Finite Group Databasebeta

← #29647174

Subgroups — #29647174

Order 15616.

1574 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#525×D61C211yesmaximal, characteristic
2#407×D61C211yesmaximal, characteristic, complemented
3C2×#16839609C211yesmaximal, characteristic, complemented
4#21444337C212yesmaximal, complemented
5#21444333C212yesmaximal, complemented
6#21444324C211yesmaximal, characteristic, complemented
7#21444323C211yesmaximal, characteristic, complemented
8#21444321C211yesmaximal, characteristic, complemented
9#21444309C212yesmaximal, complemented
10#21444307C212yesmaximal, complemented
11C61×#1504C211yesmaximal, characteristic, complemented
12C2×#41×D61C411yescharacteristic, complemented
13C23×C4×D61C2211yescharacteristic
14C2×M16×D61—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
35C22×#11758198—21no—
36C22×C4×Dic61—21no—
37#16839726C2211yescharacteristic, complemented
38#16839725—21no—
39#16839724—21no—
40#16839724C2212yes—
41C22⋊C8×D61—21no—
42C22⋊C8×D61C2212yescomplemented
43#16839609—21no—
44#16839609—21no—
45#16839609C2212yes—
46#16839609C2212yescomplemented
47C2×#14519684C2211yescharacteristic, complemented
48#16839500C2212yescomplemented
49#16839499C2212yescomplemented
50#16839498C2212yescomplemented
51#16839497C2212yescomplemented
52#16839496C2212yescomplemented
53#16839495C2212yescomplemented
54C61×#525C2211yescharacteristic
55C61×#407C2211yescharacteristic, complemented
56C2×#95×C61C2211yescharacteristic, complemented
57C61×#328C2212yescomplemented
58C61×#327C2212yescomplemented
59C24×D61D411yescharacteristic
60C2×#11758226C2×C411yescharacteristic, complemented
61C2×#11758222—21no—
62C2×#11758222C2×C411yescharacteristic
63C2×#11758224—21no—
64C2×#11758224C2×C411yescharacteristic, complemented
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×Dic61—21no—
72C23×Dic61D411yescharacteristic
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×#11758194—21no—
88C2×#11758189—22no—
89M16×D61—44no—
90C2×C8×D61—22no—
91#14519762—21no—
92#14519762—21no—
93#14519761—21no—
94#14519760—21no—
95#14519759—21no—
96#14519759—21no—
97#14519758—21no—
98#14519757C2×C411yescharacteristic, complemented
99#14519757C2×C411yescharacteristic, complemented
100#14519756C2×C411yescharacteristic
101#14519756C2311yescharacteristic
102#14519755—21no—
103#14519755—21no—
104#14519754—21no—
105#14519754—21no—
106#14519753C2×C411yescharacteristic, complemented
107#14519753C2×C411yescharacteristic, complemented
108#14519752C2×C411yescharacteristic, complemented
109#14519752C2×C411yescharacteristic, complemented
110#14519751C2×C411yescharacteristic
111#14519751C2311yescharacteristic
112#14519750—21no—
113#14519750—21no—
114#14519749—21no—
