Finite Group Databasebeta

← #29647614

Subgroups — #29647614

Order 15616.

1366 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459480C211yesmaximal, characteristic
2#21454265C211yesmaximal, characteristic, complemented
3#21448643C211yesmaximal, characteristic, complemented
4#21444385C211yesmaximal, characteristic, complemented
5#21444374C211yesmaximal, characteristic, complemented
6#21444361C211yesmaximal, characteristic, complemented
7#21444347C211yesmaximal, characteristic, complemented
8#21444346C211yesmaximal, characteristic, complemented
9#21444333C211yesmaximal, characteristic, complemented
10#21444323C211yesmaximal, characteristic, complemented
11#21444322C211yesmaximal, characteristic, complemented
12#21444309C211yesmaximal, characteristic, complemented
13C2×#16839497C211yesmaximal, characteristic, complemented
14#327×D61C211yesmaximal, characteristic, complemented
15C61×#1516C211yesmaximal, characteristic, complemented
16C2×#14519823C411yescharacteristic, complemented
17C22×#11758222C2211yescharacteristic
18C2×#14519783—21no—
19#16840433—21no—
20#16840421—21no—
21#16840408—21no—
22#16840404—21no—
23#16840404—21no—
24D4×D244—21no—
25#16840394—21no—
26#16840394—21no—
27#16840342C411yescharacteristic, complemented
28#16840342C411yescharacteristic, complemented
29#16840340C411yescharacteristic, complemented
30#16840331C411yescharacteristic, complemented
31#16840328C411yescharacteristic, complemented
32#16840328C411yescharacteristic, complemented
33#16840275C2211yescharacteristic
34#16840275C2211yescharacteristic
35C2×#14519751C2211yescharacteristic
36#121×D61C2211yescharacteristic
37#121×D61C2211yescharacteristic
38#16840242C411yescharacteristic, complemented
39C2×#14519737—21no—
40#16839728—21no—
41#16839727—21no—
42#16839727—21no—
43#16839726C2211yescharacteristic, complemented
44#16839724C2211yescharacteristic, complemented
45#16839724C2211yescharacteristic, complemented
46C22⋊C8×D61C2211yescharacteristic, complemented
47C22⋊C8×D61C2211yescharacteristic, complemented
48#16839666—21no—
49#16839640—21no—
50#16839639—21no—
51#16839624C2211yescharacteristic, complemented
52#16839621C2211yescharacteristic, complemented
53#16839609C2211yescharacteristic, complemented
54C2×#14519684C2211yescharacteristic, complemented
55#95×D61C2211yescharacteristic, complemented
56#16839499C2211yescharacteristic, complemented
57#16839499C2211yescharacteristic, complemented
58#16839497C2211yescharacteristic, complemented
59#16839497C2211yescharacteristic, complemented
60#16839497C2211yescharacteristic, complemented
61#16839497C2211yescharacteristic, complemented
62#16839496C2211yescharacteristic, complemented
63#16839496C2211yescharacteristic, complemented
64#16839495C2211yescharacteristic, complemented
65#16839495C2211yescharacteristic, complemented
66#16839495C2211yescharacteristic, complemented
67#16839495C2211yescharacteristic, complemented
68C61×#525C2211yescharacteristic
69C2×C22⋊C8×C61C2211yescharacteristic, complemented
70C61×#381C2211yescharacteristic, complemented
71C61×#328C2211yescharacteristic, complemented
72C61×#328C2211yescharacteristic, complemented
73C61×#327C2211yescharacteristic, complemented
74C61×#327C2211yescharacteristic, complemented
75#14519823—44no—
76C2×#11758226C2×C411yescharacteristic, complemented
77C2×#11758226C2×C411yescharacteristic, complemented
78C2×#11758222—21no—
79C2×#11758222—44no—
