Finite Group Databasebeta

← #30610990

Subgroups — #30610990

Order 15616.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462676C211yesmaximal, characteristic, complemented
2#21462258C211yesmaximal, characteristic, complemented
3#21461220C211yesmaximal, characteristic, complemented
4#21461215C211yesmaximal, characteristic, complemented
5#21461214C211yesmaximal, characteristic, complemented
6#21461209C211yesmaximal, characteristic, complemented
7#21461206C211yesmaximal, characteristic, complemented
8#21461205C211yesmaximal, characteristic, complemented
9#21461198C211yesmaximal, characteristic, complemented
10#21461197C211yesmaximal, characteristic, complemented
11#21461194C211yesmaximal, characteristic, complemented
12#21461191C211yesmaximal, characteristic, complemented
13D61⋊#327C211yesmaximal, characteristic, complemented
14C2×#16840613C211yesmaximal, characteristic, complemented
15#21459848C211yesmaximal, characteristic
16C2×D4×#6923—21no—
17#16840795—21no—
18#16840793—21no—
19#16840792—21no—
20#16840789—21no—
21#16840785C2211yescharacteristic, complemented
22#16840780C2211yescharacteristic, complemented
23#16840734C2211yescharacteristic, complemented
24#16840733C2211yescharacteristic, complemented
25C2×#14519834C2211yescharacteristic, complemented
26D61⋊(C22⋊C8)C2211yescharacteristic, complemented
27C4⋊C4×#6923—21no—
28C4×C4⋊#6923C2211yescharacteristic, complemented
29C22⋊C4×#6923—21no—
30C22⋊C4×#6923—21no—
31C4×C22⋊#6923C2211yescharacteristic, complemented
32C4×C22⋊#6923C2211yescharacteristic, complemented
33#16840698C2211yescharacteristic, complemented
34C2×(C2×#6923)⋊C4C2211yescharacteristic, complemented
35C2×(C2×#6923)⋊C4C2211yescharacteristic, complemented
36#16840616C2211yescharacteristic, complemented
37#16840616C2211yescharacteristic, complemented
38#16840616C2211yescharacteristic, complemented
39#16840616C2211yescharacteristic, complemented
40#16840614C2211yescharacteristic, complemented
41#16840614C2211yescharacteristic, complemented
42#16840614C2211yescharacteristic, complemented
43#16840614C2211yescharacteristic, complemented
44#16840613C2211yescharacteristic
45#16840613C2211yescharacteristic
46#16840613C2211yescharacteristic
47#16840613C2211yescharacteristic
48#16840613C2211yescharacteristic, complemented
49#16840613C2211yescharacteristic, complemented
50#16840613C2211yescharacteristic, complemented
51#16840613C2211yescharacteristic, complemented
52#16840476C411yescharacteristic, complemented
53#16840470C411yescharacteristic, complemented
54#16840462C411yescharacteristic, complemented
55#16840458C411yescharacteristic, complemented
56#16840457—21no—
57#16840431C411yescharacteristic, complemented
58#16840409—21no—
59#16840405C411yescharacteristic, complemented
60#16840402—21no—
61D4×C22⋊D61C411yescharacteristic, complemented
62#16840394—21no—
63#16840362—21no—
64#16840348—21no—
65#16840347—21no—
66#16840309C2211yescharacteristic
67#16840291C2211yescharacteristic
68#16840275C2211yescharacteristic
69#16840269C2211yescharacteristic
70C2×#14519748C2211yescharacteristic
71#121×D61C2211yescharacteristic
