Finite Group Databasebeta

← #29647663

Subgroups — #29647663

Order 15616.

1298 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459491C211yesmaximal, characteristic
2#21454269C211yesmaximal, characteristic, complemented
3#21448646C211yesmaximal, characteristic, complemented
4#21444389C211yesmaximal, characteristic, complemented
5#21444375C211yesmaximal, characteristic, complemented
6#21444372C211yesmaximal, characteristic, complemented
7#21444359C211yesmaximal, characteristic, complemented
8#21444353C211yesmaximal, characteristic, complemented
9#21444350C211yesmaximal, characteristic, complemented
10#21444337C211yesmaximal, characteristic, complemented
11#21444320C211yesmaximal, characteristic, complemented
12#21444307C211yesmaximal, characteristic, complemented
13C2×#16839498C211yesmaximal, characteristic, complemented
14#328×D61C211yesmaximal, characteristic, complemented
15C61×#1504C211yesmaximal, characteristic, complemented
16C2×#14519824C411yescharacteristic, complemented
17C22×#11758222C2211yescharacteristic
18C2×#14519785—21no—
19D4×Dic122—21no—
20#16840421—21no—
21#16840417—21no—
22#16840410—21no—
23#16840410—21no—
24#16840408—21no—
25#16840399—21no—
26#16840399—21no—
27#16840341C411yescharacteristic, complemented
28#16840341C411yescharacteristic, complemented
29#16840340C411yescharacteristic, complemented
30#16840338C411yescharacteristic, complemented
31#16840335C411yescharacteristic, complemented
32#16840335C411yescharacteristic, complemented
33#16840272C2211yescharacteristic
34#16840272C2211yescharacteristic
35C2×#14519756C2211yescharacteristic
36C22⋊Q8×D61C2211yescharacteristic
37C22⋊Q8×D61C2211yescharacteristic
38#16840242C411yescharacteristic, complemented
39C2×C4×C22⋊D61—21no—
40#16839730—21no—
41#16839727—21no—
42#16839727—21no—
43#16839724C2211yescharacteristic
44#16839724C2211yescharacteristic
45C2×C22⋊#92418C2211yescharacteristic
46C22⋊C8×D61C2211yescharacteristic
47C22⋊C8×D61C2211yescharacteristic
48#16839666—21no—
49#16839641—21no—
50#16839640—21no—
51#16839625C2211yescharacteristic
52#16839624C2211yescharacteristic
53#16839621C2211yescharacteristic
54#16839609C2211yescharacteristic
55#95×D61C2211yescharacteristic
56#16839500C2211yescharacteristic
57#16839500C2211yescharacteristic
58#16839500C2211yescharacteristic
59#16839500C2211yescharacteristic
60#16839499C2211yescharacteristic
61#16839499C2211yescharacteristic
62#16839498C2211yescharacteristic
63#16839498C2211yescharacteristic
64#16839498C2211yescharacteristic
65#16839498C2211yescharacteristic
66#16839496C2211yescharacteristic
67#16839496C2211yescharacteristic
68C61×#525C2211yescharacteristic
69C61×#407C2211yescharacteristic
70C2×#95×C61C2211yescharacteristic
71C61×#328C2211yescharacteristic
72C61×#328C2211yescharacteristic
73C61×#327C2211yescharacteristic
74C61×#327C2211yescharacteristic
75#14519824—44no—
76C2×#11758222—21no—
77C2×#11758222—44no—
78C2×#11758222C2×C411yescharacteristic
79C2×#11758222C2×C411yescharacteristic
80C2×#11758222C2×C411yescharacteristic
