Finite Group Databasebeta

← #29647542

Subgroups — #29647542

Order 15616.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459851C211yesmaximal, characteristic
2#21448452C211yesmaximal, characteristic, complemented
3#21444397C211yesmaximal, characteristic, complemented
4#21444388C211yesmaximal, characteristic, complemented
5#21444380C211yesmaximal, characteristic, complemented
6#21444376C211yesmaximal, characteristic, complemented
7#21444367C211yesmaximal, characteristic, complemented
8#21444363C211yesmaximal, characteristic, complemented
9#21444358C211yesmaximal, characteristic, complemented
10#21444349C211yesmaximal, characteristic, complemented
11#21444336C211yesmaximal, characteristic, complemented
12#21444324C211yesmaximal, characteristic, complemented
13#21444311C211yesmaximal, characteristic, complemented
14C2×#16839497C211yesmaximal, characteristic, complemented
15C61×#2974C211yesmaximal, characteristic, complemented
16#16840477C411yescharacteristic, complemented
17#16840469C411yescharacteristic, complemented
18#16840460—21no—
19#16840458C411yescharacteristic, complemented
20#16840458C411yescharacteristic, complemented
21#16840433C411yescharacteristic, complemented
22#16840408C411yescharacteristic, complemented
23#16840408C411yescharacteristic, complemented
24#16840402—21no—
25#16840402—21no—
26D4×D244C411yescharacteristic, complemented
27D4×C22⋊D61—21no—
28#16840363—21no—
29#16840345—21no—
30#16840345—21no—
31#16840312C2211yescharacteristic
32#16840296C2211yescharacteristic
33#16840273C2211yescharacteristic
34#16840273C2211yescharacteristic
35C2×#14519751C2211yescharacteristic
36C2×#14519751C2211yescharacteristic
37#16840234—21no—
38#16839655—21no—
39#16839648—21no—
40#16839642—21no—
41#16839637—21no—
42#16839630C2211yescharacteristic, complemented
43#16839628C2211yescharacteristic, complemented
44#16839625C2211yescharacteristic, complemented
45#16839622C2211yescharacteristic, complemented
46C4×C22⋊Dic61C2211yescharacteristic, complemented
47C2×#14519684C2211yescharacteristic, complemented
48#16839500C2211yescharacteristic, complemented
49#16839500C2211yescharacteristic, complemented
50#16839500C2211yescharacteristic, complemented
51#16839500C2211yescharacteristic, complemented
52#16839497C2211yescharacteristic
53#16839497C2211yescharacteristic
54#16839497C2211yescharacteristic
55#16839497C2211yescharacteristic
56#16839497C2211yescharacteristic, complemented
57#16839497C2211yescharacteristic, complemented
58#16839497C2211yescharacteristic, complemented
59#16839497C2211yescharacteristic, complemented
60#16839497C2211yescharacteristic, complemented
61#16839497C2211yescharacteristic, complemented
62#16839497C2211yescharacteristic, complemented
63#16839497C2211yescharacteristic, complemented
64C2×C4×D4×C61C2211yescharacteristic
65C61×#436—21no—
66C61×#435—21no—
67C61×#435—21no—
68C8×D4×C61—21no—
69C61×#432C2211yescharacteristic, complemented
70C61×#431C2211yescharacteristic, complemented
71C61×#407C2211yescharacteristic, complemented
