Finite Group Databasebeta

← #29647288

Subgroups — #29647288

Order 15616.

1438 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#525×D61C211yesmaximal, characteristic
2C2×#16839724C211yesmaximal, characteristic, complemented
3#21448200C211yesmaximal, characteristic, complemented
4#21444361C212yesmaximal, complemented
5#21444359C212yesmaximal, complemented
6#21444350C212yesmaximal, complemented
7#21444346C212yesmaximal, complemented
8#21444311C211yesmaximal, characteristic, complemented
9#21444310C211yesmaximal, characteristic, complemented
10#21444308C211yesmaximal, characteristic, complemented
11C61×#1501C211yesmaximal, characteristic, complemented
12C2×#41×D61C411yescharacteristic, complemented
13C23×C4×D61C2211yescharacteristic
14C22×#11758189—21no—
15#16840275C411yescharacteristic, complemented
16#16840275C2211yescharacteristic
17#16840274C411yescharacteristic, complemented
18#16840273C2211yescharacteristic
19#16840272C411yescharacteristic, complemented
20#16840272C2211yescharacteristic
21#16840271—21no—
22#16840271—21no—
23#16840270—21no—
24#16840269C411yescharacteristic, complemented
25#16840268—21no—
26#123×D61—21no—
27C22⋊Q8×D61C411yescharacteristic, complemented
28C22⋊Q8×D61C2211yescharacteristic
29#121×D61C411yescharacteristic, complemented
30#121×D61C2211yescharacteristic
31#120×D61—21no—
32C4×D4×D61—21no—
33C4×D4×D61—21no—
34C2×#14519734—21no—
35#117×D61C411yescharacteristic, complemented
36#16839724—21no—
37#16839724—21no—
38#16839724C2212yes—
39#16839724C2212yescomplemented
40C2×C22⋊#92418C2211yescharacteristic, complemented
41C2×#14519689—21no—
42#16839624C2212yes—
43#16839621C2212yescomplemented
44#16839620—21no—
45#16839617—21no—
46C4×#11758198—21no—
47C4×C22⋊Dic61C2211yescharacteristic, complemented
48#16839500C2212yescomplemented
49#16839499C2212yescomplemented
50#16839498C2212yescomplemented
51#16839497C2212yescomplemented
52#16839496C2212yescomplemented
53#16839495C2212yescomplemented
54C61×#525C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic, complemented
56C4×C22⋊C4×C61C2211yescharacteristic, complemented
57C61×#328C2212yescomplemented
58C61×#327C2212yescomplemented
59C24×D61D411yescharacteristic
60C2×#11758226C2×C411yescharacteristic
61C2×#11758222—21no—
62C2×#11758222C2×C411yescharacteristic
63C2×#11758224—21no—
64C2×#11758224C2×C411yescharacteristic
65#41×D61—44no—
66C2×Q8×D61C2×C411yescharacteristic
67C2×D4×D61—21no—
68C2×D4×D61—21no—
69C2×D4×D61—21no—
70C2×D4×D61C2×C411yescharacteristic
71C23×Dic61D411yescharacteristic
72C22×C4×D61—21no—
73C22×C4×D61—44no—
74C22×C4×D61C2×C411yescharacteristic
75C22×C4×D61C2×C411yescharacteristic
76C22×C4×D61C2×C411yescharacteristic
77C22×C4×D61C2×C411yescharacteristic
