Finite Group Databasebeta

← C2×#21457957 #30556568

Subgroups — C2×#21457957 #30556568

Order 15616.

2642 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840465C211yesmaximal, characteristic, complemented
2C2×D4×D244C211yesmaximal, characteristic, complemented
3#21457957C2116yesmaximal, direct product factor
4C2×#16840128C211yesmaximal, characteristic, complemented
5C2×#16840082C211yesmaximal, characteristic, complemented
6C2×#16840089C211yesmaximal, characteristic, complemented
7C2×#16840016C211yesmaximal, characteristic, complemented
8C2×#16839999C211yesmaximal, characteristic, complemented
9C2×#16839958C211yesmaximal, characteristic, complemented
10C2×#16839897C211yesmaximal, characteristic, complemented
11C2×#16839897C211yesmaximal, characteristic, complemented
12C2×#16839872C211yesmaximal, 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×D488C2211yescharacteristic, complemented
21C22×D488C2211yescharacteristic, complemented
22C22×#11758199C2211yescharacteristic
23C22×#11758189C2211yescharacteristic, complemented
24C22×C8×D61C2211yescharacteristic, complemented
25#16840465—24no—
26#16840465C2218yescomplemented
27D4×D244—24no—
28D4×D244C2218yescomplemented
29C2×#14519774C2211yescharacteristic
30C2×#14519772—21no—
31C2×#14519762—21no—
32C2×#14519752—21no—
33C2×#14519752C2211yescharacteristic
34C2×#14519752C2211yescharacteristic
35C2×#14519752C2211yescharacteristic, complemented
36C2×#14519752C2211yescharacteristic, complemented
37C2×#14519751—21no—
38C2×#14519747—21no—
39C2×#14519747—21no—
40C2×C4×D244C2211yescharacteristic
41C2×C4×D244C2211yescharacteristic, complemented
42C2×#14519739—21no—
43C2×#14519735C2211yescharacteristic, complemented
44C2×C4⋊C4×D61C2211yescharacteristic, complemented
45#16840128C2218yescomplemented
46#16840089C2218yescomplemented
47#16840082C2218yescomplemented
48#16840016C2218yescomplemented
49#16839999C2218yescomplemented
50#16839958C2218yescomplemented
51#16839897C2218yescomplemented
52#16839897C2218yescomplemented
53#16839872C2218yescomplemented
54#16839832C2218yescomplemented
55C2×#14519708C2211yescharacteristic, complemented
56#16839765C2218yescomplemented
57C2×#14519699C2211yescharacteristic, complemented
58C2×#14519699C2211yescharacteristic, complemented
59C2×#14519698C2211yescharacteristic
60C2×#14519697C2211yescharacteristic, complemented
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×D244—21no—
80C22×D244—21no—
81C22×D244—21no—
82C22×D244—21no—
83C22×D244—21no—
84C22×D244—21no—
85C22×D244—28no—
86C22×D244—48no—
87C22×D244D411yescharacteristic
88C22×D244C2311yescharacteristic
89C22×D244C2311yescharacteristic
90C22×D244C2311yescharacteristic
91C22×C22⋊D61—21no—
92C22×C22⋊D61—21no—
93C2×D4×D61—24no—
94C2×D4×D61—24no—
95C2×D4×D61—22no—
