Finite Group Databasebeta

← #29689664

Subgroups — #29689664

Order 15616.

1200 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459112C211yesmaximal, characteristic
2#423×D61C211yesmaximal, characteristic, complemented
3C4×#14519735C211yesmaximal, characteristic, complemented
4#21446794C212yesmaximal, complemented
5#21446645C212yesmaximal, complemented
6#21446120C212yesmaximal, complemented
7#21446118C212yesmaximal, complemented
8#21445840C211yesmaximal, characteristic, complemented
9#21445839C211yesmaximal, characteristic, complemented
10#21445836C211yesmaximal, characteristic, complemented
11C61×#1806C211yesmaximal, characteristic, complemented
12C2×M16×D61C2212yes—
13#16840316C411yescharacteristic, complemented
14#16840316C411yescharacteristic, complemented
15#16840315C2211yescharacteristic
16#16840309C411yescharacteristic, complemented
17#16840309C411yescharacteristic, complemented
18#16840308C2211yescharacteristic
19#16840299C411yescharacteristic, complemented
20#16840299C411yescharacteristic, complemented
21#16840294C411yescharacteristic, complemented
22#16840294C411yescharacteristic, complemented
23#16840292—21no—
24#16840292—21no—
25#16840290—21no—
26#16840290—21no—
27#16840274C2211yescharacteristic
28#16840271—21no—
29#16840271—21no—
30#16840269C2211yescharacteristic
31C4×#11758222—21no—
32C4×#11758222—21no—
33C4×#11758222C2211yescharacteristic
34C2×#14519735—21no—
35C2×C42×D61C2211yescharacteristic
36#16839786C2211yescharacteristic
37#16839785C2212yes—
38#16839784—21no—
39#16839784—21no—
40C4⋊C8×D61—21no—
41C4⋊C8×D61—21no—
42C2×#14519705C2212yes—
43C2×#14519704C2212yes—
44C2×#14519703C2212yes—
45C4⋊C4×Dic61—21no—
46C4×C4⋊Dic61C2211yescharacteristic
47C4×#11758198C2212yes—
48#16839609—21no—
49#16839607—21no—
50C42×Dic61C2212yes—
51#16839523C2212yes—
52#16839522C2212yes—
53#16839521C2212yes—
54C4×#41×C61C2211yescharacteristic
55C61×#423C2211yescharacteristic
56C2×#104×C61C2212yes—
57C4×C4⋊C4×C61C2211yescharacteristic
58C61×#339C2212yes—
59C2×#11758222—21no—
60C2×#11758222—21no—
61C2×#11758222C2311yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61C2311yescharacteristic
65C2×#11758194C2312yes—
66C2×#11758189—22no—
67M16×D61—42no—
68M16×D61—42no—
69C2×C8×D61—22no—
70#14519776C2×C411yescharacteristic
71#14519776C2×C411yescharacteristic
72#14519775C2×C411yescharacteristic
73#14519773C2×C411yescharacteristic
74#14519772—21no—
75#14519772—21no—
76#14519770—21no—
77#14519770—21no—
78#14519768C2×C411yescharacteristic
79#14519768C2×C411yescharacteristic
80#14519767—21no—
81#14519767—21no—
82#14519766C2×C411yescharacteristic
83#14519764C2×C411yescharacteristic
84#14519763—21no—
85#14519763—21no—
86#14519762—21no—
87#14519762—21no—
88#14519761—21no—
89#14519759—21no—
90#14519759—21no—
91#14519758—21no—
92#14519757C2×C411yescharacteristic
93#14519757C2×C411yescharacteristic
94#14519755—21no—
95#14519755—21no—
