Finite Group Databasebeta

← #29684015

Subgroups — #29684015

Order 15616.

1458 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519798C211yesmaximal, characteristic
2C2×#108×D61C211yesmaximal, characteristic, complemented
3#21454337C211yesmaximal, characteristic, complemented
4#21454333C211yesmaximal, characteristic, complemented
5C2×#16839745C211yesmaximal, characteristic, complemented
6C2×#16839743C211yesmaximal, characteristic, complemented
7#405×D61C211yesmaximal, characteristic, complemented
8#21446733C211yesmaximal, characteristic, complemented
9#21446731C211yesmaximal, characteristic, complemented
10#21446728C211yesmaximal, characteristic, complemented
11#21446726C211yesmaximal, characteristic, complemented
12#21446724C211yesmaximal, characteristic, complemented
13#21446722C211yesmaximal, characteristic, complemented
14#21446720C211yesmaximal, characteristic, complemented
15C61×#1977C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×#11758224C2211yescharacteristic
18C2×#14519798—21no—
19C2×#14519798—21no—
20C2×#14519798—21no—
21C2×#14519798—21no—
22C2×#14519798—24no—
23C2×#14519798C418yescomplemented
24C22×#11758202C2211yescharacteristic
25C22×#11758190C2211yescharacteristic
26C22×#11758199C2211yescharacteristic
27C2×M16×D61C2211yescharacteristic
28C2×M16×D61C2211yescharacteristic
29C2×M16×D61C2211yescharacteristic
30C22×C8×D61C2211yescharacteristic
31#117×D61C2211yescharacteristic
32C2×#14519713C2211yescharacteristic
33C2×#14519712C2211yescharacteristic
34C2×#14519712C2211yescharacteristic
35#108×D61—24no—
36#16839772C2211yescharacteristic
37#16839771C2211yescharacteristic
38#16839770C2211yescharacteristic
39#16839768C2211yescharacteristic
40#16839767C2211yescharacteristic
41#16839766C2211yescharacteristic
42#16839762—22no—
43#16839760—22no—
44#16839757—22no—
45#16839755—22no—
46#16839745—24no—
47#16839743—24no—
48C2×#14519696C2211yescharacteristic
49C2×#14519695C2211yescharacteristic
50C2×#14519695C2211yescharacteristic
51C2×#14519694C2211yescharacteristic
52C2×#14519693C2211yescharacteristic
53C2×#14519693C2211yescharacteristic
54#16839720C2211yescharacteristic
55#16839719—21no—
56#16839718C2211yescharacteristic
57#16839717C2211yescharacteristic
58#16839716—21no—
59#97×D61—21no—
60C4×C8×D61—21no—
61C22×SD16×C61C2211yescharacteristic
62C2×#108×C61C2211yescharacteristic
63C61×#419C2211yescharacteristic
64C61×#418C2211yescharacteristic
65C2×#101×C61C2211yescharacteristic
66C2×#100×C61C2211yescharacteristic
67C61×#405C2211yescharacteristic
68C2×#11758226—22no—
69C2×#11758226—21no—
70C2×#11758226—21no—
71C2×#11758226—21no—
72C2×#11758226—21no—
73C2×#11758226—22no—
74C2×#11758226—22no—
75C2×#11758226C2×C414yes—
76C2×#11758224—21no—
77C2×#11758224—21no—
78C2×#11758224—21no—
79C2×#11758224—21no—
80C2×#11758224—22no—
81C2×#11758224—22no—
82C2×#11758224—22no—
83C2×#11758224C2×C414yes—
84C22×Dic122C2311yescharacteristic
85C22×D244—21no—
86C22×D244C2311yescharacteristic
87C22×C22⋊D61—21no—