78C22×C4×D61D411yescharacteristic
79C22×C4×D61D411yescharacteristic
80C22×C4×D61D411yescharacteristic
81C22×C4×D61D411yescharacteristic
82C22×C4×D61D411yescharacteristic
83C22×C4×D61D411yescharacteristic
84C22×C4×D61C2311yescharacteristic
85C22×C4×D61C2311yescharacteristic
86C2×#11758189—22no—
87C2×#11758189—22no—
88C2×#11758189—44no—
89C22×#92418—21no—
90#14519762—21no—
91#14519762—21no—
92#14519761—21no—
93#14519760—21no—
94#14519759—21no—
95#14519759—21no—
96#14519758—21no—
97#14519757C2×C411yescharacteristic
98#14519757C2×C411yescharacteristic
99#14519756C2×C411yescharacteristic
100#14519756C2311yescharacteristic
101#14519755—21no—
102#14519755—21no—
103#14519754—21no—
104#14519754—21no—
105#14519753C2×C411yescharacteristic
106#14519753C2×C411yescharacteristic
107#14519752C2×C411yescharacteristic
108#14519752C2×C411yescharacteristic
109#14519751C2×C411yescharacteristic
110#14519751C2311yescharacteristic
111#14519750—21no—
112#14519750—21no—
113#14519749—21no—
114#14519749—21no—
115#14519748C2×C411yescharacteristic
116#14519748C2×C411yescharacteristic
117#14519747—21no—
118#14519747—21no—
119#14519747—21no—
120#14519746—21no—
121#14519745—21no—
122#14519745—21no—
123#14519745—21no—
124C4×D244—21no—
125C4×D244—21no—
126D4×Dic61—21no—
127D4×Dic61—21no—
128#14519739—21no—
129#14519739—21no—
130C4×C22⋊D61—21no—
131C4×C22⋊D61—21no—
132C4×C22⋊D61—21no—
133C4×C22⋊D61—21no—
134#14519737—21no—
135#14519737—21no—
136#14519737—21no—
137#14519737—21no—
138#14519736C2×C411yescharacteristic
139#14519735C2×C411yescharacteristic
140#14519735C2×C411yescharacteristic
141#14519734—21no—
142#14519734—44no—
143#14519733—21no—
144C2×#11758196—22no—
145C4⋊C4×D61—21no—
146C4⋊C4×D61—21no—
147C4⋊C4×D61C2×C411yescharacteristic
148C4⋊C4×D61C2×C411yescharacteristic
149C2×C22⋊Dic61—21no—
150C2×#11758198—22no—
151C2×#11758198—22no—
152C22⋊C4×D61—21no—
153C22⋊C4×D61—21no—
154C22⋊C4×D61—21no—
155C22⋊C4×D61—21no—
156C22⋊C4×D61—21no—
157C2×C4×Dic61—21no—
158C42×D61—21no—
159C22⋊#92418—21no—
160C22⋊#92418C2312yes—
161#14519689—22no—
162#14519689—22no—
163#14519684—22no—
164#14519684C2312yes—
165C2×#41×C61C2×C411yescharacteristic
166C23×C4×C61C2311yescharacteristic
167C22×C8×C61—21no—
168#123×C61—21no—
169C22⋊Q8×C61C2×C411yescharacteristic
170C22⋊Q8×C61C2311yescharacteristic
171#121×C61C2×C411yescharacteristic
172#121×C61C2311yescharacteristic
173#120×C61—21no—
174C4×D4×C61—21no—
175C4×D4×C61—21no—
176#117×C61C2×C411yescharacteristic
177C2×C22⋊C4×C61—21no—
178C2×C42×C61—21no—
179C22⋊C8×C61—21no—
180C22⋊C8×C61C2312yes—
181#95×C61C2312yes—
182C24×C61C2×D411yescharacteristic
183C23×D61—21no—
184C23×D61—42no—
185C23×D61—42no—
186C23×D61—42no—
187C23×D61C22⋊C411yescharacteristic
