Finite Group Databasebeta

← #29647869

Subgroups — #29647869

Order 15616.

1066 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459662C211yesmaximal, characteristic
2#21454858C211yesmaximal, characteristic, complemented
3#21448723C211yesmaximal, characteristic, complemented
4#21444381C211yesmaximal, characteristic, complemented
5#21444377C211yesmaximal, characteristic, complemented
6#21444361C211yesmaximal, characteristic, complemented
7#21444360C211yesmaximal, characteristic, complemented
8#21444359C211yesmaximal, characteristic, complemented
9#21444324C211yesmaximal, characteristic, complemented
10#21444323C211yesmaximal, characteristic, complemented
11#21444322C211yesmaximal, characteristic, complemented
12#21444320C211yesmaximal, characteristic, complemented
13#21444316C211yesmaximal, characteristic, complemented
14#21444312C211yesmaximal, characteristic, complemented
15C61×#1513C211yesmaximal, characteristic, complemented
16#16840496—21no—
17#16840495—21no—
18#16840483C411yescharacteristic, complemented
19#16840480C411yescharacteristic, complemented
20#16840476C411yescharacteristic, complemented
21#16840475C411yescharacteristic, complemented
22#16840461—21no—
23#16840457—21no—
24#16840431C411yescharacteristic, complemented
25#16840430C411yescharacteristic, complemented
26#16840414C411yescharacteristic, complemented
27#16840411C411yescharacteristic, complemented
28#16840347—21no—
29#16840345—21no—
30#16840327—21no—
31#16840314C2211yescharacteristic
32#16840307C2211yescharacteristic
33#16840275C2211yescharacteristic
34#16840273C2211yescharacteristic
35#16840272C2211yescharacteristic
36#16840241—21no—
37C2×C4×C22⋊D61C2211yescharacteristic
38C2×#14519737—21no—
39#16839838—21no—
40#16839838—21no—
41#16839837—21no—
42#16839837—21no—
43#16839812C2211yescharacteristic
44#16839812C2211yescharacteristic
45#16839726C2211yescharacteristic
46#16839724C2211yescharacteristic
47#16839724C2211yescharacteristic
48#16839657—21no—
49#16839634—21no—
50#16839633—21no—
51#16839626C2211yescharacteristic
52#16839621C2211yescharacteristic
53#16839613C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55#95×D61C2211yescharacteristic
56#16839500C2211yescharacteristic
57#16839500C2211yescharacteristic
58#16839499C2211yescharacteristic
59#16839499C2211yescharacteristic
60#16839498C2211yescharacteristic
61#16839498C2211yescharacteristic
62#16839497C2211yescharacteristic
63#16839497C2211yescharacteristic
64#16839496C2211yescharacteristic
65#16839496C2211yescharacteristic
66#16839495C2211yescharacteristic
67#16839495C2211yescharacteristic
68C61×#525C2211yescharacteristic
69C61×#407C2211yescharacteristic
70C61×#380C2211yescharacteristic
71C61×#328C2211yescharacteristic
72C61×#328C2211yescharacteristic
73C61×#327C2211yescharacteristic
74C61×#327C2211yescharacteristic
75C2×#11758226C2×C411yescharacteristic, complemented
76C2×#11758222C2×C411yescharacteristic, complemented
77C2×#11758224—21no—
78C2×#11758224C2×C411yescharacteristic, complemented
79C22×C22⋊D61D411yescharacteristic
80C23×Dic61—21no—
81C22×C4×D61—21no—
82C22×C4×D61C2311yescharacteristic
83C2×#11758194—21no—
84C2×#11758189—21no—
85C2×#11758189—21no—
86#14519776C2×C411yescharacteristic, complemented