80C2×#11758222C2×C411yescharacteristic
81C2×#11758222C2×C411yescharacteristic
82C2×#11758222C2×C411yescharacteristic
83C2×#11758222C2×C411yescharacteristic
84C2×#11758222D411yescharacteristic
85C2×#11758222D411yescharacteristic
86C2×#11758222D411yescharacteristic
87C2×#11758222D411yescharacteristic
88C22×Dic122D411yescharacteristic
89C22×D244—21no—
90C22×D244C2×C411yescharacteristic, complemented
91C22×D244D411yescharacteristic
92C22×C22⋊D61—21no—
93C22×C22⋊D61D411yescharacteristic
94C22×C22⋊D61D411yescharacteristic
95C2×D4×D61—21no—
96C2×D4×D61—21no—
97C2×D4×D61—21no—
98C2×D4×D61—21no—
99C2×D4×D61C2×C411yescharacteristic, complemented
100C2×D4×D61C2×C411yescharacteristic, complemented
101C23×Dic61—21no—
102C22×C4×D61—21no—
103C22×C4×D61C2311yescharacteristic
104C22×C4×D61C2311yescharacteristic
105#14519783—44no—
106C2×#11758194—21no—
107C2×#11758189—21no—
108C2×#11758189—21no—
109C2×C8×D61—21no—
110C2×C8×D61—21no—
111#14519774—21no—
112#14519773—21no—
113#14519773—21no—
114#14519765—21no—
115#14519763—21no—
116#14519763—21no—
117#14519762—21no—
118#14519762—21no—
119#14519756—21no—
120#14519755—21no—
121#14519755—21no—
122#14519753C2×C411yescharacteristic, complemented
123#14519753C2×C411yescharacteristic, complemented
124#14519752—21no—
125#14519752—21no—
126#14519752C2×C411yescharacteristic, complemented
127#14519752C2×C411yescharacteristic, complemented
128#14519752C2×C411yescharacteristic, complemented
129#14519752C2×C411yescharacteristic, complemented
130#14519751—21no—
131#14519751—21no—
132#14519751—21no—
133#14519751C2×C411yescharacteristic, complemented
134#14519751C2×C411yescharacteristic, complemented
135#14519751C2311yescharacteristic
136#14519751C2311yescharacteristic
137#14519750—21no—
138#14519750—21no—
139#14519750—21no—
140#14519750—21no—
141#14519750—21no—
142#14519750—21no—
143#14519749—21no—
144#14519749—21no—
145#14519749—21no—
146#14519749—21no—
147#14519748C2×C411yescharacteristic, complemented
148#14519748C2×C411yescharacteristic, complemented
149#14519747—21no—
150#14519747—21no—
151#14519747—21no—
152#14519747—21no—
153#14519747—21no—
154#14519747—21no—
155#14519745—21no—
156#14519745—21no—
157C4×Dic122—21no—
158C4×D244—21no—
159#14519739—21no—
160#14519739—21no—
161#14519737—21no—
162#14519737—21no—
163#14519737—21no—
164#14519737—21no—
165#14519737—44no—
166#14519735C2×C411yescharacteristic, complemented
167#14519735C2×C411yescharacteristic, complemented
168C2×C4⋊Dic61C2×C411yescharacteristic, complemented
169C2×#11758196—21no—
170C4⋊C4×D61C2×C411yescharacteristic, complemented
171C4⋊C4×D61C2×C411yescharacteristic, complemented
172C2×#11758198—21no—
173C2×#11758198—21no—
174C2×#11758198—21no—
175C2×#11758198—21no—
176C22⋊C4×D61—21no—
177C22⋊C4×D61—21no—
178C2×C4×Dic61—21no—
179C22⋊#92418—21no—
180C22⋊#92418C2311yescharacteristic
181C22⋊#92418C2311yescharacteristic
182#14519689—21no—
183#14519689—21no—
184#14519689—21no—
185#14519689—21no—
186#14519684—21no—
187#14519684—21no—
188#14519684—21no—
189#14519684C2311yescharacteristic
190#14519684C2311yescharacteristic
191C2×#41×C61C2×C411yescharacteristic, complemented
192C23×C4×C61C2311yescharacteristic
193C22×C8×C61—21no—
194#123×C61—21no—
195C22⋊Q8×C61C2×C411yescharacteristic, complemented
196C22⋊Q8×C61C2311yescharacteristic
197#121×C61C2×C411yescharacteristic, complemented
198#121×C61C2311yescharacteristic
199#120×C61—21no—
200C4×D4×C61—21no—
