Finite Group Databasebeta

← #29696006

Subgroups — #29696006

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×#16839884C211yesmaximal, characteristic, complemented
2#21454695C211yesmaximal, characteristic, complemented
3#21454352C211yesmaximal, characteristic, complemented
4#21454345C211yesmaximal, characteristic, complemented
5#21446724C211yesmaximal, characteristic, complemented
6#21446702C211yesmaximal, characteristic, complemented
7#21446336C211yesmaximal, characteristic, complemented
8#21446329C211yesmaximal, characteristic, complemented
9#21446197C211yesmaximal, characteristic, complemented
10#21446190C211yesmaximal, characteristic, complemented
11#21445883C211yesmaximal, characteristic, complemented
12#21445778C211yesmaximal, characteristic, complemented
13#21445773C211yesmaximal, characteristic, complemented
14#21445661C211yesmaximal, characteristic, complemented
15C2×C61×#577C211yesmaximal, characteristic
16C2×#14519784C2211yescharacteristic
17C2×#14519784C2211yescharacteristic, complemented
18#16840245C2211yescharacteristic
19#16840245C2211yescharacteristic, complemented
20#16839884—24no—
21#16839863—21no—
22#16839863—21no—
23Q16×Dic61—21no—
24D8×Dic61—21no—
25C2×#14519713C2211yescharacteristic, complemented
26C2×#14519711C2211yescharacteristic, complemented
27C2×#14519704C2211yescharacteristic
28C2×#14519704C2211yescharacteristic
29C2×#14519704C2211yescharacteristic, complemented
30#16839771—21no—
31#16839771C2211yescharacteristic, complemented
32#16839767—21no—
33#16839767C2211yescharacteristic
34#16839763—21no—
35#16839763—21no—
36#16839763C2211yescharacteristic
37#16839763C2211yescharacteristic
38#16839763C2211yescharacteristic
39#16839763C2211yescharacteristic, complemented
40#16839758—21no—
41#16839758—21no—
42#16839758C2211yescharacteristic
43C2×#14519701—21no—
44C2×#14519701C2211yescharacteristic, complemented
45C2×#14519698—21no—
46C2×#14519698C2211yescharacteristic
47C2×#14519696C2211yescharacteristic, complemented
48C2×#14519694C2211yescharacteristic
49#16839717C2211yescharacteristic, complemented
50C2×#14519687C2211yescharacteristic, complemented
51#16839669C2211yescharacteristic, complemented
52#16839665C2211yescharacteristic
53#16839530C2211yescharacteristic, complemented
54#16839530C2211yescharacteristic, complemented
55#16839526C2211yescharacteristic, complemented
56#16839523C2211yescharacteristic, complemented
57C2×2−1+4×C61C2211yescharacteristic
58C2×H(5,𝔽2)×C61C2211yescharacteristic
59C61×#577—24no—
60C61×#577C418yescomplemented
61C2×#137×C61—21no—
62C2×#137×C61C2211yescharacteristic
63C2×AGL(1,ℤ/8)×C61—21no—
64C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
65C2×#135×C61—21no—
66C2×#135×C61C2211yescharacteristic
67C22×SD16×C61—21no—
68C22×SD16×C61C2211yescharacteristic
69C2×#131×C61C2211yescharacteristic
70#14519784—22no—
71#14519784—22no—
72#14519784—41no—
73#14519784—41no—
74C2×#11758194—21no—
75C2×#11758194—21no—
76C2×#11758194C2311yescharacteristic
77C2×#11758194C2311yescharacteristic
78C2×#11758194C2311yescharacteristic
79C22×#92418—21no—
80C22×#92418—21no—
81C22×#92418C2311yescharacteristic
82Q8×Dic61—21no—
83Q8×Dic61—21no—
84D4×Dic61—21no—
