Finite Group Databasebeta

← C2×#21457349 #30555015

Subgroups — C2×#21457349 #30555015

Order 15616.

2914 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519805C211yesmaximal, characteristic, complemented
2C22×#14519799C211yesmaximal, characteristic, complemented
3C2×#16840417C211yesmaximal, characteristic, complemented
4C2×#16840408C211yesmaximal, characteristic, complemented
5#21457349C2116yesmaximal, direct product factor
6C2×#16840156C211yesmaximal, characteristic, complemented
7C2×#16840020C211yesmaximal, characteristic, complemented
8C2×#16839991C211yesmaximal, characteristic, complemented
9C2×#16839978C211yesmaximal, characteristic, complemented
10C2×#16839968C211yesmaximal, characteristic, complemented
11C2×#16839926C211yesmaximal, characteristic, complemented
12C2×#16839926C211yesmaximal, characteristic, complemented
13C2×#16839909C211yesmaximal, characteristic, complemented
14C2×#16839915C211yesmaximal, characteristic, complemented
15C2×#16839875C211yesmaximal, characteristic, complemented
16C2×C61×#435C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×#11758222C2211yescharacteristic
19C22×#11758222C2211yescharacteristic, complemented
20C23×D244C2211yescharacteristic
21C2×#14519805—28no—
22C2×#14519805C2218yescomplemented
23C2×#14519799—28no—
24C2×#14519799C2218yescomplemented
25C22×Dic244C2211yescharacteristic, complemented
26C22×Dic244C2211yescharacteristic, complemented
27C22×#11758190C2211yescharacteristic
28C22×#11758190C2211yescharacteristic
29C22×#11758190C2211yescharacteristic
30C22×#11758190C2211yescharacteristic
31C22×#11758190C2211yescharacteristic, complemented
32C22×D488C2211yescharacteristic
33C22×D488C2211yescharacteristic
34#16840417—24no—
35#16840417C2218yescomplemented
36#16840408—24no—
37#16840408C2218yescomplemented
38C2×#14519777C2211yescharacteristic, complemented
39C2×#14519765C2211yescharacteristic
40C2×#14519762—21no—
41C2×#14519759—21no—
42C2×#14519759—21no—
43C2×#14519756C2211yescharacteristic
44C2×#14519756C2211yescharacteristic
45C2×#14519756C2211yescharacteristic, complemented
46C2×#14519751C2211yescharacteristic
47C2×#14519750—21no—
48C2×#14519748—21no—
49C2×#14519745—21no—
50C2×C4×D244C2211yescharacteristic
51C2×C4×D244C2211yescharacteristic, complemented
52C2×C4⋊C4×D61—21no—
53C2×C22⋊C4×D61—21no—
54#16840156C2218yescomplemented
55#16840020C2218yescomplemented
56#16839991C2218yescomplemented
57#16839978C2218yescomplemented
58#16839968C2218yescomplemented
59#16839926C2218yescomplemented
60#16839926C2218yescomplemented
61#16839915C2218yescomplemented
62#16839909C2218yescomplemented
63#16839875C2218yescomplemented
64C2×#14519709C2211yescharacteristic, complemented
65C2×#14519702C2211yescharacteristic, complemented
66C2×#14519702C2211yescharacteristic, complemented
