Finite Group Databasebeta

← C2×#21458474 #30559592

Subgroups — C2×#21458474 #30559592

Order 15616.

1970 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840494C211yesmaximal, characteristic, complemented
2C2×#16840471C211yesmaximal, characteristic, complemented
3#21458474C2116yesmaximal, direct product factor
4C2×#16840118C211yesmaximal, characteristic, complemented
5C2×#16840116C211yesmaximal, characteristic, complemented
6C2×#16840107C211yesmaximal, characteristic, complemented
7C2×#16840055C211yesmaximal, characteristic, complemented
8C2×#16840064C211yesmaximal, characteristic, complemented
9C2×#16840063C211yesmaximal, characteristic, complemented
10C2×#16839979C211yesmaximal, characteristic, complemented
11C2×#16839955C211yesmaximal, characteristic
12C2×#16839886C211yesmaximal, characteristic, complemented
13C2×SD16×Dic61C211yesmaximal, characteristic, complemented
14C2×D8×Dic61C211yesmaximal, characteristic, complemented
15C2×C4×#11758199C211yesmaximal, characteristic, complemented
16C2×C61×#463C211yesmaximal, characteristic, complemented
17C22×#11758199C2211yescharacteristic
18#16840494—24no—
19#16840494C2218yescomplemented
20#16840471—24no—
21#16840471C2218yescomplemented
22C2×#14519776C2211yescharacteristic
23C2×#14519773C2211yescharacteristic
24C2×#14519769C2211yescharacteristic
25C2×#14519768C2211yescharacteristic
26C2×#14519766C2211yescharacteristic
27C2×#14519763—21no—
28C2×#14519761—21no—
29C2×#14519759—21no—
30C2×#14519756—21no—
31C2×#14519754—21no—
32C2×#14519754—21no—
33C2×Q8×Dic61C2211yescharacteristic
34C2×C4×Dic122C2211yescharacteristic
35C2×C4×D244C2211yescharacteristic
36C2×D4×Dic61C2211yescharacteristic
37C2×D4×Dic61C2211yescharacteristic
38C2×D4×Dic61C2211yescharacteristic
39C2×#14519737—21no—
40C22×#11758196—21no—
41#16840118C2218yescomplemented
42#16840116C2218yescomplemented
43#16840107C2218yescomplemented
44#16840064C2218yescomplemented
45#16840063C2218yescomplemented
46#16840055C2218yescomplemented
47#16839979C2218yescomplemented
48#16839955C2218yes—
49#16839886C2218yescomplemented
50SD16×Dic61C2218yescomplemented
51D8×Dic61C2218yescomplemented
52C4×#11758199C2218yescomplemented
53C2×#14519711C2211yescharacteristic
54C2×#14519710C2211yescharacteristic
55C2×#14519709C2211yescharacteristic
56C2×#14519706C2211yescharacteristic
57C2×#14519706C2211yescharacteristic
58C2×#14519701C2211yescharacteristic
59C2×#14519701C2211yescharacteristic
60C2×#14519699C2211yescharacteristic
61C2×#14519699C2211yescharacteristic
62C2×#14519698C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×C4×#92418C2211yescharacteristic
67C2×C8×Dic61C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C22×D8×C61C2211yescharacteristic
71C2×#124×C61C2211yescharacteristic
72C2×C4×D4×C61C2211yescharacteristic
73C61×#463C2218yescomplemented
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122D411yescharacteristic
79C22×D244C2311yescharacteristic
80C22×C22⋊D61—21no—
81C22×C22⋊D61—21no—
82C23×Dic61—21no—
83C23×Dic61—21no—
84C23×Dic61—21no—
85C22×C4×D61—21no—
86C2×#11758199—24no—
87C2×#11758199C2314yes—
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90#14519776—22no—
91#14519776C2314yes—
92#14519773—22no—
93#14519773C2314yes—
94#14519769—22no—
95#14519769C2314yes—
96#14519768—22no—
97#14519768C2314yes—