96#14519754—21no—
97#14519754—21no—
98#14519753C2×C411yescharacteristic
99#14519753C2×C411yescharacteristic
100#14519752C2×C411yescharacteristic
101#14519752C2×C411yescharacteristic
102#14519750—21no—
103#14519750—21no—
104#14519749—21no—
105#14519749—21no—
106#14519748C2×C411yescharacteristic
107#14519748C2×C411yescharacteristic
108#14519747—21no—
109#14519745—21no—
110C4×Dic122—21no—
111C4×Dic122—21no—
112C4×Dic122—21no—
113C4×Dic122—21no—
114C4×Dic122C2×C411yescharacteristic
115C4×Dic122C2×C411yescharacteristic
116C4×D244—21no—
117C4×D244—21no—
118C4×D244—21no—
119C4×D244—21no—
120C4×D244C2×C411yescharacteristic
121C4×D244C2×C411yescharacteristic
122C4×C22⋊D61—21no—
123C4×C22⋊D61—21no—
124C4×C22⋊D61—21no—
125C4×C22⋊D61—21no—
126C4×C22⋊D61—21no—
127C4×C22⋊D61—21no—
128C4×C22⋊D61—21no—
129C4×C22⋊D61—21no—
130C4×C22⋊D61—21no—
131C4×C22⋊D61—21no—
132#14519736—21no—
133#14519736—21no—
134#14519736C2311yescharacteristic
135#14519735—28no—
136#14519734—21no—
137#14519734—21no—
138#14519734—21no—
139#14519734—21no—
140#14519734—21no—
141C2×C4⋊Dic61—21no—
142C2×#11758198—22no—
143C2×C4×Dic61—22no—
144C2×C4×Dic61—22no—
145C2×C4×Dic61D411yescharacteristic
146C2×C4×Dic61D411yescharacteristic
147C2×C4×Dic61C2312yes—
148C2×C4×Dic61C2311yescharacteristic
149C42×D61—21no—
150C42×D61C2×C411yescharacteristic
151C42×D61C2×C411yescharacteristic
152C42×D61C2×C411yescharacteristic
153C42×D61C2×C411yescharacteristic
154C42×D61D411yescharacteristic
155C42×D61D411yescharacteristic
156C42×D61D411yescharacteristic
157C42×D61D411yescharacteristic
158C4⋊#92418—21no—
159C4⋊#92418—21no—
160#14519706—22no—
161#14519706—22no—
162#14519705—42no—
163#14519704—42no—
164#14519703—42no—
165#14519684—21no—
166#14519684—22no—
167C2×#41×C61C2311yescharacteristic
168C2×M16×C61C2312yes—
169C4×Q8×C61C2×C411yescharacteristic
170C4×Q8×C61C2×C411yescharacteristic
171C4×D4×C61—21no—
172C4×D4×C61—21no—
173C4×D4×C61C2×C411yescharacteristic
174C4×D4×C61C2×C411yescharacteristic
175#117×C61—21no—
176#117×C61C2311yescharacteristic
177C2×C4⋊C4×C61—21no—
178C2×C42×C61—21no—
179C2×C42×C61C2312yes—
180C2×C42×C61C2311yescharacteristic
181C4⋊C8×C61—21no—
182C4⋊C8×C61—21no—
183#104×C61—42no—
184#95×C61—21no—
185C23×D61C2×D411yescharacteristic
186#41×C61—21no—
187#41×C61—21no—
188#41×C61—21no—
189#41×C61—21no—
190C2×Q8×C61C22×C411yescharacteristic
191C2×D4×C61—21no—
192C2×D4×C61C22×C411yescharacteristic
193C22×C4×C61—22no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2411yescharacteristic
200C2×C22⋊D61—21no—
201C2×C22⋊D61—21no—
202C2×C22⋊D61—21no—
203C2×C22⋊D61—21no—
204C2×C22⋊D61—21no—
205C22×Dic61—22no—
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208C22×Dic61C2×D411yescharacteristic
209#11758222—21no—
210#11758222—21no—
211#11758222—21no—
212#11758222—21no—
213#11758222—44no—
214#11758222—44no—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244C22×C411yescharacteristic
