Finite Group Databasebeta

← #29647173

Subgroups — #29647173

Order 15616.

1574 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#525×D61C211yesmaximal, characteristic
2C2×#16839724C211yesmaximal, characteristic, complemented
3C4×C22⋊C4×D61C211yesmaximal, characteristic, complemented
4#21444337C212yesmaximal, complemented
5#21444333C212yesmaximal, complemented
6#21444322C212yesmaximal, complemented
7#21444320C212yesmaximal, 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—
34#117×D61C411yescharacteristic, complemented
35C2×C22⋊C4×D61—21no—
36C2×C42×D61—21no—
37#16839724—21no—
38#16839724—21no—
39#16839724C2212yes—
40#16839724C2212yescomplemented
41C2×C22⋊#92418C2211yescharacteristic, complemented
42C2×#14519689—21no—
43C22⋊C4×Dic61—21no—
44C4×#11758198—21no—
45C4×C22⋊Dic61C2211yescharacteristic, complemented
46#16839609C2212yes—
47#95×D61C2212yescomplemented
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, complemented
63C2×#11758224—21no—
64C2×#11758224C2×C411yescharacteristic
65#41×D61—44no—
66C2×Q8×D61C2×C411yescharacteristic, complemented
67C2×D4×D61—21no—
68C2×D4×D61—21no—
69C2×D4×D61—21no—
70C2×D4×D61C2×C411yescharacteristic, complemented
71C23×Dic61D411yescharacteristic
72C22×C4×D61—22no—
73C22×C4×D61—21no—
74C22×C4×D61—44no—
75C22×C4×D61C2×C411yescharacteristic
76C22×C4×D61C2×C411yescharacteristic
77C22×C4×D61C2×C411yescharacteristic
78C22×C4×D61C2×C411yescharacteristic
79C22×C4×D61D411yescharacteristic
80C22×C4×D61D411yescharacteristic
81C22×C4×D61D411yescharacteristic
82C22×C4×D61D411yescharacteristic
83C22×C4×D61D411yescharacteristic
84C22×C4×D61D411yescharacteristic
85C22×C4×D61C2311yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C2×#11758189—22no—
88C2×#11758189—22no—
89C2×#11758189—44no—
90C22×#92418—21no—
91#14519762—21no—
92#14519762—21no—
93#14519761—21no—
94#14519760—21no—
95#14519759—21no—
96#14519759—21no—
97#14519758—21no—
98#14519757C2×C411yescharacteristic
99#14519757C2×C411yescharacteristic, complemented
100#14519756C2×C411yescharacteristic, complemented
101#14519756C2311yescharacteristic
102#14519755—21no—
103#14519755—21no—
104#14519754—21no—
105#14519754—21no—
106#14519753C2×C411yescharacteristic
107#14519753C2×C411yescharacteristic, complemented
108#14519752C2×C411yescharacteristic
109#14519752C2×C411yescharacteristic, complemented
110#14519751C2×C411yescharacteristic, complemented
111#14519751C2311yescharacteristic
112#14519750—21no—
113#14519750—21no—
114#14519749—21no—
115#14519749—21no—
116#14519748C2×C411yescharacteristic
117#14519748C2×C411yescharacteristic, complemented
118#14519747—21no—
119#14519747—21no—
120#14519747—21no—
121#14519746—21no—
122#14519745—21no—
123#14519745—21no—
124#14519745—21no—
125C4×D244—21no—
126C4×D244—21no—
127D4×Dic61—21no—
128D4×Dic61—21no—
129#14519739—21no—
130#14519739—21no—
131C4×C22⋊D61—21no—
132C4×C22⋊D61—21no—
