Finite Group Databasebeta

← C2×#21449365 #29847732

Subgroups — C2×#21449365 #29847732

Order 15616.

3938 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519762C211yesmaximal, characteristic, complemented
2C22×#14519759C211yesmaximal, characteristic, complemented
3C22×#14519750C211yesmaximal, characteristic
4C22×#14519739C211yesmaximal, characteristic, complemented
5#21449365C2116yesmaximal, direct product factor
6C2×#16839692C211yesmaximal, characteristic, complemented
7C2×#16839691C211yesmaximal, characteristic, complemented
8C2×#16839677C211yesmaximal, characteristic, complemented
9C2×#16839657C211yesmaximal, characteristic, complemented
10C2×#16839656C211yesmaximal, characteristic, complemented
11C2×#16839638C211yesmaximal, characteristic, complemented
12C2×#16839638C211yesmaximal, characteristic, complemented
13C2×#16839633C211yesmaximal, characteristic, complemented
14C2×#16839619C211yesmaximal, characteristic, complemented
15C2×#95×D61C211yesmaximal, characteristic, complemented
16C2×C61×#396C211yesmaximal, characteristic, complemented
17C23×D244C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C23×C22⋊D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C23×C4×D61C2211yescharacteristic
22C23×C4×D61C2211yescharacteristic
23C23×C4×D61C2211yescharacteristic
24C2×#14519762—28no—
25C2×#14519762C2218yescomplemented
26C2×#14519759—28no—
27C2×#14519759C2218yescomplemented
28C2×#14519750—28no—
29C2×#14519750C2218yes—
30C2×#14519739—28no—
31C2×#14519739C2218yescomplemented
32C22×C4⋊Dic61C2211yescharacteristic
33C22×#11758196C2211yescharacteristic
34C22×#11758196C2211yescharacteristic
35C22×#11758196C2211yescharacteristic
36C22×#11758196C2211yescharacteristic
37C22×C22⋊Dic61C2211yescharacteristic
38C22×C22⋊Dic61C2211yescharacteristic
39C22×#11758198C2211yescharacteristic
40C22×#11758198C2211yescharacteristic
41C22×#11758198C2211yescharacteristic
42C22×#11758198C2211yescharacteristic
43C22×#11758198C2211yescharacteristic
44C22×#11758198C2211yescharacteristic
45C22×C4×Dic61C2211yescharacteristic
46#16839692C2218yescomplemented
47#16839691C2218yescomplemented
48#16839677C2218yescomplemented
49#16839657C2218yescomplemented
50#16839656C2218yescomplemented
51#16839638C2218yescomplemented
52#16839638C2218yescomplemented
53#16839633C2218yescomplemented
54#16839619C2218yescomplemented
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C2×#14519684C2211yescharacteristic
62#95×D61C2218yescomplemented
63C22×C4⋊C4×C61C2211yescharacteristic
64C22×C4⋊C4×C61C2211yescharacteristic
65C22×C4⋊C4×C61C2211yescharacteristic
66C22×C22⋊C4×C61C2211yescharacteristic
67C22×C22⋊C4×C61C2211yescharacteristic
68C22×C22⋊C4×C61C2211yescharacteristic
69C61×#396C2218yescomplemented
70C2×#95×C61C2211yescharacteristic
