Finite Group Databasebeta

← C2×#21458294 #30558581

Subgroups — C2×#21458294 #30558581

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×#16840462C211yesmaximal, characteristic, complemented
2C2×#16840417C211yesmaximal, characteristic, complemented
3#21458294C2116yesmaximal, direct product factor
4C2×#16840171C211yesmaximal, characteristic, complemented
5C2×#16840079C211yesmaximal, characteristic, complemented
6C2×#16840079C211yesmaximal, characteristic, complemented
7C2×#16840084C211yesmaximal, characteristic, complemented
8C2×#16840074C211yesmaximal, characteristic, complemented
9C2×#16840062C211yesmaximal, characteristic, complemented
10C2×#16840052C211yesmaximal, characteristic, complemented
11C2×#16840012C211yesmaximal, characteristic, complemented
12C2×#16839995C211yesmaximal, characteristic, complemented
13C2×#16839835C211yesmaximal, characteristic, complemented
14C2×#16839801C211yesmaximal, characteristic, complemented
15C2×#106×D61C211yesmaximal, characteristic, complemented
16C2×C61×#442C211yesmaximal, characteristic, complemented
17C22×#11758222—21no—
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840462—24no—
21#16840462C2218yescomplemented
22#16840417—24no—
23#16840417C2218yescomplemented
24C2×#14519777C2211yescharacteristic
25C2×#14519770—21no—
26C2×#14519769C2211yescharacteristic
27C2×#14519760—21no—
28C2×#14519759—21no—
29C2×#14519759—21no—
30C2×#14519756—21no—
31C2×#14519750—21no—
32C2×#14519748C2211yescharacteristic
33C2×#14519748C2211yescharacteristic
34C2×#14519748C2211yescharacteristic
35C2×#14519748C2211yescharacteristic
36C2×C4×D244C2211yescharacteristic
37C2×C4×C22⋊D61—21no—
38C2×#14519735C2211yescharacteristic
39C2×C4⋊C4×D61C2211yescharacteristic
40C2×C4⋊C4×D61C2211yescharacteristic
41C2×C4⋊C4×D61C2211yescharacteristic
42#16840171C2218yescomplemented
43#16840084C2218yescomplemented
44#16840079C2218yescomplemented
45#16840079C2218yescomplemented
46#16840074C2218yescomplemented
47#16840062C2218yescomplemented
48#16840052C2218yescomplemented
49#16840012C2218yescomplemented
50#16839995C2218yescomplemented
51#16839835C2218yescomplemented
52#16839801C2218yescomplemented
53C2×#14519711C2211yescharacteristic
54C2×#14519711C2211yescharacteristic
55C2×#14519710C2211yescharacteristic
56C2×#14519709C2211yescharacteristic
57C2×#14519709C2211yescharacteristic
58C2×#14519708C2211yescharacteristic
59C2×#14519708C2211yescharacteristic
60C2×#14519708C2211yescharacteristic
61#106×D61C2218yescomplemented
62C2×C4⋊#92418C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×#14519698C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519689C2211yescharacteristic
69C22×D8×C61C2211yescharacteristic
70C2×C4×D4×C61C2211yescharacteristic
71C2×C4×D4×C61C2211yescharacteristic
72C61×#442C2218yescomplemented
73C2×#106×C61C2211yescharacteristic
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C2×#11758222—28no—
78C2×#11758222—48no—
79C22×Dic122—21no—
80C22×D244D411yescharacteristic
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C22×C22⋊D61—21no—
84C22×C22⋊D61—21no—
85C22×C4×D61—21no—
86C22×C4×D61—21no—
87C22×C4×D61—21no—
88C22×C4×D61C2311yescharacteristic
