Finite Group Databasebeta

← #29647534

Subgroups — #29647534

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#21454854C211yesmaximal, characteristic, complemented
3#21444394C211yesmaximal, characteristic, complemented
4#21444386C211yesmaximal, characteristic, complemented
5#21444378C211yesmaximal, characteristic, complemented
6#21444373C211yesmaximal, characteristic, complemented
7#21444365C211yesmaximal, characteristic, complemented
8#21444360C211yesmaximal, characteristic, complemented
9#21444355C211yesmaximal, characteristic, complemented
10#21444347C211yesmaximal, characteristic, complemented
11#21444334C211yesmaximal, characteristic, complemented
12#21444321C211yesmaximal, characteristic, complemented
13#21444308C211yesmaximal, characteristic, complemented
14C2×#16839495C211yesmaximal, characteristic, complemented
15C61×#2318C211yesmaximal, 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#16839840—21no—
39#16839834—21no—
40#16839834—21no—
41D4×#92418—21no—
42#16839819C2211yescharacteristic, complemented
43#16839815C2211yescharacteristic, complemented
44#16839726C2211yescharacteristic, complemented
45#16839726C2211yescharacteristic, complemented
46C2×C22⋊#92418C2211yescharacteristic, complemented
47C2×C22⋊#92418C2211yescharacteristic, complemented
48#16839498C2211yescharacteristic, complemented
49#16839498C2211yescharacteristic, complemented
50#16839498C2211yescharacteristic, complemented
51#16839498C2211yescharacteristic, complemented
52#16839495C2211yescharacteristic
53#16839495C2211yescharacteristic
54#16839495C2211yescharacteristic
55#16839495C2211yescharacteristic
56#16839495C2211yescharacteristic, complemented
57#16839495C2211yescharacteristic, complemented
58#16839495C2211yescharacteristic, complemented
59#16839495C2211yescharacteristic, complemented
60#16839495C2211yescharacteristic, complemented
61#16839495C2211yescharacteristic, complemented
62#16839495C2211yescharacteristic, complemented
63#16839495C2211yescharacteristic, complemented
64C2×C4×D4×C61C2211yescharacteristic
65C61×#388—21no—
66C61×#387—21no—
67C61×#386—21no—
68C61×#385—21no—
69C61×#383C2211yescharacteristic, complemented
70C61×#382C2211yescharacteristic, complemented
71C61×#381C2211yescharacteristic, complemented
72C61×#380C2211yescharacteristic, complemented
73C4×C22⋊C4×C61C2211yescharacteristic, complemented
74C2×#95×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—
83C2×#11758194—21no—
84C2×#11758194—21no—
85C22×#92418—21no—
86C22×#92418—21no—
87#14519777C2×C411yescharacteristic, complemented
88#14519774C2×C411yescharacteristic, complemented
89#14519773—21no—
90#14519772—21no—
91#14519772—21no—
92#14519771—21no—
93#14519769C2×C411yescharacteristic, complemented
94#14519768—21no—
95#14519765—21no—
96#14519765C2×C411yescharacteristic, complemented
97#14519763—21no—
98#14519763—21no—
99#14519762—21no—
100#14519762—21no—
101#14519760—21no—
102#14519760—21no—
103#14519760—21no—
104#14519759—21no—
105#14519759—21no—
106#14519756C2×C411yescharacteristic
107#14519756C2×C411yescharacteristic, complemented
108#14519756C2311yescharacteristic
109#14519754—21no—
110#14519754—21no—
111#14519752—21no—