81C2×#11758222C2×C411yescharacteristic
82C2×#11758222D411yescharacteristic
83C2×#11758222D411yescharacteristic
84C2×#11758222D411yescharacteristic
85C2×#11758222D411yescharacteristic
86C2×#11758224—21no—
87C2×#11758224—21no—
88C2×#11758224C2×C411yescharacteristic, complemented
89C2×#11758224C2×C411yescharacteristic, complemented
90C22×Dic122—21no—
91C22×Dic122C2×C411yescharacteristic, complemented
92C22×Dic122D411yescharacteristic
93C2×Q8×D61C2×C411yescharacteristic, complemented
94C2×Q8×D61C2×C411yescharacteristic, complemented
95C22×D244D411yescharacteristic
96C22×C22⋊D61D411yescharacteristic
97C22×C22⋊D61D411yescharacteristic
98C22×C4×D61—21no—
99C22×C4×D61C2311yescharacteristic
100C22×C4×D61C2311yescharacteristic
101#14519785—44no—
102C2×#11758189—21no—
103C2×#11758189—21no—
104C22×#92418—21no—
105C2×C8×D61—21no—
106C2×C8×D61—21no—
107#14519777—21no—
108#14519776—21no—
109#14519776—21no—
110#14519765—21no—
111#14519763—21no—
112#14519763—21no—
113#14519762—21no—
114#14519762—21no—
115#14519761—21no—
116#14519761—21no—
117#14519759—21no—
118#14519759—21no—
119#14519759—21no—
120#14519759—21no—
121#14519757C2×C411yescharacteristic, complemented
122#14519757C2×C411yescharacteristic, complemented
123#14519757C2×C411yescharacteristic, complemented
124#14519757C2×C411yescharacteristic, complemented
125#14519756—21no—
126#14519756—21no—
127#14519756—21no—
128#14519756C2×C411yescharacteristic, complemented
129#14519756C2×C411yescharacteristic, complemented
130#14519756C2311yescharacteristic
131#14519756C2311yescharacteristic
132#14519755—21no—
133#14519755—21no—
134#14519754—21no—
135#14519754—21no—
136#14519754—21no—
137#14519754—21no—
138#14519753C2×C411yescharacteristic, complemented
139#14519753C2×C411yescharacteristic, complemented
140#14519751—21no—
141#14519750—21no—
142#14519750—21no—
143#14519749—21no—
144#14519749—21no—
145#14519749—21no—
146#14519749—21no—
147#14519748—21no—
148#14519748—21no—
149#14519748C2×C411yescharacteristic, complemented
150#14519748C2×C411yescharacteristic, complemented
151#14519745—21no—
152#14519745—21no—
153C4×Dic122—21no—
154C4×D244—21no—
155D4×Dic61—21no—
156D4×Dic61—21no—
157C4×C22⋊D61—44no—
158#14519737—21no—
159#14519737—21no—
160#14519737—21no—
161#14519737—21no—
162#14519735C2×C411yescharacteristic, complemented
163#14519735C2×C411yescharacteristic, complemented
164C2×C4⋊Dic61C2×C411yescharacteristic, complemented
165C2×#11758196—21no—
166C2×#11758196—21no—
167C4⋊C4×D61—21no—
168C4⋊C4×D61—21no—
169C4⋊C4×D61C2×C411yescharacteristic, complemented
170C4⋊C4×D61C2×C411yescharacteristic, complemented
171C2×C22⋊Dic61—21no—
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
191C2×#41×C61C2×C411yescharacteristic, complemented
192C23×C4×C61—21no—
193C23×C4×C61C2311yescharacteristic
194C2×M16×C61—21no—
195#123×C61—21no—
196C22⋊Q8×C61C2×C411yescharacteristic, complemented
197C22⋊Q8×C61C2311yescharacteristic
198#121×C61C2×C411yescharacteristic, complemented
199#121×C61C2311yescharacteristic
200#120×C61—21no—
201C4×D4×C61—21no—
202C4×D4×C61—21no—
