Finite Group Databasebeta

← C2×#21457381 #30555049

Subgroups — C2×#21457381 #30555049

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×#14519798C211yesmaximal, characteristic, complemented
3C2×#16840418C211yesmaximal, characteristic, complemented
4C2×#16840414C211yesmaximal, characteristic, complemented
5#21457381C2116yesmaximal, direct product factor
6C2×#16840153C211yesmaximal, characteristic, complemented
7C2×#16840004C211yesmaximal, characteristic, complemented
8C2×#16839971C211yesmaximal, characteristic, complemented
9C2×#16839976C211yesmaximal, characteristic, complemented
10C2×#16839927C211yesmaximal, characteristic, complemented
11C2×#16839925C211yesmaximal, characteristic, complemented
12C2×#16839905C211yesmaximal, characteristic, complemented
13C2×#16839917C211yesmaximal, characteristic, complemented
14C2×#16839861C211yesmaximal, characteristic, complemented
15C2×#16839831C211yesmaximal, characteristic, complemented
16C2×C61×#468C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758222C2211yescharacteristic
19C22×#11758224C2211yescharacteristic
20C23×Dic122C2211yescharacteristic
21C2×#14519810—28no—
22C2×#14519810C2218yescomplemented
23C2×#14519798—28no—
24C2×#14519798C2218yescomplemented
25C22×Dic244C2211yescharacteristic
26C22×Dic244C2211yescharacteristic
27C22×#11758202C2211yescharacteristic
28C22×#11758202C2211yescharacteristic
29C22×#11758190C2211yescharacteristic
30C22×#11758190C2211yescharacteristic
31C22×#11758200C2211yescharacteristic
32C22×#11758199C2211yescharacteristic
33C22×C8×D61C2211yescharacteristic
34#16840418—24no—
35#16840418C2218yescomplemented
36#16840414—24no—
37#16840414C2218yescomplemented
38C2×#14519775C2211yescharacteristic
39C2×#14519764C2211yescharacteristic
40C2×#14519763—21no—
41C2×#14519762—21no—
42C2×#14519759—21no—
43C2×#14519757C2211yescharacteristic
44C2×#14519757C2211yescharacteristic
45C2×#14519754—21no—
46C2×#14519750—21no—
47C2×#14519749—21no—
48C2×#14519742C2211yescharacteristic
49C2×D4×Dic61—21no—
50C2×#14519739C2211yescharacteristic
51C2×C4×C22⋊D61C2211yescharacteristic
52C2×C4⋊C4×D61—21no—
53#16840153C2218yescomplemented
54#16840004C2218yescomplemented
55#16839976C2218yescomplemented
56#16839971C2218yescomplemented
57#16839927C2218yescomplemented
58#16839925C2218yescomplemented
59#16839917C2218yescomplemented
60#16839905C2218yescomplemented
61#16839861C2218yescomplemented
62#16839831C2218yescomplemented
63C2×#14519706C2211yescharacteristic
64C2×#14519700C2211yescharacteristic
65C2×#14519700C2211yescharacteristic
66C2×#14519700C2211yescharacteristic
67C2×#14519697C2211yescharacteristic
68C2×C22⋊#92418C2211yescharacteristic
69C2×#14519689C2211yescharacteristic
70C2×#14519687C2211yescharacteristic
71C22×SD16×C61C2211yescharacteristic