201C4×D4×C61—21no—
202#117×C61C2×C411yescharacteristic, complemented
203C2×C22⋊C4×C61—21no—
204C22⋊C8×C61—21no—
205C22⋊C8×C61C2311yescharacteristic
206C22⋊C8×C61C2311yescharacteristic
207#95×C61—21no—
208#95×C61C2311yescharacteristic
209#95×C61C2311yescharacteristic
210C24×C61C2×D411yescharacteristic
211C23×D61—21no—
212C23×D61—21no—
213C23×D61—21no—
214C23×D61C2×D411yescharacteristic
215C23×D61C2×D411yescharacteristic
216#41×C61—42no—
217C2×Q8×C61C22×C411yescharacteristic
218C2×D4×C61—21no—
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61C22×C411yescharacteristic
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—42no—
226C22×C4×C61C22×C411yescharacteristic
227C22×C4×C61C22×C411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2411yescharacteristic
232C2×C22⋊D61—24no—
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—42no—
242C2×C22⋊D61—81no—
243C2×C22⋊D61—81no—
244C2×C22⋊D61C22⋊C411yescharacteristic
245C2×C22⋊D61C22⋊C411yescharacteristic
246C2×C22⋊D61C22⋊C411yescharacteristic
247C2×C22⋊D61C22⋊C411yescharacteristic
248C2×C22⋊D61C22⋊C411yescharacteristic
249C2×C22⋊D61C22⋊C411yescharacteristic
250C2×C22⋊D61C22⋊C411yescharacteristic
251C2×C22⋊D61C22⋊C411yescharacteristic
252C22×Dic61—21no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255C22×Dic61—42no—
256C22×Dic61—42no—
257C22×Dic61—81no—
258C22×Dic61C2×D411yescharacteristic
259C22×Dic61C2×D411yescharacteristic
260#11758226—42no—
261#11758226—42no—
262D4×D61—42no—
263D4×D61—42no—
264D4×D61—44no—
265D4×D61—44no—
266D4×D61—81no—
267D4×D61—81no—
268D4×D61—81no—
269D4×D61—81no—
270#11758222—24no—
271#11758222—24no—
272#11758222—42no—
273#11758222—42no—
274#11758222—44no—
275#11758222—42no—
276#11758222—42no—
277#11758222—42no—
278#11758222—42no—
279C2×D244—21no—
280C2×D244—21no—
281C2×D244—21no—
282C2×D244—21no—
283C2×D244—21no—
284C2×D244—21no—
285C2×D244—21no—
286C2×D244—42no—
287C2×D244—44no—
288C2×D244—42no—
289C2×D244C22⋊C411yescharacteristic
290C2×D244C22⋊C411yescharacteristic
291C2×D244C22⋊C411yescharacteristic
292C2×D244C22⋊C411yescharacteristic
293C2×D244C22×C411yescharacteristic
294C2×D244C22×C411yescharacteristic
295C2×C4×D61—21no—
296C2×C4×D61—21no—
297C2×C4×D61—21no—
298C2×C4×D61—21no—
299C2×C4×D61—42no—
300C2×C4×D61—42no—
301C2×C4×D61—42no—
302C2×C4×D61—42no—
303C2×C4×D61—81no—
304C2×C4×D61C22×C411yescharacteristic
305C2×C4×D61C22×C411yescharacteristic
306C2×C4×D61C22×C411yescharacteristic
307C2×C4×D61C22×C411yescharacteristic
308C2×C4×D61C2×D411yescharacteristic
309C2×C4×D61C2×D411yescharacteristic
310C2×C4×D61C2×D411yescharacteristic
311C2×C4×D61C2×D411yescharacteristic
312C2×Dic122—42no—
313C2×Dic122C22⋊C411yescharacteristic
314C2×Dic122C22⋊C411yescharacteristic
315C2×Dic122C22⋊C411yescharacteristic
316C2×Dic122C22⋊C411yescharacteristic
317C2×C8×C61—21no—
318C2×C8×C61—21no—
319C2×C8×C61—42no—
320C4⋊C4×C61—21no—
321C4⋊C4×C61—21no—
322C4⋊C4×C61C22×C411yescharacteristic
323C4⋊C4×C61C22×C411yescharacteristic
324C22⋊C4×C61—21no—
325C22⋊C4×C61—21no—
326C22⋊C4×C61—21no—
327C22⋊C4×C61—21no—
328C22⋊C4×C61—21no—
329C22⋊C4×C61—42no—
330C42×C61—21no—
331C22⋊Dic61—21no—
332C22⋊Dic61—21no—
333#11758198—21no—
334#11758198—21no—
335#11758198—21no—
336#11758198—21no—
337#11758198—21no—
338#11758198—21no—
339#11758198—21no—
340#11758198—21no—
341#11758198—21no—
342#11758198—21no—
343#11758198—21no—
344#11758198—21no—
345#11758198—42no—
346#11758198—42no—