88C23×Dic61—21no—
89C22×C4×D61—21no—
90C22×C4×D61C2311yescharacteristic
91#14519798—28no—
92#14519798—28no—
93#14519798—28no—
94#14519798—28no—
95C2×#11758202—21no—
96C2×#11758202—21no—
97C2×#11758202—22no—
98C2×#11758202C2×C414yescomplemented
99C2×#11758190—21no—
100C2×#11758190—21no—
101C2×#11758190—22no—
102C2×#11758190C2×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—
113M16×D61—22no—
114M16×D61—22no—
115M16×D61—22no—
116M16×D61—22no—
117M16×D61—22no—
118M16×D61D414yes—
119C22×#92418C2311yescharacteristic
120C2×C8×D61—21no—
121C2×C8×D61—21no—
122C2×C8×D61—21no—
123C2×C8×D61C2×C414yes—
124C2×C8×D61D411yescharacteristic
125C2×C8×D61D411yescharacteristic
126C2×C8×D61D411yescharacteristic
127C2×C8×D61D411yescharacteristic
128C2×C8×D61D414yes—
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#14519701—22no—
141#14519700—22no—
142#14519699—22no—
143#14519698—22no—
144#14519697—22no—
145#14519696—22no—
146#14519695—22no—
147#14519695—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×Q8×C61C2311yescharacteristic
158C22×D4×C61C2311yescharacteristic
159C2×SD16×C61—21no—
160C2×SD16×C61—21no—
161C2×SD16×C61—22no—
162C2×SD16×C61C2×C414yescomplemented
163C2×M16×C61C2311yescharacteristic
164C2×M16×C61C2311yescharacteristic
165C2×M16×C61C2311yescharacteristic
166C22×C8×C61C2311yescharacteristic
167#117×C61C2311yescharacteristic
168#108×C61—22no—
169#103×C61—22no—
170#102×C61—22no—
171#101×C61—22no—
172#100×C61—22no—
173#97×C61—21no—
174C4×C8×C61—21no—
175C24×C61—21no—
176C23×D61—21no—
177C23×D61#4111yescharacteristic
178C2×Q8×C61—21no—
179C2×Q8×C61—21no—
180C2×Q8×C61—21no—
181C2×Q8×C61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61C22×C412yes—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61C22×C412yes—
190C22×C4×C61—21no—
191C22×C4×C61C2411yescharacteristic
192C2×C22⋊D61—24no—
193C2×C22⋊D61—41no—
194C2×C22⋊D61—41no—
195C2×C22⋊D61—42no—
196C22×Dic61—21no—
197C22×Dic61—24no—
198C22×Dic61—41no—
199C22×Dic61—41no—
200C22×Dic61—42no—
201C22×Dic61#4111yescharacteristic
202#11758226—24no—
203#11758226—24no—
204#11758226—24no—
205#11758226—24no—
206#11758226—42no—
207#11758226—42no—
208#11758226—42no—
209#11758226—42no—
210#11758224—24no—
211#11758224—24no—
212#11758224—24no—
213#11758224—24no—
214#11758224—42no—
215#11758224—42no—
216#11758224—42no—
217#11758224—42no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244—21no—
221C2×D244—21no—
222C2×D244—24no—
223C2×D244—21no—
224C2×D244—41no—
225C2×D244—41no—
226C2×D244—42no—
227C2×D244C22×C412yes—
228C2×C4×D61—22no—
229C2×C4×D61—24no—
230C2×C4×D61—41no—
231C2×C4×D61—41no—
232C2×C4×D61—42no—
233C2×C4×D61C22×C412yes—
234C2×C4×D61C2×D411yescharacteristic
235C2×C4×D61C2×D411yescharacteristic
236C2×C4×D61C2×D412yes—
237C2×C4×D61C2×D411yescharacteristic
238C2×C4×D61C2×D411yescharacteristic
239C2×C4×D61C2×D412yes—
240C2×C4×D61#4112yes—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122—21no—
244C2×Dic122—21no—
245C2×Dic122—21no—
