Finite Group Databasebeta

← #29700504

Subgroups — #29700504

Order 15616.

1398 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839894C211yesmaximal, characteristic
2C2×#102×D61C211yesmaximal, characteristic, complemented
3#21448831C211yesmaximal, characteristic, complemented
4D4×#11758198C211yesmaximal, characteristic, complemented
5#21446682C211yesmaximal, characteristic, complemented
6#21446502C211yesmaximal, characteristic, complemented
7#21446438C211yesmaximal, characteristic, complemented
8#21446244C211yesmaximal, characteristic, complemented
9#21446169C211yesmaximal, characteristic, complemented
10#21446167C211yesmaximal, characteristic, complemented
11#21446066C211yesmaximal, characteristic, complemented
12#21446005C211yesmaximal, characteristic, complemented
13#102×Dic61C211yesmaximal, characteristic, complemented
14C8×#11758198C211yesmaximal, characteristic, complemented
15C2×C4×D8×C61C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C2×#14519748C2211yescharacteristic
20C2×D4×Dic61C2211yescharacteristic
21C2×C4×C22⋊D61—21no—
22C2×C4⋊C4×D61C2211yescharacteristic
23C22×#11758198—21no—
24#16839894C418yescomplemented
25C2×#14519710C2211yescharacteristic, complemented
26C2×#14519699C2211yescharacteristic
27C2×#14519699C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic, complemented
31C2×#14519697C2211yescharacteristic
32#102×D61—24no—
33C2×#14519689C2211yescharacteristic
34C2×C8×Dic61C2211yescharacteristic, complemented
35#16839665C2211yescharacteristic, complemented
36#16839664C2211yescharacteristic
37#16839663C2211yescharacteristic
38#16839660C2211yescharacteristic, complemented
39#16839656—21no—
40#16839641—21no—
41#16839639—21no—
42#16839638—21no—
43#16839635—21no—
44#16839619C2211yescharacteristic
45#16839617—21no—
46C4⋊C4×Dic61C2211yescharacteristic, complemented
47C4×#11758198C2211yescharacteristic
48#16839525C2211yescharacteristic, complemented
49#16839525C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839517C2211yescharacteristic, complemented
53#16839516C2211yescharacteristic, complemented
54C22×D8×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C2×C4×D4×C61C2211yescharacteristic, complemented
57C4×D8×C61—24no—
58C2×#107×C61C2211yescharacteristic, complemented
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic, complemented
61C2×C4×C8×C61C2211yescharacteristic, complemented
62C24×D61—21no—
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C22⋊D61—21no—
66C2×D4×D61—22no—
67C2×D4×D61—22no—
68C2×D4×D61—22no—
69C2×D4×D61—41no—
70C2×D4×D61—41no—
71C2×D4×D61C2×C414yescomplemented
72C23×Dic61—21no—
73C22×C4×D61—21no—
74C22×C4×D61C2311yescharacteristic
75C2×#11758199—41no—
76C2×#11758199—41no—
77C2×#11758199C2×C414yescomplemented
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C2×C8×D61—22no—
81C2×C8×D61—22no—
82C2×C8×D61—41no—
83#14519748—22no—
84#14519748C2×C414yescomplemented
85D4×Dic61—22no—
86D4×Dic61—41no—
87C4×C22⋊D61—44no—
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×#11758196—21no—
92C2×#11758196—21no—
93C4⋊C4×D61—22no—
94C4⋊C4×D61—41no—
95C2×C22⋊Dic61—21no—
96C2×C22⋊Dic61—21no—
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—44no—
105C2×#11758198D411yescharacteristic
106C2×#11758198D411yescharacteristic
107C2×C4×Dic61—21no—
108C2×C4×Dic61C2311yescharacteristic
109#14519710—41no—
110#14519699—22no—
111#14519699C2×C414yescomplemented
112#14519698—22no—
113#14519698—41no—
114#14519698C2×C414yescomplemented
115#14519697—22no—