72C22×M16×C61C2211yescharacteristic
73C2×C22⋊Q8×C61C2211yescharacteristic
74C2×#121×C61C2211yescharacteristic
75C61×#468C2218yescomplemented
76C2×#107×C61C2211yescharacteristic
77C2×#103×C61C2211yescharacteristic
78C2×#102×C61C2211yescharacteristic
79C2×#11758226—22no—
80C2×#11758226—24no—
81C2×#11758226—42no—
82C2×#11758226C2314yes—
83C2×#11758222—22no—
84C2×#11758222—24no—
85C2×#11758222—42no—
86C2×#11758222C2314yes—
87C2×#11758224—22no—
88C2×#11758224—24no—
89C2×#11758224—42no—
90C2×#11758224C2314yes—
91C22×Dic122—24no—
92C22×Dic122—21no—
93C22×Dic122—22no—
94C22×Dic122—42no—
95C22×Dic122C2311yescharacteristic
96C22×Dic122C2311yescharacteristic
97C22×Dic122C2314yes—
98C22×Dic122C2311yescharacteristic
99C22×D244—21no—
100C22×D244C2311yescharacteristic
101C22×C22⋊D61—21no—
102C22×C22⋊D61—21no—
103C22×C22⋊D61D411yescharacteristic
104C23×Dic61—21no—
105C23×Dic61—21no—
106C22×C4×D61—21no—
107C22×C4×D61—21no—
108C22×C4×D61—21no—
109C22×C4×D61C2311yescharacteristic
110#14519810—232no—
111#14519798—232no—
112C2×Dic244—24no—
113C2×Dic244—24no—
114C2×Dic244C2314yes—
115C2×Dic244C2314yes—
116C2×#11758202—24no—
117C2×#11758202—42no—
118C2×#11758202C2314yes—
119C2×#11758202C2314yes—
120C2×#11758190—24no—
121C2×#11758190D418yescomplemented
122C2×#11758190C2314yes—
123C2×#11758190C2314yes—
124C2×#11758200—42no—
125C2×#11758200C2314yes—
126C2×#11758199—24no—
127C2×#11758199C2314yes—
128C22×#92418C2311yescharacteristic
129C22×#92418C2311yescharacteristic
130C2×C8×D61—24no—
131C2×C8×D61C2314yes—
132#14519775—22no—
133#14519775C2314yes—
134#14519764—22no—
135#14519764C2314yes—
136#14519763—28no—
137#14519762—28no—
138#14519759—28no—
139#14519757—22no—
140#14519757—22no—
141#14519757C2314yes—
142#14519757C2314yes—
143#14519754—28no—
144#14519750—28no—
145#14519749—28no—
146#14519742—22no—
147#14519742C2314yes—
148D4×Dic61—28no—
149#14519739—22no—
150#14519739C2314yes—
151C4×C22⋊D61D414yes—
152C4×C22⋊D61C2314yes—
153C2×C4⋊Dic61—21no—
154C2×C4⋊Dic61—21no—
155C2×#11758196—21no—
156C2×#11758196—21no—
157C2×#11758196—21no—
158C2×#11758196D411yescharacteristic
159C4⋊C4×D61—28no—
160C2×C22⋊Dic61—21no—
161C2×C22⋊Dic61—21no—
162C2×C22⋊Dic61D411yescharacteristic
163C2×#11758198—21no—
164C2×#11758198—21no—
165C2×#11758198—21no—
166C2×#11758198D411yescharacteristic
167C2×C4×Dic61—21no—
168C2×C4×Dic61C2311yescharacteristic
169#14519706C2314yes—
170#14519700C2314yes—
171#14519700C2314yes—
172#14519700C2314yes—
173#14519697C2314yes—
174C22⋊#92418C2314yes—
175#14519689C2314yes—
176#14519687C2314yes—
177C22×Q8×C61C2311yescharacteristic
178C22×D4×C61—21no—
179C22×D4×C61C2311yescharacteristic
180C23×C4×C61C2311yescharacteristic
181C2×SD16×C61—24no—
182C2×SD16×C61C2314yes—
183C2×M16×C61—24no—
184C2×M16×C61C2314yes—
