Finite Group Databasebeta

← #29681291

Subgroups — #29681291

Order 15616.

1842 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840342C211yesmaximal, characteristic
2C2×#16840242C211yesmaximal, characteristic, complemented
3C2×#16839762C211yesmaximal, characteristic, complemented
4C2×#16839757C211yesmaximal, characteristic, complemented
5C2×#16839727C211yesmaximal, characteristic, complemented
6#21446141C211yesmaximal, characteristic, complemented
7#21446140C211yesmaximal, characteristic, complemented
8#21446135C211yesmaximal, characteristic, complemented
9#21446134C211yesmaximal, characteristic, complemented
10#21446128C211yesmaximal, characteristic, complemented
11#21446127C211yesmaximal, characteristic, complemented
12#21446123C211yesmaximal, characteristic, complemented
13#21445537C211yesmaximal, characteristic, complemented
14#340×D61C211yesmaximal, characteristic, complemented
15C61×#1873C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×#11758222C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840342—24no—
21#16840342C418yescomplemented
22C2×#14519755—21no—
23C2×#14519753C2211yescharacteristic
24C2×#14519752—21no—
25C2×#14519752C2211yescharacteristic
26C2×#14519751C2211yescharacteristic
27C2×#14519750—21no—
28C2×#14519750—21no—
29#16840242—24no—
30#16840242—24no—
31C2×C4×Dic122—21no—
32C2×C4×D244—21no—
33C2×#14519737—21no—
34C2×#14519737—21no—
35C2×#14519735C2211yescharacteristic
36C2×#14519735C2211yescharacteristic
37C22×C4⋊Dic61C2211yescharacteristic
38C2×C4⋊C4×D61C2211yescharacteristic
39C2×C4⋊C4×D61C2211yescharacteristic
40C2×C4⋊C4×D61C2211yescharacteristic
41#16839762—24no—
42#16839757—24no—
43C2×#14519701C2211yescharacteristic
44C2×#14519701C2211yescharacteristic
45C2×#14519699C2211yescharacteristic
46C2×#14519699C2211yescharacteristic
47C2×#14519697C2211yescharacteristic
48C2×#14519697C2211yescharacteristic
49#16839727—24no—
50C2×C22⋊#92418C2211yescharacteristic
51C2×#14519689C2211yescharacteristic
52C2×#14519689C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839525C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57#16839524C2211yescharacteristic
58#16839524C2211yescharacteristic
59C2×C22⋊Q8×C61C2211yescharacteristic
60C2×#117×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×#103×C61C2211yescharacteristic
63C2×C22⋊C8×C61C2211yescharacteristic
64C61×#340C2211yescharacteristic
65C61×#340C2211yescharacteristic
66C2×#11758226—22no—
67C2×#11758226—22no—
68C2×#11758226—22no—
69C2×#11758226—22no—
70C2×#11758226—22no—
71C2×#11758226C2×C414yescomplemented
72C2×#11758222—22no—
73C2×#11758222—22no—
74C2×#11758222—22no—
75C2×#11758222—22no—
76C2×#11758222C2×C414yes—
77C2×#11758222D414yes—
78C22×Dic122D411yescharacteristic
79C22×D244—21no—
80C22×D244—21no—
81C22×D244D411yescharacteristic
82C22×D244C2311yescharacteristic
83C22×C22⋊D61—21no—
84C22×C22⋊D61D411yescharacteristic
85C22×C22⋊D61D411yescharacteristic
86C23×Dic61—21no—
87C22×C4×D61—21no—
88C22×C4×D61—21no—
89C22×C4×D61—21no—
90C22×C4×D61—21no—
91C22×C4×D61C2311yescharacteristic
92C22×C4×D61C2311yescharacteristic
93C2×#11758189—22no—
94C2×#11758189—22no—
95C2×#11758189—22no—
96C22×#92418C2311yescharacteristic