203#117×C61C2×C411yescharacteristic, complemented
204C22⋊C8×C61—21no—
205C22⋊C8×C61C2311yescharacteristic
206C22⋊C8×C61C2311yescharacteristic
207#95×C61—21no—
208#95×C61C2311yescharacteristic
209#95×C61C2311yescharacteristic
210C24×C61C2×D411yescharacteristic
211C23×D61C2×D411yescharacteristic
212C23×D61C2×D411yescharacteristic
213#41×C61—42no—
214C2×Q8×C61C22×C411yescharacteristic
215C2×D4×C61—21no—
216C2×D4×C61—21no—
217C2×D4×C61—21no—
218C2×D4×C61C22×C411yescharacteristic
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—42no—
223C22×C4×C61—42no—
224C22×C4×C61—42no—
225C22×C4×C61—81no—
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—42no—
238C2×C22⋊D61C22⋊C411yescharacteristic
239C2×C22⋊D61C22⋊C411yescharacteristic
240C2×C22⋊D61C22⋊C411yescharacteristic
241C2×C22⋊D61C22⋊C411yescharacteristic
242C2×C22⋊D61C22⋊C411yescharacteristic
243C2×C22⋊D61C22⋊C411yescharacteristic
244C2×C22⋊D61C22⋊C411yescharacteristic
245C2×C22⋊D61C22⋊C411yescharacteristic
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61C2×D411yescharacteristic
253C22×Dic61C2×D411yescharacteristic
254Q8×D61—42no—
255Q8×D61—42no—
256#11758224—42no—
257#11758224—42no—
258#11758224—44no—
259#11758224—44no—
260#11758222—24no—
261#11758222—24no—
262#11758222—42no—
263#11758222—42no—
264#11758222—42no—
265#11758222—42no—
266#11758222—44no—
267#11758222—42no—
268#11758222—42no—
269C2×D244—42no—
270C2×D244C22⋊C411yescharacteristic
271C2×D244C22⋊C411yescharacteristic
272C2×D244C22⋊C411yescharacteristic
273C2×D244C22⋊C411yescharacteristic
274C2×C4×D61—21no—
275C2×C4×D61—21no—
276C2×C4×D61—21no—
277C2×C4×D61—21no—
278C2×C4×D61—42no—
279C2×C4×D61—42no—
280C2×C4×D61—42no—
281C2×C4×D61—42no—
282C2×C4×D61—81no—
283C2×C4×D61C22×C411yescharacteristic
284C2×C4×D61C22×C411yescharacteristic
285C2×C4×D61C22×C411yescharacteristic
286C2×C4×D61C22×C411yescharacteristic
287C2×C4×D61C2×D411yescharacteristic
288C2×C4×D61C2×D411yescharacteristic
289C2×C4×D61C2×D411yescharacteristic
290C2×C4×D61C2×D411yescharacteristic
291C2×Dic122—21no—
292C2×Dic122—21no—
293C2×Dic122—21no—
294C2×Dic122—42no—
295C2×Dic122—44no—
296C2×Dic122—42no—
297C2×Dic122C22⋊C411yescharacteristic
298C2×Dic122C22⋊C411yescharacteristic
299C2×Dic122C22⋊C411yescharacteristic
300C2×Dic122C22⋊C411yescharacteristic
301C2×Dic122C22×C411yescharacteristic
302C2×Dic122C22×C411yescharacteristic
303M16×C61—42no—
304C2×C8×C61—21no—
305C2×C8×C61—21no—
306C4⋊C4×C61—21no—
307C4⋊C4×C61—21no—
308C4⋊C4×C61C22×C411yescharacteristic
309C4⋊C4×C61C22×C411yescharacteristic
310C22⋊C4×C61—21no—
311C22⋊C4×C61—21no—
312C22⋊C4×C61—21no—
313C22⋊C4×C61—21no—
314C22⋊C4×C61—21no—
315C42×C61—21no—
316C22⋊Dic61—21no—
317C22⋊Dic61—21no—
318C22⋊Dic61—21no—
319C22⋊Dic61—21no—
320C22⋊Dic61—21no—
321C22⋊Dic61—21no—
322C22⋊Dic61—42no—
323#11758198—21no—
324#11758198—21no—
325#11758198—21no—
326#11758198—21no—
327#11758198—21no—
328#11758198—21no—
329#11758198—21no—
330#11758198—21no—
331#11758198—42no—
332#11758198—42no—
333#11758198—81no—
334C4⋊Dic61—21no—
335C4⋊Dic61—21no—
