Finite Group Databasebeta

← #29601164

Subgroups — #29601164

Order 15616.

3366 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519737C211yesmaximal, characteristic
2C22×C42×D61C211yesmaximal, characteristic, complemented
3C2×#16839638C212yesmaximal
4C2×C22⋊C4×Dic61C212yesmaximal, complemented
5C2×#16839609C211yesmaximal, characteristic, complemented
6#21444056C211yesmaximal, characteristic, complemented
7#21444054C211yesmaximal, characteristic, complemented
8#21444052C211yesmaximal, characteristic, complemented
9#21444040C212yesmaximal, complemented
10#95×Dic61C212yesmaximal, complemented
11C61×#1437C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C24×Dic61C2211yescharacteristic
14C23×C4×D61C2212yes—
15C23×C4×D61C2211yescharacteristic
16C2×#14519737—24no—
17C2×#14519737—24no—
18C2×#14519737C418yescomplemented
19C22×#11758196C2211yescharacteristic
20C22×C22⋊Dic61C2212yes—
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2212yes—
23C22×C4×Dic61C2211yescharacteristic
24C22×C4×Dic61C2212yes—
25C22×C4×Dic61C2211yescharacteristic
26C22×C4×Dic61C2212yes—
27C2×C42×D61—28no—
28C2×C42×D61—24no—
29#16839638C4116yescomplemented
30C22⋊C4×Dic61—28no—
31#16839609—24no—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2212yes—
37C2×#14519684C2212yes—
38C22×C22⋊C4×C61C2212yes—
39C22×C22⋊C4×C61C2211yescharacteristic
40C22×C42×C61C2211yescharacteristic
41C2×#95×C61C2212yes—
42C2×#95×C61C2211yescharacteristic
43C24×D61C2311yescharacteristic
44C22×C22⋊D61—22no—
45C22×C22⋊D61—22no—
46C22×C22⋊D61—24no—
47C22×C22⋊D61C2×C414yes—
48C22×C22⋊D61C2×C418yes—
49C23×Dic61—22no—
50C23×Dic61—22no—
51C23×Dic61—24no—
52C23×Dic61—24no—
53C23×Dic61C2×C414yescomplemented
54C23×Dic61C2312yes—
55C23×Dic61C2311yescharacteristic
56C23×Dic61C2311yescharacteristic
57C23×Dic61C2312yes—
58C23×Dic61C2311yescharacteristic
59C22×C4×D61—24no—
60C22×C4×D61—24no—
61C22×C4×D61—24no—
62C22×C4×D61—24no—
63C22×C4×D61—24no—
64C22×C4×D61—24no—
65C22×C4×D61—24no—
66C22×C4×D61—24no—
67C22×C4×D61C2×C414yes—
68C22×C4×D61C2×C418yescomplemented
69C22×C4×D61D414yes—
70C22×C4×D61D414yes—
71#14519737—232no—
72C2×#11758196—22no—
73C2×#11758196—22no—
74C2×#11758196C2×C414yescomplemented
75C2×C22⋊Dic61—24no—
76C2×C22⋊Dic61—24no—
77C2×C22⋊Dic61C2×C418yescomplemented
78C2×#11758198—22no—
79C2×#11758198—22no—
80C2×#11758198—24no—
81C2×#11758198—24no—
82C2×#11758198C2×C414yes—
83C2×#11758198C2×C418yescomplemented
84C2×C4×Dic61—22no—
85C2×C4×Dic61—24no—
86C2×C4×Dic61—24no—
87C2×C4×Dic61—24no—
88C2×C4×Dic61—22no—
89C2×C4×Dic61—22no—
90C2×C4×Dic61—24no—
91C2×C4×Dic61—24no—
92C2×C4×Dic61—24no—
93C2×C4×Dic61C2×C414yescomplemented
94C2×C4×Dic61D418yescomplemented
95C42×D61—232no—
96#14519684—22no—
97#14519684—24no—
98#14519684—24no—
