Finite Group Databasebeta

← #29689267

Subgroups — #29689267

Order 15616.

1882 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519751C211yesmaximal, characteristic
2#21448202C211yesmaximal, characteristic, complemented
3#21446655C214yesmaximal, complemented
4#21446654C214yesmaximal, complemented
5#21445733C214yesmaximal, complemented
6C61×#2280C211yesmaximal, characteristic, complemented
7C23×D244C411yescharacteristic, complemented
8C23×C22⋊D61C2212yes—
9C2×#14519751—21no—
10C2×#14519751—21no—
11C2×#14519751—21no—
12C2×#14519751—21no—
13C2×#14519751—21no—
14C2×#14519751—21no—
15C2×#14519751—21no—
16C2×#14519751—21no—
17C2×#14519751C412yescomplemented
18C2×#14519751C412yescomplemented
19C2×#14519751C2212yes—
20C2×#14519751C2212yes—
21C2×#14519736—21no—
22C22×C4⋊Dic61C411yescharacteristic, complemented
23C22×#11758198C412yescomplemented
24C2×#14519691C22116yescomplemented
25#16839625—21no—
26#16839622—21no—
27#16839622C2212yescomplemented
28#16839618C2212yes—
29C4×C22⋊Dic61—21no—
30C4×C22⋊Dic61C2212yescomplemented
31C24×C4×C61C2211yescharacteristic
32C2×#117×C61—21no—
33C61×#381—21no—
34C61×#380—21no—
35C61×#380C2212yescomplemented
36C61×#379C2212yes—
37C4×C22⋊C4×C61—21no—
38C4×C22⋊C4×C61C2212yescomplemented
39C24×D61C2×C412yes—
40C22×D244—21no—
41C22×D244—21no—
42C22×D244—21no—
43C22×D244—21no—
44C22×D244—44no—
45C22×D244C2×C412yes—
46C22×D244C2×C412yes—
47C22×C22⋊D61—22no—
48C22×C22⋊D61—22no—
49C22×C22⋊D61—22no—
50C22×C22⋊D61—22no—
51C22×C22⋊D61—48no—
52C22×C22⋊D61C2×C414yes—
53C22×C22⋊D61C2314yes—
54C23×Dic61C2×C412yes—
55#14519751—22no—
56#14519751—22no—
57#14519751—22no—
58#14519751—22no—
59#14519751—22no—
60#14519751—22no—
61#14519751—22no—
62#14519751—22no—
63#14519751—22no—
64#14519751—22no—
65#14519751—22no—
66#14519751—22no—
67#14519751—22no—
68#14519751—22no—
69#14519751—22no—
70#14519751—22no—
71#14519736—44no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61—22no—
77C2×C4⋊Dic61C2×C412yes—
78C2×C4⋊Dic61C2×C412yes—
79C2×C22⋊Dic61—22no—
80C2×C22⋊Dic61—22no—
81C2×C22⋊Dic61C2314yes—
82C2×#11758198—22no—
83C2×#11758198—22no—
84C2×#11758198—22no—
85C2×#11758198—22no—
86C2×#11758198C2×C414yes—
87C2×#11758198C2×C414yes—
88C2×C4×Dic61—22no—
89#14519691—416no—
90#14519684—22no—
91#14519684—22no—
92C25×C61C2311yescharacteristic
93C23×C4×C61—44no—
94C23×C4×C61C2×C411yescharacteristic
95C23×C4×C61C2×C411yescharacteristic
96C23×C4×C61C2×C411yescharacteristic
97C23×C4×C61C2×C411yescharacteristic
98C23×C4×C61D411yescharacteristic
99C23×C4×C61D411yescharacteristic
100C23×C4×C61D411yescharacteristic
101C23×C4×C61D411yescharacteristic
102C23×C4×C61D411yescharacteristic
103C23×C4×C61D411yescharacteristic
104C23×C4×C61D411yescharacteristic
105C23×C4×C61D411yescharacteristic
106C23×C4×C61C2311yescharacteristic
107C23×C4×C61C2311yescharacteristic
108#117×C61—44no—
109C2×C4⋊C4×C61—22no—
110C2×C22⋊C4×C61—22no—
111C2×C22⋊C4×C61—22no—
112C2×C22⋊C4×C61C2314yes—
113C2×C42×C61—22no—
114#95×C61—22no—
115#95×C61—22no—
116C24×C61—24no—
117C24×C61—42no—
118C24×C61—42no—
119C24×C61C22×C411yescharacteristic
120C24×C61C22×C411yescharacteristic
121C24×C61C2×D411yescharacteristic
