal, characteristic, complemented
6C2×#17986318C211yesmaximal, characteristic, complemented
7C2×#17986324C211yesmaximal, characteristic, complemented
8C2×#17986313C211yesmaximal, characteristic, complemented
9C2×#17986300C211yesmaximal, characteristic, complemented
10C2×#17986290C211yesmaximal, characteristic, complemented
11C2×#17986252C211yesmaximal, characteristic, complemented
12C2×#17986235C211yesmaximal, characteristic, complemented
13C2×#17986112C211yesmaximal, characteristic, complemented
14C2×#17986041C211yesmaximal, characteristic, complemented
15C22×#14556060C211yesmaximal, characteristic, complemented
16C2×#435×C71C211yesmaximal, characteristic, complemented
17C22×#11765864—21no—
18C22×D568C2211yescharacteristic
19#17986695—24no—
20#17986695C2218yescomplemented
21#17986653—24no—
22#17986653C2218yescomplemented
23C2×#14556128C2211yescharacteristic
24C2×#14556123—21no—
25C2×#14556120C2211yescharacteristic
26C2×#14556112—21no—
27C2×#14556112—21no—
28C2×#14556110—21no—
29C2×#14556108—21no—
30C2×#14556102C2211yescharacteristic
31C2×#14556102C2211yescharacteristic
32C2×#14556102C2211yescharacteristic
33C2×#14556102C2211yescharacteristic
34C2×#14556100—21no—
35C2×C4×D284C2211yescharacteristic
36C2×C4×D284C2211yescharacteristic
37C2×(C22⋊D71)⋊C4—21no—
38C2×#14556087C2211yescharacteristic
39C22×C4⋊Dic71C2211yescharacteristic
40C22×C4⋊Dic71C2211yescharacteristic
41C22×C4⋊Dic71C2211yescharacteristic
42#17986408C2218yescomplemented
43#17986324C2218yescomplemented
44#17986318C2218yescomplemented
45#17986318C2218yescomplemented
46#17986313C2218yescomplemented
47#17986300C2218yescomplemented
48#17986290C2218yescomplemented
49#17986252C2218yescomplemented
50#17986235C2218yescomplemented
51#17986112C2218yescomplemented
52#17986041C2218yescomplemented
53C2×#14556062C2211yescharacteristic
54C2×#14556062C2211yescharacteristic
55C2×#14556062C2211yescharacteristic
56C2×#14556060C2211yescharacteristic
57C2×#14556060C2211yescharacteristic
58C2×#14556060C2211yescharacteristic
59C2×#14556060C2211yescharacteristic
60C2×#14556060C2211yescharacteristic
61C2×#14556060C2211yescharacteristic
62C2×#14556060C2218yescomplemented
63C2×#14556050C2211yescharacteristic
64C2×#14556050C2211yescharacteristic
65C2×#14556050C2211yescharacteristic
66C2×#14556050C2211yescharacteristic
67C2×#14556050C2211yescharacteristic
68C2×#14556050C2211yescharacteristic
69C22×M16×C71C2211yescharacteristic
70C23×C8×C71C2211yescharacteristic
71C2×C4×D4×C71C2211yescharacteristic
72#435×C71C2218yescomplemented
73C2×C4⋊C8×C71C2211yescharacteristic
74C2×C22⋊C8×C71C2211yescharacteristic
