Finite Group Databasebeta

← #29700330

Subgroups — #29700330

Order 15616.

1386 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×#16839896C211yesmaximal, characteristic
2C2×#16839871C211yesmaximal, characteristic, complemented
3#21448835C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic61C211yesmaximal, characteristic, complemented
5#21446692C211yesmaximal, characteristic, complemented
6#21446513C211yesmaximal, characteristic, complemented
7#21446449C211yesmaximal, characteristic, complemented
8#21446247C211yesmaximal, characteristic, complemented
9#21446165C211yesmaximal, characteristic, complemented
10#21446164C211yesmaximal, characteristic, complemented
11#21446078C211yesmaximal, characteristic, complemented
12#21446012C211yesmaximal, characteristic, complemented
13#21445646C211yesmaximal, characteristic, complemented
14#21445595C211yesmaximal, characteristic, complemented
15C22×#102×C61C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic
20C2×D4×Dic61C2211yescharacteristic
21C2×#14519739C2211yescharacteristic, complemented
22C2×C4×C22⋊D61—21no—
23C22×C22⋊Dic61—21no—
24#16839896C418yescomplemented
25#16839871—24no—
26C2×#14519708C2211yescharacteristic, complemented
27C2×#14519708C2211yescharacteristic, complemented
28C2×#14519699C2211yescharacteristic, complemented
29C2×#14519699C2211yescharacteristic, complemented
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33C2×#14519687C2211yescharacteristic, complemented
34C2×#14519687C2211yescharacteristic, complemented
35#16839665C2211yescharacteristic
36#16839665C2211yescharacteristic
37#16839663C2211yescharacteristic, complemented
38#16839658C2211yescharacteristic, complemented
39#16839652—21no—
40#16839642—21no—
41#16839642—21no—
42#16839641—21no—
43#16839633—21no—
44#16839622C2211yescharacteristic
45#16839618—21no—
46C4⋊C4×Dic61C2211yescharacteristic, complemented
47C4×C22⋊Dic61C2211yescharacteristic
48#16839525C2211yescharacteristic, complemented
49#16839525C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53#16839516C2211yescharacteristic, complemented
54C23×D4×C61C2211yescharacteristic
55C23×C8×C61C2211yescharacteristic
56C22×C4⋊C4×C61C2211yescharacteristic
57C2×#102×C61—24no—
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C23×Dic61—21no—
65C23×Dic61—21no—
66C22×C4×D61—21no—
67C2×#11758199—22no—
68C2×#11758199—22no—
69C2×#11758199—41no—
70C2×#11758199—41no—
71C2×#11758199C2×C414yescomplemented
72C2×#11758199C2×C414yescomplemented
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75#14519751—22no—
76#14519751C2×C414yescomplemented
77D4×Dic61—22no—
78D4×Dic61—22no—
79D4×Dic61—41no—
80D4×Dic61—41no—
81#14519739—22no—
82#14519739—41no—
83C4×C22⋊D61—44no—
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×#11758196—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—44no—
96C2×C22⋊Dic61D411yescharacteristic
97C2×C22⋊Dic61D411yescharacteristic
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61C2311yescharacteristic
104C2×C4×Dic61C2311yescharacteristic
105#14519708—22no—
106#14519708—41no—
107#14519699—22no—
108#14519699—41no—
109#14519698C2×C414yescomplemented
110#14519698C2×C414yescomplemented
111C22⋊#92418C2×C414yescomplemented
112#14519687—22no—
113#14519687—41no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684D411yescharacteristic
118#14519684D411yescharacteristic
119C25×C61—21no—
120C22×D4×C61—22no—
121C22×D4×C61—22no—
