Finite Group Databasebeta

← C2×#21458545 #30559709

Subgroups — C2×#21458545 #30559709

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×#16840489C211yesmaximal, characteristic, complemented
2C2×#16840432C211yesmaximal, characteristic
3#21458545C2116yesmaximal, direct product factor
4C2×#16840125C211yesmaximal, characteristic, complemented
5C2×#16840107C211yesmaximal, characteristic, complemented
6C2×#16840060C211yesmaximal, characteristic, complemented
7C2×#16840059C211yesmaximal, characteristic, complemented
8C2×#16840040C211yesmaximal, characteristic, complemented
9C2×#16839961C211yesmaximal, characteristic, complemented
10C2×#16839961C211yesmaximal, characteristic, complemented
11C2×#16839959C211yesmaximal, characteristic, complemented
12C2×#16839890C211yesmaximal, characteristic, complemented
13C2×#16839864C211yesmaximal, characteristic, complemented
14C2×#16839859C211yesmaximal, characteristic, complemented
15C2×#16839853C211yesmaximal, characteristic, complemented
16C2×C61×#490C211yesmaximal, characteristic, complemented
17C22×#11758224—21no—
18C22×#11758190C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21#16840489—24no—
22#16840489C2218yescomplemented
23#16840432—24no—
24#16840432C2218yes—
25C2×#14519776—21no—
26C2×#14519776C2211yescharacteristic
27C2×#14519773C2211yescharacteristic
28C2×#14519773C2211yescharacteristic
29C2×#14519768C2211yescharacteristic
30C2×#14519767—21no—
31C2×#14519767—21no—
32C2×#14519749—21no—
33C2×#14519749—21no—
34C2×#14519748—21no—
35C2×C4×Dic122C2211yescharacteristic
36C2×C4×Dic122C2211yescharacteristic
37C2×#14519742—21no—
38C2×#14519742C2211yescharacteristic
39C2×#14519742C2211yescharacteristic
40C2×C4×D244C2211yescharacteristic
41C2×D4×Dic61C2211yescharacteristic
42C2×D4×Dic61C2211yescharacteristic
43#16840125C2218yescomplemented
44#16840107C2218yescomplemented
45#16840060C2218yescomplemented
46#16840059C2218yescomplemented
47#16840040C2218yescomplemented
48#16839961C2218yescomplemented
49#16839961C2218yescomplemented
50#16839959C2218yescomplemented
51#16839890C2218yescomplemented
52#16839864C2218yescomplemented
53#16839859C2218yescomplemented
54#16839853C2218yescomplemented
55C2×#14519711C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×C4⋊#92418C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519706C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519697C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C2×#127×C61C2211yescharacteristic
70C2×#125×C61C2211yescharacteristic
71C61×#490C2218yescomplemented
72C2×#102×C61C2211yescharacteristic
73C2×#102×C61C2211yescharacteristic
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C2×#11758224—28no—
78C2×#11758224—48no—
79C22×Dic122—21no—
80C22×Dic122D411yescharacteristic
81C22×Dic122C2311yescharacteristic
82C22×D244C2311yescharacteristic
83C22×C22⋊D61—21no—
84C22×C22⋊D61—21no—
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C23×Dic61—21no—
88C23×Dic61—21no—
89C22×C4×D61—21no—
90C2×#11758190—24no—
91C2×#11758190C2314yes—
92C2×#11758200—24no—
93C2×#11758200—24no—
94C2×#11758200C2314yes—
95C2×#11758200C2314yes—
96C22×#92418C2311yescharacteristic
97C22×#92418C2311yescharacteristic
98#14519776—28no—
99#14519776—22no—
100#14519776C2314yes—
101#14519773—22no—
102#14519773—22no—
103#14519773C2314yes—
104#14519773C2314yes—
105#14519768—22no—
106#14519768C2314yes—
107#14519767—28no—
108#14519767—28no—
109#14519749—28no—
110#14519749—28no—
111#14519748—28no—
