Finite Group Databasebeta

← D61⋊#1799 #30614960

Subgroups — D61⋊#1799 #30614960

Order 15616.

2066 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊#99C212yesmaximal
2C2×#16840704C212yesmaximal, complemented
3#21461682C212yesmaximal, complemented
4#21461681C212yesmaximal, complemented
5#21461680C212yesmaximal, complemented
6#21461679C212yesmaximal, complemented
7#21461516C212yesmaximal, complemented
8C2×C4×D4×D61C211yesmaximal, characteristic
9C22×C4⋊#6923—22no—
10C22×C22⋊#6923C2214yes—
11C2×#14519836C2214yes—
12D61⋊#99—28no—
13C2×#14519835C2214yes—
14#16840704—22no—
15#16840704—22no—
16#16840704C2214yescomplemented
17#16840704C2214yescomplemented
18C2×(C2×#6923)⋊C4—22no—
19#16840640C2214yescomplemented
20#16840640C2214yescomplemented
21C22×D4×D61C2211yescharacteristic
22C23×C4×D61C411yescharacteristic, complemented
23C23×C4×D61C2211yescharacteristic
24C2×C4×D244C2211yescharacteristic
25C2×D4×Dic61C411yescharacteristic, complemented
26C2×#14519739C2211yescharacteristic
27C2×C4×C22⋊D61C411yescharacteristic, complemented
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×#14519737C411yescharacteristic, complemented
30C2×#14519737C2211yescharacteristic
31C4×D4×D61—22no—
32C4×D4×D61—22no—
33C4×D4×D61—22no—
34C4×D4×D61—22no—
35C2×C4⋊C4×D61C411yescharacteristic, complemented
36C2×C22⋊C4×D61C411yescharacteristic, complemented
37C2×C22⋊C4×D61C2211yescharacteristic
38C2×C42×D61C411yescharacteristic, complemented
39C2×C4×D4×C61C411yescharacteristic, complemented
40C23×#6923—24no—
41C2×C4⋊#6923—24no—
42C2×C4⋊#6923—24no—
43C2×C4⋊#6923—48no—
44C2×C22⋊#6923—28no—
45C2×C22⋊#6923—28no—
46C2×C22⋊#6923—24no—
47C2×C22⋊#6923C2318yes—
48#14519836—28no—
49#14519835—28no—
50(C2×#6923)⋊C4—24no—
51(C2×#6923)⋊C4—24no—
52C24×D61C2×C411yescharacteristic
53C24×D61C2311yescharacteristic
54C22×D244C2311yescharacteristic
55C22×C22⋊D61C2×C411yescharacteristic
56C22×C22⋊D61C2311yescharacteristic
57C2×D4×D61—22no—
58C2×D4×D61—22no—
59C2×D4×D61—24no—
60C2×D4×D61D414yes—
61C2×D4×D61Q814yes—
62C23×Dic61C2×C411yescharacteristic
63C23×Dic61C2×C411yescharacteristic, complemented
64C22×C4×D61—21no—
65C22×C4×D61—21no—
66C22×C4×D61—21no—
67C22×C4×D61—21no—
68C22×C4×D61—44no—
69C22×C4×D61—44no—
70C22×C4×D61C2×C411yescharacteristic
71C22×C4×D61C2×C411yescharacteristic
72C22×C4×D61C2×C411yescharacteristic
73C22×C4×D61C2×C411yescharacteristic
74C22×C4×D61C2×C411yescharacteristic
75C22×C4×D61C2×C411yescharacteristic, complemented
76C22×C4×D61C2×C411yescharacteristic, complemented
77C22×C4×D61D412yes—
78C22×C4×D61D412yes—
79C22×C4×D61D412yes—
80C22×C4×D61D412yes—
81C22×C4×D61C2311yescharacteristic
82C22×C4×D61C2311yescharacteristic
83C4×D244—22no—
84C4×D244—22no—
85D4×Dic61—22no—
86D4×Dic61—22no—
87#14519739—22no—
88#14519739—22no—
89C4×C22⋊D61—22no—
90C4×C22⋊D61—22no—
