Finite Group Databasebeta

← #29706920

Subgroups — #29706920

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
2C2×#16840308C211yesmaximal, characteristic, complemented
3C22×#14519704C211yesmaximal, characteristic, complemented
4#21454336C211yesmaximal, characteristic, complemented
5C2×#16839746C211yesmaximal, characteristic, complemented
6#21446853C212yesmaximal, complemented
7#21446846C212yesmaximal, complemented
8#21446839C212yesmaximal, complemented
9#21446832C212yesmaximal, complemented
10C2×#16839521C211yesmaximal, characteristic, complemented
11C61×#3449C211yesmaximal, characteristic, complemented
12C22×#11758222C2211yescharacteristic
13#16840560—24no—
14#16840560—24no—
15C2×#14519808—21no—
16C2×#14519807C2212yes—
17C2×#14519803—21no—
18C2×#14519802C2212yes—
19C2×#14519797—22no—
20C22×#11758194C2211yescharacteristic
21C22×#11758194C2211yescharacteristic
22#16840308—24no—
23#16840308—24no—
24C2×#14519775C2211yescharacteristic, complemented
25C2×#14519773C2211yescharacteristic, complemented
26C2×#14519766C2211yescharacteristic, complemented
27C2×#14519764C2211yescharacteristic, complemented
28C2×#14519749—22no—
29C2×C4×C22⋊D61—22no—
30C22×C4×Dic61C2211yescharacteristic
31C2×#14519704—24no—
32C2×#14519704C2212yes—
33C2×#14519704C2212yes—
34#16839770C2212yescomplemented
35#16839766C2212yescomplemented
36#16839761—22no—
37#16839756—22no—
38#16839746—24no—
39C2×#14519696C2212yescomplemented
40C2×#14519694C2212yescomplemented
41#16839521C2212yescomplemented
42#16839521C2212yescomplemented
43C22×#41×C61C2211yescharacteristic
44C22×#41×C61C2211yescharacteristic
45C61×#537—22no—
46C61×#536—21no—
47C61×#536C2212yes—
48C61×#535—21no—
49C61×#535C2212yes—
50C61×#534—22no—
51C61×#532—22no—
52C61×#525—22no—
53C61×#525—22no—
54C2×#117×C61C2211yescharacteristic
55C2×#11758222—22no—
56C2×#11758222—21no—
57C2×#11758222—21no—
58C2×#11758222—21no—
59C2×#11758222—21no—
60C2×#11758222—22no—
61C2×#11758222—22no—
62C2×#11758222D414yescomplemented
63C22×Dic122C2311yescharacteristic
64C22×D244C2311yescharacteristic
65C22×C22⋊D61—22no—
66C22×C22⋊D61—21no—
67C23×Dic61—21no—
68C22×C4×D61—21no—
69#14519808—28no—
70#14519807—24no—
71#14519807—24no—
72#14519803—28no—
73#14519802—24no—
74#14519802—24no—
75#14519797—216no—
76C2×#11758202—22no—
77C2×#11758200—22no—
78C2×#11758201—22no—
79C2×#11758199—22no—
80C2×#11758194—21no—
81C2×#11758194—22no—
82C2×#11758194—21no—
83C2×#11758194—22no—
84C2×#11758194—22no—
85C2×#11758194D414yescomplemented
86C2×#11758194C2312yes—
87C2×#11758194C2312yes—
88C22×#92418—21no—
89C22×#92418—21no—
90#14519775—22no—
91#14519775—22no—
92#14519773—22no—
93#14519773—22no—
94#14519766—22no—
95#14519766—22no—
96#14519764—22no—
97#14519764—22no—
98#14519749—216no—
99C4×C22⋊D61—216no—
100C2×#11758196—22no—
101C2×C22⋊Dic61—22no—
102C2×#11758198—22no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61—22no—
105C2×C4×Dic61D414yescomplemented
106C2×C4×Dic61C2311yescharacteristic
107C2×C4×Dic61C2311yescharacteristic
108#14519704—24no—
109#14519704—24no—
110#14519700—24no—
111#14519697—24no—
112#14519696—24no—
113#14519694—24no—
114C2×#41×C61—21no—
115C2×#41×C61—21no—
