Finite Group Databasebeta

← #29686712

Subgroups — #29686712

Order 15616.

1170 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840013C211yesmaximal, characteristic
2C2×#16839872C211yesmaximal, characteristic, complemented
3C2×C4×#11758194C211yesmaximal, characteristic, complemented
4C4×#14519751C211yesmaximal, characteristic, complemented
5#21446684C211yesmaximal, characteristic, complemented
6#21446544C211yesmaximal, characteristic, complemented
7#21446505C211yesmaximal, characteristic, complemented
8#21446501C211yesmaximal, characteristic, complemented
9#21446258C211yesmaximal, characteristic, complemented
10#21446255C211yesmaximal, characteristic, complemented
11#21445850C211yesmaximal, characteristic, complemented
12#21445717C211yesmaximal, characteristic, complemented
13#21445647C211yesmaximal, characteristic, complemented
14#21445644C211yesmaximal, characteristic, complemented
15C4×#121×C61C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×C4×C22⋊D61—21no—
22#16840013C418yescomplemented
23#16839872—24no—
24C2×#14519710C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26C2×#14519708C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C4×#11758194—24no—
34C2×#14519688C2211yescharacteristic
35C2×#14519688C2211yescharacteristic
36C2×C4×#92418C2211yescharacteristic
37C2×C4×#92418C2211yescharacteristic
38#16839664C2211yescharacteristic
39#16839660C2211yescharacteristic
40#16839653—21no—
41#16839641—21no—
42#16839622C2211yescharacteristic
43C4×C4⋊Dic61C2211yescharacteristic
44C4×#11758198—21no—
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51C2×#121×C61C2211yescharacteristic
52C2×C4×D4×C61—21no—
53C2×C4×D4×C61C2211yescharacteristic
54C22×C42×C61C2211yescharacteristic
55C61×#390C2211yescharacteristic
56C61×#389C2211yescharacteristic
57C61×#388—21no—
58C61×#386—21no—
59C61×#380C2211yescharacteristic
60C4×C4⋊C4×C61C2211yescharacteristic
61C4×C22⋊C4×C61—21no—
62C22×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C22×C4×D61—21no—
65C2×#11758199—22no—
66C2×#11758199—22no—
67C2×#11758199C2×C414yescomplemented
68C2×#11758194—22no—
69C2×#11758194—22no—
70C2×#11758194—22no—
71C2×#11758194—22no—
72C2×#11758194—22no—
73C2×#11758194C2×C414yescomplemented
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78#14519751—22no—
79#14519751C2×C414yescomplemented
80C4×D244—22no—
81C4×D244—22no—
82C4×C22⋊D61—44no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×#11758196—21no—
87C2×C22⋊Dic61—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×C4×Dic61—21no—
93#14519710—22no—
94#14519708—22no—
95#14519708C2×C414yescomplemented
96#14519698—22no—
97#14519698—22no—
98#14519698C2×C414yescomplemented
99#14519697—22no—
100#14519697—22no—
101#14519697C2×C414yescomplemented
102#14519688—22no—
103#14519688D414yescomplemented
104C4×#92418—22no—
105C4×#92418—22no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109C22×D4×C61—21no—
110C22×D4×C61C2311yescharacteristic
111C23×C4×C61—21no—
112C23×C4×C61D411yescharacteristic
113C23×C4×C61D411yescharacteristic
114C23×C4×C61C2311yescharacteristic
115#121×C61—22no—
116#121×C61C2×C414yescomplemented
117C4×D4×C61—22no—
118C4×D4×C61—22no—
119C4×D4×C61—44no—
120C2×C4⋊C4×C61—21no—
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C42×C61—22no—
130C2×C42×C61—22no—
131C2×C42×C61—21no—
132C2×C42×C61D411yescharacteristic
133C2×C42×C61D411yescharacteristic
134C2×C42×C61C2311yescharacteristic
135C2×C42×C61C2311yescharacteristic
136#95×C61—21no—
137#95×C61—21no—
138#95×C61—21no—
139C24×C61—21no—
140C24×C61C2×D411yescharacteristic
141C23×D61—21no—
