Finite Group Databasebeta

← #29646236

Subgroups — #29646236

Order 15616.

1290 conjugacy classes of subgroups.

The subgroup lattice has 1058 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840410C211yesmaximal, characteristic
2#21454269C211yesmaximal, characteristic, complemented
3#21454265C211yesmaximal, characteristic, complemented
4#21444181C211yesmaximal, characteristic, complemented
5#21444181C211yesmaximal, characteristic, complemented
6#21444167C211yesmaximal, characteristic, complemented
7#21444164C211yesmaximal, characteristic, complemented
8#21444164C211yesmaximal, characteristic, complemented
9#21444154C211yesmaximal, characteristic, complemented
10#21444148C211yesmaximal, characteristic, complemented
11#21444147C211yesmaximal, characteristic, complemented
12#21444134C211yesmaximal, characteristic, complemented
13C2×#16839487C211yesmaximal, characteristic, complemented
14#324×D61C211yesmaximal, characteristic, complemented
15C61×#1468C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758224C411yescharacteristic
18C2×#14519785—21no—
19C2×#14519783—21no—
20#16840410—21no—
21#16840410—21no—
22#16840410—21no—
23#16840410—21no—
24#16840410—21no—
25#16840410—21no—
26#16840410—21no—
27#16840410—21no—
28C2×#14519776C411yescharacteristic
29C2×#14519762C411yescharacteristic
30C2×#14519761C411yescharacteristic
31C2×#14519759C2211yescharacteristic
32C2×#14519755C2211yescharacteristic
33C2×#14519754C411yescharacteristic
34C2×#14519750C411yescharacteristic
35C2×#14519749C411yescharacteristic
36C2×#14519737C411yescharacteristic
37C2×#14519737C2211yescharacteristic
38C22×#11758196C2211yescharacteristic
39C2×C4⋊C4×D61C2211yescharacteristic
40#16839730—21no—
41#16839728—21no—
42#16839727—21no—
43#16839727—21no—
44#16839727—21no—
45#16839727—21no—
46#16839726C2211yescharacteristic
47#16839724C2211yescharacteristic
48#16839724C2211yescharacteristic
49#16839724C2211yescharacteristic
50#16839724C2211yescharacteristic
51C2×C22⋊#92418C2211yescharacteristic
52C22⋊C8×D61C2211yescharacteristic
53C22⋊C8×D61C2211yescharacteristic
54C22⋊C8×D61C2211yescharacteristic
55C22⋊C8×D61C2211yescharacteristic
56#16839488C2211yescharacteristic
57#16839488C2211yescharacteristic
58#16839487C2211yescharacteristic
59#16839487C2211yescharacteristic
60#16839487C2211yescharacteristic
61#16839487C2211yescharacteristic
62#16839487C2211yescharacteristic
63#16839487C2211yescharacteristic
64#16839487C2211yescharacteristic
65#16839487C2211yescharacteristic
66#16839486C2211yescharacteristic
67#16839486C2211yescharacteristic
68C2×#123×C61C2211yescharacteristic
69C61×#407C2211yescharacteristic
70C2×C22⋊C8×C61C2211yescharacteristic
71C61×#324C2211yescharacteristic
72C61×#324C2211yescharacteristic
73C61×#323C2211yescharacteristic
74C61×#323C2211yescharacteristic
75C2×#11758222—44no—
76C2×#11758222D411yescharacteristic