67C2×#14519702C2211yescharacteristic, complemented
68C2×#14519699C2211yescharacteristic
69C2×#14519699C2211yescharacteristic
70C2×#14519699C2211yescharacteristic, complemented
71C22×M16×C61C2211yescharacteristic
72C23×C8×C61C2211yescharacteristic, complemented
73C2×C4×D4×C61C2211yescharacteristic
74C61×#435C2218yescomplemented
75C2×C4⋊C8×C61C2211yescharacteristic, complemented
76C2×C22⋊C8×C61C2211yescharacteristic
77C2×C22⋊C8×C61C2211yescharacteristic, complemented
78C2×#97×C61C2211yescharacteristic, complemented
79C24×D61—21no—
80C2×#11758222—22no—
81C2×#11758222—22no—
82C2×#11758222—22no—
83C2×#11758222—24no—
84C2×#11758222—24no—
85C2×#11758222—24no—
86C2×#11758222—42no—
87C2×#11758222—42no—
88C2×#11758222—42no—
89C2×#11758222C2314yes—
90C2×#11758222C2314yes—
91C2×#11758222C2314yescomplemented
92C22×Dic122C2311yescharacteristic
93C22×Dic122C2311yescharacteristic
94C22×Dic122C2311yescharacteristic
95C22×D244—24no—
96C22×D244—21no—
97C22×D244—22no—
98C22×D244—42no—
99C22×D244C2311yescharacteristic
100C22×D244C2314yes—
101C22×D244C2311yescharacteristic
102C22×D244C2311yescharacteristic
103C22×C22⋊D61—21no—
104C22×C22⋊D61—21no—
105C22×C22⋊D61—21no—
106C22×C22⋊D61—21no—
107C22×C4×D61—21no—
108C22×C4×D61—21no—
109C22×C4×D61—21no—
110C22×C4×D61—21no—
111C22×C4×D61—21no—
112#14519805—232no—
113#14519799—232no—
114C2×Dic244—24no—
115C2×Dic244—42no—
116C2×Dic244C2314yescomplemented
117C2×Dic244C2314yescomplemented
118C2×#11758190—24no—
119C2×#11758190—24no—
120C2×#11758190—24no—
121C2×#11758190—24no—
122C2×#11758190—42no—
123C2×#11758190C2314yes—
124C2×#11758190C2314yes—
125C2×#11758190C2314yes—
126C2×#11758190C2314yes—
127C2×#11758190C2314yescomplemented
128C2×D488—24no—
129C2×D488D418yescomplemented
130C2×D488C2314yes—
131C2×D488C2314yes—
132#14519777—22no—
133#14519777C2314yescomplemented
134#14519765—22no—
135#14519765C2314yes—
136#14519762—28no—
137#14519759—28no—
138#14519759—28no—
139#14519756—22no—
140#14519756—22no—
141#14519756—22no—
142#14519756C2314yes—
143#14519756C2314yes—
144#14519756C2314yescomplemented
145#14519751—22no—
146#14519751C2314yes—
147#14519750—28no—
148#14519748—28no—
149#14519745—28no—
150C4×D244—22no—
151C4×D244—22no—
152C4×D244C2314yes—
153C4×D244C2314yescomplemented
154C2×C4⋊Dic61—21no—
155C2×C4⋊Dic61—21no—
156C2×C4⋊Dic61C2311yescharacteristic
157C2×C4⋊Dic61C2311yescharacteristic
158C2×#11758196—21no—
159C2×#11758196—21no—
160C2×#11758196—21no—
161C4⋊C4×D61—28no—
162C2×C22⋊Dic61—21no—
163C2×C22⋊Dic61—21no—
164C2×C22⋊Dic61—21no—
165C2×#11758198—21no—
166C2×#11758198—21no—
167C2×#11758198—21no—
168C2×#11758198—21no—
169C2×#11758198—21no—
170C22⋊C4×D61—28no—
171#14519709C2314yescomplemented
172#14519702C2314yescomplemented
173#14519702C2314yescomplemented
174#14519702C2314yescomplemented
