Finite Group Databasebeta

← C2×#21456779 #30551180

Subgroups — C2×#21456779 #30551180

Order 15616.

2294 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840291C211yesmaximal, characteristic, complemented
2C2×#124×D61C211yesmaximal, characteristic, complemented
3#21456779C2116yesmaximal, direct product factor
4C2×#16840144C211yesmaximal, characteristic, complemented
5C2×#16840117C211yesmaximal, characteristic, complemented
6C2×#16840116C211yesmaximal, characteristic, complemented
7C2×#16839986C211yesmaximal, characteristic, complemented
8C2×#16839982C211yesmaximal, characteristic, complemented
9C2×#16839979C211yesmaximal, characteristic, complemented
10C2×#16839975C211yesmaximal, characteristic, complemented
11C2×#16839916C211yesmaximal, characteristic, complemented
12C2×#16839899C211yesmaximal, characteristic, complemented
13C2×#16839911C211yesmaximal, characteristic, complemented
14C2×#16839894C211yesmaximal, characteristic
15C2×#16839813C211yesmaximal, characteristic, complemented
16C2×C61×#495C211yesmaximal, characteristic, complemented
17C22×Q8×D61C2211yescharacteristic
18C22×D4×D61C2211yescharacteristic
19C22×#11758202C2211yescharacteristic, complemented
20C22×#11758200C2211yescharacteristic, complemented
21C22×#11758201C2211yescharacteristic
22C22×#11758199C2211yescharacteristic
23#16840291—24no—
24#16840291C2218yescomplemented
25C2×#14519770—21no—
26C2×#14519769C2211yescharacteristic, complemented
27C2×#14519766C2211yescharacteristic
28C2×#14519765C2211yescharacteristic
29C2×#14519764C2211yescharacteristic
30C2×#14519763—21no—
31C2×#14519763—21no—
32#124×D61—24no—
33#124×D61C2218yescomplemented
34C2×#14519759—21no—
35C2×#14519753C2211yescharacteristic
36C2×#14519748C2211yescharacteristic
37C2×Q8×Dic61C2211yescharacteristic, complemented
38C2×D4×Dic61C2211yescharacteristic, complemented
39C2×#14519737—21no—
40C2×#14519733—21no—
41C2×C22⋊C4×D61—21no—
42C2×C22⋊C4×D61—21no—
43C2×C42×D61C2211yescharacteristic
44#16840144C2218yescomplemented
45#16840117C2218yescomplemented
46#16840116C2218yescomplemented
47#16839986C2218yescomplemented
48#16839982C2218yescomplemented
49#16839979C2218yescomplemented
50#16839975C2218yescomplemented
51#16839916C2218yescomplemented
52#16839911C2218yescomplemented
53#16839899C2218yescomplemented
54#16839894C2218yes—
55#16839813C2218yescomplemented
56C2×#14519706C2211yescharacteristic, complemented
57C2×#14519706C2211yescharacteristic, complemented
58C2×#14519702C2211yescharacteristic, complemented
59C2×#14519702C2211yescharacteristic, complemented
60C2×#14519701C2211yescharacteristic, complemented
61C2×#14519701C2211yescharacteristic, complemented
62C2×#14519699C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C4×#92418C2211yescharacteristic, complemented
69C22×Q16×C61C2211yescharacteristic, complemented
70C22×SD16×C61C2211yescharacteristic
71C22×SD16×C61C2211yescharacteristic, complemented
72C22×D8×C61C2211yescharacteristic
73C2×#124×C61C2211yescharacteristic
74C2×#124×C61C2211yescharacteristic, complemented
75C61×#495C2218yescomplemented
76C2×C4×C8×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C22×Dic122—21no—
79C22×Dic122C2311yescharacteristic
80C2×Q8×D61—22no—
81C2×Q8×D61—42no—
82C2×Q8×D61—42no—
83C2×Q8×D61C2314yes—
84C22×D244C2311yescharacteristic
