Finite Group Databasebeta

← C2×#21457954 #30556565

Subgroups — C2×#21457954 #30556565

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×D4×D244C211yesmaximal, characteristic, complemented
2#21457954C2116yesmaximal, direct product factor
3C2×#16840128C211yesmaximal, characteristic, complemented
4C2×#16840080C211yesmaximal, characteristic, complemented
5C2×#16840086C211yesmaximal, characteristic, complemented
6C2×#16840059C211yesmaximal, characteristic, complemented
7C2×#16840013C211yesmaximal, characteristic, complemented
8C2×#16839996C211yesmaximal, characteristic, complemented
9C2×#16839957C211yesmaximal, characteristic, complemented
10C2×#16839895C211yesmaximal, characteristic, complemented
11C2×#16839895C211yesmaximal, characteristic, complemented
12C2×#16839872C211yesmaximal, characteristic, complemented
13C2×#16839834C211yesmaximal, characteristic, complemented
14C2×#16839766C211yesmaximal, characteristic, complemented
15C22×#14519697C211yesmaximal, characteristic, complemented
16C2×C61×#553C211yesmaximal, characteristic, complemented
17C23×D244C2211yescharacteristic
18C23×D244C2211yescharacteristic
19C22×D4×D61—21no—
20C22×#11758199C2211yescharacteristic
21C22×#11758199C2211yescharacteristic, complemented
22C22×#11758199C2211yescharacteristic, complemented
23C22×#11758194C2211yescharacteristic, complemented
24C23×#92418C2211yescharacteristic, complemented
25D4×D244—24no—
26D4×D244C2218yescomplemented
27C2×#14519774C2211yescharacteristic
28C2×#14519752—21no—
29C2×#14519751C2211yescharacteristic
30C2×#14519751C2211yescharacteristic
31C2×#14519747—21no—
32C2×#14519747—21no—
33C2×C4×D244C2211yescharacteristic
34#16840128C2218yescomplemented
35#16840086C2218yescomplemented
36#16840080C2218yescomplemented
37#16840059C2218yescomplemented
38#16840013C2218yescomplemented
39#16839996C2218yescomplemented
40#16839957C2218yescomplemented
41#16839895C2218yescomplemented
42#16839895C2218yescomplemented
43#16839872C2218yescomplemented
44#16839834C2218yescomplemented
45C2×#14519710C2211yescharacteristic, complemented
46C2×#14519708C2211yescharacteristic, complemented
47C2×#14519708C2211yescharacteristic, complemented
48C2×C4⋊#92418C2211yescharacteristic, complemented
49#16839766C2218yescomplemented
50C2×#14519698C2211yescharacteristic, complemented
51C2×#14519697C2211yescharacteristic
52C2×#14519697C2211yescharacteristic
53C2×#14519697C2211yescharacteristic
54C2×#14519697C2211yescharacteristic, complemented
55C2×#14519697C2211yescharacteristic, complemented
56C2×#14519697C2211yescharacteristic, complemented
57C2×#14519697C2211yescharacteristic, complemented
58C2×#14519697C2211yescharacteristic, complemented
59C2×#14519697C2211yescharacteristic, complemented
60C2×#14519697C2218yescomplemented
61C2×C22⋊#92418C2211yescharacteristic, complemented
62C2×C22⋊#92418C2211yescharacteristic, complemented
63C2×#14519688C2211yescharacteristic, complemented
64C61×#553—24no—
65C61×#553C2218yescomplemented
66C2×#126×C61—21no—
67C2×#125×C61C2211yescharacteristic, complemented
68C2×#123×C61—21no—