122C22×D4×C61—21no—
123C22×D4×C61—22no—
124C22×D4×C61—41no—
125C22×D4×C61—41no—
126C22×D4×C61C2×C414yescomplemented
127C22×D4×C61C2311yescharacteristic
128C22×D4×C61C2311yescharacteristic
129C23×C4×C61—21no—
130C23×C4×C61C2311yescharacteristic
131C22×C8×C61—22no—
132C22×C8×C61—22no—
133C22×C8×C61—41no—
134C22×C8×C61C2311yescharacteristic
135C22×C8×C61C2311yescharacteristic
136C2×C4⋊C4×C61—22no—
137C2×C4⋊C4×C61—21no—
138C2×C4⋊C4×C61—41no—
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61C2311yescharacteristic
141#102×C61—22no—
142#102×C61—22no—
143#102×C61—22no—
144#102×C61D414yescomplemented
145C24×C61—21no—
146C24×C61—21no—
147C24×C61—24no—
148C24×C61—42no—
149C24×C61—42no—
150C24×C61—42no—
151C24×C61—42no—
152C24×C61—81no—
153C24×C61—81no—
154C24×C61C2×D411yescharacteristic
155C23×D61—21no—
156C2×D4×C61—28no—
157C2×D4×C61—24no—
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×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—44no—
167C2×D4×C61—44no—
168C2×D4×C61—44no—
169C2×D4×C61—42no—
170C2×D4×C61—42no—
171C2×D4×C61C22×C412yes—
172C2×D4×C61C22×C412yes—
173C2×D4×C61C2×D412yes—
174C2×D4×C61#4112yes—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—42no—
182C22×C4×C61—42no—
183C22×C4×C61—81no—
184C22×C4×C61C22×C412yes—
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61#4112yes—
187C22×C4×C61C2411yescharacteristic
188C2×C22⋊D61—24no—
189C2×C22⋊D61—42no—
190C2×C22⋊D61—42no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—42no—
195C22×Dic61—42no—
196C22×Dic61—42no—
197C22×Dic61—42no—
198C22×Dic61—81no—
199C22×Dic61—81no—
200C22×Dic61C2×D411yescharacteristic
201C22×Dic61C2×D411yescharacteristic
202C22×Dic61C2×D411yescharacteristic
203C22×Dic61C2×D411yescharacteristic
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244C22×C412yes—
210C2×C4×D61—42no—
211C2×C4×D61—42no—
212C2×C4×D61—81no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61—44no—
219C2×C8×C61C2×D412yes—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—42no—
224C4⋊C4×C61C2×D412yes—
225C22⋊Dic61—22no—
226C22⋊Dic61—22no—
227C22⋊Dic61—42no—
228C22⋊Dic61—42no—
229C22⋊Dic61—42no—
230C22⋊Dic61—42no—
231C22⋊Dic61—42no—
232C22⋊Dic61—81no—
233C22⋊Dic61—81no—
234#11758199—28no—
235#11758199—44no—
236#11758198—24no—
237#11758198—42no—
238#11758198—42no—
239#11758198—81no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242C4⋊Dic61—21no—
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245C4⋊Dic61C22×C412yes—
246#11758196—42no—
247C4×Dic61—21no—
248C4×Dic61—21no—
249C4×Dic61—21no—
250C4×Dic61—21no—
251C4×Dic61—42no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418C22×C412yes—
257C2×#92418C22×C412yes—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—22no—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61—22no—
266C23×C61—48no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—48no—
278C23×C61—84no—
279C23×C61—84no—
280C23×C61—84no—
281C23×C61—84no—
282C23×C61—84no—
283C23×C61C4×D412yes—
284C23×C61AGL(1,ℤ/8)12yes—
285C23×C61AGL(1,ℤ/8)12yes—
286C23×C61C22×D411yescharacteristic
287C22×D61—22no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61—41no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61—41no—
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—22no—
297D4×C61—22no—
298D4×C61—22no—
299D4×C61—48no—
300D4×C61—41no—
301D4×C61—41no—
302D4×C61C4×D414yescomplemented
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—84no—
