Finite Group Databasebeta

← C2×#21458543 #30559707

Subgroups — C2×#21458543 #30559707

Order 15616.

2122 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×#16840488C211yesmaximal, characteristic, complemented
2C2×#16840432C211yesmaximal, characteristic
3#21458543C2116yesmaximal, direct product factor
4C2×#16840126C211yesmaximal, characteristic, complemented
5C2×#16840125C211yesmaximal, characteristic, complemented
6C2×#16840107C211yesmaximal, characteristic, complemented
7C2×#16840064C211yesmaximal, characteristic, complemented
8C2×#16840063C211yesmaximal, characteristic, complemented
9C2×#16840040C211yesmaximal, characteristic, complemented
10C2×#16839960C211yesmaximal, characteristic, complemented
11C2×#16839960C211yesmaximal, characteristic, complemented
12C2×#16839891C211yesmaximal, characteristic, complemented
13C2×#16839863C211yesmaximal, characteristic, complemented
14C2×#16839860C211yesmaximal, characteristic, complemented
15C2×SD16×Dic61C211yesmaximal, characteristic, complemented
16C2×C61×#460C211yesmaximal, characteristic, complemented
17C22×#11758224—21no—
18C22×#11758201C2211yescharacteristic
19#16840488—24no—
20#16840488C2218yescomplemented
21#16840432—24no—
22#16840432C2218yes—
23C2×#14519776—21no—
24C2×#14519776C2211yescharacteristic
25C2×#14519773C2211yescharacteristic
26C2×#14519773C2211yescharacteristic
27C2×#14519769—21no—
28C2×#14519769C2211yescharacteristic
29C2×#14519768—21no—
30C2×#14519768C2211yescharacteristic
31C2×#14519749—21no—
32C2×#14519749—21no—
33C2×#14519748—21no—
34C2×Q8×Dic61C2211yescharacteristic
35C2×Q8×Dic61C2211yescharacteristic
36C2×C4×Dic122—21no—
37C2×C4×Dic122C2211yescharacteristic
38C2×C4×D244C2211yescharacteristic
39C2×D4×Dic61C2211yescharacteristic
40C2×D4×Dic61C2211yescharacteristic
41#16840126C2218yescomplemented
42#16840125C2218yescomplemented
43#16840107C2218yescomplemented
44#16840064C2218yescomplemented
45#16840063C2218yescomplemented
46#16840040C2218yescomplemented
47#16839960C2218yescomplemented
48#16839960C2218yescomplemented
49#16839891C2218yescomplemented
50#16839863C2218yescomplemented
51#16839860C2218yescomplemented
52SD16×Dic61C2218yescomplemented
53C2×#14519711C2211yescharacteristic
54C2×#14519710C2211yescharacteristic
55C2×#14519709C2211yescharacteristic
56C2×#14519706C2211yescharacteristic
57C2×#14519706C2211yescharacteristic
58C2×#14519701C2211yescharacteristic
59C2×#14519699C2211yescharacteristic
60C2×#14519699C2211yescharacteristic
61C2×#14519698C2211yescharacteristic
62C2×#14519698C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519688C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C2×#127×C61C2211yescharacteristic
72C2×C4×Q8×C61C2211yescharacteristic
73C61×#460C2218yescomplemented
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C2×#11758224—28no—
78C2×#11758224—48no—
79C22×Dic122—21no—
80C22×Dic122D411yescharacteristic
81C22×D244C2311yescharacteristic
82C22×C22⋊D61—21no—
83C22×C22⋊D61—21no—
84C22×C22⋊D61—21no—
85C22×C22⋊D61—21no—
86C23×Dic61—21no—
87C23×Dic61—21no—
88C22×C4×D61—21no—
89C2×#11758201—24no—
90C2×#11758201C2314yes—
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93#14519776—28no—
94#14519776—22no—
95#14519776C2314yes—
96#14519773—22no—
97#14519773—22no—
98#14519773C2314yes—
99#14519773C2314yes—
100#14519769—22no—
101#14519769—28no—
102#14519769C2314yes—
103#14519768—28no—
104#14519768—22no—
105#14519768C2314yes—