133C4×C22⋊D61—21no—
134C4×C22⋊D61—21no—
135#14519737—21no—
136#14519737—21no—
137#14519737—21no—
138#14519737—21no—
139#14519736C2×C411yescharacteristic, complemented
140#14519735C2×C411yescharacteristic
141#14519735C2×C411yescharacteristic
142#14519734—21no—
143#14519733—21no—
144C4⋊C4×D61—21no—
145C4⋊C4×D61—21no—
146C4⋊C4×D61C2×C411yescharacteristic, complemented
147C4⋊C4×D61C2×C411yescharacteristic, complemented
148C2×C22⋊Dic61—21no—
149C2×#11758198—22no—
150C22⋊C4×D61—28no—
151C22⋊C4×D61—21no—
152C22⋊C4×D61—21no—
153C22⋊C4×D61—21no—
154C22⋊C4×D61—21no—
155C22⋊C4×D61—21no—
156C2×C4×Dic61—21no—
157C2×C4×Dic61—22no—
158C42×D61—21no—
159C42×D61—44no—
160C22⋊#92418—21no—
161C22⋊#92418C2312yes—
162#14519689—22no—
163#14519689—22no—
164#14519684—22no—
165#14519684C2312yes—
166C2×#41×C61C2×C411yescharacteristic, complemented
167C23×C4×C61C2311yescharacteristic
168C22×C8×C61—21no—
169#123×C61—21no—
170C22⋊Q8×C61C2×C411yescharacteristic, complemented
171C22⋊Q8×C61C2311yescharacteristic
172#121×C61C2×C411yescharacteristic, complemented
173#121×C61C2311yescharacteristic
174#120×C61—21no—
175C4×D4×C61—21no—
176C4×D4×C61—21no—
177#117×C61C2×C411yescharacteristic, complemented
178C2×C22⋊C4×C61—21no—
179C2×C42×C61—21no—
180C22⋊C8×C61—21no—
181C22⋊C8×C61C2312yes—
182#95×C61C2312yes—
183C24×C61C2×D411yescharacteristic
184C23×D61—24no—
185C23×D61—21no—
186C23×D61—42no—
187C23×D61—42no—
188C23×D61C22⋊C411yescharacteristic
189C23×D61C22⋊C411yescharacteristic
190C23×D61C22⋊C411yescharacteristic
191C23×D61C22⋊C411yescharacteristic
192C23×D61C2×D411yescharacteristic
193C23×D61C2×D411yescharacteristic
194#41×C61—42no—
195C2×Q8×C61C22×C411yescharacteristic
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61C22×C411yescharacteristic
200C22×C4×C61—22no—
201C22×C4×C61—21no—
202C22×C4×C61—42no—
203C22×C4×C61C22×C411yescharacteristic
204C22×C4×C61C22×C411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2411yescharacteristic
209C2×C22⋊D61—21no—
210C2×C22⋊D61—21no—
211C2×C22⋊D61—21no—
212C2×C22⋊D61—21no—
213C2×C22⋊D61—21no—
214C2×C22⋊D61—21no—
215C2×C22⋊D61—21no—
216C22×Dic61—22no—
217C22×Dic61—21no—
218C22×Dic61—42no—
219C22×Dic61C22⋊C411yescharacteristic
220C22×Dic61C22⋊C411yescharacteristic
221C22×Dic61C22⋊C411yescharacteristic
222C22×Dic61C22⋊C411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224C22×Dic61C2×D411yescharacteristic
225#11758226—42no—
226Q8×D61—42no—
227#11758224—42no—
228#11758224—44no—
229D4×D61—42no—
230D4×D61—44no—
231D4×D61—44no—
232D4×D61—44no—
233#11758222—44no—
234#11758222—42no—
235C2×D244—21no—
236C2×D244—21no—
237C2×D244—21no—
238C2×D244C22×C411yescharacteristic
239C2×C4×D61—24no—
240C2×C4×D61—24no—
241C2×C4×D61—24no—
242C2×C4×D61—28no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
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—42no—
256C2×C4×D61—42no—
257C2×C4×D61—44no—
258C2×C4×D61—44no—