91C4×C22⋊D61—22no—
92C4×C22⋊D61—22no—
93#14519737—22no—
94#14519737—22no—
95#14519737—22no—
96#14519737—22no—
97C2×C4⋊Dic61C2×C411yescharacteristic, complemented
98C2×#11758196C2×C411yescharacteristic, complemented
99C2×#11758196C2×C411yescharacteristic, complemented
100C4⋊C4×D61—22no—
101C4⋊C4×D61—22no—
102C2×C22⋊Dic61C2×C411yescharacteristic
103C2×C22⋊Dic61C2×C411yescharacteristic, complemented
104C2×#11758198C2×C411yescharacteristic, complemented
105C2×#11758198C2×C411yescharacteristic, complemented
106C2×#11758198C2311yescharacteristic
107C2×#11758198C2311yescharacteristic
108C22⋊C4×D61—22no—
109C22⋊C4×D61—22no—
110C22⋊C4×D61—22no—
111C22⋊C4×D61—22no—
112C2×C4×Dic61C2×C411yescharacteristic, complemented
113C2×C4×Dic61C2×C411yescharacteristic, complemented
114C2×C4×Dic61C2×C411yescharacteristic, complemented
115C42×D61—21no—
116C42×D61—21no—
117C42×D61—21no—
118C42×D61—21no—
119C22×D4×C61C2×C411yescharacteristic
120C23×C4×C61C2×C411yescharacteristic
121C23×C4×C61C2×C411yescharacteristic, complemented
122C4×D4×C61—22no—
123C4×D4×C61—22no—
124C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
125C2×C22⋊C4×C61C2×C411yescharacteristic
126C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
127C2×C42×C61C2×C411yescharacteristic, complemented
128C24×C61C22×C411yescharacteristic
129C24×C61C22×C411yescharacteristic
130C23×D61—21no—
131C23×D61—21no—
132C23×D61—22no—
133C23×D61—42no—
134C23×D61—42no—
135C23×D61—42no—
136C23×D61—42no—
137C23×D61C4⋊C414yescomplemented
138C23×D61C22×C411yescharacteristic
139C23×D61C22×C411yescharacteristic
140C23×D61C2×D412yes—
141C23×D61C2×D412yes—
142C23×D61C2×D412yes—
143C23×D61C2×Q812yes—
144C23×D61#4114yes—
145C23×D61C2411yescharacteristic
146C22×#6923—28no—
147C22×#6923—48no—
148C22×#6923—48no—
149C22×#6923—48no—
150C2×D4×C61—22no—
151C2×D4×C61—22no—
152C2×D4×C61C4⋊C414yescomplemented
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—42no—
156C22×C4×C61—42no—
157C22×C4×C61C22⋊C412yes—
158C22×C4×C61C22⋊C412yes—
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C2×C22⋊D61—22no—
165C2×C22⋊D61—22no—
166C2×C22⋊D61—22no—
167C2×C22⋊D61—22no—
168C2×C22⋊D61C4⋊C414yescomplemented
169C2×C22⋊D61C2×D412yes—
170C2×C22⋊D61C2×Q812yes—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—42no—
174C22×Dic61—42no—
175C22×Dic61C22⋊C412yes—
176C22×Dic61C22⋊C412yes—
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C22×Dic61C22×C411yescharacteristic
180C22×Dic61C22×C411yescharacteristic
181C22×Dic61C22×C411yescharacteristic
182D4×D61—28no—
183D4×D61—28no—
184D4×D61—28no—
185D4×D61—28no—
186C2×D244—22no—
187C2×D244—22no—
188C2×D244C2×D412yes—
189C2×D244C2×Q812yes—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—22no—
193C2×C4×D61—24no—
194C2×C4×D61—28no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—44no—