112C4×Dic122—22no—
113C4×Dic122D414yes—
114C4×Dic122C2314yes—
115C4×Dic122C2314yes—
116#14519742—28no—
117#14519742—22no—
118#14519742—22no—
119#14519742C2314yes—
120#14519742C2314yes—
121C4×D244—22no—
122C4×D244C2314yes—
123D4×Dic61—22no—
124D4×Dic61—22no—
125D4×Dic61C2314yes—
126D4×Dic61C2314yes—
127C2×C4⋊Dic61—21no—
128C2×C4⋊Dic61D411yescharacteristic
129C2×C4⋊Dic61C2311yescharacteristic
130C2×C4⋊Dic61C2311yescharacteristic
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196D411yescharacteristic
137C2×#11758196D411yescharacteristic
138C2×C22⋊Dic61—21no—
139C2×C22⋊Dic61—21no—
140C2×#11758198—21no—
141C2×C4×Dic61—21no—
142C2×C4×Dic61—21no—
143C2×C4×Dic61—21no—
144C2×C4×Dic61C2311yescharacteristic
145C2×C4×Dic61C2311yescharacteristic
146#14519711C2314yes—
147#14519710C2314yes—
148#14519708C2314yes—
149C4⋊#92418C2314yes—
150#14519706C2314yes—
151#14519706C2314yes—
152#14519702C2314yes—
153#14519699C2314yes—
154#14519698C2314yes—
155#14519698C2314yes—
156#14519697C2314yes—
157#14519697C2314yes—
158#14519687C2314yes—
159C8×Dic61C2314yes—
160C22×D4×C61—21no—
161C22×D4×C61—21no—
162C22×D4×C61C2311yescharacteristic
163C22×D4×C61C2311yescharacteristic
164C22×C8×C61C2311yescharacteristic
165C22×C8×C61C2311yescharacteristic
166#127×C61—22no—
167#127×C61C2314yes—
168#125×C61—22no—
169#125×C61C2314yes—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C42×C61C2311yescharacteristic
175#102×C61C2314yes—
176#102×C61C2314yes—
177#102×C61C2314yes—
178#102×C61C2314yes—
179#97×C61C2314yes—
180C24×C61—21no—
181C24×C61—21no—
182C23×D61—21no—
183C2×D4×C61—24no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—24no—
187C2×D4×C61—22no—
188C2×D4×C61—22no—
189C2×D4×C61—22no—
190C2×D4×C61—22no—
191C2×D4×C61—44no—
192C2×D4×C61—82no—
193C2×D4×C61C2412yes—
194C2×D4×C61C2412yes—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2411yescharacteristic
200C2×C22⋊D61—24no—
201C2×C22⋊D61—24no—
202C2×C22⋊D61—24no—
203C2×C22⋊D61—24no—
204C2×C22⋊D61—44no—
205C2×C22⋊D61—44no—
206C2×C22⋊D61—82no—
207C2×C22⋊D61—82no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—24no—
212C22×Dic61—24no—
213C22×Dic61—44no—
214C22×Dic61—44no—
215C22×Dic61C2×D411yescharacteristic
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219#11758224—432no—
220C2×D244—22no—
221C2×D244—22no—
222C2×D244—21no—
223C2×D244C2412yes—
224C2×C4×D61—24no—
225C2×C4×D61—44no—
226C2×Dic122—21no—
227C2×Dic122—22no—
228C2×Dic122—24no—
229C2×Dic122—24no—
230C2×Dic122—44no—
231C2×Dic122C2×D414yes—
232C2×Dic122#4114yescomplemented
233C2×Dic122C2412yes—
234C2×C8×C61—22no—
235C2×C8×C61—22no—
236C2×C8×C61C2412yes—
237C2×C8×C61C2412yes—
238C4⋊C4×C61—24no—
239C4⋊C4×C61—24no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61C2412yes—
243C4⋊C4×C61C2412yes—
244C42×C61C2×D412yes—
245C42×C61C2412yes—
246C22⋊Dic61—24no—
247C22⋊Dic61—24no—
248#11758200—28no—
249#11758200—28no—
250#11758198—24no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61—24no—
254C4⋊Dic61C2×D414yes—
255C4⋊Dic61C2412yes—
256C4⋊Dic61C2412yes—
257#11758196—24no—
258#11758196—24no—
259#11758196—24no—
260#11758196—24no—
261#11758196—24no—
262#11758196C2×D414yes—
263#11758196C2×D414yes—
264C4×Dic61—24no—
265C4×Dic61—24no—
266C4×Dic61—24no—
267C4×Dic61C2×D412yes—
268C4×Dic61C2×D412yes—
269C4×Dic61C2412yes—
270C4×Dic61C2412yes—
271C2×#92418—22no—
272C2×#92418—22no—
273C2×#92418C2412yes—
274C2×#92418C2412yes—
275#11758190—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—42no—