218C2×C4×D61—21no—
219C2×C4×D61—21no—
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—24no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—42no—
227C2×C4×D61C22⋊C411yescharacteristic
228C2×C4×D61C22⋊C411yescharacteristic
229C2×C4×D61C22⋊C411yescharacteristic
230C2×C4×D61C22⋊C411yescharacteristic
231C2×C4×D61C22⋊C411yescharacteristic
232C2×C4×D61C22⋊C411yescharacteristic
233C2×C4×D61C22⋊C411yescharacteristic
234C2×C4×D61C22⋊C411yescharacteristic
235C2×C4×D61C22×C411yescharacteristic
236C2×C4×D61C22×C411yescharacteristic
237C2×C4×D61C2×D411yescharacteristic
238C2×C4×D61C2×D411yescharacteristic
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122C22×C411yescharacteristic
242M16×C61—22no—
243M16×C61—22no—
244C2×C8×C61—22no—
245C4⋊C4×C61—24no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61C22×C411yescharacteristic
249C4⋊C4×C61C22×C411yescharacteristic
250C22⋊C4×C61—21no—
251C22⋊C4×C61—21no—
252C22⋊C4×C61—21no—
253C42×C61—21no—
254C42×C61—21no—
255C42×C61—21no—
256C42×C61—22no—
257C42×C61—22no—
258C42×C61C22×C411yescharacteristic
259C42×C61C22×C411yescharacteristic
260C42×C61C2×D411yescharacteristic
261C42×C61C2×D411yescharacteristic
262C22⋊Dic61—21no—
263C22⋊Dic61—21no—
264C22⋊Dic61—21no—
265C22⋊Dic61—21no—
266C22⋊Dic61—21no—
267#11758198—28no—
268#11758198—21no—
269#11758198—21no—
270#11758198—21no—
271#11758198—21no—
272#11758198—21no—
273#11758198—21no—
274#11758198—21no—
275#11758198—21no—
276#11758198—21no—
277#11758198—21no—
278C4⋊Dic61—24no—
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61C22×C411yescharacteristic
284C4⋊Dic61C22×C411yescharacteristic
285#11758196—21no—
286#11758196—21no—
287#11758196—21no—
288#11758196—21no—
289#11758196—21no—
290#11758196—21no—
291#11758196—21no—
292#11758196—21no—
293#11758196—21no—
294#11758196—21no—
295C4×Dic61—28no—
296C4×Dic61—21no—
297C4×Dic61—21no—
298C4×Dic61—21no—
299C4×Dic61—22no—
300C4×Dic61—22no—
301C4×Dic61—44no—
302C4×Dic61C22⋊C411yescharacteristic
303C4×Dic61C22⋊C411yescharacteristic
304C4×Dic61C22⋊C411yescharacteristic
305C4×Dic61C22⋊C411yescharacteristic
306C4×Dic61C22⋊C411yescharacteristic
307C4×Dic61C22⋊C411yescharacteristic
308C4×Dic61C22⋊C411yescharacteristic
309C4×Dic61C22⋊C411yescharacteristic
310C4×Dic61C22×C411yescharacteristic
311C4×Dic61C22×C411yescharacteristic
312C4×Dic61C2×D411yescharacteristic
313C4×Dic61C2×D411yescharacteristic
314#11758194—22no—
315#11758194—22no—
316C2×#92418—22no—
317#11758189—44no—
318C8×D61—44no—
319C23×C61—21no—
320C23×C61C22×D411yescharacteristic
321C22×D61—21no—
322C22×D61—21no—
323C22×D61—22no—
324C22×D61—21no—
325C22×D61—41no—
326C22×D61C2×C22⋊C411yescharacteristic
327C22×D61C2×C22⋊C411yescharacteristic
328Q8×C61—21no—
329Q8×C61—21no—
330D4×C61—21no—
331D4×C61—21no—
332D4×C61—41no—
333D4×C61—41no—
334C2×C4×C61—22no—
335C2×C4×C61—24no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—41no—
