Finite Group Databasebeta

← C2×#21457379 #30555047

Subgroups — C2×#21457379 #30555047

Order 15616.

2774 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519810C211yesmaximal, characteristic, complemented
2C22×#14519799C211yesmaximal, characteristic, complemented
3C2×#16840421C211yesmaximal, characteristic, complemented
4C2×#16840417C211yesmaximal, characteristic, complemented
5#21457379C2116yesmaximal, direct product factor
6C2×#16840156C211yesmaximal, characteristic, complemented
7C2×#16840008C211yesmaximal, characteristic, complemented
8C2×#16840003C211yesmaximal, characteristic, complemented
9C2×#16839973C211yesmaximal, characteristic, complemented
10C2×#16839978C211yesmaximal, characteristic, complemented
11C2×#16839926C211yesmaximal, characteristic, complemented
12C2×#16839926C211yesmaximal, characteristic, complemented
13C2×#16839909C211yesmaximal, characteristic, complemented
14C2×#16839920C211yesmaximal, characteristic, complemented
15C2×#16839864C211yesmaximal, characteristic, complemented
16C2×C61×#435C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×#11758222C2211yescharacteristic
19C22×#11758222C2211yescharacteristic
20C23×Dic122C2211yescharacteristic
21C2×#14519810—28no—
22C2×#14519810C2218yescomplemented
23C2×#14519799—28no—
24C2×#14519799C2218yescomplemented
25C22×Dic244C2211yescharacteristic
26C22×Dic244C2211yescharacteristic
27C22×Dic244C2211yescharacteristic
28C22×Dic244C2211yescharacteristic
29C22×#11758190C2211yescharacteristic
30C22×#11758190C2211yescharacteristic
31C22×#11758190C2211yescharacteristic
32C22×#11758190C2211yescharacteristic
33C22×D488C2211yescharacteristic
34#16840421—24no—
35#16840421C2218yescomplemented
36#16840417—24no—
37#16840417C2218yescomplemented
38C2×#14519777C2211yescharacteristic
39C2×#14519765C2211yescharacteristic
40C2×#14519763—21no—
41C2×#14519759—21no—
42C2×#14519759—21no—
43C2×#14519756C2211yescharacteristic
44C2×#14519756C2211yescharacteristic
45C2×#14519756C2211yescharacteristic
46C2×#14519755—21no—
47C2×#14519751C2211yescharacteristic
48C2×#14519749—21no—
49C2×#14519748—21no—
50C2×C4×Dic122C2211yescharacteristic
51C2×C4×D244C2211yescharacteristic
52C2×#14519737—21no—
53C2×C4⋊C4×D61—21no—
54#16840156C2218yescomplemented
55#16840008C2218yescomplemented
56#16840003C2218yescomplemented
57#16839978C2218yescomplemented
58#16839973C2218yescomplemented
59#16839926C2218yescomplemented
60#16839926C2218yescomplemented
61#16839920C2218yescomplemented
62#16839909C2218yescomplemented
63#16839864C2218yescomplemented
64C2×#14519711C2211yescharacteristic
65C2×#14519702C2211yescharacteristic
66C2×#14519702C2211yescharacteristic
67C2×#14519702C2211yescharacteristic
68C2×#14519702C2211yescharacteristic
69C2×#14519699C2211yescharacteristic
70C2×#14519699C2211yescharacteristic