87#14519776C2×C411yescharacteristic, complemented
88#14519775C2×C411yescharacteristic, complemented
89#14519773—21no—
90#14519773—21no—
91#14519773C2×C411yescharacteristic, complemented
92#14519772—21no—
93#14519771—21no—
94#14519770—21no—
95#14519770—21no—
96#14519767—21no—
97#14519765—21no—
98#14519764—21no—
99#14519763—21no—
100#14519763—21no—
101#14519763—21no—
102#14519763—21no—
103#14519763—21no—
104#14519762—21no—
105#14519762—21no—
106#14519760—21no—
107#14519760—21no—
108#14519759—21no—
109#14519759—21no—
110#14519758—21no—
111#14519757C2×C411yescharacteristic, complemented
112#14519756C2×C411yescharacteristic, complemented
113#14519756C2311yescharacteristic
114#14519754—21no—
115#14519753C2×C411yescharacteristic, complemented
116#14519752C2×C411yescharacteristic, complemented
117#14519751—21no—
118#14519751C2×C411yescharacteristic, complemented
119#14519751C2311yescharacteristic
120#14519750—21no—
121#14519750—21no—
122#14519750—21no—
123#14519749—21no—
124#14519749—21no—
125#14519749—21no—
126#14519749—21no—
127#14519748—21no—
128#14519748C2×C411yescharacteristic, complemented
129#14519747—21no—
130#14519746—21no—
131#14519745—21no—
132Q8×Dic61C2×C411yescharacteristic, complemented
133C4×Dic122—21no—
134#14519742—21no—
135#14519742—21no—
136#14519742C2×C411yescharacteristic, complemented
137D4×Dic61—21no—
138D4×Dic61C2×C411yescharacteristic, complemented
139#14519739—21no—
140#14519739C2×C411yescharacteristic, complemented
141C4×C22⋊D61—21no—
142C4×C22⋊D61—21no—
143C4×C22⋊D61—21no—
144C4×C22⋊D61C2×C411yescharacteristic
145C4×C22⋊D61C2×C411yescharacteristic
146C4×C22⋊D61C2×C411yescharacteristic
147C4×C22⋊D61C2×C411yescharacteristic
148C4×C22⋊D61D411yescharacteristic
149C4×C22⋊D61D411yescharacteristic
150C4×C22⋊D61D411yescharacteristic
151C4×C22⋊D61D411yescharacteristic
152#14519737—21no—
153#14519737—21no—
154#14519737—21no—
155#14519737—21no—
156#14519737—44no—
157#14519736C2×C411yescharacteristic, complemented
158#14519735C2×C411yescharacteristic, complemented
159#14519735C2×C411yescharacteristic, complemented
160#14519734—21no—
161#14519733—21no—
162#14519733—21no—
163C2×#11758196—21no—
164C2×#11758196—21no—
165C2×#11758196—21no—
166C2×#11758196—21no—
167C2×#11758196D411yescharacteristic
168C4⋊C4×D61—21no—
169C2×C22⋊Dic61D411yescharacteristic
170C2×#11758198—21no—
171C2×#11758198D411yescharacteristic
172C2×C4×Dic61—21no—
173C2×C4×Dic61C2311yescharacteristic
174#14519706—21no—
175#14519706—21no—
176C22⋊#92418—21no—
177C22⋊#92418C2311yescharacteristic
178C22⋊#92418C2311yescharacteristic
179#14519689—21no—
180#14519689—21no—
181C8×Dic61—21no—
182C8×Dic61—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684—21no—
186#14519684C2311yescharacteristic
187#14519684C2311yescharacteristic
188C2×#41×C61C2×C411yescharacteristic, complemented
189C23×C4×C61C2311yescharacteristic
190C2×M16×C61—21no—
191#123×C61—21no—
192C22⋊Q8×C61C2×C411yescharacteristic, complemented
193C22⋊Q8×C61C2311yescharacteristic
194#121×C61C2×C411yescharacteristic, complemented
195#121×C61C2311yescharacteristic
196#120×C61—21no—
197C4×D4×C61—21no—
198C4×D4×C61—21no—
199#117×C61C2×C411yescharacteristic, complemented
200C2×C4⋊C4×C61—21no—
201C2×C22⋊C4×C61—21no—
202C22⋊C8×C61—21no—
203C22⋊C8×C61C2311yescharacteristic
