Finite Group Databasebeta

← C2×#21450062 #29847621

Subgroups — C2×#21450062 #29847621

Order 15616.

4102 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519770C211yesmaximal, characteristic, complemented
2C23×C22⋊Dic61C211yesmaximal, characteristic
3#21450062C2116yesmaximal, direct product factor
4C2×#16839690C211yesmaximal, characteristic, complemented
5C2×#16839690C211yesmaximal, characteristic, complemented
6C2×#16839687C211yesmaximal, characteristic, complemented
7C2×#16839685C211yesmaximal, characteristic, complemented
8C2×#16839656C211yesmaximal, characteristic, complemented
9C2×#16839655C211yesmaximal, characteristic, complemented
10C2×#16839650C211yesmaximal, characteristic, complemented
11C2×#16839637C211yesmaximal, characteristic, complemented
12C2×#16839634C211yesmaximal, characteristic, complemented
13C2×#16839620C211yesmaximal, characteristic, complemented
14C2×#16839618C211yesmaximal, characteristic
15C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
16C2×C61×#379C211yesmaximal, characteristic
17C24×Dic61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C2×#14519770—28no—
20C2×#14519770C2218yescomplemented
21C22×C4⋊Dic61C2211yescharacteristic, complemented
22C22×C4⋊Dic61C2211yescharacteristic, complemented
23C22×#11758196C2211yescharacteristic, complemented
24C22×#11758196C2211yescharacteristic, complemented
25C22×#11758196C2211yescharacteristic, complemented
26C22×#11758196C2211yescharacteristic, complemented
27C22×C22⋊Dic61—28no—
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2218yes—
30C22×C22⋊Dic61C2211yescharacteristic
31C22×C22⋊Dic61C2211yescharacteristic
32C22×C22⋊Dic61C2211yescharacteristic
33C22×C22⋊Dic61C2211yescharacteristic
34C22×C22⋊Dic61C2211yescharacteristic
35C22×C22⋊Dic61C2211yescharacteristic
36C22×C22⋊Dic61C2211yescharacteristic
37C22×C22⋊Dic61C2211yescharacteristic
38C22×C22⋊Dic61C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic, complemented
40C22×C4×Dic61C2211yescharacteristic, complemented
41#16839690C2218yescomplemented
42#16839690C2218yescomplemented
43#16839687C2218yescomplemented
44#16839685C2218yescomplemented
45#16839656C2218yescomplemented
46#16839655C2218yescomplemented
47#16839650C2218yescomplemented
48#16839637C2218yescomplemented
49#16839634C2218yescomplemented
50#16839620C2218yescomplemented
51#16839618C2218yes—
52C22⋊C4×Dic61C2218yescomplemented
53C2×#14519684C2211yescharacteristic, complemented
54C2×#14519684C2211yescharacteristic, complemented
55C2×#14519684C2211yescharacteristic, complemented
56C2×#14519684C2211yescharacteristic, complemented
57C2×#14519684C2211yescharacteristic, complemented
58C2×#14519684C2211yescharacteristic, complemented
59C2×#14519684C2211yescharacteristic, complemented
60C2×#14519684C2211yescharacteristic, complemented
61C26×C61C2211yescharacteristic
62C22×C22⋊C4×C61C2211yescharacteristic
