Finite Group Databasebeta

← C2×#21458864 #30560996

Subgroups — C2×#21458864 #30560996

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×#16840495C211yesmaximal, characteristic, complemented
2C2×#16840432C211yesmaximal, characteristic, complemented
3#21458864C2116yesmaximal, direct product factor
4C2×#16840150C211yesmaximal, characteristic, complemented
5C2×#16840149C211yesmaximal, characteristic, complemented
6C2×#16840137C211yesmaximal, characteristic, complemented
7C2×#16839961C211yesmaximal, characteristic, complemented
8C2×#16839978C211yesmaximal, characteristic, complemented
9C2×#16839975C211yesmaximal, characteristic, complemented
10C2×#16839956C211yesmaximal, characteristic, complemented
11C2×#16839955C211yesmaximal, characteristic, complemented
12C2×#16839891C211yesmaximal, characteristic, complemented
13C2×#16839872C211yesmaximal, characteristic, complemented
14C2×#16839871C211yesmaximal, characteristic, complemented
15C2×#16839853C211yesmaximal, characteristic, complemented
16C2×C61×#459C211yesmaximal, characteristic, complemented
17C22×#11758224—21no—
18C22×#11758190C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×D488C2211yescharacteristic
22C22×#11758199C2211yescharacteristic
23C22×#11758199C2211yescharacteristic
24C22×#11758199C2211yescharacteristic
25#16840495—24no—
26#16840495C2218yescomplemented
27#16840432—24no—
28#16840432C2218yescomplemented
29C2×#14519773C2211yescharacteristic
30C2×#14519773C2211yescharacteristic
31C2×#14519773C2211yescharacteristic
32C2×#14519765C2211yescharacteristic
33C2×#14519764C2211yescharacteristic
34C2×#14519763—21no—
35C2×#14519760—21no—
36C2×#14519759—21no—
37C2×#14519749—21no—
38C2×#14519749—21no—
39C2×#14519748—21no—
40C2×C4×Dic122C2211yescharacteristic
41C2×#14519742C2211yescharacteristic
42C2×C4×D244C2211yescharacteristic
43C2×D4×Dic61C2211yescharacteristic
44C2×D4×Dic61C2211yescharacteristic
45C2×#14519739C2211yescharacteristic
46C2×C4×C22⋊D61—21no—
47#16840150C2218yescomplemented
48#16840149C2218yescomplemented
49#16840137C2218yescomplemented
50#16839978C2218yescomplemented
51#16839975C2218yescomplemented
52#16839961C2218yescomplemented
53#16839956C2218yescomplemented
54#16839955C2218yescomplemented
55#16839891C2218yescomplemented
56#16839872C2218yescomplemented
57#16839871C2218yescomplemented
58#16839853C2218yescomplemented
59C2×#14519708C2211yescharacteristic
60C2×#14519706C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519702C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519688C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×D8×C61C2211yescharacteristic
70C22×D8×C61C2211yescharacteristic
71C2×#127×C61C2211yescharacteristic
72C2×C4×D4×C61C2211yescharacteristic
73C61×#459C2218yescomplemented
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C2×#11758224—28no—
78C2×#11758224—48no—
79C22×Dic122D411yescharacteristic
80C22×Dic122C2311yescharacteristic
81C22×D244C2311yescharacteristic
82C22×D244C2311yescharacteristic
83C22×C22⋊D61—21no—
84C22×C22⋊D61—21no—
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C22×C22⋊D61—21no—
89C23×Dic61—21no—
90C23×Dic61—21no—
91C22×C4×D61—21no—
92C22×C4×D61—21no—
93C2×#11758190—42no—
94C2×#11758190C2314yes—
95C2×#11758200—24no—
96C2×#11758200—42no—
97C2×#11758200C2314yes—
98C2×#11758200C2314yes—
99C2×D488—42no—
100C2×D488C2314yes—
101C2×#11758199—24no—
102C2×#11758199—24no—
103C2×#11758199—42no—
104C2×#11758199C2314yes—
105C2×#11758199C2314yes—
106C2×#11758199C2314yes—
107C22×#92418C2311yescharacteristic
108C22×#92418C2311yescharacteristic
109#14519773—22no—
110#14519773—22no—
