Finite Group Databasebeta

← #29711159

Subgroups — #29711159

Order 15616.

2240 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519803C211yesmaximal, characteristic, complemented
2C2×#16839905C211yesmaximal, characteristic, complemented
3C2×#16839913C211yesmaximal, characteristic, complemented
4C2×#16839896C211yesmaximal, characteristic, complemented
5#21449164C211yesmaximal, characteristic, complemented
6#21446907C211yesmaximal, characteristic, complemented
7#21446890C211yesmaximal, characteristic, complemented
8#21446822C211yesmaximal, characteristic, complemented
9#21446815C211yesmaximal, characteristic, complemented
10#21446258C211yesmaximal, characteristic, complemented
11#21446167C211yesmaximal, characteristic, complemented
12#21446153C211yesmaximal, characteristic, complemented
13#21446117C211yesmaximal, characteristic, complemented
14#21445750C211yesmaximal, characteristic, complemented
15C2×D42×C61C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic, complemented
17C2×#14519803—24no—
18C2×#14519803—24no—
19C2×#14519803—24no—
20C22×#11758200C2211yescharacteristic
21C22×#11758200C2211yescharacteristic, complemented
22C22×#11758200C2211yescharacteristic, complemented
23C22×#11758199C2211yescharacteristic
24C22×#11758199C2211yescharacteristic, complemented
25C22×#11758199C2211yescharacteristic, complemented
26C22×#11758194C2211yescharacteristic, complemented
27C2×#14519756C2211yescharacteristic, complemented
28C2×#14519751C2211yescharacteristic, complemented
29#16839913—24no—
30#16839905—24no—
31#16839896—24no—
32C2×#14519700C2211yescharacteristic, complemented
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic, complemented
36C2×#14519698C2211yescharacteristic, complemented
37C2×#14519698C2211yescharacteristic, complemented
38C2×#14519698C2211yescharacteristic, complemented
39C2×#14519697C2211yescharacteristic, complemented
40C2×C22⋊#92418C2211yescharacteristic, complemented
41C2×C22⋊#92418C2211yescharacteristic, complemented
42C2×C22⋊#92418C2211yescharacteristic, complemented
43#16839677—21no—
44#16839670—21no—
45#16839668C2211yescharacteristic, complemented
46#16839664C2211yescharacteristic, complemented
47#16839638—21no—
48#16839633—21no—
49#16839622C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839517C2211yescharacteristic, complemented
53#16839517C2211yescharacteristic, complemented
54C23×D4×C61—21no—
55C23×D4×C61C2211yescharacteristic
56C23×D4×C61C2211yescharacteristic
57D42×C61—24no—
58D42×C61—24no—
59C2×#127×C61C2211yescharacteristic
60C2×#121×C61—21no—
61C2×#121×C61C2211yescharacteristic
62C2×#121×C61C2211yescharacteristic
63C2×#120×C61—21no—
64C2×#120×C61—21no—
65C2×C4×D4×C61C2211yescharacteristic
66C2×C4×D4×C61C2211yescharacteristic
67C2×#11758222—22no—
68C2×#11758222—22no—
69C2×#11758222—22no—
70C2×#11758222—22no—
71C2×#11758222—41no—
72C2×#11758222—41no—
73C22×Dic122C2311yescharacteristic
74C22×D244C2311yescharacteristic