204C22⋊C8×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206#95×C61C2311yescharacteristic
207C24×C61C2×D411yescharacteristic
208C23×D61C2×D411yescharacteristic
209#41×C61—81no—
210C2×Q8×C61C22×C411yescharacteristic
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61C22×C411yescharacteristic
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—81no—
219C22×C4×C61C22×C411yescharacteristic
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2411yescharacteristic
225C2×C22⋊D61—21no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—22no—
233C2×C22⋊D61—22no—
234C2×C22⋊D61C22⋊C411yescharacteristic
235C2×C22⋊D61C22⋊C411yescharacteristic
236C2×C22⋊D61C22⋊C411yescharacteristic
237C2×C22⋊D61C22⋊C411yescharacteristic
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—42no—
243C22×Dic61—42no—
244C22×Dic61—81no—
245C22×Dic61C2×D411yescharacteristic
246C22×Dic61C2×D411yescharacteristic
247C22×Dic61C2×D411yescharacteristic
248#11758226—81no—
249#11758224—42no—
250#11758224—42no—
251#11758224—81no—
252#11758222—81no—
253C2×D244—21no—
254C2×D244—21no—
255C2×D244C22×C411yescharacteristic
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61—42no—
260C2×C4×D61—42no—
261C2×C4×D61—81no—
262C2×C4×D61—81no—
263C2×C4×D61C22×C411yescharacteristic
264C2×C4×D61C22×C411yescharacteristic
265C2×C4×D61C2×D411yescharacteristic
266C2×C4×D61C2×D411yescharacteristic
267C2×Dic122—21no—
268C2×Dic122—21no—
269C2×Dic122C22×C411yescharacteristic
270M16×C61—81no—
271C2×C8×C61—21no—
272C2×C8×C61—21no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61—81no—
276C4⋊C4×C61C22×C411yescharacteristic
277C4⋊C4×C61C22×C411yescharacteristic
278C22⋊C4×C61—21no—
279C22⋊C4×C61—21no—
280C22⋊C4×C61—21no—
281C22⋊C4×C61—21no—
282C22⋊C4×C61—21no—
283C22⋊C4×C61—42no—
284C42×C61—21no—
285C22⋊Dic61—21no—
286C22⋊Dic61—21no—
287C22⋊Dic61—21no—
288C22⋊Dic61—21no—
289C22⋊Dic61—21no—
290C22⋊Dic61C22⋊C411yescharacteristic
291C22⋊Dic61C22⋊C411yescharacteristic
292C22⋊Dic61C22⋊C411yescharacteristic
293C22⋊Dic61C22⋊C411yescharacteristic
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—42no—
303#11758198C22⋊C411yescharacteristic
304#11758198C22⋊C411yescharacteristic
305#11758198C22⋊C411yescharacteristic
306#11758198C22⋊C411yescharacteristic
307C4⋊Dic61—21no—
308C4⋊Dic61—21no—
309C4⋊Dic61C22×C411yescharacteristic
310C4⋊Dic61C22×C411yescharacteristic
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196—42no—
320#11758196—42no—
321#11758196—81no—
322#11758196C22⋊C411yescharacteristic
323#11758196C22⋊C411yescharacteristic
324#11758196C22⋊C411yescharacteristic
325#11758196C22⋊C411yescharacteristic
326C4×Dic61—21no—
327C4×Dic61—21no—
328C4×Dic61—21no—
329C4×Dic61—21no—
330C4×Dic61—21no—
331C4×Dic61—42no—
332C4×Dic61C22×C411yescharacteristic
333C4×Dic61C22×C411yescharacteristic
334C4×Dic61C2×D411yescharacteristic
335C4×Dic61C2×D411yescharacteristic
336#11758194—81no—
337C2×#92418—21no—
338C2×#92418—21no—
339#11758189—81no—
340#11758189—81no—
341C23×C61—21no—
342C23×C61—21no—
343C23×C61—21no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61C2×C22⋊C411yescharacteristic
347C23×C61C2×C22⋊C411yescharacteristic
348C23×C61C22×D411yescharacteristic
349C22×D61—21no—
350C22×D61—21no—
351C22×D61—21no—