188C23×D61C22⋊C411yescharacteristic
189C23×D61C22⋊C411yescharacteristic
190C23×D61C22⋊C411yescharacteristic
191C23×D61C2×D411yescharacteristic
192C23×D61C2×D411yescharacteristic
193#41×C61—42no—
194C2×Q8×C61C22×C411yescharacteristic
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61C22×C411yescharacteristic
199C22×C4×C61—21no—
200C22×C4×C61—22no—
201C22×C4×C61—42no—
202C22×C4×C61C22×C411yescharacteristic
203C22×C4×C61C22×C411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2411yescharacteristic
208C2×C22⋊D61—21no—
209C2×C22⋊D61—21no—
210C2×C22⋊D61—21no—
211C2×C22⋊D61—21no—
212C2×C22⋊D61—21no—
213C2×C22⋊D61—21no—
214C2×C22⋊D61—21no—
215C22×Dic61—21no—
216C22×Dic61—22no—
217C22×Dic61—42no—
218C22×Dic61C22⋊C411yescharacteristic
219C22×Dic61C22⋊C411yescharacteristic
220C22×Dic61C22⋊C411yescharacteristic
221C22×Dic61C22⋊C411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224#11758226—42no—
225Q8×D61—42no—
226#11758224—42no—
227#11758224—44no—
228D4×D61—42no—
229D4×D61—44no—
230D4×D61—44no—
231D4×D61—44no—
232#11758222—44no—
233#11758222—42no—
234C2×D244—21no—
235C2×D244—21no—
236C2×D244—21no—
237C2×D244C22×C411yescharacteristic
238C2×C4×D61—24no—
239C2×C4×D61—24no—
240C2×C4×D61—24no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—42no—
247C2×C4×D61—42no—
248C2×C4×D61—42no—
249C2×C4×D61—42no—
250C2×C4×D61—42no—
251C2×C4×D61—42no—
252C2×C4×D61—42no—
253C2×C4×D61—42no—
254C2×C4×D61—42no—
255C2×C4×D61—44no—
256C2×C4×D61C22⋊C411yescharacteristic
257C2×C4×D61C22⋊C411yescharacteristic
258C2×C4×D61C22⋊C411yescharacteristic
259C2×C4×D61C22⋊C411yescharacteristic
260C2×C4×D61C22⋊C411yescharacteristic
261C2×C4×D61C22⋊C411yescharacteristic
262C2×C4×D61C22⋊C411yescharacteristic
263C2×C4×D61C22⋊C411yescharacteristic
264C2×C4×D61C22×C411yescharacteristic
265C2×C4×D61C22×C411yescharacteristic
266C2×C4×D61C22×C411yescharacteristic
267C2×C4×D61C22×C411yescharacteristic
268C2×C4×D61C2×D411yescharacteristic
269C2×C4×D61C2×D411yescharacteristic
270C2×C4×D61C2×D411yescharacteristic
271C2×C4×D61C2×D411yescharacteristic
272C2×Dic122—21no—
273C2×Dic122C22×C411yescharacteristic
274C2×C8×C61—22no—
275C2×C8×C61—42no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61C22×C411yescharacteristic
279C4⋊C4×C61C22×C411yescharacteristic
280C22⋊C4×C61—21no—
281C22⋊C4×C61—21no—
282C22⋊C4×C61—21no—
283C22⋊C4×C61—21no—
284C22⋊C4×C61—21no—
285C22⋊C4×C61—42no—
286C42×C61—21no—
287C42×C61—42no—
288C22⋊Dic61—21no—
289C22⋊Dic61—21no—
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292C22⋊Dic61—21no—
293C22⋊Dic61—42no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—44no—
305#11758198—44no—
306C4⋊Dic61—21no—
307C4⋊Dic61—21no—
308C4⋊Dic61C22×C411yescharacteristic