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C2×D4×D61—22no—
88C2×D4×D61—42no—
89C2×D4×D61—42no—
90C2×D4×D61C2314yes—
91C23×Dic61—21no—
92C22×C4×D61—21no—
93C22×C4×D61D411yescharacteristic
94C22×C4×D61D411yescharacteristic
95C22×C4×D61C2311yescharacteristic
96C2×#11758202—42no—
97C2×#11758202C2314yescomplemented
98C2×#11758200—42no—
99C2×#11758200C2314yescomplemented
100C2×#11758201—42no—
101C2×#11758201C2314yes—
102C2×#11758199—42no—
103C2×#11758199C2314yes—
104C22×#92418C2311yescharacteristic
105C22×#92418C2311yescharacteristic
106#14519770—28no—
107#14519769—22no—
108#14519769C2314yescomplemented
109#14519766—22no—
110#14519766C2314yes—
111#14519765—22no—
112#14519765C2314yes—
113#14519764—22no—
114#14519764C2314yes—
115#14519763—28no—
116#14519763—28no—
117#14519759—28no—
118#14519753—22no—
119#14519753C2314yes—
120#14519748—22no—
121#14519748C2314yes—
122Q8×Dic61—22no—
123Q8×Dic61C2314yescomplemented
124D4×Dic61—22no—
125D4×Dic61C2314yescomplemented
126#14519737—28no—
127#14519733—28no—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61C2311yescharacteristic
130C2×C4⋊Dic61C2311yescharacteristic
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×C22⋊Dic61—21no—
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C22⋊C4×D61—28no—
144C22⋊C4×D61—28no—
145C2×C4×Dic61—21no—
146C2×C4×Dic61D411yescharacteristic
147C2×C4×Dic61D411yescharacteristic
148C2×C4×Dic61C2311yescharacteristic
149C42×D61D414yes—
150C42×D61C2314yes—
151#14519706C2314yescomplemented
152#14519706C2314yescomplemented
153#14519702C2314yescomplemented
154#14519702C2314yescomplemented
155#14519701C2314yescomplemented
156#14519701C2314yescomplemented
157#14519699C2314yes—
158#14519699C2314yes—
159#14519698C2314yes—
160#14519698C2314yes—
161#14519689C2314yes—
162#14519689C2314yes—
163C4×#92418C2314yescomplemented
164C22×Q8×C61C2311yescharacteristic
165C22×Q8×C61C2311yescharacteristic
166C22×D4×C61C2311yescharacteristic
167C22×D4×C61C2311yescharacteristic
168C2×Q16×C61—42no—
169C2×Q16×C61C2314yescomplemented
170C2×SD16×C61—42no—
171C2×SD16×C61—42no—
172C2×SD16×C61C2314yes—
173C2×SD16×C61C2314yescomplemented
174C2×D8×C61—42no—
175C2×D8×C61C2314yes—
176C22×C8×C61C2311yescharacteristic
177C22×C8×C61C2311yescharacteristic
178#124×C61—22no—
179#124×C61—22no—
180#124×C61C2314yes—
181#124×C61C2314yescomplemented
182C2×C22⋊C4×C61—21no—
183C2×C22⋊C4×C61—21no—
184C2×C22⋊C4×C61—21no—
185C2×C22⋊C4×C61—21no—
186C2×C42×C61C2311yescharacteristic
187C4×C8×C61C2314yescomplemented
188C24×C61—21no—
189C24×C61—21no—
190C23×D61—21no—
191C23×D61—24no—
192C23×D61—44no—
193C23×D61—44no—
194C23×D61—44no—
195C23×D61C2×D411yescharacteristic
196C2×Q8×C61—21no—
197C2×Q8×C61—21no—
198C2×Q8×C61—22no—
199C2×Q8×C61—22no—
200C2×Q8×C61—22no—
201C2×Q8×C61—22no—
202C2×Q8×C61C2412yes—
203C2×Q8×C61C2412yes—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—22no—
207C2×D4×C61—22no—
208C2×D4×C61—22no—
209C2×D4×C61—22no—
210C2×D4×C61C2412yes—
211C2×D4×C61C2412yes—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2411yescharacteristic
217C2×C22⋊D61—24no—
218C2×C22⋊D61—24no—
219C2×C22⋊D61—44no—
220C2×C22⋊D61—44no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—24no—
225C22×Dic61—44no—
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229Q8×D61—44no—
230Q8×D61—44no—
231Q8×D61—48no—
232D4×D61—44no—
233D4×D61—44no—