336C4⋊Dic61—21no—
337C4⋊Dic61—21no—
338C4⋊Dic61—21no—
339C4⋊Dic61C22×C411yescharacteristic
340C4⋊Dic61C22×C411yescharacteristic
341#11758196—21no—
342#11758196—21no—
343#11758196—21no—
344#11758196—21no—
345#11758196—21no—
346#11758196—21no—
347#11758196—21no—
348#11758196—21no—
349#11758196—42no—
350C4×Dic61—21no—
351C4×Dic61—21no—
352C4×Dic61—42no—
353C2×#92418—21no—
354C2×#92418—21no—
355C2×#92418—42no—
356#11758189—42no—
357#11758189—42no—
358C8×D61—42no—
359C8×D61—42no—
360C23×C61—21no—
361C23×C61—21no—
362C23×C61—22no—
363C23×C61—21no—
364C23×C61—41no—
365C23×C61C2×C22⋊C411yescharacteristic
366C23×C61C2×C22⋊C411yescharacteristic
367C23×C61C22×D411yescharacteristic
368C22×D61—21no—
369C22×D61—21no—
370C22×D61—21no—
371C22×D61—21no—
372C22×D61—22no—
373C22×D61—41no—
374C22×D61—41no—
375C22×D61—41no—
376C22×D61C2×C22⋊C411yescharacteristic
377C22×D61C2×C22⋊C411yescharacteristic
378C22×D61C2×C22⋊C411yescharacteristic
379C22×D61C2×C22⋊C411yescharacteristic
380Q8×C61—41no—
381D4×C61—41no—
382D4×C61—41no—
383D4×C61—41no—
384D4×C61—42no—
385D4×C61—81no—
386C2×C4×C61—22no—
387C2×C4×C61—22no—
388C2×C4×C61—22no—
389C2×C4×C61—21no—
390C2×C4×C61—21no—
391C2×C4×C61—21no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
394C2×C4×C61—41no—
395C2×C4×C61—41no—
396C2×C4×C61—42no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61—41no—
400C2×C4×C61—41no—
401C2×C4×C61—41no—
402C2×C4×C61—84no—
403C2×C4×C61C2×C22⋊C411yescharacteristic
404C2×C4×C61C2×C22⋊C411yescharacteristic
405C2×C4×C61C23×C411yescharacteristic
406C2×C4×C61C22×D411yescharacteristic
407C22⋊D61—22no—
408C22⋊D61—22no—
409C22⋊D61—22no—
410C22⋊D61—22no—
411C22⋊D61—22no—
412C22⋊D61—41no—
413C22⋊D61—41no—
414C22⋊D61—42no—
415C22⋊D61—42no—
416C22⋊D61—81no—
417C22⋊D61—81no—
418C22⋊D61#9914yes—
419C2×Dic61—22no—
420C2×Dic61—21no—
421C2×Dic61—21no—
422C2×Dic61—21no—
423C2×Dic61—21no—
424C2×Dic61—41no—
425C2×Dic61—42no—
426C2×Dic61—42no—
427C2×Dic61—42no—
428C2×Dic61—41no—
429C2×Dic61—41no—
430C2×Dic61—41no—
431C2×Dic61—41no—
432C2×Dic61—41no—
433C2×Dic61—41no—
434C2×Dic61—81no—
435C2×Dic61C2×C22⋊C411yescharacteristic
436C2×Dic61C2×C22⋊C411yescharacteristic
437C2×Dic61C2×C22⋊C411yescharacteristic
438C2×Dic61C2×C22⋊C411yescharacteristic
439D244—22no—
440D244—22no—
441D244—41no—
442D244—41no—
443C4×D61—22no—
444C4×D61—22no—
445C4×D61—22no—
446C4×D61—22no—
447C4×D61—41no—
448C4×D61—41no—
449C4×D61—41no—
450C4×D61—41no—
451C4×D61—42no—
452C4×D61—42no—
453C4×D61—81no—
454C4×D61—81no—
455C4×D61—84no—
456Dic122—22no—
457Dic122—22no—
458Dic122—41no—
459Dic122—41no—
460Dic122—42no—
461Dic122—42no—
462Dic122—42no—
463Dic122—41no—
464Dic122—41no—
465C8×C61—41no—
466C8×C61—41no—
467#92418—41no—
468#92418—41no—
469#17608—611nomaximal, Sylow
470C22×C61—21no—
471C22×C61—21no—
472C22×C61—21no—
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—21no—
476C22×C61—21no—
477C22×C61—42no—
478C22×C61—42no—
479C22×C61—41no—
480C22×C61—41no—
481C22×C61—41no—
482C22×C61C2×#9912yes—
483C22×C61C22×C22⋊C411yescharacteristic
484C22×C61#57711yescharacteristic
