Finite Group Databasebeta

← D61×#1520 #29647325

Subgroups — D61×#1520 #29647325

Order 15616.

1522 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D61C211yesmaximal, characteristic
2C2×C22⋊C8×D61C211yesmaximal, characteristic
3#380×D61C211yesmaximal, characteristic
4#21444392C211yesmaximal, characteristic, complemented
5#21444391C211yesmaximal, characteristic, complemented
6#21444390C211yesmaximal, characteristic, complemented
7#21444389C214yesmaximal, complemented
8#328×D61C214yesmaximal, complemented
9C61×#1520C211yesmaximal, characteristic, complemented
10C22×Q8×D61C411yescharacteristic, complemented
11C23×C4×D61C2211yescharacteristic
12C22×C8×D61—21no—
13C2×#14519757C411yescharacteristic, complemented
14C2×#14519756C2211yescharacteristic
15C2×#14519755—21no—
16C2×#14519754—21no—
17C2×#14519753C411yescharacteristic, complemented
18C22⋊Q8×D61—21no—
19C22⋊Q8×D61—21no—
20C22⋊Q8×D61—21no—
21C22⋊Q8×D61—21no—
22C22⋊Q8×D61C412yescomplemented
23C22⋊Q8×D61C412yescomplemented
24C22⋊Q8×D61C2212yes—
25C22⋊Q8×D61C2212yes—
26C2×C4⋊C4×D61—21no—
27C2×C4⋊C4×D61—21no—
28C2×C4⋊C4×D61C411yescharacteristic, complemented
29C2×C22⋊C4×D61—21no—
30C2×C22⋊C4×D61—21no—
31C2×C22⋊#92418C2211yescharacteristic
32C2×#14519689—21no—
33C22⋊C8×D61—21no—
34C22⋊C8×D61—21no—
35C22⋊C8×D61C2212yes—
36C22⋊C8×D61C2212yes—
37#16839622C2211yescharacteristic
38#16839621C2212yes—
39#16839620—21no—
40#16839619—21no—
41#95×D61C2212yes—
42#16839500C2214yescomplemented
43#16839499C2214yescomplemented
44#16839498C2214yescomplemented
45C2×C22⋊Q8×C61C2211yescharacteristic
46C2×C22⋊C8×C61C2211yescharacteristic
47C61×#380C2211yescharacteristic
48C61×#328C2214yescomplemented
49C24×D61D411yescharacteristic
50C22×Dic122—21no—
51C22×Dic122C2×C411yescharacteristic, complemented
52C2×Q8×D61—21no—
53C2×Q8×D61—21no—
54C2×Q8×D61—44no—
55C2×Q8×D61C2×C412yes—
56C2×Q8×D61C2×C412yescomplemented
57C23×Dic61D411yescharacteristic
58C22×C4×D61—21no—
59C22×C4×D61—21no—
60C22×C4×D61—22no—
61C22×C4×D61—44no—
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61C2×C411yescharacteristic
65C22×C4×D61C2×C411yescharacteristic
66C22×C4×D61D411yescharacteristic
67C22×C4×D61D411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61C2311yescharacteristic
73C22×C4×D61C2311yescharacteristic
74C22×#92418—21no—
75C2×C8×D61—22no—
76C2×C8×D61—22no—
77C2×C8×D61—44no—
78#14519757—21no—
79#14519757—21no—
80#14519757C2×C412yes—
81#14519757C2×C412yescomplemented
82#14519756—21no—
83#14519756—21no—
84#14519756C2×C412yescomplemented
85#14519756C2312yes—
86#14519755—22no—
87#14519755—22no—
88#14519755—22no—
89#14519755—22no—
90#14519754—22no—
91#14519754—22no—
92#14519754—22no—
93#14519754—22no—
94#14519753—21no—
95#14519753—21no—
96#14519753C2×C412yes—
97#14519753C2×C412yescomplemented
98C2×C4⋊Dic61—21no—
99C2×C4⋊Dic61—21no—
100C2×C4⋊Dic61C2×C411yescharacteristic, complemented
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758196—22no—
