Finite Group Databasebeta

← #29684025

Subgroups — #29684025

Order 15616.

1562 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519801C211yesmaximal, characteristic
2C2×#16839809C211yesmaximal, characteristic, complemented
3#21454333C211yesmaximal, characteristic, complemented
4#418×D61C211yesmaximal, characteristic, complemented
5C2×#16839743C211yesmaximal, characteristic, complemented
6C2×#100×D61C211yesmaximal, characteristic, complemented
7#21454235C211yesmaximal, characteristic, complemented
8#21446730C211yesmaximal, characteristic, complemented
9#21446728C211yesmaximal, characteristic, complemented
10#21446726C211yesmaximal, characteristic, complemented
11#21446725C211yesmaximal, characteristic, complemented
12#21446722C211yesmaximal, characteristic, complemented
13#21446720C211yesmaximal, characteristic, complemented
14#21446719C211yesmaximal, characteristic, complemented
15C61×#1978C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C2×#14519801—21no—
19C2×#14519801—21no—
20C2×#14519801—21no—
21C2×#14519801—21no—
22C2×#14519801—24no—
23C2×#14519801C418yescomplemented
24C22×#11758190C2211yescharacteristic
25C22×#11758200C2211yescharacteristic
26C22×#11758199C2211yescharacteristic
27C22×#11758189C2211yescharacteristic
28C2×M16×D61C2211yescharacteristic
29C2×M16×D61C2211yescharacteristic
30C2×M16×D61C2211yescharacteristic
31#117×D61C2211yescharacteristic
32#16839809—24no—
33C2×#14519713C2211yescharacteristic, complemented
34C2×#14519712C2211yescharacteristic, complemented
35C2×#14519712C2211yescharacteristic, complemented
36#16839772C2211yescharacteristic, complemented
37#16839770C2211yescharacteristic, complemented
38#16839768C2211yescharacteristic
39#16839767C2211yescharacteristic
40#16839767C2211yescharacteristic, complemented
41#16839766C2211yescharacteristic
42#16839765—22no—
43#16839760—22no—
44#16839755—22no—
45#102×D61—22no—
46#16839743—24no—
47C2×#14519695C2211yescharacteristic, complemented
48C2×#14519695C2211yescharacteristic, complemented
49C2×#14519694C2211yescharacteristic
50C2×#14519694C2211yescharacteristic, complemented
51C2×#14519693C2211yescharacteristic
52C2×#14519693C2211yescharacteristic
53#100×D61—24no—
54#16839720C2211yescharacteristic, complemented
55#16839719—21no—
56#16839718C2211yescharacteristic, complemented
57#16839717C2211yescharacteristic, complemented
58#16839716—21no—
59#16839714—21no—
60C4×#11758189—21no—
61C22×D8×C61C2211yescharacteristic
62C2×#108×C61C2211yescharacteristic, complemented
63C61×#418C2211yescharacteristic
64C61×#418C2211yescharacteristic, complemented
65C2×#100×C61C2211yescharacteristic
66C2×#100×C61C2211yescharacteristic, complemented
67C61×#405C2211yescharacteristic, complemented
68C24×D61—21no—
69C2×#11758224—21no—
