Finite Group Databasebeta

← C2×#21457334 #30554999

Subgroups — C2×#21457334 #30554999

Order 15616.

2882 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519810C211yesmaximal, characteristic, complemented
2C23×#11758190C211yesmaximal, characteristic, complemented
3C2×D4×Dic122C211yesmaximal, characteristic, complemented
4C2×#16840408C211yesmaximal, characteristic
5#21457334C2116yesmaximal, direct product factor
6C2×#16840156C211yesmaximal, characteristic, complemented
7C2×#16840008C211yesmaximal, characteristic, complemented
8C2×#16840003C211yesmaximal, characteristic, complemented
9C2×#16839985C211yesmaximal, characteristic, complemented
10C2×#16839968C211yesmaximal, characteristic, complemented
11C2×#16839926C211yesmaximal, characteristic, complemented
12C2×#16839920C211yesmaximal, characteristic, complemented
13C2×#16839903C211yesmaximal, characteristic, complemented
14C2×#16839915C211yesmaximal, characteristic, complemented
15C2×#16839864C211yesmaximal, characteristic, complemented
16C2×C61×#435C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C23×Dic122C2211yescharacteristic
19C23×Dic122C2211yescharacteristic, complemented
20C23×D244C2211yescharacteristic
21C2×#14519810—28no—
22C2×#14519810C2218yescomplemented
23C22×Dic244C2211yescharacteristic, complemented
24C22×Dic244C2211yescharacteristic, complemented
25C22×Dic244C2211yescharacteristic, complemented
26C22×#11758190—28no—
27C22×#11758190C2211yescharacteristic
28C22×#11758190C2211yescharacteristic
29C22×#11758190C2211yescharacteristic
30C22×#11758190C2211yescharacteristic
31C22×#11758190C2211yescharacteristic
32C22×#11758190C2211yescharacteristic
33C22×#11758190C2218yescomplemented
34D4×Dic122—24no—
35D4×Dic122C2218yescomplemented
36#16840408—24no—
37#16840408C2218yes—
38C2×#14519777C2211yescharacteristic, complemented
39C2×#14519776—21no—
40C2×#14519765C2211yescharacteristic
41C2×#14519762—21no—
42C2×#14519756C2211yescharacteristic
43C2×#14519756C2211yescharacteristic
44C2×#14519756C2211yescharacteristic, complemented
45C2×#14519754—21no—
46C2×#14519754—21no—
47C2×#14519751C2211yescharacteristic
48C2×#14519750—21no—
49C2×#14519745—21no—
50C2×C4×Dic122C2211yescharacteristic, complemented
51C2×C4×D244C2211yescharacteristic
52C2×D4×Dic61—21no—
53C2×C22⋊C4×D61—21no—
54#16840156C2218yescomplemented
55#16840008C2218yescomplemented
56#16840003C2218yescomplemented
57#16839985C2218yescomplemented
58#16839968C2218yescomplemented
59#16839926C2218yescomplemented
60#16839920C2218yescomplemented
61#16839915C2218yescomplemented
62#16839903C2218yescomplemented
63#16839864C2218yescomplemented
64C2×#14519711C2211yescharacteristic, complemented
65C2×#14519702C2211yescharacteristic, complemented
