Finite Group Databasebeta

← C2×#21446996 #29707451

Subgroups — C2×#21446996 #29707451

Order 15616.

1434 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
1C2×#16840388C211yesmaximal, characteristic, complemented
2C22×#14519692C211yesmaximal, characteristic
3C22×#14519692C211yesmaximal, characteristic
4#21446996C218yesmaximal, direct product factor
5C2×#16839529C211yesmaximal, characteristic, complemented
6C2×#16839528C211yesmaximal, characteristic, complemented
7C2×#16839528C211yesmaximal, characteristic, complemented
8C22×#99×C61C211yesmaximal, characteristic
9#16840388—22no—
10#16840388—22no—
11#16840388—22no—
12#16840388C2214yescomplemented
13C2×#14519756—22no—
14C2×#14519754—22no—
15C2×#14519754—22no—
16C22×C22⋊Dic61C2211yescharacteristic
17C22×C22⋊Dic61C2211yescharacteristic
18C22×C22⋊Dic61C2211yescharacteristic
19C22×C22⋊Dic61C2211yescharacteristic
20C2×#14519692—22no—
21C2×#14519692—22no—
22C2×#14519692—22no—
23C2×#14519692—22no—
24C2×#14519692C2214yes—
25C2×#14519692C2214yes—
26#16839529C2214yescomplemented
27#16839528C2214yescomplemented
28#16839528C2214yescomplemented
29C23×D4×C61C2211yescharacteristic
30C22×C22⋊C4×C61C2211yescharacteristic
31C22×C22⋊C4×C61C2211yescharacteristic
32C2×#99×C61—22no—
33C2×#99×C61—22no—
34C2×#99×C61C2214yes—
35C22×Dic122—22no—
36C23×Dic61—21no—
37C23×Dic61—21no—
38C23×Dic61—21no—
39C23×Dic61—21no—
40#14519756—28no—
41#14519756—28no—
42#14519754—28no—
43#14519754—28no—
44#14519754—28no—
45#14519754—28no—
46C2×C4⋊Dic61—22no—
47C2×#11758196—24no—
48C2×C22⋊Dic61—21no—
49C2×C22⋊Dic61—21no—
50C2×C22⋊Dic61—21no—
51C2×C22⋊Dic61—21no—
52C2×C22⋊Dic61—21no—
53C2×C22⋊Dic61—21no—
54C2×C22⋊Dic61—21no—
55C2×C22⋊Dic61—21no—
56C2×C22⋊Dic61—21no—
57C2×C22⋊Dic61—21no—
58C2×C22⋊Dic61—21no—
59C2×C22⋊Dic61—21no—
60C2×C22⋊Dic61—21no—
61C2×C22⋊Dic61—21no—
62C2×C22⋊Dic61—21no—
63C2×C22⋊Dic61—21no—
64C2×C22⋊Dic61D412yes—
65C2×C22⋊Dic61D412yes—
66C2×C22⋊Dic61D412yes—
67C2×C22⋊Dic61D412yes—
68C2×C22⋊Dic61C2312yes—
69C2×C22⋊Dic61C2312yes—
70C2×C22⋊Dic61C2312yes—
71C2×C22⋊Dic61C2312yes—
72#14519692—28no—
73#14519692—28no—
74C25×C61Q811yescharacteristic, complemented
75C25×C61C2311yescharacteristic
76C22×D4×C61—21no—
77C22×D4×C61—21no—
78C22×D4×C61—21no—
79C22×D4×C61—21no—
80C22×D4×C61—21no—
81C22×D4×C61—21no—
82C22×D4×C61—21no—
83C22×D4×C61—21no—
84C22×D4×C61—21no—
85C22×D4×C61—21no—
86C22×D4×C61—21no—
87C22×D4×C61—21no—
88C22×D4×C61Q812yescomplemented
89C22×D4×C61C2312yes—
90C23×C4×C61—21no—
91C23×C4×C61—21no—
92C23×C4×C61Q811yescharacteristic, complemented
93C2×C22⋊C4×C61—21no—
94C2×C22⋊C4×C61—21no—
95C2×C22⋊C4×C61—21no—
96C2×C22⋊C4×C61—21no—
97C2×C22⋊C4×C61—21no—
98C2×C22⋊C4×C61—21no—
99C2×C22⋊C4×C61—21no—
100C2×C22⋊C4×C61—21no—
101C2×C22⋊C4×C61D412yes—
102C2×C22⋊C4×C61D412yes—
103C2×C22⋊C4×C61C2312yes—
104C2×C22⋊C4×C61C2312yes—
105#99×C61—28no—
106C24×C61—21no—
107C24×C61—21no—
108C24×C61—21no—
109C24×C61—21no—
110C24×C61—21no—
111C24×C61—21no—
112C24×C61—82no—
113C24×C61—82no—
114C24×C61C2×D411yescharacteristic
115C24×C61C2×D411yescharacteristic
116C24×C61C2×D411yescharacteristic
117C24×C61C2×D411yescharacteristic
118C24×C61C2×D411yescharacteristic
119C24×C61C2×D411yescharacteristic
120C24×C61C2×Q811yescharacteristic
