Finite Group Databasebeta

← D61×#2127 #29832794

Subgroups — D61×#2127 #29832794

Order 15616.

1510 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#535×D61C211yesmaximal, characteristic
2C2×#99×D61C212yesmaximal, complemented
3#21447488C211yesmaximal, characteristic, complemented
4#21447487C212yesmaximal, complemented
5#21447486C212yesmaximal, complemented
6#21447485C212yesmaximal, complemented
7#354×D61C212yesmaximal, complemented
8#353×D61C212yesmaximal, complemented
9C61×#2127C211yesmaximal, characteristic, complemented
10C2×#41×D61C411yescharacteristic, complemented
11C22×D4×D61C2211yescharacteristic
12#16840331C411yescharacteristic, complemented
13#16840330C411yescharacteristic, complemented
14#16840330C2211yescharacteristic
15#16840329C2211yescharacteristic
16#16840328—22no—
17#16840327—22no—
18#16840326C411yescharacteristic, complemented
19#16840325C411yescharacteristic, complemented
20#16840325C2211yescharacteristic
21#127×D61C411yescharacteristic, complemented
22#127×D61C2211yescharacteristic
23#124×D61C411yescharacteristic, complemented
24#124×D61C2211yescharacteristic
25#121×D61—22no—
26#120×D61—22no—
27#117×D61C411yescharacteristic, complemented
28C2×C22⋊C4×D61—22no—
29C2×#14519692C2212yescomplemented
30C2×#14519691—22no—
31#99×D61—22no—
32#99×D61—22no—
33#99×D61C2214yes—
34#99×D61C2214yescomplemented
35#16839557C2212yescomplemented
36#16839556C2214yescomplemented
37#16839555C2212yescomplemented
38#16839554C2214yescomplemented
39C61×#535C2211yescharacteristic
40C2×#99×C61C2212yescomplemented
41C61×#354C2212yescomplemented
42C61×#353C2212yescomplemented
43C24×D61D412yes—
44C2×#11758226C2×C411yescharacteristic, complemented
45C2×#11758222—21no—
46C2×#11758222C2×C411yescharacteristic, complemented
47C2×#11758224—21no—
48C2×#11758224C2×C411yescharacteristic, complemented
49#41×D61—42no—
50#41×D61—42no—
51C2×Q8×D61C2×C411yescharacteristic, complemented
52C22×D244C2×C411yescharacteristic
53C22×C22⋊D61D412yes—
54C2×D4×D61—21no—
55C2×D4×D61—22no—
56C2×D4×D61—22no—
57C2×D4×D61—42no—
58C2×D4×D61—42no—
59C2×D4×D61C2×C411yescharacteristic
60C2×D4×D61C2×C411yescharacteristic
61C2×D4×D61C2×C411yescharacteristic, complemented
62C2×D4×D61D412yes—
63C2×D4×D61D412yes—
64C2×D4×D61C2311yescharacteristic
65C2×D4×D61C2311yescharacteristic
66C22×C4×D61—21no—
67C22×C4×D61—42no—
68C22×C4×D61C2×C411yescharacteristic
69#14519774C2×C411yescharacteristic, complemented
70#14519774C2×C411yescharacteristic, complemented
71#14519773—22no—
72#14519773—22no—
73#14519773C2×C411yescharacteristic, complemented
74#14519773C2×C411yescharacteristic, complemented
75#14519773C2×C411yescharacteristic, complemented
76#14519773C2311yescharacteristic
77#14519766C2×C411yescharacteristic, complemented
78#14519766C2×C411yescharacteristic, complemented
