Finite Group Databasebeta

← #30620185

Subgroups — #30620185

Order 15616.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#11758213C211yesmaximal, characteristic, complemented
2C2×#16840759C211yesmaximal, characteristic, complemented
3C22×#14519841C211yesmaximal, characteristic, complemented
4#21462273C211yesmaximal, characteristic, complemented
5#21461984C211yesmaximal, characteristic, complemented
6#21461956C211yesmaximal, characteristic, complemented
7#21461839C211yesmaximal, characteristic, complemented
8#21461836C211yesmaximal, characteristic, complemented
9#21461802C211yesmaximal, characteristic, complemented
10#21461800C211yesmaximal, characteristic, complemented
11#21461691C211yesmaximal, characteristic, complemented
12#21461661C211yesmaximal, characteristic, complemented
13#21461660C211yesmaximal, characteristic, complemented
14#21461582C211yesmaximal, characteristic, complemented
15#21459303C211yesmaximal, characteristic
16C22×#11758213C2211yescharacteristic, complemented
17C22×#11758213C2211yescharacteristic, complemented
18C2×#14519856C2211yescharacteristic, complemented
19C22×C4×#6923C2211yescharacteristic, complemented
20#16840796—21no—
21#16840791—21no—
22#16840791—21no—
23D4×#92420—21no—
24#16840766C2211yescharacteristic, complemented
25#16840759—24no—
26C2×#14519842C2211yescharacteristic, complemented
27C2×#14519842C2211yescharacteristic, complemented
28C2×#14519842C2211yescharacteristic, complemented
29C2×#14519842C2211yescharacteristic, complemented
30C2×#14519841—24no—
31C2×#14519841C2211yescharacteristic
32C2×#14519841C2211yescharacteristic
33C2×#14519841C2211yescharacteristic
34C2×#14519841C2211yescharacteristic
35C2×#14519841C2211yescharacteristic, complemented
36C2×#14519841C2211yescharacteristic, complemented
37C2×#14519841C2211yescharacteristic, complemented
38C2×#14519841C2211yescharacteristic, complemented
39#16840733C2211yescharacteristic, complemented
40#16840733C2211yescharacteristic, complemented
41C4×#11758213C2211yescharacteristic, complemented
42#16840712—21no—
43#16840711—21no—
44#16840710—21no—
45#16840709—21no—
46C4×C4⋊#6923C2211yescharacteristic, complemented
47C4×C22⋊#6923C2211yescharacteristic, complemented
48C4×C22⋊#6923C2211yescharacteristic, complemented
49#16840698C2211yescharacteristic, complemented
50#16840632C2211yescharacteristic, complemented
51#16840632C2211yescharacteristic, complemented
52#16840632C2211yescharacteristic, complemented
53#16840632C2211yescharacteristic, complemented
54C22×#11758224C2211yescharacteristic
55C2×#41×D61C2211yescharacteristic
56#16840430C411yescharacteristic, complemented
57#16840425C411yescharacteristic, complemented
58#16840421C411yescharacteristic, complemented
59#16840420C411yescharacteristic, complemented
60#16840411C411yescharacteristic, complemented
61#16840410—21no—
62#16840407C411yescharacteristic, complemented
63#16840402—21no—
64#16840401—21no—
65D4×C22⋊D61C411yescharacteristic, complemented