105C4⋊C4×D61—22no—
106C4⋊C4×D61—22no—
107C4⋊C4×D61—21no—
108C4⋊C4×D61—21no—
109C4⋊C4×D61—22no—
110C4⋊C4×D61—22no—
111C4⋊C4×D61—44no—
112C4⋊C4×D61C2×C412yes—
113C4⋊C4×D61C2×C412yescomplemented
114C2×C22⋊Dic61—21no—
115C2×C22⋊Dic61—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—22no—
119C22⋊C4×D61—22no—
120C22⋊C4×D61—22no—
121C22⋊C4×D61—22no—
122C22⋊C4×D61—22no—
123C22⋊C4×D61—44no—
124C22⋊#92418—21no—
125C22⋊#92418C2312yes—
126#14519689—22no—
127#14519689—22no—
128#14519684—22no—
129#14519684C2312yes—
130C22×Q8×C61C2×C411yescharacteristic, complemented
131C23×C4×C61C2311yescharacteristic
132C22×C8×C61—21no—
133C22⋊Q8×C61—21no—
134C22⋊Q8×C61—21no—
135C22⋊Q8×C61C2×C412yescomplemented
136C22⋊Q8×C61C2312yes—
137C2×C4⋊C4×C61—21no—
138C2×C4⋊C4×C61—21no—
139C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C22⋊C8×C61—21no—
143C22⋊C8×C61C2312yes—
144#95×C61C2312yes—
145C24×C61C2×D411yescharacteristic
146C23×D61—42no—
147C23×D61—42no—
148C23×D61C22⋊C411yescharacteristic
149C23×D61C22⋊C411yescharacteristic
150C23×D61C22⋊C411yescharacteristic
151C23×D61C22⋊C411yescharacteristic
152C23×D61SD1614yes—
153C23×D61Q1614yes—
154C23×D61C2×D411yescharacteristic
155C23×D61C2×D411yescharacteristic
156C2×Q8×C61—21no—
157C2×Q8×C61—42no—
158C2×Q8×C61C22×C412yes—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—22no—
162C22×C4×C61—42no—
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2411yescharacteristic
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—22no—
172C22×Dic61—42no—
173C22×Dic61C22⋊C411yescharacteristic
174C22×Dic61C22⋊C411yescharacteristic
175C22×Dic61C22⋊C411yescharacteristic
176C22×Dic61C22⋊C411yescharacteristic
177C22×Dic61C2×D411yescharacteristic
178C22×Dic61C2×D411yescharacteristic
179Q8×D61—44no—
180Q8×D61—44no—
181Q8×D61—44no—
182Q8×D61—44no—
183C2×C4×D61—24no—
184C2×C4×D61—24no—
185C2×C4×D61—24no—
186C2×C4×D61—22no—
187C2×C4×D61—22no—
188C2×C4×D61—22no—
189C2×C4×D61—22no—
190C2×C4×D61—42no—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×C4×D61—42no—
194C2×C4×D61—42no—
195C2×C4×D61—42no—
196C2×C4×D61—42no—
197C2×C4×D61—42no—
198C2×C4×D61—42no—
199C2×C4×D61—44no—
200C2×C4×D61—44no—
201C2×C4×D61—44no—
202C2×C4×D61—44no—
203C2×C4×D61—44no—
204C2×C4×D61C22⋊C411yescharacteristic
205C2×C4×D61C22⋊C411yescharacteristic
206C2×C4×D61C22⋊C411yescharacteristic
207C2×C4×D61C22⋊C411yescharacteristic
208C2×C4×D61C22⋊C411yescharacteristic
209C2×C4×D61C22⋊C411yescharacteristic
210C2×C4×D61C22⋊C411yescharacteristic
211C2×C4×D61C22⋊C411yescharacteristic
212C2×C4×D61C22×C411yescharacteristic
213C2×C4×D61C22×C411yescharacteristic
214C2×C4×D61C22×C411yescharacteristic
215C2×C4×D61C22×C411yescharacteristic
216C2×C4×D61C2×D411yescharacteristic
217C2×C4×D61C2×D411yescharacteristic
218C2×C4×D61C2×D411yescharacteristic
219C2×C4×D61C2×D411yescharacteristic
220C2×Dic122—21no—
221C2×Dic122—22no—
222C2×Dic122—22no—
223C2×Dic122—44no—
