Finite Group Databasebeta

← C2×#21458295 #30558582

Subgroups — C2×#21458295 #30558582

Order 15616.

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×#16840464C211yesmaximal, characteristic, complemented
2C2×#16840412C211yesmaximal, characteristic, complemented
3#21458295C2116yesmaximal, direct product factor
4C2×#16840170C211yesmaximal, characteristic, complemented
5C2×#16840079C211yesmaximal, characteristic, complemented
6C2×#16840078C211yesmaximal, characteristic, complemented
7C2×#16840085C211yesmaximal, characteristic, complemented
8C2×#16840073C211yesmaximal, characteristic, complemented
9C2×#16840064C211yesmaximal, characteristic, complemented
10C2×#16840050C211yesmaximal, characteristic, complemented
11C2×#16840012C211yesmaximal, characteristic, complemented
12C2×#16839874C211yesmaximal, characteristic, complemented
13C2×#16839833C211yesmaximal, characteristic, complemented
14C2×#16839803C211yesmaximal, characteristic, complemented
15C22×#14519709C211yesmaximal, characteristic, complemented
16C2×C61×#466C211yesmaximal, characteristic, complemented
17C22×#11758224—21no—
18C22×#11758189C2211yescharacteristic
19#16840464—24no—
20#16840464C2218yescomplemented
21#16840412—24no—
22#16840412C2218yescomplemented
23C2×#14519776C2211yescharacteristic
24C2×#14519770—21no—
25C2×#14519768C2211yescharacteristic
26C2×#14519761—21no—
27C2×#14519759—21no—
28C2×#14519758—21no—
29C2×#14519754—21no—
30C2×#14519749—21no—
31C2×#14519748C2211yescharacteristic
32C2×#14519748C2211yescharacteristic
33C2×D4×Dic61—21no—
34C2×D4×Dic61C2211yescharacteristic
35C2×D4×Dic61C2211yescharacteristic
36C2×C4×C22⋊D61C2211yescharacteristic
37C2×#14519735C2211yescharacteristic
38C22×C4⋊Dic61C2211yescharacteristic
39C22×C4⋊Dic61C2211yescharacteristic
40C2×C4⋊C4×D61C2211yescharacteristic
41#16840170C2218yescomplemented
42#16840085C2218yescomplemented
43#16840079C2218yescomplemented
44#16840078C2218yescomplemented
45#16840073C2218yescomplemented
46#16840064C2218yescomplemented
47#16840050C2218yescomplemented
48#16840012C2218yescomplemented
49#16839874C2218yescomplemented
50#16839833C2218yescomplemented
51#16839803C2218yescomplemented
52C2×#14519710C2211yescharacteristic
53C2×#14519710C2211yescharacteristic
54C2×#14519709C2211yescharacteristic
55C2×#14519709C2211yescharacteristic
56C2×#14519709C2211yescharacteristic
57C2×#14519709C2211yescharacteristic
58C2×#14519709C2218yescomplemented
59C2×#14519708C2211yescharacteristic
60C2×#14519708C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519698C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519687C2211yescharacteristic
69C22×D8×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic
71C2×#121×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C61×#466C2218yescomplemented
74C2×#107×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C2×#11758224—28no—
78C2×#11758224—48no—
79C22×Dic122—21no—
80C22×C22⋊D61—21no—
81C22×C22⋊D61—21no—
82C22×C22⋊D61D411yescharacteristic
83C23×Dic61—21no—
84C23×Dic61—21no—
85C23×Dic61—21no—
86C23×Dic61—21no—
87C22×C4×D61—21no—
88C22×C4×D61C2311yescharacteristic
89C2×#11758189—24no—
90C2×#11758189C2314yes—
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93#14519776—22no—
94#14519776C2314yes—
95#14519770—28no—
96#14519768—22no—
97#14519768C2314yes—
98#14519761—28no—
99#14519759—28no—
100#14519758—28no—
101#14519754—28no—
102#14519749—28no—
103#14519748—22no—
104#14519748—22no—
105#14519748C2314yes—