99#14519684—24no—
100#14519684C2×C418yescomplemented
101#14519684C2×C418yescomplemented
102C25×C61C2311yescharacteristic
103C23×C4×C61C2312yes—
104C23×C4×C61C2311yescharacteristic
105C23×C4×C61C2311yescharacteristic
106C23×C4×C61C2312yes—
107C2×C22⋊C4×C61—22no—
108C2×C22⋊C4×C61—22no—
109C2×C22⋊C4×C61—24no—
110C2×C22⋊C4×C61—24no—
111C2×C22⋊C4×C61C2×C414yescomplemented
112C2×C22⋊C4×C61C2×C418yescomplemented
113C2×C42×C61—22no—
114C2×C42×C61—24no—
115#95×C61—22no—
116#95×C61—24no—
117C24×C61—21no—
118C24×C61—21no—
119C24×C61—22no—
120C24×C61—22no—
121C24×C61—22no—
122C24×C61—22no—
123C24×C61—22no—
124C24×C61C22×C412yes—
125C24×C61C22×C414yes—
126C24×C61C2411yescharacteristic
127C23×D61—22no—
128C23×D61—22no—
129C23×D61—22no—
130C23×D61—22no—
131C23×D61C22×C412yes—
132C23×D61C22×C414yes—
133C23×D61C2×D412yes—
134C23×D61C2×D412yes—
135C23×D61#4114yes—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61C22×C414yes—
153C22×C4×C61C22×C412yes—
154C22×C4×C61C22×C412yes—
155C22×C4×C61C22×C414yes—
156C22×C4×C61C2×D412yes—
157C22×C4×C61C2×D412yes—
158C22×C4×C61C2×D414yes—
159C22×C4×C61#4114yes—
160C2×C22⋊D61—28no—
161C2×C22⋊D61—28no—
162C2×C22⋊D61—216no—
163C2×C22⋊D61—216no—
164C2×C22⋊D61C42116yescomplemented
165C22×Dic61—22no—
166C22×Dic61—22no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—22no—
172C22×Dic61—22no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—22no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—28no—
183C22×Dic61—216no—
184C22×Dic61—44no—
185C22×Dic61—48no—
186C22×Dic61—44no—
187C22×Dic61C22×C412yes—
188C22×Dic61C22×C414yes—
189C22×Dic61C22×C414yes—
190C22×Dic61C22×C412yes—
191C22×Dic61C22×C414yes—
192C22×Dic61C22×C412yes—
193C22×Dic61C2×D414yes—
194C22×Dic61C2×D412yes—
195C22×Dic61C2×D412yes—
196C22×Dic61C2×D414yes—
197C22×Dic61#4114yes—
198C22×Dic61#4114yes—
199C2×C4×D61—216no—
200C2×C4×D61—216no—
201C2×C4×D61—216no—
202C2×C4×D61—216no—
203C2×C4×D61—216no—
204C2×C4×D61—216no—
205C2×C4×D61—216no—
206C2×C4×D61—216no—
207C2×C4×D61—28no—
208C2×C4×D61—216no—
209C2×C4×D61—28no—
210C2×C4×D61C22⋊C4116yescomplemented
211C22⋊C4×C61—28no—
212C22⋊C4×C61—216no—
213C42×C61—28no—
214C22⋊Dic61—216no—
215#11758198—28no—
216#11758198—216no—
217#11758196—28no—
218C4×Dic61—28no—
219C4×Dic61—28no—
220C4×Dic61—216no—
221C4×Dic61—48no—
222C23×C61—22no—
223C23×C61—22no—
224C23×C61—24no—
225C23×C61—24no—
226C23×C61—24no—
227C23×C61—24no—
228C23×C61—24no—
229C23×C61—24no—
230C23×C61—24no—
231C23×C61—24no—
232C23×C61—41no—
233C23×C61—42no—
234C23×C61—41no—
235C23×C61—42no—
236C23×C61—42no—
237C23×C61—42no—
238C23×C61—42no—
239C23×C61—42no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61C2×C4214yescomplemented
243C23×C61C23×C411yescharacteristic
