Finite Group Databasebeta

← C2×#21458858 #30560990

Subgroups — C2×#21458858 #30560990

Order 15616.

2314 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840494C211yesmaximal, characteristic, complemented
2C2×#16840432C211yesmaximal, characteristic, complemented
3#21458858C2116yesmaximal, direct product factor
4C2×#16840148C211yesmaximal, characteristic, complemented
5C2×#16840137C211yesmaximal, characteristic, complemented
6C2×#16839960C211yesmaximal, characteristic, complemented
7C2×#16839979C211yesmaximal, characteristic, complemented
8C2×#16839974C211yesmaximal, characteristic, complemented
9C2×#16839955C211yesmaximal, characteristic, complemented
10C2×#16839955C211yesmaximal, characteristic, complemented
11C2×#16839954C211yesmaximal, characteristic, complemented
12C2×#16839890C211yesmaximal, characteristic, complemented
13C2×#16839875C211yesmaximal, characteristic, complemented
14C2×#16839874C211yesmaximal, characteristic, complemented
15C2×SD16×Dic61C211yesmaximal, characteristic, complemented
16C2×C61×#496C211yesmaximal, characteristic, complemented
17C22×#11758224—21no—
18C22×#11758201C2211yescharacteristic
19C22×D488C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21C22×#11758199C2211yescharacteristic
22C22×#11758199C2211yescharacteristic
23#16840494—24no—
24#16840494C2218yescomplemented
25#16840432—24no—
26#16840432C2218yescomplemented
27C2×#14519773C2211yescharacteristic
28C2×#14519773C2211yescharacteristic
29C2×#14519773C2211yescharacteristic
30C2×#14519766C2211yescharacteristic
31C2×#14519763—21no—
32C2×#14519761—21no—
33C2×#14519759—21no—
34C2×#14519749—21no—
35C2×#14519749—21no—
36C2×#14519748—21no—
37C2×Q8×Dic61C2211yescharacteristic
38C2×C4×Dic122C2211yescharacteristic
39C2×C4×D244C2211yescharacteristic
40C2×C4×D244C2211yescharacteristic
41C2×D4×Dic61C2211yescharacteristic
42C2×D4×Dic61C2211yescharacteristic
43C2×D4×Dic61C2211yescharacteristic
44C2×#14519737—21no—
45#16840148C2218yescomplemented
46#16840137C2218yescomplemented
47#16839979C2218yescomplemented
48#16839974C2218yescomplemented
49#16839960C2218yescomplemented
50#16839955C2218yescomplemented
51#16839955C2218yescomplemented
52#16839954C2218yescomplemented
53#16839890C2218yescomplemented
54#16839875C2218yescomplemented
55#16839874C2218yescomplemented
56SD16×Dic61C2218yescomplemented
57C2×#14519709C2211yescharacteristic
58C2×C4⋊#92418C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519706C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×#14519698C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C22×D8×C61C2211yescharacteristic
72C22×D8×C61C2211yescharacteristic
73C2×#127×C61C2211yescharacteristic
74C2×#124×C61C2211yescharacteristic
75C61×#496C2218yescomplemented
76C2×#97×C61C2211yescharacteristic
77C2×#11758224—28no—
78C2×#11758224—48no—
79C22×Dic122D411yescharacteristic
80C22×D244C2311yescharacteristic
81C22×D244C2311yescharacteristic
82C22×C22⋊D61—21no—
83C22×C22⋊D61—21no—
84C22×C22⋊D61—21no—
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C23×Dic61—21no—
89C23×Dic61—21no—
90C23×Dic61—21no—
91C22×C4×D61—21no—
92C22×C4×D61—21no—