115#14519749—21no—
116#14519748C2×C411yescharacteristic, complemented
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
140#14519735C2×C411yescharacteristic, complemented
141#14519735C2×C411yescharacteristic, complemented
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×#11758198—28no—
149C2×#11758198—22no—
150C2×#11758198—22no—
151C22⋊C4×D61—21no—
152C22⋊C4×D61—21no—
153C22⋊C4×D61—21no—
154C22⋊C4×D61—21no—
155C22⋊C4×D61—21no—
156C2×C4×Dic61—22no—
157C2×C4×Dic61—22no—
158C2×C4×Dic61—44no—
159C42×D61—21no—
160C22⋊#92418—21no—
161C22⋊#92418C2312yes—
162#14519689—22no—
163#14519689—22no—
164#14519684—21no—
165#14519684C2312yes—
166C2×#41×C61C2×C411yescharacteristic
167C23×C4×C61—21no—
168C23×C4×C61C2311yescharacteristic
169C2×M16×C61—21no—
170#123×C61—21no—
171C22⋊Q8×C61C2×C411yescharacteristic
172C22⋊Q8×C61C2311yescharacteristic
173#121×C61C2×C411yescharacteristic
174#121×C61C2311yescharacteristic
175#120×C61—21no—
176C4×D4×C61—21no—
177C4×D4×C61—21no—
178#117×C61C2×C411yescharacteristic
179C22⋊C8×C61—21no—
180C22⋊C8×C61C2312yes—
181#95×C61—21no—
182#95×C61C2312yes—
183C24×C61C2×D411yescharacteristic
184C23×D61—24no—
185C23×D61—21no—
186C23×D61—42no—
187C23×D61—41no—
188C23×D61—41no—
189C23×D61C22⋊C411yescharacteristic
190C23×D61C22⋊C411yescharacteristic
191C23×D61C22⋊C411yescharacteristic
192C23×D61C22⋊C411yescharacteristic
193C23×D61C2×D411yescharacteristic
194C23×D61C2×D411yescharacteristic
195#41×C61—42no—
196C2×Q8×C61C22×C411yescharacteristic
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61C22×C411yescharacteristic
201C22×C4×C61—24no—
202C22×C4×C61—22no—
203C22×C4×C61—21no—
204C22×C4×C61—42no—
205C22×C4×C61—42no—
206C22×C4×C61—42no—
207C22×C4×C61C22×C411yescharacteristic
208C22×C4×C61C22×C411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2411yescharacteristic
213C2×C22⋊D61—21no—
214C2×C22⋊D61—21no—
215C2×C22⋊D61—21no—
216C2×C22⋊D61—21no—
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C22×Dic61—24no—
221C22×Dic61—24no—
222C22×Dic61—22no—
223C22×Dic61—21no—
224C22×Dic61—42no—
225C22×Dic61—42no—
226C22×Dic61C22⋊C411yescharacteristic
227C22×Dic61C22⋊C411yescharacteristic
228C22×Dic61C22⋊C411yescharacteristic
229C22×Dic61C22⋊C411yescharacteristic
230C22×Dic61C2×D411yescharacteristic
231C22×Dic61C2×D411yescharacteristic
232#11758226—42no—
233Q8×D61—42no—
234#11758224—42no—
235#11758224—44no—
236D4×D61—42no—
237D4×D61—42no—
238D4×D61—42no—
239D4×D61—44no—
240D4×D61—44no—
241#11758222—44no—
242#11758222—42no—
243C2×D244—21no—
244C2×D244—21no—
245C2×D244—21no—
246C2×D244C22×C411yescharacteristic
247C2×C4×D61—24no—
248C2×C4×D61—24no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—42no—
255C2×C4×D61—42no—