70C2×#11758224—21no—
71C2×#11758224—21no—
72C2×#11758224—21no—
73C2×#11758224—22no—
74C2×#11758224—22no—
75C2×#11758224—22no—
76C2×#11758224C2×C414yes—
77C22×Dic122C2311yescharacteristic
78C22×D244C2311yescharacteristic
79C22×C22⋊D61—21no—
80C22×C22⋊D61—21no—
81C2×D4×D61—21no—
82C2×D4×D61—21no—
83C2×D4×D61—21no—
84C2×D4×D61—21no—
85C2×D4×D61—22no—
86C2×D4×D61—22no—
87C2×D4×D61—22no—
88C2×D4×D61C2×C414yes—
89C23×Dic61—21no—
90C22×C4×D61C2311yescharacteristic
91#14519801—28no—
92#14519801—28no—
93#14519801—28no—
94#14519801—28no—
95C2×#11758190—21no—
96C2×#11758190—21no—
97C2×#11758190—22no—
98C2×#11758190C2×C414yescomplemented
99C2×#11758200—21no—
100C2×#11758200—21no—
101C2×#11758200—22no—
102C2×#11758200C2×C414yescomplemented
103C2×#11758199—21no—
104C2×#11758199—21no—
105C2×#11758199—22no—
106C2×#11758199C2×C414yescomplemented
107C2×#11758194C2311yescharacteristic
108C2×#11758194C2311yescharacteristic
109C2×#11758194C2311yescharacteristic
110C2×#11758189—21no—
111C2×#11758189—21no—
112C2×#11758189—21no—
113C2×#11758189C2×C414yes—
114C2×#11758189D411yescharacteristic
115C2×#11758189D411yescharacteristic
116C2×#11758189D411yescharacteristic
117C2×#11758189D411yescharacteristic
118C2×#11758189D414yes—
119M16×D61—22no—
120M16×D61—22no—
121M16×D61—22no—
122M16×D61—22no—
123M16×D61—22no—
124M16×D61D414yes—
125C22×#92418C2311yescharacteristic
126C2×C8×D61—21no—
127C2×C8×D61—21no—
128C2×C8×D61—21no—
129#14519736C2311yescharacteristic
130#14519735D412yes—
131#14519734—21no—
132#14519733—21no—
133C4⋊C4×D61D412yes—
134C22⋊C4×D61—21no—
135C42×D61—21no—
136#14519713—22no—
137#14519712—22no—
138#14519712—22no—
139#14519702—22no—
140#14519700—22no—
141#14519699—22no—
142#14519698—22no—
143#14519698—22no—
144#14519697—22no—
145#14519695—22no—
146#14519695—22no—
147#14519694—22no—
148#14519694—22no—
149#14519693—22no—
150#14519693—22no—
151#14519688—21no—
152#14519687—21no—
153#14519687—21no—
154C4×#92418—21no—
155C8×Dic61—21no—
156C8×Dic61—21no—
157C22×D4×C61C2311yescharacteristic
158C22×D4×C61C2311yescharacteristic
159C2×D8×C61—21no—
160C2×D8×C61—21no—
161C2×D8×C61—22no—
162C2×D8×C61C2×C414yescomplemented
163C2×M16×C61C2311yescharacteristic
164C2×M16×C61C2311yescharacteristic
165C2×M16×C61C2311yescharacteristic
166C22×C8×C61C2311yescharacteristic
167#117×C61C2311yescharacteristic
168#108×C61—22no—
169#102×C61—22no—
170#102×C61—22no—
171#100×C61—22no—
172#100×C61—22no—
173#97×C61—21no—
174C4×C8×C61—21no—
175C24×C61—21no—
176C24×C61—21no—
177C23×D61—21no—
178C23×D61—24no—
179C23×D61—41no—
180C23×D61—41no—
181C23×D61—42no—
182C23×D61—84no—
183C23×D61#4111yescharacteristic
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—21no—
192C2×D4×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61C22×C412yes—
