Finite Group Databasebeta

← #29700334

Subgroups — #29700334

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×#16839874C211yesmaximal, characteristic, complemented
2C22×#14519698C211yesmaximal, characteristic, complemented
3#21448839C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic61C211yesmaximal, characteristic, complemented
5#21446696C211yesmaximal, characteristic, complemented
6#21446518C211yesmaximal, characteristic, complemented
7#21446448C211yesmaximal, characteristic, complemented
8#21446248C211yesmaximal, characteristic, complemented
9#21446169C211yesmaximal, characteristic, complemented
10#21446169C211yesmaximal, characteristic, complemented
11#21446082C211yesmaximal, characteristic, complemented
12#21446014C211yesmaximal, characteristic, complemented
13#21445646C211yesmaximal, characteristic, complemented
14#21445598C211yesmaximal, characteristic, complemented
15C2×C61×#447C211yesmaximal, characteristic
16C23×#92418C2211yescharacteristic
17C2×D4×Dic61—21no—
18C2×D4×Dic61C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic
20C2×D4×Dic61C2211yescharacteristic, complemented
21C22×C4⋊Dic61C2211yescharacteristic
22C22×C22⋊Dic61—21no—
23#16839874—24no—
24C2×#14519709C2211yescharacteristic, complemented
25C2×#14519709C2211yescharacteristic, complemented
26C2×#14519698—24no—
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic, complemented
32C2×#14519698C2211yescharacteristic, complemented
33C2×#14519687C2211yescharacteristic, complemented
34C2×#14519687C2211yescharacteristic, complemented
35#16839665C2211yescharacteristic
36#16839665C2211yescharacteristic
37#16839665C2211yescharacteristic, complemented
38#16839661C2211yescharacteristic, complemented
39#16839655—21no—
40#16839642—21no—
41#16839642—21no—
42#16839642—21no—
43#16839637—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
55C22×D8×C61C2211yescharacteristic
56C22×D8×C61C2211yescharacteristic
57C2×#121×C61C2211yescharacteristic
58C61×#447C418yescomplemented
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C23×Dic61—21no—
63C23×Dic61—21no—
64C23×Dic61—21no—
65C23×Dic61—21no—
66C22×#92418—22no—
67C22×#92418—22no—
68C22×#92418—41no—
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71D4×Dic61—22no—
72D4×Dic61—22no—
73D4×Dic61—22no—
74D4×Dic61—41no—
75D4×Dic61—41no—
76D4×Dic61—41no—
77D4×Dic61—44no—
78C2×C4⋊Dic61—22no—
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61—21no—
81C2×C4⋊Dic61—41no—
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—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—21no—
96C2×C22⋊Dic61—44no—
97C2×C22⋊Dic61D411yescharacteristic
98C2×C22⋊Dic61D411yescharacteristic
99C2×C4×Dic61—21no—
100C2×C4×Dic61C2311yescharacteristic
101C2×C4×Dic61C2311yescharacteristic
102#14519709—22no—
103#14519709—41no—
104#14519698—22no—
105#14519698—22no—
106#14519698—22no—
107#14519698—22no—
108#14519698—41no—
109#14519698D414yescomplemented
110#14519687—22no—
111#14519687—41no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684D411yescharacteristic
116#14519684D411yescharacteristic
117C25×C61—21no—
118C22×D4×C61—22no—
119C22×D4×C61—22no—
120C22×D4×C61—21no—
121C22×D4×C61—21no—
122C22×D4×C61—22no—
123C22×D4×C61—41no—
124C22×D4×C61—41no—
125C22×D4×C61C2×C414yescomplemented
126C22×D4×C61C2311yescharacteristic
127C22×D4×C61C2311yescharacteristic
128C22×D4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C2×D8×C61—22no—
131C2×D8×C61—22no—
132C2×D8×C61—41no—
133C2×D8×C61—41no—
134C2×D8×C61C2×C414yescomplemented
135C2×D8×C61C2×C414yescomplemented
136C22×C8×C61C2311yescharacteristic
137C22×C8×C61C2311yescharacteristic
138#121×C61—22no—
139#121×C61C2×C414yescomplemented
140C2×C4⋊C4×C61C2311yescharacteristic
141C2×C22⋊C4×C61—21no—
142#102×C61C2×C414yescomplemented
143#102×C61C2×C414yescomplemented