246C2×Dic122C22×C412yes—
247SD16×C61—24no—
248SD16×C61—24no—
249M16×C61—21no—
250M16×C61—21no—
251M16×C61—21no—
252M16×C61—21no—
253M16×C61—21no—
254M16×C61C2×D412yes—
255C2×C8×C61—21no—
256C2×C8×C61—21no—
257C2×C8×C61—21no—
258C2×C8×C61C22×C412yes—
259C2×C8×C61C2×D411yescharacteristic
260C2×C8×C61C2×D411yescharacteristic
261C2×C8×C61C2×D412yes—
262C4⋊C4×C61C2×D412yes—
263C22⋊C4×C61—21no—
264C42×C61—21no—
265C22⋊Dic61—21no—
266#11758202—24no—
267#11758202—24no—
268#11758199—24no—
269#11758199—24no—
270#11758198—22no—
271C4⋊Dic61C2×D412yes—
272#11758196—22no—
273C4×Dic61—21no—
274C4×Dic61—22no—
275#11758194—21no—
276#11758194—21no—
277#11758194—21no—
278#11758194—21no—
279#11758194—21no—
280#11758194C2×D412yes—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418C22×C412yes—
285C2×#92418C2×D411yescharacteristic
286C2×#92418C2×D411yescharacteristic
287C2×#92418C2×D412yes—
288#11758190—24no—
289#11758190—24no—
290#11758189—24no—
291#11758189—42no—
292#11758189—42no—
293C8×D61—24no—
294C8×D61—42no—
295C8×D61—42no—
296C8×D61C22⋊C414yes—
297C8×D61C22⋊C414yes—
298C8×D61C22⋊C414yes—
299C8×D61C22⋊C414yes—
300C23×C61—22no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—82no—
304C23×C61C2×#4111yescharacteristic
305C22×D61—22no—
306C22×D61—42no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—82no—
310C22×D61C4×D412yes—
311C22×D61#12111yescharacteristic
312C22×D61#12111yescharacteristic
313C22×D61#12412yes—
314Q8×C61—22no—
315Q8×C61—22no—
316Q8×C61—41no—
317Q8×C61—41no—
318D4×C61—22no—
319D4×C61—22no—
320D4×C61—41no—
321D4×C61—41no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61C23×C411yescharacteristic
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C61C22×D411yescharacteristic
330C2×C4×C61C22×D411yescharacteristic
331C2×C4×C61C2×#4111yescharacteristic
332C22⋊D61—44no—
333C22⋊D61—44no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—44no—
339C2×Dic61—44no—
340C2×Dic61C4×D412yes—
341C2×Dic61#12111yescharacteristic
342C2×Dic61#12111yescharacteristic
343C2×Dic61#12412yes—
344D244—22no—
345D244—22no—
346D244—44no—
347D244—44no—
348D244—41no—
349D244—41no—
350C4×D61—44no—
351C4×D61—44no—
352C4×D61—44no—
353C4×D61C2×C22⋊C412yes—
354C4×D61C2×C22⋊C412yes—
355C4×D61C4×D412yes—
356C4×D61C4×D412yes—
357C4×D61#12112yes—
358C4×D61#12112yes—
359C4×D61#12712yes—
360C4×D61#12712yes—
361Dic122—22no—
362Dic122—22no—
363Dic122—41no—
364Dic122—41no—
365C8×C61—22no—
366C8×C61—41no—
367C8×C61—41no—
368C8×C61C2×C22⋊C412yes—
369C8×C61C2×C22⋊C412yes—
370#92418—22no—
371#92418—41no—
372#92418—41no—
373#92418C2×C22⋊C412yes—
374#92418C2×C22⋊C412yes—
375#21248—611nomaximal, Sylow
376C22×C61—22no—
377C22×C61—42no—
378C22×C61—82no—
379C22×C61—82no—
380C22×C61—82no—
381C22×C61C2×C4×D411yescharacteristic
382C22×C61C2×#12111yescharacteristic
383C22×C61C2×#12411yescharacteristic
384C2×D61—22no—
385C2×D61—22no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—82no—
390C2×D61—82no—
391C2×D61—82no—
