Finite Group Databasebeta

← C2×#21458218 #30558482

Subgroups — C2×#21458218 #30558482

Order 15616.

1994 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×#16840465C211yesmaximal, characteristic, complemented
2C2×#16840462C211yesmaximal, characteristic, complemented
3#21458218C2116yesmaximal, direct product factor
4C2×#16840161C211yesmaximal, characteristic, complemented
5C2×#16840082C211yesmaximal, characteristic, complemented
6C2×#16840079C211yesmaximal, characteristic, complemented
7C2×#16840089C211yesmaximal, characteristic, complemented
8C2×#16840084C211yesmaximal, characteristic, complemented
9C2×#16840063C211yesmaximal, characteristic, complemented
10C2×#16839997C211yesmaximal, characteristic, complemented
11C2×#16839997C211yesmaximal, characteristic, complemented
12C2×C4×#11758199C211yesmaximal, characteristic, complemented
13C2×#16839827C211yesmaximal, characteristic, complemented
14C2×#16839797C211yesmaximal, characteristic, complemented
15C2×#107×D61C211yesmaximal, characteristic, complemented
16C2×C61×#478C211yesmaximal, characteristic, complemented
17C22×#11758199C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840465—24no—
21#16840465C2218yescomplemented
22#16840462—24no—
23#16840462C2218yescomplemented
24C2×#14519772—21no—
25C2×#14519770—21no—
26C2×#14519769C2211yescharacteristic
27C2×#14519762—21no—
28C2×#14519760—21no—
29C2×#14519752—21no—
30C2×#14519752C2211yescharacteristic
31C2×#14519752C2211yescharacteristic
32C2×#14519750—21no—
33C2×#14519748C2211yescharacteristic
34C2×#14519748C2211yescharacteristic
35C2×C4×D244C2211yescharacteristic
36C2×C4×D244C2211yescharacteristic
37C2×#14519739—21no—
38C2×C4×C22⋊D61—21no—
39C2×#14519735C2211yescharacteristic
40C2×#14519735C2211yescharacteristic
41C2×C4⋊C4×D61C2211yescharacteristic
42C2×C4⋊C4×D61C2211yescharacteristic
43#16840161C2218yescomplemented
44#16840089C2218yescomplemented
45#16840084C2218yescomplemented
46#16840082C2218yescomplemented
47#16840079C2218yescomplemented
48#16840063C2218yescomplemented
49#16839997C2218yescomplemented
50#16839997C2218yescomplemented
51C4×#11758199C2218yescomplemented
52#16839827C2218yescomplemented
53#16839797C2218yescomplemented
54C2×#14519711C2211yescharacteristic
55C2×#14519710C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519710C2211yescharacteristic
58#107×D61C2218yescomplemented
59C2×#14519709C2211yescharacteristic
60C2×#14519708C2211yescharacteristic
61C2×#14519708C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C4×#92418C2211yescharacteristic
69C2×#125×C61C2211yescharacteristic
70C2×C4×D4×C61C2211yescharacteristic
71C61×#478C2218yescomplemented
72C2×#107×C61C2211yescharacteristic
73C2×#106×C61C2211yescharacteristic
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C22×D244—21no—
78C22×D244—21no—
79C22×D244D411yescharacteristic
80C22×D244C2311yescharacteristic
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86C22×C4×D61C2311yescharacteristic
87C22×C4×D61C2311yescharacteristic
88C2×#11758199—24no—
89C2×#11758199C2314yes—
90C22×#92418C2311yescharacteristic
91C22×#92418C2311yescharacteristic
92C2×C8×D61—24no—
93C2×C8×D61—24no—
94C2×C8×D61C2314yes—
95C2×C8×D61C2314yes—
96#14519772—28no—
97#14519770—28no—
98#14519769—22no—
99#14519769C2314yes—
100#14519762—28no—
101#14519760—28no—
102#14519752—28no—
