Finite Group Databasebeta

← #29681806

Subgroups — #29681806

Order 15616.

1994 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840274C211yesmaximal, characteristic
2C2×#117×D61C211yesmaximal, characteristic, complemented
3C2×#16839735C211yesmaximal, characteristic, complemented
4C2×#16839735C211yesmaximal, characteristic, complemented
5#21448198C211yesmaximal, characteristic, complemented
6#21446276C214yesmaximal, complemented
7#21446271C214yesmaximal, complemented
8#21445552C211yesmaximal, characteristic, complemented
9C61×#1740C211yesmaximal, characteristic, complemented
10C22×#11758222C2211yescharacteristic
11C23×C4×D61C2211yescharacteristic
12#16840274—21no—
13#16840274—21no—
14#16840274—21no—
15#16840274—21no—
16#16840274—22no—
17#16840274—22no—
18C2×#14519761C2212yes—
19C2×#14519757C412yescomplemented
20C2×#14519752C412yescomplemented
21C2×#14519747C2212yes—
22C2×C4×D244C414yescomplemented
23C2×#14519736C2211yescharacteristic
24C2×#14519736C2211yescharacteristic
25C2×#14519735—21no—
26C2×#14519734—21no—
27C2×#14519733C2212yes—
28#117×D61—24no—
29#117×D61—24no—
30C2×C4⋊C4×D61—21no—
31C2×C22⋊C4×D61C2212yes—
32C2×C42×D61—21no—
33#16839735—24no—
34#16839735—24no—
35C2×#14519691C2214yes—
36C2×#14519691C2214yes—
37#16839623C2212yes—
38#16839619—22no—
39#16839617C2212yes—
40C4×#11758198—22no—
41#16839529C2214yes—
42C2×#117×C61C2211yescharacteristic
43C2×#117×C61C2211yescharacteristic
44C2×#117×C61C2211yescharacteristic
45C61×#342C2214yes—
46C24×D61C2311yescharacteristic
47C2×#11758222—22no—
48C2×#11758222—22no—
49C2×#11758222—21no—
50C2×#11758222—21no—
51C2×#11758222—21no—
52C2×#11758222—21no—
53C2×#11758222—22no—
54C2×#11758222—22no—
55C22×Dic122C2×C411yescharacteristic, complemented
56C22×D244C2×C414yes—
57C22×D244C2×C411yescharacteristic, complemented
58C22×C22⋊D61C2312yes—
59C23×Dic61C2311yescharacteristic
60C22×C4×D61—22no—
61C22×C4×D61—22no—
62C22×C4×D61—22no—
63C22×C4×D61—22no—
64C22×C4×D61—22no—
65C22×C4×D61C2×C412yes—
66C22×C4×D61C2×C412yes—
67C22×C4×D61C2×C412yescomplemented
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61D412yes—
73C22×C4×D61D412yes—
74#14519761—24no—
75#14519761—22no—
76#14519761—22no—
77#14519757—22no—
78#14519757—22no—
79#14519757—22no—
80#14519757—22no—
81#14519752—22no—
82#14519752—22no—
83#14519752—22no—
84#14519752—22no—
85#14519747—22no—
86#14519747—24no—
87#14519747—22no—
88C4×D244—24no—
89C4×D244—24no—
90C4×D244—24no—
91C4×D244—24no—
92#14519736—22no—
93#14519736—22no—
94#14519736—22no—
95#14519736D414yescomplemented
96#14519735—28no—
97#14519734—28no—
98#14519733—24no—
99#14519733—24no—
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61—21no—
102C2×C4⋊Dic61C2×C414yescomplemented
103C2×#11758196—22no—
104C4⋊C4×D61—28no—
105C2×C22⋊Dic61C2312yes—
106C2×C22⋊Dic61C2312yes—
107C2×#11758198—22no—
108C2×#11758198—24no—
109C2×#11758198C2×C414yes—
