Finite Group Databasebeta

← #29647536

Subgroups — #29647536

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#21459839C211yesmaximal, characteristic
2#21454855C211yesmaximal, characteristic, complemented
3#21448453C211yesmaximal, characteristic, complemented
4#21444395C211yesmaximal, characteristic, complemented
5#21444385C211yesmaximal, characteristic, complemented
6#21444377C211yesmaximal, characteristic, complemented
7#21444374C211yesmaximal, characteristic, complemented
8#21444364C211yesmaximal, characteristic, complemented
9#21444361C211yesmaximal, characteristic, complemented
10#21444356C211yesmaximal, characteristic, complemented
11#21444346C211yesmaximal, characteristic, complemented
12#21444336C211yesmaximal, characteristic, complemented
13#21444310C211yesmaximal, characteristic, complemented
14C2×#16839495C211yesmaximal, characteristic, complemented
15C61×#1504C211yesmaximal, characteristic, complemented
16#16840475C411yescharacteristic, complemented
17#16840470C411yescharacteristic, complemented
18#16840464C411yescharacteristic, complemented
19#16840461—21no—
20#16840456C411yescharacteristic, complemented
21#16840431C411yescharacteristic, complemented
22#16840407—21no—
23#16840403C411yescharacteristic, complemented
24#16840400C411yescharacteristic, complemented
25#16840399—21no—
26#16840396C411yescharacteristic, complemented
27#16840394—21no—
28#16840364—21no—
29#16840348—21no—
30#16840345—21no—
31#16840307C2211yescharacteristic
32#16840298C2211yescharacteristic
33#16840275C2211yescharacteristic
34C2×#14519751C2211yescharacteristic
35#121×D61C2211yescharacteristic
36#16840234—21no—
37C2×C4×C22⋊D61C2211yescharacteristic
38#16839838—21no—
39#16839831—21no—
40#16839830—21no—
41#16839825—21no—
42#16839816C2211yescharacteristic, complemented
43#16839812C2211yescharacteristic, complemented
44#16839724C2211yescharacteristic, complemented
45C2×C22⋊#92418C2211yescharacteristic, complemented
46C22⋊C8×D61C2211yescharacteristic, complemented
47#16839651—21no—
48#16839644—21no—
49#16839641—21no—
50#16839635—21no—
51#16839629C2211yescharacteristic, complemented
52#16839626C2211yescharacteristic, complemented
53#16839624C2211yescharacteristic, complemented
54#16839621C2211yescharacteristic, complemented
55C4×C22⋊Dic61C2211yescharacteristic, complemented
56#16839499C2211yescharacteristic, complemented
57#16839499C2211yescharacteristic, complemented
58#16839497C2211yescharacteristic
59#16839497C2211yescharacteristic
60#16839497C2211yescharacteristic, complemented
61#16839497C2211yescharacteristic, complemented
62#16839496C2211yescharacteristic, complemented
63#16839496C2211yescharacteristic, complemented
64#16839495C2211yescharacteristic
65#16839495C2211yescharacteristic
66#16839495C2211yescharacteristic, complemented
67#16839495C2211yescharacteristic, complemented
68C61×#525C2211yescharacteristic
69C61×#407C2211yescharacteristic, complemented
70C2×#95×C61C2211yescharacteristic, complemented
71C61×#328C2211yescharacteristic, complemented
72C61×#328C2211yescharacteristic, complemented
73C61×#327C2211yescharacteristic, complemented
74C61×#327C2211yescharacteristic, complemented
75C2×#11758226C2×C411yescharacteristic, complemented
