Finite Group Databasebeta

← #30544340

Subgroups — #30544340

Order 15616.

2628 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840560C211yesmaximal, characteristic
2C2×#16840528C211yesmaximal, characteristic, complemented
3#21454734C218yesmaximal, complemented
4#21454726C218yesmaximal, complemented
5#21454720C218yesmaximal, complemented
6C2×#16839810C211yesmaximal, characteristic, complemented
7C2×#16839779C211yesmaximal, characteristic, complemented
8C2×#16839778C211yesmaximal, characteristic, complemented
9#21454237C211yesmaximal, characteristic, complemented
10C2×C61×#568C211yesmaximal, characteristic, complemented
11C22×#11758222C2211yescharacteristic
12#16840560C414yescomplemented
13#16840560C414yescomplemented
14#16840560C2214yes—
15#16840560C2214yes—
16C2×#14519808C412yescomplemented
17C2×#14519807C412yescomplemented
18C2×#14519803C412yescomplemented
19C2×#14519802C412yescomplemented
20C2×#14519797C2214yes—
21#16840528—22no—
22#16840528—22no—
23#16840528C2214yescomplemented
24#16840528C2214yescomplemented
25C2×#14519785—22no—
26C2×#14519783C2214yescomplemented
27C22×#11758194C2211yescharacteristic
28C22×#11758194C2211yescharacteristic
29C2×M16×D61—22no—
30C2×#14519736C2211yescharacteristic
31#16839882C22132yescomplemented
32#16839877C22132yescomplemented
33#16839810C2214yescomplemented
34#16839810C2214yescomplemented
35C2×#14519712C2214yescomplemented
36#16839779C2214yescomplemented
37#16839779C2214yescomplemented
38#16839778C2214yescomplemented
39#16839778C2214yescomplemented
40C2×#14519704C2214yescomplemented
41C2×#14519703C2214yescomplemented
42#16839720C2214yescomplemented
43#16839717C2214yescomplemented
44M16×Dic61C2214yescomplemented
45C22×#41×C61C2211yescharacteristic
46C61×#568—22no—
47C61×#568—22no—
48C61×#568C2214yescomplemented
49C61×#568C2214yescomplemented
50C2×#131×C61—22no—
51C2×#131×C61C2214yescomplemented
52C22×M16×C61—22no—
53C22×M16×C61C2211yescharacteristic
54C22×M16×C61C2211yescharacteristic
55C2×#11758222—21no—
56C2×#11758222—21no—
57C2×#11758222—21no—
58C2×#11758222—21no—
59C2×#11758222—21no—
60C2×#11758222—21no—
61C2×#11758222C2×C412yes—
62C2×#11758222C2×C412yes—
63C2×#11758222C2×C412yes—
64C2×#11758222C2312yes—
65C2×#11758222C2312yes—
66C2×#11758222C2312yes—
67C22×Dic122C2×C411yescharacteristic
68C22×D244C2×C411yescharacteristic
69C22×C22⋊D61—21no—
70C22×C4×D61—21no—
71#14519808C2×C418yes—
72#14519808C2×C418yescomplemented
73#14519807C2×C418yes—
74#14519807C2×C418yescomplemented
75#14519803C2×C418yes—
76#14519803C2×C418yescomplemented
77#14519802C2×C418yes—
78#14519802C2×C418yescomplemented
79#14519797C2×C4116yescomplemented
80#14519797C23116yes—
81C2×#11758202C2×C414yescomplemented
