Finite Group Databasebeta

← C2×#21458410 #30558725

Subgroups — C2×#21458410 #30558725

Order 15616.

2146 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×#16840475C211yesmaximal, characteristic, complemented
2C2×#16840413C211yesmaximal, characteristic, complemented
3#21458410C2116yesmaximal, direct product factor
4C2×#16840159C211yesmaximal, characteristic, complemented
5C2×#16840082C211yesmaximal, characteristic, complemented
6C2×#16840080C211yesmaximal, characteristic, complemented
7C2×#16840089C211yesmaximal, characteristic, complemented
8C2×#16840086C211yesmaximal, characteristic, complemented
9C2×#16840051C211yesmaximal, characteristic, complemented
10C2×#16840041C211yesmaximal, characteristic, complemented
11C2×#16840016C211yesmaximal, characteristic, complemented
12C2×#16840015C211yesmaximal, characteristic, complemented
13C2×#16839844C211yesmaximal, characteristic, complemented
14C2×#16839838C211yesmaximal, characteristic, complemented
15C2×#16839803C211yesmaximal, characteristic, complemented
16C2×C61×#428C211yesmaximal, characteristic, complemented
17C22×#11758222—21no—
18C22×D488C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20#16840475—24no—
21#16840475C2218yescomplemented
22#16840413—24no—
23#16840413C2218yescomplemented
24C2×#14519776C2211yescharacteristic
25C2×#14519776C2211yescharacteristic
26C2×#14519765—21no—
27C2×#14519763—21no—
28C2×#14519762—21no—
29C2×#14519760—21no—
30C2×#14519755—21no—
31C2×#14519752C2211yescharacteristic
32C2×#14519752C2211yescharacteristic
33C2×#14519751C2211yescharacteristic
34C2×#14519751C2211yescharacteristic
35C2×#14519750—21no—
36C2×#14519739C2211yescharacteristic
37C2×#14519739C2211yescharacteristic
38C2×C4×C22⋊D61C2211yescharacteristic
39C2×#14519735C2211yescharacteristic
40C2×#14519734—21no—
41C2×C4⋊C4×D61C2211yescharacteristic
42#16840159C2218yescomplemented
43#16840089C2218yescomplemented
44#16840086C2218yescomplemented
45#16840082C2218yescomplemented
46#16840080C2218yescomplemented
47#16840051C2218yescomplemented
48#16840041C2218yescomplemented
49#16840016C2218yescomplemented
50#16840015C2218yescomplemented
51#16839844C2218yescomplemented
52#16839838C2218yescomplemented
53#16839803C2218yescomplemented
54C2×#14519710C2211yescharacteristic
55C2×#14519709C2211yescharacteristic
56C2×#14519708C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519708C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519699C2211yescharacteristic
61C2×#14519699C2211yescharacteristic
62C2×#14519697C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×M16×C61C2211yescharacteristic
70C2×#117×C61C2211yescharacteristic
71C22×C4⋊C4×C61C2211yescharacteristic
72C61×#428C2218yescomplemented
73C2×#107×C61C2211yescharacteristic
74C2×#107×C61C2211yescharacteristic
75C2×#106×C61C2211yescharacteristic
76C2×#106×C61C2211yescharacteristic
77C2×#11758222—28no—
78C2×#11758222—48no—
79C22×Dic122—21no—
80C22×Dic122—21no—
81C22×D244—21no—
82C22×D244—21no—
83C22×D244C2311yescharacteristic
84C22×D244C2311yescharacteristic
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C22×C22⋊D61D411yescharacteristic
88C22×C4×D61—21no—
89C22×C4×D61—21no—
90C22×C4×D61—21no—
91C22×C4×D61C2311yescharacteristic
92C2×D488—24no—
93C2×D488C2314yes—
94C2×#11758189—24no—
95C2×#11758189C2314yes—
96C22×#92418C2311yescharacteristic
97C22×#92418C2311yescharacteristic
98#14519776—22no—
99#14519776—22no—