66C2×#14519702C2211yescharacteristic, complemented
67C2×#14519702C2211yescharacteristic, complemented
68C2×#14519702C2211yescharacteristic, complemented
69C2×#14519699C2211yescharacteristic
70C2×#14519699C2211yescharacteristic
71C22×M16×C61C2211yescharacteristic, complemented
72C23×C8×C61C2211yescharacteristic
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—24no—
82C2×#11758222—42no—
83C2×#11758222C2314yes—
84C22×Dic122—24no—
85C22×Dic122—24no—
86C22×Dic122—21no—
87C22×Dic122—21no—
88C22×Dic122—22no—
89C22×Dic122—22no—
90C22×Dic122—42no—
91C22×Dic122—42no—
92C22×Dic122C2311yescharacteristic
93C22×Dic122C2311yescharacteristic
94C22×Dic122C2311yescharacteristic
95C22×Dic122C2314yes—
96C22×Dic122C2311yescharacteristic
97C22×Dic122C2314yescomplemented
98C22×D244—24no—
99C22×D244—21no—
100C22×D244—22no—
101C22×D244—42no—
102C22×D244C2311yescharacteristic
103C22×D244C2314yes—
104C22×D244C2311yescharacteristic
105C22×C22⋊D61—21no—
106C22×C22⋊D61—21no—
107C23×Dic61—21no—
108C23×Dic61—21no—
109C22×C4×D61—21no—
110C22×C4×D61—21no—
111#14519810—232no—
112C2×Dic244—24no—
113C2×Dic244—24no—
114C2×Dic244—42no—
115C2×Dic244C2314yescomplemented
116C2×Dic244C2314yescomplemented
117C2×Dic244C2314yescomplemented
118C2×#11758190—24no—
119C2×#11758190—24no—
120C2×#11758190—24no—
121C2×#11758190—24no—
122C2×#11758190—232no—
123C2×#11758190—42no—
124C2×#11758190D418yescomplemented
125C2×#11758190C2314yes—
126C2×#11758190C2314yes—
127C2×#11758190C2314yes—
128C2×#11758190C2314yes—
129C2×#11758190C2314yes—
130C2×#11758190C2314yes—
131#14519777—22no—
132#14519777C2314yescomplemented
133#14519776—28no—
134#14519765—22no—
135#14519765C2314yes—
136#14519762—28no—
137#14519756—22no—
138#14519756—22no—
139#14519756—22no—
140#14519756C2314yes—
141#14519756C2314yes—
142#14519756C2314yescomplemented
143#14519754—28no—
144#14519754—28no—
145#14519751—22no—
146#14519751C2314yes—
147#14519750—28no—
148#14519745—28no—
149C4×Dic122—22no—
150C4×Dic122C2314yescomplemented
151C4×D244—22no—
152C4×D244C2314yes—
153D4×Dic61—28no—
154C2×C4⋊Dic61—21no—
155C2×C4⋊Dic61—21no—
156C2×C4⋊Dic61C2311yescharacteristic
157C2×C4⋊Dic61C2311yescharacteristic
158C2×#11758196—21no—
159C2×#11758196—21no—
160C2×#11758196—21no—
161C2×#11758196—21no—
162C2×C22⋊Dic61—21no—
163C2×C22⋊Dic61—21no—
164C2×C22⋊Dic61—21no—
165C2×#11758198—21no—
166C2×#11758198—21no—
167C2×#11758198—21no—
168C2×#11758198—21no—
169C22⋊C4×D61—28no—
170C2×C4×Dic61—21no—
171#14519711C2314yescomplemented
172#14519702C2314yescomplemented
173#14519702C2314yescomplemented
174#14519702C2314yescomplemented
175#14519702C2314yescomplemented
176#14519699C2314yes—
177#14519699C2314yes—
178C22×D4×C61D411yescharacteristic
