Finite Group Databasebeta

← #29706924

Subgroups — #29706924

Order 15616.

2062 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840560C211yesmaximal, characteristic, complemented
2#21459148C211yesmaximal, characteristic, complemented
3C22×#14519705C211yesmaximal, characteristic, complemented
4#21454338C211yesmaximal, characteristic, complemented
5C2×#16839746C211yesmaximal, characteristic, complemented
6#21446855C212yesmaximal, complemented
7#21446848C212yesmaximal, complemented
8#21446841C212yesmaximal, complemented
9#21446834C212yesmaximal, complemented
10C2×#16839522C211yesmaximal, characteristic, complemented
11C2×C61×#532C211yesmaximal, characteristic, complemented
12C22×#11758222C2211yescharacteristic
13#16840560—24no—
14#16840560—24no—
15C2×#14519808C2212yes—
16C2×#14519807—21no—
17C2×#14519803C2212yes—
18C2×#14519802—21no—
19C2×#14519797—22no—
20C22×#11758194C2211yescharacteristic
21C22×#11758194C2211yescharacteristic
22#16840340—22no—
23#16840336C2212yes—
24#16840333—21no—
25#16840329C2212yes—
26#16840326—21no—
27#16840321—22no—
28#16840308—22no—
29#16840273—22no—
30#16840269—22no—
31C2×#14519736C2211yescharacteristic
32C2×#14519705—24no—
33C2×#14519705C2212yes—
34C2×#14519705C2212yes—
35#16839771C2212yescomplemented
36#16839767C2212yescomplemented
37#16839763—22no—
38#16839758—22no—
39#16839746—24no—
40C2×#14519696C2212yescomplemented
41C2×#14519694C2212yescomplemented
42#16839522C2212yescomplemented
43#16839522C2212yescomplemented
44C22×#41×C61C2211yescharacteristic
45C22×#41×C61C2211yescharacteristic
46C61×#532—24no—
47C61×#532—24no—
48C2×C4⋊Q8×C61C2211yescharacteristic, complemented
49C2×#127×C61C2211yescharacteristic, complemented
50C2×#124×C61C2211yescharacteristic, complemented
51C2×#124×C61C2211yescharacteristic, complemented
52C2×#121×C61—22no—
53C2×C4×D4×C61—22no—
54C22×C42×C61C2211yescharacteristic
55C2×#11758222—21no—
56C2×#11758222—21no—
57C2×#11758222—22no—
58C2×#11758222—22no—
59C2×#11758222—22no—
60C2×#11758222—22no—
61C2×#11758222D412yescomplemented
62C2×#11758222C2312yes—
63C22×Dic122D411yescharacteristic, complemented
64C22×D244D411yescharacteristic, complemented
65C22×C22⋊D61—21no—
66C22×C4×D61—21no—
67#14519808—24no—
68#14519808—24no—
69#14519807—28no—
70#14519803—24no—
71#14519803—24no—
72#14519802—28no—
73#14519797—216no—
74C2×#11758202—22no—
75C2×#11758200—22no—
76C2×#11758201—22no—
77C2×#11758199—22no—
78C2×#11758194—21no—
79C2×#11758194—22no—
80C2×#11758194—21no—
81C2×#11758194—22no—
82C2×#11758194—22no—
83C2×#11758194D414yescomplemented
84C2×#11758194C2312yes—
85C2×#11758194C2312yes—
86C22×#92418—21no—
87C22×#92418—21no—
88#14519775—22no—
89#14519773—22no—
90#14519766—22no—
91#14519764—22no—
92#14519760—24no—
93#14519758—24no—
94#14519756—24no—
95#14519753—24no—
96#14519751—24no—
97#14519749—28no—
98#14519748—24no—
99#14519746—24no—
100#14519745—24no—
101C4×C22⋊D61—28no—
102#14519736—21no—
103#14519736—21no—
104#14519736D412yescomplemented
105#14519736C2312yes—
106C2×C4⋊Dic61D412yescomplemented
107C2×C22⋊Dic61—21no—
108C2×C4×Dic61—21no—