103#14519752—22no—
104#14519752—22no—
105#14519752C2314yes—
106#14519752C2314yes—
107#14519750—28no—
108#14519748—22no—
109#14519748—22no—
110#14519748C2314yes—
111#14519748C2314yes—
112C4×D244—22no—
113C4×D244D414yes—
114C4×D244C2314yes—
115C4×D244C2314yes—
116#14519739—28no—
117C4×C22⋊D61—28no—
118#14519735—22no—
119#14519735—22no—
120#14519735C2314yes—
121#14519735C2314yes—
122C2×C4⋊Dic61D411yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×C4⋊Dic61C2311yescharacteristic
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C4⋊C4×D61—22no—
131C4⋊C4×D61—22no—
132C4⋊C4×D61C2314yes—
133C4⋊C4×D61C2314yes—
134C2×C22⋊Dic61—21no—
135C2×C22⋊Dic61—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198D411yescharacteristic
142C2×#11758198D411yescharacteristic
143C2×C4×Dic61—21no—
144C2×C4×Dic61—21no—
145#14519711C2314yes—
146#14519710C2314yes—
147#14519710C2314yes—
148#14519710C2314yes—
149#14519709C2314yes—
150#14519708C2314yes—
151#14519708C2314yes—
152#14519699C2314yes—
153#14519699C2314yes—
154#14519698C2314yes—
155#14519697C2314yes—
156#14519689C2314yes—
157#14519689C2314yes—
158C4×#92418C2314yes—
159C22×D4×C61C2311yescharacteristic
160C23×C4×C61—21no—
161C22×C8×C61C2311yescharacteristic
162C22×C8×C61C2311yescharacteristic
163#125×C61—22no—
164#125×C61C2314yes—
165C4×D4×C61—22no—
166C4×D4×C61C2314yes—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61—21no—
169C2×C4⋊C4×C61C2311yescharacteristic
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C22⋊C4×C61—21no—
173C2×C42×C61C2311yescharacteristic
174#107×C61C2314yes—
175#106×C61C2314yes—
176C4⋊C8×C61C2314yes—
177#102×C61C2314yes—
178#102×C61C2314yes—
179C24×C61—21no—
180C23×D61—21no—
181C23×D61C2×D411yescharacteristic
182C23×D61C2×D411yescharacteristic
183C2×D4×C61—21no—
184C2×D4×C61—22no—
185C2×D4×C61—22no—
186C2×D4×C61C2412yes—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—24no—
191C22×C4×C61—82no—
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2411yescharacteristic
195C2×C22⋊D61—24no—
196C2×C22⋊D61—24no—
197C2×C22⋊D61—44no—
198C2×C22⋊D61—82no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61C2×D411yescharacteristic
203C22×Dic61C2×D411yescharacteristic
204C2×D244—24no—
205C2×D244—22no—
206C2×D244—22no—
207C2×D244—24no—
208C2×D244—21no—
209C2×D244—24no—
210C2×D244—44no—
211C2×D244—82no—
212C2×D244C2×D414yes—
213C2×D244C2412yes—
214C2×C4×D61—22no—
215C2×C4×D61—22no—
216C2×C4×D61—22no—
217C2×C4×D61—22no—
218C2×C4×D61—24no—
219C2×C4×D61—24no—
220C2×C4×D61—24no—
221C2×C4×D61—82no—
222C2×C4×D61—82no—
223C2×C4×D61—82no—
224C2×C4×D61C2×D412yes—
225C2×C4×D61C2×D412yes—
226C2×C4×D61C2412yes—
227C2×C4×D61C2412yes—
228C2×C8×C61—22no—
229C2×C8×C61—22no—
230C2×C8×C61C2412yes—
231C2×C8×C61C2412yes—
232C4⋊C4×C61—24no—
233C4⋊C4×C61—24no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61C2412yes—
238C4⋊C4×C61C2412yes—
239C4⋊C4×C61C2412yes—
240C22⋊C4×C61—24no—
241C42×C61C2×D412yes—
242C42×C61C2412yes—
243C22⋊Dic61—24no—
244C22⋊Dic61—24no—
245#11758199—28no—
246#11758198—24no—
247#11758198—24no—
248#11758198—24no—
249#11758198—24no—
250#11758198—24no—
251#11758198C2×D414yes—
252#11758198C2×D414yes—
253C4⋊Dic61—21no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61C2×D414yes—
257C4⋊Dic61C2412yes—
258C4⋊Dic61C2412yes—
259C4⋊Dic61C2412yes—
260#11758196—24no—