79#14519765C2×C411yescharacteristic, complemented
80#14519765C2×C411yescharacteristic, complemented
81#14519764C2×C411yescharacteristic, complemented
82#14519764C2311yescharacteristic
83#14519763—22no—
84#14519763—22no—
85#14519752—22no—
86#14519751—22no—
87#14519750—22no—
88#14519750—22no—
89#14519749—22no—
90#14519749—22no—
91#14519748—22no—
92#14519747—22no—
93#14519747—22no—
94#14519747—22no—
95#14519746—22no—
96#14519745—22no—
97#14519745—22no—
98#14519745—22no—
99#14519736C2×C411yescharacteristic, complemented
100#14519735—21no—
101#14519734C2×C411yescharacteristic, complemented
102#14519734C2×C411yescharacteristic, complemented
103#14519733—21no—
104C4⋊C4×D61—21no—
105C2×C22⋊Dic61—22no—
106C2×#11758198—42no—
107C22⋊C4×D61—21no—
108C22⋊C4×D61—22no—
109C22⋊C4×D61—22no—
110C22⋊C4×D61—24no—
111C22⋊C4×D61—24no—
112C22⋊C4×D61—42no—
113C22⋊C4×D61—42no—
114C42×D61C2×C411yescharacteristic, complemented
115C42×D61C2×C411yescharacteristic, complemented
116#14519692—22no—
117#14519692C2314yes—
118#14519691—24no—
119#14519691—24no—
120C2×#41×C61C2×C411yescharacteristic, complemented
121C22×D4×C61C2311yescharacteristic
122#127×C61C2×C411yescharacteristic, complemented
123#127×C61C2311yescharacteristic
124#124×C61C2×C411yescharacteristic, complemented
125#124×C61C2311yescharacteristic
126#121×C61—22no—
127#120×C61—22no—
128#117×C61C2×C411yescharacteristic, complemented
129C2×C22⋊C4×C61—22no—
130#99×C61—22no—
131#99×C61C2314yes—
132C24×C61C2×D412yes—
133C23×D61—22no—
134C23×D61—22no—
135C23×D61—22no—
136C23×D61—22no—
137C23×D61—21no—
138C23×D61—84no—
139C23×D61C22⋊C412yes—
140C23×D61C22⋊C412yes—
141C23×D61C22⋊C412yes—
142C23×D61C22⋊C411yescharacteristic
143C23×D61C2×D412yes—
144C23×D61C2×D412yes—
145#41×C61—42no—
146C2×Q8×C61C22×C411yescharacteristic, complemented
147C2×D4×C61—21no—
148C2×D4×C61—22no—
149C2×D4×C61—22no—
150C2×D4×C61—42no—
151C2×D4×C61C22×C411yescharacteristic
152C2×D4×C61C22×C411yescharacteristic, complemented
153C2×D4×C61C2×D412yes—
154C2×D4×C61C2411yescharacteristic
155C22×C4×C61—21no—
156C22×C4×C61—42no—
157C22×C4×C61C22×C411yescharacteristic
158C2×C22⋊D61—21no—
159C2×C22⋊D61—21no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61—22no—
162C2×C22⋊D61—22no—
163C2×C22⋊D61—22no—
164C2×C22⋊D61—21no—
165C2×C22⋊D61—42no—
166C2×C22⋊D61—42no—
167C2×C22⋊D61C22⋊C412yes—
168C2×C22⋊D61C22⋊C412yes—
169C2×C22⋊D61C2×D412yes—
170C2×C22⋊D61C2×D412yes—
171C22×Dic61—21no—
172C22×Dic61—42no—
173C22×Dic61C22⋊C411yescharacteristic
174#11758226—42no—
175Q8×D61—41no—
176Q8×D61—41no—
177#11758224—42no—
178#11758224—44no—
179D4×D61—41no—
180D4×D61—41no—
181D4×D61—42no—
182D4×D61—42no—
183D4×D61—42no—
184D4×D61—42no—
185D4×D61—42no—
186D4×D61—41no—
187D4×D61—41no—
188D4×D61—42no—
189D4×D61—41no—
190D4×D61—41no—