185C22×C8×C61C2311yescharacteristic
186C22×C8×C61C2311yescharacteristic
187C22⋊Q8×C61—22no—
188C22⋊Q8×C61C2314yes—
189#121×C61—22no—
190#121×C61C2314yes—
191C2×C4⋊C4×C61—21no—
192C2×C4⋊C4×C61C2311yescharacteristic
193C2×C4⋊C4×C61C2311yescharacteristic
194C2×C22⋊C4×C61—21no—
195C2×C22⋊C4×C61—21no—
196#107×C61C2314yes—
197#103×C61C2314yes—
198#102×C61C2314yes—
199C24×C61—21no—
200C24×C61C2×D411yescharacteristic
201C23×D61—21no—
202C23×D61C2×D411yescharacteristic
203C2×Q8×C61—21no—
204C2×Q8×C61—22no—
205C2×Q8×C61—22no—
206C2×Q8×C61C2412yes—
207C2×D4×C61—24no—
208C2×D4×C61—22no—
209C2×D4×C61—21no—
210C2×D4×C61—22no—
211C2×D4×C61—44no—
212C2×D4×C61C2412yes—
213C22×C4×C61—22no—
214C22×C4×C61—22no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D412yes—
220C22×C4×C61C2412yes—
221C22×C4×C61C2411yescharacteristic
222C2×C22⋊D61—24no—
223C2×C22⋊D61—24no—
224C2×C22⋊D61—42no—
225C2×C22⋊D61—44no—
226C2×C22⋊D61—44no—
227C2×C22⋊D61C2×D414yes—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—24no—
232C22×Dic61—24no—
233C22×Dic61—44no—
234C22×Dic61—44no—
235C22×Dic61C2×D411yescharacteristic
236C22×Dic61C2×D411yescharacteristic
237C22×Dic61C2×D411yescharacteristic
238#11758226—28no—
239#11758226—44no—
240#11758226—48no—
241#11758224—28no—
242#11758224—44no—
243#11758224—48no—
244#11758222—28no—
245#11758222—44no—
246#11758222—48no—
247C2×D244—21no—
248C2×D244—22no—
249C2×D244—24no—
250C2×D244—44no—
251C2×D244C2×D414yes—
252C2×D244C2412yes—
253C2×C4×D61—22no—
254C2×C4×D61—22no—
255C2×C4×D61—24no—
256C2×C4×D61—24no—
257C2×C4×D61—24no—
258C2×C4×D61—44no—
259C2×C4×D61—44no—
260C2×C4×D61—44no—
261C2×C4×D61C2×D412yes—
262C2×C4×D61C2412yes—
263C2×Dic122—21no—
264C2×Dic122—22no—
265C2×Dic122—22no—
266C2×Dic122—22no—
267C2×Dic122—22no—
268C2×Dic122—22no—
269C2×Dic122—28no—
270C2×Dic122—24no—
271C2×Dic122—21no—
272C2×Dic122—21no—
273C2×Dic122—44no—
274C2×Dic122—48no—
275C2×Dic122—44no—
276C2×Dic122C2×D414yes—
277C2×Dic122C2412yes—
278C2×Dic122C2412yes—
279C2×Dic122C2412yes—
280SD16×C61—28no—
281M16×C61—28no—
282C2×C8×C61—22no—
283C2×C8×C61C2×D414yes—
284C2×C8×C61C2412yes—
285C2×C8×C61C2412yes—
286C4⋊C4×C61—24no—
287C4⋊C4×C61—21no—
288C4⋊C4×C61—21no—
289C4⋊C4×C61C2412yes—
290C4⋊C4×C61C2412yes—
291C22⋊C4×C61—24no—
292C22⋊C4×C61—24no—
293C22⋊Dic61—24no—
294C22⋊Dic61—24no—
295C22⋊Dic61C2×D414yes—
296#11758202—28no—
297#11758202—44no—
298#11758200—44no—
299#11758199—28no—
300#11758198—24no—
301#11758198—24no—
302#11758198—24no—
303#11758198C2×D414yes—
304C4⋊Dic61—24no—
305C4⋊Dic61—24no—
306#11758196—24no—
307#11758196—24no—
308#11758196—24no—
309#11758196C2×D414yes—
310C4×Dic61—24no—
311C4×Dic61C2×D412yes—
312C4×Dic61C2412yes—
313C2×#92418—22no—
314C2×#92418—22no—
315C2×#92418C2412yes—
316C2×#92418C2412yes—
317Dic244—28no—
