Finite Group Databasebeta

← #29696008

Subgroups — #29696008

Order 15616.

1346 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840569C211yesmaximal, characteristic
2C2×#16839884C211yesmaximal, characteristic, complemented
3#21454349C211yesmaximal, characteristic, complemented
4#21454342C211yesmaximal, characteristic, complemented
5#21446722C211yesmaximal, characteristic, complemented
6#21446698C211yesmaximal, characteristic, complemented
7#21446332C211yesmaximal, characteristic, complemented
8#21446325C211yesmaximal, characteristic, complemented
9#21446195C211yesmaximal, characteristic, complemented
10#21446188C211yesmaximal, characteristic, complemented
11#21445884C211yesmaximal, characteristic, complemented
12#21445776C211yesmaximal, characteristic, complemented
13#21445771C211yesmaximal, characteristic, complemented
14#21445665C211yesmaximal, characteristic, complemented
15C61×#2951C211yesmaximal, characteristic, complemented
16C2×#14519824C2211yescharacteristic
17C2×#14519823C2211yescharacteristic
18#16840569—24no—
19#16840569C418yescomplemented
20C2×#14519809—21no—
21C2×#14519807C2211yescharacteristic
22C2×#14519802C2211yescharacteristic
23C2×#14519801—21no—
24C2×#14519798—21no—
25C22×#11758190C2211yescharacteristic
26C2×SD16×D61—21no—
27C2×#14519784C2211yescharacteristic
28C2×#14519784C2211yescharacteristic, complemented
29C2×#14519783C2211yescharacteristic
30#16839884—24no—
31C2×#14519713C2211yescharacteristic, complemented
32C2×#14519704C2211yescharacteristic
33C2×#14519704C2211yescharacteristic, complemented
34C2×#14519703C2211yescharacteristic
35#16839770—21no—
36#16839770C2211yescharacteristic, complemented
37#16839766—21no—
38#16839766C2211yescharacteristic
39#16839761—21no—
40#16839761—21no—
41#16839761C2211yescharacteristic
42#16839761C2211yescharacteristic
43#16839756—21no—
44#16839756—21no—
45#16839756C2211yescharacteristic
46C2×#14519700—21no—
47C2×#14519700C2211yescharacteristic, complemented
48C2×#14519697—21no—
49C2×#14519697C2211yescharacteristic
50C2×#14519695C2211yescharacteristic, complemented
51C2×#14519693C2211yescharacteristic
52C2×#14519687C2211yescharacteristic, complemented
53#16839667C2211yescharacteristic, complemented
54#16839663C2211yescharacteristic
55#16839531C2211yescharacteristic, complemented
56#16839531C2211yescharacteristic, complemented
57#16839526C2211yescharacteristic, complemented
58#16839521C2211yescharacteristic, complemented
59C2×#135×C61C2211yescharacteristic
60C61×#520C2211yescharacteristic
61C61×#520C2211yescharacteristic, complemented
62C61×#440—21no—
63C61×#440—21no—
64C4×Q16×C61—21no—
65C4×D8×C61—21no—
66C2×#107×C61C2211yescharacteristic, complemented
67C61×#417C2211yescharacteristic
68C61×#417C2211yescharacteristic, complemented
69C61×#405C2211yescharacteristic, complemented
70#14519824—22no—
71#14519824—22no—
72#14519824—41no—
