Finite Group Databasebeta

← #29696767

Subgroups — #29696767

Order 15616.

1172 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840464C211yesmaximal, characteristic
2#21448698C211yesmaximal, characteristic, complemented
3#21448694C211yesmaximal, characteristic, complemented
4#21446656C211yesmaximal, characteristic, complemented
5#21446653C212yesmaximal, complemented
6#21446653C212yesmaximal, complemented
7#21445805C212yesmaximal, complemented
8#21445804C211yesmaximal, characteristic, complemented
9#99×Dic61C212yesmaximal, complemented
10C4×#14519691C211yesmaximal, characteristic, complemented
11C61×#1964C211yesmaximal, characteristic, complemented
12#16840464—21no—
13#16840464—21no—
14#16840464—22no—
15#16840464—22no—
16#16840464—21no—
17#16840464—21no—
18C2×#14519770C412yescomplemented
19C2×#14519768C411yescharacteristic, complemented
20C2×#14519761C412yescomplemented
21C2×#14519749C2212yes—
22C2×#14519748C411yescharacteristic, complemented
23C2×D4×Dic61C411yescharacteristic, complemented
24C2×D4×Dic61C2212yes—
25C2×C4×C22⋊D61C2211yescharacteristic
26C2×#14519735C411yescharacteristic, complemented
27C22×C4⋊Dic61C2211yescharacteristic
28C2×#14519692C2212yes—
29C2×#14519692C2212yes—
30C2×#14519691C2211yescharacteristic
31C2×#14519691C2211yescharacteristic
32C2×#14519691C2212yes—
33#16839660—21no—
34#16839658—21no—
35#16839647—22no—
36#16839645—22no—
37#16839622C2211yescharacteristic
38#16839620C2212yes—
39#16839620C2212yes—
40C4⋊C4×Dic61—21no—
41C4×C4⋊Dic61—21no—
42C22⋊C4×Dic61C2212yes—
43C22⋊C4×Dic61C2212yes—
44C4×C22⋊Dic61C2211yescharacteristic
45#16839528C2212yes—
46#16839528C2211yescharacteristic
47#16839528C2211yescharacteristic
48C2×#121×C61C2211yescharacteristic
49C2×#99×C61C2212yes—
50C2×#99×C61C2212yes—
51C61×#380C2211yescharacteristic
52C4×C22⋊C4×C61C2211yescharacteristic
53C22×C22⋊D61C2×C412yes—
54C22×C22⋊D61C2311yescharacteristic
55C23×Dic61C2×C412yes—
56C23×Dic61C2312yes—
57C22×C4×D61C2×C411yescharacteristic
58#14519770—22no—
59#14519770—22no—
60#14519770—22no—
61#14519770—22no—
62#14519768—22no—
63#14519768—21no—
64#14519768—21no—
65#14519761—22no—
66#14519761—22no—
67#14519761—22no—
68#14519761—22no—
69#14519749—22no—
70#14519749—22no—
71#14519749—22no—
72#14519749—22no—
73#14519748—22no—
74#14519748—21no—
75#14519748—21no—
76D4×Dic61—22no—
77D4×Dic61—22no—
78D4×Dic61—22no—
79D4×Dic61—22no—
80D4×Dic61—22no—
81D4×Dic61—21no—
82D4×Dic61—21no—
83C4×C22⋊D61—21no—
84C4×C22⋊D61—21no—
85C4×C22⋊D61—21no—
86C4×C22⋊D61—21no—
87#14519735—22no—
88#14519735—21no—
89#14519735—21no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61C2×C412yes—
92C2×C4⋊Dic61C2×C411yescharacteristic
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×C4⋊Dic61C2×C412yes—
95C2×C4⋊Dic61D411yescharacteristic
96C2×C4⋊Dic61D411yescharacteristic
97C2×C4⋊Dic61D412yes—
98C2×C4⋊Dic61D412yes—
99C2×C4⋊Dic61D411yescharacteristic
100C2×C4⋊Dic61D411yescharacteristic
101C2×#11758196—22no—
102C2×#11758196—22no—
103C2×#11758196C2×C411yescharacteristic
104C2×#11758196C2×C412yes—
105C2×C22⋊Dic61C2×C412yes—
106C2×C22⋊Dic61C2×C412yes—
107C2×C22⋊Dic61C2311yescharacteristic
108C2×C22⋊Dic61C2312yes—
109C2×C22⋊Dic61C2311yescharacteristic
110C2×C22⋊Dic61C2311yescharacteristic
111C2×#11758198C2×C412yes—
112C2×#11758198C2×C411yescharacteristic
113C2×C4×Dic61—21no—