75C22×C22⋊D61—21no—
76C22×C22⋊D61—21no—
77C22×C4×D61—21no—
78#14519803—232no—
79C2×#11758200—22no—
80C2×#11758200—22no—
81C2×#11758200—22no—
82C2×#11758200—22no—
83C2×#11758200—22no—
84C2×#11758200—22no—
85C2×#11758200—22no—
86C2×#11758200—41no—
87C2×#11758200D414yescomplemented
88C2×#11758199—22no—
89C2×#11758199—22no—
90C2×#11758199—22no—
91C2×#11758199—22no—
92C2×#11758199—22no—
93C2×#11758199—22no—
94C2×#11758199—22no—
95C2×#11758199—41no—
96C2×#11758199D414yescomplemented
97C2×#11758194—22no—
98C2×#11758194—22no—
99C2×#11758194—22no—
100C22×#92418C2311yescharacteristic
101C22×#92418C2311yescharacteristic
102C22×#92418C2311yescharacteristic
103C22×#92418C2311yescharacteristic
104#14519756—22no—
105#14519756—41no—
106#14519751—22no—
107#14519751—41no—
108C2×C4⋊Dic61C2311yescharacteristic
109C2×C4⋊Dic61C2311yescharacteristic
110C2×#11758196—21no—
111C2×C22⋊Dic61—21no—
112C2×C22⋊Dic61—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116#14519700—22no—
117#14519698—22no—
118#14519698—22no—
119#14519698—22no—
120#14519698—22no—
121#14519698—41no—
122#14519698—41no—
123#14519697—22no—
124C22⋊#92418—22no—
125C22⋊#92418—22no—
126C22⋊#92418—22no—
127#14519684—21no—
128#14519684—21no—
129#14519684—21no—
130C25×C61—21no—
131C25×C61—21no—
132C22×D4×C61—22no—
133C22×D4×C61—22no—
134C22×D4×C61—28no—
135C22×D4×C61—21no—
136C22×D4×C61—21no—
137C22×D4×C61—22no—
138C22×D4×C61—22no—
139C22×D4×C61—22no—
140C22×D4×C61—22no—
141C22×D4×C61—21no—
142C22×D4×C61—22no—
143C22×D4×C61—21no—
144C22×D4×C61—21no—
145C22×D4×C61—21no—
146C22×D4×C61—41no—
147C22×D4×C61—41no—
148C22×D4×C61—41no—
149C22×D4×C61—41no—
150C22×D4×C61—44no—
151C22×D4×C61—44no—
152C22×D4×C61D411yescharacteristic
153C22×D4×C61D414yescomplemented
154C22×D4×C61C2311yescharacteristic
155C22×D4×C61C2311yescharacteristic
156C22×D4×C61C2311yescharacteristic
157C23×C4×C61—21no—
158C23×C4×C61C2311yescharacteristic
159C23×C4×C61C2311yescharacteristic
160#127×C61—22no—
161#127×C61—22no—
162#121×C61—28no—
163#121×C61—22no—
164#121×C61—22no—
165#121×C61—22no—
166#121×C61D414yescomplemented
167#120×C61—28no—
168#120×C61—28no—
169C4×D4×C61—22no—
170C4×D4×C61—22no—
171C4×D4×C61—22no—
172C4×D4×C61—22no—
173C2×C4⋊C4×C61D411yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61—21no—
177C2×C22⋊C4×C61—21no—
178C2×C22⋊C4×C61D411yescharacteristic
179C2×C22⋊C4×C61D411yescharacteristic
180C2×C42×C61C2311yescharacteristic
181C24×C61—21no—
182C24×C61—24no—
183C24×C61—21no—
184C24×C61—21no—
185C24×C61—24no—
186C24×C61—42no—
187C24×C61—42no—
188C24×C61—42no—
189C24×C61—42no—
190C24×C61—42no—
191C24×C61—42no—
192C24×C61—42no—
193C24×C61—42no—
194C24×C61—81no—
195C24×C61—81no—
196C24×C61—81no—
197C24×C61—81no—
198C24×C61C2×D411yescharacteristic
199C24×C61C2×D411yescharacteristic
200C23×D61—21no—
201C2×D4×C61—22no—
202C2×D4×C61—22no—
203C2×D4×C61—28no—
204C2×D4×C61—24no—
205C2×D4×C61—24no—
206C2×D4×C61—24no—
207C2×D4×C61—24no—
208C2×D4×C61—24no—
