Finite Group Databasebeta

← C2×#21449290 #29847715

Subgroups — C2×#21449290 #29847715

Order 15616.

3222 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519758C211yesmaximal, characteristic
2#21449290C2116yesmaximal, direct product factor
3C2×#16839700C211yesmaximal, characteristic, complemented
4C2×#16839693C211yesmaximal, characteristic, complemented
5C2×#16839690C211yesmaximal, characteristic, complemented
6C2×#16839690C211yesmaximal, characteristic, complemented
7C2×#16839646C211yesmaximal, characteristic, complemented
8C2×#16839646C211yesmaximal, characteristic, complemented
9C2×#16839642C211yesmaximal, characteristic
10C2×#16839635C211yesmaximal, characteristic, complemented
11C2×#16839635C211yesmaximal, characteristic, complemented
12C2×#16839625C211yesmaximal, characteristic, complemented
13C2×#16839623C211yesmaximal, characteristic, complemented
14C2×#16839620C211yesmaximal, characteristic, complemented
15C22×#14519684C211yesmaximal, characteristic, complemented
16C22×C4×D4×C61C211yesmaximal, characteristic
17C24×Dic61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C2×#14519758—28no—
20C2×#14519758C2218yes—
21C22×#11758196C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×C22⋊Dic61C2211yescharacteristic
31C22×C22⋊Dic61C2211yescharacteristic
32C22×C22⋊Dic61C2211yescharacteristic
33#16839700C2218yescomplemented
34#16839693C2218yescomplemented
35#16839690C2218yescomplemented
36#16839690C2218yescomplemented
37#16839646C2218yescomplemented
38#16839646C2218yescomplemented
39#16839642C2218yes—
40#16839635C2218yescomplemented
41#16839635C2218yescomplemented
42#16839625C2218yescomplemented
43#16839623C2218yescomplemented
44#16839620C2218yescomplemented
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2218yescomplemented
60C23×D4×C61C2211yescharacteristic
61C24×C4×C61C2211yescharacteristic
62C24×C4×C61C2211yescharacteristic
63C2×C4×D4×C61—28no—
64C2×C4×D4×C61C2218yes—
65C22×C4⋊C4×C61C2211yescharacteristic
66C22×C22⋊C4×C61C2211yescharacteristic
67C22×C22⋊C4×C61C2211yescharacteristic
68C22×C42×C61C2211yescharacteristic
69C23×Dic61—24no—
70C23×Dic61—24no—
71C23×Dic61—24no—
72C23×Dic61—24no—
73C23×Dic61—24no—
74C23×Dic61—42no—
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2314yes—
83C23×Dic61C2314yes—
84C23×Dic61C2311yescharacteristic
85#14519758—232no—
86C2×#11758196—24no—
87C2×#11758196—24no—
88C2×#11758196—24no—
89C2×#11758196—24no—
90C2×#11758196—42no—
91C2×#11758196—42no—
92C2×#11758196C2314yes—
93C2×#11758196C2314yes—
94C2×#11758196C2314yes—
95C2×#11758196C2314yes—
96C2×#11758196C2314yes—
97C2×#11758196C2314yes—
98C2×C22⋊Dic61—24no—
99C2×C22⋊Dic61—24no—
100C2×C22⋊Dic61—24no—
101C2×C22⋊Dic61—24no—
102C2×C22⋊Dic61—24no—
103C2×C22⋊Dic61—42no—
104C2×C22⋊Dic61C2314yes—
105C2×C22⋊Dic61C2314yes—
106C2×C22⋊Dic61C2314yes—
107C2×C22⋊Dic61C2314yes—
108C2×C22⋊Dic61C2314yes—
109C2×C22⋊Dic61C2314yes—
110#14519684C2314yes—
111#14519684C2314yes—
112#14519684C2314yes—
113#14519684C2314yes—
114#14519684C2314yes—
115#14519684C2314yes—
116#14519684C2314yes—
117#14519684C2314yes—
118#14519684C2314yes—
119#14519684C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
123#14519684C2314yes—