82C2×#11758200C2×C414yescomplemented
83C2×#11758201C2×C414yescomplemented
84C2×#11758199C2×C414yescomplemented
85#14519785—28no—
86#14519785—28no—
87#14519783—28no—
88#14519783C23116yescomplemented
89C2×#11758194—21no—
90C2×#11758194—21no—
91C2×#11758194—21no—
92C2×#11758194C2×C412yes—
93C2×#11758194C2×C412yes—
94C2×#11758194C2×C412yes—
95C2×#11758194C2×C412yes—
96C2×#11758194C2312yes—
97C2×#11758194C2312yes—
98C2×#11758194C2312yes—
99C2×#11758194C2312yes—
100C2×#11758194C2312yes—
101C2×#11758189—24no—
102M16×D61—28no—
103M16×D61—28no—
104C22×#92418—21no—
105C22×#92418C2312yes—
106C2×C8×D61—24no—
107#14519736—21no—
108#14519736—21no—
109#14519736C2312yes—
110#14519736C2312yes—
111C2×C4⋊Dic61—21no—
112C2×C22⋊Dic61—21no—
113C2×C4×Dic61C2312yes—
114#14519712C23116yescomplemented
115#14519704C23116yescomplemented
116#14519703C23116yescomplemented
117#14519687C2318yescomplemented
118C8×Dic61C2318yescomplemented
119C2×#41×C61—21no—
120C2×#41×C61—21no—
121C2×#41×C61—21no—
122C2×#41×C61—21no—
123C2×#41×C61—21no—
124C2×#41×C61—21no—
125C2×#41×C61C2×C412yes—
126C2×#41×C61C2×C412yes—
127C2×#41×C61C2×C412yes—
128C2×#41×C61C2312yes—
129C2×#41×C61C2312yes—
130C2×#41×C61C2312yes—
131C22×Q8×C61C2×C411yescharacteristic
132C22×D4×C61—21no—
133C22×D4×C61C2×C411yescharacteristic
134C23×C4×C61—21no—
135C23×C4×C61C2311yescharacteristic
136#131×C61—28no—
137#131×C61—28no—
138#131×C61—28no—
139#131×C61C23116yescomplemented
140C2×M16×C61—21no—
141C2×M16×C61—21no—
142C2×M16×C61—21no—
143C2×M16×C61—28no—
144C2×M16×C61—28no—
145C2×M16×C61—24no—
146C2×M16×C61D412yes—
147C2×M16×C61D412yes—
148C2×M16×C61D412yes—
149C2×M16×C61D412yes—
150C2×M16×C61C2312yes—
151C2×M16×C61C2312yes—
152C2×M16×C61C2312yes—
153C2×M16×C61C2312yes—
154C2×M16×C61C2312yes—
155C22×C8×C61—21no—
156C22×C8×C61—24no—
157C22×C8×C61C2312yes—
158C24×C61—21no—
159C24×C61#4111yescharacteristic
160C23×D61—21no—
161#41×C61—22no—
162#41×C61—22no—
163#41×C61—22no—
164#41×C61—22no—
165#41×C61—22no—
166#41×C61—22no—
167#41×C61—22no—
168#41×C61—22no—
169#41×C61—22no—
170#41×C61—22no—
171#41×C61—22no—
172#41×C61—22no—
173#41×C61C22×C414yes—
174#41×C61C22×C414yes—
175#41×C61C22×C414yes—
176#41×C61C2414yes—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61—21no—
180C2×Q8×C61C22×C412yes—
181C2×Q8×C61C22×C412yes—
182C2×Q8×C61C22×C412yes—
183C2×D4×C61—22no—
184C2×D4×C61—22no—
185C2×D4×C61—22no—
186C2×D4×C61—22no—
187C2×D4×C61—22no—
188C2×D4×C61—22no—
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—21no—
192C2×D4×C61C22×C412yes—
193C2×D4×C61C22×C412yes—
194C2×D4×C61C22×C412yes—
195C22×C4×C61—21no—
196C22×C4×C61—22no—
197C22×C4×C61—22no—
198C22×C4×C61—22no—
