Finite Group Databasebeta

← #29681760

Subgroups — #29681760

Order 15616.

1818 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519785C211yesmaximal, characteristic, complemented
2C2×#16840342C211yesmaximal, characteristic
3C2×#16839762C211yesmaximal, characteristic, complemented
4C2×#16839757C211yesmaximal, characteristic, complemented
5#21448408C211yesmaximal, characteristic, complemented
6#21446257C211yesmaximal, characteristic, complemented
7#21446256C211yesmaximal, characteristic, complemented
8#21446249C211yesmaximal, characteristic, complemented
9#21446246C211yesmaximal, characteristic, complemented
10#21446245C211yesmaximal, characteristic, complemented
11#21446243C211yesmaximal, characteristic, complemented
12#21446239C211yesmaximal, characteristic, complemented
13#21445537C211yesmaximal, characteristic, complemented
14#340×D61C211yesmaximal, characteristic, complemented
15C61×#1894C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×#11758222C2211yescharacteristic
18C2×#14519785—24no—
19C2×#14519785—24no—
20C2×#14519785—24no—
21C22×#11758189C2211yescharacteristic
22C22×#11758189C2211yescharacteristic
23C23×#92418C2211yescharacteristic
24C22×C8×D61C2211yescharacteristic
25C22×C8×D61C2211yescharacteristic
26#16840342—24no—
27#16840342C418yescomplemented
28C2×#14519755—21no—
29C2×#14519753C2211yescharacteristic
30C2×#14519752—21no—
31C2×#14519752C2211yescharacteristic
32C2×#14519751C2211yescharacteristic
33C2×#14519750—21no—
34C2×#14519750—21no—
35C2×#14519735C2211yescharacteristic
36C2×C4⋊C4×D61C2211yescharacteristic
37C2×C4⋊C4×D61C2211yescharacteristic
38#16839762—24no—
39#16839757—24no—
40C2×#14519701C2211yescharacteristic
41C2×#14519701C2211yescharacteristic
42C2×#14519699C2211yescharacteristic
43C2×#14519699C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×#14519697C2211yescharacteristic
46#16839666—21no—
47#16839662—21no—
48#16839640—21no—
49#16839638—21no—
50#16839622C2211yescharacteristic
51#16839619C2211yescharacteristic
52#16839619C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839525C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57#16839524C2211yescharacteristic
58#16839524C2211yescharacteristic
59C22×M16×C61C2211yescharacteristic
60C2×C22⋊Q8×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×#103×C61C2211yescharacteristic
63C61×#380C2211yescharacteristic
64C61×#340C2211yescharacteristic
65C61×#340C2211yescharacteristic
66C2×#11758226—22no—
67C2×#11758226—22no—
68C2×#11758226—22no—
69C2×#11758226—22no—
70C2×#11758226—22no—
71C2×#11758226C2×C414yes—
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
86C22×C4×D61—21no—
87C22×C4×D61—21no—
88C22×C4×D61—21no—
89C22×C4×D61C2311yescharacteristic
90C22×C4×D61C2311yescharacteristic
91#14519785—232no—
92C2×#11758189—22no—
93C2×#11758189—22no—
94C2×#11758189—22no—
95C2×#11758189—22no—
96C2×#11758189—22no—
97C2×#11758189D414yescomplemented
98C22×#92418—22no—
99C22×#92418—22no—
100C22×#92418—22no—
101C22×#92418C2311yescharacteristic
102C22×#92418C2311yescharacteristic
103C2×C8×D61—22no—
104C2×C8×D61—22no—
105C2×C8×D61—22no—