392C2×D61#39012yes—
393C2×D61#39012yes—
394C4×C61—42no—
395C4×C61—42no—
396C4×C61C22×C22⋊C411yescharacteristic
397C4×C61C2×C4×D411yescharacteristic
398C4×C61C2×#12111yescharacteristic
399C4×C61C2×#12711yescharacteristic
400Dic61—42no—
401Dic61—42no—
402Dic61#39012yes—
403Dic61#39012yes—
404C22×#135—611no—
405C22×#108—611no—
406#2896—611no—
407#2896—611no—
408C2×#413—611no—
409C2×#413—611no—
410C2×#405—611no—
411#1979—611no—
412#1979—611no—
413#1978—611no—
414#1978—611no—
415#1977—611no—
416#1977—611no—
417#1977—611no—
418#1977D6111yescharacteristic, complemented
419C2×C61—21no—
420C2×C61—21no—
421C2×C61—82no—
422C2×C61C2×#39011yescharacteristic
423C2×C61#306712yes—
424D61—22no—
425D61—22no—
426D61—82no—
427C22×#41—611no—
428C22×#41—611no—
429C2×#135—618no—
430C2×#135—1221no—
431C2×#135—1221no—
432C2×#135—1221no—
433C2×#135—1221no—
434C2×#135—1224no—
435C22×Q16—611no—
436C22×SD16—611no—
437C22×SD16C2×D6111yescharacteristic
438C22×D8—611no—
439C22×M16—611no—
440C22×M16—611no—
441C22×M16—611no—
442C23×C8—611no—
443C2×#117—611no—
444C2×#108—611no—
445C2×#108—611no—
446C2×#108—611no—
447C2×#108—1224no—
448C2×#108C2×D6111yescharacteristic
449#419—611no—
450#419—611no—
451#419—611no—
452#419C2×D6111yescharacteristic
453#418—611no—
454#418—611no—
455#418—611no—
456#418C2×D6111yescharacteristic
457#417—1222no—
458#417—1222no—
459#416—1222no—
460#416—1222no—
461#413—1224no—
462#413—1224no—
463C2×#101—611no—
464C2×#101—611no—
465C2×#101—611no—
466C2×#101C2×D6111yescharacteristic
467C2×#100—611no—
468C2×#100—611no—
469C2×#100—611no—
470C2×#100C2×D6111yescharacteristic
471#405—611no—
472#405—611no—
473#405—611no—
474#405—1221no—
475#405—1221no—
476#405C2×D6111yescharacteristic
477C2×#97—1221no—
478C2×C4×C8—1221no—
479C61#2124811yescharacteristic, complemented, Sylow
480C2×#41—614no—
481C2×#41—614no—
482C2×#41—1222no—
483C2×#41—1222no—
484C2×#41—1221no—
485C2×#41—1221no—
486C2×#41—1222no—
487C2×#41—1222no—
488C2×#41—1221no—
489C2×#41—1221no—
490C2×#41—1221no—
491C2×#41—1221no—
492C2×#41—1222no—
493C2×#41—1222no—
494C2×#41—1221no—
495C2×#41—1221no—
496C22×Q8—611no—
497C22×Q8C22×D6111yescharacteristic
498C22×D4—611no—
499C22×D4—1221no—
500C22×D4—1221no—
501C22×D4C22×D6111yescharacteristic
502C23×C4—611no—
503C23×C4—1221no—
504C23×C4—1221no—
505#135—1228no—
506#135—1228no—
507#135—1228no—
508#135—1228no—
509C2×Q16—614no—
510C2×Q16—1221no—
511C2×Q16—1221no—
512C2×Q16—1222no—
513C2×SD16—21no—
514C2×SD16—21no—
515C2×SD16—22no—
516C2×SD16—614no—
517C2×SD16—1221no—
518C2×SD16—1221no—
519C2×SD16—1222no—
520C2×SD16C4×D6114yescomplemented
521C2×D8—614no—
522C2×D8—1221no—
523C2×D8—1221no—
524C2×D8—1222no—
525C2×M16—611no—
526C2×M16—614no—
527C2×M16—611no—
528C2×M16—611no—
529C2×M16—1221no—
530C2×M16—1221no—
531C2×M16—1221no—
532C2×M16—1222no—
533C2×M16—1222no—
534C2×M16—1222no—
535C2×M16—1222no—
536C2×M16—1222no—
537C2×M16C22×D6111yescharacteristic
538C2×M16C22×D6111yescharacteristic
539C2×M16C22×D6111yescharacteristic
540C22×C8—611no—