144C22⋊C8×C61C2×C414yescomplemented
145C24×C61—21no—
146C24×C61—21no—
147C24×C61—21no—
148C24×C61—24no—
149C24×C61—42no—
150C24×C61—42no—
151C24×C61—42no—
152C24×C61—42no—
153C24×C61—81no—
154C24×C61—81no—
155C24×C61C2×D411yescharacteristic
156C2×D4×C61—28no—
157C2×D4×C61—24no—
158C2×D4×C61—24no—
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—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—44no—
173C2×D4×C61—44no—
174C2×D4×C61—44no—
175C2×D4×C61—42no—
176C2×D4×C61—42no—
177C2×D4×C61—42no—
178C2×D4×C61—42no—
179C2×D4×C61C22×C412yes—
180C2×D4×C61C22×C412yes—
181C2×D4×C61C22×C412yes—
182C2×D4×C61C2×D412yes—
183C2×D4×C61#4112yes—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61C22×C412yes—
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61#4112yes—
192C22×C4×C61C2411yescharacteristic
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—42no—
198C22×Dic61—42no—
199C22×Dic61—42no—
200C22×Dic61—42no—
201C22×Dic61—42no—
202C22×Dic61—42no—
203C22×Dic61—42no—
204C22×Dic61—42no—
205C22×Dic61—81no—
206C22×Dic61—81no—
207C22×Dic61—81no—
208C22×Dic61—81no—
209C22×Dic61C2×D411yescharacteristic
210C22×Dic61C2×D411yescharacteristic
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213D8×C61—28no—
214D8×C61—44no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61—21no—
219C2×C8×C61C22×C412yes—
220C2×C8×C61C22×C412yes—
221C4⋊C4×C61—21no—
222C4⋊C4×C61C22×C412yes—
223C22⋊C4×C61—24no—
224C22⋊Dic61—22no—
225C22⋊Dic61—22no—
226C22⋊Dic61—42no—
227C22⋊Dic61—42no—
228C22⋊Dic61—42no—
229C22⋊Dic61—42no—
230C22⋊Dic61—42no—
231C22⋊Dic61—42no—
232C22⋊Dic61—42no—
233C22⋊Dic61—81no—
234C22⋊Dic61—81no—
235C22⋊Dic61—81no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242C4⋊Dic61—21no—
243C4⋊Dic61—42no—
244C4⋊Dic61—42no—
245C4⋊Dic61C2×D412yes—
246C4×Dic61—21no—
247C4×Dic61—21no—
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×#92418—44no—
257C2×#92418C2×D412yes—
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—22no—
267C23×C61—48no—
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—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—48no—
285C23×C61—84no—
286C23×C61—84no—
287C23×C61—84no—
288C23×C61—84no—
289C23×C61—84no—
290C23×C61C4×D412yes—
291C23×C61AGL(1,ℤ/8)12yes—
292C23×C61AGL(1,ℤ/8)12yes—
293C23×C61C22×D411yescharacteristic
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—22no—
297D4×C61—22no—
298D4×C61—22no—
299D4×C61—22no—
300D4×C61—22no—
301D4×C61—48no—
302D4×C61—48no—
303D4×C61—41no—
304D4×C61—41no—
305D4×C61—41no—
306D4×C61—41no—
307D4×C61C4×D414yescomplemented
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61C4×D412yes—
318C2×C4×C61C23×C411yescharacteristic
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C2×#4111yescharacteristic
321C2×C4×C61C2×#4111yescharacteristic
322C2×C4×C61H(5,𝔽2)11yescharacteristic
323C2×C4×C61H(5,𝔽2)11yescharacteristic
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—22no—
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—41no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—84no—
349C2×Dic61—84no—
350C2×Dic61—84no—
351C2×Dic61—84no—
352C8×C61—22no—
353C8×C61—22no—
354#92418—22no—
355#92418—41no—
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—42no—
374C22×C61—42no—
375C22×C61—42no—
376C22×C61—816no—
377C22×C61—81no—
378C22×C61—81no—
379C22×C61—81no—
380C22×C61—81no—
381C22×C61—81no—
382C22×C61—81no—
383C22×C61—81no—
384C22×C61—81no—
385C22×C61#44214yescomplemented
386C22×C61C2×C4×D411yescharacteristic
387C22×C61D4211yescharacteristic
388C22×C61#54611yescharacteristic
389C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
390C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
391C22×C61#57611yescharacteristic
392C22×C61#57711yescharacteristic
393C4×C61—22no—
394C4×C61—42no—
395C4×C61C2×C4×D411yescharacteristic
396C4×C61#51811yescharacteristic
