Finite Group Databasebeta

← #30617022

Subgroups — #30617022

Order 15616.

980 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840801C211yesmaximal, characteristic
2C2×Q16×#6923C211yesmaximal, characteristic, complemented
3#21462309C211yesmaximal, characteristic
4#21462259C211yesmaximal, characteristic, complemented
5#21461987C211yesmaximal, characteristic
6#21461930C211yesmaximal, characteristic, complemented
7#21461899C211yesmaximal, characteristic, complemented
8#21461896C211yesmaximal, characteristic
9#21461815C211yesmaximal, characteristic
10#21461813C211yesmaximal, characteristic, complemented
11#21461688C211yesmaximal, characteristic, complemented
12#21461608C211yesmaximal, characteristic, complemented
13#21461592C211yesmaximal, characteristic, complemented
14#102×#6923C211yesmaximal, characteristic
15#464×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×Q8×#6923C2211yescharacteristic
19C2×D4×#6923C2211yescharacteristic
20#16840801—24no—
21Q16×#6923—24no—
22C2×#14519846C2211yescharacteristic
23C2×#14519846C2211yescharacteristic
24D61⋊(C4⋊C8)C2211yescharacteristic
25C2×#14519840C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519840C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30C2×#14519839C2211yescharacteristic
31C2×#14519831C2211yescharacteristic
32C2×C8×#6923C2211yescharacteristic
33(C2×#6923)⋊Q8C2211yescharacteristic
34#16840714C2211yescharacteristic
35#16840712—21no—
36#16840712—21no—
37#16840709—21no—
38#16840709—21no—
39#16840708C2211yescharacteristic
40C4⋊C4×#6923—21no—
41C4⋊C4×#6923—21no—
42C4⋊C4×#6923C2211yescharacteristic
43C4⋊C4×#6923C2211yescharacteristic
44C4×C4⋊#6923—21no—
45C4×C4⋊#6923C2211yescharacteristic
46#16840698—21no—
47#16840698C2211yescharacteristic
48#16840636C2211yescharacteristic
49#16840636C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×Q16×D61C2211yescharacteristic
55C2×SD16×D61C2211yescharacteristic
56#124×D61C2211yescharacteristic
57C4×Q8×D61C2211yescharacteristic
58#16839987C411yescharacteristic, complemented
59#16839986C411yescharacteristic, complemented
60#16839985C411yescharacteristic, complemented
61#16839984C411yescharacteristic, complemented
62#16839983C411yescharacteristic, complemented
63#16839982C411yescharacteristic, complemented
64#16839981C411yescharacteristic, complemented
65C4⋊C8×D61C2211yescharacteristic
66#103×D61C2211yescharacteristic
67#102×D61C2211yescharacteristic
68C61×#464C411yescharacteristic, complemented
69C23×#6923—21no—
70C2×D61⋊C8C2311yescharacteristic
71C2×D61⋊C8C2311yescharacteristic
72Q8×#6923—22no—
73Q8×#6923—22no—
74Q8×#6923—22no—
75Q8×#6923—22no—
76Q8×#6923—22no—
77Q8×#6923D414yes—
78D4×#6923—22no—
79D4×#6923—22no—
80C2×C4⋊#6923—21no—
81C2×C4⋊#6923—21no—
82C2×C4⋊#6923—21no—
83C2×C4⋊#6923—21no—
84C2×C4⋊#6923—21no—
85C2×C4⋊#6923C2311yescharacteristic
86C2×C4⋊#6923C2311yescharacteristic
87C2×C4⋊#6923C2311yescharacteristic
88C2×C4⋊#6923C2311yescharacteristic
89C2×C22⋊#6923—21no—
90C2×C22⋊#6923—21no—
91C2×C22⋊#6923—21no—
92C2×C4×#6923—21no—
93C2×C4×#6923—21no—
94C2×C4×#6923—21no—
95C2×C4×#6923—21no—
96C2×C4×#6923—21no—
97C2×C4×#6923—21no—