340C2×C4×C61—42no—
341C2×C4×C61—42no—
342C2×C4×C61—42no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—42no—
346C2×C4×C61C2×C22⋊C411yescharacteristic
347C2×C4×C61C2×C22⋊C411yescharacteristic
348C2×C4×C61C2×C22⋊C411yescharacteristic
349C2×C4×C61C2×C22⋊C411yescharacteristic
350C2×C4×C61C23×C411yescharacteristic
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61H(5,𝔽2)11yescharacteristic
353C2×C4×C61H(5,𝔽2)11yescharacteristic
354C2×C4×C612−1+411yescharacteristic
355C2×C4×C612−1+411yescharacteristic
356C22⋊D61—42no—
357C22⋊D61—41no—
358C22⋊D61—41no—
359C22⋊D61—42no—
360C22⋊D61—42no—
361C22⋊D61—42no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—24no—
367C2×Dic61—21no—
368C2×Dic61—21no—
369C2×Dic61—21no—
370C2×Dic61—42no—
371C2×Dic61—42no—
372C2×Dic61C2×C22⋊C411yescharacteristic
373C2×Dic61C2×C22⋊C411yescharacteristic
374C2×Dic61C2×C22⋊C411yescharacteristic
375C2×Dic61C2×C22⋊C411yescharacteristic
376C2×Dic61C2×C22⋊C411yescharacteristic
377C2×Dic61C2×C22⋊C411yescharacteristic
378D244—21no—
379D244—21no—
380D244—42no—
381D244—42no—
382C4×D61—22no—
383C4×D61—21no—
384C4×D61—21no—
385C4×D61—21no—
386C4×D61—21no—
387C4×D61—21no—
388C4×D61—21no—
389C4×D61—21no—
390C4×D61—21no—
391C4×D61—22no—
392C4×D61—22no—
393C4×D61—22no—
394C4×D61—22no—
395C4×D61—41no—
396C4×D61—41no—
397C4×D61—42no—
398C4×D61—41no—
399C4×D61—41no—
400C4×D61—42no—
401C4×D61#10414yescomplemented
402Dic122—21no—
403Dic122—21no—
404Dic122—42no—
405Dic122—42no—
406C8×C61—42no—
407#92418—42no—
408#21856—611nomaximal, Sylow
409C22×C61—21no—
410C22×C61—21no—
411C22×C61—41no—
412C22×C61—41no—
413C22×C61—41no—
414C22×C61C22×C22⋊C411yescharacteristic
415C22×C61#53711yescharacteristic
416C22×C61#53711yescharacteristic
417C2×D61—21no—
418C2×D61—21no—
419C2×D61—21no—
420C2×D61—21no—
421C2×D61—21no—
422C2×D61—42no—
423C2×D61—42no—
424C2×D61—41no—
425C2×D61—41no—
426C2×D61—41no—
427C2×D61C2×#10412yes—
428C4×C61—21no—
429C4×C61—21no—
430C4×C61—21no—
431C4×C61—44no—
432C4×C61—41no—
433C4×C61—41no—
434C4×C61—41no—
435C4×C61C2×#10412yes—
436C4×C61#52011yescharacteristic
437C4×C61#52011yescharacteristic
438C4×C61#53511yescharacteristic
439C4×C61#53611yescharacteristic
440Dic61—21no—
441Dic61—21no—
442Dic61—21no—
443Dic61—21no—
444Dic61—44no—
445Dic61—41no—
446Dic61—41no—
447Dic61—41no—
448Dic61C2×#10412yes—
449Dic61#42112yes—
450#3444—611no—
451C2×#423—611no—
452C4×#117—611no—
453#1994—612no—
454#1962—612no—
455#1871—612no—
456#1871—612no—
457#1806—611no—
458#1806—611no—
459#1806—611no—
460#1806D6111yescharacteristic, complemented
461C2×C61—21no—
462C2×C61—21no—
463C2×C61—81no—
464C2×C61#231111yescharacteristic
465C2×C61C22×#10411yescharacteristic
466C2×C61C2×#42111yescharacteristic
467D61—22no—
468D61—41no—
469D61—81no—
470C22×M16—612no—
471#533—611no—
472#533—611no—
473#533—611no—
474#532—611no—
475#532—611no—
476#532—611no—
477#529—611no—
478#529—611no—
