Finite Group Databasebeta

← C4×#16839910 #29685634

Subgroups — C4×#16839910 #29685634

Order 15616.

1564 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758226C211yesmaximal, characteristic, complemented
2C2×#16839910C211yesmaximal, characteristic
3C2×C4×#11758201C211yesmaximal, characteristic, complemented
4C2×C4×D488C211yesmaximal, characteristic, complemented
5C4×#14519752C211yesmaximal, characteristic, complemented
6#21446172C211yesmaximal, characteristic, complemented
7#21446168C211yesmaximal, characteristic, complemented
8#21446140C211yesmaximal, characteristic, complemented
9#21446081C211yesmaximal, characteristic, complemented
10#21446075C211yesmaximal, characteristic, complemented
11#21446021C211yesmaximal, characteristic, complemented
12#21445758C211yesmaximal, characteristic, complemented
13C4×#14519697C211yesmaximal, characteristic, complemented
14C4×#14519689C211yesmaximal, characteristic, complemented
15C4×#103×C61C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C22×D488C2211yescharacteristic
19C2×#14519752C2211yescharacteristic
20C4×#11758226—24no—
21C4×#11758226—24no—
22C2×Q8×Dic61C2211yescharacteristic
23C2×C4×D244—21no—
24C2×C4×D244—21no—
25C2×C4×D244C2211yescharacteristic
26C2×C4×D244C2211yescharacteristic
27C2×#14519739—21no—
28C2×#14519739C2211yescharacteristic
29C2×#14519735—21no—
30C2×#14519735C2211yescharacteristic
31C2×C42×D61—21no—
32C2×C42×D61C2211yescharacteristic
33#16839910C418yesdirect product factor
34C4×#11758201—24no—
35C4×D488—24no—
36C2×#14519711C2211yescharacteristic
37C2×#14519708C2211yescharacteristic
38C2×#14519701C2211yescharacteristic
39C2×#14519699C2211yescharacteristic
40C2×#14519699C2211yescharacteristic
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46C2×C4×#92418C2211yescharacteristic
47#16839663C2211yescharacteristic
48#16839661C2211yescharacteristic
49#16839654—21no—
50#16839640—21no—
51#16839619C2211yescharacteristic
52C4×#11758198—21no—
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839516C2211yescharacteristic
56#16839516C2211yescharacteristic
57C2×C4×Q8×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×C4×C8×C61C2211yescharacteristic
61C4×C4⋊C4×C61C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#340C2211yescharacteristic
64C2×#11758226—22no—
65C2×#11758226—22no—
66C2×#11758226—22no—
67C2×#11758226—22no—
68C2×#11758226—22no—
69C2×#11758226C2×C414yescomplemented
70C22×D244—21no—
71C22×D244—21no—
72C22×D244C2311yescharacteristic
73C22×D244C2311yescharacteristic
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C22×C4×D61—21no—
77C22×C4×D61—21no—
78C22×C4×D61D411yescharacteristic
79C22×C4×D61D411yescharacteristic
80C22×C4×D61C2311yescharacteristic
81C2×#11758201—22no—
82C2×#11758201—22no—
83C2×#11758201C2×C414yescomplemented
84C2×D488—22no—
85C2×D488—22no—
86C2×D488C2×C414yescomplemented
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89#14519752—22no—
90#14519752C2×C414yescomplemented
91Q8×Dic61—22no—
92Q8×Dic61—22no—
93C4×D244—28no—
94C4×D244—22no—
95C4×D244—22no—
96C4×D244—22no—
97C4×D244—44no—
98C4×D244D414yescomplemented
99#14519739—28no—
100#14519739—22no—
101#14519739—22no—
102#14519735—28no—
103#14519735—22no—
104#14519735—22no—
105C2×C4⋊Dic61—21no—
106C2×C4⋊Dic61—21no—
107C2×C4⋊Dic61C2311yescharacteristic
108C2×C4⋊Dic61C2311yescharacteristic
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×C4×Dic61—21no—
118C2×C4×Dic61—21no—