195C2×D4×C61C22×C412yes—
196C22×C4×C61C2411yescharacteristic
197C2×C22⋊D61—24no—
198C2×C22⋊D61—24no—
199C2×C22⋊D61—41no—
200C2×C22⋊D61—41no—
201C2×C22⋊D61—42no—
202C2×C22⋊D61—41no—
203C2×C22⋊D61—41no—
204C2×C22⋊D61—42no—
205C22×Dic61—21no—
206C22×Dic61—24no—
207C22×Dic61—41no—
208C22×Dic61—41no—
209C22×Dic61—42no—
210C22×Dic61#4111yescharacteristic
211#11758224—24no—
212#11758224—24no—
213#11758224—24no—
214#11758224—24no—
215#11758224—42no—
216#11758224—42no—
217#11758224—42no—
218#11758224—42no—
219D4×D61—24no—
220D4×D61—24no—
221D4×D61—24no—
222D4×D61—24no—
223D4×D61—42no—
224D4×D61—42no—
225D4×D61—42no—
226D4×D61—42no—
227C2×D244—21no—
228C2×D244—21no—
229C2×D244—21no—
230C2×D244—21no—
231C2×D244—21no—
232C2×D244C22×C412yes—
233C2×C4×D61—22no—
234C2×C4×D61C22×C412yes—
235C2×C4×D61C2×D411yescharacteristic
236C2×C4×D61C2×D411yescharacteristic
237C2×C4×D61C2×D412yes—
238C2×C4×D61C2×D411yescharacteristic
239C2×C4×D61C2×D411yescharacteristic
240C2×C4×D61C2×D412yes—
241C2×C4×D61#4112yes—
242C2×Dic122—21no—
243C2×Dic122—21no—
244C2×Dic122—21no—
245C2×Dic122—21no—
246C2×Dic122—21no—
247C2×Dic122C22×C412yes—
248D8×C61—24no—
249D8×C61—24no—
250M16×C61—21no—
251M16×C61—21no—
252M16×C61—21no—
253M16×C61—21no—
254M16×C61—21no—
255M16×C61C2×D412yes—
256C2×C8×C61—21no—
257C2×C8×C61—21no—
258C2×C8×C61—21no—
259C2×C8×C61C22×C412yes—
260C2×C8×C61C2×D411yescharacteristic
261C2×C8×C61C2×D411yescharacteristic
262C2×C8×C61C2×D412yes—
263C4⋊C4×C61C2×D412yes—
264C22⋊C4×C61—21no—
265C42×C61—21no—
266C22⋊Dic61—21no—
267#11758200—24no—
268#11758200—24no—
269#11758199—24no—
270#11758199—24no—
271#11758198—22no—
272C4⋊Dic61C2×D412yes—
273#11758196—22no—
274C4×Dic61—21no—
275C4×Dic61—22no—
276#11758194—21no—
277#11758194—21no—
278#11758194—21no—
279#11758194—21no—
280#11758194—21no—
281#11758194C2×D412yes—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418C22×C412yes—
286C2×#92418C2×D411yescharacteristic
287C2×#92418C2×D411yescharacteristic
288C2×#92418C2×D412yes—
289#11758190—24no—
290#11758190—24no—
291#11758189—24no—
292#11758189—42no—
293#11758189—42no—
294#11758189C22⋊C414yes—
295#11758189C22⋊C414yes—
296#11758189C22⋊C414yes—
297#11758189C22⋊C414yes—
298C8×D61—24no—
299C8×D61—42no—
300C8×D61—42no—
301C23×C61—22no—
302C23×C61—22no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—41no—
307C23×C61—82no—
308C23×C61—82no—
309C23×C61C2×#4111yescharacteristic
310C22×D61—22no—
311C22×D61—42no—
312C22×D61—41no—
313C22×D61—41no—
314C22×D61—44no—
315C22×D61—44no—
316C22×D61—84no—
317C22×D61—84no—
318C22×D61—88no—
319C22×D61—88no—
320C22×D61—82no—
321C22×D61C4×D412yes—
322C22×D61#12111yescharacteristic
323C22×D61#12111yescharacteristic
324C22×D61#12412yes—
325D4×C61—22no—
326D4×C61—22no—
327D4×C61—22no—
328D4×C61—22no—