110C2×#11758198C2×C414yescomplemented
111C22⋊C4×D61—24no—
112C22⋊C4×D61—24no—
113C2×C4×Dic61—21no—
114C2×C4×Dic61—22no—
115C2×C4×Dic61—21no—
116C42×D61—28no—
117#14519691—28no—
118#14519691—28no—
119#14519684—24no—
120C23×C4×C61C2311yescharacteristic
121#117×C61—22no—
122#117×C61—21no—
123#117×C61—21no—
124#117×C61—21no—
125#117×C61—21no—
126#117×C61—22no—
127#117×C61—22no—
128#117×C61D414yescomplemented
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61C2×C412yescomplemented
132C2×C22⋊C4×C61C2312yes—
133C2×C22⋊C4×C61C2312yes—
134C2×C22⋊C4×C61C2312yes—
135C2×C42×C61—21no—
136C2×C42×C61—21no—
137C2×C42×C61C2×C412yescomplemented
138C24×C61C2411yescharacteristic
139C23×D61—21no—
140C23×D61—21no—
141C23×D61—21no—
142C23×D61—21no—
143C23×D61—44no—
144C23×D61C22×C412yes—
145C23×D61C22×C412yes—
146C23×D61C2×D411yescharacteristic
147C23×D61C2×D412yes—
148C23×D61C2×D411yescharacteristic
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61C22×C414yes—
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D412yes—
159C22×C4×C61C2×D412yes—
160C22×C4×C61#4112yes—
161C22×C4×C61#4112yes—
162C2×C22⋊D61—22no—
163C2×C22⋊D61—22no—
164C2×C22⋊D61—22no—
165C2×C22⋊D61—22no—
166C2×C22⋊D61—22no—
167C2×C22⋊D61—22no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61C22×C412yes—
175C22×Dic61C22×C412yes—
176C22×Dic61C2×D412yes—
177C22×Dic61C2×D411yescharacteristic
178C22×Dic61C2×D411yescharacteristic
179#11758222—42no—
180#11758222—42no—
181#11758222—42no—
182#11758222—42no—
183#11758222—42no—
184#11758222—42no—
185#11758222—42no—
186#11758222—42no—
187C2×D244—24no—
188C2×D244—24no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—22no—
192C2×D244—22no—
193C2×D244—48no—
194C2×C4×D61—24no—
195C2×C4×D61—24no—
196C2×C4×D61—24no—
197C2×C4×D61—24no—
198C2×C4×D61—22no—
199C2×C4×D61—22no—
200C2×C4×D61—22no—
201C2×C4×D61—22no—
202C2×C4×D61—24no—
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—28no—
211C2×C4×D61—22no—
212C2×C4×D61—22no—
213C2×C4×D61—24no—
214C2×C4×D61—24no—
215C2×C4×D61—48no—
216C2×C4×D61C22⋊C412yes—
217C2×C4×D61C22⋊C412yes—
218C2×C4×D61C22⋊C412yes—
219C2×C4×D61C22⋊C412yes—
220C2×C4×D61C22⋊C412yes—
221C2×C4×D61C22⋊C412yes—
222C2×C4×D61C22⋊C412yes—
223C2×C4×D61C22⋊C412yes—
224C2×Dic122—21no—
225C2×Dic122—21no—
226C2×Dic122—22no—
227C2×Dic122—22no—
228C4⋊C4×C61—22no—
229C4⋊C4×C61—22no—
230C4⋊C4×C61—24no—
231C4⋊C4×C61—42no—
232C22⋊C4×C61—22no—
233C22⋊C4×C61—22no—
234C22⋊C4×C61—22no—
235C22⋊C4×C61—22no—
236C22⋊C4×C61—22no—
237C22⋊C4×C61C2×D414yes—
238C42×C61—22no—
239C42×C61—22no—
240C42×C61—24no—
241C42×C61—42no—
242C22⋊Dic61—22no—
243C22⋊Dic61—22no—
244C22⋊Dic61—22no—
245C22⋊Dic61C2×D414yes—
246#11758198—28no—
247#11758198—24no—
248#11758198—24no—
249#11758198—24no—
250#11758198—24no—
251#11758198—48no—
252C4⋊Dic61—24no—
253C4⋊Dic61—24no—
254C4⋊Dic61—24no—
255C4⋊Dic61—42no—
256#11758196—28no—