106#14519749—28no—
107#14519749—28no—
108#14519748—28no—
109Q8×Dic61—22no—
110Q8×Dic61—22no—
111Q8×Dic61C2314yes—
112Q8×Dic61C2314yes—
113C4×Dic122—28no—
114C4×Dic122D414yes—
115C4×Dic122C2314yes—
116C4×D244—22no—
117C4×D244C2314yes—
118D4×Dic61—22no—
119D4×Dic61—22no—
120D4×Dic61C2314yes—
121D4×Dic61C2314yes—
122C2×C4⋊Dic61—21no—
123C2×C4⋊Dic61—21no—
124C2×C4⋊Dic61—21no—
125C2×C4⋊Dic61D411yescharacteristic
126C2×C4⋊Dic61C2311yescharacteristic
127C2×C4⋊Dic61C2311yescharacteristic
128C2×C4⋊Dic61C2311yescharacteristic
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196D411yescharacteristic
134C2×#11758196D411yescharacteristic
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61—21no—
137C2×#11758198—21no—
138C2×C4×Dic61—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61C2311yescharacteristic
141C2×C4×Dic61C2311yescharacteristic
142#14519711C2314yes—
143#14519710C2314yes—
144#14519709C2314yes—
145#14519706C2314yes—
146#14519706C2314yes—
147#14519701C2314yes—
148#14519699C2314yes—
149#14519699C2314yes—
150#14519698C2314yes—
151#14519698C2314yes—
152#14519698C2314yes—
153#14519698C2314yes—
154#14519697C2314yes—
155#14519688C2314yes—
156#14519687C2314yes—
157C8×Dic61C2314yes—
158C22×Q8×C61C2311yescharacteristic
159C22×D4×C61—21no—
160C22×D4×C61—21no—
161C22×D4×C61C2311yescharacteristic
162C22×D4×C61C2311yescharacteristic
163C2×SD16×C61—24no—
164C2×SD16×C61—24no—
165C2×SD16×C61C2314yes—
166C2×SD16×C61C2314yes—
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169#127×C61—22no—
170#127×C61C2314yes—
171C4×Q8×C61—22no—
172C4×Q8×C61C2314yes—
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C42×C61—21no—
176C2×C42×C61C2311yescharacteristic
177C4⋊C8×C61C2314yes—
178#102×C61C2314yes—
179#102×C61C2314yes—
180C24×C61—21no—
181C24×C61—21no—
182C23×D61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—22no—
185C2×Q8×C61#4114yescomplemented
186C2×Q8×C61C2412yes—
187C2×D4×C61—24no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—24no—
191C2×D4×C61—22no—
192C2×D4×C61—22no—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
195C2×D4×C61—44no—
196C2×D4×C61—82no—
197C2×D4×C61C2412yes—
198C2×D4×C61C2412yes—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2411yescharacteristic
204C2×C22⋊D61—24no—
205C2×C22⋊D61—24no—
206C2×C22⋊D61—24no—
207C2×C22⋊D61—24no—
208C2×C22⋊D61—44no—
209C2×C22⋊D61—44no—
210C2×C22⋊D61—82no—
211C2×C22⋊D61—82no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—24no—
216C22×Dic61—24no—
217C22×Dic61—44no—
218C22×Dic61—44no—
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221C22×Dic61C2×D411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223#11758224—432no—
224C2×D244—22no—
225C2×D244—22no—
226C2×D244—21no—
227C2×D244C2412yes—
228C2×C4×D61—24no—
229C2×C4×D61—44no—
230C2×Dic122—24no—
231C2×Dic122—24no—
232C2×Dic122—44no—
233C2×Dic122C2×D414yes—
234SD16×C61—28no—
235SD16×C61—28no—
236C2×C8×C61—22no—
237C2×C8×C61—22no—
238C2×C8×C61C2412yes—
239C2×C8×C61C2412yes—
240C4⋊C4×C61—24no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61C2412yes—
243C42×C61—24no—
244C42×C61C2×D412yes—
245C42×C61C2412yes—
246C22⋊Dic61—24no—
247C22⋊Dic61—24no—
248#11758201—28no—
249#11758198—24no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61—24no—
254C4⋊Dic61—24no—
255C4⋊Dic61—24no—
256C4⋊Dic61C2×D414yes—
257C4⋊Dic61C2412yes—
258C4⋊Dic61C2412yes—
259C4⋊Dic61C2412yes—
260#11758196—24no—
261#11758196—24no—