329D4×C61—41no—
330D4×C61—41no—
331D4×C61—41no—
332D4×C61—41no—
333C2×C4×C61—22no—
334C2×C4×C61C23×C411yescharacteristic
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C2×#4111yescharacteristic
340C22⋊D61—44no—
341C22⋊D61—44no—
342C22⋊D61—44no—
343C22⋊D61—44no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—44no—
349C2×Dic61—44no—
350C2×Dic61C4×D412yes—
351C2×Dic61#12111yescharacteristic
352C2×Dic61#12111yescharacteristic
353C2×Dic61#12412yes—
354D244—22no—
355D244—22no—
356D244—41no—
357D244—41no—
358C4×D61—82no—
359C4×D61C2×C22⋊C412yes—
360C4×D61C2×C22⋊C412yes—
361C4×D61C4×D412yes—
362C4×D61C4×D412yes—
363C4×D61#12112yes—
364C4×D61#12112yes—
365C4×D61#12712yes—
366C4×D61#12712yes—
367Dic122—22no—
368Dic122—22no—
369Dic122—41no—
370Dic122—41no—
371C8×C61—22no—
372C8×C61—41no—
373C8×C61—41no—
374C8×C61C2×C22⋊C412yes—
375C8×C61C2×C22⋊C412yes—
376#92418—22no—
377#92418—41no—
378#92418—41no—
379#92418C2×C22⋊C412yes—
380#92418C2×C22⋊C412yes—
381#21249—611nomaximal, Sylow
382C22×C61—22no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—82no—
386C22×C61—82no—
387C22×C61—82no—
388C22×C61—82no—
389C22×C61—82no—
390C22×C61—82no—
391C22×C61C2×C4×D411yescharacteristic
392C22×C61C2×#12111yescharacteristic
393C22×C61C2×#12411yescharacteristic
394C2×D61—22no—
395C2×D61—22no—
396C2×D61—42no—
397C2×D61—42no—
398C2×D61—42no—
399C2×D61—88no—
400C2×D61—88no—
401C2×D61—82no—
402C2×D61—82no—
403C2×D61—82no—
404C2×D61#39012yes—
405C2×D61#39012yes—
406C4×C61—42no—
407C4×C61C22×C22⋊C411yescharacteristic
408C4×C61C2×C4×D411yescharacteristic
409C4×C61C2×#12111yescharacteristic
410C4×C61C2×#12711yescharacteristic
411Dic61—42no—
412Dic61—42no—
413Dic61#39012yes—
414Dic61#39012yes—
415C22×AGL(1,ℤ/8)—611no—
416C2×#430—611no—
417#2896—611no—
418C2×#418—611no—
419C2×#413—611no—
420C22×#100—611no—
421#2873—611no—
422#1978—611no—
423#1978—611no—
424#1978—611no—
425#1978D6111yescharacteristic, complemented
426#1977—611no—
427#1977—611no—
428#1977—611no—
429#1977—611no—
430C2×C61—21no—
431C2×C61—21no—
432C2×C61—82no—
433C2×C61—82no—
434C2×C61C2×#39011yescharacteristic
435C2×C61#306812yes—
436D61—22no—
437D61—22no—
438D61—82no—
439C22×#41—611no—
440C23×D4—611no—
441C2×AGL(1,ℤ/8)—618no—
442C2×AGL(1,ℤ/8)—1221no—
443C2×AGL(1,ℤ/8)—1221no—
444C2×AGL(1,ℤ/8)—1221no—
445C2×AGL(1,ℤ/8)—1221no—
446C2×AGL(1,ℤ/8)—1224no—
447C22×SD16—611no—
448C22×SD16—611no—
449C22×D8—611no—
450C22×D8C2×D6111yescharacteristic
451C22×M16—611no—
452C22×M16—611no—
453C22×M16—611no—
454C22×M16—611no—
455C2×#117—611no—
456#430—1224no—
457C2×#108—611no—
458C2×#108—611no—
459C2×#108—611no—
460C2×#108C2×D6111yescharacteristic, complemented
461#419—611no—
462#419—611no—
463#418—611no—
464#418—611no—
465#418—611no—
466#418—611no—
467#418—1222no—