485C22×C61#57811yescharacteristic
486C2×D61—21no—
487C2×D61—21no—
488C2×D61—21no—
489C2×D61—21no—
490C2×D61—21no—
491C2×D61—21no—
492C2×D61—21no—
493C2×D61—21no—
494C2×D61—21no—
495C2×D61—21no—
496C2×D61—21no—
497C2×D61—42no—
498C2×D61—42no—
499C2×D61—81no—
500C2×D61—81no—
501C2×D61C2×#9912yes—
502C4×C61—21no—
503C4×C61—21no—
504C4×C61—21no—
505C4×C61—21no—
506C4×C61—42no—
507C4×C61—41no—
508C4×C61—41no—
509C4×C61—41no—
510C4×C61—81no—
511Dic61—21no—
512Dic61—21no—
513Dic61—21no—
514Dic61—41no—
515Dic61—41no—
516Dic61—41no—
517Dic61—41no—
518Dic61—81no—
519Dic61—81no—
520Dic61C2×#9912yes—
521#3489—611no—
522#2880—611no—
523#2339—611no—
524#1520—611no—
525#1516—611no—
526#1516—611no—
527#1513—611no—
528#1511—611no—
529#1511—611no—
530#1508—611no—
531#1504—611no—
532#1504D6111yescharacteristic, complemented
533#1501—611no—
534C2×#328—611no—
535C2×#328—611no—
536C2×C61—21no—
537C2×C61—21no—
538C2×C61—22no—
539C2×C61—41no—
540C2×C61—81no—
541C2×C61C22×#9911yescharacteristic
542C2×C61#289811yescharacteristic
543C2×C61#290111yescharacteristic
544D61—22no—
545D61—41no—
546D61—41no—
547D61—41no—
548C2×2−1+4—611no—
549C22×#41—611no—
550C2×#131—1221no—
551D4×Q8—1221no—
552#548—1221no—
553#547—1221no—
554#547—1221no—
555#547—1221no—
556#546—1221no—
557#546—1221no—
558#546—1221no—
559#537—611no—
560#537—611no—
561#537—611no—
562#536—611no—
563#536—611no—
564#536—611no—
565#525—611no—
566#525—611no—
567#525C2×D6111yescharacteristic
568C2×C22⋊Q8—611no—
569C2×C22⋊Q8—611no—
570C2×C22⋊Q8—611no—
571#520—611no—
572C2×C4×D4—1221no—
573#408—1221no—
574#408—1221no—
575#408—1221no—
576#407—611no—
577#407—611no—
578#407C2×D6111yescharacteristic
579C2×C22⋊C8—611no—
580C2×C22⋊C8—611no—
581C2×C22⋊C8—611no—
582#391—1221no—
583#386—1221no—
584#386—1221no—
585#381—611no—
586#381—611no—
587#380—611no—
588C4×C22⋊C4—611no—
589C2×#95—611no—
590C2×#95C2×D6111yescharacteristic
591#328—611no—
592#328—611no—
593#328—611no—
594#328—611no—
595#328—611no—
596#328—611no—
597#328—611no—
598#328—611no—
599#328—611no—
600#328—611no—
601#328C2×D6111yescharacteristic
602#328C2×D6111yescharacteristic
603#327—611no—
604#327—611no—
605#327C2×D6111yescharacteristic
606#327C2×D6111yescharacteristic
607C61#1760811yescharacteristic, complemented, Sylow
6082−1+4—2444no—
609C2×#41—611no—
610C2×#41—611no—
611C2×#41—611no—
612C2×#41—611no—
613C2×#41—611no—
614C2×#41—611no—
615C2×#41—611no—
616C2×#41—611no—
617C2×#41—611no—
618C2×#41—611no—
619C2×#41—1221no—
620C2×#41—1221no—
621C2×#41—1221no—
622C2×#41—2444no—
623C2×#41C4×D6111yescharacteristic, complemented
624C22×Q8—611no—
625C22×Q8—611no—
626C22×Q8—611no—
627C22×Q8—611no—
628C22×Q8—1221no—
629C22×D4—611no—
630C22×D4—611no—
631C22×D4—611no—
632C23×C4—21no—
633C23×C4—611no—
634C23×C4—611no—
635C23×C4—1221no—
636C23×C4C22×D6111yescharacteristic
637#131—2444no—
638C2×M16—21no—
639C2×M16—1221no—
640C2×M16—1221no—
641C22×C8—1221no—
642C22×C8—1221no—
643C22×C8—1221no—
644C4⋊Q8—1221no—
645C4⋊Q8—1221no—
646C4⋊Q8—1221no—
647#124—1221no—
648#124—1221no—
649#124—1221no—
