Finite Group Databasebeta

← C2×#21448662 #29839221

Subgroups — C2×#21448662 #29839221

Order 15616.

4990 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519734C211yesmaximal, characteristic, complemented
2C23×#11758198C211yesmaximal, characteristic
3C22×C22⋊C4×D61C211yesmaximal, characteristic
4#21448662C2116yesmaximal, direct product factor
5C2×#16839653C211yesmaximal, characteristic, complemented
6C2×#16839653C211yesmaximal, characteristic, complemented
7C2×#16839651C211yesmaximal, characteristic, complemented
8C2×#16839651C211yesmaximal, characteristic, complemented
9C2×#16839635C211yesmaximal, characteristic, complemented
10C2×#16839634C211yesmaximal, characteristic, complemented
11C2×#16839624C211yesmaximal, characteristic, complemented
12C2×#16839621C211yesmaximal, characteristic, complemented
13C2×#16839617C211yesmaximal, characteristic
14C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
15C2×C4×#11758198C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
17C25×D61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C2×#14519734—28no—
22C2×#14519734C2218yescomplemented
23C22×#11758196C2211yescharacteristic, complemented
24C22×#11758196C2211yescharacteristic, complemented
25C22×#11758196C2211yescharacteristic, complemented
26C22×#11758196C2211yescharacteristic, complemented
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×#11758198—28no—
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2218yes—
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39C22×#11758198C2211yescharacteristic
40C22×#11758198C2211yescharacteristic
41C2×C22⋊C4×D61C4116yescomplemented
42C2×C22⋊C4×D61C2218yes—
43C22×C4×Dic61C2211yescharacteristic, complemented
44C22×C4×Dic61C2211yescharacteristic, complemented
45#16839653C2218yescomplemented
46#16839653C2218yescomplemented
47#16839651C2218yescomplemented
48#16839651C2218yescomplemented
49#16839635C2218yescomplemented
50#16839634C2218yescomplemented
51#16839624C2218yescomplemented
52#16839621C2218yescomplemented
53#16839617C2218yes—
54C22⋊C4×Dic61C2218yescomplemented
55C4×#11758198C2218yescomplemented
56C2×#14519684C2211yescharacteristic, complemented
57C2×#14519684C2211yescharacteristic, complemented
58C2×#14519684C2211yescharacteristic, complemented
59C2×#14519684C2211yescharacteristic, complemented
60C2×#14519684C2211yescharacteristic, complemented
61C2×#14519684C2211yescharacteristic, complemented
62C24×C4×C61C2211yescharacteristic
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C22⋊C4×C61C2211yescharacteristic
65C22×C42×C61C2211yescharacteristic, complemented
66C22×C42×C61C2211yescharacteristic, complemented
67C4×C22⋊C4×C61C2218yescomplemented
68C2×#95×C61C2211yescharacteristic, complemented
69C2×#95×C61C2211yescharacteristic, complemented
70C24×D61—24no—
71C24×D61—24no—
