Finite Group Databasebeta

← C2×#21446947 #29707248

Subgroups — C2×#21446947 #29707248

Order 15616.

2394 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840321C211yesmaximal, characteristic
2C22×#14519760C211yesmaximal, characteristic, complemented
3C22×#14519692C211yesmaximal, characteristic, complemented
4C22×#14519691C211yesmaximal, characteristic, complemented
5C2×#16839625C211yesmaximal, characteristic, complemented
6#21446947C218yesmaximal, direct product factor
7C2×#16839528C211yesmaximal, characteristic, complemented
8C22×#123×C61C211yesmaximal, characteristic, complemented
9C23×C22⋊D61C2211yescharacteristic
10#16840321—22no—
11#16840321—22no—
12#16840321—22no—
13#16840321C2214yes—
14C2×#14519760—24no—
15C2×#14519760—21no—
16C2×#14519760—24no—
17C2×#14519760—22no—
18C2×#14519760C2214yescomplemented
19C2×#14519758—21no—
20C2×#14519749—22no—
21C2×#14519746—21no—
22C2×#14519745—21no—
23C22×#11758196—21no—
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×#11758198—21no—
28C2×#14519692—24no—
29C2×#14519692C2214yescomplemented
30C2×#14519691—24no—
31C2×#14519691C2214yescomplemented
32#16839625—22no—
33#16839625C2214yescomplemented
34C2×#14519684—22no—
35#16839528C2214yescomplemented
36C23×D4×C61C2211yescharacteristic
37C24×C4×C61C2211yescharacteristic
38C2×#123×C61—22no—
39C2×#123×C61—24no—
40C2×#123×C61—24no—
41C2×#123×C61C2214yescomplemented
42C22×C4⋊C4×C61—21no—
43C22×C22⋊C4×C61—21no—
44C22×C22⋊C4×C61C2211yescharacteristic
45C24×D61D411yescharacteristic
46C22×C22⋊D61—22no—
47C22×C22⋊D61—21no—
48C22×C22⋊D61—21no—
49C22×C22⋊D61—22no—
50C22×C22⋊D61—22no—
51C22×C22⋊D61—21no—
52C22×C22⋊D61—21no—
53C22×C22⋊D61—22no—
54C22×C22⋊D61—22no—
55C22×C22⋊D61D412yes—
56C22×C22⋊D61C2312yes—
57C23×Dic61—21no—
58C23×Dic61—21no—
59C23×Dic61D411yescharacteristic
60C23×Dic61D412yes—
61#14519760—216no—
62#14519760—24no—
63#14519760—24no—
64#14519760—28no—
65#14519760—28no—
66#14519758—24no—
67#14519758—24no—
68#14519749—28no—
69#14519749—28no—
70#14519746—24no—
71#14519746—24no—
72#14519745—24no—
73#14519745—24no—
74C2×#11758196—28no—
75C2×#11758196—22no—
76C2×#11758196—24no—
77C2×C22⋊Dic61—22no—
78C2×C22⋊Dic61—21no—
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61—22no—
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—22no—
85C2×C22⋊Dic61—22no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61D412yes—
88C2×C22⋊Dic61D414yescomplemented
89C2×C22⋊Dic61C2312yes—
90C2×C22⋊Dic61C2312yes—
91C2×C22⋊Dic61C2312yes—
92C2×#11758198—28no—
93C2×#11758198—22no—
94C2×#11758198—24no—
95#14519692—28no—
96#14519691—28no—
97#14519684—28no—
98C25×C61D411yescharacteristic
99C25×C61C2311yescharacteristic
100C22×D4×C61—22no—
101C22×D4×C61—21no—
102C22×D4×C61—21no—
103C22×D4×C61—21no—
104C22×D4×C61—21no—
105C22×D4×C61—22no—
106C22×D4×C61—22no—
107C22×D4×C61—22no—
108C22×D4×C61D412yes—
109C22×D4×C61C2312yes—
110C23×C4×C61—21no—
111C23×C4×C61—22no—
112C23×C4×C61—21no—
113C23×C4×C61—21no—
114C23×C4×C61—21no—
115C23×C4×C61—21no—
116C23×C4×C61—22no—