72#16840235—21no—
73C4×D4×D61C2211yescharacteristic
74C61×#546C411yescharacteristic, complemented
75C23×#6923—21no—
76C23×#6923—21no—
77C2×#11758213—21no—
78C2×#11758217—21no—
79C2×D61⋊C8—21no—
80C22×#92420—21no—
81D4×#6923—28no—
82C2×C4⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C4×#6923—21no—
86C2×C4×#6923—21no—
87C2×C4×#6923—21no—
88C2×C4×#6923—21no—
89#14519844—21no—
90#14519844—21no—
91#14519834—21no—
92#14519834—21no—
93#14519834C2311yescharacteristic
94#14519834C2311yescharacteristic
95#14519834C2311yescharacteristic
96#14519834C2311yescharacteristic
97C22⋊#92420—21no—
98C22⋊#92420—21no—
99#14519832—21no—
100C4×#92420—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4—21no—
104(C2×#6923)⋊C4C2311yescharacteristic
105(C2×#6923)⋊C4C2311yescharacteristic
106(C2×#6923)⋊C4C2311yescharacteristic
107(C2×#6923)⋊C4C2311yescharacteristic
108C2×#11758226C2×C411yescharacteristic, complemented
109C2×#11758222—21no—
110C22×C22⋊D61—21no—
111C22×C22⋊D61—21no—
112C2×D4×D61—21no—
113C2×D4×D61C2×C411yescharacteristic, complemented
114C2×D4×D61D411yescharacteristic
115C22×C4×D61C2311yescharacteristic
116C22×C4×D61C2311yescharacteristic
117#14519776C2×C411yescharacteristic, complemented
118#14519773—21no—
119#14519773C2×C411yescharacteristic, complemented
120#14519772—21no—
121#14519770—21no—
122#14519770—21no—
123#14519769C2×C411yescharacteristic, complemented
124#14519767—21no—
125#14519764—21no—
126#14519763—21no—
127#14519763—21no—
128#14519762—21no—
129#14519760—21no—
130#14519759—21no—
131#14519759—21no—
132#14519759—21no—
133#14519758—21no—
134#14519757—21no—
135#14519754—21no—
136#14519753C2×C411yescharacteristic, complemented
137#14519753C2311yescharacteristic
138#14519752C2311yescharacteristic
139#14519751—21no—
140#14519751C2×C411yescharacteristic, complemented
141#14519751C2×C411yescharacteristic, complemented
142#14519750—21no—
143#14519750—21no—
144#14519750—21no—
145#14519750—21no—
146#14519749—21no—
147#14519749—21no—
148#14519749—21no—
149#14519749—21no—
150#14519748—21no—
151#14519748—21no—
152#14519748—21no—
153#14519748C2×C411yescharacteristic, complemented
154#14519748C2×C411yescharacteristic, complemented
155#14519748C2×C411yescharacteristic, complemented
156#14519748C2311yescharacteristic
157#14519748C2311yescharacteristic
158#14519747—21no—
159#14519747—21no—
160#14519746—21no—
161#14519745—21no—
162#14519745—21no—
163Q8×Dic61C2×C411yescharacteristic, complemented
164C4×D244C2×C411yescharacteristic
165C4×D244C2×C411yescharacteristic, complemented
166D4×Dic61C2×C411yescharacteristic, complemented
167D4×Dic61D411yescharacteristic
168#14519739—21no—
169#14519739D411yescharacteristic
170C4×C22⋊D61—21no—
171C4×C22⋊D61—21no—
172C4×C22⋊D61—21no—
173C4×C22⋊D61—21no—
174C4×C22⋊D61—21no—
175C4×C22⋊D61C2×C411yescharacteristic
176C4×C22⋊D61C2×C411yescharacteristic
177#14519737—21no—
178#14519737—21no—
179#14519737—21no—
180#14519737—21no—
181#14519737D411yescharacteristic
182#14519737D411yescharacteristic
183#14519736C2×C411yescharacteristic, complemented
184#14519735C2×C411yescharacteristic, complemented