114C2×C4×Dic61—22no—
115C2×C4×Dic61—22no—
116C2×C4×Dic61C2×C412yes—
117C2×C4×Dic61C2×C411yescharacteristic
118#14519692—24no—
119#14519692—42no—
120#14519691—22no—
121#14519691—22no—
122#14519691—42no—
123#14519684—21no—
124#14519684—21no—
125#14519684—22no—
126#14519684—22no—
127#14519684—22no—
128#14519684—22no—
129C22×D4×C61C2×C411yescharacteristic
130C22×D4×C61C2312yes—
131C23×C4×C61C2311yescharacteristic
132#121×C61—21no—
133#121×C61—21no—
134#121×C61—21no—
135#121×C61—21no—
136C2×C4⋊C4×C61—21no—
137C2×C4⋊C4×C61C2×C411yescharacteristic
138C2×C22⋊C4×C61C2×C412yes—
139C2×C22⋊C4×C61C2311yescharacteristic
140C2×C22⋊C4×C61C2312yes—
141C2×C22⋊C4×C61C2311yescharacteristic
142C2×C42×C61—21no—
143#99×C61—24no—
144#99×C61—42no—
145#95×C61—21no—
146#95×C61—21no—
147C24×C61C22×C412yes—
148C24×C61C2411yescharacteristic
149C23×D61C22×C411yescharacteristic
150C2×D4×C61—22no—
151C2×D4×C61—22no—
152C2×D4×C61—22no—
153C2×D4×C61—22no—
154C2×D4×C61—22no—
155C2×D4×C61—22no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—42no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—22no—
162C22×C4×C61—42no—
163C22×C4×C61C22×C412yes—
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C22×C411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C2×C22⋊D61—21no—
171C2×C22⋊D61—21no—
172C2×C22⋊D61—21no—
173C2×C22⋊D61—21no—
174C2×C22⋊D61—21no—
175C2×C22⋊D61—21no—
176C2×C22⋊D61—22no—
177C2×C22⋊D61—22no—
178C2×C22⋊D61—82no—
179C22×Dic61—21no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—21no—
183C22×Dic61—22no—
184C22×Dic61—82no—
185C22×Dic61—82no—
186C22×Dic61C22×C411yescharacteristic
187C22×Dic61C22×C411yescharacteristic
188C22×Dic61C22×C411yescharacteristic
189C22×Dic61C22×C412yes—
190C22×Dic61C22×C412yes—
191C22×Dic61C2×D412yes—
192C22×Dic61C2×D412yes—
193C22×Dic61C2×D412yes—
194C22×Dic61C2×D412yes—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—42no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—42no—
201C22⋊C4×C61—21no—
202C22⋊C4×C61—22no—
203C22⋊C4×C61—22no—
204C22⋊C4×C61—22no—
205C22⋊C4×C61—21no—
206C22⋊C4×C61—21no—
207C22⋊C4×C61—22no—
208C22⋊C4×C61#4112yes—
209C42×C61—42no—
210C22⋊Dic61—21no—
211C22⋊Dic61—21no—
212C22⋊Dic61—21no—
213C22⋊Dic61—22no—
214C22⋊Dic61—22no—
215C22⋊Dic61—22no—
216C22⋊Dic61—22no—
217C22⋊Dic61—21no—
218C22⋊Dic61—22no—
219C22⋊Dic61—22no—
220C22⋊Dic61—21no—
221C22⋊Dic61#4112yes—
222#11758198—21no—
223#11758198—21no—
224#11758198—22no—
225#11758198—22no—
226C4⋊Dic61—22no—
227C4⋊Dic61—22no—
228C4⋊Dic61—42no—
229C4⋊Dic61C22⋊C412yes—
230C4⋊Dic61C22⋊C411yescharacteristic
231C4⋊Dic61C22⋊C411yescharacteristic
232C4⋊Dic61C22⋊C412yes—
233C4⋊Dic61C22⋊C411yescharacteristic
234C4⋊Dic61C22⋊C411yescharacteristic
235C4⋊Dic61C22⋊C412yes—
236C4⋊Dic61C22⋊C412yes—
237C4⋊Dic61C22⋊C412yes—
238C4⋊Dic61C22⋊C412yes—
239#11758196—21no—
240#11758196—21no—
241#11758196—22no—
242#11758196—22no—
243#11758196—82no—
244#11758196—82no—
245C4×Dic61—21no—
246C4×Dic61—21no—
247C4×Dic61—22no—
248C4×Dic61—22no—
249C4×Dic61—42no—
250C4×Dic61—82no—
251C4×Dic61—82no—
252C23×C61—22no—
253C23×C61—22no—
254C23×C61—22no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—42no—
258C23×C61—42no—
259C23×C61C23×C411yescharacteristic
260C23×C61C22×D411yescharacteristic
261C23×C61C22×D411yescharacteristic
262C23×C61C2×#4111yescharacteristic