75C2×C22⋊C8×C71C2211yescharacteristic
76C2×#97×C71C2211yescharacteristic
77C2×#11765864—28no—
78C2×#11765864—48no—
79C22×Dic142—21no—
80C22×D284C2311yescharacteristic
81C22×D284C2311yescharacteristic
82C22×C22⋊D71—21no—
83C22×C22⋊D71—21no—
84C22×C22⋊D71—21no—
85C22×C22⋊D71—21no—
86C23×Dic71—21no—
87C23×Dic71—21no—
88C23×Dic71—21no—
89C22×C4×D71—21no—
90C22×C4×D71—21no—
91C2×D568—24no—
92C2×D568C2314yes—
93#14556128—22no—
94#14556128C2314yes—
95#14556123—28no—
96#14556120—22no—
97#14556120C2314yes—
98#14556112—28no—
99#14556112—28no—
100#14556110—28no—
101#14556108—28no—
102#14556102—22no—
103#14556102—22no—
104#14556102—22no—
105#14556102—22no—
106#14556102C2314yes—
107#14556102C2314yes—
108#14556102C2314yes—
109#14556102C2314yes—
110#14556100—28no—
111C4×D284—22no—
112C4×D284—22no—
113C4×D284C2314yes—
114C4×D284C2314yes—
115(C22⋊D71)⋊C4—28no—
116#14556087—22no—
117#14556087C2314yes—
118C2×C4⋊Dic71—22no—
119C2×C4⋊Dic71—22no—
120C2×C4⋊Dic71—22no—
121C2×C4⋊Dic71—21no—
122C2×C4⋊Dic71—21no—
123C2×C4⋊Dic71—21no—
124C2×C4⋊Dic71—21no—
125C2×C4⋊Dic71C2314yes—
126C2×C4⋊Dic71C2314yes—
127C2×C4⋊Dic71C2314yes—
128C2×C4⋊Dic71C2311yescharacteristic
129C2×C4⋊Dic71C2311yescharacteristic
130C2×C4⋊Dic71C2311yescharacteristic
131C2×C4⋊Dic71C2311yescharacteristic
132C2×C4⋊Dic71C2311yescharacteristic
133C2×C4⋊Dic71C2311yescharacteristic
134C2×Dic71⋊C4—21no—
135C2×Dic71⋊C4—21no—
136C2×C22⋊Dic71—21no—
137C2×(C2×D71)⋊C4—21no—
138C2×(C2×D71)⋊C4—21no—
139C2×(C2×D71)⋊C4—21no—
140C2×(C2×D71)⋊C4—21no—
141C2×(C2×D71)⋊C4—21no—
142C2×(C2×D71)⋊C4—21no—
143C2×C4×Dic71—21no—
144#14556062C2314yes—
145#14556062C2314yes—
146#14556062C2314yes—
147#14556060C2314yes—
148#14556060C2314yes—
149#14556060C2314yes—
150#14556060C2314yes—
151#14556060C2314yes—
152#14556060C2314yes—
153#14556050C2314yes—
154#14556050C2314yes—
155#14556050C2314yes—
156#14556050C2314yes—
157#14556050C2314yes—
158#14556050C2314yes—
159C22×D4×C71D411yescharacteristic
160C23×C4×C71C2311yescharacteristic
161C23×C4×C71C2311yescharacteristic
162C2×M16×C71—24no—
163C2×M16×C71C2314yes—
164C22×C8×C71—24no—
165C22×C8×C71C2311yescharacteristic
166C22×C8×C71C2311yescharacteristic
167C22×C8×C71C2311yescharacteristic
168C22×C8×C71C2314yes—
169C22×C8×C71C2311yescharacteristic
170C4×D4×C71D414yes—
171C4×D4×C71C2314yes—
172C2×C4⋊C4×C71D411yescharacteristic
173C2×C22⋊C4×C71D411yescharacteristic
174C2×C22⋊C4×C71D411yescharacteristic
175C2×C42×C71C2311yescharacteristic
176C4⋊C8×C71C2314yes—
177C22⋊C8×C71C2314yes—
178C22⋊C8×C71C2314yes—
179#97×C71C2314yes—
180C23×D71—21no—
181C23×D71—21no—
182#11765864—432no—
183C2×Dic142—24no—