257C4×Dic61—28no—
258C4×Dic61—24no—
259C4×Dic61—42no—
260C23×C61—42no—
261C23×C61C23×C411yescharacteristic
262C23×C61C22×D411yescharacteristic
263C23×C61C22×D411yescharacteristic
264C23×C61C22×D411yescharacteristic
265C23×C61C22×D411yescharacteristic
266C23×C61C2×#4111yescharacteristic
267C23×C61C2×#4111yescharacteristic
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—24no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—21no—
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—21no—
277C22×D61—24no—
278C22×D61—24no—
279C22×D61—22no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—42no—
283C22×D61—42no—
284C22×D61—42no—
285C22×D61—44no—
286C22×D61—44no—
287C22×D61—44no—
288C22×D61—44no—
289C22×D61—44no—
290C22×D61C2×C22⋊C412yes—
291C22×D61C2×C22⋊C412yes—
292C2×C4×C61—24no—
293C2×C4×C61—24no—
294C2×C4×C61—44no—
295C2×C4×C61—44no—
296C2×C4×C61—44no—
297C2×C4×C61—42no—
298C2×C4×C61C2×C22⋊C411yescharacteristic
299C2×C4×C61C2×C22⋊C411yescharacteristic
300C2×C4×C61C2×C22⋊C411yescharacteristic
301C2×C4×C61C2×C22⋊C411yescharacteristic
302C2×C4×C61C4×D412yes—
303C2×C4×C61C4×D412yes—
304C2×C4×C61C4×D412yes—
305C2×C4×C61C4×D412yes—
306C2×C4×C61#12012yes—
307C2×C4×C61#12012yes—
308C2×C4×C61#12112yes—
309C2×C4×C61#12112yes—
310C2×C4×C61#12112yes—
311C2×C4×C61#12112yes—
312C2×C4×C61#12312yes—
313C2×C4×C61#12312yes—
314C22⋊D61—42no—
315C22⋊D61—42no—
316C22⋊D61—42no—
317C22⋊D61—42no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—24no—
330C2×Dic61—44no—
331C2×Dic61—44no—
332C2×Dic61—42no—
333C2×Dic61C2×C22⋊C412yes—
334C2×Dic61C2×C22⋊C412yes—
335D244—48no—
336D244—48no—
337D244—42no—
338D244—42no—
339C4×D61—24no—
340C4×D61—24no—
341C4×D61—24no—
342C4×D61—24no—
343C4×D61—24no—
344C4×D61—24no—
345C4×D61—24no—
346C4×D61—24no—
347C4×D61—416no—
348C4×D61—44no—
349C4×D61—44no—
350Dic122—42no—
351Dic122—42no—
352#20983—611nomaximal, Sylow
353C22×C61—22no—
354C22×C61—22no—
355C22×C61—22no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61C22×C22⋊C411yescharacteristic
361C22×C61C2×C4×D411yescharacteristic
362C22×C61C2×C4×D411yescharacteristic
363C22×C61C2×#12011yescharacteristic
364C22×C61C2×#12111yescharacteristic
365C22×C61C2×#12111yescharacteristic
366C22×C61C2×#12311yescharacteristic
367C2×D61—24no—
368C2×D61—24no—
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—22no—
372C2×D61—22no—
373C2×D61—22no—
374C2×D61—44no—
375C2×D61—44no—
376C2×D61—44no—
377C2×D61—44no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—44no—
381C2×D61—42no—
382C2×D61—82no—
383C2×D61—82no—
384C2×D61#41014yescomplemented
385C4×C61—44no—
386C4×C61—44no—
387C4×C61—82no—
388C4×C61#38612yes—
389C4×C61#38612yes—
390C4×C61#38612yes—
391C4×C61#38612yes—
392Dic61—22no—
393Dic61—22no—
394Dic61—44no—
395Dic61—42no—
396Dic61—82no—
397C2×#525—611no—
398C22×#117—611no—
399C2×#410—611no—
400C2×#410—611no—
401#2280—611no—