347#11758198—81no—
348C4⋊Dic61—21no—
349C4⋊Dic61C22×C411yescharacteristic
350C4⋊Dic61C22×C411yescharacteristic
351#11758196—21no—
352#11758196—21no—
353#11758196—21no—
354#11758196—21no—
355#11758196—42no—
356C4×Dic61—21no—
357C4×Dic61—21no—
358C4×Dic61—42no—
359#11758194—42no—
360C2×#92418—21no—
361C2×#92418—21no—
362#11758189—42no—
363#11758189—42no—
364C8×D61—42no—
365C8×D61—42no—
366C23×C61—21no—
367C23×C61—21no—
368C23×C61—22no—
369C23×C61—21no—
370C23×C61—41no—
371C23×C61C2×C22⋊C411yescharacteristic
372C23×C61C2×C22⋊C411yescharacteristic
373C23×C61C22×D411yescharacteristic
374C22×D61—21no—
375C22×D61—21no—
376C22×D61—21no—
377C22×D61—21no—
378C22×D61—22no—
379C22×D61—21no—
380C22×D61—21no—
381C22×D61—41no—
382C22×D61—41no—
383C22×D61—41no—
384C22×D61—42no—
385C22×D61—42no—
386C22×D61—42no—
387C22×D61—81no—
388C22×D61—81no—
389C22×D61—81no—
390C22×D61—81no—
391C22×D61—81no—
392C22×D61—81no—
393C22×D61C2×C22⋊C411yescharacteristic
394C22×D61C2×C22⋊C411yescharacteristic
395C22×D61C2×C22⋊C411yescharacteristic
396C22×D61C2×C22⋊C411yescharacteristic
397Q8×C61—41no—
398D4×C61—41no—
399D4×C61—41no—
400D4×C61—41no—
401D4×C61—42no—
402D4×C61—81no—
403C2×C4×C61—22no—
404C2×C4×C61—22no—
405C2×C4×C61—21no—
406C2×C4×C61—21no—
407C2×C4×C61—21no—
408C2×C4×C61—41no—
409C2×C4×C61—41no—
410C2×C4×C61—41no—
411C2×C4×C61—41no—
412C2×C4×C61—42no—
413C2×C4×C61—41no—
414C2×C4×C61—41no—
415C2×C4×C61—41no—
416C2×C4×C61—41no—
417C2×C4×C61—41no—
418C2×C4×C61—41no—
419C2×C4×C61C2×C22⋊C411yescharacteristic
420C2×C4×C61C2×C22⋊C411yescharacteristic
421C2×C4×C61C23×C411yescharacteristic
422C2×C4×C61C22×D411yescharacteristic
423C22⋊D61—22no—
424C22⋊D61—22no—
425C22⋊D61—22no—
426C22⋊D61—22no—
427C22⋊D61—22no—
428C22⋊D61—41no—
429C22⋊D61—41no—
430C22⋊D61—42no—
431C22⋊D61—41no—
432C22⋊D61—41no—
433C22⋊D61—41no—
434C22⋊D61—41no—
435C22⋊D61—42no—
436C22⋊D61—81no—
437C22⋊D61—81no—
438C22⋊D61—81no—
439C22⋊D61—81no—
440C22⋊D61#9914yes—
441C2×Dic61—22no—
442C2×Dic61—22no—
443C2×Dic61—21no—
444C2×Dic61—21no—
445C2×Dic61—41no—
446C2×Dic61—41no—
447C2×Dic61—41no—
448C2×Dic61—41no—
449C2×Dic61—41no—
450C2×Dic61—41no—
451C2×Dic61—81no—
452C2×Dic61—84no—
453C2×Dic61C2×C22⋊C411yescharacteristic
454C2×Dic61C2×C22⋊C411yescharacteristic
455C2×Dic61C2×C22⋊C411yescharacteristic
456C2×Dic61C2×C22⋊C411yescharacteristic
457D244—22no—
458D244—22no—
459D244—41no—
460D244—41no—
461D244—41no—
462D244—41no—
463D244—42no—
464D244—42no—
465D244—42no—
466D244—81no—
467D244—81no—
468D244—81no—
469D244—81no—
470C4×D61—22no—
471C4×D61—22no—
472C4×D61—22no—
473C4×D61—22no—
474C4×D61—41no—
475C4×D61—41no—
476C4×D61—41no—
477C4×D61—41no—
478C4×D61—42no—
479C4×D61—42no—
480C4×D61—81no—
481C4×D61—81no—
482C4×D61—84no—
483Dic122—22no—
484Dic122—22no—
485Dic122—41no—
486Dic122—41no—
487C8×C61—41no—
488C8×C61—41no—
489#92418—41no—
490#92418—41no—
491#17603—611nomaximal, Sylow
492C22×C61—21no—
493C22×C61—21no—
494C22×C61—21no—
495C22×C61—21no—
496C22×C61—21no—
497C22×C61—21no—
498C22×C61—21no—
499C22×C61—42no—
500C22×C61—42no—
501C22×C61—41no—
502C22×C61—41no—
503C22×C61—41no—
504C22×C61C2×#9912yes—
505C22×C61C22×C22⋊C411yescharacteristic
506C22×C61#57611yescharacteristic
507C22×C61#57711yescharacteristic
508C2×D61—21no—
509C2×D61—21no—
510C2×D61—21no—
511C2×D61—21no—
512C2×D61—21no—
513C2×D61—21no—
514C2×D61—21no—
515C2×D61—21no—
516C2×D61—21no—
517C2×D61—21no—
518C2×D61—21no—
519C2×D61—42no—
520C2×D61—42no—
