Finite Group Databasebeta

← #29679943

Subgroups — #29679943

Order 15616.

1866 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D61C211yesmaximal, characteristic
2#21448202C211yesmaximal, characteristic, complemented
3#21445891C212yesmaximal, complemented
4#21445804C214yesmaximal, complemented
5#21445733C212yesmaximal
6C4×#14519691C214yesmaximal, complemented
7C61×#2280C211yesmaximal, characteristic, complemented
8C23×C22⋊D61C2211yescharacteristic
9C23×C4×D61C411yescharacteristic, complemented
10C2×C4×C22⋊D61—21no—
11C2×C4×C22⋊D61—21no—
12C2×C4×C22⋊D61—21no—
13C2×C4×C22⋊D61—21no—
14C2×C4×C22⋊D61—21no—
15C2×C4×C22⋊D61—21no—
16C2×C4×C22⋊D61—21no—
17C2×C4×C22⋊D61—21no—
18C2×C4×C22⋊D61C412yescomplemented
19C2×C4×C22⋊D61C412yescomplemented
20C2×C4×C22⋊D61C2212yes—
21C2×C4×C22⋊D61C2212yes—
22C2×#14519736—21no—
23C22×#11758196C411yescharacteristic, complemented
24C22×C22⋊Dic61C2211yescharacteristic
25C22×#11758198C411yescharacteristic, complemented
26C22×C4×Dic61C411yescharacteristic, complemented
27C2×#14519691C2218yes—
28#16839625—21no—
29#16839622—21no—
30#16839622C2212yescomplemented
31#16839618C2212yes—
32C4×C22⋊Dic61—21no—
33C4×C22⋊Dic61C2212yescomplemented
34#16839528C2218yescomplemented
35C24×C4×C61C2211yescharacteristic
36C2×#117×C61—21no—
37C61×#381—21no—
38C61×#380—21no—
39C61×#380C2212yescomplemented
40C61×#379C2212yes—
41C4×C22⋊C4×C61—21no—
42C4×C22⋊C4×C61C2212yescomplemented
43C24×D61C2×C411yescharacteristic
44C22×C22⋊D61—21no—
45C22×C22⋊D61—21no—
46C22×C22⋊D61—21no—
47C22×C22⋊D61—21no—
48C22×C22⋊D61—28no—
49C22×C22⋊D61C2×C412yes—
50C22×C22⋊D61C2312yes—
51C23×Dic61C2×C411yescharacteristic
52C23×Dic61C2×C411yescharacteristic
53C23×Dic61C2×C411yescharacteristic
54C22×C4×D61—21no—
55C22×C4×D61—21no—
56C22×C4×D61—21no—
57C22×C4×D61—21no—
58C22×C4×D61—44no—
59C22×C4×D61C2×C412yes—
60C22×C4×D61C2×C412yes—
61C4×C22⋊D61—22no—
62C4×C22⋊D61—22no—
63C4×C22⋊D61—22no—
64C4×C22⋊D61—22no—
65C4×C22⋊D61—22no—
66C4×C22⋊D61—22no—
67C4×C22⋊D61—22no—
68C4×C22⋊D61—22no—
69C4×C22⋊D61—22no—
70C4×C22⋊D61—22no—
71C4×C22⋊D61—22no—
72C4×C22⋊D61—22no—
73C4×C22⋊D61—22no—
74C4×C22⋊D61—22no—
75C4×C22⋊D61—22no—
76C4×C22⋊D61—22no—
77#14519736—44no—
78C2×C4⋊Dic61—22no—
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196C2×C412yes—
84C2×#11758196C2×C412yes—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—22no—
90C2×C22⋊Dic61—22no—
91C2×C22⋊Dic61C2×C412yes—
92C2×C22⋊Dic61C2314yes—
93C2×C22⋊Dic61C2312yes—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198C2×C412yes—
99C2×#11758198C2×C412yes—
100C2×C4×Dic61—21no—
101C2×C4×Dic61—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61—22no—
105C2×C4×Dic61C2×C412yes—
106C2×C4×Dic61C2×C412yes—
107#14519691—216no—
108#14519684—22no—
109#14519684—22no—
110C25×C61C2311yescharacteristic
111C23×C4×C61—44no—
112C23×C4×C61C2×C411yescharacteristic