244C23×C61C23×C412yes—
245C23×C61C22×D411yescharacteristic
246C23×C61C22×D411yescharacteristic
247C23×C61C22×D412yes—
248C23×C61C2×#4112yes—
249C23×C61C2×#4112yes—
250C23×C61C2×#4112yes—
251C23×C61C2×#4112yes—
252C22×D61—24no—
253C22×D61—24no—
254C22×D61—24no—
255C22×D61—24no—
256C22×D61—24no—
257C22×D61—24no—
258C22×D61—22no—
259C22×D61—24no—
260C22×D61—22no—
261C22×D61—24no—
262C22×D61—24no—
263C22×D61—24no—
264C22×D61—24no—
265C22×D61—24no—
266C22×D61—22no—
267C22×D61—22no—
268C22×D61C2×C4214yes—
269C22×D61C2×C22⋊C414yes—
270C22×D61#11714yes—
271C22×D61C4×D418yes—
272C22×D61C4×D418yes—
273C2×C4×C61—24no—
274C2×C4×C61—24no—
275C2×C4×C61—24no—
276C2×C4×C61—22no—
277C2×C4×C61—24no—
278C2×C4×C61—24no—
279C2×C4×C61—22no—
280C2×C4×C61—24no—
281C2×C4×C61—24no—
282C2×C4×C61—24no—
283C2×C4×C61—22no—
284C2×C4×C61—24no—
285C2×C4×C61—24no—
286C2×C4×C61—24no—
287C2×C4×C61—24no—
288C2×C4×C61—42no—
289C2×C4×C61—42no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—42no—
295C2×C4×C61C2×C22⋊C414yes—
296C2×C4×C61C4×D418yescomplemented
297C22⋊D61—232no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—24no—
301C2×Dic61—24no—
302C2×Dic61—24no—
303C2×Dic61—24no—
304C2×Dic61—24no—
305C2×Dic61—24no—
306C2×Dic61—24no—
307C2×Dic61—24no—
308C2×Dic61—22no—
309C2×Dic61—24no—
310C2×Dic61—24no—
311C2×Dic61—24no—
312C2×Dic61—24no—
313C2×Dic61—41no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—41no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61—416no—
321C2×Dic61C2×C4214yescomplemented
322C2×Dic61C2×C22⋊C414yes—
323C2×Dic61C4×D418yes—
324C2×Dic61C4×D418yescomplemented
325C2×Dic61#12014yes—
326C2×Dic61#12118yes—
327C2×Dic61#12314yes—
328C4×D61—264no—
329C4×D61—232no—
330C4×#386—611nomaximal, Sylow
331C22×C61—24no—
332C22×C61—28no—
333C22×C61—42no—
334C22×C61—44no—
335C22×C61—42no—
336C22×C61—44no—
337C22×C61—44no—
338C22×C61—44no—
339C22×C61—44no—
340C22×C61C22×C4211yescharacteristic
341C22×C61C22×C22⋊C411yescharacteristic
342C22×C61C2×#11711yescharacteristic
343C22×C61C2×C4×D412yes—
344C22×C61C2×C4×D412yes—
345C22×C61C2×C4×D412yes—
346C22×C61C2×C4×D412yes—
347C22×C61C2×C4×D412yes—
348C22×C61C4×#4112yes—
349C22×C61C4×#4112yes—
350C22×C61C4×#4112yes—
351C22×C61C2×#12011yescharacteristic
352C22×C61C2×#12112yes—
353C22×C61C2×#12311yescharacteristic
354C22×C61#52512yes—
355C22×C61#52512yes—
356C22×C61#52512yes—
357C22×C61#52912yes—
358C22×C61#52912yes—
359C22×C61#53211yescharacteristic
360C22×C61#53211yescharacteristic
361C2×D61—28no—
362C2×D61—24no—
363C2×D61—28no—
364C2×D61—24no—
365C2×D61—28no—
366C2×D61—28no—
367C2×D61—28no—
368C2×D61—28no—
369C2×D61C4×C22⋊C418yescomplemented
370C4×C61—24no—
371C4×C61—28no—
372C4×C61—42no—
373C4×C61—44no—
374Dic61—24no—
375Dic61—28no—
376Dic61—42no—
