Finite Group Databasebeta

← #29647605

Subgroups — #29647605

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#21459484C211yesmaximal, characteristic
2#21454265C211yesmaximal, characteristic, complemented
3#21448646C211yesmaximal, characteristic, complemented
4#21444385C211yesmaximal, characteristic, complemented
5#21444376C211yesmaximal, characteristic, complemented
6#21444372C211yesmaximal, characteristic, complemented
7#21444359C211yesmaximal, characteristic, complemented
8#21444348C211yesmaximal, characteristic, complemented
9#21444346C211yesmaximal, characteristic, complemented
10#21444333C211yesmaximal, characteristic, complemented
11#21444321C211yesmaximal, characteristic, complemented
12#21444320C211yesmaximal, characteristic, complemented
13#21444307C211yesmaximal, characteristic, complemented
14#327×D61C211yesmaximal, characteristic, complemented
15C2×C61×#327C211yesmaximal, characteristic, complemented
16C2×#14519822C411yescharacteristic, complemented
17C22×#11758222C2211yescharacteristic
18C2×#14519783—21no—
19#16840430—21no—
20#16840418—21no—
21#16840409—21no—
22#16840402—21no—
23#16840402—21no—
24#16840396—21no—
25D4×C22⋊D61—21no—
26D4×C22⋊D61—21no—
27#16840343C411yescharacteristic, complemented
28#16840341C411yescharacteristic, complemented
29#16840341C411yescharacteristic, complemented
30#16840329C411yescharacteristic, complemented
31#16840328C411yescharacteristic, complemented
32#16840328C411yescharacteristic, complemented
33#16840273C2211yescharacteristic
34#16840272C2211yescharacteristic
35#16840272C2211yescharacteristic
36#121×D61C2211yescharacteristic
37#121×D61C2211yescharacteristic
38#16840243C411yescharacteristic, complemented
39C2×C4×C22⋊D61—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#16839641—21no—
50#16839640—21no—
51#16839625C2211yescharacteristic, complemented
52#16839624C2211yescharacteristic, complemented
53#16839621C2211yescharacteristic, complemented
54#16839609C2211yescharacteristic, complemented
55#95×D61C2211yescharacteristic, complemented
56#16839500C2211yescharacteristic, complemented
57#16839500C2211yescharacteristic, complemented
58#16839498C2211yescharacteristic, complemented
59#16839498C2211yescharacteristic, complemented
60#16839497C2211yescharacteristic, complemented
61#16839497C2211yescharacteristic, complemented
62#16839496C2211yescharacteristic, complemented
63#16839496C2211yescharacteristic, complemented
64#16839496C2211yescharacteristic, complemented
65#16839496C2211yescharacteristic, complemented
66#16839495C2211yescharacteristic, complemented
67#16839495C2211yescharacteristic, complemented
68C2×#121×C61C2211yescharacteristic
69C2×C22⋊C8×C61C2211yescharacteristic, complemented
70C2×#95×C61C2211yescharacteristic, complemented
71C61×#327C2211yescharacteristic, complemented
72C61×#327C2211yescharacteristic, complemented
73C61×#327C2211yescharacteristic, complemented
74C61×#327C2211yescharacteristic, complemented
75#14519822—44no—
76C2×#11758222—44no—