287C22×D61—42no—
288C22×D61—42no—
289D4×C61—22no—
290D4×C61—22no—
291D4×C61—22no—
292D4×C61—22no—
293D4×C61—48no—
294D4×C61—42no—
295D4×C61—42no—
296D4×C61—84no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61C22×D412yes—
304C2×C4×C61C22×D412yes—
305C2×C4×C61C22×D411yescharacteristic
306C2×C4×C61C2×#4112yes—
307C2×C4×C612−1+412yes—
308C2×C4×C61C2511yescharacteristic
309C22⋊D61—48no—
310C22⋊D61—48no—
311C22⋊D61—84no—
312C22⋊D61—84no—
313C2×Dic61—24no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—48no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—48no—
324C2×Dic61AGL(1,ℤ/8)14yes—
325C2×Dic61C22×D412yes—
326C2×Dic61C22×D412yes—
327C2×Dic61C22×D412yes—
328C2×Dic61C22×D412yes—
329D244—22no—
330D244—22no—
331D244—42no—
332C4×D61—48no—
333Dic122—24no—
334Dic122—22no—
335Dic122—28no—
336Dic122—48no—
337Dic122C2×#4114yescomplemented
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—22no—
360C4×C61—22no—
361C4×C61—42no—
362C4×C61—42no—
363C4×C61#54812yes—
364C4×C61C22×#4111yescharacteristic
365C4×C61C2×2−1+411yescharacteristic
366Dic61—24no—
367Dic61—22no—
368Dic61—22no—
369Dic61—22no—
370Dic61—42no—
371Dic61—42no—
372Dic61C2×AGL(1,ℤ/8)14yes—
373C2×#557—611no—
374C2×#550—611no—
375#3368—6116no—
376C2×#490—611no—
377C2×#490D6111yescharacteristic, complemented
378C2×#486—611no—
379C2×#478—611no—
380C2×#478—611no—
381C2×#474—611no—
382C2×#460—611no—
383C2×#460—611no—
384C2×#460—611no—
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×SD16—611no—
399C22×SD16—611no—
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—1221no—
411C2×#125—1221no—
412C2×#125C2×D6111yescharacteristic
413C2×#121—1221no—
414C2×#121—1221no—
415C2×#121—1221no—
416C2×C4×Q8—611no—
417C2×C4×Q8—611no—
418C2×C4×Q8—611no—
419C2×C4×Q8—611no—
420C2×C4×Q8—1221no—
421C2×C4×D4—611no—
422C2×C4×D4—611no—
423C2×C4×D4—611no—
424#490—618no—
425#490C2×D6118yescomplemented
426#486—618no—
427#478—618no—
428#478—618no—
429#474—618no—
430#460—618no—
431#460—618no—
432#460—618no—
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⋊C8—611no—
443C2×#103—611no—
444C2×#102—611no—
445C2×#102—611no—
446C2×#102—611no—
447C2×#102—611no—
448C2×#102—611no—
449C2×#102C2×D6111yescharacteristic
450C2×#102C2×D6111yescharacteristic
451C2×#102C2×D6111yescharacteristic
452C2×#102C2×D6111yescharacteristic
453C2×#97—611no—
454C2×#97C2×D6111yescharacteristic
455C2×C4×C8—611no—
456C61C2×#336811yescharacteristic, complemented, Sylow
457C2×#41—1228no—
458C2×#41—2448no—
459C22×Q8—611no—
460C22×Q8—611no—
461C22×Q8—1221no—
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—614no—
475C2×SD16—614no—
476C2×SD16—614no—
477C2×SD16—1224no—
478C2×SD16—1224no—
479C2×SD16—1224no—
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—22no—
494#125—614no—
495#125—1222no—
496#125—1228no—
497#125—1228no—
498#125C22×D6114yes—
499#121—1228no—
500#121—1228no—
501#121—1228no—
502C4×Q8—614no—
503C4×Q8—614no—
504C4×Q8—614no—
505C4×Q8—614no—
506C4×Q8—614no—
507C4×Q8—1222no—
508C4×Q8—1222no—
509C4×Q8—1228no—
510C4×Q8—1222no—
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—21no—
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⋊C4C22×D6111yescharacteristic
531C2×C4⋊C4C22×D6111yescharacteristic
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C42—611no—
536C2×C42—611no—
537C2×C42—1221no—
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⋊C8—614no—
547#103—614no—
548#102—614no—
549#102—614no—