69C2×#121×C61—21no—
70C2×#121×C61C2211yescharacteristic, complemented
71C2×#121×C61C2211yescharacteristic, complemented
72C2×C4×D4×C61—21no—
73C2×C4×D4×C61C2211yescharacteristic
74C2×C4×D4×C61C2211yescharacteristic, complemented
75C2×#117×C61C2211yescharacteristic, complemented
76C22×C4⋊C4×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C24×D61—21no—
79C22×D244—24no—
80C22×D244—24no—
81C22×D244—21no—
82C22×D244—21no—
83C22×D244—21no—
84C22×D244—22no—
85C22×D244—22no—
86C22×D244—21no—
87C22×D244—42no—
88C22×D244—42no—
89C22×D244C2311yescharacteristic
90C22×D244C2311yescharacteristic
91C22×D244C2314yes—
92C22×D244C2314yes—
93C22×D244C2311yescharacteristic
94C22×C22⋊D61—21no—
95C22×C22⋊D61—21no—
96C2×D4×D61—28no—
97C2×D4×D61—48no—
98C22×C4×D61—21no—
99C2×#11758199—24no—
100C2×#11758199—42no—
101C2×#11758199—42no—
102C2×#11758199C2314yes—
103C2×#11758199C2314yescomplemented
104C2×#11758199C2314yescomplemented
105C2×#11758194—42no—
106C2×#11758194C2314yescomplemented
107C22×#92418—42no—
108C22×#92418C2311yescharacteristic
109C22×#92418C2311yescharacteristic
110C22×#92418C2311yescharacteristic
111C22×#92418C2311yescharacteristic
112C22×#92418C2314yescomplemented
113#14519774—22no—
114#14519774C2314yes—
115#14519752—28no—
116#14519751—22no—
117#14519751—22no—
118#14519751C2314yes—
119#14519751C2314yes—
120#14519747—28no—
121#14519747—28no—
122C4×D244—22no—
123C4×D244C2314yes—
124C2×C4⋊Dic61C2311yescharacteristic
125C2×#11758198—21no—
126C2×#11758198—21no—
127C2×#11758198—21no—
128#14519710C2314yescomplemented
129#14519708C2314yescomplemented
130#14519708C2314yescomplemented
131C4⋊#92418C2314yescomplemented
132#14519698C2314yescomplemented
133#14519697C2314yes—
134#14519697C2314yes—
135#14519697C2314yes—
136#14519697C2314yescomplemented
137#14519697C2314yescomplemented
138#14519697C2314yescomplemented
139#14519697C2314yescomplemented
140#14519697C2314yescomplemented
141#14519697C2314yescomplemented
142C22⋊#92418C2314yescomplemented
143C22⋊#92418C2314yescomplemented
144#14519688C2314yescomplemented
145C22×D4×C61—21no—
146C22×D4×C61—21no—
147C22×D4×C61D411yescharacteristic
148C22×D4×C61C2311yescharacteristic
149C23×C4×C61—21no—
150C23×C4×C61—21no—
151C23×C4×C61C2311yescharacteristic
152C23×C4×C61C2311yescharacteristic
153#126×C61—28no—
154#125×C61—22no—
155#125×C61C2314yescomplemented
156#123×C61—28no—
157#121×C61—28no—
158#121×C61—22no—
159#121×C61—22no—
160#121×C61C2314yescomplemented
161#121×C61C2314yescomplemented
162C4×D4×C61—28no—
163C4×D4×C61—22no—
164C4×D4×C61D414yes—
165C4×D4×C61C2314yes—
166C4×D4×C61C2314yescomplemented
167#117×C61—22no—
168#117×C61C2314yescomplemented
169C2×C4⋊C4×C61—22no—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61—21no—
173C2×C4⋊C4×C61D411yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C4⋊C4×C61C2314yescomplemented
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180C2×C22⋊C4×C61—21no—
181C2×C22⋊C4×C61—21no—
182C2×C22⋊C4×C61D411yescharacteristic
183C2×C22⋊C4×C61D411yescharacteristic
184C2×C42×C61—21no—
185C2×C42×C61C2311yescharacteristic