77C2×#11758222C2×C411yescharacteristic
78C2×#11758222C2×C411yescharacteristic
79C2×#11758222C2×C411yescharacteristic
80C2×#11758222C2×C411yescharacteristic
81C2×#11758222C2×C411yescharacteristic, complemented
82C2×#11758222D411yescharacteristic
83C2×#11758222D411yescharacteristic
84C2×#11758222D411yescharacteristic
85C2×#11758222D411yescharacteristic
86C2×#11758224—21no—
87C2×#11758224C2×C411yescharacteristic, complemented
88C2×#11758224C2×C411yescharacteristic, complemented
89C22×Dic122D411yescharacteristic
90C22×D244D411yescharacteristic
91C22×C22⋊D61—21no—
92C22×C22⋊D61—21no—
93C22×C22⋊D61D411yescharacteristic
94C22×C22⋊D61D411yescharacteristic
95C2×D4×D61—21no—
96C2×D4×D61—21no—
97C2×D4×D61—21no—
98C2×D4×D61C2×C411yescharacteristic, complemented
99C2×D4×D61C2×C411yescharacteristic, complemented
100C22×C4×D61—21no—
101C22×C4×D61C2311yescharacteristic
102C22×C4×D61C2311yescharacteristic
103#14519783—44no—
104C2×#11758194—21no—
105C2×#11758189—21no—
106C2×#11758189—21no—
107C2×C8×D61—21no—
108C2×C8×D61—21no—
109#14519773—21no—
110#14519773—21no—
111#14519773—21no—
112#14519764—21no—
113#14519763—21no—
114#14519763—21no—
115#14519760—21no—
116#14519759—21no—
117#14519759—21no—
118#14519757—21no—
119#14519757C2×C411yescharacteristic, complemented
120#14519757C2×C411yescharacteristic, complemented
121#14519756C2×C411yescharacteristic, complemented
122#14519756C2311yescharacteristic
123#14519754—21no—
124#14519754—21no—
125#14519752—21no—
126#14519752C2×C411yescharacteristic, complemented
127#14519752C2×C411yescharacteristic, complemented
128#14519751—21no—
129#14519751—21no—
130#14519751C2×C411yescharacteristic, complemented
131#14519751C2311yescharacteristic
132#14519750—21no—
133#14519750—21no—
134#14519750—21no—
135#14519750—21no—
136#14519749—21no—
137#14519749—21no—
138#14519749—21no—
139#14519749—21no—
140#14519748—21no—
141#14519748—21no—
142#14519748C2×C411yescharacteristic, complemented
143#14519748C2×C411yescharacteristic, complemented
144#14519748C2×C411yescharacteristic, complemented
145#14519748C2×C411yescharacteristic, complemented
146#14519747—21no—
147#14519747—21no—
148#14519746—21no—
149#14519746—21no—
150#14519746—21no—
151#14519745—21no—
152#14519745—21no—
153#14519745—21no—
154#14519745—21no—
155#14519742—21no—
156D4×Dic61—21no—
157D4×Dic61—21no—
158#14519739—21no—
159C4×C22⋊D61—21no—
160C4×C22⋊D61—21no—
161C4×C22⋊D61—21no—
162C4×C22⋊D61—21no—
163C4×C22⋊D61—44no—
164#14519737—21no—
165#14519737—21no—
166#14519736C2×C411yescharacteristic, complemented
167#14519735C2×C411yescharacteristic, complemented
168#14519735C2×C411yescharacteristic, complemented
169C2×#11758196—21no—
170C4⋊C4×D61C2×C411yescharacteristic, complemented
171C4⋊C4×D61C2×C411yescharacteristic, complemented
172C2×C22⋊Dic61—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
191C22×D4×C61—21no—
192C22×D4×C61C2×C411yescharacteristic, complemented
193C23×C4×C61—21no—
194C23×C4×C61C2311yescharacteristic
195C22×C8×C61—21no—
196#121×C61—21no—
197#121×C61—21no—