100#14519776C2314yes—
101#14519776C2314yes—
102#14519765—28no—
103#14519763—28no—
104#14519762—28no—
105#14519760—28no—
106#14519755—28no—
107#14519752—22no—
108#14519752—22no—
109#14519752C2314yes—
110#14519752C2314yes—
111#14519751—22no—
112#14519751—22no—
113#14519751C2314yes—
114#14519751C2314yes—
115#14519750—28no—
116#14519739—22no—
117#14519739—22no—
118#14519739C2314yes—
119#14519739C2314yes—
120C4×C22⋊D61D414yes—
121C4×C22⋊D61C2314yes—
122#14519735—22no—
123#14519735C2314yes—
124#14519734—28no—
125C2×C4⋊Dic61C2311yescharacteristic
126C2×C4⋊Dic61C2311yescharacteristic
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196D411yescharacteristic
131C4⋊C4×D61—22no—
132C4⋊C4×D61C2314yes—
133C2×C22⋊Dic61D411yescharacteristic
134C2×#11758198—21no—
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198D411yescharacteristic
142C2×C4×Dic61—21no—
143C2×C4×Dic61C2311yescharacteristic
144#14519710C2314yes—
145#14519709C2314yes—
146#14519708C2314yes—
147#14519708C2314yes—
148#14519708C2314yes—
149#14519706C2314yes—
150#14519699C2314yes—
151#14519699C2314yes—
152#14519697C2314yes—
153#14519697C2314yes—
154#14519697C2314yes—
155#14519697C2314yes—
156C22⋊#92418C2314yes—
157#14519689C2314yes—
158C8×Dic61C2314yes—
159C23×C4×C61—21no—
160C23×C4×C61C2311yescharacteristic
161C2×M16×C61—24no—
162C2×M16×C61C2314yes—
163C22×C8×C61C2311yescharacteristic
164C22×C8×C61C2311yescharacteristic
165#117×C61—22no—
166#117×C61C2314yes—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61—22no—
169C2×C4⋊C4×C61C2311yescharacteristic
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2314yes—
174C2×C22⋊C4×C61—21no—
175C2×C42×C61—21no—
176#107×C61C2314yes—
177#107×C61C2314yes—
178#106×C61C2314yes—
179#106×C61C2314yes—
180C24×C61C2×D411yescharacteristic
181C23×D61—21no—
182C23×D61—21no—
183C23×D61C2×D411yescharacteristic
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—24no—
191C22×C4×C61—44no—
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D412yes—
194C22×C4×C61C2412yes—
195C22×C4×C61C2411yescharacteristic
196C2×C22⋊D61—24no—
197C2×C22⋊D61—24no—
198C2×C22⋊D61—24no—
199C2×C22⋊D61—44no—
200C2×C22⋊D61—82no—
201C2×C22⋊D61C2×D414yes—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61C2×D411yescharacteristic
205C22×Dic61C2×D411yescharacteristic
206C22×Dic61C2×D411yescharacteristic
207#11758222—432no—
208C2×D244—22no—
209C2×D244—22no—
210C2×D244—22no—
211C2×D244—22no—
212C2×D244—24no—
213C2×D244—21no—
214C2×D244—21no—
215C2×D244—24no—
216C2×D244—44no—
217C2×D244—82no—
218C2×D244C2412yes—
219C2×D244C2412yes—
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—44no—
228C2×C4×D61C2×D412yes—
229C2×C4×D61C2412yes—
230C2×Dic122—24no—
231C2×Dic122—24no—
232C2×Dic122—44no—
233C2×Dic122—82no—
234M16×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×C61—24no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61C2412yes—
245C4⋊C4×C61C2412yes—
246C4⋊C4×C61C2412yes—
247C4⋊C4×C61C2412yes—
248C22⋊C4×C61—24no—
249C42×C61—24no—
250C22⋊Dic61C2×D414yes—
251#11758198—24no—
252#11758198—24no—
253#11758198—24no—
254#11758198—24no—
255#11758198—24no—
256#11758198—24no—
257#11758198—24no—
258#11758198C2×D414yes—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61C2412yes—
262C4⋊Dic61C2412yes—
263#11758196—24no—
264#11758196—24no—
265#11758196—24no—
266#11758196C2×D414yes—
267C4×Dic61—24no—
268C4×Dic61C2×D412yes—
269C4×Dic61C2412yes—