97C22×#92418C2311yescharacteristic
98C2×C8×D61—22no—
99C2×C8×D61—22no—
100C2×C8×D61—22no—
101#14519755—28no—
102#14519753—22no—
103#14519753C2×C414yescomplemented
104#14519752—28no—
105#14519752—22no—
106#14519752C2×C414yescomplemented
107#14519751—22no—
108#14519751C2×C414yescomplemented
109#14519750—28no—
110#14519750—28no—
111C4×Dic122—28no—
112C4×D244—28no—
113#14519737—28no—
114#14519737—28no—
115#14519735—22no—
116#14519735—22no—
117#14519735—22no—
118#14519735D414yescomplemented
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61—22no—
121C2×C4⋊Dic61—22no—
122C2×C4⋊Dic61C2311yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C4⋊C4×D61—22no—
130C4⋊C4×D61—22no—
131C4⋊C4×D61—22no—
132C4⋊C4×D61—22no—
133C4⋊C4×D61C2×C414yescomplemented
134C4⋊C4×D61D414yescomplemented
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61—21no—
142#14519701—22no—
143#14519701—22no—
144#14519699—22no—
145#14519699—22no—
146#14519697—22no—
147#14519697—22no—
148C22⋊#92418—22no—
149#14519689—22no—
150#14519689—22no—
151C22×Q8×C61C2311yescharacteristic
152C23×C4×C61C2311yescharacteristic
153C22×C8×C61C2311yescharacteristic
154C22×C8×C61C2311yescharacteristic
155C22⋊Q8×C61—22no—
156C22⋊Q8×C61C2×C414yescomplemented
157#117×C61—22no—
158#117×C61—22no—
159C2×C4⋊C4×C61—21no—
160C2×C4⋊C4×C61C2311yescharacteristic
161C2×C4⋊C4×C61C2311yescharacteristic
162C2×C4⋊C4×C61C2311yescharacteristic
163C2×C22⋊C4×C61—21no—
164C2×C22⋊C4×C61—21no—
165C2×C42×C61—21no—
166#103×C61—22no—
167#103×C61—22no—
168C22⋊C8×C61—22no—
169C24×C61C2×D411yescharacteristic
170C23×D61—21no—
171C23×D61C2×D411yescharacteristic
172C23×D61C2×D411yescharacteristic
173C2×Q8×C61—21no—
174C2×Q8×C61—21no—
175C2×Q8×C61—21no—
176C2×Q8×C61—21no—
177C2×Q8×C61—21no—
178C2×Q8×C61C22×C412yes—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61C22×C412yes—
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D412yes—
190C22×C4×C61C2411yescharacteristic
191C2×C22⋊D61—22no—
192C2×C22⋊D61—22no—
193C2×C22⋊D61—24no—
194C2×C22⋊D61—22no—
195C2×C22⋊D61—22no—
196C2×C22⋊D61—81no—
197C2×C22⋊D61—81no—
198C2×C22⋊D61C22⋊C414yes—
199C2×C22⋊D61C22⋊C414yes—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—24no—
204C22×Dic61—81no—
205C22×Dic61—81no—
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208#11758226—28no—
209#11758226—28no—
210#11758226—44no—
211#11758226—44no—
212#11758222—28no—
213#11758222—28no—
214#11758222—28no—
215#11758222—28no—
216C2×D244—22no—
217C2×D244—22no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244—21no—
221C2×D244—21no—
222C2×D244—24no—
223C2×D244—21no—
224C2×D244—24no—
225C2×D244—42no—
226C2×D244—42no—
227C2×D244—81no—
228C2×D244—81no—
229C2×D244C22⋊C414yes—
230C2×D244C22×C412yes—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—24no—
236C2×C4×D61—24no—
237C2×C4×D61—24no—
238C2×C4×D61—24no—
239C2×C4×D61—42no—
240C2×C4×D61—42no—
241C2×C4×D61—81no—
242C2×C4×D61—81no—
243C2×C4×D61—81no—
244C2×C4×D61—81no—
245C2×C4×D61—81no—
246C2×C4×D61—81no—
247C2×C4×D61C22×C412yes—
248C2×C4×D61C22×C412yes—
249C2×C4×D61C2×D412yes—
250C2×C4×D61C2×D412yes—
251C2×C4×D61C2×D412yes—
252C2×C4×D61C2×D412yes—
253C2×C4×D61#4112yes—
254C2×C4×D61#4112yes—
255C2×Dic122—22no—