72C24×D61—24no—
73C24×D61—24no—
74C24×D61—42no—
75C24×D61—42no—
76C24×D61C2×C418yes—
77C24×D61C2311yescharacteristic
78C24×D61C2314yes—
79C24×D61C2311yescharacteristic
80C23×Dic61—24no—
81C23×Dic61—24no—
82C23×Dic61—42no—
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2314yes—
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89C23×Dic61C2311yescharacteristic
90C22×C4×D61—24no—
91C22×C4×D61—24no—
92C22×C4×D61—42no—
93C22×C4×D61—42no—
94C22×C4×D61C2×C418yescomplemented
95C22×C4×D61C2×C418yescomplemented
96C22×C4×D61C2314yes—
97C22×C4×D61C2314yes—
98#14519734—232no—
99C2×#11758196—24no—
100C2×#11758196—24no—
101C2×#11758196—42no—
102C2×#11758196—42no—
103C2×#11758196C2314yescomplemented
104C2×#11758196C2314yescomplemented
105C2×#11758196C2314yescomplemented
106C2×#11758196C2314yescomplemented
107C2×C22⋊Dic61—24no—
108C2×C22⋊Dic61C2×C418yes—
109C2×C22⋊Dic61C2314yes—
110C2×C22⋊Dic61C2314yes—
111C2×#11758198—24no—
112C2×#11758198—24no—
113C2×#11758198—24no—
114C2×#11758198—24no—
115C2×#11758198—24no—
116C2×#11758198—232no—
117C2×#11758198—42no—
118C2×#11758198—42no—
119C2×#11758198C2×C418yescomplemented
120C2×#11758198C2×C418yescomplemented
121C2×#11758198D418yes—
122C2×#11758198C2314yes—
123C2×#11758198C2314yes—
124C2×#11758198C2314yes—
125C2×#11758198C2314yes—
126C2×#11758198C2314yes—
127C2×#11758198C2314yes—
128C2×#11758198C2314yes—
129C2×#11758198C2314yes—
130C2×#11758198C2314yes—
131C2×#11758198C2314yes—
132C22⋊C4×D61C2×C4164yescomplemented
133C2×C4×Dic61—24no—
134C2×C4×Dic61—42no—
135C2×C4×Dic61C2314yescomplemented
136C2×C4×Dic61C2314yescomplemented
137#14519684C2314yescomplemented
138#14519684C2314yescomplemented
139#14519684C2314yescomplemented
140#14519684C2314yescomplemented
141#14519684C2314yescomplemented
142#14519684C2314yescomplemented
143C25×C61C2311yescharacteristic
144C23×C4×C61—24no—
145C23×C4×C61—24no—
146C23×C4×C61—42no—
147C23×C4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149C23×C4×C61C2311yescharacteristic
150C23×C4×C61C2314yes—
151C23×C4×C61C2311yescharacteristic
152C23×C4×C61C2311yescharacteristic
153C23×C4×C61C2311yescharacteristic
154C2×C22⋊C4×C61—24no—
155C2×C22⋊C4×C61C2×C418yes—
156C2×C22⋊C4×C61C2314yes—
157C2×C22⋊C4×C61C2314yes—
158C2×C42×C61—24no—
159C2×C42×C61—42no—
160C2×C42×C61C2314yescomplemented
161C2×C42×C61C2314yescomplemented
162#95×C61C2314yescomplemented
163#95×C61C2314yescomplemented
164C24×C61—22no—
165C24×C61—22no—
166C24×C61—22no—
167C24×C61—22no—
168C24×C61C22×C414yes—
169C24×C61#4114yes—
170C24×C61#4114yes—
171C24×C61C2412yes—
172C24×C61C2411yescharacteristic
173C23×D61—22no—
174C23×D61—22no—
175C23×D61—22no—
176C23×D61—22no—
177C23×D61—232no—
178C23×D61—22no—
179C23×D61—28no—
180C23×D61—28no—
181C23×D61—22no—
182C23×D61—22no—
183C23×D61—22no—
184C23×D61—22no—
185C23×D61—22no—