117C23×C4×C61—21no—
118C23×C4×C61—21no—
119C23×C4×C61—22no—
120C23×C4×C61D411yescharacteristic
121C23×C4×C61D414yescomplemented
122C23×C4×C61C2312yes—
123#123×C61—216no—
124#123×C61—28no—
125#123×C61—28no—
126C2×C4⋊C4×C61—28no—
127C2×C4⋊C4×C61—24no—
128C2×C22⋊C4×C61—28no—
129C2×C22⋊C4×C61—24no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—22no—
132C2×C22⋊C4×C61D414yescomplemented
133C2×C22⋊C4×C61C2312yes—
134C24×C61—21no—
135C24×C61—22no—
136C24×C61—21no—
137C24×C61—22no—
138C24×C61—44no—
139C24×C61—44no—
140C24×C61C2×D411yescharacteristic
141C24×C61C2×D411yescharacteristic
142C24×C61C2×D411yescharacteristic
143C24×C61C2×D412yes—
144C24×C61C2×D411yescharacteristic
145C24×C61C2×D411yescharacteristic
146C24×C61C2×D412yes—
147C24×C61C2×D411yescharacteristic
148C24×C61C2×D412yes—
149C24×C61C2×D412yes—
150C24×C61#4112yes—
151C24×C61C2411yescharacteristic
152C23×D61—21no—
153C23×D61—22no—
154C23×D61—21no—
155C23×D61—22no—
156C23×D61—44no—
157C23×D61C2×D412yes—
158C2×D4×C61—24no—
159C2×D4×C61—22no—
160C2×D4×C61—22no—
161C2×D4×C61—24no—
162C2×D4×C61—22no—
163C2×D4×C61—22no—
164C2×D4×C61—22no—
165C2×D4×C61—22no—
166C2×D4×C61—22no—
167C2×D4×C61—22no—
168C2×D4×C61—42no—
169C2×D4×C61—42no—
170C2×D4×C61—42no—
171C2×D4×C61—42no—
172C2×D4×C61—42no—
173C2×D4×C61—42no—
174C2×D4×C61—42no—
175C2×D4×C61—42no—
176C22×C4×C61—24no—
177C22×C4×C61—24no—
178C22×C4×C61—22no—
179C22×C4×C61—24no—
180C22×C4×C61—24no—
181C22×C4×C61—24no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—24no—
185C22×C4×C61—24no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61—22no—
193C22×C4×C61—22no—
194C22×C4×C61—44no—
195C22×C4×C61—41no—
196C22×C4×C61—41no—
197C22×C4×C61—41no—
198C22×C4×C61—41no—
199C22×C4×C61—42no—
200C22×C4×C61—42no—
201C22×C4×C61—42no—
202C22×C4×C61—42no—
203C22×C4×C61—42no—
204C22×C4×C61—42no—
205C22×C4×C61C2×D412yes—
206C22×C4×C61C2×D414yescomplemented
207C2×C22⋊D61—22no—
208C2×C22⋊D61—22no—
209C2×C22⋊D61—24no—
210C2×C22⋊D61—24no—
211C2×C22⋊D61—22no—
212C2×C22⋊D61—22no—
213C2×C22⋊D61—22no—
214C2×C22⋊D61—22no—
215C2×C22⋊D61—22no—
216C2×C22⋊D61—22no—
217C2×C22⋊D61—28no—
218C2×C22⋊D61—42no—
219C2×C22⋊D61—42no—
220C2×C22⋊D61—42no—
221C2×C22⋊D61—42no—
222C2×C22⋊D61—42no—
223C2×C22⋊D61—42no—
224C2×C22⋊D61—42no—
225C2×C22⋊D61—42no—
226C2×C22⋊D61—84no—
227C22×Dic61—24no—
228C22×Dic61—21no—
229C22×Dic61—22no—
230C22×Dic61—21no—
231C22×Dic61—22no—
232C22×Dic61—22no—
233C22×Dic61—22no—
234C22×Dic61—22no—
235C22×Dic61—22no—
236C22×Dic61—44no—
237C22×Dic61—44no—
238C22×Dic61—44no—
239C22×Dic61—42no—
240C22×Dic61C2×D412yes—
241C22×Dic61C2×D414yes—
242C4⋊C4×C61—216no—
243C22⋊C4×C61—216no—
244C22⋊C4×C61—24no—
245C22⋊C4×C61—22no—
246C22⋊C4×C61C2×D414yescomplemented
247C22⋊Dic61—28no—
248C22⋊Dic61—22no—
249C22⋊Dic61—22no—
250C22⋊Dic61—24no—
251C22⋊Dic61—22no—
252C22⋊Dic61—22no—
253C22⋊Dic61—22no—
254C22⋊Dic61—22no—
255C22⋊Dic61—22no—
256C22⋊Dic61—42no—
257C22⋊Dic61C2×D414yescomplemented
258#11758198—216no—
259#11758198—28no—
260#11758196—216no—