106C2×C8×D61—22no—
107C2×C8×D61—22no—
108C2×C8×D61D414yescomplemented
109#14519755—28no—
110#14519753—22no—
111#14519753C2×C414yescomplemented
112#14519752—28no—
113#14519752—22no—
114#14519752C2×C414yescomplemented
115#14519751—22no—
116#14519751C2×C414yescomplemented
117#14519750—28no—
118#14519750—28no—
119#14519735—22no—
120#14519735—22no—
121C2×C4⋊Dic61C2311yescharacteristic
122C2×C4⋊Dic61C2311yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×#11758196—21no—
125C2×#11758196—21no—
126C2×#11758196—21no—
127C4⋊C4×D61—22no—
128C4⋊C4×D61—22no—
129C4⋊C4×D61—22no—
130C4⋊C4×D61C2×C414yes—
131C2×C22⋊Dic61—21no—
132C2×#11758198—21no—
133C2×#11758198—21no—
134C2×#11758198—21no—
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×C4×Dic61—21no—
139#14519701—22no—
140#14519701—22no—
141#14519699—22no—
142#14519699—22no—
143#14519697—22no—
144#14519697—22no—
145#14519684—21no—
146#14519684—21no—
147#14519684—21no—
148C22×Q8×C61C2311yescharacteristic
149C23×C4×C61C2311yescharacteristic
150C2×M16×C61—22no—
151C2×M16×C61—22no—
152C2×M16×C61—22no—
153C22×C8×C61C2311yescharacteristic
154C22×C8×C61C2311yescharacteristic
155C22⋊Q8×C61—22no—
156C22⋊Q8×C61C2×C414yescomplemented
157C2×C4⋊C4×C61—21no—
158C2×C4⋊C4×C61C2311yescharacteristic
159C2×C4⋊C4×C61C2311yescharacteristic
160C2×C4⋊C4×C61C2311yescharacteristic
161C2×C22⋊C4×C61—21no—
162C2×C22⋊C4×C61—21no—
163#103×C61—22no—
164#103×C61—22no—
165#95×C61—21no—
166C24×C61C2×D411yescharacteristic
167C23×D61—21no—
168C23×D61C2×D411yescharacteristic
169C23×D61C2×D411yescharacteristic
170C2×Q8×C61—21no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61—21no—
175C2×Q8×C61C22×C412yes—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61C22×C412yes—
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D412yes—
187C22×C4×C61C2411yescharacteristic
188C2×C22⋊D61—22no—
189C2×C22⋊D61—22no—
190C2×C22⋊D61—24no—
191C2×C22⋊D61—22no—
192C2×C22⋊D61—22no—
193C2×C22⋊D61—81no—
194C2×C22⋊D61—81no—
195C2×C22⋊D61C22⋊C414yes—
196C2×C22⋊D61C22⋊C414yes—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61C2×D411yescharacteristic
201C22×Dic61C2×D411yescharacteristic
202#11758226—28no—
203#11758226—28no—
204#11758226—44no—
205#11758226—44no—
206#11758222—28no—
207#11758222—28no—
208#11758222—28no—
209#11758222—28no—
210C2×D244—22no—
211C2×D244—22no—
212C2×D244—21no—
213C2×D244—21no—
214C2×D244—21no—
215C2×D244—21no—
216C2×D244—24no—
217C2×D244—21no—
218C2×D244—24no—
219C2×D244—42no—
220C2×D244—42no—
221C2×D244—81no—
222C2×D244—81no—
223C2×D244C22⋊C414yes—
224C2×D244C22×C412yes—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—24no—
230C2×C4×D61—24no—
231C2×C4×D61—42no—
232C2×C4×D61—42no—
233C2×C4×D61—42no—
234C2×C4×D61—81no—
235C2×C4×D61—81no—
236C2×C4×D61—81no—
237C2×C4×D61—81no—
238C2×C4×D61C22×C412yes—
239C2×C4×D61C22×C412yes—
240C2×C4×D61C2×D412yes—
241C2×C4×D61C2×D412yes—
242C2×C4×D61C2×D412yes—
243C2×C4×D61C2×D412yes—
244C2×C4×D61#4112yes—
245C2×C4×D61#4112yes—
246C2×Dic122—22no—
247C2×Dic122—22no—
248C2×Dic122C22⋊C414yes—
249M16×C61—28no—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61—21no—
