Finite Group Databasebeta

← #29718039

Subgroups — #29718039

Order 15616.

1480 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840013C211yesmaximal, characteristic, complemented
2C2×#16839907C211yesmaximal, characteristic, complemented
3C2×#16839901C211yesmaximal, characteristic, complemented
4C2×#16839771C211yesmaximal, characteristic, complemented
5#21449237C211yesmaximal, characteristic, complemented
6#21447055C211yesmaximal, characteristic, complemented
7#21447012C211yesmaximal, characteristic, complemented
8#21446896C211yesmaximal, characteristic, complemented
9#21446820C211yesmaximal, characteristic, complemented
10#21446174C211yesmaximal, characteristic, complemented
11#21446142C211yesmaximal, characteristic, complemented
12#21446117C211yesmaximal, characteristic, complemented
13#21446087C211yesmaximal, characteristic, complemented
14#21445759C211yesmaximal, characteristic, complemented
15C2×C61×#548C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C22×#11758194C2211yescharacteristic
20C2×#14519751C2211yescharacteristic
21C2×#14519751C2211yescharacteristic
22C2×#14519736C2211yescharacteristic
23#16840013—24no—
24#16839907—24no—
25#16839901—24no—
26C2×#14519708C2211yescharacteristic
27#16839771—24no—
28C2×#14519701C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41#16839677—21no—
42#16839670—21no—
43#16839664C2211yescharacteristic
44#16839662—21no—
45#16839660C2211yescharacteristic
46#16839652—21no—
47#16839622C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C22×#41×C61C2211yescharacteristic
53C23×Q8×C61C2211yescharacteristic
54C61×#548—24no—
55C61×#548—24no—
56C2×#124×C61—21no—
57C2×#124×C61C2211yescharacteristic
58C2×C22⋊Q8×C61—21no—
59C2×C22⋊Q8×C61C2211yescharacteristic
60C2×#121×C61—21no—
61C2×#121×C61C2211yescharacteristic
62C2×C4×Q8×C61C2211yescharacteristic
63C2×C4×D4×C61—21no—
64C2×C4×D4×C61C2211yescharacteristic
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C22×C22⋊D61—21no—
68C2×#11758201—22no—
69C2×#11758201—22no—
70C2×#11758201—22no—
71C2×#11758201—22no—
72C2×#11758201—41no—
73C2×#11758201—41no—
74C2×#11758199—22no—
75C2×#11758199—22no—
76C2×#11758199—41no—
77C2×#11758194—22no—
78C2×#11758194—22no—
79C2×#11758194—41no—
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84#14519751—22no—
85#14519751—22no—
86#14519751—22no—
87#14519751—41no—
88#14519736—22no—
89#14519736—41no—
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×#11758196—21no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×C4×Dic61—21no—
101#14519708—22no—
102#14519701—22no—
103#14519701—22no—
104#14519701—22no—
105#14519701—22no—
106#14519701—22no—
107#14519701D414yescomplemented
108#14519698—22no—
109#14519698—22no—
110#14519698—41no—
111#14519697—22no—
112C22⋊#92418—22no—
113C22⋊#92418—22no—
114C22⋊#92418—41no—
115#14519684—21no—
116#14519684—21no—
117C2×#41×C61—22no—
118C2×#41×C61—22no—
119C2×#41×C61—22no—
120C2×#41×C61—22no—
121C2×#41×C61—41no—
122C2×#41×C61—41no—
123C22×Q8×C61—22no—
124C22×Q8×C61—21no—
125C22×Q8×C61—22no—
126C22×Q8×C61—22no—
127C22×Q8×C61—41no—
128C22×Q8×C61—41no—
129C22×Q8×C61D414yescomplemented
130C22×Q8×C61C2311yescharacteristic
131C22×Q8×C61C2311yescharacteristic
132C22×D4×C61—21no—
133C22×D4×C61—21no—
134C22×D4×C61D411yescharacteristic
135C22×D4×C61C2311yescharacteristic
136C23×C4×C61—21no—
137C23×C4×C61—21no—
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140#124×C61—28no—
141#124×C61—22no—
142#124×C61—22no—
143C22⋊Q8×C61—28no—
144C22⋊Q8×C61—22no—
