Finite Group Databasebeta

← C2×#21457837 #30556552

Subgroups — C2×#21457837 #30556552

Order 15616.

2578 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840450C211yesmaximal, characteristic, complemented
2C2×D4×D244C211yesmaximal, characteristic
3#21457837C2116yesmaximal, direct product factor
4C2×#16840128C211yesmaximal, characteristic, complemented
5C2×#16840088C211yesmaximal, characteristic, complemented
6C2×#16840077C211yesmaximal, characteristic, complemented
7C2×#16840009C211yesmaximal, characteristic, complemented
8C2×#16839992C211yesmaximal, characteristic, complemented
9C2×#16839963C211yesmaximal, characteristic, complemented
10C2×#16839914C211yesmaximal, characteristic, complemented
11C2×#16839914C211yesmaximal, characteristic, complemented
12C2×#16839862C211yesmaximal, characteristic, complemented
13C2×#16839832C211yesmaximal, characteristic, complemented
14C2×#16839765C211yesmaximal, characteristic, complemented
15C2×#102×D61C211yesmaximal, characteristic, complemented
16C2×C61×#478C211yesmaximal, characteristic, complemented
17C23×D244—21no—
18C22×D4×D61C2211yescharacteristic
19C22×D4×D61C2211yescharacteristic
20C22×#11758190C2211yescharacteristic, complemented
21C22×#11758190C2211yescharacteristic, complemented
22C22×#11758200C2211yescharacteristic
23C22×#11758189C2211yescharacteristic, complemented
24C22×C8×D61C2211yescharacteristic, complemented
25#16840450—24no—
26#16840450C2218yescomplemented
27D4×D244—24no—
28D4×D244C2218yes—
29C2×#14519774C2211yescharacteristic
30C2×#14519772—21no—
31C2×#14519768—21no—
32C2×#14519762—21no—
33C2×#14519757C2211yescharacteristic, complemented
34C2×#14519757C2211yescharacteristic, complemented
35C2×#14519752C2211yescharacteristic
36C2×#14519752C2211yescharacteristic
37C2×#14519751—21no—
38C2×#14519747—21no—
39C2×#14519747—21no—
40C2×C4×Dic122C2211yescharacteristic, complemented
41C2×C4×D244C2211yescharacteristic
42C2×#14519735—21no—
43C2×#14519735C2211yescharacteristic, complemented
44C2×C4⋊C4×D61C2211yescharacteristic, complemented
45#16840128C2218yescomplemented
46#16840088C2218yescomplemented
47#16840077C2218yescomplemented
48#16840009C2218yescomplemented
49#16839992C2218yescomplemented
50#16839963C2218yescomplemented
51#16839914C2218yescomplemented
52#16839914C2218yescomplemented
53#16839862C2218yescomplemented
54#16839832C2218yescomplemented
55C2×#14519710C2211yescharacteristic, complemented
56#16839765C2218yescomplemented
57C2×#14519700C2211yescharacteristic, complemented
58C2×#14519699C2211yescharacteristic, complemented
59C2×#14519699C2211yescharacteristic, complemented
60C2×#14519698C2211yescharacteristic
61C2×#14519697C2211yescharacteristic, complemented
62C2×#14519697C2211yescharacteristic, complemented
63C2×#14519697C2211yescharacteristic, complemented
64C2×#14519697C2211yescharacteristic, complemented
65#102×D61C2218yescomplemented
66C2×#14519689C2211yescharacteristic, complemented
67C2×#14519689C2211yescharacteristic, complemented
68C2×#14519688C2211yescharacteristic, complemented
69C2×#125×C61C2211yescharacteristic, complemented