261#11758196—24no—
262#11758196—24no—
263#11758196—24no—
264C4×Dic61—24no—
265C4×Dic61—24no—
266C2×#92418—22no—
267C2×#92418#4114yes—
268C2×#92418C2412yes—
269C2×#92418C2412yes—
270C8×D61—28no—
271C8×D61—28no—
272C23×C61—22no—
273C23×C61—42no—
274C23×C61—42no—
275C23×C61—42no—
276C23×C61C22×D411yescharacteristic
277C22×D61—22no—
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—42no—
284C22×D61—42no—
285C22×D61—42no—
286C22×D61#13514yes—
287C22×D61C22×D412yes—
288C22×D61C22×D412yes—
289D4×C61—22no—
290D4×C61—22no—
291D4×C61—42no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—42no—
298C2×C4×C61—42no—
299C2×C4×C61—42no—
300C2×C4×C61—84no—
301C2×C4×C61C22×D412yes—
302C2×C4×C61C22×D412yes—
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C2×#4112yes—
305C2×C4×C612−1+412yes—
306C2×C4×C61C2511yescharacteristic
307C22⋊D61—48no—
308C22⋊D61—84no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61C22×D412yes—
318C2×Dic61C22×D412yes—
319D244—28no—
320D244—22no—
321D244—22no—
322D244—48no—
323D244—42no—
324D244—84no—
325C4×D61—24no—
326C4×D61—24no—
327C4×D61—22no—
328C4×D61—22no—
329C4×D61—22no—
330C4×D61—22no—
331C4×D61—84no—
332C4×D61—84no—
333C4×D61—84no—
334C8×C61—22no—
335C8×C61—22no—
336#92418—22no—
337#92418C2×#4114yes—
338C2×#3339—611nomaximal, Sylow
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—42no—
342C22×C61—84no—
343C22×C61#54712yes—
344C22×C61C2×#13512yes—
345C22×C61#57612yes—
346C22×C61C23×D411yescharacteristic
347C2×D61—28no—
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—22no—
351C2×D61—22no—
352C2×D61—22no—
353C2×D61—44no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—42no—
357C2×D61—84no—
358C2×D61C2×#13514yes—
359C4×C61—22no—
360C4×C61—22no—
361C4×C61—42no—
362C4×C61—42no—
363C4×C61—42no—
364C4×C61#54712yes—
365C4×C61C22×#4111yescharacteristic
366C4×C61C2×2−1+411yescharacteristic
367Dic61—22no—
368Dic61—22no—
369Dic61—42no—
370Dic61—42no—
371Dic61—42no—
372C2×#553—611no—
373C2×#553—611no—
374#3339—6116no—
375C2×#499—611no—
376C2×#481—611no—
377C2×#481—611no—
378C2×#482—611no—
379C2×#482—611no—
380C2×#478—611no—
381C2×#478D6111yescharacteristic, complemented
382C2×#466—611no—
383C2×#466—611no—
384C2×C4×D8—611no—
385C2×C8×D4—611no—
386C2×#427—611no—
387C22×#107—611no—
388C2×C61—82no—
389C2×C61#333914yescomplemented
390C2×C61C2×#54711yescharacteristic
391C2×C61C22×#13511yescharacteristic
392C2×C61C2×#57611yescharacteristic
393D61—24no—
394D61—42no—
395D61—82no—
396C22×D8—611no—
397C23×C8—611no—
398C23×C8—611no—
399#553—618no—
400#553—618no—
401#553—1224no—
402#553—1224no—
403C2×#126—1221no—
404C2×#126—1221no—
405C2×#125—611no—
406C2×#125C2×D6111yescharacteristic
407C2×#123—1221no—
408C2×#123—1221no—
409C2×#121—611no—
410C2×#121—611no—
411C2×#121—611no—
412C2×#121—611no—
413C2×#121—1221no—
414C2×#121—1221no—
415C2×C4×D4—611no—
416C2×C4×D4—611no—
417C2×C4×D4—1221no—
418C2×C4×D4—1221no—
419C2×C4×D4C2×D6111yescharacteristic
420C2×#117—611no—
421C2×#117—611no—
422C22×C4⋊C4—611no—
423C22×C4⋊C4—611no—
424#499—618no—
425#482—618no—
426#482—618no—
427#481—618no—
428#481—618no—
429#478—618no—
430#478C2×D6118yescomplemented
431#466—618no—
432#466—618no—
433C4×D8—618no—
434C8×D4—618no—
435#427—618no—
436C2×#107—611no—
437C2×#107—611no—
438C2×#107—611no—
439C2×#107—611no—
440C2×#107—618no—