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C22⋊C4×C61C2211yescharacteristic
65C22×C22⋊C4×C61C2211yescharacteristic
66C22×C22⋊C4×C61C2211yescharacteristic
67C22×C22⋊C4×C61C2211yescharacteristic
68C61×#379C2218yes—
69C23×Dic61—24no—
70C23×Dic61—24no—
71C23×Dic61—24no—
72C23×Dic61—24no—
73C23×Dic61—42no—
74C23×Dic61—42no—
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2314yes—
82C23×Dic61C2314yes—
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85#14519770—232no—
86C2×C4⋊Dic61—24no—
87C2×C4⋊Dic61—42no—
88C2×C4⋊Dic61C2314yescomplemented
89C2×C4⋊Dic61C2314yescomplemented
90C2×#11758196—24no—
91C2×#11758196—24no—
92C2×#11758196—42no—
93C2×#11758196—42no—
94C2×#11758196C2314yescomplemented
95C2×#11758196C2314yescomplemented
96C2×#11758196C2314yescomplemented
97C2×#11758196C2314yescomplemented
98C2×C22⋊Dic61—24no—
99C2×C22⋊Dic61—24no—
100C2×C22⋊Dic61—24no—
101C2×C22⋊Dic61—24no—
102C2×C22⋊Dic61—24no—
103C2×C22⋊Dic61—24no—
104C2×C22⋊Dic61—24no—
105C2×C22⋊Dic61—232no—
106C2×C22⋊Dic61—42no—
107C2×C22⋊Dic61—42no—
108C2×C22⋊Dic61D418yes—
109C2×C22⋊Dic61C2314yes—
110C2×C22⋊Dic61C2314yes—
111C2×C22⋊Dic61C2314yes—
112C2×C22⋊Dic61C2314yes—
113C2×C22⋊Dic61C2314yes—
114C2×C22⋊Dic61C2314yes—
115C2×C22⋊Dic61C2314yes—
116C2×C22⋊Dic61C2314yes—
117C2×C22⋊Dic61C2314yes—
118C2×C22⋊Dic61C2314yes—
119C2×C4×Dic61—24no—
120C2×C4×Dic61—42no—
121C2×C4×Dic61C2314yescomplemented
122C2×C4×Dic61C2314yescomplemented
123#14519684C2314yescomplemented
124#14519684C2314yescomplemented
125#14519684C2314yescomplemented
126#14519684C2314yescomplemented
127#14519684C2314yescomplemented
128#14519684C2314yescomplemented
129#14519684C2314yescomplemented
130#14519684C2314yescomplemented
131C25×C61—24no—
132C25×C61—24no—
133C25×C61—24no—
134C25×C61—24no—
135C25×C61—24no—
136C25×C61—42no—
137C25×C61—42no—
138C25×C61C2311yescharacteristic
139C25×C61C2311yescharacteristic
140C25×C61C2314yes—
141C25×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61—24no—
147C2×C22⋊C4×C61—24no—
148C2×C22⋊C4×C61—24no—
149C2×C22⋊C4×C61—24no—
150C2×C22⋊C4×C61—42no—
151C2×C22⋊C4×C61—42no—
152C2×C22⋊C4×C61C2314yes—
153C2×C22⋊C4×C61C2314yes—
154C2×C22⋊C4×C61C2314yes—
155C2×C22⋊C4×C61C2314yes—
156C2×C22⋊C4×C61C2314yes—
157C2×C22⋊C4×C61C2314yes—
158C24×C61—22no—
159C24×C61—22no—
160C24×C61—22no—
161C24×C61—22no—
162C24×C61—232no—
163C24×C61—28no—
164C24×C61—22no—
165C24×C61—28no—
166C24×C61—28no—
167C24×C61—22no—
168C24×C61—22no—
169C24×C61—22no—
170C24×C61—22no—
171C24×C61—22no—
172C24×C61—22no—
173C24×C61—22no—
174C24×C61—22no—
175C24×C61—22no—
176C24×C61—22no—
177C24×C61—22no—
178C24×C61—28no—
179C24×C61—28no—
180C24×C61—44no—
181C24×C61—44no—
182C24×C61—416no—
183C24×C61—416no—
184C24×C61—416no—
185C24×C61—416no—
186C24×C61—416no—
187C24×C61—416no—
188C24×C61C2×D414yes—
189C24×C61#4114yes—
190C24×C61#4114yes—
191C24×C61#4114yes—
192C24×C61#4114yes—
193C24×C61C2412yes—
194C24×C61C2412yes—
195C24×C61C2412yes—
196C24×C61C2411yescharacteristic