109#14519705—24no—
110#14519705—24no—
111#14519701—24no—
112#14519698—24no—
113#14519696—24no—
114#14519694—24no—
115C2×#41×C61—22no—
116C2×#41×C61—22no—
117C2×#41×C61—22no—
118C2×#41×C61—22no—
119C2×#41×C61—21no—
120C2×#41×C61—21no—
121C2×#41×C61—21no—
122C2×#41×C61—21no—
123C2×#41×C61—22no—
124C2×#41×C61—21no—
125C2×#41×C61—21no—
126C2×#41×C61—21no—
127C2×#41×C61—21no—
128C2×#41×C61—22no—
129C2×#41×C61—22no—
130C2×#41×C61D414yescomplemented
131C22×Q8×C61C2311yescharacteristic
132C22×Q8×C61C2311yescharacteristic
133C22×D4×C61—22no—
134C22×D4×C61—21no—
135C22×D4×C61D412yes—
136C22×D4×C61C2311yescharacteristic
137C22×D4×C61C2311yescharacteristic
138C23×C4×C61—21no—
139C23×C4×C61—21no—
140C23×C4×C61D412yes—
141C23×C4×C61C2311yescharacteristic
142C4⋊Q8×C61—22no—
143C4⋊Q8×C61—22no—
144#127×C61—22no—
145#127×C61—22no—
146#124×C61—22no—
147#124×C61—22no—
148#124×C61—22no—
149#124×C61—22no—
150#121×C61—216no—
151C4×D4×C61—216no—
152C2×C4⋊C4×C61—22no—
153C2×C22⋊C4×C61—22no—
154C2×C22⋊C4×C61—22no—
155C2×C42×C61—22no—
156C2×C42×C61—21no—
157C2×C42×C61D414yescomplemented
158C2×C42×C61C2311yescharacteristic
159C2×C42×C61C2311yescharacteristic
160C24×C61—21no—
161C24×C61C2×D412yes—
162C24×C61C2×D411yescharacteristic
163C23×D61—21no—
164#41×C61—24no—
165#41×C61—24no—
166#41×C61—24no—
167#41×C61—24no—
168#41×C61—42no—
169#41×C61—42no—
170#41×C61—42no—
171#41×C61—42no—
172#41×C61—42no—
173#41×C61—42no—
174#41×C61—42no—
175#41×C61—42no—
176#41×C61—42no—
177#41×C61—42no—
178#41×C61—42no—
179#41×C61—42no—
180C2×Q8×C61—21no—
181C2×Q8×C61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—21no—
187C2×Q8×C61—21no—
188C2×Q8×C61—21no—
189C2×Q8×C61—21no—
190C2×Q8×C61—21no—
191C2×Q8×C61C2×D412yes—
192C2×D4×C61—28no—
193C2×D4×C61—24no—
194C2×D4×C61—24no—
195C2×D4×C61—22no—
196C2×D4×C61—22no—
197C2×D4×C61—24no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—21no—
208C2×D4×C61—21no—
209C2×D4×C61—48no—
210C2×D4×C61—41no—
211C2×D4×C61—41no—
212C2×D4×C61—42no—
213C2×D4×C61C2×D412yes—
214C22×C4×C61—21no—
215C22×C4×C61—24no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—24no—
219C22×C4×C61—24no—
220C22×C4×C61—22no—
221C22×C4×C61—22no—
222C22×C4×C61—24no—
223C22×C4×C61—44no—
224C22×C4×C61—41no—
225C22×C4×C61—41no—
226C22×C4×C61—42no—
227C22×C4×C61C2×D412yes—
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D412yes—
232C22×C4×C61C2×D412yes—
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D411yescharacteristic
235C22×C4×C61C2×D412yes—
236C22×C4×C61#4112yes—
237C22×C4×C61C2411yescharacteristic
238C2×C22⋊D61—22no—
239C2×C22⋊D61—22no—
240C2×C22⋊D61—28no—
241C2×C22⋊D61—42no—
242C2×C22⋊D61—42no—
243C22×Dic61—21no—
244C22×Dic61—22no—
245#11758222—24no—
246#11758222—24no—
247#11758222—22no—
248#11758222—22no—
249#11758222—22no—
250#11758222—22no—
251#11758222—42no—
252#11758222—42no—
253#11758222—42no—
254#11758222—42no—
255C2×D244—22no—
256C2×D244—22no—
257C2×D244—21no—
258C2×D244C2×D412yes—
259C2×C4×D61—22no—
260C2×C4×D61—22no—
261C2×C4×D61—42no—
262C2×C4×D61—42no—
263C2×Dic122—22no—
