Finite Group Databasebeta

← C2×#21449265 #29847966

Subgroups — C2×#21449265 #29847966

Order 15616.

3830 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519755C211yesmaximal, characteristic, complemented
2C22×#14519755C211yesmaximal, characteristic, complemented
3C22×#14519739C211yesmaximal, characteristic
4C22×C4⋊C4×D61C211yesmaximal, characteristic, complemented
5#21449265C2116yesmaximal, direct product factor
6C2×#16839695C211yesmaximal, characteristic, complemented
7C2×#16839684C211yesmaximal, characteristic, complemented
8C2×#16839684C211yesmaximal, characteristic, complemented
9C2×#16839666C211yesmaximal, characteristic, complemented
10C2×#16839659C211yesmaximal, characteristic, complemented
11C2×#16839640C211yesmaximal, characteristic
12C2×#16839640C211yesmaximal, characteristic
13C2×#16839621C211yesmaximal, characteristic, complemented
14C2×#16839621C211yesmaximal, characteristic, complemented
15C2×#16839619C211yesmaximal, characteristic, complemented
16C2×C61×#398C211yesmaximal, characteristic, complemented
17C23×Dic122C2211yescharacteristic
18C23×D244C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C23×C4×D61C2211yescharacteristic
22C23×C4×D61C2211yescharacteristic
23C2×#14519755—28no—
24C2×#14519755—28no—
25C2×#14519755C2218yescomplemented
26C2×#14519755C2218yescomplemented
27C2×#14519739—28no—
28C2×#14519739C2218yes—
29C22×C4⋊Dic61C2211yescharacteristic
30C22×C4⋊Dic61C2211yescharacteristic
31C22×#11758196C2211yescharacteristic
32C22×#11758196C2211yescharacteristic
33C22×#11758196C2211yescharacteristic
34C22×#11758196C2211yescharacteristic
35C22×#11758196C2211yescharacteristic
36C22×#11758196C2211yescharacteristic
37C2×C4⋊C4×D61—28no—
38C2×C4⋊C4×D61C2218yescomplemented
39C22×#11758198C2211yescharacteristic
40C22×#11758198C2211yescharacteristic
41C22×#11758198C2211yescharacteristic
42C22×#11758198C2211yescharacteristic
43C22×#11758198C2211yescharacteristic
44C22×#11758198C2211yescharacteristic
45C22×#11758198C2211yescharacteristic
46C22×#11758198C2211yescharacteristic
47C22×C4×Dic61C2211yescharacteristic
48#16839695C2218yescomplemented
49#16839684C2218yescomplemented
50#16839684C2218yescomplemented
51#16839666C2218yescomplemented
52#16839659C2218yescomplemented
53#16839640C2218yes—
54#16839640C2218yes—
55#16839621C2218yescomplemented
56#16839621C2218yescomplemented
57#16839619C2218yescomplemented
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C2×#14519684C2211yescharacteristic
62C2×#14519684C2211yescharacteristic
63C22×C4⋊C4×C61C2211yescharacteristic
64C22×C4⋊C4×C61C2211yescharacteristic
65C22×C4⋊C4×C61C2211yescharacteristic
66C22×C4⋊C4×C61C2211yescharacteristic
67C61×#398C2218yescomplemented
68C2×#95×C61C2211yescharacteristic
69C2×#95×C61C2211yescharacteristic
70C2×#95×C61C2211yescharacteristic
71C24×D61C2311yescharacteristic
72C24×D61C2311yescharacteristic
73C22×Dic122—24no—
74C22×Dic122—24no—
75C22×Dic122—24no—
76C22×Dic122C2314yes—
77C22×D244—24no—
78C22×D244—24no—
79C22×D244Q818yescomplemented