93C2×#11758201—42no—
94C2×#11758201C2314yes—
95C2×D488—24no—
96C2×D488C2314yes—
97C2×#11758199—42no—
98C2×#11758199—42no—
99C2×#11758199—42no—
100C2×#11758199C2314yes—
101C2×#11758199C2314yes—
102C2×#11758199C2314yes—
103C22×#92418C2311yescharacteristic
104C22×#92418C2311yescharacteristic
105#14519773—22no—
106#14519773—22no—
107#14519773—22no—
108#14519773C2314yes—
109#14519773C2314yes—
110#14519773C2314yes—
111#14519766—22no—
112#14519766C2314yes—
113#14519763—28no—
114#14519761—28no—
115#14519759—28no—
116#14519749—28no—
117#14519749—28no—
118#14519748—28no—
119Q8×Dic61—22no—
120Q8×Dic61C2314yes—
121C4×Dic122D414yes—
122C4×Dic122C2314yes—
123C4×D244—22no—
124C4×D244—22no—
125C4×D244C2314yes—
126C4×D244C2314yes—
127D4×Dic61—22no—
128D4×Dic61—22no—
129D4×Dic61—22no—
130D4×Dic61C2314yes—
131D4×Dic61C2314yes—
132D4×Dic61C2314yes—
133#14519737—28no—
134C2×C4⋊Dic61—21no—
135C2×C4⋊Dic61D411yescharacteristic
136C2×C4⋊Dic61C2311yescharacteristic
137C2×C4⋊Dic61C2311yescharacteristic
138C2×#11758196D411yescharacteristic
139C2×#11758196D411yescharacteristic
140C2×C22⋊Dic61—21no—
141C2×C22⋊Dic61—21no—
142C2×C22⋊Dic61—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×C4×Dic61—21no—
148C2×C4×Dic61C2311yescharacteristic
149C2×C4×Dic61C2311yescharacteristic
150#14519709C2314yes—
151C4⋊#92418C2314yes—
152#14519706C2314yes—
153#14519706C2314yes—
154#14519701C2314yes—
155#14519699C2314yes—
156#14519699C2314yes—
157#14519698C2314yes—
158#14519698C2314yes—
159#14519698C2314yes—
160#14519687C2314yes—
161C8×Dic61C2314yes—
162C22×Q8×C61C2311yescharacteristic
163C22×D4×C61—21no—
164C22×D4×C61—21no—
165C22×D4×C61C2311yescharacteristic
166C22×D4×C61C2311yescharacteristic
167C22×D4×C61C2311yescharacteristic
168C2×SD16×C61—24no—
169C2×SD16×C61—42no—
170C2×SD16×C61C2314yes—
171C2×SD16×C61C2314yes—
172C2×D8×C61—24no—
173C2×D8×C61—42no—
174C2×D8×C61C2314yes—
175C2×D8×C61C2314yes—
176C22×C8×C61C2311yescharacteristic
177C22×C8×C61C2311yescharacteristic
178#127×C61—22no—
179#127×C61C2314yes—
180#124×C61—22no—
181#124×C61C2314yes—
182C2×C22⋊C4×C61—21no—
183C2×C22⋊C4×C61—21no—
184C2×C42×C61C2311yescharacteristic
185#97×C61C2314yes—
186C24×C61—21no—
187C24×C61—21no—
188C24×C61—21no—
189C23×D61—21no—
190C23×D61—21no—
191C2×Q8×C61—21no—
192C2×Q8×C61—22no—
193C2×Q8×C61—22no—
194C2×Q8×C61C2412yes—
195C2×D4×C61—24no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—24no—
200C2×D4×C61—22no—
201C2×D4×C61—22no—
202C2×D4×C61—22no—
203C2×D4×C61—22no—
204C2×D4×C61—22no—
205C2×D4×C61—22no—
206C2×D4×C61—44no—
207C2×D4×C61—82no—
208C2×D4×C61C2412yes—
209C2×D4×C61C2412yes—
210C2×D4×C61C2412yes—
211C22×C4×C61—21no—
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2411yescharacteristic
215C2×C22⋊D61—24no—
216C2×C22⋊D61—24no—
217C2×C22⋊D61—24no—
218C2×C22⋊D61—24no—
219C2×C22⋊D61—24no—
220C2×C22⋊D61—24no—
221C2×C22⋊D61—44no—
222C2×C22⋊D61—44no—
223C2×C22⋊D61—44no—
224C2×C22⋊D61—82no—
225C2×C22⋊D61—82no—
226C2×C22⋊D61—82no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—24no—
230C22×Dic61—24no—
231C22×Dic61—24no—
232C22×Dic61—44no—
233C22×Dic61—44no—
234C22×Dic61—82no—
235C22×Dic61C2×D411yescharacteristic