264C2×Dic122—22no—
265C2×Dic122—21no—
266C2×Dic122C2×D412yes—
267C4⋊C4×C61—28no—
268C22⋊C4×C61—28no—
269C22⋊C4×C61—28no—
270C42×C61—24no—
271C42×C61—21no—
272C42×C61—21no—
273C42×C61C2×D412yes—
274C42×C61C2×D412yes—
275C22⋊Dic61—28no—
276C22⋊Dic61—22no—
277C22⋊Dic61—22no—
278#11758202—28no—
279#11758201—28no—
280#11758200—28no—
281#11758199—28no—
282#11758198—28no—
283C4⋊Dic61—22no—
284C4⋊Dic61C2×D414yes—
285#11758196—28no—
286C4×Dic61—22no—
287C4×Dic61—22no—
288#11758194—24no—
289#11758194—22no—
290#11758194—22no—
291#11758194—22no—
292#11758194—42no—
293#11758194C2×D414yes—
294C2×#92418—24no—
295C2×#92418—22no—
296C2×#92418—22no—
297C2×#92418—42no—
298C23×C61—22no—
299C23×C61—22no—
300C23×C61—22no—
301C23×C61—22no—
302C23×C61—42no—
303C23×C61—44no—
304C23×C61—44no—
305C23×C61—41no—
306C23×C61—41no—
307C23×C61#12011yescharacteristic
308C23×C61#12011yescharacteristic
309C23×C61#12012yes—
310C23×C61#12112yes—
311C23×C61C22×D411yescharacteristic
312C22×D61—22no—
313C22×D61—42no—
314C22×D61—82no—
315Q8×C61—22no—
316Q8×C61—22no—
317Q8×C61—41no—
318Q8×C61—41no—
319Q8×C61—41no—
320Q8×C61—41no—
321Q8×C61—41no—
322Q8×C61—41no—
323D4×C61—22no—
324D4×C61—22no—
325D4×C61—416no—
326D4×C61—44no—
327D4×C61—44no—
328D4×C61—44no—
329D4×C61—44no—
330D4×C61—41no—
331D4×C61—41no—
332D4×C61—41no—
333D4×C61—41no—
334D4×C61—41no—
335D4×C61—41no—
336C2×C4×C61—24no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—48no—
344C2×C4×C61—42no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—44no—
348C2×C4×C61—44no—
349C2×C4×C61—44no—
350C2×C4×C61—44no—
351C2×C4×C61#12012yes—
352C2×C4×C61#12012yes—
353C2×C4×C61#12011yescharacteristic
354C2×C4×C61#12011yescharacteristic
355C2×C4×C61#12012yes—
356C2×C4×C61#12112yes—
357C2×C4×C61#12112yes—
358C2×C4×C61#12112yes—
359C2×C4×C61#12112yes—
360C2×C4×C61#12112yes—
361C2×C4×C61#12712yes—
362C2×C4×C61#12712yes—
363C2×C4×C61C22×D411yescharacteristic
364C2×C4×C61C22×D411yescharacteristic
365C2×C4×C61C22×D411yescharacteristic
366C2×C4×C61C22×D411yescharacteristic
367C2×C4×C61C22×D411yescharacteristic
368C2×C4×C61C2×#4111yescharacteristic
369C22⋊D61—42no—
370C22⋊D61—42no—
371C22⋊D61—44no—
372C22⋊D61—88no—
373C2×Dic61—24no—
374C2×Dic61—22no—
375C2×Dic61—42no—
376C2×Dic61—82no—
377D244—22no—
378D244—22no—
379D244—42no—
380C4×D61—42no—
381C4×D61—42no—
382C4×D61—44no—
383Dic122—22no—
384Dic122—22no—
385Dic122—42no—
386#92418—24no—
387#92418—42no—
388#23399—611nomaximal, Sylow
389C22×C61—22no—
390C22×C61—22no—
391C22×C61—22no—
392C22×C61—42no—
393C22×C61—42no—
394C22×C61—44no—
395C22×C61—44no—
396C22×C61—42no—
397C22×C61—42no—
398C22×C61—44no—
399C22×C61—82no—
400C22×C61—82no—
401C22×C61—82no—
402C22×C61#39212yes—
403C22×C61#39212yes—
404C22×C61C2×#12011yescharacteristic
405C22×C61C2×#12011yescharacteristic
406C22×C61C2×#12111yescharacteristic
407C2×D61—42no—
408C2×D61—44no—
409C2×D61—84no—
410C4×C61—24no—
411C4×C61—42no—
412C4×C61—42no—
413C4×C61—42no—
414C4×C61#39212yes—
415C4×C61#39212yes—
416C4×C61C2×#12011yescharacteristic
417C4×C61C2×#12111yescharacteristic