263C23×C61C2×#4111yescharacteristic
264C23×C61H(5,𝔽2)11yescharacteristic
265C23×C612−1+411yescharacteristic
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—41no—
270C22×D61—41no—
271D4×C61—42no—
272D4×C61—42no—
273D4×C61—42no—
274D4×C61—42no—
275D4×C61—42no—
276D4×C61—42no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—42no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—42no—
293C2×C4×C61—41no—
294C2×C4×C61—42no—
295C2×C4×C61C2×C22⋊C411yescharacteristic
296C2×C4×C61C2×C22⋊C411yescharacteristic
297C2×C4×C61C2×C22⋊C411yescharacteristic
298C2×C4×C61C2×C22⋊C411yescharacteristic
299C22⋊D61—41no—
300C22⋊D61—41no—
301C22⋊D61—41no—
302C22⋊D61—41no—
303C22⋊D61—82no—
304C22⋊D61—82no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—22no—
311C2×Dic61—42no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—42no—
323C2×Dic61—41no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—41no—
327C2×Dic61—82no—
328C2×Dic61—82no—
329C2×Dic61C2×C22⋊C412yes—
330C2×Dic61C2×C22⋊C412yes—
331C2×Dic61C2×C22⋊C412yes—
332C2×Dic61C2×C22⋊C412yes—
333C4×D61—42no—
334C4×D61—42no—
335#22535—611nomaximal, Sylow
336C22×C61—21no—
337C22×C61—21no—
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—21no—
341C22×C61—21no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—42no—
349C22×C61—82no—
350C22×C61—82no—
351C22×C61C22×C22⋊C411yescharacteristic
352C22×C61C4×#4111yescharacteristic
353C22×C61#52011yescharacteristic
354C22×C61#54811yescharacteristic
355C22×C61#54811yescharacteristic
356C22×C61#55011yescharacteristic
357C22×C61#55011yescharacteristic
358C2×D61—41no—
359C2×D61—41no—
360C2×D61—41no—
361C2×D61—81no—
362C2×D61—81no—
363C4×C61—21no—
364C4×C61—21no—
365C4×C61—21no—
366C4×C61—42no—
367C4×C61—42no—
368C4×C61—81no—
369C4×C61—82no—
370C4×C61#41012yes—
371Dic61—22no—
372Dic61—22no—
373Dic61—22no—
374Dic61—22no—
375Dic61—42no—
376Dic61—41no—
377Dic61—41no—
378Dic61—41no—
379Dic61—82no—
380Dic61—81no—
381C2×#553—611no—
382#2345—611no—
383#2345—611no—
384#1964—612no—
385#1964—612no—
386#1964—611no—
387#1964D6111yescharacteristic, complemented
388#1799—612no—
389#1799—611no—
390C4×#99—612no—
391C4×#99—611no—
392C2×C61—21no—
393C2×C61—21no—
394C2×C61—21no—
395C2×C61—21no—
396C2×C61—21no—
397C2×C61—21no—
398C2×C61—82no—
399C2×C61#234111yescharacteristic
400C2×C61C2×#41011yescharacteristic
401C2×C61#288311yescharacteristic
402D61—81no—
403#553—1221no—
404#553—1221no—
405#553—1222no—
406#553—1222no—
407#553—1221no—
408#553—1221no—
409C2×#126—612no—
410C2×#125—611no—
411C2×#123—612no—
412C2×#121—611no—
413C2×#121—612no—
414C2×#121C2×D6111yescharacteristic
415C2×C4×D4—611no—
416C2×C4×D4—612no—
417C2×C4×D4—611no—
418C2×#117—611no—
419C22×C4⋊C4—611no—
420C2×#99—612no—
421C2×#99—611no—
422C2×#99—611no—
423C2×#99—612no—
424C2×#99—612no—
425C2×#99C2×D6112yes—
426C2×#99C2×D6112yes—
427#389—1221no—
428#389—1221no—
429#387—1222no—
430#387—1222no—
431#380—611no—
432#380—612no—
433#380—612no—
434#380C2×D6111yescharacteristic
435C4×C4⋊C4—1221no—
436C4×C4⋊C4—1221no—
437C4×C22⋊C4—611no—
438C4×C22⋊C4—612no—
439C4×C22⋊C4—612no—
440C4×C22⋊C4C2×D6111yescharacteristic
441#342—612no—
442#342—611no—
443#342—611no—
444C61#2253511yescharacteristic, complemented, Sylow
445C22×D4—611no—
446C22×D4—612no—
447C22×D4C4×D6111yescharacteristic