197C22×C4×C61—22no—
198C22×C4×C61—22no—
199C22×C4×C61—22no—
200C22×C4×C61—22no—
201C22×C4×C61—22no—
202C22×C4×C61—22no—
203C22×C4×C61—22no—
204C22×C4×C61—22no—
205C22×C4×C61—22no—
206C22×C4×C61—22no—
207C22×C4×C61—22no—
208C22×C4×C61—22no—
209C22×C4×C61C2412yes—
210C22×C4×C61C2412yes—
211C22×C4×C61C2412yes—
212C22×C4×C61C2412yes—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—22no—
220C22×Dic61—22no—
221C22×Dic61—28no—
222C22×Dic61—28no—
223C22×Dic61—22no—
224C22×Dic61—22no—
225C22×Dic61—22no—
226C22×Dic61—22no—
227C22×Dic61—22no—
228C22×Dic61—22no—
229C22×Dic61—22no—
230C22×Dic61—22no—
231C22×Dic61—22no—
232C22×Dic61—22no—
233C22×Dic61—22no—
234C22×Dic61—22no—
235C22×Dic61—22no—
236C22×Dic61—22no—
237C22×Dic61—28no—
238C22×Dic61—28no—
239C22×Dic61—44no—
240C22×Dic61—44no—
241C22×Dic61—416no—
242C22×Dic61—416no—
243C22×Dic61C2×D414yes—
244C22×Dic61C2×D414yes—
245C22×Dic61C2412yes—
246C22×Dic61C2412yes—
247C22×Dic61C2412yes—
248C22×Dic61C2412yes—
249C22×Dic61C2412yes—
250C22×Dic61C2412yes—
251C22×Dic61C2412yes—
252C22×Dic61C2412yes—
253C22⋊C4×C61—28no—
254C22⋊C4×C61—28no—
255C22⋊C4×C61—28no—
256C22⋊C4×C61—28no—
257C22⋊C4×C61—44no—
258C22⋊C4×C61—44no—
259C22⋊Dic61—28no—
260C22⋊Dic61—28no—
261C22⋊Dic61—28no—
262C22⋊Dic61—28no—
263C22⋊Dic61—28no—
264C22⋊Dic61—28no—
265C22⋊Dic61—28no—
266C22⋊Dic61—44no—
267C22⋊Dic61—44no—
268C22⋊Dic61C2×D4116yes—
269C4⋊Dic61—28no—
270C4⋊Dic61—44no—
271#11758196—28no—
272#11758196—28no—
273#11758196—44no—
274#11758196—44no—
275C4×Dic61—28no—
276C4×Dic61—44no—
277C23×C61—28no—
278C23×C61—28no—
279C23×C61—28no—
280C23×C61—28no—
281C23×C61—28no—
282C23×C61—28no—
283C23×C61—22no—
284C23×C61—22no—
285C23×C61—22no—
286C23×C61—22no—
287C23×C61—232no—
288C23×C61—28no—
289C23×C61—28no—
290C23×C61—28no—
291C23×C61—28no—
292C23×C61—28no—
293C23×C61—28no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—22no—
299C23×C61—22no—
300C23×C61—22no—
301C23×C61—22no—
302C23×C61—22no—
303C23×C61—22no—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—416no—
307C23×C61—416no—
308C23×C61—416no—
309C23×C61—416no—
310C23×C61—416no—
311C23×C61—4128no—
312C23×C61—44no—
313C23×C61—44no—
314C23×C61—416no—
315C23×C61—44no—
316C23×C61—44no—
317C23×C61—44no—
318C23×C61—44no—
319C23×C61—44no—
320C23×C61—44no—
321C23×C61#126116yescomplemented
322C23×C61C22×D414yes—
323C23×C61C22×D412yes—
324C23×C61C2×#4114yes—
325C23×C61C2×#4114yes—
326C23×C61C2×#4114yes—
327C23×C61C2×#4114yes—
328C23×C61C2×#4112yes—
329C23×C61C2×#4112yes—
330C23×C61C2×#4112yes—
331C23×C61C2×#4112yes—
332C23×C61H(5,𝔽2)12yes—
333C23×C61H(5,𝔽2)12yes—
334C23×C61C2511yescharacteristic
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—44no—
348C2×C4×C61—44no—
349C2×C4×C61—44no—
350C2×C4×C61—44no—
351C2×Dic61—28no—
352C2×Dic61—28no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—22no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—22no—