71C22×M16×C61C2211yescharacteristic
72C23×C8×C61C2211yescharacteristic
73C2×C4×D4×C61C2211yescharacteristic
74C61×#435C2218yescomplemented
75C2×C4⋊C8×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C2×C22⋊C8×C61C2211yescharacteristic
78C2×#97×C61C2211yescharacteristic
79C2×#11758222—22no—
80C2×#11758222—22no—
81C2×#11758222—22no—
82C2×#11758222—24no—
83C2×#11758222—24no—
84C2×#11758222—24no—
85C2×#11758222—42no—
86C2×#11758222—42no—
87C2×#11758222—42no—
88C2×#11758222C2314yes—
89C2×#11758222C2314yes—
90C2×#11758222C2314yes—
91C22×Dic122—24no—
92C22×Dic122—21no—
93C22×Dic122—22no—
94C22×Dic122—42no—
95C22×Dic122C2311yescharacteristic
96C22×Dic122C2311yescharacteristic
97C22×Dic122C2311yescharacteristic
98C22×Dic122C2314yes—
99C22×Dic122C2311yescharacteristic
100C22×D244C2311yescharacteristic
101C22×D244C2311yescharacteristic
102C22×C22⋊D61—21no—
103C22×C22⋊D61—21no—
104C22×C22⋊D61—21no—
105C22×C22⋊D61—21no—
106C23×Dic61—21no—
107C22×C4×D61—21no—
108C22×C4×D61—21no—
109C22×C4×D61—21no—
110C22×C4×D61—21no—
111#14519810—232no—
112#14519799—232no—
113C2×Dic244—24no—
114C2×Dic244—24no—
115C2×Dic244—24no—
116C2×Dic244—42no—
117C2×Dic244C2314yes—
118C2×Dic244C2314yes—
119C2×Dic244C2314yes—
120C2×Dic244C2314yes—
121C2×#11758190—24no—
122C2×#11758190—24no—
123C2×#11758190—42no—
124C2×#11758190D418yescomplemented
125C2×#11758190C2314yes—
126C2×#11758190C2314yes—
127C2×#11758190C2314yes—
128C2×#11758190C2314yes—
129C2×D488—24no—
130C2×D488C2314yes—
131#14519777—22no—
132#14519777C2314yes—
133#14519765—22no—
134#14519765C2314yes—
135#14519763—28no—
136#14519759—28no—
137#14519759—28no—
138#14519756—22no—
139#14519756—22no—
140#14519756—22no—
141#14519756C2314yes—
142#14519756C2314yes—
143#14519756C2314yes—
144#14519755—28no—
145#14519751—22no—
146#14519751C2314yes—
147#14519749—28no—
148#14519748—28no—
149C4×Dic122—22no—
150C4×Dic122C2314yes—
151C4×D244—22no—
152C4×D244C2314yes—
153#14519737—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—
162C4⋊C4×D61—28no—
163C2×C22⋊Dic61—21no—
164C2×C22⋊Dic61—21no—
165C2×C22⋊Dic61—21no—
166C2×#11758198—21no—
167C2×#11758198—21no—
168C2×#11758198—21no—
169C2×#11758198—21no—
170C2×C4×Dic61—21no—
171#14519711C2314yes—
172#14519702C2314yes—
173#14519702C2314yes—
174#14519702C2314yes—
175#14519702C2314yes—
176#14519699C2314yes—
177#14519699C2314yes—
178C22×D4×C61D411yescharacteristic
179C23×C4×C61C2311yescharacteristic
180C23×C4×C61C2311yescharacteristic
181C2×M16×C61—24no—
182C2×M16×C61C2314yes—
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×C61C2314yes—
196C22⋊C8×C61C2314yes—
197C22⋊C8×C61C2314yes—
198#97×C61C2314yes—
199C24×C61C2×D411yescharacteristic
200C24×C61C2×D411yescharacteristic
201C23×D61—21no—
202C23×D61—21no—
203C2×D4×C61—42no—
204C2×D4×C61C2×D414yes—
205C22×C4×C61—22no—