441C2×#107C2×D6111yescharacteristic
442C2×#106—611no—
443C2×#106—611no—
444C2×#106—611no—
445C2×#106C2×D6111yescharacteristic
446C2×C4⋊C8C2×D6111yescharacteristic
447C2×#102—611no—
448C2×#102—611no—
449C2×#102—611no—
450C2×#102—611no—
451C2×#102C2×D6111yescharacteristic
452C2×#102C2×D6111yescharacteristic
453C2×C22⋊C8—611no—
454C2×C22⋊C8—611no—
455C2×C4×C8—611no—
456C61C2×#333911yescharacteristic, complemented, Sylow
457C22×D4—611no—
458C22×D4—611no—
459C22×D4—1221no—
460C22×D4—1221no—
461C22×D4—1221no—
462C22×D4—1221no—
463C22×D4C22×D6111yescharacteristic
464C23×C4—21no—
465C23×C4—611no—
466C23×C4—611no—
467C23×C4—1221no—
468C23×C4—1221no—
469C23×C4—1221no—
470C2×D8—614no—
471C2×D8—1224no—
472C22×C8—611no—
473C22×C8—611no—
474C22×C8—614no—
475C22×C8—614no—
476C22×C8—1224no—
477C22×C8—1224no—
478C22×C8C22×D6111yescharacteristic
479C22×C8C22×D6111yescharacteristic
480#126—1228no—
481#126—1228no—
482#125—22no—
483#125—614no—
484#125—1222no—
485#125C22×D6114yes—
486#123—1228no—
487#123—1228no—
488#121—614no—
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#121—1222no—
498C4×D4—22no—
499C4×D4—614no—
500C4×D4—614no—
501C4×D4—614no—
502C4×D4—1228no—
503C4×D4—1228no—
504C4×D4—1222no—
505C4×D4C22×D6114yes—
506#117—614no—
507#117—614no—
508#117—1222no—
509#117—1222no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—614no—
517C2×C4⋊C4—614no—
518C2×C4⋊C4—1222no—
519C2×C4⋊C4—1222no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4C22×D6111yescharacteristic
525C2×C4⋊C4C22×D6111yescharacteristic
526C2×C4⋊C4C22×D6111yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—611no—
529C2×C22⋊C4—611no—
530C2×C22⋊C4—1221no—
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—1221no—
538C2×C42—1221no—
539C2×C42C22×D6111yescharacteristic
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⋊C8C22×D6114yes—
550#102—614no—
551#102—614no—
552#102—614no—
553#102—614no—
554#102C22×D6114yes—
555#102C22×D6114yes—
556C22⋊C8—614no—
557C22⋊C8—614no—
558C4×C8—614no—
559C24—21no—
560C24—611no—
561C24—611no—
562C24—1221no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—614no—
567C2×D4—612no—
568C2×D4—1224no—
569C2×D4—1224no—
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—2444no—
580C2×D4C23×D6112yes—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—24no—
585C22×C4—82no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—612no—
589C22×C4—612no—
590C22×C4—612no—
591C22×C4—612no—
592C22×C4—1224no—
593C22×C4—1224no—
594C22×C4—1222no—
595C22×C4—1222no—
596C22×C4—1222no—
597C22×C4—1222no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1224no—
602C22×C4—4882no—
603C22×C4—4882no—
604C22×C4—4882no—
605C22×C4D4×D6111yescharacteristic
606C22×C4D4×D6111yescharacteristic
607C22×C4C23×D6111yescharacteristic
608D8—1228no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—614no—
612C2×C8—612no—
613C2×C8—612no—
614C2×C8—1228no—
615C2×C8—1228no—
616C2×C8—1222no—
617C2×C8C23×D6112yes—
618C2×C8C23×D6112yes—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—614no—
625C4⋊C4—612no—
626C4⋊C4—612no—
627C4⋊C4—612no—
628C4⋊C4—1224no—
629C4⋊C4—1224no—
630C4⋊C4—1221no—
631C4⋊C4—1221no—
632C4⋊C4—1221no—
633C4⋊C4—1224no—
634C4⋊C4—1224no—
635C4⋊C4C23×D6112yes—
636C4⋊C4C23×D6112yes—
637C4⋊C4C23×D6112yes—
638C22⋊C4—24no—
639C22⋊C4—614no—
640C22⋊C4—614no—