236C22×Dic61C2×D411yescharacteristic
237C22×Dic61C2×D411yescharacteristic
238C22×Dic61C2×D411yescharacteristic
239#11758224—432no—
240C2×D244—22no—
241C2×D244—22no—
242C2×D244—22no—
243C2×D244—22no—
244C2×D244—21no—
245C2×D244—21no—
246C2×D244C2412yes—
247C2×D244C2412yes—
248C2×C4×D61—24no—
249C2×C4×D61—24no—
250C2×C4×D61—44no—
251C2×C4×D61—82no—
252C2×Dic122—24no—
253C2×Dic122C2×D414yes—
254SD16×C61—28no—
255SD16×C61—44no—
256D8×C61—28no—
257D8×C61—44no—
258C2×C8×C61—22no—
259C2×C8×C61#4114yescomplemented
260C2×C8×C61C2412yes—
261C2×C8×C61C2412yes—
262C22⋊C4×C61—24no—
263C22⋊C4×C61—24no—
264C42×C61C2×D412yes—
265C42×C61C2412yes—
266C22⋊Dic61—24no—
267C22⋊Dic61—24no—
268C22⋊Dic61—24no—
269#11758201—44no—
270#11758199—44no—
271#11758199—44no—
272#11758199—44no—
273#11758198—24no—
274#11758198—24no—
275#11758198—24no—
276#11758198—24no—
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61—24no—
280C4⋊Dic61C2×D414yes—
281C4⋊Dic61C2412yes—
282C4⋊Dic61C2412yes—
283#11758196C2×D414yes—
284#11758196C2×D414yes—
285C4×Dic61—24no—
286C4×Dic61C2×D412yes—
287C4×Dic61C2×D412yes—
288C4×Dic61C2412yes—
289C4×Dic61C2412yes—
290C2×#92418—22no—
291C2×#92418—22no—
292C2×#92418C2412yes—
293C2×#92418C2412yes—
294D488—28no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—42no—
299C23×C61—42no—
300C23×C61—42no—
301C23×C61—42no—
302C23×C61—42no—
303C23×C61—42no—
304C23×C61—42no—
305C23×C61—42no—
306C23×C61—42no—
307C23×C61C22×D411yescharacteristic
308C22×D61—22no—
309C22×D61—22no—
310C22×D61—42no—
311C22×D61—42no—
312C22×D61—42no—
313C22×D61—42no—
314C22×D61—42no—
315C22×D61—42no—
316Q8×C61—22no—
317Q8×C61—22no—
318Q8×C61—42no—
319D4×C61—22no—
320D4×C61—22no—
321D4×C61—22no—
322D4×C61—22no—
323D4×C61—22no—
324D4×C61—22no—
325D4×C61—48no—
326D4×C61—42no—
327D4×C61—42no—
328D4×C61—42no—
329D4×C61—84no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—42no—
334C2×C4×C61C22×D412yes—
335C2×C4×C61C22×D412yes—
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61C2×#4112yes—
338C2×C4×C61H(5,𝔽2)12yes—
339C2×C4×C61C2511yescharacteristic
340C22⋊D61—48no—
341C22⋊D61—48no—
342C22⋊D61—48no—
343C22⋊D61—84no—
344C22⋊D61—84no—
345C22⋊D61—84no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—48no—
352C2×Dic61—42no—
353C2×Dic61—42no—
354C2×Dic61—48no—
355C2×Dic61—84no—
356C2×Dic61AGL(1,ℤ/8)14yes—
357C2×Dic61C22×D412yes—
358C2×Dic61C22×D412yes—
359C2×Dic61C22×D412yes—
360C2×Dic61C22×D412yes—
361D244—22no—
362D244—22no—
363D244—22no—
364D244—22no—
365D244—42no—
366D244—42no—
367C4×D61—48no—
368C4×D61—84no—
369Dic122—28no—
370C8×C61—22no—
371C8×C61C2×#4114yescomplemented
372#92418—22no—
373#92418—22no—
374C2×#3399—611nomaximal, Sylow
375C22×C61—42no—
376C22×C61—42no—
377C22×C61—42no—
378C22×C61—42no—
379C22×C61—42no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61—42no—
383C22×C61—42no—
384C22×C61—84no—
385C22×C61—84no—
386C22×C61—84no—
387C22×C61#55012yes—
388C22×C61C2×AGL(1,ℤ/8)12yes—
389C22×C61#57612yes—
390C22×C61C23×D411yescharacteristic
391C2×D61—42no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—42no—
397C2×D61—84no—
398C2×D61—84no—
399C4×C61—22no—