73#14519824C2×C414yescomplemented
74#14519823—22no—
75#14519823—22no—
76#14519823—41no—
77#14519823C2×C414yescomplemented
78C2×#11758226—21no—
79C2×#11758222—21no—
80C2×#11758222—21no—
81C2×#11758222C2311yescharacteristic
82C2×#11758224—21no—
83C2×#11758224—41no—
84C22×Dic122—21no—
85C22×Dic122C2311yescharacteristic
86C2×Q8×D61—21no—
87C22×D244—21no—
88C22×D244C2311yescharacteristic
89C2×D4×D61—21no—
90C2×D4×D61—41no—
91#14519809—28no—
92#14519807—22no—
93#14519807C2×C414yescomplemented
94#14519802—22no—
95#14519802C2×C414yescomplemented
96#14519801—28no—
97#14519798—28no—
98C2×#11758202—21no—
99C2×#11758190—21no—
100C2×#11758190—21no—
101C2×#11758190—22no—
102C2×#11758190C2×C414yescomplemented
103C2×#11758200—21no—
104C2×#11758201—21no—
105SD16×D61—28no—
106C2×#11758199—21no—
107#14519784—22no—
108#14519784—22no—
109#14519784—41no—
110#14519784—41no—
111#14519783—22no—
112#14519783C2×C414yescomplemented
113C2×#11758194—21no—
114C2×#11758194—21no—
115C2×#11758194C2311yescharacteristic
116C2×#11758194C2311yescharacteristic
117C2×#11758194C2311yescharacteristic
118C2×#11758189—21no—
119C22×#92418—21no—
120C22×#92418—21no—
121C22×#92418C2311yescharacteristic
122C2×C8×D61—21no—
123C2×#11758198—41no—
124C2×C4×Dic61C2311yescharacteristic
125#14519713—22no—
126#14519704—22no—
127#14519704—22no—
128#14519703—22no—
129#14519700—21no—
130#14519700—21no—
131#14519700—21no—
132#14519700—21no—
133#14519700—21no—
134#14519700—21no—
135#14519700D411yescharacteristic
136#14519700D411yescharacteristic
137#14519697—21no—
138#14519697—21no—
139#14519697—21no—
140#14519697—21no—
141#14519697—21no—
142#14519697—21no—
143#14519697D411yescharacteristic
144#14519697D411yescharacteristic
145#14519695—41no—
146#14519693—41no—
147#14519687—22no—
148#14519684—41no—
149C2×#41×C61C2311yescharacteristic
150C2×#41×C61C2311yescharacteristic
151#135×C61C2×C414yes—
152#135×C61D414yes—
153C2×Q16×C61D411yescharacteristic
154C2×SD16×C61D411yescharacteristic
155C2×SD16×C61D411yescharacteristic
156C2×D8×C61D411yescharacteristic
157C2×M16×C61C2311yescharacteristic
158C22×C8×C61C2311yescharacteristic
159C4×Q8×C61—21no—
160C4×Q8×C61—21no—
161C4×D4×C61—21no—
162C4×D4×C61—21no—
163C4×D4×C61—41no—
164C4×D4×C61—41no—
165#117×C61—21no—
166#117×C61—21no—
167#117×C61C2311yescharacteristic
168C2×C4⋊C4×C61—21no—
169C2×C4⋊C4×C61—21no—
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172#107×C61—21no—
173#107×C61—21no—
174#103×C61—21no—
175#103×C61—21no—
176#102×C61—21no—
177#102×C61—21no—
178#97×C61—21no—
179C4×C8×C61—21no—
180C23×D61—21no—
181C23×D61—41no—
182#41×C61—21no—
183#41×C61—21no—
184#41×C61—21no—
185#41×C61—21no—
186#41×C61C22×C412yes—
187#41×C61C22×C412yes—
188#41×C61C2×D412yes—
189#41×C61C2×D412yes—
190C2×Q8×C61C2×D411yescharacteristic
191C2×Q8×C61C2×D411yescharacteristic
192C2×D4×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61C2×D411yescharacteristic