96C2×D4×D61—22no—
97C2×D4×D61—42no—
98C2×D4×D61—42no—
99C2×D4×D61C2314yes—
100C2×D4×D61C2314yes—
101C22×C4×D61—21no—
102C22×C4×D61—21no—
103C22×C4×D61C2311yescharacteristic
104C22×C4×D61C2311yescharacteristic
105C2×D488—42no—
106C2×D488—42no—
107C2×D488C2314yescomplemented
108C2×D488C2314yescomplemented
109C2×#11758199—24no—
110C2×#11758199C2314yes—
111C2×#11758189—42no—
112C2×#11758189C2314yescomplemented
113C22×#92418C2311yescharacteristic
114C22×#92418C2311yescharacteristic
115C2×C8×D61—42no—
116C2×C8×D61C2314yescomplemented
117#14519774—22no—
118#14519774C2314yes—
119#14519772—28no—
120#14519762—28no—
121#14519752—28no—
122#14519752—22no—
123#14519752—22no—
124#14519752—22no—
125#14519752—22no—
126#14519752C2314yes—
127#14519752C2314yes—
128#14519752C2314yescomplemented
129#14519752C2314yescomplemented
130#14519751—28no—
131#14519747—28no—
132#14519747—28no—
133C4×D244—22no—
134C4×D244D414yes—
135C4×D244C2314yes—
136C4×D244C2314yescomplemented
137#14519739—28no—
138#14519735—22no—
139#14519735C2314yescomplemented
140C2×C4⋊Dic61D411yescharacteristic
141C2×C4⋊Dic61C2311yescharacteristic
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×#11758198—21no—
151C2×#11758198D411yescharacteristic
152C2×#11758198D411yescharacteristic
153C2×C4×Dic61—21no—
154#14519708C2314yescomplemented
155#14519699C2314yescomplemented
156#14519699C2314yescomplemented
157#14519698C2314yes—
158#14519697C2314yescomplemented
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—21no—
190C23×D61—24no—
191C23×D61—24no—
192C23×D61—44no—
193C23×D61—44no—
194C23×D61—44no—
195C23×D61—44no—
196C23×D61—82no—
197C23×D61—82no—
198C23×D61C2×D411yescharacteristic
199C23×D61C2×D411yescharacteristic
200C2×D4×C61—21no—
201C2×D4×C61—22no—
202C2×D4×C61#4114yes—
203C2×D4×C61C2412yes—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—24no—
208C22×C4×C61—44no—
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2411yescharacteristic
212C2×C22⋊D61—24no—
213C2×C22⋊D61—24no—
214C2×C22⋊D61—44no—
215C2×C22⋊D61—44no—
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—22no—
231C2×D244—22no—
232C2×D244—24no—
233C2×D244—24no—
234C2×D244—24no—
235C2×D244—21no—
236C2×D244—21no—
237C2×D244—24no—
238C2×D244—21no—
239C2×D244—24no—
240C2×D244—24no—
241C2×D244—432no—
242C2×D244—44no—
243C2×D244—44no—
244C2×D244—44no—
245C2×D244—44no—
246C2×D244—82no—
247C2×D244—82no—
248C2×D244C2×D414yes—
249C2×D244C2412yes—
250C2×D244C2412yes—
251C2×D244C2412yes—
252C2×C4×D61—22no—
253C2×C4×D61—22no—
254C2×C4×D61—22no—
255C2×C4×D61—22no—
256C2×C4×D61—24no—
257C2×C4×D61—24no—
258C2×C4×D61—82no—
259C2×C4×D61—82no—
260C2×C4×D61C2×D412yes—
261C2×C4×D61C2×D412yes—
262C2×C4×D61C2412yes—
263C2×C4×D61C2412yes—
264C2×C8×C61—22no—
265C2×C8×C61—22no—