98#14519766—22no—
99#14519766C2314yes—
100#14519763—28no—
101#14519761—28no—
102#14519759—28no—
103#14519756—28no—
104#14519754—28no—
105#14519754—28no—
106Q8×Dic61—22no—
107Q8×Dic61C2314yes—
108C4×Dic122D414yes—
109C4×Dic122C2314yes—
110C4×D244—22no—
111C4×D244C2314yes—
112D4×Dic61—22no—
113D4×Dic61—22no—
114D4×Dic61—22no—
115D4×Dic61C2314yes—
116D4×Dic61C2314yes—
117D4×Dic61C2314yes—
118#14519737—28no—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61—21no—
121C2×C4⋊Dic61D411yescharacteristic
122C2×C4⋊Dic61C2311yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—28no—
130C2×#11758196D411yescharacteristic
131C2×#11758196D411yescharacteristic
132C2×C22⋊Dic61—21no—
133C2×C22⋊Dic61—21no—
134C2×C22⋊Dic61—21no—
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×C4×Dic61—21no—
139C2×C4×Dic61C2311yescharacteristic
140C2×C4×Dic61C2311yescharacteristic
141#14519711C2314yes—
142#14519710C2314yes—
143#14519709C2314yes—
144#14519706C2314yes—
145#14519706C2314yes—
146#14519701C2314yes—
147#14519701C2314yes—
148#14519699C2314yes—
149#14519699C2314yes—
150#14519698C2314yes—
151#14519698C2314yes—
152#14519698C2314yes—
153#14519697C2314yes—
154C4×#92418C2314yes—
155C8×Dic61C2314yes—
156C8×Dic61C2314yes—
157C22×Q8×C61C2311yescharacteristic
158C22×D4×C61C2311yescharacteristic
159C22×D4×C61C2311yescharacteristic
160C23×C4×C61—21no—
161C2×SD16×C61—24no—
162C2×SD16×C61C2314yes—
163C2×D8×C61—24no—
164C2×D8×C61C2314yes—
165C22×C8×C61C2311yescharacteristic
166C22×C8×C61C2311yescharacteristic
167#124×C61—22no—
168#124×C61C2314yes—
169C4×D4×C61—22no—
170C4×D4×C61C2314yes—
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C22⋊C4×C61—21no—
173C2×C22⋊C4×C61—21no—
174C2×C22⋊C4×C61—21no—
175C2×C42×C61C2311yescharacteristic
176C4⋊C8×C61C2314yes—
177#103×C61C2314yes—
178#102×C61C2314yes—
179C24×C61—21no—
180C24×C61—21no—
181C23×D61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61—22no—
184C2×Q8×C61—22no—
185C2×Q8×C61C2412yes—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—22no—
189C2×D4×C61—22no—
190C2×D4×C61—22no—
191C2×D4×C61#4114yes—
192C2×D4×C61C2412yes—
193C2×D4×C61C2412yes—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—24no—
197C22×C4×C61—82no—
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2411yescharacteristic
201C2×C22⋊D61—24no—
202C2×C22⋊D61—24no—
203C2×C22⋊D61—44no—
204C2×C22⋊D61—82no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—24no—
209C22×Dic61—24no—
210C22×Dic61—24no—
211C22×Dic61—44no—
212C22×Dic61—82no—
213C22×Dic61—82no—
214C22×Dic61C2×D411yescharacteristic
215C22×Dic61C2×D411yescharacteristic
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218C2×D244—22no—
219C2×D244—22no—
220C2×D244—21no—
221C2×D244C2412yes—
222C2×C4×D61—24no—
223C2×C4×D61—82no—
224C2×Dic122—24no—
225C2×Dic122—24no—
226C2×Dic122—82no—
227C2×Dic122C2×D414yes—
228SD16×C61—28no—
229D8×C61—28no—
230C2×C8×C61—22no—
231C2×C8×C61—22no—
232C2×C8×C61C2412yes—
233C2×C8×C61C2412yes—
234C4⋊C4×C61—21no—
235C4⋊C4×C61C2412yes—
236C22⋊C4×C61—24no—
237C22⋊C4×C61—24no—
238C22⋊C4×C61—24no—
239C42×C61C2×D412yes—
240C42×C61C2412yes—
241C22⋊Dic61—24no—
242C22⋊Dic61—24no—
243C22⋊Dic61—24no—
244#11758199—28no—
245#11758198—24no—
246#11758198—24no—
247#11758198—24no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—24no—