145C22⋊Q8×C61—22no—
146#121×C61—28no—
147#121×C61—22no—
148#121×C61D414yescomplemented
149C4×Q8×C61—22no—
150C4×Q8×C61—22no—
151C4×D4×C61—28no—
152C4×D4×C61—22no—
153C4×D4×C61—22no—
154C2×C4⋊C4×C61—21no—
155C2×C4⋊C4×C61—21no—
156C2×C4⋊C4×C61D411yescharacteristic
157C2×C4⋊C4×C61C2311yescharacteristic
158C2×C22⋊C4×C61—21no—
159C2×C22⋊C4×C61—21no—
160C2×C22⋊C4×C61—21no—
161C2×C22⋊C4×C61—21no—
162C2×C22⋊C4×C61D411yescharacteristic
163C2×C22⋊C4×C61D411yescharacteristic
164C2×C42×C61—21no—
165C2×C42×C61C2311yescharacteristic
166C24×C61—21no—
167C24×C61C2×D411yescharacteristic
168C24×C61C2×D411yescharacteristic
169C23×D61—21no—
170#41×C61—44no—
171#41×C61—44no—
172#41×C61—44no—
173#41×C61—44no—
174C2×Q8×C61—24no—
175C2×Q8×C61—21no—
176C2×Q8×C61—21no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61—28no—
180C2×Q8×C61—21no—
181C2×Q8×C61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—42no—
185C2×Q8×C61—42no—
186C2×Q8×C61—44no—
187C2×Q8×C61—44no—
188C2×Q8×C61—44no—
189C2×Q8×C61C2×D412yes—
190C2×Q8×C61C2×D412yes—
191C2×Q8×C61C2×D412yes—
192C2×Q8×C61#4112yes—
193C2×D4×C61—24no—
194C2×D4×C61—22no—
195C2×D4×C61—24no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—41no—
202C2×D4×C61—41no—
203C2×D4×C61—42no—
204C2×D4×C61—42no—
205C2×D4×C61—42no—
206C2×D4×C61—42no—
207C2×D4×C61C2×D412yes—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—24no—
214C22×C4×C61—24no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—42no—
224C22×C4×C61—42no—
225C22×C4×C61—42no—
226C22×C4×C61—42no—
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D412yes—
232C22×C4×C61C2×D412yes—
233C22×C4×C61C2411yescharacteristic
234C2×C22⋊D61—42no—
235C2×C22⋊D61—42no—
236C2×C22⋊D61—42no—
237C2×C22⋊D61—81no—
238C2×C22⋊D61—81no—
239C2×C22⋊D61—81no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C2×D244—21no—
244C2×D244—21no—
245C2×D244—21no—
246C2×D244—21no—
247C2×D244—21no—
248C2×D244—21no—
249C4⋊C4×C61—24no—
250C4⋊C4×C61—24no—
251C4⋊C4×C61—22no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61C2×D412yes—
254C22⋊C4×C61—24no—
255C22⋊C4×C61—24no—
256C22⋊C4×C61—24no—
257C22⋊C4×C61—22no—
258C22⋊C4×C61—24no—
259C22⋊C4×C61—22no—
260C42×C61—24no—
261C42×C61—21no—
262C42×C61—21no—
263C22⋊Dic61—42no—
264C22⋊Dic61—81no—
265#11758201—44no—
266#11758201—44no—
267#11758199—44no—
268#11758198—42no—
269#11758198—42no—
270#11758198—42no—
271#11758198—81no—
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61C2×D412yes—
278#11758196—81no—
279C4×Dic61—42no—
280#11758194—44no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418C2×D412yes—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—22no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—41no—
308C23×C61—41no—
309C23×C61—41no—
310C23×C61—41no—
311C23×C61—41no—
312C23×C61—41no—
313C23×C61#12012yes—
314C23×C61C22×D411yescharacteristic
315C22×D61—41no—
316C22×D61—41no—
317C22×D61—41no—
318C22×D61—41no—
319C22×D61—41no—
320C22×D61—41no—
321C22×D61—41no—
322Q8×C61—22no—
323Q8×C61—22no—
324Q8×C61—22no—
325Q8×C61—22no—
326Q8×C61—22no—
327Q8×C61—48no—
328Q8×C61—41no—
329Q8×C61—41no—
330Q8×C61#12114yes—
331D4×C61—22no—
332D4×C61—22no—
333D4×C61—48no—
334D4×C61—44no—
335D4×C61—48no—
336D4×C61—41no—
337D4×C61—41no—
338C2×C4×C61—22no—
339C2×C4×C61—21no—
340C2×C4×C61—22no—
341C2×C4×C61—21no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—21no—
358C2×C4×C61—48no—
359C2×C4×C61—48no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61#12012yes—
369C2×C4×C61C22×D411yescharacteristic