119C2×C4×Dic61D411yescharacteristic
120C2×C4×Dic61D411yescharacteristic
121C2×C4×Dic61C2311yescharacteristic
122C42×D61—28no—
123C42×D61—22no—
124C42×D61—22no—
125#14519711—22no—
126#14519708—22no—
127#14519701—22no—
128#14519699—22no—
129#14519699—22no—
130#14519697—22no—
131#14519697—22no—
132#14519697C2×C414yescomplemented
133#14519689—22no—
134#14519689C2×C414yescomplemented
135C4×#92418—22no—
136#14519684—21no—
137#14519684—21no—
138C22×Q8×C61C2311yescharacteristic
139C22×C8×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141C4×Q8×C61—22no—
142C4×Q8×C61D414yescomplemented
143C2×C4⋊C4×C61—21no—
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C42×C61—21no—
148C2×C42×C61—21no—
149C2×C42×C61C2311yescharacteristic
150#103×C61—22no—
151#103×C61C2×C414yescomplemented
152C4×C8×C61—22no—
153#95×C61—21no—
154C23×D61—21no—
155C23×D61—21no—
156C23×D61C2×D411yescharacteristic
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61C22×C412yes—
161C2×Q8×C61C2×D412yes—
162C2×Q8×C61#4112yes—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2411yescharacteristic
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174C22×Dic61C2×D411yescharacteristic
175#11758226—28no—
176#11758226—28no—
177#11758226—28no—
178#11758226—28no—
179C2×D244—24no—
180C2×D244—24no—
181C2×D244—24no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—24no—
190C2×D244—21no—
191C2×D244—42no—
192C2×D244—42no—
193C2×D244C22×C412yes—
194C2×D244C22×C412yes—
195C2×D244C2×D412yes—
196C2×D244#4112yes—
197C2×C4×D61—24no—
198C2×C4×D61—24no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—24no—
204C2×C4×D61—24no—
205C2×C4×D61—24no—
206C2×C4×D61—22no—
207C2×C4×D61—22no—
208C2×C4×D61—22no—
209C2×C4×D61—22no—
210C2×C4×D61—22no—
211C2×C4×D61—41no—
212C2×C4×D61—42no—
213C2×C4×D61—42no—
214C2×C4×D61—42no—
215C2×C4×D61—42no—
216C2×C4×D61—42no—
217C2×C4×D61—42no—
218C2×C4×D61—42no—
219C2×C4×D61C22×C412yes—
220C2×C4×D61#4112yes—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61C22×C412yes—
227C4⋊C4×C61—24no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61C22×C412yes—
233C4⋊C4×C61C2×D412yes—
234C42×C61—24no—
235C42×C61—42no—
236C42×C61C2×D412yes—
237C42×C61C2×D412yes—
238#11758201—28no—
239#11758198—24no—
240#11758198—24no—
241#11758198—24no—
242#11758198—24no—
243#11758198—42no—
244#11758198—42no—
245#11758198—42no—
246#11758198—42no—
247C4⋊Dic61—24no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—42no—
252C4⋊Dic61C2×D412yes—
253C4×Dic61—24no—
254C4×Dic61—24no—
255C4×Dic61—22no—
256C4×Dic61—22no—
257C4×Dic61—21no—
258C4×Dic61—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418C22×C412yes—
265D488—28no—
266C23×C61C22×D411yescharacteristic
267C22×D61—22no—
268C22×D61—21no—
269C22×D61—22no—
270C22×D61—21no—
271C22×D61—22no—
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—22no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61C4×D412yes—
288Q8×C61—22no—
289Q8×C61—22no—
290Q8×C61—22no—
291Q8×C61C4×D414yescomplemented
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61#12012yes—
307C2×C4×C61#12012yes—
308C2×C4×C61#13512yes—
309C2×C4×C61AGL(1,ℤ/8)12yes—
310C2×C4×C61C23×C411yescharacteristic
311C2×C4×C61C22×D411yescharacteristic
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C2×#4111yescharacteristic
314C2×C4×C61C2×#4111yescharacteristic
315C2×C4×C61C2×#4111yescharacteristic