72C61×#407C2211yescharacteristic, complemented
73C2×C22⋊C8×C61C2211yescharacteristic, complemented
74C2×C22⋊C8×C61C2211yescharacteristic, complemented
75C2×#11758222—21no—
76C2×#11758222C2×C411yescharacteristic
77C2×#11758222C2×C411yescharacteristic, complemented
78C22×D244C2×C411yescharacteristic
79C22×D244C2×C411yescharacteristic, complemented
80C22×C22⋊D61—21no—
81C22×C22⋊D61—21no—
82C2×D4×D61—21no—
83C23×Dic61—21no—
84#14519777C2×C411yescharacteristic, complemented
85#14519774C2×C411yescharacteristic, complemented
86#14519773—21no—
87#14519772—21no—
88#14519772—21no—
89#14519771—21no—
90#14519769C2×C411yescharacteristic, complemented
91#14519768—21no—
92#14519765—21no—
93#14519765C2×C411yescharacteristic, complemented
94#14519763—21no—
95#14519763—21no—
96#14519762—21no—
97#14519762—21no—
98#14519760—21no—
99#14519760—21no—
100#14519760—21no—
101#14519759—21no—
102#14519759—21no—
103#14519756C2×C411yescharacteristic
104#14519756C2×C411yescharacteristic, complemented
105#14519756C2311yescharacteristic
106#14519754—21no—
107#14519754—21no—
108#14519752—21no—
109#14519751—21no—
110#14519751—21no—
111#14519751—21no—
112#14519751—21no—
113#14519751—21no—
114#14519751C2×C411yescharacteristic
115#14519751C2×C411yescharacteristic
116#14519751C2×C411yescharacteristic
117#14519751C2×C411yescharacteristic, complemented
118#14519751C2×C411yescharacteristic, complemented
119#14519751C2×C411yescharacteristic, complemented
120#14519751C2311yescharacteristic
121#14519751C2311yescharacteristic
122#14519751C2311yescharacteristic
123#14519750—21no—
124#14519750—21no—
125#14519750—21no—
126#14519750—21no—
127#14519749—21no—
128#14519749—21no—
129#14519748—21no—
130#14519747—21no—
131#14519747—21no—
132#14519746—21no—
133#14519746—21no—
134#14519745—21no—
135#14519745—21no—
136C4×Dic122C2×C411yescharacteristic, complemented
137C4×D244—21no—
138C4×D244C2×C411yescharacteristic, complemented
139C4×D244C2×C411yescharacteristic, complemented
140C4×D244C2×C411yescharacteristic, complemented
141D4×Dic61—21no—
142#14519739—21no—
143C4×C22⋊D61—21no—
144C4×C22⋊D61—21no—
145C4×C22⋊D61—21no—
146C4×C22⋊D61—21no—
147C4×C22⋊D61—21no—
148#14519737—21no—
149#14519737—21no—
150#14519736C2×C411yescharacteristic
151#14519736C2×C411yescharacteristic, complemented
152#14519735—21no—
153#14519734—21no—
154C2×C4⋊Dic61—21no—
155C2×C4⋊Dic61—21no—
156C2×C4⋊Dic61C2×C411yescharacteristic
157C2×C4⋊Dic61C2×C411yescharacteristic, complemented
158C2×C22⋊Dic61—21no—
159C2×C22⋊Dic61—21no—
160C2×C22⋊Dic61—21no—
161C2×#11758198—21no—
162C2×#11758198—21no—
163C22⋊C4×D61—21no—
164C22⋊C4×D61—21no—
165C2×C4×Dic61—21no—
166#14519684—21no—
167#14519684—21no—
168#14519684—21no—
169#14519684—21no—
170#14519684—21no—
171#14519684C2311yescharacteristic
172#14519684C2311yescharacteristic
173#14519684C2311yescharacteristic
174#14519684C2311yescharacteristic
175C22×D4×C61D411yescharacteristic
176C23×C4×C61C2311yescharacteristic
177C23×C4×C61C2311yescharacteristic
178C2×M16×C61—21no—
179C2×M16×C61—21no—
180C22×C8×C61—21no—
181C22×C8×C61—21no—