85D4×Dic61—21no—
86D4×Dic61—41no—
87D4×Dic61—41no—
88#14519736—21no—
89#14519736—21no—
90#14519736C2311yescharacteristic
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C22⋊Dic61—41no—
96C2×C4×Dic61C2311yescharacteristic
97#14519713—22no—
98#14519711—21no—
99#14519711—21no—
100#14519704—22no—
101#14519704—22no—
102#14519704—22no—
103#14519701—21no—
104#14519701—21no—
105#14519701—21no—
106#14519701—21no—
107#14519701—21no—
108#14519701—21no—
109#14519701—21no—
110#14519701—21no—
111#14519701D411yescharacteristic
112#14519701D411yescharacteristic
113#14519698—21no—
114#14519698—21no—
115#14519698—21no—
116#14519698—21no—
117#14519698—21no—
118#14519698—21no—
119#14519698—21no—
120#14519698—21no—
121#14519698D411yescharacteristic
122#14519698D411yescharacteristic
123#14519696—41no—
124#14519694—41no—
125#14519687—22no—
126#14519687—21no—
127C8×Dic61—21no—
128#14519684—41no—
1292−1+4×C61—22no—
1302−1+4×C61—22no—
1312−1+4×C61—41no—
1322−1+4×C61C2×C414yescomplemented
133H(5,𝔽2)×C61—22no—
134H(5,𝔽2)×C61—22no—
135H(5,𝔽2)×C61—41no—
136H(5,𝔽2)×C61C2×C414yescomplemented
137C2×#41×C61—21no—
138C2×#41×C61—21no—
139C2×#41×C61—21no—
140C2×#41×C61—21no—
141C2×#41×C61—41no—
142C2×#41×C61C2311yescharacteristic
143C2×#41×C61C2311yescharacteristic
144C2×#41×C61C2311yescharacteristic
145C22×Q8×C61—21no—
146C22×Q8×C61—21no—
147C22×Q8×C61C2311yescharacteristic
148C22×D4×C61—21no—
149C22×D4×C61—21no—
150C22×D4×C61—41no—
151C22×D4×C61C2311yescharacteristic
152#137×C61—22no—
153#137×C61—28no—
154#137×C61C2×C414yescomplemented
155AGL(1,ℤ/8)×C61—22no—
156AGL(1,ℤ/8)×C61—28no—
157AGL(1,ℤ/8)×C61C2×C414yescomplemented
158#135×C61—28no—
159#135×C61C2×C414yes—
160#135×C61D414yes—
161C2×Q16×C61—21no—
162C2×Q16×C61D411yescharacteristic
163C2×SD16×C61—21no—
164C2×SD16×C61—21no—
165C2×SD16×C61—28no—
166C2×SD16×C61—21no—
167C2×SD16×C61—21no—
168C2×SD16×C61—22no—
169C2×SD16×C61C2×C414yescomplemented
170C2×SD16×C61D411yescharacteristic
171C2×SD16×C61D411yescharacteristic
172C2×D8×C61—21no—
173C2×D8×C61D411yescharacteristic
174#131×C61—22no—
175#131×C61C2×C414yescomplemented
176C2×M16×C61—21no—
177C2×M16×C61C2311yescharacteristic
178C22×C8×C61—21no—
179C22×C8×C61C2311yescharacteristic
180C24×C61—21no—
181C24×C61—41no—
182#41×C61—21no—
183#41×C61—21no—
184#41×C61—21no—
185#41×C61—21no—
186#41×C61—21no—
187#41×C61—21no—
188#41×C61—24no—
189#41×C61—24no—
190#41×C61—24no—
191#41×C61—24no—
192#41×C61—44no—
193#41×C61—42no—
194#41×C61—42no—
195#41×C61—42no—
196#41×C61—42no—
197#41×C61—44no—
198#41×C61C22×C412yes—
199#41×C61C22×C412yes—
200#41×C61C22×C412yes—
201#41×C61C2×D412yes—
202#41×C61C2×D412yes—
203#41×C61#4112yes—
204C2×Q8×C61—21no—
205C2×Q8×C61—24no—
206C2×Q8×C61—24no—
207C2×Q8×C61—21no—
208C2×Q8×C61—21no—
209C2×Q8×C61—21no—
210C2×Q8×C61—21no—
211C2×Q8×C61—41no—
212C2×Q8×C61—42no—
213C2×Q8×C61—42no—
214C2×Q8×C61C22×C412yes—
215C2×Q8×C61C2×D411yescharacteristic
216C2×Q8×C61C2×D411yescharacteristic
217C2×Q8×C61C2×D411yescharacteristic
218C2×D4×C61—21no—
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61—24no—
222C2×D4×C61—24no—
223C2×D4×C61—21no—
224C2×D4×C61—21no—
225C2×D4×C61—21no—
226C2×D4×C61—21no—
227C2×D4×C61—21no—