309C4⋊Dic61C22×C411yescharacteristic
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196—44no—
317C4×Dic61—21no—
318C4×Dic61—21no—
319C4×Dic61—21no—
320C4×Dic61—42no—
321C2×#92418—22no—
322C2×#92418—42no—
323#11758189—44no—
324#11758189—44no—
325C23×C61—22no—
326C23×C61—22no—
327C23×C61—21no—
328C23×C61—41no—
329C23×C61C2×C22⋊C411yescharacteristic
330C23×C61C2×C22⋊C411yescharacteristic
331C23×C61C22×D411yescharacteristic
332C22×D61—22no—
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—21no—
340C22×D61—41no—
341C22×D61—41no—
342C22×D61—41no—
343C22×D61—41no—
344C22×D61—41no—
345C22×D61—41no—
346C22×D61—41no—
347C22×D61—41no—
348C22×D61—41no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61—42no—
352C22×D61—42no—
353C22×D61—416no—
354C22×D61—42no—
355C22×D61C2×C22⋊C411yescharacteristic
356C22×D61C2×C22⋊C411yescharacteristic
357C22×D61C2×C22⋊C411yescharacteristic
358C22×D61C2×C22⋊C411yescharacteristic
359Q8×C61—41no—
360D4×C61—41no—
361D4×C61—42no—
362D4×C61—42no—
363D4×C61—42no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—22no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—42no—
374C2×C4×C61—42no—
375C2×C4×C61—42no—
376C2×C4×C61—42no—
377C2×C4×C61C2×C22⋊C411yescharacteristic
378C2×C4×C61C2×C22⋊C411yescharacteristic
379C2×C4×C61C23×C411yescharacteristic
380C2×C4×C61C22×D411yescharacteristic
381C22⋊D61—42no—
382C22⋊D61—42no—
383C22⋊D61—42no—
384C22⋊D61—42no—
385C22⋊D61—42no—
386C22⋊D61—42no—
387C22⋊D61—42no—
388C2×Dic61—22no—
389C2×Dic61—22no—
390C2×Dic61—22no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—42no—
398C2×Dic61—42no—
399C2×Dic61—42no—
400C2×Dic61—42no—
401C2×Dic61C2×C22⋊C411yescharacteristic
402C2×Dic61C2×C22⋊C411yescharacteristic
403C2×Dic61C2×C22⋊C411yescharacteristic
404C2×Dic61C2×C22⋊C411yescharacteristic
405D244—41no—
406D244—42no—
407D244—42no—
408D244—42no—
409C4×D61—22no—
410C4×D61—22no—
411C4×D61—22no—
412C4×D61—22no—
413C4×D61—22no—
414C4×D61—22no—
415C4×D61—22no—
416C4×D61—22no—
417C4×D61—22no—
418C4×D61—41no—
419C4×D61—41no—
420C4×D61—41no—
421C4×D61—41no—
422C4×D61—41no—
423C4×D61—41no—
424C4×D61—42no—
425C4×D61—42no—
426C4×D61—42no—
427C4×D61—42no—
428C4×D61—42no—
429C4×D61#9914yes—
430Dic122—42no—
431Dic122—41no—
432C8×C61—42no—
433#92418—42no—
434#17559—611nomaximal, Sylow
435C22×C61—21no—
436C22×C61—21no—
437C22×C61—21no—
438C22×C61—21no—
439C22×C61—21no—
440C22×C61—21no—
441C22×C61—21no—
442C22×C61—44no—
443C22×C61—41no—
444C22×C61—41no—
445C22×C61—41no—
446C22×C61#42112yes—
447C22×C61C22×C22⋊C411yescharacteristic
448C22×C61#57512yes—
449C2×D61—21no—
450C2×D61—21no—
451C2×D61—21no—
452C2×D61—21no—
453C2×D61—21no—
454C2×D61—21no—
455C2×D61—21no—
456C2×D61—21no—
457C2×D61—21no—
458C2×D61—21no—