256C2×Dic122—22no—
257C2×Dic122C22⋊C414yes—
258C2×C8×C61—21no—
259C2×C8×C61—21no—
260C2×C8×C61—21no—
261C2×C8×C61—21no—
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C4⋊C4×C61—24no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61C22×C412yes—
269C4⋊C4×C61C2×D412yes—
270C4⋊C4×C61C2×D412yes—
271C22⋊C4×C61—24no—
272C22⋊C4×C61—24no—
273C42×C61—24no—
274#11758198—24no—
275#11758198—24no—
276#11758198—24no—
277#11758198—24no—
278#11758198—24no—
279C4⋊Dic61—24no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61C22×C412yes—
284C4⋊Dic61C2×D412yes—
285C4⋊Dic61C2×D412yes—
286#11758196—24no—
287#11758196—24no—
288#11758196—24no—
289#11758196—24no—
290C4×Dic61—24no—
291C4×Dic61—24no—
292C2×#92418—21no—
293C2×#92418—21no—
294C2×#92418—21no—
295C2×#92418—21no—
296C2×#92418—21no—
297C2×#92418—21no—
298#11758189—44no—
299C8×D61—44no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61C2×C22⋊C412yes—
307C23×C61C22×D411yescharacteristic
308C22×D61—21no—
309C22×D61—21no—
310C22×D61—21no—
311C22×D61—21no—
312C22×D61—21no—
313C22×D61—21no—
314C22×D61—21no—
315C22×D61—21no—
316C22×D61—21no—
317C22×D61—21no—
318C22×D61—22no—
319C22×D61—41no—
320C22×D61—41no—
321C22×D61—41no—
322C22×D61—41no—
323C22×D61—41no—
324C22×D61—41no—
325C22×D61C2×C22⋊C412yes—
326C22×D61C2×C22⋊C412yes—
327C22×D61#12012yes—
328C22×D61#12312yes—
329Q8×C61—22no—
330Q8×C61—22no—
331Q8×C61—41no—
332Q8×C61—41no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61C2×C22⋊C412yes—
352C2×C4×C61C23×C411yescharacteristic
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C2×#4111yescharacteristic
357C2×C4×C61C2×#4111yescharacteristic
358C22⋊D61—28no—
359C22⋊D61—28no—
360C22⋊D61—84no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—84no—
373C2×Dic61C2×C22⋊C412yes—
374C2×Dic61C2×C22⋊C412yes—
375C2×Dic61#12012yes—
376C2×Dic61#12312yes—
377D244—28no—
378D244—22no—
379D244—22no—
380D244—48no—
381D244—41no—
382D244—41no—
383D244—84no—
384C4×D61—22no—
385C4×D61—22no—
386C4×D61—22no—
387C4×D61—22no—
388C4×D61—48no—
389C4×D61—84no—
390C4×D61—84no—
391C4×D61—84no—
392C4×D61C4×D414yes—
393C4×D61C4×D414yes—
394C4×D61#12114yes—
395C4×D61#12114yes—
396Dic122—28no—
397C8×C61—41no—
398C8×C61—41no—
399#92418—41no—
400#92418—41no—
401#20915—611nomaximal, Sylow
402C22×C61—22no—
403C22×C61—22no—
404C22×C61—22no—
405C22×C61—41no—
406C22×C61—41no—
407C22×C61—41no—
408C22×C61—41no—
409C22×C61C22×C22⋊C411yescharacteristic
410C22×C61C2×#12011yescharacteristic
411C22×C61C2×#12311yescharacteristic
412C22×C61#57611yescharacteristic
413C22×C61#57711yescharacteristic
414C22×C61#57711yescharacteristic
415C22×C61#57811yescharacteristic
416C2×D61—22no—
417C2×D61—22no—
418C2×D61—22no—
419C2×D61—22no—
420C2×D61—22no—
421C2×D61—22no—
422C2×D61—22no—
423C2×D61—22no—
424C2×D61—22no—
425C2×D61—41no—
426C2×D61—41no—
427C2×D61—41no—
428C2×D61—41no—
429C2×D61—42no—
430C2×D61—42no—
431C2×D61—42no—
432C2×D61—81no—
433C2×D61—81no—
434C2×D61—81no—
435C2×D61—81no—
436C2×D61#38614yes—
437C4×C61—22no—
438C4×C61—42no—
439C4×C61—42no—
440C4×C61—42no—
441C4×C61—42no—
442C4×C61C2×C4×D411yescharacteristic
443C4×C61C2×C4×D411yescharacteristic
444C4×C61C2×#12111yescharacteristic
445C4×C61C2×#12111yescharacteristic