252C4⋊Dic61—24no—
253C4⋊Dic61C2×D414yes—
254C4⋊Dic61C2412yes—
255C4⋊Dic61C2412yes—
256C4⋊Dic61C2412yes—
257#11758196—24no—
258#11758196—24no—
259#11758196—24no—
260#11758196—24no—
261#11758196C2×D414yes—
262#11758196C2×D414yes—
263C4×Dic61—24no—
264C4×Dic61C2×D412yes—
265C4×Dic61C2×D412yes—
266C4×Dic61C2412yes—
267C4×Dic61C2412yes—
268C2×#92418—22no—
269C2×#92418—22no—
270C2×#92418C2412yes—
271C2×#92418C2412yes—
272C23×C61—24no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—42no—
276C23×C61—42no—
277C23×C61—42no—
278C23×C61—42no—
279C23×C61—42no—
280C23×C61C22×D411yescharacteristic
281C22×D61—22no—
282C22×D61—42no—
283C22×D61—42no—
284C22×D61—42no—
285Q8×C61—22no—
286Q8×C61—22no—
287Q8×C61—42no—
288D4×C61—24no—
289D4×C61—22no—
290D4×C61—22no—
291D4×C61—22no—
292D4×C61—42no—
293D4×C61C2×#4114yes—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
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—22no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—48no—
319C2×Dic61—84no—
320C2×Dic61—84no—
321C2×Dic61#13514yes—
322C2×Dic61C22×D412yes—
323C2×Dic61C22×D412yes—
324C2×Dic61C22×D412yes—
325C2×Dic61C22×D412yes—
326D244—22no—
327D244—22no—
328D244—42no—
329C4×D61—84no—
330Dic122—28no—
331Dic122—84no—
332C8×C61—22no—
333C8×C61—22no—
334#92418—22no—
335#92418—22no—
336C2×#3361—611nomaximal, Sylow
337C22×C61—24no—
338C22×C61—48no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—42no—
342C22×C61—42no—
343C22×C61—42no—
344C22×C61—84no—
345C22×C61#54812yes—
346C22×C61C2×#13512yes—
347C22×C61#57612yes—
348C22×C61C23×D411yescharacteristic
349C2×D61—42no—
350C2×D61—42no—
351C2×D61—42no—
352C2×D61—84no—
353C4×C61—22no—
354C4×C61—22no—
355C4×C61—42no—
356C4×C61—42no—
357C4×C61#54812yes—
358C4×C61C22×#4111yescharacteristic
359C4×C61C2×2−1+411yescharacteristic
360Dic61—22no—
361Dic61—22no—
362Dic61—22no—
363Dic61—42no—
364Dic61—42no—
365Dic61—42no—
366Dic61C2×#13514yes—
367C2×#559—611no—
368C2×#554—611no—
369#3361—6116no—
370C2×#488—611no—
371C2×#488—611no—
372C2×#486—611no—
373C2×#477—611no—
374C2×#478—611no—
375C2×#478—611no—
376C2×#463—611no—
377C2×#463D6111yescharacteristic, complemented
378C2×#459—611no—
379C2×C8×Q8—611no—
380C2×C4×SD16—611no—
381C2×C4×D8—611no—
382C2×C4×D8—611no—
383C2×C61—44no—
384C2×C61—82no—
385C2×C61#336114yescomplemented
386C2×C61C2×#54811yescharacteristic
387C2×C61C22×#13511yescharacteristic
388C2×C61C2×#57611yescharacteristic
389D61—82no—
390C22×SD16C2×D6111yescharacteristic
391C22×D8—611no—
392C22×D8C2×D6111yescharacteristic
393#559—618no—
394#559—1224no—
395#554—618no—
396#554—1224no—
397C2×C4⋊Q8—611no—
398C2×#127—611no—
399C2×#125—611no—
400C2×#125—611no—
401C2×#124—611no—
402C2×#124—1221no—
403C2×#124C2×D6111yescharacteristic
404C2×#123—1221no—
405C2×#123—1221no—
406C2×C22⋊Q8—1221no—
407C2×C22⋊Q8—1221no—
408C2×C22⋊Q8—1221no—
409C2×C4×Q8—611no—
410C2×C4×Q8—611no—
411C2×C4×D4—611no—
412C2×C4×D4—611no—
413C2×C4×D4—611no—
414C2×C4×D4—611no—
415C2×C4×D4—1221no—
416C2×C4×D4C2×D6111yescharacteristic
417C22×C4⋊C4—1221no—
418#488—618no—
419#488—618no—
420#486—618no—
421#478—618no—
422#478—618no—
423#477—618no—
424#463—618no—
425#463C2×D6118yescomplemented
426#459—618no—
427C8×Q8—618no—
428C4×SD16—618no—
429C4×D8—618no—
430C4×D8—618no—
431C2×#107—611no—
432C2×#107—611no—
433C2×#106—611no—
