Finite Group Databasebeta

← #29646922

Subgroups — #29646922

Order 15616.

1004 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459381C211yesmaximal, characteristic
2#21454781C211yesmaximal, characteristic, complemented
3#21454388C211yesmaximal, characteristic, complemented
4#21444283C211yesmaximal, characteristic, complemented
5#21444282C211yesmaximal, characteristic, complemented
6#21444272C211yesmaximal, characteristic, complemented
7#21444255C211yesmaximal, characteristic, complemented
8#21444242C211yesmaximal, characteristic, complemented
9#21444233C211yesmaximal, characteristic, complemented
10#21444231C211yesmaximal, characteristic, complemented
11#21444220C211yesmaximal, characteristic, complemented
12#21444206C211yesmaximal, characteristic, complemented
13#21444203C211yesmaximal, characteristic, complemented
14D4⋊C8×D61C211yesmaximal, characteristic, complemented
15C61×#1489C211yesmaximal, characteristic, complemented
16C2×#14519785—21no—
17#16840484C411yescharacteristic
18#16840475C411yescharacteristic
19#16840471C411yescharacteristic
20#16840461—21no—
21#16840453C411yescharacteristic
22#16840451C411yescharacteristic
23#16840445—21no—
24#16840441—21no—
25#16840436—21no—
26#16840411C411yescharacteristic
27#16840407C411yescharacteristic
28#16840400C411yescharacteristic
29#16840316C2211yescharacteristic
30#16840299C2211yescharacteristic
31#16840296—21no—
32#16840296C2211yescharacteristic
33#16840292—21no—
34#16840271—21no—
35C4×#11758222C2211yescharacteristic
36C4×#11758224C2211yescharacteristic
37C4×D4×D61C2211yescharacteristic
38C2×#14519734—21no—
39#16839890—21no—
40#16839838—21no—
41#16839835—21no—
42#16839831—21no—
43#16839815C2211yescharacteristic, complemented
44#16839813C2211yescharacteristic
45#16839813C2211yescharacteristic, complemented
46#16839790—21no—
47#16839787—21no—
48#16839787—21no—
49#16839784C2211yescharacteristic
50#16839784C2211yescharacteristic, complemented
51C2×C4⋊#92418C2211yescharacteristic, complemented
52C4⋊C8×D61C2211yescharacteristic
53C4⋊C8×D61C2211yescharacteristic, complemented
54C4×#11758189C2211yescharacteristic, complemented
55C4×C8×D61C2211yescharacteristic
56#16839494C2211yescharacteristic, complemented
57#16839494C2211yescharacteristic, complemented
58Q8⋊#92418C2211yescharacteristic, complemented
59Q8⋊#92418C2211yescharacteristic, complemented
60#16839492C2211yescharacteristic, complemented
61#16839492C2211yescharacteristic, complemented
62#16839491C2211yescharacteristic
63#16839491C2211yescharacteristic
64D4⋊#92418C2211yescharacteristic
65D4⋊#92418C2211yescharacteristic
66#16839489C2211yescharacteristic
67#16839489C2211yescharacteristic
68C4×#41×C61C2211yescharacteristic
69C61×#423C2211yescharacteristic, complemented
70C4×M16×C61C2211yescharacteristic, complemented
71C61×Q8⋊C8C2211yescharacteristic, complemented
72C61×Q8⋊C8C2211yescharacteristic, complemented
73C61×D4⋊C8C2211yescharacteristic
74C61×D4⋊C8C2211yescharacteristic
75C2×#11758222D411yescharacteristic