76C2×#11758224—21no—
77C22×D244C2×C411yescharacteristic
78C22×C22⋊D61—21no—
79C22×C22⋊D61D411yescharacteristic
80C2×D4×D61—21no—
81C2×D4×D61—21no—
82C2×D4×D61C2×C411yescharacteristic, complemented
83C22×C4×D61C2311yescharacteristic
84C2×#11758189—21no—
85C22×#92418—21no—
86C2×C8×D61—21no—
87#14519776C2×C411yescharacteristic, complemented
88#14519773—21no—
89#14519773C2×C411yescharacteristic, complemented
90#14519772—21no—
91#14519771—21no—
92#14519770—21no—
93#14519768C2×C411yescharacteristic, complemented
94#14519767—21no—
95#14519766C2×C411yescharacteristic, complemented
96#14519765—21no—
97#14519763—21no—
98#14519763—21no—
99#14519762—21no—
100#14519762—21no—
101#14519761—21no—
102#14519761—21no—
103#14519760—21no—
104#14519759—21no—
105#14519757—21no—
106#14519754—21no—
107#14519753C2×C411yescharacteristic, complemented
108#14519752—21no—
109#14519752C2×C411yescharacteristic, complemented
110#14519752C2×C411yescharacteristic, complemented
111#14519751—21no—
112#14519751—21no—
113#14519751—21no—
114#14519751C2×C411yescharacteristic
115#14519751C2×C411yescharacteristic
116#14519751C2311yescharacteristic
117#14519751C2311yescharacteristic
118#14519750—21no—
119#14519750—21no—
120#14519750—21no—
121#14519750—21no—
122#14519749—21no—
123#14519749—21no—
124#14519749—21no—
125#14519749—21no—
126#14519748—21no—
127#14519748C2×C411yescharacteristic, complemented
128#14519747—21no—
129#14519747—21no—
130#14519747—21no—
131#14519745—21no—
132#14519745—21no—
133Q8×Dic61C2×C411yescharacteristic, complemented
134C4×D244—21no—
135D4×Dic61—21no—
136D4×Dic61C2×C411yescharacteristic, complemented
137#14519739—21no—
138#14519739C2×C411yescharacteristic, complemented
139#14519739C2×C411yescharacteristic, complemented
140C4×C22⋊D61—21no—
141C4×C22⋊D61C2×C411yescharacteristic
142C4×C22⋊D61C2×C411yescharacteristic
143C4×C22⋊D61C2×C411yescharacteristic
144C4×C22⋊D61C2×C411yescharacteristic
145C4×C22⋊D61D411yescharacteristic
146C4×C22⋊D61D411yescharacteristic
147C4×C22⋊D61D411yescharacteristic
148C4×C22⋊D61D411yescharacteristic
149#14519737—21no—
150#14519737—21no—
151#14519737—21no—
152#14519737—21no—
153#14519735—21no—
154#14519735C2×C411yescharacteristic, complemented
155#14519734—21no—
156C2×C4⋊Dic61C2×C411yescharacteristic
157C2×#11758196—21no—
158C2×#11758196—21no—
159C2×#11758196D411yescharacteristic
160C4⋊C4×D61C2×C411yescharacteristic, complemented
161C2×C22⋊Dic61—21no—
162C2×C22⋊Dic61D411yescharacteristic
163C2×#11758198—21no—
164C2×#11758198—21no—
165C2×#11758198—21no—
166C2×#11758198—21no—
167C2×#11758198D411yescharacteristic
168C22⋊C4×D61—21no—
169C22⋊C4×D61—21no—
170C2×C4×Dic61—21no—
171C2×C4×Dic61C2311yescharacteristic
172#14519706—21no—
173#14519706—21no—
174C22⋊#92418—21no—
175C22⋊#92418C2311yescharacteristic
176C22⋊#92418C2311yescharacteristic
177#14519689—21no—
178#14519689—21no—
179#14519687—21no—
180C8×Dic61—21no—
181#14519684—21no—
182#14519684—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684C2311yescharacteristic
186#14519684C2311yescharacteristic
187C2×#41×C61C2×C411yescharacteristic
188C23×C4×C61—21no—
189C23×C4×C61C2311yescharacteristic
190C2×M16×C61—21no—
191#123×C61—21no—