370C2×C4×C61C22×D411yescharacteristic
371C2×C4×C61C22×D411yescharacteristic
372C2×C4×C61C2×#4111yescharacteristic
373C2×C4×C61H(5,𝔽2)11yescharacteristic
374C2×C4×C61H(5,𝔽2)11yescharacteristic
375C22⋊D61—84no—
376C22⋊D61—84no—
377C2×Dic61—22no—
378C2×Dic61—41no—
379C2×Dic61—41no—
380C2×Dic61—41no—
381C2×Dic61—41no—
382C2×Dic61—41no—
383C2×Dic61—41no—
384C2×Dic61—41no—
385C2×Dic61—41no—
386D244—41no—
387D244—41no—
388D244—41no—
389D244—41no—
390#92418—22no—
391#92418—41no—
392#92418—41no—
393#92418—41no—
394#24455—611nomaximal, Sylow
395C22×C61—22no—
396C22×C61—22no—
397C22×C61—22no—
398C22×C61—41no—
399C22×C61—41no—
400C22×C61—41no—
401C22×C61—41no—
402C22×C61—42no—
403C22×C61—41no—
404C22×C61—41no—
405C22×C61—42no—
406C22×C61—41no—
407C22×C61—42no—
408C22×C61—41no—
409C22×C61—41no—
410C22×C61—41no—
411C22×C61—41no—
412C22×C61—81no—
413C22×C61—81no—
414C22×C61—81no—
415C22×C61—81no—
416C22×C61C2×#12011yescharacteristic
417C22×C61D4211yescharacteristic
418C22×C61#54611yescharacteristic
419C22×C61#57511yescharacteristic
420C22×C61#57511yescharacteristic
421C22×C61#57711yescharacteristic
422C22×C61#57711yescharacteristic
423C2×D61—81no—
424C2×D61—81no—
425C2×D61—81no—
426C2×D61—81no—
427C2×D61—81no—
428C2×D61—81no—
429C2×D61—81no—
430C4×C61—22no—
431C4×C61—24no—
432C4×C61—41no—
433C4×C61—42no—
434C4×C61—41no—
435C4×C61—42no—
436C4×C61—41no—
437C4×C61C2×#12111yescharacteristic
438C4×C61#53411yescharacteristic
439C4×C61D4211yescharacteristic
440C4×C61#54611yescharacteristic
441Dic61—42no—
442Dic61—81no—
443Dic61—81no—
444C2×#548D6111yescharacteristic, complemented
445C2×#469—611no—
446C2×#449—611no—
447C2×#448—611no—
448C2×#419—611no—
449#2414—611no—
450#2042—611no—
451#2035—611no—
452#2012—611no—
453#2000—611no—
454#1880—611no—
455#1875—611no—
456#1870—611no—
457#1865—611no—
458#1788—611no—
459C2×C61—42no—
460C2×C61—81no—
461C2×C61—82no—
462C2×C61#241011yescharacteristic
463C2×C61#300511yescharacteristic
464C2×C61#301011yescharacteristic
465C2×C61#327111yescharacteristic
466C2×C61#327511yescharacteristic
467C2×C61#332111yescharacteristic
468C2×C61#332611yescharacteristic
469D61—161no—
470C22×#41C2×D6111yescharacteristic
471C23×Q8C2×D6111yescharacteristic
472C22×SD16—611no—
473C22×SD16—611no—
474C22×D8—611no—
475C22×M16—611no—
476#548—24no—
477#548—24no—
478C2×#124—21no—
479C2×#124C2×D6111yescharacteristic
480C2×C22⋊Q8—21no—
481C2×C22⋊Q8C2×D6111yescharacteristic
482C2×#121—21no—
483C2×#121—611no—
484C2×#121—611no—
485C2×#121C2×D6111yescharacteristic
486C2×C4×Q8C2×D6111yescharacteristic
487C2×C4×D4—21no—
488C2×C4×D4C2×D6111yescharacteristic
489C2×#117—611no—
490#469—1224no—
491#449—1224no—
492#448—1224no—
493C2×#106—611no—
494#419—1224no—
495C2×#103—611no—
496C2×#103—611no—
497C2×#103—611no—
498C2×#103—611no—
499C2×#103—611no—
500C2×#103—611no—
501C2×#102—611no—
502C2×#102—611no—
503C2×#102—611no—
504C2×#102—611no—
505C2×C22⋊C8—611no—
506C2×C22⋊C8—611no—
507C2×C22⋊C8—611no—
508#394—1221no—
509#392—1221no—
510#390—611no—
511#390—1221no—
512#389—611no—
513#388—1221no—
514#380—611no—
515#340—611no—
516#340—611no—
517#336—611no—
518#336—611no—
519C61#2445511yescharacteristic, complemented, Sylow
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—41no—
525C2×#41—41no—
526C22×Q8—21no—
527C22×Q8—22no—
528C22×Q8—22no—
529C22×Q8—22no—
530C22×Q8—41no—
531C22×Q8—41no—
532C22×Q8C22⋊D6114yescomplemented
533C22×Q8C22×D6111yescharacteristic
534C22×Q8C22×D6111yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—611no—