479#529—611no—
480#529—611no—
481#529—1221no—
482#529—1221no—
483#529—1221no—
484#529—1221no—
485#525—611no—
486#525—611no—
487#525—1221no—
488#525—1221no—
489C4×#41—611no—
490C4×#41—1221no—
491C4×#41—1221no—
492C4×#41C2×D6111yescharacteristic
493C2×#117—1221no—
494C22×C42—611no—
495#423—612no—
496#423—611no—
497#423—1221no—
498#423—1221no—
499#423C2×D6111yescharacteristic
500C2×C4⋊C8—1221no—
501C2×C4⋊C8—1221no—
502C2×#104—612no—
503C2×#104—612no—
504C2×#104—612no—
505C2×#104C2×D6112yes—
506C4×C4⋊C4—611no—
507C4×C4⋊C4—1221no—
508C4×C4⋊C4C2×D6111yescharacteristic
509C4×C22⋊C4—612no—
510C4×C22⋊C4—1221no—
511#376—1221no—
512C43—612no—
513#339—612no—
514#339—612no—
515#339—612no—
516#339C2×D6112yes—
517C61#2185611yescharacteristic, complemented, Sylow
518C2×#41—611no—
519C2×#41—1221no—
520C2×#41—1221no—
521C2×#41C22×D6111yescharacteristic
522C23×C4—611no—
523C23×C4—611no—
524C23×C4—611no—
525C2×M16—612no—
526C2×M16—1222no—
527C2×M16—2442no—
528C2×M16—2442no—
529C2×M16C22×D6112yes—
530C22×C8—1222no—
531C4⋊Q8—611no—
532C4⋊Q8—611no—
533C4⋊Q8—611no—
534#127—611no—
535#126—1221no—
536#126—1221no—
537#126—1221no—
538#126—1221no—
539#125—611no—
540#125—611no—
541#125—1221no—
542#125—1221no—
543#124—611no—
544#124—611no—
545#124—1221no—
546#124—1221no—
547#123—1221no—
548#123—1221no—
549#123—1221no—
550#123—1221no—
551#123—1221no—
552#123—1221no—
553C22⋊Q8—611no—
554C22⋊Q8—611no—
555C22⋊Q8—611no—
556C22⋊Q8—611no—
557C22⋊Q8—1221no—
558C22⋊Q8—1221no—
559C22⋊Q8—1221no—
560C22⋊Q8—1221no—
561#121—611no—
562#121—611no—
563#121—611no—
564#121—611no—
565#121—1221no—
566#121—1221no—
567#121—1221no—
568#121—1221no—
569#120—1221no—
570#120—1221no—
571C4×Q8—611no—
572C4×Q8—611no—
573C4×Q8—1221no—
574C4×Q8—1221no—
575C4×Q8—1221no—
576C4×Q8—1221no—
577C4×Q8C4×D6111yescharacteristic
578C4×Q8C4×D6111yescharacteristic
579C4×D4—21no—
580C4×D4—21no—
581C4×D4—611no—
582C4×D4—611no—
583C4×D4—1221no—
584C4×D4—1221no—
585C4×D4—1221no—
586C4×D4—1221no—
587C4×D4—1221no—
588C4×D4—1221no—
589C4×D4—1221no—
590C4×D4—1221no—
591C4×D4—1221no—
592C4×D4—1221no—
593C4×D4—1221no—
594C4×D4—1221no—
595C4×D4—1221no—
596C4×D4—1221no—
597C4×D4C4×D6111yescharacteristic
598C4×D4C4×D6111yescharacteristic
599#117—21no—
600#117—611no—
601#117—1221no—
602#117—1221no—
603#117—1221no—
604#117—1221no—
605#117—1221no—
606#117—1221no—
607#117—1228no—
608#117—1221no—
609#117C22×D6111yescharacteristic
610C2×C4⋊C4—21no—
611C2×C4⋊C4—1221no—
612C2×C22⋊C4—1222no—
613C2×C42—21no—
614C2×C42—611no—
615C2×C42—611no—
616C2×C42—611no—
617C2×C42—611no—
618C2×C42—611no—
619C2×C42—611no—
620C2×C42—611no—
621C2×C42—611no—
622C2×C42—611no—
623C2×C42—611no—
624C2×C42—611no—
625C2×C42—612no—
626C2×C42—1222no—
627C2×C42—1221no—
628C2×C42—1222no—
629C2×C42C22×D6112yes—
630C2×C42C22×D6111yescharacteristic
631C4⋊C8—21no—
632C4⋊C8—21no—
633C4⋊C8—1222no—
634C4⋊C8—1222no—
635C4⋊C8—1221no—
636C4⋊C8—1221no—