521C2×D61—41no—
522C2×D61—41no—
523C2×D61—41no—
524C2×D61—41no—
525C2×D61—41no—
526C2×D61—41no—
527C2×D61—81no—
528C2×D61—81no—
529C2×D61—162no—
530C2×D61—162no—
531C2×D61—162no—
532C2×D61C2×#9912yes—
533C4×C61—21no—
534C4×C61—21no—
535C4×C61—21no—
536C4×C61—21no—
537C4×C61—41no—
538C4×C61—41no—
539C4×C61—41no—
540C4×C61—81no—
541C4×C61—81no—
542Dic61—21no—
543Dic61—21no—
544Dic61—21no—
545Dic61—42no—
546Dic61—41no—
547Dic61—41no—
548Dic61—81no—
549Dic61C2×#9912yes—
550#3488—611no—
551#2880—611no—
552#2339—611no—
553#1519—611no—
554#1516—611no—
555#1516D6111yescharacteristic, complemented
556#1513—611no—
557#1510—611no—
558#1510—611no—
559#1507—611no—
560#1504—611no—
561#1504—611no—
562#1501—611no—
563C2×#327—611no—
564C2×#327—611no—
565C2×C61—21no—
566C2×C61—21no—
567C2×C61—22no—
568C2×C61—41no—
569C2×C61—81no—
570C2×C61C22×#9911yescharacteristic
571C2×C61#289711yescharacteristic
572C2×C61#290111yescharacteristic
573D61—22no—
574D61—41no—
575D61—41no—
576D61—41no—
577D61—81no—
578D61—81no—
579C2×H(5,𝔽2)—611no—
580C22×#41—611no—
581C2×#131—1221no—
582#550—1221no—
583#548—1221no—
584#546—1221no—
585#546—1221no—
586#546—1221no—
587D42—1221no—
588D42—1221no—
589D42—1221no—
590#537—611no—
591#537—611no—
592#537—611no—
593#535—611no—
594#535—611no—
595#535—611no—
596#525—611no—
597#525—611no—
598#525C2×D6111yescharacteristic
599C2×#121—611no—
600C2×#121—611no—
601C2×#121—611no—
602#520—611no—
603C2×C4×D4—1221no—
604#408—1221no—
605#408—1221no—
606#408—1221no—
607#407—611no—
608#407—611no—
609#407—611no—
610C2×C22⋊C8—611no—
611C2×C22⋊C8—611no—
612C2×C22⋊C8C2×D6111yescharacteristic, complemented
613#391—1221no—
614#386—1221no—
615#386—1221no—
616#381—611no—
617#381C2×D6111yescharacteristic, complemented
618#380—611no—
619C4×C22⋊C4—611no—
620C2×#95—611no—
621C2×#95—611no—
622#328—611no—
623#328—611no—
624#328C2×D6111yescharacteristic, complemented
625#328C2×D6111yescharacteristic, complemented
626#327—611no—
627#327—611no—
628#327—611no—
629#327—611no—
630#327—611no—
631#327—611no—
632#327—611no—
633#327—611no—
634#327—611no—
635#327—611no—
636#327C2×D6111yescharacteristic, complemented
637#327C2×D6111yescharacteristic, complemented
638C61#1760311yescharacteristic, complemented, Sylow
639H(5,𝔽2)—2444no—
640C2×#41—611no—
641C2×#41—611no—
642C2×#41—611no—
643C2×#41—611no—
644C2×#41—611no—
645C2×#41—611no—
646C2×#41—611no—
647C2×#41—611no—
648C2×#41—611no—
649C2×#41—611no—
650C2×#41—1221no—
651C2×#41—2444no—
652C2×#41C4×D6111yescharacteristic, complemented
653C22×Q8—611no—
654C22×D4—611no—
655C22×D4—611no—
656C22×D4—611no—
657C22×D4—611no—
658C22×D4—611no—
659C22×D4—611no—
660C22×D4—1221no—
661C22×D4—1221no—
662C22×D4—1221no—
663C22×D4—1221no—
664C22×D4—1221no—
665C22×D4—1221no—
666C23×C4—611no—
667C23×C4—611no—
668C23×C4—1221no—
669C23×C4—1221no—
670C23×C4C22×D6111yescharacteristic
671#131—2444no—
672C2×M16—1221no—
673C2×M16—1221no—
674C2×M16—1221no—
675C22×C8—21no—
676C22×C8—1221no—
677C22×C8—1221no—
678#127—1221no—
679#127—1221no—
680#127—1221no—
681#124—1221no—
682#124—1221no—
683#124—1221no—
684#123—21no—
685#123—1221no—
686#123—1221no—
687C22⋊Q8—611no—
688C22⋊Q8—611no—
689C22⋊Q8—1221no—
690C22⋊Q8—1221no—
691C22⋊Q8—1221no—
692C22⋊Q8C4×D6111yescharacteristic, complemented
693C22⋊Q8C22×D6111yescharacteristic
694#121—611no—
695#121—611no—
696#121—611no—
697#121—611no—
698#121—611no—
699#121—611no—
700#121—611no—
701#121—611no—