185#14519733—21no—
186#14519733—21no—
187C2×C4⋊Dic61C2×C411yescharacteristic, complemented
188C4⋊C4×D61C2×C411yescharacteristic, complemented
189C4⋊C4×D61D411yescharacteristic
190C2×C22⋊Dic61—21no—
191C22⋊C4×D61—21no—
192C22⋊C4×D61—21no—
193C22⋊C4×D61D411yescharacteristic
194C22⋊C4×D61D411yescharacteristic
195C42×D61C2311yescharacteristic
196C2×#41×C61C2×C411yescharacteristic, complemented
197C22×D4×C61C2×C411yescharacteristic, complemented
198#124×C61C2×C411yescharacteristic, complemented
199#123×C61—21no—
200C22⋊Q8×C61C2×C411yescharacteristic, complemented
201#121×C61—21no—
202#121×C61C2×C411yescharacteristic, complemented
203#120×C61—21no—
204C4×D4×C61C2×C411yescharacteristic
205C4×D4×C61C2×C411yescharacteristic, complemented
206C2×C22⋊C4×C61—21no—
207C24×C61—21no—
208C23×D61—21no—
209C23×D61C2×D411yescharacteristic
210C23×D61C2×D411yescharacteristic
211C22×#6923—21no—
212C22×#6923—21no—
213C22×#6923—21no—
214C22×#6923—21no—
215C22×#6923—24no—
216C22×#6923—24no—
217C22×#6923—81no—
218C22×#6923—81no—
219C22×#6923—81no—
220C22×#6923—81no—
221#41×C61—81no—
222C2×Q8×C61C22×C411yescharacteristic
223C2×D4×C61—21no—
224C2×D4×C61—21no—
225C2×D4×C61—21no—
226C2×D4×C61—81no—
227C2×D4×C61C22⋊C411yescharacteristic
228C2×D4×C61C22×C411yescharacteristic
229C2×D4×C61C22×C411yescharacteristic
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61C22×C411yescharacteristic
233C22×C4×C61C22×C411yescharacteristic
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—21no—
242C2×C22⋊D61—21no—
243C2×C22⋊D61—21no—
244C2×C22⋊D61—44no—
245C2×C22⋊D61—81no—
246C2×C22⋊D61—81no—
247C2×C22⋊D61C22⋊C411yescharacteristic
248C2×C22⋊D61C22⋊C411yescharacteristic
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61C2×D411yescharacteristic
252C22×Dic61C2×D411yescharacteristic
253#11758226—81no—
254D4×D61—24no—
255D4×D61—81no—
256D4×D61—81no—
257D4×D61—81no—
258#11758222—81no—
259#11758222—81no—
260C2×D244—21no—
261C2×D244—21no—
262C2×D244C22⋊C411yescharacteristic
263C2×D244C22×C411yescharacteristic
264C2×C4×D61—21no—
265C2×C4×D61—21no—
266C2×C4×D61—21no—
267C2×C4×D61—81no—
268C2×C4×D61—81no—
269C2×C4×D61C22×C411yescharacteristic
270C2×C4×D61C22×C411yescharacteristic
271C2×C4×D61C2×D411yescharacteristic
272C2×C4×D61C2×D411yescharacteristic
273C2×C4×D61C2×D411yescharacteristic
274C2×C4×D61C2×D411yescharacteristic
275C2×C4×D61C2×D411yescharacteristic
276C2×C4×D61C2×D411yescharacteristic
277C2×C4×D61C2411yescharacteristic
278C2×Dic122—21no—
279C22⋊#6923—24no—
280C22⋊#6923—24no—
281#11758217—81no—
282C2×#92420—21no—
283C2×#92420—21no—
284C2×#92420—21no—
285C2×#92420—21no—
286C2×#92420—81no—
287C4⋊#6923—24no—
288C4×#6923—24no—
289C4×#6923—81no—
290C4×#6923—81no—
291C4×#6923—81no—
292#11758213—81no—
293D61⋊C8—81no—
294C4⋊C4×C61—21no—
295C4⋊C4×C61C22⋊C411yescharacteristic
296C4⋊C4×C61C22×C411yescharacteristic
297C22⋊C4×C61—21no—
298C22⋊C4×C61—21no—
299C22⋊C4×C61—21no—
300C22⋊C4×C61—21no—
301C22⋊C4×C61—21no—
302C22⋊C4×C61C22⋊C411yescharacteristic
303C22⋊C4×C61C22⋊C411yescharacteristic
304C42×C61C22×C411yescharacteristic
305C22⋊Dic61—21no—
306C22⋊Dic61—21no—