175#14519699C2314yes—
176#14519699C2314yes—
177#14519699C2314yescomplemented
178C22×D4×C61D411yescharacteristic
179C23×C4×C61C2311yescharacteristic
180C23×C4×C61C2311yescharacteristic
181C2×M16×C61—24no—
182C2×M16×C61C2314yes—
183C22×C8×C61—24no—
184C22×C8×C61C2311yescharacteristic
185C22×C8×C61C2311yescharacteristic
186C22×C8×C61C2311yescharacteristic
187C22×C8×C61C2311yescharacteristic
188C22×C8×C61C2314yescomplemented
189C4×D4×C61D414yes—
190C4×D4×C61C2314yes—
191C2×C4⋊C4×C61D411yescharacteristic
192C2×C22⋊C4×C61D411yescharacteristic
193C2×C22⋊C4×C61D411yescharacteristic
194C2×C42×C61C2311yescharacteristic
195C4⋊C8×C61C2314yescomplemented
196C22⋊C8×C61C2314yes—
197C22⋊C8×C61C2314yescomplemented
198#97×C61C2314yescomplemented
199C24×C61C2×D411yescharacteristic
200C24×C61C2×D411yescharacteristic
201C23×D61—21no—
202C23×D61—21no—
203C23×D61—21no—
204C23×D61—24no—
205C23×D61—44no—
206C23×D61—44no—
207C23×D61—82no—
208C2×D4×C61—42no—
209C2×D4×C61C2×D414yes—
210C22×C4×C61—22no—
211C22×C4×C61—22no—
212C22×C4×C61—22no—
213C22×C4×C61—22no—
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D412yes—
219C22×C4×C61C2×D412yes—
220C22×C4×C61C2412yes—
221C22×C4×C61C2412yes—
222C22×C4×C61C2411yescharacteristic
223C2×C22⋊D61—24no—
224C2×C22⋊D61—24no—
225C2×C22⋊D61—24no—
226C2×C22⋊D61—24no—
227C2×C22⋊D61—44no—
228C2×C22⋊D61—44no—
229C2×C22⋊D61—44no—
230C2×C22⋊D61—82no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236#11758222—28no—
237#11758222—28no—
238#11758222—28no—
239#11758222—44no—
240#11758222—44no—
241#11758222—44no—
242#11758222—48no—
243#11758222—48no—
244#11758222—48no—
245C2×D244—21no—
246C2×D244—21no—
247C2×D244—22no—
248C2×D244—22no—
249C2×D244—22no—
250C2×D244—22no—
251C2×D244—28no—
252C2×D244—24no—
253C2×D244—21no—
254C2×D244—44no—
255C2×D244—48no—
256C2×D244—44no—
257C2×D244C2×D414yes—
258C2×D244C2×D414yes—
259C2×D244C2412yes—
260C2×D244C2412yes—
261C2×D244C2412yes—
262C2×C4×D61—24no—
263C2×C4×D61—24no—
264C2×C4×D61—24no—
265C2×C4×D61—24no—
266C2×C4×D61—24no—
267C2×C4×D61—44no—
268C2×C4×D61—44no—
269C2×C4×D61—44no—
270C2×C4×D61—44no—
271C2×C4×D61—82no—
272C2×Dic122—22no—
273C2×Dic122—22no—
274C2×Dic122—22no—
275C2×Dic122—22no—
276C2×Dic122—22no—
277C2×Dic122—22no—
278C2×Dic122—21no—
279C2×Dic122—21no—
280C2×Dic122—21no—
281C2×Dic122C2412yes—
282C2×Dic122C2412yes—
283C2×Dic122C2412yes—
284M16×C61—28no—
285C2×C8×C61—22no—
286C2×C8×C61—22no—
287C2×C8×C61—22no—
288C2×C8×C61—28no—
289C2×C8×C61C2×D414yes—
290C2×C8×C61C2412yes—
291C2×C8×C61C2412yes—
292C2×C8×C61C2412yes—
293C2×C8×C61C2412yes—
294C4⋊C4×C61C2×D414yes—
295C22⋊C4×C61C2×D414yes—
296C22⋊C4×C61C2×D414yes—
297C42×C61C2×D412yes—
298C42×C61C2412yes—
299C22⋊Dic61—24no—
300C22⋊Dic61—24no—
301C22⋊Dic61—24no—
302#11758198—24no—