89C22×C4×D61C2311yescharacteristic
90C2×#11758189—24no—
91C2×#11758189C2314yes—
92C22×#92418C2311yescharacteristic
93C22×#92418C2311yescharacteristic
94C2×C8×D61—24no—
95C2×C8×D61C2314yes—
96#14519777—22no—
97#14519777C2314yes—
98#14519770—28no—
99#14519769—22no—
100#14519769C2314yes—
101#14519760—28no—
102#14519759—28no—
103#14519759—28no—
104#14519756—28no—
105#14519750—28no—
106#14519748—22no—
107#14519748—22no—
108#14519748—22no—
109#14519748—22no—
110#14519748C2314yes—
111#14519748C2314yes—
112#14519748C2314yes—
113#14519748C2314yes—
114C4×D244D414yes—
115C4×D244C2314yes—
116C4×C22⋊D61—28no—
117#14519735—22no—
118#14519735C2314yes—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61D411yescharacteristic
121C2×C4⋊Dic61C2311yescharacteristic
122C2×C4⋊Dic61C2311yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C4⋊C4×D61—22no—
131C4⋊C4×D61—22no—
132C4⋊C4×D61—22no—
133C4⋊C4×D61C2314yes—
134C4⋊C4×D61C2314yes—
135C4⋊C4×D61C2314yes—
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61—21no—
138C2×C22⋊Dic61—21no—
139C2×C22⋊Dic61—21no—
140C2×#11758198—21no—
141C2×#11758198D411yescharacteristic
142C2×#11758198D411yescharacteristic
143C2×C4×Dic61—21no—
144#14519711C2314yes—
145#14519711C2314yes—
146#14519710C2314yes—
147#14519709C2314yes—
148#14519709C2314yes—
149#14519708C2314yes—
150#14519708C2314yes—
151#14519708C2314yes—
152C4⋊#92418C2314yes—
153#14519698C2314yes—
154#14519698C2314yes—
155#14519698C2314yes—
156#14519698C2314yes—
157#14519689C2314yes—
158#14519689C2314yes—
159C22×D4×C61C2311yescharacteristic
160C22×D4×C61C2311yescharacteristic
161C23×C4×C61—21no—
162C23×C4×C61—21no—
163C2×D8×C61—24no—
164C2×D8×C61C2314yes—
165C22×C8×C61C2311yescharacteristic
166C22×C8×C61C2311yescharacteristic
167C4×D4×C61—22no—
168C4×D4×C61—22no—
169C4×D4×C61C2314yes—
170C4×D4×C61C2314yes—
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C22⋊C4×C61—21no—
174C2×C22⋊C4×C61—21no—
175C2×C42×C61C2311yescharacteristic
176#106×C61C2314yes—
177#102×C61C2314yes—
178#102×C61C2314yes—
179#97×C61C2314yes—
180C24×C61—21no—
181C24×C61—21no—
182C23×D61C2×D411yescharacteristic
183C23×D61C2×D411yescharacteristic
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—22no—
187C2×D4×C61—22no—
188C2×D4×C61—22no—
189C2×D4×C61—22no—
190C2×D4×C61C2412yes—
191C2×D4×C61C2412yes—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—24no—
195C22×C4×C61—24no—
196C22×C4×C61—44no—
197C22×C4×C61—82no—
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2411yescharacteristic
201C2×C22⋊D61—24no—
202C2×C22⋊D61—24no—
203C2×C22⋊D61—24no—
204C2×C22⋊D61—24no—
205C2×C22⋊D61—44no—
206C2×C22⋊D61—44no—
207C2×C22⋊D61—44no—
208C2×C22⋊D61—82no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61C2×D411yescharacteristic
214C22×Dic61C2×D411yescharacteristic
215#11758222—432no—
216C2×D244—24no—
217C2×D244C2×D414yes—
218C2×C4×D61—22no—
219C2×C4×D61—22no—
220C2×C4×D61—22no—
221C2×C4×D61—22no—
222C2×C4×D61—24no—
223C2×C4×D61—24no—
224C2×C4×D61—24no—
225C2×C4×D61—44no—
226C2×C4×D61—44no—
227C2×C4×D61—82no—
228C2×C4×D61C2×D412yes—
229C2×C4×D61C2×D412yes—
230C2×C4×D61C2412yes—
231C2×C4×D61C2412yes—
232C2×Dic122—24no—
233C2×Dic122—44no—
234D8×C61—28no—