184C2×Dic142—44no—
185C2×D284—22no—
186C2×D284—22no—
187C2×D284—22no—
188C2×D284—22no—
189C2×D284—21no—
190C2×D284—21no—
191C2×D284C2412yes—
192C2×D284C2412yes—
193C2×C22⋊D71—24no—
194C2×C22⋊D71—24no—
195C2×C22⋊D71—24no—
196C2×C22⋊D71—24no—
197C2×C22⋊D71—44no—
198C2×C22⋊D71—44no—
199C2×C22⋊D71—44no—
200C2×C22⋊D71—82no—
201C22×Dic71—21no—
202C22×Dic71—21no—
203C22×Dic71—21no—
204C22×Dic71—21no—
205C22×Dic71—21no—
206C22×Dic71—24no—
207C22×Dic71—24no—
208C22×Dic71—21no—
209C22×Dic71—24no—
210C22×Dic71—44no—
211C22×Dic71—44no—
212C22×Dic71—82no—
213C2×C4×D71—24no—
214C2×C4×D71—24no—
215C2×C4×D71—44no—
216C2×C4×D71—82no—
217D568—28no—
218C4⋊Dic71—21no—
219C4⋊Dic71—21no—
220C4⋊Dic71—21no—
221C4⋊Dic71—21no—
222C4⋊Dic71—21no—
223C4⋊Dic71—24no—
224C4⋊Dic71—24no—
225C4⋊Dic71—24no—
226C4⋊Dic71—24no—
227C4⋊Dic71—21no—
228C4⋊Dic71C2412yes—
229C4⋊Dic71C2412yes—
230C4⋊Dic71C2412yes—
231C4⋊Dic71C2412yes—
232C4⋊Dic71C2412yes—
233C4⋊Dic71C2412yes—
234Dic71⋊C4—24no—
235Dic71⋊C4—24no—
236C22⋊Dic71—24no—
237(C2×D71)⋊C4—24no—
238(C2×D71)⋊C4—24no—
239(C2×D71)⋊C4—24no—
240(C2×D71)⋊C4—24no—
241(C2×D71)⋊C4—24no—
242(C2×D71)⋊C4—24no—
243C4×Dic71—24no—
244C24×C71C2×D411yescharacteristic
245C24×C71C2×D411yescharacteristic
246C2×D4×C71—24no—
247C2×D4×C71C2×D414yes—
248C22×C4×C71—22no—
249C22×C4×C71—22no—
250C22×C4×C71—22no—
251C22×C4×C71—22no—
252C22×C4×C71C2×D411yescharacteristic
253C22×C4×C71C2×D411yescharacteristic
254C22×C4×C71C2×D411yescharacteristic
255C22×C4×C71C2×D411yescharacteristic
256C22×C4×C71C2×D412yes—
257C22×C4×C71C2×D412yes—
258C22×C4×C71C2412yes—
259C22×C4×C71C2412yes—
260C22×C4×C71C2411yescharacteristic
261M16×C71—28no—
262C2×C8×C71—22no—
263C2×C8×C71—22no—
264C2×C8×C71—22no—
265C2×C8×C71—28no—
266C2×C8×C71#4114yescomplemented
267C2×C8×C71C2412yes—
268C2×C8×C71C2412yes—
269C2×C8×C71C2412yes—
270C2×C8×C71C2412yes—
271C4⋊C4×C71C2×D414yes—
272C22⋊C4×C71C2×D414yes—
273C22⋊C4×C71C2×D414yes—
274C42×C71C2×D412yes—
275C42×C71C2412yes—
276C23×C71—22no—
277C23×C71—22no—
278C23×C71—22no—
279C23×C71—22no—
280C23×C71—22no—
281C23×C71AGL(1,ℤ/8)14yes—
282C23×C71C22×D412yes—
283C23×C71C22×D412yes—
284C23×C71C22×D411yescharacteristic
285C22×D71—22no—
286C22×D71—22no—
287C22×D71—42no—
288C22×D71—42no—
289C22×D71—42no—
290C22×D71—42no—
291C22×D71—42no—
292C22×D71—42no—
293D4×C71—28no—
294C2×C4×C71—22no—
295C2×C4×C71—22no—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—24no—
299C2×C4×C71—24no—
300C2×C4×C71—22no—
301C2×C4×C71—22no—
302C2×C4×C71—22no—
303C2×C4×C71—22no—
304C2×C4×C71C22×D412yes—
305C2×C4×C71C22×D412yes—
306C2×C4×C71C22×D412yes—
307C2×C4×C71C22×D412yes—