113C23×C4×C61C2×C411yescharacteristic
114C23×C4×C61C2×C411yescharacteristic
115C23×C4×C61C2×C411yescharacteristic
116C23×C4×C61D411yescharacteristic
117C23×C4×C61D411yescharacteristic
118C23×C4×C61D411yescharacteristic
119C23×C4×C61D411yescharacteristic
120C23×C4×C61D411yescharacteristic
121C23×C4×C61D411yescharacteristic
122C23×C4×C61D411yescharacteristic
123C23×C4×C61D411yescharacteristic
124C23×C4×C61C2311yescharacteristic
125C23×C4×C61C2311yescharacteristic
126#117×C61—44no—
127C2×C4⋊C4×C61—22no—
128C2×C22⋊C4×C61—22no—
129C2×C22⋊C4×C61—22no—
130C2×C22⋊C4×C61C2314yes—
131C2×C42×C61—22no—
132#95×C61—22no—
133#95×C61—22no—
134C24×C61—24no—
135C24×C61—42no—
136C24×C61—42no—
137C24×C61C22×C411yescharacteristic
138C24×C61C22×C411yescharacteristic
139C24×C61C2×D411yescharacteristic
140C24×C61C2×D411yescharacteristic
141C24×C61C2×D411yescharacteristic
142C24×C61C2×D411yescharacteristic
143C24×C61C2411yescharacteristic
144C23×D61—21no—
145C23×D61—21no—
146C23×D61—24no—
147C23×D61—42no—
148C23×D61—42no—
149C23×D61C22×C412yes—
150C22×C4×C61—24no—
151C22×C4×C61—24no—
152C22×C4×C61—24no—
153C22×C4×C61—24no—
154C22×C4×C61—42no—
155C22×C4×C61—42no—
156C22×C4×C61—42no—
157C22×C4×C61—42no—
158C22×C4×C61—42no—
159C22×C4×C61—42no—
160C22×C4×C61—42no—
161C22×C4×C61—42no—
162C22×C4×C61—42no—
163C22×C4×C61—42no—
164C22×C4×C61—42no—
165C22×C4×C61C22⋊C411yescharacteristic
166C22×C4×C61C22⋊C411yescharacteristic
167C22×C4×C61C22⋊C411yescharacteristic
168C22×C4×C61C22⋊C411yescharacteristic
169C22×C4×C61C22⋊C411yescharacteristic
170C22×C4×C61C22⋊C411yescharacteristic
171C22×C4×C61C22⋊C411yescharacteristic
172C22×C4×C61C22⋊C411yescharacteristic
173C22×C4×C61C22⋊C411yescharacteristic
174C22×C4×C61C22⋊C411yescharacteristic
175C22×C4×C61C22⋊C411yescharacteristic
176C22×C4×C61C22⋊C411yescharacteristic
177C22×C4×C61C22⋊C411yescharacteristic
178C22×C4×C61C22⋊C411yescharacteristic
179C22×C4×C61C22⋊C411yescharacteristic
180C22×C4×C61C22⋊C411yescharacteristic
181C22×C4×C61C22×C411yescharacteristic
182C22×C4×C61C22×C411yescharacteristic
183C22×C4×C61C22×C411yescharacteristic
184C22×C4×C61C22×C411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C2×C22⋊D61—28no—
194C2×C22⋊D61—28no—
195C2×C22⋊D61—28no—
196C2×C22⋊D61—28no—
197C2×C22⋊D61—22no—
198C2×C22⋊D61—22no—
199C2×C22⋊D61—22no—
200C2×C22⋊D61—22no—
201C2×C22⋊D61—24no—
202C2×C22⋊D61—24no—
203C2×C22⋊D61—24no—
204C2×C22⋊D61#4118yes—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—24no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—24no—
213C22×Dic61—42no—
214C22×Dic61—42no—
215C22×Dic61C22×C412yes—
216C22×Dic61C22×C412yes—
217C22×Dic61C22×C412yes—
218C2×C4×D61—22no—
219C2×C4×D61—22no—
220C2×C4×D61—22no—
221C2×C4×D61—22no—
222C2×C4×D61—44no—
223C2×C4×D61—44no—
224C2×C4×D61—44no—
225C2×C4×D61—44no—
226C2×C4×D61—44no—
227C2×C4×D61—44no—
228C4⋊C4×C61—44no—