191D4×D61—42no—
192D4×D61—42no—
193D4×D61—84no—
194D4×D61—84no—
195#11758222—44no—
196#11758222—42no—
197C2×D244—21no—
198C2×D244—22no—
199C2×D244—22no—
200C2×D244—42no—
201C2×D244C22⋊C412yes—
202C2×D244C22×C411yescharacteristic
203C2×D244C22×C411yescharacteristic
204C2×D244C22×C411yescharacteristic, complemented
205C2×C4×D61—22no—
206C2×C4×D61—22no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—21no—
212C2×C4×D61—42no—
213C2×C4×D61—42no—
214C2×C4×D61—44no—
215C2×C4×D61—44no—
216C2×C4×D61—88no—
217C2×C4×D61C22⋊C411yescharacteristic
218C2×C4×D61C22⋊C411yescharacteristic
219C2×C4×D61C22×C411yescharacteristic
220C2×C4×D61C22×C411yescharacteristic
221C2×Dic122—21no—
222C2×Dic122C22×C411yescharacteristic, complemented
223C4⋊C4×C61—21no—
224C22⋊C4×C61—21no—
225C22⋊C4×C61—22no—
226C22⋊C4×C61—22no—
227C22⋊C4×C61—24no—
228C22⋊C4×C61—42no—
229C42×C61C22×C411yescharacteristic, complemented
230C42×C61C22×C411yescharacteristic, complemented
231C22⋊Dic61—21no—
232C22⋊Dic61—22no—
233C22⋊Dic61—22no—
234C22⋊Dic61—24no—
235C22⋊Dic61—42no—
236#11758198—21no—
237#11758198—21no—
238#11758198—22no—
239#11758198—22no—
240#11758198—22no—
241#11758198—22no—
242#11758198—44no—
243#11758198—44no—
244C4⋊Dic61—21no—
245#11758196—21no—
246#11758196—21no—
247C4×Dic61—21no—
248C4×Dic61—21no—
249C4×Dic61C22×C411yescharacteristic, complemented
250C4×Dic61C22×C411yescharacteristic, complemented
251C23×C61—22no—
252C23×C61—22no—
253C23×C61—21no—
254C23×C61—82no—
255C23×C61C2×C22⋊C412yes—
256C23×C61C2×C22⋊C411yescharacteristic
257C23×C61C22×D412yes—
258C22×D61—22no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—22no—
263C22×D61—22no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—22no—
267C22×D61—22no—
268C22×D61—21no—
269C22×D61—42no—
270C22×D61—48no—
271C22×D61—44no—
272C22×D61—44no—
273C22×D61—44no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—84no—
277C22×D61—82no—
278C22×D61—82no—
279C22×D61—82no—
280C22×D61—84no—
281C22×D61—84no—
282C22×D61#9912yes—
283C22×D61#9912yes—
284C22×D61C2×C22⋊C411yescharacteristic
285C22×D61C2×C22⋊C412yes—
286C22×D61C2×C22⋊C412yes—
287C22×D61C2×C22⋊C411yescharacteristic
288Q8×C61—41no—
289D4×C61—41no—
290D4×C61—42no—
291D4×C61—41no—
292D4×C61—41no—
293D4×C61—42no—
294D4×C61—82no—
295D4×C61—82no—
296C2×C4×C61—22no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—42no—
301C2×C4×C61—44no—
302C2×C4×C61—84no—
303C2×C4×C61C2×C22⋊C411yescharacteristic
304C2×C4×C61C23×C411yescharacteristic
305C22⋊D61—42no—
306C22⋊D61—42no—
307C22⋊D61—42no—
308C22⋊D61—42no—
309C22⋊D61—42no—
310C22⋊D61—42no—
311C22⋊D61—42no—
312C22⋊D61—82no—
313C22⋊D61—82no—
314C22⋊D61—82no—
315C22⋊D61—82no—
316C2×Dic61—22no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—42no—
321C2×Dic61—44no—
322C2×Dic61—84no—