199C22×C4×C61—22no—
200C22×C4×C61—22no—
201C22×C4×C61—22no—
202C22×C4×C61C22×C411yescharacteristic
203C22×C4×C61C22×C411yescharacteristic
204C22×C4×C61C22×C411yescharacteristic
205C22×C4×C61C22×C411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61#4111yescharacteristic
211C22×C4×C61#4111yescharacteristic
212C22×C4×C61#4111yescharacteristic
213C22×C4×C61C2411yescharacteristic
214C22×C4×C61C2411yescharacteristic
215C22×C4×C61C2411yescharacteristic
216C2×C22⋊D61—22no—
217C2×C22⋊D61—22no—
218C2×C22⋊D61—22no—
219C2×C22⋊D61—22no—
220C2×C22⋊D61—22no—
221C2×C22⋊D61—22no—
222C22×Dic61—21no—
223C22×Dic61—22no—
224#11758222—22no—
225#11758222—22no—
226#11758222—22no—
227#11758222—22no—
228#11758222—22no—
229#11758222—22no—
230#11758222—22no—
231#11758222—22no—
232#11758222—22no—
233#11758222—22no—
234#11758222—22no—
235#11758222—22no—
236#11758222C22×C414yes—
237#11758222C22×C414yes—
238#11758222C22×C414yes—
239#11758222C2414yes—
240C2×D244—21no—
241C2×D244—21no—
242C2×D244—21no—
243C2×D244C22×C412yes—
244C2×D244C22×C412yes—
245C2×D244C22×C412yes—
246C2×C4×D61—22no—
247C2×C4×D61—22no—
248C2×C4×D61—22no—
249C2×C4×D61—22no—
250C2×C4×D61—22no—
251C2×C4×D61—22no—
252C2×Dic122—21no—
253C2×Dic122—21no—
254C2×Dic122—21no—
255C2×Dic122C22×C412yes—
256C2×Dic122C22×C412yes—
257C2×Dic122C22×C412yes—
258M16×C61—22no—
259M16×C61—22no—
260M16×C61—22no—
261M16×C61—216no—
262M16×C61C2×D414yes—
263M16×C61C2×D414yes—
264M16×C61C2×D414yes—
265M16×C61C2×D414yes—
266M16×C61C2414yes—
267C2×C8×C61—22no—
268C2×C8×C61—22no—
269C2×C8×C61—22no—
270C2×C8×C61—216no—
271C2×C8×C61C2×D414yes—
272C2×C8×C61C2×D414yes—
273C2×C8×C61C2414yes—
274C22⋊Dic61—22no—
275C22⋊Dic61—22no—
276#11758202C22×C4116yes—
277#11758201C22×C4116yes—
278#11758200C22×C4116yes—
279#11758199C22×C4116yes—
280C4⋊Dic61—22no—
281C4⋊Dic61—22no—
282C4×Dic61—22no—
283C4×Dic61C2414yes—
284#11758194—22no—
285#11758194—22no—
286#11758194—22no—
287#11758194C22×C414yes—
288#11758194C22×C414yes—
289#11758194C22×C414yes—
290#11758194C22×C414yes—
291#11758194C2414yes—
292C2×#92418—22no—
293C2×#92418—22no—
294C2×#92418—22no—
295C2×#92418C22×C414yes—
296C2×#92418C22×C414yes—
297C2×#92418C2414yes—
298#11758189—216no—
299C8×D61—216no—
300C23×C61—22no—
301C23×C61—22no—
302C23×C61—22no—
303C23×C61—81no—
304C23×C61—82no—
305C23×C61C4×D411yescharacteristic
306C23×C61C4×D411yescharacteristic
307C23×C61C4×D411yescharacteristic
308C23×C61C4×D411yescharacteristic
309C23×C61C2×#4111yescharacteristic
310C23×C61C2×#4111yescharacteristic
311C23×C61C2×#4111yescharacteristic
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—82no—
316Q8×C61—22no—
317Q8×C61—22no—
318Q8×C61—22no—
319Q8×C61C23×C414yes—
320D4×C61—24no—