124C25×C61C2311yescharacteristic
125C25×C61C2311yescharacteristic
126C22×D4×C61—24no—
127C22×D4×C61—24no—
128C22×D4×C61D418yes—
129C22×D4×C61C2314yes—
130C23×C4×C61—24no—
131C23×C4×C61—24no—
132C23×C4×C61—24no—
133C23×C4×C61—24no—
134C23×C4×C61—42no—
135C23×C4×C61—42no—
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2314yes—
140C23×C4×C61C2314yes—
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C4×D4×C61—232no—
144C2×C4⋊C4×C61—24no—
145C2×C4⋊C4×C61C2314yes—
146C2×C22⋊C4×C61—24no—
147C2×C22⋊C4×C61—24no—
148C2×C22⋊C4×C61C2314yes—
149C2×C22⋊C4×C61C2314yes—
150C2×C42×C61—24no—
151C2×C42×C61C2314yes—
152C24×C61—22no—
153C24×C61—22no—
154C24×C61—22no—
155C24×C61—22no—
156C24×C61—22no—
157C24×C61—22no—
158C24×C61—22no—
159C24×C61—22no—
160C24×C61—22no—
161C24×C61—22no—
162C24×C61C2×D414yes—
163C24×C61C2×D414yes—
164C24×C61#4114yes—
165C24×C61#4114yes—
166C24×C61C2412yes—
167C24×C61C2412yes—
168C24×C61C2411yescharacteristic
169C2×D4×C61—232no—
170C2×D4×C61—28no—
171C2×D4×C61—28no—
172C2×D4×C61C2×D4116yes—
173C22×C4×C61—22no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—28no—
181C22×C4×C61—28no—
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—28no—
189C22×C4×C61—28no—
190C22×C4×C61—44no—
191C22×C4×C61—44no—
192C22×C4×C61—416no—
193C22×C4×C61—416no—
194C22×C4×C61C2×D414yes—
195C22×C4×C61#4114yes—
196C22×C4×C61C2412yes—
197C22×C4×C61C2412yes—
198C22×C4×C61C2412yes—
199C22×C4×C61C2412yes—
200C22×C4×C61C2412yes—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—28no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—28no—
209C22×Dic61—28no—
210C22×Dic61—28no—
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×Dic61—22no—
224C22×Dic61—22no—
225C22×Dic61—22no—
226C22×Dic61—22no—
227C22×Dic61—22no—
228C22×Dic61—28no—
229C22×Dic61—44no—
230C22×Dic61—416no—
231C22×Dic61—416no—
232C22×Dic61#4114yes—
233C22×Dic61C2412yes—
234C22×Dic61C2412yes—
235C22×Dic61C2412yes—
236C22×Dic61C2412yes—
237C22×Dic61C2412yes—
238C22×Dic61C2412yes—
239C22×Dic61C2412yes—
240C22×Dic61C2412yes—
241C4⋊C4×C61—28no—
242C22⋊C4×C61—28no—
243C22⋊C4×C61—28no—
244C42×C61—28no—
245C22⋊Dic61—28no—
246C22⋊Dic61—28no—
247C22⋊Dic61—28no—
248C22⋊Dic61—28no—
249C22⋊Dic61—28no—
250C22⋊Dic61—44no—
251#11758196—28no—
252#11758196—28no—
253#11758196—28no—
254#11758196—28no—
255#11758196—44no—
256#11758196—44no—
257C23×C61—28no—
258C23×C61—28no—
259C23×C61—28no—
260C23×C61—28no—
261C23×C61—28no—
262C23×C61—28no—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61—22no—
266C23×C61—22no—
267C23×C61—28no—
268C23×C61—28no—
269C23×C61—28no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—44no—
277C23×C61—44no—
278C23×C61—44no—
279C23×C61—44no—
280C23×C61#123116yes—
281C23×C61C22×D414yes—
282C23×C61C22×D414yes—
283C23×C61C22×D412yes—
284C23×C61C2×#4114yes—
285C23×C61C2×#4114yes—
286C23×C61C2×#4112yes—
287C23×C61C2×#4112yes—
288C23×C61C2×#4112yes—
289C23×C61C2×#4112yes—
290C23×C61H(5,𝔽2)12yes—
291C23×C612−1+412yes—
292C23×C61C2511yescharacteristic
293D4×C61—232no—
294C2×C4×C61—28no—
295C2×C4×C61—28no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—416no—
310C2×C4×C61—416no—
311C2×C4×C61—44no—
312C2×C4×C61—44no—
313C2×C4×C61—44no—
314C2×C4×C61C22×D414yes—