261#11758196—28no—
262C23×C61—24no—
263C23×C61—24no—
264C23×C61—24no—
265C23×C61—22no—
266C23×C61—22no—
267C23×C61—22no—
268C23×C61—42no—
269C23×C61—42no—
270C23×C61—42no—
271C23×C61—44no—
272C23×C61—44no—
273C23×C61—44no—
274C23×C61—44no—
275C23×C61—42no—
276C23×C61—44no—
277C23×C61—48no—
278C23×C61—42no—
279C23×C61—42no—
280C23×C61—44no—
281C23×C61—82no—
282C23×C61—84no—
283C23×C61#12011yescharacteristic
284C23×C61#12011yescharacteristic
285C23×C61#12012yes—
286C23×C61#12011yescharacteristic
287C23×C61#12012yes—
288C23×C61#12012yes—
289C23×C61#12012yes—
290C23×C61#12011yescharacteristic
291C23×C61#12112yes—
292C23×C61#12112yes—
293C23×C61#12112yes—
294C23×C61#12112yes—
295C23×C61#12112yes—
296C23×C61#12112yes—
297C23×C61#12712yes—
298C23×C61#12712yes—
299C23×C61C22×D411yescharacteristic
300C23×C61C22×D411yescharacteristic
301C23×C61C22×D411yescharacteristic
302C23×C61C22×D411yescharacteristic
303C23×C61C22×D411yescharacteristic
304C23×C61C22×D411yescharacteristic
305C23×C61C2×#4111yescharacteristic
306C22×D61—22no—
307C22×D61—22no—
308C22×D61—22no—
309C22×D61—44no—
310C22×D61—48no—
311C22×D61—42no—
312C22×D61—42no—
313C22×D61—44no—
314C22×D61—82no—
315C22×D61—84no—
316D4×C61—42no—
317D4×C61—42no—
318D4×C61—42no—
319D4×C61—42no—
320D4×C61—44no—
321D4×C61—44no—
322C2×C4×C61—24no—
323C2×C4×C61—22no—
324C2×C4×C61—24no—
325C2×C4×C61—24no—
326C2×C4×C61—22no—
327C2×C4×C61—24no—
328C2×C4×C61—22no—
329C2×C4×C61—44no—
330C2×C4×C61—48no—
331C2×C4×C61—42no—
332C2×C4×C61—42no—
333C2×C4×C61—42no—
334C2×C4×C61—42no—
335C2×C4×C61—44no—
336C2×C4×C61—44no—
337C2×C4×C61—44no—
338C2×C4×C61—44no—
339C2×C4×C61—42no—
340C2×C4×C61—42no—
341C22⋊D61—42no—
342C22⋊D61—42no—
343C22⋊D61—42no—
344C22⋊D61—42no—
345C22⋊D61—44no—
346C22⋊D61—44no—
347C22⋊D61—88no—
348C2×Dic61—22no—
349C2×Dic61—24no—
350C2×Dic61—22no—
351C2×Dic61—24no—
352C2×Dic61—22no—
353C2×Dic61—44no—
354C2×Dic61—48no—
355C2×Dic61—42no—
356C2×Dic61—42no—
357C2×Dic61—44no—
358C2×Dic61—44no—
359C2×Dic61—44no—
360C2×Dic61—42no—
361C2×Dic61—82no—
362C2×Dic61—84no—
363C2×#2022—611nomaximal, Sylow
364C22×C61—22no—
365C22×C61—22no—
366C22×C61—22no—
367C22×C61—22no—
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—24no—
371C22×C61—24no—
372C22×C61—24no—
373C22×C61—24no—
374C22×C61—24no—
375C22×C61—24no—
376C22×C61—42no—
377C22×C61—42no—
378C22×C61—42no—
379C22×C61—42no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61—41no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61—41no—
386C22×C61—44no—
387C22×C61—42no—
388C22×C61—44no—
389C22×C61—82no—
390C22×C61—84no—
391C22×C61—84no—
392C22×C61#39212yes—
393C22×C61#39212yes—
394C22×C61#39212yes—
395C22×C61#39212yes—
396C22×C61#45814yes—
397C22×C61C2×#12011yescharacteristic
398C22×C61C2×#12011yescharacteristic
399C22×C61C2×#12011yescharacteristic
400C22×C61C2×#12111yescharacteristic
401C22×C61C2×#12111yescharacteristic
402C22×C61C2×#12111yescharacteristic
403C22×C61C2×#12711yescharacteristic
404C2×D61—44no—
405C2×D61—42no—