321D4×C61—24no—
322D4×C61—24no—
323D4×C61—24no—
324D4×C61—22no—
325D4×C61—22no—
326D4×C61—22no—
327D4×C61C23×C414yes—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—24no—
332C2×C4×C61—24no—
333C2×C4×C61—24no—
334C2×C4×C61—24no—
335C2×C4×C61C4×D411yescharacteristic
336C2×C4×C61C4×D411yescharacteristic
337C2×C4×C61C4×D411yescharacteristic
338C2×C4×C61C4×D411yescharacteristic
339C2×C4×C61C4×D411yescharacteristic
340C2×C4×C61C4×D411yescharacteristic
341C2×C4×C61C4×D411yescharacteristic
342C2×C4×C61C4×D411yescharacteristic
343C2×C4×C61C4×D411yescharacteristic
344C2×C4×C61C4×D411yescharacteristic
345C2×C4×C61C4×D411yescharacteristic
346C2×C4×C61C4×D411yescharacteristic
347C2×C4×C61C23×C411yescharacteristic
348C2×C4×C61C23×C411yescharacteristic
349C2×C4×C61C23×C411yescharacteristic
350C2×C4×C61C23×C411yescharacteristic
351C2×C4×C61C23×C411yescharacteristic
352C2×C4×C61C23×C411yescharacteristic
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C22×D411yescharacteristic
357C2×C4×C61C22×D411yescharacteristic
358C2×C4×C61C22×D411yescharacteristic
359C2×C4×C61C2×#4111yescharacteristic
360C2×C4×C61C2×#4111yescharacteristic
361C2×C4×C61C2×#4111yescharacteristic
362C2×C4×C61C2511yescharacteristic
363C22⋊D61—24no—
364C22⋊D61—24no—
365C22⋊D61—24no—
366C22⋊D61—24no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—24no—
371C2×Dic61—82no—
372D244—22no—
373D244—22no—
374D244—22no—
375D244C23×C414yes—
376C4×D61—24no—
377C4×D61—24no—
378C4×D61—24no—
379C4×D61—24no—
380Dic122—22no—
381Dic122—22no—
382Dic122—22no—
383Dic122C23×C414yes—
384C8×C61—24no—
385C8×C61C22×D418yes—
386#92418—24no—
387#92418C23×C418yes—
388#60182—611nomaximal, Sylow
389C22×C61—24no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61—44no—
398C22×C61—82no—
399C22×C61—82no—
400C22×C61C2×C4×D411yescharacteristic
401C22×C61C2×C4×D411yescharacteristic
402C22×C61C2×C4×D411yescharacteristic
403C22×C61C2×C4×D411yescharacteristic
404C22×C61C2×C4×D411yescharacteristic
405C22×C61C2×C4×D411yescharacteristic
406C22×C61C22×#4111yescharacteristic
407C2×D61—24no—
408C2×D61—44no—
409C2×D61—82no—
410C2×D61—82no—
411C4×C61—24no—
412C4×C61C2×C4×D411yescharacteristic
413C4×C61C2×C4×D411yescharacteristic
414C4×C61C2×C4×D411yescharacteristic
415C4×C61C2×C4×D411yescharacteristic
416C4×C61C2×C4×D411yescharacteristic
417C4×C61C2×C4×D411yescharacteristic
418C4×C61C24×C411yescharacteristic
419C4×C61C23×D411yescharacteristic
420Dic61—24no—
421Dic61—44no—
422C2×#575—611no—
423C2×#568—611no—
424C2×#568D6111yescharacteristic, complemented
425#2957—618no—
426#2956—618no—
427#2955—618no—
428C2×#430—611no—
429C2×#421—611no—
430C2×#421—611no—
431#2873—611no—
432C2×C61—21no—