182C4×D4×C61C2×C411yescharacteristic
183C4×D4×C61C2×C411yescharacteristic
184C4×D4×C61C2×C411yescharacteristic
185C4×D4×C61C2×C411yescharacteristic
186C4×D4×C61D411yescharacteristic
187C4×D4×C61D411yescharacteristic
188C4×D4×C61D411yescharacteristic
189C4×D4×C61D411yescharacteristic
190C2×C4⋊C4×C61D411yescharacteristic
191C2×C22⋊C4×C61D411yescharacteristic
192C2×C22⋊C4×C61D411yescharacteristic
193C2×C42×C61C2311yescharacteristic
194C4⋊C8×C61—21no—
195C4⋊C8×C61—21no—
196C22⋊C8×C61—21no—
197C22⋊C8×C61—21no—
198C22⋊C8×C61—21no—
199C22⋊C8×C61—21no—
200C22⋊C8×C61C2311yescharacteristic
201C22⋊C8×C61C2311yescharacteristic
202C22⋊C8×C61C2311yescharacteristic
203C22⋊C8×C61C2311yescharacteristic
204#97×C61—21no—
205C4×C8×C61—21no—
206C24×C61C2×D411yescharacteristic
207C24×C61C2×D411yescharacteristic
208C23×D61—21no—
209C23×D61—21no—
210C2×D4×C61—42no—
211C2×D4×C61C22⋊C411yescharacteristic
212C2×D4×C61C22⋊C411yescharacteristic
213C2×D4×C61C22⋊C411yescharacteristic
214C2×D4×C61C22⋊C411yescharacteristic
215C22×C4×C61—81no—
216C22×C4×C61—81no—
217C22×C4×C61C22×C411yescharacteristic
218C22×C4×C61C22×C411yescharacteristic
219C22×C4×C61C22×C411yescharacteristic
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2411yescharacteristic
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61—21no—
235C2×C22⋊D61—21no—
236C2×C22⋊D61—21no—
237C2×C22⋊D61—21no—
238C2×C22⋊D61—21no—
239C2×C22⋊D61—21no—
240C2×C22⋊D61—21no—
241C2×C22⋊D61—81no—
242C2×C22⋊D61—81no—
243C2×C22⋊D61—81no—
244C2×C22⋊D61—81no—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—42no—
252C22×Dic61—81no—
253C22×Dic61—81no—
254D4×D61—44no—
255#11758222—81no—
256#11758222—81no—
257#11758222—81no—
258#11758222—81no—
259C2×D244—21no—
260C2×D244—21no—
261C2×D244—21no—
262C2×D244—21no—
263C2×D244—81no—
264C2×D244—81no—
265C2×D244C22×C411yescharacteristic
266C2×D244C22×C411yescharacteristic
267C2×D244C22×C411yescharacteristic
268C2×C4×D61—21no—
269C2×C4×D61—21no—
270C2×C4×D61—21no—
271C2×C4×D61—21no—
272C2×C4×D61—21no—
273C2×Dic122—21no—
274C2×Dic122C22×C411yescharacteristic
275M16×C61—81no—
276M16×C61—81no—
277C2×C8×C61—21no—
278C2×C8×C61—21no—
279C2×C8×C61—21no—
280C2×C8×C61—21no—
281C2×C8×C61—81no—
282C2×C8×C61—81no—
283C4⋊C4×C61C22⋊C411yescharacteristic
284C4⋊C4×C61C22⋊C411yescharacteristic
285C4⋊C4×C61C22⋊C411yescharacteristic
286C4⋊C4×C61C22⋊C411yescharacteristic
287C22⋊C4×C61C22⋊C411yescharacteristic
288C22⋊C4×C61C22⋊C411yescharacteristic
289C22⋊C4×C61C22⋊C411yescharacteristic
290C22⋊C4×C61C22⋊C411yescharacteristic
291C22⋊C4×C61C22⋊C411yescharacteristic
292C22⋊C4×C61C22⋊C411yescharacteristic
293C22⋊C4×C61C22⋊C411yescharacteristic
294C22⋊C4×C61C22⋊C411yescharacteristic
295C42×C61C22×C411yescharacteristic
296C42×C61C22×C411yescharacteristic
297C42×C61C2×D411yescharacteristic
298C42×C61C2×D411yescharacteristic
299C22⋊Dic61—21no—
300C22⋊Dic61—21no—
301C22⋊Dic61—21no—
302C22⋊Dic61—21no—
303C22⋊Dic61—21no—
304C22⋊Dic61—42no—
305C22⋊Dic61—81no—
306C22⋊Dic61—81no—
307#11758198—21no—
308#11758198—21no—
309#11758198—21no—