229C22⋊C4×C61—28no—
230C22⋊C4×C61—44no—
231C22⋊C4×C61—44no—
232C42×C61—44no—
233C22⋊Dic61—22no—
234C22⋊Dic61—22no—
235C22⋊Dic61—22no—
236C22⋊Dic61—22no—
237C22⋊Dic61—28no—
238C22⋊Dic61—44no—
239C22⋊Dic61—44no—
240#11758198—22no—
241#11758198—22no—
242#11758198—22no—
243#11758198—22no—
244C4⋊Dic61—44no—
245#11758196—22no—
246#11758196—22no—
247#11758196—22no—
248#11758196—22no—
249C4×Dic61—22no—
250C4×Dic61—22no—
251C4×Dic61—22no—
252C4×Dic61—22no—
253C4×Dic61—44no—
254C23×C61—22no—
255C23×C61—22no—
256C23×C61—22no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61—22no—
260C23×C61—22no—
261C23×C61—22no—
262C23×C61—22no—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61—22no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61—416no—
275C23×C61C2×C22⋊C411yescharacteristic
276C23×C61C2×C22⋊C411yescharacteristic
277C23×C61C2×C22⋊C411yescharacteristic
278C23×C61C2×C22⋊C411yescharacteristic
279C23×C61C23×C411yescharacteristic
280C23×C61C22×D411yescharacteristic
281C23×C61C22×D411yescharacteristic
282C23×C61C2×#4114yes—
283C22×D61—24no—
284C22×D61—24no—
285C22×D61—22no—
286C22×D61—22no—
287C22×D61—42no—
288C22×D61—416no—
289C22×D61—42no—
290C22×D61—42no—
291C22×D61—42no—
292C22×D61—42no—
293C22×D61—42no—
294C22×D61#11714yescomplemented
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—44no—
323C2×C4×C61—44no—
324C2×C4×C61—44no—
325C2×C4×C61#9914yescomplemented
326C2×C4×C61C2×C22⋊C411yescharacteristic
327C2×C4×C61C2×C22⋊C411yescharacteristic
328C2×C4×C61C2×C22⋊C411yescharacteristic
329C2×C4×C61C2×C22⋊C411yescharacteristic
330C2×C4×C61C2×C22⋊C411yescharacteristic
331C2×C4×C61C2×C22⋊C411yescharacteristic
332C2×C4×C61C2×C22⋊C411yescharacteristic
333C2×C4×C61C2×C22⋊C411yescharacteristic
334C22⋊D61—28no—
335C22⋊D61—28no—
336C22⋊D61—28no—
337C22⋊D61—28no—
338C2×Dic61—24no—
339C2×Dic61—24no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—42no—
345C2×Dic61—42no—
346C2×Dic61—42no—
347C2×Dic61—42no—
348C2×Dic61—42no—
349C2×Dic61—42no—
350C2×Dic61—44no—
351C2×Dic61—44no—
352C2×Dic61—44no—
353C2×Dic61#11714yescomplemented
354C4×D61—44no—
355C4×D61—44no—
356C4×D61—44no—
357C4×D61—44no—
358#20722—611nomaximal, Sylow
359C22×C61—28no—
360C22×C61—21no—
361C22×C61—21no—
362C22×C61—21no—
363C22×C61—21no—
364C22×C61—21no—
365C22×C61—21no—
366C22×C61—21no—
367C22×C61—21no—
368C22×C61—21no—
369C22×C61—21no—
370C22×C61—21no—
371C22×C61—21no—
372C22×C61—21no—
373C22×C61—21no—
374C22×C61—21no—
375C22×C61—21no—
376C22×C61—44no—
377C22×C61—44no—
378C22×C61—44no—
379C22×C61—44no—
380C22×C61—44no—
381C22×C61—44no—
382C22×C61C2×#9912yes—
383C22×C61#41012yes—
384C22×C61C22×C22⋊C411yescharacteristic
385C22×C61C2×#11712yes—
386C22×C61#52512yes—
387C22×C61#52512yes—
388C2×D61—24no—
389C2×D61—44no—
390C2×D61—48no—
391C2×D61—48no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—44no—
395C4×C61—21no—