315C2×C4×C61C2×#4114yes—
316C2×Dic61—28no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—416no—
341C2×Dic61—416no—
342C2×Dic61—44no—
343C2×Dic61—44no—
344C2×Dic61—44no—
345C2×Dic61—44no—
346C2×Dic61—44no—
347C2×Dic61—44no—
348C2×Dic61—44no—
349C2×Dic61C2×#4114yes—
350C2×#2419—611nomaximal, Sylow
351C22×C61—24no—
352C22×C61—232no—
353C22×C61—24no—
354C22×C61—24no—
355C22×C61—24no—
356C22×C61—24no—
357C22×C61—24no—
358C22×C61—24no—
359C22×C61—24no—
360C22×C61—24no—
361C22×C61—42no—
362C22×C61—416no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61C2×#12318yes—
367C22×C61C2×#12314yes—
368C22×C61#52914yes—
369C22×C61#53914yes—
370C22×C61#54614yes—
371C22×C61#54714yes—
372C22×C61#55114yes—
373C22×C61#55214yes—
374C22×C61C23×D411yescharacteristic
375C22×C61C22×#4111yescharacteristic
376C22×C61C22×#4111yescharacteristic
377C22×C61C22×#4111yescharacteristic
378C22×C61C22×#4111yescharacteristic
379C22×C61C2×H(5,𝔽2)11yescharacteristic
380C22×C61C2×2−1+411yescharacteristic
381C4×C61—24no—
382C4×C61—24no—
383C4×C61—42no—
384C4×C61—42no—
385C4×C61—42no—
386Dic61—24no—
387Dic61—42no—
388Dic61—42no—
389Dic61—42no—
390Dic61—42no—
391Dic61—42no—
392Dic61—42no—
393Dic61—42no—
394C22×#123—611no—
395C22×C4×D4D6111yescharacteristic
396#2419—6116no—
397C2×#400—611no—
398C2×#398—611no—
399C2×#397—611no—
400C2×#397—611no—
401C2×#387—611no—
402C2×#387—611no—
403C2×#386—611no—
404C2×#385—611no—
405C2×#385—611no—
406C2×#381—611no—
407C2×#381—611no—
408C2×#380—611no—
409C22×#95—611no—
410C2×C61—28no—
411C2×C61—44no—
412C2×C61#241918yescomplemented
413C2×C61C22×#12311yescharacteristic
414C2×C61C2×#52911yescharacteristic
415C2×C61C2×#53911yescharacteristic
416C2×C61C2×#54611yescharacteristic
417C2×C61C2×#54711yescharacteristic
418C2×C61C2×#55111yescharacteristic
419C2×C61C2×#55211yescharacteristic
420C23×D4C2×D6111yescharacteristic
421C24×C4—611no—
422C24×C4—611no—
423C24×C4C2×D6111yescharacteristic
424C24×C4C2×D6111yescharacteristic
425C2×#123—618no—
426C2×#123—1228no—
427C2×C4×D4—28no—
428C2×C4×D4C2×D6118yes—
429C22×C4⋊C4—611no—
430C22×C4⋊C4—611no—
431C22×C4⋊C4—611no—
432C22×C4⋊C4—611no—
433C22×C4⋊C4—611no—
434C22×C4⋊C4—611no—
435C22×C4⋊C4C2×D6111yescharacteristic
436C22×C22⋊C4—611no—
437C22×C22⋊C4—611no—
438C22×C22⋊C4—611no—
439C22×C22⋊C4—611no—
440C22×C22⋊C4—611no—
441C22×C22⋊C4—611no—
442C22×C22⋊C4C2×D6111yescharacteristic
443C22×C22⋊C4C2×D6111yescharacteristic
444C22×C42C2×D6111yescharacteristic
445#400—618no—
446#398—618no—
447#397—618no—
448#397—618no—
449#387—618no—
450#387—618no—
451#386—618no—
452#385—618no—
453#385—618no—
454#381—618no—
455#381—618no—
456#380—618no—
457C2×#95—611no—
458C2×#95—611no—
459C2×#95—611no—
460C2×#95—611no—
461C2×#95—611no—
462C2×#95—611no—
463C2×#95—611no—
464C2×#95—611no—
465C2×#95—611no—
466C2×#95—611no—
467C2×#95—611no—
468C2×#95—618no—
469C2×#95—611no—
470C2×#95—611no—
471C2×#95—611no—
472C61C2×#241911yescharacteristic, complemented, Sylow
473C25C22×D6111yescharacteristic
474C25C22×D6111yescharacteristic
475C22×D4—24no—
476C22×D4—24no—
477C22×D4C22⋊D6118yes—
478C22×D4C22×D6114yes—
479C23×C4—24no—
480C23×C4—24no—
481C23×C4—24no—
482C23×C4—24no—
483C23×C4—42no—
484C23×C4—42no—
485C23×C4—611no—