106#14519748C2314yes—
107D4×Dic61—28no—
108D4×Dic61—22no—
109D4×Dic61—22no—
110D4×Dic61C2314yes—
111D4×Dic61C2314yes—
112C4×C22⋊D61D414yes—
113C4×C22⋊D61C2314yes—
114#14519735—22no—
115#14519735C2314yes—
116C2×C4⋊Dic61—22no—
117C2×C4⋊Dic61—21no—
118C2×C4⋊Dic61—21no—
119C2×C4⋊Dic61—22no—
120C2×C4⋊Dic61—21no—
121C2×C4⋊Dic61C2314yes—
122C2×C4⋊Dic61C2311yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×C4⋊Dic61C2311yescharacteristic
126C2×C4⋊Dic61C2314yes—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196D411yescharacteristic
131C4⋊C4×D61—22no—
132C4⋊C4×D61C2314yes—
133C2×C22⋊Dic61—21no—
134C2×C22⋊Dic61—21no—
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61D411yescharacteristic
138C2×#11758198—21no—
139C2×#11758198D411yescharacteristic
140C2×C4×Dic61—21no—
141C2×C4×Dic61C2311yescharacteristic
142#14519710C2314yes—
143#14519710C2314yes—
144#14519709C2314yes—
145#14519709C2314yes—
146#14519709C2314yes—
147#14519709C2314yes—
148#14519708C2314yes—
149#14519708C2314yes—
150#14519706C2314yes—
151#14519698C2314yes—
152#14519698C2314yes—
153#14519698C2314yes—
154#14519698C2314yes—
155C22⋊#92418C2314yes—
156#14519689C2314yes—
157#14519687C2314yes—
158C22×D4×C61—21no—
159C22×D4×C61—21no—
160C22×D4×C61C2311yescharacteristic
161C22×D4×C61C2311yescharacteristic
162C23×C4×C61C2311yescharacteristic
163C2×D8×C61—24no—
164C2×D8×C61C2314yes—
165C22×C8×C61—24no—
166C22×C8×C61C2311yescharacteristic
167C22×C8×C61C2314yes—
168C22×C8×C61C2311yescharacteristic
169#121×C61—22no—
170#121×C61—22no—
171#121×C61C2314yes—
172#121×C61C2314yes—
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61—21no—
177#107×C61C2314yes—
178#102×C61C2314yes—
179#102×C61C2314yes—
180C24×C61—21no—
181C24×C61—21no—
182C24×C61C2×D411yescharacteristic
183C23×D61C2×D411yescharacteristic
184C2×D4×C61—24no—
185C2×D4×C61—24no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—22no—
189C2×D4×C61—22no—
190C2×D4×C61—22no—
191C2×D4×C61—22no—
192C2×D4×C61—44no—
193C2×D4×C61—44no—
194C2×D4×C61C2412yes—
195C2×D4×C61C2412yes—
196C22×C4×C61—22no—
197C22×C4×C61—22no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D412yes—
202C22×C4×C61C2412yes—
203C22×C4×C61C2411yescharacteristic
204C2×C22⋊D61—24no—
205C2×C22⋊D61—24no—
206C2×C22⋊D61—24no—
207C2×C22⋊D61—44no—
208C2×C22⋊D61—82no—
209C2×C22⋊D61C2×D414yes—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—24no—
215C22×Dic61—24no—
216C22×Dic61—24no—
217C22×Dic61—24no—
218C22×Dic61—44no—
219C22×Dic61—44no—
220C22×Dic61—82no—
221C22×Dic61—82no—
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224C22×Dic61C2×D411yescharacteristic
225#11758224—432no—
226C2×C4×D61—22no—
227C2×C4×D61—22no—
228C2×C4×D61—24no—
229C2×C4×D61—44no—
230C2×C4×D61C2×D412yes—
231C2×C4×D61C2412yes—
232C2×Dic122—24no—
233C2×Dic122—44no—
234D8×C61—28no—
235C2×C8×C61—22no—
236C2×C8×C61—28no—
237C2×C8×C61#4114yescomplemented
238C2×C8×C61C2412yes—
239C2×C8×C61C2412yes—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61C2412yes—
243C4⋊C4×C61C2412yes—
244C22⋊C4×C61—24no—
245C22⋊C4×C61—24no—
246C22⋊Dic61—24no—
247C22⋊Dic61—24no—
248C22⋊Dic61—24no—
249C22⋊Dic61—24no—
250C22⋊Dic61C2×D414yes—
251#11758198—24no—
252#11758198C2×D414yes—
253C4⋊Dic61—21no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61—24no—
258C4⋊Dic61—24no—
259C4⋊Dic61—24no—
260C4⋊Dic61C2412yes—
261C4⋊Dic61C2412yes—
262C4⋊Dic61C2412yes—
263C4⋊Dic61C2412yes—
264#11758196—24no—
265#11758196—24no—
266#11758196—24no—
267#11758196C2×D414yes—