235C2×C8×C61—22no—
236C2×C8×C61#4114yescomplemented
237C2×C8×C61C2412yes—
238C2×C8×C61C2412yes—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61C2412yes—
242C4⋊C4×C61C2412yes—
243C22⋊C4×C61—24no—
244C22⋊C4×C61—24no—
245C42×C61C2×D412yes—
246C42×C61C2412yes—
247C22⋊Dic61—24no—
248C22⋊Dic61—24no—
249C22⋊Dic61—24no—
250C22⋊Dic61—24no—
251#11758198—24no—
252#11758198C2×D414yes—
253#11758198C2×D414yes—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61—24no—
258C4⋊Dic61—21no—
259C4⋊Dic61C2×D414yes—
260C4⋊Dic61C2412yes—
261C4⋊Dic61C2412yes—
262C4⋊Dic61C2412yes—
263C4⋊Dic61C2412yes—
264#11758196—24no—
265#11758196—24no—
266#11758196—24no—
267#11758196—24no—
268#11758196—24no—
269C4×Dic61—24no—
270C2×#92418—22no—
271C2×#92418—22no—
272C2×#92418C2412yes—
273C2×#92418C2412yes—
274#11758189—28no—
275C8×D61—28no—
276C23×C61—22no—
277C23×C61—22no—
278C23×C61—42no—
279C23×C61—42no—
280C23×C61—42no—
281C23×C61—42no—
282C23×C61—42no—
283C23×C61—42no—
284C23×C61C22×D411yescharacteristic
285C22×D61—22no—
286C22×D61—22no—
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—22no—
290C22×D61AGL(1,ℤ/8)14yes—
291C22×D61C22×D412yes—
292C22×D61C22×D412yes—
293D4×C61—22no—
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—22no—
297D4×C61—42no—
298D4×C61—42no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—48no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61—84no—
307C2×C4×C61C22×D412yes—
308C2×C4×C61C22×D412yes—
309C2×C4×C61C22×D411yescharacteristic
310C2×C4×C61C2×#4112yes—
311C2×C4×C612−1+412yes—
312C2×C4×C61C2511yescharacteristic
313C22⋊D61—48no—
314C22⋊D61—48no—
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—42no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61C22×D412yes—
328C2×Dic61C22×D412yes—
329D244—28no—
330C4×D61—24no—
331C4×D61—24no—
332C4×D61—22no—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—22no—
336C4×D61—48no—
337C4×D61—48no—
338C4×D61—84no—
339Dic122—48no—
340C8×C61—22no—
341C8×C61C2×#4114yescomplemented
342#92418—22no—
343#92418—22no—
344C2×#3345—611nomaximal, Sylow
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61—84no—
352C22×C61—84no—
353C22×C61#54712yes—
354C22×C61C2×AGL(1,ℤ/8)12yes—
355C22×C61#57712yes—
356C22×C61C23×D411yescharacteristic
357C2×D61—28no—
358C2×D61—22no—
359C2×D61—22no—
360C2×D61—22no—
361C2×D61—22no—
362C2×D61—22no—
363C2×D61—44no—
364C2×D61C2×AGL(1,ℤ/8)14yes—
365C4×C61—22no—
366C4×C61—22no—
367C4×C61—42no—
368C4×C61—42no—
369C4×C61#54712yes—
370C4×C61C22×#4111yescharacteristic
371C4×C61C2×2−1+411yescharacteristic
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×#466—611no—
390C2×#442D6111yescharacteristic, complemented
391C2×#435—611no—
392C2×#428—611no—
393C22×#106—611no—
394C2×C61—82no—
395C2×C61—82no—
396C2×C61#334514yescomplemented
397C2×C61C2×#54711yescharacteristic
398C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
399C2×C61C2×#57711yescharacteristic
400D61—24no—
401D61—42no—
402C22×#41—1221no—
403C22×D8C2×D6111yescharacteristic
404C22×M16—611no—
405C23×C8—611no—
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—611no—
420C2×#121—611no—
421C2×#121—1221no—
422C2×C4×D4—611no—
423C2×C4×D4—1221no—