116C2×#41×C61—21no—
117C2×#41×C61—21no—
118C2×#41×C61—22no—
119C2×#41×C61—22no—
120C2×#41×C61—22no—
121C2×#41×C61—21no—
122C2×#41×C61—21no—
123C2×#41×C61—22no—
124C2×#41×C61—22no—
125C2×#41×C61—22no—
126C2×#41×C61—22no—
127C2×#41×C61—22no—
128C2×#41×C61D412yescomplemented
129C2×#41×C61C2312yes—
130C22×Q8×C61D411yescharacteristic, complemented
131C22×Q8×C61C2311yescharacteristic
132C22×D4×C61—21no—
133C22×D4×C61D412yes—
134C22×D4×C61D411yescharacteristic, complemented
135C22×D4×C61C2311yescharacteristic
136C23×C4×C61—21no—
137C23×C4×C61D412yes—
138C23×C4×C61C2311yescharacteristic
139C4⋊Q8×C61—22no—
140#127×C61—22no—
141#124×C61—22no—
142#124×C61—22no—
143#123×C61—24no—
144#123×C61—24no—
145C22⋊Q8×C61—24no—
146C22⋊Q8×C61—24no—
147#121×C61—28no—
148#121×C61—24no—
149#121×C61—24no—
150#120×C61—24no—
151#120×C61—24no—
152C4×D4×C61—28no—
153#117×C61—21no—
154#117×C61—21no—
155#117×C61D412yescomplemented
156#117×C61C2312yes—
157C2×C4⋊C4×C61D412yescomplemented
158C2×C22⋊C4×C61—21no—
159C2×C42×C61—21no—
160C24×C61—21no—
161C24×C61C2×D412yes—
162C24×C61C2×D411yescharacteristic
163C23×D61—21no—
164#41×C61—24no—
165#41×C61—24no—
166#41×C61—22no—
167#41×C61—22no—
168#41×C61—22no—
169#41×C61—22no—
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—
180#41×C61—42no—
181#41×C61—42no—
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—22no—
190C2×Q8×C61—22no—
191C2×Q8×C61C2×D412yes—
192C2×D4×C61—22no—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
195C2×D4×C61—24no—
196C2×D4×C61—24no—
197C2×D4×C61—22no—
198C2×D4×C61—28no—
199C2×D4×C61—22no—
200C2×D4×C61—21no—
201C2×D4×C61—22no—
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—42no—
209C2×D4×C61—42no—
210C2×D4×C61C2×D412yes—
211C22×C4×C61—21no—
212C22×C4×C61—22no—
213C22×C4×C61—22no—
214C22×C4×C61—22no—
215C22×C4×C61—22no—
216C22×C4×C61—24no—
217C22×C4×C61—24no—
218C22×C4×C61—22no—
219C22×C4×C61—42no—
220C22×C4×C61—42no—
221C22×C4×C61C2×D412yes—
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D412yes—
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D412yes—
227C22×C4×C61C2×D412yes—
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61#4112yes—
231C22×C4×C61C2411yescharacteristic
232C2×C22⋊D61—28no—
233C2×C22⋊D61—24no—
234C2×C22⋊D61—48no—
235C2×C22⋊D61—41no—
236C2×C22⋊D61—41no—
237C2×C22⋊D61—42no—
238C22×Dic61—21no—
239C22×Dic61—24no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—44no—
243#11758222—24no—
244#11758222—24no—
245#11758222—24no—
246#11758222—24no—
247#11758222—42no—
248#11758222—42no—
249#11758222—42no—
250#11758222—42no—
251C2×D244—21no—
252C2×D244—21no—
253C2×D244—21no—
254C2×D244—21no—
255C2×D244—21no—
256C2×D244C2×D412yes—
257C2×C4×D61—24no—
258C2×C4×D61—41no—
259C2×C4×D61—41no—
260C2×C4×D61—42no—
261C2×Dic122—21no—
262C2×Dic122—21no—
263C2×Dic122—21no—
264C2×Dic122—21no—
265C2×Dic122—21no—
266C2×Dic122C2×D412yes—
267C4⋊C4×C61—28no—
268C4⋊C4×C61—22no—
269C4⋊C4×C61C2×D414yes—
270C22⋊C4×C61—28no—
271C22⋊C4×C61—28no—
272C22⋊C4×C61—22no—
273C22⋊C4×C61—22no—
274C42×C61—22no—
275C42×C61—22no—
276C22⋊Dic61—28no—
277#11758202—28no—
278#11758201—28no—
279#11758200—28no—
280#11758199—28no—