186C24×C61—21no—
187C24×C61C2×D411yescharacteristic
188C24×C61C2×D411yescharacteristic
189C23×D61—21no—
190C23×D61—21no—
191C23×D61—21no—
192C23×D61—24no—
193C23×D61—24no—
194C23×D61—44no—
195C23×D61—44no—
196C23×D61—44no—
197C23×D61—44no—
198C23×D61—82no—
199C23×D61—82no—
200C2×D4×C61—24no—
201C2×D4×C61—24no—
202C2×D4×C61—24no—
203C2×D4×C61—21no—
204C2×D4×C61—22no—
205C2×D4×C61—22no—
206C2×D4×C61—44no—
207C2×D4×C61—82no—
208C2×D4×C61C2×D414yes—
209C2×D4×C61C2412yes—
210C22×C4×C61—22no—
211C22×C4×C61—22no—
212C22×C4×C61—22no—
213C22×C4×C61—22no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—24no—
218C22×C4×C61—24no—
219C22×C4×C61—82no—
220C22×C4×C61—82no—
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D412yes—
226C22×C4×C61C2×D412yes—
227C22×C4×C61C2412yes—
228C22×C4×C61C2412yes—
229C22×C4×C61C2411yescharacteristic
230C2×C22⋊D61—24no—
231C2×C22⋊D61—24no—
232C2×C22⋊D61—44no—
233C2×C22⋊D61—44no—
234C22×Dic61—21no—
235D4×D61—432no—
236C2×D244—21no—
237C2×D244—22no—
238C2×D244—22no—
239C2×D244—22no—
240C2×D244—22no—
241C2×D244—22no—
242C2×D244—28no—
243C2×D244—28no—
244C2×D244—24no—
245C2×D244—24no—
246C2×D244—24no—
247C2×D244—21no—
248C2×D244—21no—
249C2×D244—24no—
250C2×D244—44no—
251C2×D244—44no—
252C2×D244—48no—
253C2×D244—48no—
254C2×D244—44no—
255C2×D244—44no—
256C2×D244—44no—
257C2×D244—82no—
258C2×D244#4114yes—
259C2×D244C2412yes—
260C2×D244C2412yes—
261C2×D244C2412yes—
262C2×C4×D61—24no—
263C2×C4×D61—44no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61—24no—
267C4⋊C4×C61—24no—
268C4⋊C4×C61—24no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61C2×D414yes—
271C4⋊C4×C61C2412yes—
272C4⋊C4×C61C2412yes—
273C4⋊C4×C61C2412yes—
274C22⋊C4×C61—24no—
275C22⋊C4×C61—24no—
276C22⋊C4×C61—24no—
277C22⋊C4×C61—24no—
278C22⋊C4×C61C2×D414yes—
279C22⋊C4×C61C2×D414yes—
280C42×C61—24no—
281C42×C61C2×D412yes—
282C42×C61C2412yes—
283#11758199—28no—
284#11758199—44no—
285#11758199—44no—
286#11758198—24no—
287#11758198—24no—
288#11758198—24no—
289C4⋊Dic61—21no—
290C4⋊Dic61C2412yes—
291#11758194—44no—
292C2×#92418—22no—
293C2×#92418—22no—
294C2×#92418—22no—
295C2×#92418—22no—
296C2×#92418—44no—
297C2×#92418C2412yes—
298C2×#92418C2412yes—
299C2×#92418C2412yes—
300C2×#92418C2412yes—
301C23×C61—22no—
302C23×C61—22no—
303C23×C61—22no—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—42no—
308C23×C61—42no—
309C23×C61—42no—
310C23×C61AGL(1,ℤ/8)14yes—
311C23×C61C22×D412yes—
312C23×C61C22×D412yes—
313C23×C61C22×D411yescharacteristic
314C22×D61—24no—
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—48no—
319C22×D61—48no—
320C22×D61—42no—
321C22×D61—42no—
322C22×D61—48no—
323C22×D61—42no—
324C22×D61—42no—
325C22×D61—42no—
326C22×D61—42no—
327C22×D61—48no—
328C22×D61—42no—
329C22×D61—42no—
330C22×D61—84no—
331C22×D61—84no—
332C22×D61—816no—
333C22×D61—816no—
334D4×C61—28no—
335D4×C61—22no—
336D4×C61—22no—
337D4×C61—48no—
338D4×C61—42no—
339D4×C61—84no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—24no—
345C2×C4×C61—24no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—42no—