433C2×C61—21no—
434C2×C61—21no—
435C2×C61—21no—
436C2×C61—21no—
437C2×C61—21no—
438C2×C61—21no—
439C2×C61—44no—
440C2×C61C22×C4×D411yescharacteristic
441D61—44no—
442C22×#41—611no—
443C22×#41C2×D6111yescharacteristic
444#575—614no—
445#575—614no—
446#575—614no—
447#575—614no—
448C2×#137—612no—
449C2×#137—612no—
450C2×AGL(1,ℤ/8)—612no—
451C2×AGL(1,ℤ/8)—612no—
452C2×#135—614no—
453#568—22no—
454#568—22no—
455#568—614no—
456#568—614no—
457#568—1222no—
458#568—1222no—
459#568C2×D6114yescomplemented
460#568C2×D6114yescomplemented
461C2×#131—22no—
462C2×#131—614no—
463C2×#131—1222no—
464C2×#131C2×D6114yescomplemented
465C22×M16—22no—
466C22×M16—611no—
467C22×M16—611no—
468C22×M16—1222no—
469C22×M16C2×D6111yescharacteristic
470C22×M16C2×D6111yescharacteristic
471C2×#117—611no—
472#444—6132no—
473#443—6132no—
474#430—614no—
475#430—614no—
476C2×#108—614no—
477#421—614no—
478#421—614no—
479#421—614no—
480#421—614no—
481C2×#104—614no—
482C2×#104—614no—
483#405—614no—
484#405—614no—
485C4×M16—614no—
486C61#6018211yescharacteristic, complemented, Sylow
487C2×#41—21no—
488C2×#41—21no—
489C2×#41—21no—
490C2×#41—21no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—612no—
494C2×#41—612no—
495C2×#41—612no—
496C2×#41—612no—
497C2×#41—612no—
498C2×#41—612no—
499C2×#41—1221no—
500C2×#41—1221no—
501C2×#41—1221no—
502C2×#41—1221no—
503C2×#41—1221no—
504C2×#41—1221no—
505C2×#41C4×D6112yes—
506C2×#41C4×D6112yes—
507C2×#41C4×D6112yes—
508C2×#41C22×D6112yes—
509C2×#41C22×D6112yes—
510C2×#41C22×D6112yes—
511C22×Q8—611no—
512C22×Q8C4×D6111yescharacteristic
513C22×D4—21no—
514C22×D4—611no—
515C22×D4—1221no—
516C22×D4C4×D6111yescharacteristic
517C23×C4—21no—
518C23×C4—1221no—
519C23×C4C22×D6111yescharacteristic
520#137—618no—
521#137—618no—
522#137—618no—
523#137—618no—
524AGL(1,ℤ/8)—618no—
525AGL(1,ℤ/8)—618no—
526AGL(1,ℤ/8)—618no—
527AGL(1,ℤ/8)—618no—
528#135—6116no—
529#135—6116no—
530C2×Q16—614no—
531C2×SD16—614no—
532C2×SD16—614no—
533C2×D8—614no—
534#131—28no—
535#131—28no—
536#131—28no—
537#131—6116no—
538#131—1228no—
539#131—1228no—
540#131—1228no—
541#131C22×D61116yescomplemented
542C2×M16—21no—
543C2×M16—21no—
544C2×M16—21no—
545C2×M16—28no—
546C2×M16—28no—
547C2×M16—24no—
548C2×M16—612no—
549C2×M16—612no—
550C2×M16—612no—
551C2×M16—612no—
552C2×M16—612no—
553C2×M16—612no—
554C2×M16—612no—
555C2×M16—612no—
556C2×M16—612no—
557C2×M16—1221no—
558C2×M16—1221no—
559C2×M16—1221no—
560C2×M16—1228no—
561C2×M16—1228no—
562C2×M16—1224no—
563C2×M16C22⋊D6112yes—
564C2×M16C22⋊D6112yes—
565C2×M16C22⋊D6112yes—
566C2×M16C22⋊D6112yes—
567C2×M16C22×D6112yes—
568C2×M16C22×D6112yes—
569C2×M16C22×D6112yes—
570C2×M16C22×D6112yes—