316C2×C4×C61C4×D412yes—
317C2×C4×C61C23×C411yescharacteristic
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C2×#4111yescharacteristic
320C2×C4×C61C2×#4111yescharacteristic
321C2×C4×C61H(5,𝔽2)11yescharacteristic
322C2×C4×C61H(5,𝔽2)11yescharacteristic
323C22⋊D61—48no—
324C2×Dic61—22no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—21no—
334C2×Dic61—21no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—84no—
346C2×Dic61—84no—
347D244—22no—
348D244—22no—
349D244—41no—
350D244—41no—
351C4×D61—84no—
352C8×C61—22no—
353C8×C61—41no—
354#92418—22no—
355#92418—22no—
356#22858—611nomaximal, Sylow
357C22×C61—22no—
358C22×C61—22no—
359C22×C61—22no—
360C22×C61—22no—
361C22×C61—22no—
362C22×C61—22no—
363C22×C61—24no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—42no—
369C22×C61—42no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61—816no—
374C22×C61—81no—
375C22×C61—81no—
376C22×C61—81no—
377C22×C61—81no—
378C22×C61#44214yescomplemented
379C22×C61C2×C4×D411yescharacteristic
380C22×C61D4211yescharacteristic
381C22×C61#54611yescharacteristic
382C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
383C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
384C22×C61#57611yescharacteristic
385C22×C61#57711yescharacteristic
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—81no—
390C2×D61—81no—
391C2×D61—81no—
392C2×D61—81no—
393C4×C61—22no—
394C4×C61—42no—
395C4×C61—81no—
396C4×C61C2×C4×D411yescharacteristic
397C4×C61#51811yescharacteristic
398C4×C61#54611yescharacteristic
399C4×C61#55111yescharacteristic
400Dic61—42no—
401Dic61—41no—
402Dic61—41no—
403Dic61—41no—
404Dic61—41no—
405Dic61—81no—
406Dic61—81no—
407C2×#447—611no—
408C2×#442—611no—
409C22×#102D6111yescharacteristic, complemented
410#2361—611no—
411D4×C22⋊C4—611no—
412#1972—611no—
413#1936—611no—
414#1926—611no—
415#1893—611no—
416#1879—611no—
417#1879—611no—
418#1864—611no—
419#1853—611no—
420#1762—611no—
421#1752—611no—
422C2×C61—24no—
423C2×C61—44no—
424C2×C61—82no—
425C2×C61#235811yescharacteristic
426C2×C61C2×#44211yescharacteristic
427C2×C61#294611yescharacteristic
428C2×C61#326411yescharacteristic
429C2×C61#326511yescharacteristic
430C2×C61#330611yescharacteristic
431C2×C61#331811yescharacteristic
432D61—82no—
433C23×D4C2×D6111yescharacteristic
434C22×D8—611no—
435C22×D8—611no—
436C23×C8C2×D6111yescharacteristic
437C2×#121—611no—
438C2×C4×D4—611no—
439C2×C4×D4—611no—
440C2×C4×D4—611no—
441C2×C4×D4—1221no—
442C22×C4⋊C4C2×D6111yescharacteristic
443C22×C22⋊C4—1221no—
444#447—618no—
445#442—1224no—
446C2×#106—611no—
447C2×#106—611no—
448C2×#102—24no—
449C2×#102—611no—
450C2×#102—611no—
451C2×#102—611no—
452C2×#102—611no—
453C2×#102C2×D6111yescharacteristic
454C2×#102C2×D6111yescharacteristic
455C2×#102C2×D6111yescharacteristic
456C2×#102C2×D6111yescharacteristic
457C2×C22⋊C8—611no—
458C2×#97—611no—
459C2×#97—611no—
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#2285811yescharacteristic, complemented, Sylow
480C25—21no—
481C22×D4—22no—
482C22×D4—22no—
483C22×D4—21no—
484C22×D4—22no—
485C22×D4—41no—
486C22×D4—41no—
487C22×D4—611no—
488C22×D4—1221no—
489C22×D4C4×D6114yescomplemented
490C22×D4C22×D6111yescharacteristic
491C22×D4C22×D6111yescharacteristic
492C23×C4—21no—
493C23×C4—1221no—
494C23×C4—1221no—
495C23×C4—1221no—
496C23×C4C22×D6111yescharacteristic
497C2×D8—614no—
498C2×D8—614no—
499C2×D8—1222no—
500C2×D8—1222no—
