Finite Group Databasebeta

← C2×#21458418 #30558734

Subgroups — C2×#21458418 #30558734

Order 15616.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840464C211yesmaximal, characteristic, complemented
2C2×#16840456C211yesmaximal, characteristic, complemented
3#21458418C2116yesmaximal, direct product factor
4C2×#16840163C211yesmaximal, characteristic, complemented
5C2×#16840089C211yesmaximal, characteristic, complemented
6C2×#16840076C211yesmaximal, characteristic, complemented
7C2×#16840074C211yesmaximal, characteristic, complemented
8C2×#16840061C211yesmaximal, characteristic, complemented
9C2×#16840060C211yesmaximal, characteristic, complemented
10C2×#16840014C211yesmaximal, characteristic, complemented
11C2×#16840013C211yesmaximal, characteristic, complemented
12C2×#16839842C211yesmaximal, characteristic, complemented
13C2×#16839837C211yesmaximal, characteristic, complemented
14C2×#16839805C211yesmaximal, characteristic, complemented
15C2×#16839801C211yesmaximal, characteristic, complemented
16C2×C61×#482C211yesmaximal, characteristic, complemented
17C22×#11758199C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20#16840464—24no—
21#16840464C2218yescomplemented
22#16840456—24no—
23#16840456C2218yescomplemented
24C2×#14519771—21no—
25C2×#14519770—21no—
26C2×#14519768C2211yescharacteristic
27C2×#14519768C2211yescharacteristic
28C2×#14519761—21no—
29C2×#14519759—21no—
30C2×#14519752C2211yescharacteristic
31C2×#14519751C2211yescharacteristic
32C2×#14519750—21no—
33C2×#14519749—21no—
34C2×#14519748C2211yescharacteristic
35C2×C4×D244—21no—
36C2×D4×Dic61—21no—
37C2×D4×Dic61C2211yescharacteristic
38C2×#14519739C2211yescharacteristic
39C2×C4×C22⋊D61C2211yescharacteristic
40C2×#14519735C2211yescharacteristic
41C22×C4⋊Dic61C2211yescharacteristic
42C2×C4⋊C4×D61C2211yescharacteristic
43#16840163C2218yescomplemented
44#16840089C2218yescomplemented
45#16840076C2218yescomplemented
46#16840074C2218yescomplemented
47#16840061C2218yescomplemented
48#16840060C2218yescomplemented
49#16840014C2218yescomplemented
50#16840013C2218yescomplemented
51#16839842C2218yescomplemented
52#16839837C2218yescomplemented
53#16839805C2218yescomplemented
54#16839801C2218yescomplemented
55C2×#14519711C2211yescharacteristic
56C2×#14519711C2211yescharacteristic
57C2×#14519710C2211yescharacteristic
58C2×#14519710C2211yescharacteristic
59C2×#14519708C2211yescharacteristic
60C2×#14519708C2211yescharacteristic
61C2×#14519708C2211yescharacteristic
62C2×#14519706C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×#14519697C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C2×#121×C61C2211yescharacteristic
70C2×#117×C61C2211yescharacteristic
71C61×#482C2218yescomplemented
72C2×#107×C61C2211yescharacteristic
73C2×#106×C61C2211yescharacteristic
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C22×D244—21no—
78C22×D244C2311yescharacteristic
79C22×C22⋊D61—21no—
80C22×C22⋊D61—21no—
81C22×C22⋊D61D411yescharacteristic
82C23×Dic61—21no—
83C23×Dic61—21no—
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86C22×C4×D61C2311yescharacteristic
87C2×#11758199—24no—
88C2×#11758199C2314yes—
89C2×#11758194—24no—
90C2×#11758194C2314yes—
91C2×#11758189—24no—
92C2×#11758189C2314yes—
93C22×#92418C2311yescharacteristic
94C22×#92418C2311yescharacteristic
95#14519771—28no—
96#14519770—28no—
97#14519768—22no—