121C24×C61C2×Q811yescharacteristic
122C24×C61C2×Q812yescomplemented
123C24×C61#4111yescharacteristic
124C24×C61#4111yescharacteristic
125C24×C61#4111yescharacteristic
126C24×C61#4111yescharacteristic
127C24×C61#4111yescharacteristic
128C24×C61#4111yescharacteristic
129C24×C61C2411yescharacteristic
130C2×D4×C61—22no—
131C2×D4×C61—22no—
132C2×D4×C61—22no—
133C2×D4×C61—22no—
134C2×D4×C61—22no—
135C2×D4×C61—22no—
136C2×D4×C61—22no—
137C2×D4×C61—22no—
138C2×D4×C61—22no—
139C2×D4×C61—22no—
140C2×D4×C61—22no—
141C2×D4×C61—22no—
142C2×D4×C61—41no—
143C2×D4×C61—41no—
144C2×D4×C61—41no—
145C2×D4×C61—41no—
146C2×D4×C61—41no—
147C2×D4×C61—41no—
148C2×D4×C61—41no—
149C2×D4×C61—41no—
150C2×D4×C61—41no—
151C2×D4×C61—41no—
152C2×D4×C61—41no—
153C2×D4×C61—41no—
154C2×D4×C61—41no—
155C2×D4×C61—41no—
156C2×D4×C61—41no—
157C2×D4×C61—41no—
158C22×C4×C61—22no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—22no—
166C22×C4×C61—22no—
167C22×C4×C61—22no—
168C22×C4×C61—41no—
169C22×C4×C61—41no—
170C22×C4×C61—82no—
171C22×C4×C61—82no—
172C22×C4×C61C2×Q812yescomplemented
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—22no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—41no—
182C22×Dic61—41no—
183C22×Dic61—41no—
184C22×Dic61—41no—
185C22×Dic61—82no—
186C22×Dic61—82no—
187C22×Dic61—82no—
188C22×Dic61—82no—
189C2×Dic122—28no—
190C2×Dic122—84no—
191C22⋊C4×C61—22no—
192C22⋊C4×C61—22no—
193C22⋊C4×C61—22no—
194C22⋊C4×C61—22no—
195C22⋊C4×C61—22no—
196C22⋊C4×C61—41no—
197C22⋊C4×C61—41no—
198C22⋊C4×C61C2×D414yes—
199C22⋊Dic61—22no—
200C22⋊Dic61—22no—
201C22⋊Dic61—22no—
202C22⋊Dic61—22no—
203C22⋊Dic61—22no—
204C22⋊Dic61—22no—
205C22⋊Dic61—22no—
206C22⋊Dic61—22no—
207C22⋊Dic61—22no—
208C22⋊Dic61—22no—
209C22⋊Dic61—41no—
210C22⋊Dic61—41no—
211C22⋊Dic61—41no—
212C22⋊Dic61—41no—
213C22⋊Dic61C2×D414yes—
214C22⋊Dic61C2×D414yes—
215C4⋊Dic61—28no—
216#11758196—216no—
217C23×C61—22no—
218C23×C61—22no—
219C23×C61—22no—
220C23×C61—42no—
221C23×C61—42no—
222C23×C61—42no—
223C23×C61—42no—
224C23×C61—42no—
225C23×C61—42no—
226C23×C61—42no—
227C23×C61—41no—
228C23×C61—41no—
229C23×C61—41no—
230C23×C61—41no—
231C23×C61—82no—
232C23×C61—82no—
233C23×C61—82no—
234C23×C61—81no—
235C23×C61—81no—
236C23×C61—81no—
237C23×C61—81no—
238C23×C61—81no—
239C23×C61—81no—
240C23×C61—81no—
241C23×C61—81no—
242C23×C61—82no—
243C23×C61—82no—
244C23×C61—82no—
245C23×C61—82no—
246C23×C61#12011yescharacteristic
247C23×C61#12011yescharacteristic
248C23×C61#12011yescharacteristic
249C23×C61#12011yescharacteristic
250C23×C61C22⋊Q811yescharacteristic
251C23×C61C22⋊Q811yescharacteristic
252C23×C61C22⋊Q811yescharacteristic
253C23×C61C22⋊Q811yescharacteristic
254C23×C61C22⋊Q811yescharacteristic
255C23×C61C22⋊Q811yescharacteristic
256C23×C61C22⋊Q811yescharacteristic
257C23×C61C22⋊Q811yescharacteristic
258C23×C61C22⋊Q811yescharacteristic
259C23×C61C22⋊Q811yescharacteristic
260C23×C61C22⋊Q811yescharacteristic
261C23×C61C22⋊Q811yescharacteristic
262C23×C61#12411yescharacteristic
263C23×C61#12411yescharacteristic
264C23×C61#12411yescharacteristic
265C23×C61#12411yescharacteristic
266C23×C61#12411yescharacteristic
267C23×C61#12411yescharacteristic
268C23×C61#12411yescharacteristic
269C23×C61#12411yescharacteristic