318Dic244—28no—
319#11758190—28no—
320#11758190C2×D4116yescomplemented
321C8×D61—28no—
322C23×C61—22no—
323C23×C61—22no—
324C23×C61—22no—
325C23×C61—22no—
326C23×C61—42no—
327C23×C61—42no—
328C23×C61—42no—
329C23×C61C22×D412yes—
330C23×C61C22×D411yescharacteristic
331C22×D61—22no—
332C22×D61—24no—
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—42no—
337C22×D61—42no—
338C22×D61C22×D412yes—
339Q8×C61—22no—
340Q8×C61—22no—
341Q8×C61—42no—
342D4×C61—22no—
343D4×C61—22no—
344D4×C61—48no—
345D4×C61—42no—
346C2×C4×C61—22no—
347C2×C4×C61—24no—
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×C61C22×D412yes—
357C2×C4×C61C22×D411yescharacteristic
358C2×C4×C61C22×D412yes—
359C2×C4×C61H(5,𝔽2)12yes—
360C2×C4×C61C2511yescharacteristic
361C22⋊D61—44no—
362C22⋊D61—48no—
363C22⋊D61—48no—
364C2×Dic61—24no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—48no—
372C2×Dic61—48no—
373C2×Dic61—42no—
374C2×Dic61—42no—
375C2×Dic61C22×D412yes—
376C2×Dic61C22×D412yes—
377C2×Dic61C22×D412yes—
378D244—24no—
379D244—22no—
380D244—48no—
381D244C22×D414yes—
382C4×D61—24no—
383C4×D61—22no—
384C4×D61—22no—
385C4×D61—48no—
386C4×D61—48no—
387C4×D61—48no—
388Dic122—24no—
389Dic122—22no—
390Dic122—22no—
391Dic122—22no—
392Dic122—22no—
393Dic122—22no—
394Dic122—48no—
395Dic122—42no—
396Dic122—42no—
397Dic122C22×D414yes—
398C8×C61—22no—
399C8×C61C22×D414yes—
400#92418—22no—
401#92418—22no—
402C2×#3269—611nomaximal, Sylow
403C22×C61—22no—
404C22×C61—22no—
405C22×C61—22no—
406C22×C61—44no—
407C22×C61—42no—
408C22×C61—42no—
409C22×C61—42no—
410C22×C61—84no—
411C22×C61D4212yes—
412C22×C61#57512yes—
413C22×C61#57812yes—
414C22×C61C23×D411yescharacteristic
415C2×D61—22no—
416C2×D61—24no—
417C2×D61—22no—
418C2×D61—22no—
419C2×D61—44no—
420C2×D61—48no—
421C2×D61—42no—
422C2×D61—42no—
423C4×C61—22no—
424C4×C61—42no—
425C4×C61—42no—
426C4×C61—42no—
427C4×C61D4212yes—
428C4×C61C23×D411yescharacteristic
429C4×C61C2×H(5,𝔽2)11yescharacteristic
430Dic61—24no—
431Dic61—22no—
432Dic61—22no—
433Dic61—22no—
434Dic61—42no—
435Dic61—42no—
436C22×#137—611no—
437C22×#135—611no—
438C2×#548—611no—
439C2×#547—611no—
440#3269—6116no—
441C2×#497—611no—
442C2×#468D6111yescharacteristic, complemented
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×#435—611no—
452C2×C61—42no—
453C2×C61—82no—
454C2×C61#326914yescomplemented
455C2×C61C2×D4211yescharacteristic
456C2×C61C2×#57511yescharacteristic
457C2×C61C2×#57811yescharacteristic
458D61—42no—
459D61—44no—
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×SD16C2×D6111yescharacteristic
476C22×D8—611no—
477C22×M16C2×D6111yescharacteristic
478C23×C8—611no—
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—1221no—
491C2×C22⋊Q8C2×D6111yescharacteristic
492C2×#121—1221no—