268C4×Dic61—24no—
269C4×Dic61C2×D412yes—
270C4×Dic61C2412yes—
271C2×#92418—22no—
272C2×#92418—22no—
273C2×#92418C2412yes—
274C2×#92418C2412yes—
275#11758189—28no—
276C23×C61—22no—
277C23×C61—22no—
278C23×C61—22no—
279C23×C61—22no—
280C23×C61—42no—
281C23×C61—42no—
282C23×C61—42no—
283C23×C61—42no—
284C23×C61—42no—
285C23×C61—42no—
286C23×C61AGL(1,ℤ/8)14yes—
287C23×C61C22×D412yes—
288C23×C61C22×D411yescharacteristic
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—22no—
292C22×D61C22×D412yes—
293D4×C61—22no—
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—22no—
297D4×C61—48no—
298D4×C61—48no—
299D4×C61—42no—
300D4×C61—42no—
301C2×C4×C61—22no—
302C2×C4×C61—24no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61C22×D412yes—
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61C2×#4112yes—
312C2×C4×C612−1+412yes—
313C2×C4×C61C2511yescharacteristic
314C22⋊D61—28no—
315C22⋊D61—48no—
316C22⋊D61—84no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—48no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—48no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—84no—
331C2×Dic61—84no—
332C2×Dic61C22×D412yes—
333C2×Dic61C22×D412yes—
334C2×Dic61C22×D412yes—
335C4×D61—24no—
336C4×D61—22no—
337C4×D61—22no—
338C4×D61—48no—
339Dic122—48no—
340C8×C61—22no—
341C8×C61C2×#4114yescomplemented
342#92418—22no—
343#92418—22no—
344C2×#3345—611nomaximal, Sylow
345C22×C61—28no—
346C22×C61—22no—
347C22×C61—22no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—84no—
355C22×C61—84no—
356C22×C61#54712yes—
357C22×C61C2×AGL(1,ℤ/8)14yes—
358C22×C61C2×AGL(1,ℤ/8)12yes—
359C22×C61#57712yes—
360C22×C61C23×D411yescharacteristic
361C2×D61—22no—
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—44no—
365C4×C61—22no—
366C4×C61—42no—
367C4×C61—42no—
368C4×C61#54712yes—
369C4×C61C22×#4111yescharacteristic
370C4×C61C2×2−1+411yescharacteristic
371Dic61—22no—
372Dic61—22no—
373Dic61—22no—
374Dic61—42no—
375Dic61—42no—
376Dic61—42no—
377Dic61—42no—
378C2×#553—611no—
379C2×#547—611no—
380#3345—6116no—
381C2×#501—611no—
382C2×#481—611no—
383C2×#481—611no—
384C2×#482—611no—
385C2×#480—611no—
386C2×#478—611no—
387C2×#476—611no—
388C2×#469—611no—
389C2×#466D6111yescharacteristic, complemented
390C2×#442—611no—
391C2×#435—611no—
392C2×#428—611no—
393C22×#106—611no—
394C2×C61—24no—
395C2×C61—82no—
396C2×C61—82no—
397C2×C61#334514yescomplemented
398C2×C61C2×#54711yescharacteristic
399C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
400C2×C61C2×#57711yescharacteristic
401D61—42no—
402C22×#41—1221no—
403C22×D8C2×D6111yescharacteristic
404C22×M16—611no—
405C23×C8C2×D6111yescharacteristic
406#553—618no—
407#553—1224no—
408#547—618no—
409#547—1224no—
410C2×C4⋊Q8—611no—
411C2×#126—1221no—
412C2×#125—611no—
413C2×#123—1221no—
414C2×#123—1221no—
415C2×#123—1221no—
416C2×C22⋊Q8—1221no—
417C2×#121—611no—
418C2×#121—611no—
419C2×#121—1221no—
420C2×#121C2×D6111yescharacteristic
421C2×#121C2×D6111yescharacteristic
422C2×C4×D4—611no—
423C2×C4×D4—611no—
424C2×C4×D4—611no—
425C2×C4×D4—1221no—
426C2×#117—611no—
427C22×C4⋊C4—611no—
428C22×C4⋊C4—611no—
429C22×C4⋊C4—611no—
430#501—618no—
431#482—618no—
432#481—618no—
433#481—618no—
434#480—618no—
435#478—618no—
436#476—618no—
437#469—618no—
438#466C2×D6118yescomplemented
439#442—618no—
440#435—618no—
441#428—618no—
442C2×#107—611no—
443C2×#107—611no—
444C2×#107C2×D6111yescharacteristic
445C2×#106—611no—
446C2×#106—611no—
447C2×#106—618no—
448C2×#106—611no—