116#14519689C2×C414yescomplemented
117C8×Dic61—41no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121#14519684D411yescharacteristic
122#14519684D411yescharacteristic
123C22×D4×C61C2311yescharacteristic
124C22×D4×C61C2311yescharacteristic
125C23×C4×C61—21no—
126C23×C4×C61—21no—
127C2×D8×C61—22no—
128C2×D8×C61—22no—
129C2×D8×C61C2×C414yescomplemented
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C4×D4×C61—22no—
133C4×D4×C61—22no—
134C4×D4×C61—41no—
135C4×D4×C61—41no—
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C42×C61C2311yescharacteristic
141#107×C61—22no—
142#102×C61—22no—
143#102×C61D414yescomplemented
144C4×C8×C61—22no—
145C24×C61—21no—
146C24×C61—21no—
147C23×D61—21no—
148C23×D61—24no—
149C23×D61—42no—
150C23×D61—42no—
151C23×D61—42no—
152C23×D61—42no—
153C23×D61—81no—
154C23×D61—81no—
155C23×D61C2×D411yescharacteristic
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61C22×C412yes—
165C2×D4×C61C22×C412yes—
166C2×D4×C61C2×D412yes—
167C2×D4×C61#4112yes—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—42no—
171C22×C4×C61—42no—
172C22×C4×C61—42no—
173C22×C4×C61—42no—
174C22×C4×C61—81no—
175C22×C4×C61—81no—
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2411yescharacteristic
179C2×C22⋊D61—24no—
180C2×C22⋊D61—24no—
181C2×C22⋊D61—42no—
182C2×C22⋊D61—42no—
183C2×C22⋊D61—42no—
184C2×C22⋊D61—42no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—42no—
189C22×Dic61—42no—
190C22×Dic61—81no—
191C22×Dic61C2×D411yescharacteristic
192C22×Dic61C2×D411yescharacteristic
193C22×Dic61C2×D411yescharacteristic
194D4×D61—28no—
195D4×D61—44no—
196D4×D61—44no—
197D4×D61—44no—
198C2×D244—21no—
199C2×D244—21no—
200C2×D244—21no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244C22×C412yes—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—42no—
209C2×C4×D61—42no—
210C2×C4×D61—81no—
211C2×C4×D61C22×C412yes—
212C2×C4×D61#4112yes—
213D8×C61—28no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61C22×C412yes—
219C2×C8×C61C2×D412yes—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61C2×D412yes—
224C22⋊C4×C61—42no—
225C22⋊C4×C61—42no—
226C42×C61—21no—
227C42×C61—21no—
228C22⋊Dic61—24no—
229C22⋊Dic61—42no—
230C22⋊Dic61—42no—
231C22⋊Dic61—81no—
232#11758199—44no—
233#11758198—22no—
234#11758198—42no—
235#11758198—42no—
236#11758198—42no—
237#11758198—81no—
238#11758198—81no—
239#11758198D814yescomplemented
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242C4⋊Dic61—21no—
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245C4⋊Dic61C22×C412yes—
246#11758196—42no—
247#11758196—42no—
248C4×Dic61—21no—
249C4×Dic61—21no—
250C4×Dic61—42no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418C22×C412yes—
257C8×D61—44no—
258C23×C61—22no—
259C23×C61—22no—
260C23×C61—22no—
261C23×C61—22no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61C22×D411yescharacteristic
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—22no—
278C22×D61—48no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—48no—
286C22×D61—84no—
287C22×D61—84no—
288C22×D61—84no—
289C22×D61—84no—
290C22×D61—84no—
291C22×D61C4×D412yes—
292C22×D61C2×D812yes—
293C22×D61#13512yes—
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—22no—
297D4×C61—22no—
298D4×C61—22no—
299D4×C61—41no—
300D4×C61—41no—
301D4×C61C4×D414yescomplemented
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—22no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—84no—
314C2×C4×C61—84no—
315C2×C4×C61C2×D812yes—