122C24×C61C2×D411yescharacteristic
123C24×C61C2×D411yescharacteristic
124C24×C61C2×D411yescharacteristic
125C24×C61C2411yescharacteristic
126C23×D61—22no—
127C23×D61—22no—
128C23×D61—44no—
129C23×D61—44no—
130C23×D61—44no—
131C23×D61C22×C414yes—
132C22×C4×C61—24no—
133C22×C4×C61—24no—
134C22×C4×C61—24no—
135C22×C4×C61—24no—
136C22×C4×C61—42no—
137C22×C4×C61—42no—
138C22×C4×C61—42no—
139C22×C4×C61—42no—
140C22×C4×C61—42no—
141C22×C4×C61—42no—
142C22×C4×C61—42no—
143C22×C4×C61—42no—
144C22×C4×C61—42no—
145C22×C4×C61—42no—
146C22×C4×C61—42no—
147C22×C4×C61C22⋊C411yescharacteristic
148C22×C4×C61C22⋊C411yescharacteristic
149C22×C4×C61C22⋊C411yescharacteristic
150C22×C4×C61C22⋊C411yescharacteristic
151C22×C4×C61C22⋊C411yescharacteristic
152C22×C4×C61C22⋊C411yescharacteristic
153C22×C4×C61C22⋊C411yescharacteristic
154C22×C4×C61C22⋊C411yescharacteristic
155C22×C4×C61C22⋊C411yescharacteristic
156C22×C4×C61C22⋊C411yescharacteristic
157C22×C4×C61C22⋊C411yescharacteristic
158C22×C4×C61C22⋊C411yescharacteristic
159C22×C4×C61C22⋊C411yescharacteristic
160C22×C4×C61C22⋊C411yescharacteristic
161C22×C4×C61C22⋊C411yescharacteristic
162C22×C4×C61C22⋊C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C22×C411yescharacteristic
166C22×C4×C61C22×C411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C2×C22⋊D61—24no—
176C2×C22⋊D61—24no—
177C2×C22⋊D61—24no—
178C2×C22⋊D61—24no—
179C2×C22⋊D61—216no—
180C2×C22⋊D61—48no—
181C2×C22⋊D61—48no—
182C2×C22⋊D61—48no—
183C2×C22⋊D61—48no—
184C2×C22⋊D61—48no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—24no—
188C22×Dic61—44no—
189C22×Dic61C22×C414yes—
190C2×D244—22no—
191C2×D244—22no—
192C2×D244—22no—
193C2×D244—22no—
194C2×D244—44no—
195C2×D244—44no—
196C2×D244—44no—
197C2×D244—44no—
198C2×D244—44no—
199C2×D244—44no—
200C4⋊C4×C61—44no—
201C22⋊C4×C61—28no—
202C22⋊C4×C61—44no—
203C22⋊C4×C61—44no—
204C42×C61—44no—
205C22⋊Dic61—28no—
206C22⋊Dic61—44no—
207C22⋊Dic61—44no—
208#11758198—24no—
209#11758198—24no—
210#11758198—24no—
211#11758198—24no—
212C4⋊Dic61—22no—
213C4⋊Dic61—22no—
214C4⋊Dic61—22no—
215C4⋊Dic61—22no—
216C4⋊Dic61—44no—
217C4×Dic61—44no—
218C23×C61—22no—
219C23×C61—22no—
220C23×C61—22no—
221C23×C61—22no—
222C23×C61—22no—
223C23×C61—22no—
224C23×C61—22no—
225C23×C61—22no—
226C23×C61—22no—
227C23×C61—22no—
228C23×C61—22no—
229C23×C61—22no—
230C23×C61—41no—
231C23×C61—41no—
232C23×C61—41no—
233C23×C61—41no—
234C23×C61—41no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61—416no—
239C23×C61C2×C22⋊C411yescharacteristic
240C23×C61C2×C22⋊C411yescharacteristic
241C23×C61C2×C22⋊C411yescharacteristic
242C23×C61C2×C22⋊C411yescharacteristic
243C23×C61C23×C411yescharacteristic
244C23×C61C22×D411yescharacteristic
245C23×C61C22×D411yescharacteristic
246C23×C61H(5,𝔽2)14yes—
247C22×D61—24no—
248C22×D61—28no—
249C22×D61—44no—
250C22×D61—44no—
251C22×D61—44no—
252C22×D61—44no—
253C22×D61—44no—
254C22×D61—44no—
255C22×D61—44no—
256C22×D61—44no—
257C22×D61—816no—
258C2×C4×C61—22no—
259C2×C4×C61—22no—
260C2×C4×C61—22no—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—44no—
286C2×C4×C61—44no—
287C2×C4×C61—44no—
