Finite Group Databasebeta

← #29646496

Subgroups — #29646496

Order 15616.

1138 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519824C211yesmaximal, characteristic
2#21454938C211yesmaximal, characteristic, complemented
3#21454783C211yesmaximal, characteristic, complemented
4#21444265C211yesmaximal, characteristic, complemented
5#21444264C211yesmaximal, characteristic, complemented
6#21444258C211yesmaximal, characteristic, complemented
7#21444255C211yesmaximal, characteristic, complemented
8#21444250C211yesmaximal, characteristic, complemented
9#21444249C211yesmaximal, characteristic, complemented
10#21444246C211yesmaximal, characteristic, complemented
11#21444212C211yesmaximal, characteristic, complemented
12#21444203C211yesmaximal, characteristic, complemented
13#21444198C211yesmaximal, characteristic, complemented
14Q8⋊C8×D61C211yesmaximal, characteristic, complemented
15C61×#1488C211yesmaximal, characteristic, complemented
16C2×#14519824C411yescharacteristic
17#16840245C411yescharacteristic
18#16840242—21no—
19#16840242C411yescharacteristic
20#16840241—21no—
21#16840241—21no—
22#16840241C411yescharacteristic
23#16840241C411yescharacteristic
24#16840239—21no—
25#16840239C411yescharacteristic
26#16840238C411yescharacteristic
27#16840238C411yescharacteristic
28C4×#11758222—21no—
29C4×#11758222C2211yescharacteristic
30C4×#11758224—21no—
31C4×#11758224—21no—
32C4×#11758224C2211yescharacteristic
33C4×#11758224C2211yescharacteristic
34C2×C4×Dic122—21no—
35C2×C4×Dic122C2211yescharacteristic
36C4×Q8×D61C2211yescharacteristic
37C4×Q8×D61C2211yescharacteristic
38#16839891—21no—
39#16839890—21no—
40#16839837—21no—
41#16839837—21no—
42#16839836—21no—
43#16839836—21no—
44#16839835—21no—
45#16839832—21no—
46#16839818C2211yescharacteristic
47#16839814C2211yescharacteristic
48#16839813C2211yescharacteristic
49#16839813C2211yescharacteristic
50#16839786C2211yescharacteristic
51#16839784C2211yescharacteristic
52C4⋊C8×D61C2211yescharacteristic
53C4×#11758194C2211yescharacteristic
54C4×#11758189C2211yescharacteristic
55C4×C8×D61C2211yescharacteristic
56#16839494C2211yescharacteristic
57#16839494C2211yescharacteristic
58#16839494C2211yescharacteristic
59#16839494C2211yescharacteristic
60Q8⋊#92418C2211yescharacteristic
61Q8⋊#92418C2211yescharacteristic
62#16839492C2211yescharacteristic
63#16839492C2211yescharacteristic
64#16839492C2211yescharacteristic
65#16839492C2211yescharacteristic
66D4⋊#92418C2211yescharacteristic
67D4⋊#92418C2211yescharacteristic
68C4×#41×C61C2211yescharacteristic
69C61×#432C2211yescharacteristic
70C61×#431C2211yescharacteristic
71C61×Q8⋊C8C2211yescharacteristic
72C61×Q8⋊C8C2211yescharacteristic
73C61×D4⋊C8C2211yescharacteristic
74C61×D4⋊C8C2211yescharacteristic
75#14519824—24no—
76#14519824—24no—
77C2×#11758222—21no—
78C2×#11758222C2×C411yescharacteristic
79C2×#11758224—21no—
80C2×#11758224—21no—
81C2×#11758224C2×C411yescharacteristic