77C2×#11758222D411yescharacteristic
78C2×#11758222D411yescharacteristic
79C2×#11758222D411yescharacteristic
80C2×#11758222D411yescharacteristic
81C2×#11758222D411yescharacteristic
82C2×#11758222D411yescharacteristic
83C2×#11758222D411yescharacteristic
84C2×#11758224—21no—
85C2×#11758224—21no—
86C2×#11758224—21no—
87C2×#11758224—21no—
88C2×#11758224—44no—
89C22×Dic122C2×C411yescharacteristic
90C22×Dic122C2×C411yescharacteristic
91C22×D244C2×C411yescharacteristic
92C22×C22⋊D61C2×C411yescharacteristic
93C22×C22⋊D61C2×C411yescharacteristic
94C22×C22⋊D61C2×C411yescharacteristic
95C22×C22⋊D61C2×C411yescharacteristic
96C23×Dic61C2×C411yescharacteristic
97C23×Dic61C2×C411yescharacteristic
98C23×Dic61C2×C411yescharacteristic
99C22×C4×D61C2×C411yescharacteristic
100C22×C4×D61C2×C411yescharacteristic
101C22×C4×D61C2311yescharacteristic
102C22×C4×D61C2311yescharacteristic
103#14519785—44no—
104#14519783—44no—
105C2×#11758194—21no—
106C2×#11758189—21no—
107C2×#11758189—21no—
108C2×#11758189—21no—
109C2×#11758189—21no—
110C22×#92418—21no—
111C2×C8×D61—21no—
112C2×C8×D61—21no—
113C2×C8×D61—21no—
114C2×C8×D61—21no—
115#14519776—21no—
116#14519776—21no—
117#14519776—21no—
118#14519776—21no—
119#14519762—21no—
120#14519762—21no—
121#14519762—21no—
122#14519762—21no—
123#14519761—21no—
124#14519761—21no—
125#14519761—21no—
126#14519761—21no—
127#14519759—21no—
128#14519759—21no—
129#14519759—21no—
130#14519759—21no—
131#14519755—21no—
132#14519755—21no—
133#14519755—21no—
134#14519755—21no—
135#14519754—21no—
136#14519754—21no—
137#14519754—21no—
138#14519754—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#14519737—21no—
148#14519737—21no—
149#14519737—21no—
150#14519737—21no—
151#14519737—21no—
152#14519737—21no—
153#14519737—21no—
154#14519737—21no—
155C2×C4⋊Dic61C2×C411yescharacteristic
156C2×C4⋊Dic61C2×C411yescharacteristic
157C2×#11758196—21no—
158C2×#11758196—21no—
159C2×#11758196—21no—
160C2×#11758196—21no—
161C2×#11758196C2×C411yescharacteristic
162C2×#11758196C2×C411yescharacteristic
163C2×#11758196C2×C411yescharacteristic
164C2×#11758196C2×C411yescharacteristic
165C2×#11758196C2311yescharacteristic
166C2×#11758196C2311yescharacteristic
167C4⋊C4×D61—21no—
168C4⋊C4×D61—21no—
169C4⋊C4×D61—21no—
170C4⋊C4×D61—21no—
171C2×C22⋊Dic61C2×C411yescharacteristic
172C2×#11758198C2×C411yescharacteristic
173C2×#11758198C2×C411yescharacteristic
174C2×#11758198C2×C411yescharacteristic
175C2×#11758198C2×C411yescharacteristic
176C2×C4×Dic61C2×C411yescharacteristic
177C22⋊#92418—21no—
178C22⋊#92418—21no—
179C22⋊#92418C2311yescharacteristic
180C22⋊#92418C2311yescharacteristic
181C22⋊#92418C2311yescharacteristic
182C22⋊#92418C2311yescharacteristic
183#14519689—21no—
184#14519689—21no—
185#14519689—21no—
186#14519689—21no—
187#14519689—21no—
188#14519689—21no—
189#14519689—21no—