650#123—21no—
651#123—1221no—
652#123—1221no—
653#123—1221no—
654#123—1221no—
655#123—1221no—
656#123—1221no—
657#123—1221no—
658#123—1221no—
659C22⋊Q8—611no—
660C22⋊Q8—611no—
661C22⋊Q8—611no—
662C22⋊Q8—611no—
663C22⋊Q8—611no—
664C22⋊Q8—611no—
665C22⋊Q8—611no—
666C22⋊Q8—611no—
667C22⋊Q8—611no—
668C22⋊Q8—611no—
669C22⋊Q8—1221no—
670C22⋊Q8—1221no—
671C22⋊Q8—1221no—
672C22⋊Q8—1221no—
673C22⋊Q8—1221no—
674C22⋊Q8—1221no—
675C22⋊Q8—1221no—
676C22⋊Q8—1221no—
677C22⋊Q8—1221no—
678C22⋊Q8C4×D6111yescharacteristic, complemented
679C22⋊Q8C22×D6111yescharacteristic
680#121—611no—
681#121—611no—
682#121—1221no—
683#121—1221no—
684#121—1221no—
685#121—1221no—
686#121—1221no—
687#121—1221no—
688#121—1221no—
689#121—1221no—
690#121—1221no—
691#121C4×D6111yescharacteristic, complemented
692#121C22×D6111yescharacteristic
693#120—21no—
694#120—1221no—
695#120—1221no—
696C4×Q8—1221no—
697C4×D4—21no—
698C4×D4—21no—
699C4×D4—1221no—
700C4×D4—1221no—
701C4×D4—1221no—
702C4×D4—1221no—
703C4×D4—1221no—
704C4×D4—1221no—
705C4×D4—1221no—
706C4×D4—2444no—
707#117—611no—
708#117—611no—
709#117C4×D6111yescharacteristic, complemented
710C2×C4⋊C4—611no—
711C2×C4⋊C4—611no—
712C2×C4⋊C4—611no—
713C2×C4⋊C4—1221no—
714C2×C4⋊C4—1221no—
715C2×C4⋊C4—1221no—
716C2×C4⋊C4—1221no—
717C2×C22⋊C4—1221no—
718C2×C22⋊C4—1221no—
719C2×C22⋊C4—1221no—
720C2×C22⋊C4—1221no—
721C2×C22⋊C4—1221no—
722C2×C22⋊C4—1221no—
723C2×C22⋊C4—1221no—
724C2×C42—1221no—
725C22⋊C8—21no—
726C22⋊C8—611no—
727C22⋊C8—611no—
728C22⋊C8—1221no—
729C22⋊C8—1221no—
730C22⋊C8—1221no—
731C22⋊C8—1221no—
732C22⋊C8—1221no—
733C22⋊C8C22×D6111yescharacteristic
734C22⋊C8C22×D6111yescharacteristic
735#95—21no—
736#95—611no—
737#95—611no—
738#95—1221no—
739#95—1221no—
740#95—1221no—
741#95C22×D6111yescharacteristic
742#95C22×D6111yescharacteristic
743C24—611no—
744C24—611no—
745C24D4×D6111yescharacteristic
746#41—42no—
747#41—1224no—
748#41—1224no—
749#41—2442no—
750#41—2442no—
751#41—2442no—
752#41—2442no—
753#41—2442no—
754#41—2442no—
755#41—2444no—
756#41—2442no—
757#41—2442no—
758#41—2444no—
759#41—2444no—
760C2×Q8—611no—
761C2×Q8—611no—
762C2×Q8—611no—
763C2×Q8—611no—
764C2×Q8—611no—
765C2×Q8—611no—
766C2×Q8—1221no—
767C2×Q8—1221no—
768C2×Q8—1221no—
769C2×Q8—2442no—
770C2×Q8—2442no—
771C2×Q8—2444no—
772C2×Q8—2442no—
773C2×Q8—2442no—
774C2×Q8C2×C4×D6111yescharacteristic
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—611no—
779C2×D4—611no—
780C2×D4—611no—
781C2×D4—611no—
782C2×D4—611no—
783C2×D4—611no—
784C2×D4—611no—
785C2×D4—611no—
786C2×D4—611no—
787C2×D4—611no—
788C2×D4—611no—
789C2×D4—611no—
790C2×D4—1224no—
791C2×D4—1221no—
792C2×D4—1221no—
793C2×D4—1221no—
794C2×D4—1221no—
795C2×D4—2442no—
796C2×D4—2442no—
797C2×D4C2×C4×D6111yescharacteristic
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—42no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—81no—
805C22×C4—611no—
806C22×C4—611no—
807C22×C4—611no—
808C22×C4—611no—
809C22×C4—611no—
810C22×C4—611no—
811C22×C4—611no—
812C22×C4—611no—
813C22×C4—611no—
814C22×C4—611no—