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—22no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61C4×D412yes—
330C2×Dic61#13512yes—
331D244—216no—
332D244—22no—
333D244—22no—
334D244—22no—
335D244—22no—
336D244—22no—
337D244—48no—
338D244—41no—
339D244—41no—
340D244C4×D414yescomplemented
341C4×D61—216no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—44no—
347C4×D61—48no—
348C4×D61—44no—
349C4×D61—48no—
350C4×D61—84no—
351C8×C61—22no—
352C8×C61—41no—
353#92418—22no—
354#92418—41no—
355C4×#449—611nomaximal, Sylow
356C22×C61C2×C4×D411yescharacteristic
357C22×C61C2×#12011yescharacteristic
358C22×C61#52511yescharacteristic
359C22×C61C2×#13511yescharacteristic
360C22×C61C2×#13511yescharacteristic
361C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
362C22×C61#57511yescharacteristic
363C2×D61—22no—
364C2×D61—22no—
365C2×D61—22no—
366C2×D61—24no—
367C2×D61—41no—
368C2×D61—42no—
369C2×D61—41no—
370C2×D61—42no—
371C2×D61—42no—
372C2×D61—42no—
373C2×D61—41no—
374C2×D61—42no—
375C2×D61—41no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—81no—
381C2×D61—81no—
382C2×D61—81no—
383C2×D61—81no—
384C4×C61—22no—
385C4×C61—24no—
386C4×C61—42no—
387C4×C61—42no—
388C4×C61—81no—
389C4×C61#44914yescomplemented
390C4×C61C2×C4×D411yescharacteristic
391C4×C61C2×C4×D411yescharacteristic
392C4×C61#52511yescharacteristic
393C4×C61#52511yescharacteristic
394Dic61—22no—
395Dic61—22no—
396Dic61—41no—
397Dic61—42no—
398Dic61—81no—
399C2×C4×#41—611no—
400C2×#449—611no—
401C2×C4×SD16—611no—
402C2×C4×D8—611no—
403C4×#121—611no—
404#1880—611no—
405#1879—611no—
406#1875—611no—
407#1864—611no—
408#1863—611no—
409#1854—611no—
410#1788—611no—
411C4×#103D6111yescharacteristic, complemented
412C4×#102—611no—
413C4×C22⋊C8—611no—
414C2×C61C4×#12011yescharacteristic
415C2×C61C4×#13511yescharacteristic
416C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
417C2×C61C2×#44911yescharacteristic
418C2×C61#300211yescharacteristic
419C2×C61#310211yescharacteristic
420C2×C61#310611yescharacteristic
421D61—42no—
422D61—44no—
423D61—82no—
424C22×#41—611no—
425C22×SD16—611no—
426C22×D8—611no—
427C2×#121—611no—
428C4×#41—1224no—
429C4×#41—1224no—
430C2×C4×Q8—611no—
431C2×C4×Q8C2×D6111yescharacteristic
432C2×C4×D4—611no—
433C2×C4×D4—611no—
434C2×C4×D4—611no—
435C2×C4×D4—1221no—
436C2×C4×D4—1221no—
437C2×C4×D4—1221no—
438C2×#117—611no—
439C2×#117—1221no—
440C22×C42—611no—
441C22×C42—1221no—
442#449—618no—
443C4×SD16—1224no—
444C4×D8—1224no—
445C2×#107—611no—
446C2×#106—611no—
447C2×#103—611no—
448C2×#103C2×D6111yescharacteristic
449C2×#103C2×D6111yescharacteristic
450C2×#102—611no—
451C2×#102—611no—
452C2×#102—611no—
453C2×#102—611no—
454C2×#102—611no—
455C2×C22⋊C8—611no—
456C2×C22⋊C8—611no—
457C2×C4×C8—611no—
458C2×C4×C8C2×D6111yescharacteristic
459#390—611no—
460#389—611no—
461#388—1221no—
462#386—1221no—
463#380—611no—
464C4×C4⋊C4C2×D6111yescharacteristic
465C4×C22⋊C4—1221no—
466#340—611no—
467#340—611no—
468#340C2×D6111yescharacteristic
469#340C2×D6111yescharacteristic
470#336—611no—
471#336—611no—
472C61C4×#44911yescharacteristic, complemented, Sylow
473C2×#41—614no—
474C2×#41—1222no—
475C2×#41—1222no—
476C2×#41—1222no—
477C2×#41—1222no—
478C2×#41—1222no—
479C22×Q8C22×D6111yescharacteristic
480C22×D4—611no—
481C22×D4—611no—
482C22×D4—1221no—
483C22×D4—1221no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—611no—
487C23×C4—1221no—
488C23×C4—1221no—
489C23×C4—1221no—
490C23×C4—1221no—