362C2×Dic61—22no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—22no—
372C2×Dic61—22no—
373C2×Dic61—22no—
374C2×Dic61—22no—
375C2×Dic61—416no—
376C2×Dic61—416no—
377C2×Dic61—44no—
378C2×Dic61—44no—
379C2×Dic61—44no—
380C2×Dic61—44no—
381C2×Dic61—44no—
382C2×Dic61—44no—
383C2×Dic61C22×D414yes—
384C2×Dic61C22×D414yes—
385C2×#2480—611nomaximal, Sylow
386C22×C61—24no—
387C22×C61—24no—
388C22×C61—24no—
389C22×C61—24no—
390C22×C61—24no—
391C22×C61—24no—
392C22×C61—232no—
393C22×C61—24no—
394C22×C61—24no—
395C22×C61—24no—
396C22×C61—24no—
397C22×C61—24no—
398C22×C61—24no—
399C22×C61—464no—
400C22×C61—42no—
401C22×C61—42no—
402C22×C61—42no—
403C22×C61—42no—
404C22×C61—42no—
405C22×C61—42no—
406C22×C61—42no—
407C22×C61—42no—
408C22×C61—416no—
409C22×C61—416no—
410C22×C61#52514yes—
411C22×C61C2×#12614yes—
412C22×C61C2×#12618yescomplemented
413C22×C61#53814yes—
414C22×C61#54614yes—
415C22×C61#54614yes—
416C22×C61#55114yes—
417C22×C61#55114yes—
418C22×C61C23×D411yescharacteristic
419C22×C61C22×#4111yescharacteristic
420C22×C61C22×#4111yescharacteristic
421C22×C61C22×#4111yescharacteristic
422C22×C61C22×#4111yescharacteristic
423C22×C61C2×H(5,𝔽2)11yescharacteristic
424C22×C61C2×H(5,𝔽2)11yescharacteristic
425C4×C61—42no—
426C4×C61—42no—
427C4×C61—42no—
428C4×C61—42no—
429Dic61—24no—
430Dic61—24no—
431Dic61—42no—
432Dic61—42no—
433Dic61—42no—
434Dic61—42no—
435Dic61—42no—
436Dic61—42no—
437C22×#126—611no—
438C23×C22⋊C4—611no—
439#2480—6116no—
440C2×#397—611no—
441C2×#397—611no—
442C2×#397—611no—
443C2×#396—611no—
444C2×#388—611no—
445C2×#388—611no—
446C2×#388—611no—
447C2×#385—611no—
448C2×#385—611no—
449C2×#380—611no—
450C2×#379—611no—
451C2×#379D6111yescharacteristic
452C2×C4×C22⋊C4—611no—
453C2×C61—28no—
454C2×C61—44no—
455C2×C61—44no—
456C2×C61#248018yescomplemented
457C2×C61C2×#52511yescharacteristic
458C2×C61C22×#12611yescharacteristic
459C2×C61C2×#53811yescharacteristic
460C2×C61C2×#54611yescharacteristic
461C2×C61C2×#54611yescharacteristic
462C2×C61C2×#55111yescharacteristic
463C2×C61C2×#55111yescharacteristic
464C26C2×D6111yescharacteristic
465C24×C4—611no—
466C24×C4—611no—
467C2×#126—618no—
468C2×#126—1228no—
469C22×C4⋊C4—611no—
470C22×C4⋊C4—611no—
471C22×C4⋊C4—611no—
472C22×C4⋊C4—611no—
473C22×C4⋊C4—611no—
474C22×C4⋊C4—611no—
475C22×C22⋊C4—611no—
476C22×C22⋊C4—611no—
477C22×C22⋊C4—611no—
478C22×C22⋊C4—611no—
479C22×C22⋊C4—611no—
480C22×C22⋊C4—618no—
481C22×C22⋊C4—611no—
482C22×C22⋊C4—611no—
483C22×C22⋊C4—611no—
484C22×C22⋊C4—611no—
485C22×C22⋊C4—611no—
486C22×C22⋊C4—1228no—
487C22×C22⋊C4C2×D6111yescharacteristic
488C22×C22⋊C4C2×D6111yescharacteristic
489C22×C22⋊C4C2×D6111yescharacteristic
490C22×C22⋊C4C2×D6111yescharacteristic
491C22×C22⋊C4C2×D6111yescharacteristic
492C22×C22⋊C4C2×D6111yescharacteristic
493C22×C42—611no—
494C22×C42—611no—
495#397—618no—
496#397—618no—
497#397—618no—
498#396—618no—
499#388—618no—
500#388—618no—