459C2×D61—21no—
460C2×D61—44no—
461C2×D61—44no—
462C2×D61—44no—
463C2×D61—44no—
464C2×D61—44no—
465C2×D61—44no—
466C2×D61—41no—
467C2×D61—41no—
468C2×D61—41no—
469C2×D61—84no—
470C2×D61C2×#9912yes—
471C4×C61—21no—
472C4×C61—21no—
473C4×C61—21no—
474C4×C61—41no—
475C4×C61—41no—
476C4×C61—41no—
477C4×C61—82no—
478C4×C61C2×#9912yes—
479Dic61—21no—
480Dic61—21no—
481Dic61—21no—
482Dic61—41no—
483Dic61—41no—
484Dic61—41no—
485Dic61—82no—
486Dic61C2×#9912yes—
487C2×#525—611no—
488C2×#407—611no—
489#2280—611no—
490#1513—612no—
491#1513—612no—
492#1511—612no—
493#1510—612no—
494#1501—611no—
495#1501—611no—
496#1501—611no—
497#1501D6111yescharacteristic, complemented
498C2×C61—22no—
499C2×C61—22no—
500C2×C61—41no—
501C2×C61—81no—
502C2×C61C22×#9911yescharacteristic
503C2×C61#289611yescharacteristic
504C2×C61C2×#42111yescharacteristic
505D61—22no—
506D61—41no—
507D61—41no—
508D61—41no—
509D61—81no—
510C22×#41—611no—
511C24×C4—611no—
512C22×M16—1221no—
513#525—611no—
514#525—611no—
515#525—611no—
516#525—611no—
517#525—611no—
518#525—611no—
519#525—611no—
520#525—1221no—
521#525—1221no—
522#525—1221no—
523#525—1221no—
524#525C2×D6111yescharacteristic
525C2×#123—1221no—
526C2×C22⋊Q8—611no—
527C2×C22⋊Q8—611no—
528C2×#121—611no—
529C2×#121—611no—
530C2×#120—1221no—
531C2×C4×D4—1221no—
532C2×C4×D4—1221no—
533C2×#117—611no—
534C2×#117—1221no—
535#407—612no—
536#407—612no—
537#407—1221no—
538#407—1221no—
539C2×C22⋊C8—611no—
540C2×C22⋊C8—1221no—
541C2×C22⋊C8C2×D6111yescharacteristic, complemented
542#381—612no—
543#380—612no—
544#380—1221no—
545#379—1221no—
546C4×C22⋊C4—611no—
547C4×C22⋊C4—1221no—
548C4×C22⋊C4C2×D6111yescharacteristic, complemented
549#328—612no—
550#328—612no—
551#328—612no—
552#328C2×D6112yescomplemented
553#327—612no—
554#327—612no—
555#327—612no—
556#327C2×D6112yescomplemented
557C61#1755911yescharacteristic, complemented, Sylow
558C25—611no—
559C2×#41—611no—
560C2×#41—611no—
561C2×#41—611no—
562C2×#41—1221no—
563C2×#41—1221no—
564C2×#41—2444no—
565C2×#41C4×D6111yescharacteristic
566C22×Q8—611no—
567C22×D4—611no—
568C22×D4—1221no—
569C22×D4—1221no—
570C22×D4—1221no—
571C23×C4—611no—
572C23×C4—611no—
573C23×C4—611no—
574C23×C4—611no—
575C23×C4—611no—
576C23×C4—611no—
577C23×C4—611no—
578C23×C4—611no—
579C23×C4—611no—
580C23×C4—611no—
581C23×C4—611no—
582C23×C4—611no—
583C23×C4—611no—
584C23×C4—1221no—
585C23×C4—2444no—
586C23×C4C22×D6111yescharacteristic
587C2×M16—1222no—
588C2×M16—1222no—
589C2×M16—2444no—
590C22×C8—21no—
591C22×C8—1221no—
592#123—21no—
593#123—1221no—
594#123—1221no—
595#123—1221no—
596#123—1221no—
597#123—1221no—
598#123—1221no—
599#123—1221no—
600C22⋊Q8—611no—
601C22⋊Q8—611no—
602C22⋊Q8—611no—
603C22⋊Q8—611no—
604C22⋊Q8—611no—
