Finite Group Databasebeta

← #30555943

Subgroups — #30555943

Order 15616.

2810 conjugacy classes of subgroups.

The subgroup lattice has 1110 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840569C211yesmaximal, characteristic, complemented
2C2×#16840564C211yesmaximal, characteristic, complemented
3#21459612C211yesmaximal, characteristic, complemented
4#21459597C211yesmaximal, characteristic, complemented
5#21457406C214yesmaximal, complemented
6#21457361C214yesmaximal, complemented
7#21457316C214yesmaximal, complemented
8#21457301C214yesmaximal, complemented
9C2×#16840151C211yesmaximal, characteristic, complemented
10#21455468C211yesmaximal, characteristic, complemented
11#21455459C211yesmaximal, characteristic, complemented
12#21455313C211yesmaximal, characteristic, complemented
13#21455299C211yesmaximal, characteristic, complemented
14#21455108C211yesmaximal, characteristic, complemented
15#21455099C211yesmaximal, characteristic, complemented
16#21455090C211yesmaximal, characteristic, complemented
17#21455090C211yesmaximal, characteristic, complemented
18#21454538C211yesmaximal, characteristic, complemented
19C61×#2943C211yesmaximal, characteristic, complemented
20C2×#14519824C2211yescharacteristic, complemented
21C2×#14519823C2211yescharacteristic
22C2×#14519823C2211yescharacteristic, complemented
23C2×#14519823C2211yescharacteristic, complemented
24#16840569—28no—
25#16840564—28no—
26C2×#14519809C2212yescomplemented
27C2×#14519807C2211yescharacteristic, complemented
28C2×#14519804C2212yescomplemented
29C2×#14519804C2212yescomplemented
30C2×#14519802C2211yescharacteristic
31C2×#14519802C2211yescharacteristic, complemented
32C2×#14519802C2211yescharacteristic, complemented
33C2×#14519801C2212yescomplemented
34C2×#14519800C2212yescomplemented
35C2×#14519798C2212yescomplemented
36C22×#11758190C2211yescharacteristic, complemented
37C22×#11758190C2211yescharacteristic, complemented
38C2×SD16×D61C2212yescomplemented
39C22×D488C2211yescharacteristic, complemented
40C22×D488C2211yescharacteristic, complemented
41C2×D8×D61C2212yescomplemented
42C2×#14519783C2211yescharacteristic, complemented
43C2×#14519783C2211yescharacteristic, complemented
44#16840434C2214yescomplemented
45#16840424C2214yescomplemented
46#16840407—24no—
47#16840407C2214yescomplemented
48D4×D244—24no—
49D4×D244C2214yescomplemented
50#16840338—21no—
51#16840338C2211yescharacteristic, complemented
52#16840331—21no—
53#16840331—21no—
54#16840331—21no—
55#16840331C2211yescharacteristic
56#16840331C2211yescharacteristic, complemented
57#16840331C2211yescharacteristic, complemented
58#16840312—21no—
59#16840312—21no—
60#16840312C2211yescharacteristic
61C2×#14519774—21no—
62C2×#14519774C2211yescharacteristic, complemented
63C2×#14519765—21no—
64C2×#14519765C2211yescharacteristic, complemented
65#16840151C2214yescomplemented
66#16840151C2214yescomplemented
67#16840016C2214yescomplemented
68#16840009C2214yescomplemented
69#16839999C2214yescomplemented
70#16839992C2214yescomplemented
71#16839984C2214yescomplemented
72#16839977C2214yescomplemented
73#16839962C2214yescomplemented
74#16839957C2214yescomplemented
75#16839927C2214yescomplemented
76#16839914C2214yescomplemented
77#16839910C2214yescomplemented
78#16839910C2214yescomplemented
79#16839908C2214yescomplemented
80#16839902C2214yescomplemented
81#16839897C2214yescomplemented
82#16839897C2214yescomplemented