82C2×#11758224C2×C411yescharacteristic
83C22×Dic122—21no—
84C22×Dic122C2×C411yescharacteristic
85C2×Q8×D61C2×C411yescharacteristic
86C2×Q8×D61C2×C411yescharacteristic
87C2×#11758194—21no—
88C2×#11758194—21no—
89C2×#11758189—21no—
90C2×#11758189—21no—
91C2×C8×D61—21no—
92C2×C8×D61—21no—
93Q8×Dic61C2×C411yescharacteristic
94Q8×Dic61C2×C411yescharacteristic
95C4×Dic122—21no—
96C4×Dic122—21no—
97C4×Dic122—21no—
98C4×Dic122—21no—
99C4×Dic122—21no—
100C4×Dic122—21no—
101C4×Dic122—21no—
102C4×Dic122—21no—
103C4×Dic122—21no—
104C4×Dic122C2×C411yescharacteristic
105C4×Dic122C2×C411yescharacteristic
106C4×Dic122D411yescharacteristic
107C4×Dic122D411yescharacteristic
108C4×Dic122C2311yescharacteristic
109C4×Dic122C2311yescharacteristic
110#14519742—21no—
111#14519742—21no—
112#14519742—21no—
113#14519742—21no—
114#14519742C2×C411yescharacteristic
115#14519742C2×C411yescharacteristic
116#14519742C2×C411yescharacteristic
117#14519742C2×C411yescharacteristic
118C4×D244—21no—
119C4×D244D411yescharacteristic
120C4×D244D411yescharacteristic
121D4×Dic61—21no—
122D4×Dic61—21no—
123D4×Dic61C2×C411yescharacteristic
124D4×Dic61C2×C411yescharacteristic
125C4×C22⋊D61—21no—
126C4×C22⋊D61—21no—
127C4×C22⋊D61—21no—
128C4×C22⋊D61—21no—
129C4×C22⋊D61D411yescharacteristic
130C4×C22⋊D61D411yescharacteristic
131C4×C22⋊D61D411yescharacteristic
132C4×C22⋊D61D411yescharacteristic
133#14519737—21no—
134#14519737—21no—
135#14519737—21no—
136#14519737—21no—
137#14519737—21no—
138#14519737—21no—
139#14519736—21no—
140#14519736C2×C411yescharacteristic
141#14519735—21no—
142#14519735—21no—
143#14519735C2×C411yescharacteristic
144#14519735C2×C411yescharacteristic
145#14519734—21no—
146#14519734—21no—
147#14519734C2×C411yescharacteristic
148#14519734C2×C411yescharacteristic
149#14519733—21no—
150#14519733—21no—
151#14519733—21no—
152#14519733—21no—
153#14519733—21no—
154#14519733—21no—
155C2×C4⋊Dic61—21no—
156C2×C4⋊Dic61C2×C411yescharacteristic
157C2×#11758196—21no—
158C2×#11758196—21no—
159C2×#11758196—21no—
160C4⋊C4×D61—21no—
161C4⋊C4×D61—21no—
162C4⋊C4×D61C2×C411yescharacteristic
163C4⋊C4×D61C2×C411yescharacteristic
164C2×C4×Dic61—21no—
165C2×C4×Dic61—21no—
166C2×C4×Dic61—21no—
167C42×D61—21no—
168C42×D61—21no—
169C42×D61C2311yescharacteristic
170C42×D61C2311yescharacteristic
171C4⋊#92418—21no—
172C4⋊#92418C2311yescharacteristic
173C4⋊#92418C2311yescharacteristic
174#14519706—21no—
175#14519706—21no—
176#14519706—21no—
177#14519706—21no—
178#14519689—21no—
179#14519689—21no—
180#14519689—21no—
181#14519689—21no—
182#14519688—21no—
183#14519687—21no—
184#14519687—21no—
185C4×#92418C2311yescharacteristic
186C4×#92418C2311yescharacteristic
187C8×Dic61—21no—
188C8×Dic61—21no—
189C2×#41×C61C2×C411yescharacteristic
190C4×Q8×C61C2×C411yescharacteristic
191C4×Q8×C61C2311yescharacteristic
192C4×D4×C61—21no—
193C4×D4×C61—21no—
194C4×D4×C61C2×C411yescharacteristic
195C4×D4×C61C2311yescharacteristic
196#117×C61—21no—