256C2×C4×D61—42no—
257C2×C4×D61—42no—
258C2×C4×D61—42no—
259C2×C4×D61—42no—
260C2×C4×D61—42no—
261C2×C4×D61—42no—
262C2×C4×D61—44no—
263C2×C4×D61—42no—
264C2×C4×D61—42no—
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×D61C22⋊C411yescharacteristic
273C2×C4×D61C22×C411yescharacteristic
274C2×C4×D61C22×C411yescharacteristic
275C2×C4×D61C22×C411yescharacteristic
276C2×C4×D61C22×C411yescharacteristic
277C2×C4×D61C2×D411yescharacteristic
278C2×C4×D61C2×D411yescharacteristic
279C2×C4×D61C2×D411yescharacteristic
280C2×C4×D61C2×D411yescharacteristic
281C2×Dic122—21no—
282C2×Dic122C22×C411yescharacteristic
283M16×C61—42no—
284C2×C8×C61—22no—
285C4⋊C4×C61—21no—
286C4⋊C4×C61—21no—
287C4⋊C4×C61C22×C411yescharacteristic
288C4⋊C4×C61C22×C411yescharacteristic
289C22⋊C4×C61—21no—
290C22⋊C4×C61—21no—
291C22⋊C4×C61—21no—
292C22⋊C4×C61—21no—
293C22⋊C4×C61—21no—
294C42×C61—21no—
295C22⋊Dic61—21no—
296C22⋊Dic61—21no—
297C22⋊Dic61—21no—
298C22⋊Dic61—21no—
299C22⋊Dic61—21no—
300#11758198—28no—
301#11758198—28no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—21no—
306#11758198—21no—
307#11758198—21no—
308#11758198—21no—
309#11758198—21no—
310#11758198—21no—
311#11758198—21no—
312C4⋊Dic61—21no—
313C4⋊Dic61—21no—
314C4⋊Dic61C22×C411yescharacteristic
315C4⋊Dic61C22×C411yescharacteristic
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322C4×Dic61—21no—
323C4×Dic61—21no—
324C4×Dic61—21no—
325C4×Dic61—44no—
326C4×Dic61—44no—
327#11758194—42no—
328C2×#92418—22no—
329#11758189—44no—
330C8×D61—44no—
331C23×C61—21no—
332C23×C61—21no—
333C23×C61—22no—
334C23×C61—22no—
335C23×C61—21no—
336C23×C61C2×C22⋊C411yescharacteristic
337C23×C61C2×C22⋊C411yescharacteristic
338C23×C61C22×D411yescharacteristic
339C22×D61—21no—
340C22×D61—21no—
341C22×D61—21no—
342C22×D61—21no—
343C22×D61—22no—
344C22×D61—22no—
345C22×D61—22no—
346C22×D61—22no—
347C22×D61—22no—
348C22×D61—22no—
349C22×D61—22no—
350C22×D61—21no—
351C22×D61—41no—
352C22×D61—41no—
353C22×D61—41no—
354C22×D61—41no—
355C22×D61—41no—
356C22×D61—41no—
357C22×D61—41no—
358C22×D61—41no—
359C22×D61—42no—
360C22×D61—42no—
361C22×D61—48no—
362C22×D61—48no—
363C22×D61—42no—
364C22×D61#10414yes—
365C22×D61C2×C22⋊C411yescharacteristic
366C22×D61C2×C22⋊C411yescharacteristic
367C22×D61C2×C22⋊C411yescharacteristic
368C22×D61C2×C22⋊C411yescharacteristic
369Q8×C61—41no—
370D4×C61—41no—
371D4×C61—41no—
372D4×C61—41no—
373D4×C61—42no—
374D4×C61—42no—
375C2×C4×C61—22no—
376C2×C4×C61—22no—
377C2×C4×C61—24no—
378C2×C4×C61—21no—
379C2×C4×C61—21no—
380C2×C4×C61—21no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—42no—
386C2×C4×C61—42no—
387C2×C4×C61—48no—
388C2×C4×C61—42no—
389C2×C4×C61C2×C22⋊C411yescharacteristic