76C2×#11758224C2×C411yescharacteristic
77C2×D4×D61C2×C411yescharacteristic
78C22×C4×D61—21no—
79#14519785—44no—
80C2×#11758189—21no—
81C2×#11758189—21no—
82C2×#11758189—21no—
83C22×#92418—21no—
84C2×C8×D61—21no—
85C2×C8×D61—21no—
86C2×C8×D61—21no—
87#14519776C2×C411yescharacteristic
88#14519775C2×C411yescharacteristic
89#14519772—21no—
90#14519772—21no—
91#14519771—21no—
92#14519771—21no—
93#14519771—21no—
94#14519770—21no—
95#14519769—21no—
96#14519769C2×C411yescharacteristic
97#14519768C2×C411yescharacteristic
98#14519767—21no—
99#14519767—21no—
100#14519766C2×C411yescharacteristic
101#14519765—21no—
102#14519765C2×C411yescharacteristic
103#14519763—21no—
104#14519762—21no—
105#14519762—21no—
106#14519761—21no—
107#14519760—21no—
108#14519760—21no—
109#14519760—21no—
110#14519759—21no—
111#14519758—21no—
112#14519757C2×C411yescharacteristic
113#14519756—21no—
114#14519756C2×C411yescharacteristic
115#14519755—21no—
116#14519755—21no—
117#14519754—21no—
118#14519754—21no—
119#14519753C2×C411yescharacteristic
120#14519753C2×C411yescharacteristic
121#14519752C2×C411yescharacteristic
122#14519751—21no—
123#14519751C2×C411yescharacteristic
124#14519750—21no—
125#14519749—21no—
126#14519749—21no—
127#14519747—21no—
128#14519745—21no—
129C4×Dic122—21no—
130C4×Dic122C2×C411yescharacteristic
131C4×Dic122D411yescharacteristic
132C4×Dic122C2311yescharacteristic
133#14519742C2×C411yescharacteristic
134C4×D244—21no—
135C4×D244C2×C411yescharacteristic
136C4×D244D411yescharacteristic
137C4×D244C2311yescharacteristic
138D4×Dic61C2×C411yescharacteristic
139D4×Dic61C2×C411yescharacteristic
140#14519739C2×C411yescharacteristic
141C4×C22⋊D61—21no—
142C4×C22⋊D61—21no—
143C4×C22⋊D61—21no—
144C4×C22⋊D61C2×C411yescharacteristic
145C4×C22⋊D61C2×C411yescharacteristic
146C4×C22⋊D61D411yescharacteristic
147C4×C22⋊D61D411yescharacteristic
148#14519737—21no—
149#14519737—21no—
150#14519736D411yescharacteristic
151#14519735C2×C411yescharacteristic
152#14519734—21no—
153#14519734—21no—
154#14519734—21no—
155#14519734—21no—
156#14519734—21no—
157#14519734—21no—
158#14519734—21no—
159#14519734D411yescharacteristic
160#14519734D411yescharacteristic
161#14519733—21no—
162C2×#11758196—21no—
163C2×#11758196—21no—
164C4⋊C4×D61C2×C411yescharacteristic
165C2×#11758198—21no—
166C2×#11758198—21no—
167C22⋊C4×D61—21no—
168C2×C4×Dic61—21no—
169C42×D61C2311yescharacteristic
170C42×D61C2311yescharacteristic
171C4⋊#92418—21no—
172C4⋊#92418—21no—
173C4⋊#92418C2311yescharacteristic
174C4⋊#92418C2311yescharacteristic
175#14519706—21no—
176#14519706—21no—
177#14519706—21no—
178#14519706—21no—
179#14519706—21no—
180#14519706—21no—
181C22⋊#92418—21no—
182#14519689—21no—
183#14519689—21no—
184#14519687—21no—
185C4×#92418C2311yescharacteristic
186C4×#92418C2311yescharacteristic
187C8×Dic61—21no—
188C2×#41×C61C2×C411yescharacteristic
189C2×M16×C61—21no—
190C2×M16×C61—21no—
191C4×Q8×C61C2×C411yescharacteristic
192C4×Q8×C61C2311yescharacteristic
193C4×D4×C61—21no—
194C4×D4×C61—21no—