262#11758196—24no—
263#11758196—24no—
264#11758196C2×D414yes—
265#11758196C2×D414yes—
266C4×Dic61—24no—
267C4×Dic61—24no—
268C4×Dic61C2×D412yes—
269C4×Dic61C2×D412yes—
270C4×Dic61C2412yes—
271C4×Dic61C2412yes—
272C2×#92418—22no—
273C2×#92418—22no—
274C2×#92418C2412yes—
275C2×#92418C2412yes—
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—42no—
287C22×D61—42no—
288C22×D61—42no—
289Q8×C61—24no—
290Q8×C61—22no—
291Q8×C61C2×#4114yescomplemented
292D4×C61—22no—
293D4×C61—22no—
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—48no—
297D4×C61—42no—
298D4×C61—42no—
299D4×C61—84no—
300C2×C4×C61—24no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—42no—
306C2×C4×C61C22×D412yes—
307C2×C4×C61C22×D412yes—
308C2×C4×C61C22×D411yescharacteristic
309C2×C4×C61C2×#4112yes—
310C2×C4×C612−1+412yes—
311C2×C4×C61C2511yescharacteristic
312C22⋊D61—48no—
313C22⋊D61—48no—
314C22⋊D61—84no—
315C22⋊D61—84no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—48no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—48no—
327C2×Dic61AGL(1,ℤ/8)14yes—
328C2×Dic61C22×D412yes—
329C2×Dic61C22×D412yes—
330C2×Dic61C22×D412yes—
331C2×Dic61C22×D412yes—
332D244—22no—
333D244—22no—
334D244—42no—
335C4×D61—48no—
336Dic122—28no—
337Dic122—48no—
338C8×C61—22no—
339C8×C61—22no—
340#92418—22no—
341#92418—22no—
342C2×#3368—611nomaximal, Sylow
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—42no—
349C22×C61—84no—
350C22×C61—84no—
351C22×C61#54812yes—
352C22×C61C2×AGL(1,ℤ/8)12yes—
353C22×C61#57712yes—
354C22×C61C23×D411yescharacteristic
355C2×D61—42no—
356C2×D61—42no—
357C2×D61—42no—
358C2×D61—84no—
359C4×C61—24no—
360C4×C61—22no—
361C4×C61—22no—
362C4×C61—42no—
363C4×C61#54812yes—
364C4×C61C22×#4111yescharacteristic
365C4×C61C2×2−1+411yescharacteristic
366Dic61—22no—
367Dic61—22no—
368Dic61—22no—
369Dic61—42no—
370Dic61—42no—
371Dic61—42no—
372Dic61C2×AGL(1,ℤ/8)14yes—
373C2×#557—611no—
374C2×#550—611no—
375#3368—6116no—
376C2×#490—611no—
377C2×#490—611no—
378C2×#486—611no—
379C2×#478—611no—
380C2×#478—611no—
381C2×#474—611no—
382C2×#460—611no—
383C2×#460—611no—
384C2×#460D6111yescharacteristic, complemented
385C2×#446—611no—
386C2×#440—611no—
387C2×#440—611no—
388C2×C4×SD16—611no—
389C2×C61—82no—
390C2×C61—82no—
391C2×C61#336814yescomplemented
392C2×C61C2×#54811yescharacteristic
393C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
394C2×C61C2×#57711yescharacteristic
395D61—82no—
396C22×#41—1221no—
397C22×SD16—611no—
398C22×SD16C2×D6111yescharacteristic
399C22×SD16C2×D6111yescharacteristic
400#557—618no—
401#557—1224no—
402#550—618no—
403#550—1224no—
404C2×C4⋊Q8—611no—
405C2×C4⋊Q8—1221no—
406C2×#127—611no—
407C2×#127—611no—
408C2×#127C2×D6111yescharacteristic
409C2×#125—611no—
410C2×#125—611no—
411C2×#125—1221no—
412C2×#125—1221no—
413C2×#121—1221no—
414C2×#121—1221no—
415C2×#121—1221no—
416C2×C4×Q8—611no—
417C2×C4×Q8—611no—
418C2×C4×Q8—611no—
419C2×C4×Q8—1221no—
420C2×C4×Q8C2×D6111yescharacteristic
421C2×C4×D4—611no—
422C2×C4×D4—611no—
423C2×C4×D4—611no—
424#490—618no—
425#490—618no—
426#486—618no—
427#478—618no—
428#478—618no—
429#474—618no—
430#460—618no—
431#460—618no—
432#460C2×D6118yescomplemented
433#446—618no—
434#440—618no—
435#440—618no—
436C4×SD16—618no—
437C2×#107—611no—
438C2×#107—611no—
439C2×#106—611no—
440C2×C4⋊C8—611no—
441C2×C4⋊C8—611no—
442C2×C4⋊C8C2×D6111yescharacteristic
443C2×#103—611no—
444C2×#102—611no—
445C2×#102—611no—