390C2×C4×C61C2×C22⋊C411yescharacteristic
391C2×C4×C61C23×C411yescharacteristic
392C2×C4×C61C22×D411yescharacteristic
393C22⋊D61—42no—
394C22⋊D61—42no—
395C22⋊D61—41no—
396C22⋊D61—41no—
397C22⋊D61—42no—
398C22⋊D61—42no—
399C22⋊D61—42no—
400C22⋊D61—42no—
401C2×Dic61—22no—
402C2×Dic61—22no—
403C2×Dic61—22no—
404C2×Dic61—22no—
405C2×Dic61—22no—
406C2×Dic61—24no—
407C2×Dic61—21no—
408C2×Dic61—21no—
409C2×Dic61—21no—
410C2×Dic61—42no—
411C2×Dic61—48no—
412C2×Dic61—42no—
413C2×Dic61—42no—
414C2×Dic61#9914yes—
415C2×Dic61C2×C22⋊C411yescharacteristic
416C2×Dic61C2×C22⋊C411yescharacteristic
417C2×Dic61C2×C22⋊C411yescharacteristic
418C2×Dic61C2×C22⋊C411yescharacteristic
419D244—41no—
420D244—42no—
421D244—42no—
422D244—42no—
423C4×D61—22no—
424C4×D61—22no—
425C4×D61—22no—
426C4×D61—22no—
427C4×D61—22no—
428C4×D61—22no—
429C4×D61—22no—
430C4×D61—22no—
431C4×D61—41no—
432C4×D61—41no—
433C4×D61—41no—
434C4×D61—41no—
435C4×D61—41no—
436C4×D61—41no—
437C4×D61—41no—
438C4×D61—41no—
439C4×D61—42no—
440C4×D61—42no—
441C4×D61—42no—
442C4×D61—42no—
443C4×D61—42no—
444Dic122—42no—
445Dic122—41no—
446C8×C61—42no—
447#92418—42no—
448#17542—611nomaximal, Sylow
449C22×C61—24no—
450C22×C61—24no—
451C22×C61—21no—
452C22×C61—21no—
453C22×C61—21no—
454C22×C61—21no—
455C22×C61—21no—
456C22×C61—21no—
457C22×C61—41no—
458C22×C61—41no—
459C22×C61—41no—
460C22×C61C2×#9912yes—
461C22×C61C2×#10412yes—
462C22×C61C22×C22⋊C411yescharacteristic
463C22×C61#57511yescharacteristic
464C22×C61#57511yescharacteristic
465C2×D61—21no—
466C2×D61—21no—
467C2×D61—21no—
468C2×D61—21no—
469C2×D61—21no—
470C2×D61—21no—
471C2×D61—21no—
472C2×D61—21no—
473C2×D61—21no—
474C2×D61—21no—
475C2×D61—44no—
476C2×D61—42no—
477C2×D61—42no—
478C2×D61—44no—
479C2×D61—42no—
480C2×D61—42no—
481C2×D61—44no—
482C2×D61—44no—
483C2×D61—41no—
484C2×D61—41no—
485C2×D61—41no—
486C2×D61—84no—
487C2×D61C2×#10412yes—
488C2×D61C2×#10412yes—
489C4×C61—21no—
490C4×C61—21no—
491C4×C61—21no—
492C4×C61—21no—
493C4×C61—44no—
494C4×C61—41no—
495C4×C61—41no—
496C4×C61—41no—
497Dic61—21no—
498Dic61—21no—
499Dic61—44no—
500Dic61—41no—
501Dic61—41no—
502Dic61—41no—
503Dic61C2×#9912yes—
504Dic61C2×#9912yes—
505C2×#525—611no—
506C2×#407—611no—
507C2×C4×C22⋊C4—611no—
508#1508—612no—
509#1507—612no—
510#1504—611no—
511#1504—611no—
512#1504—611no—
513#1504D6111yescharacteristic, complemented
514#1501—612no—
515#1501—612no—
516C2×C61—21no—
517C2×C61—21no—
518C2×C61—22no—
519C2×C61—22no—
520C2×C61—81no—
521C2×C61C22×#9911yescharacteristic
522C2×C61#289611yescharacteristic
523C2×C61C22×#10411yescharacteristic
524D61—22no—
525D61—22no—
526D61—41no—
527D61—41no—
528D61—81no—
529C22×#41—611no—
530C24×C4—611no—
531C22×M16—1221no—
532#525—611no—
533#525—611no—