70C2×C4×D4×C61C2211yescharacteristic
71C61×#478C2218yescomplemented
72C2×#107×C61C2211yescharacteristic, complemented
73C2×#106×C61C2211yescharacteristic, complemented
74C2×C4⋊C8×C61C2211yescharacteristic, complemented
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C24×D61—21no—
78C24×D61—21no—
79C22×Dic122C2311yescharacteristic
80C22×D244—21no—
81C22×D244—21no—
82C22×D244—21no—
83C22×D244—21no—
84C22×D244—28no—
85C22×D244—48no—
86C22×D244D411yescharacteristic
87C22×D244C2311yescharacteristic
88C22×D244C2311yescharacteristic
89C22×C22⋊D61—21no—
90C22×C22⋊D61—21no—
91C2×D4×D61—24no—
92C2×D4×D61—24no—
93C2×D4×D61—22no—
94C2×D4×D61—22no—
95C2×D4×D61—42no—
96C2×D4×D61—42no—
97C2×D4×D61C2314yes—
98C2×D4×D61C2314yes—
99C22×C4×D61—21no—
100C22×C4×D61C2311yescharacteristic
101C22×C4×D61C2311yescharacteristic
102C2×#11758190—42no—
103C2×#11758190—42no—
104C2×#11758190C2314yescomplemented
105C2×#11758190C2314yescomplemented
106C2×#11758200—24no—
107C2×#11758200C2314yes—
108C2×#11758189—42no—
109C2×#11758189C2314yescomplemented
110C22×#92418C2311yescharacteristic
111C22×#92418C2311yescharacteristic
112C2×C8×D61—42no—
113C2×C8×D61C2314yescomplemented
114#14519774—22no—
115#14519774C2314yes—
116#14519772—28no—
117#14519768—28no—
118#14519762—28no—
119#14519757—22no—
120#14519757—22no—
121#14519757C2314yescomplemented
122#14519757C2314yescomplemented
123#14519752—22no—
124#14519752—22no—
125#14519752C2314yes—
126#14519752C2314yes—
127#14519751—28no—
128#14519747—28no—
129#14519747—28no—
130C4×Dic122—22no—
131C4×Dic122C2314yescomplemented
132C4×D244D414yes—
133C4×D244C2314yes—
134#14519735—22no—
135#14519735—28no—
136#14519735C2314yescomplemented
137C2×C4⋊Dic61—21no—
138C2×C4⋊Dic61—21no—
139C2×C4⋊Dic61D411yescharacteristic
140C2×C4⋊Dic61C2311yescharacteristic
141C2×#11758196—21no—
142C2×#11758196—21no—
143C4⋊C4×D61—22no—
144C4⋊C4×D61C2314yescomplemented
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×#11758198D411yescharacteristic
151C2×#11758198D411yescharacteristic
152C2×C4×Dic61—21no—
153C2×C4×Dic61—21no—
154#14519710C2314yescomplemented
155#14519700C2314yescomplemented
156#14519699C2314yescomplemented
157#14519699C2314yescomplemented
158#14519698C2314yes—
159#14519697C2314yescomplemented
160#14519697C2314yescomplemented
161#14519697C2314yescomplemented
162#14519697C2314yescomplemented
163#14519689C2314yescomplemented
164#14519689C2314yescomplemented
165#14519688C2314yescomplemented
166C22×D4×C61C2311yescharacteristic
167C23×C4×C61—21no—
168C22×C8×C61C2311yescharacteristic
169C22×C8×C61C2311yescharacteristic
170#125×C61—22no—
171#125×C61C2314yescomplemented
172C4×D4×C61—22no—
173C4×D4×C61C2314yes—
174C2×C4⋊C4×C61—21no—
175C2×C4⋊C4×C61—21no—
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C4⋊C4×C61C2311yescharacteristic
179C2×C22⋊C4×C61—21no—
180C2×C42×C61C2311yescharacteristic
181#107×C61C2314yescomplemented
182#106×C61C2314yescomplemented
183C4⋊C8×C61C2314yescomplemented
184#102×C61C2314yes—
185#102×C61C2314yes—
186C24×C61—21no—
187C23×D61—21no—
188C23×D61—21no—
189C23×D61—24no—
190C23×D61—24no—