702#121—611no—
703#121—611no—
704#121—1221no—
705#121—1221no—
706#121—1221no—
707#121—1221no—
708#121—1221no—
709#121—1221no—
710#121—1221no—
711#121—1221no—
712#121—1221no—
713#121—1221no—
714#121—1221no—
715#121—1221no—
716#121—1221no—
717#121—1221no—
718#121—1221no—
719#121C4×D6111yescharacteristic, complemented
720#121C22×D6111yescharacteristic
721#120—21no—
722#120—1221no—
723#120—1221no—
724#120—1221no—
725#120—1221no—
726#120—1221no—
727#120—1221no—
728#120—1221no—
729#120—1221no—
730C4×Q8—1221no—
731C4×D4—21no—
732C4×D4—21no—
733C4×D4—1221no—
734C4×D4—1221no—
735C4×D4—1221no—
736C4×D4—1221no—
737C4×D4—1221no—
738C4×D4—1221no—
739C4×D4—1221no—
740C4×D4—2444no—
741#117—611no—
742#117—611no—
743#117C4×D6111yescharacteristic, complemented
744C2×C4⋊C4—611no—
745C2×C4⋊C4—611no—
746C2×C4⋊C4—611no—
747C2×C4⋊C4—1221no—
748C2×C22⋊C4—21no—
749C2×C22⋊C4—1221no—
750C2×C22⋊C4—1221no—
751C2×C22⋊C4—1221no—
752C2×C22⋊C4—1221no—
753C2×C22⋊C4—1221no—
754C2×C22⋊C4—1221no—
755C2×C42—1221no—
756C22⋊C8—21no—
757C22⋊C8—611no—
758C22⋊C8—611no—
759C22⋊C8—1221no—
760C22⋊C8—1221no—
761C22⋊C8—1221no—
762C22⋊C8—1221no—
763C22⋊C8—1221no—
764C22⋊C8C22×D6111yescharacteristic
765C22⋊C8C22×D6111yescharacteristic
766#95—21no—
767#95—611no—
768#95—611no—
769#95—1221no—
770#95—1221no—
771#95—1221no—
772#95C22×D6111yescharacteristic
773#95C22×D6111yescharacteristic
774C24—611no—
775C24—611no—
776C24—1221no—
777C24—1221no—
778C24—1221no—
779C24D4×D6111yescharacteristic
780#41—42no—
781#41—1224no—
782#41—1224no—
783#41—2442no—
784#41—2442no—
785#41—2442no—
786#41—2442no—
787#41—2442no—
788#41—2442no—
789#41—2444no—
790#41—2442no—
791#41—2442no—
792C2×Q8—611no—
793C2×Q8—611no—
794C2×Q8—611no—
795C2×Q8—611no—
796C2×Q8—2442no—
797C2×Q8C2×C4×D6111yescharacteristic
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—611no—
802C2×D4—611no—
803C2×D4—611no—
804C2×D4—611no—
805C2×D4—611no—
806C2×D4—611no—
807C2×D4—611no—
808C2×D4—611no—
809C2×D4—611no—
810C2×D4—611no—
811C2×D4—611no—
812C2×D4—611no—
813C2×D4—611no—
814C2×D4—611no—
815C2×D4—1221no—
816C2×D4—1221no—
817C2×D4—1221no—
818C2×D4—1221no—
819C2×D4—1221no—
820C2×D4—1221no—
821C2×D4—1221no—
822C2×D4—1221no—
823C2×D4—1224no—
824C2×D4—1221no—
825C2×D4—1221no—
826C2×D4—1221no—
827C2×D4—1221no—
828C2×D4—1221no—
829C2×D4—1221no—
830C2×D4—1221no—
831C2×D4—4881no—
832C2×D4—4881no—
833C2×D4—4881no—
834C2×D4—4881no—
835C2×D4—4881no—
836C2×D4—4881no—
837C2×D4—2442no—
838C2×D4—2442no—
839C2×D4—2444no—
840C2×D4—2442no—
841C2×D4—2442no—
842C2×D4—2444no—
843C2×D4—2444no—
844C2×D4—2442no—
845C2×D4C2×C4×D6111yescharacteristic
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—42no—
850C22×C4—611no—
851C22×C4—611no—
852C22×C4—611no—
853C22×C4—611no—
854C22×C4—611no—
855C22×C4—611no—
856C22×C4—611no—
857C22×C4—611no—
858C22×C4—611no—
859C22×C4—611no—
860C22×C4—1221no—
861C22×C4—1221no—
862C22×C4—1221no—
863C22×C4—1221no—
864C22×C4—1221no—
865C22×C4—1221no—
866C22×C4—1221no—
867C22×C4—4881no—
868C22×C4—4881no—
869C22×C4—2442no—
870C22×C4—2442no—
871C22×C4—2442no—
872C22×C4—2442no—
873C22×C4—2442no—
874C22×C4—2442no—
875C22×C4C2×C4×D6111yescharacteristic
876C22×C4C2×C4×D6111yescharacteristic
877C22×C4D4×D6111yescharacteristic
878C22×C4D4×D6111yescharacteristic
879C22×C4D4×D6111yescharacteristic
880C22×C4C23×D6111yescharacteristic
881M16—2442no—
882M16—2442no—
883M16—2442no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—42no—