323C2×Dic61C2×C22⋊C411yescharacteristic
324C2×Dic61C2×C22⋊C411yescharacteristic
325D244—42no—
326D244—41no—
327D244—41no—
328D244—41no—
329D244—42no—
330D244—82no—
331D244—82no—
332C4×D61—21no—
333C4×D61—21no—
334C4×D61—22no—
335C4×D61—21no—
336C4×D61—21no—
337C4×D61—22no—
338C4×D61—42no—
339C4×D61—42no—
340C4×D61—42no—
341C4×D61—42no—
342C4×D61—41no—
343C4×D61—41no—
344C4×D61—88no—
345C4×D61—88no—
346Dic122—42no—
347Dic122—41no—
348C2×#2127—611nomaximal, Sylow
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—41no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—44no—
355C22×C61—42no—
356C22×C61—41no—
357C22×C61—82no—
358C22×C61C2×#9912yes—
359C22×C61C22×C22⋊C411yescharacteristic
360C2×D61—22no—
361C2×D61—24no—
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—42no—
365C2×D61—41no—
366C2×D61—44no—
367C2×D61—44no—
368C2×D61—44no—
369C2×D61—44no—
370C2×D61—44no—
371C2×D61—42no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—41no—
375C2×D61—82no—
376C2×D61—82no—
377C2×D61—82no—
378C2×D61—82no—
379C2×D61—82no—
380C2×D61—82no—
381C2×D61—82no—
382C2×D61C2×#9911yescharacteristic
383C2×D61C2×#9912yes—
384C2×D61C2×#9911yescharacteristic
385C4×C61—21no—
386C4×C61—21no—
387C4×C61—41no—
388C4×C61—41no—
389C4×C61—41no—
390C4×C61—84no—
391Dic61—21no—
392Dic61—21no—
393Dic61—41no—
394Dic61—41no—
395Dic61—41no—
396Dic61—84no—
397C2×#535—611no—
398C22×#99—612no—
399#2127—612no—
400#2127—612no—
401#2127—612no—
402#2127—611no—
403#2127D6111yescharacteristic, direct product factor
404C2×#354—612no—
405C2×#353—612no—
406C2×C61—21no—
407C2×C61—22no—
408C2×C61—42no—
409C2×C61—42no—
410C2×C61—81no—
411C2×C61C22×#9911yescharacteristic
412D61—22no—
413D61—21no—
414D61—42no—
415D61—42no—
416D61—81no—
417D61#212712yesdirect product factor
418C22×#41—611no—
419C23×D4—611no—
420#535—611no—
421#535—611no—
422#535—611no—
423#535—611no—
424#535—611no—
425#535—611no—
426#535—611no—
427#535—1222no—
428#535—1222no—
429#535C2×D6111yescharacteristic
430C2×#127—611no—
431C2×#127—611no—
432C2×#124—611no—
433C2×#124—611no—
434C2×#121—1222no—
435C2×#120—1222no—
436C2×#117—611no—
437C22×C22⋊C4—1222no—
438C2×#99—612no—
439C2×#99—614no—
440C2×#99—614no—
441C2×#99—1222no—
442C2×#99—1222no—
443C2×#99—1222no—
444C2×#99C2×D6112yescomplemented
445#354—612no—
446#354—614no—
447#354C2×D6112yescomplemented
448#353—612no—
449#353—614no—
450#353C2×D6112yescomplemented
451C61C2×#212711yescharacteristic, complemented, Sylow
452C25—612no—
453C2×#41—611no—
454C2×#41—611no—
455C2×#41—611no—
456C2×#41—1221no—
457C2×#41—1221no—
458C2×#41—2442no—
459C2×#41—2442no—
460C2×#41C4×D6111yescharacteristic, complemented
461C22×Q8—611no—
462C22×D4—612no—
463C22×D4—611no—
464C22×D4—611no—
465C22×D4—612no—
466C22×D4—612no—
467C22×D4—611no—
468C22×D4—611no—
469C22×D4—611no—