98C2×C4×#6923C2311yescharacteristic
99C2×C4×#6923C2311yescharacteristic
100#14519846—22no—
101#14519846—22no—
102#14519844—21no—
103C4⋊#92420—21no—
104#14519840—22no—
105#14519840—22no—
106#14519840—22no—
107#14519840—22no—
108#14519839—22no—
109#14519839—22no—
110#14519831—22no—
111C8×#6923—22no—
112(C2×#6923)⋊C4—21no—
113(C2×#6923)⋊C4—21no—
114(C2×#6923)⋊C4—21no—
115(C2×#6923)⋊C4—21no—
116(C2×#6923)⋊C4—21no—
117(C2×#6923)⋊C4D411yescharacteristic
118(C2×#6923)⋊C4D411yescharacteristic
119(C2×#6923)⋊C4D411yescharacteristic
120(C2×#6923)⋊C4D411yescharacteristic
121C2×Q8×D61C2311yescharacteristic
122C2×Q8×D61C2311yescharacteristic
123C2×D4×D61C2311yescharacteristic
124C2×Dic244C2×C411yescharacteristic, complemented
125C2×#11758202C2×C411yescharacteristic, complemented
126C2×#11758202C2×C411yescharacteristic, complemented
127Q16×D61—22no—
128Q16×D61—22no—
129C2×#11758190C2×C411yescharacteristic
130C2×#11758200C2×C411yescharacteristic
131C2×#11758201C2×C411yescharacteristic
132SD16×D61—22no—
133SD16×D61—22no—
134C2×C8×D61C2311yescharacteristic
135C2×C8×D61C2311yescharacteristic
136#14519766C2×C411yescharacteristic
137#14519765C2×C411yescharacteristic
138#14519764C2×C411yescharacteristic
139#14519763—21no—
140#14519763—21no—
141Q8×Dic61C2×C411yescharacteristic, complemented
142C4×Dic122—21no—
143C4×Dic122C2×C411yescharacteristic, complemented
144#14519742—21no—
145#14519742C2×C411yescharacteristic, complemented
146C4⋊C4×D61—21no—
147C4⋊C4×D61C2311yescharacteristic
148C22⋊C4×D61—21no—
149C22⋊C4×D61—21no—
150C42×D61—21no—
151C42×D61C2311yescharacteristic
152C4⋊#92418C2×C411yescharacteristic, complemented
153#14519706C2×C411yescharacteristic, complemented
154#14519706C2×C411yescharacteristic, complemented
155#14519702C2×C411yescharacteristic, complemented
156#14519701C2×C411yescharacteristic, complemented
157#14519700C2×C411yescharacteristic, complemented
158#14519699C2×C411yescharacteristic
159#14519698C2×C411yescharacteristic
160#14519697C2×C411yescharacteristic
161C2×Q16×C61C2×C411yescharacteristic, complemented
162C2×SD16×C61C2×C411yescharacteristic
163#124×C61C2×C411yescharacteristic
164C4×Q8×C61C2×C411yescharacteristic, complemented
165C4⋊C8×C61C2×C411yescharacteristic, complemented
166#103×C61C2×C411yescharacteristic, complemented
167#102×C61C2×C411yescharacteristic
168C23×D61—21no—
169C22×#6923—21no—
170C22×#6923—21no—
171C22×#6923—21no—
172C22×#6923—21no—
173C22×#6923—42no—
174C22×#6923—81no—
175C22×#6923—81no—
176C22×#6923C2×D411yescharacteristic
177C22×#6923C2×D411yescharacteristic
178C22×#6923C2×D411yescharacteristic
179C22×#6923C2×D411yescharacteristic
180C2×Q8×C61C22×C411yescharacteristic
181C2×Q8×C61C22×C411yescharacteristic
182C2×D4×C61C22×C411yescharacteristic
183C2×C22⋊D61—21no—
184Q8×D61—21no—
185Q8×D61—21no—
186Q8×D61—21no—
187Q8×D61—21no—
188Q8×D61—21no—
189Q8×D61—21no—
190Q8×D61C2×D412yes—
191Q8×D61#4112yes—
192D4×D61—21no—
193D4×D61—21no—
194D4×D61—21no—
195D4×D61—21no—
196C2×D244C22×C411yescharacteristic
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61C2×D411yescharacteristic
201C2×C4×D61C2×D411yescharacteristic