354C2×C4×C61—42no—
355C2×C4×C61—42no—
356C2×C4×C61—84no—
357C2×C4×C61—84no—
358C2×C4×C61C22×D412yes—
359C2×C4×C61C22×D412yes—
360C2×C4×C61C22×D412yes—
361C2×C4×C61C22×D412yes—
362C2×C4×C61C22×D411yescharacteristic
363C2×C4×C61C2×#4112yes—
364C2×C4×C61H(5,𝔽2)12yes—
365C2×C4×C61C2511yescharacteristic
366C22⋊D61—48no—
367C22⋊D61—48no—
368C2×Dic61—22no—
369C2×Dic61—42no—
370D244—24no—
371D244—22no—
372D244—22no—
373D244—22no—
374D244—22no—
375D244—22no—
376D244—48no—
377D244—48no—
378D244—48no—
379D244—42no—
380D244—42no—
381D244—84no—
382D244C2×#4114yes—
383C4×D61—48no—
384#92418—22no—
385#92418—22no—
386#92418—22no—
387#92418—22no—
388C2×#3318—611nomaximal, Sylow
389C22×C61—22no—
390C22×C61—28no—
391C22×C61—22no—
392C22×C61—22no—
393C22×C61—22no—
394C22×C61—22no—
395C22×C61—44no—
396C22×C61—42no—
397C22×C61—42no—
398C22×C61—42no—
399C22×C61—84no—
400C22×C61#54612yes—
401C22×C61C2×AGL(1,ℤ/8)14yes—
402C22×C61C2×AGL(1,ℤ/8)12yes—
403C22×C61#57612yes—
404C22×C61C23×D411yescharacteristic
405C2×D61—24no—
406C2×D61—48no—
407C2×D61—42no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—42no—
412C2×D61—42no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—816no—
416C2×D61—816no—
417C2×D61—84no—
418C2×D61—84no—
419C4×C61—22no—
420C4×C61—22no—
421C4×C61—22no—
422C4×C61—22no—
423C4×C61—42no—
424C4×C61—42no—
425C4×C61—42no—
426C4×C61#54612yes—
427C4×C61C22×#4111yescharacteristic
428C4×C61C2×H(5,𝔽2)11yescharacteristic
429Dic61—42no—
430C2×#553D6111yescharacteristic, complemented
431C2×D42—611no—
432#3318—6116no—
433C2×#490—611no—
434C2×#481—611no—
435C2×#482—611no—
436C2×#478—611no—
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—24no—
447C2×C61—42no—
448C2×C61—82no—
449C2×C61#331814yescomplemented
450C2×C61C2×#54611yescharacteristic
451C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
452C2×C61C2×#57611yescharacteristic
453D61—44no—
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—24no—
465#553C2×D6118yescomplemented
466D42—618no—
467D42—1224no—
468C2×#127—611no—
469C2×#126—21no—
470C2×#125C2×D6111yescharacteristic, complemented
471C2×#123—21no—
472C2×#121—21no—
473C2×#121—611no—
474C2×#121—611no—
475C2×#121—1221no—
476C2×#121C2×D6111yescharacteristic, complemented
477C2×#121C2×D6111yescharacteristic, complemented
478C2×#120—1221no—
479C2×#120—1221no—
480C2×C4×D4—21no—
481C2×C4×D4—611no—
482C2×C4×D4C2×D6111yescharacteristic
483C2×C4×D4C2×D6111yescharacteristic, complemented
484C2×#117C2×D6111yescharacteristic, complemented
485C22×C4⋊C4C2×D6111yescharacteristic, complemented
486#490—618no—
487#482—618no—
488#481—618no—
489#478—618no—
490#469—618no—
491#466—618no—
492#459—618no—
493#447—618no—
494#447—618no—
495#442—618no—
496#435—618no—
497C2×#107—611no—
498C2×#106—611no—
499C2×#106—611no—
500C2×C4⋊C8—611no—
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—611no—
511C2×#102—611no—
512C2×#102—618no—
513C2×C22⋊C8—611no—
514C2×C22⋊C8—611no—
515C2×#97—611no—
516C61C2×#331811yescharacteristic, complemented, Sylow
517C25—1221no—
518C25—1221no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—611no—