83#16839835C2214yescomplemented
84#16839835C2214yescomplemented
85#16839786C2211yescharacteristic, complemented
86#16839770C2211yescharacteristic, complemented
87#16839766C2211yescharacteristic, complemented
88#16839766C2211yescharacteristic, complemented
89#16839766C2211yescharacteristic, complemented
90#16839728C2211yescharacteristic, complemented
91#16839728C2211yescharacteristic, complemented
92C2×#135×C61C2211yescharacteristic
93C4×#41×C61C2211yescharacteristic, complemented
94C4×#41×C61C2211yescharacteristic, complemented
95C61×#442C2212yescomplemented
96C61×#441C2212yescomplemented
97C61×#440C2212yescomplemented
98C61×#440C2212yescomplemented
99C61×#427C2211yescharacteristic, complemented
100C61×#416C2211yescharacteristic, complemented
101C61×#416C2211yescharacteristic, complemented
102C2×#97×C61C2211yescharacteristic, complemented
103#14519824—24no—
104#14519824—42no—
105#14519823—24no—
106#14519823—24no—
107#14519823—24no—
108#14519823—42no—
109#14519823—42no—
110#14519823—42no—
111C2×#11758226C2312yes—
112C2×#11758226C2312yes—
113C2×#11758226C2312yes—
114C2×#11758222—21no—
115C2×#11758222—21no—
116C2×#11758222—21no—
117C2×#11758222—21no—
118C2×#11758222C2311yescharacteristic
119C2×#11758222C2311yescharacteristic
120C2×#11758224—22no—
121C2×#11758224C2312yes—
122C22×Dic122—21no—
123C22×Dic122C2311yescharacteristic
124C2×Q8×D61C2312yes—
125C22×D244—22no—
126C22×D244—21no—
127C22×D244—21no—
128C22×D244—21no—
129C22×D244—24no—
130C22×D244C2311yescharacteristic
131C22×D244C2311yescharacteristic
132C22×D244C2311yescharacteristic
133C2×D4×D61—22no—
134C2×D4×D61—22no—
135C2×D4×D61—22no—
136C2×D4×D61C2312yes—
137C2×D4×D61C2312yes—
138C2×D4×D61C2312yes—
139#14519809—28no—
140#14519807—24no—
141#14519804—28no—
142#14519804—28no—
143#14519802—24no—
144#14519802—24no—
145#14519802—24no—
146#14519801—28no—
147#14519800—28no—
148#14519798—28no—
149C2×#11758202C2312yes—
150C2×#11758190—24no—
151C2×#11758190—42no—
152C2×#11758190C2312yes—
153C2×#11758190C2312yes—
154C2×#11758190C2314yes—
155C2×#11758200C2312yes—
156C2×#11758201C2312yes—
157C2×#11758201C2312yes—
158C2×#11758201C2312yes—
159SD16×D61—28no—
160C2×D488—24no—
161C2×D488—42no—
162C2×D488C2312yes—
163C2×D488C2312yes—
164C2×D488C2314yes—
165C2×#11758199C2312yes—
166C2×#11758199C2312yes—
167C2×#11758199C2312yes—
168D8×D61—28no—
169#14519783—24no—
170#14519783—24no—
171C2×#11758194C2311yescharacteristic
172C2×#11758194C2311yescharacteristic
173C2×#11758189C2312yes—
174C2×#11758189C2312yes—
175C2×C8×D61C2312yes—
176C2×C8×D61C2312yes—
177#14519777—21no—
178#14519777D411yescharacteristic
179#14519774—21no—
180#14519774—21no—
181#14519774—24no—
182#14519774—21no—
183#14519774—21no—
184#14519774—21no—
185#14519774D411yescharacteristic
186#14519774C2314yes—
187#14519765—21no—
188#14519765—21no—
189#14519765—21no—
190#14519765—21no—
191#14519765—21no—
192#14519765—21no—
193#14519765—24no—
194#14519765D411yescharacteristic
195#14519765D411yescharacteristic
196#14519765C2314yes—
197#14519761—22no—
198#14519761—24no—
199#14519757—24no—
200#14519757C2314yes—
201#14519752—24no—
202#14519752—24no—
203#14519752—24no—
204#14519752C2314yes—
205#14519752C2314yes—
206#14519752C2314yes—
207#14519751—24no—
208#14519751—24no—
209#14519751D414yes—
210#14519747—22no—
211#14519747—22no—
212#14519747—22no—
213#14519747—24no—
214#14519747—24no—
215#14519747—24no—
216C4×D244—24no—
217C4×D244—24no—
218C4×D244C2314yes—