538C22×D4—1221no—
539C22×D4—1221no—
540C22×D4C22⋊D6111yescharacteristic
541C22×D4C22×D6111yescharacteristic
542C23×C4—21no—
543C23×C4—21no—
544C23×C4C22×D6111yescharacteristic
545C23×C4C22×D6111yescharacteristic
546C2×SD16—1222no—
547C2×SD16—1222no—
548C2×SD16—1222no—
549C2×SD16—1222no—
550C2×SD16—2441no—
551C2×SD16—2441no—
552C2×D8—1222no—
553C2×D8—1222no—
554C2×D8—2441no—
555C2×M16—1222no—
556C2×M16—1222no—
557C2×M16—2441no—
558C22×C8—611no—
559C22×C8—611no—
560C22×C8—611no—
561C22×C8—611no—
562#124—28no—
563#124—22no—
564#124—22no—
565C22⋊Q8—28no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568#121—28no—
569#121—22no—
570#121—1222no—
571#121—1222no—
572#121—1222no—
573#121—2441no—
574#121C22⋊D6114yescomplemented
575C4×Q8—22no—
576C4×Q8—22no—
577C4×D4—28no—
578C4×D4—22no—
579C4×D4—22no—
580#117—1222no—
581#117—2441no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—611no—
585C2×C4⋊C4—611no—
586C2×C4⋊C4—611no—
587C2×C4⋊C4—1221no—
588C2×C4⋊C4C22⋊D6111yescharacteristic
589C2×C4⋊C4C22×D6111yescharacteristic
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—1221no—
595C2×C22⋊C4—1221no—
596C2×C22⋊C4—1221no—
597C2×C22⋊C4—1221no—
598C2×C22⋊C4—1221no—
599C2×C22⋊C4—1221no—
600C2×C22⋊C4C22⋊D6111yescharacteristic
601C2×C22⋊C4C22⋊D6111yescharacteristic
602C2×C42—21no—
603C2×C42—1221no—
604C2×C42C22×D6111yescharacteristic
605#106—1222no—
606#103—614no—
607#103—1222no—
608#103—1222no—
609#103—1222no—
610#103—1222no—
611#103—1222no—
612#102—1222no—
613#102—1222no—
614#102—1222no—
615#102—2441no—
616C22⋊C8—1222no—
617C22⋊C8—1222no—
618C22⋊C8—2441no—
619#95—1221no—
620#95—1221no—
621C24—21no—
622C24—1221no—
623C24C2×C22⋊D6111yescharacteristic
624C24C2×C22⋊D6111yescharacteristic
625#41—44no—
626#41—44no—
627#41—44no—
628#41—44no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—24no—
634C2×Q8—28no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—42no—
640C2×Q8—42no—
641C2×Q8—44no—
642C2×Q8—44no—
643C2×Q8—44no—
644C2×Q8D4×D6112yes—
645C2×Q8#1175822412yes—
646C2×Q8C2×C22⋊D6112yes—
647C2×Q8C2×C22⋊D6112yes—
648C2×D4—24no—
649C2×D4—22no—
650C2×D4—24no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—41no—
657C2×D4—41no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—1221no—
663C2×D4—1221no—
664C2×D4—1221no—
665C2×D4—1221no—
666C2×D4—1221no—
667C2×D4—1221no—
668C2×D4—4881no—
669C2×D4—4881no—
670C2×D4—4881no—
671C2×D4—2442no—
672C2×D4—2442no—
673C2×D4—2442no—
674C2×D4C2×C22⋊D6112yes—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—24no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—24no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—1221no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4C2×C22⋊D6111yescharacteristic
698C22×C4C2×C22⋊D6111yescharacteristic
699C22×C4C2×C22⋊D6111yescharacteristic
700C22×C4C2×C22⋊D6112yes—
701C22×C4C2×C22⋊D6112yes—
702C22×C4C2×C22⋊D6111yescharacteristic
703C22×C4C23×D6111yescharacteristic
704SD16—2444no—
705SD16—2444no—
706D8—2444no—
707M16—2444no—
708C2×C8—612no—
709C2×C8—1221no—
710C2×C8—1221no—
711C2×C8—1221no—
712C2×C8—1221no—
713C2×C8—1221no—
714C2×C8—1221no—
715C2×C8—1221no—
716C2×C8—1221no—
717C2×C8—1221no—
718C2×C8—1221no—
719C2×C8—1221no—
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—21no—
723C4⋊C4—22no—
724C4⋊C4—612no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4—1221no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4—4881no—
731C4⋊C4C2×C22⋊D6112yes—
732C22⋊C4—24no—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—22no—