112#14519751—21no—
113#14519751—21no—
114#14519751—21no—
115#14519751—21no—
116#14519751—21no—
117#14519751C2×C411yescharacteristic
118#14519751C2×C411yescharacteristic
119#14519751C2×C411yescharacteristic
120#14519751C2×C411yescharacteristic, complemented
121#14519751C2×C411yescharacteristic, complemented
122#14519751C2×C411yescharacteristic, complemented
123#14519751C2311yescharacteristic
124#14519751C2311yescharacteristic
125#14519751C2311yescharacteristic
126#14519750—21no—
127#14519750—21no—
128#14519750—21no—
129#14519750—21no—
130#14519749—21no—
131#14519749—21no—
132#14519748—21no—
133#14519747—21no—
134#14519747—21no—
135#14519746—21no—
136#14519746—21no—
137#14519745—21no—
138#14519745—21no—
139C4×Dic122C2×C411yescharacteristic, complemented
140C4×D244—21no—
141C4×D244C2×C411yescharacteristic, complemented
142C4×D244C2×C411yescharacteristic, complemented
143C4×D244C2×C411yescharacteristic, complemented
144D4×Dic61—21no—
145#14519739—21no—
146C4×C22⋊D61—21no—
147C4×C22⋊D61—21no—
148C4×C22⋊D61—21no—
149C4×C22⋊D61—21no—
150C4×C22⋊D61—21no—
151#14519737—21no—
152#14519737—21no—
153#14519736C2×C411yescharacteristic
154#14519736C2×C411yescharacteristic, complemented
155#14519735—21no—
156#14519734—21no—
157C2×C4⋊Dic61C2×C411yescharacteristic
158C2×C4⋊Dic61C2×C411yescharacteristic, complemented
159C2×#11758198—21no—
160C2×#11758198—21no—
161C22⋊C4×D61—21no—
162C22⋊C4×D61—21no—
163C4⋊#92418—21no—
164C4⋊#92418—21no—
165C22⋊#92418—21no—
166C22⋊#92418—21no—
167C22⋊#92418—21no—
168C22⋊#92418—21no—
169C22⋊#92418C2311yescharacteristic
170C22⋊#92418C2311yescharacteristic
171C22⋊#92418C2311yescharacteristic
172C22⋊#92418C2311yescharacteristic
173#14519688—21no—
174C4×#92418—21no—
175C22×D4×C61D411yescharacteristic
176C23×C4×C61—21no—
177C23×C4×C61C2311yescharacteristic
178C23×C4×C61C2311yescharacteristic
179C4×D4×C61C2×C411yescharacteristic
180C4×D4×C61C2×C411yescharacteristic
181C4×D4×C61C2×C411yescharacteristic
182C4×D4×C61C2×C411yescharacteristic
183C4×D4×C61D411yescharacteristic
184C4×D4×C61D411yescharacteristic
185C4×D4×C61D411yescharacteristic
186C4×D4×C61D411yescharacteristic
187C2×C4⋊C4×C61—21no—
188C2×C4⋊C4×C61—21no—
189C2×C4⋊C4×C61D411yescharacteristic
190C2×C22⋊C4×C61—21no—
191C2×C22⋊C4×C61—21no—
192C2×C22⋊C4×C61—21no—
193C2×C22⋊C4×C61D411yescharacteristic
194C2×C22⋊C4×C61D411yescharacteristic
195C2×C42×C61—21no—
196C2×C42×C61C2311yescharacteristic
197#95×C61—21no—
198#95×C61—21no—
199#95×C61—21no—
200#95×C61—21no—
201#95×C61—21no—
202#95×C61C2311yescharacteristic
203#95×C61C2311yescharacteristic
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
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—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—42no—
220C22×C4×C61—81no—
221C22×C4×C61—81no—
222C22×C4×C61—81no—
223C22×C4×C61—81no—
224C22×C4×C61C22×C411yescharacteristic
225C22×C4×C61C22×C411yescharacteristic
226C22×C4×C61C22×C411yescharacteristic
227C22×C4×C61C22×C411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D411yescharacteristic
235C22×C4×C61C2×D411yescharacteristic
236C22×C4×C61C2411yescharacteristic
237C2×C22⋊D61—21no—
238C2×C22⋊D61—21no—
239C2×C22⋊D61—21no—
240C2×C22⋊D61—21no—