192C22⋊Q8×C61C2×C411yescharacteristic
193C22⋊Q8×C61C2311yescharacteristic
194#121×C61C2×C411yescharacteristic
195#121×C61C2311yescharacteristic
196#120×C61—21no—
197C4×D4×C61—21no—
198C4×D4×C61—21no—
199#117×C61C2×C411yescharacteristic
200C22⋊C8×C61—21no—
201C22⋊C8×C61C2311yescharacteristic
202C22⋊C8×C61C2311yescharacteristic
203#95×C61—21no—
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C24×C61C2×D411yescharacteristic
207C23×D61—21no—
208C23×D61—21no—
209C23×D61C2×D411yescharacteristic
210#41×C61—81no—
211C2×Q8×C61C22×C411yescharacteristic
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61C22×C411yescharacteristic
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×C61C22×C411yescharacteristic
224C22×C4×C61C22×C411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2411yescharacteristic
229C2×C22⋊D61—21no—
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—42no—
238C2×C22⋊D61—81no—
239C2×C22⋊D61—81no—
240C2×C22⋊D61C22⋊C411yescharacteristic
241C2×C22⋊D61C22⋊C411yescharacteristic
242C2×C22⋊D61C22⋊C411yescharacteristic
243C2×C22⋊D61C22⋊C411yescharacteristic
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61C2×D411yescharacteristic
249C22×Dic61C2×D411yescharacteristic
250C22×Dic61C2×D411yescharacteristic
251#11758226—81no—
252#11758224—81no—
253#11758224—81no—
254D4×D61—44no—
255D4×D61—81no—
256D4×D61—81no—
257D4×D61—81no—
258C2×D244—21no—
259C2×D244—21no—
260C2×D244—21no—
261C2×D244—21no—
262C2×D244—81no—
263C2×D244C22×C411yescharacteristic
264C2×D244C22×C411yescharacteristic
265C2×C4×D61—21no—
266C2×C4×D61—21no—
267C2×C4×D61—21no—
268C2×C4×D61—21no—
269C2×C4×D61—81no—
270C2×C4×D61C22×C411yescharacteristic
271C2×C4×D61C22×C411yescharacteristic
272C2×C4×D61C2×D411yescharacteristic
273C2×C4×D61C2×D411yescharacteristic
274C2×Dic122—21no—
275M16×C61—81no—
276C2×C8×C61—21no—
277C2×C8×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61C22×C411yescharacteristic
281C4⋊C4×C61C22×C411yescharacteristic
282C22⋊C4×C61—21no—
283C22⋊C4×C61—21no—
284C22⋊C4×C61—21no—
285C22⋊C4×C61—21no—
286C22⋊C4×C61—21no—
287C42×C61—21no—
288C22⋊Dic61—21no—
289C22⋊Dic61—21no—
290C22⋊Dic61—42no—
291C22⋊Dic61C22⋊C411yescharacteristic
292C22⋊Dic61C22⋊C411yescharacteristic
293C22⋊Dic61C22⋊C411yescharacteristic
294C22⋊Dic61C22⋊C411yescharacteristic
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—21no—
306#11758198—21no—
307#11758198—81no—
308#11758198—81no—
309#11758198C22⋊C411yescharacteristic
310#11758198C22⋊C411yescharacteristic
311#11758198C22⋊C411yescharacteristic
312#11758198C22⋊C411yescharacteristic
313C4⋊Dic61—21no—
314C4⋊Dic61—21no—
315C4⋊Dic61—21no—
316C4⋊Dic61C22×C411yescharacteristic
317C4⋊Dic61C22×C411yescharacteristic
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322#11758196—81no—
323#11758196—81no—
324#11758196C22⋊C411yescharacteristic
325#11758196C22⋊C411yescharacteristic
326#11758196C22⋊C411yescharacteristic
327#11758196C22⋊C411yescharacteristic
328C4×Dic61—21no—
329C4×Dic61—21no—
330C4×Dic61—81no—
331C4×Dic61C22×C411yescharacteristic
332C4×Dic61C22×C411yescharacteristic
333C4×Dic61C2×D411yescharacteristic
334C4×Dic61C2×D411yescharacteristic
335C2×#92418—21no—
336C2×#92418—21no—
337C2×#92418—81no—