186C23×D61—232no—
187C23×D61—28no—
188C23×D61—28no—
189C23×D61—416no—
190C23×D61—44no—
191C23×D61—44no—
192C23×D61—416no—
193C23×D61—416no—
194C23×D61—416no—
195C23×D61—416no—
196C23×D61C22×C414yes—
197C23×D61C22×C4116yes—
198C23×D61C22×C414yes—
199C23×D61C2×D414yes—
200C23×D61#4114yes—
201C23×D61C2412yes—
202C23×D61C2412yes—
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×C61—22no—
210C22×C4×C61—22no—
211C22×C4×C61—22no—
212C22×C4×C61—22no—
213C22×C4×C61—28no—
214C22×C4×C61—22no—
215C22×C4×C61—22no—
216C22×C4×C61—22no—
217C22×C4×C61—22no—
218C22×C4×C61—22no—
219C22×C4×C61—28no—
220C22×C4×C61—44no—
221C22×C4×C61—416no—
222C22×C4×C61C22×C414yes—
223C22×C4×C61C22×C414yes—
224C22×C4×C61C2×D414yes—
225C22×C4×C61C2412yes—
226C22×C4×C61C2412yes—
227C22×C4×C61C2412yes—
228C22×C4×C61C2412yes—
229C22×C4×C61C2412yes—
230C22×C4×C61C2412yes—
231C22×Dic61—22no—
232C22×Dic61—22no—
233C22×Dic61—22no—
234C22×Dic61—22no—
235C22×Dic61—22no—
236C22×Dic61—22no—
237C22×Dic61—22no—
238C22×Dic61—22no—
239C22×Dic61—28no—
240C22×Dic61—22no—
241C22×Dic61—22no—
242C22×Dic61—22no—
243C22×Dic61—22no—
244C22×Dic61—22no—
245C22×Dic61—22no—
246C22×Dic61—22no—
247C22×Dic61—28no—
248C22×Dic61—44no—
249C22×Dic61—416no—
250C22×Dic61C22×C414yes—
251C22×Dic61C22×C414yes—
252C22×Dic61C2×D414yes—
253C22×Dic61C2412yes—
254C22×Dic61C2412yes—
255C22×Dic61C2412yes—
256C22×Dic61C2412yes—
257C22×Dic61C2412yes—
258C22×Dic61C2412yes—
259C2×C4×D61—232no—
260C2×C4×D61—28no—
261C2×C4×D61—28no—
262C2×C4×D61—416no—
263C2×C4×D61—44no—
264C2×C4×D61—44no—
265C2×C4×D61C22×C4116yescomplemented
266C2×C4×D61C22×C4116yescomplemented
267C22⋊C4×C61—28no—
268C22⋊C4×C61C22×C4116yes—
269C42×C61—28no—
270C42×C61—44no—
271C22⋊Dic61—28no—
272C22⋊Dic61C22×C4116yes—
273#11758198—28no—
274#11758198—28no—
275#11758198—28no—
276#11758198—28no—
277#11758198—28no—
278#11758198—44no—
279#11758198—44no—
280#11758198C22×C4116yescomplemented
281#11758198C22×C4116yescomplemented
282#11758198C2×D4116yes—
283#11758196—28no—
284#11758196—28no—
285#11758196—44no—
286#11758196—44no—
287C4×Dic61—28no—
288C4×Dic61—44no—
289C23×C61—28no—
290C23×C61—28no—
291C23×C61—28no—
292C23×C61—28no—
293C23×C61—28no—
294C23×C61—28no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—22no—
299C23×C61#117116yescomplemented
300C23×C61C23×C414yes—
301C23×C61C23×C412yes—
302C23×C61C22×D412yes—
303C23×C61C2×#4114yes—
304C23×C61C2×#4114yes—
305C23×C61C2×#4112yes—
306C23×C61C2×#4112yes—
307C23×C61C2×#4112yes—
308C23×C61H(5,𝔽2)12yes—
309C23×C61H(5,𝔽2)12yes—
310C23×C61C2511yescharacteristic
311C22×D61—28no—
312C22×D61—28no—
313C22×D61—28no—
314C22×D61—28no—
315C22×D61—28no—
316C22×D61—28no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—28no—
322C22×D61—232no—
323C22×D61—28no—
324C22×D61—28no—