66#16840394—21no—
67#16840311C2211yescharacteristic
68#16840307—21no—
69#16840275C2211yescharacteristic
70#16840272C2211yescharacteristic
71#16840270—21no—
72#16840268—21no—
73C4×#11758224C2211yescharacteristic
74C2×#14519737—21no—
75C4×D4×D61C2211yescharacteristic
76C61×#546C411yescharacteristic, complemented
77C23×#6923—21no—
78C2×#11758213—22no—
79C2×#11758213—22no—
80C2×#11758213—21no—
81C2×#11758213—21no—
82C2×#11758213—41no—
83C2×#11758213—41no—
84C2×#11758213C2311yescharacteristic
85C2×#11758213C2311yescharacteristic
86C2×#11758213C2311yescharacteristic
87C2×#11758213C2311yescharacteristic
88C22×#92420—21no—
89C22×#92420—21no—
90#14519856—22no—
91#14519856—41no—
92C2×C4⋊#6923—21no—
93C2×C4⋊#6923—21no—
94C2×C22⋊#6923—21no—
95C2×C22⋊#6923—21no—
96C2×C22⋊#6923—21no—
97C2×C4×#6923—22no—
98C2×C4×#6923—21no—
99C2×C4×#6923—41no—
100C2×C4×#6923C2311yescharacteristic
101C2×C4×#6923C2311yescharacteristic
102C2×C4×#6923C2311yescharacteristic
103C2×C4×#6923C2311yescharacteristic
104C4⋊#92420—21no—
105C4⋊#92420—21no—
106#14519842—22no—
107#14519842—22no—
108#14519842—41no—
109#14519842—41no—
110#14519841—22no—
111#14519841—22no—
112#14519841—22no—
113#14519841—22no—
114#14519841—22no—
115#14519841—41no—
116#14519841—41no—
117#14519841D414yescomplemented
118#14519834—21no—
119#14519834—21no—
120C22⋊#92420—21no—
121C22⋊#92420—21no—
122#14519832—21no—
123C4×#92420—21no—
124(C2×#6923)⋊C4—21no—
125(C2×#6923)⋊C4—21no—
126(C2×#6923)⋊C4—21no—
127(C2×#6923)⋊C4—21no—
128(C2×#6923)⋊C4—21no—
129C2×#11758226C2311yescharacteristic
130C2×#11758222—21no—
131C2×#11758222C2×C411yescharacteristic, complemented
132C2×#11758224—22no—
133C2×#11758224—22no—
134C2×#11758224—21no—
135C2×#11758224—21no—
136C2×#11758224—21no—
137C2×#11758224—41no—
138C2×#11758224—41no—
139C2×#11758224C2×C411yescharacteristic
140C2×#11758224C2×C411yescharacteristic
141C2×#11758224C2311yescharacteristic
142C2×#11758224C2311yescharacteristic
143#41×D61—22no—
144#41×D61—22no—
145#41×D61—41no—
146#41×D61—41no—
147C22×Dic122C2×C411yescharacteristic
148C2×Q8×D61C2×C411yescharacteristic, complemented
149C22×C22⋊D61—21no—
150C22×C22⋊D61—21no—
151C2×D4×D61—21no—
152C2×D4×D61C2×C411yescharacteristic, complemented
153C2×D4×D61D411yescharacteristic
154C23×Dic61—21no—
155C22×C4×D61—21no—
156C22×C4×D61C2311yescharacteristic
157C22×C4×D61C2311yescharacteristic
158#14519776—21no—
159#14519775C2×C411yescharacteristic, complemented
160#14519773—21no—
161#14519773C2×C411yescharacteristic, complemented
162#14519765C2×C411yescharacteristic, complemented
163#14519763—21no—
164#14519763—21no—
165#14519762—21no—
166#14519761—21no—
167#14519760—21no—
168#14519759—21no—
169#14519758—21no—
170#14519757C2×C411yescharacteristic, complemented
171#14519756C2×C411yescharacteristic, complemented
172#14519755—21no—
173#14519755—21no—
174#14519754—21no—
175#14519754—21no—
176#14519753C2×C411yescharacteristic
177#14519752C2×C411yescharacteristic