202C2×C4×D61C2411yescharacteristic
203C2×Dic122—21no—
204C2×Dic122—21no—
205C2×Dic122C22×C411yescharacteristic
206C2×Dic122C22×C411yescharacteristic
207C22⋊#6923—42no—
208C22⋊#6923—81no—
209C22⋊#6923—81no—
210C2×#92420—21no—
211C2×#92420—21no—
212C4⋊#6923—24no—
213C4⋊#6923—24no—
214C4⋊#6923—21no—
215C4⋊#6923—21no—
216C4⋊#6923—21no—
217C4⋊#6923—21no—
218C4⋊#6923—21no—
219C4⋊#6923—21no—
220C4⋊#6923—42no—
221C4⋊#6923—81no—
222C4⋊#6923—81no—
223C4⋊#6923C2×D412yes—
224C4⋊#6923#4112yes—
225C4×#6923—24no—
226C4×#6923—24no—
227C4×#6923—21no—
228C4×#6923—21no—
229C4×#6923—42no—
230C4×#6923—81no—
231C4×#6923—81no—
232C4×#6923—81no—
233C4×#6923C2×D412yes—
234C4×#6923#4112yes—
235D61⋊C8—21no—
236D61⋊C8—21no—
237D61⋊C8—21no—
238D61⋊C8—21no—
239Q16×C61—22no—
240SD16×C61—22no—
241C2×C8×C61C22×C411yescharacteristic
242C2×C8×C61C22×C411yescharacteristic
243C4⋊C4×C61—21no—
244C4⋊C4×C61C22×C411yescharacteristic
245C22⋊C4×C61—21no—
246C22⋊C4×C61—21no—
247C42×C61—21no—
248C42×C61C22×C411yescharacteristic
249C22⋊Dic61—21no—
250C22⋊Dic61—21no—
251#11758202—22no—
252#11758202—22no—
253#11758201—22no—
254#11758200—22no—
255#11758198—21no—
256#11758198—21no—
257#11758198—21no—
258#11758198—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61C22×C411yescharacteristic
261#11758196—21no—
262#11758196—21no—
263#11758196—21no—
264C4×Dic61—21no—
265C4×Dic61—21no—
266C4×Dic61—21no—
267C4×Dic61C22×C411yescharacteristic
268C4×Dic61#4111yescharacteristic
269C4×Dic61#4111yescharacteristic
270C2×#92418C22×C411yescharacteristic
271C2×#92418C22×C411yescharacteristic
272Dic244—22no—
273#11758190—22no—
274C8×D61—21no—
275C8×D61—21no—
276C8×D61—21no—
277C8×D61—21no—
278C23×C61—21no—
279C22×D61—21no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61C22×D411yescharacteristic
287C2×#6923—21no—
288C2×#6923—21no—
289C2×#6923—21no—
290C2×#6923—21no—
291C2×#6923—22no—
292C2×#6923—21no—
293C2×#6923—21no—
294C2×#6923—22no—
295C2×#6923—21no—
296C2×#6923—21no—
297C2×#6923—21no—
298C2×#6923—21no—
299C2×#6923—41no—
300C2×#6923—41no—
301C2×#6923—41no—
302C2×#6923—41no—
303C2×#6923—41no—
304C2×#6923—41no—
305C2×#6923—41no—
306C2×#6923—41no—
307C2×#6923—41no—
308C2×#6923—41no—
309C2×#6923—84no—
310C2×#6923#12112yes—
311C2×#6923#12112yes—
312Q8×C61—21no—
313Q8×C61—21no—
314Q8×C61—21no—
315Q8×C61C4×D412yes—
316D4×C61—21no—
317D4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61C4×D411yescharacteristic
322C2×C4×C61C4×D411yescharacteristic
323C2×C4×C61C23×C411yescharacteristic
324C22⋊D61—41no—
325C22⋊D61—41no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61C4×D411yescharacteristic
330C2×Dic61C4×D411yescharacteristic
331C2×Dic61C2×#4111yescharacteristic
332D244—21no—
333D244—21no—
334C4×D61—22no—
335C4×D61—22no—
336C4×D61—21no—
337C4×D61—21no—
338C4×D61—21no—
339C4×D61—21no—
340C4×D61—41no—
341C4×D61—41no—
342C4×D61—41no—
343C4×D61—41no—
344C4×D61C22×D411yescharacteristic
345C4×D61C2×#4111yescharacteristic
346C4×D61C2×#4111yescharacteristic
347C4×D61C2×#4111yescharacteristic
348Dic122—21no—
349Dic122—22no—
350Dic122—22no—
351Dic122—21no—
352Dic122—21no—
353Dic122—41no—
354Dic122—41no—
355Dic122C4×D412yes—