206C22×C4×C61—22no—
207C22×C4×C61—22no—
208C22×C4×C61—22no—
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D412yes—
213C22×C4×C61C2×D412yes—
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2412yes—
216C22×C4×C61C2412yes—
217C22×C4×C61C2411yescharacteristic
218C2×C22⋊D61—24no—
219C2×C22⋊D61—24no—
220C2×C22⋊D61—24no—
221C2×C22⋊D61—24no—
222C2×C22⋊D61—44no—
223C2×C22⋊D61—44no—
224C2×C22⋊D61—44no—
225C2×C22⋊D61—44no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—24no—
232C22×Dic61—21no—
233C22×Dic61—44no—
234#11758222—28no—
235#11758222—28no—
236#11758222—28no—
237#11758222—44no—
238#11758222—44no—
239#11758222—44no—
240#11758222—48no—
241#11758222—48no—
242#11758222—48no—
243C2×D244—21no—
244C2×D244—22no—
245C2×D244—22no—
246C2×D244—22no—
247C2×D244—21no—
248C2×D244C2×D414yes—
249C2×D244C2412yes—
250C2×D244C2412yes—
251C2×C4×D61—24no—
252C2×C4×D61—24no—
253C2×C4×D61—24no—
254C2×C4×D61—24no—
255C2×C4×D61—44no—
256C2×C4×D61—44no—
257C2×C4×D61—44no—
258C2×C4×D61—44no—
259C2×Dic122—21no—
260C2×Dic122—22no—
261C2×Dic122—22no—
262C2×Dic122—22no—
263C2×Dic122—22no—
264C2×Dic122—22no—
265C2×Dic122—22no—
266C2×Dic122—22no—
267C2×Dic122—28no—
268C2×Dic122—24no—
269C2×Dic122—21no—
270C2×Dic122—21no—
271C2×Dic122—21no—
272C2×Dic122—44no—
273C2×Dic122—48no—
274C2×Dic122—44no—
275C2×Dic122C2×D414yes—
276C2×Dic122C2412yes—
277C2×Dic122C2412yes—
278C2×Dic122C2412yes—
279C2×Dic122C2412yes—
280M16×C61—28no—
281C2×C8×C61—22no—
282C2×C8×C61—22no—
283C2×C8×C61—22no—
284C2×C8×C61—28no—
285C2×C8×C61C2×D414yes—
286C2×C8×C61C2412yes—
287C2×C8×C61C2412yes—
288C2×C8×C61C2412yes—
289C2×C8×C61C2412yes—
290C4⋊C4×C61C2×D414yes—
291C22⋊C4×C61C2×D414yes—
292C22⋊C4×C61C2×D414yes—
293C42×C61C2×D412yes—
294C42×C61C2412yes—
295C22⋊Dic61—24no—
296C22⋊Dic61—24no—
297C22⋊Dic61—24no—
298#11758198—24no—
299#11758198—24no—
300#11758198—24no—
301#11758198—24no—
302C4⋊Dic61—24no—
303C4⋊Dic61—24no—
304C4⋊Dic61—21no—
305C4⋊Dic61—21no—
306C4⋊Dic61C2412yes—
307C4⋊Dic61C2412yes—
308#11758196—24no—
309#11758196—24no—
310#11758196—24no—
311#11758196—24no—
312C4×Dic61—24no—
313Dic244—28no—
314Dic244—28no—
315Dic244—28no—
316Dic244—44no—
317D488—28no—
318#11758190—28no—
319#11758190—28no—
320#11758190—44no—
321#11758190C2×D4116yescomplemented
322C23×C61—22no—
323C23×C61—22no—
324C23×C61—22no—
325C23×C61—22no—
326C23×C61—22no—
327C23×C61—22no—
328C23×C61C22×D412yes—
329C23×C61C22×D412yes—
330C23×C61C22×D411yescharacteristic
331C22×D61—24no—
332C22×D61—22no—
333C22×D61—22no—
334C22×D61—42no—
335C22×D61—42no—
336C22×D61—42no—
337C22×D61—42no—
338C22×D61—42no—
339D4×C61—44no—
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×C61C22×D412yes—
351C2×C4×C61C22×D412yes—
352C2×C4×C61C22×D412yes—
353C2×C4×C61C22×D412yes—
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C22×D412yes—