179C23×C4×C61C2311yescharacteristic
180C23×C4×C61C2311yescharacteristic
181C2×M16×C61—24no—
182C2×M16×C61C2314yescomplemented
183C22×C8×C61—24no—
184C22×C8×C61C2314yes—
185C22×C8×C61C2311yescharacteristic
186C22×C8×C61C2311yescharacteristic
187C22×C8×C61C2311yescharacteristic
188C22×C8×C61C2311yescharacteristic
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—24no—
204C23×D61—44no—
205C23×D61—44no—
206C23×D61—82no—
207C2×D4×C61—24no—
208C2×D4×C61C2×D414yes—
209C22×C4×C61—22no—
210C22×C4×C61—22no—
211C22×C4×C61—22no—
212C22×C4×C61—22no—
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D412yes—
217C22×C4×C61C2×D412yes—
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2412yes—
220C22×C4×C61C2412yes—
221C22×C4×C61C2411yescharacteristic
222C2×C22⋊D61—24no—
223C2×C22⋊D61—24no—
224C2×C22⋊D61—44no—
225C2×C22⋊D61—82no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—24no—
232C22×Dic61—24no—
233C22×Dic61—21no—
234C22×Dic61—44no—
235C22×Dic61—44no—
236#11758222—28no—
237#11758222—44no—
238#11758222—48no—
239C2×D244—21no—
240C2×D244—22no—
241C2×D244—22no—
242C2×D244—22no—
243C2×D244—28no—
244C2×D244—24no—
245C2×D244—21no—
246C2×D244—44no—
247C2×D244—48no—
248C2×D244—44no—
249C2×D244C2×D414yes—
250C2×D244C2412yes—
251C2×D244C2412yes—
252C2×C4×D61—24no—
253C2×C4×D61—24no—
254C2×C4×D61—44no—
255C2×C4×D61—82no—
256C2×Dic122—21no—
257C2×Dic122—22no—
258C2×Dic122—22no—
259C2×Dic122—22no—
260C2×Dic122—22no—
261C2×Dic122—22no—
262C2×Dic122—22no—
263C2×Dic122—22no—
264C2×Dic122—28no—
265C2×Dic122—28no—
266C2×Dic122—24no—
267C2×Dic122—21no—
268C2×Dic122—21no—
269C2×Dic122—24no—
270C2×Dic122—21no—
271C2×Dic122—44no—
272C2×Dic122—44no—
273C2×Dic122—48no—
274C2×Dic122—48no—
275C2×Dic122—44no—
276C2×Dic122—44no—
277C2×Dic122C2×D414yes—
278C2×Dic122C2412yes—
279C2×Dic122C2412yes—
280C2×Dic122C2412yes—
281C2×Dic122C2412yes—
282M16×C61—28no—
283C2×C8×C61—22no—
284C2×C8×C61—22no—
285C2×C8×C61—22no—
286C2×C8×C61—28no—
287C2×C8×C61C2×D414yes—
288C2×C8×C61C2412yes—
289C2×C8×C61C2412yes—
290C2×C8×C61C2412yes—
291C2×C8×C61C2412yes—
292C4⋊C4×C61C2×D414yes—
293C22⋊C4×C61C2×D414yes—
294C22⋊C4×C61C2×D414yes—
295C42×C61C2×D412yes—
296C42×C61C2412yes—
297C22⋊Dic61—24no—
298C22⋊Dic61—24no—
299C22⋊Dic61—24no—
300#11758198—24no—
301#11758198—24no—
302#11758198—24no—
303#11758198—24no—
304C4⋊Dic61—24no—
305C4⋊Dic61—24no—
306C4⋊Dic61—21no—
307C4⋊Dic61—21no—
308C4⋊Dic61C2412yes—
309C4⋊Dic61C2412yes—
310#11758196—24no—
311#11758196—24no—
312#11758196—24no—
313#11758196—24no—
314C4×Dic61—24no—
315Dic244—28no—
316Dic244—28no—
317Dic244—44no—
318#11758190—28no—
319#11758190—28no—
320#11758190—28no—
321#11758190—28no—
322#11758190—44no—
323#11758190C2×D4116yescomplemented