71C24×D61C2311yescharacteristic
72C24×D61C2311yescharacteristic
73C22×D244—24no—
74C22×D244—24no—
75C22×D244D418yes—
76C22×D244C2314yes—
77C22×C22⋊D61—24no—
78C22×C22⋊D61—24no—
79C22×C22⋊D61—24no—
80C22×C22⋊D61—24no—
81C22×C22⋊D61—24no—
82C22×C22⋊D61—42no—
83C22×C22⋊D61C2314yes—
84C22×C22⋊D61C2314yes—
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89C23×Dic61C2311yescharacteristic
90C23×Dic61C2311yescharacteristic
91C22×C4×D61—24no—
92C22×C4×D61—24no—
93C22×C4×D61—24no—
94C22×C4×D61—24no—
95C22×C4×D61—24no—
96C22×C4×D61—24no—
97C22×C4×D61—24no—
98C22×C4×D61—24no—
99C22×C4×D61—24no—
100C22×C4×D61—42no—
101C22×C4×D61—42no—
102C22×C4×D61—42no—
103C22×C4×D61C2314yes—
104C22×C4×D61C2314yes—
105C22×C4×D61C2314yes—
106C22×C4×D61C2314yes—
107#14519762—232no—
108#14519759—232no—
109#14519750—232no—
110#14519739—232no—
111C2×C4⋊Dic61—24no—
112C2×C4⋊Dic61C2314yes—
113C2×#11758196—24no—
114C2×#11758196—24no—
115C2×#11758196—24no—
116C2×#11758196—24no—
117C2×#11758196C2314yes—
118C2×#11758196C2314yes—
119C2×#11758196C2314yes—
120C2×#11758196C2314yes—
121C2×C22⋊Dic61—24no—
122C2×C22⋊Dic61—24no—
123C2×C22⋊Dic61C2314yes—
124C2×C22⋊Dic61C2314yes—
125C2×#11758198—24no—
126C2×#11758198—24no—
127C2×#11758198—24no—
128C2×#11758198—24no—
129C2×#11758198—24no—
130C2×#11758198D418yescomplemented
131C2×#11758198C2314yes—
132C2×#11758198C2314yes—
133C2×#11758198C2314yes—
134C2×#11758198C2314yes—
135C2×#11758198C2314yes—
136C2×#11758198C2314yes—
137C2×C4×Dic61—24no—
138C2×C4×Dic61C2314yes—
139#14519684C2314yes—
140#14519684C2314yes—
141#14519684C2314yes—
142#14519684C2314yes—
143#14519684C2314yes—
144#14519684C2314yes—
145#14519684C2314yes—
146C25×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149C23×C4×C61C2311yescharacteristic
150C23×C4×C61C2311yescharacteristic
151C23×C4×C61C2311yescharacteristic
152C23×C4×C61C2311yescharacteristic
153C2×C4⋊C4×C61—24no—
154C2×C4⋊C4×C61—24no—
155C2×C4⋊C4×C61—42no—
156C2×C4⋊C4×C61C2314yes—
157C2×C4⋊C4×C61C2314yes—
158C2×C4⋊C4×C61C2314yes—
159C2×C22⋊C4×C61—24no—
160C2×C22⋊C4×C61—24no—
161C2×C22⋊C4×C61—42no—
162C2×C22⋊C4×C61C2314yes—
163C2×C22⋊C4×C61C2314yes—
164C2×C22⋊C4×C61C2314yes—
165#95×C61C2314yes—
166C24×C61—22no—
167C24×C61—22no—
168C24×C61—22no—
169C24×C61—22no—
170C24×C61—22no—
171C24×C61—22no—
172C24×C61—22no—
173C24×C61C2412yes—
174C24×C61C2411yescharacteristic
175C23×D61—22no—
176C23×D61—22no—
177C23×D61—22no—
178C23×D61—22no—
179C23×D61—22no—
180C23×D61—22no—
181C23×D61—22no—
182C23×D61—22no—
183C23×D61—22no—
184C23×D61—22no—
185C23×D61C2×D414yes—
186C23×D61C2×D414yes—
187C23×D61C2×D414yes—
188C23×D61#4114yes—
189C23×D61C2412yes—
190C23×D61C2412yes—
191C22×C4×C61—22no—
192C22×C4×C61—22no—
193C22×C4×C61—22no—
194C22×C4×C61—22no—