191C23×D61—44no—
192C23×D61—44no—
193C23×D61—44no—
194C23×D61—44no—
195C23×D61—82no—
196C23×D61—82no—
197C23×D61C2×D411yescharacteristic
198C23×D61C2×D411yescharacteristic
199C2×D4×C61—21no—
200C2×D4×C61—22no—
201C2×D4×C61#4114yes—
202C2×D4×C61C2412yes—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—24no—
207C22×C4×C61—44no—
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2411yescharacteristic
211C2×C22⋊D61—24no—
212C2×C22⋊D61—24no—
213C2×C22⋊D61—44no—
214C2×C22⋊D61—44no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219D4×D61—28no—
220D4×D61—28no—
221D4×D61—44no—
222D4×D61—44no—
223D4×D61—48no—
224D4×D61—48no—
225C2×D244—24no—
226C2×D244—22no—
227C2×D244—22no—
228C2×D244—22no—
229C2×D244—22no—
230C2×D244—24no—
231C2×D244—24no—
232C2×D244—21no—
233C2×D244—21no—
234C2×D244—24no—
235C2×D244—24no—
236C2×D244—432no—
237C2×D244—44no—
238C2×D244—44no—
239C2×D244—44no—
240C2×D244—82no—
241C2×D244C2×D414yes—
242C2×D244C2412yes—
243C2×D244C2412yes—
244C2×C4×D61—22no—
245C2×C4×D61—22no—
246C2×C4×D61—22no—
247C2×C4×D61—22no—
248C2×C4×D61—24no—
249C2×C4×D61—44no—
250C2×C4×D61C2×D412yes—
251C2×C4×D61C2×D412yes—
252C2×C4×D61C2412yes—
253C2×C4×D61C2412yes—
254C2×Dic122—22no—
255C2×Dic122—22no—
256C2×Dic122—21no—
257C2×Dic122C2412yes—
258C2×C8×C61—22no—
259C2×C8×C61—22no—
260C2×C8×C61C2412yes—
261C2×C8×C61C2412yes—
262C4⋊C4×C61—24no—
263C4⋊C4×C61—24no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61C2412yes—
268C4⋊C4×C61C2412yes—
269C4⋊C4×C61C2412yes—
270C22⋊C4×C61—24no—
271C42×C61C2×D412yes—
272C42×C61C2412yes—
273#11758200—28no—
274#11758198—24no—
275#11758198—24no—
276#11758198—24no—
277#11758198—24no—
278#11758198—24no—
279#11758198C2×D414yes—
280#11758198C2×D414yes—
281C4⋊Dic61—21no—
282C4⋊Dic61—24no—
283C4⋊Dic61—24no—
284C4⋊Dic61C2×D414yes—
285C4⋊Dic61C2412yes—
286#11758196—24no—
287#11758196—24no—
288C4×Dic61—24no—
289C4×Dic61—24no—
290C2×#92418—22no—
291C2×#92418—22no—
292C2×#92418C2412yes—
293C2×#92418C2412yes—
294#11758190—44no—
295#11758190—44no—
296#11758189—44no—
297C8×D61—44no—
298C23×C61—24no—
299C23×C61—22no—
300C23×C61—42no—
301C23×C61—42no—
302C23×C61C22×D411yescharacteristic
303C22×D61—22no—
304C22×D61—22no—
305C22×D61—22no—
306C22×D61—22no—
307C22×D61—22no—
308C22×D61—22no—
309C22×D61—22no—
310C22×D61—48no—
311C22×D61—48no—
312C22×D61—48no—
313C22×D61—42no—
314C22×D61—42no—
315C22×D61—42no—
316C22×D61—42no—
317C22×D61—42no—
318C22×D61—42no—
319C22×D61—48no—
320C22×D61—84no—
321C22×D61—84no—
322C22×D61—816no—
323C22×D61—816no—
324C22×D61AGL(1,ℤ/8)14yes—
325C22×D61C22×D412yes—
326C22×D61C22×D412yes—
327D4×C61—24no—
328D4×C61—22no—
329D4×C61C2×#4114yes—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—48no—
336C2×C4×C61—42no—
337C2×C4×C61—42no—
338C2×C4×C61—42no—
339C2×C4×C61C22×D412yes—
340C2×C4×C61C22×D412yes—
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C2×#4112yes—
343C2×C4×C61H(5,𝔽2)12yes—
344C2×C4×C61C2511yescharacteristic
345C22⋊D61—48no—
346C22⋊D61—48no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—42no—
352C2×Dic61—42no—
353C2×Dic61C22×D412yes—
354C2×Dic61C22×D412yes—