310#11758198—21no—
311#11758198—21no—
312#11758198—21no—
313#11758198—21no—
314#11758198—21no—
315#11758198—21no—
316#11758198—21no—
317#11758198—21no—
318#11758198—21no—
319#11758198—21no—
320#11758198—21no—
321C4⋊Dic61—21no—
322C4⋊Dic61—21no—
323C4⋊Dic61—21no—
324C4⋊Dic61—81no—
325C4⋊Dic61—81no—
326C4⋊Dic61C22×C411yescharacteristic
327C4⋊Dic61C22×C411yescharacteristic
328C4⋊Dic61C22×C411yescharacteristic
329C4⋊Dic61C22×C411yescharacteristic
330#11758196—21no—
331#11758196—21no—
332#11758196—21no—
333#11758196—21no—
334#11758196—21no—
335#11758196—21no—
336C4×Dic61—21no—
337C4×Dic61—21no—
338C4×Dic61—21no—
339C4×Dic61—81no—
340C23×C61—21no—
341C23×C61—21no—
342C23×C61—22no—
343C23×C61—21no—
344C23×C61—21no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—41no—
348C23×C61C2×C22⋊C411yescharacteristic
349C23×C61C2×C22⋊C411yescharacteristic
350C23×C61C2×C22⋊C411yescharacteristic
351C23×C61C2×C22⋊C411yescharacteristic
352C23×C61C22×D411yescharacteristic
353C22×D61—21no—
354C22×D61—21no—
355C22×D61—21no—
356C22×D61—42no—
357C22×D61—42no—
358C22×D61—81no—
359C22×D61—81no—
360C22×D61—81no—
361C22×D61—81no—
362D4×C61—22no—
363D4×C61—22no—
364D4×C61—41no—
365D4×C61—41no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61C2×C22⋊C411yescharacteristic
381C2×C4×C61C2×C22⋊C411yescharacteristic
382C2×C4×C61C2×C22⋊C411yescharacteristic
383C2×C4×C61C2×C22⋊C411yescharacteristic
384C2×C4×C61C2×C22⋊C411yescharacteristic
385C2×C4×C61C2×C22⋊C411yescharacteristic
386C2×C4×C61C2×C22⋊C411yescharacteristic
387C2×C4×C61C2×C22⋊C411yescharacteristic
388C2×C4×C61C23×C411yescharacteristic
389C2×C4×C61C22×D411yescharacteristic
390C22⋊D61—42no—
391C22⋊D61—41no—
392C22⋊D61—41no—
393C22⋊D61—41no—
394C22⋊D61—41no—
395C22⋊D61—41no—
396C22⋊D61—41no—
397C22⋊D61—42no—
398C22⋊D61—81no—
399C22⋊D61—81no—
400C22⋊D61—81no—
401C22⋊D61—81no—
402C22⋊D61—81no—
403C22⋊D61—81no—
404C2×Dic61—21no—
405C2×Dic61—21no—
406C2×Dic61—21no—
407C2×Dic61—21no—
408C2×Dic61—21no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411C2×Dic61—41no—
412C2×Dic61—41no—
413C2×Dic61—41no—
414C2×Dic61—41no—
415C2×Dic61—41no—
416C2×Dic61—41no—
417C2×Dic61—41no—
418C2×Dic61—41no—
419C2×Dic61—41no—
420C2×Dic61—41no—
421C2×Dic61—81no—
422C2×Dic61—81no—
423C2×Dic61—84no—
424D244—41no—
425D244—41no—
426D244—41no—
427D244—42no—
428D244—81no—
429D244—81no—
430D244—81no—
431C4×D61—42no—
432C4×D61—81no—
433C4×D61—81no—
434C4×D61—81no—
435C4×D61—81no—
436Dic122—41no—
437Dic122—81no—
438C8×C61—41no—
439C8×C61—41no—
440C8×C61—41no—
441C8×C61—41no—
442#17597—611nomaximal, Sylow
443C22×C61—21no—
444C22×C61—21no—
445C22×C61—21no—
446C22×C61—21no—
447C22×C61—21no—
448C22×C61—21no—
449C22×C61—21no—
450C22×C61—21no—
451C22×C61—21no—
452C22×C61—21no—
453C22×C61—21no—
454C22×C61—21no—
455C22×C61—21no—
456C22×C61—42no—
457C22×C61—42no—
458C22×C61—81no—
459C22×C61—81no—
460C22×C61#42112yes—
461C22×C61C22×C22⋊C411yescharacteristic
462C22×C61#57611yescharacteristic
463C22×C61#57711yescharacteristic
464C2×D61—41no—
465C2×D61—41no—