446C2×#102—611no—
447C2×#102—611no—
448C2×#102—611no—
449C2×#102—611no—
450C2×#102—611no—
451C2×#102C2×D6111yescharacteristic
452C2×#102C2×D6111yescharacteristic
453C2×#97—611no—
454C2×#97—611no—
455C2×C4×C8—611no—
456C61C2×#336811yescharacteristic, complemented, Sylow
457C2×#41—1228no—
458C2×#41—2448no—
459C22×Q8—611no—
460C22×Q8—1221no—
461C22×Q8C22×D6111yescharacteristic
462C22×D4—21no—
463C22×D4—21no—
464C22×D4—611no—
465C22×D4—1221no—
466C22×D4—1221no—
467C22×D4—1221no—
468C22×D4—1221no—
469C22×D4C22×D6111yescharacteristic
470C22×D4C22×D6111yescharacteristic
471C23×C4—1221no—
472C23×C4—1221no—
473C23×C4—1221no—
474C2×SD16—24no—
475C2×SD16—24no—
476C2×SD16—614no—
477C2×SD16—1224no—
478C2×SD16C22×D6114yes—
479C2×SD16C22×D6114yes—
480C22×C8—611no—
481C22×C8—611no—
482C22×C8C22×D6111yescharacteristic
483C22×C8C22×D6111yescharacteristic
484C4⋊Q8—614no—
485C4⋊Q8—1222no—
486C4⋊Q8—1228no—
487#127—22no—
488#127—614no—
489#127—614no—
490#127—1222no—
491#127—1222no—
492#127C22×D6114yes—
493#125—614no—
494#125—614no—
495#125—1228no—
496#125—1222no—
497#125—1228no—
498#125—1222no—
499#121—1228no—
500#121—1228no—
501#121—1228no—
502C4×Q8—22no—
503C4×Q8—614no—
504C4×Q8—614no—
505C4×Q8—614no—
506C4×Q8—614no—
507C4×Q8—1228no—
508C4×Q8—1222no—
509C4×Q8—1222no—
510C4×Q8C22×D6114yes—
511C4×D4—614no—
512C4×D4—614no—
513C4×D4—614no—
514C4×D4—1222no—
515C4×D4—1222no—
516C4×D4—1222no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—611no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4C22×D6111yescharacteristic
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C42—21no—
536C2×C42—611no—
537C2×C42—611no—
538C2×C42—1221no—
539C2×C42—1221no—
540C2×C42C22×D6111yescharacteristic
541#107—614no—
542#107—614no—
543#106—614no—
544C4⋊C8—614no—
545C4⋊C8—614no—
546C4⋊C8C22×D6114yes—
547#103—614no—
548#102—614no—
549#102—614no—
550#102—614no—
551#102—614no—
552#102—614no—
553#102—614no—
554#102—614no—
555#102C22×D6114yes—
556#102C22×D6114yes—
557#97—614no—
558#97—614no—
559C4×C8—614no—
560C24—21no—
561C24—21no—
562C24—1221no—
563#41—24432no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—614no—
567C2×Q8—1224no—
568C2×Q8—1224no—
569C2×Q8—2444no—
570C2×Q8#1175822414yescomplemented
571C2×Q8C23×D6112yes—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—24no—
575C2×D4—24no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—44no—
581C2×D4—82no—
582C2×D4—612no—
583C2×D4—1224no—
584C2×D4—1224no—
585C2×D4—1224no—
586C2×D4—1224no—
587C2×D4—1221no—
588C2×D4—1222no—
589C2×D4—1222no—
590C2×D4—4882no—
591C2×D4—4882no—
592C2×D4—2444no—
593C2×D4—2444no—
594C2×D4C23×D6112yes—
595C2×D4C23×D6112yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—1224no—
603C22×C4—1224no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1224no—
608C22×C4—2444no—
609C22×C4—2444no—
610C22×C4—2444no—
611C22×C4D4×D6111yescharacteristic
612C22×C4D4×D6111yescharacteristic
613C22×C4C23×D6111yescharacteristic
614SD16—28no—
615SD16—28no—
616SD16—1228no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—612no—
620C2×C8—612no—
621C2×C8—1222no—
622C2×C8—1222no—
623C2×C8C23×D6112yes—
624C2×C8C23×D6112yes—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—614no—
628C4⋊C4—614no—
629C4⋊C4—614no—
630C4⋊C4—612no—
631C4⋊C4—612no—
632C4⋊C4—612no—
633C4⋊C4—1224no—
634C4⋊C4—1224no—
635C4⋊C4—1224no—
636C4⋊C4—1224no—
637C4⋊C4—1224no—
638C4⋊C4—1221no—
639C4⋊C4—1221no—
640C4⋊C4—1221no—