303#11758198—24no—
304#11758198—24no—
305#11758198—24no—
306#11758198—24no—
307C4⋊Dic61—24no—
308C4⋊Dic61—24no—
309C4⋊Dic61—21no—
310C4⋊Dic61—21no—
311C4⋊Dic61C2412yes—
312C4⋊Dic61C2412yes—
313#11758196—24no—
314#11758196—24no—
315#11758196—24no—
316Dic244—28no—
317Dic244—44no—
318D488—28no—
319D488C2×D4116yescomplemented
320#11758190—28no—
321#11758190—28no—
322#11758190—28no—
323#11758190—28no—
324#11758190—44no—
325C23×C61—22no—
326C23×C61—22no—
327C23×C61—22no—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—22no—
331C23×C61C22×D412yes—
332C23×C61C22×D412yes—
333C23×C61C22×D411yescharacteristic
334C22×D61—24no—
335C22×D61—24no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—48no—
340C22×D61—42no—
341C22×D61—42no—
342C22×D61—42no—
343C22×D61—42no—
344C22×D61—48no—
345C22×D61—42no—
346C22×D61—42no—
347C22×D61—42no—
348C22×D61—84no—
349C22×D61—816no—
350D4×C61—44no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—24no—
356C2×C4×C61—24no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61C22×D412yes—
362C2×C4×C61C22×D412yes—
363C2×C4×C61C22×D412yes—
364C2×C4×C61C22×D412yes—
365C2×C4×C61C22×D411yescharacteristic
366C2×C4×C61C22×D412yes—
367C2×C4×C61H(5,𝔽2)12yes—
368C2×C4×C61C2511yescharacteristic
369C22⋊D61—48no—
370C22⋊D61—48no—
371C22⋊D61—48no—
372C22⋊D61—84no—
373C2×Dic61—22no—
374C2×Dic61—22no—
375C2×Dic61—22no—
376C2×Dic61—22no—
377C2×Dic61—22no—
378C2×Dic61—42no—
379C2×Dic61—42no—
380C2×Dic61—42no—
381C2×Dic61—42no—
382C2×Dic61—42no—
383D244—24no—
384D244—24no—
385D244—22no—
386D244—22no—
387D244—22no—
388D244—22no—
389D244—48no—
390D244—42no—
391D244C22×D414yes—
392D244C22×D414yes—
393C4×D61—48no—
394C4×D61—48no—
395C4×D61—48no—
396C4×D61—48no—
397C4×D61—84no—
398Dic122—22no—
399Dic122—22no—
400Dic122—22no—
401Dic122—22no—
402Dic122—22no—
403Dic122—22no—
404Dic122—42no—
405Dic122—42no—
406Dic122—42no—
407C8×C61—22no—
408C8×C61—22no—
409C8×C61—22no—
410C8×C61C22×D414yes—
411C2×#3267—611nomaximal, Sylow
412C22×C61—22no—
413C22×C61—22no—
414C22×C61—22no—
415C22×C61—22no—
416C22×C61—22no—
417C22×C61—22no—
418C22×C61—44no—
419C22×C61—44no—
420C22×C61D4212yes—
421C22×C61#57512yes—
422C22×C61#57712yes—
423C22×C61C23×D411yescharacteristic
424C2×D61—24no—
425C2×D61—24no—
426C2×D61—48no—
427C2×D61—48no—
428C2×D61—42no—
429C2×D61—42no—
430C2×D61—42no—
431C2×D61—42no—
432C2×D61—42no—
433C2×D61—42no—
434C2×D61—42no—
435C2×D61—816no—
436C2×D61—84no—
437C4×C61—22no—
438C4×C61—22no—
439C4×C61—22no—
440C4×C61—22no—
441C4×C61D4212yes—
442C4×C61C23×D411yescharacteristic
443C4×C61C2×H(5,𝔽2)11yescharacteristic
444Dic61—42no—
445Dic61—42no—
446Dic61—42no—
447Dic61—42no—
448Dic61—42no—
449C22×AGL(1,ℤ/8)—611no—
450C22×#135—611no—
451C2×#547—611no—
452C2×#546—611no—
453#3267—6116no—
454C2×#497—611no—
455C2×#470—611no—