98#14519768—22no—
99#14519768C2314yes—
100#14519768C2314yes—
101#14519761—28no—
102#14519759—28no—
103#14519752—22no—
104#14519752C2314yes—
105#14519751—22no—
106#14519751C2314yes—
107#14519750—28no—
108#14519749—28no—
109#14519748—22no—
110#14519748C2314yes—
111C4×D244—28no—
112D4×Dic61—28no—
113D4×Dic61—22no—
114D4×Dic61C2314yes—
115#14519739—22no—
116#14519739C2314yes—
117C4×C22⋊D61D414yes—
118C4×C22⋊D61C2314yes—
119#14519735—22no—
120#14519735C2314yes—
121C2×C4⋊Dic61—22no—
122C2×C4⋊Dic61—21no—
123C2×C4⋊Dic61—21no—
124C2×C4⋊Dic61—21no—
125C2×C4⋊Dic61C2314yes—
126C2×C4⋊Dic61C2311yescharacteristic
127C2×C4⋊Dic61C2311yescharacteristic
128C2×C4⋊Dic61C2311yescharacteristic
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196D411yescharacteristic
133C4⋊C4×D61—22no—
134C4⋊C4×D61C2314yes—
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61D411yescharacteristic
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198D411yescharacteristic
143C2×C4×Dic61—21no—
144C2×C4×Dic61C2311yescharacteristic
145#14519711C2314yes—
146#14519711C2314yes—
147#14519710C2314yes—
148#14519710C2314yes—
149#14519708C2314yes—
150#14519708C2314yes—
151#14519708C2314yes—
152#14519706C2314yes—
153#14519699C2314yes—
154#14519699C2314yes—
155#14519698C2314yes—
156#14519697C2314yes—
157#14519689C2314yes—
158C8×Dic61C2314yes—
159C22×D4×C61—21no—
160C22×D4×C61C2311yescharacteristic
161C23×C4×C61C2311yescharacteristic
162C22×C8×C61C2311yescharacteristic
163C22×C8×C61C2311yescharacteristic
164#121×C61—22no—
165#121×C61C2314yes—
166#117×C61—22no—
167#117×C61C2314yes—
168C2×C4⋊C4×C61C2311yescharacteristic
169C2×C4⋊C4×C61C2311yescharacteristic
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C22⋊C4×C61—21no—
172C2×C22⋊C4×C61—21no—
173C2×C42×C61—21no—
174#107×C61C2314yes—
175#106×C61C2314yes—
176#102×C61C2314yes—
177#102×C61C2314yes—
178C22⋊C8×C61C2314yes—
179C24×C61—21no—
180C24×C61C2×D411yescharacteristic
181C23×D61—21no—
182C23×D61C2×D411yescharacteristic
183C2×D4×C61—24no—
184C2×D4×C61—21no—
185C2×D4×C61—22no—
186C2×D4×C61—22no—
187C2×D4×C61—44no—
188C2×D4×C61C2412yes—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D412yes—
196C22×C4×C61C2412yes—
197C22×C4×C61C2411yescharacteristic
198C2×C22⋊D61—24no—
199C2×C22⋊D61—24no—
200C2×C22⋊D61—42no—
201C2×C22⋊D61—82no—
202C2×C22⋊D61—82no—
203C2×C22⋊D61C2×D414yes—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—24no—
208C22×Dic61—24no—
209C22×Dic61—82no—
210C22×Dic61—82no—
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213C22×Dic61C2×D411yescharacteristic
214C2×D244—22no—
215C2×D244—22no—
216C2×D244—24no—
217C2×D244—21no—
218C2×D244—44no—
219C2×D244C2412yes—
220C2×C4×D61—22no—
221C2×C4×D61—22no—
222C2×C4×D61—24no—
223C2×C4×D61—24no—
224C2×C4×D61—82no—
225C2×C4×D61—82no—
226C2×C4×D61C2×D412yes—
227C2×C4×D61C2412yes—
228C2×C8×C61—22no—
229C2×C8×C61—22no—
230C2×C8×C61C2412yes—
231C2×C8×C61C2412yes—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61C2412yes—
236C4⋊C4×C61C2412yes—
237C4⋊C4×C61C2412yes—
238C22⋊C4×C61—24no—
239C22⋊C4×C61—24no—
240C42×C61—24no—
241C22⋊Dic61—24no—
242C22⋊Dic61—24no—
243C22⋊Dic61C2×D414yes—
244#11758199—28no—
245#11758198—24no—
246#11758198—24no—
247#11758198—24no—
248#11758198—24no—
249#11758198C2×D414yes—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61—24no—
254C4⋊Dic61—24no—
255C4⋊Dic61—24no—
256C4⋊Dic61C2412yes—