270C23×C61#12411yescharacteristic
271C23×C61#12411yescharacteristic
272C23×C61#12411yescharacteristic
273C23×C61#12411yescharacteristic
274C23×C61C22×D411yescharacteristic
275C23×C61C22×D411yescharacteristic
276C23×C61C22×D411yescharacteristic
277C23×C61C22×Q811yescharacteristic
278C23×C61C2×#4111yescharacteristic
279C23×C61C2×#4111yescharacteristic
280C23×C61C2×#4111yescharacteristic
281D4×C61—42no—
282D4×C61—42no—
283D4×C61—42no—
284D4×C61—42no—
285D4×C61—42no—
286D4×C61—42no—
287D4×C61—42no—
288D4×C61—42no—
289C2×C4×C61—24no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—44no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—42no—
299C2×C4×C61—82no—
300C2×C4×C61—82no—
301C2×C4×C61—82no—
302C2×C4×C61—82no—
303C2×C4×C61—82no—
304C2×Dic61—24no—
305C2×Dic61—24no—
306C2×Dic61—44no—
307C2×Dic61—44no—
308C2×Dic61—42no—
309C2×Dic61—42no—
310C2×Dic61—82no—
311C2×Dic61—82no—
312C2×Dic61—82no—
313C2×Dic61—82no—
314C2×Dic61—82no—
315C2×Dic61—82no—
316C2×Dic61—82no—
317C2×Dic61—82no—
318C2×Dic61—82no—
319C2×Dic61—82no—
320Dic122—88no—
321C2×#2032—611nomaximal, Sylow
322C22×C61—22no—
323C22×C61—22no—
324C22×C61—22no—
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—22no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—42no—
358C22×C61—82no—
359C22×C61—82no—
360C22×C61—82no—
361C22×C61—82no—
362C22×C61—82no—
363C22×C61—82no—
364C22×C61—82no—
365C22×C61#39311yescharacteristic
366C22×C61#39311yescharacteristic
367C22×C61#39311yescharacteristic
368C22×C61#39311yescharacteristic
369C22×C61#39311yescharacteristic
370C22×C61#39311yescharacteristic
371C22×C61#39311yescharacteristic
372C22×C61#39311yescharacteristic
373C22×C61C2×#12011yescharacteristic
374C22×C61C2×C22⋊Q811yescharacteristic
375C22×C61C2×C22⋊Q811yescharacteristic
376C22×C61C2×C22⋊Q811yescharacteristic
377C22×C61C2×#12411yescharacteristic
378C22×C61C2×#12411yescharacteristic
379C22×C61C2×#12411yescharacteristic
380C4×C61—44no—
381C4×C61—42no—
382C4×C61—82no—
383Dic61—44no—
384Dic61—44no—
385Dic61—82no—
386Dic61—82no—
387C2×#543—611no—
388C22×#99—611no—
389C22×#99—611no—
390C22×#99D6111yescharacteristic
391#2032—618no—
392C2×#342—611no—
393C2×#342—611no—
394C2×#342—611no—
395C2×C61—21no—
396C2×C61—21no—
397C2×C61—21no—
398C2×C61—21no—
399C2×C61—21no—
400C2×C61—21no—
401C2×C61—21no—
402C2×C61—21no—
403C2×C61—21no—
404C2×C61—21no—
405C2×C61—21no—
406C2×C61—21no—
407C2×C61—21no—
408C2×C61—21no—
409C2×C61—82no—
410C2×C61#203212yescomplemented
411C2×C61C2×#39311yescharacteristic
412C23×D4C2×D6111yescharacteristic
413#543—614no—
414#543—1222no—
415#543—1222no—
416#543—1222no—
417C2×C22⋊Q8—1222no—
418C2×C22⋊Q8—1222no—
419C2×C22⋊Q8—1222no—
420C22×C22⋊C4—611no—
421C22×C22⋊C4—611no—
422C22×C22⋊C4—611no—
423C22×C22⋊C4—611no—
424C22×C22⋊C4C2×D6111yescharacteristic
425C22×C22⋊C4C2×D6111yescharacteristic
426C2×#99—22no—
427C2×#99—22no—
428C2×#99—614no—
429C2×#99—614no—
430C2×#99—1222no—
431C2×#99—1222no—
432C2×#99—1222no—
433C2×#99—1222no—
434C2×#99C2×D6114yes—
435#342—614no—
436#342—614no—
437#342—614no—
438C61C2×#203211yescharacteristic, complemented, Sylow
439C25Dic12211yescharacteristic, complemented
440C25C22×D6111yescharacteristic
441C22×Q8—1222no—
442C22×D4—21no—
443C22×D4—21no—