377Dic61—44no—
378Dic61#38618yescomplemented
379C22×C4×D4—611no—
380C23×C42—611no—
381C2×#386—612no—
382C2×C4×C22⋊C4—611no—
383C2×C4×C22⋊C4—612no—
384#1437—611no—
385#1437D6111yescharacteristic, complemented
386#1436—611no—
387#1436—611no—
388C22⋊#95—612no—
389C4×#95—612no—
390C2×C61—44no—
391C2×C61C2×C4×C22⋊C411yescharacteristic
392C2×C61C42×D412yes—
393C2×C61C2×#38611yescharacteristic
394C2×C61#229012yes—
395C2×C61#229711yescharacteristic
396C2×C61C4×#12012yes—
397C2×C61C4×#12112yes—
398C2×C61C4×#12112yes—
399C2×C61C4×#12312yes—
400D61—28no—
401C23×D4—611no—
402C24×C4—611no—
403C24×C4—611no—
404C24×C4—612no—
405C2×C4×D4—618no—
406C2×C4×D4—1224no—
407C2×C4×D4—1224no—
408C22×C4⋊C4—611no—
409C22×C22⋊C4—612no—
410C22×C22⋊C4—611no—
411C22×C22⋊C4—612no—
412C22×C22⋊C4C2×D6111yescharacteristic
413C22×C22⋊C4C2×D6112yes—
414C22×C42—612no—
415C22×C42—611no—
416C22×C42—611no—
417C22×C42—612no—
418C22×C42—1228no—
419C22×C42—1224no—
420C22×C42C2×D6111yescharacteristic
421#386—6116no—
422C4×C22⋊C4—1224no—
423C4×C22⋊C4—1228no—
424C2×#95—612no—
425C2×#95—612no—
426C2×#95—612no—
427C2×#95—612no—
428C2×#95—612no—
429C2×#95—611no—
430C2×#95C2×D6112yes—
431C2×#95C2×D6111yescharacteristic
432C61C4×#38611yescharacteristic, complemented, Sylow
433C25—611no—
434C25C22×D6111yescharacteristic
435C22×D4—614no—
436C22×D4—618no—
437C22×D4—1222no—
438C22×D4—1222no—
439C22×D4—1224no—
440C23×C4—611no—
441C23×C4—612no—
442C23×C4—611no—
443C23×C4—614no—
444C23×C4—614no—
445C23×C4—614no—
446C23×C4—614no—
447C23×C4—612no—
448C23×C4—611no—
449C23×C4—618no—
450C23×C4—1224no—
451C23×C4—1224no—
452C23×C4—1224no—
453C23×C4—1224no—
454C23×C4—1224no—
455C23×C4—1224no—
456C23×C4—1222no—
457C23×C4—1222no—
458C23×C4—1224no—
459C23×C4—1224no—
460C23×C4—1224no—
461C23×C4—1224no—
462C23×C4C22×D6112yes—
463C23×C4C22×D6111yescharacteristic
464C23×C4C22×D6111yescharacteristic
465C23×C4C22×D6112yes—
466C4×D4—12232no—
467C2×C4⋊C4—614no—
468C2×C4⋊C4—1222no—
469C2×C4⋊C4—1222no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—618no—
475C2×C22⋊C4—614no—
476C2×C22⋊C4—618no—
477C2×C22⋊C4—1222no—
478C2×C22⋊C4—1222no—
479C2×C22⋊C4—1224no—
480C2×C22⋊C4—1224no—
481C2×C22⋊C4—1224no—
482C2×C22⋊C4—1224no—
483C2×C22⋊C4C4×D6114yescomplemented
484C2×C22⋊C4C4×D6118yescomplemented
485C2×C42—22no—
486C2×C42—24no—
487C2×C42—614no—
488C2×C42—618no—
489C2×C42—12232no—
490C2×C42—1222no—
491C2×C42—1222no—
492C2×C42—1224no—
493C2×C42—1224no—
494C2×C42—1224no—
495C2×C42—1222no—
496C2×C42—1224no—
497C2×C42—1224no—
498C2×C42—1224no—
499#95—22no—
500#95—24no—
501#95—618no—
502#95—618no—
503#95—1224no—
504#95—1224no—
505#95—1224no—
506#95—1222no—
507C24—22no—
508C24—21no—
509C24—21no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—612no—