308C2×C4×C71C22×D411yescharacteristic
309C2×C4×C71C2×#4112yes—
310C2×C4×C712−1+412yes—
311C2×C4×C71C2511yescharacteristic
312C22⋊D71—48no—
313C22⋊D71—48no—
314C22⋊D71—48no—
315C22⋊D71—84no—
316C2×Dic71—22no—
317C2×Dic71—22no—
318C2×Dic71—22no—
319C2×Dic71—22no—
320C2×Dic71—22no—
321C2×Dic71—22no—
322C2×Dic71—48no—
323C2×Dic71—42no—
324C2×Dic71—42no—
325C2×Dic71—42no—
326C2×Dic71—48no—
327C2×Dic71—42no—
328C2×Dic71—42no—
329C2×Dic71—42no—
330C2×Dic71—84no—
331D284—22no—
332D284—22no—
333D284—22no—
334D284—22no—
335D284—42no—
336D284—42no—
337C4×D71—48no—
338C4×D71—84no—
339Dic142—48no—
340C8×C71—22no—
341C8×C71—22no—
342C8×C71—22no—
343C8×C71C2×#4114yescomplemented
344C22×C71—28no—
345C22×C71—22no—
346C22×C71—22no—
347C22×C71—22no—
348C22×C71—22no—
349C22×C71—22no—
350C22×C71—44no—
351C22×C71#54712yes—
352C22×C71C2×AGL(1,ℤ/8)14yes—
353C22×C71C2×AGL(1,ℤ/8)12yes—
354C22×C71#57712yes—
355C22×C71C23×D411yescharacteristic
356C2×D71—42no—
357C2×D71—42no—
358C2×D71—42no—
359C2×D71—42no—
360C2×D71—42no—
361C2×D71—42no—
362C2×D71—84no—
363C2×D71—84no—
364C4×C71—22no—
365C4×C71—22no—
366C4×C71—22no—
367C4×C71—22no—
368C4×C71#54712yes—
369C4×C71C22×#4111yescharacteristic
370C4×C71C2×2−1+411yescharacteristic
371Dic71—42no—
372Dic71—42no—
373Dic71—42no—
374Dic71—42no—
375Dic71—42no—
376Dic71—42no—
377C2×#3345—711nomaximal, Sylow
378C2×C71—24no—
379C2×C71—42no—
380C2×C71#334514yescomplemented
381C2×C71C2×#54711yescharacteristic
382C2×C71C22×AGL(1,ℤ/8)11yescharacteristic
383C2×C71C2×#57711yescharacteristic
384D71—82no—
385D71—82no—
386C2×#553—711no—
387C2×#547—711no—
388#3345—7116no—
389C2×#501—711no—
390C2×#481—711no—
391C2×#481—711no—
392C2×#482—711no—
393C2×#480—711no—
394C2×#478—711no—
395C2×#476—711no—
396C2×#469—711no—
397C2×#466—711no—
398C2×#442—711no—
399C2×#435D7111yescharacteristic, complemented
400C2×#428—711no—
401C22×#106—711no—
402C71C2×#334511yescharacteristic, complemented, Sylow
403C22×#41—1421no—
404C22×D8—711no—
405C22×M16C2×D7111yescharacteristic
406C23×C8C2×D7111yescharacteristic
407#553—718no—
408#553—1424no—
409#547—718no—
410#547—1424no—
411C2×C4⋊Q8—711no—
412C2×#126—1421no—
413C2×#125—711no—
414C2×#123—1421no—
415C2×#123—1421no—
416C2×#123—1421no—
417C2×C22⋊Q8—1421no—
418C2×#121—711no—
419C2×#121—711no—
420C2×#121—711no—
421C2×#121—711no—
422C2×#121—1421no—
423C2×C4×D4—711no—
424C2×C4×D4—711no—
425C2×C4×D4—1421no—
426C2×C4×D4C2×D7111yescharacteristic
427C2×#117—711no—
428C22×C4⋊C4—711no—
429C22×C4⋊C4—711no—
430C22×C4⋊C4—711no—
431#501—718no—
432#482—718no—
433#481—718no—
434#481—718no—
435#480—718no—
436#478—718no—