80C22×D244C2314yes—
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C22×C4×D61—24no—
88C22×C4×D61—24no—
89C22×C4×D61—24no—
90C22×C4×D61—24no—
91C22×C4×D61—24no—
92C22×C4×D61—24no—
93C22×C4×D61—24no—
94C22×C4×D61—24no—
95C22×C4×D61—24no—
96C22×C4×D61—42no—
97C22×C4×D61—42no—
98C22×C4×D61D418yes—
99C22×C4×D61C2314yes—
100C22×C4×D61C2314yes—
101C22×C4×D61C2314yes—
102C22×C4×D61C2314yes—
103#14519755—232no—
104#14519755—232no—
105#14519739—232no—
106C2×C4⋊Dic61—24no—
107C2×C4⋊Dic61—42no—
108C2×C4⋊Dic61C2314yes—
109C2×C4⋊Dic61C2314yes—
110C2×#11758196—24no—
111C2×#11758196—24no—
112C2×#11758196—24no—
113C2×#11758196—24no—
114C2×#11758196—42no—
115C2×#11758196D418yescomplemented
116C2×#11758196C2314yes—
117C2×#11758196C2314yes—
118C2×#11758196C2314yes—
119C2×#11758196C2314yes—
120C2×#11758196C2314yes—
121C2×#11758196C2314yes—
122C4⋊C4×D61—232no—
123C2×#11758198—24no—
124C2×#11758198—24no—
125C2×#11758198—24no—
126C2×#11758198—24no—
127C2×#11758198—24no—
128C2×#11758198—24no—
129C2×#11758198—42no—
130C2×#11758198—42no—
131C2×#11758198C2314yes—
132C2×#11758198C2314yes—
133C2×#11758198C2314yes—
134C2×#11758198C2314yes—
135C2×#11758198C2314yes—
136C2×#11758198C2314yes—
137C2×#11758198C2314yes—
138C2×#11758198C2314yes—
139C2×C4×Dic61—24no—
140C2×C4×Dic61C2314yes—
141#14519684C2314yes—
142#14519684C2314yes—
143#14519684C2314yes—
144#14519684C2314yes—
145#14519684C2314yes—
146C23×C4×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—24no—
156C2×C4⋊C4×C61—24no—
157C2×C4⋊C4×C61C2314yes—
158C2×C4⋊C4×C61C2314yes—
159C2×C4⋊C4×C61C2314yes—
160C2×C4⋊C4×C61C2314yes—
161#95×C61C2314yes—
162#95×C61C2314yes—
163#95×C61C2314yes—
164C24×C61C2411yescharacteristic
165C23×D61—22no—
166C23×D61—22no—
167C23×D61—22no—
168C23×D61—22no—
169C23×D61—22no—
170C23×D61—22no—
171C23×D61—22no—
172C23×D61—22no—
173C23×D61—22no—
174C23×D61—22no—
175C23×D61C2×D414yes—
176C23×D61C2×Q814yes—
177C23×D61C2×Q814yes—
178C23×D61#4114yes—
179C23×D61C2412yes—
180C23×D61C2412yes—
181C22×C4×C61—22no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
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×C61C2×D414yes—
200C22×C4×C61C2×D414yes—
201C22×C4×C61C2×Q814yes—
202C22×C4×C61C2412yes—
203C22×C4×C61C2412yes—
204C22×C4×C61C2412yes—
205C22×C4×C61C2412yes—
206C22×C4×C61C2412yes—
207C22×C4×C61C2412yes—
208C22×C4×C61C2412yes—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—22no—
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—22no—
222C22×Dic61—22no—
223C22×Dic61C2×D414yes—
224C22×Dic61C2×D414yes—
225C22×Dic61C2×D414yes—
226C22×Dic61#4114yes—
227C22×Dic61C2412yes—
228C22×Dic61C2412yes—
229C22×Dic61C2412yes—
230C22×Dic61C2412yes—
231C22×Dic61C2412yes—
232C22×Dic61C2412yes—
233C2×D244—232no—
234C2×D244—28no—
235C2×D244—28no—
236C2×D244C2×Q8116yescomplemented
237C2×C4×D61—232no—
238C2×C4×D61—28no—
239C2×C4×D61—28no—
240C2×C4×D61—28no—
241C2×C4×D61—28no—
242C2×C4×D61—28no—
243C2×C4×D61—28no—
244C2×C4×D61—28no—
245C2×C4×D61—28no—
246C2×C4×D61—28no—
247C2×C4×D61—44no—
248C2×C4×D61—44no—