195C22×C4×C61—22no—
196C22×C4×C61—22no—
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×C61C2×D414yes—
208C22×C4×C61C2×D414yes—
209C22×C4×C61C2412yes—
210C22×C4×C61C2412yes—
211C22×C4×C61C2412yes—
212C22×C4×C61C2412yes—
213C22×C4×C61C2412yes—
214C22×C4×C61C2412yes—
215C2×C22⋊D61—28no—
216C2×C22⋊D61—28no—
217C2×C22⋊D61—28no—
218C2×C22⋊D61—28no—
219C2×C22⋊D61—28no—
220C2×C22⋊D61—44no—
221C2×C22⋊D61—416no—
222C2×C22⋊D61—416no—
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—22no—
238C22×Dic61C2×D414yes—
239C22×Dic61#4114yes—
240C22×Dic61#4114yes—
241C22×Dic61C2412yes—
242C22×Dic61C2412yes—
243C22×Dic61C2412yes—
244C22×Dic61C2412yes—
245C22×Dic61C2412yes—
246C22×Dic61C2412yes—
247C2×D244—232no—
248C2×D244—28no—
249C2×D244—28no—
250C2×D244C2×D4116yes—
251C2×C4×D61—28no—
252C2×C4×D61—28no—
253C2×C4×D61—28no—
254C2×C4×D61—28no—
255C2×C4×D61—28no—
256C2×C4×D61—28no—
257C2×C4×D61—28no—
258C2×C4×D61—28no—
259C2×C4×D61—28no—
260C2×C4×D61—44no—
261C2×C4×D61—44no—
262C2×C4×D61—44no—
263C2×C4×D61—416no—
264C2×C4×D61—416no—
265C2×C4×D61—416no—
266C2×C4×D61—416no—
267C4⋊C4×C61—28no—
268C4⋊C4×C61—28no—
269C4⋊C4×C61—44no—
270C22⋊C4×C61—28no—
271C22⋊C4×C61—28no—
272C22⋊C4×C61—44no—
273C22⋊Dic61—28no—
274C22⋊Dic61—28no—
275#11758198—28no—
276#11758198—28no—
277#11758198—28no—
278#11758198—28no—
279#11758198—28no—
280#11758198C2×D4116yescomplemented
281C4⋊Dic61—28no—
282#11758196—28no—
283#11758196—28no—
284#11758196—28no—
285#11758196—28no—
286C4×Dic61—28no—
287C23×C61—22no—
288C23×C61—22no—
289C23×C61—22no—
290C23×C61—22no—
291C23×C61—22no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—44no—
295C23×C61—44no—
296C23×C61—44no—
297C23×C61—44no—
298C23×C61—44no—
299C23×C61—44no—
300C23×C61—44no—
301C23×C61C22×D412yes—
302C23×C61C22×D412yes—
303C23×C61C2×#4112yes—
304C23×C61C2×#4112yes—
305C23×C61C2×#4112yes—
306C23×C61H(5,𝔽2)12yes—
307C23×C612−1+412yes—
308C23×C61C2511yescharacteristic
309C22×D61—28no—
310C22×D61—28no—
311C22×D61—28no—
312C22×D61—28no—
313C22×D61—28no—
314C22×D61—28no—
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—28no—
320C22×D61—28no—
321C22×D61—28no—
322C22×D61—22no—
323C22×D61—22no—
324C22×D61—22no—
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—22no—
328C22×D61—44no—
329C22×D61—44no—
330C22×D61—44no—
331C22×D61—44no—
332C22×D61#121116yes—
333C22×D61C22×D414yes—
334C22×D61C22×D414yes—
335C22×D61C22×D414yes—
336C22×D61C2×#4114yes—
337C2×C4×C61—28no—
338C2×C4×C61—28no—
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—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—44no—
356C2×C4×C61—44no—
357C2×C4×C61—44no—
358C2×C4×C61—44no—
359C2×C4×C61C22×D414yes—
360C2×C4×C61C22×D414yes—
361C22⋊D61—416no—
362C22⋊D61—416no—
363C2×Dic61—28no—
364C2×Dic61—28no—