209C2×D4×C61—24no—
210C2×D4×C61—22no—
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61—21no—
216C2×D4×C61—21no—
217C2×D4×C61—21no—
218C2×D4×C61—21no—
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61—21no—
224C2×D4×C61—44no—
225C2×D4×C61—44no—
226C2×D4×C61—44no—
227C2×D4×C61—42no—
228C2×D4×C61—42no—
229C2×D4×C61—42no—
230C2×D4×C61—42no—
231C2×D4×C61—42no—
232C2×D4×C61—44no—
233C2×D4×C61—44no—
234C2×D4×C61—432no—
235C2×D4×C61—44no—
236C2×D4×C61—42no—
237C2×D4×C61—42no—
238C2×D4×C61—42no—
239C2×D4×C61—42no—
240C2×D4×C61—44no—
241C2×D4×C61—42no—
242C2×D4×C61—81no—
243C2×D4×C61—81no—
244C2×D4×C61C2×D412yes—
245C2×D4×C61C2×D412yes—
246C2×D4×C61C2×D412yes—
247C2×D4×C61C2×D412yes—
248C2×D4×C61C2×D412yes—
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61—21no—
252C22×C4×C61—21no—
253C22×C4×C61—24no—
254C22×C4×C61—21no—
255C22×C4×C61—21no—
256C22×C4×C61—21no—
257C22×C4×C61—21no—
258C22×C4×C61—21no—
259C22×C4×C61—21no—
260C22×C4×C61—21no—
261C22×C4×C61—42no—
262C22×C4×C61—42no—
263C22×C4×C61C2×D411yescharacteristic
264C22×C4×C61C2×D411yescharacteristic
265C22×C4×C61C2×D411yescharacteristic
266C22×C4×C61C2×D412yes—
267C22×C4×C61C2×D412yes—
268C22×C4×C61C2×D411yescharacteristic
269C22×C4×C61C2411yescharacteristic
270C2×C22⋊D61—42no—
271C2×C22⋊D61—42no—
272C2×C22⋊D61—42no—
273C2×C22⋊D61—42no—
274C2×C22⋊D61—42no—
275C2×C22⋊D61—81no—
276C22×Dic61—21no—
277C22×Dic61—21no—
278C22×Dic61—21no—
279#11758222—28no—
280#11758222—44no—
281#11758222—44no—
282#11758222—44no—
283C2×D244—21no—
284C2×D244—21no—
285C2×D244—21no—
286C2×D244—21no—
287C2×D244—21no—
288C2×D244C2×D412yescomplemented
289C2×C4×D61—42no—
290C2×C4×D61—42no—
291C2×C4×D61—42no—
292C2×Dic122—21no—
293C2×Dic122—21no—
294C2×Dic122—21no—
295C2×Dic122—21no—
296C2×Dic122—21no—
297C2×Dic122C2×D412yescomplemented
298C4⋊C4×C61—22no—
299C4⋊C4×C61—21no—
300C4⋊C4×C61C2×D412yes—
301C22⋊C4×C61—24no—
302C22⋊C4×C61—24no—
303C22⋊C4×C61—22no—
304C22⋊C4×C61—24no—
305C22⋊C4×C61—22no—
306C42×C61—21no—
307C42×C61—21no—
308C22⋊Dic61—42no—
309C22⋊Dic61—81no—
310#11758200—28no—
311#11758200—28no—
312#11758200—44no—
313#11758199—28no—
314#11758199—28no—
315#11758199—44no—
316#11758198—42no—
317#11758198—42no—
318#11758198—81no—
319C4⋊Dic61—21no—
320C4⋊Dic61—21no—
321C4⋊Dic61—21no—
322C4⋊Dic61—21no—
323#11758196—42no—
324#11758194—28no—
325C2×#92418—21no—
326C2×#92418—21no—
327C2×#92418—21no—
328C2×#92418—21no—
329C2×#92418—21no—
330C2×#92418—21no—
331C2×#92418—21no—
332C2×#92418—21no—
333C2×#92418—21no—
334C2×#92418—21no—
335C2×#92418C2×D412yescomplemented
336C2×#92418C2×D412yescomplemented
337C23×C61—21no—
338C23×C61—22no—
339C23×C61—21no—
340C23×C61—21no—
341C23×C61—21no—
342C23×C61—21no—
343C23×C61—22no—
344C23×C61—22no—
345C23×C61—21no—
346C23×C61—21no—
347C23×C61—21no—
348C23×C61—21no—
349C23×C61—21no—
350C23×C61—21no—
351C23×C61—21no—
352C23×C61—22no—
353C23×C61—22no—
354C23×C61—48no—
355C23×C61—48no—
356C23×C61—48no—