641C4⋊C4—1224no—
642C4⋊C4—1224no—
643C4⋊C4C23×D6112yes—
644C22⋊C4—1224no—
645C22⋊C4—1224no—
646C22⋊C4—1224no—
647C42—24no—
648C42—612no—
649C42—612no—
650C42—612no—
651C42—612no—
652C42—1224no—
653C42—1224no—
654C42D4×D6112yes—
655C42C23×D6112yes—
656C23—22no—
657C23—22no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—1222no—
665C23—2442no—
666C23—2442no—
667C23—2442no—
668C23C2×D4×D6111yescharacteristic
669Q8—22no—
670Q8—24no—
671Q8—1228no—
672Q8—2448no—
673Q8C2×#1175822414yescomplemented
674D4—22no—
675D4—22no—
676D4—22no—
677D4—22no—
678D4—48no—
679D4—42no—
680D4—42no—
681D4—84no—
682D4—1222no—
683D4—1222no—
684D4—4884no—
685D4—4884no—
686D4—2448no—
687D4—2448no—
688D4—2442no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—42no—
695C2×C4—614no—
696C2×C4—612no—
697C2×C4—612no—
698C2×C4—612no—
699C2×C4—612no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—2448no—
707C2×C4—2448no—
708C2×C4—2448no—
709C2×C4—2442no—
710C2×C4—2442no—
711C2×C4—2442no—
712C2×C4C2×D4×D6112yes—
713C2×C4C2×D4×D6112yes—
714C2×C4C2×D4×D6111yescharacteristic
715C2×C4C2×#1175822412yes—
716C2×C4#1451982412yes—
717C2×C4C24×D6111yescharacteristic
718C8—22no—
719C8—22no—
720C8—1222no—
721C8—1222no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—84no—
729C22—84no—
730C22—4884no—
731C22—2442no—
732C22—2442no—
733C22—2442no—
734C22#1684041812yes—
735C22AGL(1,ℤ/8)×D6112yes—
736C22#1684056812yes—
737C22C22×D4×D6111yescharacteristic
738C4—22no—
739C4—24no—
740C4—22no—
741C4—42no—
742C4—614no—
743C4—1222no—
744C4—1222no—
745C4—1222no—
746C4—2442no—
747C4—2442no—
748C4—2442no—
749C4#1684041812yes—
750C4C22×#1175822411yescharacteristic
751C4C2×#1451982411yescharacteristic
752C2—82no—
753C2—82no—
754C2—4882no—
755C2#2145854314yesdirect product factor
756C2C2×#1684041811yescharacteristic
757C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
758C2C2×#1684056811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#460C2
socleC23×C61C22×D4
prime radicalC2×#16840432C2
hypercenterC2×#460D61
hypocenterC61C2×#3368
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C2×#16840488C2semidirect
3. #21458543C2direct (N × H)
4. C2×#16840126C2semidirect
5. C2×#16840125C2semidirect
6. C2×#16840107C2semidirect
7. C2×#16840064C2semidirect
8. C2×#16840063C2semidirect
9. C2×#16840040C2semidirect
10. C2×#16839960C2semidirect
11. C2×#16839960C2semidirect
12. C2×#16839891C2semidirect
13. C2×#16839863C2semidirect
14. C2×#16839860C2semidirect
15. C2×SD16×Dic61C2semidirect
16. C2×C61×#460C2semidirect
20. #16840488C22semidirect
41. #16840126C22semidirect
42. #16840125C22semidirect
43. #16840107C22semidirect
44. #16840064C22semidirect
45. #16840063C22semidirect
46. #16840040C22semidirect
47. #16839960C22semidirect
48. #16839960C22semidirect
49. #16839891C22semidirect
50. #16839863C22semidirect
51. #16839860C22semidirect
52. SD16×Dic61C22semidirect
73. C61×#460C22semidirect
185. C2×Q8×C61#41semidirect
291. Q8×C61C2×#41semidirect
384. C2×#460D61semidirect
391. C2×C61#3368semidirect
432. #460C2×D61semidirect
456. C61C2×#3368semidirect
570. C2×Q8#11758224semidirect
673. Q8C2×#11758224semidirect
755. C2#21458543direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404882
C2×#168404322
#214585432
C2×#168401262
C2×#168401252
C2×#168401072
C2×#168400642
C2×#168400632
C2×#168400402
C2×#168399602
C2×#168398912
C2×#168398632
C2×#168398602
C2×SD16×Dic612
C2×C61×#4602
C2×#336861