178#14519751—21no—
179#14519751C2×C411yescharacteristic
180#14519750—21no—
181#14519750—21no—
182#14519750—21no—
183#14519750—21no—
184#14519749—21no—
185#14519749—21no—
186#14519749—21no—
187#14519749—21no—
188#14519748C2×C411yescharacteristic, complemented
189#14519747—21no—
190#14519747—21no—
191#14519746—21no—
192#14519745—21no—
193#14519745—21no—
194C4×Dic122C2×C411yescharacteristic, complemented
195#14519742C2×C411yescharacteristic, complemented
196C4×D244C2×C411yescharacteristic
197D4×Dic61—21no—
198D4×Dic61C2×C411yescharacteristic, complemented
199D4×Dic61D411yescharacteristic
200#14519739—21no—
201#14519739D411yescharacteristic
202C4×C22⋊D61—21no—
203C4×C22⋊D61C2×C411yescharacteristic
204C4×C22⋊D61C2×C411yescharacteristic
205#14519737—21no—
206#14519737—21no—
207#14519737—21no—
208#14519737—21no—
209#14519737—21no—
210#14519737—21no—
211#14519737—21no—
212#14519737—21no—
213#14519737—21no—
214#14519737D411yescharacteristic
215#14519737D411yescharacteristic
216#14519735C2311yescharacteristic
217#14519733—21no—
218C2×#11758196—21no—
219C4⋊C4×D61D411yescharacteristic
220C2×#11758198—21no—
221C22⋊C4×D61D411yescharacteristic
222C22⋊C4×D61D411yescharacteristic
223C2×C4×Dic61—21no—
224C42×D61C2311yescharacteristic
225C2×#41×C61C2×C411yescharacteristic, complemented
226C22×D4×C61C2×C411yescharacteristic
227#124×C61C2×C411yescharacteristic, complemented
228#123×C61—21no—
229C22⋊Q8×C61C2×C411yescharacteristic
230#121×C61—21no—
231#121×C61C2×C411yescharacteristic, complemented
232#120×C61—21no—
233C4×D4×C61C2×C411yescharacteristic
234C4×D4×C61C2×C411yescharacteristic, complemented
235C2×C22⋊C4×C61—21no—
236C24×C61—21no—
237C23×D61—21no—
238C23×D61C2×D411yescharacteristic
239C23×D61C2×D411yescharacteristic
240C22×#6923—21no—
241C22×#6923—21no—
242C22×#6923—21no—
243C22×#6923—21no—
244C22×#6923—42no—
245C22×#6923—42no—
246C22×#6923—42no—
247#41×C61—22no—
248#41×C61—41no—
249C2×Q8×C61C22×C411yescharacteristic
250C2×D4×C61—22no—
251C2×D4×C61—21no—
252C2×D4×C61—21no—
253C2×D4×C61—21no—
254C2×D4×C61—41no—
255C2×D4×C61C22⋊C411yescharacteristic
256C2×D4×C61C22×C411yescharacteristic
257C2×D4×C61C22×C411yescharacteristic
258C22×C4×C61—21no—
259C22×C4×C61—21no—
260C22×C4×C61C22×C411yescharacteristic
261C22×C4×C61C22×C411yescharacteristic
262C2×C22⋊D61—21no—
263C2×C22⋊D61—21no—
264C2×C22⋊D61—21no—
265C2×C22⋊D61—21no—
266C2×C22⋊D61—21no—
267C2×C22⋊D61—21no—
268C2×C22⋊D61—21no—
269C2×C22⋊D61—21no—
270C2×C22⋊D61—21no—
271C2×C22⋊D61—21no—
272C2×C22⋊D61—42no—
273C2×C22⋊D61—42no—
274C2×C22⋊D61—44no—
275C2×C22⋊D61C22⋊C411yescharacteristic
276C2×C22⋊D61C22⋊C411yescharacteristic
277C22×Dic61—21no—
278C22×Dic61—21no—
279C22×Dic61—21no—
280C22×Dic61—21no—
281C22×Dic61—21no—
282C22×Dic61—21no—
283C22×Dic61—42no—
284C22×Dic61—42no—
285C22×Dic61C2×D411yescharacteristic
286C22×Dic61C2×D411yescharacteristic
287#11758226—21no—
288#11758226—21no—
289#11758226—21no—
290#11758226—21no—
291Q8×D61—22no—