270C2×#92418—22no—
271C2×#92418—22no—
272C2×#92418C2412yes—
273C2×#92418C2412yes—
274D488—28no—
275#11758189—28no—
276C23×C61—22no—
277C23×C61—22no—
278C23×C61—22no—
279C23×C61C22×D412yes—
280C23×C61C22×D411yescharacteristic
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—42no—
287C22×D61—42no—
288C22×D61—42no—
289C22×D61—42no—
290C22×D61—42no—
291C22×D61—42no—
292C22×D61C22×D412yes—
293C2×C4×C61—22no—
294C2×C4×C61—24no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—48no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61C22×D412yes—
307C2×C4×C61C22×D411yescharacteristic
308C2×C4×C61C2×#4112yes—
309C2×C4×C612−1+412yes—
310C2×C4×C61C2511yescharacteristic
311C22⋊D61—28no—
312C22⋊D61—48no—
313C22⋊D61—84no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61AGL(1,ℤ/8)14yes—
321C2×Dic61C22×D412yes—
322C2×Dic61C22×D412yes—
323C2×Dic61C22×D412yes—
324D244—22no—
325D244—22no—
326D244—22no—
327D244—22no—
328D244—48no—
329D244—42no—
330D244—42no—
331D244—84no—
332C4×D61—24no—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—48no—
336C4×D61—48no—
337C4×D61—48no—
338Dic122—48no—
339Dic122—84no—
340C8×C61—22no—
341C8×C61C2×#4114yescomplemented
342#92418—22no—
343#92418—22no—
344C2×#3354—611nomaximal, Sylow
345C22×C61—22no—
346C22×C61—22no—
347C22×C61—22no—
348C22×C61—44no—
349C22×C61#54712yes—
350C22×C61C2×AGL(1,ℤ/8)12yes—
351C22×C61#57712yes—
352C22×C61C23×D411yescharacteristic
353C2×D61—22no—
354C2×D61—22no—
355C2×D61—22no—
356C2×D61—44no—
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—42no—
363C2×D61—84no—
364C2×D61—84no—
365C4×C61—22no—
366C4×C61—42no—
367C4×C61—42no—
368C4×C61—42no—
369C4×C61—42no—
370C4×C61#54712yes—
371C4×C61C22×#4111yescharacteristic
372C4×C61C2×2−1+411yescharacteristic
373Dic61—22no—
374Dic61—22no—
375Dic61—42no—
376Dic61—42no—
377Dic61C2×AGL(1,ℤ/8)14yes—
378C2×#555—611no—
379C2×#547—611no—
380#3354—6116no—
381C2×#498—611no—
382C2×#481—611no—
383C2×#481—611no—
384C2×#482—611no—
385C2×#482—611no—
386C2×#476—611no—
387C2×#474—611no—
388C2×#469—611no—
389C2×#469—611no—
390C2×C4×D8—611no—
391C2×#436—611no—
392C2×#428—611no—
393C2×#428D6111yescharacteristic, complemented
394C2×C61—42no—
395C2×C61#335414yescomplemented
396C2×C61C2×#54711yescharacteristic
397C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
398C2×C61C2×#57711yescharacteristic
399D61—42no—
400D61—82no—
401D61—82no—
402C22×#41—1221no—
403C22×D8—611no—
404C22×M16—611no—
405C22×M16C2×D6111yescharacteristic
406#555—618no—
407#555—1224no—
408#547—618no—
409#547—1224no—
410C2×C4⋊Q8—611no—
411C2×C4⋊Q8—611no—
412C2×#124—1221no—
413C2×#124—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—611no—
424C2×C4×D4—611no—
425C2×#117—611no—
426C2×#117—1221no—
427C2×#117C2×D6111yescharacteristic
428C22×C4⋊C4—611no—
429C22×C4⋊C4C2×D6111yescharacteristic
430#498—618no—
431#482—618no—
432#482—618no—
433#481—618no—
434#481—618no—
435#476—618no—
436#474—618no—
437#469—618no—
438#469—618no—
439C4×D8—618no—
440#436—618no—
441#428—618no—
442#428C2×D6118yescomplemented
443C2×#107—611no—
444C2×#107C2×D6111yescharacteristic
445C2×#107C2×D6111yescharacteristic
446C2×#106—611no—
447C2×#106—611no—
448C2×#106—611no—
449C2×#106—611no—
450C2×#106C2×D6111yescharacteristic
451C2×#106C2×D6111yescharacteristic
452C2×C4⋊C8—611no—
453C2×#102—611no—
454C2×#102—611no—
455C2×#102—611no—
456C2×#102—611no—
457C2×#102—611no—
458C2×#102—611no—