356#92420—41no—
357#92420—41no—
358C8×C61—21no—
359C8×C61—21no—
360#92418—21no—
361#92418—21no—
362#21512—611nomaximal, Sylow
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61C2×C4×D411yescharacteristic
367C2×D61—41no—
368C2×D61—41no—
369C2×D61—41no—
370C2×D61—81no—
371C2×D61—81no—
372C2×D61—81no—
373C2×D61—81no—
374C2×D61C2×#12111yescharacteristic
375C2×D61#52511yescharacteristic
376C2×D61#57611yescharacteristic
377C2×D61#57711yescharacteristic
378C2×D61#57811yescharacteristic
379C2×D61#57811yescharacteristic
380#6923—22no—
381#6923—22no—
382#6923—41no—
383#6923—41no—
384#6923—42no—
385#6923—42no—
386#6923—81no—
387#6923—81no—
388C4×C61—21no—
389C4×C61—21no—
390C4×C61—22no—
391C4×C61—41no—
392C4×C61—41no—
393C4×C61C2×C4×D411yescharacteristic
394C4×C61C4×#4111yescharacteristic
395Dic61—21no—
396Dic61—21no—
397Dic61—22no—
398Dic61—41no—
399Dic61—41no—
400Dic61#52911yescharacteristic
401Dic61#53211yescharacteristic
402C2×#464—611no—
403C2×#440—611no—
404C2×C4×Q16—611no—
405#2326—611no—
406#2276—611no—
407#1983—611no—
408#1947—611no—
409#1928—611no—
410#1925—611no—
411#1880—611no—
412#1878—611no—
413#1803—611no—
414#1768—611no—
415#1763—611no—
416C4×#102—611no—
417C2×C61—81no—
418C2×C61C4×#12111yescharacteristic
419C2×C61#294711yescharacteristic
420C2×C61#295111yescharacteristic
421D61—81no—
422D61#304411yescharacteristic
423D61#304511yescharacteristic
424D61#312111yescharacteristic
425D61#312411yescharacteristic
426C22×Q16—611no—
427C22×SD16—611no—
428C2×#124—611no—
429C2×C4×Q8—611no—
430C2×C4×Q8—611no—
431C2×C4×Q8—611no—
432C2×C4×Q8—611no—
433C2×C4×D4—611no—
434#464—611no—
435#464—611no—
436#464—611no—
437#464—611no—
438#464—611no—
439#464—611no—
440#464—611no—
441#464#692311yescharacteristic, complemented
442#440—1224no—
443C4×Q16—1224no—
444C2×#107—611no—
445C2×#107—611no—
446C2×C4⋊C8—611no—
447C2×C4⋊C8—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#103—611no—
451C2×#103—611no—
452C2×#103—611no—
453C2×#102—611no—
454C2×#102—611no—
455C2×#102—611no—
456C2×#97—611no—
457C2×C4×C8—611no—
458#391—611no—
459#390—611no—
460#388—1221no—
461#388—1221no—
462#385—1221no—
463#385—1221no—
464#384—611no—
465C4×C4⋊C4—611no—
466C4×C4⋊C4—611no—
467C4×C4⋊C4—611no—
468C4×C4⋊C4—1221no—
469C4×C4⋊C4—1221no—
470C4×C4⋊C4—1221no—
471#376—611no—
472#376—1221no—
473#340—611no—
474#340—611no—
475#340—611no—
476#340—611no—
477#336—611no—
478#336—611no—
479C61#2151211yescharacteristic, complemented, Sylow
480C22×Q8—611no—
481C22×Q8—611no—
482C22×D4—611no—
483C23×C4—1221no—
484C2×Q16—611no—
485C2×Q16—611no—
486C2×Q16—611no—
487C2×Q16—1222no—
488C2×Q16—1222no—
489C2×Q16C2×#692311yescharacteristic, complemented
490C2×SD16—611no—
491C2×SD16—611no—
492C2×SD16—611no—
493C2×SD16—1222no—
494C2×SD16—1222no—
495C2×SD16C2×#692311yescharacteristic
496C22×C8—611no—
497C22×C8—611no—
498C22×C8—611no—
499C22×C8—611no—
500#124—611no—
501#124—611no—
502#124—611no—
503#124—1221no—
504#124—1221no—
505#124C2×#692311yescharacteristic
506C4×Q8—614no—
507C4×Q8—611no—
508C4×Q8—611no—
509C4×Q8—611no—
510C4×Q8—1221no—
511C4×Q8—1221no—
512C4×Q8—1222no—
513C4×Q8—1222no—
514C4×Q8—1222no—