234D4×D61—48no—
235C2×D244—22no—
236C2×D244—22no—
237C2×D244—21no—
238C2×D244C2412yes—
239C2×C4×D61—24no—
240C2×C4×D61—22no—
241C2×C4×D61—22no—
242C2×C4×D61—24no—
243C2×C4×D61—42no—
244C2×C4×D61—44no—
245C2×C4×D61C2×D414yes—
246C2×C4×D61C2×D412yes—
247C2×C4×D61C2×D414yes—
248C2×C4×D61C2412yes—
249C2×Dic122—22no—
250C2×Dic122—22no—
251C2×Dic122—21no—
252C2×Dic122—24no—
253C2×Dic122—44no—
254C2×Dic122C2412yes—
255Q16×C61—44no—
256SD16×C61—44no—
257SD16×C61—44no—
258D8×C61—44no—
259C2×C8×C61—22no—
260C2×C8×C61—22no—
261C2×C8×C61C2412yes—
262C2×C8×C61C2412yes—
263C22⋊C4×C61—24no—
264C22⋊C4×C61—24no—
265C22⋊C4×C61—24no—
266C22⋊C4×C61—24no—
267C42×C61C2×D412yes—
268C42×C61C2412yes—
269C22⋊Dic61—24no—
270C22⋊Dic61—24no—
271C22⋊Dic61—24no—
272C22⋊Dic61—24no—
273#11758202—44no—
274#11758201—44no—
275#11758200—44no—
276#11758199—44no—
277#11758198—24no—
278#11758198—24no—
279#11758198—24no—
280#11758198—24no—
281#11758198—24no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61—24no—
285C4⋊Dic61C2412yes—
286C4⋊Dic61C2412yes—
287#11758196—24no—
288#11758196—24no—
289#11758196—24no—
290C4×Dic61—24no—
291C4×Dic61C2×D412yes—
292C4×Dic61C2×D414yes—
293C4×Dic61C2×D414yes—
294C4×Dic61C2412yes—
295C2×#92418—22no—
296C2×#92418—22no—
297C2×#92418C2412yes—
298C2×#92418C2412yes—
299C23×C61—22no—
300C23×C61—22no—
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—22no—
311C22×D61—48no—
312C22×D61—48no—
313C22×D61—42no—
314C22×D61—42no—
315C22×D61—42no—
316C22×D61—48no—
317C22×D61—816no—
318C22×D61#13514yes—
319C22×D61C22×D412yes—
320Q8×C61—22no—
321Q8×C61—22no—
322Q8×C61—22no—
323Q8×C61—22no—
324Q8×C61—42no—
325Q8×C61—42no—
326D4×C61—22no—
327D4×C61—22no—
328D4×C61—22no—
329D4×C61—22no—
330D4×C61—42no—
331D4×C61—42no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—42no—
337C2×C4×C61—42no—
338C2×C4×C61C22×D412yes—
339C2×C4×C61C22×D412yes—
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61H(5,𝔽2)12yes—
342C2×C4×C61H(5,𝔽2)12yes—
343C2×C4×C61C2511yescharacteristic
344C22⋊D61—48no—
345C22⋊D61—48no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—48no—
353C2×Dic61—42no—
354C2×Dic61—42no—
355C2×Dic61—42no—
356C2×Dic61C22×D412yes—
357C2×Dic61C22×D412yes—
358C2×Dic61C22×D412yes—
359D244—22no—
360D244—22no—
361D244—42no—
362C4×D61—28no—
363C4×D61—24no—
364C4×D61—22no—
365C4×D61—22no—
366C4×D61—44no—
367C4×D61—48no—
368Dic122—22no—
369Dic122—22no—
370Dic122—48no—
371Dic122—42no—
372C8×C61—22no—
373C8×C61—22no—
374#92418—22no—
375#92418—22no—
376C2×#3211—611nomaximal, Sylow
377C22×C61—42no—
378C22×C61—42no—
379C22×C61—42no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61—42no—
383C22×C61—84no—
384C22×C61—84no—
385C22×C61#53512yes—
386C22×C61C2×#13512yes—
387C22×C61#57512yes—
388C22×C61C23×D411yescharacteristic
389C2×D61—22no—
390C2×D61—28no—
391C2×D61—22no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—816no—
396C2×D61—84no—
397C2×D61C2×#13514yes—
398C4×C61—22no—
399C4×C61—22no—
400C4×C61—42no—
401C4×C61—42no—
402C4×C61#53512yes—
403C4×C61C2×H(5,𝔽2)11yescharacteristic
404C4×C61C2×H(5,𝔽2)11yescharacteristic
405Dic61—22no—
406Dic61—22no—
407Dic61—22no—
408Dic61—42no—
409Dic61—42no—
410Dic61—42no—
411C2×#529—611no—
412C22×#124—611no—
413#3211—6116no—
414C2×#495—611no—
415C2×#495D6111yescharacteristic, complemented
416C2×#488—611no—