459C2×C22⋊C8—611no—
460C2×C22⋊C8—611no—
461C2×C4×C8—611no—
462C61C2×#335411yescharacteristic, complemented, Sylow
463C2×#41—1228no—
464C2×#41—2448no—
465C22×Q8—1221no—
466C22×Q8—1221no—
467C22×D4—611no—
468C22×D4—611no—
469C22×D4—611no—
470C22×D4—1221no—
471C22×D4—1221no—
472C22×D4—1221no—
473C22×D4—1221no—
474C23×C4—21no—
475C23×C4—611no—
476C23×C4—1221no—
477C23×C4—1221no—
478C23×C4—1221no—
479C23×C4C22×D6111yescharacteristic
480C2×D8—614no—
481C2×D8—1224no—
482C2×M16—24no—
483C2×M16—614no—
484C2×M16—1224no—
485C2×M16C22×D6114yes—
486C22×C8—611no—
487C22×C8—611no—
488C22×C8C22×D6111yescharacteristic
489C22×C8C22×D6111yescharacteristic
490C4⋊Q8—614no—
491C4⋊Q8—614no—
492C4⋊Q8—1222no—
493C4⋊Q8—1222no—
494#124—1228no—
495#124—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—614no—
509C4×D4—614no—
510C4×D4—614no—
511C4×D4—614no—
512C4×D4—1222no—
513C4×D4—1222no—
514#117—22no—
515#117—614no—
516#117—1228no—
517#117—1222no—
518#117C22×D6114yes—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—614no—
525C2×C4⋊C4—1222no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4C22×D6111yescharacteristic
530C2×C4⋊C4C22×D6111yescharacteristic
531C2×C4⋊C4C22×D6114yes—
532C2×C4⋊C4C22×D6111yescharacteristic
533C2×C4⋊C4C22×D6111yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—611no—
536C2×C22⋊C4—611no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C22⋊C4—1221no—
544C2×C42—21no—
545C2×C42—611no—
546C2×C42—1221no—
547#107—614no—
548#107C22×D6114yes—
549#107C22×D6114yes—
550#106—614no—
551#106—614no—
552#106—614no—
553#106—614no—
554#106C22×D6114yes—
555#106C22×D6114yes—
556C4⋊C8—614no—
557#102—614no—
558#102—614no—
559#102—614no—
560#102—614no—
561#102—614no—
562#102—614no—
563C22⋊C8—614no—
564C22⋊C8—614no—
565C4×C8—614no—
566C24—611no—
567C24—1221no—
568C24—1221no—
569C24D4×D6111yescharacteristic
570#41—24432no—
571C2×Q8—1224no—
572C2×Q8—1224no—
573C2×Q8—4882no—
574C2×Q8—2444no—
575C2×D4—614no—
576C2×D4—612no—
577C2×D4—612no—
578C2×D4—1224no—
579C2×D4—1224no—
580C2×D4—1224no—
581C2×D4—1224no—
582C2×D4—1224no—
583C2×D4—1221no—
584C2×D4—1221no—
585C2×D4—1222no—
586C2×D4—1222no—
587C2×D4—1222no—
588C2×D4—1222no—
589C2×D4—4882no—
590C2×D4—4882no—
591C2×D4—2444no—
592C2×D4—2444no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—24no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—44no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—612no—
605C22×C4—612no—
606C22×C4—1224no—
607C22×C4—1224no—
608C22×C4—1224no—
609C22×C4—1222no—
610C22×C4—1222no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—2444no—
614C22×C4—2444no—
615C22×C4—2444no—
616C22×C4D4×D6112yes—
617C22×C4D4×D6111yescharacteristic
618C22×C4C23×D6112yes—
619C22×C4C23×D6111yescharacteristic
620D8—1228no—
621M16—28no—
622M16—1228no—
623C2×C8—22no—
624C2×C8—612no—
625C2×C8—612no—
626C2×C8—1222no—
627C2×C8—1222no—
628C2×C8#1175822214yescomplemented
629C2×C8C23×D6112yes—
630C2×C8C23×D6112yes—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—614no—
637C4⋊C4—612no—
638C4⋊C4—612no—
639C4⋊C4—1224no—
640C4⋊C4—1224no—
641C4⋊C4—1224no—
642C4⋊C4—1221no—
643C4⋊C4—1221no—
644C4⋊C4C23×D6112yes—
645C4⋊C4C23×D6112yes—
646C4⋊C4C23×D6112yes—
647C4⋊C4C23×D6112yes—
648C22⋊C4—24no—
649C22⋊C4—614no—
650C22⋊C4—614no—
651C22⋊C4—1224no—
652C22⋊C4—1224no—
653C22⋊C4—1224no—
654C22⋊C4—1224no—
655C22⋊C4—1224no—
656C22⋊C4—1224no—
657C22⋊C4—1224no—
658C42—24no—