418C4×C61C2×#12111yescharacteristic
419C4×C61C2×#12711yescharacteristic
420Dic61—42no—
421Dic61—44no—
422C2×#575—611no—
423#3449—611no—
424C2×#532D6111yescharacteristic, complemented
425C22×#104—611no—
426#2896—611no—
427C2×#413—611no—
428#2005—612no—
429#2004—612no—
430#2003—612no—
431#2002—612no—
432C2×#339—611no—
433C2×C61—21no—
434C2×C61—22no—
435C2×C61—21no—
436C2×C61—22no—
437C2×C61—82no—
438C2×C61—82no—
439C2×C61C2×#39211yescharacteristic
440C2×C61#301812yes—
441D61—82no—
442C22×#41—611no—
443C22×#41C2×D6111yescharacteristic
444C22×#41C2×D6111yescharacteristic
445#575—1224no—
446#575—1224no—
447C2×#137—612no—
448C2×#137—1221no—
449C2×AGL(1,ℤ/8)—612no—
450C2×AGL(1,ℤ/8)—1221no—
451C2×#135—1222no—
452C22×M16—611no—
453C22×M16—611no—
454#537—1222no—
455#536—612no—
456#536—1221no—
457#535—612no—
458#535—1221no—
459#534—1222no—
460#532—24no—
461#532—24no—
462#532—1222no—
463C2×C4⋊Q8C2×D6111yescharacteristic, complemented
464C2×#127C2×D6111yescharacteristic, complemented
465C2×#124C2×D6111yescharacteristic, complemented
466C2×#124C2×D6111yescharacteristic, complemented
467#525—1222no—
468#525—1222no—
469C2×#121—22no—
470C2×C4×D4—22no—
471C2×#117—611no—
472C22×C42C2×D6111yescharacteristic
473C2×#104—612no—
474C2×#104—612no—
475C2×#104—1224no—
476#419—612no—
477#418—612no—
478#417—1222no—
479#416—1222no—
480#413—1224no—
481C2×#101—612no—
482C2×#100—612no—
483#339—612no—
484#339—612no—
485C61#2339911yescharacteristic, complemented, Sylow
486C2×#41—21no—
487C2×#41—21no—
488C2×#41—21no—
489C2×#41—21no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—21no—
496C2×#41—21no—
497C2×#41—22no—
498C2×#41—21no—
499C2×#41—21no—
500C2×#41—22no—
501C2×#41—612no—
502C2×#41—612no—
503C2×#41—1221no—
504C2×#41—1221no—
505C2×#41—1222no—
506C2×#41—1222no—
507C2×#41—1222no—
508C2×#41—1222no—
509C2×#41C22⋊D6114yescomplemented
510C22×Q8—611no—
511C22×Q8C22×D6111yescharacteristic
512C22×Q8C22×D6111yescharacteristic
513C22×D4—22no—
514C22×D4—21no—
515C22×D4—611no—
516C22×D4—1221no—
517C22×D4C22⋊D6112yes—
518C22×D4C22×D6111yescharacteristic
519C22×D4C22×D6111yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—1221no—
523C23×C4C22⋊D6112yes—
524C23×C4C22×D6111yescharacteristic
525#137—1224no—
526#137—1228no—
527#137—1224no—
528AGL(1,ℤ/8)—1224no—
529AGL(1,ℤ/8)—1228no—
530AGL(1,ℤ/8)—1224no—
531#135—12216no—
532C2×Q16—1222no—
533C2×SD16—1222no—
534C2×SD16—1222no—
535C2×D8—1222no—
536C2×M16—614no—
537C2×M16—612no—
538C2×M16—612no—
539C2×M16—1221no—
540C2×M16—1222no—
541C2×M16—1221no—
542C2×M16—1222no—
543C2×M16—1222no—
544C22×C8—1221no—
545C22×C8—1221no—
546C4⋊Q8—22no—
547C4⋊Q8—22no—
548C4⋊Q8—1222no—
549#127—22no—
550#127—22no—
551#127—1222no—
552#124—22no—
553#124—22no—
554#124—22no—
555#124—22no—
556#124—1222no—
557#124—1222no—
558#123—1224no—
559#123—1224no—
560C22⋊Q8—1224no—
561C22⋊Q8—1224no—
562#121—216no—
563#121—1224no—
564#121—1224no—
565#121—1228no—
566#120—1224no—
567#120—1224no—
568C4×D4—216no—
569C4×D4—1228no—
570#117—612no—
571#117—612no—
572#117—1221no—