493C2×#121—1221no—
494C2×#121C2×D6111yescharacteristic
495C2×C4×Q8—611no—
496C2×C4×D4—611no—
497C2×C4×D4—611no—
498C2×C4×D4—1221no—
499C22×C4⋊C4—1221no—
500#497—618no—
501#468C2×D6118yescomplemented
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#435—618no—
511C2×#107C2×D6111yescharacteristic
512C2×C4⋊C8—611no—
513C2×#103—611no—
514C2×#103—611no—
515C2×#103—611no—
516C2×#103C2×D6111yescharacteristic
517C2×#102—611no—
518C2×#102C2×D6111yescharacteristic
519C2×C22⋊C8—611no—
520C2×C22⋊C8—611no—
521C2×#97—611no—
522C61C2×#326911yescharacteristic, complemented, Sylow
523C2×#41—614no—
524C2×#41—614no—
525C2×#41—614no—
526C2×#41—1224no—
527C2×#41—1222no—
528C2×#41—1222no—
529C2×#41—1222no—
530C2×#41—1224no—
531C2×#41—1224no—
532C2×#41—2442no—
533C2×#41—2442no—
534C2×#41—2442no—
535C22×Q8—611no—
536C22×Q8—611no—
537C22×Q8—611no—
538C22×Q8—614no—
539C22×Q8—1224no—
540C22×Q8—1221no—
541C22×Q8—1222no—
542C22×Q8—2442no—
543C22×Q8C22×D6111yescharacteristic
544C22×D4—21no—
545C22×D4—611no—
546C22×D4—611no—
547C22×D4—1221no—
548C22×D4—1221no—
549C22×D4—1221no—
550C22×D4C22×D6111yescharacteristic
551C23×C4—611no—
552C23×C4—1221no—
553C23×C4—1221no—
554C23×C4—1221no—
555C23×C4—1221no—
556C23×C4—1221no—
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—24no—
569C2×SD16—614no—
570C2×SD16—618no—
571C2×SD16—614no—
572C2×SD16—614no—
573C2×SD16—1224no—
574C2×SD16—2442no—
575C2×SD16C22×D6114yes—
576C2×D8—614no—
577C2×D8—1224no—
578C2×M16—24no—
579C2×M16C22×D6114yes—
580C22×C8—611no—
581C22×C8—611no—
582C22×C8—614no—
583C22×C8—1224no—
584C22×C8C22×D6111yescharacteristic
585C22×C8C22×D6111yescharacteristic
586C4⋊Q8—614no—
587C4⋊Q8—1222no—
588#124—614no—
589#124—1222no—
590#124—1228no—
591#123—1228no—
592#123—1228no—
593C22⋊Q8—22no—
594C22⋊Q8—614no—
595C22⋊Q8—614no—
596C22⋊Q8—1228no—
597C22⋊Q8—1222no—
598C22⋊Q8—1222no—
599C22⋊Q8C22×D6114yes—
600#121—22no—
601#121—1228no—
602#121—1228no—
603#121C22×D6114yes—
604C4×Q8—614no—
605C4×Q8—1222no—
606C4×D4—614no—
607C4×D4—614no—
608C4×D4—614no—
609C4×D4—1222no—
610C4×D4—1228no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—611no—
613C2×C4⋊C4—1228no—
614C2×C4⋊C4—1221no—
615C2×C4⋊C4—1221no—
616C2×C4⋊C4—1221no—
617C2×C4⋊C4—1221no—
618C2×C4⋊C4—1221no—
619C2×C4⋊C4C22×D6111yescharacteristic
620C2×C4⋊C4C22×D6111yescharacteristic
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—611no—
624C2×C22⋊C4—611no—
625C2×C22⋊C4—1221no—
626C2×C22⋊C4—1221no—
627C2×C22⋊C4—1221no—
628C2×C22⋊C4—1221no—
629C2×C22⋊C4—1221no—
630C2×C42—611no—
631C2×C42—1221no—
632#107C22×D6114yes—
633C4⋊C8—614no—
634#103—614no—
635#103—614no—
636#103—614no—
637#103C22×D6114yes—
638#102—614no—
639#102C22×D6114yes—
640C22⋊C8—614no—
641C22⋊C8—614no—
642#97—614no—
643C24—21no—
644C24—611no—
645C24—1221no—