266C2×C8×C61C2412yes—
267C2×C8×C61C2412yes—
268C4⋊C4×C61—24no—
269C4⋊C4×C61—24no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61—21no—
273C4⋊C4×C61C2412yes—
274C4⋊C4×C61C2412yes—
275C4⋊C4×C61C2412yes—
276C22⋊C4×C61—24no—
277C42×C61C2×D412yes—
278C42×C61C2412yes—
279#11758199—28no—
280#11758198—24no—
281#11758198—24no—
282#11758198—24no—
283#11758198—24no—
284#11758198—24no—
285#11758198—24no—
286#11758198C2×D414yes—
287#11758198C2×D414yes—
288C4⋊Dic61—21no—
289C4⋊Dic61C2×D414yes—
290C4⋊Dic61C2412yes—
291#11758196—24no—
292C4×Dic61—24no—
293C2×#92418—22no—
294C2×#92418—22no—
295C2×#92418C2412yes—
296C2×#92418C2412yes—
297D488—44no—
298D488—44no—
299#11758189—44no—
300C8×D61—44no—
301C23×C61—24no—
302C23×C61—22no—
303C23×C61—42no—
304C23×C61—42no—
305C23×C61C22×D411yescharacteristic
306C22×D61—22no—
307C22×D61—22no—
308C22×D61—22no—
309C22×D61—22no—
310C22×D61—22no—
311C22×D61—22no—
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—48no—
315C22×D61—48no—
316C22×D61—48no—
317C22×D61—42no—
318C22×D61—42no—
319C22×D61—42no—
320C22×D61—42no—
321C22×D61—42no—
322C22×D61—42no—
323C22×D61—42no—
324C22×D61—42no—
325C22×D61—42no—
326C22×D61—48no—
327C22×D61—84no—
328C22×D61—84no—
329C22×D61—816no—
330C22×D61—816no—
331C22×D61AGL(1,ℤ/8)14yes—
332C22×D61C22×D412yes—
333C22×D61C22×D412yes—
334D4×C61—24no—
335D4×C61—22no—
336D4×C61C2×#4114yes—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—48no—
343C2×C4×C61—42no—
344C2×C4×C61—42no—
345C2×C4×C61—42no—
346C2×C4×C61C22×D412yes—
347C2×C4×C61C22×D412yes—
348C2×C4×C61C22×D411yescharacteristic
349C2×C4×C61C2×#4112yes—
350C2×C4×C61H(5,𝔽2)12yes—
351C2×C4×C61C2511yescharacteristic
352C22⋊D61—48no—
353C22⋊D61—48no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—42no—
358C2×Dic61C22×D412yes—
359C2×Dic61C22×D412yes—
360D244—28no—
361D244—22no—
362D244—22no—
363D244—22no—
364D244—22no—
365D244—22no—
366D244—22no—
367D244—48no—
368D244—48no—
369D244—48no—
370D244—48no—
371D244—42no—
372D244—42no—
373D244—42no—
374D244—84no—
375D244—84no—
376C4×D61—24no—
377C4×D61—24no—
378C4×D61—22no—
379C4×D61—22no—
380C4×D61—22no—
381C4×D61—22no—
382C4×D61—84no—
383C4×D61—84no—
384C8×C61—22no—
385C8×C61—22no—
386#92418—22no—
387#92418—22no—
388C2×#3318—611nomaximal, Sylow
389C22×C61—24no—
390C22×C61—48no—
391C22×C61—42no—
392C22×C61—42no—
393C22×C61#54612yes—
394C22×C61C2×AGL(1,ℤ/8)12yes—
395C22×C61#57612yes—
396C22×C61C23×D411yescharacteristic
397C2×D61—22no—
398C2×D61—28no—
399C2×D61—22no—
400C2×D61—22no—
401C2×D61—22no—
402C2×D61—22no—
403C2×D61—44no—
404C2×D61—42no—
405C2×D61—42no—
406C2×D61—42no—
407C2×D61—42no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—42no—
412C2×D61—42no—
413C2×D61—816no—
414C2×D61—816no—
415C2×D61—84no—
416C2×D61—84no—