338#11758189—81no—
339C8×D61—81no—
340C23×C61—21no—
341C23×C61—21no—
342C23×C61—22no—
343C23×C61—21no—
344C23×C61—41no—
345C23×C61C2×C22⋊C411yescharacteristic
346C23×C61C2×C22⋊C411yescharacteristic
347C23×C61C22×D411yescharacteristic
348C22×D61—21no—
349C22×D61—21no—
350C22×D61—21no—
351C22×D61—21no—
352C22×D61—41no—
353C22×D61—41no—
354C22×D61—42no—
355C22×D61—42no—
356C22×D61—81no—
357C22×D61—81no—
358C22×D61—81no—
359C22×D61—81no—
360C22×D61C2×C22⋊C411yescharacteristic
361C22×D61C2×C22⋊C411yescharacteristic
362Q8×C61—41no—
363D4×C61—41no—
364D4×C61—41no—
365D4×C61—41no—
366D4×C61—42no—
367D4×C61—81no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
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—81no—
384C2×C4×C61—84no—
385C2×C4×C61C2×C22⋊C411yescharacteristic
386C2×C4×C61C2×C22⋊C411yescharacteristic
387C2×C4×C61C23×C411yescharacteristic
388C2×C4×C61C22×D411yescharacteristic
389C22⋊D61—22no—
390C22⋊D61—22no—
391C22⋊D61—41no—
392C22⋊D61—41no—
393C22⋊D61—42no—
394C22⋊D61—41no—
395C22⋊D61—41no—
396C22⋊D61—41no—
397C22⋊D61—41no—
398C22⋊D61—81no—
399C22⋊D61—81no—
400C22⋊D61—81no—
401C22⋊D61—81no—
402C22⋊D61—81no—
403C2×Dic61—21no—
404C2×Dic61—21no—
405C2×Dic61—21no—
406C2×Dic61—21no—
407C2×Dic61—41no—
408C2×Dic61—41no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411C2×Dic61—41no—
412C2×Dic61—41no—
413C2×Dic61—41no—
414C2×Dic61—41no—
415C2×Dic61—81no—
416C2×Dic61—81no—
417C2×Dic61C2×C22⋊C411yescharacteristic
418C2×Dic61C2×C22⋊C411yescharacteristic
419C2×Dic61C2×C22⋊C411yescharacteristic
420C2×Dic61C2×C22⋊C411yescharacteristic
421C2×Dic61C2×C22⋊C411yescharacteristic
422C2×Dic61C2×C22⋊C411yescharacteristic
423D244—41no—
424D244—41no—
425D244—42no—
426D244—81no—
427D244—81no—
428D244—81no—
429C4×D61—41no—
430C4×D61—41no—
431C4×D61—41no—
432C4×D61—41no—
433C4×D61—42no—
434C4×D61—81no—
435C4×D61—81no—
436C4×D61—81no—
437Dic122—81no—
438C8×C61—41no—
439C8×C61—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—42no—
451C22×C61—42no—
452C22×C61—41no—
453C22×C61—41no—
454C22×C61—41no—
455C22×C61#42112yes—
456C22×C61C22×C22⋊C411yescharacteristic
457C22×C61#57611yescharacteristic
458C22×C61#57711yescharacteristic
459C2×D61—21no—
460C2×D61—21no—
461C2×D61—21no—
462C2×D61—21no—
463C2×D61—21no—
464C2×D61—21no—
465C2×D61—41no—
466C2×D61—41no—
467C2×D61—41no—
468C2×D61—41no—
469C2×D61—41no—
470C2×D61—41no—
471C2×D61—81no—
472C2×D61—81no—
473C2×D61—162no—
474C2×D61—162no—
475C4×C61—21no—
476C4×C61—21no—
477C4×C61—21no—
478C4×C61—21no—
479C4×C61—41no—
480C4×C61—41no—
481C4×C61—41no—
482C4×C61—81no—
483C4×C61—81no—
484Dic61—21no—
485Dic61—21no—
486Dic61—21no—
487Dic61—21no—
488Dic61—21no—
489Dic61—21no—
490Dic61—41no—
491Dic61—41no—
492Dic61—81no—
493Dic61—81no—
494#3519—611no—
495#2974—611no—
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#1504D6111yescharacteristic, complemented
507#1501—611no—
508C2×#327—611no—
509C2×C61—21no—
510C2×C61—21no—
511C2×C61—22no—
512C2×C61—41no—
513C2×C61—81no—
514C2×C61#288311yescharacteristic
515C2×C61#289711yescharacteristic
516C2×C61C2×#42111yescharacteristic
517D61—41no—
518D61—41no—
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#525C2×D6111yescharacteristic
