Finite Group Databasebeta

← D61⋊#1899 #30615715

Subgroups — D61⋊#1899 #30615715

Order 15616.

2066 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519856C211yesmaximal, characteristic, complemented
2C2×D61⋊#99C212yesmaximal
3C2×#16840705C211yesmaximal, characteristic, complemented
4#21461843C214yesmaximal, complemented
5#21461842C214yesmaximal, complemented
6#21461516C212yesmaximal, complemented
7C2×#123×D61C211yesmaximal, characteristic
8C2×#14519856—28no—
9C2×#14519856—22no—
10C2×#14519856C2214yescomplemented
11C22×C4⋊#6923—21no—
12C22×C22⋊#6923C2212yes—
13C22×C22⋊#6923C2212yes—
14C22×C4×#6923—21no—
15C2×#14519836C2214yes—
16D61⋊#99—28no—
17C2×#14519835C2214yes—
18#16840705—21no—
19#16840705—21no—
20#16840705C2214yescomplemented
21C2×(C2×#6923)⋊C4—22no—
22#16840640C2218yescomplemented
23C22×D4×D61C2211yescharacteristic
24C23×C4×D61C2211yescharacteristic
25C2×#14519762C2212yes—
26C2×#14519761C411yescharacteristic, complemented
27C2×#14519760C411yescharacteristic, complemented
28C2×#14519759C2212yes—
29C2×#14519758C411yescharacteristic, complemented
30#123×D61—21no—
31#123×D61—21no—
32#123×D61—21no—
33#123×D61—21no—
34#123×D61—22no—
35#123×D61—22no—
36C2×C4⋊C4×D61C412yescomplemented
37C2×C22⋊C4×D61C412yescomplemented
38C2×C22⋊C4×D61C2211yescharacteristic
39C2×#123×C61C411yescharacteristic, complemented
40C23×#6923—22no—
41C23×#6923—22no—
42#14519856—216no—
43#14519856—216no—
44C2×C4⋊#6923—28no—
45C2×C4⋊#6923—24no—
46C2×C22⋊#6923—22no—
47C2×C22⋊#6923—24no—
48C2×C22⋊#6923—24no—
49C2×C22⋊#6923—24no—
50C2×C22⋊#6923—22no—
51C2×C22⋊#6923D418yes—
52C2×C22⋊#6923C2314yes—
53C2×C22⋊#6923C2314yes—
54C2×C4×#6923—28no—
55C2×C4×#6923—24no—
56#14519836—28no—
57#14519835—28no—
58(C2×#6923)⋊C4—24no—
59(C2×#6923)⋊C4—24no—
60C24×D61C2×C411yescharacteristic
61C24×D61C2311yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C22⋊D61C2×C411yescharacteristic
64C22×C22⋊D61C2311yescharacteristic
65C2×D4×D61—24no—
66C2×D4×D61—21no—
67C2×D4×D61—21no—
68C2×D4×D61—21no—
69C2×D4×D61—21no—
70C2×D4×D61—24no—
71C23×Dic61C2×C411yescharacteristic
72C22×C4×D61—24no—
73C22×C4×D61—24no—
74C22×C4×D61C2×C411yescharacteristic
75C22×C4×D61C2×C412yes—
76C22×C4×D61C2×C412yes—
77C22×C4×D61D411yescharacteristic
78C22×C4×D61D411yescharacteristic
79C22×C4×D61D411yescharacteristic
80C22×C4×D61D411yescharacteristic
81C22×C4×D61D412yes—
82C22×C4×D61D412yes—
83C22×C4×D61C2312yes—
84#14519762—22no—
85#14519762—22no—
86#14519762—22no—
87#14519762—22no—
88#14519761—21no—
89#14519761—21no—
90#14519761—22no—
91#14519760—21no—
92#14519760—21no—
93#14519760—22no—
94#14519759—22no—
95#14519759—22no—
96#14519759—22no—
97#14519759—22no—
98#14519758—21no—
99#14519758—21no—
100#14519758—22no—
101C2×C4⋊Dic61C2×C412yescomplemented
102C2×#11758196C2×C412yescomplemented