219C2×#11758198—22no—
220C2×#11758198—24no—
221C4⋊#92418C2314yes—
222#14519700C2314yes—
223#14519697C2314yes—
224#14519697C2314yes—
225#14519697C2314yes—
226#14519689C2314yes—
227#14519689C2314yes—
228C2×#41×C61C2311yescharacteristic
229C2×#41×C61C2311yescharacteristic
230#135×C61D418yescomplemented
231C2×Q16×C61C2311yescharacteristic
232C2×SD16×C61C2311yescharacteristic
233C2×SD16×C61C2311yescharacteristic
234C2×D8×C61C2311yescharacteristic
235C22×C8×C61C2311yescharacteristic
236C22×C8×C61C2311yescharacteristic
237C4×Q8×C61C2312yes—
238C4×Q8×C61C2312yes—
239C4×D4×C61—22no—
240C4×D4×C61—22no—
241C4×D4×C61C2312yes—
242C4×D4×C61C2312yes—
243#117×C61—21no—
244#117×C61—21no—
245#117×C61C2311yescharacteristic
246#117×C61C2311yescharacteristic
247C2×C42×C61—21no—
248C2×C42×C61—21no—
249C2×C42×C61C2311yescharacteristic
250#107×C61C2312yes—
251#106×C61C2312yes—
252#103×C61C2312yes—
253#103×C61C2312yes—
254#102×C61C2312yes—
255#102×C61C2312yes—
256#97×C61C2312yes—
257#97×C61C2312yes—
258C23×D61—21no—
259C23×D61—21no—
260C23×D61—21no—
261C23×D61—22no—
262C23×D61—22no—
263C23×D61—22no—
264#41×C61—22no—
265#41×C61—22no—
266#41×C61C2×D414yes—
267#41×C61C2×D414yescomplemented
268C2×Q8×C61C2411yescharacteristic
269C2×Q8×C61C2411yescharacteristic
270C2×D4×C61—21no—
271C2×D4×C61—21no—
272C2×D4×C61C2411yescharacteristic
273C2×D4×C61C2411yescharacteristic
274C22×C4×C61—21no—
275C22×C4×C61—21no—
276C22×C4×C61—22no—
277C22×C4×C61—22no—
278C22×C4×C61C2×D412yes—
279C22×C4×C61C2411yescharacteristic
280C2×C22⋊D61—22no—
281C2×C22⋊D61—22no—
282C2×C22⋊D61—22no—
283C2×C22⋊D61—22no—
284C2×C22⋊D61C2×D412yes—
285C2×C22⋊D61C2×D412yes—
286C22×Dic61—21no—
287C22×Dic61—22no—
288#11758226—24no—
289#11758226—24no—
290#11758226—24no—
291#11758226—42no—
292#11758226—42no—
293#11758226—42no—
294Q8×D61—24no—
295Q8×D61—42no—
296#11758224—24no—
297#11758224—42no—
298#11758224—48no—
299D4×D61—24no—
300D4×D61—24no—
301D4×D61—24no—
302D4×D61—42no—
303D4×D61—42no—
304D4×D61—42no—
305D4×D61—48no—
306D4×D61—48no—
307D4×D61—48no—
308#11758222—22no—
309#11758222—22no—
310#11758222—22no—
311#11758222—22no—
312#11758222—44no—
313#11758222—44no—
314#11758222—44no—
315#11758222—44no—
316C2×D244—22no—
317C2×D244—22no—
318C2×D244—22no—
319C2×D244—22no—
320C2×D244—22no—
321C2×D244—22no—
322C2×D244—22no—
323C2×D244—22no—
324C2×D244—22no—
325C2×D244—24no—
326C2×D244—21no—
327C2×D244—21no—
328C2×D244—21no—
329C2×D244—24no—
330C2×D244—24no—
331C2×D244—24no—
332C2×D244—24no—
333C2×D244—44no—
334C2×D244—44no—
335C2×D244—44no—
336C2×D244—88no—
337C2×D244—84no—
338C2×D244C2×D411yescharacteristic
339C2×D244C2×D411yescharacteristic
340C2×D244C2×D414yes—
341C2×D244C2412yes—
342C2×D244C2412yes—
343C2×D244C2412yes—
344C2×C4×D61—22no—
345C2×C4×D61—22no—
346C2×C4×D61—22no—
347C2×C4×D61—22no—
348C2×C4×D61C2412yes—
349C2×C4×D61C2412yes—
350C2×Dic122—22no—
351C2×Dic122—22no—
352C2×Dic122—21no—
353C2×Dic122—22no—
354C2×Dic122—44no—
355C2×Dic122C2×D411yescharacteristic
356C2×Dic122C2×D411yescharacteristic
357C2×Dic122C2412yes—
358Q16×C61C2×D414yescomplemented
359SD16×C61C2×D414yescomplemented
360SD16×C61C2×D414yescomplemented
361D8×C61C2×D414yescomplemented
362C2×C8×C61—22no—
363C2×C8×C61C2×D414yescomplemented
364C2×C8×C61C2412yes—
365C2×C8×C61C2411yescharacteristic
366C2×C8×C61C2411yescharacteristic
367C4⋊C4×C61—22no—
368C4⋊C4×C61—22no—
369C4⋊C4×C61C2412yes—
370C4⋊C4×C61C2412yes—
371C22⋊C4×C61—21no—