224C2×Dic122—42no—
225C2×Dic122C22×C412yes—
226C2×C8×C61—22no—
227C2×C8×C61—42no—
228C4⋊C4×C61—22no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—22no—
231C4⋊C4×C61—42no—
232C4⋊C4×C61C22×C412yes—
233C22⋊C4×C61—22no—
234C22⋊C4×C61—22no—
235C22⋊C4×C61—42no—
236C22⋊Dic61—22no—
237C22⋊Dic61—22no—
238C22⋊Dic61—42no—
239#11758198—22no—
240#11758198—22no—
241#11758198—22no—
242#11758198—22no—
243#11758198—44no—
244C4⋊Dic61—21no—
245C4⋊Dic61—22no—
246C4⋊Dic61—22no—
247C4⋊Dic61—42no—
248C4⋊Dic61C22×C412yes—
249#11758196—22no—
250#11758196—22no—
251#11758196—22no—
252#11758196—22no—
253#11758196—22no—
254#11758196—22no—
255#11758196—44no—
256C2×#92418—22no—
257C2×#92418—42no—
258C8×D61—44no—
259C8×D61—44no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61C2×C22⋊C411yescharacteristic
263C23×C61C2×C22⋊C411yescharacteristic
264C23×C61C2×SD1612yes—
265C23×C61C2×Q1612yes—
266C23×C61C22×D411yescharacteristic
267C22×D61—22no—
268C22×D61—22no—
269C22×D61—22no—
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—48no—
274C22×D61—48no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61#10314yes—
282C22×D61#10314yes—
283C22×D61#10314yes—
284C22×D61#10314yes—
285C22×D61C2×C22⋊C411yescharacteristic
286C22×D61C2×C22⋊C411yescharacteristic
287C22×D61C2×C22⋊C411yescharacteristic
288C22×D61C2×C22⋊C411yescharacteristic
289C22×D61C2×SD1612yes—
290C22×D61C2×SD1612yes—
291C22×D61C2×Q1612yes—
292C22×D61C2×Q1612yes—
293Q8×C61—42no—
294Q8×C61—42no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61C2×C22⋊C411yescharacteristic
309C2×C4×C61C2×C22⋊C411yescharacteristic
310C2×C4×C61C23×C411yescharacteristic
311C2×C4×C61C22×D411yescharacteristic
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—42no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61C2×C22⋊C411yescharacteristic
326C2×Dic61C2×C22⋊C411yescharacteristic
327C2×Dic61C2×C22⋊C411yescharacteristic
328C2×Dic61C2×C22⋊C411yescharacteristic
329C4×D61—22no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—22no—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—22no—
336C4×D61—22no—
337C4×D61—22no—
338C4×D61—41no—
339C4×D61—41no—
340C4×D61—41no—
341C4×D61—41no—
342C4×D61—41no—
343C4×D61—41no—
344C4×D61—44no—
345C4×D61—44no—
346C4×D61—44no—
347C4×D61—44no—
348C4×D61—88no—
349C4×D61#9914yes—
350Dic122—44no—
351Dic122—42no—
352Dic122—44no—
353Dic122—42no—
354C8×C61—42no—
355#92418—42no—
356C2×#1520—611nomaximal, Sylow
357C22×C61—21no—
358C22×C61—21no—
359C22×C61—21no—
360C22×C61—21no—
361C22×C61—21no—
362C22×C61—21no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61C2×#10312yes—
366C22×C61C2×#10312yes—
367C22×C61C22×C22⋊C411yescharacteristic
368C22×C61C22×SD1611yescharacteristic
369C22×C61C22×Q1611yescharacteristic
370C2×D61—21no—
371C2×D61—21no—
372C2×D61—21no—
373C2×D61—21no—
374C2×D61—21no—
375C2×D61—21no—
376C2×D61—24no—
377C2×D61—28no—
378C2×D61—28no—
379C2×D61—24no—
380C2×D61—44no—
