Finite Group Databasebeta

← C2×#21456792 #30551230

Subgroups — C2×#21456792 #30551230

Order 15616.

2218 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840308C211yesmaximal, characteristic, complemented
2C2×#16840293C211yesmaximal, characteristic, complemented
3#21456792C2116yesmaximal, direct product factor
4C2×#16840145C211yesmaximal, characteristic, complemented
5C2×#16840143C211yesmaximal, characteristic, complemented
6C2×#16840118C211yesmaximal, characteristic, complemented
7C2×#16840115C211yesmaximal, characteristic, complemented
8C2×#16839971C211yesmaximal, characteristic, complemented
9C2×#16839961C211yesmaximal, characteristic, complemented
10C2×#16839965C211yesmaximal, characteristic, complemented
11C2×#16839955C211yesmaximal, characteristic, complemented
12C2×#16839926C211yesmaximal, characteristic, complemented
13C2×#16839924C211yesmaximal, characteristic, complemented
14C2×#16839905C211yesmaximal, characteristic, complemented
15C2×#16839812C211yesmaximal, characteristic, complemented
16C2×C61×#449C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×Dic244C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758190C2211yescharacteristic
21C22×#11758200C2211yescharacteristic
22C22×#11758200C2211yescharacteristic
23C22×#11758199C2211yescharacteristic
24#16840308—24no—
25#16840308C2218yescomplemented
26C2×#14519775C2211yescharacteristic
27C2×#14519773C2211yescharacteristic
28#16840293—24no—
29#16840293C2218yescomplemented
30C2×#14519770—21no—
31C2×#14519768C2211yescharacteristic
32C2×#14519766C2211yescharacteristic
33C2×#14519764C2211yescharacteristic
34C2×#14519764C2211yescharacteristic
35C2×#14519758—21no—
36C2×#14519756C2211yescharacteristic
37C2×#14519749—21no—
38C2×#14519749—21no—
39C2×#14519742C2211yescharacteristic
40C2×D4×Dic61—21no—
41C2×D4×Dic61C2211yescharacteristic
42C2×C4×C22⋊D61—21no—
43C2×C4×C22⋊D61—21no—
44C2×#14519733—21no—
45C22×C4×Dic61C2211yescharacteristic
46#16840145C2218yescomplemented
47#16840143C2218yescomplemented
48#16840118C2218yescomplemented
49#16840115C2218yescomplemented
50#16839971C2218yescomplemented
51#16839965C2218yescomplemented
52#16839961C2218yescomplemented
53#16839955C2218yescomplemented
54#16839926C2218yescomplemented
55#16839924C2218yescomplemented
56#16839905C2218yescomplemented
57#16839812C2218yescomplemented
58C2×#14519706C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×C8×Dic61C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×#41×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C22×D8×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C61×#449C2218yescomplemented
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C2×#11758222—22no—
78C2×#11758222—42no—
79C2×#11758222—42no—
80C2×#11758222C2314yes—
81C22×Dic122C2311yescharacteristic
82C22×Dic122C2311yescharacteristic
83C22×D244C2311yescharacteristic
84C22×C22⋊D61—21no—
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C23×Dic61—21no—
88C23×Dic61D411yescharacteristic
89C23×Dic61D411yescharacteristic
90C22×C4×D61—21no—
91C2×Dic244—42no—