197#117×C61C2×C411yescharacteristic
198C2×C42×C61—21no—
199C2×C42×C61C2311yescharacteristic
200C4⋊C8×C61—21no—
201C4⋊C8×C61C2311yescharacteristic
202C4⋊C8×C61C2311yescharacteristic
203C22⋊C8×C61—21no—
204C22⋊C8×C61—21no—
205#97×C61—21no—
206C4×C8×C61C2311yescharacteristic
207C4×C8×C61C2311yescharacteristic
208#41×C61—22no—
209#41×C61—22no—
210C2×Q8×C61C22×C411yescharacteristic
211C2×D4×C61—21no—
212C2×D4×C61C22×C411yescharacteristic
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61C22×C411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C2×C22⋊D61C22⋊C411yescharacteristic
222C2×C22⋊D61C22⋊C411yescharacteristic
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229Q8×D61—22no—
230Q8×D61—22no—
231Q8×D61—22no—
232Q8×D61M1614yescomplemented
233#11758224—28no—
234#11758224—28no—
235#11758224—22no—
236#11758224—22no—
237#11758224—22no—
238#11758224M1614yescomplemented
239#11758222—28no—
240#11758222—22no—
241#11758222—22no—
242C2×D244C22⋊C411yescharacteristic
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61C22×C411yescharacteristic
248C2×C4×D61C22×C411yescharacteristic
249C2×C4×D61C2×D411yescharacteristic
250C2×C4×D61C2×D411yescharacteristic
251C2×C4×D61C2×D411yescharacteristic
252C2×C4×D61C2×D411yescharacteristic
253C2×Dic122—28no—
254C2×Dic122—21no—
255C2×Dic122—21no—
256C2×Dic122—21no—
257C2×Dic122—22no—
258C2×Dic122—22no—
259C2×Dic122C22⋊C411yescharacteristic
260C2×Dic122C22×C411yescharacteristic
261C2×Dic122C22×C411yescharacteristic
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61C22×C411yescharacteristic
269C4⋊C4×C61C22×C411yescharacteristic
270C22⋊C4×C61—21no—
271C22⋊C4×C61—21no—
272C22⋊C4×C61—21no—
273C42×C61—21no—
274C42×C61—21no—
275C42×C61—21no—
276C42×C61C22×C411yescharacteristic
277C42×C61C2×D411yescharacteristic
278C42×C61C2×D411yescharacteristic
279C42×C61C2411yescharacteristic
280C22⋊Dic61—21no—
281C22⋊Dic61—21no—
282C22⋊Dic61C22⋊C411yescharacteristic
283C22⋊Dic61C22⋊C411yescharacteristic
284#11758198—21no—
285#11758198—21no—
286#11758198C22⋊C411yescharacteristic
287#11758198C22⋊C411yescharacteristic
288#11758198C22⋊C411yescharacteristic
289#11758198C22⋊C411yescharacteristic
290C4⋊Dic61—21no—
291C4⋊Dic61—21no—
292C4⋊Dic61—21no—
293C4⋊Dic61C22⋊C411yescharacteristic
294C4⋊Dic61C22⋊C411yescharacteristic
295C4⋊Dic61C22×C411yescharacteristic
296C4⋊Dic61C22×C411yescharacteristic
297#11758196—21no—
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307#11758196C22⋊C411yescharacteristic
308#11758196C22⋊C411yescharacteristic
309#11758196C22⋊C411yescharacteristic
310#11758196C22⋊C411yescharacteristic
311C4×Dic61—21no—
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61—21no—
315C4×Dic61—21no—
316C4×Dic61—21no—
317C4×Dic61—21no—
318C4×Dic61—21no—
319C4×Dic61—21no—
320C4×Dic61—21no—
321C4×Dic61—21no—
322C4×Dic61—21no—
323C4×Dic61C22×C411yescharacteristic
324C4×Dic61C22×C411yescharacteristic
325C4×Dic61C2×D411yescharacteristic