372C22⋊C4×C61—21no—
373C22⋊C4×C61—22no—
374C22⋊C4×C61—22no—
375C42×C61—21no—
376C42×C61—21no—
377C42×C61—22no—
378C42×C61—22no—
379C42×C61C2×D411yescharacteristic
380C42×C61C2×D411yescharacteristic
381C42×C61C2412yes—
382#11758202—24no—
383#11758201—24no—
384#11758201—24no—
385#11758201—24no—
386#11758200—24no—
387#11758199—24no—
388#11758199—24no—
389#11758199—24no—
390#11758198—24no—
391#11758198—24no—
392#11758198—24no—
393#11758198—24no—
394#11758198—24no—
395#11758198—24no—
396#11758198C2×D414yes—
397#11758198C2×D414yes—
398C4⋊Dic61—24no—
399C4⋊Dic61C2×D414yes—
400#11758194—22no—
401#11758194—22no—
402C2×#92418C2412yes—
403C2×#92418C2412yes—
404D488—24no—
405D488—24no—
406D488—44no—
407#11758190—24no—
408#11758190—24no—
409#11758190—44no—
410#11758189—24no—
411#11758189—24no—
412C8×D61—24no—
413C8×D61—24no—
414C23×C61—21no—
415C23×C61—21no—
416C23×C61C22×D411yescharacteristic
417C22×D61—22no—
418C22×D61—22no—
419C22×D61—22no—
420C22×D61—44no—
421C22×D61—44no—
422C22×D61—44no—
423C22×D61—42no—
424C22×D61—42no—
425C22×D61—42no—
426C22×D61—84no—
427C22×D61—84no—
428C22×D61—84no—
429C22×D61—82no—
430C22×D61—82no—
431C22×D61—82no—
432C22×D61C22×D412yes—
433C22×D61C22×D412yes—
434Q8×C61—21no—
435Q8×C61—21no—
436Q8×C61C22×D412yes—
437Q8×C61C22×D412yes—
438D4×C61—24no—
439D4×C61—24no—
440D4×C61—21no—
441D4×C61—21no—
442D4×C61C22×D412yes—
443D4×C61C22×D412yes—
444C2×C4×C61—21no—
445C2×C4×C61—21no—
446C2×C4×C61—24no—
447C2×C4×C61—24no—
448C2×C4×C61—22no—
449C2×C4×C61—22no—
450C2×C4×C61—42no—
451C2×C4×C61—44no—
452C2×C4×C61—82no—
453C2×C4×C61C22×D412yes—
454C2×C4×C61C22×D412yes—
455C2×C4×C61C22×D411yescharacteristic
456C2×C4×C61C22×D412yes—
457C2×C4×C61H(5,𝔽2)12yes—
458C2×C4×C61C2511yescharacteristic
459C22⋊D61—24no—
460C22⋊D61—24no—
461C22⋊D61—44no—
462C22⋊D61—44no—
463C22⋊D61—44no—
464C22⋊D61—44no—
465C2×Dic61—22no—
466C2×Dic61—44no—
467C2×Dic61—42no—
468C2×Dic61C22×D412yes—
469C2×Dic61C22×D412yes—
470D244—22no—
471D244—22no—
472D244—22no—
473D244—22no—
474D244—22no—
475D244—22no—
476D244—22no—
477D244—22no—
478D244—44no—
479D244—44no—
480D244—44no—
481D244—44no—
482D244—48no—
483D244—42no—
484D244—42no—
485D244—42no—
486D244—84no—
487D244—84no—
488D244—84no—
489D244—84no—
490C4×D61—22no—
491C4×D61—22no—
492C4×D61—22no—
493C4×D61—22no—
494C4×D61—44no—
495C4×D61—44no—
496C4×D61—44no—
497C4×D61—44no—
498Dic122—22no—
499Dic122—22no—
500Dic122—22no—
501Dic122—22no—
502Dic122—44no—
503Dic122—42no—
504C8×C61—22no—
505C8×C61C22×D412yes—
506C8×C61C22×D412yes—
507#92418—22no—
508#92418—22no—
509#61082—611nomaximal, Sylow
510C22×C61—22no—
511C22×C61—22no—
512C22×C61—22no—
513C22×C61—42no—
514C22×C61—42no—
515C22×C61D4212yes—
516C22×C61C23×D411yescharacteristic
517C2×D61—24no—
518C2×D61—24no—
519C2×D61—22no—
520C2×D61—22no—
521C2×D61—44no—
522C2×D61—44no—
523C2×D61—44no—
524C2×D61—42no—
525C2×D61—42no—
526C2×D61—42no—
527C2×D61—164no—
528C2×D61—164no—
529C2×D61—164no—
530C2×D61—162no—
531C2×D61—162no—
532C2×D61—162no—
533C4×C61—22no—
534C4×C61—22no—
535C4×C61—22no—
536C4×C61—22no—
537C4×C61—42no—
538C4×C61—42no—
539C4×C61D4212yes—
540C4×C61C23×D411yescharacteristic
541C4×C61C2×H(5,𝔽2)11yescharacteristic
542Dic61—22no—
543Dic61—22no—
544Dic61—42no—
545C2×#577—611no—
546C2×#576—611no—
547#3500—611no—
548#3498—611no—
549#3271—614no—
550#3268—614no—
551#3265—614no—
552#3264—614no—
553C2×#496—611no—
554#3058—611no—
555#3057—611no—
556#3040—611no—
557#3038—611no—