887C2×C8—1221no—
888C2×C8—1221no—
889C2×C8—2442no—
890C2×C8—2442no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—611no—
894C4⋊C4—611no—
895C4⋊C4—1221no—
896C4⋊C4—1221no—
897C4⋊C4—1221no—
898C4⋊C4—1221no—
899C4⋊C4—1221no—
900C4⋊C4—2442no—
901C4⋊C4C2×C4×D6111yescharacteristic
902C4⋊C4C2×C4×D6111yescharacteristic
903C22⋊C4—21no—
904C22⋊C4—21no—
905C22⋊C4—21no—
906C22⋊C4—21no—
907C22⋊C4—21no—
908C22⋊C4—42no—
909C22⋊C4—1221no—
910C22⋊C4—1221no—
911C22⋊C4—1221no—
912C22⋊C4—1221no—
913C22⋊C4—1221no—
914C22⋊C4—1221no—
915C22⋊C4—1221no—
916C22⋊C4—1221no—
917C22⋊C4—1221no—
918C22⋊C4—1221no—
919C22⋊C4—1221no—
920C22⋊C4—1221no—
921C22⋊C4—1221no—
922C22⋊C4—1221no—
923C22⋊C4—4881no—
924C22⋊C4—2442no—
925C22⋊C4—2442no—
926C42—21no—
927C42—1221no—
928C42—1221no—
929C42—2442no—
930C23—22no—
931C23—21no—
932C23—21no—
933C23—21no—
934C23—41no—
935C23—611no—
936C23—611no—
937C23—611no—
938C23—611no—
939C23—1222no—
940C23—1221no—
941C23—1221no—
942C23—1221no—
943C23—1221no—
944C23—1221no—
945C23—1221no—
946C23—4881no—
947C23—4881no—
948C23—4881no—
949C23—4881no—
950C23—4881no—
951C23—4881no—
952C23—2441no—
953C23—2441no—
954C23—2441no—
955C23—2442no—
956C23—2442no—
957C23—2442no—
958C23C22⋊C4×D6111yescharacteristic
959C23C22⋊C4×D6111yescharacteristic
960C23C2×D4×D6111yescharacteristic
961Q8—41no—
962Q8—1222no—
963Q8—1222no—
964Q8—2441no—
965Q8—2441no—
966D4—41no—
967D4—42no—
968D4—41no—
969D4—41no—
970D4—81no—
971D4—614no—
972D4—1222no—
973D4—1222no—
974D4—1222no—
975D4—1222no—
976D4—1222no—
977D4—1222no—
978D4—1222no—
979D4—4881no—
980D4—4881no—
981D4—4881no—
982D4—4881no—
983D4—4881no—
984D4—4881no—
985D4—4881no—
986D4—4881no—
987D4—2441no—
988D4—2441no—
989D4—2441no—
990D4—2441no—
991D4—2442no—
992D4—2442no—
993D4—2442no—
994D4—2442no—
995D4—2441no—
996D4—2441no—
997D4—2442no—
998D4—2441no—
999D4—2441no—
1000D4—2441no—
1001D4—2441no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—42no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—611no—
1019C2×C4—611no—
1020C2×C4—611no—
1021C2×C4—611no—
1022C2×C4—1222no—
1023C2×C4—1222no—
1024C2×C4—1222no—
1025C2×C4—1222no—
1026C2×C4—1222no—
1027C2×C4—1222no—
1028C2×C4—1221no—
1029C2×C4—1221no—
1030C2×C4—4881no—
1031C2×C4—4881no—
1032C2×C4—4884no—
1033C2×C4—4884no—
1034C2×C4—4881no—
1035C2×C4—2441no—
1036C2×C4—2441no—
1037C2×C4—2441no—
1038C2×C4—2441no—
1039C2×C4—2442no—
1040C2×C4—2442no—
1041C2×C4—2441no—
1042C2×C4—2441no—
1043C2×C4—2441no—
1044C2×C4—2441no—
1045C2×C4—2441no—
1046C2×C4—2441no—
1047C2×C4C22⋊C4×D6111yescharacteristic
1048C2×C4C22⋊C4×D6111yescharacteristic
1049C2×C4C22×C4×D6111yescharacteristic
1050C2×C4C2×D4×D6111yescharacteristic
1051C8—41no—
1052C8—41no—
1053C8—2441no—
1054C8—2441no—
1055C22—21no—
1056C22—21no—
1057C22—21no—
1058C22—21no—
1059C22—21no—
1060C22—21no—
1061C22—21no—
1062C22—42no—
1063C22—42no—
1064C22—41no—
1065C22—41no—
1066C22—41no—
1067C22—612no—
1068C22—1221no—
1069C22—1221no—
1070C22—1221no—
1071C22—1221no—
1072C22—1221no—
1073C22—1221no—
1074C22—1221no—
1075C22—1221no—
1076C22—1221no—
1077C22—1221no—
1078C22—1221no—
1079C22—9762no—
1080C22—9762no—
1081C22—9762no—
1082C22—4881no—
1083C22—4881no—
1084C22—2442no—
1085C22—2442no—
1086C22—2441no—
1087C22—2441no—
1088C22—2441no—
1089C22—2441no—
1090C22—2441no—
1091C22—2441no—
1092C22#99×D6112yes—
1093C22C2×C22⋊C4×D6111yescharacteristic
1094C22#1684056411yescharacteristic
1095C22#1684056911yescharacteristic