307C22⋊Dic61—21no—
308C22⋊Dic61—21no—
309C22⋊Dic61—21no—
310C22⋊Dic61—21no—
311C22⋊Dic61—21no—
312C22⋊Dic61C22⋊C411yescharacteristic
313C22⋊Dic61C22⋊C411yescharacteristic
314#11758198—21no—
315#11758198—21no—
316#11758198—21no—
317#11758198—21no—
318#11758198—21no—
319#11758198—21no—
320#11758198—21no—
321#11758198C22⋊C411yescharacteristic
322#11758198C22⋊C411yescharacteristic
323#11758198C22⋊C411yescharacteristic
324#11758198C22⋊C411yescharacteristic
325C4⋊Dic61—21no—
326C4⋊Dic61—21no—
327C4⋊Dic61C22⋊C411yescharacteristic
328C4⋊Dic61C22×C411yescharacteristic
329C4⋊Dic61C22×C411yescharacteristic
330C4⋊Dic61C22×C411yescharacteristic
331#11758196—21no—
332#11758196—21no—
333#11758196—21no—
334#11758196—21no—
335#11758196—21no—
336#11758196—21no—
337#11758196C22⋊C411yescharacteristic
338#11758196C22⋊C411yescharacteristic
339C4×Dic61—21no—
340C4×Dic61—21no—
341C4×Dic61—21no—
342C4×Dic61C22×C411yescharacteristic
343C4×Dic61C2×D411yescharacteristic
344C4×Dic61C2×D411yescharacteristic
345C23×C61—21no—
346C23×C61—21no—
347C23×C61—42no—
348C23×C61—81no—
349C23×C61—81no—
350C23×C61C2×C22⋊C411yescharacteristic
351C23×C61C2×C22⋊C411yescharacteristic
352C22×D61—22no—
353C22×D61—21no—
354C22×D61—21no—
355C22×D61—21no—
356C22×D61—21no—
357C22×D61—22no—
358C22×D61—21no—
359C22×D61—41no—
360C22×D61—41no—
361C22×D61—42no—
362C22×D61—81no—
363C22×D61—81no—
364C22×D61C2×C22⋊C411yescharacteristic
365C22×D61C2×C22⋊C411yescharacteristic
366C22×D61C22×D411yescharacteristic
367C2×#6923—22no—
368C2×#6923—22no—
369C2×#6923—22no—
370C2×#6923—22no—
371C2×#6923—41no—
372C2×#6923—41no—
373C2×#6923—41no—
374C2×#6923—41no—
375C2×#6923—41no—
376C2×#6923—41no—
377C2×#6923—41no—
378C2×#6923—41no—
379C2×#6923—84no—
380C2×#6923—84no—
381Q8×C61—41no—
382D4×C61—22no—
383D4×C61—41no—
384D4×C61—41no—
385D4×C61—81no—
386D4×C61—81no—
387D4×C61—81no—
388C2×C4×C61—21no—
389C2×C4×C61—21no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—81no—
393C2×C4×C61—81no—
394C2×C4×C61C2×C22⋊C411yescharacteristic
395C2×C4×C61C2×C22⋊C411yescharacteristic
396C2×C4×C61C2×C22⋊C411yescharacteristic
397C2×C4×C61C2×C22⋊C411yescharacteristic
398C2×C4×C61C23×C411yescharacteristic
399C22⋊D61—22no—
400C22⋊D61—42no—
401C22⋊D61—41no—
402C22⋊D61—41no—
403C22⋊D61—41no—
404C22⋊D61—41no—
405C22⋊D61—42no—
406C22⋊D61—42no—
407C22⋊D61—81no—
408C22⋊D61—81no—
409C22⋊D61—81no—
410C22⋊D61—81no—
411C22⋊D61—81no—
412C22⋊D61#10414yes—
413C2×Dic61—21no—
414C2×Dic61—21no—
415C2×Dic61—21no—
416C2×Dic61—41no—
417C2×Dic61—41no—
418C2×Dic61—42no—
419C2×Dic61—81no—
420C2×Dic61C2×C22⋊C411yescharacteristic
421C2×Dic61C2×C22⋊C411yescharacteristic
422C2×Dic61C2×C22⋊C411yescharacteristic
423C2×Dic61C2×C22⋊C411yescharacteristic
424C2×Dic61C22×D411yescharacteristic
425D244—22no—
426D244—41no—
427D244—41no—
428D244—41no—
429D244—81no—
430C4×D61—21no—
431C4×D61—21no—
432C4×D61—22no—
433C4×D61—41no—
434C4×D61—41no—
435C4×D61—41no—
436C4×D61—41no—
437C4×D61—41no—
438C4×D61—41no—
439C4×D61—41no—
440C4×D61—81no—
441C4×D61—81no—
442C4×D61—81no—
443Dic122—81no—
444#92420—41no—
445#92420—41no—
446#92420—41no—
447#92420—41no—