204C2×C4×D61—42no—
205C2×C4×D61—44no—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×C4×D61—44no—
209C2×C4×D61—44no—
210C2×C4×D61—44no—
211C2×C4×D61—44no—
212C2×C4×D61—44no—
213C2×C4×D61—42no—
214C2×C4×D61—42no—
215C2×C4×D61—42no—
216C2×C4×D61—42no—
217C2×C4×D61C22⋊C411yescharacteristic
218C2×C4×D61C22⋊C411yescharacteristic
219C2×C4×D61C22⋊C411yescharacteristic
220C2×C4×D61C22⋊C412yes—
221C2×C4×D61C22⋊C412yes—
222C2×C4×D61C22⋊C411yescharacteristic
223C2×C4×D61C4⋊C414yescomplemented
224C2×C4×D61C2×D412yes—
225C2×C4×D61C2×D412yes—
226C2×C4×D61C2×D412yes—
227C2×C4×D61C2×D412yes—
228C22⋊#6923—28no—
229C22⋊#6923—28no—
230C22⋊#6923—48no—
231C4⋊#6923—48no—
232C4⋊#6923—48no—
233C4⋊C4×C61—22no—
234C22⋊C4×C61—22no—
235C22⋊C4×C61—22no—
236C42×C61—21no—
237C42×C61—21no—
238C22⋊Dic61—22no—
239C22⋊Dic61—22no—
240#11758198—22no—
241#11758198—22no—
242#11758198—22no—
243#11758198—22no—
244C4⋊Dic61—22no—
245#11758196—22no—
246#11758196—22no—
247C4×Dic61—21no—
248C4×Dic61—21no—
249C4×Dic61—21no—
250C4×Dic61—21no—
251C4×Dic61—21no—
252C4×Dic61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61C2×C22⋊C412yes—
260C23×C61C2×C4⋊C412yes—
261C23×C61C2×C4⋊C412yescomplemented
262C23×C61#11712yes—
263C23×C61C23×C411yescharacteristic
264C22×D61—22no—
265C22×D61—24no—
266C22×D61—22no—
267C22×D61—24no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—24no—
271C22×D61—24no—
272C22×D61—44no—
273C22×D61—44no—
274C22×D61—48no—
275C22×D61—42no—
276C22×D61—41no—
277C22×D61—42no—
278C22×D61—41no—
279C22×D61—42no—
280C22×D61—42no—
281C22×D61—48no—
282C22×D61—48no—
283C22×D61—42no—
284C22×D61—42no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61C2×C22⋊C411yescharacteristic
288C22×D61C2×C22⋊C411yescharacteristic
289C22×D61C2×C4⋊C412yes—
290C22×D61C2×C4⋊C412yescomplemented
291C22×D61#11712yes—
292C22×D61#12114yes—
293C22×D61#12114yes—
294C22×D61C22⋊Q814yes—
295C22×D61C22⋊Q814yes—
296C22×D61C22×D412yes—
297C22×D61C22×D411yescharacteristic
298C22×D61C22×Q811yescharacteristic
299C22×D61C2×#4112yes—
300C2×#6923—48no—
301C2×#6923—48no—
302C2×#6923—48no—
303C2×#6923—816no—
304D4×C61—28no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—22no—
308C2×C4×C61—24no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—42no—
312C2×C4×C61—41no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61C2×C22⋊C411yescharacteristic
318C2×C4×C61C2×C22⋊C412yes—
319C2×C4×C61C2×C22⋊C411yescharacteristic
320C2×C4×C61C2×C4⋊C412yescomplemented
321C22⋊D61—28no—
322C22⋊D61—24no—
323C22⋊D61—24no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—22no—
327C2×Dic61—24no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—42no—
331C2×Dic61—41no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61C2×C22⋊C411yescharacteristic
337C2×Dic61C2×C22⋊C412yes—
338C2×Dic61C2×C22⋊C411yescharacteristic