281#11758198—28no—
282#11758196—28no—
283C4×Dic61—24no—
284C4×Dic61—21no—
285C4×Dic61—21no—
286C4×Dic61C2×D412yes—
287C4×Dic61C2×D412yes—
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—42no—
305C23×C61—82no—
306C23×C61#12011yescharacteristic
307C23×C61#12011yescharacteristic
308C23×C61#12012yes—
309C23×C61#12112yes—
310C23×C61C22×D411yescharacteristic
311C22×D61—22no—
312C22×D61—44no—
313C22×D61—41no—
314C22×D61—41no—
315Q8×C61—22no—
316Q8×C61—22no—
317Q8×C61—41no—
318Q8×C61—41no—
319Q8×C61—41no—
320Q8×C61—41no—
321Q8×C61—42no—
322D4×C61—22no—
323D4×C61—22no—
324D4×C61—42no—
325D4×C61—42no—
326D4×C61—44no—
327D4×C61—44no—
328D4×C61—44no—
329D4×C61—41no—
330D4×C61—41no—
331D4×C61—41no—
332D4×C61—41no—
333D4×C61—42no—
334D4×C61—88no—
335C2×C4×C61—22no—
336C2×C4×C61—24no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—42no—
341C2×C4×C61—42no—
342C2×C4×C61—42no—
343C2×C4×C61—44no—
344C2×C4×C61—44no—
345C2×C4×C61—44no—
346C2×C4×C61—82no—
347C2×C4×C61#12012yes—
348C2×C4×C61#12012yes—
349C2×C4×C61#12012yes—
350C2×C4×C61#12011yescharacteristic
351C2×C4×C61#12011yescharacteristic
352C2×C4×C61#12112yes—
353C2×C4×C61#12112yes—
354C2×C4×C61#12112yes—
355C2×C4×C61#12112yes—
356C2×C4×C61#12112yes—
357C2×C4×C61#12712yes—
358C2×C4×C61#12712yes—
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61C22×D411yescharacteristic
361C2×C4×C61C22×D411yescharacteristic
362C2×C4×C61C22×D411yescharacteristic
363C2×C4×C61C22×D411yescharacteristic
364C2×C4×C61C2×#4111yescharacteristic
365C22⋊D61—416no—
366C22⋊D61—44no—
367C22⋊D61—44no—
368C2×Dic61—24no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—22no—
372C2×Dic61—48no—
373C2×Dic61—42no—
374C2×Dic61—41no—
375C2×Dic61—41no—
376D244—22no—
377D244—22no—
378D244—41no—
379D244—41no—
380C4×D61—44no—
381C4×D61—44no—
382Dic122—22no—
383Dic122—22no—
384Dic122—41no—
385Dic122—41no—
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—42no—
396C22×C61—42no—
397C22×C61—44no—
398C22×C61—44no—
399C22×C61—82no—
400C22×C61—84no—
401C22×C61#39212yes—
402C22×C61#39212yes—
403C22×C61C2×#12011yescharacteristic
404C22×C61C2×#12011yescharacteristic
405C22×C61C2×#12111yescharacteristic
406C2×D61—44no—
407C2×D61—42no—
408C2×D61—82no—
409C2×D61—82no—
410C4×C61—42no—
411C4×C61—42no—
412C4×C61—44no—
413C4×C61#39212yes—
414C4×C61#39212yes—
415C4×C61C2×#12011yescharacteristic
416C4×C61C2×#12111yescharacteristic
417C4×C61C2×#12111yescharacteristic
418C4×C61C2×#12711yescharacteristic
419Dic61—24no—
420Dic61—42no—
421Dic61—42no—
422C2×#575—611no—
423#3449D6111yescharacteristic, complemented
424C2×#532—611no—
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—21no—
435C2×C61—22no—
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—22no—
455#536—21no—
456#536C2×D6112yes—
457#535—21no—
458#535C2×D6112yes—
459#534—22no—
460#532—22no—
461#532—1224no—
462#532—1224no—
463C2×C4⋊Q8—611no—
464C2×#127—611no—
465C2×#124—611no—
466C2×#124—611no—
467#525—22no—
468#525—22no—
469C2×#121—1222no—
470C2×C4×D4—1222no—
471C2×#117C2×D6111yescharacteristic
472C22×C42—611no—
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—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—21no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—21no—