571C2×M16C22×D6112yes—
572C22×C8—21no—
573C22×C8—24no—
574C22×C8—612no—
575C22×C8—1221no—
576C22×C8—1224no—
577C22×C8C22×D6112yes—
578#117—612no—
579#117—612no—
580#117—1221no—
581#117—1221no—
582C2×C4⋊C4—1221no—
583C2×C22⋊C4—1221no—
584C2×C42—612no—
585#108—6116no—
586#104—6116no—
587#104—6116no—
588#97—618no—
589C4×C8—618no—
590C24—21no—
591C24—1221no—
592C24#1175822211yescharacteristic
593#41—22no—
594#41—22no—
595#41—22no—
596#41—22no—
597#41—22no—
598#41—22no—
599#41—22no—
600#41—22no—
601#41—22no—
602#41—22no—
603#41—22no—
604#41—22no—
605#41—614no—
606#41—614no—
607#41—614no—
608#41—614no—
609#41—1222no—
610#41—1222no—
611#41—1222no—
612#41—1222no—
613#41—1222no—
614#41—1222no—
615#41—1222no—
616#41—1222no—
617#41—1222no—
618#41—1222no—
619#41—1222no—
620#41—1222no—
621#41C2×C4×D6114yes—
622#41C2×C4×D6114yes—
623#41C2×C4×D6114yes—
624#41C23×D6114yes—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—612no—
629C2×Q8—612no—
630C2×Q8—612no—
631C2×Q8—1221no—
632C2×Q8—1221no—
633C2×Q8—1221no—
634C2×Q8C2×C4×D6112yes—
635C2×Q8C2×C4×D6112yes—
636C2×Q8C2×C4×D6112yes—
637C2×D4—22no—
638C2×D4—22no—
639C2×D4—22no—
640C2×D4—22no—
641C2×D4—22no—
642C2×D4—22no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—612no—
647C2×D4—612no—
648C2×D4—612no—
649C2×D4—1222no—
650C2×D4—1222no—
651C2×D4—1222no—
652C2×D4—1222no—
653C2×D4—1222no—
654C2×D4—1222no—
655C2×D4—1221no—
656C2×D4—1221no—
657C2×D4—1221no—
658C2×D4C2×C4×D6112yes—
659C2×D4C2×C4×D6112yes—
660C2×D4C2×C4×D6112yes—
661C22×C4—21no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—1221no—
669C22×C4—1222no—
670C22×C4—1222no—
671C22×C4—1222no—
672C22×C4—1222no—
673C22×C4—1222no—
674C22×C4—1222no—
675C22×C4—1222no—
676C22×C4C2×C4×D6111yescharacteristic
677C22×C4C2×C4×D6111yescharacteristic
678C22×C4C2×C4×D6111yescharacteristic
679C22×C4C2×C4×D6111yescharacteristic
680C22×C4#1175822211yescharacteristic
681C22×C4#1175822211yescharacteristic
682C22×C4#1175822211yescharacteristic
683C22×C4C2×C22⋊D6111yescharacteristic
684C22×C4C2×C22⋊D6111yescharacteristic
685C22×C4C2×C22⋊D6111yescharacteristic
686C22×C4C2×C22⋊D6111yescharacteristic
687C22×C4C23×D6111yescharacteristic
688C22×C4C23×D6111yescharacteristic
689C22×C4C23×D6111yescharacteristic
690Q16—6116no—
691SD16—6116no—
692SD16—6116no—
693D8—6116no—
694M16—22no—
695M16—22no—
696M16—22no—
697M16—216no—
698M16—614no—
699M16—614no—
700M16—614no—
701M16—614no—
702M16—614no—
703M16—1222no—
704M16—1222no—
705M16—1222no—
706M16—12216no—
707M16C2×C22⋊D6114yes—
708M16C2×C22⋊D6114yes—
709M16C2×C22⋊D6114yes—
710M16C2×C22⋊D6114yes—
711M16C23×D6114yes—
712C2×C8—22no—
713C2×C8—22no—
714C2×C8—22no—
715C2×C8—216no—
716C2×C8—614no—
717C2×C8—614no—