357C23×C61—48no—
358C23×C61—41no—
359C23×C61—41no—
360C23×C61—41no—
361C23×C61—41no—
362C23×C61—41no—
363C23×C61—41no—
364C23×C61—41no—
365C23×C61—41no—
366C23×C61—41no—
367C23×C61—41no—
368C23×C61—41no—
369C23×C61—41no—
370C23×C61—41no—
371C23×C61—41no—
372C23×C61—41no—
373C23×C61—41no—
374C23×C61—84no—
375C23×C61—84no—
376C23×C61—84no—
377C23×C61—84no—
378C23×C61—84no—
379C23×C61—84no—
380C23×C61—84no—
381C23×C61—84no—
382C23×C61—84no—
383C23×C61—84no—
384C23×C61#12012yes—
385C23×C61AGL(1,ℤ/8)12yescomplemented
386C23×C61C22×D411yescharacteristic
387C22×D61—22no—
388C22×D61—41no—
389C22×D61—41no—
390C22×D61—41no—
391C22×D61—41no—
392C22×D61—41no—
393C22×D61—41no—
394D4×C61—28no—
395D4×C61—22no—
396D4×C61—22no—
397D4×C61—22no—
398D4×C61—22no—
399D4×C61—22no—
400D4×C61—22no—
401D4×C61—22no—
402D4×C61—48no—
403D4×C61—48no—
404D4×C61—48no—
405D4×C61—48no—
406D4×C61—48no—
407D4×C61—41no—
408D4×C61—41no—
409D4×C61—41no—
410D4×C61—41no—
411D4×C61—84no—
412D4×C61#12014yes—
413C2×C4×C61—21no—
414C2×C4×C61—21no—
415C2×C4×C61—21no—
416C2×C4×C61—21no—
417C2×C4×C61—22no—
418C2×C4×C61—22no—
419C2×C4×C61—22no—
420C2×C4×C61—22no—
421C2×C4×C61—21no—
422C2×C4×C61—21no—
423C2×C4×C61—22no—
424C2×C4×C61—21no—
425C2×C4×C61—21no—
426C2×C4×C61—21no—
427C2×C4×C61—21no—
428C2×C4×C61—48no—
429C2×C4×C61—41no—
430C2×C4×C61—41no—
431C2×C4×C61—41no—
432C2×C4×C61—41no—
433C2×C4×C61—41no—
434C2×C4×C61—41no—
435C2×C4×C61#12012yes—
436C2×C4×C61AGL(1,ℤ/8)12yescomplemented
437C2×C4×C61C22×D411yescharacteristic
438C2×C4×C61C22×D411yescharacteristic
439C2×C4×C61C22×D411yescharacteristic
440C2×C4×C61C22×D411yescharacteristic
441C2×C4×C61H(5,𝔽2)11yescharacteristic
442C2×C4×C61H(5,𝔽2)11yescharacteristic
443C22⋊D61—48no—
444C22⋊D61—84no—
445C2×Dic61—22no—
446C2×Dic61—41no—
447C2×Dic61—41no—
448C2×Dic61—41no—
449C2×Dic61—41no—
450C2×Dic61—41no—
451C2×Dic61—41no—
452C2×Dic61—41no—
453C2×Dic61—41no—
454D244—22no—
455D244—22no—
456D244—41no—
457D244—41no—
458C4×D61—48no—
459Dic122—22no—
460Dic122—22no—
461Dic122—41no—
462Dic122—41no—
463#92418—22no—
464#92418—22no—
465#92418—41no—
466#92418—41no—
467#23860—611nomaximal, Sylow
468C22×C61—22no—
469C22×C61—24no—
470C22×C61—22no—
471C22×C61—22no—
472C22×C61—22no—
473C22×C61—22no—
474C22×C61—22no—
475C22×C61—41no—
476C22×C61—42no—
477C22×C61—41no—
478C22×C61—42no—
479C22×C61—41no—
480C22×C61—42no—
481C22×C61—41no—
482C22×C61—42no—
483C22×C61—41no—
484C22×C61—41no—
485C22×C61—42no—
486C22×C61—41no—
487C22×C61—41no—
488C22×C61—42no—
489C22×C61—42no—
490C22×C61—42no—
491C22×C61—42no—
492C22×C61—42no—
493C22×C61—42no—
494C22×C61—42no—
495C22×C61—816no—
496C22×C61—816no—
497C22×C61—81no—
498C22×C61—81no—
499C22×C61—81no—
500C22×C61—81no—
501C22×C61—81no—
502C22×C61—81no—
503C22×C61—81no—
504C22×C61—81no—
505C22×C61C2×#12011yescharacteristic
506C22×C61D4211yescharacteristic
507C22×C61D4211yescharacteristic
508C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