288C2×C4×C61#9914yescomplemented
289C2×C4×C61C2×C22⋊C411yescharacteristic
290C2×C4×C61C2×C22⋊C411yescharacteristic
291C2×C4×C61C2×C22⋊C411yescharacteristic
292C2×C4×C61C2×C22⋊C411yescharacteristic
293C2×C4×C61C2×C22⋊C411yescharacteristic
294C2×C4×C61C2×C22⋊C411yescharacteristic
295C2×C4×C61C2×C22⋊C411yescharacteristic
296C2×C4×C61C2×C22⋊C411yescharacteristic
297C22⋊D61—48no—
298C22⋊D61—48no—
299C22⋊D61—48no—
300C22⋊D61—48no—
301C2×Dic61—24no—
302C2×Dic61—28no—
303C2×Dic61—44no—
304C2×Dic61—44no—
305C2×Dic61—44no—
306C2×Dic61—44no—
307C2×Dic61—44no—
308D244—44no—
309D244—44no—
310D244—44no—
311D244—44no—
312#21793—611nomaximal, Sylow
313C22×C61—28no—
314C22×C61—21no—
315C22×C61—21no—
316C22×C61—21no—
317C22×C61—21no—
318C22×C61—21no—
319C22×C61—21no—
320C22×C61—21no—
321C22×C61—21no—
322C22×C61—21no—
323C22×C61—21no—
324C22×C61—21no—
325C22×C61—21no—
326C22×C61—21no—
327C22×C61—21no—
328C22×C61—21no—
329C22×C61—21no—
330C22×C61—44no—
331C22×C61—44no—
332C22×C61—44no—
333C22×C61—44no—
334C22×C61—44no—
335C22×C61—44no—
336C22×C61C2×#9912yes—
337C22×C61#41012yes—
338C22×C61C22×C22⋊C411yescharacteristic
339C22×C61#51812yes—
340C22×C61#53512yes—
341C22×C61#53512yes—
342C2×D61—44no—
343C2×D61—44no—
344C2×D61—44no—
345C2×D61—88no—
346C2×D61—88no—
347C2×D61—88no—
348C4×C61—21no—
349C4×C61—21no—
350C4×C61—21no—
351C4×C61—21no—
352C4×C61—21no—
353C4×C61—21no—
354C4×C61—84no—
355C4×C61C2×#9912yes—
356C4×C61C2×#9912yes—
357Dic61—44no—
358Dic61—84no—
359C22×#121—611no—
360#2280—611no—
361#2280D6111yescharacteristic, complemented
362#1964—614no—
363#1964—614no—
364#1781—614no—
365C2×C61—22no—
366C2×C61—22no—
367C2×C61—22no—
368C2×C61—22no—
369C2×C61—22no—
370C2×C61—41no—
371C2×C61—41no—
372C2×C61#230911yescharacteristic
373C2×C61C22×#9911yescharacteristic
374C2×C61C2×#41011yescharacteristic
375D61—84no—
376C23×D4—612no—
377C23×D4—611no—
378C24×C4C2×D6111yescharacteristic
379C2×#121—612no—
380C2×#121—612no—
381C2×#121—612no—
382C2×#121—612no—
383C2×#121—1221no—
384C2×#121—1221no—
385C2×#121—1221no—
386C2×#121—1221no—
387C2×#121—1221no—
388C2×#121—1221no—
389C2×#121—1221no—
390C2×#121—1221no—
391C2×#117—21no—
392C2×#117—1221no—
393C22×C4⋊C4—611no—
394C22×C22⋊C4—612no—
395C2×#99—6116no—
396#381—21no—
397#381—1221no—
398#380—21no—
399#380—612no—
400#380—1221no—
401#380C2×D6112yescomplemented
402#379—612no—
403#379C2×D6112yes—
404C4×C22⋊C4—21no—
405C4×C22⋊C4—612no—
406C4×C22⋊C4—1221no—
407C4×C22⋊C4C2×D6112yescomplemented
408C61#2179311yescharacteristic, complemented, Sylow
409C25—612no—
410C25C22×D6111yescharacteristic
411C22×D4—614no—
412C22×D4—614no—
413C22×D4—612no—
414C22×D4—612no—
415C22×D4—1222no—
416C22×D4—1222no—
417C22×D4—1222no—
418C22×D4—1222no—
419C22×D4—1221no—
420C22×D4—1221no—
421C22×D4—1221no—
422C22×D4—1221no—
423C22×D4—2444no—
424C22×D4—2448no—
425C23×C4—44no—
426C23×C4—612no—
427C23×C4C4×D6111yescharacteristic
428C23×C4C4×D6111yescharacteristic
429C23×C4C4×D6111yescharacteristic
430C23×C4C4×D6111yescharacteristic
431C23×C4D24411yescharacteristic
432C23×C4D24411yescharacteristic
433C23×C4D24411yescharacteristic
434C23×C4D24411yescharacteristic
435C23×C4C22⋊D6111yescharacteristic