466C2×D61—41no—
467C2×D61—41no—
468C2×D61—41no—
469C2×D61—41no—
470C2×D61—41no—
471C2×D61—41no—
472C2×D61—41no—
473C2×D61—162no—
474C2×D61—162no—
475C4×C61—21no—
476C4×C61—21no—
477C4×C61—21no—
478C4×C61—21no—
479C4×C61—21no—
480C4×C61—21no—
481C4×C61—21no—
482C4×C61—21no—
483C4×C61—21no—
484C4×C61—21no—
485Dic61—41no—
486Dic61—41no—
487Dic61—41no—
488Dic61—41no—
489Dic61—41no—
490Dic61—81no—
491Dic61—81no—
492Dic61—81no—
493Dic61—81no—
494#3519—611no—
495#2974D6111yescharacteristic, complemented
496#2318—611no—
497#1521—611no—
498#1519—611no—
499#1517—611no—
500#1516—611no—
501#1514—611no—
502#1513—611no—
503#1512—611no—
504#1510—611no—
505#1507—611no—
506#1504—611no—
507#1501—611no—
508C2×#327—611no—
509C2×C61—21no—
510C2×C61—21no—
511C2×C61—22no—
512C2×C61—41no—
513C2×C61—41no—
514C2×C61—41no—
515C2×C61#288311yescharacteristic
516C2×C61#289711yescharacteristic
517C2×C61C2×#42111yescharacteristic
518D61—81no—
519D61—81no—
520D61—81no—
521#555—611no—
522#554—611no—
523#553—611no—
524#553—611no—
525#553—1221no—
526#550—611no—
527#546—611no—
528#546—611no—
529#546—1221no—
530#546—1221no—
531D42—611no—
532D42—1221no—
533#540—1221no—
534#538—1221no—
535#538—1221no—
536#532—611no—
537#529—611no—
538#525—611no—
539#525—611no—
540C2×#121—611no—
541C2×#121—611no—
542#518—1221no—
543C2×C4×D4C2×D6111yescharacteristic
544#436—21no—
545#435—21no—
546#435—21no—
547C8×D4—21no—
548#432C2×D6111yescharacteristic, complemented
549#431C2×D6111yescharacteristic, complemented
550#407C2×D6111yescharacteristic, complemented
551#407C2×D6111yescharacteristic, complemented
552C2×C22⋊C8C2×D6111yescharacteristic, complemented
553C2×C22⋊C8C2×D6111yescharacteristic, complemented
554#388—1221no—
555#387—1221no—
556#386—1221no—
557#385—1221no—
558#383—611no—
559#382—611no—
560#381—611no—
561#380—611no—
562C4×C22⋊C4—611no—
563C2×#95—611no—
564#328—611no—
565#328—611no—
566#328—611no—
567#328—611no—
568#327—611no—
569#327—611no—
570#327—611no—
571#327—611no—
572#327—611no—
573#327—611no—
574#327—611no—
575#327—611no—
576#327—611no—
577#327—611no—
578#327—611no—
579#327—611no—
580C61#1759711yescharacteristic, complemented, Sylow
581C2×#41—611no—
582C2×#41—611no—
583C2×#41—1221no—
584C22×D4—611no—
585C22×D4—611no—
586C22×D4—1221no—
587C22×D4—1221no—
588C22×D4—1221no—
589C22×D4D24411yescharacteristic
590C23×C4—1221no—
591C23×C4C22×D6111yescharacteristic
592C23×C4C22×D6111yescharacteristic
593C2×M16—21no—
594C2×M16—21no—
595C22×C8—21no—
596C22×C8—21no—
597C4⋊Q8—611no—
598#127—611no—
599#127—1221no—
600#126—1221no—
601#126—1221no—
602#126—1221no—
603#125—611no—
604#125—1221no—
605#124—611no—
606#124—1221no—
607#124—1221no—
608#124—1221no—
609#123—1221no—
610#123—1221no—
611#123—1221no—
612#123—1221no—
613#123—1221no—
614#123—1221no—
615#123—1221no—
616C22⋊Q8—611no—
617C22⋊Q8—611no—
618C22⋊Q8—611no—
619C22⋊Q8—1221no—
620C22⋊Q8—1221no—
621#121—611no—
622#121—611no—
623#121—611no—
624#121—611no—
625#121—611no—
626#121—611no—
627#121—611no—
628#121—611no—
629#121—611no—
630#121—1221no—
631#121—1221no—