257C4⋊Dic61C2412yes—
258C4⋊Dic61C2412yes—
259#11758196—24no—
260#11758196—24no—
261#11758196—24no—
262#11758196C2×D414yes—
263C4×Dic61—24no—
264C4×Dic61C2×D412yes—
265C4×Dic61C2412yes—
266#11758194—28no—
267C2×#92418—22no—
268C2×#92418#4114yes—
269C2×#92418C2412yes—
270C2×#92418C2412yes—
271#11758189—28no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—42no—
277C23×C61—42no—
278C23×C61—42no—
279C23×C61C22×D412yes—
280C23×C61C22×D411yescharacteristic
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—42no—
286C22×D61—42no—
287C22×D61—42no—
288C22×D61C22×D412yes—
289D4×C61—22no—
290D4×C61—22no—
291D4×C61—48no—
292D4×C61—42no—
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—42no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61C22×D412yes—
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C2×#4112yes—
306C2×C4×C612−1+412yes—
307C2×C4×C61C2511yescharacteristic
308C22⋊D61—44no—
309C22⋊D61—84no—
310C22⋊D61—84no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61—84no—
321C2×Dic61—84no—
322C2×Dic61C22×D412yes—
323C2×Dic61C22×D412yes—
324C2×Dic61C22×D412yes—
325D244—22no—
326D244—22no—
327D244—48no—
328D244—42no—
329C4×D61—24no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—84no—
333C4×D61—84no—
334C8×C61—22no—
335C8×C61—22no—
336#92418—22no—
337#92418C2×#4114yes—
338C2×#3355—611nomaximal, Sylow
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—44no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—84no—
347C22×C61#54712yes—
348C22×C61#57512yes—
349C22×C61#57612yes—
350C22×C61C23×D411yescharacteristic
351C2×D61—22no—
352C2×D61—22no—
353C2×D61—22no—
354C2×D61—44no—
355C2×D61—42no—
356C2×D61—42no—
357C2×D61—42no—
358C2×D61—84no—
359C4×C61—22no—
360C4×C61—42no—
361C4×C61—42no—
362C4×C61—42no—
363C4×C61#54712yes—
364C4×C61C22×#4111yescharacteristic
365C4×C61C2×2−1+411yescharacteristic
366Dic61—22no—
367Dic61—22no—
368Dic61—22no—
369Dic61—42no—
370Dic61—42no—
371Dic61—42no—
372C2×#553—611no—
373C2×#553—611no—
374#3355—6116no—
375C2×#499—611no—
376C2×#482—611no—
377C2×#482D6111yescharacteristic, complemented
378C2×#480—611no—
379C2×#480—611no—
380C2×#478—611no—
381C2×#478—611no—
382C2×#469—611no—
383C2×#469—611no—
384C2×C4×D8—611no—
385C2×#436—611no—
386C2×#428—611no—
387C2×#428—611no—
388C2×C61—42no—
389C2×C61—82no—
390C2×C61#335514yescomplemented
391C2×C61C2×#54711yescharacteristic
392C2×C61C2×#57511yescharacteristic
393C2×C61C2×#57611yescharacteristic
394D61—42no—
395D61—82no—
396C22×D8—611no—
397C22×M16—611no—
398C22×M16—611no—
399#553—618no—
400#553—618no—
401#553—1224no—
402#553—1224no—
403C2×#126—1221no—
404C2×#126—1221no—
405C2×#125—611no—
406C2×#125—611no—
407C2×#123—1221no—
408C2×#123—1221no—
409C2×#121—611no—
410C2×#121—611no—
411C2×#121—611no—
412C2×#121—1221no—
413C2×#121—1221no—
414C2×#121C2×D6111yescharacteristic
415C2×C4×D4—611no—
416C2×C4×D4—611no—
417C2×C4×D4—611no—
418C2×C4×D4—1221no—
419C2×C4×D4—1221no—
420C2×#117—611no—
421C2×#117C2×D6111yescharacteristic
422C22×C4⋊C4—611no—
423C22×C4⋊C4—611no—
424#499—618no—
425#482—618no—
426#482C2×D6118yescomplemented
427#480—618no—
428#480—618no—
429#478—618no—
430#478—618no—
431#469—618no—
432#469—618no—
433C4×D8—618no—
434#436—618no—
435#428—618no—
436#428—618no—
437C2×#107—611no—
438C2×#107—611no—
439C2×#107—611no—
440C2×#107—611no—
441C2×#107C2×D6111yescharacteristic
442C2×#106—611no—