228C2×D4×C61—42no—
229C2×D4×C61—42no—
230C2×D4×C61—41no—
231C2×D4×C61—41no—
232C2×D4×C61—44no—
233C2×D4×C61—44no—
234C2×D4×C61—41no—
235C2×D4×C61C22×C412yes—
236C2×D4×C61C2×D411yescharacteristic
237C2×D4×C61C2×D411yescharacteristic
238C2×D4×C61C2×D411yescharacteristic
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—41no—
244C22×C4×C61—41no—
245C22×C4×C61—41no—
246C22×C4×C61C2411yescharacteristic
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—41no—
251C22×Dic61—41no—
252Q16×C61—24no—
253Q16×C61C22⋊C414yescomplemented
254SD16×C61—24no—
255SD16×C61—24no—
256SD16×C61—24no—
257SD16×C61—24no—
258SD16×C61C22⋊C414yescomplemented
259SD16×C61C22⋊C414yescomplemented
260D8×C61—24no—
261D8×C61C22⋊C414yescomplemented
262M16×C61—21no—
263M16×C61—24no—
264M16×C61C22×C412yes—
265C2×C8×C61—21no—
266C2×C8×C61—24no—
267C2×C8×C61C22×C412yes—
268C2×C8×C61C2×D411yescharacteristic
269C2×C8×C61C2×D411yescharacteristic
270C2×C8×C61C2×D412yes—
271C22⋊Dic61—21no—
272C22⋊Dic61—41no—
273C22⋊Dic61—41no—
274C22⋊Dic61—82no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61—41no—
280C4⋊Dic61—41no—
281C4⋊Dic61C2×D411yescharacteristic
282C4⋊Dic61C2×D411yescharacteristic
283C4×Dic61—21no—
284C4×Dic61—21no—
285C4×Dic61—21no—
286C4×Dic61—41no—
287C4×Dic61—41no—
288#11758194—21no—
289#11758194—21no—
290#11758194—21no—
291#11758194—21no—
292#11758194—21no—
293#11758194—21no—
294#11758194—42no—
295#11758194—42no—
296C2×#92418—21no—
297C2×#92418—21no—
298C2×#92418—21no—
299C2×#92418—21no—
300C2×#92418—21no—
301C2×#92418—42no—
302C2×#92418—42no—
303C2×#92418C2×D411yescharacteristic
304C2×#92418C2×D411yescharacteristic
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—21no—
308C23×C61—22no—
309C23×C61—44no—
310C23×C61—41no—
311C23×C61—41no—
312C23×C61—81no—
313C23×C61—81no—
314C23×C61—161no—
315C23×C61—161no—
316C23×C61H(5,𝔽2)11yescharacteristic
317Q8×C61—21no—
318Q8×C61—21no—
319Q8×C61—21no—
320Q8×C61—22no—
321Q8×C61—22no—
322Q8×C61—44no—
323Q8×C61—41no—
324Q8×C61—41no—
325Q8×C61C2×C22⋊C412yes—
326Q8×C61C2×C22⋊C412yes—
327Q8×C61C4×D412yes—
328D4×C61—22no—
329D4×C61—22no—
330D4×C61—22no—
331D4×C61—22no—
332D4×C61—22no—
333D4×C61—22no—
334D4×C61—22no—
335D4×C61—22no—
336D4×C61—21no—
337D4×C61—21no—
338D4×C61—21no—
339D4×C61—44no—
340D4×C61—44no—
341D4×C61—44no—
342D4×C61—41no—
343D4×C61—41no—
344D4×C61C2×C22⋊C412yes—
345D4×C61C2×C22⋊C412yes—
346D4×C61C4×D412yes—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—44no—
358C2×C4×C61—44no—
359C2×C4×C61—44no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61C23×C411yescharacteristic
363C2×C4×C61C22×D411yescharacteristic
364C2×C4×C61C22×D411yescharacteristic
365C2×C4×C61C22×D411yescharacteristic
366C2×C4×C61C2×#4111yescharacteristic
367C2×C4×C61H(5,𝔽2)11yescharacteristic
368C2×Dic61—21no—
369C2×Dic61—21no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—41no—
373C2×Dic61—41no—
374C2×Dic61—41no—
375C2×Dic61—81no—
376C2×Dic61—81no—
377C2×Dic61—161no—
378C2×Dic61—161no—
379C8×C61—22no—
380C8×C61C2×C22⋊C412yes—
381C8×C61C2×C22⋊C412yes—
382#92418—21no—
383#92418—21no—
384#92418—41no—
385#92418—41no—
386#92418—41no—
387#22464—611nomaximal, Sylow