468#418C2×D6111yescharacteristic
469#418C2×D6111yescharacteristic, complemented
470#417—1222no—
471#416—1222no—
472C2×#102—1222no—
473#413—1224no—
474C2×#101—611no—
475C2×#101—611no—
476C2×#100—611no—
477C2×#100—611no—
478C2×#100—611no—
479C2×#100—611no—
480C2×#100—1224no—
481C2×#100C2×D6111yescharacteristic
482C2×#100C2×D6111yescharacteristic, complemented
483#405—611no—
484#405—611no—
485#405—611no—
486#405—1221no—
487#405—1221no—
488#405C2×D6111yescharacteristic, complemented
489C4×M16—1221no—
490C4×M16—1221no—
491C61#2124911yescharacteristic, complemented, Sylow
492C25—1221no—
493C2×#41—614no—
494C2×#41—1222no—
495C2×#41—1221no—
496C2×#41—1221no—
497C2×#41—1222no—
498C2×#41—1222no—
499C2×#41—1221no—
500C2×#41—1221no—
501C22×Q8—611no—
502C22×D4—614no—
503C22×D4—611no—
504C22×D4—1221no—
505C22×D4—1221no—
506C22×D4—1222no—
507C22×D4—1222no—
508C22×D4—1221no—
509C22×D4—1221no—
510C22×D4—1222no—
511C22×D4—1221no—
512C22×D4—1221no—
513C22×D4C22×D6111yescharacteristic
514C22×D4C22×D6111yescharacteristic
515C23×C4—611no—
516C23×C4—1221no—
517AGL(1,ℤ/8)—1228no—
518AGL(1,ℤ/8)—1228no—
519AGL(1,ℤ/8)—1228no—
520AGL(1,ℤ/8)—1228no—
521C2×SD16—614no—
522C2×SD16—614no—
523C2×SD16—1221no—
524C2×SD16—1221no—
525C2×SD16—1222no—
526C2×SD16—1221no—
527C2×SD16—1221no—
528C2×SD16—1222no—
529C2×D8—21no—
530C2×D8—21no—
531C2×D8—22no—
532C2×D8—614no—
533C2×D8—1221no—
534C2×D8—1221no—
535C2×D8—1222no—
536C2×D8C4×D6114yescomplemented
537C2×M16—614no—
538C2×M16—611no—
539C2×M16—611no—
540C2×M16—611no—
541C2×M16—611no—
542C2×M16—614no—
543C2×M16—611no—
544C2×M16—614no—
545C2×M16—611no—
546C2×M16—611no—
547C2×M16—1221no—
548C2×M16—1221no—
549C2×M16—1221no—
550C2×M16—1222no—
551C2×M16—1222no—
552C2×M16—1222no—
553C2×M16—1222no—
554C2×M16—1222no—
555C2×M16C22×D6111yescharacteristic
556C2×M16C22×D6111yescharacteristic
557C2×M16C22×D6111yescharacteristic
558C22×C8—611no—
559C22×C8—1221no—
560C22×C8—1221no—
561C22×C8—1221no—
562C22×C8C22×D6111yescharacteristic
563#117—611no—
564#117—612no—
565#117—1221no—
566#117—1221no—
567#117C22×D6111yescharacteristic
568C2×C4⋊C4—612no—
569C2×C22⋊C4—1221no—
570C2×C42—1221no—
571#108—22no—
572#108—1222no—
573#108—1222no—
574#108—1222no—
575#103—1222no—
576#103—1222no—
577#102—22no—
578#102—22no—
579#102—1222no—
580#102—1222no—
581#102—1222no—
582#102—1222no—
583#101—1222no—
584#101—1222no—
585#100—22no—
586#100—22no—
587#100—1222no—
588#100—1222no—
589#100—1222no—
590#100—1222no—
591#97—21no—
592#97—1221no—
593#97—1221no—
594#97—1221no—
595C4×C8—21no—
596C4×C8—1221no—
597C4×C8—1221no—
598C4×C8—1221no—
599C24—21no—
600C24—21no—
601C24—611no—
602C24—1224no—
603C24—1221no—
604C24—4884no—
605C24—2441no—
606C24—2441no—
607C24—2442no—
608#41—1224no—
609#41—1224no—
610#41—1224no—
611#41—1224no—