632#121—1221no—
633#121—1221no—
634#121—1221no—
635#121—1221no—
636#121—1221no—
637#121—1221no—
638#121—1221no—
639#121—1221no—
640#121—1221no—
641#121—1221no—
642#121—1221no—
643#120—1221no—
644#120—1221no—
645#120—1221no—
646#120—1221no—
647#120—1221no—
648#120—1221no—
649C4×Q8—611no—
650C4×D4—611no—
651C4×D4—611no—
652C4×D4—611no—
653C4×D4—1221no—
654C4×D4—1221no—
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×D4C4×D6111yescharacteristic
664C4×D4C4×D6111yescharacteristic
665C4×D4C4×D6111yescharacteristic
666C4×D4C4×D6111yescharacteristic
667C4×D4C22⋊D6111yescharacteristic
668C4×D4C22⋊D6111yescharacteristic
669C4×D4C22⋊D6111yescharacteristic
670C4×D4C22⋊D6111yescharacteristic
671#117—611no—
672#117—611no—
673#117—1221no—
674#117—1221no—
675C2×C4⋊C4—611no—
676C2×C4⋊C4—611no—
677C2×C4⋊C4—1221no—
678C2×C4⋊C4—1221no—
679C2×C4⋊C4D24411yescharacteristic
680C2×C22⋊C4—1221no—
681C2×C22⋊C4—1221no—
682C2×C22⋊C4—1221no—
683C2×C22⋊C4—1221no—
684C2×C22⋊C4—1221no—
685C2×C22⋊C4—1221no—
686C2×C22⋊C4—1221no—
687C2×C22⋊C4D24411yescharacteristic
688C2×C22⋊C4D24411yescharacteristic
689C2×C42—1221no—
690C2×C42C22×D6111yescharacteristic
691C4⋊C8—21no—
692C4⋊C8—21no—
693C22⋊C8—21no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696C22⋊C8—21no—
697C22⋊C8C22×D6111yescharacteristic
698C22⋊C8C22×D6111yescharacteristic
699C22⋊C8C22×D6111yescharacteristic
700C22⋊C8C22×D6111yescharacteristic
701#97—21no—
702C4×C8—21no—
703#95—611no—
704#95—611no—
705#95—611no—
706#95—611no—
707#95—1221no—
708#95—1221no—
709#95—1221no—
710#95—1221no—
711#95—1221no—
712C24—1221no—
713C24—1221no—
714C24C2×D24411yescharacteristic
715C24C2×D24411yescharacteristic
716#41—4881no—
717#41—4881no—
718#41—4881no—
719#41—4881no—
720C2×Q8—611no—
721C2×Q8—1221no—
722C2×D4—42no—
723C2×D4—611no—
724C2×D4—611no—
725C2×D4—611no—
726C2×D4—1221no—
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—1221no—
738C2×D4—1221no—
739C2×D4—1221no—
740C2×D4—1221no—
741C2×D4—4881no—
742C2×D4—4881no—
743C2×D4—4881no—
744C2×D4—4881no—
745C2×D4—4881no—
746C2×D4—4881no—
747C2×D4—2444no—
748C2×D4#1175819811yescharacteristic
749C2×D4#1175819811yescharacteristic
750C2×D4#1175819811yescharacteristic
751C2×D4#1175819811yescharacteristic
752C22×C4—81no—
753C22×C4—81no—
754C22×C4—1221no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—1221no—
760C22×C4—1221no—
761C22×C4—1221no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—4881no—
766C22×C4—4881no—
767C22×C4—2442no—
768C22×C4C2×C4×D6111yescharacteristic
769C22×C4C2×C4×D6111yescharacteristic
770C22×C4C2×C4×D6111yescharacteristic
771C22×C4C2×C4×D6111yescharacteristic
772C22×C4C2×D24411yescharacteristic
773C22×C4C2×D24411yescharacteristic
774C22×C4C2×D24411yescharacteristic
775C22×C4C2×D24411yescharacteristic
776C22×C4C2×C22⋊D6111yescharacteristic
777C22×C4C2×C22⋊D6111yescharacteristic
778C22×C4C2×C22⋊D6111yescharacteristic
779C22×C4C2×C22⋊D6111yescharacteristic
780C22×C4C23×D6111yescharacteristic
781M16—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C2×C8—81no—