292Q8×D61—41no—
293#11758224—22no—
294#11758224—21no—
295#11758224—21no—
296#11758224—21no—
297#11758224—21no—
298#11758224—21no—
299#11758224—21no—
300#11758224—22no—
301#11758224—41no—
302#11758224—41no—
303#11758224—42no—
304#11758224—42no—
305#11758224—42no—
306#11758224—42no—
307#11758224—42no—
308#11758224—42no—
309#11758224C2×D412yes—
310#11758224#4112yes—
311D4×D61—22no—
312D4×D61—41no—
313D4×D61—42no—
314D4×D61—42no—
315D4×D61—42no—
316#11758222—22no—
317#11758222—41no—
318#11758222—42no—
319#11758222—42no—
320C2×D244—21no—
321C2×D244—21no—
322C2×D244C22⋊C411yescharacteristic
323C2×D244C22×C411yescharacteristic
324C2×C4×D61—21no—
325C2×C4×D61—21no—
326C2×C4×D61—21no—
327C2×C4×D61—21no—
328C2×C4×D61—21no—
329C2×C4×D61—21no—
330C2×C4×D61—21no—
331C2×C4×D61—21no—
332C2×C4×D61—21no—
333C2×C4×D61—21no—
334C2×C4×D61—21no—
335C2×C4×D61—42no—
336C2×C4×D61—42no—
337C2×C4×D61C22×C411yescharacteristic
338C2×C4×D61C22×C411yescharacteristic
339C2×C4×D61C2×D411yescharacteristic
340C2×C4×D61C2×D411yescharacteristic
341C2×C4×D61C2×D411yescharacteristic
342C2×C4×D61C2×D411yescharacteristic
343C2×C4×D61C2×D411yescharacteristic
344C2×C4×D61C2×D411yescharacteristic
345C2×C4×D61C2411yescharacteristic
346C2×Dic122—22no—
347C2×Dic122—21no—
348C2×Dic122—21no—
349C2×Dic122—41no—
350C2×Dic122C22×C411yescharacteristic
351C2×Dic122C22×C411yescharacteristic
352C22⋊#6923—42no—
353C22⋊#6923—42no—
354C22⋊#6923—42no—
355C2×#92420—21no—
356C2×#92420—21no—
357C2×#92420—21no—
358C2×#92420—21no—
359C2×#92420—42no—
360C2×#92420—42no—
361C4⋊#6923—42no—
362C4⋊#6923—42no—
363C4×#6923—21no—
364C4×#6923—21no—
365C4×#6923—21no—
366C4×#6923—21no—
367C4×#6923—21no—
368C4×#6923—21no—
369C4×#6923—21no—
370C4×#6923—42no—
371C4×#6923C2×D412yescomplemented
372#11758213—21no—
373#11758213—21no—
374#11758213—21no—
375#11758213—21no—
376#11758213—21no—
377#11758213—21no—
378#11758213—21no—
379#11758213—42no—
380#11758213—42no—
381#11758213C2×D412yescomplemented
382C4⋊C4×C61—21no—
383C4⋊C4×C61C22⋊C411yescharacteristic
384C4⋊C4×C61C22×C411yescharacteristic
385C22⋊C4×C61—21no—
386C22⋊C4×C61—21no—
387C22⋊C4×C61—21no—
388C22⋊C4×C61—21no—
389C22⋊C4×C61—21no—
390C22⋊C4×C61C22⋊C411yescharacteristic
391C22⋊C4×C61C22⋊C411yescharacteristic
392C42×C61C22×C411yescharacteristic
393C22⋊Dic61—21no—
394C22⋊Dic61—21no—
395C22⋊Dic61—21no—
396C22⋊Dic61C22⋊C411yescharacteristic
397C22⋊Dic61C22⋊C411yescharacteristic
398#11758198—21no—
399#11758198—21no—
400#11758198—21no—
401#11758198—21no—
402#11758198—21no—
403#11758198—21no—
404#11758198—21no—
405#11758198C22⋊C411yescharacteristic
406#11758198C22⋊C411yescharacteristic
407#11758198C22⋊C411yescharacteristic
408#11758198C22⋊C411yescharacteristic
409C4⋊Dic61—21no—
410C4⋊Dic61C22⋊C411yescharacteristic
411C4⋊Dic61C22×C411yescharacteristic
412#11758196—21no—
413#11758196—21no—
414#11758196—21no—
415#11758196—21no—
416#11758196—21no—
417#11758196—21no—
418#11758196C22⋊C411yescharacteristic