195C4×D4×C61C2×C411yescharacteristic
196C4×D4×C61C2311yescharacteristic
197#117×C61—21no—
198#117×C61C2×C411yescharacteristic
199C2×C42×C61—21no—
200C2×C42×C61C2311yescharacteristic
201C4⋊C8×C61—21no—
202C4⋊C8×C61C2311yescharacteristic
203C4⋊C8×C61C2311yescharacteristic
204#97×C61—21no—
205C4×C8×C61C2311yescharacteristic
206C4×C8×C61C2311yescharacteristic
207C23×D61—21no—
208#41×C61—22no—
209#41×C61—41no—
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⋊D61—21no—
222C2×C22⋊D61C22⋊C411yescharacteristic
223C2×C22⋊D61C22⋊C411yescharacteristic
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227#11758224—22no—
228#11758224—41no—
229D4×D61—22no—
230D4×D61—41no—
231#11758222—22no—
232#11758222—22no—
233C2×D244—21no—
234C2×D244C22⋊C411yescharacteristic
235C2×D244C22×C411yescharacteristic
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—42no—
240C2×C4×D61—42no—
241C2×C4×D61C22×C411yescharacteristic
242C2×C4×D61C22×C411yescharacteristic
243C2×C4×D61C2×D411yescharacteristic
244C2×C4×D61C2×D411yescharacteristic
245C2×C4×D61C2×D411yescharacteristic
246C2×C4×D61C2×D411yescharacteristic
247C2×Dic122—21no—
248C2×Dic122C22⋊C411yescharacteristic
249C2×Dic122C22×C411yescharacteristic
250M16×C61—42no—
251M16×C61—42no—
252C2×C8×C61—21no—
253C2×C8×C61—21no—
254C2×C8×C61—21no—
255C2×C8×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61C22×C411yescharacteristic
259C4⋊C4×C61C22×C411yescharacteristic
260C22⋊C4×C61—21no—
261C22⋊C4×C61—21no—
262C22⋊C4×C61—21no—
263C42×C61—21no—
264C42×C61—21no—
265C42×C61—21no—
266C42×C61C22×C411yescharacteristic
267C42×C61C2×D411yescharacteristic
268C42×C61C2×D411yescharacteristic
269C42×C61C2411yescharacteristic
270C22⋊Dic61—21no—
271C22⋊Dic61—21no—
272C22⋊Dic61—21no—
273C22⋊Dic61C22⋊C411yescharacteristic
274C22⋊Dic61C22⋊C411yescharacteristic
275#11758198—21no—
276#11758198—21no—
277#11758198—21no—
278#11758198—21no—
279#11758198—21no—
280#11758198—21no—
281#11758198—21no—
282#11758198—21no—
283#11758198—21no—
284#11758198—21no—
285#11758198—21no—
286#11758198—21no—
287#11758198C22⋊C411yescharacteristic
288#11758198C22⋊C411yescharacteristic
289#11758198C22⋊C411yescharacteristic
290#11758198C22⋊C411yescharacteristic
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#11758196—21no—
308#11758196—21no—
309#11758196C22⋊C411yescharacteristic
310#11758196C22⋊C411yescharacteristic
311#11758196C22⋊C411yescharacteristic
312#11758196C22⋊C411yescharacteristic
313C4×Dic61—21no—
314C4×Dic61—21no—
315C4×Dic61—21no—
316C4×Dic61C22×C411yescharacteristic
317C4×Dic61C22×C411yescharacteristic
318C4×Dic61C2×D411yescharacteristic
319C4×Dic61C2×D411yescharacteristic
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C2×#92418—21no—
323C2×#92418—21no—
324C2×#92418—21no—
325C2×#92418—21no—
326C2×#92418—42no—
327#11758189—42no—
328#11758189—42no—
329#11758189—42no—
330C8×D61—42no—
331C8×D61—42no—
332C8×D61—42no—
333C23×C61—21no—
334C23×C61C2×C22⋊C411yescharacteristic
335C22×D61—21no—
336C22×D61—42no—