449C2×#106—611no—
450C2×#106—611no—
451C2×#106—611no—
452C2×C4⋊C8—611no—
453C2×#102—611no—
454C2×#102—611no—
455C2×#102—611no—
456C2×#102—611no—
457C2×#102C2×D6111yescharacteristic
458C2×#102C2×D6111yescharacteristic
459C2×C22⋊C8—611no—
460C2×C22⋊C8—611no—
461C2×#97—611no—
462C61C2×#334511yescharacteristic, complemented, Sylow
463C2×#41—1228no—
464C2×#41—2448no—
465C22×Q8—1221no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4—611no—
469C22×D4—1221no—
470C22×D4—1221no—
471C22×D4C22×D6111yescharacteristic
472C22×D4C22×D6111yescharacteristic
473C23×C4—611no—
474C23×C4—1221no—
475C23×C4—1221no—
476C23×C4—1221no—
477C23×C4—1221no—
478C23×C4—1221no—
479C23×C4C22×D6111yescharacteristic
480C2×D8—24no—
481C2×D8C22×D6114yes—
482C2×M16—614no—
483C2×M16—1224no—
484C22×C8—24no—
485C22×C8—611no—
486C22×C8—611no—
487C22×C8C22×D6111yescharacteristic
488C22×C8C22×D6114yes—
489C22×C8C22×D6111yescharacteristic
490C4⋊Q8—614no—
491C4⋊Q8—1222no—
492#126—1228no—
493#125—614no—
494#125—1222no—
495#123—1228no—
496#123—1228no—
497#123—1228no—
498C22⋊Q8—1228no—
499#121—22no—
500#121—22no—
501#121—614no—
502#121—614no—
503#121—1222no—
504#121—1222no—
505#121—1228no—
506#121C22×D6114yes—
507#121C22×D6114yes—
508C4×D4—614no—
509C4×D4—614no—
510C4×D4—614no—
511C4×D4—614no—
512C4×D4—1222no—
513C4×D4—1222no—
514C4×D4—1228no—
515#117—614no—
516#117—1222no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—611no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—614no—
523C2×C4⋊C4—614no—
524C2×C4⋊C4—614no—
525C2×C4⋊C4—1222no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4—1222no—
533C2×C4⋊C4—1222no—
534C2×C4⋊C4C22×D6111yescharacteristic
535C2×C4⋊C4C22×D6111yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—611no—
539C2×C22⋊C4—611no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1221no—
545C2×C42—611no—
546C2×C42—1221no—
547#107—614no—
548#107—614no—
549#107C22×D6114yes—
550#106—614no—
551#106—614no—
552#106—614no—
553#106—614no—
554#106—614no—
555#106—614no—
556C4⋊C8—614no—
557#102—614no—
558#102—614no—
559#102—614no—
560#102—614no—
561#102C22×D6114yes—
562#102C22×D6114yes—
563C22⋊C8—614no—
564C22⋊C8—614no—
565#97—614no—
566C24—21no—
567C24—21no—
568C24—611no—
569C24D4×D6111yescharacteristic
570#41—24432no—
571C2×Q8—1224no—
572C2×Q8—2444no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—44no—
582C2×D4—44no—
583C2×D4—614no—
584C2×D4—1224no—
585C2×D4—1224no—
586C2×D4—1224no—
587C2×D4—4882no—
588C2×D4—2444no—
589C2×D4C23×D6112yes—
590C2×D4C23×D6112yes—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—612no—
599C22×C4—612no—
600C22×C4—1224no—
601C22×C4—1224no—
602C22×C4—1224no—
603C22×C4—1222no—
604C22×C4—1222no—
605C22×C4—1224no—
606C22×C4—1224no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—4882no—
612C22×C4—4882no—
613C22×C4—2444no—
614C22×C4—2444no—
615C22×C4—2444no—
616C22×C4D4×D6112yes—
617C22×C4D4×D6111yescharacteristic
618C22×C4C23×D6112yes—
619C22×C4C23×D6111yescharacteristic
620D8—28no—
621M16—1228no—
622C2×C8—22no—
623C2×C8—28no—
624C2×C8—612no—
625C2×C8—612no—
626C2×C8—1222no—
627C2×C8—1222no—
628C2×C8#1175822414yescomplemented
629C2×C8C23×D6112yes—
630C2×C8C23×D6112yes—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—614no—
634C4⋊C4—612no—
635C4⋊C4—612no—
636C4⋊C4—612no—
637C4⋊C4—612no—
638C4⋊C4—1224no—
639C4⋊C4—1224no—
640C4⋊C4—1224no—
641C4⋊C4—1224no—
642C4⋊C4—1221no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—1224no—
647C4⋊C4—1224no—