515C4×Q8—1222no—
516C4×Q8—1222no—
517C4×Q8C2×#692311yescharacteristic, complemented
518C4×D4—1222no—
519C4×D4—1222no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—611no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C42—611no—
537C2×C42—611no—
538C2×C42—611no—
539C2×C42—1221no—
540C2×C42—1221no—
541C2×C42—1221no—
542C2×C42—1221no—
543C2×C42—1221no—
544C2×C42—1221no—
545C2×C42—1221no—
546#107—1222no—
547#107—1222no—
548C4⋊C8—611no—
549C4⋊C8—611no—
550C4⋊C8—611no—
551C4⋊C8—1221no—
552C4⋊C8—1221no—
553C4⋊C8C2×#692311yescharacteristic, complemented
554#103—611no—
555#103—611no—
556#103—611no—
557#103—1222no—
558#103—1222no—
559#103—1222no—
560#103—1222no—
561#103C2×#692311yescharacteristic, complemented
562#102—611no—
563#102—611no—
564#102—611no—
565#102—1222no—
566#102—1222no—
567#102C2×#692311yescharacteristic
568#97—1222no—
569C4×C8—1222no—
570#95—611no—
571#95—611no—
572#95—611no—
573#95—611no—
574#95—1221no—
575#95—1221no—
576#95—1221no—
577#95—1221no—
578#95—1221no—
579C24—1221no—
580C2×Q8—612no—
581C2×Q8—612no—
582C2×Q8—611no—
583C2×Q8—611no—
584C2×Q8—1221no—
585C2×Q8—1221no—
586C2×Q8—1221no—
587C2×Q8—1221no—
588C2×Q8—1221no—
589C2×Q8—1221no—
590C2×Q8—1221no—
591C2×Q8—1221no—
592C2×Q8C22×#692311yescharacteristic
593C2×Q8C22×#692311yescharacteristic
594C2×D4—611no—
595C2×D4—1221no—
596C2×D4—1221no—
597C2×D4—1221no—
598C2×D4—1221no—
599C2×D4—1221no—
600C2×D4C22×#692311yescharacteristic
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—4881no—
616C22×C4—4881no—
617C22×C4—2442no—
618Q16—22no—
619Q16—1222no—
620Q16—1222no—
621Q16—1222no—
622SD16—22no—
623SD16—1222no—
624SD16—1222no—
625SD16—1222no—
626C2×C8—611no—
627C2×C8—611no—
628C2×C8—1221no—
629C2×C8—1221no—
630C2×C8—1221no—
631C2×C8—1221no—
632C2×C8—1221no—
633C2×C8—1221no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8—1221no—
637C2×C8—1221no—
638C2×C8C22×#692311yescharacteristic
639C2×C8C22×#692311yescharacteristic
640C4⋊C4—21no—
641C4⋊C4—612no—
642C4⋊C4—612no—
643C4⋊C4—611no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—1221no—
647C4⋊C4—1221no—
648C4⋊C4—1221no—
649C4⋊C4—1224no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1224no—
655C4⋊C4—1221no—
656C4⋊C4—4881no—
657C4⋊C4—4881no—
658C4⋊C4—2442no—
659C4⋊C4C22×#692311yescharacteristic
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—1221no—
663C22⋊C4—1221no—
664C22⋊C4—1221no—
665C22⋊C4—1221no—
666C22⋊C4—1221no—
667C22⋊C4—1221no—
668C22⋊C4—4881no—
669C22⋊C4—4881no—
670C22⋊C4—2442no—
671C42—21no—
672C42—612no—
673C42—612no—
674C42—611no—
675C42—611no—
676C42—611no—
677C42—1221no—
678C42—1221no—
679C42—1221no—
680C42—1221no—
681C42—1224no—
682C42—1224no—
683C42—1221no—
684C42—4881no—
685C42—4881no—
686C42—4881no—
687C42—2442no—
688C42C22×#692311yescharacteristic
689C23—21no—
690C23—611no—
691C23—1221no—
692C23—2441no—
693C23—2441no—
694C23—2441no—
695C23—2441no—
696C23—2441no—
697C23—2441no—
698Q8—21no—
699Q8—21no—
700Q8—21no—
701Q8—612no—
702Q8—1222no—
703Q8—1222no—
704Q8—1221no—
705Q8—1221no—
706Q8—1221no—
707Q8—2441no—
708Q8—2441no—
709Q8D4×#692312yes—
710D4—21no—
711D4—21no—
712D4—1221no—