494C2×#41—21no—
495C2×#41—21no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—614no—
501C2×#41—1222no—
502C2×#41—1222no—
503C2×#41—1222no—
504C2×#41—1221no—
505C2×#41—1221no—
506C2×#41—1221no—
507C2×#41—1221no—
508C2×#41C22⋊D6112yescomplemented
509C2×#41C22×D6112yes—
510C22×Q8—611no—
511C22×Q8C22⋊D6111yescharacteristic, complemented
512C22×Q8C22×D6111yescharacteristic
513C22×D4—21no—
514C22×D4—611no—
515C22×D4—1222no—
516C22×D4—1221no—
517C22×D4C22⋊D6112yes—
518C22×D4C22⋊D6111yescharacteristic, complemented
519C22×D4C22×D6111yescharacteristic
520C23×C4—21no—
521C23×C4—1221no—
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—1222no—
540C2×M16—1221no—
541C2×M16—1221no—
542C2×M16—1222no—
543C2×M16—1222no—
544C22×C8—1221no—
545C22×C8—1221no—
546C4⋊Q8—22no—
547C4⋊Q8—1222no—
548C4⋊Q8—1222no—
549#127—22no—
550#127—1222no—
551#127—1222no—
552#124—22no—
553#124—22no—
554#124—1222no—
555#124—1222no—
556#124—1222no—
557#124—1222no—
558#123—24no—
559#123—24no—
560C22⋊Q8—24no—
561C22⋊Q8—24no—
562#121—24no—
563#121—28no—
564#121—24no—
565#121—12216no—
566#120—24no—
567#120—24no—
568C4×D4—28no—
569C4×D4—12216no—
570#117—21no—
571#117—21no—
572#117C22⋊D6112yescomplemented
573#117C22×D6112yes—
574C2×C4⋊C4—1222no—
575C2×C4⋊C4C22⋊D6112yescomplemented
576C2×C22⋊C4—21no—
577C2×C22⋊C4—1222no—
578C2×C22⋊C4—1222no—
579C2×C42—21no—
580C2×C42—614no—
581C2×C42—611no—
582C2×C42—611no—
583C2×C42—1222no—
584C2×C42—1221no—
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—22no—
596#41—22no—
597#41—22no—
598#41—22no—
599#41—24no—
600#41—24no—
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—42no—
612#41—42no—
613#41—1224no—
614#41—1224no—
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—22no—
629C2×Q8—22no—
630C2×Q8—612no—
631C2×Q8—1221no—
632C2×Q8—1221no—
633C2×Q8—1221no—
634C2×Q8—1221no—
635C2×Q8—1221no—
636C2×Q8C2×C22⋊D6112yes—
637C2×D4—22no—
638C2×D4—24no—
639C2×D4—22no—
640C2×D4—22no—
641C2×D4—22no—
642C2×D4—24no—
643C2×D4—28no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—22no—
651C2×D4—21no—
652C2×D4—22no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—612no—
656C2×D4—1228no—
657C2×D4—1224no—
658C2×D4—1221no—
659C2×D4—1221no—
660C2×D4—1221no—
661C2×D4—1221no—
662C2×D4—1221no—
663C2×D4—2448no—
664C2×D4—2441no—
665C2×D4—2441no—
666C2×D4—2442no—
667C2×D4C2×C22⋊D6112yes—
668C22×C4—21no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—24no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—24no—
676C22×C4—42no—
677C22×C4—42no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—1224no—
682C22×C4—1224no—
683C22×C4—2444no—
684C22×C4—2441no—
685C22×C4—2441no—
686C22×C4—2442no—
687C22×C4D4×D6112yes—
688C22×C4D4×D6112yes—
689C22×C4D4×D6112yes—
690C22×C4#1175822412yes—
691C22×C4C2×C22⋊D6112yes—
692C22×C4C2×C22⋊D6111yescharacteristic
693C22×C4C2×C22⋊D6111yescharacteristic
694C22×C4C2×C22⋊D6111yescharacteristic
695C22×C4C2×C22⋊D6111yescharacteristic
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—22no—
714C4⋊C4—1228no—
715C4⋊C4C2×C22⋊D6114yes—
716C22⋊C4—28no—
717C22⋊C4—28no—