406C2×D61—44no—
407C2×D61—84no—
408C2×D61—84no—
409C2×D61—82no—
410C4×C61—44no—
411C4×C61—44no—
412C4×C61—42no—
413Dic61—44no—
414Dic61—42no—
415Dic61—44no—
416Dic61—82no—
417C2×#534—611no—
418C22×#123—611no—
419C22×#123D6111yescharacteristic, complemented
420C22×#99—611no—
421C22×#99—611no—
422C2×#381—611no—
423#2022—618no—
424C2×#342—611no—
425C2×C61—21no—
426C2×C61—21no—
427C2×C61—21no—
428C2×C61—21no—
429C2×C61—22no—
430C2×C61—21no—
431C2×C61—22no—
432C2×C61—21no—
433C2×C61—22no—
434C2×C61—82no—
435C2×C61#202214yescomplemented
436C2×C61C2×#39211yescharacteristic
437C2×C61C2×#45812yes—
438D61—82no—
439C23×D4—611no—
440C23×D4C2×D6111yescharacteristic
441C24×C4C2×D6111yescharacteristic
442#534—614no—
443#534—1222no—
444#534—1222no—
445#534—1222no—
446C2×#123—22no—
447C2×#123—24no—
448C2×#123—24no—
449C2×#123—614no—
450C2×#123—1224no—
451C2×#123—1222no—
452C2×#123—1221no—
453C2×#123—1221no—
454C2×#123—1224no—
455C2×#123C2×D6114yescomplemented
456C2×#121—1222no—
457C2×#120—1221no—
458C2×#120—1221no—
459C22×C4⋊C4—21no—
460C22×C4⋊C4—1221no—
461C22×C22⋊C4—21no—
462C22×C22⋊C4—611no—
463C22×C22⋊C4—611no—
464C22×C22⋊C4—611no—
465C22×C22⋊C4—1221no—
466C22×C22⋊C4C2×D6111yescharacteristic
467C2×#99—614no—
468C2×#99—614no—
469C2×#99—1224no—
470C2×#99—1224no—
471#381—614no—
472#381—1222no—
473C2×#95—1222no—
474#342—614no—
475C61C2×#202211yescharacteristic, complemented, Sylow
476C25—611no—
477C25C22⋊D6111yescharacteristic
478C25C22×D6111yescharacteristic
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—21no—
482C22×D4—21no—
483C22×D4—22no—
484C22×D4—22no—
485C22×D4—22no—
486C22×D4—22no—
487C22×D4—612no—
488C22×D4—612no—
489C22×D4—1222no—
490C22×D4—1221no—
491C22×D4—1222no—
492C22×D4—1221no—
493C22×D4—1222no—
494C22×D4—1221no—
495C22×D4—1222no—
496C22×D4—1221no—
497C22×D4—1222no—
498C22×D4C22⋊D6112yes—
499C22×D4C22×D6112yes—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—22no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—22no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—22no—
510C23×C4—611no—
511C23×C4—612no—
512C23×C4—1221no—
513C23×C4—1221no—
514C23×C4C22⋊D6111yescharacteristic
515C23×C4C22⋊D6114yescomplemented
516C23×C4C22×D6112yes—
517#123—216no—
518#123—28no—
519#123—28no—
520#123—1228no—
521#123—12216no—
522#123—1224no—
523#123—1224no—
524#123—1224no—
525#123—1224no—
526#123—1228no—
527#121—1228no—
528#121—1228no—
529#120—1224no—
530#120—1224no—
531#120—1224no—
532#120—1224no—
533C2×C4⋊C4—28no—
534C2×C4⋊C4—24no—
535C2×C4⋊C4—1224no—
536C2×C4⋊C4—1228no—
537C2×C4⋊C4—1222no—
538C2×C22⋊C4—28no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—614no—
543C2×C22⋊C4—612no—
544C2×C22⋊C4—612no—
545C2×C22⋊C4—612no—
546C2×C22⋊C4—612no—
547C2×C22⋊C4—1224no—
548C2×C22⋊C4—1228no—
549C2×C22⋊C4—1222no—
550C2×C22⋊C4—1222no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1222no—
556C2×C22⋊C4—1221no—
557C2×C22⋊C4—1222no—
558C2×C22⋊C4—1222no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4C22⋊D6114yescomplemented