396C4×C61—21no—
397C4×C61—21no—
398C4×C61—21no—
399C4×C61—21no—
400C4×C61—21no—
401C4×C61—84no—
402C4×C61C2×#9912yes—
403C4×C61C2×#9912yes—
404Dic61—24no—
405Dic61—42no—
406Dic61—42no—
407Dic61—84no—
408C22×C4×D4—611no—
409#2280—611no—
410#2280D6111yescharacteristic, complemented
411#1819—612no—
412#1799—614no—
413#1781—612no—
414C4×#99—614no—
415C2×C61—22no—
416C2×C61—22no—
417C2×C61—22no—
418C2×C61—22no—
419C2×C61—22no—
420C2×C61—41no—
421C2×C61—41no—
422C2×C61#228011yescharacteristic
423C2×C61C22×#9911yescharacteristic
424C2×C61C2×#41011yescharacteristic
425D61—44no—
426C23×D4—611no—
427C24×C4—611no—
428C24×C4C2×D6111yescharacteristic
429C2×C4×D4—612no—
430C2×C4×D4—612no—
431C2×C4×D4—612no—
432C2×C4×D4—612no—
433C2×C4×D4—1221no—
434C2×C4×D4—1221no—
435C2×C4×D4—1221no—
436C2×C4×D4—1221no—
437C2×C4×D4—1221no—
438C2×C4×D4—1221no—
439C2×C4×D4—1221no—
440C2×C4×D4—1221no—
441C2×#117—21no—
442C2×#117—1221no—
443C22×C4⋊C4—611no—
444C22×C22⋊C4—611no—
445C22×C22⋊C4—611no—
446C22×C42—611no—
447C2×#99—618no—
448#381—21no—
449#381—1221no—
450#380—21no—
451#380—612no—
452#380—1221no—
453#380C2×D6112yescomplemented
454#379—612no—
455#379C2×D6112yes—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—612no—
458C4×C22⋊C4—1221no—
459C4×C22⋊C4C2×D6112yescomplemented
460#342—618no—
461C61#2072211yescharacteristic, complemented, Sylow
462C25—611no—
463C25C22×D6111yescharacteristic
464C22×D4—612no—
465C22×D4—612no—
466C22×D4—1228no—
467C22×D4—1221no—
468C22×D4—1221no—
469C22×D4—1221no—
470C22×D4—1221no—
471C23×C4—44no—
472C23×C4—611no—
473C23×C4—611no—
474C23×C4—611no—
475C23×C4—612no—
476C23×C4—612no—
477C23×C4—1221no—
478C23×C4—1221no—
479C23×C4—1221no—
480C23×C4—1221no—
481C23×C4—2444no—
482C23×C4C4×D6111yescharacteristic
483C23×C4C4×D6111yescharacteristic
484C23×C4C4×D6111yescharacteristic
485C23×C4C4×D6111yescharacteristic
486C23×C4D24411yescharacteristic
487C23×C4D24411yescharacteristic
488C23×C4D24411yescharacteristic
489C23×C4D24411yescharacteristic
490C23×C4C22⋊D6111yescharacteristic
491C23×C4C22⋊D6111yescharacteristic
492C23×C4C22⋊D6111yescharacteristic
493C23×C4C22⋊D6111yescharacteristic
494C23×C4C22×D6111yescharacteristic
495C23×C4C22×D6111yescharacteristic
496C4×D4—1222no—
497C4×D4—1222no—
498C4×D4—1222no—
499C4×D4—1222no—
500C4×D4—1222no—
501C4×D4—1222no—
502C4×D4—1222no—
503C4×D4—1222no—
504C4×D4—1222no—
505C4×D4—1222no—
506C4×D4—1222no—
507C4×D4—1222no—
508C4×D4—1222no—
509C4×D4—1222no—
510C4×D4—1222no—
511C4×D4—1222no—
512#117—44no—
513#117—2444no—
514C2×C4⋊C4—22no—
515C2×C4⋊C4—612no—
516C2×C4⋊C4—612no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1222no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—612no—
525C2×C22⋊C4—612no—
526C2×C22⋊C4—612no—
527C2×C22⋊C4—612no—
528C2×C22⋊C4—614no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1222no—
538C2×C22⋊C4—1222no—