316C2×C4×C61C23×C411yescharacteristic
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C2×#4111yescharacteristic
319C2×C4×C61C2×#4111yescharacteristic
320C2×C4×C61H(5,𝔽2)11yescharacteristic
321C2×C4×C61H(5,𝔽2)11yescharacteristic
322C22⋊D61—48no—
323C22⋊D61—48no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—22no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—84no—
341C2×Dic61C4×D412yes—
342C2×Dic61C2×D812yes—
343D244—22no—
344D244—22no—
345D244—41no—
346D244—41no—
347C4×D61—22no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—84no—
352C8×C61—22no—
353C8×C61—22no—
354#92418—22no—
355#92418—41no—
356#22870—611nomaximal, Sylow
357C22×C61—24no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61—81no—
368C22×C61—81no—
369C22×C61—81no—
370C22×C61—81no—
371C22×C61C2×C4×D411yescharacteristic
372C22×C61D4211yescharacteristic
373C22×C61#54611yescharacteristic
374C22×C61C22×D811yescharacteristic
375C22×C61C2×#13511yescharacteristic
376C22×C61#57611yescharacteristic
377C22×C61#57711yescharacteristic
378C2×D61—22no—
379C2×D61—22no—
380C2×D61—22no—
381C2×D61—22no—
382C2×D61—22no—
383C2×D61—22no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—816no—
388C2×D61—81no—
389C2×D61—81no—
390C2×D61—81no—
391C2×D61—81no—
392C2×D61C4×D814yescomplemented
393C4×C61—22no—
394C4×C61—42no—
395C4×C61—41no—
396C4×C61—81no—
397C4×C61C2×C4×D411yescharacteristic
398C4×C61#51811yescharacteristic
399C4×C61#54611yescharacteristic
400C4×C61#55111yescharacteristic
401Dic61—22no—
402Dic61—22no—
403Dic61—42no—
404Dic61—41no—
405Dic61—81no—
406Dic61—81no—
407C2×#447—611no—
408C2×C4×D8D6111yescharacteristic, complemented
409C22×#102—611no—
410#2361—611no—
411D4×C22⋊C4—611no—
412#1970—611no—
413#1934—611no—
414#1925—611no—
415#1893—611no—
416#1879—611no—
417#1879—611no—
418#1862—611no—
419#1852—611no—
420C4×#102—611no—
421C8×C22⋊C4—611no—
422C2×C61—44no—
423C2×C61—82no—
424C2×C61#235811yescharacteristic
425C2×C61C2×C4×D811yescharacteristic
426C2×C61#294611yescharacteristic
427C2×C61D4×D811yescharacteristic
428C2×C61#328211yescharacteristic
429C2×C61#329411yescharacteristic
430C2×C61#329711yescharacteristic
431D61—24no—
432D61—82no—
433C23×D4—611no—
434C22×D8—611no—
435C22×D8C2×D6111yescharacteristic
436C23×C8—611no—
437C2×#121—611no—
438C2×C4×D4—611no—
439C2×C4×D4—1221no—
440C2×C4×D4C2×D6111yescharacteristic
441C2×C4×D4C2×D6111yescharacteristic, complemented
442C22×C4⋊C4—611no—
443C22×C22⋊C4—1221no—
444#447—618no—
445C4×D8—24no—
446C2×#107—611no—
447C2×#107C2×D6111yescharacteristic, complemented
448C2×#102—611no—
449C2×#102—611no—
450C2×#102—611no—
451C2×#102—611no—
452C2×#102—611no—
453C2×#102—611no—
454C2×#102—1224no—
455C2×#102C2×D6111yescharacteristic
456C2×#102C2×D6111yescharacteristic, complemented
457C2×C22⋊C8—611no—
458C2×C4×C8—611no—
459C2×C4×C8C2×D6111yescharacteristic, complemented
460#390—611no—
461#390—611no—
462#390—611no—
463#389—611no—
464#388—1221no—
465#386—1221no—
466#386—1221no—
467#386—1221no—
468#385—1221no—
469#380—611no—
470#379—1221no—
471C4×C4⋊C4—611no—
472C4×C22⋊C4—611no—
473#340—611no—
474#340—611no—
475#340—611no—
476#340—611no—
477#336—611no—
478#336—611no—
479C61#2287011yescharacteristic, complemented, Sylow
480C25—1221no—
481C22×D4—614no—
482C22×D4—611no—
483C22×D4—1222no—
484C22×D4—1221no—
485C22×D4—1222no—
486C22×D4—1222no—
487C22×D4—1221no—
488C22×D4—2441no—
489C22×D4—2441no—
490C22×D4C22×D6111yescharacteristic
491C22×D4C22×D6111yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—611no—