501C2×D8—2441no—
502C2×D8—2441no—
503C22×C8—22no—
504C22×C8—22no—
505C22×C8—41no—
506C22×C8—611no—
507C22×C8—611no—
508C22×C8C22×D6111yescharacteristic
509C22×C8C22×D6111yescharacteristic
510#121—614no—
511#121—1222no—
512C4×D4—1222no—
513C4×D4—1222no—
514C4×D4—1222no—
515C4×D4—2441no—
516C4×D4—2441no—
517C4×D4—2441no—
518C4×D4—2444no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—41no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—611no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4C22×D6111yescharacteristic
527C2×C4⋊C4C22×D6111yescharacteristic
528C2×C22⋊C4—611no—
529C2×C22⋊C4—611no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
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—611no—
544C2×C42—1221no—
545#106—1222no—
546#106—2441no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—614no—
551#102—614no—
552#102—1222no—
553#102—2441no—
554#102C22⋊D6114yescomplemented
555C22⋊C8—614no—
556#97—1222no—
557#97—2441no—
558#95—611no—
559#95—611no—
560#95—1221no—
561#95—1221no—
562#95—1221no—
563C24—21no—
564C24—21no—
565C24—24no—
566C24—42no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—81no—
571C24—81no—
572C24—1221no—
573C24D4×D6111yescharacteristic
574C2×D4—28no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—24no—
584C2×D4—44no—
585C2×D4—44no—
586C2×D4—44no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—612no—
590C2×D4—1224no—
591C2×D4—1221no—
592C2×D4—1221no—
593C2×D4—1221no—
594C2×D4—1221no—
595C2×D4—1221no—
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—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—81no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—4881no—
619C22×C4—4881no—
620C22×C4—4881no—
621C22×C4—2442no—
622C22×C4—2442no—
623C22×C4—2442no—
624C22×C4—2442no—
625C22×C4—2442no—
626C22×C4—2442no—
627C22×C4C2×C4×D6112yes—
628C22×C4D4×D6111yescharacteristic
629C22×C4#1175822412yes—
630C22×C4C23×D6111yescharacteristic
631D8—1228no—
632D8—2444no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—44no—
639C2×C8—612no—
640C2×C8—612no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8—1221no—
644C2×C8—1221no—
645C2×C8C2×C22⋊D6112yes—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—42no—
650C4⋊C4—612no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1221no—
656C4⋊C4—2442no—
657C4⋊C4C2×C22⋊D6112yes—
658C22⋊C4—1222no—
659C22⋊C4—1222no—
660C22⋊C4—1224no—
661C22⋊C4—4881no—
662C22⋊C4—4881no—
663C22⋊C4—4881no—
664C22⋊C4—2442no—
665C22⋊C4—2442no—
666C22⋊C4—2442no—
667C22⋊C4—2442no—
668C22⋊C4—2442no—
669C22⋊C4—2442no—
670C22⋊C4—2442no—
671C42—1221no—
672C42—1221no—
673C42—1221no—
674C42—1221no—
675C42—2442no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—48no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—48no—
694C23—41no—
695C23—41no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—1222no—
702C23—2441no—
703C23—2441no—
704C23—2441no—
705C23—2441no—
706C23—2441no—
707C23—2441no—
708C23#1451973712yes—
709C23#1451980112yes—
710C23#1451980412yes—
711C23C2×D4×D6111yescharacteristic
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—48no—
718D4—41no—
719D4—41no—
720D4—1222no—
721D4—1222no—
722D4—2448no—
723D4—2441no—
724D4—2441no—
725D4C4×C22⋊D6114yescomplemented
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—84no—
739C2×C4—1222no—
740C2×C4—1221no—
741C2×C4—1221no—
742C2×C4—1221no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1221no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—1221no—