815C22×C4—1221no—
816C22×C4—1221no—
817C22×C4—1221no—
818C22×C4—1221no—
819C22×C4—1221no—
820C22×C4—1221no—
821C22×C4—1221no—
822C22×C4—1221no—
823C22×C4—1221no—
824C22×C4—1221no—
825C22×C4—4881no—
826C22×C4—2442no—
827C22×C4—2442no—
828C22×C4—2442no—
829C22×C4—2442no—
830C22×C4C2×C4×D6111yescharacteristic
831C22×C4C2×C4×D6111yescharacteristic
832C22×C4D4×D6111yescharacteristic
833C22×C4D4×D6111yescharacteristic
834C22×C4D4×D6111yescharacteristic
835C22×C4C23×D6111yescharacteristic
836M16—42no—
837M16—2442no—
838M16—2442no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—1221no—
842C2×C8—1221no—
843C2×C8—2442no—
844C2×C8—2442no—
845C2×C8—2442no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—611no—
849C4⋊C4—611no—
850C4⋊C4—1221no—
851C4⋊C4—1221no—
852C4⋊C4—1221no—
853C4⋊C4—1221no—
854C4⋊C4—1221no—
855C4⋊C4—1221no—
856C4⋊C4—1221no—
857C4⋊C4—1221no—
858C4⋊C4—1221no—
859C4⋊C4—1221no—
860C4⋊C4—1221no—
861C4⋊C4—1221no—
862C4⋊C4—1221no—
863C4⋊C4—2442no—
864C4⋊C4C2×C4×D6111yescharacteristic
865C4⋊C4C2×C4×D6111yescharacteristic
866C22⋊C4—21no—
867C22⋊C4—21no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—21no—
871C22⋊C4—1221no—
872C22⋊C4—1221no—
873C22⋊C4—1221no—
874C22⋊C4—1221no—
875C22⋊C4—1221no—
876C22⋊C4—1221no—
877C22⋊C4—1221no—
878C22⋊C4—1221no—
879C22⋊C4—1221no—
880C22⋊C4—1221no—
881C22⋊C4—1221no—
882C22⋊C4—1221no—
883C22⋊C4—1221no—
884C22⋊C4—1221no—
885C22⋊C4—4881no—
886C22⋊C4—2442no—
887C22⋊C4—2442no—
888C22⋊C4—2442no—
889C42—21no—
890C42—1221no—
891C42—1221no—
892C42—2442no—
893C23—22no—
894C23—21no—
895C23—21no—
896C23—21no—
897C23—41no—
898C23—611no—
899C23—611no—
900C23—611no—
901C23—611no—
902C23—1222no—
903C23—1221no—
904C23—1221no—
905C23—1221no—
906C23—1221no—
907C23—2441no—
908C23—2441no—
909C23—2441no—
910C23C22⋊C4×D6111yescharacteristic
911C23C22⋊C4×D6111yescharacteristic
912C23C2×D4×D6111yescharacteristic
913Q8—41no—
914Q8—1222no—
915Q8—1222no—
916Q8—2441no—
917Q8—2441no—
918Q8—2441no—
919Q8—2441no—
920Q8—2442no—
921Q8—2442no—
922Q8—2442no—
923D4—41no—
924D4—42no—
925D4—41no—
926D4—41no—
927D4—81no—
928D4—614no—
929D4—1222no—
930D4—1222no—
931D4—1222no—
932D4—1222no—
933D4—1222no—
934D4—1222no—
935D4—1222no—
936D4—4881no—
937D4—4881no—
938D4—2441no—
939D4—2441no—
940D4—2441no—
941D4—2441no—
942D4—2442no—
943D4—2442no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—42no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—84no—
961C2×C4—611no—
962C2×C4—611no—
963C2×C4—611no—
964C2×C4—611no—
965C2×C4—1222no—
966C2×C4—1222no—
967C2×C4—1222no—
968C2×C4—1222no—
969C2×C4—1222no—
970C2×C4—1221no—
971C2×C4—1221no—
972C2×C4—1221no—
973C2×C4—1221no—
974C2×C4—4884no—
975C2×C4—4881no—
976C2×C4—4881no—
977C2×C4—4881no—
978C2×C4—2441no—
979C2×C4—2441no—
980C2×C4—2441no—
981C2×C4—2441no—
982C2×C4—2442no—
983C2×C4—2442no—
984C2×C4—2442no—
985C2×C4—2441no—
986C2×C4—2442no—
987C2×C4—2441no—
988C2×C4—2441no—
989C2×C4—2441no—
990C2×C4—2441no—
991C2×C4—2441no—
992C2×C4—2441no—
993C2×C4—2442no—
994C2×C4C22⋊C4×D6111yescharacteristic
995C2×C4C22⋊C4×D6111yescharacteristic