448#17547—611nomaximal, Sylow
449C22×C61—21no—
450C22×C61—21no—
451C22×C61—21no—
452C22×C61—21no—
453C22×C61—21no—
454C22×C61—41no—
455C22×C61—41no—
456C22×C61—41no—
457C22×C61—41no—
458C22×C61—41no—
459C22×C61—41no—
460C22×C61—162no—
461C22×C61C2×#10412yes—
462C22×C61C22×C22⋊C411yescharacteristic
463C2×D61—21no—
464C2×D61—21no—
465C2×D61—21no—
466C2×D61—21no—
467C2×D61—21no—
468C2×D61—21no—
469C2×D61—21no—
470C2×D61—42no—
471C2×D61—42no—
472C2×D61—42no—
473C2×D61—42no—
474C2×D61—41no—
475C2×D61—41no—
476C2×D61—41no—
477C2×D61—162no—
478C2×D61C2×#10412yes—
479C2×D61#57611yescharacteristic
480C2×D61#57711yescharacteristic
481#6923—42no—
482#6923—42no—
483#6923—42no—
484#6923—42no—
485C4×C61—21no—
486C4×C61—21no—
487C4×C61—21no—
488C4×C61—21no—
489C4×C61—21no—
490C4×C61—41no—
491C4×C61—41no—
492Dic61—21no—
493Dic61—21no—
494Dic61—21no—
495Dic61—21no—
496Dic61—41no—
497Dic61—41no—
498Dic61—41no—
499Dic61C2×#10412yes—
500#3519—611no—
501#2974—611no—
502#2275—611no—
503#1509—611no—
504#1507—611no—
505#1507—611no—
506#1505—611no—
507#1504—611no—
508#1504—611no—
509#1502—611no—
510#1501—611no—
511#1501—611no—
512#1500—611no—
513C2×#327—611no—
514C2×#327—611no—
515C2×C61—22no—
516C2×C61—41no—
517C2×C61—81no—
518C2×C61—81no—
519C2×C61#288311yescharacteristic
520C2×C61#289711yescharacteristic
521C2×C61C22×#10411yescharacteristic
522D61—21no—
523D61—21no—
524D61—22no—
525D61—41no—
526D61—81no—
527#555—611no—
528#554—611no—
529#553—611no—
530#553—611no—
531#553—1221no—
532#550—611no—
533#546—611no—
534#546—1221no—
535#546—1221no—
536#546#692311yescharacteristic, complemented
537D42—611no—
538D42—1221no—
539#540—1221no—
540#538—1221no—
541#538—1221no—
542#532—611no—
543#529—611no—
544#525—611no—
545#525—611no—
546C2×#121—611no—
547C2×#121—611no—
548#518—1221no—
549C2×C4×D4—611no—
550C2×C4×D4—1221no—
551#436—1221no—
552#435—1221no—
553#435—1221no—
554C8×D4—1221no—
555#432—611no—
556#431—611no—
557#407—611no—
558#407—611no—
559C2×C22⋊C8—611no—
560C2×C22⋊C8—611no—
561C4×C4⋊C4—611no—
562C4×C4⋊C4—1221no—
563C4×C22⋊C4—611no—
564C4×C22⋊C4—611no—
565C4×C22⋊C4—1221no—
566C4×C22⋊C4—1221no—
567#376—611no—
568C2×#95—611no—
569C2×#95—611no—
570#328—611no—
571#328—611no—
572#328—611no—
573#328—611no—
574#327—611no—
575#327—611no—
576#327—611no—
577#327—611no—
578#327—611no—
579#327—611no—
580#327—611no—
581#327—611no—
582#327—611no—
583#327—611no—
584#327—611no—
585#327—611no—
586C61#1754711yescharacteristic, complemented, Sylow
587C2×#41—611no—
588C2×#41—1221no—
589C2×#41C2×#692311yescharacteristic, complemented
590C22×D4—611no—
591C22×D4—611no—
592C22×D4—1221no—
593C22×D4—1221no—
594C22×D4—1221no—
595C22×D4C2×#692311yescharacteristic, complemented
596C23×C4—611no—
597C23×C4—611no—
598C23×C4—1221no—
599C23×C4—1221no—
600C2×M16—1221no—
601C2×M16—1221no—
602C22×C8—1221no—
603C22×C8—1221no—
604C4⋊Q8—611no—
605#127—611no—
606#127—1221no—
607#126—1221no—
608#126—1221no—
609#126—1221no—
610#125—611no—
611#125—1221no—
612#124—1221no—
613#124—1221no—
614#124—1221no—
615#124C2×#692311yescharacteristic, complemented
616#123—21no—
617#123—1221no—