456C2×#465—611no—
457C2×#463—611no—
458C2×#461—611no—
459C2×#452—611no—
460C2×#452—611no—
461C2×#449—611no—
462C2×#450—611no—
463C2×#442—611no—
464C2×#435D6111yescharacteristic, complemented
465C2×C61—42no—
466C2×C61—42no—
467C2×C61#326714yescomplemented
468C2×C61C2×D4211yescharacteristic
469C2×C61C2×#57511yescharacteristic
470C2×C61C2×#57711yescharacteristic
471D61—44no—
472D61—44no—
473D61—82no—
474C22×#41—611no—
475C22×#41—611no—
476C22×#41—611no—
477C23×D4—611no—
478C2×AGL(1,ℤ/8)—618no—
479C2×AGL(1,ℤ/8)—1228no—
480C2×#135—618no—
481C2×#135—1228no—
482C22×Q16—611no—
483C22×Q16—611no—
484C22×SD16—611no—
485C22×SD16—611no—
486C22×SD16—611no—
487C22×SD16—611no—
488C22×SD16—611no—
489C22×D8—611no—
490C22×D8—611no—
491C22×M16C2×D6111yescharacteristic
492C23×C8C2×D6111yescharacteristic, complemented
493#547—618no—
494#547—1224no—
495#546—618no—
496#546—1224no—
497C2×C4⋊Q8—611no—
498C2×#124—611no—
499C2×#123—1221no—
500C2×#123—1221no—
501C2×#123—1221no—
502C2×C22⋊Q8—611no—
503C2×C22⋊Q8—611no—
504C2×C22⋊Q8—611no—
505C2×#121—611no—
506C2×#121—1221no—
507C2×#121—1221no—
508C2×#120—1221no—
509C2×C4×D4—611no—
510C2×C4×D4—611no—
511C2×C4×D4C2×D6111yescharacteristic
512C22×C4⋊C4—1221no—
513C22×C22⋊C4—1221no—
514#497—618no—
515#470—618no—
516#465—618no—
517#463—618no—
518#461—618no—
519#452—618no—
520#452—618no—
521#450—618no—
522#449—618no—
523#442—618no—
524#435C2×D6118yescomplemented
525C2×#106—611no—
526C2×C4⋊C8C2×D6111yescharacteristic, complemented
527C2×#103—611no—
528C2×#103—611no—
529C2×#103—611no—
530C2×#102—611no—
531C2×#102—611no—
532C2×#102—611no—
533C2×C22⋊C8C2×D6111yescharacteristic
534C2×C22⋊C8C2×D6111yescharacteristic, complemented
535C2×#97C2×D6111yescharacteristic, complemented
536C61C2×#326711yescharacteristic, complemented, Sylow
537C25—1221no—
538C2×#41—614no—
539C2×#41—614no—
540C2×#41—614no—
541C2×#41—1224no—
542C2×#41—1224no—
543C2×#41—1224no—
544C2×#41—1222no—
545C2×#41—1222no—
546C2×#41—1222no—
547C2×#41—2442no—
548C2×#41—2442no—
549C2×#41—2442no—
550C22×Q8—611no—
551C22×Q8—611no—
552C22×Q8—611no—
553C22×D4—611no—
554C22×D4—611no—
555C22×D4—611no—
556C22×D4—614no—
557C22×D4—1224no—
558C22×D4—1221no—
559C22×D4—1221no—
560C22×D4—1221no—
561C22×D4—1221no—
562C22×D4—1221no—
563C22×D4—1222no—
564C22×D4—2442no—
565C22×D4D24411yescharacteristic
566C23×C4—1221no—
567C23×C4—1221no—
568C23×C4—1221no—
569C23×C4—1221no—
570C23×C4—1221no—
571C23×C4C22×D6111yescharacteristic
572C23×C4C22×D6111yescharacteristic
573AGL(1,ℤ/8)—12232no—
574#135—12232no—
575C2×Q16—614no—
576C2×Q16—614no—
577C2×Q16—1224no—
578C2×Q16—2442no—
579C2×SD16—614no—
580C2×SD16—614no—
581C2×SD16—614no—
582C2×SD16—614no—
583C2×SD16—614no—
584C2×SD16—1224no—
585C2×SD16—1224no—
586C2×SD16—1224no—
587C2×SD16—1224no—
588C2×SD16—2442no—