718C22⋊C4—22no—
719C22⋊C4—22no—
720C22⋊C4—1228no—
721C22⋊C4—1228no—
722C42—22no—
723C42—22no—
724C42—612no—
725C42—612no—
726C42—1221no—
727C42—1221no—
728C42—1224no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—42no—
734C23—44no—
735C23—42no—
736C23—82no—
737C23—1222no—
738C23—2444no—
739C23—2441no—
740C23—2441no—
741C23#1451974512yes—
742C23#1451974611yescharacteristic
743C23#1451974611yescharacteristic
744C23#1451974912yes—
745C23C22×C22⋊D6111yescharacteristic
746Q8—22no—
747Q8—22no—
748Q8—41no—
749Q8—41no—
750Q8—41no—
751Q8—41no—
752Q8—42no—
753Q8—1222no—
754Q8—1222no—
755Q8—2441no—
756Q8—2441no—
757D4—22no—
758D4—22no—
759D4—42no—
760D4—42no—
761D4—44no—
762D4—44no—
763D4—44no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—42no—
769D4—88no—
770D4—1222no—
771D4—1222no—
772D4—24416no—
773D4—2444no—
774D4—2444no—
775D4—2441no—
776D4—2441no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—82no—
789C2×C4—1224no—
790C2×C4—1222no—
791C2×C4—1222no—
792C2×C4—1222no—
793C2×C4—2448no—
794C2×C4—2442no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2444no—
798C2×C4—2444no—
799C2×C4#1451974512yes—
800C2×C4#1451974512yes—
801C2×C4#1451974512yes—
802C2×C4#1451974611yescharacteristic
803C2×C4#1451974611yescharacteristic
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—42no—
826C22—42no—
827C22—44no—
828C22—44no—
829C22—82no—
830C22—84no—
831C22—4882no—
832C22—4882no—
833C22—2444no—
834C22—2442no—
835C22#1683967012yes—
836C22#1683967012yes—
837C22C2×#1451974511yescharacteristic
838C22C2×#1451974611yescharacteristic
839C22C2×#1451974911yescharacteristic
840C4—42no—
841C4—42no—
842C4—44no—
843C4—1224no—
844C4—2442no—
845C4—2442no—
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#2145516812yes—
subgroupG/H
centerC2×C4#14519746
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#3449C2
socleC22×C61C2×#120
hypercenter#3449D61
hypocenterC61#23399
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#16840560C2semidirect
2. C2×#16840308C2semidirect
3. C22×#14519704C2semidirect
4. #21454336C2semidirect
5. C2×#16839746C2semidirect
6. #21446853C2semidirect
7. #21446846C2semidirect
8. #21446839C2semidirect
9. #21446832C2semidirect
10. C2×#16839521C2semidirect
11. C61×#3449C2semidirect
24. C2×#14519775C22semidirect
25. C2×#14519773C22semidirect
26. C2×#14519766C22semidirect
27. C2×#14519764C22semidirect
34. #16839770C22semidirect
35. #16839766C22semidirect
39. C2×#14519696C22semidirect
40. C2×#14519694C22semidirect
41. #16839521C22semidirect
42. #16839521C22semidirect
62. C2×#11758222D4semidirect
85. C2×#11758194D4semidirect
105. C2×C4×Dic61D4semidirect
128. C2×#41×C61D4semidirect
130. C22×Q8×C61D4semidirect
134. C22×D4×C61D4semidirect
155. #117×C61D4semidirect
157. C2×C4⋊C4×C61D4semidirect
423. #3449D61semidirect
485. C61#23399semidirect
508. C2×#41C22⋊D61semidirect
511. C22×Q8C22⋊D61semidirect
518. C22×D4C22⋊D61semidirect
572. #117C22⋊D61semidirect
575. C2×C4⋊C4C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168405602
C2×#168403082
C22×#145197042
#214543362
C2×#168397462
#214468532
#214468462
#214468392
#214468322
C2×#168395212
C61×#34492
#2339961