326C4×Dic61C2×D411yescharacteristic
327C4×Dic61C2×D411yescharacteristic
328C4×Dic61C2×D411yescharacteristic
329#11758194—42no—
330#11758194—81no—
331C2×#92418—21no—
332C2×#92418—21no—
333C2×#92418—21no—
334C2×#92418—21no—
335#11758189—42no—
336#11758189—81no—
337C8×D61—42no—
338C8×D61—81no—
339C23×C61—21no—
340C23×C61C2×C22⋊C411yescharacteristic
341C22×D61C2×C22⋊C411yescharacteristic
342C22×D61C2×C22⋊C411yescharacteristic
343Q8×C61—21no—
344Q8×C61C2×M1612yes—
345D4×C61—24no—
346D4×C61—21no—
347D4×C61C2×M1612yes—
348C2×C4×C61—24no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—81no—
360C2×C4×C61C2×C22⋊C411yescharacteristic
361C2×C4×C61C2×C22⋊C411yescharacteristic
362C2×C4×C61C2×C22⋊C411yescharacteristic
363C2×C4×C61C23×C411yescharacteristic
364C2×C4×C61C22×D411yescharacteristic
365C2×C4×C61C22×D411yescharacteristic
366C22⋊D61—24no—
367C22⋊D61—22no—
368C22⋊D61—24no—
369C22⋊D61—22no—
370C2×Dic61—24no—
371C2×Dic61—24no—
372C2×Dic61—21no—
373C2×Dic61—21no—
374C2×Dic61—24no—
375C2×Dic61—21no—
376C2×Dic61—21no—
377C2×Dic61—81no—
378C2×Dic61—81no—
379C2×Dic61—81no—
380C2×Dic61C2×C22⋊C411yescharacteristic
381C2×Dic61C2×C22⋊C411yescharacteristic
382C2×Dic61C2×C22⋊C411yescharacteristic
383C2×Dic61C2×C22⋊C411yescharacteristic
384C2×Dic61C2×C22⋊C411yescharacteristic
385C2×Dic61C2×C22⋊C411yescharacteristic
386D244—22no—
387C4×D61—24no—
388C4×D61—24no—
389C4×D61—21no—
390C4×D61—21no—
391C4×D61—21no—
392C4×D61—21no—
393C4×D61—21no—
394C4×D61—21no—
395C4×D61—41no—
396C4×D61—41no—
397C4×D61—81no—
398C4×D61—81no—
399C4×D61C2×M1612yes—
400C4×D61C2×M1612yes—
401Dic122—24no—
402Dic122—24no—
403Dic122—21no—
404Dic122—21no—
405Dic122—22no—
406Dic122—24no—
407Dic122C2×M1612yes—
408Dic122C2×M1612yes—
409C8×C61—41no—
410C8×C61—41no—
411C8×C61—41no—
412C8×C61—41no—
413#92418—22no—
414#92418—41no—
415#92418—41no—
416#92418—41no—
417#17454—611nomaximal, Sylow
418C22×C61—21no—
419C22×C61—22no—
420C22×C61—21no—
421C22×C61—21no—
422C22×C61—41no—
423C22×C61—41no—
424C22×C61C22×C22⋊C411yescharacteristic
425C2×D61—21no—
426C2×D61—21no—
427C2×D61—21no—
428C2×D61—21no—
429C2×D61—21no—
430C2×D61#40712yes—
431C4×C61—21no—
432C4×C61—22no—
433C4×C61—21no—
434C4×C61—21no—
435C4×C61—21no—
436C4×C61—41no—
437C4×C61—41no—
438C4×C61C22×M1611yescharacteristic
439C4×C61C22×M1611yescharacteristic
440C4×C61#57711yescharacteristic
441C4×C61#57811yescharacteristic
442Dic61—21no—
443Dic61—22no—
444Dic61—22no—
445Dic61—21no—
446Dic61—21no—
447Dic61—21no—
448Dic61—21no—
449Dic61—41no—
450Dic61—41no—
451Dic61#40712yes—
452C4×2−1+4—611no—
453#2989—611no—
454#2965—611no—
455#1491—611no—
456#1491—611no—
457#1489—611no—
458#1489—611no—
459#1488—611no—
460#1488D6111yescharacteristic, complemented
461#1487—611no—
462#1487—611no—
463#1479—611no—
464#1477—611no—
465#1476—611no—
466C2×Q8⋊C8—611no—
467C2×C61—41no—
468C2×C61—42no—
469C2×C61C2×#40711yescharacteristic
470C2×C61#289811yescharacteristic
471C2×C61#290111yescharacteristic