437#476—718no—
438#469—718no—
439#466—718no—
440#442—718no—
441#435C2×D7118yescomplemented
442#428—718no—
443C2×#107—711no—
444C2×#107—711no—
445C2×#107—711no—
446C2×#106—711no—
447C2×#106—711no—
448C2×#106—711no—
449C2×#106—711no—
450C2×#106—718no—
451C2×#106—711no—
452C2×#106—711no—
453C2×C4⋊C8C2×D7111yescharacteristic
454C2×#102—711no—
455C2×#102—711no—
456C2×#102—711no—
457C2×#102—711no—
458C2×#102—711no—
459C2×#102—711no—
460C2×C22⋊C8C2×D7111yescharacteristic
461C2×C22⋊C8C2×D7111yescharacteristic
462C2×#97C2×D7111yescharacteristic
463C2×#41—2848no—
464C2×#41—1428no—
465C22×Q8—1421no—
466C22×D4—711no—
467C22×D4—711no—
468C22×D4—1421no—
469C22×D4—1421no—
470C22×D4—1421no—
471C22×D4—1421no—
472C22×D4D28411yescharacteristic
473C23×C4—1421no—
474C23×C4—1421no—
475C23×C4—1421no—
476C23×C4—1421no—
477C23×C4—1421no—
478C23×C4C22×D7111yescharacteristic
479C23×C4C22×D7111yescharacteristic
480C2×D8—714no—
481C2×D8—1424no—
482C2×M16—24no—
483C2×M16C22×D7114yes—
484C22×C8—24no—
485C22×C8C22×D7111yescharacteristic
486C22×C8C22×D7114yes—
487C22×C8C22×D7111yescharacteristic
488C22×C8C22×D7111yescharacteristic
489C22×C8C22×D7111yescharacteristic
490C4⋊Q8—714no—
491C4⋊Q8—1422no—
492#126—1428no—
493#125—714no—
494#125—1422no—
495#123—1428no—
496#123—1428no—
497#123—1428no—
498C22⋊Q8—1428no—
499#121—714no—
500#121—714no—
501#121—714no—
502#121—714no—
503#121—1428no—
504#121—1422no—
505#121—1422no—
506#121—1422no—
507#121—1422no—
508C4×D4—714no—
509C4×D4—714no—
510C4×D4—1428no—
511C4×D4—1422no—
512C4×D4—1422no—
513C4×D4D28414yes—
514C4×D4C22×D7114yes—
515#117—714no—
516#117—1422no—
517C2×C4⋊C4—711no—
518C2×C4⋊C4—711no—
519C2×C4⋊C4—711no—
520C2×C4⋊C4—711no—
521C2×C4⋊C4—711no—
522C2×C4⋊C4—714no—
523C2×C4⋊C4—714no—
524C2×C4⋊C4—714no—
525C2×C4⋊C4—711no—
526C2×C4⋊C4—1421no—
527C2×C4⋊C4—1421no—
528C2×C4⋊C4—1421no—
529C2×C4⋊C4—1422no—
530C2×C4⋊C4—1422no—
531C2×C4⋊C4—1422no—
532C2×C4⋊C4—1421no—
533C2×C4⋊C4—1421no—
534C2×C4⋊C4—1421no—
535C2×C4⋊C4D28411yescharacteristic
536C2×C22⋊C4—1421no—
537C2×C22⋊C4—1421no—
538C2×C22⋊C4—1421no—
539C2×C22⋊C4—1421no—
540C2×C22⋊C4—1421no—
541C2×C22⋊C4—1421no—
542C2×C22⋊C4—1421no—
543C2×C22⋊C4D28411yescharacteristic
544C2×C22⋊C4D28411yescharacteristic
545C2×C42—1421no—
546C2×C42C22×D7111yescharacteristic
547#107—714no—
548#107—714no—
549#107—714no—
550#106—714no—
551#106—714no—
552#106—714no—
553#106—714no—
554#106—714no—
555#106—714no—
556C4⋊C8C22×D7114yes—
557#102—714no—
558#102—714no—
559#102—714no—
560#102—714no—
561#102—714no—
562#102—714no—
563C22⋊C8C22×D7114yes—
564C22⋊C8C22×D7114yes—
565#97C22×D7114yes—
566C24—1421no—