448C22×D4C22×D6112yes—
449C23×C4—612no—
450C23×C4—612no—
451C23×C4—611no—
452C23×C4C22×D6111yescharacteristic
453#126—1222no—
454#126—1222no—
455#126—1222no—
456#126—1222no—
457#125—1222no—
458#125—1221no—
459#125—1221no—
460#123—1222no—
461#123—1222no—
462#123—1222no—
463#123—1222no—
464#121—21no—
465#121—21no—
466#121—21no—
467#121—21no—
468#121—1222no—
469#121—1221no—
470#121—1221no—
471#121—1222no—
472#121—1222no—
473#121—1222no—
474#121—1222no—
475C4×D4—1222no—
476C4×D4—1221no—
477C4×D4—1221no—
478C4×D4—1222no—
479C4×D4—1222no—
480C4×D4—1222no—
481C4×D4—1222no—
482C4×D4—1221no—
483C4×D4—1221no—
484C4×D4—1221no—
485C4×D4—1221no—
486#117—1222no—
487#117—1221no—
488#117—1221no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—611no—
491C2×C4⋊C4—611no—
492C2×C4⋊C4—612no—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—612no—
496C2×C4⋊C4—612no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—612no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—612no—
502C2×C4⋊C4—1222no—
503C2×C4⋊C4—1222no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4C4×D6111yescharacteristic
506C2×C22⋊C4—611no—
507C2×C22⋊C4—612no—
508C2×C22⋊C4—612no—
509C2×C22⋊C4—611no—
510C2×C22⋊C4—612no—
511C2×C22⋊C4—611no—
512C2×C22⋊C4—612no—
513C2×C22⋊C4—611no—
514C2×C22⋊C4C4×D6112yes—
515C2×C22⋊C4C22×D6112yes—
516C2×C22⋊C4C22×D6111yescharacteristic
517C2×C22⋊C4C22×D6111yescharacteristic
518C2×C42—21no—
519C2×C42—612no—
520C2×C42—611no—
521C2×C42—1222no—
522C2×C42—1222no—
523C2×C42—1221no—
524#99—24no—
525#99—42no—
526#99—1222no—
527#99—1224no—
528#99—1222no—
529#99—2442no—
530#99—2442no—
531#95—21no—
532#95—21no—
533#95—1222no—
534#95—1222no—
535#95—1222no—
536#95—1222no—
537#95—1221no—
538#95—1221no—
539C24—611no—
540C24C2×C4×D6112yes—
541C24C23×D6111yescharacteristic
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—42no—
551C2×D4—1222no—
552C2×D4—1222no—
553C2×D4—1221no—
554C2×D4—1221no—
555C2×D4—1221no—
556C2×D4—1221no—
557C2×D4—1221no—
558C2×D4—1221no—
559C2×D4—4882no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—42no—
564C22×C4—612no—
565C22×C4—612no—
566C22×C4—612no—
567C22×C4—612no—
568C22×C4—612no—
569C22×C4—612no—
570C22×C4—611no—
571C22×C4—611no—
572C22×C4—611no—
573C22×C4—1222no—
574C22×C4—1222no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—1222no—
579C22×C4—1221no—
580C22×C4—4882no—
581C22×C4—4882no—
582C22×C4—2442no—
583C22×C4C2×C4×D6112yes—
584C22×C4C2×C4×D6111yescharacteristic
585C22×C4C2×C4×D6111yescharacteristic
586C22×C4D4×D6111yescharacteristic
587C22×C4D4×D6111yescharacteristic
588C22×C4D4×D6111yescharacteristic
589C22×C4D4×D6111yescharacteristic
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—42no—
593C4⋊C4—612no—
594C4⋊C4—611no—
595C4⋊C4—611no—
596C4⋊C4—612no—
597C4⋊C4—611no—
598C4⋊C4—611no—
599C4⋊C4—612no—
600C4⋊C4—612no—
601C4⋊C4—612no—
602C4⋊C4—612no—
603C4⋊C4—1222no—
604C4⋊C4—1222no—
605C4⋊C4—1222no—
606C4⋊C4—1222no—
607C4⋊C4—1221no—
608C4⋊C4—1221no—
609C4⋊C4—4882no—
610C4⋊C4—4882no—
611C4⋊C4—2442no—
612C22⋊C4—21no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—21no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—22no—
619C22⋊C4—612no—
620C22⋊C4—1222no—
621C22⋊C4—1222no—
622C22⋊C4—1222no—
623C22⋊C4—1222no—
624C22⋊C4—1222no—
625C22⋊C4—1222no—
626C22⋊C4—1221no—
627C22⋊C4—1221no—
628C22⋊C4—1221no—