402#1899—614no—
403#1898—614no—
404#1740—611no—
405#1740D6111yescharacteristic, complemented
406C2×C61—21no—
407C2×C61—21no—
408C2×C61—21no—
409C2×C61—21no—
410C2×C61—21no—
411C2×C61—21no—
412C2×C61C2×#38611yescharacteristic
413C2×C61C2×#41012yes—
414D61—24no—
415D61—42no—
416D61—82no—
417C22×#41—611no—
418C24×C4—611no—
419#525—1221no—
420#525—1221no—
421#525—1221no—
422#525—1222no—
423#525—1222no—
424#525—1221no—
425C2×#123—612no—
426C2×C22⋊Q8—612no—
427C2×#121—612no—
428C2×#120—612no—
429C2×C4×D4—614no—
430C2×#117—611no—
431C2×#117—611no—
432C2×#117—612no—
433C2×#117—1221no—
434C2×#117—1221no—
435C2×#117—1224no—
436C2×#117—1224no—
437C2×#117C2×D6111yescharacteristic
438C2×#117C2×D6111yescharacteristic
439C2×#117C2×D6111yescharacteristic
440C22×C4⋊C4—1221no—
441C22×C22⋊C4—612no—
442C22×C42—1221no—
443#410—1224no—
444#410—1224no—
445C2×#99—614no—
446C2×#99—614no—
447#381—612no—
448#380—1222no—
449#379—612no—
450C4×C22⋊C4—1222no—
451#342—614no—
452#342C2×D6114yes—
453C61#2098311yescharacteristic, complemented, Sylow
454C25—611no—
455C2×#41—1222no—
456C2×#41—1222no—
457C2×#41—1221no—
458C2×#41—1221no—
459C2×#41—1221no—
460C2×#41—1221no—
461C2×#41—1222no—
462C2×#41—1222no—
463C22×Q8—611no—
464C22×D4—612no—
465C22×D4—611no—
466C22×D4—614no—
467C23×C4—611no—
468C23×C4—612no—
469C23×C4—612no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—611no—
473C23×C4—612no—
474C23×C4—612no—
475C23×C4—611no—
476C23×C4—612no—
477C23×C4—1222no—
478C23×C4—1222no—
479C23×C4—1222no—
480C23×C4—1222no—
481C23×C4—1222no—
482C23×C4C22×D6111yescharacteristic
483#123—1224no—
484#123—1222no—
485#123—1222no—
486C22⋊Q8—1222no—
487C22⋊Q8—1222no—
488C22⋊Q8—1222no—
489C22⋊Q8—1222no—
490#121—1222no—
491#121—1222no—
492#121—1222no—
493#121—1222no—
494#120—1222no—
495#120—1224no—
496#120—1222no—
497C4×D4—1224no—
498C4×D4—1224no—
499C4×D4—1224no—
500C4×D4—1224no—
501#117—22no—
502#117—21no—
503#117—21no—
504#117—21no—
505#117—21no—
506#117—22no—
507#117—22no—
508#117—614no—
509#117—1228no—
510#117—1224no—
511#117—1228no—
512#117—1222no—
513#117—1224no—
514#117—1222no—
515#117—1222no—
516#117D24414yescomplemented
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—614no—
520C2×C4⋊C4—1228no—
521C2×C4⋊C4—1222no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4C4×D6112yescomplemented
525C2×C22⋊C4—612no—
526C2×C22⋊C4—614no—
527C2×C22⋊C4—614no—
528C2×C22⋊C4—612no—
529C2×C22⋊C4—1224no—
530C2×C22⋊C4—1222no—
531C2×C22⋊C4—1224no—
532C2×C22⋊C4—1224no—
533C2×C22⋊C4C22×D6112yes—
534C2×C22⋊C4C22×D6112yes—
535C2×C22⋊C4C22×D6112yes—
536C2×C42—21no—
537C2×C42—21no—
538C2×C42—1228no—
539C2×C42—1222no—
540C2×C42—1221no—
541C2×C42—1221no—
542C2×C42C4×D6112yescomplemented
543#99—1228no—
544#99—1228no—
545#95—1224no—
546C24—611no—
547C24—612no—
548C24—612no—
549C24—611no—
550C24—612no—
551C24—1221no—
552C24—1221no—
553C24—1221no—
554C24—1221no—