397C4×C61#54611yescharacteristic
398C4×C61#55111yescharacteristic
399Dic61—41no—
400Dic61—42no—
401Dic61—41no—
402Dic61—41no—
403Dic61—41no—
404Dic61—81no—
405Dic61—81no—
406Dic61—81no—
407C2×#447D6111yescharacteristic
408C2×#442—611no—
409C22×#102—611no—
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—82no—
426C2×C61#235811yescharacteristic
427C2×C61C2×#44211yescharacteristic
428C2×C61#294611yescharacteristic
429C2×C61#326411yescharacteristic
430C2×C61#326511yescharacteristic
431C2×C61#330611yescharacteristic
432C2×C61#331811yescharacteristic
433C23×D4C2×D6111yescharacteristic
434C22×D8C2×D6111yescharacteristic
435C22×D8C2×D6111yescharacteristic
436C23×C8—611no—
437C2×#121C2×D6111yescharacteristic
438C2×C4×D4—611no—
439C2×C4×D4—611no—
440C2×C4×D4—611no—
441C2×C4×D4—1221no—
442C22×C4⋊C4—611no—
443C22×C22⋊C4—1221no—
444#447Dic6118yescomplemented
445#442—1224no—
446C2×#106—611no—
447C2×#106—611no—
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
457C2×C22⋊C8C2×D6111yescharacteristic
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—21no—
485C22×D4—22no—
486C22×D4—41no—
487C22×D4—41no—
488C22×D4C2×Dic6114yescomplemented
489C22×D4C22×D6111yescharacteristic
490C22×D4C22×D6111yescharacteristic
491C22×D4C22×D6111yescharacteristic
492C23×C4—1221no—
493C23×C4—1221no—
494C23×C4—1221no—
495C23×C4—1221no—
496C23×C4C22×D6111yescharacteristic
497C2×D8—22no—
498C2×D8—22no—
499C2×D8—41no—
500C2×D8—41no—
501C2×D8C2×Dic6114yescomplemented
502C2×D8C2×Dic6114yescomplemented
503C22×C8—611no—
504C22×C8—611no—
505C22×C8—1222no—
506C22×C8—1222no—
507C22×C8—2441no—
508C22×C8C22×D6111yescharacteristic
509C22×C8C22×D6111yescharacteristic
510#121—22no—
511#121C2×Dic6114yescomplemented
512C4×D4—1222no—
513C4×D4—1222no—
514C4×D4—1222no—
515C4×D4—2441no—
516C4×D4—2441no—
517C4×D4—2441no—
518C4×D4—2444no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—1222no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—2441no—
527C2×C4⋊C4C22×D6111yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—611no—
530C2×C22⋊C4—611no—
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—614no—
548#102—1222no—
549#102—1222no—
550#102—1222no—
551#102—1222no—
552#102—2441no—
553#102C2×Dic6114yescomplemented
554#102C2×Dic6114yescomplemented
555C22⋊C8C2×Dic6114yescomplemented
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—21no—
566C24—24no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—42no—
571C24—81no—
572C24—81no—
573C24D4×D6111yescharacteristic
574C2×D4—28no—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—24no—
590C2×D4—44no—
591C2×D4—44no—
592C2×D4—44no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4D4×D6112yes—
598C2×D4#1175822412yes—
599C2×D4C22×Dic6112yes—
600C2×D4C22×Dic6112yes—
601C2×D4C22×Dic6112yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—4881no—
616C22×C4—4881no—
617C22×C4—4881no—
618C22×C4—4881no—
619C22×C4—2442no—
620C22×C4—2442no—
621C22×C4—2442no—
622C22×C4—2442no—
623C22×C4—2442no—
624C22×C4—2442no—
625C22×C4—2442no—
626C22×C4—2442no—
627C22×C4D4×D6111yescharacteristic
628C22×C4#1175822412yes—
629C22×C4C22×Dic6112yes—
630C22×C4C23×D6111yescharacteristic
631D8—28no—
632D8—44no—
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×C8C22×Dic6112yes—
645C2×C8C22×Dic6112yes—
646C4⋊C4—21no—
647C4⋊C4—612no—
648C4⋊C4—1221no—
649C4⋊C4—1221no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—2442no—
656C4⋊C4—2442no—
657C4⋊C4C22×Dic6112yes—
658C22⋊C4—24no—
659C22⋊C4—1222no—
660C22⋊C4—1222no—
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—22no—
685C23—48no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—48no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—84no—
704C23—84no—
705C23—84no—
706C23—84no—
707C23—84no—
708C23D4×Dic6112yes—
709C23#1451980112yes—
710C23#1451980112yes—