541C22×C8—614no—
542C22×C8—611no—
543C22×C8—611no—
544C22×C8—611no—
545C22×C8—611no—
546C22×C8—614no—
547C22×C8—1221no—
548C22×C8—1221no—
549C22×C8—1221no—
550C22×C8C22×D6111yescharacteristic
551#117—611no—
552#117—612no—
553#117—1221no—
554#117—1221no—
555#117C22×D6111yescharacteristic
556C2×C4⋊C4—612no—
557C2×C22⋊C4—1221no—
558C2×C42—1221no—
559#108—22no—
560#108—1222no—
561#108—1222no—
562#108—1222no—
563#103—22no—
564#103—1222no—
565#103—1222no—
566#103—1222no—
567#102—22no—
568#102—1222no—
569#102—1222no—
570#102—1222no—
571#101—22no—
572#101—1222no—
573#101—1222no—
574#101—1222no—
575#100—22no—
576#100—1222no—
577#100—1222no—
578#100—1222no—
579#97—21no—
580#97—1221no—
581#97—1221no—
582#97—1221no—
583C4×C8—21no—
584C4×C8—1221no—
585C4×C8—1221no—
586C4×C8—1221no—
587C24—21no—
588C24—611no—
589C24—1221no—
590#41—1224no—
591#41—1224no—
592#41—1224no—
593#41—1224no—
594#41—1224no—
595#41—1224no—
596#41—1224no—
597#41—1224no—
598#41—2442no—
599#41—2442no—
600#41—2442no—
601#41—2442no—
602#41—2442no—
603#41—2442no—
604#41—2442no—
605#41—2442no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—612no—
612C2×Q8—1221no—
613C2×Q8—1221no—
614C2×Q8—1221no—
615C2×Q8—1221no—
616C2×Q8—1221no—
617C2×Q8C2×C4×D6112yes—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—612no—
624C2×D4—1224no—
625C2×D4—1224no—
626C2×D4—1221no—
627C2×D4—1221no—
628C2×D4—1221no—
629C2×D4—1221no—
630C2×D4—1221no—
631C2×D4—2441no—
632C2×D4—2441no—
633C2×D4—2442no—
634C2×D4—2441no—
635C2×D4—2441no—
636C2×D4—2442no—
637C2×D4C2×C4×D6112yes—
638C22×C4—21no—
639C22×C4—611no—
640C22×C4—612no—
641C22×C4—611no—
642C22×C4—611no—
643C22×C4—611no—
644C22×C4—611no—
645C22×C4—612no—
646C22×C4—612no—
647C22×C4—612no—
648C22×C4—1224no—
649C22×C4—1222no—
650C22×C4—1224no—
651C22×C4—1221no—
652C22×C4—2441no—
653C22×C4—2441no—
654C22×C4—2442no—
655C22×C4—2441no—
656C22×C4—2441no—
657C22×C4—2442no—
658C22×C4C23×D6111yescharacteristic
659Q16—1224no—
660Q16—1224no—
661SD16—24no—
662SD16—24no—
663SD16—1224no—
664SD16—1224no—
665D8—1224no—
666D8—1224no—
667M16—21no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16—21no—
672M16—612no—
673M16—1224no—
674M16—1221no—
675M16—1221no—
676M16—1221no—
677M16—1221no—
678M16—1221no—
679M16—2442no—
680M16—2442no—
681M16D4×D6112yes—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—612no—
686C2×C8—611no—
687C2×C8—611no—
688C2×C8—612no—
689C2×C8—614no—
690C2×C8—614no—
691C2×C8—614no—
692C2×C8—614no—
693C2×C8—1224no—
694C2×C8—1221no—
695C2×C8—1221no—
696C2×C8—1221no—
697C2×C8—2442no—
698C2×C8—2442no—
699C2×C8C2×C4×D6112yes—
700C2×C8D4×D6111yescharacteristic
701C2×C8D4×D6111yescharacteristic
702C2×C8D4×D6112yes—
703C4⋊C4—612no—
704C4⋊C4—1222no—
705C4⋊C4D4×D6112yes—
706C22⋊C4—21no—
707C22⋊C4—1222no—
708C22⋊C4—1221no—
709C42—21no—
710C42—1222no—
711C42—1221no—
712C23—22no—
713C23—41no—
714C23—41no—
715C23—82no—
716C23—611no—
717C23—611no—
718C23—612no—
719C23—612no—
720C23—1222no—
721C23—4882no—