522C22×D4—611no—
523C22×D4—611no—
524C22×D4—614no—
525C22×D4—614no—
526C22×D4—1224no—
527C22×D4—1224no—
528C22×D4—1221no—
529C22×D4—1221no—
530C22×D4—1228no—
531C22×D4—1221no—
532C22×D4—1221no—
533C22×D4—1221no—
534C22×D4—1221no—
535C22×D4—1222no—
536C22×D4—1222no—
537C22×D4—2442no—
538C22×D4—2442no—
539C22×D4—2448no—
540C22×D4C22⋊D6111yescharacteristic
541C22×D4C22×D6111yescharacteristic
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—1221no—
545C23×C4C22×D6111yescharacteristic
546C23×C4C22×D6111yescharacteristic
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—611no—
558C22×C8—611no—
559C22×C8—614no—
560C22×C8—2442no—
561#127—614no—
562#127—1222no—
563#126—28no—
564#125—22no—
565#125C22×D6114yescomplemented
566#123—28no—
567#121—28no—
568#121—22no—
569#121—22no—
570#121—614no—
571#121—614no—
572#121—1222no—
573#121—1222no—
574#121—1228no—
575#121C22×D6114yescomplemented
576#121C22×D6114yescomplemented
577#120—1228no—
578#120—1228no—
579C4×D4—28no—
580C4×D4—22no—
581C4×D4—614no—
582C4×D4—1222no—
583C4×D4C22⋊D6114yes—
584C4×D4C22×D6114yes—
585C4×D4C22×D6114yescomplemented
586#117—22no—
587#117C22×D6114yescomplemented
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—611no—
593C2×C4⋊C4C22⋊D6111yescharacteristic
594C2×C4⋊C4C22×D6111yescharacteristic
595C2×C4⋊C4C22×D6111yescharacteristic
596C2×C4⋊C4C22×D6111yescharacteristic
597C2×C4⋊C4C22×D6114yescomplemented
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—1221no—
603C2×C22⋊C4—1221no—
604C2×C22⋊C4—1221no—
605C2×C22⋊C4C22⋊D6111yescharacteristic
606C2×C22⋊C4C22⋊D6111yescharacteristic
607C2×C42—21no—
608C2×C42C22×D6111yescharacteristic
609#107—614no—
610#106—614no—
611#106—614no—
612C4⋊C8—614no—
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#102—614no—
622#102—614no—
623C22⋊C8—614no—
624C22⋊C8—614no—
625#97—614no—
626C24—21no—
627C24—1221no—
628C24—1224no—
629C24—1224no—
630C24—1221no—
631C24—1221no—
632C24—4882no—
633C24—4882no—
634C24—2444no—
635C24—2444no—
636C24—2444no—
637C24—2444no—
638C24C2×C22⋊D6111yescharacteristic
639C24C2×C22⋊D6111yescharacteristic
640C2×D4—24no—
641C2×D4—24no—
642C2×D4—24no—
643C2×D4—21no—
644C2×D4—22no—
645C2×D4—22no—
646C2×D4—44no—
647C2×D4—82no—
648C2×D4—614no—
649C2×D4—612no—
650C2×D4—612no—
651C2×D4—612no—
652C2×D4—1228no—
653C2×D4—1228no—
654C2×D4—1224no—
655C2×D4—1224no—
656C2×D4—1221no—
657C2×D4—1224no—
658C2×D4—1224no—
659C2×D4—1224no—
660C2×D4—1224no—
661C2×D4—1221no—
662C2×D4—1221no—
663C2×D4—1222no—
664C2×D4—1222no—
665C2×D4—1222no—
666C2×D4—1222no—
667C2×D4—1222no—
668C2×D4—4882no—
669C2×D4—2444no—
670C2×D4—2444no—
671C2×D4—2448no—
672C2×D4—2448no—
673C2×D4—2444no—
674C2×D4—2444no—
675C2×D4—2444no—
676C2×D4—24432no—
677C2×D4—2444no—
678C2×D4—2444no—
679C2×D4C2×C22⋊D6114yes—
680C2×D4C23×D6112yes—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—24no—
689C22×C4—24no—
690C22×C4—82no—
691C22×C4—82no—
692C22×C4—1221no—
693C22×C4—1224no—
694C22×C4—2444no—
695C22×C4C2×C22⋊D6112yes—
696C22×C4C2×C22⋊D6112yes—
697C22×C4C2×C22⋊D6111yescharacteristic