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—22no—
328C22×D61—22no—
329C22×D61—22no—
330C22×D61—22no—
331C22×D61—232no—
332C22×D61—416no—
333C22×D61—4128no—
334C22×D61—416no—
335C22×D61—416no—
336C22×D61—416no—
337C22×D61—416no—
338C22×D61—44no—
339C22×D61—44no—
340C22×D61—44no—
341C22×D61—44no—
342C22×D61C4×D4116yes—
343C22×D61C23×C414yes—
344C22×D61C23×C414yes—
345C22×D61C22×D414yes—
346C22×D61C2×#4114yes—
347C2×C4×C61—28no—
348C2×C4×C61—28no—
349C2×C4×C61—28no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—416no—
366C2×C4×C61—44no—
367C2×C4×C61—44no—
368C2×C4×C61—44no—
369C2×C4×C61C23×C414yes—
370C2×C4×C61C23×C414yes—
371C2×C4×C61C22×D414yes—
372C2×Dic61—28no—
373C2×Dic61—28no—
374C2×Dic61—28no—
375C2×Dic61—22no—
376C2×Dic61—22no—
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—22no—
380C2×Dic61—22no—
381C2×Dic61—22no—
382C2×Dic61—22no—
383C2×Dic61—22no—
384C2×Dic61—22no—
385C2×Dic61—22no—
386C2×Dic61—22no—
387C2×Dic61—22no—
388C2×Dic61—22no—
389C2×Dic61—22no—
390C2×Dic61—416no—
391C2×Dic61—44no—
392C2×Dic61—44no—
393C2×Dic61—44no—
394C2×Dic61C23×C414yes—
395C2×Dic61C23×C414yes—
396C2×Dic61C22×D414yes—
397C4×D61—232no—
398C4×D61—416no—
399C2×#2342—611nomaximal, Sylow
400C22×C61—232no—
401C22×C61—24no—
402C22×C61—24no—
403C22×C61—24no—
404C22×C61—24no—
405C22×C61—24no—
406C22×C61—24no—
407C22×C61C2×#11714yes—
408C22×C61C2×#11718yescomplemented
409C22×C61C2×C4×D414yes—
410C22×C61#51814yes—
411C22×C61#54614yes—
412C22×C61#54614yes—
413C22×C61#55114yes—
414C22×C61#55114yes—
415C22×C61C24×C411yescharacteristic
416C22×C61C23×D411yescharacteristic
417C22×C61C22×#4111yescharacteristic
418C22×C61C22×#4111yescharacteristic
419C22×C61C22×#4111yescharacteristic
420C22×C61C2×H(5,𝔽2)11yescharacteristic
421C22×C61C2×H(5,𝔽2)11yescharacteristic
422C2×D61—232no—
423C2×D61—24no—
424C2×D61—24no—
425C2×D61—24no—
426C2×D61—24no—
427C2×D61—24no—
428C2×D61—24no—
429C2×D61—24no—
430C2×D61—24no—
431C2×D61—24no—
432C2×D61—464no—
433C2×D61—416no—
434C2×D61—42no—
435C2×D61—42no—
436C2×D61—42no—
437C2×D61—42no—
438C2×D61C2×C4×D418yes—
439C4×C61—24no—
440C4×C61—24no—
441C4×C61—24no—
442C4×C61—42no—
443C4×C61—42no—
444C4×C61—42no—
445Dic61—24no—
446Dic61—24no—
447Dic61—24no—
448Dic61—42no—
449Dic61—42no—
450Dic61—42no—
451C22×#117—611no—
452C23×C22⋊C4—611no—
453C23×C22⋊C4—611no—
454#2342—6116no—
455C2×#388—611no—
456C2×#388—611no—
457C2×#388—611no—
458C2×#388—611no—
459C2×#385—611no—
460C2×#385—611no—
461C2×#381—611no—
462C2×#380—611no—
463C2×#379—611no—
464C2×C4×C22⋊C4—611no—
465C2×C4×C22⋊C4—611no—
466C2×C4×C22⋊C4D6111yescharacteristic, complemented
467C2×C61—28no—
468C2×C61#234218yescomplemented
469C2×C61C22×#11711yescharacteristic
470C2×C61C22×C4×D411yescharacteristic
471C2×C61C2×#51811yescharacteristic
472C2×C61C2×#54611yescharacteristic
473C2×C61C2×#54611yescharacteristic