486C23×C4—614no—
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—611no—
491C23×C4—611no—
492C23×C4—611no—
493C23×C4—611no—
494C23×C4—614no—
495C23×C4—1224no—
496C23×C4—1224no—
497C23×C4—1224no—
498C23×C4—1224no—
499C23×C4—1224no—
500C23×C4—2442no—
501C23×C4C22×D6111yescharacteristic
502C23×C4C22×D6111yescharacteristic
503C23×C4C22×D6111yescharacteristic
504C23×C4C22×D6114yes—
505C23×C4C22×D6114yes—
506C23×C4C22×D6111yescharacteristic
507C23×C4C22×D6111yescharacteristic
508#123—12232no—
509C4×D4—232no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—614no—
512C2×C4⋊C4—614no—
513C2×C4⋊C4—614no—
514C2×C4⋊C4—614no—
515C2×C4⋊C4—614no—
516C2×C4⋊C4—614no—
517C2×C4⋊C4—1224no—
518C2×C4⋊C4—1224no—
519C2×C4⋊C4—1224no—
520C2×C4⋊C4—1224no—
521C2×C4⋊C4—2442no—
522C2×C4⋊C4—2442no—
523C2×C4⋊C4C22×D6114yes—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—614no—
527C2×C22⋊C4—614no—
528C2×C22⋊C4—614no—
529C2×C22⋊C4—614no—
530C2×C22⋊C4—614no—
531C2×C22⋊C4—614no—
532C2×C22⋊C4—1224no—
533C2×C22⋊C4—1224no—
534C2×C22⋊C4—1224no—
535C2×C22⋊C4—1224no—
536C2×C22⋊C4—1224no—
537C2×C22⋊C4—2442no—
538C2×C22⋊C4C22×D6114yes—
539C2×C22⋊C4C22×D6114yes—
540C2×C42—24no—
541C2×C42C22×D6114yes—
542#95—614no—
543#95—614no—
544#95—614no—
545#95—614no—
546#95—614no—
547#95—614no—
548#95—614no—
549#95—614no—
550#95—614no—
551#95—614no—
552#95—614no—
553#95—614no—
554#95—614no—
555#95—614no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24#1175822214yes—
567C24#1175822214yes—
568C24C2×C22⋊D6114yes—
569C24C2×C22⋊D6114yes—
570C24C23×D6112yes—
571C24C23×D6112yes—
572C24C23×D6111yescharacteristic
573C2×D4—28no—
574C2×D4—28no—
575C2×D4—232no—
576C2×D4C2×C22⋊D61116yes—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—28no—
585C22×C4—28no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—28no—
593C22×C4—28no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—416no—
597C22×C4—416no—
598C22×C4—614no—
599C22×C4—612no—
600C22×C4—612no—
601C22×C4—612no—
602C22×C4—612no—
603C22×C4—612no—
604C22×C4—612no—
605C22×C4—612no—
606C22×C4—612no—
607C22×C4—1228no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1228no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4—1222no—
622C22×C4—1228no—
623C22×C4—1228no—
624C22×C4—1228no—
625C22×C4—1222no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—1222no—
630C22×C4—1222no—
631C22×C4—1222no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4—2444no—
636C22×C4—24416no—
637C22×C4—24416no—
638C22×C4#1175822414yes—
639C22×C4C2×C22⋊D6114yes—
640C22×C4C23×D6112yes—
641C22×C4C23×D6112yes—
642C22×C4C23×D6112yes—
643C22×C4C23×D6112yes—
644C22×C4C23×D6112yes—
645C4⋊C4—28no—
646C4⋊C4—1228no—
647C4⋊C4—1228no—
648C4⋊C4—1228no—
649C4⋊C4—1228no—
650C4⋊C4—2444no—
651C4⋊C4—2444no—
652C22⋊C4—28no—
653C22⋊C4—28no—
654C22⋊C4—1228no—
655C22⋊C4—1228no—
656C22⋊C4—1228no—
657C22⋊C4—1228no—
658C22⋊C4—1228no—
659C22⋊C4—2444no—
660C42—28no—
661C23—28no—
662C23—28no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—28no—
668C23—28no—
669C23—28no—
670C23—28no—
671C23—28no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—28no—
679C23—28no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23#14519760116yes—