417C2×D61—84no—
418C2×D61C2×AGL(1,ℤ/8)14yes—
419C4×C61—22no—
420C4×C61—22no—
421C4×C61—42no—
422C4×C61—42no—
423C4×C61—42no—
424C4×C61#54612yes—
425C4×C61C22×#4111yescharacteristic
426C4×C61C2×H(5,𝔽2)11yescharacteristic
427Dic61—22no—
428Dic61—22no—
429Dic61—42no—
430C2×#553—611no—
431C2×D42—611no—
432#3318—6116no—
433C2×#490—611no—
434C2×#481—611no—
435C2×#482—611no—
436C2×#478D6111yescharacteristic, complemented
437C2×#469—611no—
438C2×#466—611no—
439C2×#459—611no—
440C2×#447—611no—
441C2×#447—611no—
442C2×#442—611no—
443C2×#435—611no—
444C2×#418—611no—
445C22×#102—611no—
446C2×C61—44no—
447C2×C61#331814yescomplemented
448C2×C61C2×#54611yescharacteristic
449C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
450C2×C61C2×#57611yescharacteristic
451D61—24no—
452D61—42no—
453D61—82no—
454D61—82no—
455D61—82no—
456C23×D4—611no—
457C23×D4—611no—
458C23×D4—1221no—
459C22×D8—611no—
460C22×D8—611no—
461C22×D8—611no—
462C22×M16—611no—
463C23×C8—611no—
464#553—618no—
465#553—1224no—
466D42—618no—
467D42—1224no—
468C2×#127—611no—
469C2×#126—1221no—
470C2×#125C2×D6111yescharacteristic, complemented
471C2×#123—1221no—
472C2×#121—611no—
473C2×#121—611no—
474C2×#121—611no—
475C2×#121—611no—
476C2×#121—1221no—
477C2×#121—1221no—
478C2×#120—1221no—
479C2×#120—1221no—
480C2×C4×D4—611no—
481C2×C4×D4—611no—
482C2×C4×D4—1221no—
483C2×C4×D4C2×D6111yescharacteristic
484C2×#117—611no—
485C22×C4⋊C4—611no—
486#490—618no—
487#482—618no—
488#481—618no—
489#478C2×D6118yescomplemented
490#469—618no—
491#466—618no—
492#459—618no—
493#447—618no—
494#447—618no—
495#442—618no—
496#435—618no—
497C2×#107C2×D6111yescharacteristic, complemented
498C2×#106—611no—
499C2×#106C2×D6111yescharacteristic, complemented
500C2×C4⋊C8C2×D6111yescharacteristic, complemented
501#418—618no—
502C2×#102—611no—
503C2×#102—611no—
504C2×#102—611no—
505C2×#102—611no—
506C2×#102—611no—
507C2×#102—611no—
508C2×#102—611no—
509C2×#102—611no—
510C2×#102—618no—
511C2×#102C2×D6111yescharacteristic
512C2×#102C2×D6111yescharacteristic
513C2×C22⋊C8—611no—
514C2×C22⋊C8—611no—
515C2×#97—611no—
516C61C2×#331811yescharacteristic, complemented, Sylow
517C25—1221no—
518C25—1221no—
519C22×D4—614no—
520C22×D4—614no—
521C22×D4—611no—
522C22×D4—611no—
523C22×D4—611no—
524C22×D4—611no—
525C22×D4—1228no—
526C22×D4—1221no—
527C22×D4—1221no—
528C22×D4—1221no—
529C22×D4—1221no—
530C22×D4—1222no—
531C22×D4—1222no—
532C22×D4—1221no—
533C22×D4—1221no—
534C22×D4—1224no—
535C22×D4—1224no—
536C22×D4—1221no—
537C22×D4—1221no—
538C22×D4—2448no—
539C22×D4—2442no—
540C22×D4—2442no—
541C22×D4C22×D6111yescharacteristic
542C23×C4—21no—
543C23×C4—611no—
544C23×C4—611no—
545C23×C4—1221no—
546C23×C4—1221no—
547C2×D8—614no—
548C2×D8—614no—
549C2×D8—614no—
550C2×D8—1224no—