103C2×#11758196C2×C412yescomplemented
104C4⋊C4×D61—22no—
105C4⋊C4×D61—22no—
106C4⋊C4×D61—22no—
107C4⋊C4×D61—22no—
108C2×C22⋊Dic61C2×C411yescharacteristic
109C2×C22⋊Dic61C2×C412yescomplemented
110C2×#11758198C2×C412yescomplemented
111C2×#11758198C2×C412yescomplemented
112C2×#11758198C2312yes—
113C22⋊C4×D61—21no—
114C22⋊C4×D61—21no—
115C22⋊C4×D61—21no—
116C22⋊C4×D61—21no—
117C22⋊C4×D61—22no—
118C22⋊C4×D61—22no—
119C22⋊C4×D61—22no—
120C22⋊C4×D61—22no—
121C22×D4×C61C2×C411yescharacteristic
122C23×C4×C61C2×C411yescharacteristic
123#123×C61—21no—
124#123×C61—21no—
125#123×C61—22no—
126C2×C4⋊C4×C61C2×C412yescomplemented
127C2×C22⋊C4×C61C2×C411yescharacteristic
128C2×C22⋊C4×C61C2×C412yescomplemented
129C24×C61C22×C411yescharacteristic
130C24×C61C22×C411yescharacteristic
131C23×D61—21no—
132C23×D61—21no—
133C23×D61—24no—
134C23×D61—44no—
135C23×D61—44no—
136C23×D61C22×C411yescharacteristic
137C23×D61C22×C411yescharacteristic
138C23×D61C2×D411yescharacteristic
139C23×D61C2×D411yescharacteristic
140C23×D61C2×D411yescharacteristic
141C23×D61C2×D411yescharacteristic
142C23×D61C2×D414yes—
143C23×D61#4114yes—
144C23×D61C2411yescharacteristic
145C22×#6923—28no—
146C22×#6923—24no—
147C22×#6923—24no—
148C22×#6923—48no—
149C22×#6923—48no—
150C22×#6923—44no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—24no—
154C22×C4×C61—24no—
155C22×C4×C61C22⋊C411yescharacteristic
156C22×C4×C61C22⋊C411yescharacteristic
157C22×C4×C61C22⋊C412yes—
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C22×C412yes—
160C22×C4×C61C22×C412yes—
161C2×C22⋊D61—21no—
162C2×C22⋊D61—21no—
163C2×C22⋊D61—24no—
164C2×C22⋊D61—22no—
165C2×C22⋊D61—21no—
166C2×C22⋊D61—21no—
167C2×C22⋊D61—22no—
168C22×Dic61—24no—
169C22×Dic61C22⋊C411yescharacteristic
170C22×Dic61C22⋊C411yescharacteristic
171C22×Dic61C22⋊C412yes—
172C22×Dic61C22×C411yescharacteristic
173C22×Dic61C22×C412yes—
174C22×Dic61C22×C412yes—
175D4×D61—42no—
176D4×D61—42no—
177D4×D61—44no—
178D4×D61—44no—
179D4×D61—42no—
180D4×D61—42no—
181C2×D244—22no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—22no—
185C2×C4×D61—28no—
186C2×C4×D61—22no—
187C2×C4×D61—22no—
188C2×C4×D61—24no—
189C2×C4×D61—28no—
190C2×C4×D61—24no—
191C2×C4×D61—24no—
192C2×C4×D61—22no—
193C2×C4×D61—22no—
194C2×C4×D61—24no—
195C2×C4×D61—24no—
196C2×C4×D61—24no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—22no—
200C2×C4×D61—22no—
201C2×C4×D61—24no—
202C2×C4×D61—44no—
203C2×C4×D61C22⋊C412yes—
204C2×C4×D61C22⋊C412yes—
205C2×C4×D61C22⋊C412yes—
206C2×C4×D61C22⋊C412yes—
207C2×C4×D61C2×D412yes—
208C2×C4×D61C2×D412yes—
209C2×C4×D61C2×D412yes—
210C2×C4×D61C2×D412yes—
211C22⋊#6923—28no—
212C22⋊#6923—24no—
213C22⋊#6923—24no—
214C22⋊#6923—24no—
215C22⋊#6923—44no—
216C22⋊#6923C2×D418yes—
217C4⋊#6923—216no—
218C4×#6923—216no—