381C2×D61—44no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61C2×#9912yes—
385C2×D61C2×#10312yes—
386C2×D61C2×#10312yes—
387C2×D61C2×#10312yes—
388C2×D61C2×#10312yes—
389C2×D61#42112yes—
390C4×C61—21no—
391C4×C61—21no—
392C4×C61—21no—
393C4×C61—42no—
394C4×C61—42no—
395C4×C61—82no—
396C4×C61C2×#9912yes—
397Dic61—21no—
398Dic61—21no—
399Dic61—21no—
400Dic61—42no—
401Dic61—42no—
402Dic61—82no—
403Dic61C2×#9912yes—
404C22×C22⋊Q8—611no—
405C22×C22⋊C8—611no—
406C2×#380—611no—
407#1520—611no—
408#1520—611no—
409#1520—614no—
410#1520—611no—
411#1520D6111yescharacteristic, direct product factor
412C2×#328—614no—
413C2×C61—21no—
414C2×C61—21no—
415C2×C61—22no—
416C2×C61—22no—
417C2×C61C22×#9911yescharacteristic
418C2×C61C22×#10311yescharacteristic
419C2×C61C2×#42111yescharacteristic
420D61—22no—
421D61—22no—
422D61—22no—
423D61#152014yesdirect product factor
424C23×Q8—611no—
425C24×C4—611no—
426C23×C8—1221no—
427C2×C22⋊Q8—611no—
428C2×C22⋊Q8—611no—
429C2×C22⋊Q8—612no—
430C2×C22⋊Q8—612no—
431C2×C22⋊Q8—612no—
432C2×C22⋊Q8—612no—
433C2×C22⋊Q8—611no—
434C2×C22⋊Q8—1221no—
435C2×C22⋊Q8—1221no—
436C2×C22⋊Q8—1221no—
437C2×C22⋊Q8—1221no—
438C2×C22⋊Q8—1221no—
439C2×C22⋊Q8—1221no—
440C2×C22⋊Q8C2×D6111yescharacteristic
441C22×C4⋊C4—611no—
442C22×C4⋊C4—1221no—
443C22×C4⋊C4—1221no—
444C22×C22⋊C4—1221no—
445C22×C22⋊C4—1221no—
446C2×C22⋊C8—611no—
447C2×C22⋊C8—612no—
448C2×C22⋊C8—612no—
449C2×C22⋊C8—1221no—
450C2×C22⋊C8—1221no—
451C2×C22⋊C8—1221no—
452C2×C22⋊C8C2×D6111yescharacteristic
453#380—611no—
454#380—612no—
455#380—1221no—
456#380—1221no—
457#380C2×D6111yescharacteristic
458C2×#95—612no—
459#328—614no—
460#328—614no—
461#328—614no—
462#328C2×D6114yescomplemented
463C61C2×#152011yescharacteristic, complemented, Sylow
464C25—611no—
465C22×Q8—612no—
466C22×Q8—612no—
467C22×Q8—611no—
468C22×Q8—1221no—
469C22×Q8—1221no—
470C22×Q8—1221no—
471C22×Q8—2444no—
472C22×Q8C4×D6111yescharacteristic, complemented
473C23×C4—611no—
474C23×C4—611no—
475C23×C4—611no—
476C23×C4—611no—
477C23×C4—611no—
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—1221no—
487C23×C4—1221no—
488C23×C4—1222no—
489C23×C4—2444no—
490C23×C4C22×D6111yescharacteristic
491C22×C8—21no—
492C22×C8—1222no—
493C22×C8—1222no—
494C22×C8—1221no—
495C22×C8—2444no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—612no—
499C22⋊Q8—612no—
500C22⋊Q8—612no—
501C22⋊Q8—612no—
502C22⋊Q8—612no—
503C22⋊Q8—612no—
504C22⋊Q8—1222no—
505C22⋊Q8—1222no—
506C22⋊Q8—1222no—
507C22⋊Q8—1222no—
508C22⋊Q8—1222no—
509C22⋊Q8—1222no—
510C22⋊Q8—1222no—
511C22⋊Q8—1222no—
512C22⋊Q8—1221no—
513C22⋊Q8—1221no—
514C22⋊Q8—1221no—
515C22⋊Q8—1221no—
516C22⋊Q8—1221no—
517C22⋊Q8—1221no—
518C22⋊Q8C4×D6112yescomplemented
519C22⋊Q8C22×D6112yes—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—612no—
524C2×C4⋊C4—612no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4—1222no—
528C2×C4⋊C4—1222no—
529C2×C4⋊C4—1222no—