190#14519689—21no—
191C22×D4×C61C2×C411yescharacteristic
192C23×C4×C61C2311yescharacteristic
193C2×M16×C61—21no—
194C22×C8×C61—21no—
195#123×C61—21no—
196#123×C61—21no—
197#123×C61—21no—
198#123×C61—21no—
199C2×C4⋊C4×C61C2×C411yescharacteristic
200C2×C4⋊C4×C61C2311yescharacteristic
201C2×C22⋊C4×C61C2×C411yescharacteristic
202C2×C22⋊C4×C61C2×C411yescharacteristic
203C2×C22⋊C4×C61C2311yescharacteristic
204C22⋊C8×C61—21no—
205C22⋊C8×C61—21no—
206C22⋊C8×C61C2311yescharacteristic
207C22⋊C8×C61C2311yescharacteristic
208C22⋊C8×C61C2311yescharacteristic
209C22⋊C8×C61C2311yescharacteristic
210C24×C61C22×C411yescharacteristic
211C24×C61C22×C411yescharacteristic
212C23×D61C22×C411yescharacteristic
213C23×D61C22×C411yescharacteristic
214C2×D4×C61—21no—
215C2×D4×C61—21no—
216C2×D4×C61—42no—
217C22×C4×C61—42no—
218C22×C4×C61C22×C411yescharacteristic
219C22×C4×C61C22×C411yescharacteristic
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C22×C411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2411yescharacteristic
227C2×C22⋊D61—24no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—22no—
233C2×C22⋊D61—41no—
234C2×C22⋊D61—42no—
235C2×C22⋊D61—42no—
236C2×C22⋊D61C22⋊C411yescharacteristic
237C2×C22⋊D61C22⋊C411yescharacteristic
238C2×C22⋊D61C22⋊C411yescharacteristic
239C2×C22⋊D61C22⋊C411yescharacteristic
240C2×C22⋊D61C22⋊C411yescharacteristic
241C2×C22⋊D61C22⋊C411yescharacteristic
242C2×C22⋊D61C22⋊C411yescharacteristic
243C2×C22⋊D61C22⋊C411yescharacteristic
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—22no—
251C22×Dic61—41no—
252C22×Dic61—42no—
253C22×Dic61—42no—
254C22×Dic61C22×C411yescharacteristic
255C22×Dic61C22×C411yescharacteristic
256C22×Dic61C22×C411yescharacteristic
257C22×Dic61C22×C411yescharacteristic
258C22×Dic61C22×C411yescharacteristic
259C22×Dic61C22×C411yescharacteristic
260#11758224—44no—
261#11758224—44no—
262#11758224—44no—
263#11758224—44no—
264#11758222—24no—
265#11758222—24no—
266#11758222—42no—
267#11758222—42no—
268#11758222—42no—
269#11758222—42no—
270#11758222—42no—
271#11758222—42no—
272C2×D244—42no—
273C2×D244C22⋊C411yescharacteristic
274C2×D244C22⋊C411yescharacteristic
275C2×D244C22⋊C411yescharacteristic
276C2×D244C22⋊C411yescharacteristic
277C2×C4×D61—21no—
278C2×C4×D61—21no—
279C2×C4×D61—21no—
280C2×C4×D61—21no—
281C2×C4×D61—22no—
282C2×C4×D61—42no—
283C2×C4×D61—42no—
284C2×C4×D61—41no—
285C2×C4×D61—42no—
286C2×C4×D61C2×D411yescharacteristic
287C2×C4×D61C2×D411yescharacteristic
288C2×C4×D61C2×D411yescharacteristic
289C2×C4×D61C2×D411yescharacteristic
290C2×C4×D61C2×D411yescharacteristic
291C2×C4×D61C2×D411yescharacteristic
292C2×C4×D61C2×D411yescharacteristic
293C2×C4×D61C2×D411yescharacteristic
294C2×Dic122—21no—
295C2×Dic122—21no—
296C2×Dic122—42no—
297C2×Dic122—42no—
298C2×Dic122C22⋊C411yescharacteristic
299C2×Dic122C22⋊C411yescharacteristic