722C23—2442no—
723C23—2441no—
724C23—2441no—
725C23#41×D6111yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—41no—
729Q8—41no—
730Q8—1222no—
731Q8—1222no—
732Q8—2441no—
733Q8—2441no—
734D4—22no—
735D4—22no—
736D4—41no—
737D4—41no—
738D4—1222no—
739D4—1222no—
740D4—2444no—
741D4—2444no—
742D4—2444no—
743D4—2444no—
744D4—2441no—
745D4—2441no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—612no—
751C2×C4—611no—
752C2×C4—611no—
753C2×C4—612no—
754C2×C4—612no—
755C2×C4—612no—
756C2×C4—612no—
757C2×C4—612no—
758C2×C4—612no—
759C2×C4—612no—
760C2×C4—612no—
761C2×C4—612no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—2444no—
765C2×C4—2444no—
766C2×C4—2444no—
767C2×C4—2444no—
768C2×C4—2444no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4C22×C4×D6111yescharacteristic
772C2×C4C2×D4×D6111yescharacteristic
773C2×C4C2×D4×D6111yescharacteristic
774C2×C4C2×D4×D6111yescharacteristic
775C2×C4C2×D4×D6111yescharacteristic
776C2×C4#41×D6111yescharacteristic
777C8—22no—
778C8—41no—
779C8—41no—
780C8—612no—
781C8—612no—
782C8—1222no—
783C8—2441no—
784C8—2441no—
785C8C22⋊C4×D6112yes—
786C8C22⋊C4×D6112yes—
787C22—22no—
788C22—42no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—612no—
793C22—612no—
794C22—1222no—
795C22—1222no—
796C22—4882no—
797C22—4882no—
798C22—4882no—
799C22—2442no—
800C22—2442no—
801C22—2442no—
802C22C4×D4×D6111yescharacteristic
803C22#121×D6111yescharacteristic
804C22#124×D6111yescharacteristic
805C4—42no—
806C4—42no—
807C4—612no—
808C4—612no—
809C4—2442no—
810C4—2442no—
811C4C2×C22⋊C4×D6111yescharacteristic
812C4C4×D4×D6111yescharacteristic
813C4#121×D6111yescharacteristic
814C4#127×D6111yescharacteristic
815C2—21no—
816C2—21no—
817C2—82no—
818C2—1222no—
819C2—1222no—
820C2—4882no—
821C2#390×D6111yescharacteristic
822C2#2145553412yes—
subgroupG/H
centerC22#121×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1977C2
socleC22×C61C2×#121
prime radicalC22×#14519798C2
cosocleC22×C4×C61C24
hypercenter#1977D61
hypocenterC61#21248
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1977

Complements

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

NH ≅ G/Ntype
2. C2×#108×D61C2semidirect
3. #21454337C2semidirect
4. #21454333C2semidirect
5. C2×#16839745C2semidirect
6. C2×#16839743C2semidirect
7. #405×D61C2semidirect
8. #21446733C2semidirect
9. #21446731C2semidirect
10. #21446728C2semidirect
11. #21446726C2semidirect
12. #21446724C2semidirect
13. #21446722C2semidirect
14. #21446720C2semidirect
15. C61×#1977C2semidirect
23. C2×#14519798C4semidirect
98. C2×#11758202C2×C4semidirect
102. C2×#11758190C2×C4semidirect
106. C2×#11758199C2×C4semidirect
162. C2×SD16×C61C2×C4semidirect
418. #1977D61semidirect
479. C61#21248semidirect
520. C2×SD16C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145197982
C2×#108×D612
#214543372
#214543332
C2×#168397452
C2×#168397432
#405×D612
#214467332
#214467312
#214467282
#214467262
#214467242
#214467222
#214467202
C61×#19772
#2124861