470C22×D4—611no—
471C22×D4—1222no—
472C22×D4—1222no—
473C22×D4—1221no—
474C22×D4—2442no—
475C22×D4—2442no—
476C22×D4C22×D6111yescharacteristic
477C23×C4—611no—
478C23×C4—1221no—
479C23×C4—2442no—
480#127—611no—
481#127—611no—
482#127—611no—
483#127—611no—
484#127—611no—
485#127—611no—
486#127—1222no—
487#127—1222no—
488#127C4×D6111yescharacteristic, complemented
489#127C22×D6111yescharacteristic
490#124—611no—
491#124—611no—
492#124—611no—
493#124—611no—
494#124—611no—
495#124—611no—
496#124—1222no—
497#124—1222no—
498#124C4×D6111yescharacteristic, complemented
499#124C22×D6111yescharacteristic
500#121—22no—
501#121—1222no—
502#121—1222no—
503#121—1222no—
504#121—1222no—
505#121—1222no—
506#121—1222no—
507#121—1222no—
508#120—22no—
509#120—1222no—
510#120—1222no—
511#120—1222no—
512#120—1222no—
513#120—1222no—
514#120—1222no—
515#120—1222no—
516#117—611no—
517#117—611no—
518#117—611no—
519#117—1221no—
520#117—1221no—
521#117C4×D6111yescharacteristic, complemented
522C2×C4⋊C4—1221no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1222no—
526C2×C22⋊C4—1222no—
527C2×C22⋊C4—1224no—
528C2×C22⋊C4—1224no—
529C2×C22⋊C4—1222no—
530C2×C22⋊C4—2442no—
531C2×C22⋊C4—2442no—
532C2×C22⋊C4—2442no—
533C2×C42—611no—
534C2×C42—611no—
535#99—22no—
536#99—614no—
537#99—1224no—
538#99—1224no—
539#99—1222no—
540#99C22×D6114yes—
541C24—611no—
542C24—612no—
543C24—612no—
544C24—612no—
545C24—612no—
546C24—612no—
547C24—1222no—
548C24—1222no—
549C24—1222no—
550C24—1222no—
551C24—1221no—
552C24—4884no—
553C24D4×D6112yes—
554#41—42no—
555#41—2442no—
556#41—2444no—
557#41—2444no—
558#41—2442no—
559#41—2442no—
560C2×Q8—611no—
561C2×Q8—1221no—
562C2×Q8—2441no—
563C2×Q8—2441no—
564C2×Q8C2×C4×D6111yescharacteristic, complemented
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—42no—
569C2×D4—612no—
570C2×D4—612no—
571C2×D4—612no—
572C2×D4—612no—
573C2×D4—611no—
574C2×D4—611no—
575C2×D4—611no—
576C2×D4—612no—
577C2×D4—1222no—
578C2×D4—1222no—
579C2×D4—1221no—
580C2×D4—1221no—
581C2×D4—1222no—
582C2×D4—1222no—
583C2×D4—1222no—
584C2×D4—1222no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—4884no—
588C2×D4—4884no—
589C2×D4—2442no—
590C2×D4—2442no—
591C2×D4—2442no—
592C2×D4—2441no—
593C2×D4—2441no—
594C2×D4—2441no—
595C2×D4—2441no—
596C2×D4—2442no—
597C2×D4—2442no—
598C2×D4—2442no—
599C2×D4—2442no—
600C2×D4—2441no—
601C2×D4—2441no—
602C2×D4—2442no—
603C2×D4—2442no—
604C2×D4—2442no—
605C2×D4—2442no—
606C2×D4C2×C4×D6111yescharacteristic
607C2×D4C2×C4×D6111yescharacteristic, complemented
608C2×D4D4×D6112yes—
609C2×D4C23×D6111yescharacteristic
610C22×C4—21no—
611C22×C4—42no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—1221no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—4888no—
626C22×C4—2442no—
627C22×C4—2442no—