339C2×Dic61C2×C4⋊C412yescomplemented
340D244—24no—
341D244—24no—
342C4×D61—24no—
343C4×D61—24no—
344C4×D61—22no—
345C4×D61—24no—
346C4×D61—24no—
347C4×D61—22no—
348C4×D61—24no—
349C4×D61—22no—
350C4×D61—42no—
351C4×D61—42no—
352C4×D61—42no—
353C4×D61—42no—
354C4×D61—42no—
355C4×D61—42no—
356C4×D61—42no—
357C4×D61—42no—
358C4×D61—42no—
359C4×D61—42no—
360C4×D61—42no—
361C4×D61#9914yescomplemented
362C2×#1799—611nomaximal, Sylow
363C22×C61—21no—
364C22×C61—22no—
365C22×C61—21no—
366C22×C61—22no—
367C22×C61—22no—
368C22×C61—42no—
369C22×C61—42no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61#38014yes—
375C22×C61C22×C22⋊C411yescharacteristic
376C22×C61C22×C4⋊C411yescharacteristic
377C22×C61C2×#11711yescharacteristic
378C2×D61—21no—
379C2×D61—22no—
380C2×D61—21no—
381C2×D61—22no—
382C2×D61—28no—
383C2×D61—24no—
384C2×D61—24no—
385C2×D61—28no—
386C2×D61—22no—
387C2×D61—44no—
388C2×D61—44no—
389C2×D61—41no—
390C2×D61—41no—
391C2×D61—42no—
392C2×D61—48no—
393C2×D61—42no—
394C2×D61—41no—
395C2×D61—41no—
396C2×D61—48no—
397C2×D61—42no—
398C2×D61#38012yes—
399C2×D61#38012yes—
400C2×D61C2×#9912yes—
401C2×D61#41012yes—
402C2×D61C2×#12112yes—
403C2×D61C2×C22⋊Q812yes—
404#6923—88no—
405C4×C61—21no—
406C4×C61—22no—
407C4×C61—22no—
408C4×C61—41no—
409C4×C61—41no—
410C4×C61C2×#9912yescomplemented
411Dic61—21no—
412Dic61—22no—
413Dic61—22no—
414Dic61—41no—
415Dic61—41no—
416Dic61C2×#9912yescomplemented
417C22×C4×D4—611no—
418C22×#99—612no—
419C2×#380—612no—
420#1799—612no—
421#1799—612no—
422#1799—612no—
423#1799—612no—
424C2×#342—612no—
425C2×C61—21no—
426C2×C61—21no—
427C2×C61—24no—
428C2×C61—42no—
429C2×C61C2×#38011yescharacteristic
430C2×C61C22×#9911yescharacteristic
431C2×C61C2×#41011yescharacteristic
432D61—22no—
433D61—22no—
434D61—22no—
435D61—42no—
436D61#179914yescomplemented
437C23×D4—611no—
438C24×C4—611no—
439C24×C4—611no—
440C2×C4×D4—611no—
441C2×C4×D4—611no—
442C2×C4×D4—611no—
443C2×C4×D4—611no—
444C2×C4×D4—611no—
445C2×C4×D4—611no—
446C2×C4×D4—611no—
447C2×C4×D4—1222no—
448C2×C4×D4—1222no—
449C2×C4×D4—1222no—
450C2×C4×D4—1222no—
451C2×C4×D4#692311yescharacteristic, complemented
452C22×C4⋊C4—611no—
453C22×C4⋊C4—1222no—
454C22×C22⋊C4—611no—
455C22×C22⋊C4—611no—
456C22×C22⋊C4—614no—
457C22×C42—611no—
458C2×#99—614no—
459C2×#99—614no—
460C2×#99—1228no—
461#380—614no—
462#380—614no—
463#380—1222no—
464#380—1222no—
465C2×#95—1222no—
466#342—614no—
467#342—614no—
468C61C2×#179911yescharacteristic, complemented, Sylow
469C25—611no—
470C25—611no—
471C22×D4—611no—
472C22×D4—611no—
473C22×D4—614no—
474C22×D4—614no—
475C22×D4—611no—
476C22×D4—1222no—
477C22×D4—1222no—
478C22×D4—1224no—
479C22×D4C2×#692311yescharacteristic
480C23×C4—611no—
481C23×C4—612no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—612no—
485C23×C4—612no—
486C23×C4—612no—