472D61—22no—
473D61—41no—
474C2×2−1+4—611no—
475#520—611no—
476#520—611no—
477#520—611no—
478#520—611no—
479#520—1221no—
480#520—1221no—
481#520—1221no—
482#519—611no—
483#519—611no—
484#519—611no—
485#519—1221no—
486C4×#41—611no—
487C4×#41—611no—
488C4×#41—611no—
489C4×#41—1221no—
490C4×#41—1221no—
491C4×#41—1221no—
492C4×#41C2×D6111yescharacteristic
493C2×C4×Q8—611no—
494C2×C4×Q8—611no—
495C2×C4×Q8—611no—
496C2×C4×Q8—1221no—
497#446—1221no—
498#446—1221no—
499#436—1221no—
500#436—1221no—
501#435—1221no—
502#435—1221no—
503#435—1221no—
504#435—1221no—
505#432—611no—
506#432C2×D6111yescharacteristic
507#431—611no—
508#431—611no—
509#431—611no—
510#431C2×D6111yescharacteristic
511#423—611no—
512#423—611no—
513C2×C4⋊C8—611no—
514C4×M16—611no—
515C4×M16—611no—
516C2×C4×C8—611no—
517Q8⋊C8—611no—
518Q8⋊C8—611no—
519Q8⋊C8—611no—
520Q8⋊C8—611no—
521Q8⋊C8—611no—
522Q8⋊C8—611no—
523Q8⋊C8—611no—
524Q8⋊C8—611no—
525Q8⋊C8—611no—
526Q8⋊C8—611no—
527Q8⋊C8C2×D6111yescharacteristic
528Q8⋊C8C2×D6111yescharacteristic
529D4⋊C8—611no—
530D4⋊C8—611no—
531D4⋊C8C2×D6111yescharacteristic
532D4⋊C8C2×D6111yescharacteristic
533C61#1745411yescharacteristic, complemented, Sylow
5342−1+4—1224no—
5352−1+4—1224no—
536C2×#41—611no—
537C2×#41—611no—
538C2×#41—611no—
539C2×#41—1221no—
540C2×#41—1221no—
541C2×#41—1221no—
542C2×#41C4×D6111yescharacteristic
543C22×Q8—611no—
544C22×Q8—611no—
545C22×Q8—611no—
546C22×Q8—1221no—
547C2×M16—1221no—
548C2×M16—1221no—
549C2×M16—1221no—
550C2×M16—1221no—
551C22×C8—1221no—
552C22×C8—1221no—
553C4×Q8—611no—
554C4×Q8—611no—
555C4×Q8—611no—
556C4×Q8—611no—
557C4×Q8—611no—
558C4×Q8—611no—
559C4×Q8—611no—
560C4×Q8—611no—
561C4×Q8—611no—
562C4×Q8—611no—
563C4×Q8—611no—
564C4×Q8—611no—
565C4×Q8—1221no—
566C4×Q8—1221no—
567C4×Q8—1221no—
568C4×Q8—1221no—
569C4×Q8—1221no—
570C4×Q8—1221no—
571C4×Q8—1221no—
572C4×Q8—1221no—
573C4×Q8—1221no—
574C4×Q8—1221no—
575C4×Q8—1221no—
576C4×Q8—1221no—
577C4×Q8—1221no—
578C4×Q8C4×D6111yescharacteristic
579C4×Q8C22×D6111yescharacteristic
580C4×D4—21no—
581C4×D4—21no—
582C4×D4—611no—
583C4×D4—611no—
584C4×D4—611no—
585C4×D4—611no—
586C4×D4—611no—
587C4×D4—611no—
588C4×D4—611no—
589C4×D4—611no—
590C4×D4—1221no—
591C4×D4—1221no—
592C4×D4—1221no—
593C4×D4—1221no—
594C4×D4—1221no—
595C4×D4—1221no—
596C4×D4—1221no—
597C4×D4—1221no—
598C4×D4—1221no—
599C4×D4—1221no—
600C4×D4—1221no—
601C4×D4—1221no—
602C4×D4—1221no—
603C4×D4C4×D6111yescharacteristic
604C4×D4C22×D6111yescharacteristic
605#117—21no—
606#117—611no—
607#117—611no—
608#117—611no—
609#117—611no—
610#117—611no—
611#117—1221no—
612#117—1221no—
613#117—1221no—
614#117—1221no—
615#117—1221no—
616#117—1221no—
617#117—1221no—
618#117—1221no—
619#117—1221no—
620#117—1221no—
621#117—1221no—
622#117C4×D6111yescharacteristic
623C2×C4⋊C4—611no—
624C2×C4⋊C4—611no—
625C2×C4⋊C4—611no—
626C2×C4⋊C4—1221no—
627C2×C4⋊C4—1221no—
628C2×C4⋊C4—1221no—
629C2×C4⋊C4—1221no—
630C2×C4⋊C4—1221no—