198#121×C61C2×C411yescharacteristic, complemented
199#121×C61C2×C411yescharacteristic, complemented
200#121×C61C2311yescharacteristic
201#121×C61C2311yescharacteristic
202C2×C4⋊C4×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×C61—21no—
211C24×C61C2×D411yescharacteristic
212C23×D61—21no—
213C23×D61—21no—
214C23×D61C2×D411yescharacteristic
215C23×D61C2×D411yescharacteristic
216C2×D4×C61—21no—
217C2×D4×C61—21no—
218C2×D4×C61—21no—
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61—42no—
222C2×D4×C61—81no—
223C2×D4×C61—81no—
224C2×D4×C61C22×C411yescharacteristic
225C2×D4×C61C22×C411yescharacteristic
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—42no—
230C22×C4×C61—42no—
231C22×C4×C61—42no—
232C22×C4×C61—81no—
233C22×C4×C61C22×C411yescharacteristic
234C22×C4×C61C22×C411yescharacteristic
235C22×C4×C61C2×D411yescharacteristic
236C22×C4×C61C2×D411yescharacteristic
237C22×C4×C61C2×D411yescharacteristic
238C22×C4×C61C2411yescharacteristic
239C2×C22⋊D61—24no—
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—21no—
249C2×C22⋊D61—21no—
250C2×C22⋊D61—21no—
251C2×C22⋊D61—42no—
252C2×C22⋊D61—44no—
253C2×C22⋊D61—44no—
254C2×C22⋊D61C22⋊C411yescharacteristic
255C2×C22⋊D61C22⋊C411yescharacteristic
256C2×C22⋊D61C22⋊C411yescharacteristic
257C2×C22⋊D61C22⋊C411yescharacteristic
258C2×C22⋊D61C22⋊C411yescharacteristic
259C2×C22⋊D61C22⋊C411yescharacteristic
260C2×C22⋊D61C22⋊C411yescharacteristic
261C2×C22⋊D61C22⋊C411yescharacteristic
262C22×Dic61—21no—
263C22×Dic61—21no—
264C22×Dic61—21no—
265C22×Dic61—21no—
266C22×Dic61C2×D411yescharacteristic
267C22×Dic61C2×D411yescharacteristic
268#11758224—44no—
269#11758224—42no—
270#11758224—42no—
271D4×D61—42no—
272D4×D61—42no—
273D4×D61—44no—
274D4×D61—81no—
275D4×D61—81no—
276D4×D61—81no—
277D4×D61—81no—
278#11758222—24no—
279#11758222—24no—
280#11758222—42no—
281#11758222—42no—
282#11758222—42no—
283#11758222—42no—
284#11758222—42no—
285#11758222—42no—
286#11758222—42no—
287C2×D244—21no—
288C2×D244—21no—
289C2×D244—42no—
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—42no—
299C2×C4×D61—42no—
300C2×C4×D61—42no—
301C2×C4×D61—42no—
302C2×C4×D61—81no—
303C2×C4×D61C22×C411yescharacteristic
304C2×C4×D61C22×C411yescharacteristic
305C2×C4×D61C22×C411yescharacteristic
306C2×C4×D61C22×C411yescharacteristic
307C2×C4×D61C2×D411yescharacteristic
308C2×C4×D61C2×D411yescharacteristic
309C2×C4×D61C2×D411yescharacteristic
310C2×C4×D61C2×D411yescharacteristic
311C2×Dic122—42no—
312C2×Dic122C22⋊C411yescharacteristic
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×C61C22×C411yescharacteristic
322C4⋊C4×C61C22×C411yescharacteristic
323C22⋊C4×C61—21no—
324C22⋊C4×C61—21no—
325C22⋊C4×C61—21no—
326C22⋊C4×C61—21no—
327C22⋊Dic61—21no—
328C22⋊Dic61—21no—
329C22⋊Dic61—21no—
330C22⋊Dic61—21no—
331C22⋊Dic61—21no—
332C22⋊Dic61—21no—
333C22⋊Dic61—21no—
334C22⋊Dic61—42no—
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—42no—
344#11758198—42no—
345#11758198—81no—
346C4⋊Dic61—21no—
347C4⋊Dic61—21no—