573#117—1221no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—612no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—22no—
578C2×C22⋊C4—1221no—
579C2×C42—21no—
580C2×C42—22no—
581C2×C42—1221no—
582C2×C42C22⋊D6114yescomplemented
583C2×C42C22×D6111yescharacteristic
584C2×C42C22×D6111yescharacteristic
585#104—1224no—
586#104—1224no—
587#103—1224no—
588#102—1224no—
589#101—1224no—
590#100—1224no—
591C24—21no—
592C24—1221no—
593C24C2×C22⋊D6112yes—
594C24C2×C22⋊D6111yescharacteristic
595#41—24no—
596#41—24no—
597#41—24no—
598#41—24no—
599#41—42no—
600#41—42no—
601#41—42no—
602#41—42no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41—42no—
607#41—42no—
608#41—42no—
609#41—42no—
610#41—42no—
611#41—1222no—
612#41—1222no—
613#41—1222no—
614#41—1222no—
615#41—1224no—
616#41—1224no—
617#41—2442no—
618#41—2442no—
619#41—2442no—
620#41—2442no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—612no—
633C2×Q8—1221no—
634C2×Q8—1222no—
635C2×Q8—1222no—
636C2×Q8C2×C22⋊D6112yes—
637C2×D4—28no—
638C2×D4—22no—
639C2×D4—22no—
640C2×D4—24no—
641C2×D4—24no—
642C2×D4—24no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—48no—
655C2×D4—41no—
656C2×D4—41no—
657C2×D4—42no—
658C2×D4—612no—
659C2×D4—1228no—
660C2×D4—1222no—
661C2×D4—1222no—
662C2×D4—1222no—
663C2×D4—1221no—
664C2×D4—1222no—
665C2×D4—2442no—
666C2×D4—2442no—
667C2×D4C2×C22⋊D6112yes—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—24no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—44no—
678C22×C4—41no—
679C22×C4—41no—
680C22×C4—42no—
681C22×C4—1222no—
682C22×C4—1221no—
683C22×C4—1222no—
684C22×C4—1222no—
685C22×C4—2442no—
686C22×C4—2442no—
687C22×C4D4×D6111yescharacteristic
688C22×C4D4×D6111yescharacteristic
689C22×C4D4×D6112yes—
690C22×C4D4×D6111yescharacteristic
691C22×C4D4×D6111yescharacteristic
692C22×C4#1175822412yes—
693C22×C4C2×C22⋊D6112yes—
694C22×C4C2×C22⋊D6112yes—
695C22×C4C2×C22⋊D6112yes—
696C22×C4C2×C22⋊D6111yescharacteristic
697C22×C4C23×D6111yescharacteristic
698Q16—1228no—
699SD16—1228no—
700SD16—1228no—
701D8—1228no—
702M16—614no—
703M16—1222no—
704M16—1224no—
705M16—1222no—
706M16—1222no—
707M16—2442no—
708C2×C8—1222no—
709C2×C8—1224no—
710C2×C8—1222no—
711C2×C8—2442no—
712C4⋊C4—28no—
713C4⋊C4—614no—
714C4⋊C4—1228no—
715C4⋊C4—1222no—
716C22⋊C4—28no—
717C22⋊C4—28no—
718C22⋊C4—1228no—
719C22⋊C4—1228no—
720C22⋊C4—1222no—
721C22⋊C4—1222no—
722C42—21no—
723C42—21no—
724C42—24no—
725C42—1222no—
726C42—1222no—
727C42C2×C22⋊D6112yes—
728C42C2×C22⋊D6112yes—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—42no—
734C23—44no—
735C23—44no—
736C23—41no—
737C23—41no—
738C23—1222no—
739C23—4882no—
740C23—2442no—
741C23#1451974511yescharacteristic
742C23#1451974511yescharacteristic
743C23#1451974612yes—
744C23#1451974912yes—
745C23C22×C22⋊D6111yescharacteristic
746Q8—22no—
747Q8—22no—
748Q8—41no—
749Q8—41no—
750Q8—41no—
751Q8—41no—
752Q8—41no—
753Q8—41no—
754Q8—1222no—
755Q8—1222no—
756Q8—2442no—
757D4—22no—
758D4—22no—
759D4—416no—
760D4—44no—
761D4—44no—
762D4—44no—
763D4—44no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—41no—