355D244—28no—
356D244—22no—
357D244—22no—
358D244—22no—
359D244—22no—
360D244—48no—
361D244—48no—
362D244—48no—
363D244—42no—
364D244—42no—
365D244—84no—
366C4×D61—24no—
367C4×D61—24no—
368C4×D61—22no—
369C4×D61—22no—
370C4×D61—22no—
371C4×D61—22no—
372C4×D61—48no—
373Dic122—22no—
374Dic122—22no—
375Dic122—42no—
376C8×C61—22no—
377C8×C61—22no—
378#92418—22no—
379#92418—22no—
380C2×#3310—611nomaximal, Sylow
381C22×C61—24no—
382C22×C61—48no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61#54612yes—
386C22×C61C2×AGL(1,ℤ/8)12yes—
387C22×C61#57712yes—
388C22×C61C23×D411yescharacteristic
389C2×D61—22no—
390C2×D61—28no—
391C2×D61—22no—
392C2×D61—22no—
393C2×D61—22no—
394C2×D61—22no—
395C2×D61—44no—
396C2×D61—42no—
397C2×D61—42no—
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—42no—
401C2×D61—42no—
402C2×D61—816no—
403C2×D61—816no—
404C2×D61—84no—
405C2×D61—84no—
406C2×D61C2×AGL(1,ℤ/8)14yes—
407C4×C61—22no—
408C4×C61—22no—
409C4×C61—42no—
410C4×C61—42no—
411C4×C61—42no—
412C4×C61#54612yes—
413C4×C61C22×#4111yescharacteristic
414C4×C61C2×H(5,𝔽2)11yescharacteristic
415Dic61—22no—
416Dic61—22no—
417Dic61—42no—
418Dic61—42no—
419C2×#552—611no—
420C2×D42—611no—
421#3310—6116no—
422C2×#490—611no—
423C2×#482—611no—
424C2×#480—611no—
425C2×#478D6111yescharacteristic, complemented
426C2×#468—611no—
427C2×#465—611no—
428C2×#460—611no—
429C2×#450—611no—
430C2×#450—611no—
431C2×#440—611no—
432C2×#435—611no—
433C2×#418—611no—
434C22×#102—611no—
435C2×C61—44no—
436C2×C61#331014yescomplemented
437C2×C61C2×#54611yescharacteristic
438C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
439C2×C61C2×#57711yescharacteristic
440D61—24no—
441D61—42no—
442D61—82no—
443D61—82no—
444C23×D4—611no—
445C23×D4—611no—
446C23×D4—1221no—
447C22×SD16—611no—
448C22×SD16—611no—
449C22×SD16—611no—
450C22×M16—611no—
451C23×C8—611no—
452#552—618no—
453#552—1224no—
454D42—618no—
455D42—1224no—
456C2×#127—611no—
457C2×#126—1221no—
458C2×#125—1221no—
459C2×#125C2×D6111yescharacteristic, complemented
460C2×#123—1221no—
461C2×C22⋊Q8—611no—
462C2×C22⋊Q8—611no—
463C2×#121—611no—
464C2×#121—611no—
465C2×#121—1221no—
466C2×#120—1221no—
467C2×#120—1221no—
468C2×C4×Q8—611no—
469C2×C4×D4—611no—
470C2×C4×D4C2×D6111yescharacteristic
471C2×#117—611no—
472C2×#117—1221no—
473C22×C4⋊C4—611no—
474#490—618no—
475#482—618no—
476#480—618no—
477#478C2×D6118yescomplemented
478#468—618no—
479#465—618no—
480#460—618no—
481#450—618no—
482#450—618no—
483#440—618no—
484#435—618no—
485C2×#107—611no—
486C2×#107C2×D6111yescharacteristic, complemented
487C2×#106C2×D6111yescharacteristic, complemented
488C2×C4⋊C8C2×D6111yescharacteristic, complemented
489#418—618no—
490C2×#103—611no—
491C2×#102—611no—
492C2×#102—611no—
493C2×#102—611no—
494C2×#102—611no—
495C2×#102—611no—
496C2×#102—611no—
497C2×#102—611no—
498C2×#102—618no—
499C2×#102C2×D6111yescharacteristic
500C2×#102C2×D6111yescharacteristic
501C2×C22⋊C8—611no—
502C2×C22⋊C8—611no—
503C2×#97—611no—
504C61C2×#331011yescharacteristic, complemented, Sylow
505C25—1221no—
506C25—1221no—
507C22×Q8—611no—
508C22×D4—614no—