300C2×Dic122C22⋊C411yescharacteristic
301C2×Dic122C22⋊C411yescharacteristic
302M16×C61—42no—
303C2×C8×C61—21no—
304C2×C8×C61—21no—
305C2×C8×C61—21no—
306C2×C8×C61—21no—
307C2×C8×C61—42no—
308C4⋊C4×C61—21no—
309C4⋊C4×C61—21no—
310C4⋊C4×C61—21no—
311C4⋊C4×C61—21no—
312C22⋊C4×C61—21no—
313C22⋊C4×C61—21no—
314C22⋊C4×C61—21no—
315C22⋊C4×C61—21no—
316C22⋊C4×C61—21no—
317C22⋊C4×C61—21no—
318C22⋊Dic61—21no—
319C22⋊Dic61—21no—
320#11758198—21no—
321#11758198—21no—
322#11758198—21no—
323#11758198—21no—
324#11758198—21no—
325#11758198—21no—
326#11758198—21no—
327#11758198—21no—
328C4⋊Dic61—21no—
329C4⋊Dic61—21no—
330C4⋊Dic61—21no—
331C4⋊Dic61—21no—
332#11758196—21no—
333#11758196—21no—
334#11758196—21no—
335#11758196—21no—
336#11758196—21no—
337#11758196—21no—
338#11758196—21no—
339#11758196—21no—
340#11758196—21no—
341#11758196—21no—
342#11758196—21no—
343#11758196—21no—
344C4×Dic61—21no—
345C4×Dic61—21no—
346#11758194—42no—
347C2×#92418—21no—
348C2×#92418—21no—
349C2×#92418—21no—
350C2×#92418—21no—
351C2×#92418—42no—
352#11758189—42no—
353#11758189—42no—
354#11758189—42no—
355#11758189—42no—
356C8×D61—42no—
357C8×D61—42no—
358C8×D61—42no—
359C8×D61—42no—
360C23×C61—21no—
361C23×C61—21no—
362C23×C61—22no—
363C23×C61—21no—
364C23×C61—21no—
365C23×C61—21no—
366C23×C61—41no—
367C23×C61—41no—
368C23×C61—41no—
369C23×C61C2×C22⋊C411yescharacteristic
370C23×C61C2×C22⋊C411yescharacteristic
371C23×C61C23×C411yescharacteristic
372C22×D61—21no—
373C22×D61—21no—
374C22×D61—21no—
375C22×D61—21no—
376C22×D61—22no—
377C22×D61—41no—
378C22×D61—41no—
379C22×D61—41no—
380C22×D61C2×C22⋊C411yescharacteristic
381C22×D61C2×C22⋊C411yescharacteristic
382C22×D61C2×C22⋊C411yescharacteristic
383C22×D61C2×C22⋊C411yescharacteristic
384D4×C61—42no—
385D4×C61—42no—
386C2×C4×C61—22no—
387C2×C4×C61—22no—
388C2×C4×C61—21no—
389C2×C4×C61—21no—
390C2×C4×C61—21no—
391C2×C4×C61—21no—
392C2×C4×C61—21no—
393C2×C4×C61—41no—
394C2×C4×C61—41no—
395C2×C4×C61—41no—
396C2×C4×C61—41no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61C2×C22⋊C411yescharacteristic
400C2×C4×C61C2×C22⋊C411yescharacteristic
401C2×C4×C61C22×D411yescharacteristic
402C2×C4×C61C22×D411yescharacteristic
403C22⋊D61—22no—
404C22⋊D61—22no—
405C22⋊D61—22no—
406C22⋊D61—22no—
407C22⋊D61—22no—
408C22⋊D61—41no—
409C22⋊D61—41no—
410C22⋊D61—42no—
411C22⋊D61—42no—
412C22⋊D61—42no—
413C22⋊D61—42no—
414C22⋊D61#9914yes—
415C2×Dic61—21no—
416C2×Dic61—21no—
417C2×Dic61—22no—
418C2×Dic61—21no—
419C2×Dic61—21no—
420C2×Dic61—21no—
421C2×Dic61—21no—
422C2×Dic61—21no—
423C2×Dic61—41no—
424C2×Dic61—42no—
425C2×Dic61—42no—
426C2×Dic61—42no—
427C2×Dic61—42no—
428C2×Dic61—42no—
429C2×Dic61—42no—
430C2×Dic61—41no—
431C2×Dic61—41no—
432C2×Dic61C2×C22⋊C411yescharacteristic
433C2×Dic61C2×C22⋊C411yescharacteristic
434C2×Dic61C2×C22⋊C411yescharacteristic