646C24D4×D6111yescharacteristic
647#41—1228no—
648#41—1228no—
649#41—1228no—
650#41—2444no—
651#41—2448no—
652#41—2444no—
653#41—2448no—
654#41—2444no—
655#41—2448no—
656C2×Q8—21no—
657C2×Q8—22no—
658C2×Q8—22no—
659C2×Q8—614no—
660C2×Q8—612no—
661C2×Q8—612no—
662C2×Q8—612no—
663C2×Q8—1228no—
664C2×Q8—1221no—
665C2×Q8—1224no—
666C2×Q8—1221no—
667C2×Q8—1221no—
668C2×Q8—1222no—
669C2×Q8—1222no—
670C2×Q8—1222no—
671C2×Q8—1222no—
672C2×Q8—1222no—
673C2×Q8—2444no—
674C2×Q8—2444no—
675C2×Q8—2448no—
676C2×Q8C23×D6112yes—
677C2×D4—24no—
678C2×D4—22no—
679C2×D4—21no—
680C2×D4—22no—
681C2×D4—44no—
682C2×D4—614no—
683C2×D4—614no—
684C2×D4—612no—
685C2×D4—1224no—
686C2×D4—1224no—
687C2×D4—1224no—
688C2×D4—1221no—
689C2×D4—1222no—
690C2×D4—2444no—
691C2×D4—2442no—
692C2×D4—2444no—
693C2×D4—2444no—
694C2×D4C23×D6112yes—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—611no—
701C22×C4—611no—
702C22×C4—611no—
703C22×C4—612no—
704C22×C4—612no—
705C22×C4—1224no—
706C22×C4—1224no—
707C22×C4—1224no—
708C22×C4—1221no—
709C22×C4—1222no—
710C22×C4—1222no—
711C22×C4—1224no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1224no—
715C22×C4—2444no—
716C22×C4—2444no—
717C22×C4—2444no—
718C22×C4—2444no—
719C22×C4—2444no—
720C22×C4D4×D6112yes—
721C22×C4D4×D6111yescharacteristic
722C22×C4C23×D6112yes—
723C22×C4C23×D6111yescharacteristic
724Q16—1228no—
725Q16—1228no—
726Q16—1228no—
727Q16—2444no—
728SD16—28no—
729SD16—6116no—
730SD16—1228no—
731SD16—2444no—
732D8—1228no—
733M16—28no—
734C2×C8—22no—
735C2×C8—612no—
736C2×C8—612no—
737C2×C8—1222no—
738C2×C8—1222no—
739C2×C8—1228no—
740C2×C8D4×D6114yes—
741C2×C8C23×D6112yes—
742C2×C8C23×D6112yes—
743C4⋊C4—24no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—614no—
747C4⋊C4—1224no—
748C4⋊C4—1224no—
749C4⋊C4—1224no—
750C4⋊C4—1224no—
751C4⋊C4—1224no—
752C4⋊C4C23×D6112yes—
753C4⋊C4C23×D6112yes—
754C22⋊C4—24no—
755C22⋊C4—24no—
756C22⋊C4—614no—
757C22⋊C4—614no—
758C22⋊C4—1224no—
759C22⋊C4—1224no—
760C22⋊C4—1224no—
761C22⋊C4—1224no—
762C22⋊C4—1224no—
763C42—612no—
764C42—612no—
765C42—1224no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—612no—
774C23—1222no—
775C23—1222no—
776C23—1222no—
777C23—1222no—
778C23—1224no—
779C23—2442no—
780C23—2442no—
781C23C2×D4×D6112yes—
782C23C2×D4×D6111yescharacteristic
783Q8—22no—
784Q8—22no—
785Q8—42no—
786Q8—614no—
787Q8—1222no—
788Q8—1224no—
789Q8—1222no—
790Q8—1222no—
791Q8—1222no—
792Q8—1222no—
793Q8—2448no—
794Q8—2442no—
795Q8—2442no—
796D4—22no—
797D4—22no—
798D4—48no—
799D4—42no—
800D4—614no—
801D4—1222no—
802D4—1224no—
803D4—2448no—
804D4—2444no—
805D4—2448no—
806D4—2448no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—24no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—612no—
818C2×C4—612no—
819C2×C4—612no—