629C22⋊C4—1221no—
630C22⋊C4—1221no—
631C22⋊C4—1222no—
632C22⋊C4—1221no—
633C22⋊C4—1222no—
634C22⋊C4—1221no—
635C22⋊C4#1175822412yes—
636C42—42no—
637C42—1222no—
638C42—1222no—
639C42—1221no—
640C42—1221no—
641C42—4882no—
642C42—4882no—
643C42—2442no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—41no—
648C23—41no—
649C23—42no—
650C23—42no—
651C23—1221no—
652C23—1221no—
653C23—1221no—
654C23—2441no—
655C23—2441no—
656C23C22×C4×D6111yescharacteristic
657C23C2×D4×D6111yescharacteristic
658C23C2×D4×D6111yescharacteristic
659C23#41×D6111yescharacteristic
660C23C2×#1175822411yescharacteristic
661C23#1451982211yescharacteristic
662C23#1451982411yescharacteristic
663D4—42no—
664D4—42no—
665D4—42no—
666D4—42no—
667D4—42no—
668D4—42no—
669D4—4882no—
670D4—4882no—
671D4—2441no—
672D4—2441no—
673D4—2441no—
674D4—2441no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—612no—
694C2×C4—612no—
695C2×C4—612no—
696C2×C4—612no—
697C2×C4—1221no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—1222no—
703C2×C4—4882no—
704C2×C4—4882no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4—2442no—
708C2×C4—2442no—
709C2×C4—2442no—
710C2×C4—2442no—
711C2×C4—2442no—
712C2×C4—2442no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2442no—
716C2×C4—2442no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2442no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4C22⋊C4×D6111yescharacteristic
724C2×C4C22⋊C4×D6111yescharacteristic
725C2×C4C22⋊C4×D6111yescharacteristic
726C2×C4C22⋊C4×D6111yescharacteristic
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—82no—
741C22—82no—
742C22—4881no—
743C22—4881no—
744C22—2441no—
745C22—2441no—
746C22—2441no—
747C22C2×C22⋊C4×D6111yescharacteristic
748C22C4×#1175822411yescharacteristic
749C22#1684024111yescharacteristic
750C22#1684041811yescharacteristic
751C22#1684042011yescharacteristic
752C22#1684043011yescharacteristic
753C22#1684043211yescharacteristic
754C4—21no—
755C4—21no—
756C4—21no—
757C4—42no—
758C4—42no—
759C4—82no—
760C4—81no—
761C4—1222no—
762C4—1222no—
763C4—1222no—
764C4—1222no—
765C4—4881no—
766C4—4882no—
767C4—2442no—
768C4—2441no—
769C4—2441no—
770C4—2441no—
771C4#1683973412yes—
772C2—21no—
773C2—21no—
774C2—21no—
775C2—21no—
776C2—21no—
777C2—21no—
778C2—82no—
779C2—4881no—
780C2#2144865811yescharacteristic
781C2C2×#1683973411yescharacteristic
782C2#2145427811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1964C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840464C2
cosocleC24×C61C24
hypercenter#1964D61
hypocenterC61#22535
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. #21448698C2semidirect
3. #21448694C2semidirect
4. #21446656C2semidirect
5. #21446653C2semidirect
6. #21446653C2semidirect
7. #21445805C2semidirect
8. #21445804C2semidirect
9. #99×Dic61C2semidirect
10. C4×#14519691C2semidirect
11. C61×#1964C2semidirect
18. C2×#14519770C4semidirect
19. C2×#14519768C4semidirect
20. C2×#14519761C4semidirect
22. C2×#14519748C4semidirect
23. C2×D4×Dic61C4semidirect
26. C2×#14519735C4semidirect
387. #1964D61semidirect
444. C61#22535semidirect

Maximal subgroups

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

subgroupindex
C2×#168404642
#214486982
#214486942
#214466562
#214466532
#214458052
#214458042
#99×Dic612
C4×#145196912
C61×#19642
#2253561