501#388—618no—
502#385—618no—
503#385—618no—
504#380—618no—
505#379—618no—
506#379C2×D6118yes—
507C4×C22⋊C4—618no—
508C2×#95—611no—
509C2×#95—611no—
510C2×#95—611no—
511C2×#95—611no—
512C2×#95—611no—
513C2×#95—611no—
514C2×#95—611no—
515C2×#95—611no—
516C61C2×#248011yescharacteristic, complemented, Sylow
517C25—24no—
518C25—24no—
519C25—24no—
520C25—24no—
521C25—24no—
522C25—42no—
523C25—42no—
524C25C22×D6111yescharacteristic
525C25C22×D6111yescharacteristic
526C25C22×D6114yes—
527C25C22×D6111yescharacteristic
528C23×C4—611no—
529C23×C4—611no—
530C23×C4—611no—
531C23×C4—611no—
532C23×C4—611no—
533C23×C4—611no—
534C23×C4—611no—
535C23×C4—611no—
536C23×C4—614no—
537C23×C4—614no—
538C23×C4—1224no—
539C23×C4—1224no—
540C23×C4—1224no—
541C23×C4—1224no—
542C23×C4—2442no—
543C23×C4—2442no—
544C23×C4C22×D6111yescharacteristic
545C23×C4C22×D6111yescharacteristic
546C23×C4C22×D6111yescharacteristic
547C23×C4C22×D6111yescharacteristic
548#126—12232no—
549C2×C4⋊C4—614no—
550C2×C4⋊C4—614no—
551C2×C4⋊C4—614no—
552C2×C4⋊C4—614no—
553C2×C4⋊C4—614no—
554C2×C4⋊C4—614no—
555C2×C4⋊C4—1224no—
556C2×C4⋊C4—1224no—
557C2×C4⋊C4—1224no—
558C2×C4⋊C4—2442no—
559C2×C4⋊C4—2442no—
560C2×C4⋊C4—2442no—
561C2×C22⋊C4—24no—
562C2×C22⋊C4—24no—
563C2×C22⋊C4—24no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4—618no—
568C2×C22⋊C4—614no—
569C2×C22⋊C4—614no—
570C2×C22⋊C4—614no—
571C2×C22⋊C4—614no—
572C2×C22⋊C4—614no—
573C2×C22⋊C4—614no—
574C2×C22⋊C4—614no—
575C2×C22⋊C4—614no—
576C2×C22⋊C4—614no—
577C2×C22⋊C4—614no—
578C2×C22⋊C4—12232no—
579C2×C22⋊C4—1224no—
580C2×C22⋊C4—1224no—
581C2×C22⋊C4—1224no—
582C2×C22⋊C4—1224no—
583C2×C22⋊C4—1224no—
584C2×C22⋊C4—1224no—
585C2×C22⋊C4—1224no—
586C2×C22⋊C4—2442no—
587C2×C22⋊C4—2442no—
588C2×C22⋊C4C22×D6114yes—
589C2×C22⋊C4C22×D6114yes—
590C2×C22⋊C4C22×D6114yes—
591C2×C22⋊C4C22×D6114yes—
592C2×C22⋊C4C22×D6114yes—
593C2×C22⋊C4C22×D6114yes—
594C2×C42—614no—
595C2×C42—614no—
596C2×C42—1224no—
597C2×C42—2442no—
598#95—614no—
599#95—614no—
600#95—614no—
601#95—614no—
602#95—614no—
603#95—614no—
604#95—614no—
605#95—614no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—232no—
611C24—28no—
612C24—22no—
613C24—28no—
614C24—28no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—28no—
627C24—28no—
628C24—44no—
629C24—44no—
630C24—416no—
631C24—416no—
632C24—416no—
633C24—416no—
634C24—416no—
635C24—416no—
636C24#1175822214yes—
637C24D4×D6114yes—
638C24#1175822414yes—
639C24#1175822414yes—
640C24#1175822414yes—
641C24C23×D6112yes—
642C24C23×D6112yes—
643C24C23×D6112yes—
644C24C23×D6111yescharacteristic
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—614no—
658C22×C4—614no—
659C22×C4—612no—
660C22×C4—612no—
661C22×C4—612no—
662C22×C4—612no—
663C22×C4—612no—
664C22×C4—612no—
665C22×C4—612no—
666C22×C4—612no—
667C22×C4—1228no—
668C22×C4—1228no—
669C22×C4—1222no—
670C22×C4—1222no—
671C22×C4—1222no—
672C22×C4—1222no—
673C22×C4—1222no—