435C2×Dic61C2×C22⋊C411yescharacteristic
436C2×Dic61#13112yescomplemented
437D244—22no—
438D244—22no—
439D244—41no—
440D244—41no—
441C4×D61—22no—
442C4×D61—22no—
443C4×D61—22no—
444C4×D61—22no—
445C4×D61—41no—
446C4×D61—41no—
447C4×D61—41no—
448C4×D61—41no—
449C4×D61—42no—
450C4×D61—42no—
451C4×D61—42no—
452C4×D61—42no—
453Dic122—22no—
454Dic122—22no—
455Dic122—41no—
456Dic122—41no—
457Dic122—42no—
458Dic122—42no—
459C8×C61—41no—
460C8×C61—41no—
461C8×C61—41no—
462C8×C61—41no—
463#92418—41no—
464#92418—41no—
465#92418—41no—
466#92418—41no—
467#17416—611nomaximal, Sylow
468C22×C61—21no—
469C22×C61—21no—
470C22×C61—21no—
471C22×C61—21no—
472C22×C61—21no—
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—42no—
476C22×C61—42no—
477C22×C61—41no—
478C22×C61—41no—
479C22×C61—41no—
480C22×C61—81no—
481C22×C61—81no—
482C22×C61C2×#9912yes—
483C22×C61C22×C22⋊C411yescharacteristic
484C22×C61C2×#13111yescharacteristic
485C22×C61#56811yescharacteristic
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—41no—
507C4×C61—41no—
508C4×C61—41no—
509Dic61—22no—
510Dic61—21no—
511Dic61—21no—
512Dic61—21no—
513Dic61—41no—
514Dic61—41no—
515Dic61—41no—
516Dic61C2×#9912yes—
517C2×#547—611no—
518#2880—611no—
519#2880—611no—
520#1472—611no—
521#1472—611no—
522#1468—611no—
523#1468—611no—
524#1468—611no—
525#1468D6111yescharacteristic, complemented
526#1465—611no—
527#1463—611no—
528#1463—611no—
529#1459—611no—
530C2×#324—611no—
531C2×#324—611no—
532C2×C61—21no—
533C2×C61—21no—
534C2×C61—22no—
535C2×C61—41no—
536C2×C61—81no—
537C2×C61#288011yescharacteristic
538C2×C61C22×#9911yescharacteristic
539C2×C61#288911yescharacteristic
540D61—22no—
541D61—41no—
542D61—41no—
543D61—41no—
544C22×#41—611no—
545C22×#41—611no—
546C2×#131—1221no—
547C2×#131—1221no—
548#547—1221no—
549#547—1221no—
550#547—1221no—
551#547—1221no—
552#547—1221no—
553#547—1221no—
554#547—1221no—
555#547—1221no—
556C2×C4⋊Q8—611no—
557C2×#123—611no—
558C2×#123—611no—
559C2×#123—611no—
560C2×#123C2×D6111yescharacteristic
561C2×C22⋊Q8—611no—
562C2×C22⋊Q8—611no—
563C2×#121—611no—
564C2×#121—611no—
565C2×C4×D4—611no—
566C2×C4×D4—611no—
567C22×C4⋊C4—611no—
568C22×C4⋊C4—611no—
569#408—1221no—
570#408—1221no—
571#408—1221no—
572#408—1221no—
573#408—1221no—
574#408—1221no—
575#407—611no—
576#407—611no—
577#407—611no—
578#407—611no—
579#407—611no—
580#407C2×D6111yescharacteristic
581C2×C22⋊C8—611no—
582C2×C22⋊C8—611no—
583C2×C22⋊C8—611no—
584C2×C22⋊C8—611no—
585C2×C22⋊C8—611no—
586C2×C22⋊C8C2×D6111yescharacteristic
587#324—611no—
588#324—611no—
589#324—611no—
590#324—611no—
591#324—611no—
592#324—611no—
593#324—611no—
594#324—611no—
595#324—611no—
596#324—611no—
597#324C2×D6111yescharacteristic
598#324C2×D6111yescharacteristic
599#323—611no—
600#323—611no—
601#323C2×D6111yescharacteristic
602#323C2×D6111yescharacteristic