443C2×#106—611no—
444C2×#106—611no—
445C2×#106C2×D6111yescharacteristic
446C2×C4⋊C8—611no—
447C2×#102—611no—
448C2×#102—611no—
449C2×#102—611no—
450C2×#102—611no—
451C2×#102C2×D6111yescharacteristic
452C2×#102C2×D6111yescharacteristic
453C2×C22⋊C8—611no—
454C2×C22⋊C8C2×D6111yescharacteristic
455C2×C4×C8—611no—
456C61C2×#335511yescharacteristic, complemented, Sylow
457C22×D4—21no—
458C22×D4—611no—
459C22×D4—611no—
460C22×D4—1221no—
461C22×D4—1221no—
462C22×D4—1221no—
463C22×D4C22×D6111yescharacteristic
464C23×C4—611no—
465C23×C4—1221no—
466C23×C4—1221no—
467C23×C4—1221no—
468C23×C4—1221no—
469C23×C4C22×D6111yescharacteristic
470C2×D8—614no—
471C2×D8—1224no—
472C2×M16—614no—
473C2×M16—614no—
474C2×M16—1224no—
475C2×M16—1224no—
476C22×C8—611no—
477C22×C8—611no—
478C22×C8C22×D6111yescharacteristic
479C22×C8C22×D6111yescharacteristic
480#126—1228no—
481#126—1228no—
482#125—614no—
483#125—614no—
484#125—1222no—
485#125—1222no—
486#123—1228no—
487#123—1228no—
488#121—22no—
489#121—614no—
490#121—614no—
491#121—614no—
492#121—1228no—
493#121—1222no—
494#121—1222no—
495#121—1228no—
496#121—1222no—
497#121C22×D6114yes—
498C4×D4—614no—
499C4×D4—614no—
500C4×D4—614no—
501C4×D4—614no—
502C4×D4—1228no—
503C4×D4—1222no—
504C4×D4—1222no—
505C4×D4—1228no—
506#117—22no—
507#117—614no—
508#117—1222no—
509#117C22×D6114yes—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—614no—
515C2×C4⋊C4—614no—
516C2×C4⋊C4—1222no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1222no—
524C2×C4⋊C4C22×D6111yescharacteristic
525C2×C4⋊C4C22×D6111yescharacteristic
526C2×C4⋊C4C22×D6111yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—611no—
530C2×C22⋊C4—611no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C42—21no—
538C2×C42—611no—
539C2×C42—1221no—
540#107—614no—
541#107—614no—
542#107—614no—
543#107—614no—
544#107C22×D6114yes—
545#106—614no—
546#106—614no—
547#106—614no—
548#106C22×D6114yes—
549C4⋊C8—614no—
550#102—614no—
551#102—614no—
552#102—614no—
553#102—614no—
554#102C22×D6114yes—
555#102C22×D6114yes—
556C22⋊C8—614no—
557C22⋊C8C22×D6114yes—
558C4×C8—614no—
559C24—21no—
560C24—611no—
561C24—1221no—
562C24D4×D6111yescharacteristic
563C2×D4—24no—
564C2×D4—21no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—44no—
568C2×D4—614no—
569C2×D4—612no—
570C2×D4—1224no—
571C2×D4—1224no—
572C2×D4—1224no—
573C2×D4—1221no—
574C2×D4—1222no—
575C2×D4—1222no—
576C2×D4—4882no—
577C2×D4—4882no—
578C2×D4—2444no—
579C2×D4—2442no—
580C2×D4C23×D6112yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—612no—
590C22×C4—612no—
591C22×C4—1224no—
592C22×C4—1224no—
593C22×C4—1224no—
594C22×C4—1222no—
595C22×C4—1222no—
596C22×C4—1224no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—4882no—
601C22×C4—4882no—
602C22×C4—4882no—
603C22×C4—4882no—
604C22×C4D4×D6112yes—
605C22×C4D4×D6111yescharacteristic
606C22×C4C23×D6112yes—
607C22×C4C23×D6111yescharacteristic
608D8—1228no—
609M16—1228no—
610M16—1228no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—614no—
614C2×C8—612no—
615C2×C8—612no—
616C2×C8—1222no—
617C2×C8C23×D6112yes—
618C2×C8C23×D6112yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—614no—
623C4⋊C4—612no—
624C4⋊C4—612no—
625C4⋊C4—612no—
626C4⋊C4—1224no—
627C4⋊C4—1224no—
628C4⋊C4—1224no—
629C4⋊C4—1224no—
630C4⋊C4—1224no—
631C4⋊C4—1221no—
632C4⋊C4—1221no—
633C4⋊C4—1221no—
634C4⋊C4—1224no—