551C2×D8—2442no—
552C2×D8—2442no—
553C2×M16—614no—
554C2×M16—2442no—
555C22×C8—611no—
556C22×C8—611no—
557C22×C8—614no—
558C22×C8—2442no—
559C22×C8C22×D6111yescharacteristic
560C22×C8C22×D6111yescharacteristic
561#127—614no—
562#127—1222no—
563#126—1228no—
564#125—22no—
565#125C22×D6114yescomplemented
566#123—1228no—
567#121—614no—
568#121—614no—
569#121—614no—
570#121—614no—
571#121—1222no—
572#121—1222no—
573#121—1222no—
574#121—1222no—
575#121—1228no—
576#121—1228no—
577#120—1228no—
578#120—1228no—
579C4×D4—22no—
580C4×D4—614no—
581C4×D4—614no—
582C4×D4—614no—
583C4×D4—1228no—
584C4×D4—1222no—
585C4×D4C22×D6114yes—
586#117—614no—
587#117—1222no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—611no—
591C2×C4⋊C4—611no—
592C2×C4⋊C4—614no—
593C2×C4⋊C4—1222no—
594C2×C4⋊C4—1221no—
595C2×C4⋊C4C22×D6111yescharacteristic
596C2×C4⋊C4C22×D6111yescharacteristic
597C2×C4⋊C4C22×D6111yescharacteristic
598C2×C22⋊C4—21no—
599C2×C22⋊C4—611no—
600C2×C22⋊C4—611no—
601C2×C22⋊C4—1221no—
602C2×C22⋊C4—1221no—
603C2×C22⋊C4—1221no—
604C2×C22⋊C4—1221no—
605C2×C22⋊C4—1221no—
606C2×C22⋊C4—1221no—
607C2×C42—1221no—
608C2×C42C22×D6111yescharacteristic
609#107C22×D6114yescomplemented
610#106—614no—
611#106C22×D6114yescomplemented
612C4⋊C8C22×D6114yescomplemented
613#102—614no—
614#102—614no—
615#102—614no—
616#102—614no—
617#102—614no—
618#102—614no—
619#102—614no—
620#102—614no—
621#102C22×D6114yes—
622#102C22×D6114yes—
623C22⋊C8—614no—
624C22⋊C8—614no—
625#97—614no—
626C24—21no—
627C24—611no—
628C24—611no—
629C24—1224no—
630C24—1224no—
631C24—1221no—
632C24—1221no—
633C24—1221no—
634C24—4882no—
635C24—4882no—
636C24—2444no—
637C24—2444no—
638C24—2444no—
639C24—2444no—
640C2×D4—21no—
641C2×D4—22no—
642C2×D4—614no—
643C2×D4—612no—
644C2×D4—612no—
645C2×D4—612no—
646C2×D4—1224no—
647C2×D4—1224no—
648C2×D4—1224no—
649C2×D4—1224no—
650C2×D4—1224no—
651C2×D4—1224no—
652C2×D4—1224no—
653C2×D4—1228no—
654C2×D4—1228no—
655C2×D4—1224no—
656C2×D4—1221no—
657C2×D4—1224no—
658C2×D4—1221no—
659C2×D4—1221no—
660C2×D4—1222no—
661C2×D4—1222no—
662C2×D4—1222no—
663C2×D4—1222no—
664C2×D4—1222no—
665C2×D4—1222no—
666C2×D4—4882no—
667C2×D4—4882no—
668C2×D4—2444no—
669C2×D4—24432no—
670C2×D4—2444no—
671C2×D4—2444no—
672C2×D4—2444no—
673C2×D4—2444no—
674C2×D4—2444no—
675C2×D4—2448no—
676C2×D4—2448no—
677C2×D4—2444no—
678C2×D4—2444no—
679C2×D4#1175822614yes—
680C2×D4C23×D6112yes—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—24no—
685C22×C4—44no—
686C22×C4—611no—
687C22×C4—611no—
688C22×C4—612no—
689C22×C4—612no—
690C22×C4—612no—
691C22×C4—612no—
692C22×C4—1224no—
693C22×C4—1222no—
694C22×C4—1222no—
695C22×C4—1222no—
696C22×C4—1222no—
697C22×C4—1221no—
698C22×C4—1224no—
699C22×C4—4882no—
700C22×C4—4882no—
701C22×C4D4×D6111yescharacteristic