348C4⋊Dic61C22×C411yescharacteristic
349C4⋊Dic61C22×C411yescharacteristic
350#11758196—21no—
351#11758196—21no—
352#11758196—21no—
353#11758196—21no—
354#11758196—42no—
355C4×Dic61—21no—
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—21no—
371C23×C61—41no—
372C23×C61—42no—
373C23×C61—81no—
374C23×C61—81no—
375C23×C61C2×C22⋊C411yescharacteristic
376C23×C61C2×C22⋊C411yescharacteristic
377C23×C61C22×D411yescharacteristic
378C22×D61—21no—
379C22×D61—21no—
380C22×D61—21no—
381C22×D61—21no—
382C22×D61—22no—
383C22×D61—21no—
384C22×D61—41no—
385C22×D61—41no—
386C22×D61—41no—
387C22×D61—42no—
388C22×D61—42no—
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
397D4×C61—41no—
398D4×C61—41no—
399D4×C61—42no—
400D4×C61—41no—
401D4×C61—41no—
402D4×C61—41no—
403D4×C61—41no—
404D4×C61—81no—
405D4×C61—81no—
406C2×C4×C61—22no—
407C2×C4×C61—22no—
408C2×C4×C61—22no—
409C2×C4×C61—21no—
410C2×C4×C61—21no—
411C2×C4×C61—41no—
412C2×C4×C61—41no—
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×C61—41no—
420C2×C4×C61—81no—
421C2×C4×C61—84no—
422C2×C4×C61C2×C22⋊C411yescharacteristic
423C2×C4×C61C2×C22⋊C411yescharacteristic
424C2×C4×C61C23×C411yescharacteristic
425C2×C4×C61C22×D411yescharacteristic
426C22⋊D61—22no—
427C22⋊D61—22no—
428C22⋊D61—22no—
429C22⋊D61—22no—
430C22⋊D61—22no—
431C22⋊D61—41no—
432C22⋊D61—41no—
433C22⋊D61—42no—
434C22⋊D61—42no—
435C22⋊D61—41no—
436C22⋊D61—41no—
437C22⋊D61—42no—
438C22⋊D61—42no—
439C22⋊D61—42no—
440C22⋊D61—81no—
441C22⋊D61—81no—
442C22⋊D61—81no—
443C22⋊D61—81no—
444C22⋊D61—81no—
445C22⋊D61#9914yes—
446C2×Dic61—22no—
447C2×Dic61—21no—
448C2×Dic61—21no—
449C2×Dic61—21no—
450C2×Dic61—41no—
451C2×Dic61—42no—
452C2×Dic61—42no—
453C2×Dic61—41no—
454C2×Dic61—41no—
455C2×Dic61—41no—
456C2×Dic61—41no—
457C2×Dic61—41no—
458C2×Dic61—41no—
459C2×Dic61C2×C22⋊C411yescharacteristic
460C2×Dic61C2×C22⋊C411yescharacteristic
461C2×Dic61C2×C22⋊C411yescharacteristic
462C2×Dic61C2×C22⋊C411yescharacteristic
463D244—22no—
464D244—22no—
465D244—41no—
466D244—41no—
467D244—41no—
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—81no—
480C4×D61—81no—
481C4×D61—84no—
482Dic122—22no—
483Dic122—22no—
484Dic122—41no—
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×C61—41no—
505C22×C61—41no—
506C22×C61—41no—
507C22×C61—162no—
508C22×C61C2×#9912yes—
509C22×C61C22×C22⋊C411yescharacteristic
510C22×C61#57611yescharacteristic
511C22×C61#57711yescharacteristic
512C2×D61—21no—
513C2×D61—21no—
514C2×D61—21no—
515C2×D61—21no—
516C2×D61—21no—
517C2×D61—21no—
518C2×D61—21no—
519C2×D61—21no—
520C2×D61—21no—
521C2×D61—21no—
522C2×D61—21no—
523C2×D61—42no—
524C2×D61—42no—
525C2×D61—41no—
526C2×D61—41no—
527C2×D61—41no—
528C2×D61—81no—
529C2×D61—81no—
530C2×D61—162no—
531C2×D61—162no—
532C2×D61C2×#9912yes—
533C4×C61—21no—
534C4×C61—21no—
535C4×C61—21no—
536C4×C61—21no—
537C4×C61—42no—
538C4×C61—41no—
539C4×C61—41no—
540C4×C61—81no—
541Dic61—21no—
542Dic61—21no—
543Dic61—21no—
544Dic61—41no—
545Dic61—41no—
546Dic61—41no—
547Dic61—81no—