641C22⋊C4—1224no—
642C22⋊C4—1224no—
643C22⋊C4—1224no—
644C22⋊C4—1224no—
645C22⋊C4—1224no—
646C22⋊C4—1224no—
647C22⋊C4—1224no—
648C42—1224no—
649C42—1224no—
650C42D4×D6112yes—
651C42C23×D6112yes—
652C23—22no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—614no—
657C23—612no—
658C23—612no—
659C23—1222no—
660C23—1222no—
661C23—1222no—
662C23—1222no—
663C23—1222no—
664C23—1222no—
665C23—2442no—
666C23—2442no—
667C23—2442no—
668C23C2×D4×D6111yescharacteristic
669D4—22no—
670D4—22no—
671D4—42no—
672D4—1228no—
673D4—1222no—
674D4—1222no—
675D4—4884no—
676D4—4884no—
677D4—2448no—
678D4—2448no—
679D4—2442no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—84no—
689C2×C4—612no—
690C2×C4—612no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1224no—
698C2×C4—1224no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—4884no—
703C2×C4—4884no—
704C2×C4—4884no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4—2442no—
708C2×C4C2×D4×D6112yes—
709C2×C4C2×D4×D6112yes—
710C2×C4C2×D4×D6111yescharacteristic
711C2×C4#41×D6112yes—
712C2×C4#1451982512yes—
713C2×C4C24×D6111yescharacteristic
714C8—22no—
715C8—22no—
716C8—614no—
717C8—1222no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—84no—
722C22—614no—
723C22—1228no—
724C22—1222no—
725C22—1222no—
726C22—1222no—
727C22—1222no—
728C22—1222no—
729C22—4884no—
730C22—2442no—
731C22—2442no—
732C22—2442no—
733C22—2444no—
734C22#1684041412yes—
735C22#135×D6112yes—
736C22#1684056612yes—
737C22C22×D4×D6111yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—1222no—
744C4—1222no—
745C4—2442no—
746C4—2442no—
747C4—2442no—
748C4#1684041412yes—
749C4C2×#41×D6111yescharacteristic
750C4C2×#1451982511yescharacteristic
751C2—82no—
752C2—1224no—
753C2—4882no—
754C2—2442no—
755C2#2145821814yesdirect product factor
756C2C2×#1684041411yescharacteristic
757C2C2×#135×D6111yescharacteristic
758C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#478C2
socleC23×C61C22×D4
hypercenterC2×#478D61
hypocenterC61C2×#3339
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#16840465C2semidirect
2. C2×#16840462C2semidirect
3. #21458218C2direct (N × H)
4. C2×#16840161C2semidirect
5. C2×#16840082C2semidirect
6. C2×#16840079C2semidirect
7. C2×#16840089C2semidirect
8. C2×#16840084C2semidirect
9. C2×#16840063C2semidirect
10. C2×#16839997C2semidirect
11. C2×#16839997C2semidirect
12. C2×C4×#11758199C2semidirect
13. C2×#16839827C2semidirect
14. C2×#16839797C2semidirect
15. C2×#107×D61C2semidirect
16. C2×C61×#478C2semidirect
21. #16840465C22semidirect
23. #16840462C22semidirect
43. #16840161C22semidirect
44. #16840089C22semidirect
45. #16840084C22semidirect
46. #16840082C22semidirect
47. #16840079C22semidirect
48. #16840063C22semidirect
49. #16839997C22semidirect
50. #16839997C22semidirect
51. C4×#11758199C22semidirect
52. #16839827C22semidirect
53. #16839797C22semidirect
58. #107×D61C22semidirect
71. C61×#478C22semidirect
381. C2×#478D61semidirect
389. C2×C61#3339semidirect
430. #478C2×D61semidirect
456. C61C2×#3339semidirect
755. C2#21458218direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404652
C2×#168404622
#214582182
C2×#168401612
C2×#168400822
C2×#168400792
C2×#168400892
C2×#168400842
C2×#168400632
C2×#168399972
C2×C4×#117581992
C2×#168398272
C2×#168397972
C2×#107×D612
C2×C61×#4782
C2×#333961