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—22no—
391C22×C61—22no—
392C22×C61—22no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61—41no—
399C22×C61—42no—
400C22×C61—82no—
401C22×C61—81no—
402C22×C61—81no—
403C22×C61—161no—
404C22×C61—164no—
405C22×C61#51811yescharacteristic
406C22×C61D4211yescharacteristic
407C22×C61#54611yescharacteristic
408C4×C61—22no—
409C4×C61—22no—
410C4×C61—22no—
411C4×C61—42no—
412C4×C61C22×C22⋊C411yescharacteristic
413C4×C61C2×C4×D411yescharacteristic
414C4×C61D4211yescharacteristic
415C4×C61#54611yescharacteristic
416Dic61—41no—
417Dic61—41no—
418Dic61—81no—
419Dic61—81no—
420Dic61—81no—
421C2×#577D6111yescharacteristic
422C2×#444—611no—
423#2951—611no—
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×C61—42no—
441C2×C61—82no—
442C2×C61D4×C22⋊C411yescharacteristic
443C2×C61#328811yescharacteristic
444C2×C61#328911yescharacteristic
445C2×2−1+4C2×D6111yescharacteristic
446C2×H(5,𝔽2)C2×D6111yescharacteristic
447#577—24no—
448#577Dic6118yescomplemented
449C2×#137—21no—
450C2×#137C2×D6111yescharacteristic
451C2×AGL(1,ℤ/8)—21no—
452C2×AGL(1,ℤ/8)C2×D6111yescharacteristic
453C2×#135—21no—
454C2×#135C2×D6111yescharacteristic
455C22×SD16—21no—
456C22×SD16C2×D6111yescharacteristic
457C2×#131—611no—
458C2×#131—611no—
459C2×#131C2×D6111yescharacteristic
460#520—611no—
461#520—611no—
462#444—1224no—
463#440—1221no—
464#440—1221no—
465C4×Q16—1221no—
466C4×D8—1221no—
467C2×#108—611no—
468C2×#107—611no—
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—611no—
479#417—611no—
480#417—1221no—
481#417—1221no—
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#405—611no—
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—22no—
5012−1+4—22no—
5022−1+4—41no—
5032−1+4C2×Dic6114yescomplemented
504H(5,𝔽2)—22no—
505H(5,𝔽2)—22no—
506H(5,𝔽2)—41no—
507H(5,𝔽2)C2×Dic6114yescomplemented
508C2×#41—21no—
509C2×#41—21no—
510C2×#41—21no—
511C2×#41—21no—
512C2×#41—41no—
513C2×#41C22×D6111yescharacteristic
514C2×#41C22×D6111yescharacteristic
515C2×#41C22×D6111yescharacteristic
516C22×Q8—21no—
517C22×Q8—21no—
518C22×Q8C22×D6111yescharacteristic
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—41no—
522C22×D4C22×D6111yescharacteristic
523#137—22no—
524#137—28no—
525#137C2×Dic6114yescomplemented
526AGL(1,ℤ/8)—22no—
527AGL(1,ℤ/8)—28no—
528AGL(1,ℤ/8)C2×Dic6114yescomplemented
529#135—28no—
530#135C2×Dic6114yes—
531#135C22⋊D6114yes—
532C2×Q16—21no—
533C2×Q16C22⋊D6111yescharacteristic
534C2×SD16—21no—
535C2×SD16—21no—
536C2×SD16—28no—
537C2×SD16—21no—
538C2×SD16—21no—
539C2×SD16—22no—
540C2×SD16C2×Dic6114yescomplemented
541C2×SD16C22⋊D6111yescharacteristic
542C2×SD16C22⋊D6111yescharacteristic
543C2×D8—21no—
544C2×D8C22⋊D6111yescharacteristic
545#131—22no—
546#131—1222no—
547#131—1222no—
548#131—2441no—
549#131—2441no—
550#131C2×Dic6114yescomplemented
551C2×M16—21no—
552C2×M16—611no—
553C2×M16—611no—
554C2×M16—611no—
555C2×M16—1221no—
556C2×M16—1221no—
557C2×M16C22×D6111yescharacteristic
558C22×C8—21no—
559C22×C8—611no—
560C22×C8—1221no—
561C22×C8—1221no—
562C22×C8C22×D6111yescharacteristic
563C4×Q8—1221no—
564C4×Q8—1221no—
565C4×D4—1221no—
566C4×D4—1221no—
567C4×D4—2441no—
568C4×D4—2441no—