736C22⋊C4—24no—
737C22⋊C4—22no—
738C22⋊C4—4881no—
739C22⋊C4—4881no—
740C22⋊C4—2442no—
741C22⋊C4—2442no—
742C22⋊C4—2442no—
743C22⋊C4—2442no—
744C42—24no—
745C42—21no—
746C42—21no—
747C42—2442no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—22no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—2441no—
769C23—2441no—
770C23—2441no—
771C23—2441no—
772C23—2441no—
773C23—2441no—
774C23—2441no—
775C23#1451974612yes—
776C23C22×C22⋊D6111yescharacteristic
777Q8—22no—
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—22no—
782Q8—48no—
783Q8—41no—
784Q8—41no—
785Q8#1451974914yes—
786D4—22no—
787D4—22no—
788D4—48no—
789D4—44no—
790D4—48no—
791D4—41no—
792D4—41no—
793D4—4884no—
794D4—4884no—
795D4—2441no—
796D4—2441no—
797D4—2441no—
798D4—2441no—
799C2×C4—22no—
800C2×C4—21no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—48no—
820C2×C4—48no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—1222no—
830C2×C4—2441no—
831C2×C4—2441no—
832C2×C4—2441no—
833C2×C4—2441no—
834C2×C4—2441no—
835C2×C4—2441no—
836C2×C4—2441no—
837C2×C4—2441no—
838C2×C4#1451974612yes—
839C2×C4C2×D4×D6111yescharacteristic
840C2×C4C22×C22⋊D6111yescharacteristic
841C2×C4C22×C22⋊D6111yescharacteristic
842C2×C4C2×#1175822411yescharacteristic
843C2×C4#1451982211yescharacteristic
844C2×C4#1451982211yescharacteristic
845C8—1222no—
846C8—2441no—
847C8—2441no—
848C8—2441no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—42no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—42no—
863C22—42no—
864C22—41no—
865C22—41no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—4881no—
871C22—4881no—
872C22—4881no—
873C22—4881no—
874C22—4881no—
875C22—4881no—
876C22—4881no—
877C22C2×#1451974611yescharacteristic
878C22D4×C22⋊D6111yescharacteristic
879C22#1684040611yescharacteristic
880C22#1684056011yescharacteristic
881C22#1684056011yescharacteristic
882C22#1684057011yescharacteristic
883C22#1684057011yescharacteristic
884C4—22no—
885C4—24no—
886C4—41no—
887C4—41no—
888C4—42no—
889C4—41no—
890C4—42no—
891C4—4881no—
892C4—4881no—
893C4—2442no—
894C4C2×#1451974911yescharacteristic
895C4#1684032111yescharacteristic
896C4D4×C22⋊D6111yescharacteristic
897C4#1684040611yescharacteristic
898C2—42no—
899C2—81no—
900C2—82no—
901C2—9761no—
902C2#2144919311yescharacteristic
903C2#2145506111yescharacteristic
904C2#2145510511yescharacteristic
905C2#2145740511yescharacteristic
906C2#2145745111yescharacteristic
907C2#2145800511yescharacteristic
908C2#2145807211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#548C2
socleC23×C61C22×D4
hypercenterC2×#548D61
hypocenterC61#24455
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#16840013C2semidirect
2. C2×#16839907C2semidirect
3. C2×#16839901C2semidirect
4. C2×#16839771C2semidirect
5. #21449237C2semidirect
6. #21447055C2semidirect
7. #21447012C2semidirect
8. #21446896C2semidirect
9. #21446820C2semidirect
10. #21446174C2semidirect
11. #21446142C2semidirect
12. #21446117C2semidirect
13. #21446087C2semidirect
14. #21445759C2semidirect
15. C2×C61×#548C2semidirect
107. #14519701D4semidirect
129. C22×Q8×C61D4semidirect
148. #121×C61D4semidirect
444. C2×#548D61semidirect
519. C61#24455semidirect
532. C22×Q8C22⋊D61semidirect
574. #121C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168400132
C2×#168399072
C2×#168399012
C2×#168397712
#214492372
#214470552
#214470122
#214468962
#214468202
#214461742
#214461422
#214461172
#214460872
#214457592
C2×C61×#5482
#2445561