589C2×D8—618no—
590C2×D8—614no—
591C2×D8—614no—
592C2×D8—1224no—
593C2×M16—24no—
594C2×M16C22×D6114yes—
595C22×C8—24no—
596C22×C8C22×D6111yescharacteristic
597C22×C8C22×D6111yescharacteristic
598C22×C8C22×D6111yescharacteristic
599C22×C8C22×D6111yescharacteristic
600C22×C8C22×D6114yescomplemented
601C4⋊Q8—614no—
602C4⋊Q8—1222no—
603#124—614no—
604#124—1222no—
605#123—1228no—
606#123—1228no—
607#123—1228no—
608C22⋊Q8—614no—
609C22⋊Q8—614no—
610C22⋊Q8—614no—
611C22⋊Q8—1222no—
612C22⋊Q8—1222no—
613C22⋊Q8—1222no—
614#121—614no—
615#121—1228no—
616#121—1222no—
617#121—1228no—
618#120—1228no—
619C4×D4—614no—
620C4×D4—614no—
621C4×D4—1222no—
622C4×D4—1222no—
623C4×D4D24414yes—
624C4×D4C22×D6114yes—
625C2×C4⋊C4—611no—
626C2×C4⋊C4—611no—
627C2×C4⋊C4—1221no—
628C2×C4⋊C4—1221no—
629C2×C4⋊C4—1221no—
630C2×C4⋊C4—1221no—
631C2×C4⋊C4—1221no—
632C2×C4⋊C4—1228no—
633C2×C4⋊C4D24411yescharacteristic
634C2×C22⋊C4—1221no—
635C2×C22⋊C4—1221no—
636C2×C22⋊C4—1221no—
637C2×C22⋊C4—1221no—
638C2×C22⋊C4—1221no—
639C2×C22⋊C4—1221no—
640C2×C22⋊C4—1221no—
641C2×C22⋊C4—1221no—
642C2×C22⋊C4—1228no—
643C2×C22⋊C4D24411yescharacteristic
644C2×C22⋊C4D24411yescharacteristic
645C2×C42C22×D6111yescharacteristic
646#106—614no—
647C4⋊C8C22×D6114yescomplemented
648#103—614no—
649#103—614no—
650#103—614no—
651#102—614no—
652#102—614no—
653#102—614no—
654C22⋊C8C22×D6114yes—
655C22⋊C8C22×D6114yescomplemented
656#97C22×D6114yescomplemented
657C24—1221no—
658C24—1221no—
659C24—1224no—
660C24—1221no—
661C24—4882no—
662C24—2444no—
663C24—2444no—
664C24C2×D24411yescharacteristic
665C24C2×D24411yescharacteristic
666#41—1228no—
667#41—1228no—
668#41—1228no—
669#41—2444no—
670#41—2444no—
671#41—2444no—
672#41—2448no—
673#41—2448no—
674#41—2448no—
675C2×Q8—612no—
676C2×Q8—612no—
677C2×Q8—612no—
678C2×Q8—1221no—
679C2×Q8—1221no—
680C2×Q8—1221no—
681C2×Q8—1222no—
682C2×Q8—1222no—
683C2×Q8—1222no—
684C2×Q8—1222no—
685C2×Q8—1222no—
686C2×Q8—1222no—
687C2×D4—42no—
688C2×D4—614no—
689C2×D4—614no—
690C2×D4—612no—
691C2×D4—612no—
692C2×D4—612no—
693C2×D4—1228no—
694C2×D4—1224no—
695C2×D4—1224no—
696C2×D4—1224no—
697C2×D4—1224no—
698C2×D4—1222no—
699C2×D4—1221no—
700C2×D4—1221no—
701C2×D4—1224no—
702C2×D4—1221no—
703C2×D4—1222no—
704C2×D4—1222no—
705C2×D4—1222no—
706C2×D4—4882no—
707C2×D4—2444no—
708C2×D4—2448no—
709C2×D4—2444no—
710C2×D4—2444no—
711C2×D4—2444no—
712C2×D4—2444no—
713C2×D4C2×D24414yes—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1224no—
724C22×C4—1224no—
725C22×C4—1224no—
726C22×C4—1224no—
727C22×C4—1224no—
728C22×C4—4882no—
729C22×C4—2444no—
730C22×C4—2444no—
731C22×C4—2444no—
732C22×C4—2444no—
733C22×C4C2×D24412yes—
734C22×C4C2×D24412yes—
735C22×C4C2×D24411yescharacteristic
736C22×C4C2×D24411yescharacteristic
737C22×C4C2×D24411yescharacteristic