558#3010—611no—
559#3009—611no—
560#3008—611no—
561#3008—611no—
562#2943D6111yescharacteristic, complemented
563#2932—611no—
564C2×C61—22no—
565C2×C61—42no—
566C2×C61—42no—
567C2×C61C2×D4211yescharacteristic
568C2×C61#358512yes—
569D61—42no—
570D61—42no—
571D61—82no—
572D61—82no—
573D61—82no—
574C2×2−1+4—611no—
575C2×H(5,𝔽2)—611no—
576C2×H(5,𝔽2)—611no—
577C2×H(5,𝔽2)—611no—
578#577—1228no—
579#576—1228no—
580C2×#137—611no—
581C2×#137—612no—
582C2×AGL(1,ℤ/8)—611no—
583C2×AGL(1,ℤ/8)—611no—
584C2×AGL(1,ℤ/8)—611no—
585C2×AGL(1,ℤ/8)—612no—
586C2×AGL(1,ℤ/8)—612no—
587C2×AGL(1,ℤ/8)—612no—
588C2×#135—612no—
589C2×#135—612no—
590C2×#135C2×D6111yescharacteristic
591C22×SD16—612no—
592C22×SD16—611no—
593C22×SD16—611no—
594C22×D8—612no—
595C22×D8—611no—
596C22×D8—611no—
597C2×#131—611no—
598C2×#131—611no—
599#550—614no—
600#548—614no—
601#546—614no—
602#546—1224no—
603D42—614no—
604D42—1224no—
605#536—611no—
606#536—1221no—
607#535—611no—
608#535—611no—
609#535—611no—
610#535—1221no—
611#535—1221no—
612#535—1221no—
613#532—611no—
614#532—1221no—
615#532—1221no—
616C2×#127—611no—
617C2×#127—1221no—
618C2×#124—611no—
619C2×#124—1221no—
620C4×#41C2×D6111yescharacteristic, complemented
621C4×#41C2×D6111yescharacteristic, complemented
622#496—614no—
623#496—614no—
624#469—614no—
625#468—614no—
626#466—614no—
627#465—614no—
628#464—614no—
629#463—614no—
630#460—614no—
631#459—614no—
632#452—614no—
633#450—614no—
634#449—614no—
635#449—614no—
636#449—614no—
637#448—614no—
638#447—614no—
639#447—614no—
640#442C2×D6112yescomplemented
641#441C2×D6112yescomplemented
642#440C2×D6112yescomplemented
643#440C2×D6112yescomplemented
644#435—614no—
645#435—614no—
646#427C2×D6111yescharacteristic, complemented
647#423—611no—
648#419—611no—
649#418—611no—
650#418—611no—
651#418—611no—
652#416C2×D6111yescharacteristic, complemented
653#416C2×D6111yescharacteristic, complemented
654#408—611no—
655#408—611no—
656C2×#97C2×D6111yescharacteristic, complemented
657C61#6108211yescharacteristic, complemented, Sylow
6582−1+4—1224no—
6592−1+4—2442no—
660H(5,𝔽2)—1224no—
661H(5,𝔽2)—1224no—
662H(5,𝔽2)—1224no—
663H(5,𝔽2)—2442no—
664H(5,𝔽2)—2442no—
665H(5,𝔽2)—2442no—
666C2×#41—611no—
667C2×#41—611no—
668C2×#41—612no—
669C2×#41—612no—
670C2×#41—612no—
671C2×#41—612no—
672C2×#41—1221no—
673C2×#41—1221no—
674C2×#41—1221no—
675C2×#41—1221no—
676C2×#41—1222no—
677C2×#41C22×D6111yescharacteristic
678C2×#41C22×D6111yescharacteristic
679C22×Q8—612no—
680C22×Q8—611no—
681C22×Q8—1221no—
682C22×D4—612no—
683C22×D4—612no—
684C22×D4—612no—
685C22×D4—611no—
686C22×D4—611no—
687C22×D4—611no—
688C22×D4—1224no—
689C22×D4—1221no—
690C22×D4—1221no—
691C22×D4—1221no—
692C22×D4—1222no—
693C22×D4—1222no—
694C22×D4—1222no—
695C22×D4—1222no—
696#137—1224no—
697#137—1228no—
698AGL(1,ℤ/8)—1224no—
699AGL(1,ℤ/8)—1224no—
700AGL(1,ℤ/8)—1224no—
701AGL(1,ℤ/8)—1228no—
702AGL(1,ℤ/8)—1228no—
703AGL(1,ℤ/8)—1228no—
704#135—1228no—
705#135—1228no—
706#135D24418yescomplemented
707C2×Q16—612no—
708C2×Q16C22×D6111yescharacteristic
709C2×SD16—612no—
710C2×SD16—612no—
711C2×SD16—612no—
712C2×SD16—612no—
713C2×SD16—612no—
714C2×SD16—612no—
715C2×SD16—614no—
716C2×SD16—1228no—
717C2×SD16—1224no—
718C2×SD16—2442no—
719C2×SD16C22×D6111yescharacteristic
720C2×SD16C22×D6111yescharacteristic
721C2×D8—612no—
722C2×D8—612no—
723C2×D8—612no—
724C2×D8—612no—
725C2×D8—612no—
726C2×D8—614no—
727C2×D8—1228no—
728C2×D8—1224no—