259C2×C4×D61—44no—
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×D61C22×C411yescharacteristic
269C2×C4×D61C22×C411yescharacteristic
270C2×C4×D61C22×C411yescharacteristic
271C2×C4×D61C22×C411yescharacteristic
272C2×C4×D61C2×D411yescharacteristic
273C2×C4×D61C2×D411yescharacteristic
274C2×C4×D61C2×D411yescharacteristic
275C2×C4×D61C2×D411yescharacteristic
276C2×Dic122—21no—
277C2×Dic122C22×C411yescharacteristic
278C2×C8×C61—22no—
279C2×C8×C61—42no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61C22×C411yescharacteristic
283C4⋊C4×C61C22×C411yescharacteristic
284C22⋊C4×C61—24no—
285C22⋊C4×C61—21no—
286C22⋊C4×C61—21no—
287C22⋊C4×C61—21no—
288C22⋊C4×C61—21no—
289C22⋊C4×C61—21no—
290C42×C61—21no—
291C42×C61—42no—
292C22⋊Dic61—24no—
293C22⋊Dic61—21no—
294C22⋊Dic61—21no—
295C22⋊Dic61—21no—
296C22⋊Dic61—21no—
297C22⋊Dic61—21no—
298#11758198—28no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—21no—
306#11758198—21no—
307#11758198—21no—
308#11758198—21no—
309C4⋊Dic61—21no—
310C4⋊Dic61—21no—
311C4⋊Dic61C22×C411yescharacteristic
312C4⋊Dic61C22×C411yescharacteristic
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319C4×Dic61—21no—
320C4×Dic61—21no—
321C4×Dic61—21no—
322C4×Dic61—44no—
323C4×Dic61—42no—
324C2×#92418—22no—
325C2×#92418—42no—
326#11758189—44no—
327#11758189—44no—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—21no—
331C23×C61—41no—
332C23×C61C2×C22⋊C411yescharacteristic
333C23×C61C2×C22⋊C411yescharacteristic
334C23×C61C22×D411yescharacteristic
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—22no—
343C22×D61—22no—
344C22×D61—22no—
345C22×D61—21no—
346C22×D61—41no—
347C22×D61—41no—
348C22×D61—41no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—41no—
353C22×D61—416no—
354C22×D61—42no—
355C22×D61—42no—
356C22×D61—42no—
357C22×D61#10414yes—
358C22×D61C2×C22⋊C411yescharacteristic
359C22×D61C2×C22⋊C411yescharacteristic
360C22×D61C2×C22⋊C411yescharacteristic
361C22×D61C2×C22⋊C411yescharacteristic
362Q8×C61—41no—
363D4×C61—41no—
364D4×C61—42no—
365D4×C61—42no—
366D4×C61—42no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—22no—
370C2×C4×C61—24no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—42no—
378C2×C4×C61—42no—
379C2×C4×C61—42no—
380C2×C4×C61C2×C22⋊C411yescharacteristic
381C2×C4×C61C2×C22⋊C411yescharacteristic
382C2×C4×C61C23×C411yescharacteristic
383C2×C4×C61C22×D411yescharacteristic
384C22⋊D61—42no—
385C22⋊D61—42no—
386C22⋊D61—42no—
387C22⋊D61—42no—
388C22⋊D61—42no—
389C22⋊D61—42no—
390C22⋊D61—42no—
391C2×Dic61—22no—
392C2×Dic61—22no—
393C2×Dic61—22no—
394C2×Dic61—24no—
395C2×Dic61—21no—
396C2×Dic61—21no—
397C2×Dic61—21no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—42no—
402C2×Dic61—42no—
403C2×Dic61—42no—
404C2×Dic61C2×C22⋊C411yescharacteristic
405C2×Dic61C2×C22⋊C411yescharacteristic
406C2×Dic61C2×C22⋊C411yescharacteristic
407C2×Dic61C2×C22⋊C411yescharacteristic