605C22⋊Q8—611no—
606C22⋊Q8—1221no—
607C22⋊Q8—1221no—
608C22⋊Q8—1221no—
609C22⋊Q8—1221no—
610C22⋊Q8C4×D6111yescharacteristic
611C22⋊Q8C22×D6111yescharacteristic
612#121—611no—
613#121—611no—
614#121—611no—
615#121—611no—
616#121—611no—
617#121—611no—
618#121—1221no—
619#121—1221no—
620#121—1221no—
621#121—1221no—
622#121C4×D6111yescharacteristic
623#121C22×D6111yescharacteristic
624#120—21no—
625#120—1221no—
626#120—1221no—
627#120—1221no—
628#120—1221no—
629#120—1221no—
630#120—1221no—
631#120—1221no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—1221no—
635C4×D4—1221no—
636C4×D4—1221no—
637C4×D4—1221no—
638C4×D4—1221no—
639C4×D4—1221no—
640C4×D4—1221no—
641C4×D4—1221no—
642C4×D4—1221no—
643C4×D4—1221no—
644C4×D4—1221no—
645C4×D4—1221no—
646C4×D4—1221no—
647C4×D4—1221no—
648#117—611no—
649#117—611no—
650#117—611no—
651#117—1221no—
652#117—1221no—
653#117—2444no—
654#117C4×D6111yescharacteristic
655C2×C4⋊C4—611no—
656C2×C4⋊C4—611no—
657C2×C4⋊C4—1221no—
658C2×C4⋊C4—1221no—
659C2×C4⋊C4—1222no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—1221no—
662C2×C22⋊C4—1221no—
663C2×C22⋊C4—1221no—
664C2×C22⋊C4—1221no—
665C2×C22⋊C4—1221no—
666C2×C22⋊C4—1222no—
667C2×C22⋊C4—1222no—
668C2×C22⋊C4—1221no—
669C2×C42—21no—
670C2×C42—1221no—
671C2×C42—1221no—
672C22⋊C8—21no—
673C22⋊C8—612no—
674C22⋊C8—1222no—
675C22⋊C8—1222no—
676C22⋊C8—1221no—
677C22⋊C8C22×D6112yes—
678#95—612no—
679#95—1222no—
680#95C22×D6112yes—
681C24—611no—
682C24—611no—
683C24—611no—
684C24—611no—
685C24—611no—
686C24—611no—
687C24—1221no—
688C24—2442no—
689C24—2442no—
690C24—2442no—
691C24D4×D6111yescharacteristic
692#41—42no—
693#41—2442no—
694#41—2444no—
695#41—2444no—
696#41—2442no—
697#41—2442no—
698C2×Q8—611no—
699C2×Q8—1221no—
700C2×Q8—2442no—
701C2×Q8C2×C4×D6111yescharacteristic
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—611no—
706C2×D4—1221no—
707C2×D4—1221no—
708C2×D4—1221no—
709C2×D4—1221no—
710C2×D4—1221no—
711C2×D4—1221no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—1221no—
716C2×D4—2442no—
717C2×D4—2444no—
718C2×D4—2444no—
719C2×D4—2444no—
720C2×D4C2×C4×D6111yescharacteristic
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—42no—
724C22×C4—611no—
725C22×C4—611no—
726C22×C4—611no—
727C22×C4—611no—
728C22×C4—611no—
729C22×C4—611no—
730C22×C4—611no—
731C22×C4—611no—
732C22×C4—611no—
733C22×C4—611no—
734C22×C4—611no—
735C22×C4—611no—
736C22×C4—611no—
737C22×C4—611no—
738C22×C4—611no—
739C22×C4—611no—
740C22×C4—611no—
741C22×C4—611no—
742C22×C4—611no—
743C22×C4—611no—
744C22×C4—611no—
745C22×C4—611no—
746C22×C4—1224no—
747C22×C4—1224no—
748C22×C4—1224no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—1221no—
755C22×C4—1222no—
756C22×C4—2442no—