674C22×C4—1222no—
675C22×C4—1222no—
676C22×C4—1222no—
677C22×C4—1222no—
678C22×C4—1222no—
679C22×C4—1222no—
680C22×C4—1222no—
681C22×C4—1228no—
682C22×C4—1222no—
683C22×C4—1222no—
684C22×C4—1222no—
685C22×C4—1228no—
686C22×C4—1222no—
687C22×C4—1222no—
688C22×C4—1222no—
689C22×C4—1222no—
690C22×C4—1222no—
691C22×C4—1222no—
692C22×C4—1222no—
693C22×C4—2444no—
694C22×C4—2444no—
695C22×C4—24416no—
696C22×C4—24416no—
697C22×C4C23×D6112yes—
698C22×C4C23×D6112yes—
699C22×C4C23×D6112yes—
700C22×C4C23×D6112yes—
701C4⋊C4—1228no—
702C4⋊C4—1228no—
703C4⋊C4—1228no—
704C4⋊C4—2444no—
705C4⋊C4—2444no—
706C4⋊C4—2444no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—28no—
710C22⋊C4—28no—
711C22⋊C4—44no—
712C22⋊C4—44no—
713C22⋊C4—6116no—
714C22⋊C4—1228no—
715C22⋊C4—1228no—
716C22⋊C4—1228no—
717C22⋊C4—1228no—
718C22⋊C4—1228no—
719C22⋊C4—1228no—
720C22⋊C4—1228no—
721C22⋊C4—2444no—
722C22⋊C4—2444no—
723C42—1228no—
724C42—2444no—
725C23—28no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—28no—
731C23—28no—
732C23—28no—
733C23—28no—
734C23—28no—
735C23—232no—
736C23—28no—
737C23—28no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—28no—
751C23—28no—
752C23—28no—
753C23—28no—
754C23—416no—
755C23—416no—
756C23—416no—
757C23—416no—
758C23—4128no—
759C23—416no—
760C23—44no—
761C23—44no—
762C23—416no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23#14519770116yescomplemented
770C23C2×D4×D6114yes—
771C23C2×D4×D6112yes—
772C23C2×#1175822414yes—
773C23C2×#1175822414yes—
774C23C2×#1175822414yes—
775C23C2×#1175822412yes—
776C23C2×#1175822412yes—
777C23C2×#1175822412yes—
778C23C2×#1175822214yes—
779C23C2×#1175822212yes—
780C23#1451982212yes—
781C23#1451982212yes—
782C23C24×D6111yescharacteristic
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—614no—
800C2×C4—614no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1228no—
806C2×C4—1228no—
807C2×C4—1222no—
808C2×C4—1222no—
809C2×C4—1222no—
810C2×C4—1222no—
811C2×C4—1222no—
812C2×C4—1222no—
813C2×C4—1222no—
814C2×C4—1222no—
815C2×C4—1222no—
816C2×C4—1222no—
817C2×C4—1222no—
818C2×C4—1222no—
819C2×C4—1222no—
820C2×C4—1222no—
821C2×C4—1222no—
822C2×C4—1222no—
823C2×C4—1222no—
824C2×C4—1222no—
825C2×C4—24416no—
826C2×C4—24416no—
827C2×C4—2444no—
828C2×C4—2444no—
829C2×C4—2444no—
830C2×C4—2444no—
831C2×C4—2444no—
832C2×C4—2444no—
833C22—24no—
834C22—24no—
835C22—232no—
836C22—24no—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—464no—
847C22—42no—
848C22—42no—
849C22—416no—
850C22—416no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22#1684026814yes—
858C22C2×#1451977014yes—
859C22C2×#1451977018yescomplemented
860C22#1684034714yes—
861C22#1684039914yes—
862C22#1684040214yes—
863C22#1684043814yes—
864C22#1684044314yes—
865C22C22×D4×D6111yescharacteristic
866C22C22×#1175822411yescharacteristic
867C22C22×#1175822411yescharacteristic
868C22C22×#1175822411yescharacteristic
869C22C22×#1175822211yescharacteristic