324C23×C61—22no—
325C23×C61—22no—
326C23×C61—22no—
327C23×C61—22no—
328C23×C61—22no—
329C23×C61#13714yescomplemented
330C23×C61C22×D412yes—
331C23×C61C22×D412yes—
332C23×C61C22×D411yescharacteristic
333C22×D61—24no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—48no—
337C22×D61—42no—
338C22×D61—42no—
339C22×D61—42no—
340C22×D61—42no—
341C22×D61—48no—
342C22×D61—42no—
343C22×D61—84no—
344C22×D61—816no—
345D4×C61—28no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—24no—
351C2×C4×C61—24no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61C22×D412yes—
357C2×C4×C61C22×D412yes—
358C2×C4×C61C22×D412yes—
359C2×C4×C61C22×D412yes—
360C2×C4×C61C22×D411yescharacteristic
361C2×C4×C61C22×D412yes—
362C2×C4×C61H(5,𝔽2)12yes—
363C2×C4×C61C2511yescharacteristic
364C22⋊D61—48no—
365C22⋊D61—84no—
366C2×Dic61—24no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—22no—
372C2×Dic61—22no—
373C2×Dic61—48no—
374C2×Dic61—48no—
375C2×Dic61—42no—
376C2×Dic61—42no—
377C2×Dic61—42no—
378C2×Dic61—42no—
379C2×Dic61—42no—
380D244—24no—
381D244—22no—
382D244—22no—
383D244—22no—
384D244—48no—
385D244—42no—
386D244C22×D414yes—
387C4×D61—48no—
388C4×D61—84no—
389Dic122—24no—
390Dic122—22no—
391Dic122—22no—
392Dic122—22no—
393Dic122—22no—
394Dic122—22no—
395Dic122—22no—
396Dic122—22no—
397Dic122—48no—
398Dic122—48no—
399Dic122—42no—
400Dic122—42no—
401Dic122—42no—
402Dic122C22×D414yes—
403C8×C61—22no—
404C8×C61—22no—
405C8×C61—22no—
406C8×C61C22×D414yes—
407C2×#3266—611nomaximal, Sylow
408C22×C61—22no—
409C22×C61—28no—
410C22×C61—22no—
411C22×C61—22no—
412C22×C61—22no—
413C22×C61—22no—
414C22×C61—44no—
415C22×C61D4212yes—
416C22×C61C2×#13712yes—
417C22×C61C2×#13714yescomplemented
418C22×C61#57712yes—
419C22×C61C23×D411yescharacteristic
420C2×D61—24no—
421C2×D61—48no—
422C2×D61—42no—
423C2×D61—42no—
424C2×D61—42no—
425C2×D61—42no—
426C2×D61—42no—
427C2×D61—816no—
428C2×D61—84no—
429C4×C61—22no—
430C4×C61—22no—
431C4×C61—22no—
432C4×C61—22no—
433C4×C61D4212yes—
434C4×C61C23×D411yescharacteristic
435C4×C61C2×H(5,𝔽2)11yescharacteristic
436Dic61—24no—
437Dic61—42no—
438Dic61—42no—
439Dic61—42no—
440Dic61—42no—
441Dic61—42no—
442C22×#137—611no—
443C23×SD16—611no—
444C2×D4×Q8—611no—
445C2×#546—611no—
446#3266—6116no—
447C2×#497—611no—
448C2×#468—611no—
449C2×#467—611no—
450C2×#464—611no—
451C2×#461—611no—
452C2×#452—611no—
453C2×#451—611no—
454C2×#448—611no—
455C2×#450—611no—
456C2×#440—611no—
457C2×#435D6111yescharacteristic, complemented
458C2×C61—24no—
459C2×C61—42no—
460C2×C61#326614yescomplemented
461C2×C61C2×D4211yescharacteristic
462C2×C61C22×#13711yescharacteristic
463C2×C61C2×#57711yescharacteristic
464D61—44no—
465D61—82no—
466C22×#41—611no—