195C2×D4×C61C2×D411yescharacteristic
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—41no—
201C22×C4×C61—41no—
202C22×C4×C61C2411yescharacteristic
203C2×C22⋊D61—21no—
204C2×C22⋊D61—41no—
205C2×C22⋊D61—41no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—41no—
209#11758226—24no—
210#11758226—42no—
211Q8×D61—24no—
212Q8×D61—42no—
213#11758224—24no—
214#11758224—42no—
215#11758224—44no—
216#11758224—44no—
217D4×D61—24no—
218D4×D61—42no—
219D4×D61—44no—
220D4×D61—44no—
221#11758222—21no—
222#11758222—21no—
223#11758222—24no—
224#11758222—24no—
225#11758222—42no—
226#11758222—42no—
227#11758222C22×C412yes—
228#11758222#4112yes—
229C2×D244—21no—
230C2×D244—21no—
231C2×D244—21no—
232C2×D244—21no—
233C2×D244—24no—
234C2×D244—21no—
235C2×D244—42no—
236C2×D244—41no—
237C2×D244C22×C412yes—
238C2×D244C2×D411yescharacteristic
239C2×C4×D61—21no—
240C2×C4×D61—41no—
241C2×C4×D61—41no—
242C2×Dic122—21no—
243C2×Dic122—21no—
244C2×Dic122—21no—
245C2×Dic122—21no—
246C2×Dic122—24no—
247C2×Dic122—21no—
248C2×Dic122—42no—
249C2×Dic122—41no—
250C2×Dic122C22×C412yes—
251C2×Dic122C2×D411yescharacteristic
252Q16×C61C22⋊C414yescomplemented
253SD16×C61C22⋊C414yescomplemented
254SD16×C61C22⋊C414yescomplemented
255D8×C61C22⋊C414yescomplemented
256M16×C61—21no—
257M16×C61—21no—
258C2×C8×C61—21no—
259C2×C8×C61C22×C412yes—
260C2×C8×C61C2×D412yes—
261C2×C8×C61C2×D411yescharacteristic
262C2×C8×C61C2×D411yescharacteristic
263C4⋊C4×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—41no—
268C4⋊C4×C61—41no—
269C4⋊C4×C61C2×D411yescharacteristic
270C4⋊C4×C61C2×D411yescharacteristic
271C22⋊C4×C61—21no—
272C22⋊C4×C61—41no—
273C22⋊C4×C61—41no—
274C42×C61—21no—
275C42×C61—41no—
276C42×C61—41no—
277#11758202—24no—
278#11758201—24no—
279#11758200—24no—
280#11758199—24no—
281#11758198—82no—
282C4×Dic61—21no—
283C4×Dic61—21no—
284#11758194—21no—
285#11758194—21no—
286#11758194—21no—
287#11758194—21no—
288#11758194—21no—
289#11758194—42no—
290#11758194—42no—
291#11758194C22×C412yes—
292C2×#92418—21no—
293C2×#92418—21no—
294C2×#92418—21no—
295C2×#92418—21no—
296C2×#92418—21no—
297C2×#92418—42no—
298C2×#92418—42no—
299C2×#92418C2×D411yescharacteristic
300C2×#92418C2×D411yescharacteristic
301#11758190—24no—
302#11758190—24no—
303#11758189—24no—
304C8×D61—24no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61H(5,𝔽2)11yescharacteristic
308C22×D61—21no—
309C22×D61—22no—
310C22×D61—44no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61—81no—
314C22×D61—81no—
315C22×D61—161no—
316C22×D61—161no—
317Q8×C61—21no—
318Q8×C61—21no—
319Q8×C61C2×C22⋊C412yes—
320Q8×C61C2×C22⋊C412yes—
321D4×C61—22no—
322D4×C61—22no—
323D4×C61—22no—
324D4×C61—22no—
325D4×C61—21no—
326D4×C61—21no—
327D4×C61C2×C22⋊C412yes—
328D4×C61C2×C22⋊C412yes—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—81no—
340C2×C4×C61—81no—