729C2×D8—2442no—
730C2×D8C22×D6111yescharacteristic
731#131—1224no—
732#131—1224no—
733C2×M16—611no—
734C2×M16—611no—
735C2×M16—612no—
736C2×M16—612no—
737C22×C8—612no—
738C22×C8—612no—
739C22×C8C22×D6111yescharacteristic
740C22×C8C22×D6111yescharacteristic
741C4⋊Q8—611no—
742C4⋊Q8—1221no—
743#127—611no—
744#127—614no—
745#127—1221no—
746#127—1221no—
747#127—1224no—
748#127—1221no—
749#127—1221no—
750#127—1221no—
751#124—611no—
752#124—611no—
753#124—614no—
754#124—1224no—
755#124—1221no—
756#124—1221no—
757#124—1221no—
758#124—1221no—
759#124—1221no—
760#124—1221no—
761#123—1224no—
762#123—1222no—
763C22⋊Q8—614no—
764C22⋊Q8—1224no—
765#121—614no—
766#121—614no—
767#121—614no—
768#121—614no—
769#121—1224no—
770#121—1224no—
771#121—1224no—
772#121—1224no—
773#121—1224no—
774#120—1224no—
775#120—1224no—
776#120—1222no—
777#120—1222no—
778#120—1222no—
779#120—1224no—
780C4×Q8C22×D6112yes—
781C4×Q8C22×D6112yes—
782C4×D4—22no—
783C4×D4—22no—
784C4×D4—614no—
785C4×D4—1224no—
786C4×D4—1224no—
787C4×D4C22×D6112yes—
788C4×D4C22×D6112yes—
789#117—21no—
790#117—21no—
791#117C22×D6111yescharacteristic
792#117C22×D6111yescharacteristic
793C2×C22⋊C4—1224no—
794C2×C22⋊C4—1222no—
795C2×C42—21no—
796C2×C42—21no—
797C2×C42C22×D6111yescharacteristic
798#107C22×D6112yes—
799#106C22×D6112yes—
800C4⋊C8—614no—
801#103—614no—
802#103C22×D6112yes—
803#103C22×D6112yes—
804#102—614no—
805#102—614no—
806#102—614no—
807#102C22×D6112yes—
808#102C22×D6112yes—
809C22⋊C8—614no—
810C22⋊C8—614no—
811#97C22×D6112yes—
812#97C22×D6112yes—
813C24—1222no—
814C24—1222no—
815C24—1222no—
816C24—1221no—
817C24—1221no—
818C24—1221no—
819#41—22no—
820#41—22no—
821#41—1222no—
822#41—1222no—
823#41—1222no—
824#41—1222no—
825#41—1224no—
826#41—1224no—
827#41—1224no—
828#41—1224no—
829#41—2444no—
830#41—2444no—
831#41—2444no—
832#41—2444no—
833#41—2442no—
834#41—2442no—
835#41—2442no—
836#41—2442no—
837#41—2448no—
838#41C2×D24414yes—
839#41C2×D24414yescomplemented
840C2×Q8—611no—
841C2×Q8—611no—
842C2×Q8—612no—
843C2×Q8—1222no—
844C2×Q8—1221no—
845C2×Q8—1224no—
846C2×Q8—1222no—
847C2×Q8—1222no—
848C2×Q8—2444no—
849C2×Q8—2442no—
850C2×Q8C23×D6111yescharacteristic
851C2×Q8C23×D6111yescharacteristic
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—612no—
855C2×D4—612no—
856C2×D4—611no—
857C2×D4—611no—
858C2×D4—614no—
859C2×D4—612no—
860C2×D4—612no—
861C2×D4—612no—
862C2×D4—1224no—
863C2×D4—1224no—
864C2×D4—1224no—
865C2×D4—1222no—
866C2×D4—1222no—
867C2×D4—1222no—
868C2×D4—1222no—
869C2×D4—1222no—
870C2×D4—1222no—
871C2×D4—1224no—
872C2×D4—1224no—
873C2×D4—1224no—
874C2×D4—1222no—
875C2×D4—1224no—
876C2×D4—1224no—
877C2×D4—1221no—
878C2×D4—1221no—
879C2×D4—1221no—
880C2×D4—1222no—
881C2×D4—1222no—
882C2×D4—1222no—
883C2×D4—1222no—
884C2×D4—1222no—
885C2×D4—1222no—
886C2×D4—4884no—
887C2×D4—4888no—
888C2×D4—2444no—
889C2×D4—2444no—
890C2×D4—2444no—
891C2×D4—2442no—
892C2×D4—2442no—
893C2×D4—2442no—
894C2×D4—2448no—
895C2×D4—2448no—
896C2×D4—2448no—
897C2×D4C23×D6111yescharacteristic
898C2×D4C23×D6111yescharacteristic
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—22no—
902C22×C4—22no—
903C22×C4—612no—
904C22×C4—612no—
905C22×C4—1222no—
906C22×C4—1222no—
907C22×C4—1222no—
908C22×C4—1222no—
909C22×C4—1222no—
910C22×C4—1221no—
911C22×C4D4×D6112yes—
912C22×C4C23×D6111yescharacteristic
913Q16—1224no—
914Q16C2×D24414yescomplemented
915SD16—1224no—
916SD16—1224no—
917SD16—1224no—