567C24—1421no—
568C24C2×D28411yescharacteristic
569C24C2×D28411yescharacteristic
570#41—28432no—
571C2×Q8—2844no—
572C2×Q8—1424no—
573C2×D4—24no—
574C2×D4—2844no—
575C2×D4—2844no—
576C2×D4—2844no—
577C2×D4—5682no—
578C2×D4—712no—
579C2×D4—712no—
580C2×D4—1424no—
581C2×D4—1424no—
582C2×D4—1424no—
583C2×D4—1424no—
584C2×D4—1421no—
585C2×D4—1421no—
586C2×D4—1422no—
587C2×D4—1422no—
588C2×D4—1422no—
589C2×D4—1422no—
590C2×D4C2×D28414yes—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—2844no—
596C22×C4—2844no—
597C22×C4—2844no—
598C22×C4—5682no—
599C22×C4—5682no—
600C22×C4—1424no—
601C22×C4—1424no—
602C22×C4—1421no—
603C22×C4—1421no—
604C22×C4—1421no—
605C22×C4—1421no—
606C22×C4—1421no—
607C22×C4—1421no—
608C22×C4—1424no—
609C22×C4—1424no—
610C22×C4—1424no—
611C22×C4C2×D28412yes—
612C22×C4C2×D28412yes—
613C22×C4C2×D28411yescharacteristic
614C22×C4C2×D28411yescharacteristic
615C22×C4C2×D28411yescharacteristic
616C22×C4C2×D28411yescharacteristic
617C22×C4C23×D7112yes—
618C22×C4C23×D7112yes—
619C22×C4C23×D7111yescharacteristic
620D8—1428no—
621M16—28no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—28no—
626C2×C8#1176586414yescomplemented
627C2×C8C23×D7112yes—
628C2×C8C23×D7112yes—
629C2×C8C23×D7112yes—
630C2×C8C23×D7112yes—
631C4⋊C4—712no—
632C4⋊C4—712no—
633C4⋊C4—712no—
634C4⋊C4—712no—
635C4⋊C4—712no—
636C4⋊C4—712no—
637C4⋊C4—1424no—
638C4⋊C4—1424no—
639C4⋊C4—1421no—
640C4⋊C4—1421no—
641C4⋊C4—1421no—
642C4⋊C4—1421no—
643C4⋊C4—1421no—
644C4⋊C4—1424no—
645C4⋊C4—1424no—
646C4⋊C4—1424no—
647C4⋊C4—1421no—
648C4⋊C4—1424no—
649C4⋊C4C2×D28414yes—
650C22⋊C4—1424no—
651C22⋊C4—1424no—
652C22⋊C4—1424no—
653C22⋊C4—1424no—
654C22⋊C4—1424no—
655C22⋊C4—1424no—
656C22⋊C4—1424no—
657C22⋊C4C2×D28414yes—
658C22⋊C4C2×D28414yes—
659C42—1424no—
660C42C2×D28412yes—
661C42C23×D7112yes—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—2842no—
668C23—2842no—
669C23—2842no—
670C23—2842no—
671C23—2842no—
672C23—2842no—
673C23—1422no—
674C23—1422no—
675C23#1455615614yes—
676C23C22×D28412yes—
677C23C22×D28412yes—
678C23C22×D28411yescharacteristic
679Q8—2848no—
680D4—28no—
681D4—2848no—
682D4—2848no—
683D4—2848no—
684D4—2842no—
685D4—2842no—
686D4—5684no—
687D4—1422no—
688D4—1422no—
689D4—1422no—
690D4—1422no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—2848no—
702C2×C4—2848no—
703C2×C4—2842no—
704C2×C4—2842no—
705C2×C4—2842no—
706C2×C4—2848no—
707C2×C4—2842no—
708C2×C4—2842no—
709C2×C4—2842no—
710C2×C4—5684no—
711C2×C4—5684no—
712C2×C4—1422no—
713C2×C4—1422no—
714C2×C4—1422no—
715C2×C4—1422no—
716C2×C4—1422no—
717C2×C4—1422no—
718C2×C4C22×D28412yes—