417C2×#488—611no—
418C2×#464—611no—
419C2×#464—611no—
420C2×#463—611no—
421C2×#463—611no—
422C2×#451—611no—
423C2×#448—611no—
424C2×#450—611no—
425C2×#447—611no—
426C2×#431—611no—
427C2×C61—82no—
428C2×C61—82no—
429C2×C61#321114yescomplemented
430C2×C61C2×#53511yescharacteristic
431C2×C61C22×#13511yescharacteristic
432C2×C61C2×#57511yescharacteristic
433D61—24no—
434D61—82no—
435C23×Q8—611no—
436C23×D4—611no—
437C22×Q16—611no—
438C22×Q16C2×D6111yescharacteristic, complemented
439C22×SD16—611no—
440C22×SD16—611no—
441C22×SD16C2×D6111yescharacteristic
442C22×SD16C2×D6111yescharacteristic, complemented
443C22×D8—611no—
444C22×D8C2×D6111yescharacteristic
445#529—618no—
446#529—1224no—
447C2×#126—1221no—
448C2×#125—611no—
449C2×#124—611no—
450C2×#124—611no—
451C2×#124—618no—
452C2×#124—611no—
453C2×#124—1221no—
454C2×#124—1221no—
455C2×#124—1224no—
456C2×#124C2×D6111yescharacteristic
457C2×#124C2×D6111yescharacteristic, complemented
458C2×#123—1221no—
459C2×C22⋊Q8—611no—
460C2×#121—611no—
461C2×C4×Q8—611no—
462C2×C4×D4—611no—
463C2×C4×D4—1221no—
464C2×#117—1221no—
465C22×C22⋊C4—1221no—
466C22×C22⋊C4—1221no—
467C22×C42—611no—
468#495—618no—
469#495C2×D6118yescomplemented
470#488—618no—
471#488—618no—
472#464—618no—
473#464—618no—
474#463—618no—
475#463—618no—
476#451—618no—
477#450—618no—
478#448—618no—
479#447—618no—
480#431—618no—
481C2×C4⋊C8—611no—
482C2×C4⋊C8—611no—
483C2×#103—611no—
484C2×#103—611no—
485C2×#103—611no—
486C2×#103—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×C22⋊C8—611no—
492C2×C22⋊C8—611no—
493C2×C4×C8—611no—
494C2×C4×C8C2×D6111yescharacteristic, complemented
495C61C2×#321111yescharacteristic, complemented, Sylow
496C25—1221no—
497C22×Q8—614no—
498C22×Q8—611no—
499C22×Q8—1221no—
500C22×Q8—1222no—
501C22×Q8—2442no—
502C22×Q8—2442no—
503C22×Q8C22×D6111yescharacteristic
504C22×Q8C22×D6111yescharacteristic
505C22×D4—614no—
506C22×D4—611no—
507C22×D4—1222no—
508C22×D4—1221no—
509C22×D4—1221no—
510C22×D4—2442no—
511C22×D4—2442no—
512C22×D4C22×D6111yescharacteristic
513C22×D4C22×D6111yescharacteristic
514C23×C4—611no—
515C23×C4—611no—
516C23×C4—611no—
517C23×C4—1221no—
518C23×C4—1221no—
519C2×Q16—42no—
520C2×Q16—614no—
521C2×Q16—2442no—
522C2×Q16C22×D6114yescomplemented
523C2×SD16—42no—
524C2×SD16—42no—
525C2×SD16—614no—
526C2×SD16—614no—
527C2×SD16—2442no—
528C2×SD16—2442no—
529C2×SD16C22×D6114yes—
530C2×SD16C22×D6114yescomplemented
531C2×D8—42no—
532C2×D8—614no—
533C2×D8—2442no—
534C2×D8C22×D6114yes—
535C22×C8—611no—
536C22×C8—611no—
537C22×C8C22×D6111yescharacteristic
538C22×C8C22×D6111yescharacteristic
539#126—1228no—
540#125—614no—
541#125—1222no—
542#124—22no—
543#124—22no—
544#124—614no—
545#124—614no—
546#124—614no—
547#124—1228no—
548#124—1228no—
549#124—1222no—
550#124—1222no—
551#124—1222no—
552#124C22×D6114yes—
553#124C22×D6114yescomplemented
554#123—1228no—
555C22⋊Q8—614no—
556C22⋊Q8—1222no—
557#121—614no—
558#121—1222no—
559C4×Q8—614no—
560C4×Q8—1222no—
561C4×D4—614no—
562C4×D4—1222no—
563C4×D4—1228no—
564#117—1228no—
565C2×C4⋊C4—611no—
566C2×C4⋊C4—611no—
567C2×C4⋊C4—1221no—
568C2×C4⋊C4—1221no—
569C2×C4⋊C4—1221no—
570C2×C4⋊C4—1221no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—1228no—
576C2×C22⋊C4—1228no—
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×C22⋊C4—1221no—
585C2×C22⋊C4—1221no—