467C23×Q8—611no—
468C23×Q8—611no—
469C23×D4—611no—
470C2×#137—618no—
471C2×#137—1228no—
472C22×Q16—611no—
473C22×Q16—611no—
474C22×Q16—611no—
475C22×SD16—611no—
476C22×SD16—611no—
477C22×SD16—611no—
478C22×SD16—611no—
479C22×SD16—611no—
480C22×SD16—618no—
481C22×SD16—611no—
482C22×SD16—1228no—
483C22×M16C2×D6111yescharacteristic, complemented
484C23×C8C2×D6111yescharacteristic
485D4×Q8—618no—
486D4×Q8—1224no—
487#546—618no—
488#546—1224no—
489C2×C4⋊Q8—611no—
490C2×C4⋊Q8—1221no—
491C2×#124—611no—
492C2×#123—1221no—
493C2×C22⋊Q8—611no—
494C2×C22⋊Q8—611no—
495C2×C22⋊Q8—611no—
496C2×C22⋊Q8—1221no—
497C2×C22⋊Q8—1221no—
498C2×#121—611no—
499C2×#121—1221no—
500C2×#120—1221no—
501C2×C4×Q8—611no—
502C2×C4×D4—611no—
503C2×C4×D4—1221no—
504C2×C4×D4C2×D6111yescharacteristic
505C22×C22⋊C4—1221no—
506#497—618no—
507#468—618no—
508#467—618no—
509#464—618no—
510#461—618no—
511#452—618no—
512#451—618no—
513#450—618no—
514#448—618no—
515#440—618no—
516#435C2×D6118yescomplemented
517C2×#107—611no—
518C2×C4⋊C8C2×D6111yescharacteristic, complemented
519C2×#103—611no—
520C2×#103—611no—
521C2×#103—611no—
522C2×#103—611no—
523C2×#102—611no—
524C2×#102—611no—
525C2×C22⋊C8C2×D6111yescharacteristic
526C2×C22⋊C8C2×D6111yescharacteristic, complemented
527C2×#97C2×D6111yescharacteristic, complemented
528C61C2×#326611yescharacteristic, complemented, Sylow
529C25—1221no—
530C2×#41—614no—
531C2×#41—1224no—
532C2×#41—1222no—
533C2×#41—2442no—
534C22×Q8—611no—
535C22×Q8—611no—
536C22×Q8—611no—
537C22×Q8—611no—
538C22×Q8—614no—
539C22×Q8—614no—
540C22×Q8—1224no—
541C22×Q8—1224no—
542C22×Q8—1221no—
543C22×Q8—1221no—
544C22×Q8—1222no—
545C22×Q8—1222no—
546C22×Q8—2442no—
547C22×Q8—2442no—
548C22×D4—611no—
549C22×D4—611no—
550C22×D4—614no—
551C22×D4—1224no—
552C22×D4—1221no—
553C22×D4—1221no—
554C22×D4—1221no—
555C22×D4—1222no—
556C22×D4—2442no—
557C22×D4D24411yescharacteristic
558C23×C4—1221no—
559C23×C4—1221no—
560C23×C4—1221no—
561C23×C4—1221no—
562C23×C4C22×D6111yescharacteristic
563C23×C4C22×D6111yescharacteristic
564#137—12232no—
565C2×Q16—614no—
566C2×Q16—614no—
567C2×Q16—614no—
568C2×Q16—1224no—
569C2×Q16—1224no—
570C2×Q16—2442no—
571C2×SD16—618no—
572C2×SD16—614no—
573C2×SD16—614no—
574C2×SD16—614no—
575C2×SD16—614no—
576C2×SD16—614no—
577C2×SD16—614no—
578C2×SD16—12232no—
579C2×SD16—1224no—
580C2×SD16—1224no—
581C2×SD16—1224no—
582C2×SD16—1224no—
583C2×SD16—2442no—
584C2×M16—24no—
585C2×M16C22×D6114yescomplemented
586C22×C8—24no—
587C22×C8C22×D6111yescharacteristic
588C22×C8C22×D6114yes—
589C22×C8C22×D6111yescharacteristic
590C22×C8C22×D6111yescharacteristic
591C22×C8C22×D6111yescharacteristic
592C4⋊Q8—614no—
593C4⋊Q8—1228no—
594C4⋊Q8—1222no—
595#124—614no—