540C2×#121—611no—
541C2×#121—611no—
542#518—1221no—
543C2×C4×D4—611no—
544#436—1221no—
545#435—1221no—
546#435—1221no—
547C8×D4—1221no—
548#432—611no—
549#431—611no—
550#407—611no—
551#407C2×D6111yescharacteristic, complemented
552C2×C22⋊C8—611no—
553C2×C22⋊C8—611no—
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×#95C2×D6111yescharacteristic, complemented
564#328—611no—
565#328—611no—
566#328C2×D6111yescharacteristic, complemented
567#328C2×D6111yescharacteristic, complemented
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#327C2×D6111yescharacteristic, complemented
579#327C2×D6111yescharacteristic, complemented
580C61#1759711yescharacteristic, complemented, Sylow
581C2×#41—611no—
582C2×#41—1221no—
583C2×#41C4×D6111yescharacteristic
584C22×D4—611no—
585C22×D4—611no—
586C22×D4—611no—
587C22×D4—1221no—
588C22×D4—1221no—
589C22×D4—1221no—
590C23×C4—21no—
591C23×C4—611no—
592C23×C4C22×D6111yescharacteristic
593C2×M16—21no—
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—21no—
610#123—1221no—
611#123—1221no—
612#123—1221no—
613#123—1221no—
614#123—1221no—
615#123—1221no—
616C22⋊Q8—611no—
617C22⋊Q8—1221no—
618C22⋊Q8—1221no—
619C22⋊Q8C4×D6111yescharacteristic
620C22⋊Q8C22×D6111yescharacteristic
621#121—611no—
622#121—611no—
623#121—611no—
624#121—611no—
625#121—611no—
626#121—611no—
627#121—611no—
628#121—1221no—
629#121—1221no—
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#121C4×D6111yescharacteristic
642#121C22×D6111yescharacteristic
643#120—21no—
644#120—1221no—
645#120—1221no—
646#120—1221no—
647#120—1221no—
648#120—1221no—
649C4×Q8—611no—
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—611no—
653C4×D4—611no—
654C4×D4—611no—
655C4×D4—611no—
656C4×D4—611no—
657C4×D4—611no—
658C4×D4—611no—
659C4×D4—611no—
660C4×D4—611no—
661C4×D4—611no—
662C4×D4—611no—
663C4×D4—1221no—
664C4×D4—1221no—
665C4×D4—1221no—
666C4×D4—1221no—
667C4×D4—1221no—
668C4×D4—1221no—
669C4×D4—1221no—
670C4×D4—1221no—
671#117—611no—
672#117—1221no—
673#117—1221no—
674#117C4×D6111yescharacteristic
675C2×C4⋊C4—611no—
676C2×C4⋊C4—611no—
677C2×C4⋊C4—611no—
678C2×C4⋊C4—1221no—
679C2×C4⋊C4—1221no—
680C2×C22⋊C4—611no—
681C2×C22⋊C4—611no—
682C2×C22⋊C4—1221no—
683C2×C22⋊C4—1221no—
684C2×C22⋊C4—1221no—
685C2×C22⋊C4—1221no—
686C2×C22⋊C4—1221no—
687C2×C22⋊C4—1221no—
688C2×C22⋊C4—1221no—
689C2×C42—611no—
690C2×C42—1221no—
691C4⋊C8—1221no—
692C4⋊C8—1221no—
693C22⋊C8—21no—
694C22⋊C8—611no—
695C22⋊C8—611no—
696C22⋊C8—1221no—
697C22⋊C8—1221no—
698C22⋊C8—1221no—
699C22⋊C8C22×D6111yescharacteristic
700C22⋊C8C22×D6111yescharacteristic
701#97—1221no—
702C4×C8—1221no—
703#95—21no—
704#95—611no—
705#95—611no—
706#95—1221no—
707#95—1221no—
708#95—1221no—
709#95—1221no—
710#95C22×D6111yescharacteristic
711#95C22×D6111yescharacteristic
712C24—611no—
713C24—1221no—
714C24—1221no—
715C24D4×D6111yescharacteristic
716#41—81no—
717#41—4881no—
718#41—4881no—
719#41—4881no—
720C2×Q8—1221no—
721C2×Q8C2×C4×D6111yescharacteristic
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—611no—
726C2×D4—611no—
727C2×D4—611no—
728C2×D4—611no—
729C2×D4—611no—
730C2×D4—611no—
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—1221no—
742C2×D4—1221no—
743C2×D4—4881no—