698C22×C4C2×C22⋊D6111yescharacteristic
699C22×C4C2×C22⋊D6111yescharacteristic
700C22×C4C2×C22⋊D6111yescharacteristic
701C22×C4C23×D6112yes—
702C22×C4C23×D6112yes—
703C22×C4C23×D6111yescharacteristic
704D8—1228no—
705D8—2444no—
706D8—2444no—
707M16—2444no—
708C2×C8—612no—
709C2×C8—612no—
710C2×C8—612no—
711C2×C8—612no—
712C2×C8—1222no—
713C2×C8—1222no—
714C2×C8—1222no—
715C2×C8—1222no—
716C2×C8—2444no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—24no—
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—21no—
723C4⋊C4—612no—
724C4⋊C4—1221no—
725C4⋊C4C2×C22⋊D6114yes—
726C4⋊C4C23×D6112yes—
727C4⋊C4C23×D6112yes—
728C4⋊C4C23×D6112yes—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—24no—
732C22⋊C4—24no—
733C22⋊C4—1224no—
734C22⋊C4—1224no—
735C22⋊C4—1224no—
736C22⋊C4C2×C22⋊D6114yes—
737C22⋊C4C2×C22⋊D6114yes—
738C42—24no—
739C42C2×C22⋊D6112yes—
740C42C23×D6112yes—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—1222no—
751C23—1224no—
752C23—1222no—
753C23—1222no—
754C23—48816no—
755C23—4884no—
756C23—4884no—
757C23—48816no—
758C23—2448no—
759C23—2448no—
760C23—2448no—
761C23—2448no—
762C23—2442no—
763C23—2442no—
764C23—2442no—
765C23—2442no—
766C23—2442no—
767C23—2442no—
768C23—2442no—
769C23—2442no—
770C23#1451980214yes—
771C23C22×C22⋊D6112yes—
772C23C22×C22⋊D6112yes—
773C23C22×C22⋊D6111yescharacteristic
774D4—28no—
775D4—22no—
776D4—22no—
777D4—48no—
778D4—42no—
779D4—84no—
780D4—614no—
781D4—1222no—
782D4—1222no—
783D4—1222no—
784D4—1222no—
785D4—1222no—
786D4—1224no—
787D4—4884no—
788D4—2448no—
789D4—2448no—
790D4—2448no—
791D4—2448no—
792D4—2448no—
793D4—2442no—
794D4—2442no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—84no—
812C2×C4—84no—
813C2×C4—1222no—
814C2×C4—2448no—
815C2×C4—2442no—
816C2×C4C22×C22⋊D6112yes—
817C2×C4C22×C22⋊D6112yes—
818C2×C4C22×C22⋊D6112yes—
819C2×C4C22×C22⋊D6112yes—
820C2×C4C22×C22⋊D6111yescharacteristic
821C2×C4#41×D6112yes—
822C2×C4#1451982312yes—
823C2×C4C24×D6111yescharacteristic
824C8—1222no—
825C8—1222no—
826C8—1222no—
827C8—1222no—
828C22—28no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—44no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—84no—
839C22—1224no—
840C22—48816no—
841C22—48816no—
842C22—4884no—
843C22—4884no—
844C22—2442no—
845C22—2442no—
846C22—2442no—
847C22—2442no—
848C22—2442no—
849C22—2442no—
850C22—2448no—
851C22—2442no—
852C22—2442no—
853C22#1684040012yes—
854C22C2×#1451980214yes—
855C22C2×#1451980212yes—
856C22#1684056512yes—
857C22C23×C22⋊D6111yescharacteristic
858C4—22no—
859C4—22no—
860C4—22no—
861C4—22no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—2442no—
866C4#1684040012yes—
867C4C2×#41×D6111yescharacteristic
868C4C2×#1451982311yescharacteristic
869C2—24no—
870C2—42no—
871C2—82no—
872C2—4882no—
873C2—4882no—
874C2—2444no—
875C2#2145795414yesdirect product factor
876C2C2×#1684040011yescharacteristic
877C2C22×#1451980211yescharacteristic
878C2C2×#1684056511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#553C2
socleC23×C61C22×D4
hypercenterC2×#553D61
hypocenterC61C2×#3318