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—611no—
491C23×C4—611no—
492C23×C4—611no—
493C23×C4—611no—
494C23×C4—611no—
495C23×C4—1221no—
496C23×C4—1221no—
497C23×C4—1221no—
498C23×C4—1221no—
499C23×C4—1224no—
500C23×C4—2444no—
501C23×C4—2444no—
502C23×C4C2×#692311yescharacteristic
503C23×C4C2×#692311yescharacteristic, complemented
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—1222no—
507C4×D4—1222no—
508C4×D4—1222no—
509C4×D4—1222no—
510C4×D4—1222no—
511C4×D4—1222no—
512C4×D4—1222no—
513C4×D4—1222no—
514C4×D4—1222no—
515C4×D4—1222no—
516C4×D4—1222no—
517C4×D4—1222no—
518C4×D4—1222no—
519C4×D4—1222no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—1222no—
524C2×C4⋊C4—1222no—
525C2×C4⋊C4—1224no—
526C2×C4⋊C4—1224no—
527C2×C4⋊C4—2448no—
528C2×C4⋊C4C2×#692311yescharacteristic, complemented
529C2×C22⋊C4—611no—
530C2×C22⋊C4—611no—
531C2×C22⋊C4—611no—
532C2×C22⋊C4—611no—
533C2×C22⋊C4—611no—
534C2×C22⋊C4—611no—
535C2×C22⋊C4—618no—
536C2×C22⋊C4—1222no—
537C2×C22⋊C4—1222no—
538C2×C22⋊C4—1222no—
539C2×C22⋊C4—1222no—
540C2×C22⋊C4—1228no—
541C2×C22⋊C4—1228no—
542C2×C22⋊C4—1224no—
543C2×C22⋊C4C2×#692311yescharacteristic
544C2×C22⋊C4C2×#692311yescharacteristic, complemented
545C2×C42—611no—
546C2×C42—611no—
547C2×C42—611no—
548C2×C42—1221no—
549C2×C42—1221no—
550C2×C42—1221no—
551C2×C42—1221no—
552C2×C42C2×#692311yescharacteristic, complemented
553#99—1228no—
554#99—1228no—
555#95—1224no—
556#95—1224no—
557C24—612no—
558C24—611no—
559C24—612no—
560C24—612no—
561C24—612no—
562C24—614no—
563C24—611no—
564C24—614no—
565C24—611no—
566C24—1221no—
567C24—1221no—
568C24—1222no—
569C24—2442no—
570C24—2442no—
571C24—2442no—
572C24—2442no—
573C24C22×#692311yescharacteristic
574C24C22×#692311yescharacteristic
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—614no—
578C2×D4—612no—
579C2×D4—612no—
580C2×D4—612no—
581C2×D4—612no—
582C2×D4—1222no—
583C2×D4—1222no—
584C2×D4—1228no—
585C2×D4—1228no—
586C2×D4—1228no—
587C2×D4—1228no—
588C2×D4—1222no—
589C2×D4—1222no—
590C2×D4—1222no—
591C2×D4—1222no—
592C2×D4C4⋊#692314yescomplemented
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—611no—
598C22×C4—612no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—612no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—612no—
607C22×C4—612no—
608C22×C4—612no—
609C22×C4—614no—
610C22×C4—612no—
611C22×C4—612no—
612C22×C4—612no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—1228no—
616C22×C4—1224no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1222no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1228no—
631C22×C4—2442no—
632C22×C4—2444no—
633C22×C4—2442no—
634C22×C4—2444no—
635C22×C4—2444no—
636C22×C4—2442no—
637C22×C4—2444no—
638C22×C4—2442no—
639C22×C4—2444no—
640C22×C4—2444no—
641C22×C4—2444no—
642C22×C4—2442no—
643C22×C4—2442no—