424C2×C4×D4C2×D6111yescharacteristic
425C2×C4×D4C2×D6111yescharacteristic
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#466—618no—
439#442C2×D6118yescomplemented
440#435—618no—
441#428—618no—
442C2×#107—611no—
443C2×#107—611no—
444C2×#107—611no—
445C2×#106—611no—
446C2×#106—611no—
447C2×#106—611no—
448C2×#106—611no—
449C2×#106—611no—
450C2×#106—618no—
451C2×#106C2×D6111yescharacteristic
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×#97C2×D6111yescharacteristic
462C61C2×#334511yescharacteristic, complemented, Sylow
463C2×#41—1228no—
464C2×#41—2448no—
465C22×Q8—1221no—
466C22×D4—611no—
467C22×D4—1221no—
468C22×D4—1221no—
469C22×D4—1221no—
470C22×D4—1221no—
471C22×D4C22×D6111yescharacteristic
472C22×D4C22×D6111yescharacteristic
473C23×C4—21no—
474C23×C4—21no—
475C23×C4—611no—
476C23×C4—611no—
477C23×C4—1221no—
478C23×C4—1221no—
479C23×C4—1221no—
480C2×D8—24no—
481C2×D8C22×D6114yes—
482C2×M16—614no—
483C2×M16—1224no—
484C22×C8—611no—
485C22×C8—611no—
486C22×C8—614no—
487C22×C8—1224no—
488C22×C8C22×D6111yescharacteristic
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—614no—
500#121—614no—
501#121—614no—
502#121—614no—
503#121—1228no—
504#121—1222no—
505#121—1222no—
506#121—1222no—
507#121—1222no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—614no—
511C4×D4—614no—
512C4×D4—1228no—
513C4×D4C22×D6114yes—
514C4×D4C22×D6114yes—
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—1222no—
527C2×C4⋊C4—1222no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4—1221no—
533C2×C4⋊C4—1221no—
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—1221no—
546C2×C42C22×D6111yescharacteristic
547#107—614no—
548#107—614no—
549#107—614no—
550#106—614no—
551#106—614no—
552#106—614no—
553#106—614no—
554#106—614no—
555#106C22×D6114yes—
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#97C22×D6114yes—
566C24—21no—
567C24—21no—
568C24—611no—
569C24—611no—
570#41—24432no—
571C2×Q8—1224no—
572C2×Q8—2444no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—614no—
580C2×D4—1224no—
581C2×D4—1224no—
582C2×D4—1224no—
583C2×D4—1224no—
584C2×D4—1224no—
585C2×D4—4882no—
586C2×D4—2444no—
587C2×D4—2444no—
588C2×D4—2444no—
589C2×D4C23×D6112yes—
590C2×D4C23×D6112yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—44no—
596C22×C4—82no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—612no—
600C22×C4—612no—
601C22×C4—612no—
602C22×C4—612no—
603C22×C4—1224no—
604C22×C4—1224no—
605C22×C4—1224no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—4882no—
615C22×C4—2444no—
616C22×C4—2444no—
617C22×C4D4×D6111yescharacteristic
618C22×C4D4×D6111yescharacteristic
619C22×C4C23×D6111yescharacteristic
620D8—28no—
621M16—1228no—
622C2×C8—22no—
623C2×C8—612no—
624C2×C8—612no—
625C2×C8—1222no—
626C2×C8—1222no—
627C2×C8—1228no—
628C2×C8#1175822214yescomplemented
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—1221no—
642C4⋊C4—1221no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—1224no—
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—1224no—
660C42D4×D6112yes—
661C42C23×D6112yes—
662C23—22no—
663C23—22no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—614no—
671C23—612no—
672C23—612no—