253C2×C8×C61—21no—
254C2×C8×C61C2×D412yes—
255C2×C8×C61C2×D412yes—
256C4⋊C4×C61—24no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61C22×C412yes—
263C22⋊C4×C61—24no—
264C22⋊C4×C61—81no—
265C22⋊Dic61—81no—
266#11758198—24no—
267#11758198—24no—
268#11758198—24no—
269#11758198—42no—
270#11758198—81no—
271#11758198—81no—
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61C22×C412yes—
278#11758196—24no—
279#11758196—24no—
280#11758196—42no—
281C4×Dic61—42no—
282C2×#92418—28no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418C2×D412yes—
288C2×#92418C2×D412yes—
289#11758189—28no—
290#11758189—28no—
291C8×D61—28no—
292C8×D61—28no—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61C2×C22⋊C412yes—
300C23×C61C22×D411yescharacteristic
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—21no—
304C22×D61—21no—
305C22×D61—21no—
306C22×D61—21no—
307C22×D61—21no—
308C22×D61—21no—
309C22×D61—21no—
310C22×D61—21no—
311C22×D61—22no—
312C22×D61—41no—
313C22×D61—41no—
314C22×D61—41no—
315C22×D61—41no—
316C22×D61—41no—
317C22×D61—41no—
318C22×D61C2×C22⋊C412yes—
319C22×D61C2×C22⋊C412yes—
320C22×D61#12112yes—
321C22×D61#12112yes—
322Q8×C61—22no—
323Q8×C61—22no—
324Q8×C61—41no—
325Q8×C61—41no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61C2×C22⋊C412yes—
345C2×C4×C61C23×C411yescharacteristic
346C2×C4×C61C22×D411yescharacteristic
347C2×C4×C61C22×D411yescharacteristic
348C2×C4×C61C22×D411yescharacteristic
349C2×C4×C61C2×#4111yescharacteristic
350C2×C4×C61C2×#4111yescharacteristic
351C22⋊D61—28no—
352C22⋊D61—28no—
353C22⋊D61—84no—
354C2×Dic61—21no—
355C2×Dic61—21no—
356C2×Dic61—22no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61C2×C22⋊C412yes—
366C2×Dic61C2×C22⋊C412yes—
367C2×Dic61#12112yes—
368C2×Dic61#12112yes—
369D244—28no—
370D244—22no—
371D244—22no—
372D244—48no—
373D244—41no—
374D244—41no—
375D244—84no—
376C4×D61—22no—
377C4×D61—22no—
378C4×D61—22no—
379C4×D61—22no—
380C4×D61—48no—
381C4×D61—84no—
382C4×D61—84no—
383C4×D61C4×D414yes—
384C4×D61C4×D414yes—
385C4×D61#12014yes—
386C4×D61#12314yes—
387Dic122—28no—
388C8×C61—22no—
389C8×C61—22no—
390#92418—22no—
391#92418—22no—
392#20976—611nomaximal, Sylow
393C22×C61—22no—
394C22×C61—22no—
395C22×C61—22no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61—41no—
399C22×C61—41no—
400C22×C61C22×C22⋊C411yescharacteristic
401C22×C61C2×#12111yescharacteristic
402C22×C61C2×#12111yescharacteristic
403C22×C61#57611yescharacteristic
404C22×C61#57711yescharacteristic
405C22×C61#57711yescharacteristic
406C22×C61#57811yescharacteristic
407C2×D61—22no—
408C2×D61—22no—
409C2×D61—22no—
410C2×D61—22no—
411C2×D61—22no—
412C2×D61—22no—
413C2×D61—22no—
414C2×D61—22no—
415C2×D61—22no—
416C2×D61—41no—
417C2×D61—41no—
418C2×D61—41no—
419C2×D61—41no—
420C2×D61—42no—
421C2×D61—42no—
422C2×D61—42no—
423C2×D61—81no—
424C2×D61—81no—
425C2×D61—81no—
426C2×D61—81no—
427C2×D61#38614yes—
428C4×C61—22no—
429C4×C61—42no—
430C4×C61—42no—
431C4×C61—81no—
432C4×C61—81no—
433C4×C61C2×C4×D411yescharacteristic
434C4×C61C2×C4×D411yescharacteristic
435C4×C61C2×#12011yescharacteristic