249C2×C4×D61—416no—
250C2×C4×D61—416no—
251C2×C4×D61—416no—
252C2×C4×D61C2×D4116yes—
253C2×Dic122—28no—
254C2×Dic122—28no—
255C2×Dic122—28no—
256C2×Dic122—416no—
257C4⋊C4×C61—28no—
258C4⋊C4×C61—28no—
259C4⋊C4×C61—28no—
260C4⋊C4×C61—28no—
261#11758198—28no—
262#11758198—28no—
263#11758198—28no—
264#11758198—28no—
265#11758198—28no—
266#11758198—28no—
267#11758198—44no—
268#11758198—44no—
269C4⋊Dic61—28no—
270C4⋊Dic61—44no—
271#11758196—28no—
272#11758196—28no—
273#11758196—28no—
274#11758196—28no—
275#11758196—44no—
276#11758196C2×D4116yescomplemented
277C4×Dic61—28no—
278C23×C61C22×D412yes—
279C23×C61C22×D412yes—
280C23×C61C22×Q812yes—
281C23×C61C2×#4112yes—
282C23×C61C2×#4112yes—
283C23×C61H(5,𝔽2)12yes—
284C23×C612−1+412yes—
285C23×C61C2511yescharacteristic
286C22×D61—28no—
287C22×D61—28no—
288C22×D61—28no—
289C22×D61—28no—
290C22×D61—28no—
291C22×D61—28no—
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—28no—
297C22×D61—28no—
298C22×D61—28no—
299C22×D61—22no—
300C22×D61—22no—
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—22no—
305C22×D61—44no—
306C22×D61—44no—
307C22×D61—44no—
308C22×D61—44no—
309C22×D61C22⋊Q8116yescomplemented
310C22×D61C22×D414yes—
311C22×D61C22×Q814yes—
312C22×D61C22×Q814yes—
313C22×D61C2×#4114yes—
314C2×C4×C61—28no—
315C2×C4×C61—28no—
316C2×C4×C61—28no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—44no—
336C2×C4×C61—44no—
337C2×C4×C61—44no—
338C2×C4×C61—44no—
339C2×C4×C61C22×D414yes—
340C2×C4×C61C22×D414yes—
341C2×C4×C61C22×Q814yes—
342C2×Dic61—28no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—44no—
358C2×Dic61—44no—
359C2×Dic61—44no—
360C2×Dic61—44no—
361C2×Dic61#121116yes—
362C2×Dic61C22×D414yes—
363C2×Dic61C22×D414yes—
364C2×Dic61C22×D414yes—
365C2×Dic61C2×#4114yes—
366D244—232no—
367C4×D61—232no—
368C4×D61—416no—
369C4×D61—416no—
370C4×D61—416no—
371Dic122—416no—
372C2×#2417—611nomaximal, Sylow
373C22×C61C2×#12114yes—
374C22×C61C2×C22⋊Q814yes—
375C22×C61#53714yes—
376C22×C61#54614yes—
377C22×C61D4×Q814yes—
378C22×C61#55214yes—
379C22×C61#55414yes—
380C22×C61C23×D411yescharacteristic
381C22×C61C23×D411yescharacteristic
382C22×C61C23×Q811yescharacteristic
383C22×C61C22×#4111yescharacteristic
384C22×C61C22×#4111yescharacteristic
385C22×C61C2×H(5,𝔽2)11yescharacteristic
386C22×C61C2×2−1+411yescharacteristic
387C2×D61—24no—
388C2×D61—232no—
389C2×D61—24no—
390C2×D61—24no—
391C2×D61—24no—
392C2×D61—24no—
393C2×D61—24no—
394C2×D61—24no—
395C2×D61—24no—
396C2×D61—24no—
397C2×D61—42no—
398C2×D61—416no—
399C2×D61—42no—
400C2×D61—42no—
401C2×D61—42no—
402C2×D61C2×C22⋊Q818yescomplemented
403C4×C61—24no—
404C4×C61—24no—
405C4×C61—24no—
406C4×C61—42no—
407C4×C61—42no—
408C4×C61—42no—
409C4×C61—42no—
410Dic61—24no—
411Dic61—42no—
412Dic61—42no—
413Dic61—42no—
414Dic61—42no—
415Dic61C2×#12118yes—
416C22×C22⋊Q8—611no—
417C22×C22⋊Q8—611no—
418C22×C4×D4—611no—
419C23×C4⋊C4—611no—
420#2417—6116no—
421C2×#398—611no—
422C2×#398D6111yescharacteristic, complemented
423C2×#396—611no—
424C2×#396—611no—