436C23×C4C22⋊D6111yescharacteristic
437C23×C4C22⋊D6111yescharacteristic
438C23×C4C22⋊D6111yescharacteristic
439C23×C4C22×D6111yescharacteristic
440C23×C4C22×D6111yescharacteristic
441#121—1222no—
442#121—1222no—
443#121—1222no—
444#121—1222no—
445#121—1222no—
446#121—1222no—
447#121—1222no—
448#121—1222no—
449#121—1222no—
450#121—1222no—
451#121—1222no—
452#121—1222no—
453#121—1222no—
454#121—1222no—
455#121—1222no—
456#121—1222no—
457#117—44no—
458#117—2444no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—612no—
461C2×C4⋊C4—612no—
462C2×C4⋊C4—1221no—
463C2×C4⋊C4—1221no—
464C2×C4⋊C4—1221no—
465C2×C4⋊C4—1221no—
466C2×C4⋊C4—1222no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—614no—
470C2×C22⋊C4—614no—
471C2×C22⋊C4—614no—
472C2×C22⋊C4—1222no—
473C2×C22⋊C4—1222no—
474C2×C22⋊C4—1222no—
475C2×C22⋊C4—1222no—
476C2×C22⋊C4—1222no—
477C2×C22⋊C4—1222no—
478C2×C22⋊C4C22×D6114yes—
479C2×C42—22no—
480C2×C42—1222no—
481#99—24416no—
482#95—22no—
483#95—22no—
484#95—1222no—
485#95—1222no—
486C24—24no—
487C24—42no—
488C24—42no—
489C24—614no—
490C24—1222no—
491C24—1222no—
492C24—2444no—
493C24—2444no—
494C24—2444no—
495C24C2×C4×D6111yescharacteristic
496C24C2×C4×D6111yescharacteristic
497C24C2×D24411yescharacteristic
498C24C2×D24411yescharacteristic
499C24C2×C22⋊D6111yescharacteristic
500C24C2×C22⋊D6111yescharacteristic
501C24C23×D6111yescharacteristic
502C2×D4—1224no—
503C2×D4—1224no—
504C2×D4—12216no—
505C2×D4—1224no—
506C2×D4—1224no—
507C2×D4—1222no—
508C2×D4—1222no—
509C2×D4—1222no—
510C2×D4—1222no—
511C2×D4—2444no—
512C2×D4—2444no—
513C2×D4—2444no—
514C2×D4—2444no—
515C2×D4—2444no—
516C2×D4—2448no—
517C2×D4—2448no—
518C2×D4—2448no—
519C2×D4—2448no—
520C2×D4—2448no—
521C2×D4—2444no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—614no—
538C22×C4—1222no—
539C22×C4—1222no—
540C22×C4—1224no—
541C22×C4—2444no—
542C22×C4#1175819811yescharacteristic
543C22×C4#1175819811yescharacteristic
544C22×C4#1175819811yescharacteristic
545C22×C4#1175819811yescharacteristic
546C22×C4#1175819811yescharacteristic
547C22×C4#1175819811yescharacteristic
548C22×C4#1175819811yescharacteristic
549C22×C4#1175819811yescharacteristic
550C22×C4#1175819811yescharacteristic
551C22×C4#1175819811yescharacteristic
552C22×C4#1175819811yescharacteristic
553C22×C4#1175819811yescharacteristic
554C22×C4#1175819811yescharacteristic
555C22×C4#1175819811yescharacteristic
556C22×C4#1175819811yescharacteristic
557C22×C4#1175819811yescharacteristic
558C22×C4C2×C4×D6111yescharacteristic
559C22×C4C2×C4×D6111yescharacteristic
560C22×C4C2×C4×D6111yescharacteristic
561C22×C4C2×C4×D6111yescharacteristic
562C22×C4C2×D24411yescharacteristic
563C22×C4C2×D24411yescharacteristic
564C22×C4C2×D24411yescharacteristic
565C22×C4C2×D24411yescharacteristic
566C22×C4C2×C22⋊D6111yescharacteristic
567C22×C4C2×C22⋊D6111yescharacteristic
568C22×C4C2×C22⋊D6111yescharacteristic
569C22×C4C2×C22⋊D6111yescharacteristic
570C4⋊C4—44no—
571C4⋊C4—1222no—
572C4⋊C4—1222no—
573C4⋊C4—1222no—
574C4⋊C4—1222no—
575C4⋊C4—2444no—
576C22⋊C4—28no—
577C22⋊C4—44no—
578C22⋊C4—44no—
579C22⋊C4—1224no—
580C22⋊C4—1224no—
581C22⋊C4—1224no—