408D244—41no—
409D244—42no—
410D244—42no—
411D244—42no—
412C4×D61—22no—
413C4×D61—22no—
414C4×D61—22no—
415C4×D61—22no—
416C4×D61—22no—
417C4×D61—22no—
418C4×D61—22no—
419C4×D61—22no—
420C4×D61—22no—
421C4×D61—41no—
422C4×D61—41no—
423C4×D61—41no—
424C4×D61—41no—
425C4×D61—41no—
426C4×D61—41no—
427C4×D61—42no—
428C4×D61—416no—
429C4×D61—42no—
430C4×D61—42no—
431C4×D61—42no—
432C4×D61—42no—
433C4×D61#9914yes—
434Dic122—42no—
435Dic122—41no—
436C8×C61—42no—
437#92418—42no—
438#17542—611nomaximal, Sylow
439C22×C61—21no—
440C22×C61—21no—
441C22×C61—21no—
442C22×C61—21no—
443C22×C61—21no—
444C22×C61—21no—
445C22×C61—21no—
446C22×C61—44no—
447C22×C61—41no—
448C22×C61—41no—
449C22×C61—41no—
450C22×C61C2×#10412yes—
451C22×C61C22×C22⋊C411yescharacteristic
452C22×C61#57512yes—
453C2×D61—28no—
454C2×D61—21no—
455C2×D61—21no—
456C2×D61—21no—
457C2×D61—21no—
458C2×D61—21no—
459C2×D61—21no—
460C2×D61—21no—
461C2×D61—21no—
462C2×D61—21no—
463C2×D61—44no—
464C2×D61—44no—
465C2×D61—44no—
466C2×D61—44no—
467C2×D61—44no—
468C2×D61—41no—
469C2×D61—41no—
470C2×D61—41no—
471C2×D61—84no—
472C2×D61C2×#9912yes—
473C2×D61C2×#10412yes—
474C2×D61C2×#10412yes—
475C4×C61—21no—
476C4×C61—21no—
477C4×C61—21no—
478C4×C61—44no—
479C4×C61—41no—
480C4×C61—41no—
481C4×C61—41no—
482C4×C61C2×#9912yes—
483Dic61—21no—
484Dic61—21no—
485Dic61—21no—
486Dic61—44no—
487Dic61—41no—
488Dic61—41no—
489Dic61—41no—
490Dic61C2×#9912yes—
491C2×#525—611no—
492C2×#407—611no—
493C2×C4×C22⋊C4—611no—
494#1508—612no—
495#1507—612no—
496#1504—612no—
497#1504—612no—
498#1501—611no—
499#1501—611no—
500#1501—611no—
501#1501D6111yescharacteristic, complemented
502C2×C61—22no—
503C2×C61—22no—
504C2×C61—41no—
505C2×C61—81no—
506C2×C61C22×#9911yescharacteristic
507C2×C61#289611yescharacteristic
508C2×C61C22×#10411yescharacteristic
509D61—22no—
510D61—22no—
511D61—22no—
512D61—41no—
513D61—81no—
514C22×#41—611no—
515C24×C4—611no—
516C22×M16—1221no—
517#525—611no—
518#525—611no—
519#525—611no—
520#525—611no—
521#525—611no—
522#525—611no—
523#525—611no—
524#525—1221no—
525#525—1221no—
526#525—1221no—
527#525—1221no—
528#525C2×D6111yescharacteristic
529C2×#123—1221no—
530C2×C22⋊Q8—611no—
531C2×C22⋊Q8—611no—
532C2×#121—611no—
533C2×#121—611no—
534C2×#120—1221no—
535C2×C4×D4—1221no—
536C2×C4×D4—1221no—
537C2×#117—611no—
538C22×C22⋊C4—1221no—
539C22×C42—1221no—
540#407—612no—
541#407—612no—
542#407—1221no—
543#407—1221no—
544C2×C22⋊C8—611no—
545C2×C22⋊C8—1221no—
546C2×C22⋊C8C2×D6111yescharacteristic, complemented
547C4×C22⋊C4—611no—
548C4×C22⋊C4—612no—
549C4×C22⋊C4—1221no—
550C4×C22⋊C4—1221no—
551C4×C22⋊C4C2×D6111yescharacteristic, complemented
552C2×#95—612no—
553#328—612no—
554#328—612no—
555#328—612no—
556#328C2×D6112yescomplemented
557#327—612no—
558#327—612no—
559#327—612no—
560#327C2×D6112yescomplemented
561C61#1754211yescharacteristic, complemented, Sylow