425C2×#391—611no—
426C2×#389—611no—
427C2×#386—611no—
428C2×#386—611no—
429C2×#380—611no—
430C2×#380—611no—
431C2×#380—611no—
432C2×C61#241718yescomplemented
433C2×C61C22×#12111yescharacteristic
434C2×C61C22×C22⋊Q811yescharacteristic
435C2×C61C2×#53711yescharacteristic
436C2×C61C2×#54611yescharacteristic
437C2×C61C2×D4×Q811yescharacteristic
438C2×C61C2×#55211yescharacteristic
439C2×C61C2×#55411yescharacteristic
440D61—28no—
441D61—44no—
442C23×Q8—611no—
443C23×D4—611no—
444C24×C4—611no—
445C24×C4—611no—
446C24×C4—611no—
447C24×C4—611no—
448C2×C22⋊Q8—618no—
449C2×C22⋊Q8—618no—
450C2×C22⋊Q8—1228no—
451C2×C22⋊Q8—1228no—
452C2×C4×D4—618no—
453C2×C4×D4—1228no—
454C22×C4⋊C4—611no—
455C22×C4⋊C4—611no—
456C22×C4⋊C4—611no—
457C22×C4⋊C4—611no—
458C22×C4⋊C4—611no—
459C22×C4⋊C4—611no—
460C22×C4⋊C4—611no—
461C22×C4⋊C4—611no—
462C22×C4⋊C4—618no—
463C22×C4⋊C4—1228no—
464C22×C4⋊C4C2×D6111yescharacteristic
465C22×C4⋊C4C2×D6111yescharacteristic
466C22×C4⋊C4C2×D6111yescharacteristic
467C22×C4⋊C4C2×D6111yescharacteristic
468C22×C22⋊C4—611no—
469C22×C22⋊C4—611no—
470C22×C22⋊C4—611no—
471C22×C22⋊C4—611no—
472C22×C22⋊C4—611no—
473C22×C22⋊C4—611no—
474C22×C22⋊C4—611no—
475C22×C22⋊C4—611no—
476C22×C42—611no—
477#398—618no—
478#398C2×D6118yescomplemented
479#396—618no—
480#396—618no—
481#391—618no—
482#389—618no—
483#386—618no—
484#386—618no—
485#380—618no—
486#380—618no—
487#380—618no—
488C2×#95—611no—
489C2×#95—611no—
490C2×#95—611no—
491C2×#95—611no—
492C2×#95—611no—
493C2×#95C2×D6111yescharacteristic
494C2×#95C2×D6111yescharacteristic
495C2×#95C2×D6111yescharacteristic
496C61C2×#241711yescharacteristic, complemented, Sylow
497C25—611no—
498C25—611no—
499C22×Q8—614no—
500C22×Q8—1224no—
501C22×Q8—1224no—
502C22×Q8—1224no—
503C22×D4—618no—
504C22×D4—614no—
505C22×D4—1224no—
506C22×D4—1224no—
507C23×C4—611no—
508C23×C4—611no—
509C23×C4—618no—
510C23×C4—614no—
511C23×C4—611no—
512C23×C4—611no—
513C23×C4—611no—
514C23×C4—611no—
515C23×C4—614no—
516C23×C4—614no—
517C23×C4—614no—
518C23×C4—1224no—
519C23×C4—1224no—
520C23×C4—1224no—
521C23×C4—1224no—
522C23×C4—1224no—
523C23×C4—1224no—
524C23×C4—1224no—
525C23×C4—1224no—
526C23×C4—1224no—
527C23×C4—2442no—
528C23×C4—2442no—
529C23×C4C22×D6111yescharacteristic
530C23×C4C22×D6111yescharacteristic
531C23×C4C22×D6111yescharacteristic
532C23×C4C22×D6111yescharacteristic
533C23×C4C22×D6111yescharacteristic
534C23×C4C22×D6111yescharacteristic
535C23×C4C22×D6111yescharacteristic
536C22⋊Q8—12232no—
537C22⋊Q8—12232no—
538C4×D4—12232no—
539C2×C4⋊C4—24no—
540C2×C4⋊C4—24no—
541C2×C4⋊C4—24no—
542C2×C4⋊C4—24no—
543C2×C4⋊C4—618no—
544C2×C4⋊C4—614no—
545C2×C4⋊C4—614no—
546C2×C4⋊C4—614no—
547C2×C4⋊C4—614no—
548C2×C4⋊C4—614no—
549C2×C4⋊C4—614no—
550C2×C4⋊C4—614no—
551C2×C4⋊C4—614no—
552C2×C4⋊C4—12232no—
553C2×C4⋊C4—1224no—
554C2×C4⋊C4—1224no—
555C2×C4⋊C4—1224no—
556C2×C4⋊C4—1224no—
557C2×C4⋊C4—1224no—
558C2×C4⋊C4—2442no—
559C2×C4⋊C4—2442no—
560C2×C4⋊C4C22×D6114yes—
561C2×C4⋊C4C22×D6114yes—
562C2×C4⋊C4C22×D6114yes—