596#124—1222no—
597#123—1228no—
598C22⋊Q8—614no—
599C22⋊Q8—614no—
600C22⋊Q8—614no—
601C22⋊Q8—1222no—
602C22⋊Q8—1222no—
603C22⋊Q8—1222no—
604C22⋊Q8—1228no—
605C22⋊Q8—1228no—
606#121—614no—
607#121—1222no—
608#121—1228no—
609#120—1228no—
610C4×Q8—614no—
611C4×Q8—1222no—
612C4×D4—614no—
613C4×D4—1228no—
614C4×D4—1222no—
615C4×D4D24414yes—
616C4×D4C22×D6114yes—
617C2×C4⋊C4—611no—
618C2×C4⋊C4—611no—
619C2×C4⋊C4—1221no—
620C2×C4⋊C4—1221no—
621C2×C4⋊C4—1221no—
622C2×C4⋊C4—1221no—
623C2×C4⋊C4—1221no—
624C2×C4⋊C4—1221no—
625C2×C4⋊C4D24411yescharacteristic
626C2×C22⋊C4—1221no—
627C2×C22⋊C4—1221no—
628C2×C22⋊C4—1221no—
629C2×C22⋊C4—1221no—
630C2×C22⋊C4—1221no—
631C2×C22⋊C4—1221no—
632C2×C22⋊C4—1221no—
633C2×C22⋊C4—1228no—
634C2×C22⋊C4D24411yescharacteristic
635C2×C22⋊C4D24411yescharacteristic
636C2×C42—1221no—
637C2×C42C22×D6111yescharacteristic
638#107—614no—
639C4⋊C8C22×D6114yescomplemented
640#103—614no—
641#103—614no—
642#103—614no—
643#103—614no—
644#102—614no—
645#102—614no—
646C22⋊C8C22×D6114yes—
647C22⋊C8C22×D6114yescomplemented
648#97C22×D6114yescomplemented
649C24—1221no—
650C24—1224no—
651C24—1221no—
652C24—4882no—
653C24—2444no—
654C24—2444no—
655C24C2×D24411yescharacteristic
656C24C2×D24411yescharacteristic
657#41—1228no—
658#41—2444no—
659#41—2448no—
660C2×Q8—614no—
661C2×Q8—612no—
662C2×Q8—612no—
663C2×Q8—612no—
664C2×Q8—612no—
665C2×Q8—1228no—
666C2×Q8—1228no—
667C2×Q8—1221no—
668C2×Q8—1221no—
669C2×Q8—1224no—
670C2×Q8—1224no—
671C2×Q8—1221no—
672C2×Q8—1221no—
673C2×Q8—1222no—
674C2×Q8—1222no—
675C2×Q8—1222no—
676C2×Q8—1222no—
677C2×Q8—1222no—
678C2×Q8—1222no—
679C2×Q8—1222no—
680C2×Q8—2444no—
681C2×Q8—2444no—
682C2×Q8—2444no—
683C2×Q8—2444no—
684C2×Q8—2448no—
685C2×Q8—2448no—
686C2×D4—24no—
687C2×D4—614no—
688C2×D4—612no—
689C2×D4—612no—
690C2×D4—1228no—
691C2×D4—1224no—
692C2×D4—1224no—
693C2×D4—1222no—
694C2×D4—1221no—
695C2×D4—1224no—
696C2×D4—1221no—
697C2×D4—1222no—
698C2×D4—1222no—
699C2×D4—4882no—
700C2×D4—2444no—
701C2×D4—2448no—
702C2×D4—2444no—
703C2×D4—2444no—
704C2×D4C2×D24414yes—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—1221no—
710C22×C4—1224no—
711C22×C4—1224no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1224no—
718C22×C4—1224no—
719C22×C4—4882no—
720C22×C4—2444no—
721C22×C4—2444no—
722C22×C4—2444no—
723C22×C4C2×D24412yes—
724C22×C4C2×D24412yes—
725C22×C4C2×D24411yescharacteristic
726C22×C4C2×D24411yescharacteristic
727C22×C4C2×D24411yescharacteristic
728C22×C4C2×D24411yescharacteristic
729C22×C4C23×D6112yes—
730C22×C4C23×D6112yes—
731C22×C4C23×D6111yescharacteristic
732Q16—1228no—
733Q16—1228no—
734Q16—2444no—
735SD16—6116no—
736SD16—1228no—
737SD16—1228no—
738SD16—1228no—
739SD16—1228no—
740SD16—2444no—