352C22×D61—41no—
353C22×D61—41no—
354C22×D61C2×C22⋊C411yescharacteristic
355C22×D61C2×C22⋊C411yescharacteristic
356Q8×C61—41no—
357D4×C61—41no—
358D4×C61—41no—
359D4×C61—41no—
360D4×C61—81no—
361D4×C61—81no—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—81no—
378C2×C4×C61C2×C22⋊C411yescharacteristic
379C2×C4×C61C2×C22⋊C411yescharacteristic
380C2×C4×C61C23×C411yescharacteristic
381C2×C4×C61C22×D411yescharacteristic
382C22⋊D61—22no—
383C22⋊D61—22no—
384C22⋊D61—22no—
385C22⋊D61—22no—
386C22⋊D61—41no—
387C22⋊D61—41no—
388C22⋊D61—42no—
389C22⋊D61—81no—
390C22⋊D61—81no—
391C22⋊D61—81no—
392C22⋊D61—81no—
393C22⋊D61—81no—
394C2×Dic61—22no—
395C2×Dic61—21no—
396C2×Dic61—21no—
397C2×Dic61—21no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—42no—
403C2×Dic61—41no—
404C2×Dic61—41no—
405C2×Dic61—41no—
406C2×Dic61—81no—
407C2×Dic61—84no—
408C2×Dic61C2×C22⋊C411yescharacteristic
409C2×Dic61C2×C22⋊C411yescharacteristic
410C2×Dic61C2×C22⋊C411yescharacteristic
411C2×Dic61C2×C22⋊C411yescharacteristic
412C2×Dic61C2×C22⋊C411yescharacteristic
413C2×Dic61C2×C22⋊C411yescharacteristic
414C2×Dic61AGL(1,ℤ/8)12yes—
415C2×Dic61#13712yes—
416D244—41no—
417D244—81no—
418D244—81no—
419C4×D61—41no—
420C4×D61—41no—
421C4×D61—41no—
422C4×D61—41no—
423C4×D61—42no—
424C4×D61—81no—
425C4×D61—81no—
426C4×D61—84no—
427Dic122—42no—
428Dic122—41no—
429Dic122—81no—
430C8×C61—41no—
431C8×C61—41no—
432#92418—41no—
433#92418—41no—
434#17630—611nomaximal, Sylow
435C22×C61—21no—
436C22×C61—21no—
437C22×C61—21no—
438C22×C61—21no—
439C22×C61—21no—
440C22×C61—21no—
441C22×C61—21no—
442C22×C61—21no—
443C22×C61—42no—
444C22×C61—42no—
445C22×C61—41no—
446C22×C61—41no—
447C22×C61—41no—
448C22×C61C22×C22⋊C411yescharacteristic
449C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
450C22×C61C2×#13711yescharacteristic
451C2×D61—21no—
452C2×D61—21no—
453C2×D61—21no—
454C2×D61—21no—
455C2×D61—21no—
456C2×D61—21no—
457C2×D61—42no—
458C2×D61—42no—
459C2×D61—41no—
460C2×D61—41no—
461C2×D61—41no—
462C4×C61—21no—
463C4×C61—21no—
464C4×C61—21no—
465C4×C61—21no—
466C4×C61—41no—
467C4×C61—41no—
468C4×C61—41no—
469C4×C61—81no—
470C4×C61—81no—
471Dic61—21no—
472Dic61—21no—
473Dic61—21no—
474Dic61—21no—
475Dic61—42no—
476Dic61—41no—
477Dic61—41no—
478Dic61—41no—
479Dic61—81no—
480Dic61#41712yes—
481Dic61#41712yes—
482#3506—611no—
483#2975—611no—
484#2349—611no—
485#1518—611no—
486#1517—611no—
487#1513—611no—
488#1513—611no—
489#1513—611no—
490#1513D6111yescharacteristic, complemented
491#1504—611no—
492#1504—611no—
493#1504—611no—
494#1504—611no—
495#1503—611no—
496#1502—611no—
497C2×C61—21no—
498C2×C61—21no—
499C2×C61—41no—
500C2×C61—41no—
501C2×C61—81no—
502C2×C61#288311yescharacteristic
503C2×C61C2×#41711yescharacteristic
504C2×C61#290111yescharacteristic
505D61—41no—
506D61—41no—
507D61—81no—
508#559—1221no—
509#559—1221no—
510#556—611no—
511#556—611no—
512#555—611no—
513#555—611no—
514#553—1221no—
515#553—1221no—
516#550—611no—
517#550—611no—
518#547—611no—
519#547—611no—
520#538—1221no—
521#538—1221no—
522#535—1221no—
523#533—611no—
524#532—611no—
525#525—611no—
526#525—611no—
527#525—611no—
528#525C2×D6111yescharacteristic
529#520—1221no—
530C2×C4×D4—611no—
531C2×C4×D4—1221no—
532#436—1221no—
533#436—1221no—