365C2×Dic61—28no—
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—22no—
376C2×Dic61—22no—
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—22no—
380C2×Dic61—22no—
381C2×Dic61—44no—
382C2×Dic61—44no—
383C2×Dic61—44no—
384C2×Dic61C22×D414yes—
385C2×Dic61C2×#4114yes—
386C2×Dic61C2×#4114yes—
387D244—232no—
388C4×D61—416no—
389C4×D61—416no—
390C4×D61—416no—
391C4×D61—416no—
392C2×#2425—611nomaximal, Sylow
393C22×C61—42no—
394C22×C61—42no—
395C22×C61—42no—
396C22×C61—42no—
397C22×C61—42no—
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—88no—
401C22×C61C2×#12114yes—
402C22×C61#52914yes—
403C22×C61#53914yes—
404C22×C61#54614yes—
405C22×C61#54614yes—
406C22×C61#54714yes—
407C22×C61#54714yes—
408C22×C61C23×D411yescharacteristic
409C22×C61C23×D411yescharacteristic
410C22×C61C22×#4111yescharacteristic
411C22×C61C22×#4111yescharacteristic
412C22×C61C22×#4111yescharacteristic
413C22×C61C2×H(5,𝔽2)11yescharacteristic
414C22×C61C2×2−1+411yescharacteristic
415C2×D61—24no—
416C2×D61—232no—
417C2×D61—24no—
418C2×D61—24no—
419C2×D61—24no—
420C2×D61—24no—
421C2×D61—24no—
422C2×D61—24no—
423C2×D61—24no—
424C2×D61—24no—
425C2×D61—42no—
426C2×D61—416no—
427C2×D61—42no—
428C2×D61—42no—
429C2×D61—42no—
430C2×D61C2×#12118yes—
431C4×C61—24no—
432C4×C61—24no—
433C4×C61—42no—
434C4×C61—42no—
435C4×C61—42no—
436C4×C61—42no—
437Dic61—24no—
438Dic61—24no—
439Dic61—24no—
440Dic61—42no—
441Dic61—42no—
442Dic61—42no—
443C22×#123—611no—
444C22×#123—611no—
445C22×#121—611no—
446C22×C4×D4—611no—
447#2425—6116no—
448C2×#398—611no—
449C2×#397—611no—
450C2×#396D6111yescharacteristic, complemented
451C2×#394—611no—
452C2×#389—611no—
453C2×#388—611no—
454C2×#386—611no—
455C2×#386—611no—
456C2×#385—611no—
457C2×#380—611no—
458C22×#95—611no—
459C2×C61—82no—
460C2×C61#242518yescomplemented
461C2×C61C22×#12111yescharacteristic
462C2×C61C2×#52911yescharacteristic
463C2×C61C2×#53911yescharacteristic
464C2×C61C2×#54611yescharacteristic
465C2×C61C2×#54611yescharacteristic
466C2×C61C2×#54711yescharacteristic
467C2×C61C2×#54711yescharacteristic
468D61—28no—
469D61—44no—
470C23×D4—611no—
471C23×D4—611no—
472C23×D4—611no—
473C24×C4—611no—
474C24×C4—611no—
475C24×C4—611no—
476C24×C4—611no—
477C2×#123—618no—
478C2×#123—618no—
479C2×#123—1228no—
480C2×#123—1228no—
481C2×#121—618no—
482C2×#121—1228no—
483C2×C4×D4—618no—
484C2×C4×D4—1228no—
485C22×C4⋊C4—611no—
486C22×C4⋊C4—611no—
487C22×C4⋊C4—611no—
488C22×C4⋊C4—611no—
489C22×C4⋊C4—611no—
490C22×C4⋊C4C2×D6111yescharacteristic
491C22×C4⋊C4C2×D6111yescharacteristic
492C22×C4⋊C4C2×D6111yescharacteristic
493C22×C22⋊C4—611no—
494C22×C22⋊C4—611no—
495C22×C22⋊C4—611no—
496C22×C22⋊C4—611no—
497C22×C22⋊C4—611no—
498C22×C22⋊C4—611no—
499C22×C22⋊C4—611no—
500C22×C22⋊C4—611no—