400C4×C61—22no—
401C4×C61—42no—
402C4×C61#55012yes—
403C4×C61C22×#4111yescharacteristic
404C4×C61C2×H(5,𝔽2)11yescharacteristic
405Dic61—22no—
406Dic61—22no—
407Dic61—22no—
408Dic61—42no—
409Dic61—42no—
410Dic61C2×AGL(1,ℤ/8)14yes—
411C2×#559—611no—
412C2×#550—611no—
413#3399—6116no—
414C2×#496—611no—
415C2×#496D6111yescharacteristic, complemented
416C2×#493—611no—
417C2×#460—611no—
418C2×#463—611no—
419C2×#463—611no—
420C2×#459—611no—
421C2×#459—611no—
422C2×#459—611no—
423C2×#446—611no—
424C2×#442—611no—
425C2×#442—611no—
426C2×C4×SD16—611no—
427C2×C61—82no—
428C2×C61—82no—
429C2×C61—82no—
430C2×C61#339914yescomplemented
431C2×C61C2×#55011yescharacteristic
432C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
433C2×C61C2×#57611yescharacteristic
434D61—82no—
435D61—82no—
436C22×#41—1221no—
437C22×SD16—611no—
438C22×SD16C2×D6111yescharacteristic
439C22×SD16C2×D6111yescharacteristic
440C22×D8—611no—
441C22×D8—611no—
442C22×D8—611no—
443C22×D8—611no—
444C22×D8C2×D6111yescharacteristic
445C22×D8C2×D6111yescharacteristic
446#559—618no—
447#559—1224no—
448#550—618no—
449#550—1224no—
450C2×#127—611no—
451C2×#127—611no—
452C2×#127—611no—
453C2×#127C2×D6111yescharacteristic
454C2×#124—611no—
455C2×#124—1221no—
456C2×#124C2×D6111yescharacteristic
457C2×#123—1221no—
458C2×#123—1221no—
459C2×#121—1221no—
460C2×#121—1221no—
461C2×#121—1221no—
462C2×C4×Q8—611no—
463C2×C4×Q8—611no—
464C2×C4×D4—611no—
465C2×C4×D4—611no—
466C2×C4×D4—611no—
467C2×C4×D4—611no—
468C2×C4×D4—611no—
469C2×C4×D4—1221no—
470#496—618no—
471#496C2×D6118yescomplemented
472#493—618no—
473#463—618no—
474#463—618no—
475#460—618no—
476#459—618no—
477#459—618no—
478#459—618no—
479#446—618no—
480#442—618no—
481#442—618no—
482C4×SD16—618no—
483C2×#106—611no—
484C2×C4⋊C8—611no—
485C2×C4⋊C8—611no—
486C2×C4⋊C8—611no—
487C2×#103—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102—611no—
492C2×#102—611no—
493C2×#97—611no—
494C2×#97C2×D6111yescharacteristic
495C2×C4×C8—611no—
496C61C2×#339911yescharacteristic, complemented, Sylow
497C2×#41—1228no—
498C2×#41—2448no—
499C22×Q8—611no—
500C22×Q8C22×D6111yescharacteristic
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—611no—
504C22×D4—611no—
505C22×D4—1221no—
506C22×D4—1221no—
507C22×D4—1221no—
508C22×D4—1221no—
509C22×D4—1221no—
510C22×D4—1221no—
511C22×D4C22×D6111yescharacteristic
512C22×D4C22×D6111yescharacteristic
513C22×D4C22×D6111yescharacteristic
514C23×C4—1221no—
515C23×C4—1221no—
516C23×C4—1221no—
517C23×C4—1221no—
518C23×C4—1221no—
519C2×SD16—24no—
520C2×SD16—42no—
521C2×SD16—614no—
522C2×SD16—2442no—
523C2×SD16C22×D6114yes—
524C2×SD16C22×D6114yes—
525C2×D8—24no—
526C2×D8—42no—
527C2×D8—614no—
528C2×D8—614no—
529C2×D8—614no—
530C2×D8—614no—
531C2×D8—1224no—
532C2×D8—2442no—
533C2×D8—2442no—
534C2×D8—2442no—
535C2×D8C22×D6114yes—
536C2×D8C22×D6114yes—
537C22×C8—611no—
538C22×C8—611no—
539C22×C8C22×D6111yescharacteristic
540C22×C8C22×D6111yescharacteristic
541#127—22no—
542#127—614no—
543#127—614no—
544#127—614no—
545#127—1222no—
546#127—1222no—
547#127—1222no—
548#127C22×D6114yes—
549#124—22no—
550#124—614no—
551#124—1222no—