474C2×C61C2×#55111yescharacteristic
475C2×C61C2×#55111yescharacteristic
476D61—28no—
477D61—44no—
478C26—611no—
479C24×C4—611no—
480C24×C4—611no—
481C24×C4—611no—
482C24×C4C2×D6111yescharacteristic
483C2×#117—618no—
484C2×#117—1228no—
485C22×C4⋊C4—611no—
486C22×C4⋊C4—611no—
487C22×C4⋊C4—611no—
488C22×C4⋊C4—611no—
489C22×C22⋊C4—611no—
490C22×C22⋊C4—611no—
491C22×C22⋊C4—611no—
492C22×C22⋊C4—611no—
493C22×C22⋊C4—6116no—
494C22×C22⋊C4—618no—
495C22×C22⋊C4—611no—
496C22×C22⋊C4—618no—
497C22×C22⋊C4—611no—
498C22×C22⋊C4—611no—
499C22×C22⋊C4—611no—
500C22×C22⋊C4—611no—
501C22×C22⋊C4—611no—
502C22×C22⋊C4—611no—
503C22×C22⋊C4—611no—
504C22×C22⋊C4—1228no—
505C22×C22⋊C4C2×D6111yescharacteristic
506C22×C22⋊C4C2×D6111yescharacteristic
507C22×C42—611no—
508C22×C42—611no—
509C22×C42C2×D6111yescharacteristic, complemented
510C22×C42C2×D6111yescharacteristic, complemented
511#388—618no—
512#388—618no—
513#388—618no—
514#388—618no—
515#385—618no—
516#385—618no—
517#381—618no—
518#380—618no—
519#379—618no—
520C4×C22⋊C4—618no—
521C4×C22⋊C4—618no—
522C4×C22⋊C4C2×D6118yescomplemented
523C2×#95—611no—
524C2×#95—611no—
525C2×#95—611no—
526C2×#95—611no—
527C2×#95—611no—
528C2×#95—611no—
529C2×#95C2×D6111yescharacteristic, complemented
530C2×#95C2×D6111yescharacteristic, complemented
531C61C2×#234211yescharacteristic, complemented, Sylow
532C25—611no—
533C25—611no—
534C25—618no—
535C25—614no—
536C25—1224no—
537C25—1224no—
538C25—1224no—
539C25—1224no—
540C25—2442no—
541C25—2442no—
542C25C22×D6111yescharacteristic
543C23×C4—24no—
544C23×C4—24no—
545C23×C4—42no—
546C23×C4—611no—
547C23×C4—611no—
548C23×C4—611no—
549C23×C4—618no—
550C23×C4—614no—
551C23×C4—618no—
552C23×C4—614no—
553C23×C4—611no—
554C23×C4—611no—
555C23×C4—611no—
556C23×C4—614no—
557C23×C4—1224no—
558C23×C4—1224no—
559C23×C4—1224no—
560C23×C4—1224no—
561C23×C4—2442no—
562C23×C4—2442no—
563C23×C4—2442no—
564C23×C4C22×D6111yescharacteristic
565C23×C4C22×D6111yescharacteristic
566C23×C4C22×D6111yescharacteristic
567C23×C4C22×D6114yes—
568C23×C4C22×D6111yescharacteristic
569C23×C4C22×D6111yescharacteristic
570C23×C4C22×D6111yescharacteristic
571#117—12232no—
572C2×C4⋊C4—614no—
573C2×C4⋊C4—614no—
574C2×C4⋊C4—614no—
575C2×C4⋊C4—614no—
576C2×C4⋊C4—1224no—
577C2×C4⋊C4—1224no—
578C2×C4⋊C4—2442no—
579C2×C4⋊C4—2442no—
580C2×C22⋊C4—24no—
581C2×C22⋊C4—618no—
582C2×C22⋊C4—614no—
583C2×C22⋊C4—618no—
584C2×C22⋊C4—618no—
585C2×C22⋊C4—618no—
586C2×C22⋊C4—614no—
587C2×C22⋊C4—614no—
588C2×C22⋊C4—614no—
589C2×C22⋊C4—6164no—
590C2×C22⋊C4—614no—
591C2×C22⋊C4—614no—
592C2×C22⋊C4—614no—
593C2×C22⋊C4—614no—
594C2×C22⋊C4—614no—
595C2×C22⋊C4—614no—
596C2×C22⋊C4—614no—
597C2×C22⋊C4—614no—
598C2×C22⋊C4—12232no—
599C2×C22⋊C4—1224no—
600C2×C22⋊C4—1224no—
601C2×C22⋊C4—1224no—
602C2×C22⋊C4—1224no—
603C2×C22⋊C4—1224no—