337C22×D61—42no—
338C22×D61—81no—
339C22×D61C2×C22⋊C411yescharacteristic
340C22×D61C2×C22⋊C411yescharacteristic
341Q8×C61—21no—
342Q8×C61—21no—
343D4×C61—21no—
344D4×C61—42no—
345D4×C61#13112yescomplemented
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—41no—
354C2×C4×C61—42no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—81no—
358C2×C4×C61C2×C22⋊C411yescharacteristic
359C2×C4×C61C2×C22⋊C411yescharacteristic
360C2×C4×C61C2×C22⋊C411yescharacteristic
361C2×C4×C61C23×C411yescharacteristic
362C2×C4×C61C22×D411yescharacteristic
363C2×C4×C61C22×D411yescharacteristic
364C22⋊D61—22no—
365C22⋊D61—22no—
366C22⋊D61—42no—
367C22⋊D61—42no—
368C22⋊D61—81no—
369C2×Dic61—21no—
370C2×Dic61—21no—
371C2×Dic61—21no—
372C2×Dic61—42no—
373C2×Dic61—42no—
374C2×Dic61—81no—
375C2×Dic61C2×C22⋊C411yescharacteristic
376C2×Dic61C2×C22⋊C411yescharacteristic
377C2×Dic61C2×C22⋊C411yescharacteristic
378C2×Dic61C2×C22⋊C411yescharacteristic
379C2×Dic61C2×C22⋊C411yescharacteristic
380C2×Dic61C2×C22⋊C411yescharacteristic
381D244—22no—
382D244—21no—
383D244—21no—
384D244—81no—
385C4×D61—21no—
386C4×D61—21no—
387C4×D61—21no—
388C4×D61—21no—
389C4×D61—21no—
390C4×D61—21no—
391C4×D61—41no—
392C4×D61—41no—
393C4×D61—42no—
394C4×D61—41no—
395C4×D61—41no—
396C4×D61—42no—
397C4×D61AGL(1,ℤ/8)12yes—
398C4×D61#13712yes—
399Dic122—22no—
400Dic122—21no—
401Dic122—21no—
402Dic122—81no—
403C8×C61—22no—
404C8×C61—41no—
405C8×C61—41no—
406C8×C61—41no—
407#92418—41no—
408#92418—41no—
409#92418—41no—
410#92418—41no—
411#17512—611nomaximal, Sylow
412C22×C61—22no—
413C22×C61—21no—
414C22×C61—21no—
415C22×C61—21no—
416C22×C61—41no—
417C22×C61—41no—
418C22×C61C22×C22⋊C411yescharacteristic
419C2×D61—21no—
420C2×D61—21no—
421C2×D61—21no—
422C2×D61—21no—
423C2×D61—21no—
424C2×D61—41no—
425C2×D61—41no—
426C2×D61—41no—
427C2×D61—84no—
428C2×D61#41712yes—
429C4×C61—21no—
430C4×C61—21no—
431C4×C61—21no—
432C4×C61—21no—
433C4×C61—41no—
434C4×C61—41no—
435C4×C61—41no—
436C4×C61C2×#13111yescharacteristic
437C4×C61#56811yescharacteristic
438C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
439C4×C61C2×#13711yescharacteristic
440Dic61—21no—
441Dic61—21no—
442Dic61—21no—
443Dic61—21no—
444Dic61—21no—
445Dic61—41no—
446Dic61—41no—
447Dic61—41no—
448Dic61#41712yes—
449#3475—611no—
450#2965—611no—
451#2906—611no—
452#1495—611no—
453#1495—611no—
454#1493—611no—
455#1489—611no—
456#1489D6111yescharacteristic, complemented
457#1486—611no—
458#1483—611no—
459#1483—611no—
460#1481—611no—
461#1477—611no—
462#1477—611no—
463C2×D4⋊C8—611no—
464C2×C61—42no—
465C2×C61—41no—
466C2×C61#288011yescharacteristic
467C2×C61C2×#41711yescharacteristic
468C2×C61#290111yescharacteristic
469D61—22no—
470D61—41no—
471D61—81no—
472C2×#131—1221no—
473#556—611no—
474#555—611no—
475#554—611no—
476#553—1221no—
477#552—611no—
478#552—611no—
479#552—1221no—
480#551—1221no—
481#551—1221no—
482#547—611no—
483#546—611no—
484#546—611no—
485#533—611no—
486#529—611no—
487#529—611no—
488#529—1221no—
489#529—1221no—