142C2×D4×C61—24no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—42no—
149C2×D4×C61—42no—
150C2×D4×C61C22×C412yes—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—41no—
163C22×C4×C61—41no—
164C22×C4×C61—42no—
165C22×C4×C61—42no—
166C22×C4×C61—42no—
167C22×C4×C61C22×C412yes—
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61#4112yes—
174C22×C4×C61C2411yescharacteristic
175C2×C22⋊D61—24no—
176C2×C22⋊D61—42no—
177C2×C22⋊D61—42no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244C22×C412yes—
187C2×C4×D61—42no—
188C2×C4×D61—42no—
189C2×C4×D61—42no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—42no—
196C4⋊C4×C61C22×C412yes—
197C22⋊C4×C61—24no—
198C22⋊C4×C61—42no—
199C22⋊C4×C61—42no—
200C22⋊C4×C61—42no—
201C22⋊C4×C61—42no—
202C42×C61—22no—
203C42×C61—22no—
204C42×C61—21no—
205C42×C61—21no—
206C42×C61—42no—
207C42×C61C2×D412yes—
208C42×C61#4112yes—
209C22⋊Dic61—42no—
210#11758199—28no—
211#11758198—24no—
212#11758198—42no—
213#11758198—42no—
214#11758198—42no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61C22×C412yes—
221#11758196—42no—
222C4×Dic61—42no—
223#11758194—28no—
224#11758194—28no—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418C22×C412yes—
232C2×#92418C22×C412yes—
233C2×#92418C2×D412yes—
234C2×#92418C2×D412yes—
235C2×#92418#4112yes—
236C2×#92418#4112yes—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—22no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61C4×D412yes—
251C23×C61C22×D411yescharacteristic
252C22×D61—22no—
253C22×D61—41no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259D4×C61—22no—
260D4×C61—22no—
261D4×C61—48no—
262D4×C61—41no—
263D4×C61—41no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—44no—
280C2×C4×C61—44no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—84no—
290C2×C4×C61C4×D412yes—
291C2×C4×C61#12112yes—
292C2×C4×C61#12112yes—
293C2×C4×C61AGL(1,ℤ/8)12yes—
294C2×C4×C61AGL(1,ℤ/8)12yes—
295C2×C4×C61C23×C411yescharacteristic
296C2×C4×C61C22×D411yescharacteristic
297C2×C4×C61C2×#4111yescharacteristic
298C2×C4×C61C2×#4111yescharacteristic
299C2×C4×C61C2×#4111yescharacteristic
300C2×C4×C61C2×#4111yescharacteristic
301C22⋊D61—48no—
302C2×Dic61—22no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311D244—22no—
312D244—22no—
313D244—41no—
314D244—41no—
315C4×D61—84no—
316#92418—22no—
317#92418—22no—
318#92418—22no—
319#92418C4×D414yescomplemented
320#21538—611nomaximal, Sylow
321C22×C61—22no—
322C22×C61—22no—
323C22×C61—22no—
324C22×C61—41no—
325C22×C61—41no—
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—42no—
329C22×C61—42no—
330C22×C61—42no—
331C22×C61—81no—
332C22×C61—81no—
333C22×C61—81no—
334C22×C61—81no—
335C22×C61C2×C4×D411yescharacteristic
336C22×C61C2×#12111yescharacteristic
337C22×C61#53211yescharacteristic
338C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
339C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
340C22×C61#57511yescharacteristic
341C22×C61#57511yescharacteristic
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—81no—
346C2×D61—81no—
347C2×D61—81no—
348C2×D61—81no—
349C4×C61—22no—
350C4×C61—22no—
351C4×C61—22no—
352C4×C61—22no—
353C4×C61—22no—
354C4×C61—42no—
355C4×C61—81no—
356C4×C61—81no—
357C4×C61C2×C4×D411yescharacteristic
358C4×C61C4×#4111yescharacteristic
359C4×C61#52511yescharacteristic
360C4×C61#52911yescharacteristic
361Dic61—42no—
362Dic61—81no—
363Dic61—81no—
364C2×#469—611no—
365C2×#442—611no—
366C2×C4×M16—611no—
367C4×#121—611no—
368C4×#121D6111yescharacteristic, complemented
369#1970—611no—
370#1941—611no—
371#1934—611no—
372#1934—611no—
373#1895—611no—