444C22×D4—21no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—21no—
452C22×D4—21no—
453C22×D4—21no—
454C22×D4Dic12212yescomplemented
455C22×D4C22×D6112yes—
456C23×C4—21no—
457C23×C4—21no—
458C23×C4—1221no—
459C23×C4—1221no—
460C23×C4—1221no—
461C23×C4—1221no—
462C23×C4Dic12211yescharacteristic, complemented
463C22⋊Q8—1228no—
464C22⋊Q8—1228no—
465C22⋊Q8—1228no—
466C22⋊Q8—1228no—
467C22⋊Q8—1228no—
468C22⋊Q8—1228no—
469C2×C4⋊C4—1224no—
470C2×C4⋊C4—1222no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—612no—
480C2×C22⋊C4—612no—
481C2×C22⋊C4—612no—
482C2×C22⋊C4—612no—
483C2×C22⋊C4—612no—
484C2×C22⋊C4—612no—
485C2×C22⋊C4—612no—
486C2×C22⋊C4—612no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1221no—
490C2×C22⋊C4—1221no—
491C2×C22⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4C22⋊D6112yes—
504C2×C22⋊C4C22⋊D6112yes—
505C2×C22⋊C4C22×D6112yes—
506C2×C22⋊C4C22×D6112yes—
507#99—28no—
508#99—1228no—
509#99—1228no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—82no—
517C24—82no—
518C24C2×Dic12211yescharacteristic
519C24C2×Dic12211yescharacteristic
520C24C2×Dic12212yescomplemented
521C24#1175822211yescharacteristic
522C24#1175822211yescharacteristic
523C24D4×D6111yescharacteristic
524C24D4×D6111yescharacteristic
525C24D4×D6111yescharacteristic
526C24D4×D6111yescharacteristic
527C24#1175822411yescharacteristic
528C24#1175822411yescharacteristic
529C24#1175822411yescharacteristic
530C24#1175822411yescharacteristic
531C24C2×C22⋊D6111yescharacteristic
532C24C2×C22⋊D6111yescharacteristic
533C24C23×D6111yescharacteristic
534C2×Q8—1228no—
535C2×Q8—4884no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—41no—
549C2×D4—41no—
550C2×D4—41no—
551C2×D4—41no—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—41no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—82no—
577C22×C4—82no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—4882no—
587C22×C4—4882no—
588C22×C4—4882no—
589C22×C4—4882no—
590C22×C4—2441no—
591C22×C4—2441no—
592C22×C4—2441no—
593C22×C4—2441no—
594C22×C4C2×Dic12212yescomplemented
595C4⋊C4—12216no—
596C4⋊C4—1228no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—41no—
603C22⋊C4—41no—
604C22⋊C4—614no—
605C22⋊C4—614no—
606C22⋊C4—1222no—
607C22⋊C4—1222no—
608C22⋊C4—1222no—
609C22⋊C4—1222no—
610C22⋊C4—1222no—
611C22⋊C4—1222no—
612C22⋊C4—1222no—
613C22⋊C4—1222no—
614C22⋊C4—1222no—
615C22⋊C4—1222no—
616C22⋊C4—2441no—
617C22⋊C4—2441no—
618C22⋊C4—2441no—
619C22⋊C4—2441no—
620C22⋊C4C2×C22⋊D6114yes—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—82no—
636C23—82no—
637C23—82no—
638C23—81no—
639C23—81no—
640C23—81no—
641C23—81no—
642C23—81no—
643C23—81no—
644C23—81no—
645C23—81no—
646C23—82no—
647C23—82no—
648C23—82no—
649C23—82no—
650C23#1451974511yescharacteristic
651C23#1451974511yescharacteristic
652C23#1451974511yescharacteristic
653C23#1451974511yescharacteristic
654C23#1451975411yescharacteristic
655C23#1451975411yescharacteristic
656C23#1451975411yescharacteristic
657C23#1451975411yescharacteristic
658C23#1451975411yescharacteristic
659C23#1451975411yescharacteristic
660C23#1451975411yescharacteristic
661C23#1451975411yescharacteristic
662C23#1451975611yescharacteristic
663C23#1451975611yescharacteristic
664C23#1451975611yescharacteristic