644C22×C4—2442no—
645C22×C4—2442no—
646C22×C4—2442no—
647C22×C4—2448no—
648C22×C4—2448no—
649C22×C4—2448no—
650C22×C4C22⋊#692312yes—
651C22×C4C22⋊#692312yes—
652C22×C4C22×#692311yescharacteristic
653C22×C4C22×#692311yescharacteristic
654C22×C4C22×#692311yescharacteristic
655C22×C4C22×#692311yescharacteristic
656C22×C4C22×#692311yescharacteristic
657C4⋊C4—22no—
658C4⋊C4—1222no—
659C4⋊C4—1222no—
660C4⋊C4—1222no—
661C4⋊C4—2448no—
662C4⋊C4—2448no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—1222no—
666C22⋊C4—1222no—
667C22⋊C4—1222no—
668C22⋊C4—1222no—
669C22⋊C4—1222no—
670C22⋊C4—1222no—
671C22⋊C4—1228no—
672C22⋊C4—1228no—
673C22⋊C4—2448no—
674C42—21no—
675C42—21no—
676C42—1221no—
677C42—1221no—
678C42—1221no—
679C42—1221no—
680C42—1221no—
681C42—1221no—
682C23—21no—
683C23—21no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—611no—
689C23—614no—
690C23—614no—
691C23—611no—
692C23—612no—
693C23—612no—
694C23—612no—
695C23—614no—
696C23—614no—
697C23—611no—
698C23—611no—
699C23—612no—
700C23—612no—
701C23—1224no—
702C23—1222no—
703C23—1224no—
704C23—1222no—
705C23—1224no—
706C23—1224no—
707C23—1221no—
708C23—1221no—
709C23—2441no—
710C23—2442no—
711C23—2441no—
712C23—2442no—
713C23—2441no—
714C23—2441no—
715C23—2442no—
716C23—2442no—
717C23—2444no—
718C23—2444no—
719C23—2448no—
720C23—2448no—
721C23—2442no—
722C23—2448no—
723C23—2442no—
724C23C2×C22⋊#692312yes—
725C23C2×C4⋊#692312yes—
726C23C2×C4⋊#692312yescomplemented
727C23#1451985612yes—
728C23C23×#692311yescharacteristic
729D4—28no—
730D4—1224no—
731D4—1224no—
732D4—1224no—
733D4—1224no—
734D4—1228no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—611no—
748C2×C4—614no—
749C2×C4—611no—
750C2×C4—612no—
751C2×C4—612no—
752C2×C4—1224no—
753C2×C4—1222no—
754C2×C4—1224no—
755C2×C4—1222no—
756C2×C4—1224no—
757C2×C4—1224no—
758C2×C4—1224no—
759C2×C4—1222no—
760C2×C4—1221no—
761C2×C4—1221no—
762C2×C4—1224no—
763C2×C4—1222no—
764C2×C4—1221no—
765C2×C4—1221no—
766C2×C4—48816no—
767C2×C4—2442no—
768C2×C4—2442no—
769C2×C4—2442no—
770C2×C4—2442no—
771C2×C4—2442no—
772C2×C4—2442no—
773C2×C4—2442no—
774C2×C4—2442no—
775C2×C4—2442no—
776C2×C4—2442no—
777C2×C4—2442no—
778C2×C4—2441no—
779C2×C4—2442no—
780C2×C4—2442no—
781C2×C4—2448no—
782C2×C4—2448no—
783C2×C4—2448no—
784C2×C4—2442no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4C2×C22⋊#692311yescharacteristic
788C2×C4C2×C22⋊#692312yes—
789C2×C4C2×C22⋊#692311yescharacteristic
790C2×C4C2×C4⋊#692312yescomplemented
791C22—21no—
792C22—22no—
793C22—21no—
794C22—22no—
795C22—22no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—41no—
801C22—41no—
802C22—612no—
803C22—612no—
804C22—612no—
805C22—612no—
806C22—612no—
807C22—612no—
808C22—1228no—
809C22—1228no—
810C22—1224no—
811C22—1224no—
812C22—1222no—
813C22—1221no—
814C22—1222no—