534#525—611no—
535#525—611no—
536#525—611no—
537#525—611no—
538#525—611no—
539#525—1221no—
540#525—1221no—
541#525—1221no—
542#525—1221no—
543#525C2×D6111yescharacteristic
544C2×#123—1221no—
545C2×C22⋊Q8—611no—
546C2×C22⋊Q8—611no—
547C2×#121—611no—
548C2×#121—611no—
549C2×#120—1221no—
550C2×C4×D4—1221no—
551C2×C4×D4—1221no—
552C2×#117—611no—
553C22×C22⋊C4—1221no—
554C22×C42—1221no—
555#407—611no—
556#407—612no—
557#407—1221no—
558#407—1221no—
559#407C2×D6111yescharacteristic, complemented
560C2×C22⋊C8—612no—
561C2×C22⋊C8—1221no—
562C4×C22⋊C4—612no—
563C4×C22⋊C4—612no—
564C4×C22⋊C4—1221no—
565C4×C22⋊C4—1221no—
566C2×#95—611no—
567C2×#95C2×D6111yescharacteristic, complemented
568#328—612no—
569#328—612no—
570#328—612no—
571#328C2×D6112yescomplemented
572#327—612no—
573#327—612no—
574#327—612no—
575#327C2×D6112yescomplemented
576C61#1754211yescharacteristic, complemented, Sylow
577C25—611no—
578C2×#41—611no—
579C2×#41—611no—
580C2×#41—611no—
581C2×#41—1221no—
582C2×#41—1221no—
583C2×#41—2444no—
584C2×#41C4×D6111yescharacteristic
585C22×Q8—611no—
586C22×D4—611no—
587C22×D4—1221no—
588C22×D4—1221no—
589C22×D4—1221no—
590C23×C4—21no—
591C23×C4—611no—
592C23×C4—611no—
593C23×C4—611no—
594C23×C4—611no—
595C23×C4—611no—
596C23×C4—611no—
597C23×C4—611no—
598C23×C4—611no—
599C23×C4—611no—
600C23×C4—611no—
601C23×C4—611no—
602C23×C4—611no—
603C23×C4—611no—
604C23×C4—1221no—
605C23×C4—1221no—
606C23×C4—2444no—
607C23×C4C22×D6111yescharacteristic
608C2×M16—21no—
609C2×M16—1222no—
610C2×M16—1221no—
611C2×M16—2444no—
612C22×C8—1222no—
613#123—21no—
614#123—1221no—
615#123—1221no—
616#123—1221no—
617#123—1221no—
618#123—1221no—
619#123—1221no—
620#123—1221no—
621C22⋊Q8—611no—
622C22⋊Q8—611no—
623C22⋊Q8—611no—
624C22⋊Q8—611no—
625C22⋊Q8—611no—
626C22⋊Q8—611no—
627C22⋊Q8—1221no—
628C22⋊Q8—1221no—
629C22⋊Q8—1221no—
630C22⋊Q8—1221no—
631C22⋊Q8C4×D6111yescharacteristic
632C22⋊Q8C22×D6111yescharacteristic
633#121—611no—
634#121—611no—
635#121—611no—
636#121—611no—
637#121—611no—
638#121—611no—
639#121—1221no—
640#121—1221no—
641#121—1221no—
642#121—1221no—
643#121C4×D6111yescharacteristic
644#121C22×D6111yescharacteristic
645#120—21no—
646#120—1221no—
647#120—1221no—
648#120—1221no—
649#120—1221no—
650#120—1221no—
651#120—1221no—
652#120—1221no—
653C4×D4—21no—
654C4×D4—21no—
655C4×D4—1221no—
656C4×D4—1221no—
657C4×D4—1221no—
658C4×D4—1221no—
659C4×D4—1221no—
660C4×D4—1221no—
661C4×D4—1221no—
662C4×D4—1221no—
663C4×D4—1221no—
664C4×D4—1221no—
665C4×D4—1221no—
666C4×D4—1221no—
667C4×D4—1221no—
668C4×D4—1221no—
669#117—611no—
670#117—611no—
671#117—611no—
672#117—1221no—
673#117—1221no—
674#117C4×D6111yescharacteristic
675C2×C4⋊C4—611no—
676C2×C4⋊C4—611no—