702C22×C4D4×D6111yescharacteristic
703C22×C4C23×D6111yescharacteristic
704D8—1228no—
705D8—2444no—
706D8—2444no—
707M16—2444no—
708C2×C8—22no—
709C2×C8—22no—
710C2×C8—612no—
711C2×C8—612no—
712C2×C8—1222no—
713C2×C8—1222no—
714C2×C8—2444no—
715C2×C8C23×D6112yes—
716C2×C8C23×D6112yes—
717C4⋊C4—24no—
718C4⋊C4—24no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—614no—
723C4⋊C4—612no—
724C4⋊C4—1224no—
725C4⋊C4—1221no—
726C4⋊C4C23×D6112yes—
727C4⋊C4C23×D6112yes—
728C4⋊C4C23×D6112yes—
729C22⋊C4—24no—
730C22⋊C4—614no—
731C22⋊C4—614no—
732C22⋊C4—1224no—
733C22⋊C4—1224no—
734C22⋊C4—1224no—
735C22⋊C4—1224no—
736C22⋊C4—1224no—
737C22⋊C4—1224no—
738C42—1224no—
739C42D4×D6112yes—
740C42C23×D6112yes—
741C23—22no—
742C23—24no—
743C23—42no—
744C23—42no—
745C23—614no—
746C23—612no—
747C23—612no—
748C23—1222no—
749C23—1222no—
750C23—1222no—
751C23—1222no—
752C23—1222no—
753C23—1222no—
754C23—1222no—
755C23—1222no—
756C23—48816no—
757C23—4884no—
758C23—4884no—
759C23—48816no—
760C23—2448no—
761C23—2448no—
762C23—2448no—
763C23—2448no—
764C23—2442no—
765C23—2442no—
766C23—2442no—
767C23—2442no—
768C23—2442no—
769C23—2442no—
770C23—2442no—
771C23—2442no—
772C23—2442no—
773C23C2×D4×D6111yescharacteristic
774D4—22no—
775D4—24no—
776D4—1228no—
777D4—1222no—
778D4—1222no—
779D4—1222no—
780D4—1222no—
781D4—1222no—
782D4—1222no—
783D4—4884no—
784D4—4884no—
785D4—2448no—
786D4—2448no—
787D4—2448no—
788D4—2448no—
789D4—2448no—
790D4—2448no—
791D4—2442no—
792D4—2442no—
793D4—2442no—
794D4C2×#1175822614yes—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—48no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—612no—
805C2×C4—612no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—1222no—
809C2×C4—1222no—
810C2×C4—1222no—
811C2×C4—1222no—
812C2×C4—1224no—
813C2×C4—1224no—
814C2×C4—1222no—
815C2×C4—4884no—
816C2×C4—4884no—
817C2×C4—2442no—
818C2×C4C2×D4×D6112yes—
819C2×C4C2×D4×D6112yes—
820C2×C4C2×D4×D6111yescharacteristic
821C2×C4C2×#1175822612yes—
822C2×C4#1451982312yes—
823C2×C4C24×D6111yescharacteristic
824C8—22no—
825C8—22no—
826C8—1222no—
827C8—1222no—
828C22—24no—
829C22—48no—
830C22—42no—
831C22—42no—
832C22—614no—
833C22—1228no—
834C22—1222no—
835C22—1222no—
836C22—1222no—
837C22—1222no—
838C22—1222no—
839C22—48816no—
840C22—48816no—
841C22—4884no—
842C22—4884no—
843C22—4884no—
844C22—2442no—
845C22—2442no—
846C22—2442no—
847C22—2442no—
848C22—2442no—
849C22—2442no—
850C22—2442no—
851C22—2442no—
852C22—2442no—
853C22—2444no—
854C22#1684040312yes—
855C22AGL(1,ℤ/8)×D6112yes—
856C22#1684056412yes—
857C22C22×D4×D6111yescharacteristic
858C4—22no—
859C4—22no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—1222no—
864C4—1222no—
865C4—2442no—
866C4#1684040312yes—