918SD16—1224no—
919SD16—1224no—
920SD16—1224no—
921SD16—2444no—
922SD16C2×D24414yescomplemented
923SD16C2×D24414yescomplemented
924D8—1224no—
925D8—1224no—
926D8—1224no—
927D8—1224no—
928D8—1224no—
929D8—2444no—
930D8C2×D24414yescomplemented
931M16—1222no—
932M16—1222no—
933M16—1224no—
934M16—1224no—
935C2×C8—22no—
936C2×C8—612no—
937C2×C8—612no—
938C2×C8—1224no—
939C2×C8—1224no—
940C2×C8C2×D24414yescomplemented
941C2×C8C23×D6112yes—
942C2×C8C23×D6111yescharacteristic
943C2×C8C23×D6111yescharacteristic
944C4⋊C4—22no—
945C4⋊C4—22no—
946C4⋊C4—614no—
947C4⋊C4—1224no—
948C4⋊C4C23×D6112yes—
949C4⋊C4C23×D6112yes—
950C22⋊C4—21no—
951C22⋊C4—21no—
952C22⋊C4—22no—
953C22⋊C4—22no—
954C22⋊C4—614no—
955C22⋊C4—614no—
956C22⋊C4—1224no—
957C22⋊C4—1224no—
958C22⋊C4—1224no—
959C22⋊C4—1224no—
960C22⋊C4—1224no—
961C22⋊C4—1224no—
962C42—21no—
963C42—21no—
964C42—22no—
965C42—22no—
966C42D4×D6111yescharacteristic
967C42D4×D6111yescharacteristic
968C42C23×D6112yes—
969C23—21no—
970C23—21no—
971C23—612no—
972C23—612no—
973C23—1222no—
974C23—1222no—
975C23—1222no—
976C23—4882no—
977C23—4882no—
978C23—4882no—
979C23—4884no—
980C23—4884no—
981C23—4884no—
982C23—2444no—
983C23—2444no—
984C23—2444no—
985C23—2442no—
986C23—2442no—
987C23—2442no—
988C23C2×D4×D6111yescharacteristic
989Q8—21no—
990Q8—21no—
991Q8—1222no—
992Q8—1222no—
993Q8—1222no—
994Q8—1222no—
995Q8—2444no—
996Q8—2442no—
997Q8C22×D24412yes—
998Q8C22×D24412yes—
999D4—24no—
1000D4—24no—
1001D4—21no—
1002D4—21no—
1003D4—1224no—
1004D4—1224no—
1005D4—1222no—
1006D4—1222no—
1007D4—1222no—
1008D4—1222no—
1009D4—1222no—
1010D4—1222no—
1011D4—1222no—
1012D4—1222no—
1013D4—4884no—
1014D4—4884no—
1015D4—4884no—
1016D4—4884no—
1017D4—2444no—
1018D4—2444no—
1019D4—2444no—
1020D4—2444no—
1021D4—2448no—
1022D4—2444no—
1023D4—2444no—
1024D4—2444no—
1025D4—2444no—
1026D4—2442no—
1027D4—2442no—
1028D4—2442no—
1029D4C22×D24412yes—
1030D4C22×D24412yes—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—42no—
1038C2×C4—44no—
1039C2×C4—82no—
1040C2×C4—612no—
1041C2×C4—612no—
1042C2×C4—1222no—
1043C2×C4—1222no—
1044C2×C4—1222no—
1045C2×C4—1222no—
1046C2×C4—1222no—
1047C2×C4—2444no—
1048C2×C4—2444no—
1049C2×C4—2444no—
1050C2×C4—2444no—
1051C2×C4—2444no—
1052C2×C4—2442no—
1053C2×C4C2×D4×D6112yes—
1054C2×C4C2×D4×D6112yes—
1055C2×C4C2×D4×D6111yescharacteristic
1056C2×C4C22×D24412yes—
1057C2×C4#1451982312yes—
1058C2×C4C24×D6111yescharacteristic
1059C8—22no—
1060C8—1222no—
1061C8—1222no—
1062C8C22×D24412yes—
1063C8C22×D24412yes—
1064C22—22no—
1065C22—22no—
1066C22—22no—
1067C22—42no—
1068C22—42no—
1069C22—1222no—
1070C22—1222no—
1071C22—1224no—
1072C22—1224no—
1073C22—9762no—
1074C22—9762no—
1075C22—9762no—
1076C22—9764no—
1077C22—9764no—
1078C22—9764no—
1079C22—2442no—
1080C22—2442no—
1081C22—2442no—
1082C22—2444no—
1083C22—2444no—
1084C22—2444no—
1085C22D4×D24412yes—
1086C22C22×D4×D6111yescharacteristic
1087C4—22no—
1088C4—22no—
1089C4—22no—
1090C4—22no—
1091C4—42no—
1092C4—42no—
1093C4—1222no—
1094C4—1222no—
1095C4—2442no—
1096C4D4×D24412yes—
1097C4C23×D24411yescharacteristic
1098C4C2×#1451982311yescharacteristic
1099C2—22no—
1100C2—42no—
1101C2—42no—
1102C2—4882no—
1103C2—4882no—
1104C2—4882no—
1105C2—2442no—
1106C2—2442no—
1107C2C2×D4×D24411yescharacteristic
1108C2#2146059612yes—
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#2943C2
socleC22×C61C23×D4
hypercenter#2943D61
hypocenterC61#61082