555C24—2444no—
556C24C23×D6111yescharacteristic
557#41—2442no—
558#41—2442no—
559#41—2442no—
560#41—2442no—
561#41—2442no—
562#41—2442no—
563#41—2442no—
564#41—2442no—
565C2×Q8—1221no—
566C2×Q8—1221no—
567C2×Q8—1222no—
568C2×Q8—1222no—
569C2×D4—1224no—
570C2×D4—1224no—
571C2×D4—1222no—
572C2×D4—1222no—
573C2×D4—1222no—
574C2×D4—1222no—
575C2×D4—1222no—
576C2×D4—1222no—
577C2×D4—1221no—
578C2×D4—1221no—
579C2×D4—1222no—
580C2×D4—1222no—
581C2×D4—2448no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—612no—
585C22×C4—612no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—612no—
589C22×C4—612no—
590C22×C4—612no—
591C22×C4—612no—
592C22×C4—612no—
593C22×C4—612no—
594C22×C4—612no—
595C22×C4—612no—
596C22×C4—612no—
597C22×C4—1228no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1224no—
603C22×C4—1224no—
604C22×C4—1224no—
605C22×C4—1224no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1224no—
611C22×C4—1224no—
612C22×C4—1224no—
613C22×C4—1224no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4—1224no—
622C22×C4—1224no—
623C22×C4—1222no—
624C22×C4—2448no—
625C22×C4C2×C4×D6114yes—
626C22×C4C2×C4×D6111yescharacteristic
627C22×C4C2×C4×D6111yescharacteristic
628C22×C4C2×D24412yes—
629C22×C4#1175822212yes—
630C22×C4D4×D6111yescharacteristic
631C22×C4D4×D6111yescharacteristic
632C22×C4D4×D6111yescharacteristic
633C22×C4D4×D6111yescharacteristic
634C22×C4D4×D6112yes—
635C22×C4#1175822612yes—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—24no—
639C4⋊C4—42no—
640C4⋊C4—1224no—
641C4⋊C4—1224no—
642C4⋊C4—1228no—
643C4⋊C4—1224no—
644C4⋊C4—2442no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—614no—
651C22⋊C4—1224no—
652C22⋊C4—1224no—
653C22⋊C4—1224no—
654C22⋊C4—1224no—
655C22⋊C4—1228no—
656C22⋊C4—1222no—
657C22⋊C4—1222no—
658C22⋊C4—1222no—
659C22⋊C4—2448no—
660C22⋊C4C2×D24414yes—
661C42—22no—
662C42—22no—
663C42—24no—
664C42—42no—
665C42—1228no—
666C42—1224no—
667C42—2442no—
668C23—42no—
669C23—612no—
670C23—612no—
671C23—1224no—
672C23—1224no—
673C23—1224no—
674C23—1221no—
675C23—1221no—
676C23—1222no—
677C23—1222no—
678C23—1221no—
679C23—1222no—
680C23—1222no—
681C23—1221no—
682C23—1222no—
683C23—1222no—
684C23—1222no—
685C23—2442no—
686C23—2442no—
687C23—2442no—
688C23—2444no—
689C23—2444no—
690C23—2444no—
691C23—2444no—
692C23—2444no—
693C23C22×C4×D6111yescharacteristic
694C23C2×D4×D6111yescharacteristic
695C23C2×D4×D6111yescharacteristic
696C23C2×D4×D6111yescharacteristic
697C23C22×D24411yescharacteristic
698C23C2×#1175822211yescharacteristic
699C23C2×#1175822611yescharacteristic
700Q8—2442no—
701Q8—2442no—
702D4—2448no—
703D4—2448no—
704D4—2442no—
705D4—2442no—
706D4—2442no—
707D4—2442no—
708D4—2442no—
709D4—2442no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—612no—
717C2×C4—612no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1221no—
725C2×C4—1221no—