665C23#1451975611yescharacteristic
666C23#1451976311yescharacteristic
667C23#1451976311yescharacteristic
668C23#1451976311yescharacteristic
669C23#1451976311yescharacteristic
670C23#1451976311yescharacteristic
671C23#1451976311yescharacteristic
672C23#1451976311yescharacteristic
673C23#1451976311yescharacteristic
674C23#1451976411yescharacteristic
675C23#1451976411yescharacteristic
676C23#1451976411yescharacteristic
677C23#1451976411yescharacteristic
678C23C2×D4×D6111yescharacteristic
679C23C2×D4×D6111yescharacteristic
680C23C22×C22⋊D6111yescharacteristic
681C23C22×Dic12211yescharacteristic
682C23C2×#1175822411yescharacteristic
683C23C2×#1175822411yescharacteristic
684C23C2×#1175822211yescharacteristic
685Q8—4888no—
686D4—42no—
687D4—42no—
688D4—42no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—42no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—44no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4—82no—
707C2×C4—82no—
708C2×C4—82no—
709C2×C4—1224no—
710C2×C4—1224no—
711C2×C4—4882no—
712C2×C4—4882no—
713C2×C4—4882no—
714C2×C4—4882no—
715C2×C4—4882no—
716C2×C4—4882no—
717C2×C4—4882no—
718C2×C4—4882no—
719C2×C4—4882no—
720C2×C4—4882no—
721C2×C4—2442no—
722C2×C4—2442no—
723C2×C4—2444no—
724C2×C4—2444no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—42no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22#1683967411yescharacteristic
769C22#1683967411yescharacteristic
770C22#1683967411yescharacteristic
771C22#1683967411yescharacteristic
772C22#1683967411yescharacteristic
773C22#1683967411yescharacteristic
774C22#1683967411yescharacteristic
775C22#1683967411yescharacteristic
776C22C2×#1451974511yescharacteristic
777C22C2×#1451975411yescharacteristic
778C22C2×#1451975411yescharacteristic
779C22C2×#1451975611yescharacteristic
780C22C2×#1451976311yescharacteristic
781C22C2×#1451976311yescharacteristic
782C22C2×#1451976411yescharacteristic
783C4—44no—
784C4—42no—
785C4—82no—
786C4—4882no—
787C4—4882no—
788C4—2444no—
789C4—2444no—
790C2—21no—
791C2—21no—
792C2—21no—
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—82no—
805C2#2144699612yesdirect product factor
806C2C2×#1683967411yescharacteristic
subgroupG/H
centerC22#16839674
commutator, cosocleC24×C61C24
FrattiniC24C23×D61
FittingC22×#99×C61C2
socleC22×C61#393
prime radicalC23×D4×C61C22
hypercenterC22×#99D61
hypocenterC61C2×#2032
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C25 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
1. C2×#16840388C2semidirect
4. #21446996C2direct (N × H)
5. C2×#16839529C2semidirect
6. C2×#16839528C2semidirect
7. C2×#16839528C2semidirect
12. #16840388C22semidirect
26. #16839529C22semidirect
27. #16839528C22semidirect
28. #16839528C22semidirect
74. C25×C61Q8semidirect
88. C22×D4×C61Q8semidirect
92. C23×C4×C61Q8semidirect
122. C24×C61C2×Q8semidirect
172. C22×C4×C61C2×Q8semidirect
410. C2×C61#2032semidirect
438. C61C2×#2032semidirect
439. C25Dic122semidirect
454. C22×D4Dic122semidirect
462. C23×C4Dic122semidirect
520. C24C2×Dic122semidirect
594. C22×C4C2×Dic122semidirect
805. C2#21446996direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403882
C22×#145196922
#214469962
C2×#168395292
C2×#168395282
C22×#99×C612
C2×#203261