530C2×C4⋊C4—1222no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4—1221no—
533C2×C4⋊C4—1221no—
534C2×C4⋊C4—1221no—
535C2×C4⋊C4—1222no—
536C2×C4⋊C4—1221no—
537C2×C4⋊C4—2444no—
538C2×C4⋊C4C4×D6111yescharacteristic, complemented
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—1222no—
542C2×C22⋊C4—1222no—
543C2×C22⋊C4—1222no—
544C2×C22⋊C4—1222no—
545C2×C22⋊C4—1221no—
546C2×C22⋊C4—1221no—
547C2×C22⋊C4—1221no—
548C2×C22⋊C4—1222no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—2444no—
551C22⋊C8—21no—
552C22⋊C8—612no—
553C22⋊C8—1222no—
554C22⋊C8—1222no—
555C22⋊C8—1221no—
556C22⋊C8C22×D6112yes—
557#95—612no—
558#95—1222no—
559#95C22×D6112yes—
560C24—611no—
561C24—611no—
562C24—611no—
563C24—611no—
564C24—611no—
565C24—611no—
566C24—614no—
567C24—614no—
568C24—2442no—
569C24—2442no—
570C24D4×D6111yescharacteristic
571C2×Q8—21no—
572C2×Q8—42no—
573C2×Q8—612no—
574C2×Q8—1222no—
575C2×Q8—1222no—
576C2×Q8—1221no—
577C2×Q8—2442no—
578C2×Q8—2444no—
579C2×Q8—2444no—
580C2×Q8—2444no—
581C2×Q8—2444no—
582C2×Q8—2444no—
583C2×Q8C2×C4×D6112yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—42no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—611no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—1224no—
611C22×C4—1224no—
612C22×C4—1224no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1222no—
620C22×C4—2442no—
621C22×C4—2442no—
622C22×C4—2442no—
623C22×C4—2442no—
624C22×C4—2442no—
625C22×C4—2442no—
626C22×C4—2442no—
627C22×C4—2442no—
628C22×C4—2442no—
629C22×C4—2444no—
630C22×C4—2444no—
631C22×C4—2444no—
632C22×C4—2444no—
633C22×C4—2444no—
634C22×C4—2442no—
635C22×C4C2×C4×D6111yescharacteristic
636C22×C4C2×C4×D6111yescharacteristic
637C22×C4D4×D6111yescharacteristic
638C22×C4D4×D6111yescharacteristic
639C22×C4D4×D6111yescharacteristic
640C22×C4C23×D6111yescharacteristic
641C2×C8—22no—
642C2×C8—42no—
643C2×C8—1222no—
644C2×C8—2444no—
645C2×C8—2444no—
646C2×C8—2442no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—21no—
650C4⋊C4—42no—
651C4⋊C4—612no—
652C4⋊C4—1222no—
653C4⋊C4—1222no—
654C4⋊C4—1222no—
655C4⋊C4—1222no—
656C4⋊C4—1222no—
657C4⋊C4—1222no—
658C4⋊C4—1222no—
659C4⋊C4—1221no—
660C4⋊C4—1222no—
661C4⋊C4—2442no—
662C4⋊C4—2444no—
663C4⋊C4C2×C4×D6112yes—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—42no—
667C22⋊C4—1222no—
668C22⋊C4—1222no—
669C22⋊C4—1222no—
670C22⋊C4—1222no—
671C22⋊C4—1222no—
672C22⋊C4—1222no—
673C22⋊C4—2444no—
674C22⋊C4—2442no—
675C23—41no—
676C23—41no—
677C23—611no—
678C23—611no—
679C23—611no—
680C23—611no—
681C23—614no—
682C23—614no—
683C23—612no—
684C23—612no—
685C23—614no—
686C23—614no—
687C23—612no—
688C23—612no—
689C23—1222no—
690C23—1222no—
691C23—1222no—
692C23—1222no—
693C23—1222no—
694C23—1222no—
695C23—2441no—
696C23—2441no—
697C23—2441no—
698C23—2441no—
699C23—2441no—
700C23—2441no—
701C23—2448no—
702C23—2448no—
703C23C22⋊C4×D6111yescharacteristic
704C23C22⋊C4×D6111yescharacteristic
705C23SD16×D6112yes—