586C2×C42—611no—
587C2×C42—611no—
588C2×C42—611no—
589C2×C42—614no—
590C2×C42—614no—
591C2×C42—1221no—
592C2×C42C22×D6111yescharacteristic
593C4⋊C8—614no—
594C4⋊C8—614no—
595#103—614no—
596#103—614no—
597#103—614no—
598#103—614no—
599#102—614no—
600#102—614no—
601#102—614no—
602#102—614no—
603C22⋊C8—614no—
604C22⋊C8—614no—
605C4×C8—614no—
606C4×C8C22×D6114yescomplemented
607C24—21no—
608C24—21no—
609C24—611no—
610C24—1224no—
611C24—1221no—
612C24—2444no—
613C24—2444no—
614C24—2444no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—22no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8—22no—
621C2×Q8—612no—
622C2×Q8—1224no—
623C2×Q8—1221no—
624C2×Q8—1222no—
625C2×Q8—1222no—
626C2×Q8—2444no—
627C2×Q8—2444no—
628C2×Q8—2444no—
629C2×Q8—2448no—
630C2×Q8C23×D6112yes—
631C2×Q8C23×D6112yes—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—22no—
637C2×D4—22no—
638C2×D4—612no—
639C2×D4—1224no—
640C2×D4—1224no—
641C2×D4—1221no—
642C2×D4—1222no—
643C2×D4—1222no—
644C2×D4—2444no—
645C2×D4—2444no—
646C2×D4—2448no—
647C2×D4—2444no—
648C2×D4—2444no—
649C2×D4C23×D6112yes—
650C2×D4C23×D6112yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—611no—
654C22×C4—611no—
655C22×C4—611no—
656C22×C4—614no—
657C22×C4—612no—
658C22×C4—612no—
659C22×C4—614no—
660C22×C4—1224no—
661C22×C4—1224no—
662C22×C4—1224no—
663C22×C4—1222no—
664C22×C4—1222no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—2442no—
669C22×C4—2444no—
670C22×C4—2444no—
671C22×C4D4×D6111yescharacteristic
672C22×C4D4×D6111yescharacteristic
673C22×C4C23×D6111yescharacteristic
674Q16—44no—
675Q16—2444no—
676SD16—44no—
677SD16—44no—
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—612no—
691C4⋊C4—612no—
692C4⋊C4—1224no—
693C4⋊C4—1224no—
694C4⋊C4—1221no—
695C4⋊C4—1221no—
696C4⋊C4—1224no—
697C4⋊C4—1224no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—1224no—
703C22⋊C4—1224no—
704C22⋊C4—1224no—
705C22⋊C4—1224no—
706C22⋊C4—1224no—
707C22⋊C4—1224no—
708C22⋊C4—1224no—
709C22⋊C4—1224no—
710C22⋊C4—1224no—
711C42—614no—
712C42—612no—
713C42—614no—
714C42—612no—
715C42—1224no—
716C42D4×D6112yes—
717C42C23×D6112yes—
718C23—22no—
719C23—22no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—614no—
727C23—612no—
728C23—1222no—
729C23—1222no—
730C23—1222no—
731C23—48816no—
732C23—2448no—
733C23—2448no—
734C23—2448no—
735C23—2442no—
736C23—2442no—
737C23—2442no—
738C23C2×D4×D6111yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—22no—
742Q8—22no—
743Q8—42no—
744Q8—42no—
745Q8—1222no—
746Q8—1222no—
747Q8—2448no—
748Q8—2442no—
749D4—22no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—42no—
754D4—42no—
755D4—1222no—
756D4—1222no—
757D4—2448no—
758D4—2448no—
759D4—2442no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—612no—
767C2×C4—612no—
768C2×C4—612no—
769C2×C4—1228no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1224no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—2444no—
780C2×C4—2448no—
781C2×C4—2448no—
782C2×C4—2442no—
783C2×C4—2442no—
784C2×C4—2442no—
785C2×C4C2×D4×D6112yes—
786C2×C4C2×D4×D6112yes—
787C2×C4C2×D4×D6111yescharacteristic
788C2×C4#1451982212yes—
789C2×C4#1451982212yes—
790C2×C4C24×D6111yescharacteristic
791C8—22no—
792C8—22no—
793C8—1222no—
794C8—1222no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—84no—
802C22—84no—
803C22—614no—