628C22×C4—2444no—
629C22×C4—2444no—
630C22×C4—2442no—
631C22×C4C2×C4×D6111yescharacteristic
632C4⋊C4—21no—
633C4⋊C4—1221no—
634C4⋊C4—1221no—
635C4⋊C4—1221no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—21no—
639C22⋊C4—24no—
640C22⋊C4—42no—
641C22⋊C4—1221no—
642C22⋊C4—1221no—
643C22⋊C4—1222no—
644C22⋊C4—1222no—
645C22⋊C4—1222no—
646C22⋊C4—1222no—
647C22⋊C4—1222no—
648C22⋊C4—1222no—
649C22⋊C4—1221no—
650C22⋊C4—1224no—
651C22⋊C4—2444no—
652C22⋊C4—2444no—
653C22⋊C4—2442no—
654C42—611no—
655C42—611no—
656C42—1221no—
657C42—1221no—
658C42C2×C4×D6111yescharacteristic, complemented
659C42C2×C4×D6111yescharacteristic, complemented
660C23—22no—
661C23—22no—
662C23—21no—
663C23—82no—
664C23—611no—
665C23—612no—
666C23—611no—
667C23—612no—
668C23—612no—
669C23—612no—
670C23—1222no—
671C23—1222no—
672C23—1222no—
673C23—1222no—
674C23—1222no—
675C23—1222no—
676C23—1222no—
677C23—1222no—
678C23—1222no—
679C23—1222no—
680C23—1221no—
681C23—4884no—
682C23—4882no—
683C23—4882no—
684C23—4882no—
685C23—4884no—
686C23—4884no—
687C23—2441no—
688C23—2441no—
689C23—2442no—
690C23—2444no—
691C23—2444no—
692C23—2444no—
693C23—2448no—
694C23C22⋊C4×D6112yes—
695C23C22⋊C4×D6111yescharacteristic
696C23C2×D4×D6112yes—
697Q8—41no—
698Q8—2441no—
699Q8—2442no—
700D4—41no—
701D4—42no—
702D4—41no—
703D4—41no—
704D4—42no—
705D4—82no—
706D4—82no—
707D4—4882no—
708D4—4882no—
709D4—4882no—
710D4—4882no—
711D4—4882no—
712D4—4882no—
713D4—2442no—
714D4—2441no—
715D4—2441no—
716D4—2441no—
717D4—2442no—
718D4—2442no—
719D4—2442no—
720D4—2442no—
721D4—2442no—
722D4—2442no—
723D4—2442no—
724D4—2442no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—84no—
732C2×C4—611no—
733C2×C4—611no—
734C2×C4—1221no—
735C2×C4—1221no—
736C2×C4—1221no—
737C2×C4—1221no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1221no—
742C2×C4—1221no—
743C2×C4—1221no—
744C2×C4—4888no—
745C2×C4—4888no—
746C2×C4—4884no—
747C2×C4—2442no—
748C2×C4—2442no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2442no—
752C2×C4—2442no—
753C2×C4—2442no—
754C2×C4—2444no—
755C2×C4C22⋊C4×D6111yescharacteristic
756C2×C4C22×C4×D6111yescharacteristic
757C22—22no—
758C22—22no—
759C22—41no—
760C22—42no—
761C22—42no—
762C22—44no—
763C22—42no—
764C22—41no—
765C22—82no—
766C22—611no—
767C22—611no—
768C22—612no—
769C22—1222no—
770C22—1224no—
771C22—1222no—
772C22—1222no—
773C22—4882no—
774C22—4882no—
775C22—4882no—
776C22—4882no—
777C22—4882no—
778C22—4882no—
779C22—4882no—
780C22—2441no—
781C22—2442no—
782C22—2442no—
783C22—2442no—
784C22—2442no—
785C22—2444no—
786C22—2444no—
787C22—2444no—
788C22—2444no—
789C22—2444no—
790C22—2441no—
791C22#99×D6112yes—
792C22C2×C22⋊C4×D6111yescharacteristic
793C4—21no—
794C4—21no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—84no—
799C4—1221no—
800C4—1221no—