603C61#1741611yescharacteristic, complemented, Sylow
604C2×#41—611no—
605C2×#41—611no—
606C2×#41—611no—
607C2×#41—611no—
608C2×#41—611no—
609C2×#41—611no—
610C2×#41—611no—
611C2×#41—611no—
612C2×#41—1221no—
613C2×#41—1221no—
614C2×#41—1221no—
615C2×#41—1221no—
616C2×#41—2444no—
617C2×#41—2444no—
618C22×Q8—611no—
619C22×Q8—611no—
620C22×D4—611no—
621C22×D4—611no—
622C22×D4—611no—
623C22×D4—611no—
624C22×D4—611no—
625C22×D4C4×D6111yescharacteristic
626C23×C4—611no—
627C23×C4—611no—
628C23×C4—611no—
629C23×C4—611no—
630C23×C4—611no—
631C23×C4—611no—
632C23×C4—611no—
633C23×C4C22×D6111yescharacteristic
634#131—2444no—
635#131—2444no—
636C2×M16—21no—
637C2×M16—1221no—
638C2×M16—1221no—
639C2×M16—1221no—
640C2×M16—1221no—
641C2×M16—1221no—
642C22×C8—21no—
643C22×C8—1221no—
644C22×C8—1221no—
645C22×C8—1221no—
646C22×C8—1221no—
647C22×C8—1221no—
648C4⋊Q8—1221no—
649C4⋊Q8—1221no—
650C4⋊Q8—1221no—
651C4⋊Q8—1221no—
652#123—21no—
653#123—21no—
654#123—21no—
655#123—21no—
656#123—1221no—
657#123—1221no—
658#123—1221no—
659#123—1221no—
660#123—1221no—
661#123—1221no—
662#123—1221no—
663#123—1221no—
664#123—1221no—
665#123—1221no—
666#123—1221no—
667#123—1221no—
668C22⋊Q8—1221no—
669C22⋊Q8—1221no—
670C22⋊Q8—1221no—
671C22⋊Q8—1221no—
672C22⋊Q8—1221no—
673C22⋊Q8—1221no—
674C22⋊Q8—1221no—
675C22⋊Q8—1221no—
676#121—1221no—
677#121—1221no—
678#121—1221no—
679#121—1221no—
680#121—1221no—
681#121—1221no—
682#121—1221no—
683#121—1221no—
684C4×D4—1221no—
685C4×D4—1221no—
686C4×D4—1221no—
687C4×D4—1221no—
688C4×D4—1221no—
689C4×D4—1221no—
690C4×D4—1221no—
691C4×D4—1221no—
692C2×C4⋊C4—611no—
693C2×C4⋊C4—611no—
694C2×C4⋊C4—611no—
695C2×C4⋊C4—611no—
696C2×C4⋊C4—611no—
697C2×C4⋊C4—611no—
698C2×C4⋊C4—611no—
699C2×C4⋊C4—611no—
700C2×C4⋊C4—1221no—
701C2×C4⋊C4—1221no—
702C2×C4⋊C4—1221no—
703C2×C4⋊C4—1221no—
704C2×C4⋊C4—1221no—
705C2×C4⋊C4—1221no—
706C2×C4⋊C4—1221no—
707C2×C4⋊C4—1221no—
708C2×C4⋊C4C4×D6111yescharacteristic
709C2×C4⋊C4C22×D6111yescharacteristic
710C2×C22⋊C4—611no—
711C2×C22⋊C4—611no—
712C2×C22⋊C4—611no—
713C2×C22⋊C4—611no—
714C2×C22⋊C4—611no—
715C2×C22⋊C4C4×D6111yescharacteristic
716C2×C22⋊C4C4×D6111yescharacteristic
717C2×C22⋊C4C22×D6111yescharacteristic
718C2×C42—611no—
719C22⋊C8—21no—
720C22⋊C8—21no—
721C22⋊C8—611no—
722C22⋊C8—611no—
723C22⋊C8—611no—
724C22⋊C8—611no—
725C22⋊C8—1221no—
726C22⋊C8—1221no—
727C22⋊C8—1221no—
728C22⋊C8—1221no—
729C22⋊C8—1221no—
730C22⋊C8—1221no—
731C22⋊C8—1221no—
732C22⋊C8—1221no—
733C22⋊C8—1221no—
734C22⋊C8—1221no—
735C22⋊C8C22×D6111yescharacteristic
736C22⋊C8C22×D6111yescharacteristic
737C22⋊C8C22×D6111yescharacteristic
738C22⋊C8C22×D6111yescharacteristic
739C24—611no—
740C24—611no—
741C24C2×C4×D6111yescharacteristic
742C24C2×C4×D6111yescharacteristic
743#41—1224no—
744#41—1224no—
745#41—2442no—
746#41—2442no—
747#41—2442no—
748#41—2442no—
749#41—2442no—
750#41—2442no—