741M16—28no—
742C2×C8—22no—
743C2×C8—22no—
744C2×C8—22no—
745C2×C8—28no—
746C2×C8D4×D6114yes—
747C2×C8C23×D6112yes—
748C2×C8C23×D6112yes—
749C2×C8C23×D6112yes—
750C2×C8C23×D6112yes—
751C4⋊C4—612no—
752C4⋊C4—612no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1224no—
756C4⋊C4—1224no—
757C4⋊C4—1224no—
758C4⋊C4—1224no—
759C4⋊C4—1224no—
760C4⋊C4—1224no—
761C4⋊C4C2×D24414yes—
762C22⋊C4—1224no—
763C22⋊C4—1224no—
764C22⋊C4—1224no—
765C22⋊C4—1224no—
766C22⋊C4—1224no—
767C22⋊C4—1224no—
768C22⋊C4—1224no—
769C22⋊C4C2×D24414yes—
770C22⋊C4C2×D24414yes—
771C42—1224no—
772C42C2×D24412yes—
773C42C23×D6112yes—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—1222no—
780C23—1224no—
781C23—1222no—
782C23—48816no—
783C23—4884no—
784C23—2448no—
785C23—2442no—
786C23—2448no—
787C23—2442no—
788C23—2442no—
789C23—2442no—
790C23—2442no—
791C23#1451981014yescomplemented
792C23C22×D24412yes—
793C23C22×D24412yes—
794C23C22×D24411yescharacteristic
795Q8—614no—
796Q8—1222no—
797Q8—1224no—
798Q8—1222no—
799Q8—1222no—
800Q8—1222no—
801Q8—1222no—
802Q8—1222no—
803Q8—1222no—
804Q8—2448no—
805Q8—2448no—
806Q8—2442no—
807Q8—2442no—
808Q8—2442no—
809D4—28no—
810D4—614no—
811D4—1222no—
812D4—1222no—
813D4—1222no—
814D4—1224no—
815D4—4884no—
816D4—2448no—
817D4—2448no—
818D4—2442no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—1222no—
830C2×C4—1224no—
831C2×C4—1222no—
832C2×C4—1222no—
833C2×C4—1222no—
834C2×C4—1222no—
835C2×C4—1222no—
836C2×C4—4884no—
837C2×C4—2448no—
838C2×C4—2448no—
839C2×C4—2448no—
840C2×C4—2442no—
841C2×C4—2442no—
842C2×C4—2442no—
843C2×C4—2442no—
844C2×C4—2442no—
845C2×C4C2×D4×D6112yes—
846C2×C4C22×D24412yes—
847C2×C4C22×D24412yes—
848C2×C4C22×D24412yes—
849C2×C4C22×D24412yes—
850C2×C4C22×D24411yescharacteristic
851C2×C4#1451982312yes—
852C2×C4C24×D6111yescharacteristic
853C8—22no—
854C8—22no—
855C8—22no—
856C8C2×D4×D6114yes—
857C22—22no—
858C22—22no—
859C22—28no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—44no—
864C22—1224no—
865C22—48816no—
866C22—4884no—
867C22—2442no—
868C22—2442no—
869C22—2442no—
870C22—2442no—
871C22—2442no—
872C22—2448no—
873C22D4×D24412yes—
874C22C2×#1451981012yes—
875C22C2×#1451981014yescomplemented
876C22#1684057412yes—
877C22C23×D24411yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—1224no—
883C4—2442no—
884C4—2442no—
885C4—2442no—
886C4—2442no—
887C4—2442no—
888C4D4×D24412yes—
889C4C22×D4×D6111yescharacteristic
890C4C2×#1451982311yescharacteristic
891C2—24no—
892C2—42no—
893C2—4882no—
894C2—2444no—
895C2#2145733414yesdirect product factor
896C2C2×D4×D24411yescharacteristic
897C2C22×#1451981011yescharacteristic
898C2C2×#1684057411yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#435C2