677C2×C4⋊C4—1221no—
678C2×C4⋊C4—1221no—
679C2×C22⋊C4—1221no—
680C2×C22⋊C4—1221no—
681C2×C22⋊C4—1221no—
682C2×C22⋊C4—1221no—
683C2×C22⋊C4—1221no—
684C2×C22⋊C4—1222no—
685C2×C22⋊C4—1222no—
686C2×C22⋊C4—1228no—
687C2×C42—1221no—
688C2×C42—1222no—
689C2×C42—1222no—
690C2×C42—2444no—
691C22⋊C8—21no—
692C22⋊C8—612no—
693C22⋊C8—1222no—
694C22⋊C8—1222no—
695C22⋊C8—1221no—
696C22⋊C8C22×D6112yes—
697#95—21no—
698#95—612no—
699#95—1221no—
700#95C22×D6112yes—
701C24—611no—
702C24—611no—
703C24—611no—
704C24—611no—
705C24—611no—
706C24—611no—
707C24—1224no—
708C24—1221no—
709C24—2442no—
710C24—2441no—
711C24—2441no—
712C24D4×D6111yescharacteristic
713#41—42no—
714#41—2442no—
715#41—2444no—
716#41—2444no—
717#41—2442no—
718#41—2442no—
719C2×Q8—611no—
720C2×Q8—1221no—
721C2×Q8—2442no—
722C2×Q8C2×C4×D6111yescharacteristic
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—611no—
727C2×D4—1221no—
728C2×D4—1221no—
729C2×D4—1221no—
730C2×D4—1221no—
731C2×D4—1221no—
732C2×D4—1221no—
733C2×D4—1221no—
734C2×D4—1221no—
735C2×D4—1221no—
736C2×D4—1221no—
737C2×D4—2442no—
738C2×D4—2444no—
739C2×D4—2444no—
740C2×D4—2442no—
741C2×D4—2442no—
742C2×D4C2×C4×D6111yescharacteristic
743C22×C4—24no—
744C22×C4—22no—
745C22×C4—21no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—611no—
750C22×C4—611no—
751C22×C4—611no—
752C22×C4—611no—
753C22×C4—611no—
754C22×C4—611no—
755C22×C4—611no—
756C22×C4—611no—
757C22×C4—611no—
758C22×C4—611no—
759C22×C4—611no—
760C22×C4—611no—
761C22×C4—611no—
762C22×C4—611no—
763C22×C4—611no—
764C22×C4—611no—
765C22×C4—611no—
766C22×C4—611no—
767C22×C4—611no—
768C22×C4—611no—
769C22×C4—611no—
770C22×C4—611no—
771C22×C4—1224no—
772C22×C4—1224no—
773C22×C4—1221no—
774C22×C4—1221no—
775C22×C4—1221no—
776C22×C4—1221no—
777C22×C4—1224no—
778C22×C4—1221no—
779C22×C4—1224no—
780C22×C4—1222no—
781C22×C4—1221no—
782C22×C4—2442no—
783C22×C4—2442no—
784C22×C4—2442no—
785C22×C4—2442no—
786C22×C4—2442no—
787C22×C4—2442no—
788C22×C4—2442no—
789C22×C4—2442no—
790C22×C4—2442no—
791C22×C4—2442no—
792C22×C4—2444no—
793C22×C4—2442no—
794C22×C4—2442no—
795C22×C4C2×C4×D6111yescharacteristic
796C22×C4C2×C4×D6111yescharacteristic
797C22×C4D4×D6111yescharacteristic
798C22×C4D4×D6111yescharacteristic
799C22×C4D4×D6111yescharacteristic
800C22×C4C23×D6111yescharacteristic
801M16—42no—
802M16—2444no—
803M16—2442no—
804C2×C8—22no—
805C2×C8—1222no—
806C2×C8—2444no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—611no—
810C4⋊C4—611no—
811C4⋊C4—1221no—
812C4⋊C4—1221no—
813C4⋊C4—1221no—
814C4⋊C4—1221no—
815C4⋊C4—1221no—
816C4⋊C4—1221no—
817C4⋊C4—1221no—
818C4⋊C4—1221no—
819C4⋊C4C2×C4×D6111yescharacteristic
820C4⋊C4C2×C4×D6111yescharacteristic