509C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
510C22×C61#57611yescharacteristic
511C22×C61#57711yescharacteristic
512C2×D61—42no—
513C2×D61—42no—
514C2×D61—42no—
515C2×D61—81no—
516C2×D61—81no—
517C2×D61—81no—
518C2×D61—81no—
519C4×C61—22no—
520C4×C61—22no—
521C4×C61—41no—
522C4×C61—42no—
523C4×C61—41no—
524C4×C61C2×#12011yescharacteristic
525C4×C61#53411yescharacteristic
526C4×C61D4211yescharacteristic
527C4×C61D4211yescharacteristic
528Dic61—42no—
529Dic61—81no—
530Dic61—81no—
531C22×AGL(1,ℤ/8)—611no—
532C2×D42D6111yescharacteristic, complemented
533C2×#449—611no—
534C2×#450—611no—
535C2×#447—611no—
536#2407—611no—
537#2014—611no—
538#2011—611no—
539#2000—611no—
540#1999—611no—
541#1895—611no—
542#1879—611no—
543#1877—611no—
544#1870—611no—
545#1786—611no—
546C2×C61—42no—
547C2×C61—42no—
548C2×C61—44no—
549C2×C61—82no—
550C2×C61—82no—
551C2×C61#240311yescharacteristic
552C2×C61#300311yescharacteristic
553C2×C61#301211yescharacteristic
554C2×C61#326411yescharacteristic
555C2×C61#326511yescharacteristic
556C2×C61#327211yescharacteristic
557C2×C61#327411yescharacteristic
558D61—82no—
559C22×#41—611no—
560C23×D4—21no—
561C23×D4C2×D6111yescharacteristic
562C23×D4C2×D6111yescharacteristic
563C2×AGL(1,ℤ/8)—1224no—
564C2×AGL(1,ℤ/8)—1224no—
565C2×AGL(1,ℤ/8)—1224no—
566C22×SD16—611no—
567C22×SD16—611no—
568C22×SD16—611no—
569C22×D8—611no—
570C22×D8—611no—
571C22×D8—611no—
572C22×M16—611no—
573D42—24no—
574D42—24no—
575C2×#127C2×D6111yescharacteristic
576C2×C22⋊Q8—611no—
577C2×#121—21no—
578C2×#121—611no—
579C2×#121C2×D6111yescharacteristic
580C2×#121C2×D6111yescharacteristic
581C2×#120—21no—
582C2×#120—21no—
583C2×C4×D4C2×D6111yescharacteristic
584C2×C4×D4C2×D6111yescharacteristic
585#450—1224no—
586#449—1224no—
587#447—1224no—
588C2×#103—611no—
589C2×#102—611no—
590C2×#102—611no—
591C2×#102—611no—
592C2×#102—611no—
593C2×#102—611no—
594C2×#102—611no—
595C2×#102—611no—
596C2×C22⋊C8—611no—
597C2×C22⋊C8—611no—
598C2×C22⋊C8—611no—
599#394—1221no—
600#392—1221no—
601#391—611no—
602#390—611no—
603#386—1221no—
604#385—1221no—
605#380—611no—
606#340—611no—
607#340—611no—
608#336—611no—
609#336—611no—
610C61#2386011yescharacteristic, complemented, Sylow
611C25—21no—
612C25—21no—
613C2×#41—1222no—
614C2×#41—1222no—
615C2×#41—1222no—
616C2×#41—1222no—
617C2×#41—2441no—
618C2×#41—2441no—
619C22×Q8—611no—
620C22×D4—22no—
621C22×D4—22no—
622C22×D4—28no—
623C22×D4—21no—
624C22×D4—21no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—21no—
630C22×D4—21no—
631C22×D4—21no—
632C22×D4—22no—
633C22×D4—21no—
634C22×D4—41no—
635C22×D4—41no—
636C22×D4—41no—
637C22×D4—41no—
638C22×D4—44no—
639C22×D4—44no—
640C22×D4—611no—
641C22×D4—1221no—
642C22×D4—1221no—
643C22×D4C22⋊D6111yescharacteristic
644C22×D4C22⋊D6114yescomplemented
645C22×D4C22×D6111yescharacteristic
646C22×D4C22×D6111yescharacteristic
647C22×D4C22×D6111yescharacteristic
648C23×C4—21no—
649C23×C4—1221no—