659C42—612no—
660C42—612no—
661C42—1224no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—612no—
666C23—1222no—
667C23—1222no—
668C23—1222no—
669C23—1222no—
670C23—1222no—
671C23—2442no—
672C23—2442no—
673C23—2442no—
674C23—2442no—
675C23—2442no—
676C23—2442no—
677C23C2×D4×D6112yes—
678C23C2×D4×D6111yescharacteristic
679Q8—4884no—
680Q8—2448no—
681D4—1228no—
682D4—1222no—
683D4—1222no—
684D4—1222no—
685D4—1222no—
686D4—4884no—
687D4—4884no—
688D4—2448no—
689D4—2448no—
690D4—2442no—
691D4—2442no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—48no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—614no—
706C2×C4—612no—
707C2×C4—612no—
708C2×C4—612no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1224no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—2448no—
717C2×C4—2448no—
718C2×C4—2448no—
719C2×C4—2442no—
720C2×C4—2442no—
721C2×C4C2×D4×D6112yes—
722C2×C4C2×D4×D6111yescharacteristic
723C2×C4C2×#1175822212yes—
724C2×C4#1451982512yes—
725C2×C4C24×D6111yescharacteristic
726C8—22no—
727C8—1222no—
728C8—1222no—
729C8C2×#1175822214yescomplemented
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—1222no—
735C22—1222no—
736C22—1222no—
737C22—4884no—
738C22—4884no—
739C22—2442no—
740C22—2442no—
741C22—2442no—
742C22—2442no—
743C22—2442no—
744C22—2442no—
745C22—2444no—
746C22#1684041312yes—
747C22AGL(1,ℤ/8)×D6112yes—
748C22#1684057112yes—
749C22C22×D4×D6111yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—614no—
756C4—1222no—
757C4—1222no—
758C4—2442no—
759C4—2442no—
760C4#1684041312yes—
761C4C22×#1175822211yescharacteristic
762C4C2×#1451982511yescharacteristic
763C2—42no—
764C2—4882no—
765C2—4882no—
766C2—2442no—
767C2#2145841014yesdirect product factor
768C2C2×#1684041311yescharacteristic
769C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
770C2C2×#1684057111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#428C2
socleC23×C61C22×D4
hypercenterC2×#428D61
hypocenterC61C2×#3354
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#16840475C2semidirect
2. C2×#16840413C2semidirect
3. #21458410C2direct (N × H)
4. C2×#16840159C2semidirect
5. C2×#16840082C2semidirect
6. C2×#16840080C2semidirect
7. C2×#16840089C2semidirect
8. C2×#16840086C2semidirect
9. C2×#16840051C2semidirect
10. C2×#16840041C2semidirect
11. C2×#16840016C2semidirect
12. C2×#16840015C2semidirect
13. C2×#16839844C2semidirect
14. C2×#16839838C2semidirect
15. C2×#16839803C2semidirect
16. C2×C61×#428C2semidirect
21. #16840475C22semidirect
23. #16840413C22semidirect
42. #16840159C22semidirect
43. #16840089C22semidirect
44. #16840086C22semidirect
45. #16840082C22semidirect
46. #16840080C22semidirect
47. #16840051C22semidirect
48. #16840041C22semidirect
49. #16840016C22semidirect
50. #16840015C22semidirect
51. #16839844C22semidirect
52. #16839838C22semidirect
53. #16839803C22semidirect
72. C61×#428C22semidirect
236. C2×C8×C61#41semidirect
341. C8×C61C2×#41semidirect
393. C2×#428D61semidirect
395. C2×C61#3354semidirect
442. #428C2×D61semidirect
462. C61C2×#3354semidirect
628. C2×C8#11758222semidirect
729. C8C2×#11758222semidirect
767. C2#21458410direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404752
C2×#168404132
#214584102
C2×#168401592
C2×#168400822
C2×#168400802
C2×#168400892
C2×#168400862
C2×#168400512
C2×#168400412
C2×#168400162
C2×#168400152
C2×#168398442
C2×#168398382
C2×#168398032
C2×C61×#4282
C2×#335461