548Dic61—81no—
549Dic61C2×#9912yes—
550#3488—611no—
551#2880—611no—
552#2339—611no—
553#1519—611no—
554#1516—611no—
555#1516—611no—
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×#327D6111yescharacteristic, complemented
565C2×C61—21no—
566C2×C61—21no—
567C2×C61—22no—
568C2×C61—41no—
569C2×C61—81no—
570C2×C61—81no—
571C2×C61C22×#9911yescharacteristic
572C2×C61#289711yescharacteristic
573C2×C61#290111yescharacteristic
574D61—22no—
575D61—41no—
576D61—41no—
577D61—41no—
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#525—611no—
599C2×#121—611no—
600C2×#121—611no—
601C2×#121C2×D6111yescharacteristic
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#381—611no—
618#380—611no—
619C4×C22⋊C4—611no—
620C2×#95—611no—
621C2×#95C2×D6111yescharacteristic, complemented
622#328—611no—
623#328—611no—
624#328—611no—
625#328—611no—
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#327C2×D6111yescharacteristic, complemented
635#327C2×D6111yescharacteristic, complemented
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—611no—
651C2×#41—1221no—
652C2×#41—2444no—
653C22×Q8—611no—
654C22×D4—21no—
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×D4C4×D6111yescharacteristic, complemented
666C23×C4—21no—
667C23×C4—611no—
668C23×C4—611no—
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—1221no—
685#123—1221no—
686#123—1221no—
687C22⋊Q8—611no—
688C22⋊Q8—611no—
689C22⋊Q8—611no—
690C22⋊Q8—611no—
691C22⋊Q8—1221no—
692C22⋊Q8—1221no—
693C22⋊Q8—1221no—
694#121—21no—
695#121—21no—
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#121C4×D6111yescharacteristic, complemented
718#121C4×D6111yescharacteristic, complemented
719#121C22×D6111yescharacteristic
720#121C22×D6111yescharacteristic
721#120—1221no—
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—1221no—
732C4×D4—1221no—
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#117—611no—
744C2×C4⋊C4—611no—
745C2×C4⋊C4—611no—
746C2×C4⋊C4—1221no—
747C2×C4⋊C4C4×D6111yescharacteristic, complemented
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—21no—
775C24—611no—
776C24—611no—
777C24—1221no—
778C24—1221no—
779C24D4×D6111yescharacteristic
780#41—1224no—
781#41—1224no—
782#41—2442no—
783#41—2442no—
784#41—2442no—
785#41—2442no—
786#41—2442no—
787#41—2442no—
788#41—2442no—
789#41—2442no—
790#41—2442no—
791#41—2444no—
792C2×Q8—611no—
793C2×Q8—611no—
794C2×Q8—611no—
795C2×Q8—611no—
796C2×Q8—611no—
797C2×Q8—2442no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—42no—
804C2×D4—81no—
805C2×D4—81no—
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—611no—
816C2×D4—611no—
817C2×D4—611no—
818C2×D4—611no—
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—1221no—
832C2×D4—1221no—
833C2×D4—4881no—
834C2×D4—4881no—
835C2×D4—4881no—
836C2×D4—4881no—
837C2×D4—2442no—
838C2×D4—2442no—
839C2×D4—2442no—
840C2×D4—2444no—
841C2×D4—2444no—
842C2×D4—2442no—
843C2×D4—2444no—
844C2×D4C2×C4×D6111yescharacteristic
845C2×D4C2×C4×D6111yescharacteristic
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—81no—