569#117—611no—
570#117—1221no—
571#117—1221no—
572C2×C4⋊C4—611no—
573C2×C4⋊C4—611no—
574C2×C4⋊C4—1221no—
575C2×C4⋊C4—1221no—
576C2×C22⋊C4—2441no—
577C2×C42—611no—
578#108—1222no—
579#107—1221no—
580#107—1221no—
581#104—1222no—
582#104—1222no—
583#104—1222no—
584#103—611no—
585#103—611no—
586#103—1221no—
587#103—1221no—
588#103—1221no—
589#103—1221no—
590#103—1221no—
591#103—1221no—
592#103—1221no—
593#103—1221no—
594#102—611no—
595#102—611no—
596#102—1221no—
597#102—1221no—
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—1222no—
607#97—1221no—
608C4×C8—1221no—
609#95—2441no—
610C24—21no—
611C24—41no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—24no—
619#41—24no—
620#41—24no—
621#41—24no—
622#41—44no—
623#41—42no—
624#41—42no—
625#41—42no—
626#41—42no—
627#41—44no—
628#41#1175822412yes—
629#41C22×Dic6112yes—
630#41C22×Dic6112yes—
631#41C22×Dic6112yes—
632#41C2×C22⋊D6112yes—
633#41C2×C22⋊D6112yes—
634C2×Q8—21no—
635C2×Q8—24no—
636C2×Q8—24no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—41no—
642C2×Q8—42no—
643C2×Q8—42no—
644C2×Q8D4×D6111yescharacteristic
645C2×Q8C22×Dic6112yes—
646C2×Q8C2×C22⋊D6111yescharacteristic
647C2×Q8C2×C22⋊D6111yescharacteristic
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—41no—
661C2×D4—41no—
662C2×D4—44no—
663C2×D4—44no—
664C2×D4—41no—
665C2×D4D4×D6111yescharacteristic
666C2×D4C22×Dic6112yes—
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—41no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—2441no—
680C22×C4—2441no—
681C22×C4C23×D6111yescharacteristic
682Q16—24no—
683Q16C22⋊Dic6114yescomplemented
684SD16—24no—
685SD16—24no—
686SD16—24no—
687SD16—24no—
688SD16C22⋊Dic6114yescomplemented
689SD16C22⋊Dic6114yescomplemented
690D8—24no—
691D8C22⋊Dic6114yescomplemented
692M16—21no—
693M16—24no—
694M16—1221no—
695M16—1221no—
696M16—1221no—
697M16—1221no—
698M16—1221no—
699M16—1221no—
700M16—2442no—
701M16—2442no—
702M16C22×Dic6112yes—
703C2×C8—21no—
704C2×C8—24no—
705C2×C8—611no—
706C2×C8—611no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—1221no—
711C2×C8—1221no—
712C2×C8—2442no—
713C2×C8—2442no—
714C2×C8C22×Dic6112yes—
715C2×C8C2×C22⋊D6111yescharacteristic
716C2×C8C2×C22⋊D6111yescharacteristic
717C2×C8C2×C22⋊D6112yes—
718C4⋊C4—611no—
719C4⋊C4—611no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—2441no—
725C4⋊C4—2441no—
726C22⋊C4—1221no—
727C22⋊C4—4882no—
728C22⋊C4—2441no—
729C22⋊C4—2441no—
730C42—1221no—
731C42—1221no—
732C42—1221no—
733C42—2441no—
734C42—2441no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—22no—
739C23—44no—
740C23—41no—
741C23—41no—
742C23—81no—
743C23—81no—
744C23—161no—
745C23—161no—
746C23#1451982211yescharacteristic
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—22no—
751Q8—22no—
752Q8—44no—
753Q8—41no—
754Q8—41no—
755Q8C2×C22⋊Dic6112yes—
756Q8C2×C22⋊Dic6112yes—
757Q8D4×Dic6112yes—
758D4—22no—
759D4—22no—
760D4—22no—
761D4—22no—
762D4—22no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—21no—
767D4—21no—
768D4—21no—
769D4—44no—
770D4—44no—
771D4—44no—
772D4—41no—
773D4—41no—
774D4C2×C22⋊Dic6112yes—
775D4C2×C22⋊Dic6112yes—
776D4D4×Dic6112yes—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—1221no—