757C22×C4—2442no—
758C22×C4—2442no—
759C22×C4—2444no—
760C22×C4—2442no—
761C22×C4—2442no—
762C22×C4—2442no—
763C22×C4—2442no—
764C22×C4—2442no—
765C22×C4—2442no—
766C22×C4—2442no—
767C22×C4C2×C4×D6111yescharacteristic
768C22×C4C2×C4×D6111yescharacteristic
769C22×C4D4×D6111yescharacteristic
770C22×C4D4×D6111yescharacteristic
771C22×C4D4×D6111yescharacteristic
772C22×C4C23×D6111yescharacteristic
773M16—2444no—
774M16—2444no—
775C2×C8—22no—
776C2×C8—42no—
777C2×C8—1222no—
778C2×C8—2442no—
779C4⋊C4—21no—
780C4⋊C4—21no—
781C4⋊C4—611no—
782C4⋊C4—611no—
783C4⋊C4—1221no—
784C4⋊C4—1221no—
785C4⋊C4—1221no—
786C4⋊C4—1221no—
787C4⋊C4—1221no—
788C4⋊C4—1221no—
789C4⋊C4—1221no—
790C4⋊C4—1221no—
791C4⋊C4—2444no—
792C4⋊C4C2×C4×D6111yescharacteristic
793C4⋊C4C2×C4×D6111yescharacteristic
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—42no—
800C22⋊C4—1221no—
801C22⋊C4—1221no—
802C22⋊C4—1221no—
803C22⋊C4—1221no—
804C22⋊C4—1221no—
805C22⋊C4—1221no—
806C22⋊C4—1221no—
807C22⋊C4—1221no—
808C22⋊C4—1221no—
809C22⋊C4—1221no—
810C22⋊C4—1221no—
811C22⋊C4—1221no—
812C22⋊C4—1221no—
813C22⋊C4—1221no—
814C22⋊C4—1221no—
815C22⋊C4—2444no—
816C22⋊C4—2444no—
817C22⋊C4—2442no—
818C42—21no—
819C42—42no—
820C42—1221no—
821C42—1221no—
822C42—1221no—
823C42—2442no—
824C23—22no—
825C23—22no—
826C23—21no—
827C23—41no—
828C23—611no—
829C23—611no—
830C23—611no—
831C23—611no—
832C23—1222no—
833C23—1222no—
834C23—1222no—
835C23—1222no—
836C23—1222no—
837C23—1222no—
838C23—1222no—
839C23—1221no—
840C23—2441no—
841C23—2441no—
842C23—2441no—
843C23—2441no—
844C23—2441no—
845C23—2441no—
846C23—2441no—
847C23—2441no—
848C23—2441no—
849C23—2441no—
850C23—2441no—
851C23—2442no—
852C23—2442no—
853C23—2442no—
854C23—24416no—
855C23C22⋊C4×D6111yescharacteristic
856C23C22⋊C4×D6111yescharacteristic
857C23C2×D4×D6111yescharacteristic
858Q8—41no—
859Q8—2441no—
860Q8—2442no—
861D4—41no—
862D4—42no—
863D4—42no—
864D4—42no—
865D4—2441no—
866D4—2442no—
867D4—2442no—
868D4—2442no—
869D4—2442no—
870D4—2442no—
871D4—2442no—
872D4—2442no—
873D4—2442no—
874D4—2442no—
875D4—2442no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—611no—
890C2×C4—614no—
891C2×C4—611no—
892C2×C4—611no—
893C2×C4—611no—
894C2×C4—1222no—
895C2×C4—1222no—
896C2×C4—1222no—
897C2×C4—1222no—
898C2×C4—1222no—
899C2×C4—1222no—
900C2×C4—1222no—
901C2×C4—1222no—
902C2×C4—1222no—
903C2×C4—1222no—
904C2×C4—1222no—
905C2×C4—1222no—
906C2×C4—1221no—
907C2×C4—1221no—
908C2×C4—1221no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4—2442no—
916C2×C4—2442no—
917C2×C4—2442no—
918C2×C4—2442no—
919C2×C4—2442no—
920C2×C4—2441no—
921C2×C4—2441no—
922C2×C4—2441no—
923C2×C4—2442no—
924C2×C4—2442no—
925C2×C4—2442no—
926C2×C4—2442no—