612#41—2442no—
613#41—2442no—
614#41—2442no—
615#41—2442no—
616C2×Q8—612no—
617C2×Q8—1221no—
618C2×Q8—1221no—
619C2×Q8—1221no—
620C2×Q8—1221no—
621C2×Q8—1221no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—612no—
633C2×D4—1224no—
634C2×D4—1224no—
635C2×D4—1224no—
636C2×D4—1224no—
637C2×D4—1224no—
638C2×D4—1224no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4—1221no—
644C2×D4—2442no—
645C2×D4—2442no—
646C2×D4—2442no—
647C2×D4—2442no—
648C2×D4—2441no—
649C2×D4—2441no—
650C2×D4—2442no—
651C2×D4—2441no—
652C2×D4—2441no—
653C2×D4—2442no—
654C2×D4C2×C4×D6112yes—
655C2×D4C2×C4×D6112yes—
656C22×C4—611no—
657C22×C4—612no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—612no—
663C22×C4—612no—
664C22×C4—612no—
665C22×C4—1222no—
666C22×C4—1224no—
667C22×C4—1221no—
668C22×C4—2441no—
669C22×C4—2441no—
670C22×C4—2442no—
671C22×C4C23×D6111yescharacteristic
672SD16—1224no—
673SD16—1224no—
674SD16—1224no—
675SD16—1224no—
676D8—24no—
677D8—24no—
678D8—1224no—
679D8—1224no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—614no—
686M16—614no—
687M16—614no—
688M16—614no—
689M16—612no—
690M16—1224no—
691M16—1221no—
692M16—1221no—
693M16—1221no—
694M16—1221no—
695M16—1221no—
696M16—2442no—
697M16—2442no—
698M16D4×D6112yes—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—612no—
703C2×C8—611no—
704C2×C8—611no—
705C2×C8—612no—
706C2×C8—1224no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—2442no—
711C2×C8—2442no—
712C2×C8C2×C4×D6112yes—
713C2×C8D4×D6111yescharacteristic
714C2×C8D4×D6111yescharacteristic
715C2×C8D4×D6112yes—
716C4⋊C4—612no—
717C4⋊C4—1222no—
718C4⋊C4D4×D6112yes—
719C22⋊C4—21no—
720C22⋊C4—1222no—
721C22⋊C4—1221no—
722C42—21no—
723C42—1222no—
724C42—1221no—
725C23—22no—
726C23—22no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—82no—
732C23—82no—
733C23—611no—
734C23—611no—
735C23—612no—
736C23—612no—
737C23—1222no—
738C23—4882no—
739C23—4884no—
740C23—4884no—
741C23—4888no—
742C23—4888no—
743C23—2442no—
744C23—2444no—
745C23—2444no—
746C23—2441no—
747C23—2441no—
748C23#41×D6111yescharacteristic
749Q8—1222no—
750Q8—1222no—
751Q8—2441no—
752Q8—2441no—
753D4—22no—
754D4—22no—
755D4—22no—
756D4—22no—
757D4—41no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—1222no—
762D4—1222no—
763D4—2444no—
764D4—2444no—
765D4—2444no—
766D4—2444no—
767D4—2441no—
768D4—2441no—
769C2×C4—22no—
770C2×C4—612no—
771C2×C4—611no—
772C2×C4—611no—
773C2×C4—612no—
774C2×C4—612no—
775C2×C4—612no—
776C2×C4—612no—
777C2×C4—612no—
778C2×C4—612no—
779C2×C4—612no—
780C2×C4—612no—
781C2×C4—612no—
782C2×C4—1222no—
783C2×C4—1222no—
784C2×C4—4882no—
785C2×C4—2444no—
786C2×C4—2444no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4C22×C4×D6111yescharacteristic
790C2×C4C2×D4×D6111yescharacteristic