738C22×C4C2×D24411yescharacteristic
739C22×C4C23×D6112yes—
740C22×C4C23×D6112yes—
741C22×C4C23×D6111yescharacteristic
742Q16—1228no—
743Q16—2444no—
744SD16—1228no—
745SD16—1228no—
746SD16—1228no—
747SD16—1228no—
748SD16—2444no—
749D8—6116no—
750D8—1228no—
751M16—28no—
752C2×C8—22no—
753C2×C8—22no—
754C2×C8—22no—
755C2×C8—28no—
756C2×C8D4×D6114yes—
757C2×C8C23×D6112yes—
758C2×C8C23×D6112yes—
759C2×C8C23×D6112yes—
760C2×C8C23×D6112yes—
761C4⋊C4—612no—
762C4⋊C4—612no—
763C4⋊C4—1221no—
764C4⋊C4—1221no—
765C4⋊C4—1224no—
766C4⋊C4—1224no—
767C4⋊C4—1224no—
768C4⋊C4—1224no—
769C4⋊C4—1224no—
770C4⋊C4C2×D24414yes—
771C22⋊C4—1224no—
772C22⋊C4—1224no—
773C22⋊C4—1224no—
774C22⋊C4—1224no—
775C22⋊C4—1224no—
776C22⋊C4—1224no—
777C22⋊C4—1224no—
778C22⋊C4—1224no—
779C22⋊C4C2×D24414yes—
780C22⋊C4C2×D24414yes—
781C42C2×D24412yes—
782C42C23×D6112yes—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—1222no—
790C23—1222no—
791C23—1224no—
792C23—1224no—
793C23—1222no—
794C23—4884no—
795C23—48816no—
796C23—2448no—
797C23—2448no—
798C23—2442no—
799C23—2442no—
800C23—2442no—
801C23—2442no—
802C23—2442no—
803C23—2442no—
804C23—2442no—
805C23C22×D24412yes—
806C23C22×D24412yes—
807C23C22×D24411yescharacteristic
808Q8—1222no—
809Q8—1222no—
810Q8—1222no—
811Q8—1222no—
812Q8—1222no—
813Q8—1222no—
814Q8—2442no—
815Q8—2442no—
816Q8—2442no—
817D4—44no—
818D4—614no—
819D4—614no—
820D4—1222no—
821D4—1222no—
822D4—1222no—
823D4—1222no—
824D4—1224no—
825D4—1224no—
826D4—4884no—
827D4—2448no—
828D4—2448no—
829D4—2448no—
830D4—2448no—
831D4—2442no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—1222no—
843C2×C4—1222no—
844C2×C4—1222no—
845C2×C4—1222no—
846C2×C4—1222no—
847C2×C4—4884no—
848C2×C4—2448no—
849C2×C4—2448no—
850C2×C4—2448no—
851C2×C4—2448no—
852C2×C4—2442no—
853C2×C4—2442no—
854C2×C4—2442no—
855C2×C4—2442no—
856C2×C4—2442no—
857C2×C4C2×D4×D6112yes—
858C2×C4C22×D24412yes—
859C2×C4C22×D24412yes—
860C2×C4C22×D24412yes—
861C2×C4C22×D24412yes—
862C2×C4C22×D24411yescharacteristic
863C2×C4#1451982312yes—
864C2×C4C24×D6111yescharacteristic
865C8—22no—
866C8—22no—
867C8—22no—
868C8C2×D4×D6114yes—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—44no—
876C22—44no—
877C22—1224no—
878C22—1224no—
879C22—48816no—
880C22—4884no—
881C22—2442no—
882C22—2442no—
883C22—2442no—
884C22—2442no—
885C22—2442no—
886C22—2442no—
887C22—2442no—
888C22—2448no—
889C22—2448no—
890C22D4×D24412yes—
891C22#1684056212yes—
892C22#1684057412yes—
893C22C23×D24411yescharacteristic
894C4—22no—
895C4—22no—
896C4—22no—
897C4—22no—
898C4—2442no—
899C4—2442no—
900C4—2442no—
901C4—2442no—
902C4—2442no—
903C4D4×D24412yes—
904C4C22×D4×D6111yescharacteristic
905C4C2×#1451982311yescharacteristic
906C2—42no—
907C2—42no—
908C2—4882no—
909C2—2444no—
910C2—2444no—