713D4—1221no—
714D4—2441no—
715D4—2441no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—611no—
720C2×C4—611no—
721C2×C4—611no—
722C2×C4—611no—
723C2×C4—611no—
724C2×C4—612no—
725C2×C4—612no—
726C2×C4—611no—
727C2×C4—611no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—1221no—
733C2×C4—1221no—
734C2×C4—1221no—
735C2×C4—1221no—
736C2×C4—1221no—
737C2×C4—1221no—
738C2×C4—1221no—
739C2×C4—1221no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1221no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1221no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—1221no—
749C2×C4—4884no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4D4×#692311yescharacteristic
765C2×C4D4×#692311yescharacteristic
766C2×C4C23×#692311yescharacteristic
767C8—21no—
768C8—21no—
769C8—1221no—
770C8—1221no—
771C8—2441no—
772C8—2441no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—611no—
777C22—611no—
778C22—611no—
779C22—611no—
780C22—611no—
781C22—611no—
782C22—4881no—
783C22—4881no—
784C22—4881no—
785C22—4881no—
786C22—2441no—
787C22—2441no—
788C22—2441no—
789C22C2×D4×#692311yescharacteristic
790C4—22no—
791C4—21no—
792C4—21no—
793C4—41no—
794C4—41no—
795C4—611no—
796C4—611no—
797C4—1222no—
798C4—1222no—
799C4—1222no—
800C4—1221no—
801C4—1221no—
802C4—4881no—
803C4—4881no—
804C4—2441no—
805C4—2441no—
806C4—2442no—
807C4—2442no—
808C4—2441no—
809C4—2441no—
810C4C2×D4×#692311yescharacteristic
811C4#41×#692311yescharacteristic
812C2—81no—
813C2—611no—
814C2—611no—
815C2—611no—
816C2—611no—
817C2—4881no—
818C2#121×#692311yescharacteristic
819C2#2146257711yescharacteristic
820C2#2146258111yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#464C4
socleC22×C61C2×C4×D4
prime radicalC2×D4×D61C23
cosocleC2×C4×D61C24
hypercenter#464#6923
hypocenterC61#21512
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. C2×Q16×#6923C2semidirect
4. #21462259C2semidirect
6. #21461930C2semidirect
7. #21461899C2semidirect
10. #21461813C2semidirect
11. #21461688C2semidirect
12. #21461608C2semidirect
13. #21461592C2semidirect
58. #16839987C4semidirect
59. #16839986C4semidirect
60. #16839985C4semidirect
61. #16839984C4semidirect
62. #16839983C4semidirect
63. #16839982C4semidirect
64. #16839981C4semidirect
68. C61×#464C4semidirect
124. C2×Dic244C2×C4semidirect
125. C2×#11758202C2×C4semidirect
126. C2×#11758202C2×C4semidirect
141. Q8×Dic61C2×C4semidirect
143. C4×Dic122C2×C4semidirect
145. #14519742C2×C4semidirect
152. C4⋊#92418C2×C4semidirect
153. #14519706C2×C4semidirect
154. #14519706C2×C4semidirect
155. #14519702C2×C4semidirect
156. #14519701C2×C4semidirect
157. #14519700C2×C4semidirect
161. C2×Q16×C61C2×C4semidirect
164. C4×Q8×C61C2×C4semidirect
165. C4⋊C8×C61C2×C4semidirect
166. #103×C61C2×C4semidirect
441. #464#6923semidirect
479. C61#21512semidirect
489. C2×Q16C2×#6923semidirect
517. C4×Q8C2×#6923semidirect
553. C4⋊C8C2×#6923semidirect
561. #103C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168408012
C2×Q16×#69232
#214623092
#214622592
#214619872
#214619302
#214618992
#214618962
#214618152
#214618132
#214616882
#214616082
#214615922
#102×#69232
#464×D612
#2151261