341C2×C4×C61—161no—
342C2×C4×C61—161no—
343C2×C4×C61C23×C411yescharacteristic
344C2×C4×C61C22×D411yescharacteristic
345C2×C4×C61C22×D411yescharacteristic
346C2×C4×C61C22×D411yescharacteristic
347C2×C4×C61C2×#4111yescharacteristic
348C2×C4×C61H(5,𝔽2)11yescharacteristic
349C22⋊D61—22no—
350C22⋊D61—22no—
351C22⋊D61—44no—
352C22⋊D61—44no—
353C2×Dic61—21no—
354C2×Dic61—22no—
355C2×Dic61—44no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361D244—22no—
362D244—22no—
363D244—21no—
364D244—44no—
365D244—41no—
366D244—41no—
367D244C4×D412yes—
368C4×D61—22no—
369C4×D61—22no—
370C4×D61—44no—
371C4×D61—44no—
372Dic122—21no—
373Dic122—22no—
374Dic122—22no—
375Dic122—44no—
376Dic122—41no—
377Dic122—41no—
378Dic122C4×D412yes—
379C8×C61—41no—
380C8×C61C2×C22⋊C412yes—
381C8×C61C2×C22⋊C412yes—
382#92418—22no—
383#92418—21no—
384#92418—21no—
385#92418—41no—
386#92418—41no—
387#22464—611nomaximal, Sylow
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—22no—
391C22×C61—22no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61#51811yescharacteristic
397C22×C61D4211yescharacteristic
398C22×C61#54611yescharacteristic
399C2×D61—22no—
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—42no—
403C2×D61—81no—
404C2×D61—81no—
405C2×D61—82no—
406C2×D61—164no—
407C2×D61—161no—
408C4×C61—22no—
409C4×C61—22no—
410C4×C61—41no—
411C4×C61—41no—
412C4×C61—81no—
413C4×C61—81no—
414C4×C61C22×C22⋊C411yescharacteristic
415C4×C61C2×C4×D411yescharacteristic
416C4×C61D4211yescharacteristic
417C4×C61#54611yescharacteristic
418Dic61—22no—
419Dic61—42no—
420Dic61—81no—
421C2×#577—611no—
422C2×#444—611no—
423#2951D6111yescharacteristic, complemented
424#2898—611no—
425#2897—611no—
426#1977—611no—
427#1973—611no—
428#1908—611no—
429#1907—611no—
430#1883—611no—
431#1882—611no—
432#1816—611no—
433#1793—611no—
434#1792—611no—
435#1765—611no—
436C2×C61—21no—
437C2×C61—21no—
438C2×C61—42no—
439C2×C61—42no—
440C2×C61D4×C22⋊C411yescharacteristic
441C2×C61#328811yescharacteristic
442C2×C61#328911yescharacteristic
443D61—42no—
444D61—82no—
445C2×2−1+4—611no—
446C2×H(5,𝔽2)—611no—
447#577—618no—
448#577—1224no—
449C2×#137—611no—
450C2×#137—1221no—
451C2×AGL(1,ℤ/8)—611no—
452C2×AGL(1,ℤ/8)—1221no—
453C2×#135—1221no—
454C2×#135C2×D6111yescharacteristic
455C22×SD16—611no—
456C22×SD16—1221no—
457C2×#131—611no—
458C2×#131—611no—
459C2×#131—611no—
460#520C2×D6111yescharacteristic
461#520C2×D6111yescharacteristic, complemented
462#444—1224no—
463#440—21no—
464#440—21no—
465C4×Q16—21no—
466C4×D8—21no—
467C2×#108—611no—
468C2×#107C2×D6111yescharacteristic, complemented
469C2×#104—611no—
470C2×#104—611no—
471C2×#104—611no—
472#419—611no—
473#419—1221no—
474#418—611no—
475#418—1221no—
476#417—611no—
477#417—611no—
478#417—1221no—
479#417—1221no—
480#417C2×D6111yescharacteristic
481#417C2×D6111yescharacteristic, complemented
482#416—611no—
483#416—1221no—