241C2×C22⋊D61—21no—
242C2×C22⋊D61—21no—
243C2×C22⋊D61—21no—
244C2×C22⋊D61—21no—
245C2×C22⋊D61—21no—
246C2×C22⋊D61—21no—
247C2×C22⋊D61—21no—
248C2×C22⋊D61—81no—
249C2×C22⋊D61—81no—
250C2×C22⋊D61—81no—
251C2×C22⋊D61—81no—
252C22×Dic61—21no—
253C22×Dic61—21no—
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
275C4⋊C4×C61—81no—
276C4⋊C4×C61—81no—
277C4⋊C4×C61C22⋊C411yescharacteristic
278C4⋊C4×C61C22⋊C411yescharacteristic
279C4⋊C4×C61C22⋊C411yescharacteristic
280C4⋊C4×C61C22⋊C411yescharacteristic
281C22⋊C4×C61—42no—
282C22⋊C4×C61—81no—
283C22⋊C4×C61—81no—
284C22⋊C4×C61C22⋊C411yescharacteristic
285C22⋊C4×C61C22⋊C411yescharacteristic
286C22⋊C4×C61C22⋊C411yescharacteristic
287C22⋊C4×C61C22⋊C411yescharacteristic
288C22⋊C4×C61C22⋊C411yescharacteristic
289C22⋊C4×C61C22⋊C411yescharacteristic
290C22⋊C4×C61C22⋊C411yescharacteristic
291C22⋊C4×C61C22⋊C411yescharacteristic
292C42×C61—81no—
293C42×C61C22×C411yescharacteristic
294C42×C61C22×C411yescharacteristic
295C42×C61C2×D411yescharacteristic
296C42×C61C2×D411yescharacteristic
297C22⋊Dic61—21no—
298C22⋊Dic61—21no—
299C22⋊Dic61—21no—
300C22⋊Dic61—21no—
301C22⋊Dic61—21no—
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—
312#11758198—21no—
313#11758198—21no—
314#11758198—21no—
315#11758198—21no—
316C4⋊Dic61—21no—
317C4⋊Dic61—21no—
318C4⋊Dic61—21no—
319C4⋊Dic61C22×C411yescharacteristic
320C4⋊Dic61C22×C411yescharacteristic
321C4⋊Dic61C22×C411yescharacteristic
322C4⋊Dic61C22×C411yescharacteristic
323#11758196—21no—
324#11758196—21no—
325#11758196—21no—
326#11758196—21no—
327#11758196—21no—
328#11758196—21no—
329C4×Dic61—21no—
330C4×Dic61—21no—
331C4×Dic61—21no—
332#11758194—81no—
333#11758194—81no—
334C2×#92418—21no—
335C2×#92418—21no—
336C2×#92418—21no—
337C2×#92418—21no—
338C2×#92418—81no—
339C2×#92418—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×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—84no—
393C2×C4×C61C2×C22⋊C411yescharacteristic
394C2×C4×C61C2×C22⋊C411yescharacteristic
395C2×C4×C61C2×C22⋊C411yescharacteristic
396C2×C4×C61C2×C22⋊C411yescharacteristic
397C2×C4×C61C2×C22⋊C411yescharacteristic
398C2×C4×C61C2×C22⋊C411yescharacteristic
399C2×C4×C61C2×C22⋊C411yescharacteristic
400C2×C4×C61C2×C22⋊C411yescharacteristic
401C2×C4×C61C23×C411yescharacteristic
402C2×C4×C61C22×D411yescharacteristic
403C22⋊D61—42no—
404C22⋊D61—41no—
405C22⋊D61—41no—
406C22⋊D61—41no—
407C22⋊D61—41no—
408C22⋊D61—41no—
409C22⋊D61—41no—
410C22⋊D61—42no—
411C22⋊D61—81no—
412C22⋊D61—81no—
413C22⋊D61—81no—
414C22⋊D61—81no—
415C22⋊D61—81no—
416C22⋊D61—81no—
417C2×Dic61—21no—
418C2×Dic61—21no—
419C2×Dic61—21no—
420C2×Dic61—21no—
421C2×Dic61—21no—
422C2×Dic61—81no—
423C2×Dic61—81no—
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—
438#92418—41no—
439#92418—41no—
440#92418—41no—
441#92418—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—
485C4×C61—81no—
486C4×C61—81no—
487C4×C61—81no—
488C4×C61—81no—
489Dic61—41no—
490Dic61—41no—
491Dic61—41no—
492Dic61—41no—
493Dic61—41no—
494#3519—611no—
495#2974—611no—
496#2318D6111yescharacteristic, complemented
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—1221no—
545#435—1221no—
546#435—1221no—