490#525—1221no—
491C4×#41—611no—
492C4×#41—611no—
493C4×#41C2×D6111yescharacteristic
494C2×C4×D4—611no—
495C2×#117—1221no—
496#446—1221no—
497#436—1221no—
498#435—1221no—
499#435—1221no—
500#431—611no—
501#431—611no—
502#431—611no—
503#424—1221no—
504#424—1221no—
505#424—1221no—
506#423—611no—
507#423—611no—
508#423C2×D6111yescharacteristic, complemented
509C2×C4⋊C8—611no—
510C2×C4⋊C8—611no—
511C2×C4⋊C8—611no—
512C4×M16—611no—
513C4×M16C2×D6111yescharacteristic, complemented
514C2×C4×C8—611no—
515Q8⋊C8—611no—
516Q8⋊C8—611no—
517Q8⋊C8—611no—
518Q8⋊C8—611no—
519Q8⋊C8—611no—
520Q8⋊C8—611no—
521Q8⋊C8C2×D6111yescharacteristic, complemented
522Q8⋊C8C2×D6111yescharacteristic, complemented
523D4⋊C8—611no—
524D4⋊C8—611no—
525D4⋊C8—611no—
526D4⋊C8—611no—
527D4⋊C8—611no—
528D4⋊C8—611no—
529D4⋊C8C2×D6111yescharacteristic
530D4⋊C8C2×D6111yescharacteristic
531C61#1751211yescharacteristic, complemented, Sylow
532C2×#41—611no—
533C2×#41—611no—
534C2×#41C4×D6111yescharacteristic
535C22×D4—611no—
536C23×C4—1221no—
537#131—2444no—
538C2×M16—21no—
539C2×M16—21no—
540C2×M16—1221no—
541C2×M16—1221no—
542C2×M16—1221no—
543C22×C8—1221no—
544C22×C8—1221no—
545C22×C8—1221no—
546C22×C8—1221no—
547C4⋊Q8—611no—
548C4⋊Q8—611no—
549#126—1221no—
550#126—1221no—
551#126—1221no—
552#126—1221no—
553#126—1221no—
554#126—1221no—
555#125—611no—
556#125—611no—
557#125—1221no—
558#125—1221no—
559#125—1221no—
560#124—611no—
561#124—611no—
562#124—1221no—
563#124—1221no—
564#123—1221no—
565#123—1221no—
566#123—1221no—
567#123—1221no—
568#123—1221no—
569#123—1221no—
570#123—1221no—
571#123—1221no—
572C22⋊Q8—611no—
573C22⋊Q8—611no—
574C22⋊Q8—611no—
575C22⋊Q8—611no—
576C22⋊Q8—1221no—
577C22⋊Q8—1221no—
578C22⋊Q8—1221no—
579C22⋊Q8—1221no—
580C22⋊Q8—1221no—
581#121—611no—
582#121—611no—
583#121—1221no—
584#121—1221no—
585#121—1221no—
586#121—1221no—
587#120—1221no—
588#120—1221no—
589C4×Q8—611no—
590C4×Q8—611no—
591C4×Q8—611no—
592C4×Q8—611no—
593C4×Q8—1221no—
594C4×Q8C4×D6111yescharacteristic
595C4×Q8C22×D6111yescharacteristic
596C4×D4—21no—
597C4×D4—21no—
598C4×D4—611no—
599C4×D4—611no—
600C4×D4—611no—
601C4×D4—611no—
602C4×D4—611no—
603C4×D4—611no—
604C4×D4—611no—
605C4×D4—611no—
606C4×D4—611no—
607C4×D4—611no—
608C4×D4—1221no—
609C4×D4—1221no—
610C4×D4—1221no—
611C4×D4—1221no—
612C4×D4—1221no—
613C4×D4—1221no—
614C4×D4C4×D6111yescharacteristic
615C4×D4C22×D6111yescharacteristic
616#117—21no—
617#117—611no—
618#117—611no—
619#117—611no—
620#117—611no—
621#117—1221no—
622#117—1221no—
623#117—1221no—
624#117—1221no—
625#117—1221no—
626#117—1221no—
627#117—1221no—
628#117—1221no—
629#117C4×D6111yescharacteristic
630C2×C4⋊C4—611no—
631C2×C4⋊C4—1221no—
632C2×C4⋊C4—1221no—
633C2×C22⋊C4—1221no—
634C2×C22⋊C4—1221no—
635C2×C22⋊C4—1221no—
636C2×C42—21no—
637C2×C42—611no—
638C2×C42—611no—
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⋊C8—1221no—
650C4⋊C8—1221no—
651C4⋊C8—1221no—
652C4⋊C8C22×D6111yescharacteristic
653C4⋊C8C22×D6111yescharacteristic
654C22⋊C8—1221no—