501C22×C22⋊C4C2×D6111yescharacteristic
502C22×C22⋊C4C2×D6111yescharacteristic
503C22×C22⋊C4C2×D6111yescharacteristic
504C22×C42—611no—
505#398—618no—
506#397—618no—
507#396C2×D6118yescomplemented
508#394—618no—
509#389—618no—
510#388—618no—
511#386—618no—
512#386—618no—
513#385—618no—
514#380—618no—
515C2×#95—611no—
516C2×#95—611no—
517C2×#95—611no—
518C2×#95—611no—
519C2×#95—611no—
520C2×#95—611no—
521C2×#95—611no—
522C2×#95—618no—
523C2×#95C2×D6111yescharacteristic
524C61C2×#242511yescharacteristic, complemented, Sylow
525C25—611no—
526C25—611no—
527C25C22×D6111yescharacteristic
528C22×D4—614no—
529C22×D4—614no—
530C22×D4—618no—
531C22×D4—614no—
532C22×D4—1224no—
533C22×D4—1224no—
534C22×D4—1224no—
535C22×D4—1224no—
536C22×D4—1224no—
537C22×D4—1224no—
538C22×D4—1224no—
539C22×D4—2442no—
540C23×C4—611no—
541C23×C4—611no—
542C23×C4—611no—
543C23×C4—611no—
544C23×C4—611no—
545C23×C4—611no—
546C23×C4—614no—
547C23×C4—614no—
548C23×C4—614no—
549C23×C4—614no—
550C23×C4—1224no—
551C23×C4—1224no—
552C23×C4—1224no—
553C23×C4—1224no—
554C23×C4—1224no—
555C23×C4—1224no—
556C23×C4—1224no—
557C23×C4—1224no—
558C23×C4—1224no—
559C23×C4—2442no—
560C23×C4—2442no—
561C23×C4—2442no—
562C23×C4C22×D6111yescharacteristic
563C23×C4C22×D6111yescharacteristic
564C23×C4C22×D6111yescharacteristic
565C23×C4C22×D6111yescharacteristic
566C23×C4C22×D6111yescharacteristic
567C23×C4C22×D6111yescharacteristic
568#123—12232no—
569#123—12232no—
570#121—12232no—
571C4×D4—12232no—
572C2×C4⋊C4—24no—
573C2×C4⋊C4—24no—
574C2×C4⋊C4—42no—
575C2×C4⋊C4—614no—
576C2×C4⋊C4—614no—
577C2×C4⋊C4—614no—
578C2×C4⋊C4—614no—
579C2×C4⋊C4—614no—
580C2×C4⋊C4—1224no—
581C2×C4⋊C4—1224no—
582C2×C4⋊C4—1224no—
583C2×C4⋊C4—1224no—
584C2×C4⋊C4—1224no—
585C2×C4⋊C4C22×D6114yes—
586C2×C4⋊C4C22×D6114yes—
587C2×C4⋊C4C22×D6114yes—
588C2×C22⋊C4—24no—
589C2×C22⋊C4—24no—
590C2×C22⋊C4—42no—
591C2×C22⋊C4—618no—
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—614no—
599C2×C22⋊C4—614no—
600C2×C22⋊C4—1224no—
601C2×C22⋊C4—1224no—
602C2×C22⋊C4—1224no—
603C2×C22⋊C4—1224no—
604C2×C22⋊C4—1224no—
605C2×C22⋊C4—1224no—
606C2×C22⋊C4—1224no—
607C2×C22⋊C4C22×D6114yes—
608C2×C22⋊C4C22×D6114yes—
609C2×C22⋊C4C22×D6114yes—
610C2×C42—614no—
611C2×C42—1224no—
612#95—614no—
613#95—614no—
614#95—614no—
615#95—614no—
616#95—614no—
617#95—614no—
618#95—614no—
619#95C22×D6114yes—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—614no—
628C24—614no—
629C24—614no—
630C24—612no—
631C24—614no—
632C24—612no—
633C24—1222no—
634C24—1222no—
635C24—1222no—
636C24—1222no—
637C24—1222no—
638C24—1222no—
639C24—1222no—
640C24—1222no—
641C24—1222no—
642C24—1222no—
643C24C23×D6112yes—
644C24C23×D6111yescharacteristic
645C2×D4—6116no—
646C2×D4—1228no—
647C2×D4—12232no—
648C2×D4—1228no—