604C2×C22⋊C4—1224no—
605C2×C22⋊C4—2442no—
606C2×C22⋊C4—2442no—
607C2×C22⋊C4C4×D6118yes—
608C2×C22⋊C4C22×D6114yes—
609C2×C22⋊C4C22×D6114yes—
610C2×C42—24no—
611C2×C42—42no—
612C2×C42—614no—
613C2×C42—614no—
614C2×C42—1224no—
615C2×C42—2442no—
616C2×C42C22×D6114yescomplemented
617C2×C42C22×D6114yescomplemented
618#95—614no—
619#95—614no—
620#95—614no—
621#95—614no—
622#95—614no—
623#95—614no—
624#95C22×D6114yescomplemented
625#95C22×D6114yescomplemented
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—614no—
631C24—614no—
632C24—614no—
633C24—612no—
634C24—614no—
635C24—612no—
636C24—6116no—
637C24—1228no—
638C24—12232no—
639C24—1228no—
640C24—1222no—
641C24—1222no—
642C24—1222no—
643C24—1222no—
644C24—1222no—
645C24—1222no—
646C24—1228no—
647C24—1228no—
648C24—1222no—
649C24—1222no—
650C24—1222no—
651C24—1222no—
652C24—12232no—
653C24—24416no—
654C24—2444no—
655C24—2444no—
656C24—24416no—
657C24—24416no—
658C24—24416no—
659C24—24416no—
660C24C2×C4×D6114yes—
661C24#1175822214yes—
662C24#1175822214yes—
663C24C23×D6112yes—
664C24C23×D6111yescharacteristic
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—28no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—28no—
682C22×C4—44no—
683C22×C4—416no—
684C22×C4—614no—
685C22×C4—614no—
686C22×C4—614no—
687C22×C4—612no—
688C22×C4—612no—
689C22×C4—612no—
690C22×C4—6116no—
691C22×C4—6116no—
692C22×C4—612no—
693C22×C4—612no—
694C22×C4—612no—
695C22×C4—1228no—
696C22×C4—12232no—
697C22×C4—1228no—
698C22×C4—1228no—
699C22×C4—1222no—
700C22×C4—1222no—
701C22×C4—1222no—
702C22×C4—1222no—
703C22×C4—1222no—
704C22×C4—1222no—
705C22×C4—1222no—
706C22×C4—1222no—
707C22×C4—1222no—
708C22×C4—1222no—
709C22×C4—1222no—
710C22×C4—1228no—
711C22×C4—1222no—
712C22×C4—1222no—
713C22×C4—1222no—
714C22×C4—1222no—
715C22×C4—24416no—
716C22×C4—2444no—
717C22×C4—2444no—
718C22×C4—2444no—
719C22×C4—24416no—
720C22×C4C2×C4×D6114yes—
721C22×C4C2×C4×D6114yes—
722C22×C4D4×D6114yes—
723C22×C4C23×D6112yes—
724C22×C4C23×D6112yes—
725C22×C4C23×D6112yes—
726C22×C4C23×D6112yes—
727C22×C4C23×D6112yes—
728C22×C4C23×D6112yes—
729C4⋊C4—1228no—
730C4⋊C4—1228no—
731C4⋊C4—2444no—
732C4⋊C4—2444no—
733C22⋊C4—28no—
734C22⋊C4—6116no—
735C22⋊C4—6116no—
736C22⋊C4—6116no—
737C22⋊C4—6116no—
738C22⋊C4—1228no—
739C22⋊C4—1228no—
740C22⋊C4—1228no—
741C22⋊C4—1228no—
742C22⋊C4—1228no—
743C22⋊C4—1228no—
744C22⋊C4—2444no—
745C22⋊C4—2444no—
746C22⋊C4C2×C4×D61116yes—
747C42—28no—
748C42—44no—
749C42—1228no—
750C42—2444no—
751C23—28no—
752C23—28no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—28no—
758C23—28no—
759C23—28no—
760C23—28no—
761C23—6116no—
762C23—614no—
763C23—614no—
764C23—614no—
765C23—614no—
766C23—12232no—
767C23—1228no—
768C23—1228no—
769C23—1222no—
770C23—1222no—
771C23—1222no—
772C23—1222no—
773C23—1228no—