356C2×C4×C61H(5,𝔽2)12yes—
357C2×C4×C61C2511yescharacteristic
358C22⋊D61—48no—
359C22⋊D61—48no—
360C22⋊D61—48no—
361C22⋊D61—48no—
362C2×Dic61—24no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—48no—
370C2×Dic61—42no—
371C2×Dic61—42no—
372C2×Dic61—42no—
373C2×Dic61—42no—
374C2×Dic61—42no—
375D244—24no—
376D244—22no—
377D244—22no—
378D244—22no—
379D244—42no—
380D244C22×D414yes—
381C4×D61—48no—
382C4×D61—48no—
383C4×D61—48no—
384C4×D61—48no—
385Dic122—24no—
386Dic122—22no—
387Dic122—22no—
388Dic122—22no—
389Dic122—22no—
390Dic122—22no—
391Dic122—22no—
392Dic122—22no—
393Dic122—48no—
394Dic122—42no—
395Dic122—42no—
396Dic122—42no—
397Dic122C22×D414yes—
398C8×C61—22no—
399C8×C61—22no—
400C8×C61—22no—
401C8×C61C22×D414yes—
402C2×#3269—611nomaximal, Sylow
403C22×C61—22no—
404C22×C61—22no—
405C22×C61—22no—
406C22×C61—22no—
407C22×C61—22no—
408C22×C61—22no—
409C22×C61—44no—
410C22×C61—44no—
411C22×C61D4212yes—
412C22×C61#57512yes—
413C22×C61#57812yes—
414C22×C61C23×D411yescharacteristic
415C2×D61—24no—
416C2×D61—48no—
417C2×D61—42no—
418C2×D61—42no—
419C2×D61—42no—
420C2×D61—42no—
421C2×D61—42no—
422C2×D61—84no—
423C4×C61—22no—
424C4×C61—22no—
425C4×C61—22no—
426C4×C61—22no—
427C4×C61D4212yes—
428C4×C61C23×D411yescharacteristic
429C4×C61C2×H(5,𝔽2)11yescharacteristic
430Dic61—24no—
431Dic61—42no—
432Dic61—42no—
433Dic61—42no—
434Dic61—42no—
435Dic61—42no—
436C22×#137—611no—
437C22×#135—611no—
438C2×#548—611no—
439C2×#547—611no—
440#3269—6116no—
441C2×#497—611no—
442C2×#468—611no—
443C2×#467—611no—
444C2×#462—611no—
445C2×#463—611no—
446C2×#452—611no—
447C2×#452—611no—
448C2×#449—611no—
449C2×#451—611no—
450C2×#440—611no—
451C2×#435D6111yescharacteristic, complemented
452C2×C61—42no—
453C2×C61—42no—
454C2×C61#326914yescomplemented
455C2×C61C2×D4211yescharacteristic
456C2×C61C2×#57511yescharacteristic
457C2×C61C2×#57811yescharacteristic
458D61—44no—
459D61—82no—
460C22×#41—611no—
461C22×#41—611no—
462C22×#41—611no—
463C23×Q8—611no—
464C2×#137—618no—
465C2×#137—1228no—
466C2×#135—618no—
467C2×#135—1228no—
468C22×Q16—611no—
469C22×Q16—611no—
470C22×Q16—611no—
471C22×Q16—611no—
472C22×SD16—611no—
473C22×SD16—611no—
474C22×SD16—611no—
475C22×SD16—611no—
476C22×D8—611no—
477C22×M16C2×D6111yescharacteristic
478C23×C8C2×D6111yescharacteristic
479#548—618no—
480#548—1224no—
481#547—618no—
482#547—1224no—
483C2×C4⋊Q8—611no—
484C2×#124—611no—
485C2×#124—1221no—
486C2×#123—1221no—
487C2×#123—1221no—
488C2×C22⋊Q8—611no—
489C2×C22⋊Q8—611no—
490C2×C22⋊Q8—611no—
491C2×C22⋊Q8—1221no—
492C2×#121—611no—
493C2×#121—1221no—
494C2×#121—1221no—
495C2×C4×Q8—611no—
496C2×C4×D4—611no—
497C2×C4×D4—1221no—
498C2×C4×D4C2×D6111yescharacteristic
499C22×C4⋊C4—1221no—
500#497—618no—
501#468—618no—
502#467—618no—
503#463—618no—