92C2×Dic244C2314yes—
93C2×#11758202—42no—
94C2×#11758202C2314yes—
95C2×#11758190—42no—
96C2×#11758190C2314yes—
97C2×#11758200—42no—
98C2×#11758200—42no—
99C2×#11758200C2314yes—
100C2×#11758200C2314yes—
101C2×#11758199—42no—
102C2×#11758199C2314yes—
103C22×#92418C2311yescharacteristic
104C22×#92418C2311yescharacteristic
105#14519775—22no—
106#14519775C2314yes—
107#14519773—22no—
108#14519773C2314yes—
109#14519770—28no—
110#14519768—22no—
111#14519768C2314yes—
112#14519766—22no—
113#14519766C2314yes—
114#14519764—22no—
115#14519764—22no—
116#14519764C2314yes—
117#14519764C2314yes—
118#14519758—28no—
119#14519756—22no—
120#14519756C2314yes—
121#14519749—28no—
122#14519749—28no—
123#14519742—22no—
124#14519742C2314yes—
125D4×Dic61—28no—
126D4×Dic61—22no—
127D4×Dic61C2314yes—
128C4×C22⋊D61—28no—
129C4×C22⋊D61—28no—
130#14519733—28no—
131C2×C4⋊Dic61—21no—
132C2×C4⋊Dic61C2311yescharacteristic
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196—21no—
138C2×C22⋊Dic61—21no—
139C2×C22⋊Dic61—21no—
140C2×C22⋊Dic61—21no—
141C2×C22⋊Dic61—21no—
142C2×C22⋊Dic61—21no—
143C2×C22⋊Dic61—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×C4×Dic61—21no—
147C2×C4×Dic61D411yescharacteristic
148C2×C4×Dic61D411yescharacteristic
149C2×C4×Dic61D414yes—
150C2×C4×Dic61C2311yescharacteristic
151C2×C4×Dic61C2311yescharacteristic
152C2×C4×Dic61C2314yes—
153#14519706C2314yes—
154#14519706C2314yes—
155#14519702C2314yes—
156#14519701C2314yes—
157#14519700C2314yes—
158#14519699C2314yes—
159#14519698C2314yes—
160#14519697C2314yes—
161C22⋊#92418C2314yes—
162C8×Dic61C2314yes—
163C8×Dic61C2314yes—
164C2×#41×C61—22no—
165C2×#41×C61—42no—
166C2×#41×C61—42no—
167C2×#41×C61C2314yes—
168C22×Q8×C61C2311yescharacteristic
169C22×D4×C61—21no—
170C22×D4×C61—21no—
171C22×D4×C61C2311yescharacteristic
172C22×D4×C61C2311yescharacteristic
173C23×C4×C61—21no—
174C23×C4×C61C2311yescharacteristic
175C2×SD16×C61—42no—
176C2×SD16×C61C2314yes—
177C2×D8×C61—42no—
178C2×D8×C61C2314yes—
179C22×C8×C61C2311yescharacteristic
180C22×C8×C61C2311yescharacteristic
181#121×C61—22no—
182#121×C61C2314yes—
183C2×C4⋊C4×C61C2311yescharacteristic
184C2×C22⋊C4×C61—21no—
185#103×C61C2314yes—
186#102×C61C2314yes—
187C22⋊C8×C61C2314yes—
188C24×C61—21no—
189C24×C61—21no—
190C24×C61C2×D411yescharacteristic
191C23×D61—21no—
192#41×C61—44no—
193#41×C61—44no—
194#41×C61—48no—
195C2×Q8×C61—21no—
196C2×Q8×C61—22no—
197C2×Q8×C61—22no—
198C2×Q8×C61C2412yes—
199C2×D4×C61—24no—
200C2×D4×C61—24no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—22no—
204C2×D4×C61—22no—
205C2×D4×C61—22no—
206C2×D4×C61—22no—
207C2×D4×C61—44no—
208C2×D4×C61—44no—
209C2×D4×C61C2412yes—
210C2×D4×C61C2412yes—
211C22×C4×C61—22no—
212C22×C4×C61—22no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—24no—
216C22×C4×C61—44no—
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D412yes—
219C22×C4×C61C2412yes—
220C22×C4×C61C2411yescharacteristic
221C2×C22⋊D61—24no—
222C2×C22⋊D61—24no—
223C2×C22⋊D61—24no—
224C2×C22⋊D61—44no—
225C2×C22⋊D61—44no—
226C2×C22⋊D61—44no—