495C23×C4—1221no—
496C23×C4—1221no—
497C2×D8—22no—
498C2×D8—22no—
499C2×D8—614no—
500C2×D8—2441no—
501C2×D8—2441no—
502C2×D8C4×D6114yescomplemented
503C22×C8—611no—
504C22×C8—611no—
505C22×C8—1222no—
506C22×C8—1222no—
507C22×C8—2441no—
508C22×C8C22×D6111yescharacteristic
509C22×C8C22×D6111yescharacteristic
510#121—614no—
511#121—1222no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—41no—
515C4×D4—41no—
516C4×D4—1222no—
517C4×D4—2441no—
518C4×D4—2444no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—1222no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—2441no—
526C2×C4⋊C4C22×D6111yescharacteristic
527C2×C4⋊C4C22×D6111yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—611no—
531C2×C22⋊C4—611no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—2444no—
542C2×C42—611no—
543C2×C42—1221no—
544C2×C42C22×D6111yescharacteristic
545#107—22no—
546#107—2441no—
547#102—22no—
548#102—614no—
549#102—614no—
550#102—1222no—
551#102—1222no—
552#102—1222no—
553#102—2441no—
554#102C22⋊D6114yescomplemented
555C22⋊C8—614no—
556C4×C8—22no—
557C4×C8—2441no—
558#95—611no—
559#95—611no—
560#95—1221no—
561#95—1221no—
562#95—1221no—
563C24—21no—
564C24—21no—
565C24—611no—
566C24—1224no—
567C24—1221no—
568C24—4881no—
569C24—4881no—
570C24—2442no—
571C24—2442no—
572C24—2442no—
573C24—2442no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—612no—
583C2×D4—1224no—
584C2×D4—1228no—
585C2×D4—1224no—
586C2×D4—1221no—
587C2×D4—1221no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4—1221no—
591C2×D4—2444no—
592C2×D4—2444no—
593C2×D4—2444no—
594C2×D4—2442no—
595C2×D4—2442no—
596C2×D4—2442no—
597C2×D4—2442no—
598C2×D4C2×C4×D6112yes—
599C2×D4C2×C4×D6112yes—
600C2×D4#1175822212yes—
601C2×D4C2×C22⋊D6112yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—81no—
609C22×C4—81no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—612no—
613C22×C4—612no—
614C22×C4—611no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—4881no—
623C22×C4—4881no—
624C22×C4—2442no—
625C22×C4—2442no—
626C22×C4—2442no—
627C22×C4—2442no—
628C22×C4D4×D6111yescharacteristic
629C22×C4D4×D6111yescharacteristic
630C22×C4C23×D6111yescharacteristic
631D8—28no—
632D8—2444no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—612no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8—2444no—
644C2×C8C2×C4×D6112yes—
645C2×C8C2×C22⋊D6112yes—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—612no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—2442no—
656C4⋊C4—2442no—
657C4⋊C4C2×C22⋊D6112yes—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—614no—
661C22⋊C4—1222no—
662C22⋊C4—1224no—
663C22⋊C4—4881no—
664C22⋊C4—4881no—
665C22⋊C4—4881no—
666C22⋊C4—2442no—
667C22⋊C4—2442no—
668C22⋊C4—2442no—
669C22⋊C4—2442no—
670C22⋊C4—2442no—
671C42—21no—
672C42—21no—
673C42—1221no—
674C42—1221no—
675C42—2442no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—612no—
691C23—612no—
692C23—612no—
693C23—1221no—
694C23—1221no—
695C23—1221no—
696C23—1221no—
697C23—1222no—
698C23—4884no—
699C23—4884no—
700C23—4884no—
701C23—4884no—
702C23—4884no—
703C23—2448no—
704C23—2448no—
705C23—2441no—
706C23—2441no—
707C23—2441no—
708C23—2441no—
709C23—2441no—
710C23—2441no—
711C23C2×D4×D6111yescharacteristic
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—41no—
718D4—41no—
719D4—1222no—
720D4—1222no—
721D4—2448no—
722D4—2448no—
723D4—2441no—
724D4—2441no—
725D4C4×C22⋊D6114yescomplemented
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—84no—