673C23—1222no—
674C23—1222no—
675C23—1222no—
676C23—1222no—
677C23—1222no—
678C23C2×D4×D6111yescharacteristic
679Q8—2448no—
680D4—22no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—42no—
685D4—42no—
686D4—1228no—
687D4—4884no—
688D4—2448no—
689D4—2448no—
690D4—2448no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—48no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—84no—
699C2×C4—612no—
700C2×C4—612no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—1224no—
708C2×C4—1224no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—4884no—
714C2×C4—2448no—
715C2×C4—2448no—
716C2×C4—2442no—
717C2×C4—2442no—
718C2×C4—2442no—
719C2×C4—2442no—
720C2×C4C2×D4×D6112yes—
721C2×C4C2×D4×D6112yes—
722C2×C4C2×D4×D6111yescharacteristic
723C2×C4C2×#1175822212yes—
724C2×C4#1451982412yes—
725C2×C4C24×D6111yescharacteristic
726C8—22no—
727C8—1222no—
728C8—1222no—
729C8C2×#1175822214yescomplemented
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—84no—
737C22—84no—
738C22—614no—
739C22—1222no—
740C22—1222no—
741C22—1228no—
742C22—1222no—
743C22—1222no—
744C22—1222no—
745C22—2444no—
746C22#1684041712yes—
747C22AGL(1,ℤ/8)×D6112yes—
748C22#1684057212yes—
749C22C22×D4×D6111yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—1222no—
755C4—1222no—
756C4—2442no—
757C4—2442no—
758C4—2442no—
759C4—2442no—
760C4#1684041712yes—
761C4C22×#1175822211yescharacteristic
762C4C2×#1451982411yescharacteristic
763C2—82no—
764C2—82no—
765C2—1224no—
766C2—2442no—
767C2#2145829414yesdirect product factor
768C2C2×#1684041711yescharacteristic
769C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
770C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#442C2
socleC23×C61C22×D4
hypercenterC2×#442D61
hypocenterC61C2×#3345
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#16840462C2semidirect
2. C2×#16840417C2semidirect
3. #21458294C2direct (N × H)
4. C2×#16840171C2semidirect
5. C2×#16840079C2semidirect
6. C2×#16840079C2semidirect
7. C2×#16840084C2semidirect
8. C2×#16840074C2semidirect
9. C2×#16840062C2semidirect
10. C2×#16840052C2semidirect
11. C2×#16840012C2semidirect
12. C2×#16839995C2semidirect
13. C2×#16839835C2semidirect
14. C2×#16839801C2semidirect
15. C2×#106×D61C2semidirect
16. C2×C61×#442C2semidirect
21. #16840462C22semidirect
23. #16840417C22semidirect
42. #16840171C22semidirect
43. #16840084C22semidirect
44. #16840079C22semidirect
45. #16840079C22semidirect
46. #16840074C22semidirect
47. #16840062C22semidirect
48. #16840052C22semidirect
49. #16840012C22semidirect
50. #16839995C22semidirect
51. #16839835C22semidirect
52. #16839801C22semidirect
61. #106×D61C22semidirect
72. C61×#442C22semidirect
236. C2×C8×C61#41semidirect
341. C8×C61C2×#41semidirect
390. C2×#442D61semidirect
396. C2×C61#3345semidirect
439. #442C2×D61semidirect
462. C61C2×#3345semidirect
628. C2×C8#11758222semidirect
729. C8C2×#11758222semidirect
767. C2#21458294direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404622
C2×#168404172
#214582942
C2×#168401712
C2×#168400792
C2×#168400842
C2×#168400742
C2×#168400622
C2×#168400522
C2×#168400122
C2×#168399952
C2×#168398352
C2×#168398012
C2×#106×D612
C2×C61×#4422
C2×#334561