227C22×Dic61—24no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—24no—
232C22×Dic61—42no—
233C22×Dic61—44no—
234C22×Dic61C2×D411yescharacteristic
235C22×Dic61C2×D411yescharacteristic
236C22×Dic61C2×D411yescharacteristic
237C22×Dic61C2×D414yes—
238C22×Dic61C2×D414yes—
239C22×Dic61C2×D411yescharacteristic
240#11758222—44no—
241#11758222—44no—
242#11758222—48no—
243C2×D244—22no—
244C2×D244—22no—
245C2×D244—21no—
246C2×D244C2412yes—
247C2×C4×D61—24no—
248C2×C4×D61—44no—
249C2×Dic122—22no—
250C2×Dic122—22no—
251C2×Dic122—22no—
252C2×Dic122—22no—
253C2×Dic122—21no—
254C2×Dic122—21no—
255C2×Dic122C2412yes—
256C2×Dic122C2412yes—
257SD16×C61—44no—
258D8×C61—44no—
259C2×C8×C61—22no—
260C2×C8×C61—22no—
261C2×C8×C61C2412yes—
262C2×C8×C61C2412yes—
263C4⋊C4×C61—21no—
264C4⋊C4×C61C2412yes—
265C22⋊C4×C61—24no—
266C22⋊Dic61—24no—
267C22⋊Dic61—24no—
268C22⋊Dic61—24no—
269C22⋊Dic61—24no—
270C22⋊Dic61—24no—
271C22⋊Dic61—24no—
272#11758202—44no—
273#11758200—44no—
274#11758200—44no—
275#11758199—44no—
276#11758198—24no—
277#11758198—24no—
278C4⋊Dic61—21no—
279C4⋊Dic61—24no—
280C4⋊Dic61C2412yes—
281#11758196—24no—
282#11758196—24no—
283#11758196—24no—
284#11758196—24no—
285#11758196—24no—
286C4×Dic61—24no—
287C4×Dic61C2×D414yes—
288C4×Dic61C2×D414yes—
289C4×Dic61C2×D412yes—
290C4×Dic61C2×D412yes—
291C4×Dic61C2412yes—
292C4×Dic61C2412yes—
293C2×#92418—22no—
294C2×#92418—22no—
295C2×#92418C2412yes—
296C2×#92418C2412yes—
297Dic244—44no—
298#11758190—44no—
299C23×C61—22no—
300C23×C61—22no—
301C23×C61—22no—
302C23×C61—22no—
303C23×C61—22no—
304C23×C61—42no—
305C23×C61—42no—
306C23×C61—42no—
307C23×C61—42no—
308C23×C61—42no—
309C23×C61—42no—
310C23×C61C22×D412yes—
311C23×C61C22×D411yescharacteristic
312C22×D61—22no—
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—48no—
324D4×C61—48no—
325D4×C61—42no—
326D4×C61—42no—
327C2×C4×C61—22no—
328C2×C4×C61—24no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—48no—
334C2×C4×C61—42no—
335C2×C4×C61—42no—
336C2×C4×C61C22×D412yes—
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61H(5,𝔽2)12yes—
339C2×C4×C61H(5,𝔽2)12yes—
340C2×C4×C61C2511yescharacteristic
341C22⋊D61—48no—
342C22⋊D61—48no—
343C22⋊D61—48no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—28no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—44no—
352C2×Dic61—42no—
353C2×Dic61—42no—
354C2×Dic61—42no—
355C2×Dic61—48no—
356C2×Dic61#13514yes—
357C2×Dic61C22×D412yes—
358C2×Dic61C22×D412yes—
359C2×Dic61C22×D412yes—
360C2×Dic61C22×D412yes—
361D244—22no—
362D244—22no—
363D244—42no—
364C4×D61—48no—
365Dic122—22no—
366Dic122—22no—
367Dic122—22no—
368Dic122—22no—
369Dic122—42no—
370Dic122—42no—
371C8×C61—22no—
372C8×C61—22no—
373#92418—22no—
374#92418—22no—
375C2×#3212—611nomaximal, Sylow
376C22×C61—22no—
377C22×C61—22no—
378C22×C61—22no—
379C22×C61—44no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61—42no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—84no—
387C22×C61—84no—
388C22×C61#53512yes—
389C22×C61C2×#13512yes—
390C22×C61#57512yes—
391C22×C61C23×D411yescharacteristic