655C22⋊C8—1221no—
656C22⋊C8—1221no—
657#97—21no—
658#97—1221no—
659C4×C8—611no—
660C4×C8—611no—
661C4×C8—1221no—
662C4×C8C22×D6111yescharacteristic
663C4×C8C22×D6111yescharacteristic
664C24—1221no—
665#41—22no—
666#41—41no—
667#41—1222no—
668#41—1222no—
669#41—1222no—
670#41—2441no—
671C2×Q8—611no—
672C2×Q8—611no—
673C2×Q8—1221no—
674C2×Q8C2×C4×D6111yescharacteristic
675C2×D4—21no—
676C2×D4—611no—
677C2×D4—611no—
678C2×D4—611no—
679C2×D4—611no—
680C2×D4—1221no—
681C2×D4—1221no—
682C2×D4—1222no—
683C2×D4—1221no—
684C2×D4—1221no—
685C2×D4—2441no—
686C2×D4C2×C4×D6111yescharacteristic
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—611no—
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—611no—
694C22×C4—611no—
695C22×C4—611no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—2442no—
703C22×C4—2442no—
704C22×C4C2×C4×D6111yescharacteristic
705C22×C4D4×D6111yescharacteristic
706C22×C4D4×D6111yescharacteristic
707M16—42no—
708M16—42no—
709M16—2442no—
710M16—2442no—
711M16—2442no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—1221no—
717C2×C8—1221no—
718C2×C8—1221no—
719C2×C8—1221no—
720C2×C8—2442no—
721C2×C8—2442no—
722C2×C8—2442no—
723C2×C8—2442no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—611no—
727C4⋊C4—611no—
728C4⋊C4—611no—
729C4⋊C4—611no—
730C4⋊C4—611no—
731C4⋊C4—611no—
732C4⋊C4—611no—
733C4⋊C4—611no—
734C4⋊C4—1221no—
735C4⋊C4—1221no—
736C4⋊C4—1221no—
737C4⋊C4—1221no—
738C4⋊C4—1221no—
739C4⋊C4—1221no—
740C4⋊C4—1221no—
741C4⋊C4—1221no—
742C4⋊C4—1221no—
743C4⋊C4—1221no—
744C4⋊C4—1221no—
745C4⋊C4—1221no—
746C4⋊C4—1221no—
747C4⋊C4—1221no—
748C4⋊C4C2×C4×D6111yescharacteristic
749C4⋊C4C2×C4×D6111yescharacteristic
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—611no—
754C22⋊C4—611no—
755C22⋊C4—611no—
756C22⋊C4—611no—
757C22⋊C4—611no—
758C22⋊C4—611no—
759C22⋊C4—1221no—
760C22⋊C4—1221no—
761C22⋊C4—1221no—
762C22⋊C4—1221no—
763C22⋊C4—1221no—
764C22⋊C4—1221no—
765C22⋊C4—1221no—
766C22⋊C4—1221no—
767C22⋊C4—1221no—
768C22⋊C4—1221no—
769C22⋊C4—1221no—
770C22⋊C4—1221no—
771C22⋊C4—1221no—
772C22⋊C4—1221no—
773C22⋊C4—1221no—
774C42—21no—
775C42—21no—
776C42—21no—
777C42—611no—
778C42—611no—
779C42—611no—
780C42—611no—
781C42—611no—
782C42—611no—
783C42—1221no—
784C42—1221no—
785C42—1221no—
786C42C2×C4×D6111yescharacteristic
787C42D4×D6111yescharacteristic
788C42D4×D6111yescharacteristic
789C42C23×D6111yescharacteristic
790C23—21no—
791C23—611no—
792C23—611no—
793C23—1221no—
794C23—4881no—
795C23—2442no—
796C23—2442no—
797C23C22⋊C4×D6111yescharacteristic
798Q8—21no—
799Q8—21no—
800Q8—1222no—
801Q8—1221no—
802Q8—1221no—
803Q8—4881no—
804D4—21no—
805D4—42no—
806D4—1222no—
807D4—1222no—
808D4—1222no—
809D4—1221no—
810D4—1221no—
811D4—4881no—
812D4—4881no—
813D4—2442no—
814D4—2442no—
815D4#1451978512yescomplemented
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—81no—
828C2×C4—611no—
829C2×C4—612no—
830C2×C4—612no—
831C2×C4—611no—
832C2×C4—611no—
833C2×C4—611no—
834C2×C4—611no—
835C2×C4—611no—