815C22—1221no—
816C22—1222no—
817C22—2441no—
818C22—2441no—
819C22—2442no—
820C22—2444no—
821C22—2444no—
822C22—2442no—
823C22—2442no—
824C22—2448no—
825C22—2448no—
826C22—2441no—
827C22—2441no—
828C22#1684070414yes—
829C22C22×C22⋊#692311yescharacteristic
830C22C22×C4⋊#692311yescharacteristic
831C22C2×#1451985611yescharacteristic
832C4—21no—
833C4—22no—
834C4—22no—
835C4—41no—
836C4—41no—
837C4—612no—
838C4—1222no—
839C4—1221no—
840C4—1222no—
841C4—4888no—
842C4—2441no—
843C4—2441no—
844C4D61⋊#9912yescomplemented
845C2—21no—
846C2—21no—
847C2—24no—
848C2—42no—
849C2—614no—
850C2—1222no—
851C2—1222no—
852C2—1222no—
853C2—2442no—
854C2C2×#1684070411yescharacteristic
855C2C2×D61⋊#9911yescharacteristic
856C2D61⋊#41011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C4×D4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×D61C22
cosocleC23×D61C24
hypercenterC2×C4×D4#6923
hypocenterC61C2×#1799
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#16840704C2semidirect
3. #21461682C2semidirect
4. #21461681C2semidirect
5. #21461680C2semidirect
6. #21461679C2semidirect
7. #21461516C2semidirect
16. #16840704C22semidirect
17. #16840704C22semidirect
19. #16840640C22semidirect
20. #16840640C22semidirect
22. C23×C4×D61C4semidirect
25. C2×D4×Dic61C4semidirect
27. C2×C4×C22⋊D61C4semidirect
29. C2×#14519737C4semidirect
35. C2×C4⋊C4×D61C4semidirect
36. C2×C22⋊C4×D61C4semidirect
38. C2×C42×D61C4semidirect
39. C2×C4×D4×C61C4semidirect
63. C23×Dic61C2×C4semidirect
75. C22×C4×D61C2×C4semidirect
76. C22×C4×D61C2×C4semidirect
97. C2×C4⋊Dic61C2×C4semidirect
98. C2×#11758196C2×C4semidirect
99. C2×#11758196C2×C4semidirect
103. C2×C22⋊Dic61C2×C4semidirect
104. C2×#11758198C2×C4semidirect
105. C2×#11758198C2×C4semidirect
112. C2×C4×Dic61C2×C4semidirect
113. C2×C4×Dic61C2×C4semidirect
114. C2×C4×Dic61C2×C4semidirect
121. C23×C4×C61C2×C4semidirect
124. C2×C4⋊C4×C61C2×C4semidirect
126. C2×C22⋊C4×C61C2×C4semidirect
127. C2×C42×C61C2×C4semidirect
137. C23×D61C4⋊C4semidirect
152. C2×D4×C61C4⋊C4semidirect
168. C2×C22⋊D61C4⋊C4semidirect
223. C2×C4×D61C4⋊C4semidirect
261. C23×C61C2×C4⋊C4semidirect
290. C22×D61C2×C4⋊C4semidirect
320. C2×C4×C61C2×C4⋊C4semidirect
339. C2×Dic61C2×C4⋊C4semidirect
361. C4×D61#99semidirect
410. C4×C61C2×#99semidirect
416. Dic61C2×#99semidirect
436. D61#1799semidirect
451. C2×C4×D4#6923semidirect
468. C61C2×#1799semidirect
503. C23×C4C2×#6923semidirect
528. C2×C4⋊C4C2×#6923semidirect
544. C2×C22⋊C4C2×#6923semidirect
552. C2×C42C2×#6923semidirect
592. C2×D4C4⋊#6923semidirect
726. C23C2×C4⋊#6923semidirect
790. C2×C4C2×C4⋊#6923semidirect
844. C4D61⋊#99semidirect

Maximal subgroups

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

subgroupindex
C2×D61⋊#992
C2×#168407042
#214616822
#214616812
#214616802
#214616792
#214615162
C2×C4×D4×D612
C2×#179961