744C2×D4—4881no—
745C2×D4—4881no—
746C2×D4—4881no—
747C2×D4—4881no—
748C2×D4—4881no—
749C2×D4—2444no—
750C2×D4—2442no—
751C2×D4C2×C4×D6111yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—42no—
756C22×C4—81no—
757C22×C4—81no—
758C22×C4—81no—
759C22×C4—611no—
760C22×C4—611no—
761C22×C4—611no—
762C22×C4—611no—
763C22×C4—611no—
764C22×C4—611no—
765C22×C4—611no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—4881no—
775C22×C4C2×C4×D6111yescharacteristic
776C22×C4C2×C4×D6111yescharacteristic
777C22×C4D4×D6111yescharacteristic
778C22×C4D4×D6111yescharacteristic
779C22×C4D4×D6111yescharacteristic
780C22×C4C23×D6111yescharacteristic
781M16—81no—
782M16—4881no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—1221no—
786C2×C8—1221no—
787C2×C8—4881no—
788C2×C8—4881no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—611no—
792C4⋊C4—611no—
793C4⋊C4—611no—
794C4⋊C4—611no—
795C4⋊C4—611no—
796C4⋊C4—611no—
797C4⋊C4—1221no—
798C4⋊C4—1221no—
799C4⋊C4—1221no—
800C4⋊C4—1221no—
801C4⋊C4—1221no—
802C4⋊C4—1221no—
803C4⋊C4—1221no—
804C4⋊C4—4881no—
805C4⋊C4—4881no—
806C4⋊C4C2×C4×D6111yescharacteristic
807C4⋊C4C2×C4×D6111yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—611no—
814C22⋊C4—611no—
815C22⋊C4—611no—
816C22⋊C4—611no—
817C22⋊C4—611no—
818C22⋊C4—611no—
819C22⋊C4—611no—
820C22⋊C4—611no—
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—1221no—
831C22⋊C4—1221no—
832C22⋊C4—1221no—
833C22⋊C4—1221no—
834C22⋊C4—1221no—
835C22⋊C4—4881no—
836C22⋊C4—4881no—
837C22⋊C4—2442no—
838C42—21no—
839C42—611no—
840C42—611no—
841C42—611no—
842C42—611no—
843C42—1221no—
844C42—1221no—
845C42—4881no—
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—41no—
851C23—611no—
852C23—611no—
853C23—1221no—
854C23—1221no—
855C23—1221no—
856C23—1221no—
857C23—4881no—
858C23—4881no—
859C23—4881no—
860C23—4881no—
861C23—2441no—
862C23—2441no—
863C23—2442no—
864C23—2442no—
865C23C22⋊C4×D6111yescharacteristic
866C23C22⋊C4×D6111yescharacteristic
867C23C2×D4×D6111yescharacteristic
868Q8—41no—
869Q8—4881no—
870D4—41no—
871D4—42no—
872D4—41no—
873D4—41no—
874D4—81no—
875D4—1222no—
876D4—1222no—
877D4—4881no—
878D4—4881no—
879D4—4881no—
880D4—4881no—
881D4—4881no—
882D4—4881no—
883D4—4881no—
884D4—4881no—
885D4—2441no—
886D4—2441no—
887D4—2442no—
888D4—2441no—
889D4—2441no—
890D4—2442no—
891D4—2441no—
892D4—2441no—
893D4—2441no—
894D4—2441no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
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—81no—
911C2×C4—84no—
912C2×C4—611no—
913C2×C4—611no—
914C2×C4—611no—
915C2×C4—611no—
916C2×C4—611no—
917C2×C4—611no—
918C2×C4—1221no—
919C2×C4—1221no—
920C2×C4—1221no—
921C2×C4—1221no—
922C2×C4—4881no—
923C2×C4—4881no—
924C2×C4—4881no—
925C2×C4—4881no—
926C2×C4—4881no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2442no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4—2441no—
940C2×C4C22⋊C4×D6111yescharacteristic
941C2×C4C22⋊C4×D6111yescharacteristic
942C2×C4C22×C4×D6111yescharacteristic
943C2×C4C2×D4×D6111yescharacteristic
944C8—41no—
945C8—41no—
946C8—2441no—
947C8—2441no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—42no—
956C22—42no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—1221no—