618#123—1221no—
619#123—1221no—
620#123—1221no—
621#123—1221no—
622#123—1221no—
623C22⋊Q8—611no—
624C22⋊Q8—611no—
625C22⋊Q8—1221no—
626C22⋊Q8—1221no—
627C22⋊Q8C2×#692311yescharacteristic, complemented
628#121—21no—
629#121—611no—
630#121—611no—
631#121—611no—
632#121—611no—
633#121—611no—
634#121—611no—
635#121—611no—
636#121—611no—
637#121—1221no—
638#121—1221no—
639#121—1221no—
640#121—1221no—
641#121—1221no—
642#121—1221no—
643#121—1221no—
644#121—1221no—
645#121—1221no—
646#121—1221no—
647#121—1221no—
648#121—1221no—
649#121C2×#692311yescharacteristic, complemented
650#120—21no—
651#120—1221no—
652#120—1221no—
653#120—1221no—
654#120—1221no—
655#120—1221no—
656C4×Q8—611no—
657C4×D4—611no—
658C4×D4—611no—
659C4×D4—611no—
660C4×D4—611no—
661C4×D4—611no—
662C4×D4—611no—
663C4×D4—611no—
664C4×D4—611no—
665C4×D4—611no—
666C4×D4—1221no—
667C4×D4—1221no—
668C4×D4—1221no—
669C4×D4—1221no—
670C4×D4—1221no—
671C4×D4—1221no—
672C4×D4—1221no—
673C4×D4—1221no—
674C4×D4—1221no—
675C4×D4—1228no—
676C4×D4—1221no—
677C4×D4C2×#692311yescharacteristic
678C4×D4C2×#692311yescharacteristic, complemented
679#117—611no—
680#117—611no—
681#117—1221no—
682#117—1221no—
683C2×C4⋊C4—611no—
684C2×C4⋊C4—611no—
685C2×C4⋊C4—611no—
686C2×C4⋊C4—1221no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—611no—
689C2×C22⋊C4—611no—
690C2×C22⋊C4—1221no—
691C2×C22⋊C4—1221no—
692C2×C22⋊C4—1221no—
693C2×C22⋊C4—1221no—
694C2×C22⋊C4—1221no—
695C2×C42—611no—
696C2×C42—1221no—
697C2×C42—1221no—
698C2×C42—1221no—
699C2×C42—1221no—
700C4⋊C8—1221no—
701C4⋊C8—1221no—
702C22⋊C8—611no—
703C22⋊C8—611no—
704C22⋊C8—611no—
705C22⋊C8—611no—
706C22⋊C8—1221no—
707C22⋊C8—1221no—
708C22⋊C8—1221no—
709C22⋊C8—1221no—
710#97—1221no—
711C4×C8—1221no—
712#95—611no—
713#95—611no—
714#95—611no—
715#95—611no—
716#95—1221no—
717#95—1221no—
718#95—1221no—
719C24—21no—
720C24—611no—
721C24—611no—
722C24—1221no—
723#41—81no—
724#41—4881no—
725#41—4881no—
726#41—4881no—
727C2×Q8—1221no—
728C2×Q8C22×#692311yescharacteristic
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—81no—
733C2×D4—611no—
734C2×D4—611no—
735C2×D4—611no—
736C2×D4—611no—
737C2×D4—1221no—
738C2×D4—1221no—
739C2×D4—1221no—
740C2×D4—1221no—
741C2×D4—1221no—
742C2×D4—1224no—
743C2×D4—1221no—
744C2×D4—1221no—
745C2×D4—1221no—
746C2×D4—1221no—
747C2×D4—1221no—
748C2×D4—1221no—
749C2×D4—1221no—
750C2×D4—4881no—
751C2×D4—4881no—
752C2×D4—4881no—
753C2×D4—4881no—
754C2×D4—4881no—
755C2×D4—2444no—
756C2×D4C22⋊#692311yescharacteristic
757C2×D4C22×#692311yescharacteristic
758C2×D4C22×#692311yescharacteristic
759C22×C4—21no—
760C22×C4—21no—
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—611no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—1221no—
775C22×C4—1224no—
776C22×C4—1224no—
777C22×C4—1221no—
778C22×C4—1221no—
779C22×C4—1221no—
780C22×C4—1221no—
781C22×C4—1221no—
782C22×C4—1221no—
783C22×C4—4881no—
784C22×C4—4881no—
785C22×C4—4881no—
786C22×C4—4881no—
787C22×C4—4881no—
788C22×C4—4881no—
789C22×C4C22×#692311yescharacteristic
790C22×C4C22×#692311yescharacteristic
791M16—4881no—
792M16—4881no—
793C2×C8—1221no—