635C4⋊C4C23×D6112yes—
636C4⋊C4C23×D6112yes—
637C4⋊C4C23×D6112yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—614no—
641C22⋊C4—614no—
642C22⋊C4—1224no—
643C22⋊C4—1224no—
644C22⋊C4—1224no—
645C22⋊C4—1224no—
646C22⋊C4—1224no—
647C22⋊C4—1224no—
648C42—24no—
649C42—612no—
650C42—612no—
651C42—1224no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—612no—
660C23—1222no—
661C23—1222no—
662C23—1222no—
663C23—1222no—
664C23—2442no—
665C23—2442no—
666C23—2442no—
667C23C2×D4×D6112yes—
668C23C2×D4×D6111yescharacteristic
669D4—22no—
670D4—22no—
671D4—48no—
672D4—42no—
673D4—1222no—
674D4—1222no—
675D4—4884no—
676D4—4884no—
677D4—2448no—
678D4—2444no—
679D4—2442no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—612no—
691C2×C4—612no—
692C2×C4—612no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1224no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—4884no—
703C2×C4—4884no—
704C2×C4—4884no—
705C2×C4—4884no—
706C2×C4—2442no—
707C2×C4—2442no—
708C2×C4—2442no—
709C2×C4C2×D4×D6112yes—
710C2×C4C2×D4×D6111yescharacteristic
711C2×C4#41×D6112yes—
712C2×C4#1451982412yes—
713C2×C4C24×D6111yescharacteristic
714C8—22no—
715C8—22no—
716C8—614no—
717C8—1222no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—44no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—1222no—
727C22—1222no—
728C22—1222no—
729C22—4884no—
730C22—2442no—
731C22—2442no—
732C22—2442no—
733C22—2444no—
734C22#1684041012yes—
735C22#1684055812yes—
736C22#1684056412yes—
737C22C22×D4×D6111yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—1222no—
743C4—1222no—
744C4—1222no—
745C4—2442no—
746C4—2442no—
747C4—2442no—
748C4#1684041012yes—
749C4C2×#41×D6111yescharacteristic
750C4C2×#1451982411yescharacteristic
751C2—42no—
752C2—82no—
753C2—4882no—
754C2—2442no—
755C2#2145841814yesdirect product factor
756C2C2×#1684041011yescharacteristic
757C2C2×#1684055811yescharacteristic
758C2C2×#1684056411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#482C2
socleC23×C61C22×D4
hypercenterC2×#482D61
hypocenterC61C2×#3355
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#16840464C2semidirect
2. C2×#16840456C2semidirect
3. #21458418C2direct (N × H)
4. C2×#16840163C2semidirect
5. C2×#16840089C2semidirect
6. C2×#16840076C2semidirect
7. C2×#16840074C2semidirect
8. C2×#16840061C2semidirect
9. C2×#16840060C2semidirect
10. C2×#16840014C2semidirect
11. C2×#16840013C2semidirect
12. C2×#16839842C2semidirect
13. C2×#16839837C2semidirect
14. C2×#16839805C2semidirect
15. C2×#16839801C2semidirect
16. C2×C61×#482C2semidirect
21. #16840464C22semidirect
23. #16840456C22semidirect
43. #16840163C22semidirect
44. #16840089C22semidirect
45. #16840076C22semidirect
46. #16840074C22semidirect
47. #16840061C22semidirect
48. #16840060C22semidirect
49. #16840014C22semidirect
50. #16840013C22semidirect
51. #16839842C22semidirect
52. #16839837C22semidirect
53. #16839805C22semidirect
54. #16839801C22semidirect
71. C61×#482C22semidirect
377. C2×#482D61semidirect
390. C2×C61#3355semidirect
426. #482C2×D61semidirect
456. C61C2×#3355semidirect
755. C2#21458418direct (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×#168404562
#214584182
C2×#168401632
C2×#168400892
C2×#168400762
C2×#168400742
C2×#168400612
C2×#168400602
C2×#168400142
C2×#168400132
C2×#168398422
C2×#168398372
C2×#168398052
C2×#168398012
C2×C61×#4822
C2×#335561