563C2×C4⋊C4C22×D6114yes—
564C2×C22⋊C4—614no—
565C2×C22⋊C4—614no—
566C2×C22⋊C4—614no—
567C2×C22⋊C4—614no—
568C2×C22⋊C4—614no—
569C2×C22⋊C4—614no—
570C2×C22⋊C4—614no—
571C2×C22⋊C4—614no—
572C2×C22⋊C4—1224no—
573C2×C22⋊C4—1224no—
574C2×C22⋊C4—1224no—
575C2×C22⋊C4—1224no—
576C2×C22⋊C4—1224no—
577C2×C22⋊C4—1224no—
578C2×C22⋊C4—2442no—
579C2×C22⋊C4—2442no—
580C2×C42—614no—
581C2×C42—1224no—
582#95—614no—
583#95—614no—
584#95—614no—
585#95—614no—
586#95—614no—
587#95C22×D6114yes—
588#95C22×D6114yes—
589#95C22×D6114yes—
590C24—614no—
591C24—614no—
592C24—614no—
593C24—612no—
594C24—614no—
595C24—612no—
596C24—1222no—
597C24—1222no—
598C24—1222no—
599C24—1222no—
600C24—1222no—
601C24—1222no—
602C24—1222no—
603C24—1222no—
604C24—1222no—
605C24—1222no—
606C24C23×D6111yescharacteristic
607C2×Q8—1228no—
608C2×Q8—1228no—
609C2×Q8—1228no—
610C2×Q8—24416no—
611C2×D4—6116no—
612C2×D4—1228no—
613C2×D4—12232no—
614C2×D4—1228no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—614no—
634C22×C4—614no—
635C22×C4—614no—
636C22×C4—612no—
637C22×C4—614no—
638C22×C4—612no—
639C22×C4—6116no—
640C22×C4—612no—
641C22×C4—612no—
642C22×C4—612no—
643C22×C4—612no—
644C22×C4—1228no—
645C22×C4—12232no—
646C22×C4—1228no—
647C22×C4—1228no—
648C22×C4—1228no—
649C22×C4—1228no—
650C22×C4—1228no—
651C22×C4—1228no—
652C22×C4—1228no—
653C22×C4—1222no—
654C22×C4—1222no—
655C22×C4—1222no—
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—1222no—
665C22×C4—1222no—
666C22×C4—1222no—
667C22×C4—1228no—
668C22×C4—2444no—
669C22×C4—2444no—
670C22×C4—24416no—
671C22×C4—24416no—
672C22×C4—24416no—
673C22×C4D4×D6114yes—
674C22×C4D4×D6114yes—
675C22×C4Q8×D6114yes—
676C22×C4C23×D6112yes—
677C22×C4C23×D6112yes—
678C22×C4C23×D6112yes—
679C22×C4C23×D6112yes—
680C22×C4C23×D6112yes—
681C22×C4C23×D6112yes—
682C22×C4C23×D6112yes—
683C4⋊C4—28no—
684C4⋊C4—28no—
685C4⋊C4—28no—
686C4⋊C4—28no—
687C4⋊C4—6116no—
688C4⋊C4—1228no—
689C4⋊C4—1228no—
690C4⋊C4—1228no—
691C4⋊C4—1228no—
692C4⋊C4—1228no—
693C4⋊C4—2444no—
694C4⋊C4—2444no—
695C22⋊C4—1228no—
696C22⋊C4—1228no—
697C22⋊C4—1228no—
698C22⋊C4—1228no—
699C22⋊C4—1228no—
700C22⋊C4—1228no—
701C22⋊C4—2444no—
702C22⋊C4—2444no—
703C42—1228no—
704C23—6116no—
705C23—614no—
706C23—614no—
707C23—614no—
708C23—614no—
709C23—1228no—
710C23—1228no—
711C23—1222no—
712C23—1222no—
713C23—1222no—
714C23—1222no—
715C23—1228no—
716C23—1228no—
717C23—1228no—
718C23—1228no—
719C23—1228no—
720C23—1228no—
721C23—1222no—
722C23—1222no—
723C23—1222no—
724C23—1222no—
725C23—1222no—
726C23—1222no—
727C23—1228no—
728C23—2444no—
729C23—2444no—
730C23—2444no—
731C23—2444no—
732C23C2×D4×D6112yes—
733C23C2×D4×D6112yes—
734C23C2×Q8×D6112yes—
735C23#41×D6112yes—
736C23#41×D6112yes—
737C23#1451982312yes—
738C23#1451982512yes—
739C23C24×D6111yescharacteristic
740Q8—24416no—
741D4—12232no—
742C2×C4—28no—
743C2×C4—28no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—28no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—6116no—
768C2×C4—614no—
769C2×C4—614no—
770C2×C4—614no—
771C2×C4—614no—