794C2×C8—1221no—
795C2×C8—1221no—
796C2×C8—1221no—
797C2×C8—4881no—
798C2×C8—4881no—
799C4⋊C4—21no—
800C4⋊C4—611no—
801C4⋊C4—611no—
802C4⋊C4—611no—
803C4⋊C4—611no—
804C4⋊C4—611no—
805C4⋊C4—611no—
806C4⋊C4—1221no—
807C4⋊C4—1221no—
808C4⋊C4—1221no—
809C4⋊C4—1221no—
810C4⋊C4—1221no—
811C4⋊C4—1224no—
812C4⋊C4—1221no—
813C4⋊C4—1221no—
814C4⋊C4—1221no—
815C4⋊C4C22⋊#692311yescharacteristic
816C4⋊C4C22×#692311yescharacteristic
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—611no—
823C22⋊C4—611no—
824C22⋊C4—611no—
825C22⋊C4—611no—
826C22⋊C4—611no—
827C22⋊C4—611no—
828C22⋊C4—1221no—
829C22⋊C4—1221no—
830C22⋊C4—1221no—
831C22⋊C4—1221no—
832C22⋊C4—1221no—
833C22⋊C4—1221no—
834C22⋊C4—1221no—
835C22⋊C4—1221no—
836C22⋊C4—1221no—
837C22⋊C4—1221no—
838C22⋊C4—1224no—
839C22⋊C4—1224no—
840C22⋊C4—1221no—
841C22⋊C4—1221no—
842C22⋊C4—1221no—
843C22⋊C4—1221no—
844C22⋊C4C22⋊#692311yescharacteristic
845C22⋊C4C22⋊#692311yescharacteristic
846C42—611no—
847C42—611no—
848C42—611no—
849C42—1221no—
850C42—1221no—
851C42—1224no—
852C42—1221no—
853C42—4881no—
854C42—4881no—
855C42—4881no—
856C42C22×#692311yescharacteristic
857C23—21no—
858C23—21no—
859C23—42no—
860C23—81no—
861C23—81no—
862C23—611no—
863C23—611no—
864C23—611no—
865C23—1222no—
866C23—1221no—
867C23—1221no—
868C23—1221no—
869C23—1221no—
870C23—1222no—
871C23—1221no—
872C23—4881no—
873C23—4881no—
874C23—2441no—
875C23—2441no—
876C23—2442no—
877C23C2×C22⋊#692311yescharacteristic
878C23C2×C22⋊#692311yescharacteristic
879Q8—41no—
880Q8—4881no—
881D4—22no—
882D4—41no—
883D4—41no—
884D4—81no—
885D4—81no—
886D4—81no—
887D4—614no—
888D4—1222no—
889D4—1222no—
890D4—4881no—
891D4—4881no—
892D4—4881no—
893D4—4881no—
894D4—4881no—
895D4—4881no—
896D4—2441no—
897D4—2441no—
898D4—2441no—
899D4—2442no—
900D4—2441no—
901D4—2441no—
902D4—2441no—
903D4—2441no—
904D4—2442no—
905D4—2442no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—81no—
911C2×C4—81no—
912C2×C4—611no—
913C2×C4—611no—
914C2×C4—611no—
915C2×C4—611no—
916C2×C4—611no—
917C2×C4—1222no—
918C2×C4—1221no—
919C2×C4—1221no—
920C2×C4—1222no—
921C2×C4—1222no—
922C2×C4—1222no—
923C2×C4—1222no—
924C2×C4—1221no—
925C2×C4—1221no—
926C2×C4—1221no—
927C2×C4—4881no—
928C2×C4—4881no—
929C2×C4—4881no—
930C2×C4—4881no—
931C2×C4—4884no—
932C2×C4—4884no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4—2441no—
940C2×C4—2442no—
941C2×C4—2441no—
942C2×C4—2441no—
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×C4C2×C22⋊#692311yescharacteristic
952C2×C4C2×C22⋊#692311yescharacteristic
953C2×C4C2×C22⋊#692311yescharacteristic
954C2×C4C2×C22⋊#692311yescharacteristic
955C2×C4C23×#692311yescharacteristic
956C8—2441no—
957C8—2441no—
958C8—2441no—
959C8—2441no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—162no—
972C22—611no—
973C22—611no—
974C22—612no—
975C22—1221no—
976C22—1221no—
977C22—1221no—
978C22—1221no—
979C22—1221no—
980C22—1221no—
981C22—1221no—
982C22—9762no—
983C22—2442no—
984C22—2442no—
985C22—2442no—
986C22—2442no—
987C22—2441no—
988C22—2441no—
989C22—2441no—
990C22D61⋊#10412yes—
991C22C22×C22⋊#692311yescharacteristic