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2943

Complements

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

NH ≅ G/Ntype
1. C2×#16840569C2semidirect
2. C2×#16840564C2semidirect
3. #21459612C2semidirect
4. #21459597C2semidirect
5. #21457406C2semidirect
6. #21457361C2semidirect
7. #21457316C2semidirect
8. #21457301C2semidirect
9. C2×#16840151C2semidirect
10. #21455468C2semidirect
11. #21455459C2semidirect
12. #21455313C2semidirect
13. #21455299C2semidirect
14. #21455108C2semidirect
15. #21455099C2semidirect
16. #21455090C2semidirect
17. #21455090C2semidirect
18. #21454538C2semidirect
19. C61×#2943C2semidirect
20. C2×#14519824C22semidirect
22. C2×#14519823C22semidirect
23. C2×#14519823C22semidirect
26. C2×#14519809C22semidirect
27. C2×#14519807C22semidirect
28. C2×#14519804C22semidirect
29. C2×#14519804C22semidirect
31. C2×#14519802C22semidirect
32. C2×#14519802C22semidirect
33. C2×#14519801C22semidirect
34. C2×#14519800C22semidirect
35. C2×#14519798C22semidirect
36. C22×#11758190C22semidirect
37. C22×#11758190C22semidirect
38. C2×SD16×D61C22semidirect
39. C22×D488C22semidirect
40. C22×D488C22semidirect
41. C2×D8×D61C22semidirect
42. C2×#14519783C22semidirect
43. C2×#14519783C22semidirect
44. #16840434C22semidirect
45. #16840424C22semidirect
47. #16840407C22semidirect
49. D4×D244C22semidirect
51. #16840338C22semidirect
56. #16840331C22semidirect
57. #16840331C22semidirect
62. C2×#14519774C22semidirect
64. C2×#14519765C22semidirect
65. #16840151C22semidirect
66. #16840151C22semidirect
67. #16840016C22semidirect
68. #16840009C22semidirect
69. #16839999C22semidirect
70. #16839992C22semidirect
71. #16839984C22semidirect
72. #16839977C22semidirect
73. #16839962C22semidirect
74. #16839957C22semidirect
75. #16839927C22semidirect
76. #16839914C22semidirect
77. #16839910C22semidirect
78. #16839910C22semidirect
79. #16839908C22semidirect
80. #16839902C22semidirect
81. #16839897C22semidirect
82. #16839897C22semidirect
83. #16839835C22semidirect
84. #16839835C22semidirect
85. #16839786C22semidirect
86. #16839770C22semidirect
87. #16839766C22semidirect
88. #16839766C22semidirect
89. #16839766C22semidirect
90. #16839728C22semidirect
91. #16839728C22semidirect
93. C4×#41×C61C22semidirect
94. C4×#41×C61C22semidirect
95. C61×#442C22semidirect
96. C61×#441C22semidirect
97. C61×#440C22semidirect
98. C61×#440C22semidirect
99. C61×#427C22semidirect
100. C61×#416C22semidirect
101. C61×#416C22semidirect
102. C2×#97×C61C22semidirect
230. #135×C61D4semidirect
267. #41×C61C2×D4semidirect
358. Q16×C61C2×D4semidirect
359. SD16×C61C2×D4semidirect
360. SD16×C61C2×D4semidirect
361. D8×C61C2×D4semidirect
363. C2×C8×C61C2×D4semidirect
562. #2943D61semidirect
620. C4×#41C2×D61semidirect
621. C4×#41C2×D61semidirect
640. #442C2×D61semidirect
641. #441C2×D61semidirect
642. #440C2×D61semidirect
643. #440C2×D61semidirect
646. #427C2×D61semidirect
652. #416C2×D61semidirect
653. #416C2×D61semidirect
656. C2×#97C2×D61semidirect
657. C61#61082semidirect
706. #135D244semidirect
839. #41C2×D244semidirect
914. Q16C2×D244semidirect
922. SD16C2×D244semidirect
923. SD16C2×D244semidirect
930. D8C2×D244semidirect
940. C2×C8C2×D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168405692
C2×#168405642
#214596122
#214595972
#214574062
#214573612
#214573162
#214573012
C2×#168401512
#214554682
#214554592
#214553132
#214552992
#214551082
#214550992
#214550902
#214545382
C61×#29432
#6108261