751#41—2444no—
752#41—2444no—
753#41—2444no—
754#41—2444no—
755C2×Q8—611no—
756C2×Q8—611no—
757C2×Q8—611no—
758C2×Q8—611no—
759C2×Q8—1221no—
760C2×Q8—1221no—
761C2×Q8—2442no—
762C2×Q8—2442no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—42no—
766C2×D4—611no—
767C2×D4—611no—
768C2×D4—611no—
769C2×D4—611no—
770C2×D4—611no—
771C2×D4—611no—
772C2×D4—611no—
773C2×D4—611no—
774C2×D4—611no—
775C2×D4—611no—
776C2×D4—611no—
777C2×D4—611no—
778C2×D4—1222no—
779C2×D4—1224no—
780C2×D4—1221no—
781C2×D4—1221no—
782C2×D4—1221no—
783C2×D4—1221no—
784C2×D4—2442no—
785C2×D4—2441no—
786C2×D4—2442no—
787C2×D4—2442no—
788C22×C4—42no—
789C22×C4—611no—
790C22×C4—611no—
791C22×C4—611no—
792C22×C4—611no—
793C22×C4—611no—
794C22×C4—611no—
795C22×C4—611no—
796C22×C4—611no—
797C22×C4—611no—
798C22×C4—611no—
799C22×C4—611no—
800C22×C4—611no—
801C22×C4—611no—
802C22×C4—611no—
803C22×C4—1222no—
804C22×C4—1221no—
805C22×C4—1221no—
806C22×C4—1221no—
807C22×C4—1221no—
808C22×C4—1221no—
809C22×C4—1221no—
810C22×C4—1222no—
811C22×C4—1221no—
812C22×C4—1221no—
813C22×C4—1221no—
814C22×C4—1221no—
815C22×C4—2441no—
816C22×C4—2442no—
817C22×C4—2442no—
818C22×C4—2442no—
819C22×C4—2441no—
820C22×C4—2442no—
821C22×C4—2442no—
822C22×C4C2×C4×D6111yescharacteristic
823C22×C4C2×C4×D6111yescharacteristic
824C22×C4C2×C4×D6111yescharacteristic
825C22×C4C2×C4×D6111yescharacteristic
826C22×C4D4×D6111yescharacteristic
827C22×C4D4×D6111yescharacteristic
828C22×C4D4×D6111yescharacteristic
829C22×C4D4×D6111yescharacteristic
830C22×C4C23×D6111yescharacteristic
831M16—42no—
832M16—2442no—
833M16—2442no—
834M16—2442no—
835M16—2442no—
836M16—2442no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—42no—
842C2×C8—1221no—
843C2×C8—1221no—
844C2×C8—1221no—
845C2×C8—1221no—
846C2×C8—2442no—
847C2×C8—2442no—
848C2×C8—2442no—
849C2×C8—2442no—
850C2×C8—2442no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
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—1221no—
864C4⋊C4—1221no—
865C4⋊C4—1221no—
866C4⋊C4—1221no—
867C4⋊C4—1221no—
868C4⋊C4—1221no—
869C4⋊C4—1221no—
870C4⋊C4—1221no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—21no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
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—1221no—
886C22⋊C4—1221no—
887C42—1221no—
888C42—1221no—
889C23—22no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—21no—
895C23—41no—
896C23—41no—
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
912C23C22×C4×D6111yescharacteristic
913Q8—1222no—
914Q8—1222no—
915Q8—2441no—
916Q8—2441no—
917Q8—2442no—
918Q8—2442no—
919D4—42no—
920D4—42no—
921D4—614no—
922D4—1222no—
923D4—1222no—
924D4—1222no—
925D4—1222no—
926D4—1222no—
927D4—1222no—
928D4—1222no—
929D4—2441no—
930D4—2441no—
931D4—2441no—
932D4—2441no—
933D4—2442no—
934D4—2442no—
935D4—2442no—