484#416—1221no—
485C2×#103—611no—
486C2×#103—1221no—
487C2×#102—611no—
488C2×#102—1221no—
489C2×#101—611no—
490C2×#100—611no—
491#405C2×D6111yescharacteristic, complemented
492C2×#97—611no—
493#391—611no—
494#390—611no—
495#343—611no—
496#343—611no—
497#341—611no—
498#339—611no—
499C61#2246411yescharacteristic, complemented, Sylow
5002−1+4—614no—
5012−1+4—1222no—
5022−1+4—1222no—
5032−1+4—2441no—
504H(5,𝔽2)—614no—
505H(5,𝔽2)—1222no—
506H(5,𝔽2)—1222no—
507H(5,𝔽2)—2441no—
508C2×#41—611no—
509C2×#41—1221no—
510C2×#41—1221no—
511C2×#41—1221no—
512C2×#41—1221no—
513C2×#41—2441no—
514C2×#41C22×D6111yescharacteristic
515C2×#41C22×D6111yescharacteristic
516C22×Q8—611no—
517C22×Q8—1221no—
518C22×Q8—1221no—
519C22×D4—611no—
520C22×D4—1221no—
521C22×D4—1221no—
522C22×D4—2441no—
523#137—614no—
524#137—1222no—
525#137—1228no—
526AGL(1,ℤ/8)—614no—
527AGL(1,ℤ/8)—1222no—
528AGL(1,ℤ/8)—1228no—
529#135—1228no—
530#135C4×D6114yes—
531#135D24414yes—
532C2×Q16—1221no—
533C2×Q16C22⋊D6111yescharacteristic
534C2×SD16—614no—
535C2×SD16—1221no—
536C2×SD16—1221no—
537C2×SD16—1228no—
538C2×SD16—1222no—
539C2×SD16—1221no—
540C2×SD16—1221no—
541C2×SD16C22⋊D6111yescharacteristic
542C2×SD16C22⋊D6111yescharacteristic
543C2×D8—1221no—
544C2×D8C22⋊D6111yescharacteristic
545#131—614no—
546#131—1222no—
547#131—1222no—
548#131—1222no—
549#131—2441no—
550#131—2441no—
551C2×M16—611no—
552C2×M16—611no—
553C2×M16—611no—
554C2×M16—1221no—
555C2×M16—1221no—
556C2×M16—1221no—
557C2×M16C22×D6111yescharacteristic
558C22×C8—611no—
559C22×C8—1221no—
560C22×C8—1221no—
561C22×C8—1221no—
562C22×C8C22×D6111yescharacteristic
563C4×Q8—21no—
564C4×Q8—21no—
565C4×D4—21no—
566C4×D4—21no—
567C4×D4—41no—
568C4×D4—41no—
569#117—21no—
570#117—21no—
571#117C22×D6111yescharacteristic
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4C22×D6111yescharacteristic
575C2×C4⋊C4C22×D6111yescharacteristic
576C2×C22⋊C4—2441no—
577C2×C42—611no—
578#108—1222no—
579#107—21no—
580#107—21no—
581#104—1222no—
582#104—1222no—
583#104—1222no—
584#103—21no—
585#103—21no—
586#103—611no—
587#103—611no—
588#103—1221no—
589#103—1221no—
590#103—1221no—
591#103—1221no—
592#103—1221no—
593#103—1221no—
594#102—21no—
595#102—21no—
596#102—611no—
597#102—611no—
598#102—1221no—
599#102—1221no—
600#102—1221no—
601#102—1221no—
602#102—1221no—
603#102—1221no—
604#101—2441no—
605#100—2441no—
606#97—21no—
607#97—1222no—
608C4×C8—21no—
609#95—2441no—
610C24—1221no—
611C24—2441no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—612no—
617#41—612no—
618#41—1224no—
619#41—1224no—
620#41—1221no—
621#41—1221no—
622#41—1224no—
623#41—1224no—
624#41—2442no—
625#41—2442no—
626#41—2444no—
627#41—2442no—
628#41—2442no—
629#41—2444no—
630#41C2×C4×D6112yes—
631#41C2×C4×D6112yes—
632#41C2×D24412yes—
633#41C2×D24412yes—
634C2×Q8—612no—
635C2×Q8—611no—
636C2×Q8—1224no—
637C2×Q8—1221no—