774C23—1228no—
775C23—1228no—
776C23—1228no—
777C23—1228no—
778C23—12232no—
779C23—1228no—
780C23—1228no—
781C23—1222no—
782C23—1222no—
783C23—1222no—
784C23—1222no—
785C23—1222no—
786C23—1222no—
787C23—24416no—
788C23—24416no—
789C23—24416no—
790C23—24416no—
791C23—24416no—
792C23—244128no—
793C23—2444no—
794C23—2444no—
795C23—2444no—
796C23—2444no—
797C23#14519734116yescomplemented
798C23C22×C4×D6114yes—
799C23C22×C4×D6112yes—
800C23C2×D4×D6112yes—
801C23#41×D6112yes—
802C23C2×#1175822214yes—
803C23C2×#1175822214yes—
804C23C2×#1175822212yes—
805C23C2×#1175822212yes—
806C23#1451982212yes—
807C23#1451982312yes—
808C23C24×D6111yescharacteristic
809C2×C4—28no—
810C2×C4—28no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—28no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—416no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—614no—
832C2×C4—614no—
833C2×C4—614no—
834C2×C4—12232no—
835C2×C4—1228no—
836C2×C4—1228no—
837C2×C4—1222no—
838C2×C4—1222no—
839C2×C4—1222no—
840C2×C4—1222no—
841C2×C4—1222no—
842C2×C4—1222no—
843C2×C4—1228no—
844C2×C4—1222no—
845C2×C4—1222no—
846C2×C4—1222no—
847C2×C4—1222no—
848C2×C4—1222no—
849C2×C4—1222no—
850C2×C4—1222no—
851C2×C4—1222no—
852C2×C4—1222no—
853C2×C4—24416no—
854C2×C4—24416no—
855C2×C4—2444no—
856C2×C4—2444no—
857C2×C4—2444no—
858C2×C4C22×C4×D6114yes—
859C2×C4C22×C4×D6114yes—
860C2×C4C2×D4×D6114yes—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—232no—
868C22—618no—
869C22—1224no—
870C22—1224no—
871C22—1224no—
872C22—1224no—
873C22—1224no—
874C22—1224no—
875C22—12232no—
876C22—1224no—
877C22—1224no—
878C22—1224no—
879C22—24464no—
880C22—2442no—
881C22—2442no—
882C22—2442no—
883C22—2442no—
884C22—24416no—
885C22C2×#1451973414yes—
886C22C2×#1451973418yescomplemented
887C22C4×D4×D6114yes—
888C22#1684023414yes—
889C22#1684040214yes—
890C22#1684040814yes—
891C22#1684043614yes—
892C22#1684044114yes—
893C22C23×C4×D6111yescharacteristic
894C22C22×D4×D6111yescharacteristic
895C22C2×#41×D6111yescharacteristic
896C22C22×#1175822211yescharacteristic
897C22C22×#1175822211yescharacteristic
898C22C2×#1451982211yescharacteristic
899C22C2×#1451982311yescharacteristic
900C4—24no—
901C4—24no—
902C4—24no—
903C4—42no—
904C4—42no—
905C4—42no—
906C4—1224no—
907C4—1224no—
908C4—1224no—
909C4—2442no—
910C4—2442no—
911C4—2442no—
912C2—28no—
913C2—1228no—
914C2—2444no—
915C2#2144866218yesdirect product factor
916C2C22×#1451973411yescharacteristic
917C2C2×C4×D4×D6111yescharacteristic
918C2C2×#1684023411yescharacteristic
919C2C2×#1684040211yescharacteristic
920C2C2×#1684040811yescharacteristic
921C2C2×#1684043611yescharacteristic
922C2C2×#1684044111yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C4×C22⋊C4×C61C2
socleC24×C61C24
prime radicalC25×D61C22
cosocleC23×C61C25
hypercenterC2×C4×C22⋊C4D61