867C4C22×#1175822611yescharacteristic
868C4C2×#1451982311yescharacteristic
869C2—44no—
870C2—1224no—
871C2—4882no—
872C2—4882no—
873C2—4882no—
874C2—2442no—
875C2#2145795714yesdirect product factor
876C2C2×#1684040311yescharacteristic
877C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
878C2C2×#1684056411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#478C2
socleC23×C61C22×D4
hypercenterC2×#478D61
hypocenterC61C2×#3318
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×#16840465C2semidirect
2. C2×D4×D244C2semidirect
3. #21457957C2direct (N × H)
4. C2×#16840128C2semidirect
5. C2×#16840082C2semidirect
6. C2×#16840089C2semidirect
7. C2×#16840016C2semidirect
8. C2×#16839999C2semidirect
9. C2×#16839958C2semidirect
10. C2×#16839897C2semidirect
11. C2×#16839897C2semidirect
12. C2×#16839872C2semidirect
13. C2×#16839832C2semidirect
14. C2×#16839765C2semidirect
15. C2×#102×D61C2semidirect
16. C2×C61×#478C2semidirect
20. C22×D488C22semidirect
21. C22×D488C22semidirect
23. C22×#11758189C22semidirect
24. C22×C8×D61C22semidirect
26. #16840465C22semidirect
28. D4×D244C22semidirect
35. C2×#14519752C22semidirect
36. C2×#14519752C22semidirect
41. C2×C4×D244C22semidirect
43. C2×#14519735C22semidirect
44. C2×C4⋊C4×D61C22semidirect
45. #16840128C22semidirect
46. #16840089C22semidirect
47. #16840082C22semidirect
48. #16840016C22semidirect
49. #16839999C22semidirect
50. #16839958C22semidirect
51. #16839897C22semidirect
52. #16839897C22semidirect
53. #16839872C22semidirect
54. #16839832C22semidirect
55. C2×#14519708C22semidirect
56. #16839765C22semidirect
57. C2×#14519699C22semidirect
58. C2×#14519699C22semidirect
60. C2×#14519697C22semidirect
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
107. C2×D488C23semidirect
108. C2×D488C23semidirect
112. C2×#11758189C23semidirect
116. C2×C8×D61C23semidirect
128. #14519752C23semidirect
129. #14519752C23semidirect
136. C4×D244C23semidirect
139. #14519735C23semidirect
144. C4⋊C4×D61C23semidirect
154. #14519708C23semidirect
155. #14519699C23semidirect
156. #14519699C23semidirect
158. #14519697C23semidirect
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
436. C2×#478D61semidirect
447. C2×C61#3318semidirect
470. C2×#125C2×D61semidirect
489. #478C2×D61semidirect
497. C2×#107C2×D61semidirect
499. C2×#106C2×D61semidirect
500. C2×C4⋊C8C2×D61semidirect
516. C61C2×#3318semidirect
565. #125C22×D61semidirect
609. #107C22×D61semidirect
611. #106C22×D61semidirect
612. C4⋊C8C22×D61semidirect
875. C2#21457957direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404652
C2×D4×D2442
#214579572
C2×#168401282
C2×#168400822
C2×#168400892
C2×#168400162
C2×#168399992
C2×#168399582
C2×#168398972
C2×#168398722
C2×#168398322
C2×#168397652
C2×#102×D612
C2×C61×#4782
C2×#331861