772C2×C4—12232no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—1228no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—1222no—
782C2×C4—1222no—
783C2×C4—1222no—
784C2×C4—1222no—
785C2×C4—1222no—
786C2×C4—1222no—
787C2×C4—1222no—
788C2×C4—24416no—
789C2×C4—24416no—
790C2×C4—24416no—
791C2×C4—2444no—
792C2×C4—2444no—
793C2×C4—2444no—
794C2×C4—2444no—
795C2×C4C2×D4×D6114yes—
796C2×C4C2×D4×D6114yes—
797C2×C4C2×Q8×D6114yes—
798C22—618no—
799C22—12232no—
800C22—1224no—
801C22—1224no—
802C22—1224no—
803C22—1224no—
804C22—1224no—
805C22—1224no—
806C22—1224no—
807C22—1224no—
808C22—1224no—
809C22—24416no—
810C22—2442no—
811C22—2442no—
812C22—2442no—
813C22—2442no—
814C22#121×D6114yes—
815C22C22⋊Q8×D6114yes—
816C22#1684034214yes—
817C22#1684040414yes—
818C22#1684042714yes—
819C22#1684044414yes—
820C22#1684046814yes—
821C22C22×D4×D6111yescharacteristic
822C22C22×D4×D6111yescharacteristic
823C22C22×Q8×D6111yescharacteristic
824C22C2×#41×D6111yescharacteristic
825C22C2×#41×D6111yescharacteristic
826C22C2×#1451982311yescharacteristic
827C22C2×#1451982511yescharacteristic
828C4—24no—
829C4—24no—
830C4—24no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—618no—
836C4—1224no—
837C4—2442no—
838C4—2442no—
839C4—2442no—
840C4—2442no—
841C2—1228no—
842C2—2444no—
843C2#2144926518yesdirect product factor
844C2C2×#121×D6111yescharacteristic
845C2C2×C22⋊Q8×D6111yescharacteristic
846C2C2×#1684034211yescharacteristic
847C2C2×#1684040411yescharacteristic
848C2C2×#1684042711yescharacteristic
849C2C2×#1684044411yescharacteristic
850C2C2×#1684046811yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#398C2
socleC24×C61C24
prime radicalC23×D244C22
hypercenterC2×#398D61
hypocenterC61C2×#2417
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C22×#14519755C2semidirect
2. C22×#14519755C2semidirect
4. C22×C4⋊C4×D61C2semidirect
5. #21449265C2direct (N × H)
6. C2×#16839695C2semidirect
7. C2×#16839684C2semidirect
8. C2×#16839684C2semidirect
9. C2×#16839666C2semidirect
10. C2×#16839659C2semidirect
13. C2×#16839621C2semidirect
14. C2×#16839621C2semidirect
15. C2×#16839619C2semidirect
16. C2×C61×#398C2semidirect
25. C2×#14519755C22semidirect
26. C2×#14519755C22semidirect
38. C2×C4⋊C4×D61C22semidirect
48. #16839695C22semidirect
49. #16839684C22semidirect
50. #16839684C22semidirect
51. #16839666C22semidirect
52. #16839659C22semidirect
55. #16839621C22semidirect
56. #16839621C22semidirect
57. #16839619C22semidirect
67. C61×#398C22semidirect
79. C22×D244Q8semidirect
115. C2×#11758196D4semidirect
236. C2×D244C2×Q8semidirect
276. #11758196C2×D4semidirect
309. C22×D61C22⋊Q8semidirect
402. C2×D61C2×C22⋊Q8semidirect
422. C2×#398D61semidirect
432. C2×C61#2417semidirect
478. #398C2×D61semidirect
496. C61C2×#2417semidirect
843. C2#21449265direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197552
C22×#145197392
C22×C4⋊C4×D612
#214492652
C2×#168396952
C2×#168396842
C2×#168396662
C2×#168396592
C2×#168396402
C2×#168396212
C2×#168396192
C2×C61×#3982
C2×#241761