446Dic61—22no—
447Dic61—42no—
448Dic61—42no—
449Dic61—42no—
450Dic61#38614yes—
451C2×#537—611no—
452C2×#520—611no—
453C2×#417—611no—
454C2×#416—611no—
455C2×#408—611no—
456#1875—611no—
457#1875—611no—
458#1874—611no—
459#1874—611no—
460#1873—611no—
461#1873D6111yescharacteristic, complemented
462#1872—611no—
463#1872—611no—
464#1736—611no—
465C2×#340—611no—
466C2×C61—42no—
467C2×C61C2×#38611yescharacteristic
468C2×C61#289711yescharacteristic
469C2×C61#289811yescharacteristic
470C2×C61#301211yescharacteristic
471C2×C61#301311yescharacteristic
472C2×C61#309811yescharacteristic
473C2×C61#309911yescharacteristic
474D61—24no—
475D61—42no—
476D61—82no—
477C22×#41—611no—
478C22×#41—611no—
479C22×M16—611no—
480C23×C8—611no—
481#537—618no—
482#537—1224no—
483C2×C22⋊Q8—611no—
484C2×C22⋊Q8—1221no—
485C2×C22⋊Q8C2×D6111yescharacteristic
486C2×#121—611no—
487C2×#121—611no—
488C2×#121—1221no—
489C2×#121—1221no—
490C2×#121—1221no—
491#520—1224no—
492#520—1224no—
493C2×C4×Q8—1221no—
494C2×C4×D4—1221no—
495C2×C4×D4—1221no—
496C2×C4×D4—1221no—
497C2×#117—611no—
498C2×#117—611no—
499C2×#117C2×D6111yescharacteristic
500C22×C4⋊C4—611no—
501C22×C4⋊C4—611no—
502C22×C4⋊C4—611no—
503C22×C4⋊C4—611no—
504#417—1224no—
505#416—1224no—
506C2×#103—611no—
507C2×#103—611no—
508C2×#103C2×D6111yescharacteristic
509C2×#103C2×D6111yescharacteristic
510C2×#102—611no—
511C2×#102—611no—
512C2×#102—611no—
513C2×#102—611no—
514#408—1224no—
515C2×C22⋊C8—611no—
516C2×C22⋊C8—611no—
517C2×C22⋊C8—611no—
518C2×C22⋊C8C2×D6111yescharacteristic
519#340—611no—
520#340—611no—
521#340—611no—
522#340—611no—
523#340—611no—
524#340—611no—
525#340C2×D6111yescharacteristic
526#340C2×D6111yescharacteristic
527C61#2091511yescharacteristic, complemented, Sylow
528C2×#41—614no—
529C2×#41—614no—
530C2×#41—614no—
531C2×#41—1222no—
532C2×#41—1222no—
533C2×#41—1222no—
534C2×#41—1222no—
535C2×#41—1222no—
536C2×#41—1222no—
537C2×#41—1222no—
538C2×#41—1222no—
539C2×#41—1222no—
540C22×Q8—611no—
541C22×Q8C22×D6111yescharacteristic
542C22×D4—611no—
543C22×D4—611no—
544C22×D4—611no—
545C22×D4—611no—
546C22×D4—1221no—
547C22×D4—1221no—
548C22×D4—1221no—
549C23×C4—611no—
550C23×C4—611no—
551C23×C4—1221no—
552C23×C4—1221no—
553C23×C4—1221no—
554C23×C4—1221no—
555C23×C4—1221no—
556C23×C4C22×D6111yescharacteristic
557C2×M16—1222no—
558C2×M16—1222no—
559C2×M16—1222no—
560C22×C8—611no—
561C22×C8—611no—
562C22×C8—1222no—
563C22×C8—1222no—
564C22×C8—1222no—
565C22×C8C22×D6111yescharacteristic
566C22×C8C22×D6111yescharacteristic
567C22⋊Q8—22no—
568C22⋊Q8—614no—
569C22⋊Q8—1228no—
570C22⋊Q8—1222no—
571C22⋊Q8C4×D6114yescomplemented
572#121—614no—
573#121—614no—
574#121—1228no—
575#121—1228no—
576#121—1222no—
577#121—1228no—
578#121—1222no—
579C4×Q8—1228no—
580C4×D4—1228no—
581C4×D4—1228no—
582C4×D4—1228no—
583#117—22no—
584#117—22no—
585#117—614no—
586#117—1222no—
587#117—1222no—
588#117—1222no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—611no—
591C2×C4⋊C4—611no—
592C2×C4⋊C4—611no—
593C2×C4⋊C4—614no—
594C2×C4⋊C4—614no—
595C2×C4⋊C4—1222no—
596C2×C4⋊C4—1222no—
597C2×C4⋊C4—1222no—
598C2×C4⋊C4—1222no—
599C2×C4⋊C4—1222no—
600C2×C4⋊C4—1221no—
601C2×C4⋊C4—1221no—
602C2×C4⋊C4—1221no—