515C24—614no—
516C24—612no—
517C24—612no—
518C24—614no—
519C24—1222no—
520C24—1222no—
521C24—1222no—
522C24—1222no—
523C24C2×C4×D6114yes—
524C24C2×C4×D6112yes—
525C24C23×D6111yescharacteristic
526C2×D4—6116no—
527C2×D4—1228no—
528C2×D4—1228no—
529C2×D4—12216no—
530C2×D4—12216no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—612no—
548C22×C4—614no—
549C22×C4—612no—
550C22×C4—612no—
551C22×C4—614no—
552C22×C4—614no—
553C22×C4—614no—
554C22×C4—612no—
555C22×C4—614no—
556C22×C4—614no—
557C22×C4—6116no—
558C22×C4—614no—
559C22×C4—612no—
560C22×C4—1228no—
561C22×C4—12216no—
562C22×C4—12216no—
563C22×C4—12216no—
564C22×C4—1228no—
565C22×C4—12216no—
566C22×C4—12216no—
567C22×C4—12216no—
568C22×C4—12216no—
569C22×C4—12216no—
570C22×C4—1228no—
571C22×C4—12216no—
572C22×C4—1222no—
573C22×C4—1222no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—12216no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—2444no—
591C22×C4—2448no—
592C22×C4—2444no—
593C22×C4C2×C4×D6114yes—
594C22×C4C2×C4×D6112yes—
595C22×C4C2×C4×D6112yes—
596C22×C4C2×C4×D6114yes—
597C22×C4D4×D6112yes—
598C22×C4D4×D6112yes—
599C22×C4D4×D6114yes—
600C22×C4#1175822414yes—
601C4⋊C4—1228no—
602C22⋊C4—28no—
603C22⋊C4—216no—
604C22⋊C4—1228no—
605C22⋊C4—12216no—
606C22⋊C4—12216no—
607C42—28no—
608C42—12216no—
609C42—1228no—
610C42—1228no—
611C42—2448no—
612C23—22no—
613C23—22no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—41no—
623C23—42no—
624C23—41no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—41no—
631C23—41no—
632C23—614no—
633C23—614no—
634C23—614no—
635C23—618no—
636C23—618no—
637C23—1224no—
638C23—1224no—
639C23—1224no—
640C23—1224no—
641C23—1224no—
642C23—1224no—
643C23—1222no—
644C23—1224no—
645C23—1222no—
646C23—1224no—
647C23—1224no—
648C23—1224no—
649C23—1224no—
650C23—1224no—
651C23—1222no—
652C23—1222no—
653C23C42×D6114yescomplemented
654C23C22×C4×D6111yescharacteristic
655C23C22×C4×D6112yes—
656C23C2×D4×D6111yescharacteristic
657C23C2×D4×D6111yescharacteristic
658C23C2×D4×D6112yes—
659C23#41×D6112yes—
660C23#41×D6112yes—
661C23#41×D6112yes—
662C23C2×#1175822412yes—
663D4—12232no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—614no—
687C2×C4—618no—
688C2×C4—614no—
689C2×C4—618no—
690C2×C4—614no—
691C2×C4—614no—
692C2×C4—618no—
693C2×C4—12232no—
694C2×C4—12264no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1224no—
698C2×C4—1224no—
699C2×C4—1224no—
700C2×C4—1224no—
701C2×C4—1224no—
702C2×C4—1224no—
703C2×C4—1224no—
704C2×C4—1224no—
705C2×C4—1222no—
706C2×C4—1224no—
707C2×C4—1224no—
708C2×C4—1224no—
709C2×C4—1224no—
710C2×C4—24416no—
711C2×C4—2441no—
712C2×C4—2442no—
713C2×C4—2442no—
714C2×C4—2441no—
715C2×C4—2442no—
716C2×C4—2442no—
717C2×C4—2442no—