534#436—1221no—
535#436—1221no—
536#431—611no—
537#431—611no—
538#407—611no—
539#407—611no—
540#407—611no—
541#407C2×D6111yescharacteristic
542#389—1221no—
543#385—1221no—
544#385—1221no—
545#382—611no—
546#380—611no—
547#380C2×D6111yescharacteristic
548C4×C4⋊C4—611no—
549C2×#95—611no—
550C2×#95—611no—
551#328—611no—
552#328—611no—
553#328—611no—
554#328—611no—
555#328—611no—
556#328—611no—
557#328C2×D6111yescharacteristic
558#328C2×D6111yescharacteristic
559#327—611no—
560#327—611no—
561#327—611no—
562#327—611no—
563#327—611no—
564#327—611no—
565#327C2×D6111yescharacteristic
566#327C2×D6111yescharacteristic
567C61#1763011yescharacteristic, complemented, Sylow
568C2×#41—611no—
569C2×#41—611no—
570C2×#41—611no—
571C2×#41—1221no—
572C2×#41C4×D6111yescharacteristic, complemented
573C22×D4—611no—
574C23×C4—611no—
575C23×C4—1221no—
576C23×C4—1221no—
577C23×C4C22×D6111yescharacteristic
578C2×M16—21no—
579C2×M16—1221no—
580C2×M16—1221no—
581C2×M16—1221no—
582C4⋊Q8—611no—
583C4⋊Q8—611no—
584C4⋊Q8—611no—
585#127—611no—
586#127—1221no—
587#127—1221no—
588#126—1221no—
589#126—1221no—
590#126—1221no—
591#126—1221no—
592#125—1221no—
593#124—1221no—
594#124—1221no—
595#124—1221no—
596#124—1221no—
597#124—1221no—
598#124—1221no—
599#124—1221no—
600#123—21no—
601#123—1221no—
602#123—1221no—
603#123—1221no—
604#123—1221no—
605#123—1221no—
606#123—1221no—
607#123—1221no—
608C22⋊Q8—611no—
609C22⋊Q8—611no—
610C22⋊Q8—611no—
611C22⋊Q8—611no—
612C22⋊Q8—1221no—
613C22⋊Q8C4×D6111yescharacteristic, complemented
614C22⋊Q8C22×D6111yescharacteristic
615#121—611no—
616#121—611no—
617#121—611no—
618#121—611no—
619#121—1221no—
620#121—1221no—
621#121—1221no—
622#121—1221no—
623#121—1221no—
624#121—1221no—
625#121—1221no—
626#121—1221no—
627#121—1221no—
628#121C4×D6111yescharacteristic, complemented
629#121C22×D6111yescharacteristic
630#120—21no—
631#120—1221no—
632#120—1221no—
633#120—1221no—
634C4×Q8—611no—
635C4×Q8—611no—
636C4×Q8—1221no—
637C4×Q8—1221no—
638C4×Q8—1221no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—611no—
642C4×D4—611no—
643C4×D4—611no—
644C4×D4—611no—
645C4×D4—611no—
646C4×D4—611no—
647C4×D4—611no—
648C4×D4—611no—
649C4×D4—611no—
650C4×D4—611no—
651C4×D4—1221no—
652C4×D4—1221no—
653C4×D4—1221no—
654C4×D4—1221no—
655C4×D4—1221no—
656C4×D4—1221no—
657C4×D4—1221no—
658C4×D4—1221no—
659C4×D4—1221no—
660C4×D4—2444no—
661#117—611no—
662#117—611no—
663#117—611no—
664#117—1221no—
665#117—1221no—
666#117—1221no—
667#117C4×D6111yescharacteristic, complemented
668C2×C4⋊C4—21no—
669C2×C4⋊C4—611no—
670C2×C4⋊C4—1221no—
671C2×C4⋊C4—1221no—
672C2×C4⋊C4—1221no—
673C2×C4⋊C4—1221no—
674C2×C4⋊C4—1221no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—611no—
677C2×C22⋊C4—611no—
678C2×C22⋊C4—1221no—
679C2×C42—611no—
680C2×C42—1221no—
681C4⋊C8—1221no—
682C4⋊C8—1221no—
683C22⋊C8—21no—
684C22⋊C8—611no—
685C22⋊C8—611no—
686C22⋊C8—1221no—
687C22⋊C8—1221no—
688C22⋊C8—1221no—
689C22⋊C8C22×D6111yescharacteristic
690C22⋊C8C22×D6111yescharacteristic
691C4×C8—1221no—
692C4×C8—1221no—
693#95—611no—
694#95—611no—
695#95—1221no—
696#95—1221no—
697#95—1221no—
698#95C22×D6111yescharacteristic
699#95C22×D6111yescharacteristic
700C24—611no—
701C24D4×D6111yescharacteristic
702#41—81no—
703#41—4881no—