649C2×D4—1228no—
650C2×D4—1228no—
651C2×D4—1228no—
652C2×D4—1228no—
653C2×D4—1228no—
654C2×D4—2444no—
655C2×D4—24416no—
656C2×D4—24416no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
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—614no—
674C22×C4—614no—
675C22×C4—614no—
676C22×C4—612no—
677C22×C4—612no—
678C22×C4—612no—
679C22×C4—612no—
680C22×C4—612no—
681C22×C4—612no—
682C22×C4—1228no—
683C22×C4—1228no—
684C22×C4—1228no—
685C22×C4—1228no—
686C22×C4—1228no—
687C22×C4—1228no—
688C22×C4—1228no—
689C22×C4—1228no—
690C22×C4—1222no—
691C22×C4—1222no—
692C22×C4—1222no—
693C22×C4—1222no—
694C22×C4—1222no—
695C22×C4—1222no—
696C22×C4—1222no—
697C22×C4—1222no—
698C22×C4—1222no—
699C22×C4—1222no—
700C22×C4—1222no—
701C22×C4—1222no—
702C22×C4—1222no—
703C22×C4—1222no—
704C22×C4—1222no—
705C22×C4—1228no—
706C22×C4—2444no—
707C22×C4—2444no—
708C22×C4—2444no—
709C22×C4—24416no—
710C22×C4—24416no—
711C22×C4—24416no—
712C22×C4—24416no—
713C22×C4D4×D6114yes—
714C22×C4D4×D6114yes—
715C22×C4C23×D6112yes—
716C22×C4C23×D6112yes—
717C22×C4C23×D6112yes—
718C22×C4C23×D6112yes—
719C22×C4C23×D6112yes—
720C22×C4C23×D6112yes—
721C4⋊C4—28no—
722C4⋊C4—28no—
723C4⋊C4—44no—
724C4⋊C4—1228no—
725C4⋊C4—1228no—
726C4⋊C4—1228no—
727C4⋊C4—1228no—
728C4⋊C4—1228no—
729C22⋊C4—28no—
730C22⋊C4—28no—
731C22⋊C4—44no—
732C22⋊C4—6116no—
733C22⋊C4—1228no—
734C22⋊C4—1228no—
735C22⋊C4—1228no—
736C22⋊C4—1228no—
737C22⋊C4—1228no—
738C22⋊C4—1228no—
739C22⋊C4—1228no—
740C42—1228no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23—44no—
755C23—6116no—
756C23—614no—
757C23—614no—
758C23—614no—
759C23—614no—
760C23—1228no—
761C23—1222no—
762C23—1222no—
763C23—1222no—
764C23—1222no—
765C23—1228no—
766C23—1228no—
767C23—1228no—
768C23—1228no—
769C23—1228no—
770C23—1228no—
771C23—1222no—
772C23—1222no—
773C23—1222no—
774C23—1222no—
775C23—1222no—
776C23—1222no—
777C23—1228no—
778C23—1228no—
779C23—2444no—
780C23—2444no—
781C23—2444no—
782C23—2444no—
783C23C2×D4×D6112yes—
784C23C2×D4×D6112yes—
785C23#41×D6112yes—
786C23#41×D6112yes—
787C23#41×D6112yes—
788C23#1451982212yes—
789C23#1451982512yes—
790C23C24×D6111yescharacteristic
791D4—12232no—
792D4—24416no—
793D4—24416no—
794C2×C4—28no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—28no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—614no—
817C2×C4—614no—
818C2×C4—614no—
819C2×C4—1222no—
820C2×C4—1222no—
821C2×C4—1222no—
822C2×C4—1222no—
823C2×C4—1222no—
824C2×C4—1222no—
825C2×C4—1228no—
826C2×C4—1228no—
827C2×C4—1228no—
828C2×C4—1222no—
829C2×C4—1222no—
830C2×C4—1222no—
831C2×C4—1222no—
832C2×C4—1222no—
833C2×C4—1222no—
834C2×C4—1222no—
835C2×C4—1222no—
836C2×C4—1222no—
837C2×C4—24416no—
838C2×C4—24416no—
839C2×C4—24416no—
840C2×C4—24416no—
841C2×C4—2444no—