504#462—618no—
505#452—618no—
506#452—618no—
507#451—618no—
508#449—618no—
509#440—618no—
510#435C2×D6118yescomplemented
511C2×#107—611no—
512C2×C4⋊C8C2×D6111yescharacteristic
513C2×#103—611no—
514C2×#103—611no—
515C2×#103—611no—
516C2×#103—611no—
517C2×#102—611no—
518C2×#102—611no—
519C2×C22⋊C8C2×D6111yescharacteristic
520C2×C22⋊C8C2×D6111yescharacteristic
521C2×#97C2×D6111yescharacteristic
522C61C2×#326911yescharacteristic, complemented, Sylow
523C2×#41—614no—
524C2×#41—614no—
525C2×#41—614no—
526C2×#41—1224no—
527C2×#41—1224no—
528C2×#41—1224no—
529C2×#41—1222no—
530C2×#41—1222no—
531C2×#41—1222no—
532C2×#41—2442no—
533C2×#41—2442no—
534C2×#41—2442no—
535C22×Q8—611no—
536C22×Q8—611no—
537C22×Q8—611no—
538C22×Q8—611no—
539C22×Q8—614no—
540C22×Q8—1224no—
541C22×Q8—1221no—
542C22×Q8—1222no—
543C22×Q8—2442no—
544C22×D4—611no—
545C22×D4—611no—
546C22×D4—1221no—
547C22×D4—1221no—
548C22×D4—1221no—
549C22×D4—1221no—
550C22×D4D24411yescharacteristic
551C23×C4—1221no—
552C23×C4—1221no—
553C23×C4—1221no—
554C23×C4—1221no—
555C23×C4—1221no—
556C23×C4C22×D6111yescharacteristic
557C23×C4C22×D6111yescharacteristic
558#137—12232no—
559#135—12232no—
560C2×Q16—614no—
561C2×Q16—614no—
562C2×Q16—614no—
563C2×Q16—614no—
564C2×Q16—1224no—
565C2×Q16—1224no—
566C2×Q16—1224no—
567C2×Q16—2442no—
568C2×SD16—618no—
569C2×SD16—614no—
570C2×SD16—614no—
571C2×SD16—614no—
572C2×SD16—614no—
573C2×SD16—1224no—
574C2×SD16—1224no—
575C2×SD16—2442no—
576C2×D8—614no—
577C2×D8—1224no—
578C2×M16—24no—
579C2×M16C22×D6114yes—
580C22×C8—24no—
581C22×C8C22×D6111yescharacteristic
582C22×C8C22×D6114yes—
583C22×C8C22×D6111yescharacteristic
584C22×C8C22×D6111yescharacteristic
585C22×C8C22×D6111yescharacteristic
586C4⋊Q8—614no—
587C4⋊Q8—1222no—
588#124—614no—
589#124—1228no—
590#124—1222no—
591#123—1228no—
592#123—1228no—
593C22⋊Q8—614no—
594C22⋊Q8—614no—
595C22⋊Q8—614no—
596C22⋊Q8—1222no—
597C22⋊Q8—1222no—
598C22⋊Q8—1222no—
599C22⋊Q8—1228no—
600#121—614no—
601#121—1228no—
602#121—1228no—
603#121—1222no—
604C4×Q8—614no—
605C4×Q8—1222no—
606C4×D4—614no—
607C4×D4—1228no—
608C4×D4—1222no—
609C4×D4D24414yes—
610C4×D4C22×D6114yes—
611C2×C4⋊C4—611no—
612C2×C4⋊C4—611no—
613C2×C4⋊C4—1221no—
614C2×C4⋊C4—1221no—
615C2×C4⋊C4—1221no—
616C2×C4⋊C4—1221no—
617C2×C4⋊C4—1221no—
618C2×C4⋊C4—1221no—
619C2×C4⋊C4—1228no—
620C2×C4⋊C4D24411yescharacteristic
621C2×C22⋊C4—1221no—
622C2×C22⋊C4—1221no—
623C2×C22⋊C4—1221no—
624C2×C22⋊C4—1221no—
625C2×C22⋊C4—1221no—
626C2×C22⋊C4—1221no—
627C2×C22⋊C4—1221no—
628C2×C22⋊C4D24411yescharacteristic
629C2×C22⋊C4D24411yescharacteristic
630C2×C42—1221no—
631C2×C42C22×D6111yescharacteristic
632#107—614no—
633C4⋊C8C22×D6114yes—
634#103—614no—
635#103—614no—
636#103—614no—
637#103—614no—
638#102—614no—
639#102—614no—
640C22⋊C8C22×D6114yes—