491C2×SD16—614no—
492C2×SD16—1222no—
493C2×SD16—1222no—
494C2×D8—614no—
495C2×D8—1222no—
496C2×D8—1222no—
497C22×C8—611no—
498C22×C8—611no—
499C22×C8C22×D6111yescharacteristic
500C22×C8C22×D6111yescharacteristic
501#121—614no—
502#121—1222no—
503C4×Q8—22no—
504C4×Q8—1222no—
505C4×Q8—1222no—
506C4×Q8D24414yescomplemented
507C4×D4—614no—
508C4×D4—1228no—
509C4×D4—1222no—
510C4×D4—1228no—
511C4×D4—1222no—
512C4×D4—1222no—
513C4×D4—1222no—
514C4×D4—1222no—
515C4×D4—2444no—
516#117—1222no—
517#117—1228no—
518#117—1222no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4C22×D6111yescharacteristic
525C2×C4⋊C4C22×D6111yescharacteristic
526C2×C4⋊C4C22×D6111yescharacteristic
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C42—21no—
536C2×C42—21no—
537C2×C42—611no—
538C2×C42—611no—
539C2×C42—611no—
540C2×C42—1228no—
541C2×C42—1221no—
542C2×C42—1221no—
543C2×C42—1222no—
544C2×C42—1222no—
545C2×C42C22×D6111yescharacteristic
546#107—1222no—
547#106—1222no—
548#103—22no—
549#103—1222no—
550#103C4×D6114yescomplemented
551#102—614no—
552#102—1222no—
553#102—1222no—
554#102—1222no—
555#102—1222no—
556C22⋊C8—614no—
557C22⋊C8—1222no—
558C4×C8—22no—
559C4×C8—1222no—
560#95—21no—
561#95—1221no—
562#95—1221no—
563C24—611no—
564C24—1221no—
565C24—1221no—
566#41—1228no—
567#41—1228no—
568#41—1228no—
569#41—1228no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8C2×C4×D6112yes—
574C2×Q8C2×D24412yes—
575C2×Q8#1175822212yes—
576C2×D4—612no—
577C2×D4—612no—
578C2×D4—612no—
579C2×D4—612no—
580C2×D4—1224no—
581C2×D4—1224no—
582C2×D4—1224no—
583C2×D4—1224no—
584C2×D4—1221no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—1221no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4—1221no—
591C2×D4—1221no—
592C2×D4—2442no—
593C2×D4—2442no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—612no—
601C22×C4—612no—
602C22×C4—611no—
603C22×C4—1224no—
604C22×C4—1222no—
605C22×C4—1224no—
606C22×C4—1224no—
607C22×C4—1224no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1224no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1221no—
619C22×C4—2441no—
620C22×C4—2442no—
621C22×C4—2442no—
622C22×C4—2442no—
623C22×C4—2442no—
624C22×C4—2442no—
625C22×C4—2442no—
626C22×C4—2442no—
627C22×C4D4×D6111yescharacteristic
628C22×C4D4×D6111yescharacteristic
629C22×C4C23×D6111yescharacteristic
630SD16—1228no—
631D8—1228no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—612no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8C2×C4×D6112yes—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—24no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—612no—
650C4⋊C4—1224no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—2442no—
655C4⋊C4C2×C4×D6112yes—
656C4⋊C4C2×D24412yes—
657C22⋊C4—1224no—
658C22⋊C4—1224no—
659C22⋊C4—1224no—
660C22⋊C4—1224no—
661C22⋊C4—2442no—
662C22⋊C4—2442no—
663C22⋊C4—2442no—
664C22⋊C4—2442no—
665C42—24no—
666C42—42no—
667C42—1224no—
668C42—1224no—
669C42—1221no—
670C42—1221no—
671C42—1222no—
672C42—1222no—
673C42C2×D24412yes—
674C42D4×D6112yes—
675C23—612no—
676C23—1222no—
677C23—1222no—
678C23—1221no—
679C23—1222no—
680C23—1221no—
681C23—1221no—
682C23—1221no—
683C23—1221no—
684C23—1221no—
685C23—1222no—
686C23—2441no—
687C23—2441no—
688C23—2441no—
689C23—2441no—
690C23—2441no—
691C23—2441no—
692C23—2441no—
693C23—2441no—
694C23—2441no—
695C23—2441no—
696C23C2×D4×D6111yescharacteristic
697Q8—22no—
698Q8—22no—
699Q8—22no—