436C4×C61C2×#12311yescharacteristic
437Dic61—22no—
438Dic61—42no—
439Dic61—81no—
440Dic61—81no—
441Dic61#38614yes—
442C22×#131—611no—
443C2×#537—611no—
444C2×#417—611no—
445C2×#416—611no—
446#2311—611no—
447#1895—611no—
448#1895—611no—
449#1894—611no—
450#1894D6111yescharacteristic, complemented
451#1893—611no—
452#1893—611no—
453#1892—611no—
454#1892—611no—
455#1736—611no—
456C2×#340—611no—
457C2×C61—42no—
458C2×C61C2×#38611yescharacteristic
459C2×C61#289711yescharacteristic
460C2×C61#289811yescharacteristic
461C2×C61#306011yescharacteristic
462C2×C61#306111yescharacteristic
463C2×C61#306211yescharacteristic
464C2×C61#306311yescharacteristic
465D61—24no—
466D61—42no—
467D61—82no—
468C22×#41—611no—
469C22×#41—611no—
470C2×#131—1224no—
471C2×#131—1224no—
472C2×#131—1224no—
473C22×M16—611no—
474C22×M16—611no—
475C22×M16C2×D6111yescharacteristic
476C23×C8—611no—
477C23×C8—611no—
478C23×C8—611no—
479#537—618no—
480#537—1224no—
481C2×C22⋊Q8—611no—
482C2×C22⋊Q8—1221no—
483C2×C22⋊Q8C2×D6111yescharacteristic
484C2×#121—611no—
485C2×#121—611no—
486C2×#121—1221no—
487C2×#121—1221no—
488C2×#121—1221no—
489C2×#117—611no—
490C22×C4⋊C4—611no—
491C22×C4⋊C4—611no—
492#417—1224no—
493#416—1224no—
494C2×#103—611no—
495C2×#103—611no—
496C2×#103C2×D6111yescharacteristic
497C2×#103C2×D6111yescharacteristic
498C2×#102—611no—
499C2×#102—611no—
500C2×#102—611no—
501C2×#102—611no—
502#391—1221no—
503#390—1221no—
504#386—1221no—
505#386—1221no—
506#380—611no—
507#380—611no—
508#380—611no—
509#380C2×D6111yescharacteristic
510#340—611no—
511#340—611no—
512#340—611no—
513#340—611no—
514#340—611no—
515#340—611no—
516#340C2×D6111yescharacteristic
517#340C2×D6111yescharacteristic
518C61#2097611yescharacteristic, complemented, Sylow
519C2×#41—614no—
520C2×#41—614no—
521C2×#41—614no—
522C2×#41—1222no—
523C2×#41—1222no—
524C2×#41—1222no—
525C2×#41—1222no—
526C2×#41—1222no—
527C2×#41—1222no—
528C2×#41—1222no—
529C2×#41—1222no—
530C2×#41—1222no—
531C22×Q8—611no—
532C22×Q8C22×D6111yescharacteristic
533C22×D4—611no—
534C22×D4—611no—
535C22×D4—611no—
536C22×D4—611no—
537C22×D4—1221no—
538C22×D4—1221no—
539C22×D4—1221no—
540C23×C4—611no—
541C23×C4—611no—
542C23×C4—1221no—
543C23×C4—1221no—
544C23×C4—1221no—
545C23×C4C22×D6111yescharacteristic
546#131—12232no—
547C2×M16—22no—
548C2×M16—22no—
549C2×M16—22no—
550C2×M16—614no—
551C2×M16—1222no—
552C2×M16—1222no—
553C2×M16—1222no—
554C2×M16—1222no—
555C2×M16—1222no—
556C22×C8—611no—
557C22×C8—611no—
558C22×C8—614no—
559C22×C8—1222no—
560C22×C8—1222no—
561C22×C8—1222no—
562C22×C8—1222no—
563C22×C8—1222no—
564C22×C8—1222no—
565C22×C8—1222no—
566C22×C8—1222no—
567C22×C8C22×D6111yescharacteristic
568C22×C8C22×D6111yescharacteristic
569C22⋊Q8—22no—
570C22⋊Q8—614no—
571C22⋊Q8—1228no—
572C22⋊Q8—1222no—
573C22⋊Q8C4×D6114yescomplemented
574#121—614no—
575#121—614no—
576#121—1228no—
577#121—1228no—
578#121—1222no—
579#121—1228no—
580#121—1222no—
581#117—1222no—
582#117—1222no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—611no—
585C2×C4⋊C4—614no—
586C2×C4⋊C4—611no—
587C2×C4⋊C4—611no—
588C2×C4⋊C4—1222no—
589C2×C4⋊C4—1222no—