927C2×C4C22⋊C4×D6111yescharacteristic
928C2×C4C22⋊C4×D6111yescharacteristic
929C2×C4C22×C4×D6111yescharacteristic
930C2×C4C2×D4×D6111yescharacteristic
931C8—42no—
932C8—2442no—
933C22—21no—
934C22—21no—
935C22—21no—
936C22—21no—
937C22—21no—
938C22—21no—
939C22—21no—
940C22—44no—
941C22—41no—
942C22—41no—
943C22—41no—
944C22—612no—
945C22—1221no—
946C22—1221no—
947C22—1221no—
948C22—1221no—
949C22—1221no—
950C22—1221no—
951C22—1221no—
952C22—1221no—
953C22—1221no—
954C22—1221no—
955C22—1221no—
956C22—4884no—
957C22—2444no—
958C22—2444no—
959C22—2444no—
960C22—2444no—
961C22—2444no—
962C22—2444no—
963C22—2441no—
964C22—2441no—
965C22—2441no—
966C22#1683977712yes—
967C22C2×C22⋊C4×D6111yescharacteristic
968C22#1684055912yes—
969C4—21no—
970C4—21no—
971C4—21no—
972C4—41no—
973C4—41no—
974C4—41no—
975C4—82no—
976C4—612no—
977C4—1221no—
978C4—1221no—
979C4—1221no—
980C4—4882no—
981C4—2441no—
982C4—2441no—
983C4—2441no—
984C4#99×D6112yes—
985C2—22no—
986C2—22no—
987C2—41no—
988C2—81no—
989C2—1222no—
990C2—4881no—
991C2—2441no—
992C2—2441no—
993C2—2441no—
994C2C2×#99×D6111yescharacteristic
995C2#2145433411yescharacteristic
996C2C2×#1683977711yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1501C2
socleC22×C61C22×C22⋊C4
prime radical#525×D61C2
cosocleC22×C4×C61C24
hypercenter#1501D61
hypocenterC61#17559
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1501

Complements

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

NH ≅ G/Ntype
2. C2×#16839724C2semidirect
3. #21448200C2semidirect
4. #21444361C2semidirect
5. #21444359C2semidirect
6. #21444350C2semidirect
7. #21444346C2semidirect
8. #21444311C2semidirect
9. #21444310C2semidirect
10. #21444308C2semidirect
11. C61×#1501C2semidirect
12. C2×#41×D61C4semidirect
15. #16840275C4semidirect
17. #16840274C4semidirect
19. #16840272C4semidirect
24. #16840269C4semidirect
27. C22⋊Q8×D61C4semidirect
29. #121×D61C4semidirect
35. #117×D61C4semidirect
39. #16839724C22semidirect
40. C2×C22⋊#92418C22semidirect
43. #16839621C22semidirect
47. C4×C22⋊Dic61C22semidirect
48. #16839500C22semidirect
49. #16839499C22semidirect
50. #16839498C22semidirect
51. #16839497C22semidirect
52. #16839496C22semidirect
53. #16839495C22semidirect
55. C2×C22⋊C8×C61C22semidirect
56. C4×C22⋊C4×C61C22semidirect
57. C61×#328C22semidirect
58. C61×#327C22semidirect
497. #1501D61semidirect
541. C2×C22⋊C8C2×D61semidirect
548. C4×C22⋊C4C2×D61semidirect
552. #328C2×D61semidirect
556. #327C2×D61semidirect
557. C61#17559semidirect

Maximal subgroups

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

subgroupindex
#525×D612
C2×#168397242
#214482002
#214443612
#214443592
#214443502
#214443462
#214443112
#214443102
#214443082
C61×#15012
#1755961