219C4⋊C4×C61—22no—
220C4⋊C4×C61—22no—
221C22⋊C4×C61—21no—
222C22⋊C4×C61—21no—
223C22⋊C4×C61—22no—
224C22⋊C4×C61—22no—
225C22⋊Dic61—21no—
226C22⋊Dic61—21no—
227C22⋊Dic61—22no—
228C22⋊Dic61—22no—
229#11758198—22no—
230#11758198—22no—
231#11758198—22no—
232#11758198—22no—
233#11758198—22no—
234#11758198—22no—
235C4⋊Dic61—22no—
236C4⋊Dic61—22no—
237#11758196—22no—
238#11758196—22no—
239#11758196—22no—
240#11758196—22no—
241C23×C61—21no—
242C23×C61—22no—
243C23×C61—42no—
244C23×C61—42no—
245C23×C61C2×C22⋊C411yescharacteristic
246C23×C61C2×C22⋊C411yescharacteristic
247C23×C61C4×D414yes—
248C23×C61C23×C411yescharacteristic
249C22×D61—24no—
250C22×D61—24no—
251C22×D61—24no—
252C22×D61—21no—
253C22×D61—22no—
254C22×D61—48no—
255C22×D61—48no—
256C22×D61—42no—
257C22×D61—42no—
258C22×D61—42no—
259C22×D61—44no—
260C22×D61—42no—
261C22×D61—42no—
262C22×D61—44no—
263C22×D61—42no—
264C22×D61—88no—
265C22×D61C2×C22⋊C411yescharacteristic
266C22×D61C2×C22⋊C411yescharacteristic
267C22×D61C4×D414yes—
268C22×D61#12012yes—
269C22×D61#12012yes—
270C22×D61#12114yes—
271C22×D61#12114yes—
272C22×D61#12312yes—
273C22×D61#12312yes—
274C22×D61C22×D411yescharacteristic
275C22×D61C22×D411yescharacteristic
276C22×D61C22×D412yes—
277C22×D61C2×#4112yes—
278C2×#6923—28no—
279C2×#6923—48no—
280C2×#6923—416no—
281C2×#6923—48no—
282C2×#6923—44no—
283C2×#6923—88no—
284D4×C61—42no—
285D4×C61—42no—
286C2×C4×C61—24no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—24no—
290C2×C4×C61—21no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—42no—
294C2×C4×C61C2×C22⋊C412yes—
295C2×C4×C61C2×C22⋊C412yes—
296C22⋊D61—42no—
297C22⋊D61—42no—
298C22⋊D61—41no—
299C22⋊D61—42no—
300C22⋊D61—41no—
301C2×Dic61—24no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—24no—
305C2×Dic61—21no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—42no—
309C2×Dic61C2×C22⋊C412yes—
310C2×Dic61C2×C22⋊C412yes—
311D244—41no—
312D244—42no—
313D244—41no—
314C4×D61—22no—
315C4×D61—22no—
316C4×D61—24no—
317C4×D61—24no—
318C4×D61—22no—
319C4×D61—22no—
320C4×D61—24no—
321C4×D61—24no—
322C4×D61—24no—
323C4×D61—24no—
324C4×D61—44no—
325C4×D61—42no—
326C4×D61—42no—
327C4×D61—44no—
328C2×#1899—611nomaximal, Sylow
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—44no—
333C22×C61—42no—
334C22×C61—41no—
335C22×C61—82no—
336C22×C61#38612yes—
337C22×C61#38612yes—
338C22×C61C22×C22⋊C411yescharacteristic
339C22×C61C2×C4×D412yes—
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—22no—
343C2×D61—24no—
344C2×D61—28no—
345C2×D61—28no—
346C2×D61—24no—
347C2×D61—42no—
348C2×D61—44no—
349C2×D61—42no—
350C2×D61—42no—
351C2×D61—42no—
352C2×D61—42no—
353C2×D61—41no—
354C2×D61—84no—
355C2×D61—84no—
356C2×D61—82no—
357C2×D61#38612yes—
358C2×D61#38612yes—
359C2×D61#41014yes—