820C2×C4—1222no—
821C2×C4—1222no—
822C2×C4—1222no—
823C2×C4—1222no—
824C2×C4—1224no—
825C2×C4—1222no—
826C2×C4—1222no—
827C2×C4—1224no—
828C2×C4—1222no—
829C2×C4—1222no—
830C2×C4—2448no—
831C2×C4—2448no—
832C2×C4—2448no—
833C2×C4—2448no—
834C2×C4—2448no—
835C2×C4—2442no—
836C2×C4—2442no—
837C2×C4C2×D4×D6112yes—
838C2×C4C2×D4×D6112yes—
839C2×C4C2×D4×D6111yescharacteristic
840C2×C4#1451982312yes—
841C2×C4C24×D6111yescharacteristic
842C8—22no—
843C8—1222no—
844C8—1222no—
845C8C2×D4×D6114yes—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—44no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—84no—
854C22—1222no—
855C22—1224no—
856C22—1222no—
857C22—1222no—
858C22—2442no—
859C22—2442no—
860C22—2444no—
861C22—2448no—
862C22#1684039612yes—
863C22#1684055812yes—
864C22#1684057812yes—
865C22C22×D4×D6111yescharacteristic
866C4—22no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—1222no—
871C4—1224no—
872C4—1222no—
873C4—1222no—
874C4—2442no—
875C4—2442no—
876C4#1684039612yes—
877C4C22×D4×D6111yescharacteristic
878C4C2×#1451982311yescharacteristic
879C2—42no—
880C2—82no—
881C2—2442no—
882C2—2444no—
883C2#2145738114yesdirect product factor
884C2C2×#1684039611yescharacteristic
885C2C2×#1684055811yescharacteristic
886C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#468C2
socleC23×C61C22×D4
hypercenterC2×#468D61
hypocenterC61C2×#3269
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C22×#14519810C2semidirect
2. C22×#14519798C2semidirect
3. C2×#16840418C2semidirect
4. C2×#16840414C2semidirect
5. #21457381C2direct (N × H)
6. C2×#16840153C2semidirect
7. C2×#16840004C2semidirect
8. C2×#16839971C2semidirect
9. C2×#16839976C2semidirect
10. C2×#16839927C2semidirect
11. C2×#16839925C2semidirect
12. C2×#16839905C2semidirect
13. C2×#16839917C2semidirect
14. C2×#16839861C2semidirect
15. C2×#16839831C2semidirect
16. C2×C61×#468C2semidirect
22. C2×#14519810C22semidirect
24. C2×#14519798C22semidirect
35. #16840418C22semidirect
37. #16840414C22semidirect
53. #16840153C22semidirect
54. #16840004C22semidirect
55. #16839976C22semidirect
56. #16839971C22semidirect
57. #16839927C22semidirect
58. #16839925C22semidirect
59. #16839917C22semidirect
60. #16839905C22semidirect
61. #16839861C22semidirect
62. #16839831C22semidirect
75. C61×#468C22semidirect
121. C2×#11758190D4semidirect
320. #11758190C2×D4semidirect
442. C2×#468D61semidirect
454. C2×C61#3269semidirect
501. #468C2×D61semidirect
522. C61C2×#3269semidirect
883. C2#21457381direct (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×#145197982
C2×#168404182
C2×#168404142
#214573812
C2×#168401532
C2×#168400042
C2×#168399712
C2×#168399762
C2×#168399272
C2×#168399252
C2×#168399052
C2×#168399172
C2×#168398612
C2×#168398312
C2×C61×#4682
C2×#326961