637#104—42no—
638#104—2442no—
639#104—2442no—
640#104—2442no—
641#95—21no—
642#95—1222no—
643#95—1221no—
644C24—611no—
645#41—21no—
646#41—21no—
647#41—21no—
648#41—21no—
649#41—1221no—
650#41—1221no—
651#41—1221no—
652#41—1221no—
653#41—2444no—
654#41—2444no—
655C2×Q8—611no—
656C2×Q8—1221no—
657C2×Q8—1221no—
658C2×Q8C2×C4×D6111yescharacteristic
659C2×D4—21no—
660C2×D4—611no—
661C2×D4—1221no—
662C2×D4—1221no—
663C2×D4—1221no—
664C2×D4—1221no—
665C2×D4—1221no—
666C2×D4—1221no—
667C2×D4—1221no—
668C2×D4C2×C4×D6111yescharacteristic
669C22×C4—22no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—611no—
674C22×C4—611no—
675C22×C4—611no—
676C22×C4—611no—
677C22×C4—611no—
678C22×C4—611no—
679C22×C4—611no—
680C22×C4—611no—
681C22×C4—611no—
682C22×C4—611no—
683C22×C4—611no—
684C22×C4—611no—
685C22×C4—611no—
686C22×C4—611no—
687C22×C4—611no—
688C22×C4—1224no—
689C22×C4—1221no—
690C22×C4—1221no—
691C22×C4—1221no—
692C22×C4—1221no—
693C22×C4—1222no—
694C22×C4—1221no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—2442no—
698C22×C4D4×D6111yescharacteristic
699C22×C4D4×D6111yescharacteristic
700C22×C4C23×D6111yescharacteristic
701M16—22no—
702M16—22no—
703M16—1222no—
704M16—1222no—
705M16—2444no—
706C2×C8—22no—
707C2×C8—1222no—
708C2×C8—2444no—
709C4⋊C4—24no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—611no—
713C4⋊C4—611no—
714C4⋊C4—1221no—
715C4⋊C4—1221no—
716C4⋊C4—1221no—
717C4⋊C4—1221no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C4⋊C4—1224no—
727C4⋊C4—1221no—
728C4⋊C4—1221no—
729C4⋊C4C2×C4×D6111yescharacteristic
730C4⋊C4C2×C4×D6111yescharacteristic
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—1221no—
735C22⋊C4—1221no—
736C22⋊C4—1221no—
737C22⋊C4—1221no—
738C22⋊C4—1221no—
739C22⋊C4—1221no—
740C22⋊C4—1221no—
741C22⋊C4—1221no—
742C22⋊C4—1228no—
743C22⋊C4—1221no—
744C22⋊C4—1221no—
745C22⋊C4—1221no—
746C22⋊C4—1221no—
747C22⋊C4—1221no—
748C22⋊C4—1221no—
749C22⋊C4—1221no—
750C42—21no—
751C42—21no—
752C42—21no—
753C42—22no—
754C42—22no—
755C42—611no—
756C42—611no—
757C42—611no—
758C42—611no—
759C42—611no—
760C42—611no—
761C42—611no—
762C42—611no—
763C42—611no—
764C42—611no—
765C42—611no—
766C42—611no—
767C42—1228no—
768C42—1221no—
769C42—1221no—
770C42—1221no—
771C42—1222no—
772C42—1222no—
773C42—2444no—
774C42C2×C4×D6111yescharacteristic
775C42C2×C4×D6111yescharacteristic
776C42D4×D6111yescharacteristic
777C42D4×D6111yescharacteristic
778C23—21no—
779C23—611no—
780C23—611no—
781C23—1222no—
782C23—1221no—
783C23—1221no—
784C23—1221no—
785C23—2441no—
786C23C2×D4×D6111yescharacteristic
787Q8—21no—
788Q8—21no—
789Q8—1221no—
790Q8—1221no—
791Q8—2442no—
792Q8—2442no—
793D4—21no—
794D4—21no—
795D4—41no—
796D4—41no—
797D4—1221no—
798D4—1221no—
799D4—2442no—
800D4—2442no—
801D4—2442no—
802D4—2442no—
803D4—2442no—
804D4—2442no—
805D4—2441no—
806D4—2441no—
807C2×C4—22no—
808C2×C4—24no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—611no—