360C2×D61C2×#12011yescharacteristic
361C2×D61C2×#12112yes—
362C2×D61C2×#12311yescharacteristic
363#6923—48no—
364#6923—84no—
365C4×C61—22no—
366C4×C61—22no—
367C4×C61—42no—
368C4×C61—41no—
369Dic61—22no—
370Dic61—22no—
371Dic61—42no—
372Dic61—41no—
373C22×#123—611no—
374C22×#117—611no—
375C22×#99—612no—
376C2×#381—611no—
377#1899—614no—
378#1899—614no—
379C2×#342—612no—
380C2×C61—22no—
381C2×C61—22no—
382C2×C61—22no—
383C2×C61—81no—
384C2×C61C2×#38611yescharacteristic
385C2×C61C2×#41012yes—
386D61—21no—
387D61—22no—
388D61—22no—
389D61—21no—
390D61—81no—
391D61#189914yescomplemented
392C23×D4—611no—
393C24×C4—611no—
394C2×#123—611no—
395C2×#123—611no—
396C2×#123—612no—
397C2×#123—611no—
398C2×#123—612no—
399C2×#123—1221no—
400C2×#123—1222no—
401C2×#123—1222no—
402C2×#123—1221no—
403C2×#123—1221no—
404C2×#123—1221no—
405C2×#123#692311yescharacteristic, complemented
406C2×#117—614no—
407C2×#117—1228no—
408C2×#117—1222no—
409C22×C4⋊C4—612no—
410C22×C4⋊C4—1221no—
411C22×C22⋊C4—612no—
412C22×C22⋊C4—611no—
413C22×C22⋊C4—612no—
414C22×C22⋊C4—612no—
415C22×C42—1221no—
416C2×#99—614no—
417C2×#99—614no—
418C2×#99—1228no—
419#381—614no—
420#381—1221no—
421#381—1221no—
422C2×#95—1222no—
423#342—618no—
424C61C2×#189911yescharacteristic, complemented, Sylow
425C25—611no—
426C25—611no—
427C22×D4—611no—
428C22×D4—611no—
429C22×D4—611no—
430C22×D4—1221no—
431C22×D4—1221no—
432C22×D4—1221no—
433C22×D4—1221no—
434C22×D4—1224no—
435C22×D4—1224no—
436C22×D4C2×#692311yescharacteristic
437C23×C4—611no—
438C23×C4—611no—
439C23×C4—612no—
440C23×C4—612no—
441C23×C4—611no—
442C23×C4—611no—
443C23×C4—611no—
444C23×C4—612no—
445C23×C4—612no—
446C23×C4—611no—
447C23×C4—612no—
448C23×C4—1224no—
449C23×C4—1224no—
450C23×C4—1222no—
451C23×C4—1222no—
452C23×C4C2×#692311yescharacteristic
453#123—21no—
454#123—22no—
455#123—21no—
456#123—1222no—
457#123—1222no—
458#123—1222no—
459#123—1222no—
460#123—1221no—
461#123—1222no—
462#123—1221no—
463#123—1222no—
464#123—1222no—
465#123—1222no—
466#123—1222no—
467#123—1221no—
468#123—1222no—
469#123—1221no—
470#123—1221no—
471#123—1222no—
472#123—1221no—
473#117—12216no—
474#117—12216no—
475C2×C4⋊C4—612no—
476C2×C4⋊C4—612no—
477C2×C4⋊C4—612no—
478C2×C4⋊C4—1222no—
479C2×C4⋊C4—1222no—
480C2×C4⋊C4—1222no—
481C2×C4⋊C4—1222no—
482C2×C4⋊C4—1224no—
483C2×C4⋊C4—1228no—
484C2×C4⋊C4C2×#692312yescomplemented
485C2×C22⋊C4—614no—
486C2×C22⋊C4—618no—
487C2×C22⋊C4—611no—
488C2×C22⋊C4—612no—
489C2×C22⋊C4—612no—
490C2×C22⋊C4—612no—
491C2×C22⋊C4—612no—
492C2×C22⋊C4—614no—
493C2×C22⋊C4—1222no—
494C2×C22⋊C4—1222no—
495C2×C22⋊C4—1222no—
496C2×C22⋊C4—1222no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1222no—
502C2×C22⋊C4—1224no—
503C2×C22⋊C4—1224no—
504C2×C22⋊C4—1224no—
505C2×C22⋊C4—1222no—