706C23Q16×D6112yes—
707C23C2×D4×D6111yescharacteristic
708Q8—42no—
709Q8—42no—
710Q8—2442no—
711Q8—2444no—
712Q8—2444no—
713Q8—2442no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—611no—
728C2×C4—614no—
729C2×C4—611no—
730C2×C4—611no—
731C2×C4—611no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—4888no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2444no—
754C2×C4—2444no—
755C2×C4—2444no—
756C2×C4—2444no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2442no—
761C2×C4—2442no—
762C2×C4—2442no—
763C2×C4—2442no—
764C2×C4—2442no—
765C2×C4C22⋊C4×D6111yescharacteristic
766C2×C4C22⋊C4×D6111yescharacteristic
767C2×C4C22×C4×D6111yescharacteristic
768C2×C4C2×D4×D6111yescharacteristic
769C8—42no—
770C8—2442no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—42no—
778C22—42no—
779C22—612no—
780C22—612no—
781C22—612no—
782C22—612no—
783C22—612no—
784C22—612no—
785C22—1224no—
786C22—1228no—
787C22—1228no—
788C22—1224no—
789C22—1221no—
790C22—1221no—
791C22—1221no—
792C22—1221no—
793C22—1221no—
794C22—1221no—
795C22—2442no—
796C22—2444no—
797C22—2444no—
798C22—2442no—
799C22#103×D6112yes—
800C22#103×D6112yes—
801C22C2×C22⋊C4×D6111yescharacteristic
802C22C2×SD16×D6111yescharacteristic
803C22C2×Q16×D6111yescharacteristic
804C4—21no—
805C4—21no—
806C4—21no—
807C4—42no—
808C4—42no—
809C4—82no—
810C4—612no—
811C4—1221no—
812C4—1221no—
813C4—1221no—
814C4—4882no—
815C4—2442no—
816C4—2442no—
817C4#99×D6112yes—
818C2—21no—
819C2—22no—
820C2—22no—
821C2—21no—
822C2—614no—
823C2—1222no—
824C2—1222no—
825C2—1222no—
826C2C2×#99×D6111yescharacteristic
827C2C2×#103×D6111yescharacteristic
828C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1520C2
socleC22×C61C22×C22⋊C4
prime radicalC24×D61D4
cosocleC22×C4×C61C24
hypercenter#1520D61
hypocenterC61C2×#1520
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
4. #21444392C2semidirect
5. #21444391C2semidirect
6. #21444390C2semidirect
7. #21444389C2semidirect
8. #328×D61C2semidirect
9. C61×#1520C2semidirect
10. C22×Q8×D61C4semidirect
13. C2×#14519757C4semidirect
17. C2×#14519753C4semidirect
22. C22⋊Q8×D61C4semidirect
23. C22⋊Q8×D61C4semidirect
28. C2×C4⋊C4×D61C4semidirect
42. #16839500C22semidirect
43. #16839499C22semidirect
44. #16839498C22semidirect
48. C61×#328C22semidirect
51. C22×Dic122C2×C4semidirect
56. C2×Q8×D61C2×C4semidirect
81. #14519757C2×C4semidirect
84. #14519756C2×C4semidirect
97. #14519753C2×C4semidirect
100. C2×C4⋊Dic61C2×C4semidirect
113. C4⋊C4×D61C2×C4semidirect
130. C22×Q8×C61C2×C4semidirect
135. C22⋊Q8×C61C2×C4semidirect
139. C2×C4⋊C4×C61C2×C4semidirect
411. #1520D61direct (N × H)
423. D61#1520direct (N × H)
462. #328C2×D61semidirect
463. C61C2×#1520semidirect
472. C22×Q8C4×D61semidirect
518. C22⋊Q8C4×D61semidirect
538. C2×C4⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D612
C2×C22⋊C8×D612
#380×D612
#214443922
#214443912
#214443902
#214443892
#328×D612
C61×#15202
C2×#152061