911C2#2145734914yesdirect product factor
912C2C2×D4×D24411yescharacteristic
913C2C2×#1684056211yescharacteristic
914C2C2×#1684057411yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#435C2
socleC23×C61C22×D4
hypercenterC2×#435D61
hypocenterC61C2×#3267
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C22×#14519805C2semidirect
2. C22×#14519799C2semidirect
3. C2×#16840417C2semidirect
4. C2×#16840408C2semidirect
5. #21457349C2direct (N × H)
6. C2×#16840156C2semidirect
7. C2×#16840020C2semidirect
8. C2×#16839991C2semidirect
9. C2×#16839978C2semidirect
10. C2×#16839968C2semidirect
11. C2×#16839926C2semidirect
12. C2×#16839926C2semidirect
13. C2×#16839909C2semidirect
14. C2×#16839915C2semidirect
15. C2×#16839875C2semidirect
16. C2×C61×#435C2semidirect
19. C22×#11758222C22semidirect
22. C2×#14519805C22semidirect
24. C2×#14519799C22semidirect
25. C22×Dic244C22semidirect
26. C22×Dic244C22semidirect
31. C22×#11758190C22semidirect
35. #16840417C22semidirect
37. #16840408C22semidirect
38. C2×#14519777C22semidirect
45. C2×#14519756C22semidirect
51. C2×C4×D244C22semidirect
54. #16840156C22semidirect
55. #16840020C22semidirect
56. #16839991C22semidirect
57. #16839978C22semidirect
58. #16839968C22semidirect
59. #16839926C22semidirect
60. #16839926C22semidirect
61. #16839915C22semidirect
62. #16839909C22semidirect
63. #16839875C22semidirect
64. C2×#14519709C22semidirect
65. C2×#14519702C22semidirect
66. C2×#14519702C22semidirect
67. C2×#14519702C22semidirect
70. C2×#14519699C22semidirect
72. C23×C8×C61C22semidirect
74. C61×#435C22semidirect
75. C2×C4⋊C8×C61C22semidirect
77. C2×C22⋊C8×C61C22semidirect
78. C2×#97×C61C22semidirect
91. C2×#11758222C23semidirect
116. C2×Dic244C23semidirect
117. C2×Dic244C23semidirect
127. C2×#11758190C23semidirect
129. C2×D488D4semidirect
133. #14519777C23semidirect
144. #14519756C23semidirect
153. C4×D244C23semidirect
171. #14519709C23semidirect
172. #14519702C23semidirect
173. #14519702C23semidirect
174. #14519702C23semidirect
177. #14519699C23semidirect
188. C22×C8×C61C23semidirect
195. C4⋊C8×C61C23semidirect
197. C22⋊C8×C61C23semidirect
198. #97×C61C23semidirect
319. D488C2×D4semidirect
464. C2×#435D61semidirect
467. C2×C61#3267semidirect
492. C23×C8C2×D61semidirect
524. #435C2×D61semidirect
526. C2×C4⋊C8C2×D61semidirect
534. C2×C22⋊C8C2×D61semidirect
535. C2×#97C2×D61semidirect
536. C61C2×#3267semidirect
600. C22×C8C22×D61semidirect
647. C4⋊C8C22×D61semidirect
655. C22⋊C8C22×D61semidirect
656. #97C22×D61semidirect
911. C2#21457349direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198052
C22×#145197992
C2×#168404172
C2×#168404082
#214573492
C2×#168401562
C2×#168400202
C2×#168399912
C2×#168399782
C2×#168399682
C2×#168399262
C2×#168399092
C2×#168399152
C2×#168398752
C2×C61×#4352
C2×#326761