506C2×C22⋊C4C2×#692311yescharacteristic
507C2×C22⋊C4C2×#692312yescomplemented
508C2×C42—1224no—
509C2×C42—1228no—
510#99—1228no—
511#99—1228no—
512#95—1224no—
513#95—1224no—
514C24—611no—
515C24—611no—
516C24—611no—
517C24—611no—
518C24—611no—
519C24—614no—
520C24—614no—
521C24—611no—
522C24—611no—
523C24—1224no—
524C24—1221no—
525C24—1221no—
526C24—2444no—
527C24—2444no—
528C24C22×#692311yescharacteristic
529C24C22×#692311yescharacteristic
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—24no—
533C2×D4—1222no—
534C2×D4—1221no—
535C2×D4—1221no—
536C2×D4—1222no—
537C2×D4—1222no—
538C2×D4—1221no—
539C2×D4—1221no—
540C2×D4—1222no—
541C2×D4—1221no—
542C2×D4—1221no—
543C2×D4—1224no—
544C2×D4—2442no—
545C2×D4—2444no—
546C2×D4—2442no—
547C2×D4—2442no—
548C2×D4—2444no—
549C2×D4—2442no—
550C22×C4—24no—
551C22×C4—611no—
552C22×C4—612no—
553C22×C4—611no—
554C22×C4—612no—
555C22×C4—612no—
556C22×C4—612no—
557C22×C4—612no—
558C22×C4—612no—
559C22×C4—612no—
560C22×C4—612no—
561C22×C4—612no—
562C22×C4—612no—
563C22×C4—611no—
564C22×C4—612no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4—1224no—
568C22×C4—1224no—
569C22×C4—1228no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1224no—
573C22×C4—1224no—
574C22×C4—1224no—
575C22×C4—1228no—
576C22×C4—1224no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—1224no—
582C22×C4—1224no—
583C22×C4—1228no—
584C22×C4—1224no—
585C22×C4—1224no—
586C22×C4—2444no—
587C22×C4—2444no—
588C22×C4—2448no—
589C22×C4—2448no—
590C22×C4C22⋊#692311yescharacteristic
591C22×C4C22⋊#692312yes—
592C22×C4C22⋊#692311yescharacteristic
593C22×C4C22×#692311yescharacteristic
594C22×C4C22×#692312yes—
595C22×C4C22×#692312yes—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—1222no—
599C4⋊C4—1222no—
600C4⋊C4—1222no—
601C4⋊C4—1222no—
602C4⋊C4—12216no—
603C4⋊C4—1222no—
604C4⋊C4—1222no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—618no—
610C22⋊C4—1222no—
611C22⋊C4—1222no—
612C22⋊C4—1222no—
613C22⋊C4—1222no—
614C22⋊C4—1222no—
615C22⋊C4—1222no—
616C22⋊C4—1228no—
617C22⋊C4—1224no—
618C22⋊C4—1221no—
619C22⋊C4—1221no—
620C22⋊C4—1222no—
621C22⋊C4—1222no—
622C22⋊C4—1224no—
623C22⋊C4—1224no—
624C22⋊C4—2444no—
625C42—12216no—
626C23—21no—
627C23—22no—
628C23—42no—
629C23—42no—
630C23—611no—
631C23—612no—
632C23—614no—
633C23—612no—
634C23—611no—
635C23—611no—
636C23—611no—
637C23—614no—
638C23—612no—
639C23—614no—
640C23—612no—
641C23—612no—
642C23—612no—
643C23—1224no—
644C23—1224no—
645C23—1224no—
646C23—1222no—
647C23—1221no—
648C23—4888no—
649C23—2442no—
650C23—2442no—
651C23—2442no—
652C23—2442no—
653C23—2442no—
654C23—2442no—
655C23—2444no—
656C23—2448no—
657C23—2448no—
658C23—2444no—
659C23C2×C22⋊#692311yescharacteristic
660C23C2×C22⋊#692311yescharacteristic
661C23D4×#692314yes—
662C23C23×#692311yescharacteristic