726C2×C4—1224no—
727C2×C4—1224no—
728C2×C4—1224no—
729C2×C4—1224no—
730C2×C4—1224no—
731C2×C4—1224no—
732C2×C4—1224no—
733C2×C4—1224no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1224no—
738C2×C4—24416no—
739C2×C4—2444no—
740C2×C4—2442no—
741C2×C4—2444no—
742C2×C4—2444no—
743C2×C4—2444no—
744C2×C4C22⋊C4×D6111yescharacteristic
745C2×C4C22⋊C4×D6111yescharacteristic
746C2×C4C22⋊C4×D6111yescharacteristic
747C2×C4C22⋊C4×D6111yescharacteristic
748C2×C4#1451973912yes—
749C2×C4#1451973912yes—
750C2×C4C4×D24412yes—
751C2×C4C4×D24412yes—
752C2×C4#1451974712yes—
753C2×C4#1451974712yes—
754C2×C4#1451975012yes—
755C2×C4#1451975012yes—
756C2×C4#1451975212yes—
757C2×C4#1451975212yes—
758C2×C4#1451976212yes—
759C2×C4#1451976212yes—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—614no—
768C22—1224no—
769C22—1224no—
770C22—1222no—
771C22—1222no—
772C22—1222no—
773C22—1222no—
774C22—1222no—
775C22—4882no—
776C22—4882no—
777C22—2444no—
778C22—2444no—
779C22—2444no—
780C22—2444no—
781C22—2442no—
782C22—2442no—
783C22—2442no—
784C22—2444no—
785C22C2×C22⋊C4×D6111yescharacteristic
786C22C2×#1451973911yescharacteristic
787C22C2×C4×D24411yescharacteristic
788C22C2×#1451974711yescharacteristic
789C22C2×#1451975011yescharacteristic
790C22C2×#1451975211yescharacteristic
791C22C2×#1451976211yescharacteristic
792C4—44no—
793C4—44no—
794C4—82no—
795C4—1222no—
796C4—1222no—
797C4—4882no—
798C4—2444no—
799C4—2442no—
800C4#1683964012yes—
801C4#1683964012yes—
802C4#1683964012yes—
803C4#1683964012yes—
804C2—21no—
805C2—21no—
806C2—21no—
807C2—21no—
808C2—21no—
809C2—21no—
810C2—1224no—
811C2—4882no—
812C2—2442no—
813C2C2×#1683964011yescharacteristic
814C2#410×D6112yes—
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1740C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840274C2
cosocleC24×C61C24
hypercenter#1740D61
hypocenterC61#20983
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1740

Complements

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

NH ≅ G/Ntype
2. C2×#117×D61C2semidirect
3. C2×#16839735C2semidirect
4. C2×#16839735C2semidirect
5. #21448198C2semidirect
6. #21446276C2semidirect
7. #21446271C2semidirect
8. #21445552C2semidirect
9. C61×#1740C2semidirect
19. C2×#14519757C4semidirect
20. C2×#14519752C4semidirect
22. C2×C4×D244C4semidirect
55. C22×Dic122C2×C4semidirect
57. C22×D244C2×C4semidirect
67. C22×C4×D61C2×C4semidirect
95. #14519736D4semidirect
102. C2×C4⋊Dic61C2×C4semidirect
110. C2×#11758198C2×C4semidirect
128. #117×C61D4semidirect
131. C2×C4⋊C4×C61C2×C4semidirect
137. C2×C42×C61C2×C4semidirect
384. C2×D61#410semidirect
405. #1740D61semidirect
453. C61#20983semidirect
516. #117D244semidirect
524. C2×C4⋊C4C4×D61semidirect
542. C2×C42C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402742
C2×#117×D612
C2×#168397352
#214481982
#214462762
#214462712
#214455522
C61×#17402
#2098361