509C22×D4—614no—
510C22×D4—611no—
511C22×D4—611no—
512C22×D4—611no—
513C22×D4—1228no—
514C22×D4—1221no—
515C22×D4—1221no—
516C22×D4—1222no—
517C22×D4—1222no—
518C22×D4—1221no—
519C22×D4—1221no—
520C22×D4—1224no—
521C22×D4—1224no—
522C22×D4—1221no—
523C22×D4—1221no—
524C22×D4—2448no—
525C22×D4—2442no—
526C22×D4—2442no—
527C22×D4C22×D6111yescharacteristic
528C23×C4—21no—
529C23×C4—611no—
530C23×C4—611no—
531C23×C4—1221no—
532C2×SD16—614no—
533C2×SD16—614no—
534C2×SD16—614no—
535C2×SD16—1224no—
536C2×SD16—2442no—
537C2×SD16—2442no—
538C2×M16—614no—
539C2×M16—2442no—
540C22×C8—611no—
541C22×C8—611no—
542C22×C8—614no—
543C22×C8—2442no—
544C22×C8C22×D6111yescharacteristic
545C22×C8C22×D6111yescharacteristic
546#127—614no—
547#127—1222no—
548#126—1228no—
549#125—22no—
550#125—1228no—
551#125C22×D6114yescomplemented
552#123—1228no—
553C22⋊Q8—614no—
554C22⋊Q8—614no—
555C22⋊Q8—1222no—
556C22⋊Q8—1222no—
557#121—614no—
558#121—614no—
559#121—1222no—
560#121—1222no—
561#121—1228no—
562#120—1228no—
563#120—1228no—
564C4×Q8—614no—
565C4×Q8—1222no—
566C4×D4—22no—
567C4×D4—614no—
568C4×D4—614no—
569C4×D4C22×D6114yes—
570#117—614no—
571#117—1228no—
572#117—1222no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—611no—
576C2×C4⋊C4—611no—
577C2×C4⋊C4—614no—
578C2×C4⋊C4—1222no—
579C2×C4⋊C4—1221no—
580C2×C4⋊C4—1221no—
581C2×C4⋊C4—1221no—
582C2×C4⋊C4—1221no—
583C2×C4⋊C4C22×D6111yescharacteristic
584C2×C4⋊C4C22×D6111yescharacteristic
585C2×C4⋊C4C22×D6111yescharacteristic
586C2×C22⋊C4—21no—
587C2×C22⋊C4—611no—
588C2×C22⋊C4—611no—
589C2×C22⋊C4—1221no—
590C2×C22⋊C4—1221no—
591C2×C22⋊C4—1221no—
592C2×C22⋊C4—1221no—
593C2×C22⋊C4—1221no—
594C2×C42—1221no—
595C2×C42—1221no—
596C2×C42C22×D6111yescharacteristic
597#107—614no—
598#107C22×D6114yescomplemented
599#106C22×D6114yescomplemented
600C4⋊C8C22×D6114yescomplemented
601#103—614no—
602#102—614no—
603#102—614no—
604#102—614no—
605#102—614no—
606#102—614no—
607#102—614no—
608#102—614no—
609#102C22×D6114yes—
610#102C22×D6114yes—
611C22⋊C8—614no—
612C22⋊C8—614no—
613#97—614no—
614C24—21no—
615C24—611no—
616C24—611no—
617C24—1224no—
618C24—1224no—
619C24—1221no—
620C24—1221no—
621C24—4882no—
622C24—4882no—
623C24—2444no—
624C24—2444no—
625C24—2444no—
626C24—2444no—
627C2×Q8—612no—
628C2×Q8—1221no—
629C2×Q8—1222no—
630C2×Q8—1222no—
631C2×D4—21no—
632C2×D4—22no—
633C2×D4—614no—
634C2×D4—612no—
635C2×D4—612no—
636C2×D4—1224no—
637C2×D4—1224no—
638C2×D4—1224no—
639C2×D4—1224no—
640C2×D4—1224no—
641C2×D4—1228no—
642C2×D4—1228no—
643C2×D4—1224no—
644C2×D4—1224no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4—1222no—
648C2×D4—1222no—
649C2×D4—1222no—
650C2×D4—1222no—
651C2×D4—4882no—
652C2×D4—2444no—
653C2×D4—24432no—
654C2×D4—2444no—
655C2×D4—2444no—
656C2×D4—2444no—
657C2×D4—2444no—
658C2×D4—2448no—
659C2×D4—2448no—
660C2×D4—2444no—
661C2×D4—2444no—
662C2×D4#1175822614yes—
663C2×D4C23×D6112yes—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—24no—
668C22×C4—44no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—612no—
672C22×C4—612no—
673C22×C4—612no—
674C22×C4—612no—