820C2×C4—611no—
821C2×C4—614no—
822C2×C4—611no—
823C2×C4—611no—
824C2×C4—611no—
825C2×C4—611no—
826C2×C4—1222no—
827C2×C4—1222no—
828C2×C4—1222no—
829C2×C4—1222no—
830C2×C4—1222no—
831C2×C4—1222no—
832C2×C4—1221no—
833C2×C4—1221no—
834C2×C4—1221no—
835C2×C4—1221no—
836C2×C4—1221no—
837C2×C4—1221no—
838C2×C4—1222no—
839C2×C4—1221no—
840C2×C4—1221no—
841C2×C4—1221no—
842C2×C4—1221no—
843C2×C4—1224no—
844C2×C4—1221no—
845C2×C4—1221no—
846C2×C4—1221no—
847C2×C4—2441no—
848C2×C4—2441no—
849C2×C4—2442no—
850C2×C4—2442no—
851C2×C4—2442no—
852C2×C4—2442no—
853C2×C4—2441no—
854C2×C4—2441no—
855C2×C4C22⋊C4×D6111yescharacteristic
856C2×C4C22⋊C4×D6111yescharacteristic
857C2×C4C22⋊C4×D6111yescharacteristic
858C2×C4C22⋊C4×D6111yescharacteristic
859C2×C4C22×C4×D6111yescharacteristic
860C2×C4C2×D4×D6111yescharacteristic
861C2×C4#1451982211yescharacteristic
862C2×C4#1451982311yescharacteristic
863C2×C4#1451982411yescharacteristic
864C2×C4#1451982511yescharacteristic
865C8—42no—
866C8—2442no—
867C22—21no—
868C22—21no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—612no—
873C22—1221no—
874C22—1221no—
875C22—1221no—
876C22—1221no—
877C22—1221no—
878C22—2442no—
879C22—2442no—
880C22—2441no—
881C22—2441no—
882C22—2441no—
883C22C2×C22⋊C4×D6111yescharacteristic
884C22#1684034111yescharacteristic
885C22#1684034211yescharacteristic
886C4—21no—
887C4—21no—
888C4—21no—
889C4—44no—
890C4—41no—
891C4—41no—
892C4—41no—
893C4—612no—
894C4—612no—
895C4—1221no—
896C4—1221no—
897C4—1221no—
898C4—1221no—
899C4—2444no—
900C4—2441no—
901C4—2441no—
902C4—2441no—
903C4#104×D6112yes—
904C4#1684024211yescharacteristic
905C4#1684024311yescharacteristic
906C4#1684032811yescharacteristic
907C4#1684033511yescharacteristic
908C2—21no—
909C2—21no—
910C2—81no—
911C2—1222no—
912C2—4881no—
913C2—2441no—
914C2#2144840811yescharacteristic
915C2C2×#104×D6111yescharacteristic
916C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1806C2
socleC22×C61C22×C22⋊C4
prime radical#21459112C2
cosocleC22×C4×C61C24
hypercenter#1806D61
hypocenterC61#21856
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #423×D61C2semidirect
3. C4×#14519735C2semidirect
4. #21446794C2semidirect
5. #21446645C2semidirect
6. #21446120C2semidirect
7. #21446118C2semidirect
8. #21445840C2semidirect
9. #21445839C2semidirect
10. #21445836C2semidirect
11. C61×#1806C2semidirect
13. #16840316C4semidirect
14. #16840316C4semidirect
16. #16840309C4semidirect
17. #16840309C4semidirect
19. #16840299C4semidirect
20. #16840299C4semidirect
21. #16840294C4semidirect
22. #16840294C4semidirect
401. C4×D61#104semidirect
460. #1806D61semidirect
517. C61#21856semidirect

Maximal subgroups

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

subgroupindex
#214591122
#423×D612
C4×#145197352
#214467942
#214466452
#214461202
#214461182
#214458402
#214458392
#214458362
C61×#18062
#2185661