789C4⋊C4—611no—
790C4⋊C4—611no—
791C4⋊C4—611no—
792C4⋊C4—611no—
793C4⋊C4—1221no—
794C4⋊C4—1221no—
795C4⋊C4—1221no—
796C4⋊C4—1221no—
797C4⋊C4—1221no—
798C4⋊C4—1221no—
799C4⋊C4—1221no—
800C4⋊C4—1221no—
801C4⋊C4—1221no—
802C4⋊C4—4881no—
803C4⋊C4—4881no—
804C4⋊C4#1175819811yescharacteristic
805C4⋊C4#1175819811yescharacteristic
806C4⋊C4#1175819811yescharacteristic
807C4⋊C4#1175819811yescharacteristic
808C22⋊C4—1221no—
809C22⋊C4—1221no—
810C22⋊C4—1221no—
811C22⋊C4—1221no—
812C22⋊C4—1221no—
813C22⋊C4—1221no—
814C22⋊C4—1221no—
815C22⋊C4—1221no—
816C22⋊C4—1221no—
817C22⋊C4—1221no—
818C22⋊C4—1221no—
819C22⋊C4—1221no—
820C22⋊C4—1221no—
821C22⋊C4—1221no—
822C22⋊C4—1221no—
823C22⋊C4—1221no—
824C22⋊C4—1221no—
825C22⋊C4—1221no—
826C22⋊C4—1221no—
827C22⋊C4—4881no—
828C22⋊C4—4881no—
829C22⋊C4—2442no—
830C22⋊C4#1175819811yescharacteristic
831C22⋊C4#1175819811yescharacteristic
832C22⋊C4#1175819811yescharacteristic
833C22⋊C4#1175819811yescharacteristic
834C22⋊C4#1175819811yescharacteristic
835C22⋊C4#1175819811yescharacteristic
836C22⋊C4#1175819811yescharacteristic
837C22⋊C4#1175819811yescharacteristic
838C42—1221no—
839C42—1221no—
840C42—1221no—
841C42—4881no—
842C42C2×C4×D6111yescharacteristic
843C42C2×C4×D6111yescharacteristic
844C42C2×C22⋊D6111yescharacteristic
845C42C2×C22⋊D6111yescharacteristic
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—1221no—
855C23—1221no—
856C23—1221no—
857C23—4881no—
858C23—4881no—
859C23—4881no—
860C23—4881no—
861C23—2442no—
862C23—2442no—
863C23C2×#1175819811yescharacteristic
864C23C2×#1175819811yescharacteristic
865C23C2×#1175819811yescharacteristic
866C23C2×#1175819811yescharacteristic
867C23C22×D24411yescharacteristic
868Q8—4881no—
869Q8—2441no—
870D4—22no—
871D4—22no—
872D4—41no—
873D4—41no—
874D4—4881no—
875D4—4881no—
876D4—4881no—
877D4—4881no—
878D4—4881no—
879D4—4881no—
880D4—4881no—
881D4—4881no—
882D4—4881no—
883D4—2441no—
884D4—2441no—
885D4—2441no—
886D4—2442no—
887D4—2442no—
888D4—2442no—
889D4—2441no—
890D4—2441no—
891D4—2441no—
892D4—2441no—
893D4—2441no—
894D4—2441no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—1221no—
910C2×C4—1221no—
911C2×C4—1221no—
912C2×C4—1221no—
913C2×C4—1221no—
914C2×C4—4881no—
915C2×C4—4881no—
916C2×C4—4881no—
917C2×C4—4881no—
918C2×C4—4884no—
919C2×C4—4881no—
920C2×C4—4881no—
921C2×C4—2442no—
922C2×C4—2441no—
923C2×C4—2441no—
924C2×C4—2441no—
925C2×C4—2441no—
926C2×C4—2441no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4C2×#1175819811yescharacteristic
935C2×C4C2×#1175819811yescharacteristic
936C2×C4C2×#1175819811yescharacteristic
937C2×C4C2×#1175819811yescharacteristic
938C2×C4C2×#1175819811yescharacteristic
939C2×C4C2×#1175819811yescharacteristic
940C2×C4C2×#1175819811yescharacteristic
941C2×C4C2×#1175819811yescharacteristic
942C2×C4C22×C4×D6111yescharacteristic
943C2×C4C22×C22⋊D6111yescharacteristic
944C8—41no—
945C8—41no—
946C8—41no—
947C8—41no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—42no—
962C22—42no—
963C22—81no—
964C22—81no—
965C22—9762no—
966C22—9762no—
967C22—2441no—