996C2×C4C22×C4×D6111yescharacteristic
997C2×C4C2×D4×D6111yescharacteristic
998C8—41no—
999C8—41no—
1000C8—2441no—
1001C8—2441no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—42no—
1010C22—42no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—612no—
1015C22—1221no—
1016C22—1221no—
1017C22—1221no—
1018C22—1221no—
1019C22—1221no—
1020C22—1221no—
1021C22—1221no—
1022C22—1221no—
1023C22—1221no—
1024C22—1221no—
1025C22—1221no—
1026C22—4881no—
1027C22—4881no—
1028C22—2442no—
1029C22—2442no—
1030C22#99×D6112yes—
1031C22C2×C22⋊C4×D6111yescharacteristic
1032C22#1684057211yescharacteristic
1033C22#1684057811yescharacteristic
1034C4—21no—
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—42no—
1039C4—41no—
1040C4—41no—
1041C4—41no—
1042C4—81no—
1043C4—612no—
1044C4—1221no—
1045C4—1221no—
1046C4—1221no—
1047C4—4881no—
1048C4—4881no—
1049C4—2441no—
1050C4—2441no—
1051C4—2441no—
1052C4—2441no—
1053C2—21no—
1054C2—21no—
1055C2—22no—
1056C2—41no—
1057C2—81no—
1058C2—1222no—
1059C2—2441no—
1060C2—2441no—
1061C2—2441no—
1062C2C2×#99×D6111yescharacteristic
1063C2#2145435011yescharacteristic
1064C2#2145436311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1504C2
socleC22×C61C22×C22⋊C4
prime radical#21459491C2
cosocleC22×C4×C61C24
hypercenter#1504D61
hypocenterC61#17608
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. #21454269C2semidirect
3. #21448646C2semidirect
4. #21444389C2semidirect
5. #21444375C2semidirect
6. #21444372C2semidirect
7. #21444359C2semidirect
8. #21444353C2semidirect
9. #21444350C2semidirect
10. #21444337C2semidirect
11. #21444320C2semidirect
12. #21444307C2semidirect
13. C2×#16839498C2semidirect
14. #328×D61C2semidirect
15. C61×#1504C2semidirect
16. C2×#14519824C4semidirect
27. #16840341C4semidirect
28. #16840341C4semidirect
29. #16840340C4semidirect
30. #16840338C4semidirect
31. #16840335C4semidirect
32. #16840335C4semidirect
38. #16840242C4semidirect
88. C2×#11758224C2×C4semidirect
89. C2×#11758224C2×C4semidirect
91. C22×Dic122C2×C4semidirect
93. C2×Q8×D61C2×C4semidirect
94. C2×Q8×D61C2×C4semidirect
121. #14519757C2×C4semidirect
122. #14519757C2×C4semidirect
123. #14519757C2×C4semidirect
124. #14519757C2×C4semidirect
128. #14519756C2×C4semidirect
129. #14519756C2×C4semidirect
138. #14519753C2×C4semidirect
139. #14519753C2×C4semidirect
149. #14519748C2×C4semidirect
150. #14519748C2×C4semidirect
162. #14519735C2×C4semidirect
163. #14519735C2×C4semidirect
164. C2×C4⋊Dic61C2×C4semidirect
169. C4⋊C4×D61C2×C4semidirect
170. C4⋊C4×D61C2×C4semidirect
191. C2×#41×C61C2×C4semidirect
196. C22⋊Q8×C61C2×C4semidirect
198. #121×C61C2×C4semidirect
203. #117×C61C2×C4semidirect
532. #1504D61semidirect
607. C61#17608semidirect
623. C2×#41C4×D61semidirect
678. C22⋊Q8C4×D61semidirect
691. #121C4×D61semidirect
709. #117C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214594912
#214542692
#214486462
#214443892
#214443752
#214443722
#214443592
#214443532
#214443502
#214443372
#214443202
#214443072
C2×#168394982
#328×D612
C61×#15042
#1760861