641C22⋊C8C22×D6114yes—
642#97C22×D6114yes—
643C24—1221no—
644C24—1221no—
645C24C2×D24411yescharacteristic
646C24C2×D24411yescharacteristic
647#41—1228no—
648#41—1228no—
649#41—1228no—
650#41—2444no—
651#41—2444no—
652#41—2444no—
653#41—2448no—
654#41—2448no—
655#41—2448no—
656C2×Q8—614no—
657C2×Q8—612no—
658C2×Q8—612no—
659C2×Q8—612no—
660C2×Q8—612no—
661C2×Q8—1228no—
662C2×Q8—1221no—
663C2×Q8—1224no—
664C2×Q8—1221no—
665C2×Q8—1221no—
666C2×Q8—1221no—
667C2×Q8—1222no—
668C2×Q8—1222no—
669C2×Q8—1222no—
670C2×Q8—1222no—
671C2×Q8—1222no—
672C2×Q8—1222no—
673C2×Q8—1222no—
674C2×Q8—2444no—
675C2×Q8—2444no—
676C2×Q8—2448no—
677C2×D4—42no—
678C2×D4—614no—
679C2×D4—612no—
680C2×D4—612no—
681C2×D4—1224no—
682C2×D4—1224no—
683C2×D4—1224no—
684C2×D4—1224no—
685C2×D4—1222no—
686C2×D4—1221no—
687C2×D4—1221no—
688C2×D4—1222no—
689C2×D4—1222no—
690C2×D4—2444no—
691C2×D4—2444no—
692C2×D4—2444no—
693C2×D4—2444no—
694C2×D4C2×D24414yes—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—1221no—
700C22×C4—1224no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1224no—
707C22×C4—1224no—
708C22×C4—1224no—
709C22×C4—1224no—
710C22×C4—2444no—
711C22×C4—2444no—
712C22×C4—2444no—
713C22×C4—2444no—
714C22×C4—2444no—
715C22×C4C2×D24412yes—
716C22×C4C2×D24412yes—
717C22×C4C2×D24411yescharacteristic
718C22×C4C2×D24411yescharacteristic
719C22×C4C2×D24411yescharacteristic
720C22×C4C2×D24411yescharacteristic
721C22×C4C23×D6112yes—
722C22×C4C23×D6112yes—
723C22×C4C23×D6111yescharacteristic
724Q16—1228no—
725Q16—1228no—
726Q16—1228no—
727Q16—2444no—
728SD16—6116no—
729SD16—1228no—
730SD16—1228no—
731SD16—2444no—
732D8—1228no—
733M16—28no—
734C2×C8—22no—
735C2×C8—22no—
736C2×C8—22no—
737C2×C8—28no—
738C2×C8D4×D6114yes—
739C2×C8C23×D6112yes—
740C2×C8C23×D6112yes—
741C2×C8C23×D6112yes—
742C2×C8C23×D6112yes—
743C4⋊C4—612no—
744C4⋊C4—612no—
745C4⋊C4—1221no—
746C4⋊C4—1221no—
747C4⋊C4—1224no—
748C4⋊C4—1224no—
749C4⋊C4—1224no—
750C4⋊C4—1224no—
751C4⋊C4—1224no—
752C4⋊C4—1224no—
753C4⋊C4C2×D24414yes—
754C22⋊C4—1224no—
755C22⋊C4—1224no—
756C22⋊C4—1224no—
757C22⋊C4—1224no—
758C22⋊C4—1224no—
759C22⋊C4—1224no—
760C22⋊C4—1224no—
761C22⋊C4C2×D24414yes—
762C22⋊C4C2×D24414yes—
763C42—1224no—
764C42C2×D24412yes—
765C42C23×D6112yes—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—1222no—
773C23—1224no—
774C23—1222no—
775C23—2442no—
776C23—2442no—
777C23—2442no—
778C23—2442no—
779C23—2442no—
780C23C22×D24412yes—
781C23C22×D24412yes—
782C23C22×D24411yescharacteristic
783Q8—614no—
784Q8—1222no—
785Q8—1224no—
786Q8—1222no—
787Q8—1222no—
788Q8—1222no—
789Q8—1222no—
790Q8—1222no—
791Q8—1222no—
792Q8—2448no—
793Q8—2442no—
794Q8—2442no—
795Q8—2442no—
796D4—44no—
797D4—614no—
798D4—1222no—
799D4—1222no—
800D4—1222no—
801D4—1224no—
802D4—2448no—
803D4—2448no—
804D4—2448no—