853C22×C4—611no—
854C22×C4—611no—
855C22×C4—611no—
856C22×C4—611no—
857C22×C4—611no—
858C22×C4—611no—
859C22×C4—611no—
860C22×C4—611no—
861C22×C4—611no—
862C22×C4—611no—
863C22×C4—1221no—
864C22×C4—1221no—
865C22×C4—1221no—
866C22×C4—1221no—
867C22×C4—1221no—
868C22×C4—1221no—
869C22×C4—1221no—
870C22×C4—4881no—
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—611no—
893C4⋊C4—611no—
894C4⋊C4—1221no—
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—1221no—
908C22⋊C4—1221no—
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—4881no—
923C22⋊C4—2442no—
924C22⋊C4—2442no—
925C22⋊C4—2442no—
926C42—1221no—
927C42—1221no—
928C42—1221no—
929C42—2442no—
930C23—22no—
931C23—21no—
932C23—21no—
933C23—21no—
934C23—21no—
935C23—41no—
936C23—42no—
937C23—81no—
938C23—81no—
939C23—611no—
940C23—611no—
941C23—611no—
942C23—611no—
943C23—1222no—
944C23—1221no—
945C23—1221no—
946C23—1221no—
947C23—1221no—
948C23—1221no—
949C23—4881no—
950C23—4881no—
951C23—4881no—
952C23—4881no—
953C23—2441no—
954C23—2441no—
955C23—2441no—
956C23—2442no—
957C23—2442no—
958C23C22⋊C4×D6111yescharacteristic
959C23C22⋊C4×D6111yescharacteristic
960C23C2×D4×D6111yescharacteristic
961Q8—1222no—
962Q8—1222no—
963Q8—2441no—
964Q8—2441no—
965Q8—2441no—
966D4—41no—
967D4—41no—
968D4—42no—
969D4—41no—
970D4—41no—
971D4—41no—
972D4—41no—
973D4—81no—
974D4—81no—
975D4—614no—
976D4—1222no—
977D4—1222no—
978D4—1222no—
979D4—1222no—
980D4—1222no—
981D4—1222no—
982D4—1222no—
983D4—4881no—
984D4—4881no—
985D4—4881no—
986D4—4881no—
987D4—4881no—
988D4—4881no—
989D4—4881no—
990D4—2441no—
991D4—2441no—
992D4—2441no—
993D4—2442no—
994D4—2441no—
995D4—2441no—
996D4—2442no—
997D4—2442no—
998D4—2442no—
999D4—2442no—
1000D4—2441no—
1001D4—2441no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—81no—
1017C2×C4—84no—
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—1221no—
1028C2×C4—1221no—
1029C2×C4—1221no—
1030C2×C4—4884no—
1031C2×C4—4881no—
1032C2×C4—4881no—
1033C2×C4—2441no—
1034C2×C4—2441no—
1035C2×C4—2441no—
1036C2×C4—2441no—
1037C2×C4—2442no—
1038C2×C4—2442no—
1039C2×C4—2441no—
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—41no—
1068C22—41no—
1069C22—41no—
1070C22—162no—
1071C22—612no—
1072C22—1221no—
1073C22—1221no—
1074C22—1221no—
1075C22—1221no—
1076C22—1221no—
1077C22—1221no—
1078C22—1221no—
1079C22—1221no—
1080C22—1221no—
1081C22—1221no—
1082C22—1221no—
1083C22—9762no—
1084C22—9762no—
1085C22—4881no—
1086C22—4881no—
1087C22—2442no—
1088C22—2442no—
1089C22—2441no—
1090C22—2441no—
1091C22—2441no—
1092C22#99×D6112yes—
1093C22C2×C22⋊C4×D6111yescharacteristic
1094C22#1684056311yescharacteristic
1095C22#1684056811yescharacteristic
1096C4—21no—
1097C4—21no—
1098C4—21no—
1099C4—21no—
1100C4—42no—
1101C4—41no—
1102C4—41no—
1103C4—81no—
1104C4—612no—
1105C4—1221no—
1106C4—1221no—
1107C4—1221no—
1108C4—4881no—
1109C4—4881no—
1110C4—2441no—
1111C4—2441no—
1112C4—2441no—
1113C2—21no—
1114C2—21no—
1115C2—22no—
1116C2—41no—
1117C2—81no—