718C2×C8—614no—
719C2×C8—1222no—
720C2×C8—1222no—
721C2×C8—1222no—
722C2×C8—12216no—
723C2×C8C2×C22⋊D6114yes—
724C2×C8C2×C22⋊D6114yes—
725C2×C8C23×D6114yes—
726C4⋊C4—1222no—
727C4⋊C4—1222no—
728C22⋊C4—1222no—
729C22⋊C4—1222no—
730C42—614no—
731C42—1222no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—81no—
736C23—82no—
737C23—1222no—
738C23—1222no—
739C23—1222no—
740C23—4882no—
741C23C4×C22⋊D6111yescharacteristic
742C23C4×C22⋊D6111yescharacteristic
743C23C4×C22⋊D6111yescharacteristic
744C23C4×C22⋊D6111yescharacteristic
745C23C2×#1175822211yescharacteristic
746C23C2×#1175822211yescharacteristic
747C23C2×#1175822211yescharacteristic
748Q8—22no—
749Q8—22no—
750Q8—22no—
751Q8—614no—
752Q8—1222no—
753Q8—1222no—
754Q8—1222no—
755Q8C22×C4×D6114yes—
756D4—24no—
757D4—24no—
758D4—24no—
759D4—24no—
760D4—22no—
761D4—22no—
762D4—22no—
763D4—614no—
764D4—1224no—
765D4—1224no—
766D4—1224no—
767D4—1224no—
768D4—1222no—
769D4—1222no—
770D4—1222no—
771D4C22×C4×D6114yes—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—1222no—
782C2×C4—1224no—
783C2×C4—1224no—
784C2×C4—1224no—
785C2×C4—1224no—
786C2×C4—1224no—
787C2×C4—4882no—
788C2×C4C4×C22⋊D6111yescharacteristic
789C2×C4C4×C22⋊D6111yescharacteristic
790C2×C4C4×C22⋊D6111yescharacteristic
791C2×C4C4×C22⋊D6111yescharacteristic
792C2×C4C4×C22⋊D6111yescharacteristic
793C2×C4C4×C22⋊D6111yescharacteristic
794C2×C4C4×C22⋊D6111yescharacteristic
795C2×C4C4×C22⋊D6111yescharacteristic
796C2×C4C4×C22⋊D6111yescharacteristic
797C2×C4C4×C22⋊D6111yescharacteristic
798C2×C4C4×C22⋊D6111yescharacteristic
799C2×C4C4×C22⋊D6111yescharacteristic
800C2×C4C22×C4×D6111yescharacteristic
801C2×C4C22×C4×D6111yescharacteristic
802C2×C4C22×C4×D6111yescharacteristic
803C2×C4C22×C4×D6111yescharacteristic
804C2×C4C22×C4×D6111yescharacteristic
805C2×C4C22×C4×D6111yescharacteristic
806C2×C4C22×C22⋊D6111yescharacteristic
807C2×C4C22×C22⋊D6111yescharacteristic
808C2×C4C22×C22⋊D6111yescharacteristic
809C2×C4C22×C22⋊D6111yescharacteristic
810C2×C4C22×C22⋊D6111yescharacteristic
811C2×C4C22×C22⋊D6111yescharacteristic
812C2×C4C2×#1175822211yescharacteristic
813C2×C4C2×#1175822211yescharacteristic
814C2×C4C2×#1175822211yescharacteristic
815C2×C4C24×D6111yescharacteristic
816C8—24no—
817C8—618no—
818C8—1224no—
819C8C22×C22⋊D6118yes—
820C22—24no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—44no—
829C22—82no—
830C22—82no—
831C22—1224no—
832C22—4882no—
833C22—4882no—
834C22—2444no—
835C22C2×C4×C22⋊D6111yescharacteristic
836C22C2×C4×C22⋊D6111yescharacteristic
837C22C2×C4×C22⋊D6111yescharacteristic
838C22C2×C4×C22⋊D6111yescharacteristic
839C22C2×C4×C22⋊D6111yescharacteristic
840C22C2×C4×C22⋊D6111yescharacteristic