111#14519773—22no—
112#14519773C2314yes—
113#14519773C2314yes—
114#14519773C2314yes—
115#14519765—22no—
116#14519765C2314yes—
117#14519764—22no—
118#14519764C2314yes—
119#14519763—28no—
120#14519760—28no—
121#14519759—28no—
122#14519749—28no—
123#14519749—28no—
124#14519748—28no—
125C4×Dic122D414yes—
126C4×Dic122C2314yes—
127#14519742—22no—
128#14519742C2314yes—
129C4×D244—22no—
130C4×D244C2314yes—
131D4×Dic61—22no—
132D4×Dic61—22no—
133D4×Dic61C2314yes—
134D4×Dic61C2314yes—
135#14519739—22no—
136#14519739C2314yes—
137C4×C22⋊D61—28no—
138C2×C4⋊Dic61D411yescharacteristic
139C2×C4⋊Dic61C2311yescharacteristic
140C2×#11758196—21no—
141C2×#11758196D411yescharacteristic
142C2×#11758196D411yescharacteristic
143C2×C22⋊Dic61—21no—
144C2×C22⋊Dic61—21no—
145C2×C22⋊Dic61—21no—
146C2×C22⋊Dic61—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×#11758198—21no—
151C2×C4×Dic61—21no—
152C2×C4×Dic61C2311yescharacteristic
153C2×C4×Dic61C2311yescharacteristic
154#14519708C2314yes—
155#14519706C2314yes—
156#14519706C2314yes—
157#14519702C2314yes—
158#14519699C2314yes—
159#14519698C2314yes—
160#14519697C2314yes—
161#14519688C2314yes—
162#14519687C2314yes—
163C8×Dic61C2314yes—
164C22×D4×C61—21no—
165C22×D4×C61—21no—
166C22×D4×C61C2311yescharacteristic
167C22×D4×C61C2311yescharacteristic
168C22×D4×C61C2311yescharacteristic
169C23×C4×C61—21no—
170C2×D8×C61—42no—
171C2×D8×C61—42no—
172C2×D8×C61C2314yes—
173C2×D8×C61C2314yes—
174C22×C8×C61C2311yescharacteristic
175C22×C8×C61C2311yescharacteristic
176#127×C61—22no—
177#127×C61C2314yes—
178C4×D4×C61—22no—
179C4×D4×C61C2314yes—
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C22⋊C4×C61—21no—
182C2×C42×C61C2311yescharacteristic
183C4⋊C8×C61C2314yes—
184#102×C61C2314yes—
185#102×C61C2314yes—
186C24×C61—21no—
187C24×C61—21no—
188C24×C61—21no—
189C23×D61—21no—
190C23×D61—21no—
191C2×D4×C61—24no—
192C2×D4×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—24no—
196C2×D4×C61—22no—
197C2×D4×C61—22no—
198C2×D4×C61—22no—
199C2×D4×C61—22no—
200C2×D4×C61—22no—
201C2×D4×C61—22no—
202C2×D4×C61—44no—
203C2×D4×C61—82no—
204C2×D4×C61C2412yes—
205C2×D4×C61C2412yes—
206C2×D4×C61C2412yes—
207C22×C4×C61—21no—
208C22×C4×C61—24no—
209C22×C4×C61—82no—
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2411yescharacteristic
213C2×C22⋊D61—24no—
214C2×C22⋊D61—24no—
215C2×C22⋊D61—24no—
216C2×C22⋊D61—24no—
217C2×C22⋊D61—24no—
218C2×C22⋊D61—24no—
219C2×C22⋊D61—44no—
220C2×C22⋊D61—44no—
221C2×C22⋊D61—44no—
222C2×C22⋊D61—82no—
223C2×C22⋊D61—82no—
224C2×C22⋊D61—82no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—24no—
228C22×Dic61—24no—
229C22×Dic61—44no—
230C22×Dic61—44no—
231C22×Dic61C2×D411yescharacteristic
232C22×Dic61C2×D411yescharacteristic
233C22×Dic61C2×D411yescharacteristic
234C22×Dic61C2×D411yescharacteristic
235#11758224—432no—
236C2×D244—22no—
237C2×D244—22no—
238C2×D244—22no—
239C2×D244—22no—
240C2×D244—21no—
241C2×D244—21no—
242C2×D244C2412yes—
243C2×D244C2412yes—
244C2×C4×D61—24no—
245C2×C4×D61—24no—
246C2×C4×D61—44no—
247C2×C4×D61—82no—
248C2×Dic122—24no—
249C2×Dic122—22no—
250C2×Dic122—22no—
251C2×Dic122—21no—
252C2×Dic122C2×D414yes—
253C2×Dic122C2412yes—
254D8×C61—44no—
255D8×C61—44no—
256C2×C8×C61—22no—
257C2×C8×C61—22no—
258C2×C8×C61C2412yes—
259C2×C8×C61C2412yes—
260C4⋊C4×C61—21no—
261C4⋊C4×C61C2412yes—
262C22⋊C4×C61—24no—
263C42×C61C2×D412yes—
264C42×C61C2412yes—
265C22⋊Dic61—24no—
266C22⋊Dic61—24no—
267C22⋊Dic61—24no—
268C22⋊Dic61—24no—
269#11758200—28no—
270#11758200—44no—
271#11758199—28no—
272#11758199—28no—
273#11758199—44no—
274#11758198—24no—
275#11758198—24no—
276#11758198—24no—