374#1895—611no—
375#1809—611no—
376#1776—611no—
377#1762—611no—
378#1762—611no—
379C2×C61—42no—
380C2×C61—82no—
381C2×C61C4×#12111yescharacteristic
382C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
383C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
384C2×C61#305511yescharacteristic
385C2×C61#305511yescharacteristic
386C2×C61#318311yescharacteristic
387C2×C61#318411yescharacteristic
388D61—82no—
389C22×D8—611no—
390C22×M16—611no—
391C22×M16—611no—
392C2×#121—611no—
393C2×#121C2×D6111yescharacteristic
394C2×C4×D4—21no—
395C2×C4×D4—611no—
396C2×C4×D4—1221no—
397C2×C4×D4C2×D6111yescharacteristic
398C22×C42C2×D6111yescharacteristic
399#469—618no—
400#442—1224no—
401C2×#107—611no—
402C2×#106—611no—
403C2×#106—611no—
404C2×#102—611no—
405C2×#102—611no—
406C2×#102—611no—
407C2×#102—611no—
408C2×#102—611no—
409C2×#102—611no—
410C4×M16—1224no—
411C2×#97—611no—
412C2×#97—611no—
413C2×C4×C8—611no—
414C2×C4×C8—611no—
415#390—611no—
416#390C2×D6111yescharacteristic
417#389—611no—
418#389C2×D6111yescharacteristic
419#388—21no—
420#388—1221no—
421#386—21no—
422#386—1221no—
423#380—611no—
424#380C2×D6111yescharacteristic
425C4×C4⋊C4—611no—
426C4×C4⋊C4C2×D6111yescharacteristic
427C4×C22⋊C4—21no—
428C4×C22⋊C4—1221no—
429#340—611no—
430#340—611no—
431#340—611no—
432#340—611no—
433#340—611no—
434#340—611no—
435C61#2153811yescharacteristic, complemented, Sylow
436C22×D4—21no—
437C22×D4—611no—
438C22×D4—1221no—
439C22×D4C22×D6111yescharacteristic
440C23×C4—21no—
441C23×C4—1221no—
442C23×C4C22⋊D6111yescharacteristic
443C23×C4C22⋊D6111yescharacteristic
444C23×C4C22×D6111yescharacteristic
445C2×D8—614no—
446C2×D8—1222no—
447C2×D8—1222no—
448C2×M16—614no—
449C2×M16—1222no—
450C2×M16—1222no—
451C2×M16—1222no—
452C2×M16—1222no—
453C2×M16—1222no—
454C22×C8—611no—
455C22×C8—611no—
456C22×C8—611no—
457C22×C8—611no—
458#121—22no—
459#121—614no—
460#121—1222no—
461#121C4×D6114yescomplemented
462C4×D4—22no—
463C4×D4—22no—
464C4×D4—44no—
465C4×D4—1222no—
466C4×D4—1222no—
467C4×D4—2444no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—1221no—
473C2×C4⋊C4C22×D6111yescharacteristic
474C2×C4⋊C4C22×D6111yescharacteristic
475C2×C4⋊C4C22×D6111yescharacteristic
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
484C2×C22⋊C4—1221no—
485C2×C22⋊C4—1221no—
486C2×C42—22no—
487C2×C42—22no—
488C2×C42—21no—
489C2×C42—1221no—
490C2×C42C22⋊D6111yescharacteristic
491C2×C42C22⋊D6111yescharacteristic
492C2×C42C22×D6111yescharacteristic
493C2×C42C22×D6111yescharacteristic
494#107—1222no—
495#106—614no—
496#106—1222no—
497#102—614no—
498#102—614no—
499#102—1222no—
500#102—1222no—
501#102—1222no—
502#102—1222no—
503#97—614no—
504#97—1222no—
505C4×C8—1222no—
506C4×C8—1222no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—1221no—
511#95—1221no—
512#95—1221no—
513C24—21no—
514C24—1221no—
515C24C2×C22⋊D6111yescharacteristic
516C2×D4—24no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—612no—
525C2×D4—1224no—
526C2×D4—1221no—
527C2×D4—1221no—
528C2×D4—1221no—
529C2×D4—1221no—
530C2×D4—1221no—
531C2×D4—2442no—
532C2×D4—2442no—
533C2×D4C2×C4×D6112yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—2442no—
554C22×C4—2442no—
555C22×C4—2442no—
556C22×C4C2×C4×D6112yes—
557C22×C4#1175822212yes—
558C22×C4C2×C22⋊D6111yescharacteristic
559C22×C4C2×C22⋊D6111yescharacteristic
560C22×C4C2×C22⋊D6111yescharacteristic
561C22×C4C2×C22⋊D6111yescharacteristic
562C22×C4C2×C22⋊D6111yescharacteristic
563C22×C4C23×D6111yescharacteristic
564D8—1228no—
565M16—1228no—
566M16—1228no—
567C2×C8—612no—
568C2×C8—612no—
569C2×C8—612no—
570C2×C8—612no—