561C2×C22⋊C4C22×D6112yes—
562#99—1228no—
563#99—1228no—
564#95—1228no—
565C24—21no—
566C24—22no—
567C24—21no—
568C24—22no—
569C24—44no—
570C24—44no—
571C24—612no—
572C24—1221no—
573C24—1222no—
574C24—1222no—
575C24—1221no—
576C24—2444no—
577C24D4×D6111yescharacteristic
578C24D4×D6111yescharacteristic
579C24D4×D6111yescharacteristic
580C24D4×D6111yescharacteristic
581C24D4×D6112yes—
582C24#1175822412yes—
583C24C2×C22⋊D6111yescharacteristic
584C24C2×C22⋊D6112yes—
585C24C2×C22⋊D6111yescharacteristic
586C24C2×C22⋊D6112yes—
587C24C2×C22⋊D6112yes—
588C24C23×D6111yescharacteristic
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—24no—
598C2×D4—24no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—1228no—
608C2×D4—1222no—
609C2×D4—1222no—
610C2×D4—1222no—
611C2×D4—1222no—
612C2×D4—1222no—
613C2×D4—1222no—
614C2×D4—1222no—
615C2×D4—1222no—
616C2×D4—1224no—
617C2×D4—1224no—
618C2×D4—4884no—
619C2×D4—2442no—
620C2×D4—2442no—
621C2×D4—2442no—
622C2×D4—2442no—
623C2×D4—2442no—
624C2×D4—2442no—
625C2×D4—2442no—
626C2×D4—2442no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—24no—
635C22×C4—24no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—24no—
639C22×C4—24no—
640C22×C4—22no—
641C22×C4—24no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—22no—
645C22×C4—44no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—612no—
657C22×C4—614no—
658C22×C4—1222no—
659C22×C4—1222no—
660C22×C4—1224no—
661C22×C4—1222no—
662C22×C4—1221no—
663C22×C4—1222no—
664C22×C4—1221no—
665C22×C4—1222no—
666C22×C4—1222no—
667C22×C4—2444no—
668C22×C4—2442no—
669C22×C4—2444no—
670C22×C4—2444no—
671C22×C4C2×C22⋊D6112yes—
672C22×C4C2×C22⋊D6114yescomplemented
673C4⋊C4—216no—
674C4⋊C4—12216no—
675C4⋊C4—1228no—
676C22⋊C4—216no—
677C22⋊C4—22no—
678C22⋊C4—24no—
679C22⋊C4—614no—
680C22⋊C4—12216no—
681C22⋊C4—1228no—
682C22⋊C4—1228no—
683C22⋊C4—1222no—
684C22⋊C4—1222no—
685C22⋊C4—1222no—
686C22⋊C4—1222no—
687C22⋊C4—1222no—
688C22⋊C4—1224no—
689C22⋊C4—1222no—
690C22⋊C4—1222no—
691C22⋊C4—2442no—
692C22⋊C4C2×C22⋊D6114yescomplemented
693C23—24no—
694C23—24no—
695C23—24no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—44no—
700C23—42no—
701C23—42no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—42no—
706C23—42no—
707C23—44no—
708C23—48no—
709C23—44no—
710C23—42no—
711C23—42no—
712C23—82no—
713C23—84no—
714C23—1222no—
715C23—1222no—
716C23—1222no—
717C23—4884no—
718C23—4882no—
719C23—2448no—
720C23—2444no—
721C23—2444no—
722C23—2442no—
723C23—2442no—
724C23#1451974511yescharacteristic
725C23#1451974511yescharacteristic
726C23#1451974512yes—
727C23#1451974511yescharacteristic
728C23#1451974512yes—
729C23#1451974511yescharacteristic
730C23#1451974612yes—
731C23#1451974612yes—
732C23#1451974812yes—
733C23#1451974812yes—
734C23#1451974912yes—
735C23#1451974912yes—
736C23#1451974912yes—
737C23#1451974912yes—
738C23#1451977312yes—
739C23#1451977312yes—
740C23C2×D4×D6111yescharacteristic
741C23C2×D4×D6111yescharacteristic
742C23C2×D4×D6111yescharacteristic