552#124—1228no—
553#124C22×D6114yes—
554#123—1228no—
555#123—1228no—
556#121—1228no—
557#121—1228no—
558#121—1228no—
559C4×Q8—614no—
560C4×Q8—614no—
561C4×Q8—614no—
562C4×Q8—1222no—
563C4×D4—614no—
564C4×D4—614no—
565C4×D4—614no—
566C4×D4—614no—
567C4×D4—614no—
568C4×D4—1222no—
569C4×D4—1222no—
570C4×D4—1222no—
571C4×D4—1228no—
572C4×D4—1222no—
573C4×D4—1222no—
574C2×C4⋊C4—611no—
575C2×C4⋊C4—611no—
576C2×C4⋊C4—611no—
577C2×C4⋊C4—611no—
578C2×C4⋊C4—611no—
579C2×C4⋊C4—1221no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—1221no—
583C2×C22⋊C4—1221no—
584C2×C22⋊C4—1221no—
585C2×C22⋊C4—1221no—
586C2×C22⋊C4—1221no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C42—611no—
590C2×C42—611no—
591C2×C42—1221no—
592C2×C42C22×D6111yescharacteristic
593#106—614no—
594C4⋊C8—614no—
595C4⋊C8—614no—
596C4⋊C8—614no—
597#103—614no—
598#102—614no—
599#102—614no—
600#102—614no—
601#102—614no—
602#102—614no—
603#97—614no—
604#97C22×D6114yes—
605C4×C8—614no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—1221no—
610C24—1221no—
611#41—24432no—
612C2×Q8—21no—
613C2×Q8—22no—
614C2×Q8—22no—
615C2×Q8—614no—
616C2×Q8—1224no—
617C2×Q8C23×D6112yes—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—44no—
630C2×D4—82no—
631C2×D4—612no—
632C2×D4—612no—
633C2×D4—1224no—
634C2×D4—1224no—
635C2×D4—1224no—
636C2×D4—1224no—
637C2×D4—1224no—
638C2×D4—1224no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1222no—
642C2×D4—1222no—
643C2×D4—1222no—
644C2×D4—1222no—
645C2×D4—4882no—
646C2×D4—4882no—
647C2×D4—4882no—
648C2×D4—2444no—
649C2×D4—2444no—
650C2×D4—2444no—
651C2×D4C23×D6112yes—
652C2×D4C23×D6112yes—
653C2×D4C23×D6112yes—
654C22×C4—21no—
655C22×C4—611no—
656C22×C4—611no—
657C22×C4—611no—
658C22×C4—611no—
659C22×C4—1224no—
660C22×C4—1224no—
661C22×C4—1224no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1224no—
665C22×C4—1224no—
666C22×C4—4882no—
667C22×C4—4882no—
668C22×C4—2444no—
669C22×C4—2444no—
670C22×C4—2444no—
671C22×C4D4×D6111yescharacteristic
672C22×C4D4×D6111yescharacteristic
673C22×C4C23×D6111yescharacteristic
674SD16—28no—
675SD16—44no—
676SD16—2444no—
677D8—28no—
678D8—44no—
679D8—1228no—
680D8—2444no—
681D8—2444no—
682D8—2444no—
683C2×C8—22no—
684C2×C8—612no—
685C2×C8—612no—
686C2×C8—1222no—
687C2×C8—1222no—
688C2×C8#1175822414yescomplemented
689C2×C8C23×D6112yes—
690C2×C8C23×D6112yes—
691C4⋊C4—614no—
692C4⋊C4—614no—
693C4⋊C4—614no—
694C4⋊C4—612no—
695C4⋊C4—612no—
696C4⋊C4—1224no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C22⋊C4—24no—
700C22⋊C4—24no—
701C22⋊C4—1224no—
702C22⋊C4—1224no—
703C22⋊C4—1224no—
704C22⋊C4—1224no—
705C22⋊C4—1224no—
706C22⋊C4—1224no—
707C22⋊C4—1224no—
708C42—612no—
709C42—612no—
710C42—612no—
711C42—612no—
712C42—1224no—
713C42D4×D6112yes—
714C42C23×D6112yes—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—1222no—
728C23—1222no—
729C23—2442no—
730C23—2442no—
731C23—2442no—
732C23—2442no—
733C23—2442no—
734C23—2442no—
735C23C2×D4×D6111yescharacteristic
736Q8—22no—
737Q8—22no—
738Q8—42no—
739Q8—1228no—
740D4—22no—
741D4—22no—
742D4—22no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—48no—
747D4—42no—