992C4—21no—
993C4—21no—
994C4—21no—
995C4—21no—
996C4—21no—
997C4—41no—
998C4—41no—
999C4—612no—
1000C4—1221no—
1001C4—1221no—
1002C4—1221no—
1003C4—1221no—
1004C4—2442no—
1005C4—2442no—
1006C4—2442no—
1007C4—2442no—
1008C4—2441no—
1009C4—2441no—
1010C4—2441no—
1011C2—22no—
1012C2—41no—
1013C2—81no—
1014C2—81no—
1015C2—1221no—
1016C2—1221no—
1017C2—1222no—
1018C2—4881no—
1019C2—2441no—
1020C2#2146241811yescharacteristic
1021C2#2146244011yescharacteristic
1022C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#546C4
socleC22×C61C22×C22⋊C4
prime radical#21459848C2
cosocleC2×C4×D61C24
hypercenter#546#6923
hypocenterC61#17547
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #21462676C2semidirect
2. #21462258C2semidirect
3. #21461220C2semidirect
4. #21461215C2semidirect
5. #21461214C2semidirect
6. #21461209C2semidirect
7. #21461206C2semidirect
8. #21461205C2semidirect
9. #21461198C2semidirect
10. #21461197C2semidirect
11. #21461194C2semidirect
12. #21461191C2semidirect
13. D61⋊#327C2semidirect
14. C2×#16840613C2semidirect
21. #16840785C22semidirect
22. #16840780C22semidirect
23. #16840734C22semidirect
24. #16840733C22semidirect
25. C2×#14519834C22semidirect
26. D61⋊(C22⋊C8)C22semidirect
28. C4×C4⋊#6923C22semidirect
31. C4×C22⋊#6923C22semidirect
32. C4×C22⋊#6923C22semidirect
33. #16840698C22semidirect
34. C2×(C2×#6923)⋊C4C22semidirect
35. C2×(C2×#6923)⋊C4C22semidirect
36. #16840616C22semidirect
37. #16840616C22semidirect
38. #16840616C22semidirect
39. #16840616C22semidirect
40. #16840614C22semidirect
41. #16840614C22semidirect
42. #16840614C22semidirect
43. #16840614C22semidirect
48. #16840613C22semidirect
49. #16840613C22semidirect
50. #16840613C22semidirect
51. #16840613C22semidirect
52. #16840476C4semidirect
53. #16840470C4semidirect
54. #16840462C4semidirect
55. #16840458C4semidirect
57. #16840431C4semidirect
59. #16840405C4semidirect
61. D4×C22⋊D61C4semidirect
74. C61×#546C4semidirect
108. C2×#11758226C2×C4semidirect
113. C2×D4×D61C2×C4semidirect
117. #14519776C2×C4semidirect
119. #14519773C2×C4semidirect
123. #14519769C2×C4semidirect
136. #14519753C2×C4semidirect
140. #14519751C2×C4semidirect
141. #14519751C2×C4semidirect
153. #14519748C2×C4semidirect
154. #14519748C2×C4semidirect
155. #14519748C2×C4semidirect
163. Q8×Dic61C2×C4semidirect
165. C4×D244C2×C4semidirect
166. D4×Dic61C2×C4semidirect
183. #14519736C2×C4semidirect
184. #14519735C2×C4semidirect
187. C2×C4⋊Dic61C2×C4semidirect
188. C4⋊C4×D61C2×C4semidirect
196. C2×#41×C61C2×C4semidirect
197. C22×D4×C61C2×C4semidirect
198. #124×C61C2×C4semidirect
200. C22⋊Q8×C61C2×C4semidirect
202. #121×C61C2×C4semidirect
205. C4×D4×C61C2×C4semidirect
536. #546#6923semidirect
586. C61#17547semidirect
589. C2×#41C2×#6923semidirect
595. C22×D4C2×#6923semidirect
615. #124C2×#6923semidirect
627. C22⋊Q8C2×#6923semidirect
649. #121C2×#6923semidirect
678. C4×D4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214626762
#214622582
#214612202
#214612152
#214612142
#214612092
#214612062
#214612052
#214611982
#214611972
#214611942
#214611912
D61⋊#3272
C2×#168406132
#214598482
#1754761