650C23×C4C22×D6111yescharacteristic
651C23×C4C22×D6111yescharacteristic
652AGL(1,ℤ/8)—12232no—
653C2×SD16—614no—
654C2×SD16—1222no—
655C2×SD16—1222no—
656C2×SD16—1222no—
657C2×SD16—1222no—
658C2×SD16—1222no—
659C2×SD16—1222no—
660C2×SD16—1222no—
661C2×SD16—2441no—
662C2×D8—614no—
663C2×D8—1222no—
664C2×D8—1222no—
665C2×D8—1222no—
666C2×D8—1222no—
667C2×D8—1222no—
668C2×D8—1222no—
669C2×D8—1222no—
670C2×D8—2441no—
671C2×M16—1222no—
672C2×M16—1222no—
673C2×M16—1222no—
674C22×C8—611no—
675C22×C8—611no—
676C22×C8—611no—
677C22×C8—611no—
678#127—22no—
679#127—22no—
680C22⋊Q8—1222no—
681C22⋊Q8—2441no—
682#121—28no—
683#121—22no—
684#121—22no—
685#121—22no—
686#121—1222no—
687#121—2441no—
688#121C22⋊D6114yescomplemented
689#120—28no—
690#120—28no—
691C4×D4—22no—
692C4×D4—22no—
693C4×D4—22no—
694C4×D4—22no—
695C2×C4⋊C4—611no—
696C2×C4⋊C4—611no—
697C2×C4⋊C4—1221no—
698C2×C4⋊C4C22⋊D6111yescharacteristic
699C2×C4⋊C4C22×D6111yescharacteristic
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—1221no—
704C2×C22⋊C4—1221no—
705C2×C22⋊C4—1221no—
706C2×C22⋊C4—1221no—
707C2×C22⋊C4—1221no—
708C2×C22⋊C4C22⋊D6111yescharacteristic
709C2×C22⋊C4C22⋊D6111yescharacteristic
710C2×C42C22×D6111yescharacteristic
711#103—1222no—
712#102—1222no—
713#102—1222no—
714#102—1222no—
715#102—1222no—
716#102—1222no—
717#102—2441no—
718#102—2441no—
719C22⋊C8—1222no—
720C22⋊C8—1222no—
721C22⋊C8—1222no—
722#95—1221no—
723#95—1221no—
724#95—1221no—
725C24—21no—
726C24—24no—
727C24—21no—
728C24—21no—
729C24—24no—
730C24—42no—
731C24—42no—
732C24—42no—
733C24—42no—
734C24—42no—
735C24—42no—
736C24—42no—
737C24—42no—
738C24—81no—
739C24—81no—
740C24—81no—
741C24—81no—
742C24—1221no—
743C24C2×C22⋊D6111yescharacteristic
744C24C2×C22⋊D6111yescharacteristic
745#41—1228no—
746#41—2444no—
747#41—2444no—
748#41—2444no—
749C2×Q8—612no—
750C2×Q8—1221no—
751C2×Q8—1221no—
752C2×Q8—1221no—
753C2×Q8—1221no—
754C2×Q8—1221no—
755C2×D4—22no—
756C2×D4—22no—
757C2×D4—28no—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—24no—
761C2×D4—24no—
762C2×D4—24no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—24no—
777C2×D4—22no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—42no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—432no—
789C2×D4—44no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—42no—
793C2×D4—42no—
794C2×D4—44no—
795C2×D4—42no—
796C2×D4—81no—
797C2×D4—81no—
798C2×D4—612no—
799C2×D4—1221no—
800C2×D4—1221no—
801C2×D4—1221no—
802C2×D4—1221no—
803C2×D4—1221no—
804C2×D4—4881no—
805C2×D4—2442no—
806C2×D4—2442no—
807C2×D4—2442no—
808C2×D4—2442no—
809C2×D4—2442no—
810C2×D4D4×D6112yes—
811C2×D4D4×D6112yes—
812C2×D4C2×C22⋊D6112yes—
813C2×D4C2×C22⋊D6112yes—
814C2×D4C2×C22⋊D6112yes—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—24no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—1221no—
830C22×C4—1221no—
831C22×C4—1221no—
832C22×C4—2442no—
833C22×C4—2442no—
834C22×C4—2442no—
835C22×C4C2×C22⋊D6111yescharacteristic