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—84no—
396C4×C61—22no—
397C4×C61—42no—
398C4×C61—42no—
399C4×C61#53512yes—
400C4×C61C2×H(5,𝔽2)11yescharacteristic
401C4×C61C2×H(5,𝔽2)11yescharacteristic
402Dic61—22no—
403Dic61—22no—
404Dic61—22no—
405Dic61—42no—
406Dic61—42no—
407Dic61—42no—
408Dic61C2×#13514yes—
409C2×#532—611no—
410C2×#529—611no—
411#3212—6116no—
412C2×#495—611no—
413C2×#495—611no—
414C2×#488—611no—
415C2×#488—611no—
416C2×#462—611no—
417C2×#460—611no—
418C2×#461—611no—
419C2×#459—611no—
420C2×#452—611no—
421C2×#452—611no—
422C2×#449—611no—
423C2×#449D6111yescharacteristic, complemented
424C2×#431—611no—
425C2×C61—42no—
426C2×C61—82no—
427C2×C61—82no—
428C2×C61#321214yescomplemented
429C2×C61C2×#53511yescharacteristic
430C2×C61C22×#13511yescharacteristic
431C2×C61C2×#57511yescharacteristic
432D61—82no—
433C22×#41—611no—
434C22×#41C2×D6111yescharacteristic
435C22×Q16—611no—
436C22×Q16—611no—
437C22×SD16—611no—
438C22×SD16—611no—
439C22×SD16—611no—
440C22×SD16C2×D6111yescharacteristic
441C22×D8—611no—
442C22×D8C2×D6111yescharacteristic
443#532—618no—
444#532—1224no—
445C2×C4⋊Q8—611no—
446C2×#127—611no—
447#529—618no—
448#529—1224no—
449C2×#126—1221no—
450C2×#125—611no—
451C2×#124—611no—
452C2×#124—611no—
453C2×#124—611no—
454C2×#123—1221no—
455C2×C22⋊Q8—611no—
456C2×#121—1221no—
457C2×#121—1221no—
458C2×#121C2×D6111yescharacteristic
459C2×C4×Q8—611no—
460C2×C4×D4—611no—
461C2×C4×D4—1221no—
462C2×C4×D4—1221no—
463C2×C4×D4—1221no—
464C2×#117—1221no—
465C22×C42—611no—
466#495—618no—
467#495—618no—
468#488—618no—
469#488—618no—
470#462—618no—
471#461—618no—
472#460—618no—
473#459—618no—
474#452—618no—
475#452—618no—
476#449—618no—
477#449C2×D6118yescomplemented
478#431—618no—
479C2×C4⋊C8—611no—
480C2×C4⋊C8—611no—
481C2×#103—611no—
482C2×#103—611no—
483C2×#103—611no—
484C2×#103C2×D6111yescharacteristic
485C2×#102—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102C2×D6111yescharacteristic
489C2×C22⋊C8—611no—
490C2×C22⋊C8C2×D6111yescharacteristic
491C2×C4×C8—611no—
492C2×C4×C8—611no—
493C61C2×#321211yescharacteristic, complemented, Sylow
494C2×#41—22no—
495C2×#41—42no—
496C2×#41—42no—
497C2×#41—614no—
498C2×#41—1222no—
499C2×#41—2442no—
500C2×#41—2442no—
501C2×#41C22×D6114yes—
502C22×Q8—611no—
503C22×Q8—611no—
504C22×Q8C22×D6111yescharacteristic
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—611no—
508C22×D4—1221no—
509C22×D4—1221no—
510C22×D4—1221no—
511C22×D4C22×D6111yescharacteristic
512C22×D4C22×D6111yescharacteristic
513C23×C4—21no—
514C23×C4—611no—
515C23×C4—611no—
516C23×C4—1221no—
517C23×C4—1221no—
518C23×C4C22×D6111yescharacteristic
519C2×Q16—614no—
520C2×Q16—614no—
521C2×Q16—2442no—
522C2×Q16—2442no—
523C2×SD16—42no—
524C2×SD16—614no—
525C2×SD16—614no—
526C2×SD16—614no—
527C2×SD16—2442no—
528C2×SD16—2442no—
529C2×SD16—2442no—
530C2×SD16C22×D6114yes—
531C2×D8—42no—
532C2×D8—614no—
533C2×D8—2442no—
534C2×D8C22×D6114yes—
535C22×C8—611no—
536C22×C8—611no—
537C22×C8C22×D6111yescharacteristic
538C22×C8C22×D6111yescharacteristic
539C4⋊Q8—614no—
540C4⋊Q8—1222no—