704#41—4881no—
705#41—4881no—
706#41—2442no—
707#41—2442no—
708C2×Q8—611no—
709C2×Q8—1221no—
710C2×Q8—1221no—
711C2×Q8C2×C4×D6111yescharacteristic
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—611no—
716C2×D4—611no—
717C2×D4—611no—
718C2×D4—611no—
719C2×D4—611no—
720C2×D4—1221no—
721C2×D4—1221no—
722C2×D4—1222no—
723C2×D4—1222no—
724C2×D4—1221no—
725C2×D4—1221no—
726C2×D4—1221no—
727C2×D4—1221no—
728C2×D4—1221no—
729C2×D4—1221no—
730C2×D4—1221no—
731C2×D4C2×C4×D6111yescharacteristic
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—81no—
736C22×C4—611no—
737C22×C4—611no—
738C22×C4—611no—
739C22×C4—611no—
740C22×C4—611no—
741C22×C4—611no—
742C22×C4—611no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—4881no—
751C22×C4—4881no—
752C22×C4—4881no—
753C22×C4—2442no—
754C22×C4—2442no—
755C22×C4—2442no—
756C22×C4—2442no—
757C22×C4C2×C4×D6111yescharacteristic
758C22×C4C2×C4×D6111yescharacteristic
759C22×C4D4×D6111yescharacteristic
760C22×C4D4×D6111yescharacteristic
761C22×C4D4×D6111yescharacteristic
762C22×C4C23×D6111yescharacteristic
763M16—81no—
764M16—4881no—
765M16—4881no—
766M16—4881no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—1221no—
770C2×C8—1221no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—81no—
774C4⋊C4—611no—
775C4⋊C4—611no—
776C4⋊C4—611no—
777C4⋊C4—611no—
778C4⋊C4—611no—
779C4⋊C4—611no—
780C4⋊C4—1221no—
781C4⋊C4—1221no—
782C4⋊C4—1221no—
783C4⋊C4—1221no—
784C4⋊C4—1221no—
785C4⋊C4—1221no—
786C4⋊C4—1221no—
787C4⋊C4—1221no—
788C4⋊C4—1221no—
789C4⋊C4—1221no—
790C4⋊C4—4881no—
791C4⋊C4—2442no—
792C4⋊C4—2442no—
793C4⋊C4C2×C4×D6111yescharacteristic
794C4⋊C4C2×C4×D6111yescharacteristic
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—42no—
801C22⋊C4—611no—
802C22⋊C4—611no—
803C22⋊C4—611no—
804C22⋊C4—611no—
805C22⋊C4—611no—
806C22⋊C4—611no—
807C22⋊C4—611no—
808C22⋊C4—611no—
809C22⋊C4—1221no—
810C22⋊C4—1221no—
811C22⋊C4—1221no—
812C22⋊C4—1221no—
813C22⋊C4—1221no—
814C22⋊C4—1221no—
815C22⋊C4—1221no—
816C22⋊C4—1221no—
817C22⋊C4—1221no—
818C22⋊C4—1221no—
819C22⋊C4—1221no—
820C22⋊C4—1221no—
821C22⋊C4—1221no—
822C22⋊C4—2442no—
823C42—21no—
824C42—611no—
825C42—611no—
826C42—611no—
827C42—611no—
828C42—1221no—
829C42—1221no—
830C42—1221no—
831C42—1221no—
832C42—1221no—
833C42—2442no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—41no—
838C23—41no—
839C23—611no—
840C23—611no—
841C23—1221no—
842C23—1221no—
843C23—1221no—
844C23—2441no—
845C23—2441no—
846C23C22⋊C4×D6111yescharacteristic
847C23C22⋊C4×D6111yescharacteristic
848C23C2×D4×D6111yescharacteristic
849Q8—41no—
850Q8—4881no—
851Q8—2441no—
852Q8—2442no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—1222no—
859D4—1222no—
860D4—1222no—
861D4—1222no—
862D4—4881no—
863D4—4881no—
864D4—4881no—
865D4—4881no—
866D4—4881no—
867D4—4881no—
868D4—4881no—
869D4—2441no—
870D4—2442no—
871D4—2441no—
872D4—2441no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—81no—
889C2×C4—611no—
890C2×C4—611no—
891C2×C4—612no—
892C2×C4—612no—
893C2×C4—611no—
894C2×C4—611no—
895C2×C4—611no—
896C2×C4—611no—
897C2×C4—1222no—
898C2×C4—1221no—
899C2×C4—1221no—
900C2×C4—1221no—
901C2×C4—4881no—
902C2×C4—4881no—
903C2×C4—4884no—
904C2×C4—4881no—
905C2×C4—4884no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2442no—