711C23C2×D4×D6111yescharacteristic
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—48no—
720D4—48no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4D4×Dic6114yescomplemented
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—1221no—
736C2×C4—1221no—
737C2×C4—1221no—
738C2×C4—1221no—
739C2×C4—1221no—
740C2×C4—1221no—
741C2×C4—1221no—
742C2×C4—1221no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1222no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—4884no—
749C2×C4—4884no—
750C2×C4—4884no—
751C2×C4—4884no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
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×C4D4×Dic6112yes—
764C2×C4C23×Dic6111yescharacteristic
765C2×C4C2×D4×D6111yescharacteristic
766C2×C4C2×#1175822411yescharacteristic
767C2×C4C2×#1175822411yescharacteristic
768C2×C4#1451982211yescharacteristic
769C2×C4#1451982211yescharacteristic
770C8—22no—
771C8—22no—
772C8—1222no—
773C8—2441no—
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—42no—
791C22—42no—
792C22—42no—
793C22—816no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22#1683987414yescomplemented
803C22C2×D4×Dic6111yescharacteristic
804C22#1684039411yescharacteristic
805C22#1684039911yescharacteristic
806C22C2×#1451980111yescharacteristic
807C22C2×#1451980111yescharacteristic
808C22#1684056611yescharacteristic
809C22#1684057211yescharacteristic
810C4—22no—
811C4—42no—
812C4—4881no—
813C4—4881no—
814C4—4881no—
815C4—2441no—
816C4—2441no—
817C4—2441no—
818C4—2442no—
819C4—2441no—
820C4C2×D4×Dic6111yescharacteristic
821C4#1684023711yescharacteristic
822C4#1684039911yescharacteristic
823C4#1684044311yescharacteristic
824C2—24no—
825C2—44no—
826C2—82no—
827C2—82no—
828C2#2144880311yescharacteristic
829C2C2×#1683987411yescharacteristic
830C2#2145465211yescharacteristic
831C2#2145729211yescharacteristic
832C2#2145731811yescharacteristic
833C2#2145778411yescharacteristic
834C2#2145796411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#447C2
socleC23×C61C22×D4
cosocleC22×C4×C61C24
hypercenterC2×#447D61
hypocenterC61#22858
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C2×#16839874C2semidirect
2. C22×#14519698C2semidirect
3. #21448839C2semidirect
4. D4×C22⋊Dic61C2semidirect
5. #21446696C2semidirect
6. #21446518C2semidirect
7. #21446448C2semidirect
8. #21446248C2semidirect
9. #21446169C2semidirect
10. #21446169C2semidirect
11. #21446082C2semidirect
12. #21446014C2semidirect
13. #21445646C2semidirect
14. #21445598C2semidirect
20. C2×D4×Dic61C22semidirect
24. C2×#14519709C22semidirect
25. C2×#14519709C22semidirect
31. C2×#14519698C22semidirect
32. C2×#14519698C22semidirect
33. C2×#14519687C22semidirect
34. C2×#14519687C22semidirect
37. #16839665C22semidirect
38. #16839661C22semidirect
46. C4⋊C4×Dic61C22semidirect
48. #16839525C22semidirect
49. #16839525C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839516C22semidirect
53. #16839516C22semidirect
58. C61×#447C4semidirect
109. #14519698D4semidirect
125. C22×D4×C61C2×C4semidirect
134. C2×D8×C61C2×C4semidirect
135. C2×D8×C61C2×C4semidirect
139. #121×C61C2×C4semidirect
142. #102×C61C2×C4semidirect
143. #102×C61C2×C4semidirect
144. C22⋊C8×C61C2×C4semidirect
307. D4×C61C4×D4semidirect
385. C22×C61#442semidirect
444. #447Dic61semidirect
479. C61#22858semidirect
488. C22×D4C2×Dic61semidirect
501. C2×D8C2×Dic61semidirect
502. C2×D8C2×Dic61semidirect
511. #121C2×Dic61semidirect
553. #102C2×Dic61semidirect
554. #102C2×Dic61semidirect
555. C22⋊C8C2×Dic61semidirect
725. D4D4×Dic61semidirect
802. C22#16839874semidirect

Maximal subgroups

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

subgroupindex
C2×#168398742
C22×#145196982
#214488392
D4×C22⋊Dic612
#214466962
#214465182
#214464482
#214462482
#214461692
#214460822
#214460142
#214456462
#214455982
C2×C61×#4472
#2285861