571C2×C8—612no—
572C2×C8—612no—
573C2×C8—1221no—
574C2×C8—1221no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—42no—
585C4⋊C4—612no—
586C4⋊C4—1221no—
587C4⋊C4—1221no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—2442no—
592C4⋊C4C2×C4×D6112yes—
593C22⋊C4—24no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—1224no—
599C22⋊C4—2442no—
600C22⋊C4—2442no—
601C22⋊C4—2442no—
602C22⋊C4—2442no—
603C42—21no—
604C42—21no—
605C42—22no—
606C42—22no—
607C42—42no—
608C42—2442no—
609C42D4×D6112yes—
610C42#1175822412yes—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—1222no—
625C23—2441no—
626C23—2441no—
627C23—2441no—
628C23—2441no—
629C23—2441no—
630C23—2441no—
631C23C4×C22⋊D6112yes—
632C23C22×C22⋊D6111yescharacteristic
633D4—22no—
634D4—22no—
635D4—48no—
636D4—41no—
637D4—41no—
638D4—1222no—
639D4—1222no—
640D4—2448no—
641D4—2441no—
642D4—2441no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—84no—
669C2×C4—1222no—
670C2×C4—4884no—
671C2×C4—2441no—
672C2×C4—2441no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4C4×C22⋊D6112yes—
680C2×C4#1451974912yes—
681C2×C4#1451974912yes—
682C2×C4#1451980212yes—
683C2×C4#1451980312yes—
684C2×C4C22×C4×D6111yescharacteristic
685C2×C4C2×D4×D6111yescharacteristic
686C2×C4#41×D6111yescharacteristic
687C2×C4#41×D6111yescharacteristic
688C2×C4C2×#1175822411yescharacteristic
689C2×C4C2×#1175822211yescharacteristic
690C8—614no—
691C8—1222no—
692C8—1222no—
693C8—1222no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—4881no—
709C22—4881no—
710C22—4881no—
711C22—4881no—
712C22—2442no—
713C22—2442no—
714C22—2442no—
715C22C2×C4×C22⋊D6111yescharacteristic
716C22C2×#1451974911yescharacteristic
717C22#1684030811yescharacteristic
718C22C2×#1451980211yescharacteristic
719C22C2×#1451980311yescharacteristic
720C22#1684056011yescharacteristic
721C22#1684056011yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—42no—
728C4—81no—
729C4—81no—
730C4—4881no—
731C4—4881no—
732C4—2442no—
733C4C4×D4×D6111yescharacteristic
734C4C4×#1175822411yescharacteristic
735C4#1684027111yescharacteristic
736C4#1684029211yescharacteristic
737C2—42no—
738C2—82no—
739C2—4882no—
740C2C4×#1451974911yescharacteristic
741C2C4×#1451980211yescharacteristic
742C2C4×#1451980311yescharacteristic
743C2#2145543411yescharacteristic
744C2#2145544011yescharacteristic
745C2#2145654211yescharacteristic
746C2#2145655311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×#121×C61C2
socleC23×C61C22×D4
prime radicalC2×#16840013C2
cosocleC22×C4×C61C24
hypercenterC4×#121D61
hypocenterC61#21538
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. C2×#16839872C2semidirect
3. C2×C4×#11758194C2semidirect
4. C4×#14519751C2semidirect
5. #21446684C2semidirect
6. #21446544C2semidirect
7. #21446505C2semidirect
8. #21446501C2semidirect
9. #21446258C2semidirect
10. #21446255C2semidirect
11. #21445850C2semidirect
12. #21445717C2semidirect
13. #21445647C2semidirect
14. #21445644C2semidirect
15. C4×#121×C61C2semidirect
22. #16840013C4semidirect
67. C2×#11758199C2×C4semidirect
73. C2×#11758194C2×C4semidirect
79. #14519751C2×C4semidirect
95. #14519708C2×C4semidirect
98. #14519698C2×C4semidirect
101. #14519697C2×C4semidirect
103. #14519688D4semidirect
116. #121×C61C2×C4semidirect
319. #92418C4×D4semidirect
368. C4×#121D61semidirect
435. C61#21538semidirect
461. #121C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168400132
C2×#168398722
C2×C4×#117581942
C4×#145197512
#214466842
#214465442
#214465052
#214465012
#214462582
#214462552
#214458502
#214457172
#214456472
#214456442
C4×#121×C612
#2153861