748D4—42no—
749D4—42no—
750D4—84no—
751D4—1222no—
752D4—1222no—
753D4—1222no—
754D4—1222no—
755D4—4884no—
756D4—4884no—
757D4—4884no—
758D4—2448no—
759D4—2448no—
760D4—2448no—
761D4—2442no—
762D4—2442no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—42no—
767C2×C4—614no—
768C2×C4—612no—
769C2×C4—612no—
770C2×C4—612no—
771C2×C4—612no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—4884no—
778C2×C4—4884no—
779C2×C4—2448no—
780C2×C4—2448no—
781C2×C4—2448no—
782C2×C4—2442no—
783C2×C4—2442no—
784C2×C4C2×D4×D6112yes—
785C2×C4C2×D4×D6112yes—
786C2×C4C2×D4×D6111yescharacteristic
787C2×C4C2×#1175822412yes—
788C2×C4#1451982212yes—
789C2×C4C24×D6111yescharacteristic
790C8—22no—
791C8—1222no—
792C8—1222no—
793C8C2×#1175822414yescomplemented
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—84no—
804C22—84no—
805C22—84no—
806C22—4884no—
807C22—4884no—
808C22—2442no—
809C22—2442no—
810C22—2442no—
811C22—2442no—
812C22—2442no—
813C22—2442no—
814C22#1684043212yes—
815C22AGL(1,ℤ/8)×D6112yes—
816C22#1684056612yes—
817C22C22×D4×D6111yescharacteristic
818C4—22no—
819C4—22no—
820C4—42no—
821C4—614no—
822C4—1222no—
823C4—1222no—
824C4—1222no—
825C4—2442no—
826C4—2442no—
827C4#1684043212yes—
828C4C22×#1175822411yescharacteristic
829C4C2×#1451982211yescharacteristic
830C2—82no—
831C2—82no—
832C2—82no—
833C2—4882no—
834C2—4882no—
835C2#2145885814yesdirect product factor
836C2C2×#1684043211yescharacteristic
837C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
838C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#496C2
socleC23×C61C22×D4
hypercenterC2×#496D61
hypocenterC61C2×#3399
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#496

Complements

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

NH ≅ G/Ntype
1. C2×#16840494C2semidirect
2. C2×#16840432C2semidirect
3. #21458858C2direct (N × H)
4. C2×#16840148C2semidirect
5. C2×#16840137C2semidirect
6. C2×#16839960C2semidirect
7. C2×#16839979C2semidirect
8. C2×#16839974C2semidirect
9. C2×#16839955C2semidirect
10. C2×#16839955C2semidirect
11. C2×#16839954C2semidirect
12. C2×#16839890C2semidirect
13. C2×#16839875C2semidirect
14. C2×#16839874C2semidirect
15. C2×SD16×Dic61C2semidirect
16. C2×C61×#496C2semidirect
24. #16840494C22semidirect
26. #16840432C22semidirect
45. #16840148C22semidirect
46. #16840137C22semidirect
47. #16839979C22semidirect
48. #16839974C22semidirect
49. #16839960C22semidirect
50. #16839955C22semidirect
51. #16839955C22semidirect
52. #16839954C22semidirect
53. #16839890C22semidirect
54. #16839875C22semidirect
55. #16839874C22semidirect
56. SD16×Dic61C22semidirect
75. C61×#496C22semidirect
259. C2×C8×C61#41semidirect
371. C8×C61C2×#41semidirect
415. C2×#496D61semidirect
430. C2×C61#3399semidirect
471. #496C2×D61semidirect
496. C61C2×#3399semidirect
688. C2×C8#11758224semidirect
793. C8C2×#11758224semidirect
835. C2#21458858direct (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×#168404322
#214588582
C2×#168401482
C2×#168401372
C2×#168399602
C2×#168399792
C2×#168399742
C2×#168399552
C2×#168399542
C2×#168398902
C2×#168398752
C2×#168398742
C2×SD16×Dic612
C2×C61×#4962
C2×#339961