539C2×C22⋊C4C22×D6114yes—
540C2×C42—22no—
541C2×C42—612no—
542C2×C42—612no—
543C2×C42—1221no—
544C2×C42—1221no—
545C2×C42—1221no—
546C2×C42—1221no—
547C2×C42—1222no—
548#99—12216no—
549#95—22no—
550#95—22no—
551#95—1222no—
552#95—1222no—
553C24—24no—
554C24—42no—
555C24—42no—
556C24—612no—
557C24—1224no—
558C24—1221no—
559C24—1221no—
560C24—2442no—
561C24—2442no—
562C24C2×C4×D6111yescharacteristic
563C24C2×C4×D6111yescharacteristic
564C24C2×D24411yescharacteristic
565C24C2×D24411yescharacteristic
566C24C2×C22⋊D6111yescharacteristic
567C24C2×C22⋊D6111yescharacteristic
568C24C23×D6111yescharacteristic
569C2×D4—618no—
570C2×D4—1224no—
571C2×D4—1224no—
572C2×D4—1228no—
573C2×D4—1228no—
574C2×D4—1228no—
575C2×D4—1228no—
576C2×D4—1222no—
577C2×D4—1222no—
578C2×D4—1224no—
579C2×D4—1222no—
580C2×D4—1222no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—612no—
597C22×C4—612no—
598C22×C4—612no—
599C22×C4—1224no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1224no—
611C22×C4—2444no—
612C22×C4—2444no—
613C22×C4—2444no—
614C22×C4—2444no—
615C22×C4—2444no—
616C22×C4—2444no—
617C22×C4—2442no—
618C22×C4—2442no—
619C22×C4#1175819811yescharacteristic
620C22×C4#1175819811yescharacteristic
621C22×C4#1175819811yescharacteristic
622C22×C4#1175819811yescharacteristic
623C22×C4#1175819811yescharacteristic
624C22×C4#1175819811yescharacteristic
625C22×C4#1175819811yescharacteristic
626C22×C4#1175819811yescharacteristic
627C22×C4#1175819811yescharacteristic
628C22×C4#1175819811yescharacteristic
629C22×C4#1175819811yescharacteristic
630C22×C4#1175819811yescharacteristic
631C22×C4#1175819811yescharacteristic
632C22×C4#1175819811yescharacteristic
633C22×C4#1175819811yescharacteristic
634C22×C4#1175819811yescharacteristic
635C22×C4C2×C4×D6111yescharacteristic
636C22×C4C2×C4×D6111yescharacteristic
637C22×C4C2×C4×D6111yescharacteristic
638C22×C4C2×C4×D6111yescharacteristic
639C22×C4C2×D24411yescharacteristic
640C22×C4C2×D24411yescharacteristic
641C22×C4C2×D24411yescharacteristic
642C22×C4C2×D24411yescharacteristic
643C22×C4C2×C22⋊D6111yescharacteristic
644C22×C4C2×C22⋊D6111yescharacteristic
645C22×C4C2×C22⋊D6111yescharacteristic
646C22×C4C2×C22⋊D6111yescharacteristic
647C4⋊C4—44no—
648C4⋊C4—1222no—
649C4⋊C4—1222no—
650C4⋊C4—1222no—
651C4⋊C4—1222no—
652C4⋊C4—2444no—
653C22⋊C4—28no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—1222no—
657C22⋊C4—1222no—
658C22⋊C4—1222no—
659C22⋊C4—1222no—
660C22⋊C4—1222no—
661C22⋊C4—1222no—
662C22⋊C4—1222no—
663C22⋊C4—1222no—
664C22⋊C4—1228no—
665C22⋊C4—2444no—
666C22⋊C4—2444no—
667C42—44no—
668C42—1222no—
669C42—1222no—
670C42—1222no—
671C42—1222no—
672C42—2444no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—416no—
694C23—614no—
695C23—1224no—
696C23—1224no—
697C23—1222no—
698C23—1222no—
699C23—2442no—
700C23—2442no—
701C23—2442no—
702C23—24416no—