hypocenterC61C2×#2342
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#14519734C2semidirect
4. #21448662C2direct (N × H)
5. C2×#16839653C2semidirect
6. C2×#16839653C2semidirect
7. C2×#16839651C2semidirect
8. C2×#16839651C2semidirect
9. C2×#16839635C2semidirect
10. C2×#16839634C2semidirect
11. C2×#16839624C2semidirect
12. C2×#16839621C2semidirect
14. C2×C22⋊C4×Dic61C2semidirect
15. C2×C4×#11758198C2semidirect
16. C2×C4×C22⋊C4×C61C2semidirect
22. C2×#14519734C22semidirect
23. C22×#11758196C22semidirect
24. C22×#11758196C22semidirect
25. C22×#11758196C22semidirect
26. C22×#11758196C22semidirect
41. C2×C22⋊C4×D61C4semidirect
43. C22×C4×Dic61C22semidirect
44. C22×C4×Dic61C22semidirect
45. #16839653C22semidirect
46. #16839653C22semidirect
47. #16839651C22semidirect
48. #16839651C22semidirect
49. #16839635C22semidirect
50. #16839634C22semidirect
51. #16839624C22semidirect
52. #16839621C22semidirect
54. C22⋊C4×Dic61C22semidirect
55. C4×#11758198C22semidirect
56. C2×#14519684C22semidirect
57. C2×#14519684C22semidirect
58. C2×#14519684C22semidirect
59. C2×#14519684C22semidirect
60. C2×#14519684C22semidirect
61. C2×#14519684C22semidirect
65. C22×C42×C61C22semidirect
66. C22×C42×C61C22semidirect
67. C4×C22⋊C4×C61C22semidirect
68. C2×#95×C61C22semidirect
69. C2×#95×C61C22semidirect
94. C22×C4×D61C2×C4semidirect
95. C22×C4×D61C2×C4semidirect
103. C2×#11758196C23semidirect
104. C2×#11758196C23semidirect
105. C2×#11758196C23semidirect
106. C2×#11758196C23semidirect
119. C2×#11758198C2×C4semidirect
120. C2×#11758198C2×C4semidirect
132. C22⋊C4×D61C2×C4semidirect
135. C2×C4×Dic61C23semidirect
136. C2×C4×Dic61C23semidirect
137. #14519684C23semidirect
138. #14519684C23semidirect
139. #14519684C23semidirect
140. #14519684C23semidirect
141. #14519684C23semidirect
142. #14519684C23semidirect
160. C2×C42×C61C23semidirect
161. C2×C42×C61C23semidirect
162. #95×C61C23semidirect
163. #95×C61C23semidirect
265. C2×C4×D61C22×C4semidirect
266. C2×C4×D61C22×C4semidirect
280. #11758198C22×C4semidirect
281. #11758198C22×C4semidirect
299. C23×C61#117semidirect
408. C22×C61C2×#117semidirect
466. C2×C4×C22⋊C4D61semidirect
468. C2×C61#2342semidirect
509. C22×C42C2×D61semidirect
510. C22×C42C2×D61semidirect
522. C4×C22⋊C4C2×D61semidirect
529. C2×#95C2×D61semidirect
530. C2×#95C2×D61semidirect
531. C61C2×#2342semidirect
616. C2×C42C22×D61semidirect
617. C2×C42C22×D61semidirect
624. #95C22×D61semidirect
625. #95C22×D61semidirect
797. C23#14519734semidirect
886. C22C2×#14519734semidirect
915. C2#21448662direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197342
C23×#117581982
C22×C22⋊C4×D612
#214486622
C2×#168396532
C2×#168396512
C2×#168396352
C2×#168396342
C2×#168396242
C2×#168396212
C2×#168396172
C2×C22⋊C4×Dic612
C2×C4×#117581982
C2×C4×C22⋊C4×C612
C2×#234261