1118C2—81no—
1119C2—1222no—
1120C2—4881no—
1121C2—2441no—
1122C2—2441no—
1123C2—2441no—
1124C2C2×#99×D6111yescharacteristic
1125C2#2145434011yescharacteristic
1126C2#2145436311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#327C2
socleC22×C61C22×C22⋊C4
prime radical#21459484C2
cosocleC22×C4×C61C24
hypercenterC2×#327D61
hypocenterC61#17603
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. #21454265C2semidirect
3. #21448646C2semidirect
4. #21444385C2semidirect
5. #21444376C2semidirect
6. #21444372C2semidirect
7. #21444359C2semidirect
8. #21444348C2semidirect
9. #21444346C2semidirect
10. #21444333C2semidirect
11. #21444321C2semidirect
12. #21444320C2semidirect
13. #21444307C2semidirect
14. #327×D61C2semidirect
15. C2×C61×#327C2semidirect
16. C2×#14519822C4semidirect
27. #16840343C4semidirect
28. #16840341C4semidirect
29. #16840341C4semidirect
30. #16840329C4semidirect
31. #16840328C4semidirect
32. #16840328C4semidirect
38. #16840243C4semidirect
43. #16839726C22semidirect
44. #16839724C22semidirect
45. #16839724C22semidirect
46. C22⋊C8×D61C22semidirect
47. C22⋊C8×D61C22semidirect
51. #16839625C22semidirect
52. #16839624C22semidirect
53. #16839621C22semidirect
54. #16839609C22semidirect
55. #95×D61C22semidirect
56. #16839500C22semidirect
57. #16839500C22semidirect
58. #16839498C22semidirect
59. #16839498C22semidirect
60. #16839497C22semidirect
61. #16839497C22semidirect
62. #16839496C22semidirect
63. #16839496C22semidirect
64. #16839496C22semidirect
65. #16839496C22semidirect
66. #16839495C22semidirect
67. #16839495C22semidirect
69. C2×C22⋊C8×C61C22semidirect
70. C2×#95×C61C22semidirect
71. C61×#327C22semidirect
72. C61×#327C22semidirect
73. C61×#327C22semidirect
74. C61×#327C22semidirect
81. C2×#11758222C2×C4semidirect
87. C2×#11758224C2×C4semidirect
88. C2×#11758224C2×C4semidirect
98. C2×D4×D61C2×C4semidirect
99. C2×D4×D61C2×C4semidirect
119. #14519757C2×C4semidirect
120. #14519757C2×C4semidirect
121. #14519756C2×C4semidirect
126. #14519752C2×C4semidirect
127. #14519752C2×C4semidirect
130. #14519751C2×C4semidirect
142. #14519748C2×C4semidirect
143. #14519748C2×C4semidirect
144. #14519748C2×C4semidirect
145. #14519748C2×C4semidirect
166. #14519736C2×C4semidirect
167. #14519735C2×C4semidirect
168. #14519735C2×C4semidirect
170. C4⋊C4×D61C2×C4semidirect
171. C4⋊C4×D61C2×C4semidirect
192. C22×D4×C61C2×C4semidirect
198. #121×C61C2×C4semidirect
199. #121×C61C2×C4semidirect
202. C2×C4⋊C4×C61C2×C4semidirect
564. C2×#327D61semidirect
612. C2×C22⋊C8C2×D61semidirect
621. C2×#95C2×D61semidirect
634. #327C2×D61semidirect
635. #327C2×D61semidirect
636. #327C2×D61semidirect
637. #327C2×D61semidirect
638. C61#17603semidirect
665. C22×D4C4×D61semidirect
717. #121C4×D61semidirect
718. #121C4×D61semidirect
747. C2×C4⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214594842
#214542652
#214486462
#214443852
#214443762
#214443722
#214443592
#214443482
#214443462
#214443332
#214443212
#214443202
#214443072
#327×D612
C2×C61×#3272
#1760361