718C2×C4C22⋊C4×D6114yes—
719C2×C4#1451973718yescomplemented
720C22—24no—
721C22—28no—
722C22—42no—
723C22—44no—
724C22—42no—
725C22—44no—
726C22—44no—
727C22—44no—
728C22—44no—
729C22—618no—
730C22—1224no—
731C22—1228no—
732C22—1224no—
733C22—1228no—
734C22—1228no—
735C22—1228no—
736C22—1228no—
737C22—1228no—
738C22C2×C42×D6111yescharacteristic
739C22C2×C22⋊C4×D6111yescharacteristic
740C22#117×D6111yescharacteristic
741C22C4×D4×D6112yes—
742C22C4×D4×D6112yes—
743C22C4×D4×D6112yes—
744C22C4×D4×D6112yes—
745C22C2×#1451973712yes—
746C22C4×#1175822412yes—
747C22C4×#1175822412yes—
748C22#1684023012yes—
749C22#120×D6111yescharacteristic
750C22#121×D6112yes—
751C22#123×D6111yescharacteristic
752C22#1684027012yes—
753C22#1684027212yes—
754C22#1684027212yes—
755C22#1684029112yes—
756C22#1684029512yes—
757C22#1684031011yescharacteristic
758C22#1684031111yescharacteristic
759C4—24no—
760C4—28no—
761C4—42no—
762C4—44no—
763C4—618no—
764C4—1228no—
765C4—1224no—
766C4—2442no—
767C4—2444no—
768C2—44no—
769C2—1228no—
770C2C4×C22⋊C4×D6111yescharacteristic
771C2C4×#1451973712yes—
772C2#386×D6111yescharacteristic
773C2#2144826112yes—
774C2#2144830611yescharacteristic
775C2#2144832412yes—
776C2#2144833112yes—
777C2#2144833512yes—
778C2#2144834612yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC61×#1437C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenter#1437D61
hypocenterC61C4×#386
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C22×C42×D61C2semidirect
4. C2×C22⋊C4×Dic61C2semidirect
5. C2×#16839609C2semidirect
6. #21444056C2semidirect
7. #21444054C2semidirect
8. #21444052C2semidirect
9. #21444040C2semidirect
10. #95×Dic61C2semidirect
11. C61×#1437C2semidirect
18. C2×#14519737C4semidirect
29. #16839638C4semidirect
53. C23×Dic61C2×C4semidirect
68. C22×C4×D61C2×C4semidirect
74. C2×#11758196C2×C4semidirect
77. C2×C22⋊Dic61C2×C4semidirect
83. C2×#11758198C2×C4semidirect
93. C2×C4×Dic61C2×C4semidirect
94. C2×C4×Dic61D4semidirect
100. #14519684C2×C4semidirect
101. #14519684C2×C4semidirect
111. C2×C22⋊C4×C61C2×C4semidirect
112. C2×C22⋊C4×C61C2×C4semidirect
164. C2×C22⋊D61C42semidirect
210. C2×C4×D61C22⋊C4semidirect
242. C23×C61C2×C42semidirect
296. C2×C4×C61C4×D4semidirect
321. C2×Dic61C2×C42semidirect
324. C2×Dic61C4×D4semidirect
369. C2×D61C4×C22⋊C4semidirect
378. Dic61#386semidirect
385. #1437D61semidirect
432. C61C4×#386semidirect
483. C2×C22⋊C4C4×D61semidirect
484. C2×C22⋊C4C4×D61semidirect
653. C23C42×D61semidirect
719. C2×C4#14519737semidirect

Maximal subgroups

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

subgroupindex
C22×#145197372
C22×C42×D612
C2×#168396382
C2×C22⋊C4×Dic612
C2×#168396092
#214440562
#214440542
#214440522
#214440402
#95×Dic612
C61×#14372
C4×#38661