936D4—2442no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—611no—
951C2×C4—611no—
952C2×C4—611no—
953C2×C4—611no—
954C2×C4—612no—
955C2×C4—1222no—
956C2×C4—1222no—
957C2×C4—1222no—
958C2×C4—1222no—
959C2×C4—1222no—
960C2×C4—1221no—
961C2×C4—1221no—
962C2×C4—1221no—
963C2×C4—1221no—
964C2×C4—1221no—
965C2×C4—1221no—
966C2×C4—1221no—
967C2×C4—2441no—
968C2×C4—2441no—
969C2×C4—2441no—
970C2×C4—2441no—
971C2×C4—2442no—
972C2×C4—2442no—
973C2×C4—2442no—
974C2×C4—2442no—
975C2×C4—2442no—
976C2×C4—2441no—
977C2×C4—2442no—
978C2×C4—2442no—
979C2×C4—2442no—
980C2×C4—2442no—
981C2×C4—2442no—
982C2×C4—2441no—
983C2×C4—2441no—
984C2×C4C22⋊C4×D6111yescharacteristic
985C2×C4C22⋊C4×D6111yescharacteristic
986C2×C4C2×D4×D6111yescharacteristic
987C2×C4C2×D4×D6111yescharacteristic
988C8—41no—
989C8—41no—
990C8—41no—
991C8—41no—
992C8—2441no—
993C8—2441no—
994C8—2441no—
995C8—2441no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—42no—
1004C22—42no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—81no—
1009C22—81no—
1010C22—612no—
1011C22—1221no—
1012C22—1221no—
1013C22—1221no—
1014C22—1221no—
1015C22—1221no—
1016C22—1221no—
1017C22—1221no—
1018C22—1221no—
1019C22—1221no—
1020C22—1221no—
1021C22—1221no—
1022C22—4881no—
1023C22—4881no—
1024C22—2442no—
1025C22—2442no—
1026C22#99×D6112yes—
1027C22C2×C22⋊C4×D6111yescharacteristic
1028C22#131×D6111yescharacteristic
1029C22#1684052711yescharacteristic
1030C4—21no—
1031C4—21no—
1032C4—21no—
1033C4—21no—
1034C4—41no—
1035C4—41no—
1036C4—41no—
1037C4—612no—
1038C4—1222no—
1039C4—1221no—
1040C4—1221no—
1041C4—1221no—
1042C4—2441no—
1043C4—2441no—
1044C4—2441no—
1045C2—21no—
1046C2—21no—
1047C2—22no—
1048C2—41no—
1049C2—81no—
1050C2—1222no—
1051C2—2441no—
1052C2—2441no—
1053C2—2441no—
1054C2#2145426711yescharacteristic
1055C2C2×#99×D6111yescharacteristic
1056C2#2145430011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1468C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840410C2
cosocleC22×C4×C61C24
hypercenter#1468D61
hypocenterC61#17416
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1468

Complements

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

NH ≅ G/Ntype
2. #21454269C2semidirect
3. #21454265C2semidirect
4. #21444181C2semidirect
5. #21444181C2semidirect
6. #21444167C2semidirect
7. #21444164C2semidirect
8. #21444164C2semidirect
9. #21444154C2semidirect
10. #21444148C2semidirect
11. #21444147C2semidirect
12. #21444134C2semidirect
13. C2×#16839487C2semidirect
14. #324×D61C2semidirect
15. C61×#1468C2semidirect
436. C2×Dic61#131semidirect
525. #1468D61semidirect
603. C61#17416semidirect

Maximal subgroups

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

subgroupindex
C2×#168404102
#214542692
#214542652
#214441812
#214441672
#214441642
#214441542
#214441482
#214441472
#214441342
C2×#168394872
#324×D612
C61×#14682
#1741661