841C22C22×#1175822211yescharacteristic
842C4—24no—
843C4—1224no—
844C4—2444no—
845C4C2×C4×C22⋊D6111yescharacteristic
846C4C2×C4×C22⋊D6111yescharacteristic
847C4C2×C4×C22⋊D6111yescharacteristic
848C4C2×C4×C22⋊D6111yescharacteristic
849C4C2×C4×C22⋊D6111yescharacteristic
850C4C2×C4×C22⋊D6111yescharacteristic
851C4C23×C4×D6111yescharacteristic
852C4C23×C22⋊D6111yescharacteristic
853C2—21no—
854C2—21no—
855C2—21no—
856C2—21no—
857C2—21no—
858C2—21no—
859C2—21no—
860C2—44no—
861C2—2444no—
862C2C22×C4×C22⋊D6111yescharacteristic
subgroupG/H
centerC4C23×C22⋊D61
commutatorC4×C61C24×C4
FrattiniC2×C4C24×D61
FittingC2×C61×#568C2
socleC2×C61C22×C4×D4
prime radicalC2×#16840560C2
cosocleC2×C4×C61C25
hypercenterC2×#568D61
hypocenterC61#60182
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×M16 ◁ C2×#568

Complements

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

NH ≅ G/Ntype
2. C2×#16840528C2semidirect
3. #21454734C2semidirect
4. #21454726C2semidirect
5. #21454720C2semidirect
6. C2×#16839810C2semidirect
7. C2×#16839779C2semidirect
8. C2×#16839778C2semidirect
9. #21454237C2semidirect
10. C2×C61×#568C2semidirect
12. #16840560C4semidirect
13. #16840560C4semidirect
16. C2×#14519808C4semidirect
17. C2×#14519807C4semidirect
18. C2×#14519803C4semidirect
19. C2×#14519802C4semidirect
23. #16840528C22semidirect
24. #16840528C22semidirect
26. C2×#14519783C22semidirect
31. #16839882C22semidirect
32. #16839877C22semidirect
33. #16839810C22semidirect
34. #16839810C22semidirect
35. C2×#14519712C22semidirect
36. #16839779C22semidirect
37. #16839779C22semidirect
38. #16839778C22semidirect
39. #16839778C22semidirect
40. C2×#14519704C22semidirect
41. C2×#14519703C22semidirect
42. #16839720C22semidirect
43. #16839717C22semidirect
44. M16×Dic61C22semidirect
48. C61×#568C22semidirect
49. C61×#568C22semidirect
51. C2×#131×C61C22semidirect
72. #14519808C2×C4semidirect
74. #14519807C2×C4semidirect
76. #14519803C2×C4semidirect
78. #14519802C2×C4semidirect
79. #14519797C2×C4semidirect
81. C2×#11758202C2×C4semidirect
82. C2×#11758200C2×C4semidirect
83. C2×#11758201C2×C4semidirect
84. C2×#11758199C2×C4semidirect
88. #14519783C23semidirect
114. #14519712C23semidirect
115. #14519704C23semidirect
116. #14519703C23semidirect
117. #14519687C23semidirect
118. C8×Dic61C23semidirect
139. #131×C61C23semidirect
424. C2×#568D61semidirect
459. #568C2×D61semidirect
460. #568C2×D61semidirect
464. C2×#131C2×D61semidirect
486. C61#60182semidirect
541. #131C22×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168405602
C2×#168405282
#214547342
#214547262
#214547202
C2×#168398102
C2×#168397792
C2×#168397782
#214542372
C2×C61×#5682
#6018261