836C22×C4C2×C22⋊D6111yescharacteristic
837C22×C4C2×C22⋊D6112yes—
838C22×C4C2×C22⋊D6112yes—
839C22×C4C2×C22⋊D6111yescharacteristic
840C22×C4C2×C22⋊D6111yescharacteristic
841C22×C4C23×D6111yescharacteristic
842SD16—1228no—
843SD16—1228no—
844SD16—2444no—
845D8—1228no—
846D8—1228no—
847D8—2444no—
848M16—1228no—
849C2×C8—612no—
850C2×C8—612no—
851C2×C8—1221no—
852C2×C8—1221no—
853C2×C8—1221no—
854C2×C8—1221no—
855C2×C8—1221no—
856C2×C8—1221no—
857C2×C8—1221no—
858C2×C8—1221no—
859C2×C8—1221no—
860C2×C8—1221no—
861C4⋊C4—21no—
862C4⋊C4—22no—
863C4⋊C4—1221no—
864C4⋊C4—1221no—
865C4⋊C4—1221no—
866C4⋊C4—1221no—
867C4⋊C4—2442no—
868C4⋊C4C2×C22⋊D6112yes—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—22no—
872C22⋊C4—24no—
873C22⋊C4—22no—
874C22⋊C4—4881no—
875C22⋊C4—4881no—
876C22⋊C4—2442no—
877C22⋊C4—2442no—
878C22⋊C4—2442no—
879C42—21no—
880C42—21no—
881C23—21no—
882C23—22no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—21no—
888C23—21no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—48no—
899C23—48no—
900C23—48no—
901C23—48no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—84no—
919C23—84no—
920C23—84no—
921C23—84no—
922C23—84no—
923C23—84no—
924C23—84no—
925C23—84no—
926C23—84no—
927C23—84no—
928C23—1222no—
929C23—2441no—
930C23—2441no—
931C23—2441no—
932C23—2441no—
933C23—2441no—
934C23—2441no—
935C23#1451974612yes—
936C23#1451980312yescomplemented
937C23C22×C22⋊D6111yescharacteristic
938Q8—1222no—
939Q8—1222no—
940Q8—2441no—
941Q8—2441no—
942D4—28no—
943D4—22no—
944D4—22no—
945D4—22no—
946D4—22no—
947D4—22no—
948D4—22no—
949D4—22no—
950D4—48no—
951D4—48no—
952D4—48no—
953D4—48no—
954D4—48no—
955D4—41no—
956D4—41no—
957D4—41no—
958D4—41no—
959D4—84no—
960D4—1222no—
961D4—1222no—
962D4—4884no—
963D4—2448no—
964D4—2441no—
965D4—2441no—
966D4#1451974514yes—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—48no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—1222no—
990C2×C4—2448no—
991C2×C4—2441no—
992C2×C4—2441no—
993C2×C4—2441no—
994C2×C4—2441no—
995C2×C4—2441no—
996C2×C4—2441no—
997C2×C4—2441no—
998C2×C4—2441no—
999C2×C4#1451974612yes—
1000C2×C4#1451980312yescomplemented
1001C2×C4C2×D4×D6111yescharacteristic
1002C2×C4C2×D4×D6111yescharacteristic
1003C2×C4C22×C22⋊D6111yescharacteristic
1004C2×C4C22×C22⋊D6111yescharacteristic
1005C2×C4#1451982211yescharacteristic
1006C2×C4#1451982211yescharacteristic
1007C8—1222no—
1008C8—1222no—
1009C8—2441no—
1010C8—2441no—
1011C22—22no—
1012C22—22no—
1013C22—22no—
1014C22—22no—
1015C22—24no—
1016C22—22no—
1017C22—22no—
1018C22—41no—
1019C22—41no—
1020C22—42no—
1021C22—41no—
1022C22—42no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—41no—
1027C22—42no—
1028C22—41no—
1029C22—42no—
1030C22—41no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—42no—
1038C22—816no—
1039C22—816no—
1040C22—81no—
1041C22—81no—
1042C22—81no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—4881no—