842C2×C4—2444no—
843C2×C4—2444no—
844C2×C4C2×D4×D6114yes—
845C2×C4C2×D4×D6114yes—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—88no—
854C22—618no—
855C22—1224no—
856C22—1224no—
857C22—1224no—
858C22—1224no—
859C22—1224no—
860C22—12232no—
861C22—1224no—
862C22—1224no—
863C22—1224no—
864C22—1224no—
865C22—2442no—
866C22—2442no—
867C22—2442no—
868C22—24416no—
869C22—2442no—
870C22#121×D6114yes—
871C22#1684029514yes—
872C22#1684035814yes—
873C22#1684040114yes—
874C22#1684040914yes—
875C22#1684041414yes—
876C22#1684041414yes—
877C22C22×D4×D6111yescharacteristic
878C22C22×D4×D6111yescharacteristic
879C22C2×#41×D6111yescharacteristic
880C22C2×#41×D6111yescharacteristic
881C22C2×#41×D6111yescharacteristic
882C22C2×#1451982211yescharacteristic
883C22C2×#1451982511yescharacteristic
884C4—24no—
885C4—24no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—1224no—
891C4—1224no—
892C4—1224no—
893C4—2442no—
894C4—2442no—
895C4—2442no—
896C2—82no—
897C2—1228no—
898C2—2444no—
899C2#2144936518yesdirect product factor
900C2C2×#121×D6111yescharacteristic
901C2C2×#1684029511yescharacteristic
902C2C2×#1684035811yescharacteristic
903C2C2×#1684040111yescharacteristic
904C2C2×#1684040911yescharacteristic
905C2C2×#1684041411yescharacteristic
906C2C2×#1684041411yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#396C2
socleC24×C61C24
prime radicalC22×#14519750C2
hypercenterC2×#396D61
hypocenterC61C2×#2425
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#14519762C2semidirect
2. C22×#14519759C2semidirect
4. C22×#14519739C2semidirect
5. #21449365C2direct (N × H)
6. C2×#16839692C2semidirect
7. C2×#16839691C2semidirect
8. C2×#16839677C2semidirect
9. C2×#16839657C2semidirect
10. C2×#16839656C2semidirect
11. C2×#16839638C2semidirect
12. C2×#16839638C2semidirect
13. C2×#16839633C2semidirect
14. C2×#16839619C2semidirect
15. C2×#95×D61C2semidirect
16. C2×C61×#396C2semidirect
25. C2×#14519762C22semidirect
27. C2×#14519759C22semidirect
31. C2×#14519739C22semidirect
46. #16839692C22semidirect
47. #16839691C22semidirect
48. #16839677C22semidirect
49. #16839657C22semidirect
50. #16839656C22semidirect
51. #16839638C22semidirect
52. #16839638C22semidirect
53. #16839633C22semidirect
54. #16839619C22semidirect
62. #95×D61C22semidirect
69. C61×#396C22semidirect
130. C2×#11758198D4semidirect
280. #11758198C2×D4semidirect
450. C2×#396D61semidirect
460. C2×C61#2425semidirect
507. #396C2×D61semidirect
524. C61C2×#2425semidirect
899. C2#21449365direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197622
C22×#145197592
C22×#145197502
C22×#145197392
#214493652
C2×#168396922
C2×#168396912
C2×#168396772
C2×#168396572
C2×#168396562
C2×#168396382
C2×#168396332
C2×#168396192
C2×#95×D612
C2×C61×#3962
C2×#242561