638C2×Q8—1224no—
639C2×Q8—1221no—
640C2×Q8—1221no—
641C2×Q8—1221no—
642C2×Q8—1221no—
643C2×Q8—2441no—
644C2×Q8—2442no—
645C2×Q8—2442no—
646C2×Q8C2×C22⋊D6111yescharacteristic
647C2×Q8C2×C22⋊D6111yescharacteristic
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—612no—
651C2×D4—611no—
652C2×D4—1224no—
653C2×D4—1221no—
654C2×D4—1224no—
655C2×D4—1221no—
656C2×D4—1221no—
657C2×D4—1221no—
658C2×D4—1221no—
659C2×D4—1221no—
660C2×D4—2442no—
661C2×D4—2441no—
662C2×D4—2442no—
663C2×D4—2441no—
664C2×D4—2444no—
665C2×D4—2444no—
666C2×D4—2441no—
667C2×D4C2×C22⋊D6111yescharacteristic
668C2×D4C2×C22⋊D6111yescharacteristic
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—41no—
674C22×C4—41no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—2441no—
679C22×C4—2441no—
680C22×C4—2441no—
681C22×C4C23×D6111yescharacteristic
682Q16—1224no—
683Q16#1175819814yescomplemented
684SD16—1224no—
685SD16—1224no—
686SD16—1224no—
687SD16—1224no—
688SD16#1175819814yescomplemented
689SD16#1175819814yescomplemented
690D8—1224no—
691D8#1175819814yescomplemented
692M16—21no—
693M16—21no—
694M16—612no—
695M16—1221no—
696M16—1224no—
697M16—1221no—
698M16—1221no—
699M16—1221no—
700M16—1221no—
701M16—2442no—
702M16—2442no—
703C2×C8—21no—
704C2×C8—611no—
705C2×C8—611no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1224no—
710C2×C8—1221no—
711C2×C8—1221no—
712C2×C8—2442no—
713C2×C8—2442no—
714C2×C8C2×C4×D6112yes—
715C2×C8C2×D24412yes—
716C2×C8C2×C22⋊D6111yescharacteristic
717C2×C8C2×C22⋊D6111yescharacteristic
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—41no—
723C4⋊C4—41no—
724C4⋊C4D4×D6111yescharacteristic
725C4⋊C4D4×D6111yescharacteristic
726C22⋊C4—21no—
727C22⋊C4—41no—
728C22⋊C4—41no—
729C22⋊C4—4882no—
730C42—21no—
731C42—41no—
732C42—41no—
733C42—1221no—
734C42—1221no—
735C23—21no—
736C23—21no—
737C23—1221no—
738C23—1222no—
739C23—9761no—
740C23—9761no—
741C23—4881no—
742C23—4881no—
743C23—2444no—
744C23—2441no—
745C23—2441no—
746C23#1451982211yescharacteristic
747Q8—21no—
748Q8—21no—
749Q8—612no—
750Q8—1221no—
751Q8—1222no—
752Q8—1222no—
753Q8—2444no—
754Q8—2441no—
755Q8—2441no—
756Q8C2×#1175819812yes—
757Q8C2×#1175819812yes—
758D4—22no—
759D4—22no—
760D4—22no—
761D4—22no—
762D4—21no—
763D4—21no—
764D4—612no—
765D4—1222no—
766D4—1222no—
767D4—1222no—
768D4—1222no—
769D4—1221no—
770D4—2444no—
771D4—2444no—
772D4—2444no—
773D4—2441no—
774D4—2441no—
775D4C2×#1175819812yes—
776D4C2×#1175819812yes—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—161no—
790C2×C4—161no—
791C2×C4—1221no—
792C2×C4—1222no—
793C2×C4—1222no—
794C2×C4—1222no—
795C2×C4—2444no—
796C2×C4—2444no—
797C2×C4—2444no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4C22×C4×D6111yescharacteristic
804C2×C4C2×D4×D6111yescharacteristic
805C2×C4C22×C22⋊D6111yescharacteristic
806C2×C4C22×D24411yescharacteristic
807C2×C4#41×D6111yescharacteristic