911C2×C4—2442no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4—2441no—
916C2×C4—2441no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4C22⋊C4×D6111yescharacteristic
920C2×C4C22⋊C4×D6111yescharacteristic
921C2×C4C22×C4×D6111yescharacteristic
922C2×C4C2×D4×D6111yescharacteristic
923C8—41no—
924C8—41no—
925C8—2441no—
926C8—2441no—
927C22—21no—
928C22—21no—
929C22—21no—
930C22—21no—
931C22—21no—
932C22—21no—
933C22—21no—
934C22—21no—
935C22—42no—
936C22—42no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—1221no—
941C22—1221no—
942C22—1221no—
943C22—1221no—
944C22—1221no—
945C22—1221no—
946C22—2442no—
947C22—2442no—
948C22—2441no—
949C22—2441no—
950C22—2441no—
951C22C2×C22⋊C4×D6111yescharacteristic
952C22AGL(1,ℤ/8)×D6111yescharacteristic
953C22#137×D6111yescharacteristic
954C4—21no—
955C4—21no—
956C4—21no—
957C4—21no—
958C4—41no—
959C4—41no—
960C4—41no—
961C4—81no—
962C4—81no—
963C4—612no—
964C4—612no—
965C4—1221no—
966C4—1221no—
967C4—1221no—
968C4—1221no—
969C4—4881no—
970C4—2442no—
971C4—2441no—
972C4—2441no—
973C4—2441no—
974C2—21no—
975C2—21no—
976C2—41no—
977C2—41no—
978C2—81no—
979C2—4881no—
980C2—2441no—
981C2—2441no—
982C2#2145427711yescharacteristic
983C2#417×D6111yescharacteristic
984C2#2145436511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1513C2
socleC22×C61C22×C22⋊C4
prime radical#21459662C2
cosocleC22×C4×C61C24
hypercenter#1513D61
hypocenterC61#17630
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1513

Complements

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

NH ≅ G/Ntype
2. #21454858C2semidirect
3. #21448723C2semidirect
4. #21444381C2semidirect
5. #21444377C2semidirect
6. #21444361C2semidirect
7. #21444360C2semidirect
8. #21444359C2semidirect
9. #21444324C2semidirect
10. #21444323C2semidirect
11. #21444322C2semidirect
12. #21444320C2semidirect
13. #21444316C2semidirect
14. #21444312C2semidirect
15. C61×#1513C2semidirect
18. #16840483C4semidirect
19. #16840480C4semidirect
20. #16840476C4semidirect
21. #16840475C4semidirect
24. #16840431C4semidirect
25. #16840430C4semidirect
26. #16840414C4semidirect
27. #16840411C4semidirect
75. C2×#11758226C2×C4semidirect
76. C2×#11758222C2×C4semidirect
78. C2×#11758224C2×C4semidirect
86. #14519776C2×C4semidirect
87. #14519776C2×C4semidirect
88. #14519775C2×C4semidirect
91. #14519773C2×C4semidirect
111. #14519757C2×C4semidirect
112. #14519756C2×C4semidirect
115. #14519753C2×C4semidirect
116. #14519752C2×C4semidirect
118. #14519751C2×C4semidirect
128. #14519748C2×C4semidirect
132. Q8×Dic61C2×C4semidirect
136. #14519742C2×C4semidirect
138. D4×Dic61C2×C4semidirect
140. #14519739C2×C4semidirect
157. #14519736C2×C4semidirect
158. #14519735C2×C4semidirect
159. #14519735C2×C4semidirect
188. C2×#41×C61C2×C4semidirect
192. C22⋊Q8×C61C2×C4semidirect
194. #121×C61C2×C4semidirect
199. #117×C61C2×C4semidirect
490. #1513D61semidirect
567. C61#17630semidirect
572. C2×#41C4×D61semidirect
613. C22⋊Q8C4×D61semidirect
628. #121C4×D61semidirect
667. #117C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214596622
#214548582
#214487232
#214443812
#214443772
#214443612
#214443602
#214443592
#214443242
#214443232
#214443222
#214443202
#214443162
#214443122
C61×#15132
#1763061