1096C4—21no—
1097C4—21no—
1098C4—21no—
1099C4—21no—
1100C4—41no—
1101C4—41no—
1102C4—41no—
1103C4—81no—
1104C4—81no—
1105C4—612no—
1106C4—1221no—
1107C4—1221no—
1108C4—1221no—
1109C4—4881no—
1110C4—2442no—
1111C4—2441no—
1112C4—2441no—
1113C2—21no—
1114C2—21no—
1115C2—22no—
1116C2—41no—
1117C2—81no—
1118C2—1222no—
1119C2—4881no—
1120C2—4881no—
1121C2—2441no—
1122C2—2441no—
1123C2—2441no—
1124C2C2×#99×D6111yescharacteristic
1125C2#2145434111yescharacteristic
1126C2#2145436511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1516C2
socleC22×C61C22×C22⋊C4
prime radical#21459480C2
cosocleC22×C4×C61C24
hypercenter#1516D61
hypocenterC61#17603
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1516

Complements

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

NH ≅ G/Ntype
2. #21454265C2semidirect
3. #21448643C2semidirect
4. #21444385C2semidirect
5. #21444374C2semidirect
6. #21444361C2semidirect
7. #21444347C2semidirect
8. #21444346C2semidirect
9. #21444333C2semidirect
10. #21444323C2semidirect
11. #21444322C2semidirect
12. #21444309C2semidirect
13. C2×#16839497C2semidirect
14. #327×D61C2semidirect
15. C61×#1516C2semidirect
16. C2×#14519823C4semidirect
27. #16840342C4semidirect
28. #16840342C4semidirect
29. #16840340C4semidirect
30. #16840331C4semidirect
31. #16840328C4semidirect
32. #16840328C4semidirect
38. #16840242C4semidirect
43. #16839726C22semidirect
44. #16839724C22semidirect
45. #16839724C22semidirect
46. C22⋊C8×D61C22semidirect
47. C22⋊C8×D61C22semidirect
51. #16839624C22semidirect
52. #16839621C22semidirect
53. #16839609C22semidirect
54. C2×#14519684C22semidirect
55. #95×D61C22semidirect
56. #16839499C22semidirect
57. #16839499C22semidirect
58. #16839497C22semidirect
59. #16839497C22semidirect
60. #16839497C22semidirect
61. #16839497C22semidirect
62. #16839496C22semidirect
63. #16839496C22semidirect
64. #16839495C22semidirect
65. #16839495C22semidirect
66. #16839495C22semidirect
67. #16839495C22semidirect
69. C2×C22⋊C8×C61C22semidirect
70. C61×#381C22semidirect
71. C61×#328C22semidirect
72. C61×#328C22semidirect
73. C61×#327C22semidirect
74. C61×#327C22semidirect
76. C2×#11758226C2×C4semidirect
77. C2×#11758226C2×C4semidirect
90. C22×D244C2×C4semidirect
99. C2×D4×D61C2×C4semidirect
100. C2×D4×D61C2×C4semidirect
122. #14519753C2×C4semidirect
123. #14519753C2×C4semidirect
126. #14519752C2×C4semidirect
127. #14519752C2×C4semidirect
128. #14519752C2×C4semidirect
129. #14519752C2×C4semidirect
133. #14519751C2×C4semidirect
134. #14519751C2×C4semidirect
147. #14519748C2×C4semidirect
148. #14519748C2×C4semidirect
166. #14519735C2×C4semidirect
167. #14519735C2×C4semidirect
168. C2×C4⋊Dic61C2×C4semidirect
170. C4⋊C4×D61C2×C4semidirect
171. C4⋊C4×D61C2×C4semidirect
191. C2×#41×C61C2×C4semidirect
195. C22⋊Q8×C61C2×C4semidirect
197. #121×C61C2×C4semidirect
202. #117×C61C2×C4semidirect
555. #1516D61semidirect
612. C2×C22⋊C8C2×D61semidirect
617. #381C2×D61semidirect
624. #328C2×D61semidirect
625. #328C2×D61semidirect
636. #327C2×D61semidirect
637. #327C2×D61semidirect
638. C61#17603semidirect
652. C2×#41C4×D61semidirect
692. C22⋊Q8C4×D61semidirect
719. #121C4×D61semidirect
743. #117C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214594802
#214542652
#214486432
#214443852
#214443742
#214443612
#214443472
#214443462
#214443332
#214443232
#214443222
#214443092
C2×#168394972
#327×D612
C61×#15162
#1760361