968C22—2441no—
969C22—2441no—
970C22—2441no—
971C22—2441no—
972C22—2441no—
973C22—2441no—
974C22—2441no—
975C22—2441no—
976C22#1683977812yes—
977C22C22×#1175819811yescharacteristic
978C22#1684056711yescharacteristic
979C22#1684057411yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—4881no—
991C4—4881no—
992C4—4881no—
993C4—4881no—
994C4—2441no—
995C4—2441no—
996C4—2441no—
997C4—2441no—
998C4—2441no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—41no—
1004C2—41no—
1005C2—4881no—
1006C2—4881no—
1007C2—4881no—
1008C2#2145427911yescharacteristic
1009C2#2145434611yescharacteristic
1010C2C2×#1683977811yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2974C2
socleC22×C61C22×C22⋊C4
prime radical#21459851C2
cosocleC22×C4×C61C24
hypercenter#2974D61
hypocenterC61#17597
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #21448452C2semidirect
3. #21444397C2semidirect
4. #21444388C2semidirect
5. #21444380C2semidirect
6. #21444376C2semidirect
7. #21444367C2semidirect
8. #21444363C2semidirect
9. #21444358C2semidirect
10. #21444349C2semidirect
11. #21444336C2semidirect
12. #21444324C2semidirect
13. #21444311C2semidirect
14. C2×#16839497C2semidirect
15. C61×#2974C2semidirect
16. #16840477C4semidirect
17. #16840469C4semidirect
19. #16840458C4semidirect
20. #16840458C4semidirect
21. #16840433C4semidirect
22. #16840408C4semidirect
23. #16840408C4semidirect
26. D4×D244C4semidirect
42. #16839630C22semidirect
43. #16839628C22semidirect
44. #16839625C22semidirect
45. #16839622C22semidirect
46. C4×C22⋊Dic61C22semidirect
47. C2×#14519684C22semidirect
48. #16839500C22semidirect
49. #16839500C22semidirect
50. #16839500C22semidirect
51. #16839500C22semidirect
56. #16839497C22semidirect
57. #16839497C22semidirect
58. #16839497C22semidirect
59. #16839497C22semidirect
60. #16839497C22semidirect
61. #16839497C22semidirect
62. #16839497C22semidirect
63. #16839497C22semidirect
69. C61×#432C22semidirect
70. C61×#431C22semidirect
71. C61×#407C22semidirect
72. C61×#407C22semidirect
73. C2×C22⋊C8×C61C22semidirect
74. C2×C22⋊C8×C61C22semidirect
77. C2×#11758222C2×C4semidirect
79. C22×D244C2×C4semidirect
84. #14519777C2×C4semidirect
85. #14519774C2×C4semidirect
90. #14519769C2×C4semidirect
93. #14519765C2×C4semidirect
104. #14519756C2×C4semidirect
117. #14519751C2×C4semidirect
118. #14519751C2×C4semidirect
119. #14519751C2×C4semidirect
136. C4×Dic122C2×C4semidirect
138. C4×D244C2×C4semidirect
139. C4×D244C2×C4semidirect
140. C4×D244C2×C4semidirect
151. #14519736C2×C4semidirect
157. C2×C4⋊Dic61C2×C4semidirect
495. #2974D61semidirect
548. #432C2×D61semidirect
549. #431C2×D61semidirect
550. #407C2×D61semidirect
551. #407C2×D61semidirect
552. C2×C22⋊C8C2×D61semidirect
553. C2×C22⋊C8C2×D61semidirect
580. C61#17597semidirect

Maximal subgroups

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

subgroupindex
#214598512
#214484522
#214443972
#214443882
#214443802
#214443762
#214443672
#214443632
#214443582
#214443492
#214443362
#214443242
#214443112
C2×#168394972
C61×#29742
#1759761