791C2×C4C2×D4×D6111yescharacteristic
792C2×C4C2×D4×D6111yescharacteristic
793C2×C4C2×D4×D6111yescharacteristic
794C2×C4#41×D6111yescharacteristic
795C8—22no—
796C8—41no—
797C8—41no—
798C8—612no—
799C8—612no—
800C8—1222no—
801C8—2441no—
802C8—2441no—
803C8C22⋊C4×D6112yes—
804C8C22⋊C4×D6112yes—
805C22—22no—
806C22—42no—
807C22—42no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—82no—
814C22—612no—
815C22—612no—
816C22—1222no—
817C22—1222no—
818C22—4882no—
819C22—4882no—
820C22—4888no—
821C22—4888no—
822C22—4882no—
823C22—2442no—
824C22—2442no—
825C22—2442no—
826C22C4×D4×D6111yescharacteristic
827C22#121×D6111yescharacteristic
828C22#124×D6111yescharacteristic
829C4—42no—
830C4—612no—
831C4—612no—
832C4—2442no—
833C4—2442no—
834C4C2×C22⋊C4×D6111yescharacteristic
835C4C4×D4×D6111yescharacteristic
836C4#121×D6111yescharacteristic
837C4#127×D6111yescharacteristic
838C2—21no—
839C2—21no—
840C2—82no—
841C2—82no—
842C2—1222no—
843C2—1222no—
844C2—4882no—
845C2#390×D6111yescharacteristic
846C2#2145554512yes—
subgroupG/H
centerC22#121×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1978C2
socleC22×C61C2×#121
prime radicalC22×#14519801C2
cosocleC22×C4×C61C24
hypercenter#1978D61
hypocenterC61#21249
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1978

Complements

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

NH ≅ G/Ntype
2. C2×#16839809C2semidirect
3. #21454333C2semidirect
4. #418×D61C2semidirect
5. C2×#16839743C2semidirect
6. C2×#100×D61C2semidirect
7. #21454235C2semidirect
8. #21446730C2semidirect
9. #21446728C2semidirect
10. #21446726C2semidirect
11. #21446725C2semidirect
12. #21446722C2semidirect
13. #21446720C2semidirect
14. #21446719C2semidirect
15. C61×#1978C2semidirect
23. C2×#14519801C4semidirect
33. C2×#14519713C22semidirect
34. C2×#14519712C22semidirect
35. C2×#14519712C22semidirect
36. #16839772C22semidirect
37. #16839770C22semidirect
40. #16839767C22semidirect
47. C2×#14519695C22semidirect
48. C2×#14519695C22semidirect
50. C2×#14519694C22semidirect
54. #16839720C22semidirect
56. #16839718C22semidirect
57. #16839717C22semidirect
62. C2×#108×C61C22semidirect
64. C61×#418C22semidirect
66. C2×#100×C61C22semidirect
67. C61×#405C22semidirect
98. C2×#11758190C2×C4semidirect
102. C2×#11758200C2×C4semidirect
106. C2×#11758199C2×C4semidirect
162. C2×D8×C61C2×C4semidirect
425. #1978D61semidirect
460. C2×#108C2×D61semidirect
469. #418C2×D61semidirect
482. C2×#100C2×D61semidirect
488. #405C2×D61semidirect
491. C61#21249semidirect
536. C2×D8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145198012
C2×#168398092
#214543332
#418×D612
C2×#168397432
C2×#100×D612
#214542352
#214467302
#214467282
#214467262
#214467252
#214467222
#214467202
#214467192
C61×#19782
#2124961