805D4—2448no—
806D4—2442no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—1222no—
818C2×C4—1224no—
819C2×C4—1222no—
820C2×C4—1222no—
821C2×C4—1222no—
822C2×C4—1222no—
823C2×C4—1222no—
824C2×C4—2448no—
825C2×C4—2448no—
826C2×C4—2448no—
827C2×C4—2448no—
828C2×C4—2448no—
829C2×C4—2442no—
830C2×C4—2442no—
831C2×C4—2442no—
832C2×C4—2442no—
833C2×C4—2442no—
834C2×C4C2×D4×D6112yes—
835C2×C4C22×D24412yes—
836C2×C4C22×D24412yes—
837C2×C4C22×D24412yes—
838C2×C4C22×D24412yes—
839C2×C4C22×D24411yescharacteristic
840C2×C4#1451982312yes—
841C2×C4C24×D6111yescharacteristic
842C8—22no—
843C8—22no—
844C8—22no—
845C8C2×D4×D6114yes—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—44no—
853C22—44no—
854C22—1224no—
855C22—4884no—
856C22—2442no—
857C22—2442no—
858C22—2442no—
859C22—2442no—
860C22—2442no—
861C22—2448no—
862C22D4×D24412yes—
863C22#1684056212yes—
864C22#1684057912yes—
865C22C23×D24411yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—1224no—
871C4—2442no—
872C4—2442no—
873C4—2442no—
874C4—2442no—
875C4—2442no—
876C4D4×D24412yes—
877C4C22×D4×D6111yescharacteristic
878C4C2×#1451982311yescharacteristic
879C2—42no—
880C2—42no—
881C2—4882no—
882C2—2444no—
883C2#2145737914yesdirect product factor
884C2C2×D4×D24411yescharacteristic
885C2C2×#1684056211yescharacteristic
886C2C2×#1684057911yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#435C2
socleC23×C61C22×D4
hypercenterC2×#435D61
hypocenterC61C2×#3269
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. C22×#14519799C2semidirect
3. C2×#16840421C2semidirect
4. C2×#16840417C2semidirect
5. #21457379C2direct (N × H)
6. C2×#16840156C2semidirect
7. C2×#16840008C2semidirect
8. C2×#16840003C2semidirect
9. C2×#16839973C2semidirect
10. C2×#16839978C2semidirect
11. C2×#16839926C2semidirect
12. C2×#16839926C2semidirect
13. C2×#16839909C2semidirect
14. C2×#16839920C2semidirect
15. C2×#16839864C2semidirect
16. C2×C61×#435C2semidirect
22. C2×#14519810C22semidirect
24. C2×#14519799C22semidirect
35. #16840421C22semidirect
37. #16840417C22semidirect
54. #16840156C22semidirect
55. #16840008C22semidirect
56. #16840003C22semidirect
57. #16839978C22semidirect
58. #16839973C22semidirect
59. #16839926C22semidirect
60. #16839926C22semidirect
61. #16839920C22semidirect
62. #16839909C22semidirect
63. #16839864C22semidirect
74. C61×#435C22semidirect
124. C2×#11758190D4semidirect
321. #11758190C2×D4semidirect
451. C2×#435D61semidirect
454. C2×C61#3269semidirect
510. #435C2×D61semidirect
522. C61C2×#3269semidirect
883. C2#21457379direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198102
C22×#145197992
C2×#168404212
C2×#168404172
#214573792
C2×#168401562
C2×#168400082
C2×#168400032
C2×#168399732
C2×#168399782
C2×#168399262
C2×#168399092
C2×#168399202
C2×#168398642
C2×C61×#4352
C2×#326961