603C2×C4⋊C4—1221no—
604C2×C4⋊C4—1221no—
605C2×C4⋊C4—1222no—
606C2×C4⋊C4C22×D6111yescharacteristic
607C2×C4⋊C4C22×D6111yescharacteristic
608C2×C4⋊C4C22×D6111yescharacteristic
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—1221no—
612C2×C22⋊C4—1221no—
613C2×C22⋊C4—1221no—
614C2×C22⋊C4—1221no—
615C2×C22⋊C4—1221no—
616C2×C42—21no—
617C2×C42—1221no—
618C2×C42—1221no—
619#103—22no—
620#103—22no—
621#103—1222no—
622#103—1222no—
623#102—1222no—
624#102—1222no—
625#102—1222no—
626#102—1222no—
627C22⋊C8—22no—
628C22⋊C8—1222no—
629C22⋊C8—1222no—
630C22⋊C8—1222no—
631C24—611no—
632C24—611no—
633C24—1221no—
634C24D4×D6111yescharacteristic
635#41—1228no—
636#41—1228no—
637#41—1228no—
638#41—1228no—
639#41—1228no—
640#41—1228no—
641#41—2444no—
642#41—2444no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—614no—
649C2×Q8—1222no—
650C2×Q8—1222no—
651C2×Q8C2×C4×D6112yes—
652C2×D4—614no—
653C2×D4—614no—
654C2×D4—612no—
655C2×D4—614no—
656C2×D4—1222no—
657C2×D4—1222no—
658C2×D4—1224no—
659C2×D4—1224no—
660C2×D4—1222no—
661C2×D4—1222no—
662C2×D4—1222no—
663C2×D4—1222no—
664C2×D4—1224no—
665C2×D4—1221no—
666C2×D4—1221no—
667C2×D4—1221no—
668C2×D4—1221no—
669C2×D4—1221no—
670C2×D4—4881no—
671C2×D4—4881no—
672C2×D4—4881no—
673C2×D4—4881no—
674C2×D4—2442no—
675C2×D4—2442no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—611no—
685C22×C4—612no—
686C22×C4—612no—
687C22×C4—612no—
688C22×C4—612no—
689C22×C4—612no—
690C22×C4—612no—
691C22×C4—611no—
692C22×C4—612no—
693C22×C4—612no—
694C22×C4—1224no—
695C22×C4—1224no—
696C22×C4—1224no—
697C22×C4—1224no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1224no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—4881no—
707C22×C4—4881no—
708C22×C4—4881no—
709C22×C4—4881no—
710C22×C4—4881no—
711C22×C4—4881no—
712C22×C4—4881no—
713C22×C4—4881no—
714C22×C4—2442no—
715C22×C4—2442no—
716C22×C4C2×C4×D6112yes—
717C22×C4D4×D6112yes—
718C22×C4D4×D6111yescharacteristic
719C22×C4C23×D6111yescharacteristic
720M16—2444no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—1221no—
728C2×C8—1221no—
729C2×C8—1221no—
730C2×C8—1221no—
731C2×C8—1221no—
732C2×C8—1221no—
733C2×C8—2444no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—24no—
738C4⋊C4—612no—
739C4⋊C4—612no—
740C4⋊C4—612no—
741C4⋊C4—1224no—
742C4⋊C4—1224no—
743C4⋊C4—1224no—
744C4⋊C4—1224no—
745C4⋊C4—1224no—
746C4⋊C4—1221no—
747C4⋊C4—1221no—
748C4⋊C4—1221no—
749C4⋊C4C2×C4×D6112yes—
750C4⋊C4D4×D6112yes—
751C4⋊C4D4×D6112yes—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—1224no—
755C22⋊C4—1224no—
756C22⋊C4—1224no—
757C22⋊C4—1224no—
758C22⋊C4—1224no—
759C42—24no—
760C42—1224no—
761C42—1224no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—612no—
769C23—612no—
770C23—612no—
771C23—612no—
772C23—1221no—
773C23—1221no—
774C23—1221no—
775C23—1221no—
776C23—1221no—
777C23—1221no—
778C23—1221no—
779C23—1221no—
780C23—1221no—
781C23—1221no—
782C23—1222no—
783C23—2441no—
784C23—2441no—
785C23—2441no—
786C23—2441no—
787C23—2441no—
788C23—2441no—
789C23C22⋊C4×D6112yes—
790C23C2×D4×D6111yescharacteristic
791Q8—22no—
792Q8—22no—
793Q8—41no—
794Q8—41no—
795Q8—1228no—
796D4—1228no—
797D4—1228no—
798D4—1228no—
799D4—1222no—
800D4—1222no—