547C8×D4—1221no—
548#432—611no—
549#431—611no—
550#407—611no—
551#407—611no—
552C2×C22⋊C8—611no—
553C2×C22⋊C8—611no—
554#388—21no—
555#387—21no—
556#386—21no—
557#385—21no—
558#383C2×D6111yescharacteristic, complemented
559#382C2×D6111yescharacteristic, complemented
560#381C2×D6111yescharacteristic, complemented
561#380C2×D6111yescharacteristic, complemented
562C4×C22⋊C4C2×D6111yescharacteristic, complemented
563C2×#95C2×D6111yescharacteristic, complemented
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×D4C22⋊D6111yescharacteristic
590C23×C4—21no—
591C23×C4C22×D6111yescharacteristic
592C23×C4C22×D6111yescharacteristic
593C2×M16—1221no—
594C2×M16—1221no—
595C22×C8—1221no—
596C22×C8—1221no—
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×D4D24411yescharacteristic
668C4×D4D24411yescharacteristic
669C4×D4D24411yescharacteristic
670C4×D4D24411yescharacteristic
671#117—611no—
672#117—611no—
673#117—1221no—
674#117—1221no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—611no—
678C2×C4⋊C4—611no—
679C2×C4⋊C4C22⋊D6111yescharacteristic
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—1221no—
684C2×C22⋊C4—1221no—
685C2×C22⋊C4—1221no—
686C2×C22⋊C4—1221no—
687C2×C22⋊C4C22⋊D6111yescharacteristic
688C2×C22⋊C4C22⋊D6111yescharacteristic
689C2×C42—21no—
690C2×C42C22×D6111yescharacteristic
691C4⋊C8—1221no—
692C4⋊C8—1221no—
693C22⋊C8—611no—
694C22⋊C8—611no—
695C22⋊C8—611no—
696C22⋊C8—611no—
697C22⋊C8—1221no—
698C22⋊C8—1221no—
699C22⋊C8—1221no—
700C22⋊C8—1221no—
701#97—1221no—
702C4×C8—1221no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95C22×D6111yescharacteristic
709#95C22×D6111yescharacteristic
710#95C22×D6111yescharacteristic
711#95C22×D6111yescharacteristic
712C24—1221no—
713C24—1221no—
714C24C2×C22⋊D6111yescharacteristic
715C24C2×C22⋊D6111yescharacteristic
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—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—42no—
757C22×C4—81no—
758C22×C4—81no—
759C22×C4—81no—
760C22×C4—81no—
761C22×C4—1221no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
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—4881no—
782M16—4881no—
783C2×C8—1221no—
784C2×C8—1221no—
785C2×C8—1221no—
786C2×C8—1221no—
787C2×C8—4881no—
788C2×C8—4881no—
789C4⋊C4—81no—
790C4⋊C4—81no—
791C4⋊C4—611no—
792C4⋊C4—611no—
793C4⋊C4—611no—
794C4⋊C4—611no—
795C4⋊C4—1221no—
796C4⋊C4—1221no—
797C4⋊C4—1221no—
798C4⋊C4—1221no—
799C4⋊C4—1221no—
800C4⋊C4—1221no—
801C4⋊C4—1221no—
802C4⋊C4—1221no—
803C4⋊C4—1221no—
804C4⋊C4#1175819811yescharacteristic
805C4⋊C4#1175819811yescharacteristic
806C4⋊C4#1175819811yescharacteristic
807C4⋊C4#1175819811yescharacteristic
808C22⋊C4—42no—
809C22⋊C4—81no—
810C22⋊C4—81no—
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—1221no—
828C22⋊C4—1221no—
829C22⋊C4—1221no—
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—81no—
839C42—1221no—
840C42—1221no—
841C42—1221no—
842C42C2×C4×D6111yescharacteristic
843C42C2×C4×D6111yescharacteristic
844C42C2×D24411yescharacteristic
845C42C2×D24411yescharacteristic
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×C22⋊D6111yescharacteristic
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—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—84no—