434C2×C4⋊C8—611no—
435C2×C4⋊C8—611no—
436C2×C4⋊C8C2×D6111yescharacteristic
437C2×#103—611no—
438C2×#103—611no—
439C2×#103C2×D6111yescharacteristic
440C2×#102—611no—
441C2×#102—611no—
442C2×#102—611no—
443C2×#102—611no—
444C2×#102—611no—
445C2×#102—611no—
446C2×#102C2×D6111yescharacteristic
447C2×C4×C8—611no—
448C2×C4×C8—611no—
449C2×C4×C8—611no—
450C61C2×#336111yescharacteristic, complemented, Sylow
451C22×Q8—611no—
452C22×Q8—1221no—
453C22×Q8C22×D6111yescharacteristic
454C22×D4—611no—
455C22×D4—1221no—
456C22×D4—1221no—
457C22×D4C22×D6111yescharacteristic
458C22×D4C22×D6111yescharacteristic
459C23×C4—21no—
460C23×C4—1221no—
461C23×C4—1221no—
462C23×C4—1221no—
463C23×C4—1221no—
464C2×SD16—24no—
465C2×SD16C22×D6114yes—
466C2×D8—24no—
467C2×D8—614no—
468C2×D8—1224no—
469C2×D8C22×D6114yes—
470C22×C8—611no—
471C22×C8—611no—
472C22×C8C22×D6111yescharacteristic
473C22×C8C22×D6111yescharacteristic
474C4⋊Q8—614no—
475C4⋊Q8—1222no—
476#127—614no—
477#127—1222no—
478#125—614no—
479#125—614no—
480#125—1222no—
481#125—1222no—
482#124—22no—
483#124—614no—
484#124—1222no—
485#124—1228no—
486#124C22×D6114yes—
487#123—1228no—
488#123—1228no—
489C22⋊Q8—1228no—
490C22⋊Q8—1228no—
491C22⋊Q8—1228no—
492C4×Q8—614no—
493C4×Q8—614no—
494C4×Q8—614no—
495C4×Q8—1222no—
496C4×D4—22no—
497C4×D4—614no—
498C4×D4—614no—
499C4×D4—614no—
500C4×D4—614no—
501C4×D4—1222no—
502C4×D4—1222no—
503C4×D4—1222no—
504C4×D4—1228no—
505C4×D4—1222no—
506C4×D4C22×D6114yes—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—1228no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4C22×D6111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C42—611no—
531C2×C42—611no—
532C2×C42—1221no—
533C2×C42C22×D6111yescharacteristic
534#107—614no—
535#107—614no—
536#106—614no—
537C4⋊C8—614no—
538C4⋊C8—614no—
539C4⋊C8C22×D6114yes—
540#103—614no—
541#103—614no—
542#103C22×D6114yes—
543#102—614no—
544#102—614no—
545#102—614no—
546#102—614no—
547#102—614no—
548#102—614no—
549#102C22×D6114yes—
550C4×C8—614no—
551C4×C8—614no—
552C4×C8—614no—
553C24—21no—
554C24—21no—
555C24—1221no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—614no—
560C2×Q8—1224no—
561C2×Q8—1224no—
562C2×Q8—4882no—
563C2×Q8C23×D6112yes—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—612no—
570C2×D4—1224no—
571C2×D4—1224no—
572C2×D4—1221no—
573C2×D4—1222no—
574C2×D4—1222no—
575C2×D4—4882no—
576C2×D4—2444no—
577C2×D4#1175822414yes—
578C2×D4C23×D6112yes—
579C2×D4C23×D6112yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—24no—
583C22×C4—82no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—1224no—
589C22×C4—1224no—
590C22×C4—1224no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1224no—
595C22×C4—4882no—
596C22×C4—4882no—
597C22×C4—4882no—
598C22×C4—2444no—
599C22×C4D4×D6111yescharacteristic
600C22×C4D4×D6111yescharacteristic
601C22×C4C23×D6111yescharacteristic
602SD16—28no—
603D8—28no—
604D8—1228no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—612no—
608C2×C8—612no—
609C2×C8—1222no—
610C2×C8—1222no—
611C2×C8C23×D6112yes—
612C2×C8C23×D6112yes—
613C4⋊C4—21no—
614C4⋊C4—614no—
615C4⋊C4—614no—
616C4⋊C4—614no—
617C4⋊C4—612no—
618C4⋊C4—612no—
619C4⋊C4—612no—
620C4⋊C4—1224no—
621C4⋊C4—1224no—
622C4⋊C4—1224no—
623C4⋊C4—1224no—
624C4⋊C4—1221no—
625C4⋊C4—1221no—
626C4⋊C4—1221no—
627C4⋊C4—1224no—