749C2×C4—1221no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—4884no—
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×C4#1451973712yes—
764C2×C4C22×C4×D6111yescharacteristic
765C2×C4C22×C22⋊D6111yescharacteristic
766C2×C4C2×#1175822411yescharacteristic
767C2×C4C2×#1175822211yescharacteristic
768C2×C4#1451982211yescharacteristic
769C2×C4#1451982211yescharacteristic
770C8—22no—
771C8—41no—
772C8—1222no—
773C8—1222no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—24no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—816no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—4881no—
796C22—4881no—
797C22—4881no—
798C22—4881no—
799C22—2442no—
800C22—2442no—
801C22—2442no—
802C22#1683987114yescomplemented
803C22C2×#1451973711yescharacteristic
804C22D4×C22⋊D6111yescharacteristic
805C22#1684040211yescharacteristic
806C22C2×#1451980111yescharacteristic
807C22C2×#1451980411yescharacteristic
808C22#1684056311yescharacteristic
809C22#1684056811yescharacteristic
810C4—22no—
811C4—42no—
812C4—81no—
813C4—4881no—
814C4—4881no—
815C4—2442no—
816C4—2441no—
817C4—2441no—
818C4—2441no—
819C4—2441no—
820C4C2×C4×C22⋊D6111yescharacteristic
821C4#1684023511yescharacteristic
822C4#1684040611yescharacteristic
823C4#1684043811yescharacteristic
824C2—24no—
825C2—44no—
826C2—82no—
827C2—4882no—
828C2#2144879811yescharacteristic
829C2C2×#1683987111yescharacteristic
830C2#2145464511yescharacteristic
831C2#2145729911yescharacteristic
832C2#2145731411yescharacteristic
833C2#2145777611yescharacteristic
834C2#2145795611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC22×#102×C61C2
socleC23×C61C22×D4
prime radicalC2×#16839896C2
cosocleC22×C4×C61C24
hypercenterC22×#102D61
hypocenterC61#22858
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C2×#16839871C2semidirect
3. #21448835C2semidirect
4. D4×C22⋊Dic61C2semidirect
5. #21446692C2semidirect
6. #21446513C2semidirect
7. #21446449C2semidirect
8. #21446247C2semidirect
9. #21446165C2semidirect
10. #21446164C2semidirect
11. #21446078C2semidirect
12. #21446012C2semidirect
13. #21445646C2semidirect
14. #21445595C2semidirect
15. C22×#102×C61C2semidirect
21. C2×#14519739C22semidirect
24. #16839896C4semidirect
26. C2×#14519708C22semidirect
27. C2×#14519708C22semidirect
28. C2×#14519699C22semidirect
29. C2×#14519699C22semidirect
33. C2×#14519687C22semidirect
34. C2×#14519687C22semidirect
37. #16839663C22semidirect
38. #16839658C22semidirect
46. C4⋊C4×Dic61C22semidirect
48. #16839525C22semidirect
49. #16839525C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839516C22semidirect
53. #16839516C22semidirect
71. C2×#11758199C2×C4semidirect
72. C2×#11758199C2×C4semidirect
76. #14519751C2×C4semidirect
109. #14519698C2×C4semidirect
110. #14519698C2×C4semidirect
111. C22⋊#92418C2×C4semidirect
126. C22×D4×C61C2×C4semidirect
144. #102×C61D4semidirect
302. D4×C61C4×D4semidirect
378. C22×C61#442semidirect
409. C22×#102D61semidirect
479. C61#22858semidirect
489. C22×D4C4×D61semidirect
554. #102C22⋊D61semidirect
725. D4C4×C22⋊D61semidirect
802. C22#16839871semidirect

Maximal subgroups

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

subgroupindex
C2×#168398962
C2×#168398712
#214488352
D4×C22⋊Dic612
#214466922
#214465132
#214464492
#214462472
#214461652
#214461642
#214460782
#214460122
#214456462
#214455952
C22×#102×C612
#2285861