socleC23×C61C22×D4
prime radicalC2×#16840408C2
hypercenterC2×#435D61
hypocenterC61C2×#3266
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×#14519810C2semidirect
2. C23×#11758190C2semidirect
3. C2×D4×Dic122C2semidirect
5. #21457334C2direct (N × H)
6. C2×#16840156C2semidirect
7. C2×#16840008C2semidirect
8. C2×#16840003C2semidirect
9. C2×#16839985C2semidirect
10. C2×#16839968C2semidirect
11. C2×#16839926C2semidirect
12. C2×#16839920C2semidirect
13. C2×#16839903C2semidirect
14. C2×#16839915C2semidirect
15. C2×#16839864C2semidirect
16. C2×C61×#435C2semidirect
19. C23×Dic122C22semidirect
22. C2×#14519810C22semidirect
23. C22×Dic244C22semidirect
24. C22×Dic244C22semidirect
25. C22×Dic244C22semidirect
33. C22×#11758190C22semidirect
35. D4×Dic122C22semidirect
38. C2×#14519777C22semidirect
44. C2×#14519756C22semidirect
50. C2×C4×Dic122C22semidirect
54. #16840156C22semidirect
55. #16840008C22semidirect
56. #16840003C22semidirect
57. #16839985C22semidirect
58. #16839968C22semidirect
59. #16839926C22semidirect
60. #16839920C22semidirect
61. #16839915C22semidirect
62. #16839903C22semidirect
63. #16839864C22semidirect
64. C2×#14519711C22semidirect
65. C2×#14519702C22semidirect
66. C2×#14519702C22semidirect
67. C2×#14519702C22semidirect
68. C2×#14519702C22semidirect
71. C22×M16×C61C22semidirect
74. C61×#435C22semidirect
75. C2×C4⋊C8×C61C22semidirect
77. C2×C22⋊C8×C61C22semidirect
78. C2×#97×C61C22semidirect
97. C22×Dic122C23semidirect
115. C2×Dic244C23semidirect
116. C2×Dic244C23semidirect
117. C2×Dic244C23semidirect
124. C2×#11758190D4semidirect
132. #14519777C23semidirect
142. #14519756C23semidirect
150. C4×Dic122C23semidirect
171. #14519711C23semidirect
172. #14519702C23semidirect
173. #14519702C23semidirect
174. #14519702C23semidirect
175. #14519702C23semidirect
182. C2×M16×C61C23semidirect
195. C4⋊C8×C61C23semidirect
197. C22⋊C8×C61C23semidirect
198. #97×C61C23semidirect
323. #11758190C2×D4semidirect
329. C23×C61#137semidirect
417. C22×C61C2×#137semidirect
457. C2×#435D61semidirect
460. C2×C61#3266semidirect
483. C22×M16C2×D61semidirect
516. #435C2×D61semidirect
518. C2×C4⋊C8C2×D61semidirect
526. C2×C22⋊C8C2×D61semidirect
527. C2×#97C2×D61semidirect
528. C61C2×#3266semidirect
585. C2×M16C22×D61semidirect
639. C4⋊C8C22×D61semidirect
647. C22⋊C8C22×D61semidirect
648. #97C22×D61semidirect
791. C23#14519810semidirect
875. C22C2×#14519810semidirect
895. C2#21457334direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198102
C23×#117581902
C2×D4×Dic1222
C2×#168404082
#214573342
C2×#168401562
C2×#168400082
C2×#168400032
C2×#168399852
C2×#168399682
C2×#168399262
C2×#168399202
C2×#168399032
C2×#168399152
C2×#168398642
C2×C61×#4352
C2×#326661