541#127—614no—
542#127—1222no—
543#126—1228no—
544#125—614no—
545#125—1222no—
546#124—614no—
547#124—614no—
548#124—614no—
549#124—1222no—
550#124—1222no—
551#124—1222no—
552#123—1228no—
553C22⋊Q8—614no—
554C22⋊Q8—1222no—
555#121—22no—
556#121—1228no—
557#121—1228no—
558#121C22×D6114yes—
559C4×Q8—614no—
560C4×Q8—1222no—
561C4×D4—614no—
562C4×D4—1228no—
563C4×D4—1228no—
564C4×D4—1222no—
565C4×D4—1228no—
566#117—1228no—
567C2×C4⋊C4—611no—
568C2×C4⋊C4—1221no—
569C2×C4⋊C4—1221no—
570C2×C4⋊C4—1221no—
571C2×C4⋊C4—1221no—
572C2×C4⋊C4—1221no—
573C2×C4⋊C4—1221no—
574C2×C4⋊C4C22×D6111yescharacteristic
575C2×C22⋊C4—21no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4—1221no—
580C2×C22⋊C4—1221no—
581C2×C22⋊C4—1221no—
582C2×C22⋊C4—1221no—
583C2×C22⋊C4—1221no—
584C2×C42—611no—
585C2×C42—611no—
586C2×C42—614no—
587C2×C42—611no—
588C2×C42—611no—
589C2×C42—614no—
590C2×C42—1221no—
591C4⋊C8—614no—
592C4⋊C8—614no—
593#103—614no—
594#103—614no—
595#103—614no—
596#103C22×D6114yes—
597#102—614no—
598#102—614no—
599#102—614no—
600#102C22×D6114yes—
601C22⋊C8—614no—
602C22⋊C8C22×D6114yes—
603C4×C8—614no—
604C4×C8—614no—
605C24—21no—
606C24—21no—
607C24—1221no—
608C24D4×D6111yescharacteristic
609#41—44no—
610#41—44no—
611#41—48no—
612#41—2444no—
613#41—2444no—
614#41—2448no—
615C2×Q8—21no—
616C2×Q8—22no—
617C2×Q8—22no—
618C2×Q8—612no—
619C2×Q8—612no—
620C2×Q8—1221no—
621C2×Q8—1221no—
622C2×Q8—1222no—
623C2×Q8—1222no—
624C2×Q8—1222no—
625C2×Q8—1222no—
626C2×Q8C23×D6112yes—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—44no—
636C2×D4—44no—
637C2×D4—612no—
638C2×D4—1224no—
639C2×D4—1224no—
640C2×D4—1224no—
641C2×D4—1221no—
642C2×D4—1222no—
643C2×D4—1222no—
644C2×D4—2444no—
645C2×D4—2444no—
646C2×D4—2444no—
647C2×D4C23×D6112yes—
648C2×D4C23×D6112yes—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—24no—
654C22×C4—44no—
655C22×C4—611no—
656C22×C4—614no—
657C22×C4—611no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—614no—
661C22×C4—1224no—
662C22×C4—1224no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1224no—
667C22×C4—2444no—
668C22×C4—2444no—
669C22×C4—2442no—
670C22×C4D4×D6112yes—
671C22×C4D4×D6111yescharacteristic
672C22×C4C23×D6112yes—
673C22×C4C23×D6111yescharacteristic
674Q16—2444no—
675Q16—2444no—
676SD16—44no—
677SD16—2444no—
678SD16—2444no—
679SD16—2444no—
680D8—44no—
681D8—2444no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—612no—
685C2×C8—612no—
686C2×C8—1222no—
687C2×C8—1222no—
688C2×C8C23×D6112yes—
689C2×C8C23×D6112yes—
690C4⋊C4—21no—
691C4⋊C4—612no—
692C4⋊C4—1224no—
693C4⋊C4—1224no—
694C4⋊C4—1224no—
695C4⋊C4—1224no—
696C4⋊C4—1224no—
697C4⋊C4—1221no—
698C4⋊C4—1224no—
699C4⋊C4C23×D6112yes—
700C22⋊C4—24no—
701C22⋊C4—1224no—
702C22⋊C4—1224no—
703C22⋊C4—1224no—
704C22⋊C4—1224no—
705C22⋊C4—1224no—
706C22⋊C4—1224no—
707C22⋊C4—1224no—
708C22⋊C4—1224no—
709C42—614no—
710C42—614no—
711C42—612no—
712C42—612no—
713C42—612no—
714C42—612no—
715C42—1224no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—1222no—
728C23—2442no—
729C23—2442no—
730C23—2442no—