562C25—611no—
563C2×#41—611no—
564C2×#41—611no—
565C2×#41—611no—
566C2×#41—1221no—
567C2×#41—1221no—
568C2×#41—2444no—
569C2×#41C4×D6111yescharacteristic, complemented
570C22×Q8—611no—
571C22×D4—611no—
572C22×D4—1221no—
573C22×D4—1221no—
574C22×D4—1221no—
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—611no—
585C23×C4—611no—
586C23×C4—611no—
587C23×C4—611no—
588C23×C4—1221no—
589C23×C4—1222no—
590C23×C4—2444no—
591C23×C4C22×D6111yescharacteristic
592C2×M16—1222no—
593C2×M16—1222no—
594C2×M16—2444no—
595C22×C8—21no—
596C22×C8—1221no—
597#123—21no—
598#123—1221no—
599#123—1221no—
600#123—1221no—
601#123—1221no—
602#123—1221no—
603#123—1221no—
604#123—1221no—
605C22⋊Q8—611no—
606C22⋊Q8—611no—
607C22⋊Q8—611no—
608C22⋊Q8—611no—
609C22⋊Q8—611no—
610C22⋊Q8—611no—
611C22⋊Q8—1221no—
612C22⋊Q8—1221no—
613C22⋊Q8—1221no—
614C22⋊Q8—1221no—
615C22⋊Q8C4×D6111yescharacteristic, complemented
616C22⋊Q8C22×D6111yescharacteristic
617#121—611no—
618#121—611no—
619#121—611no—
620#121—611no—
621#121—611no—
622#121—611no—
623#121—1221no—
624#121—1221no—
625#121—1221no—
626#121—1221no—
627#121C4×D6111yescharacteristic, complemented
628#121C22×D6111yescharacteristic
629#120—21no—
630#120—1221no—
631#120—1221no—
632#120—1221no—
633#120—1221no—
634#120—1221no—
635#120—1221no—
636#120—1221no—
637C4×D4—21no—
638C4×D4—21no—
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—
648C4×D4—1221no—
649C4×D4—1221no—
650C4×D4—1221no—
651C4×D4—1221no—
652C4×D4—1221no—
653#117—611no—
654#117—611no—
655#117—611no—
656#117—1221no—
657#117—1221no—
658#117C4×D6111yescharacteristic, complemented
659C2×C4⋊C4—611no—
660C2×C4⋊C4—611no—
661C2×C4⋊C4—1221no—
662C2×C4⋊C4—1221no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—1221no—
665C2×C22⋊C4—1221no—
666C2×C22⋊C4—1221no—
667C2×C22⋊C4—1221no—
668C2×C22⋊C4—1221no—
669C2×C22⋊C4—1228no—
670C2×C22⋊C4—1222no—
671C2×C22⋊C4—1221no—
672C2×C42—21no—
673C2×C42—1221no—
674C2×C42—1222no—
675C2×C42—1221no—
676C2×C42—2444no—
677C22⋊C8—21no—
678C22⋊C8—612no—
679C22⋊C8—1222no—
680C22⋊C8—1222no—
681C22⋊C8—1221no—
682C22⋊C8C22×D6112yes—
683#95—612no—
684#95—1222no—
685#95C22×D6112yes—
686C24—611no—
687C24—611no—
688C24—611no—
689C24—611no—
690C24—611no—
691C24—611no—
692C24—1224no—
693C24—1221no—
694C24—2442no—
695C24—2442no—
696C24D4×D6111yescharacteristic
697#41—42no—
698#41—2442no—
699#41—2444no—
700#41—2444no—
701#41—2442no—
702#41—2442no—
703C2×Q8—611no—
704C2×Q8—1221no—
705C2×Q8—2442no—
706C2×Q8C2×C4×D6111yescharacteristic
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—611no—
711C2×D4—1221no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—1221no—
716C2×D4—1221no—
717C2×D4—1221no—
718C2×D4—1221no—
719C2×D4—1221no—
720C2×D4—1221no—
721C2×D4—2442no—
722C2×D4—2444no—
723C2×D4—2444no—
724C2×D4—2444no—
725C2×D4C2×C4×D6111yescharacteristic
726C22×C4—22no—
727C22×C4—21no—
728C22×C4—42no—