675C22×C4—1224no—
676C22×C4—1222no—
677C22×C4—1222no—
678C22×C4—1222no—
679C22×C4—1222no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4—2444no—
683C22×C4D4×D6111yescharacteristic
684C22×C4D4×D6111yescharacteristic
685C22×C4C23×D6111yescharacteristic
686SD16—1228no—
687SD16—2444no—
688SD16—2444no—
689M16—2444no—
690C2×C8—22no—
691C2×C8—22no—
692C2×C8—612no—
693C2×C8—612no—
694C2×C8—1222no—
695C2×C8—1222no—
696C2×C8—2444no—
697C2×C8C23×D6112yes—
698C2×C8C23×D6112yes—
699C4⋊C4—24no—
700C4⋊C4—24no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—614no—
705C4⋊C4—612no—
706C4⋊C4—1224no—
707C4⋊C4—1224no—
708C4⋊C4—1224no—
709C4⋊C4—1221no—
710C4⋊C4—1224no—
711C4⋊C4C23×D6112yes—
712C4⋊C4C23×D6112yes—
713C4⋊C4C23×D6112yes—
714C22⋊C4—24no—
715C22⋊C4—614no—
716C22⋊C4—614no—
717C22⋊C4—1224no—
718C22⋊C4—1224no—
719C22⋊C4—1224no—
720C22⋊C4—1224no—
721C22⋊C4—1224no—
722C42—1224no—
723C42—1224no—
724C42D4×D6112yes—
725C42C23×D6112yes—
726C23—22no—
727C23—24no—
728C23—42no—
729C23—42no—
730C23—614no—
731C23—612no—
732C23—612no—
733C23—1222no—
734C23—1222no—
735C23—1222no—
736C23—1222no—
737C23—1222no—
738C23—1222no—
739C23—1222no—
740C23—48816no—
741C23—4884no—
742C23—4884no—
743C23—48816no—
744C23—2448no—
745C23—2448no—
746C23—2448no—
747C23—2448no—
748C23—2442no—
749C23—2442no—
750C23—2442no—
751C23—2442no—
752C23—2442no—
753C23—2442no—
754C23C2×D4×D6111yescharacteristic
755Q8—1222no—
756Q8—1222no—
757Q8—2442no—
758D4—22no—
759D4—24no—
760D4—1228no—
761D4—1222no—
762D4—1222no—
763D4—1222no—
764D4—1222no—
765D4—4884no—
766D4—2448no—
767D4—2448no—
768D4—2448no—
769D4—2448no—
770D4—2448no—
771D4—2442no—
772D4—2442no—
773D4C2×#1175822614yes—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—48no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—612no—
784C2×C4—612no—
785C2×C4—1222no—
786C2×C4—1222no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—1222no—
790C2×C4—1222no—
791C2×C4—1224no—
792C2×C4—1224no—
793C2×C4—1222no—
794C2×C4—1222no—
795C2×C4—2448no—
796C2×C4—2442no—
797C2×C4—2442no—
798C2×C4C2×D4×D6112yes—
799C2×C4C2×D4×D6112yes—
800C2×C4C2×D4×D6111yescharacteristic
801C2×C4C2×#1175822612yes—
802C2×C4#1451982312yes—
803C2×C4C24×D6111yescharacteristic
804C8—22no—
805C8—22no—
806C8—1222no—
807C8—1222no—
808C22—24no—
809C22—42no—
810C22—42no—
811C22—48no—
812C22—614no—
813C22—1222no—
814C22—1222no—
815C22—1228no—
816C22—1222no—
817C22—1222no—
818C22—1222no—
819C22—48816no—
820C22—48816no—
821C22—4884no—
822C22—4884no—
823C22—2442no—
824C22—2442no—
825C22—2442no—
826C22—2442no—
827C22—2442no—
828C22—2442no—
829C22—2444no—
830C22#1684040312yes—
831C22AGL(1,ℤ/8)×D6112yes—
832C22#1684056912yes—
833C22C22×D4×D6111yescharacteristic
834C4—22no—
835C4—22no—
836C4—42no—
837C4—42no—
838C4—42no—
839C4—1222no—
840C4—1222no—
841C4—2442no—
842C4—2442no—
843C4#1684040312yes—
844C4C22×#1175822611yescharacteristic
845C4C2×#1451982311yescharacteristic
846C2—44no—
847C2—1224no—
848C2—4882no—
849C2—4882no—
850C2—2442no—
851C2#2145783714yesdirect product factor
852C2C2×#1684040311yescharacteristic