922C2×C4—1221no—
923C2×C4—1221no—
924C2×C4—1221no—
925C2×C4—1221no—
926C2×C4—1221no—
927C2×C4—4881no—
928C2×C4—4881no—
929C2×C4—4881no—
930C2×C4—4881no—
931C2×C4—4881no—
932C2×C4—4881no—
933C2×C4—2442no—
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×D24411yescharacteristic
944C8—2441no—
945C8—2441no—
946C8—2441no—
947C8—2441no—
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#1683978012yes—
977C22C22×#1175819811yescharacteristic
978C22#1684056511yescharacteristic
979C22#1684057011yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—81no—
991C4—81no—
992C4—81no—
993C4—81no—
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#2145434211yescharacteristic
1010C2C2×#1683978011yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2318C2
socleC22×C61C22×C22⋊C4
prime radical#21459851C2
cosocleC22×C4×C61C24
hypercenter#2318D61
hypocenterC61#17597
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2318

Complements

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

NH ≅ G/Ntype
2. #21454854C2semidirect
3. #21444394C2semidirect
4. #21444386C2semidirect
5. #21444378C2semidirect
6. #21444373C2semidirect
7. #21444365C2semidirect
8. #21444360C2semidirect
9. #21444355C2semidirect
10. #21444347C2semidirect
11. #21444334C2semidirect
12. #21444321C2semidirect
13. #21444308C2semidirect
14. C2×#16839495C2semidirect
15. C61×#2318C2semidirect
16. #16840477C4semidirect
17. #16840469C4semidirect
19. #16840458C4semidirect
20. #16840458C4semidirect
21. #16840433C4semidirect
22. #16840408C4semidirect
23. #16840408C4semidirect
26. D4×D244C4semidirect
42. #16839819C22semidirect
43. #16839815C22semidirect
44. #16839726C22semidirect
45. #16839726C22semidirect
46. C2×C22⋊#92418C22semidirect
47. C2×C22⋊#92418C22semidirect
48. #16839498C22semidirect
49. #16839498C22semidirect
50. #16839498C22semidirect
51. #16839498C22semidirect
56. #16839495C22semidirect
57. #16839495C22semidirect
58. #16839495C22semidirect
59. #16839495C22semidirect
60. #16839495C22semidirect
61. #16839495C22semidirect
62. #16839495C22semidirect
63. #16839495C22semidirect
69. C61×#383C22semidirect
70. C61×#382C22semidirect
71. C61×#381C22semidirect
72. C61×#380C22semidirect
73. C4×C22⋊C4×C61C22semidirect
74. C2×#95×C61C22semidirect
77. C2×#11758222C2×C4semidirect
79. C22×D244C2×C4semidirect
87. #14519777C2×C4semidirect
88. #14519774C2×C4semidirect
93. #14519769C2×C4semidirect
96. #14519765C2×C4semidirect
107. #14519756C2×C4semidirect
120. #14519751C2×C4semidirect
121. #14519751C2×C4semidirect
122. #14519751C2×C4semidirect
139. C4×Dic122C2×C4semidirect
141. C4×D244C2×C4semidirect
142. C4×D244C2×C4semidirect
143. C4×D244C2×C4semidirect
154. #14519736C2×C4semidirect
158. C2×C4⋊Dic61C2×C4semidirect
496. #2318D61semidirect
558. #383C2×D61semidirect
559. #382C2×D61semidirect
560. #381C2×D61semidirect
561. #380C2×D61semidirect
562. C4×C22⋊C4C2×D61semidirect
563. C2×#95C2×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
#214548542
#214443942
#214443862
#214443782
#214443732
#214443652
#214443602
#214443552
#214443472
#214443342
#214443212
#214443082
C2×#168394952
C61×#23182
#1759761