648C4⋊C4C23×D6112yes—
649C4⋊C4C23×D6112yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—614no—
653C22⋊C4—614no—
654C22⋊C4—1224no—
655C22⋊C4—1224no—
656C22⋊C4—1224no—
657C22⋊C4—1224no—
658C22⋊C4—1224no—
659C42—612no—
660C42—612no—
661C42—1224no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—612no—
673C23—1222no—
674C23—1222no—
675C23—1222no—
676C23#1451980114yes—
677C23C2×D4×D6112yes—
678C23C2×D4×D6111yescharacteristic
679Q8—2448no—
680D4—22no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—48no—
685D4—48no—
686D4—42no—
687D4—42no—
688D4—1228no—
689D4—4884no—
690D4—2448no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—612no—
700C2×C4—612no—
701C2×C4—612no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—1224no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—4884no—
713C2×C4—4884no—
714C2×C4—2448no—
715C2×C4—2448no—
716C2×C4—2442no—
717C2×C4—2442no—
718C2×C4—2448no—
719C2×C4—2442no—
720C2×C4—2442no—
721C2×C4C2×D4×D6112yes—
722C2×C4C2×D4×D6111yescharacteristic
723C2×C4C2×#1175822412yes—
724C2×C4#1451982412yes—
725C2×C4C24×D6111yescharacteristic
726C8—22no—
727C8—1222no—
728C8—1222no—
729C8C2×#1175822414yescomplemented
730C22—22no—
731C22—22no—
732C22—28no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—84no—
740C22—84no—
741C22—1222no—
742C22—1222no—
743C22—1222no—
744C22—2444no—
745C22#1684041212yes—
746C22C2×#1451980114yes—
747C22C2×#1451980112yes—
748C22#1684056912yes—
749C22C22×D4×D6111yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—1222no—
754C4—1222no—
755C4—1222no—
756C4—2442no—
757C4—2442no—
758C4—2442no—
759C4—2442no—
760C4#1684041212yes—
761C4C22×#1175822411yescharacteristic
762C4C2×#1451982411yescharacteristic
763C2—24no—
764C2—82no—
765C2—82no—
766C2—2442no—
767C2#2145829514yesdirect product factor
768C2C2×#1684041211yescharacteristic
769C2C22×#1451980111yescharacteristic
770C2C2×#1684056911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#466C2
socleC23×C61C22×D4
hypercenterC2×#466D61
hypocenterC61C2×#3345
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C2×#16840464C2semidirect
2. C2×#16840412C2semidirect
3. #21458295C2direct (N × H)
4. C2×#16840170C2semidirect
5. C2×#16840079C2semidirect
6. C2×#16840078C2semidirect
7. C2×#16840085C2semidirect
8. C2×#16840073C2semidirect
9. C2×#16840064C2semidirect
10. C2×#16840050C2semidirect
11. C2×#16840012C2semidirect
12. C2×#16839874C2semidirect
13. C2×#16839833C2semidirect
14. C2×#16839803C2semidirect
15. C22×#14519709C2semidirect
16. C2×C61×#466C2semidirect
20. #16840464C22semidirect
22. #16840412C22semidirect
41. #16840170C22semidirect
42. #16840085C22semidirect
43. #16840079C22semidirect
44. #16840078C22semidirect
45. #16840073C22semidirect
46. #16840064C22semidirect
47. #16840050C22semidirect
48. #16840012C22semidirect
49. #16839874C22semidirect
50. #16839833C22semidirect
51. #16839803C22semidirect
58. C2×#14519709C22semidirect
73. C61×#466C22semidirect
237. C2×C8×C61#41semidirect
341. C8×C61C2×#41semidirect
389. C2×#466D61semidirect
397. C2×C61#3345semidirect
438. #466C2×D61semidirect
462. C61C2×#3345semidirect
628. C2×C8#11758224semidirect
729. C8C2×#11758224semidirect
767. C2#21458295direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404642
C2×#168404122
#214582952
C2×#168401702
C2×#168400792
C2×#168400782
C2×#168400852
C2×#168400732
C2×#168400642
C2×#168400502
C2×#168400122
C2×#168398742
C2×#168398332
C2×#168398032
C22×#145197092
C2×C61×#4662
C2×#334561