853C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
854C2C2×#1684056911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#478C2
socleC23×C61C22×D4
prime radicalC2×D4×D244C2
hypercenterC2×#478D61
hypocenterC61C2×#3310
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#16840450C2semidirect
3. #21457837C2direct (N × H)
4. C2×#16840128C2semidirect
5. C2×#16840088C2semidirect
6. C2×#16840077C2semidirect
7. C2×#16840009C2semidirect
8. C2×#16839992C2semidirect
9. C2×#16839963C2semidirect
10. C2×#16839914C2semidirect
11. C2×#16839914C2semidirect
12. C2×#16839862C2semidirect
13. C2×#16839832C2semidirect
14. C2×#16839765C2semidirect
15. C2×#102×D61C2semidirect
16. C2×C61×#478C2semidirect
20. C22×#11758190C22semidirect
21. C22×#11758190C22semidirect
23. C22×#11758189C22semidirect
24. C22×C8×D61C22semidirect
26. #16840450C22semidirect
33. C2×#14519757C22semidirect
34. C2×#14519757C22semidirect
40. C2×C4×Dic122C22semidirect
43. C2×#14519735C22semidirect
44. C2×C4⋊C4×D61C22semidirect
45. #16840128C22semidirect
46. #16840088C22semidirect
47. #16840077C22semidirect
48. #16840009C22semidirect
49. #16839992C22semidirect
50. #16839963C22semidirect
51. #16839914C22semidirect
52. #16839914C22semidirect
53. #16839862C22semidirect
54. #16839832C22semidirect
55. C2×#14519710C22semidirect
56. #16839765C22semidirect
57. C2×#14519700C22semidirect
58. C2×#14519699C22semidirect
59. C2×#14519699C22semidirect
61. C2×#14519697C22semidirect
62. C2×#14519697C22semidirect
63. C2×#14519697C22semidirect
64. C2×#14519697C22semidirect
65. #102×D61C22semidirect
66. C2×#14519689C22semidirect
67. C2×#14519689C22semidirect
68. C2×#14519688C22semidirect
69. C2×#125×C61C22semidirect
71. C61×#478C22semidirect
72. C2×#107×C61C22semidirect
73. C2×#106×C61C22semidirect
74. C2×C4⋊C8×C61C22semidirect
104. C2×#11758190C23semidirect
105. C2×#11758190C23semidirect
109. C2×#11758189C23semidirect
113. C2×C8×D61C23semidirect
121. #14519757C23semidirect
122. #14519757C23semidirect
131. C4×Dic122C23semidirect
136. #14519735C23semidirect
144. C4⋊C4×D61C23semidirect
154. #14519710C23semidirect
155. #14519700C23semidirect
156. #14519699C23semidirect
157. #14519699C23semidirect
159. #14519697C23semidirect
160. #14519697C23semidirect
161. #14519697C23semidirect
162. #14519697C23semidirect
163. #14519689C23semidirect
164. #14519689C23semidirect
165. #14519688C23semidirect
171. #125×C61C23semidirect
181. #107×C61C23semidirect
182. #106×C61C23semidirect
183. C4⋊C8×C61C23semidirect
425. C2×#478D61semidirect
436. C2×C61#3310semidirect
459. C2×#125C2×D61semidirect
477. #478C2×D61semidirect
486. C2×#107C2×D61semidirect
487. C2×#106C2×D61semidirect
488. C2×C4⋊C8C2×D61semidirect
504. C61C2×#3310semidirect
551. #125C22×D61semidirect
598. #107C22×D61semidirect
599. #106C22×D61semidirect
600. C4⋊C8C22×D61semidirect
851. C2#21457837direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404502
C2×D4×D2442
#214578372
C2×#168401282
C2×#168400882
C2×#168400772
C2×#168400092
C2×#168399922
C2×#168399632
C2×#168399142
C2×#168398622
C2×#168398322
C2×#168397652
C2×#102×D612
C2×C61×#4782
C2×#331061