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—611no—
747C22×C4—611no—
748C22×C4—611no—
749C22×C4—611no—
750C22×C4—611no—
751C22×C4—1224no—
752C22×C4—1224no—
753C22×C4—1224no—
754C22×C4—1221no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—1228no—
759C22×C4—1221no—
760C22×C4—1222no—
761C22×C4—1221no—
762C22×C4—2442no—
763C22×C4—2442no—
764C22×C4—2442no—
765C22×C4—2442no—
766C22×C4—2442no—
767C22×C4—2442no—
768C22×C4—2442no—
769C22×C4—2442no—
770C22×C4—2442no—
771C22×C4—2444no—
772C22×C4—2444no—
773C22×C4—2444no—
774C22×C4—2442no—
775C22×C4C2×C4×D6111yescharacteristic
776C22×C4C2×C4×D6111yescharacteristic
777C22×C4D4×D6111yescharacteristic
778C22×C4D4×D6111yescharacteristic
779C22×C4D4×D6111yescharacteristic
780C22×C4C23×D6111yescharacteristic
781M16—2444no—
782M16—2444no—
783C2×C8—22no—
784C2×C8—42no—
785C2×C8—1222no—
786C2×C8—2442no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—611no—
790C4⋊C4—611no—
791C4⋊C4—1221no—
792C4⋊C4—1221no—
793C4⋊C4—1221no—
794C4⋊C4—1221no—
795C4⋊C4—1221no—
796C4⋊C4—1221no—
797C4⋊C4—1221no—
798C4⋊C4—1221no—
799C4⋊C4C2×C4×D6111yescharacteristic
800C4⋊C4C2×C4×D6111yescharacteristic
801C22⋊C4—24no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—21no—
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—1228no—
816C22⋊C4—1221no—
817C22⋊C4—1221no—
818C22⋊C4—1224no—
819C22⋊C4—1221no—
820C22⋊C4—1221no—
821C22⋊C4—1221no—
822C22⋊C4—1221no—
823C22⋊C4—1221no—
824C42—21no—
825C42—42no—
826C42—1221no—
827C42—1221no—
828C42—1221no—
829C42—2442no—
830C42—2444no—
831C23—22no—
832C23—22no—
833C23—21no—
834C23—41no—
835C23—611no—
836C23—611no—
837C23—611no—
838C23—614no—
839C23—611no—
840C23—1222no—
841C23—1222no—
842C23—1222no—
843C23—1222no—
844C23—1222no—
845C23—1222no—
846C23—1222no—
847C23—1222no—
848C23—1222no—
849C23—1222no—
850C23—1221no—
851C23—2441no—
852C23—2441no—
853C23—2441no—
854C23—2441no—
855C23—2441no—
856C23—2441no—
857C23—2441no—
858C23—2442no—
859C23—2442no—
860C23—2442no—
861C23—24416no—
862C23C22⋊C4×D6111yescharacteristic
863C23C22⋊C4×D6111yescharacteristic
864C23C2×D4×D6111yescharacteristic
865Q8—41no—
866Q8—2441no—
867Q8—2442no—
868D4—41no—
869D4—42no—
870D4—42no—
871D4—42no—
872D4—2441no—
873D4—2442no—
874D4—2442no—
875D4—2442no—
876D4—2442no—
877D4—2442no—
878D4—2442no—
879D4—2442no—
880D4—2442no—
881D4—2442no—
882D4—2442no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—24no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—611no—
897C2×C4—614no—
898C2×C4—611no—
899C2×C4—611no—
900C2×C4—611no—
901C2×C4—1222no—
902C2×C4—1222no—
903C2×C4—1222no—
904C2×C4—1222no—
905C2×C4—1222no—
906C2×C4—1222no—
907C2×C4—1222no—
908C2×C4—1222no—
909C2×C4—1222no—
910C2×C4—1222no—
911C2×C4—1222no—
912C2×C4—1222no—
913C2×C4—1224no—
914C2×C4—1221no—
915C2×C4—1221no—
916C2×C4—1221no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4—2441no—
920C2×C4—2441no—
921C2×C4—2441no—