961C22—1221no—
962C22—1221no—
963C22—1221no—
964C22—1221no—
965C22—1221no—
966C22—9762no—
967C22—9762no—
968C22—4881no—
969C22—4881no—
970C22—2441no—
971C22—2441no—
972C22—2441no—
973C22—2441no—
974C22—2441no—
975C22—2441no—
976C22#1683977712yes—
977C22C2×C22⋊C4×D6111yescharacteristic
978C22#1684056611yescharacteristic
979C22#1684057111yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—81no—
988C4—81no—
989C4—1221no—
990C4—1221no—
991C4—1221no—
992C4—1221no—
993C4—1221no—
994C4—1221no—
995C4—4881no—
996C4—4881no—
997C4—2441no—
998C4—2441no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—81no—
1004C2—4881no—
1005C2—4881no—
1006C2—2441no—
1007C2—2441no—
1008C2#2145427711yescharacteristic
1009C2#2145434311yescharacteristic
1010C2C2×#1683977711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1504C2
socleC22×C61C22×C22⋊C4
prime radical#21459839C2
cosocleC22×C4×C61C24
hypercenter#1504D61
hypocenterC61#17597
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. #21454855C2semidirect
3. #21448453C2semidirect
4. #21444395C2semidirect
5. #21444385C2semidirect
6. #21444377C2semidirect
7. #21444374C2semidirect
8. #21444364C2semidirect
9. #21444361C2semidirect
10. #21444356C2semidirect
11. #21444346C2semidirect
12. #21444336C2semidirect
13. #21444310C2semidirect
14. C2×#16839495C2semidirect
15. C61×#1504C2semidirect
16. #16840475C4semidirect
17. #16840470C4semidirect
18. #16840464C4semidirect
20. #16840456C4semidirect
21. #16840431C4semidirect
23. #16840403C4semidirect
24. #16840400C4semidirect
26. #16840396C4semidirect
42. #16839816C22semidirect
43. #16839812C22semidirect
44. #16839724C22semidirect
45. C2×C22⋊#92418C22semidirect
46. C22⋊C8×D61C22semidirect
51. #16839629C22semidirect
52. #16839626C22semidirect
53. #16839624C22semidirect
54. #16839621C22semidirect
55. C4×C22⋊Dic61C22semidirect
56. #16839499C22semidirect
57. #16839499C22semidirect
60. #16839497C22semidirect
61. #16839497C22semidirect
62. #16839496C22semidirect
63. #16839496C22semidirect
66. #16839495C22semidirect
67. #16839495C22semidirect
69. C61×#407C22semidirect
70. C2×#95×C61C22semidirect
71. C61×#328C22semidirect
72. C61×#328C22semidirect
73. C61×#327C22semidirect
74. C61×#327C22semidirect
75. C2×#11758226C2×C4semidirect
82. C2×D4×D61C2×C4semidirect
87. #14519776C2×C4semidirect
89. #14519773C2×C4semidirect
93. #14519768C2×C4semidirect
95. #14519766C2×C4semidirect
107. #14519753C2×C4semidirect
109. #14519752C2×C4semidirect
110. #14519752C2×C4semidirect
127. #14519748C2×C4semidirect
133. Q8×Dic61C2×C4semidirect
136. D4×Dic61C2×C4semidirect
138. #14519739C2×C4semidirect
139. #14519739C2×C4semidirect
154. #14519735C2×C4semidirect
160. C4⋊C4×D61C2×C4semidirect
506. #1504D61semidirect
551. #407C2×D61semidirect
563. C2×#95C2×D61semidirect
566. #328C2×D61semidirect
567. #328C2×D61semidirect
578. #327C2×D61semidirect
579. #327C2×D61semidirect
580. C61#17597semidirect

Maximal subgroups

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

subgroupindex
#214598392
#214548552
#214484532
#214443952
#214443852
#214443772
#214443742
#214443642
#214443612
#214443562
#214443462
#214443362
#214443102
C2×#168394952
C61×#15042
#1759761