804C22—1222no—
805C22—1228no—
806C22—1222no—
807C22—48816no—
808C22—4884no—
809C22—2442no—
810C22—2442no—
811C22—2442no—
812C22#1684032512yes—
813C22#135×D6112yes—
814C22#1684055912yes—
815C22C22×D4×D6111yescharacteristic
816C4—22no—
817C4—22no—
818C4—42no—
819C4—42no—
820C4—1222no—
821C4—1222no—
822C4—1222no—
823C4—2442no—
824C4—2442no—
825C4—2442no—
826C4#1684032512yes—
827C4C2×#1451982211yescharacteristic
828C4C2×#1451982211yescharacteristic
829C2—82no—
830C2—82no—
831C2—1224no—
832C2—4882no—
833C2#2145677914yesdirect product factor
834C2C2×#1684032511yescharacteristic
835C2C2×#135×D6111yescharacteristic
836C2C2×#1684055911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#495C2
socleC23×C61C22×D4
prime radicalC2×#16839894C2
hypercenterC2×#495D61
hypocenterC61C2×#3211
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#495

Complements

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

NH ≅ G/Ntype
1. C2×#16840291C2semidirect
2. C2×#124×D61C2semidirect
3. #21456779C2direct (N × H)
4. C2×#16840144C2semidirect
5. C2×#16840117C2semidirect
6. C2×#16840116C2semidirect
7. C2×#16839986C2semidirect
8. C2×#16839982C2semidirect
9. C2×#16839979C2semidirect
10. C2×#16839975C2semidirect
11. C2×#16839916C2semidirect
12. C2×#16839899C2semidirect
13. C2×#16839911C2semidirect
15. C2×#16839813C2semidirect
16. C2×C61×#495C2semidirect
19. C22×#11758202C22semidirect
20. C22×#11758200C22semidirect
24. #16840291C22semidirect
26. C2×#14519769C22semidirect
33. #124×D61C22semidirect
37. C2×Q8×Dic61C22semidirect
38. C2×D4×Dic61C22semidirect
44. #16840144C22semidirect
45. #16840117C22semidirect
46. #16840116C22semidirect
47. #16839986C22semidirect
48. #16839982C22semidirect
49. #16839979C22semidirect
50. #16839975C22semidirect
51. #16839916C22semidirect
52. #16839911C22semidirect
53. #16839899C22semidirect
55. #16839813C22semidirect
56. C2×#14519706C22semidirect
57. C2×#14519706C22semidirect
58. C2×#14519702C22semidirect
59. C2×#14519702C22semidirect
60. C2×#14519701C22semidirect
61. C2×#14519701C22semidirect
68. C2×C4×#92418C22semidirect
69. C22×Q16×C61C22semidirect
71. C22×SD16×C61C22semidirect
74. C2×#124×C61C22semidirect
75. C61×#495C22semidirect
76. C2×C4×C8×C61C22semidirect
97. C2×#11758202C23semidirect
99. C2×#11758200C23semidirect
108. #14519769C23semidirect
123. Q8×Dic61C23semidirect
125. D4×Dic61C23semidirect
151. #14519706C23semidirect
152. #14519706C23semidirect
153. #14519702C23semidirect
154. #14519702C23semidirect
155. #14519701C23semidirect
156. #14519701C23semidirect
163. C4×#92418C23semidirect
169. C2×Q16×C61C23semidirect
173. C2×SD16×C61C23semidirect
181. #124×C61C23semidirect
187. C4×C8×C61C23semidirect
415. C2×#495D61semidirect
429. C2×C61#3211semidirect
438. C22×Q16C2×D61semidirect
442. C22×SD16C2×D61semidirect
457. C2×#124C2×D61semidirect
469. #495C2×D61semidirect
494. C2×C4×C8C2×D61semidirect
495. C61C2×#3211semidirect
522. C2×Q16C22×D61semidirect
530. C2×SD16C22×D61semidirect
553. #124C22×D61semidirect
606. C4×C8C22×D61semidirect
833. C2#21456779direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402912
C2×#124×D612
#214567792
C2×#168401442
C2×#168401172
C2×#168401162
C2×#168399862
C2×#168399822
C2×#168399792
C2×#168399752
C2×#168399162
C2×#168398992
C2×#168399112
C2×#168398942
C2×#168398132
C2×C61×#4952
C2×#321161