922C2×C4—2441no—
923C2×C4—2442no—
924C2×C4—2442no—
925C2×C4—24416no—
926C2×C4—2442no—
927C2×C4—2442no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2442no—
932C2×C4—2442no—
933C2×C4—2442no—
934C2×C4—2442no—
935C2×C4C22⋊C4×D6111yescharacteristic
936C2×C4C22⋊C4×D6111yescharacteristic
937C2×C4C22×C4×D6111yescharacteristic
938C2×C4C2×D4×D6111yescharacteristic
939C8—42no—
940C8—2442no—
941C22—21no—
942C22—21no—
943C22—21no—
944C22—21no—
945C22—21no—
946C22—21no—
947C22—21no—
948C22—44no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—612no—
953C22—612no—
954C22—612no—
955C22—1228no—
956C22—1221no—
957C22—1221no—
958C22—1221no—
959C22—1221no—
960C22—1221no—
961C22—1221no—
962C22—1221no—
963C22—1221no—
964C22—1221no—
965C22—4884no—
966C22—2444no—
967C22—2444no—
968C22—2444no—
969C22—2444no—
970C22—2444no—
971C22—2441no—
972C22—2441no—
973C22—2441no—
974C22#104×D6112yes—
975C22C2×C22⋊C4×D6111yescharacteristic
976C22#1684055912yes—
977C4—21no—
978C4—21no—
979C4—21no—
980C4—44no—
981C4—41no—
982C4—41no—
983C4—41no—
984C4—612no—
985C4—1221no—
986C4—1221no—
987C4—1221no—
988C4—2444no—
989C4—2441no—
990C4—2441no—
991C4—2441no—
992C4#99×D6112yes—
993C2—22no—
994C2—22no—
995C2—41no—
996C2—81no—
997C2—1222no—
998C2—1222no—
999C2—1222no—
1000C2—4881no—
1001C2—2441no—
1002C2C2×#99×D6111yescharacteristic
1003C2#2145433411yescharacteristic
1004C2C2×#104×D6111yescharacteristic
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#17542
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. C4×C22⋊C4×D61C2semidirect
4. #21444337C2semidirect
5. #21444333C2semidirect
6. #21444322C2semidirect
7. #21444320C2semidirect
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
34. #117×D61C4semidirect
40. #16839724C22semidirect
41. C2×C22⋊#92418C22semidirect
45. C4×C22⋊Dic61C22semidirect
47. #95×D61C22semidirect
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
62. C2×#11758222C2×C4semidirect
66. C2×Q8×D61C2×C4semidirect
70. C2×D4×D61C2×C4semidirect
99. #14519757C2×C4semidirect
100. #14519756C2×C4semidirect
107. #14519753C2×C4semidirect
109. #14519752C2×C4semidirect
110. #14519751C2×C4semidirect
117. #14519748C2×C4semidirect
139. #14519736C2×C4semidirect
146. C4⋊C4×D61C2×C4semidirect
147. C4⋊C4×D61C2×C4semidirect
166. C2×#41×C61C2×C4semidirect
170. C22⋊Q8×C61C2×C4semidirect
172. #121×C61C2×C4semidirect
177. #117×C61C2×C4semidirect
501. #1501D61semidirect
546. C2×C22⋊C8C2×D61semidirect
551. C4×C22⋊C4C2×D61semidirect
556. #328C2×D61semidirect
560. #327C2×D61semidirect
561. C61#17542semidirect
569. C2×#41C4×D61semidirect
615. C22⋊Q8C4×D61semidirect
627. #121C4×D61semidirect
658. #117C4×D61semidirect

Maximal subgroups

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

subgroupindex
#525×D612
C2×#168397242
C4×C22⋊C4×D612
#214443372
#214443332
#214443222
#214443202
#214443112
#214443102
#214443082
C61×#15012
#1754261