836C2×C4—1221no—
837C2×C4—1221no—
838C2×C4—1221no—
839C2×C4—1221no—
840C2×C4—1221no—
841C2×C4—1221no—
842C2×C4—1221no—
843C2×C4—1221no—
844C2×C4—1221no—
845C2×C4—4881no—
846C2×C4—2441no—
847C2×C4—2441no—
848C2×C4—2442no—
849C2×C4—2442no—
850C2×C4—2442no—
851C2×C4—2442no—
852C2×C4—2441no—
853C2×C4—2441no—
854C2×C4C22⋊C4×D6111yescharacteristic
855C2×C4C22⋊C4×D6111yescharacteristic
856C2×C4C22⋊C4×D6111yescharacteristic
857C2×C4C22×C4×D6111yescharacteristic
858C2×C4C2×D4×D6111yescharacteristic
859C2×C4C2×D4×D6111yescharacteristic
860C8—22no—
861C8—41no—
862C8—41no—
863C8—41no—
864C8—2441no—
865C8—2441no—
866C8—2441no—
867C8—2441no—
868C22—21no—
869C22—21no—
870C22—22no—
871C22—21no—
872C22—41no—
873C22—41no—
874C22—612no—
875C22—1221no—
876C22—1221no—
877C22—1221no—
878C22—1221no—
879C22—1221no—
880C22—4884no—
881C22—2441no—
882C22—2441no—
883C22—2441no—
884C22C2×C22⋊C4×D6111yescharacteristic
885C4—21no—
886C4—21no—
887C4—21no—
888C4—21no—
889C4—41no—
890C4—41no—
891C4—41no—
892C4—612no—
893C4—1221no—
894C4—1221no—
895C4—1221no—
896C4—1221no—
897C4—1221no—
898C4—2441no—
899C4—2441no—
900C4—2441no—
901C4C2×#1451978511yescharacteristic
902C4#1684052811yescharacteristic
903C4AGL(1,ℤ/8)×D6111yescharacteristic
904C4#137×D6111yescharacteristic
905C2—41no—
906C2—42no—
907C2—1222no—
908C2—4881no—
909C2—2441no—
910C2#2145426911yescharacteristic
911C2#417×D6111yescharacteristic
912C2#2145436311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1489C2
socleC22×C61C22×C22⋊C4
prime radical#21459381C2
cosocleC42×C61C24
hypercenter#1489D61
hypocenterC61#17512
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1489

Complements

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

NH ≅ G/Ntype
2. #21454781C2semidirect
3. #21454388C2semidirect
4. #21444283C2semidirect
5. #21444282C2semidirect
6. #21444272C2semidirect
7. #21444255C2semidirect
8. #21444242C2semidirect
9. #21444233C2semidirect
10. #21444231C2semidirect
11. #21444220C2semidirect
12. #21444206C2semidirect
13. #21444203C2semidirect
14. D4⋊C8×D61C2semidirect
15. C61×#1489C2semidirect
43. #16839815C22semidirect
45. #16839813C22semidirect
50. #16839784C22semidirect
51. C2×C4⋊#92418C22semidirect
53. C4⋊C8×D61C22semidirect
54. C4×#11758189C22semidirect
56. #16839494C22semidirect
57. #16839494C22semidirect
58. Q8⋊#92418C22semidirect
59. Q8⋊#92418C22semidirect
60. #16839492C22semidirect
61. #16839492C22semidirect
69. C61×#423C22semidirect
70. C4×M16×C61C22semidirect
71. C61×Q8⋊C8C22semidirect
72. C61×Q8⋊C8C22semidirect
345. D4×C61#131semidirect
456. #1489D61semidirect
508. #423C2×D61semidirect
513. C4×M16C2×D61semidirect
521. Q8⋊C8C2×D61semidirect
522. Q8⋊C8C2×D61semidirect
531. C61#17512semidirect
815. D4#14519785semidirect

Maximal subgroups

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

subgroupindex
#214593812
#214547812
#214543882
#214442832
#214442822
#214442722
#214442552
#214442422
#214442332
#214442312
#214442202
#214442062
#214442032
D4⋊C8×D612
C61×#14892
#1751261