793C2×C4—1221no—
794C2×C4—9761no—
795C2×C4—9761no—
796C2×C4—4881no—
797C2×C4—4881no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4C23×Dic6111yescharacteristic
804C2×C4C2×D4×D6111yescharacteristic
805C2×C4C22×C22⋊D6111yescharacteristic
806C2×C4C22×C22⋊D6111yescharacteristic
807C2×C4C2×#1175822411yescharacteristic
808C2×C4#1451982211yescharacteristic
809C8—22no—
810C8—1221no—
811C8—1221no—
812C8—2441no—
813C8—2441no—
814C8—2441no—
815C8C2×C22⋊Dic6112yes—
816C8C2×C22⋊Dic6112yes—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—42no—
829C22—82no—
830C22—81no—
831C22—81no—
832C22—161no—
833C22—164no—
834C22#1684023711yescharacteristic
835C22D4×C22⋊D6111yescharacteristic
836C22#1684040611yescharacteristic
837C4—22no—
838C4—22no—
839C4—22no—
840C4—42no—
841C4—4881no—
842C4—4881no—
843C4—4881no—
844C4—2441no—
845C4—2441no—
846C4C22×C22⋊Dic6111yescharacteristic
847C4C2×D4×Dic6111yescharacteristic
848C4D4×C22⋊D6111yescharacteristic
849C4#1684040611yescharacteristic
850C2—21no—
851C2—21no—
852C2—42no—
853C2—42no—
854C2—42no—
855C2—82no—
856C2D4×C22⋊Dic6111yescharacteristic
857C2#2145758111yescharacteristic
858C2#2145759211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#577C2
socleC22×C61D42
cosocleC22×C4×C61C24
hypercenterC2×#577D61
hypocenterC61#22464
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#577

Complements

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

NH ≅ G/Ntype
1. C2×#16839884C2semidirect
2. #21454695C2semidirect
3. #21454352C2semidirect
4. #21454345C2semidirect
5. #21446724C2semidirect
6. #21446702C2semidirect
7. #21446336C2semidirect
8. #21446329C2semidirect
9. #21446197C2semidirect
10. #21446190C2semidirect
11. #21445883C2semidirect
12. #21445778C2semidirect
13. #21445773C2semidirect
14. #21445661C2semidirect
17. C2×#14519784C22semidirect
19. #16840245C22semidirect
25. C2×#14519713C22semidirect
26. C2×#14519711C22semidirect
29. C2×#14519704C22semidirect
31. #16839771C22semidirect
39. #16839763C22semidirect
44. C2×#14519701C22semidirect
47. C2×#14519696C22semidirect
49. #16839717C22semidirect
50. C2×#14519687C22semidirect
51. #16839669C22semidirect
53. #16839530C22semidirect
54. #16839530C22semidirect
55. #16839526C22semidirect
56. #16839523C22semidirect
60. C61×#577C4semidirect
132. 2−1+4×C61C2×C4semidirect
136. H(5,𝔽2)×C61C2×C4semidirect
154. #137×C61C2×C4semidirect
157. AGL(1,ℤ/8)×C61C2×C4semidirect
169. C2×SD16×C61C2×C4semidirect
175. #131×C61C2×C4semidirect
253. Q16×C61C22⋊C4semidirect
258. SD16×C61C22⋊C4semidirect
259. SD16×C61C22⋊C4semidirect
261. D8×C61C22⋊C4semidirect
448. #577Dic61semidirect
499. C61#22464semidirect
503. 2−1+4C2×Dic61semidirect
507. H(5,𝔽2)C2×Dic61semidirect
525. #137C2×Dic61semidirect
528. AGL(1,ℤ/8)C2×Dic61semidirect
540. C2×SD16C2×Dic61semidirect
550. #131C2×Dic61semidirect
683. Q16C22⋊Dic61semidirect
688. SD16C22⋊Dic61semidirect
689. SD16C22⋊Dic61semidirect
691. D8C22⋊Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398842
#214546952
#214543522
#214543452
#214467242
#214467022
#214463362
#214463292
#214461972
#214461902
#214458832
#214457782
#214457732
#214456612
C2×C61×#5772
#2246461