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—1221no—
827C22⋊C4—1221no—
828C22⋊C4—1221no—
829C22⋊C4—1221no—
830C22⋊C4—1221no—
831C22⋊C4—1221no—
832C22⋊C4—1221no—
833C22⋊C4—1221no—
834C22⋊C4—1228no—
835C22⋊C4—1228no—
836C22⋊C4—1221no—
837C22⋊C4—1221no—
838C22⋊C4—1221no—
839C22⋊C4—1221no—
840C22⋊C4—1221no—
841C22⋊C4—1221no—
842C22⋊C4—1221no—
843C42—21no—
844C42—1221no—
845C42—1221no—
846C42—1221no—
847C42—2444no—
848C42—2444no—
849C23—22no—
850C23—22no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—611no—
855C23—611no—
856C23—614no—
857C23—611no—
858C23—611no—
859C23—1222no—
860C23—1222no—
861C23—1222no—
862C23—1222no—
863C23—1222no—
864C23—1222no—
865C23—1222no—
866C23—1221no—
867C23—1221no—
868C23—1221no—
869C23—1221no—
870C23—1221no—
871C23—2441no—
872C23—2441no—
873C23—2441no—
874C23—2441no—
875C23—2441no—
876C23—2441no—
877C23—2441no—
878C23—2441no—
879C23—2448no—
880C23—2448no—
881C23—2442no—
882C23—2442no—
883C23—2442no—
884C23C22⋊C4×D6111yescharacteristic
885C23C22⋊C4×D6111yescharacteristic
886C23C2×D4×D6111yescharacteristic
887Q8—41no—
888Q8—2441no—
889Q8—2442no—
890D4—41no—
891D4—42no—
892D4—42no—
893D4—41no—
894D4—41no—
895D4—2441no—
896D4—2442no—
897D4—2442no—
898D4—2442no—
899D4—2442no—
900D4—2442no—
901D4—2442no—
902D4—2442no—
903D4—2442no—
904D4—2442no—
905D4—2441no—
906D4—2441no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—24no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—48no—
920C2×C4—42no—
921C2×C4—611no—
922C2×C4—611no—
923C2×C4—614no—
924C2×C4—611no—
925C2×C4—611no—
926C2×C4—1222no—
927C2×C4—1222no—
928C2×C4—1222no—
929C2×C4—1222no—
930C2×C4—1222no—
931C2×C4—1222no—
932C2×C4—1222no—
933C2×C4—1222no—
934C2×C4—1222no—
935C2×C4—1222no—
936C2×C4—1222no—
937C2×C4—1222no—
938C2×C4—1222no—
939C2×C4—1224no—
940C2×C4—1221no—
941C2×C4—1221no—
942C2×C4—1221no—
943C2×C4—2441no—
944C2×C4—2441no—
945C2×C4—2441no—
946C2×C4—2441no—
947C2×C4—2441no—
948C2×C4—2441no—
949C2×C4—2441no—
950C2×C4—2441no—
951C2×C4—2442no—
952C2×C4—2442no—
953C2×C4—2442no—
954C2×C4—2442no—
955C2×C4—2442no—
956C2×C4—2442no—
957C2×C4—2442no—
958C2×C4—2448no—
959C2×C4—2442no—
960C2×C4C22⋊C4×D6111yescharacteristic
961C2×C4C22⋊C4×D6111yescharacteristic
962C2×C4C22×C4×D6111yescharacteristic
963C2×C4C2×D4×D6111yescharacteristic
964C8—42no—
965C8—2442no—
966C22—24no—
967C22—24no—
968C22—21no—
969C22—21no—
970C22—21no—
971C22—21no—
972C22—21no—
973C22—21no—
974C22—41no—
975C22—41no—
976C22—41no—
977C22—612no—
978C22—612no—
979C22—1221no—
980C22—1221no—
981C22—1221no—
982C22—1221no—
983C22—1221no—
984C22—1221no—
985C22—1221no—
986C22—1221no—
987C22—1221no—
988C22—1221no—
989C22—4884no—
990C22—2444no—
991C22—2442no—
992C22—2442no—
993C22—2442no—
994C22—2442no—