590C2×C4⋊C4—1222no—
591C2×C4⋊C4—1221no—
592C2×C4⋊C4—1221no—
593C2×C4⋊C4—1221no—
594C2×C4⋊C4C22×D6111yescharacteristic
595C2×C4⋊C4C22×D6111yescharacteristic
596C2×C4⋊C4C22×D6111yescharacteristic
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—1221no—
600C2×C22⋊C4—1221no—
601C2×C22⋊C4—1221no—
602C2×C22⋊C4—1221no—
603C2×C22⋊C4—1221no—
604C2×C22⋊C4—1221no—
605C2×C22⋊C4—1221no—
606C2×C42—1221no—
607#103—22no—
608#103—22no—
609#103—1222no—
610#103—1222no—
611#102—1222no—
612#102—1222no—
613#102—1222no—
614#102—1222no—
615#95—21no—
616#95—1221no—
617#95—1221no—
618#95—1221no—
619C24—611no—
620C24—611no—
621C24—1221no—
622C24D4×D6111yescharacteristic
623#41—1228no—
624#41—1228no—
625#41—1228no—
626#41—1228no—
627#41—1228no—
628#41—1228no—
629#41—2444no—
630#41—2444no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—614no—
637C2×Q8—1222no—
638C2×Q8—1222no—
639C2×Q8C2×C4×D6112yes—
640C2×D4—614no—
641C2×D4—614no—
642C2×D4—612no—
643C2×D4—614no—
644C2×D4—1222no—
645C2×D4—1222no—
646C2×D4—1224no—
647C2×D4—1224no—
648C2×D4—1222no—
649C2×D4—1222no—
650C2×D4—1222no—
651C2×D4—1222no—
652C2×D4—1224no—
653C2×D4—1221no—
654C2×D4—1221no—
655C2×D4—1221no—
656C2×D4—1221no—
657C2×D4—1221no—
658C2×D4—4881no—
659C2×D4—4881no—
660C2×D4—4881no—
661C2×D4—4881no—
662C2×D4—2442no—
663C2×D4—2442no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—611no—
673C22×C4—612no—
674C22×C4—612no—
675C22×C4—612no—
676C22×C4—612no—
677C22×C4—612no—
678C22×C4—612no—
679C22×C4—611no—
680C22×C4—612no—
681C22×C4—612no—
682C22×C4—1224no—
683C22×C4—1224no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—1221no—
690C22×C4—1221no—
691C22×C4—4881no—
692C22×C4—4881no—
693C22×C4—4881no—
694C22×C4—4881no—
695C22×C4—2442no—
696C22×C4—2442no—
697C22×C4—2442no—
698C22×C4C2×C4×D6112yes—
699C22×C4D4×D6112yes—
700C22×C4D4×D6111yescharacteristic
701C22×C4C23×D6111yescharacteristic
702M16—28no—
703M16—1228no—
704M16—1228no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—612no—
710C2×C8—612no—
711C2×C8—1228no—
712C2×C8—1228no—
713C2×C8—1228no—
714C2×C8—1221no—
715C2×C8—1221no—
716C2×C8—1221no—
717C2×C8—1221no—
718C2×C8D4×D6112yes—
719C2×C8D4×D6112yes—
720C4⋊C4—21no—
721C4⋊C4—24no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—612no—
727C4⋊C4—1224no—
728C4⋊C4—1224no—
729C4⋊C4—1221no—
730C4⋊C4—1221no—
731C4⋊C4—1221no—
732C4⋊C4—1221no—
733C4⋊C4—1221no—
734C4⋊C4—2442no—
735C4⋊C4C2×C4×D6112yes—
736C22⋊C4—24no—
737C22⋊C4—81no—
738C22⋊C4—1224no—
739C22⋊C4—1224no—
740C22⋊C4—1224no—
741C22⋊C4—4881no—
742C22⋊C4—4881no—
743C22⋊C4—4881no—
744C22⋊C4—2442no—
745C42—2442no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—612no—
753C23—612no—
754C23—612no—
755C23—612no—
756C23—1221no—
757C23—1221no—
758C23—1221no—
759C23—1221no—
760C23—1221no—
761C23—1221no—
762C23—1221no—
763C23—1221no—
764C23—1221no—
765C23—1221no—
766C23—1222no—
767C23—2441no—
768C23—2441no—
769C23—2441no—
770C23—2441no—
771C23—2441no—
772C23—2441no—
773C23C22⋊C4×D6112yes—
774C23C2×D4×D6111yescharacteristic
775Q8—22no—
776Q8—22no—
777Q8—41no—
778Q8—41no—
779Q8—1228no—
780D4—1228no—
781D4—1228no—