685C23C22×C22⋊D6114yes—
686C23C22×C22⋊D6114yes—
687C23C22×C22⋊D6112yes—
688C23#41×D6112yes—
689C23C2×#1175822412yes—
690C23C2×#1175822214yes—
691C23C2×#1175822214yes—
692C23C2×#1175822212yes—
693C23C2×#1175822212yes—
694C23#1451982212yes—
695C23#1451982412yes—
696C23C24×D6111yescharacteristic
697D4—232no—
698C2×C4—28no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—28no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—416no—
714C2×C4—416no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—614no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1228no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—24416no—
744C2×C4—24416no—
745C2×C4—2444no—
746C2×C4—2444no—
747C2×C4—2444no—
748C2×C4—2444no—
749C2×C4—2444no—
750C2×C4—2444no—
751C2×C4—2444no—
752C2×C4C22×C22⋊D6114yes—
753C2×C4C2×#1175822414yes—
754C22—24no—
755C22—232no—
756C22—24no—
757C22—24no—
758C22—24no—
759C22—24no—
760C22—24no—
761C22—24no—
762C22—24no—
763C22—24no—
764C22—416no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22C2×#1451976018yes—
770C22C2×#1451976014yes—
771C22#1684029214yes—
772C22#1684035414yes—
773C22#1684040614yes—
774C22#1684041114yes—
775C22#1684044114yes—
776C22#1684045214yes—
777C22C23×C22⋊D6111yescharacteristic
778C22C2×#41×D6111yescharacteristic
779C22C22×#1175822411yescharacteristic
780C22C22×#1175822211yescharacteristic
781C22C22×#1175822211yescharacteristic
782C22C2×#1451982211yescharacteristic
783C22C2×#1451982411yescharacteristic
784C4—24no—
785C4—24no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—1224no—
790C4—2442no—
791C4—2442no—
792C4—2442no—
793C4—2442no—
794C4—2442no—
795C4—2442no—
796C4—2442no—
797C2—28no—
798C2—44no—
799C2#2144929018yesdirect product factor
800C2C22×#1451976011yescharacteristic
801C2C2×#1684029211yescharacteristic
802C2C2×#1684035411yescharacteristic
803C2C2×#1684040611yescharacteristic
804C2C2×#1684041111yescharacteristic
805C2C2×#1684044111yescharacteristic
806C2C2×#1684045211yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC22×C4×D4×C61C2
socleC24×C61C24
prime radicalC23×D4×C61C22
hypercenterC22×C4×D4D61
hypocenterC61C2×#2419
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. #21449290C2direct (N × H)
3. C2×#16839700C2semidirect
4. C2×#16839693C2semidirect
5. C2×#16839690C2semidirect
6. C2×#16839690C2semidirect
7. C2×#16839646C2semidirect
8. C2×#16839646C2semidirect
10. C2×#16839635C2semidirect
11. C2×#16839635C2semidirect
12. C2×#16839625C2semidirect
13. C2×#16839623C2semidirect
14. C2×#16839620C2semidirect
15. C22×#14519684C2semidirect
33. #16839700C22semidirect
34. #16839693C22semidirect
35. #16839690C22semidirect
36. #16839690C22semidirect
37. #16839646C22semidirect
38. #16839646C22semidirect
40. #16839635C22semidirect
41. #16839635C22semidirect
42. #16839625C22semidirect
43. #16839623C22semidirect
44. #16839620C22semidirect
59. C2×#14519684C22semidirect
412. C2×C61#2419semidirect
472. C61C2×#2419semidirect
799. C2#21449290direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197582
#214492902
C2×#168397002
C2×#168396932
C2×#168396902
C2×#168396462
C2×#168396422
C2×#168396352
C2×#168396252
C2×#168396232
C2×#168396202
C22×#145196842
C22×C4×D4×C612
C2×#241961