731C23C2×D4×D6112yes—
732C23C2×D4×D6111yescharacteristic
733Q8—22no—
734Q8—22no—
735Q8—42no—
736Q8—1222no—
737Q8—1222no—
738Q8—1222no—
739Q8—1222no—
740Q8—2442no—
741Q8—2442no—
742D4—22no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—48no—
747D4—48no—
748D4—42no—
749D4—42no—
750D4—1222no—
751D4—1222no—
752D4—2448no—
753D4—2448no—
754D4—2448no—
755D4—2442no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—48no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—614no—
766C2×C4—612no—
767C2×C4—612no—
768C2×C4—612no—
769C2×C4—612no—
770C2×C4—1228no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—2448no—
778C2×C4—2448no—
779C2×C4—2444no—
780C2×C4—2442no—
781C2×C4—2442no—
782C2×C4—2442no—
783C2×C4C2×D4×D6112yes—
784C2×C4C2×D4×D6111yescharacteristic
785C2×C4#1451982212yes—
786C2×C4#1451982212yes—
787C2×C4C24×D6111yescharacteristic
788C8—22no—
789C8—22no—
790C8—1222no—
791C8—1222no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—44no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—84no—
803C22—84no—
804C22—4884no—
805C22—2442no—
806C22—2442no—
807C22—2442no—
808C22#1684032712yes—
809C22#135×D6112yes—
810C22#1684055812yes—
811C22C22×D4×D6111yescharacteristic
812C4—22no—
813C4—42no—
814C4—42no—
815C4—614no—
816C4—1222no—
817C4—1222no—
818C4—1222no—
819C4—2442no—
820C4—2442no—
821C4—2442no—
822C4#1684032712yes—
823C4C2×#1451982211yescharacteristic
824C4C2×#1451982211yescharacteristic
825C2—42no—
826C2—82no—
827C2—82no—
828C2—4882no—
829C2#2145679214yesdirect product factor
830C2C2×#1684032711yescharacteristic
831C2C2×#135×D6111yescharacteristic
832C2C2×#1684055811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#449C2
socleC23×C61C22×D4
hypercenterC2×#449D61
hypocenterC61C2×#3212
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#16840308C2semidirect
2. C2×#16840293C2semidirect
3. #21456792C2direct (N × H)
4. C2×#16840145C2semidirect
5. C2×#16840143C2semidirect
6. C2×#16840118C2semidirect
7. C2×#16840115C2semidirect
8. C2×#16839971C2semidirect
9. C2×#16839961C2semidirect
10. C2×#16839965C2semidirect
11. C2×#16839955C2semidirect
12. C2×#16839926C2semidirect
13. C2×#16839924C2semidirect
14. C2×#16839905C2semidirect
15. C2×#16839812C2semidirect
16. C2×C61×#449C2semidirect
25. #16840308C22semidirect
29. #16840293C22semidirect
46. #16840145C22semidirect
47. #16840143C22semidirect
48. #16840118C22semidirect
49. #16840115C22semidirect
50. #16839971C22semidirect
51. #16839965C22semidirect
52. #16839961C22semidirect
53. #16839955C22semidirect
54. #16839926C22semidirect
55. #16839924C22semidirect
56. #16839905C22semidirect
57. #16839812C22semidirect
73. C61×#449C22semidirect
423. C2×#449D61semidirect
428. C2×C61#3212semidirect
477. #449C2×D61semidirect
493. C61C2×#3212semidirect
829. C2#21456792direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403082
C2×#168402932
#214567922
C2×#168401452
C2×#168401432
C2×#168401182
C2×#168401152
C2×#168399712
C2×#168399612
C2×#168399652
C2×#168399552
C2×#168399262
C2×#168399242
C2×#168399052
C2×#168398122
C2×C61×#4492
C2×#321261