550#102—614no—
551#102—614no—
552#102—614no—
553#102C22×D6114yes—
554#102C22×D6114yes—
555#102C22×D6114yes—
556#102C22×D6114yes—
557#97—614no—
558#97C22×D6114yes—
559C4×C8—614no—
560C24—21no—
561C24—21no—
562C24—1221no—
563#41—24432no—
564C2×Q8—614no—
565C2×Q8—614no—
566C2×Q8—612no—
567C2×Q8—1224no—
568C2×Q8—1224no—
569C2×Q8—1221no—
570C2×Q8—1222no—
571C2×Q8—2444no—
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—1228no—
615SD16—1228no—
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—24no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—614no—
630C4⋊C4—614no—
631C4⋊C4—614no—
632C4⋊C4—612no—
633C4⋊C4—612no—
634C4⋊C4—1224no—
635C4⋊C4—1224no—
636C4⋊C4—1224no—
637C4⋊C4—1224no—
638C4⋊C4—1224no—
639C4⋊C4—1221no—
640C4⋊C4—1221no—
641C4⋊C4—1224no—
642C4⋊C4C23×D6112yes—
643C4⋊C4C23×D6112yes—
644C22⋊C4—1224no—
645C22⋊C4—1224no—
646C22⋊C4—1224no—
647C42—612no—
648C42—612no—
649C42—612no—
650C42—612no—
651C42—1224no—
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—614no—
670Q8—1228no—
671Q8—1222no—
672Q8—1224no—
673Q8—2448no—
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—22no—
693C2×C4—42no—
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—1224no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—2448no—
708C2×C4—2448no—
709C2×C4—2448no—
710C2×C4—2442no—
711C2×C4—2442no—
712C2×C4C2×D4×D6112yes—
713C2×C4C2×D4×D6112yes—
714C2×C4C2×D4×D6111yescharacteristic
715C2×C4#41×D6112yes—
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#1684042012yes—
735C22AGL(1,ℤ/8)×D6112yes—
736C22#1684057212yes—
737C22C22×D4×D6111yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—614no—
743C4—1222no—
744C4—1224no—
745C4—1222no—
746C4—1222no—
747C4—2442no—
748C4—2442no—
749C4#1684042012yes—
750C4C2×#41×D6111yescharacteristic
751C4C2×#1451982411yescharacteristic
752C2—82no—
753C2—82no—
754C2—4882no—
755C2#2145854514yesdirect product factor
756C2C2×#1684042011yescharacteristic
757C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
758C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#490C2
socleC23×C61C22×D4
prime radicalC2×#16840432C2
hypercenterC2×#490D61
hypocenterC61C2×#3368
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
1. C2×#16840489C2semidirect
3. #21458545C2direct (N × H)
4. C2×#16840125C2semidirect
5. C2×#16840107C2semidirect
6. C2×#16840060C2semidirect
7. C2×#16840059C2semidirect
8. C2×#16840040C2semidirect
9. C2×#16839961C2semidirect
10. C2×#16839961C2semidirect
11. C2×#16839959C2semidirect
12. C2×#16839890C2semidirect
13. C2×#16839864C2semidirect
14. C2×#16839859C2semidirect
15. C2×#16839853C2semidirect
16. C2×C61×#490C2semidirect
22. #16840489C22semidirect
43. #16840125C22semidirect
44. #16840107C22semidirect
45. #16840060C22semidirect
46. #16840059C22semidirect
47. #16840040C22semidirect
48. #16839961C22semidirect
49. #16839961C22semidirect
50. #16839959C22semidirect
51. #16839890C22semidirect
52. #16839864C22semidirect
53. #16839859C22semidirect
54. #16839853C22semidirect
71. C61×#490C22semidirect
232. C2×Dic122#41semidirect
337. Dic122C2×#41semidirect
377. C2×#490D61semidirect
391. C2×C61#3368semidirect
425. #490C2×D61semidirect
456. C61C2×#3368semidirect
755. C2#21458545direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404892
C2×#168404322
#214585452
C2×#168401252
C2×#168401072
C2×#168400602
C2×#168400592
C2×#168400402
C2×#168399612
C2×#168399592
C2×#168398902
C2×#168398642
C2×#168398592
C2×#168398532
C2×C61×#4902
C2×#336861