770D4—1222no—
771D4—1222no—
772D4—4888no—
773D4—2442no—
774D4—2442no—
775D4—2444no—
776D4—2442no—
777C2×C4—24no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—48no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—1224no—
793C2×C4—1222no—
794C2×C4—4882no—
795C2×C4—2442no—
796C2×C4—2442no—
797C2×C4—2442no—
798C2×C4—2444no—
799C2×C4#1451974512yes—
800C2×C4#1451974512yes—
801C2×C4#1451974511yescharacteristic
802C2×C4#1451974511yescharacteristic
803C2×C4#1451974612yes—
804C2×C4#1451974812yes—
805C2×C4#1451974812yes—
806C2×C4#1451974912yes—
807C2×C4#1451974912yes—
808C2×C4#1451974912yes—
809C2×C4#1451977312yes—
810C2×C4#1451977312yes—
811C2×C4C2×D4×D6111yescharacteristic
812C2×C4C2×D4×D6111yescharacteristic
813C2×C4C2×D4×D6111yescharacteristic
814C2×C4C22×C22⋊D6111yescharacteristic
815C2×C4C22×C22⋊D6111yescharacteristic
816C2×C4C2×#1175822411yescharacteristic
817C8—1224no—
818C8—2442no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—82no—
830C22—82no—
831C22—82no—
832C22—4884no—
833C22—2442no—
834C22—2444no—
835C22#1683967012yes—
836C22#1683967012yes—
837C22C2×#1451974511yescharacteristic
838C22C2×#1451974611yescharacteristic
839C22C2×#1451974911yescharacteristic
840C4—24no—
841C4—42no—
842C4—42no—
843C4—42no—
844C4—2442no—
845C4—2444no—
846C4#1683967012yes—
847C4#1683967012yes—
848C4C2×#1451974511yescharacteristic
849C4C2×#1451974811yescharacteristic
850C4C2×#1451974911yescharacteristic
851C4C2×#1451977311yescharacteristic
852C2—21no—
853C2—21no—
854C2—22no—
855C2—22no—
856C2—82no—
857C2—82no—
858C2—4882no—
859C2C2×#1683967011yescharacteristic
860C2#2145516712yes—
subgroupG/H
centerC2×C4#14519745
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#532C2
socleC22×C61C2×#120
hypercenterC2×#532D61
hypocenterC61#23399
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. C2×#16840560C2semidirect
2. #21459148C2semidirect
3. C22×#14519705C2semidirect
4. #21454338C2semidirect
5. C2×#16839746C2semidirect
6. #21446855C2semidirect
7. #21446848C2semidirect
8. #21446841C2semidirect
9. #21446834C2semidirect
10. C2×#16839522C2semidirect
11. C2×C61×#532C2semidirect
35. #16839771C22semidirect
36. #16839767C22semidirect
40. C2×#14519696C22semidirect
41. C2×#14519694C22semidirect
42. #16839522C22semidirect
43. #16839522C22semidirect
48. C2×C4⋊Q8×C61C22semidirect
49. C2×#127×C61C22semidirect
50. C2×#124×C61C22semidirect
51. C2×#124×C61C22semidirect
61. C2×#11758222D4semidirect
63. C22×Dic122D4semidirect
64. C22×D244D4semidirect
83. C2×#11758194D4semidirect
104. #14519736D4semidirect
106. C2×C4⋊Dic61D4semidirect
130. C2×#41×C61D4semidirect
157. C2×C42×C61D4semidirect
424. C2×#532D61semidirect
463. C2×C4⋊Q8C2×D61semidirect
464. C2×#127C2×D61semidirect
465. C2×#124C2×D61semidirect
466. C2×#124C2×D61semidirect
485. C61#23399semidirect
509. C2×#41C22⋊D61semidirect
582. C2×C42C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168405602
#214591482
C22×#145197052
#214543382
C2×#168397462
#214468552
#214468482
#214468412
#214468342
C2×#168395222
C2×C61×#5322
#2339961