808C2×C4#1451982311yescharacteristic
809C8—41no—
810C8—1222no—
811C8—1221no—
812C8—1221no—
813C8—2441no—
814C8—2441no—
815C8C2×#1175819812yes—
816C8C2×#1175819812yes—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—1222no—
826C22—9761no—
827C22—9764no—
828C22—4882no—
829C22—4881no—
830C22—4881no—
831C22—2442no—
832C22—2441no—
833C22—2441no—
834C22#1684023411yescharacteristic
835C22D4×C22⋊D6111yescharacteristic
836C22#1684040711yescharacteristic
837C4—22no—
838C4—22no—
839C4—41no—
840C4—41no—
841C4—81no—
842C4—81no—
843C4—1222no—
844C4—4881no—
845C4—2442no—
846C4C22×#1175819811yescharacteristic
847C4C4×D4×D6111yescharacteristic
848C4D4×D24411yescharacteristic
849C4#1684040011yescharacteristic
850C2—21no—
851C2—21no—
852C2—42no—
853C2—42no—
854C2—4882no—
855C2—2442no—
856C2D4×#1175819811yescharacteristic
857C2#2145758311yescharacteristic
858C2#2145759011yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2951C2
socleC22×C61D42
prime radicalC2×#16840569C2
cosocleC22×C4×C61C24
hypercenter#2951D61
hypocenterC61#22464
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2951

Complements

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

NH ≅ G/Ntype
2. C2×#16839884C2semidirect
3. #21454349C2semidirect
4. #21454342C2semidirect
5. #21446722C2semidirect
6. #21446698C2semidirect
7. #21446332C2semidirect
8. #21446325C2semidirect
9. #21446195C2semidirect
10. #21446188C2semidirect
11. #21445884C2semidirect
12. #21445776C2semidirect
13. #21445771C2semidirect
14. #21445665C2semidirect
15. C61×#2951C2semidirect
19. #16840569C4semidirect
28. C2×#14519784C22semidirect
31. C2×#14519713C22semidirect
33. C2×#14519704C22semidirect
36. #16839770C22semidirect
47. C2×#14519700C22semidirect
50. C2×#14519695C22semidirect
52. C2×#14519687C22semidirect
53. #16839667C22semidirect
55. #16839531C22semidirect
56. #16839531C22semidirect
57. #16839526C22semidirect
58. #16839521C22semidirect
61. C61×#520C22semidirect
66. C2×#107×C61C22semidirect
68. C61×#417C22semidirect
69. C61×#405C22semidirect
73. #14519824C2×C4semidirect
77. #14519823C2×C4semidirect
93. #14519807C2×C4semidirect
95. #14519802C2×C4semidirect
102. C2×#11758190C2×C4semidirect
112. #14519783C2×C4semidirect
252. Q16×C61C22⋊C4semidirect
253. SD16×C61C22⋊C4semidirect
254. SD16×C61C22⋊C4semidirect
255. D8×C61C22⋊C4semidirect
423. #2951D61semidirect
461. #520C2×D61semidirect
468. C2×#107C2×D61semidirect
481. #417C2×D61semidirect
491. #405C2×D61semidirect
499. C61#22464semidirect
683. Q16#11758198semidirect
688. SD16#11758198semidirect
689. SD16#11758198semidirect
691. D8#11758198semidirect

Maximal subgroups

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

subgroupindex
C2×#168405692
C2×#168398842
#214543492
#214543422
#214467222
#214466982
#214463322
#214463252
#214461952
#214461882
#214458842
#214457762
#214457712
#214456652
C61×#29512
#2246461