801C4—4884no—
802C4—2441no—
803C4—2441no—
804C4—2441no—
805C2—21no—
806C2—22no—
807C2—42no—
808C2—42no—
809C2—81no—
810C2—612no—
811C2—1221no—
812C2—1222no—
813C2—4881no—
814C2—2442no—
815C2—2442no—
816C2C2×#99×D6111yescharacteristic
subgroupG/H
centerC2C2×#99×D61
commutatorC2×C4×C61C23×C4
FrattiniC2×D4C23×D61
FittingC61×#2127C2
socleC2×C61C22×#99
prime radical#535×D61C2
cosocleC2×D4×C61C24
hypercenter#2127D61
hypocenterC61C2×#2127
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ #2127

Complements

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

NH ≅ G/Ntype
2. C2×#99×D61C2semidirect
3. #21447488C2semidirect
4. #21447487C2semidirect
5. #21447486C2semidirect
6. #21447485C2semidirect
7. #354×D61C2semidirect
8. #353×D61C2semidirect
9. C61×#2127C2semidirect
10. C2×#41×D61C4semidirect
12. #16840331C4semidirect
13. #16840330C4semidirect
18. #16840326C4semidirect
19. #16840325C4semidirect
21. #127×D61C4semidirect
23. #124×D61C4semidirect
27. #117×D61C4semidirect
29. C2×#14519692C22semidirect
34. #99×D61C22semidirect
35. #16839557C22semidirect
36. #16839556C22semidirect
37. #16839555C22semidirect
38. #16839554C22semidirect
40. C2×#99×C61C22semidirect
41. C61×#354C22semidirect
42. C61×#353C22semidirect
44. C2×#11758226C2×C4semidirect
46. C2×#11758222C2×C4semidirect
48. C2×#11758224C2×C4semidirect
51. C2×Q8×D61C2×C4semidirect
61. C2×D4×D61C2×C4semidirect
69. #14519774C2×C4semidirect
70. #14519774C2×C4semidirect
73. #14519773C2×C4semidirect
74. #14519773C2×C4semidirect
75. #14519773C2×C4semidirect
77. #14519766C2×C4semidirect
78. #14519766C2×C4semidirect
79. #14519765C2×C4semidirect
80. #14519765C2×C4semidirect
81. #14519764C2×C4semidirect
99. #14519736C2×C4semidirect
101. #14519734C2×C4semidirect
102. #14519734C2×C4semidirect
114. C42×D61C2×C4semidirect
115. C42×D61C2×C4semidirect
120. C2×#41×C61C2×C4semidirect
122. #127×C61C2×C4semidirect
124. #124×C61C2×C4semidirect
128. #117×C61C2×C4semidirect
146. C2×Q8×C61C22×C4semidirect
152. C2×D4×C61C22×C4semidirect
204. C2×D244C22×C4semidirect
222. C2×Dic122C22×C4semidirect
229. C42×C61C22×C4semidirect
230. C42×C61C22×C4semidirect
249. C4×Dic61C22×C4semidirect
250. C4×Dic61C22×C4semidirect
403. #2127D61direct (N × H)
417. D61#2127direct (N × H)
444. C2×#99C2×D61semidirect
447. #354C2×D61semidirect
450. #353C2×D61semidirect
451. C61C2×#2127semidirect
460. C2×#41C4×D61semidirect
488. #127C4×D61semidirect
498. #124C4×D61semidirect
521. #117C4×D61semidirect
564. C2×Q8C2×C4×D61semidirect
607. C2×D4C2×C4×D61semidirect
658. C42C2×C4×D61semidirect
659. C42C2×C4×D61semidirect

Maximal subgroups

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

subgroupindex
#535×D612
C2×#99×D612
#214474882
#214474872
#214474862
#214474852
#354×D612
#353×D612
C61×#21272
C2×#212761