700Q8C4×D24414yescomplemented
701D4—614no—
702D4—12216no—
703D4—1222no—
704D4—1222no—
705D4—1222no—
706D4—1222no—
707D4—1222no—
708D4—2448no—
709D4—2441no—
710D4—2441no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—612no—
726C2×C4—612no—
727C2×C4—12216no—
728C2×C4—1221no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1221no—
738C2×C4—1221no—
739C2×C4—1221no—
740C2×C4—4884no—
741C2×C4—2444no—
742C2×C4—2448no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2444no—
749C2×C4—2448no—
750C2×C4#1451974712yes—
751C2×C4#1451974712yes—
752C2×C4#1451980012yes—
753C2×C4#1451980412yes—
754C2×C4C22×C4×D6111yescharacteristic
755C2×C4C2×D4×D6111yescharacteristic
756C2×C4C22×D24411yescharacteristic
757C2×C4#41×D6111yescharacteristic
758C2×C4#41×D6111yescharacteristic
759C2×C4C2×#1175822211yescharacteristic
760C8—22no—
761C8—41no—
762C8—1222no—
763C8—2441no—
764C22—1222no—
765C22—1224no—
766C22—1222no—
767C22—1222no—
768C22—4881no—
769C22—4881no—
770C22—4881no—
771C22—4881no—
772C22—2442no—
773C22—2442no—
774C22—2442no—
775C22—2441no—
776C22—2442no—
777C22—2442no—
778C22—2441no—
779C22—2442no—
780C22—2441no—
781C22—2442no—
782C22—2441no—
783C22—2442no—
784C22—2442no—
785C22C4×D4×D6111yescharacteristic
786C22C2×#1451974711yescharacteristic
787C22#1684027111yescharacteristic
788C22#135×D6111yescharacteristic
789C22C2×#1451980011yescharacteristic
790C22C2×#1451980411yescharacteristic
791C22#1684055911yescharacteristic
792C4—24no—
793C4—22no—
794C4—42no—
795C4—42no—
796C4—81no—
797C4—1222no—
798C4—1222no—
799C4—4881no—
800C4—2441no—
801C4—2442no—
802C4#1683991014yesdirect product factor
803C4C4×D4×D6111yescharacteristic
804C4C2×C4×D24411yescharacteristic
805C4#1684027111yescharacteristic
806C4#1684027411yescharacteristic
807C2—4882no—
808C2—2442no—
809C2—2444no—
810C2C4×#1451974711yescharacteristic
811C2C4×#1451980011yescharacteristic
812C2C4×#1451980411yescharacteristic
813C2C2×#1683991011yescharacteristic
814C2#2145503911yescharacteristic
815C2#2145584311yescharacteristic
816C2#2145587711yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×#103×C61C2
socleC23×C61C22×D4
prime radicalC2×#16839910C2
cosocleC22×C4×C61C24
hypercenterC4×#103D61
hypocenterC61C4×#449
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
1. C2×C4×#11758226C2semidirect
3. C2×C4×#11758201C2semidirect
4. C2×C4×D488C2semidirect
5. C4×#14519752C2semidirect
6. #21446172C2semidirect
7. #21446168C2semidirect
8. #21446140C2semidirect
9. #21446081C2semidirect
10. #21446075C2semidirect
11. #21446021C2semidirect
12. #21445758C2semidirect
13. C4×#14519697C2semidirect
14. C4×#14519689C2semidirect
15. C4×#103×C61C2semidirect
33. #16839910C4direct (N × H)
69. C2×#11758226C2×C4semidirect
83. C2×#11758201C2×C4semidirect
86. C2×D488C2×C4semidirect
90. #14519752C2×C4semidirect
98. C4×D244D4semidirect
132. #14519697C2×C4semidirect
134. #14519689C2×C4semidirect
142. C4×Q8×C61D4semidirect
151. #103×C61C2×C4semidirect
291. Q8×C61C4×D4semidirect
340. D244C4×D4semidirect
389. C4×C61#449semidirect
411. C4×#103D61semidirect
472. C61C4×#449semidirect
506. C4×Q8D244semidirect
550. #103C4×D61semidirect
700. Q8C4×D244semidirect
802. C4#16839910direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#117582262
C2×#168399102
C2×C4×#117582012
C2×C4×D4882
C4×#145197522
#214461722
#214461682
#214461402
#214460812
#214460752
#214460212
#214457582
C4×#145196972
C4×#145196892
C4×#103×C612
C4×#44961