719C2×C4C22×D28412yes—
720C2×C4C22×D28412yes—
721C2×C4C22×D28412yes—
722C2×C4C22×D28411yescharacteristic
723C2×C4C2×#1176586412yes—
724C2×C4#1455617512yes—
725C2×C4C24×D7111yescharacteristic
726C8—22no—
727C8—22no—
728C8—22no—
729C8C2×#1176586414yescomplemented
730C22—22no—
731C22—22no—
732C22—28no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—2842no—
738C22—2842no—
739C22—2842no—
740C22—2842no—
741C22—2842no—
742C22—2842no—
743C22—5684no—
744C22—5684no—
745C22#1798665312yes—
746C22C2×#1455615614yes—
747C22C2×#1455615612yes—
748C22#1798681112yes—
749C22C23×D28411yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—2842no—
755C4—2842no—
756C4—2842no—
757C4—2842no—
758C4—2842no—
759C4—2842no—
760C4#1798665312yes—
761C4C22×#1176586411yescharacteristic
762C4C2×#1455617511yescharacteristic
763C2—24no—
764C2—42no—
765C2—5682no—
766C2—5682no—
767C2#2260081214yesdirect product factor
768C2C2×#1798665311yescharacteristic
769C2C22×#1455615611yescharacteristic
770C2C2×#1798681111yescharacteristic
subgroupG/H
centerC23C22×D284
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#435×C71C2
socleC23×C71C22×D4
hypercenterC2×#435D71
hypocenterC71C2×#3345
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#17986695C2semidirect
2. C2×#17986653C2semidirect
3. #22600812C2direct (N × H)
4. C2×#17986408C2semidirect
5. C2×#17986318C2semidirect
6. C2×#17986318C2semidirect
7. C2×#17986324C2semidirect
8. C2×#17986313C2semidirect
9. C2×#17986300C2semidirect
10. C2×#17986290C2semidirect
11. C2×#17986252C2semidirect
12. C2×#17986235C2semidirect
13. C2×#17986112C2semidirect
14. C2×#17986041C2semidirect
15. C22×#14556060C2semidirect
16. C2×#435×C71C2semidirect
20. #17986695C22semidirect
22. #17986653C22semidirect
42. #17986408C22semidirect
43. #17986324C22semidirect
44. #17986318C22semidirect
45. #17986318C22semidirect
46. #17986313C22semidirect
47. #17986300C22semidirect
48. #17986290C22semidirect
49. #17986252C22semidirect
50. #17986235C22semidirect
51. #17986112C22semidirect
52. #17986041C22semidirect
62. C2×#14556060C22semidirect
72. #435×C71C22semidirect
266. C2×C8×C71#41semidirect
343. C8×C71C2×#41semidirect
380. C2×C71#3345semidirect
399. C2×#435D71semidirect
402. C71C2×#3345semidirect
441. #435C2×D71semidirect
626. C2×C8#11765864semidirect
729. C8C2×#11765864semidirect
767. C2#22600812direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866952
C2×#179866532
#226008122
C2×#179864082
C2×#179863182
C2×#179863242
C2×#179863132
C2×#179863002
C2×#179862902
C2×#179862522
C2×#179862352
C2×#179861122
C2×#179860412
C22×#145560602
C2×#435×C712
C2×#334571