703C23—2442no—
704C23—2442no—
705C23—2442no—
706C23C2×#1175819811yescharacteristic
707C23C2×#1175819811yescharacteristic
708C23C2×#1175819811yescharacteristic
709C23C2×#1175819811yescharacteristic
710C23C22×C4×D6111yescharacteristic
711C23C22×C22⋊D6111yescharacteristic
712C23C22×D24411yescharacteristic
713C23#41×D6114yes—
714D4—1228no—
715D4—1228no—
716D4—1228no—
717D4—1228no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—614no—
749C2×C4—1224no—
750C2×C4—1224no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—2444no—
756C2×C4—2444no—
757C2×C4—2444no—
758C2×C4—2444no—
759C2×C4—2444no—
760C2×C4—2442no—
761C2×C4—2442no—
762C2×C4—2442no—
763C2×C4—2442no—
764C2×C4—2444no—
765C2×C4—2444no—
766C2×C4—2442no—
767C2×C4—2442no—
768C2×C4#1451969114yescomplemented
769C2×C4C2×#1175819811yescharacteristic
770C2×C4C2×#1175819811yescharacteristic
771C2×C4C2×#1175819811yescharacteristic
772C2×C4C2×#1175819811yescharacteristic
773C2×C4C2×#1175819811yescharacteristic
774C2×C4C2×#1175819811yescharacteristic
775C2×C4C2×#1175819811yescharacteristic
776C2×C4C2×#1175819811yescharacteristic
777C22—28no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22—1224no—
801C22—2444no—
802C22—2444no—
803C22—2448no—
804C22—2448no—
805C22—2442no—
806C22—2442no—
807C22C2×#1451969112yes—
808C22#1683973512yes—
809C22C22×#1175819811yescharacteristic
810C22#117×D6112yes—
811C22#1684026912yes—
812C22#1684027412yes—
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—84no—
820C4—1224no—
821C4—4884no—
822C4—2442no—
823C4—2442no—
824C4C2×#1451969112yes—
825C4C2×#1451969112yes—
826C2—22no—
827C2—22no—
828C2—22no—
829C2—22no—
830C2—22no—
831C2—41no—
832C2—41no—
833C2—2444no—
834C2#2144819811yescharacteristic
835C2C22×#1451969111yescharacteristic
836C2C2×#1683973511yescharacteristic
subgroupG/H
centerC2×C4C2×#11758198
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#2280C2
socleC22×C61C22×C22⋊C4
prime radicalC23×C22⋊D61C22
cosocleC24×C61C24
hypercenter#2280D61
hypocenterC61#20722
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. #21448202C2semidirect
3. #21445891C2semidirect
4. #21445804C2semidirect
6. C4×#14519691C2semidirect
7. C61×#2280C2semidirect
9. C23×C4×D61C4semidirect
18. C2×C4×C22⋊D61C4semidirect
19. C2×C4×C22⋊D61C4semidirect
23. C22×#11758196C4semidirect
25. C22×#11758198C4semidirect
26. C22×C4×Dic61C4semidirect
30. #16839622C22semidirect
33. C4×C22⋊Dic61C22semidirect
34. #16839528C22semidirect
39. C61×#380C22semidirect
42. C4×C22⋊C4×C61C22semidirect
294. C22×D61#117semidirect
325. C2×C4×C61#99semidirect
353. C2×Dic61#117semidirect
410. #2280D61semidirect
453. #380C2×D61semidirect
459. C4×C22⋊C4C2×D61semidirect
461. C61#20722semidirect
768. C2×C4#14519691semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D612
#214482022
#214458912
#214458042
#214457332
C4×#145196912
C61×#22802
#2072261