738C2×C4—84no—
739C2×C4—612no—
740C2×C4—612no—
741C2×C4—1221no—
742C2×C4—1221no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—1221no—
753C2×C4—4884no—
754C2×C4—4884no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4D8×D6112yes—
764C2×C4C22×C4×D6111yescharacteristic
765C2×C4C22×C22⋊D6111yescharacteristic
766C2×C4#41×D6111yescharacteristic
767C2×C4C2×#1175822211yescharacteristic
768C2×C4#1451982211yescharacteristic
769C2×C4#1451982311yescharacteristic
770C8—22no—
771C8—22no—
772C8—1222no—
773C8—2441no—
774C22—24no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—614no—
789C22—1222no—
790C22—1222no—
791C22—1222no—
792C22—1222no—
793C22—1222no—
794C22—1222no—
795C22—48816no—
796C22—4881no—
797C22—4881no—
798C22—4881no—
799C22—4881no—
800C22—2442no—
801C22—2442no—
802C22—2442no—
803C22C4×D4×D6111yescharacteristic
804C22D4×C22⋊D6111yescharacteristic
805C22#1684040811yescharacteristic
806C22C2×D8×D6111yescharacteristic
807C22#135×D6111yescharacteristic
808C22#1684056311yescharacteristic
809C22#1684056911yescharacteristic
810C4—22no—
811C4—42no—
812C4—41no—
813C4—81no—
814C4—1222no—
815C4—1222no—
816C4—4881no—
817C4—4881no—
818C4—2441no—
819C4—2442no—
820C4C2×C4×C22⋊D6111yescharacteristic
821C4#1684023411yescharacteristic
822C4#1684040011yescharacteristic
823C4#1684044111yescharacteristic
824C2—44no—
825C2—82no—
826C2—1224no—
827C2—4882no—
828C2#2144879611yescharacteristic
829C2C4×D8×D6111yescharacteristic
830C2#2145464411yescharacteristic
831C2D8×C22⋊D6111yescharacteristic
832C2#2145752011yescharacteristic
833C2#2145763411yescharacteristic
834C2#2145767411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C4×D8×C61C2
socleC23×C61C22×D4
prime radicalC2×#16839894C2
cosocleC22×C4×C61C24
hypercenterC2×C4×D8D61
hypocenterC61#22870
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
2. C2×#102×D61C2semidirect
3. #21448831C2semidirect
4. D4×#11758198C2semidirect
5. #21446682C2semidirect
6. #21446502C2semidirect
7. #21446438C2semidirect
8. #21446244C2semidirect
9. #21446169C2semidirect
10. #21446167C2semidirect
11. #21446066C2semidirect
12. #21446005C2semidirect
13. #102×Dic61C2semidirect
14. C8×#11758198C2semidirect
15. C2×C4×D8×C61C2semidirect
24. #16839894C4semidirect
25. C2×#14519710C22semidirect
30. C2×#14519698C22semidirect
34. C2×C8×Dic61C22semidirect
35. #16839665C22semidirect
38. #16839660C22semidirect
46. C4⋊C4×Dic61C22semidirect
48. #16839525C22semidirect
49. #16839525C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839517C22semidirect
53. #16839516C22semidirect
56. C2×C4×D4×C61C22semidirect
58. C2×#107×C61C22semidirect
60. C2×#102×C61C22semidirect
61. C2×C4×C8×C61C22semidirect
71. C2×D4×D61C2×C4semidirect
77. C2×#11758199C2×C4semidirect
84. #14519748C2×C4semidirect
111. #14519699C2×C4semidirect
114. #14519698C2×C4semidirect
116. #14519689C2×C4semidirect
129. C2×D8×C61C2×C4semidirect
143. #102×C61D4semidirect
239. #11758198D8semidirect
301. D4×C61C4×D4semidirect
392. C2×D61C4×D8semidirect
408. C2×C4×D8D61semidirect
441. C2×C4×D4C2×D61semidirect
447. C2×#107C2×D61semidirect
456. C2×#102C2×D61semidirect
459. C2×C4×C8C2×D61semidirect
479. C61#22870semidirect
502. C2×D8C4×D61semidirect
554. #102C22⋊D61semidirect
725. D4C4×C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398942
C2×#102×D612
#214488312
D4×#117581982
#214466822
#214465022
#214464382
#214462442
#214461692
#214461672
#214460662
#214460052
#102×Dic612
C8×#117581982
C2×C4×D8×C612
#2287061