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×D4×D244C2semidirect
2. #21457954C2direct (N × H)
3. C2×#16840128C2semidirect
4. C2×#16840080C2semidirect
5. C2×#16840086C2semidirect
6. C2×#16840059C2semidirect
7. C2×#16840013C2semidirect
8. C2×#16839996C2semidirect
9. C2×#16839957C2semidirect
10. C2×#16839895C2semidirect
11. C2×#16839895C2semidirect
12. C2×#16839872C2semidirect
13. C2×#16839834C2semidirect
14. C2×#16839766C2semidirect
15. C22×#14519697C2semidirect
16. C2×C61×#553C2semidirect
21. C22×#11758199C22semidirect
22. C22×#11758199C22semidirect
23. C22×#11758194C22semidirect
24. C23×#92418C22semidirect
26. D4×D244C22semidirect
34. #16840128C22semidirect
35. #16840086C22semidirect
36. #16840080C22semidirect
37. #16840059C22semidirect
38. #16840013C22semidirect
39. #16839996C22semidirect
40. #16839957C22semidirect
41. #16839895C22semidirect
42. #16839895C22semidirect
43. #16839872C22semidirect
44. #16839834C22semidirect
45. C2×#14519710C22semidirect
46. C2×#14519708C22semidirect
47. C2×#14519708C22semidirect
48. C2×C4⋊#92418C22semidirect
49. #16839766C22semidirect
50. C2×#14519698C22semidirect
54. C2×#14519697C22semidirect
55. C2×#14519697C22semidirect
56. C2×#14519697C22semidirect
57. C2×#14519697C22semidirect
58. C2×#14519697C22semidirect
59. C2×#14519697C22semidirect
60. C2×#14519697C22semidirect
61. C2×C22⋊#92418C22semidirect
62. C2×C22⋊#92418C22semidirect
63. C2×#14519688C22semidirect
65. C61×#553C22semidirect
67. C2×#125×C61C22semidirect
70. C2×#121×C61C22semidirect
71. C2×#121×C61C22semidirect
74. C2×C4×D4×C61C22semidirect
75. C2×#117×C61C22semidirect
76. C22×C4⋊C4×C61C22semidirect
103. C2×#11758199C23semidirect
104. C2×#11758199C23semidirect
106. C2×#11758194C23semidirect
112. C22×#92418C23semidirect
128. #14519710C23semidirect
129. #14519708C23semidirect
130. #14519708C23semidirect
131. C4⋊#92418C23semidirect
132. #14519698C23semidirect
136. #14519697C23semidirect
137. #14519697C23semidirect
138. #14519697C23semidirect
139. #14519697C23semidirect
140. #14519697C23semidirect
141. #14519697C23semidirect
142. C22⋊#92418C23semidirect
143. C22⋊#92418C23semidirect
144. #14519688C23semidirect
155. #125×C61C23semidirect
160. #121×C61C23semidirect
161. #121×C61C23semidirect
166. C4×D4×C61C23semidirect
168. #117×C61C23semidirect
177. C2×C4⋊C4×C61C23semidirect
430. C2×#553D61semidirect
449. C2×C61#3318semidirect
465. #553C2×D61semidirect
470. C2×#125C2×D61semidirect
476. C2×#121C2×D61semidirect
477. C2×#121C2×D61semidirect
483. C2×C4×D4C2×D61semidirect
484. C2×#117C2×D61semidirect
485. C22×C4⋊C4C2×D61semidirect
516. C61C2×#3318semidirect
565. #125C22×D61semidirect
575. #121C22×D61semidirect
576. #121C22×D61semidirect
585. C4×D4C22×D61semidirect
587. #117C22×D61semidirect
597. C2×C4⋊C4C22×D61semidirect
875. C2#21457954direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×D2442
#214579542
C2×#168401282
C2×#168400802
C2×#168400862
C2×#168400592
C2×#168400132
C2×#168399962
C2×#168399572
C2×#168398952
C2×#168398722
C2×#168398342
C2×#168397662
C22×#145196972
C2×C61×#5532
C2×#331861