782D4—1228no—
783D4—1222no—
784D4—1222no—
785D4—4884no—
786D4—4884no—
787D4—2448no—
788D4—2441no—
789D4—2441no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—612no—
809C2×C4—612no—
810C2×C4—612no—
811C2×C4—614no—
812C2×C4—614no—
813C2×C4—614no—
814C2×C4—614no—
815C2×C4—612no—
816C2×C4—1221no—
817C2×C4—1221no—
818C2×C4—1222no—
819C2×C4—1222no—
820C2×C4—1222no—
821C2×C4—1222no—
822C2×C4—1222no—
823C2×C4—4884no—
824C2×C4—4884no—
825C2×C4—2448no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4—2441no—
832C2×C4—2441no—
833C2×C4—2441no—
834C2×C4C22⋊C4×D6112yes—
835C2×C4C22×C4×D6111yescharacteristic
836C2×C4C2×D4×D6111yescharacteristic
837C2×C4C2×D4×D6111yescharacteristic
838C2×C4C2×D4×D6111yescharacteristic
839C2×C4#41×D6111yescharacteristic
840C2×C4#41×D6111yescharacteristic
841C8—22no—
842C8—22no—
843C8—1222no—
844C8—1222no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—614no—
853C22—1222no—
854C22—1222no—
855C22—1222no—
856C22—1222no—
857C22—1222no—
858C22—1222no—
859C22—1222no—
860C22—1222no—
861C22—1222no—
862C22—4881no—
863C22—4881no—
864C22—4881no—
865C22—4881no—
866C22—2442no—
867C22—2442no—
868C22—2442no—
869C22—2441no—
870C22—2441no—
871C22—2441no—
872C22—2441no—
873C22C2×C22⋊C4×D6111yescharacteristic
874C22#121×D6111yescharacteristic
875C22#121×D6111yescharacteristic
876C22#1684056611yescharacteristic
877C22#1684057111yescharacteristic
878C22#1684057111yescharacteristic
879C22#1684057811yescharacteristic
880C4—22no—
881C4—42no—
882C4—42no—
883C4—81no—
884C4—81no—
885C4—614no—
886C4—1222no—
887C4—4881no—
888C4—4881no—
889C4—2442no—
890C4C4×D4×D6111yescharacteristic
891C4C4×D4×D6111yescharacteristic
892C4#120×D6111yescharacteristic
893C4#123×D6111yescharacteristic
894C2—42no—
895C2—1224no—
896C2—4882no—
897C2—2442no—
898C2#386×D6111yescharacteristic
899C2#2145434311yescharacteristic
900C2#2145435111yescharacteristic
901C2#2145548311yescharacteristic
902C2#2145548711yescharacteristic
903C2#2145549411yescharacteristic
904C2#2145550711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1894C2
socleC23×C61C22×D4
prime radicalC2×#16840342C2
cosocleC22×C4×C61C24
hypercenter#1894D61
hypocenterC61#20976
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
1. C22×#14519785C2semidirect
3. C2×#16839762C2semidirect
4. C2×#16839757C2semidirect
5. #21448408C2semidirect
6. #21446257C2semidirect
7. #21446256C2semidirect
8. #21446249C2semidirect
9. #21446246C2semidirect
10. #21446245C2semidirect
11. #21446243C2semidirect
12. #21446239C2semidirect
13. #21445537C2semidirect
14. #340×D61C2semidirect
15. C61×#1894C2semidirect
27. #16840342C4semidirect
97. C2×#11758189D4semidirect
108. C2×C8×D61D4semidirect
111. #14519753C2×C4semidirect
114. #14519752C2×C4semidirect
116. #14519751C2×C4semidirect
156. C22⋊Q8×C61C2×C4semidirect
450. #1894D61semidirect
518. C61#20976semidirect
573. C22⋊Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145197852
C2×#168403422
C2×#168397622
C2×#168397572
#214484082
#214462572
#214462562
#214462492
#214462462
#214462452
#214462432
#214462392
#214455372
#340×D612
C61×#18942
#2097661