801D4—4884no—
802D4—4884no—
803D4—2448no—
804D4—2441no—
805D4—2441no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—612no—
825C2×C4—612no—
826C2×C4—612no—
827C2×C4—614no—
828C2×C4—614no—
829C2×C4—614no—
830C2×C4—614no—
831C2×C4—612no—
832C2×C4—1221no—
833C2×C4—1221no—
834C2×C4—1222no—
835C2×C4—1222no—
836C2×C4—1222no—
837C2×C4—1222no—
838C2×C4—1222no—
839C2×C4—1222no—
840C2×C4—1222no—
841C2×C4—4884no—
842C2×C4—4884no—
843C2×C4—4884no—
844C2×C4—4884no—
845C2×C4—2448no—
846C2×C4—2441no—
847C2×C4—2441no—
848C2×C4—2441no—
849C2×C4—2441no—
850C2×C4—2441no—
851C2×C4—2441no—
852C2×C4C22⋊C4×D6112yes—
853C2×C4C22×C4×D6111yescharacteristic
854C2×C4C2×D4×D6111yescharacteristic
855C2×C4C2×D4×D6111yescharacteristic
856C2×C4C2×D4×D6111yescharacteristic
857C2×C4#41×D6111yescharacteristic
858C2×C4#41×D6111yescharacteristic
859C8—41no—
860C8—41no—
861C8—2441no—
862C8—2441no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—614no—
871C22—1222no—
872C22—1222no—
873C22—1222no—
874C22—1222no—
875C22—1222no—
876C22—1222no—
877C22—1222no—
878C22—1222no—
879C22—1222no—
880C22—4881no—
881C22—4881no—
882C22—4881no—
883C22—4881no—
884C22—2442no—
885C22—2442no—
886C22—2442no—
887C22—2441no—
888C22—2441no—
889C22—2441no—
890C22—2441no—
891C22C2×C22⋊C4×D6111yescharacteristic
892C22#120×D6111yescharacteristic
893C22#123×D6111yescharacteristic
894C22#1684056411yescharacteristic
895C22#1684056911yescharacteristic
896C22#1684057111yescharacteristic
897C22#1684057811yescharacteristic
898C4—22no—
899C4—42no—
900C4—42no—
901C4—42no—
902C4—42no—
903C4—614no—
904C4—1222no—
905C4—2442no—
906C4—2442no—
907C4—2442no—
908C4C4×D4×D6111yescharacteristic
909C4C4×D4×D6111yescharacteristic
910C4#121×D6111yescharacteristic
911C4#121×D6111yescharacteristic
912C2—42no—
913C2—1224no—
914C2—4882no—
915C2—2442no—
916C2#386×D6111yescharacteristic
917C2#2145434111yescharacteristic
918C2#2145435111yescharacteristic
919C2#2145512711yescharacteristic
920C2#2145513811yescharacteristic
921C2#2145580011yescharacteristic
922C2#2145580511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1873C2
socleC23×C61C22×D4
prime radicalC2×#16840342C2
cosocleC22×C4×C61C24
hypercenter#1873D61
hypocenterC61#20915
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
2. C2×#16840242C2semidirect
3. C2×#16839762C2semidirect
4. C2×#16839757C2semidirect
5. C2×#16839727C2semidirect
6. #21446141C2semidirect
7. #21446140C2semidirect
8. #21446135C2semidirect
9. #21446134C2semidirect
10. #21446128C2semidirect
11. #21446127C2semidirect
12. #21446123C2semidirect
13. #21445537C2semidirect
14. #340×D61C2semidirect
15. C61×#1873C2semidirect
21. #16840342C4semidirect
71. C2×#11758226C2×C4semidirect
103. #14519753C2×C4semidirect
106. #14519752C2×C4semidirect
108. #14519751C2×C4semidirect
118. #14519735D4semidirect
133. C4⋊C4×D61C2×C4semidirect
134. C4⋊C4×D61D4semidirect
156. C22⋊Q8×C61C2×C4semidirect
461. #1873D61semidirect
527. C61#20915semidirect
571. C22⋊Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403422
C2×#168402422
C2×#168397622
C2×#168397572
C2×#168397272
#214461412
#214461402
#214461352
#214461342
#214461282
#214461272
#214461232
#214455372
#340×D612
C61×#18732
#2091561