582C22⋊C4—1224no—
583C22⋊C4—1228no—
584C22⋊C4—2444no—
585C22⋊C4—2444no—
586C42—44no—
587C42—2444no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—416no—
609C23—1228no—
610C23—1224no—
611C23—48816no—
612C23—2444no—
613C23—2444no—
614C23—2444no—
615C23—2444no—
616C23—2444no—
617C23—2444no—
618C23—2444no—
619C23—2444no—
620C23C2×#1175819811yescharacteristic
621C23C2×#1175819811yescharacteristic
622C23C2×#1175819811yescharacteristic
623C23C2×#1175819811yescharacteristic
624C23C22×C4×D6111yescharacteristic
625C23C22×C22⋊D6111yescharacteristic
626C23C22×D24411yescharacteristic
627C23#1451982314yes—
628D4—2444no—
629D4—2444no—
630D4—2448no—
631D4—2448no—
632D4—2448no—
633D4—2448no—
634D4—2444no—
635D4—2444no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—1224no—
667C2×C4—1228no—
668C2×C4—2444no—
669C2×C4—2444no—
670C2×C4—2444no—
671C2×C4—2444no—
672C2×C4—2444no—
673C2×C4#1451969114yescomplemented
674C2×C4C2×#1175819811yescharacteristic
675C2×C4C2×#1175819811yescharacteristic
676C2×C4C2×#1175819811yescharacteristic
677C2×C4C2×#1175819811yescharacteristic
678C2×C4C2×#1175819811yescharacteristic
679C2×C4C2×#1175819811yescharacteristic
680C2×C4C2×#1175819811yescharacteristic
681C2×C4C2×#1175819811yescharacteristic
682C22—28no—
683C22—21no—
684C22—21no—
685C22—21no—
686C22—21no—
687C22—21no—
688C22—21no—
689C22—21no—
690C22—21no—
691C22—21no—
692C22—21no—
693C22—21no—
694C22—21no—
695C22—21no—
696C22—21no—
697C22—21no—
698C22—21no—
699C22—44no—
700C22—44no—
701C22—44no—
702C22—44no—
703C22—44no—
704C22—44no—
705C22—4888no—
706C22—4888no—
707C22—4888no—
708C22—2444no—
709C22—2444no—
710C22—2444no—
711C22C2×#1451969112yes—
712C22#1683973512yes—
713C22C22×#1175819811yescharacteristic
714C22#1684023612yes—
715C22#1684032612yes—
716C22#1684033112yes—
717C4—21no—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—21no—
722C4—21no—
723C4—84no—
724C4—4884no—
725C4—2444no—
726C4C2×#1451969112yes—
727C4C2×#1451969112yes—
728C2—22no—
729C2—22no—
730C2—22no—
731C2—22no—
732C2—22no—
733C2—41no—
734C2—41no—
735C2—4884no—
736C2#2144839911yescharacteristic
737C2C22×#1451969111yescharacteristic
738C2C2×#1683973511yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#2280C2
socleC22×C61C22×C22⋊C4
prime radicalC22×#14519751C2
cosocleC24×C61C24
hypercenter#2280D61
hypocenterC61#21793
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. #21448202C2semidirect
3. #21446655C2semidirect
4. #21446654C2semidirect
5. #21445733C2semidirect
6. C61×#2280C2semidirect
7. C23×D244C4semidirect
17. C2×#14519751C4semidirect
18. C2×#14519751C4semidirect
22. C22×C4⋊Dic61C4semidirect
23. C22×#11758198C4semidirect
24. C2×#14519691C22semidirect
27. #16839622C22semidirect
30. C4×C22⋊Dic61C22semidirect
35. C61×#380C22semidirect
38. C4×C22⋊C4×C61C22semidirect
288. C2×C4×C61#99semidirect
361. #2280D61semidirect
401. #380C2×D61semidirect
407. C4×C22⋊C4C2×D61semidirect
408. C61#21793semidirect
673. C2×C4#14519691semidirect

Maximal subgroups

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

subgroupindex
C22×#145197512
#214482022
#214466552
#214466542
#214457332
C61×#22802
#2179361