277#11758198—24no—
278C4⋊Dic61—21no—
279C4⋊Dic61C2×D414yes—
280C4⋊Dic61C2412yes—
281#11758196—24no—
282#11758196C2×D414yes—
283#11758196C2×D414yes—
284C4×Dic61—24no—
285C4×Dic61C2×D412yes—
286C4×Dic61C2×D412yes—
287C4×Dic61C2412yes—
288C4×Dic61C2412yes—
289C2×#92418—22no—
290C2×#92418#4114yescomplemented
291C2×#92418C2412yes—
292C2×#92418C2412yes—
293D488—44no—
294#11758190—44no—
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—
316D4×C61—22no—
317D4×C61—22no—
318D4×C61—22no—
319D4×C61—22no—
320D4×C61—22no—
321D4×C61—22no—
322D4×C61—48no—
323D4×C61—42no—
324D4×C61—42no—
325D4×C61—42no—
326D4×C61—84no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—42no—
331C2×C4×C61—84no—
332C2×C4×C61C22×D412yes—
333C2×C4×C61C22×D412yes—
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C2×#4112yes—
336C2×C4×C61H(5,𝔽2)12yes—
337C2×C4×C61C2511yescharacteristic
338C22⋊D61—48no—
339C22⋊D61—48no—
340C22⋊D61—48no—
341C22⋊D61—84no—
342C22⋊D61—84no—
343C22⋊D61—84no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—48no—
350C2×Dic61—42no—
351C2×Dic61—42no—
352C2×Dic61—48no—
353C2×Dic61AGL(1,ℤ/8)14yes—
354C2×Dic61C22×D412yes—
355C2×Dic61C22×D412yes—
356C2×Dic61C22×D412yes—
357C2×Dic61C22×D412yes—
358D244—22no—
359D244—22no—
360D244—22no—
361D244—22no—
362D244—42no—
363D244—42no—
364C4×D61—48no—
365C4×D61—84no—
366Dic122—28no—
367Dic122—22no—
368Dic122—22no—
369Dic122—42no—
370C8×C61—22no—
371C8×C61—22no—
372#92418—22no—
373#92418C2×#4114yescomplemented
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×#496—611no—
416C2×#493—611no—
417C2×#460—611no—
418C2×#463—611no—
419C2×#463—611no—
420C2×#459—611no—
421C2×#459—611no—
422C2×#459D6111yescharacteristic, complemented
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×SD16—611no—
439C22×SD16—611no—
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—611no—
456C2×#124—1221no—
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—1221no—
469C2×C4×D4C2×D6111yescharacteristic
470#496—618no—
471#496—618no—
472#493—618no—
473#463—618no—
474#463—618no—
475#460—618no—
476#459—618no—
477#459—618no—
478#459C2×D6118yescomplemented
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⋊C8C2×D6111yescharacteristic
487C2×#103—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102C2×D6111yescharacteristic
492C2×#102C2×D6111yescharacteristic
493C2×#97—611no—
494C2×#97—611no—
495C2×C4×C8—611no—
496C61C2×#339911yescharacteristic, complemented, Sylow
497C2×#41—1228no—
498C2×#41—2448no—
499C22×Q8—611no—
500C22×Q8—611no—
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—21no—
515C23×C4—1221no—
516C23×C4—1221no—
517C23×C4—1221no—
518C23×C4—1221no—
519C2×SD16—614no—
520C2×SD16—614no—
521C2×SD16—614no—
522C2×SD16—1224no—
523C2×SD16—2442no—
524C2×SD16—2442no—
525C2×D8—42no—
526C2×D8—42no—
527C2×D8—614no—
528C2×D8—614no—
529C2×D8—614no—
530C2×D8—614no—
531C2×D8—1224no—
532C2×D8—1224no—
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—614no—
550#124—614no—
551#124—1222no—
552#124—1228no—
553#124—1222no—
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—22no—
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×D4C22×D6114yes—
574C2×C4⋊C4—611no—
575C2×C4⋊C4—611no—
576C2×C4⋊C4—611no—
577C2×C4⋊C4—611no—
578C2×C4⋊C4—1221no—
579C2×C4⋊C4C22×D6111yescharacteristic
580C2×C22⋊C4—21no—
581C2×C22⋊C4—1221no—
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⋊C8C22×D6114yes—
597#103—614no—
598#102—614no—
599#102—614no—
600#102—614no—
601#102C22×D6114yes—
602#102C22×D6114yes—
603#97—614no—
604#97—614no—
605C4×C8—614no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—1221no—