628C4⋊C4—1224no—
629C4⋊C4C23×D6112yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—1224no—
634C22⋊C4—1224no—
635C22⋊C4—1224no—
636C22⋊C4—1224no—
637C22⋊C4—1224no—
638C22⋊C4—1224no—
639C42—612no—
640C42—612no—
641C42—612no—
642C42—612no—
643C42—1224no—
644C42D4×D6112yes—
645C42C23×D6112yes—
646C23—22no—
647C23—24no—
648C23—22no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—1222no—
655C23—2442no—
656C23—2442no—
657C23—2442no—
658C23C2×D4×D6111yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—42no—
662Q8—1228no—
663Q8—4884no—
664D4—22no—
665D4—22no—
666D4—22no—
667D4—24no—
668D4—42no—
669D4—1222no—
670D4—1222no—
671D4—4884no—
672D4—2448no—
673D4—2442no—
674D4C2×#1175822414yes—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—84no—
682C2×C4—614no—
683C2×C4—612no—
684C2×C4—612no—
685C2×C4—612no—
686C2×C4—612no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—4884no—
694C2×C4—4884no—
695C2×C4—4884no—
696C2×C4—2448no—
697C2×C4—2442no—
698C2×C4—2442no—
699C2×C4—2442no—
700C2×C4C2×D4×D6112yes—
701C2×C4C2×D4×D6112yes—
702C2×C4C2×D4×D6111yescharacteristic
703C2×C4C2×#1175822412yes—
704C2×C4#1451982412yes—
705C2×C4C24×D6111yescharacteristic
706C8—22no—
707C8—22no—
708C8—1222no—
709C8—1222no—
710C22—24no—
711C22—48no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22—4884no—
719C22—2442no—
720C22—2442no—
721C22—2442no—
722C22#1684041812yes—
723C22#135×D6112yes—
724C22#1684056612yes—
725C22C22×D4×D6111yescharacteristic
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—614no—
731C4—1222no—
732C4—1222no—
733C4—1222no—
734C4—2442no—
735C4—2442no—
736C4—2442no—
737C4#1684041812yes—
738C4C22×#1175822411yescharacteristic
739C4C2×#1451982411yescharacteristic
740C2—44no—
741C2—82no—
742C2—4882no—
743C2#2145847414yesdirect product factor
744C2C2×#1684041811yescharacteristic
745C2C2×#135×D6111yescharacteristic
746C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#463C2
socleC23×C61C22×D4
prime radicalC2×#16839955C2
hypercenterC2×#463D61
hypocenterC61C2×#3361
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#16840494C2semidirect
2. C2×#16840471C2semidirect
3. #21458474C2direct (N × H)
4. C2×#16840118C2semidirect
5. C2×#16840116C2semidirect
6. C2×#16840107C2semidirect
7. C2×#16840055C2semidirect
8. C2×#16840064C2semidirect
9. C2×#16840063C2semidirect
10. C2×#16839979C2semidirect
12. C2×#16839886C2semidirect
13. C2×SD16×Dic61C2semidirect
14. C2×D8×Dic61C2semidirect
15. C2×C4×#11758199C2semidirect
16. C2×C61×#463C2semidirect
19. #16840494C22semidirect
21. #16840471C22semidirect
41. #16840118C22semidirect
42. #16840116C22semidirect
43. #16840107C22semidirect
44. #16840064C22semidirect
45. #16840063C22semidirect
46. #16840055C22semidirect
47. #16839979C22semidirect
49. #16839886C22semidirect
50. SD16×Dic61C22semidirect
51. D8×Dic61C22semidirect
52. C4×#11758199C22semidirect
73. C61×#463C22semidirect
377. C2×#463D61semidirect
385. C2×C61#3361semidirect
425. #463C2×D61semidirect
450. C61C2×#3361semidirect
743. C2#21458474direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404942
C2×#168404712
#214584742
C2×#168401182
C2×#168401162
C2×#168401072
C2×#168400552
C2×#168400642
C2×#168400632
C2×#168399792
C2×#168399552
C2×#168398862
C2×SD16×Dic612
C2×D8×Dic612
C2×C4×#117581992
C2×C61×#4632
C2×#336161