631C2×C4⋊C4—1221no—
632C2×C42—21no—
633C2×C42—611no—
634C2×C42—611no—
635C2×C42—1221no—
636C2×C42—1221no—
637C2×C42—1221no—
638C2×C42—1221no—
639C2×C42—1221no—
640C2×C42C22×D6111yescharacteristic
641C4⋊C8—21no—
642C4⋊C8—611no—
643C4⋊C8—611no—
644C4⋊C8—1221no—
645C4⋊C8—1221no—
646C4⋊C8—1221no—
647C4⋊C8—1221no—
648C4⋊C8—1221no—
649C4⋊C8C22×D6111yescharacteristic
650C4⋊C8C22×D6111yescharacteristic
651C22⋊C8—21no—
652C22⋊C8—21no—
653C22⋊C8—1221no—
654C22⋊C8—1221no—
655C22⋊C8—1221no—
656C22⋊C8—1221no—
657#97—21no—
658#97—1221no—
659#97—1221no—
660#97—1221no—
661C4×C8—611no—
662C4×C8—611no—
663C4×C8—1221no—
664C4×C8—1221no—
665C4×C8C22×D6111yescharacteristic
666C4×C8C22×D6111yescharacteristic
667#41—22no—
668#41—22no—
669#41—614no—
670#41—1222no—
671#41—1222no—
672#41—1228no—
673#41—1222no—
674#41—1222no—
675#41—1228no—
676#41—1228no—
677#41—1222no—
678C2×Q8—611no—
679C2×Q8—614no—
680C2×Q8—611no—
681C2×Q8—611no—
682C2×Q8—1221no—
683C2×Q8—1221no—
684C2×Q8—1222no—
685C2×Q8—1222no—
686C2×Q8—1228no—
687C2×Q8—1222no—
688C2×Q8—1222no—
689C2×Q8—1222no—
690C2×Q8—1221no—
691C2×Q8C2×C4×D6111yescharacteristic
692C2×D4—21no—
693C2×D4—611no—
694C2×D4—611no—
695C2×D4—611no—
696C2×D4—1221no—
697C2×D4—1221no—
698C2×D4C2×C4×D6111yescharacteristic
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—611no—
703C22×C4—611no—
704C22×C4—611no—
705C22×C4—611no—
706C22×C4—611no—
707C22×C4—611no—
708C22×C4—1221no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4C2×C4×D6111yescharacteristic
719C22×C4D4×D6111yescharacteristic
720C22×C4D4×D6111yescharacteristic
721M16—4881no—
722M16—4881no—
723M16—2442no—
724M16—2442no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—1221no—
730C2×C8—1221no—
731C2×C8—1221no—
732C2×C8—1221no—
733C2×C8—4881no—
734C2×C8—2442no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—611no—
738C4⋊C4—611no—
739C4⋊C4—611no—
740C4⋊C4—611no—
741C4⋊C4—611no—
742C4⋊C4—611no—
743C4⋊C4—611no—
744C4⋊C4—611no—
745C4⋊C4—1221no—
746C4⋊C4—1221no—
747C4⋊C4—1221no—
748C4⋊C4—1221no—
749C4⋊C4—1221no—
750C4⋊C4—1221no—
751C4⋊C4—1221no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4C2×C4×D6111yescharacteristic
759C4⋊C4C2×C4×D6111yescharacteristic
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—21no—
763C22⋊C4—611no—
764C22⋊C4—611no—
765C22⋊C4—611no—
766C22⋊C4—611no—
767C22⋊C4—611no—
768C22⋊C4—611no—
769C22⋊C4—1221no—
770C22⋊C4—1221no—
771C22⋊C4—1221no—
772C22⋊C4—1221no—
773C42—21no—
774C42—21no—
775C42—21no—
776C42—611no—
777C42—611no—
778C42—611no—
779C42—611no—
780C42—611no—
781C42—611no—
782C42—1221no—
783C42—1221no—
784C42—1221no—
785C42—1221no—
786C42—1221no—
787C42—1221no—
788C42—1221no—
789C42—1221no—
790C42—1221no—
791C42—1221no—
792C42—1221no—
793C42—1221no—
794C42C2×C4×D6111yescharacteristic
795C42D4×D6111yescharacteristic
796C42D4×D6111yescharacteristic
797C42C23×D6111yescharacteristic
798C23—21no—
799C23—611no—
800C23—611no—
801C23C22⋊C4×D6111yescharacteristic