743C23C22×C22⋊D6111yescharacteristic
744C23C22×C22⋊D6111yescharacteristic
745C23C22×C22⋊D6111yescharacteristic
746C23C2×#1175822411yescharacteristic
747D4—42no—
748D4—42no—
749D4—42no—
750D4—42no—
751D4—44no—
752D4—44no—
753D4—4888no—
754D4—2442no—
755D4—2442no—
756D4—2442no—
757D4—2442no—
758D4—2444no—
759D4—2444no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—22no—
767C2×C4—48no—
768C2×C4—44no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—1224no—
780C2×C4—1224no—
781C2×C4—1222no—
782C2×C4—1222no—
783C2×C4—1222no—
784C2×C4—4884no—
785C2×C4—4882no—
786C2×C4—2444no—
787C2×C4—2442no—
788C2×C4—2448no—
789C2×C4—2444no—
790C2×C4—2444no—
791C2×C4—2442no—
792C2×C4—2442no—
793C2×C4—2444no—
794C22—24no—
795C22—24no—
796C22—24no—
797C22—24no—
798C22—24no—
799C22—24no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—44no—
817C22—42no—
818C22—44no—
819C22—82no—
820C22—84no—
821C22—84no—
822C22—4882no—
823C22—4884no—
824C22—4884no—
825C22—2444no—
826C22—2442no—
827C22—2444no—
828C22#1683967012yes—
829C22#1683967012yes—
830C22#1683967012yes—
831C22#1683967012yes—
832C22#1683995114yes—
833C22C2×#1451974511yescharacteristic
834C22C2×#1451974511yescharacteristic
835C22C2×#1451974611yescharacteristic
836C22C2×#1451974811yescharacteristic
837C22C2×#1451974911yescharacteristic
838C22C2×#1451974911yescharacteristic
839C22C2×#1451977311yescharacteristic
840C4—44no—
841C4—44no—
842C4—42no—
843C4—4882no—
844C4—2444no—
845C4—2442no—
846C4—2444no—
847C2—21no—
848C2—21no—
849C2—21no—
850C2—21no—
851C2—22no—
852C2—21no—
853C2—22no—
854C2—21no—
855C2—22no—
856C2—82no—
857C2—4882no—
858C2#2144694714yesdirect product factor
859C2C2×#1683967011yescharacteristic
860C2C2×#1683995112yes—
subgroupG/H
centerC23#14519745
commutator, cosocleC24×C61C24
FrattiniC24C23×D61
FittingC22×#123×C61C2
socleC23×C61#120
prime radicalC2×#16840321C2
hypercenterC22×#123D61
hypocenterC61C2×#2022
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C25 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
2. C22×#14519760C2semidirect
3. C22×#14519692C2semidirect
4. C22×#14519691C2semidirect
5. C2×#16839625C2semidirect
6. #21446947C2direct (N × H)
7. C2×#16839528C2semidirect
8. C22×#123×C61C2semidirect
18. C2×#14519760C22semidirect
29. C2×#14519692C22semidirect
31. C2×#14519691C22semidirect
33. #16839625C22semidirect
35. #16839528C22semidirect
41. C2×#123×C61C22semidirect
88. C2×C22⋊Dic61D4semidirect
121. C23×C4×C61D4semidirect
132. C2×C22⋊C4×C61D4semidirect
206. C22×C4×C61C2×D4semidirect
246. C22⋊C4×C61C2×D4semidirect
257. C22⋊Dic61C2×D4semidirect
419. C22×#123D61semidirect
435. C2×C61#2022semidirect
455. C2×#123C2×D61semidirect
475. C61C2×#2022semidirect
515. C23×C4C22⋊D61semidirect
560. C2×C22⋊C4C22⋊D61semidirect
672. C22×C4C2×C22⋊D61semidirect
692. C22⋊C4C2×C22⋊D61semidirect
858. C2#21446947direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403212
C22×#145197602
C22×#145196922
C22×#145196912
C2×#168396252
#214469472
C2×#168395282
C22×#123×C612
C2×#202261