663D4—42no—
664D4—42no—
665D4—2441no—
666D4—2442no—
667D4—2441no—
668D4—2441no—
669D4—2442no—
670D4—2441no—
671D4—2442no—
672D4—2442no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—612no—
682C2×C4—612no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1224no—
686C2×C4—1224no—
687C2×C4—1224no—
688C2×C4—1224no—
689C2×C4—1224no—
690C2×C4—1224no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1224no—
696C2×C4—1224no—
697C2×C4—1228no—
698C2×C4—1222no—
699C2×C4—1221no—
700C2×C4—1222no—
701C2×C4—4888no—
702C2×C4—2442no—
703C2×C4—2442no—
704C2×C4—2444no—
705C2×C4—2444no—
706C2×C4—2444no—
707C2×C4—2448no—
708C2×C4—24416no—
709C2×C4—2448no—
710C2×C4—2442no—
711C2×C4C2×C22⋊#692312yes—
712C2×C4C2×C22⋊#692312yes—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—42no—
718C22—41no—
719C22—82no—
720C22—614no—
721C22—612no—
722C22—611no—
723C22—612no—
724C22—612no—
725C22—611no—
726C22—1228no—
727C22—1224no—
728C22—1228no—
729C22—1224no—
730C22—1222no—
731C22—1222no—
732C22—1222no—
733C22—4882no—
734C22—4884no—
735C22—4884no—
736C22—2442no—
737C22—2442no—
738C22—2444no—
739C22—2442no—
740C22—2442no—
741C22—2442no—
742C22—2441no—
743C22#1684071012yes—
744C22#1684071012yes—
745C22C22×C22⋊#692311yescharacteristic
746C22C2×D4×#692312yes—
747C4—22no—
748C4—22no—
749C4—42no—
750C4—41no—
751C4—1222no—
752C4—1222no—
753C4—4884no—
754C4—2448no—
755C4—2442no—
756C4—2441no—
757C2—22no—
758C2—22no—
759C2—22no—
760C2—81no—
761C2—614no—
762C2—1222no—
763C2—1221no—
764C2—1222no—
765C2—1221no—
766C2—4881no—
767C2C2×#1684071011yescharacteristic
768C2D61⋊#41012yes—
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#123×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×D61C22
cosocleC23×D61C24
hypercenterC2×#123#6923
hypocenterC61C2×#1899
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C22×#14519856C2semidirect
3. C2×#16840705C2semidirect
4. #21461843C2semidirect
5. #21461842C2semidirect
6. #21461516C2semidirect
10. C2×#14519856C22semidirect
20. #16840705C22semidirect
22. #16840640C22semidirect
26. C2×#14519761C4semidirect
27. C2×#14519760C4semidirect
29. C2×#14519758C4semidirect
36. C2×C4⋊C4×D61C4semidirect
37. C2×C22⋊C4×D61C4semidirect
39. C2×#123×C61C4semidirect
101. C2×C4⋊Dic61C2×C4semidirect
102. C2×#11758196C2×C4semidirect
103. C2×#11758196C2×C4semidirect
109. C2×C22⋊Dic61C2×C4semidirect
110. C2×#11758198C2×C4semidirect
111. C2×#11758198C2×C4semidirect
126. C2×C4⋊C4×C61C2×C4semidirect
128. C2×C22⋊C4×C61C2×C4semidirect
391. D61#1899semidirect
405. C2×#123#6923semidirect
424. C61C2×#1899semidirect
484. C2×C4⋊C4C2×#6923semidirect
507. C2×C22⋊C4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C22×#145198562
C2×D61⋊#992
C2×#168407052
#214618432
#214618422
#214615162
C2×#123×D612
C2×#189961