610C24—1221no—
611#41—24432no—
612C2×Q8—614no—
613C2×Q8—612no—
614C2×Q8—1224no—
615C2×Q8—1221no—
616C2×Q8—1222no—
617C2×Q8—1222no—
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—24no—
656C22×C4—82no—
657C22×C4—611no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—611no—
661C22×C4—1224no—
662C22×C4—1224no—
663C22×C4—1224no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1224no—
667C22×C4—4882no—
668C22×C4—2444no—
669C22×C4—2444no—
670C22×C4—2444no—
671C22×C4D4×D6111yescharacteristic
672C22×C4D4×D6111yescharacteristic
673C22×C4C23×D6111yescharacteristic
674SD16—1228no—
675SD16—2444no—
676SD16—2444no—
677D8—44no—
678D8—44no—
679D8—1228no—
680D8—1228no—
681D8—2444no—
682D8—2444no—
683C2×C8—22no—
684C2×C8—22no—
685C2×C8—614no—
686C2×C8—612no—
687C2×C8—612no—
688C2×C8—1222no—
689C2×C8C23×D6112yes—
690C2×C8C23×D6112yes—
691C4⋊C4—21no—
692C4⋊C4—614no—
693C4⋊C4—614no—
694C4⋊C4—614no—
695C4⋊C4—612no—
696C4⋊C4—1224no—
697C4⋊C4—1221no—
698C4⋊C4C23×D6112yes—
699C22⋊C4—24no—
700C22⋊C4—1224no—
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—1228no—
737Q8—1222no—
738Q8—1222no—
739Q8—2442no—
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—84no—
768C2×C4—614no—
769C2×C4—612no—
770C2×C4—612no—
771C2×C4—612no—
772C2×C4—612no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—1222no—
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×C4#41×D6112yes—
788C2×C4#1451982212yes—
789C2×C4C24×D6111yescharacteristic
790C8—22no—
791C8—22no—
792C8—614no—
793C8—1222no—
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#1684043012yes—
815C22AGL(1,ℤ/8)×D6112yes—
816C22#1684056312yes—
817C22C22×D4×D6111yescharacteristic
818C4—22no—
819C4—22no—
820C4—42no—
821C4—614no—
822C4—1222no—
823C4—1222no—
824C4—1222no—
825C4—2442no—
826C4—2442no—
827C4#1684043012yes—
828C4C2×#41×D6111yescharacteristic
829C4C2×#1451982211yescharacteristic
830C2—82no—
831C2—82no—
832C2—82no—
833C2—4882no—
834C2—4882no—
835C2#2145886414yesdirect product factor
836C2C2×#1684043011yescharacteristic
837C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
838C2C2×#1684056311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#459C2
socleC23×C61C22×D4
hypercenterC2×#459D61
hypocenterC61C2×#3399
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#16840495C2semidirect
2. C2×#16840432C2semidirect
3. #21458864C2direct (N × H)
4. C2×#16840150C2semidirect
5. C2×#16840149C2semidirect
6. C2×#16840137C2semidirect
7. C2×#16839961C2semidirect
8. C2×#16839978C2semidirect
9. C2×#16839975C2semidirect
10. C2×#16839956C2semidirect
11. C2×#16839955C2semidirect
12. C2×#16839891C2semidirect
13. C2×#16839872C2semidirect
14. C2×#16839871C2semidirect
15. C2×#16839853C2semidirect
16. C2×C61×#459C2semidirect
26. #16840495C22semidirect
28. #16840432C22semidirect
47. #16840150C22semidirect
48. #16840149C22semidirect
49. #16840137C22semidirect
50. #16839978C22semidirect
51. #16839975C22semidirect
52. #16839961C22semidirect
53. #16839956C22semidirect
54. #16839955C22semidirect
55. #16839891C22semidirect
56. #16839872C22semidirect
57. #16839871C22semidirect
58. #16839853C22semidirect
73. C61×#459C22semidirect
290. C2×#92418#41semidirect
373. #92418C2×#41semidirect
422. C2×#459D61semidirect
430. C2×C61#3399semidirect
478. #459C2×D61semidirect
496. C61C2×#3399semidirect
835. C2#21458864direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404952
C2×#168404322
#214588642
C2×#168401502
C2×#168401492
C2×#168401372
C2×#168399612
C2×#168399782
C2×#168399752
C2×#168399562
C2×#168399552
C2×#168398912
C2×#168398722
C2×#168398712
C2×#168398532
C2×C61×#4592
C2×#339961