1049C22—4881no—
1050C22—4881no—
1051C22—4881no—
1052C22—2442no—
1053C22—2442no—
1054C22—2442no—
1055C22C2×#1451974611yescharacteristic
1056C22D4×C22⋊D6111yescharacteristic
1057C22D4×C22⋊D6111yescharacteristic
1058C22C2×#1451980311yescharacteristic
1059C22C2×#1451980311yescharacteristic
1060C22#1684056511yescharacteristic
1061C22#1684057311yescharacteristic
1062C4—22no—
1063C4—22no—
1064C4—41no—
1065C4—41no—
1066C4—42no—
1067C4—4881no—
1068C4—4881no—
1069C4—2442no—
1070C4C2×#1451974511yescharacteristic
1071C4#1684032111yescharacteristic
1072C4D4×C22⋊D6111yescharacteristic
1073C4D4×C22⋊D6111yescharacteristic
1074C2—42no—
1075C2—42no—
1076C2—44no—
1077C2—82no—
1078C2—82no—
1079C2—4882no—
1080C2#2144912911yescharacteristic
1081C2#2145504611yescharacteristic
1082C2#2145512311yescharacteristic
1083C2#2145729511yescharacteristic
1084C2#2145731011yescharacteristic
1085C2#2145741511yescharacteristic
1086C2#2145743511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×D42×C61C2
socleC23×C61C22×D4
hypercenterC2×D42D61
hypocenterC61#23860
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. C22×#14519803C2semidirect
2. C2×#16839905C2semidirect
3. C2×#16839913C2semidirect
4. C2×#16839896C2semidirect
5. #21449164C2semidirect
6. #21446907C2semidirect
7. #21446890C2semidirect
8. #21446822C2semidirect
9. #21446815C2semidirect
10. #21446258C2semidirect
11. #21446167C2semidirect
12. #21446153C2semidirect
13. #21446117C2semidirect
14. #21445750C2semidirect
15. C2×D42×C61C2semidirect
16. C22×#11758222C22semidirect
21. C22×#11758200C22semidirect
22. C22×#11758200C22semidirect
24. C22×#11758199C22semidirect
25. C22×#11758199C22semidirect
26. C22×#11758194C22semidirect
27. C2×#14519756C22semidirect
28. C2×#14519751C22semidirect
32. C2×#14519700C22semidirect
35. C2×#14519698C22semidirect
36. C2×#14519698C22semidirect
37. C2×#14519698C22semidirect
38. C2×#14519698C22semidirect
39. C2×#14519697C22semidirect
40. C2×C22⋊#92418C22semidirect
41. C2×C22⋊#92418C22semidirect
42. C2×C22⋊#92418C22semidirect
45. #16839668C22semidirect
46. #16839664C22semidirect
49. #16839622C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839517C22semidirect
53. #16839517C22semidirect
87. C2×#11758200D4semidirect
96. C2×#11758199D4semidirect
153. C22×D4×C61D4semidirect
166. #121×C61D4semidirect
288. C2×D244C2×D4semidirect
297. C2×Dic122C2×D4semidirect
335. C2×#92418C2×D4semidirect
336. C2×#92418C2×D4semidirect
385. C23×C61AGL(1,ℤ/8)semidirect
436. C2×C4×C61AGL(1,ℤ/8)semidirect
532. C2×D42D61semidirect
610. C61#23860semidirect
644. C22×D4C22⋊D61semidirect
688. #121C22⋊D61semidirect
936. C23#14519803semidirect
1000. C2×C4#14519803semidirect

Maximal subgroups

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

subgroupindex
C22×#145198032
C2×#168399052
C2×#168399132
C2×#168398962
#214491642
#214469072
#214468902
#214468222
#214468152
#214462582
#214461672
#214461532
#214461172
#214457502
C2×D42×C612
#2386061