995C22—2444no—
996C22—2444no—
997C22—2444no—
998C22—2441no—
999C22—2441no—
1000C22—2441no—
1001C22#99×D6112yes—
1002C22#104×D6112yes—
1003C22C2×C22⋊C4×D6111yescharacteristic
1004C22#1684055811yescharacteristic
1005C22#1684056111yescharacteristic
1006C4—21no—
1007C4—21no—
1008C4—21no—
1009C4—21no—
1010C4—44no—
1011C4—41no—
1012C4—41no—
1013C4—41no—
1014C4—612no—
1015C4—612no—
1016C4—1221no—
1017C4—1221no—
1018C4—2444no—
1019C4—2441no—
1020C4—2441no—
1021C4—2441no—
1022C2—21no—
1023C2—21no—
1024C2—22no—
1025C2—22no—
1026C2—81no—
1027C2—1222no—
1028C2—1222no—
1029C2—4881no—
1030C2—2441no—
1031C2—2441no—
1032C2C2×#99×D6111yescharacteristic
1033C2#2145433511yescharacteristic
1034C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1504C2
socleC22×C61C22×C22⋊C4
prime radical#525×D61C2
cosocleC22×C4×C61C24
hypercenter#1504D61
hypocenterC61#17542
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1504

Complements

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

NH ≅ G/Ntype
2. #407×D61C2semidirect
3. C2×#16839609C2semidirect
4. #21444337C2semidirect
5. #21444333C2semidirect
6. #21444324C2semidirect
7. #21444323C2semidirect
8. #21444321C2semidirect
9. #21444309C2semidirect
10. #21444307C2semidirect
11. C61×#1504C2semidirect
12. C2×#41×D61C4semidirect
15. #16840275C4semidirect
17. #16840274C4semidirect
19. #16840272C4semidirect
24. #16840269C4semidirect
27. C22⋊Q8×D61C4semidirect
29. #121×D61C4semidirect
34. #117×D61C4semidirect
37. #16839726C22semidirect
42. C22⋊C8×D61C22semidirect
46. #16839609C22semidirect
47. C2×#14519684C22semidirect
48. #16839500C22semidirect
49. #16839499C22semidirect
50. #16839498C22semidirect
51. #16839497C22semidirect
52. #16839496C22semidirect
53. #16839495C22semidirect
55. C61×#407C22semidirect
56. C2×#95×C61C22semidirect
57. C61×#328C22semidirect
58. C61×#327C22semidirect
60. C2×#11758226C2×C4semidirect
64. C2×#11758224C2×C4semidirect
66. C2×Q8×D61C2×C4semidirect
70. C2×D4×D61C2×C4semidirect
98. #14519757C2×C4semidirect
99. #14519757C2×C4semidirect
106. #14519753C2×C4semidirect
107. #14519753C2×C4semidirect
108. #14519752C2×C4semidirect
109. #14519752C2×C4semidirect
116. #14519748C2×C4semidirect
117. #14519748C2×C4semidirect
140. #14519735C2×C4semidirect
141. #14519735C2×C4semidirect
146. C4⋊C4×D61C2×C4semidirect
147. C4⋊C4×D61C2×C4semidirect
513. #1504D61semidirect
559. #407C2×D61semidirect
567. C2×#95C2×D61semidirect
571. #328C2×D61semidirect
575. #327C2×D61semidirect
576. C61#17542semidirect

Maximal subgroups

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

subgroupindex
#525×D612
#407×D612
C2×#168396092
#214443372
#214443332
#214443242
#214443232
#214443212
#214443092
#214443072
C61×#15042
#1754261