870C22C2×#1451982211yescharacteristic
871C22C2×#1451982211yescharacteristic
872C4—42no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—1224no—
877C4—1224no—
878C4—2442no—
879C4—2442no—
880C4—2442no—
881C4—2442no—
882C4—2442no—
883C4—2442no—
884C2—28no—
885C2—44no—
886C2—44no—
887C2#2145006218yesdirect product factor
888C2C2×#1684026811yescharacteristic
889C2C22×#1451977011yescharacteristic
890C2C2×#1684034711yescharacteristic
891C2C2×#1684039911yescharacteristic
892C2C2×#1684040211yescharacteristic
893C2C2×#1684043811yescharacteristic
894C2C2×#1684044311yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#379C2
socleC24×C61C24
prime radicalC26×C61C22
hypercenterC2×#379D61
hypocenterC61C2×#2480
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
1. C22×#14519770C2semidirect
3. #21450062C2direct (N × H)
4. C2×#16839690C2semidirect
5. C2×#16839690C2semidirect
6. C2×#16839687C2semidirect
7. C2×#16839685C2semidirect
8. C2×#16839656C2semidirect
9. C2×#16839655C2semidirect
10. C2×#16839650C2semidirect
11. C2×#16839637C2semidirect
12. C2×#16839634C2semidirect
13. C2×#16839620C2semidirect
15. C2×C22⋊C4×Dic61C2semidirect
20. C2×#14519770C22semidirect
21. C22×C4⋊Dic61C22semidirect
22. C22×C4⋊Dic61C22semidirect
23. C22×#11758196C22semidirect
24. C22×#11758196C22semidirect
25. C22×#11758196C22semidirect
26. C22×#11758196C22semidirect
39. C22×C4×Dic61C22semidirect
40. C22×C4×Dic61C22semidirect
41. #16839690C22semidirect
42. #16839690C22semidirect
43. #16839687C22semidirect
44. #16839685C22semidirect
45. #16839656C22semidirect
46. #16839655C22semidirect
47. #16839650C22semidirect
48. #16839637C22semidirect
49. #16839634C22semidirect
50. #16839620C22semidirect
52. C22⋊C4×Dic61C22semidirect
53. C2×#14519684C22semidirect
54. C2×#14519684C22semidirect
55. C2×#14519684C22semidirect
56. C2×#14519684C22semidirect
57. C2×#14519684C22semidirect
58. C2×#14519684C22semidirect
59. C2×#14519684C22semidirect
60. C2×#14519684C22semidirect
88. C2×C4⋊Dic61C23semidirect
89. C2×C4⋊Dic61C23semidirect
94. C2×#11758196C23semidirect
95. C2×#11758196C23semidirect
96. C2×#11758196C23semidirect
97. C2×#11758196C23semidirect
121. C2×C4×Dic61C23semidirect
122. C2×C4×Dic61C23semidirect
123. #14519684C23semidirect
124. #14519684C23semidirect
125. #14519684C23semidirect
126. #14519684C23semidirect
127. #14519684C23semidirect
128. #14519684C23semidirect
129. #14519684C23semidirect
130. #14519684C23semidirect
321. C23×C61#126semidirect
412. C22×C61C2×#126semidirect
456. C2×C61#2480semidirect
516. C61C2×#2480semidirect
769. C23#14519770semidirect
859. C22C2×#14519770semidirect
887. C2#21450062direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197702
C23×C22⋊Dic612
#214500622
C2×#168396902
C2×#168396872
C2×#168396852
C2×#168396562
C2×#168396552
C2×#168396502
C2×#168396372
C2×#168396342
C2×#168396202
C2×#168396182
C2×C22⋊C4×Dic612
C2×C61×#3792
C2×#248061