802Q8—21no—
803Q8—612no—
804Q8—612no—
805Q8—1222no—
806Q8—1224no—
807Q8—1224no—
808Q8—1224no—
809Q8—1221no—
810Q8—1221no—
811Q8M16×D6112yes—
812D4—24no—
813D4—21no—
814D4—1222no—
815D4—1222no—
816D4—1222no—
817D4—1224no—
818D4—1224no—
819D4M16×D6112yes—
820C2×C4—24no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—81no—
832C2×C4—611no—
833C2×C4—612no—
834C2×C4—612no—
835C2×C4—611no—
836C2×C4—611no—
837C2×C4—611no—
838C2×C4—611no—
839C2×C4—611no—
840C2×C4—1224no—
841C2×C4—1224no—
842C2×C4—1224no—
843C2×C4—1224no—
844C2×C4—1224no—
845C2×C4—1221no—
846C2×C4—1221no—
847C2×C4—1221no—
848C2×C4—1221no—
849C2×C4—1221no—
850C2×C4—1221no—
851C2×C4—1221no—
852C2×C4—1221no—
853C2×C4—1221no—
854C2×C4—1221no—
855C2×C4—4881no—
856C2×C4—4881no—
857C2×C4—4881no—
858C2×C4—4881no—
859C2×C4—4881no—
860C2×C4—2441no—
861C2×C4—2441no—
862C2×C4C22⋊C4×D6111yescharacteristic
863C2×C4C22⋊C4×D6111yescharacteristic
864C2×C4C22⋊C4×D6111yescharacteristic
865C2×C4C22×C4×D6111yescharacteristic
866C2×C4C2×D4×D6111yescharacteristic
867C2×C4C2×D4×D6111yescharacteristic
868C8—41no—
869C8—41no—
870C8—41no—
871C8—41no—
872C8—1222no—
873C8—2441no—
874C8—2441no—
875C8—2441no—
876C22—21no—
877C22—21no—
878C22—21no—
879C22—22no—
880C22—41no—
881C22—41no—
882C22—612no—
883C22—1221no—
884C22—1221no—
885C22—1221no—
886C22—1221no—
887C22—1221no—
888C22C2×C22⋊C4×D6111yescharacteristic
889C4—21no—
890C4—21no—
891C4—21no—
892C4—21no—
893C4—22no—
894C4—41no—
895C4—41no—
896C4—612no—
897C4—1221no—
898C4—1221no—
899C4—1221no—
900C4—1221no—
901C4—1221no—
902C4—1222no—
903C4—1222no—
904C4—2441no—
905C4—2441no—
906C4C2×M16×D6111yescharacteristic
907C4C2×M16×D6111yescharacteristic
908C4#1684056911yescharacteristic
909C4#1684057611yescharacteristic
910C2—41no—
911C2—42no—
912C2—1222no—
913C2—2441no—
914C2#407×D6111yescharacteristic
915C2#2145434811yescharacteristic
916C2#2145436511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1488C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519824C4
cosocleC42×C61C24
hypercenter#1488D61
hypocenterC61#17454
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1488

Complements

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

NH ≅ G/Ntype
2. #21454938C2semidirect
3. #21454783C2semidirect
4. #21444265C2semidirect
5. #21444264C2semidirect
6. #21444258C2semidirect
7. #21444255C2semidirect
8. #21444250C2semidirect
9. #21444249C2semidirect
10. #21444246C2semidirect
11. #21444212C2semidirect
12. #21444203C2semidirect
13. #21444198C2semidirect
14. Q8⋊C8×D61C2semidirect
15. C61×#1488C2semidirect
232. Q8×D61M16semidirect
238. #11758224M16semidirect
460. #1488D61semidirect
533. C61#17454semidirect

Maximal subgroups

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

subgroupindex
C4×#145198242
#214549382
#214547832
#214442652
#214442642
#214442582
#214442552
#214442502
#214442492
#214442462
#214442122
#214442032
#214441982
Q8⋊C8×D612
C61×#14882
#1745461