419#11758196C22⋊C411yescharacteristic
420C4×Dic61—21no—
421C4×Dic61—21no—
422C4×Dic61—21no—
423C4×Dic61C22×C411yescharacteristic
424C4×Dic61C2×D411yescharacteristic
425C4×Dic61C2×D411yescharacteristic
426C23×C61—21no—
427C23×C61—21no—
428C23×C61—42no—
429C23×C61—42no—
430C23×C61—81no—
431C23×C61C2×C22⋊C411yescharacteristic
432C23×C61C2×C22⋊C411yescharacteristic
433C22×D61—22no—
434C22×D61—21no—
435C22×D61—21no—
436C22×D61—21no—
437C22×D61—21no—
438C22×D61—21no—
439C22×D61—41no—
440C22×D61—41no—
441C22×D61—41no—
442C22×D61—42no—
443C22×D61—42no—
444C22×D61—81no—
445C22×D61C2×C22⋊C411yescharacteristic
446C22×D61C2×C22⋊C411yescharacteristic
447C22×D61C22×D411yescharacteristic
448C2×#6923—22no—
449C2×#6923—22no—
450C2×#6923—41no—
451C2×#6923—41no—
452C2×#6923—41no—
453C2×#6923—48no—
454C2×#6923—41no—
455C2×#6923—41no—
456C2×#6923—41no—
457C2×#6923—41no—
458C2×#6923—41no—
459C2×#6923—41no—
460C2×#6923—41no—
461Q8×C61—21no—
462Q8×C61—21no—
463D4×C61—22no—
464D4×C61—21no—
465D4×C61—21no—
466D4×C61—21no—
467D4×C61—42no—
468D4×C61—42no—
469D4×C61—81no—
470D4×C61C4×D412yes—
471C2×C4×C61—21no—
472C2×C4×C61—21no—
473C2×C4×C61—21no—
474C2×C4×C61—21no—
475C2×C4×C61—21no—
476C2×C4×C61—21no—
477C2×C4×C61—42no—
478C2×C4×C61—81no—
479C2×C4×C61C2×C22⋊C411yescharacteristic
480C2×C4×C61C2×C22⋊C411yescharacteristic
481C2×C4×C61C2×C22⋊C411yescharacteristic
482C2×C4×C61C2×C22⋊C411yescharacteristic
483C2×C4×C61C23×C411yescharacteristic
484C22⋊D61—22no—
485C22⋊D61—22no—
486C22⋊D61—22no—
487C22⋊D61—41no—
488C22⋊D61—42no—
489C22⋊D61—42no—
490C22⋊D61—42no—
491C22⋊D61—42no—
492C22⋊D61—42no—
493C22⋊D61—42no—
494C22⋊D61—42no—
495C22⋊D61—41no—
496C22⋊D61—41no—
497C22⋊D61—81no—
498C2×Dic61—21no—
499C2×Dic61—21no—
500C2×Dic61—21no—
501C2×Dic61—22no—
502C2×Dic61—21no—
503C2×Dic61—21no—
504C2×Dic61—22no—
505C2×Dic61—21no—
506C2×Dic61—21no—
507C2×Dic61—42no—
508C2×Dic61—42no—
509C2×Dic61—42no—
510C2×Dic61—42no—
511C2×Dic61—41no—
512C2×Dic61—41no—
513C2×Dic61C2×C22⋊C411yescharacteristic
514C2×Dic61C2×C22⋊C411yescharacteristic
515C2×Dic61C2×C22⋊C411yescharacteristic
516C2×Dic61C2×C22⋊C411yescharacteristic
517C2×Dic61C22×D411yescharacteristic
518D244—21no—
519D244—21no—
520D244—41no—
521D244—41no—
522D244—41no—
523D244—81no—
524C4×D61—21no—
525C4×D61—21no—
526C4×D61—21no—
527C4×D61—21no—
528C4×D61—21no—
529C4×D61—21no—
530C4×D61—21no—
531C4×D61—21no—
532C4×D61—21no—
533C4×D61—21no—
534C4×D61—21no—
535C4×D61—21no—
536C4×D61—41no—
537C4×D61—41no—
538C4×D61—42no—
539C4×D61—42no—
540C4×D61—41no—
541C4×D61—41no—
542C4×D61C22×D411yescharacteristic
543C4×D61C2×#4111yescharacteristic
544C4×D61H(5,𝔽2)11yescharacteristic
545C4×D61H(5,𝔽2)11yescharacteristic
546Dic122—21no—
547Dic122—21no—
548Dic122—21no—
549Dic122—42no—
550Dic122—42no—
551Dic122C4×D412yes—
552#92420—22no—
553#92420—41no—
554#92420—41no—
555#92420—41no—
556#22434—611nomaximal, Sylow
557C22×C61—21no—
558C22×C61—21no—
559C22×C61—22no—
560C22×C61—21no—
561C22×C61—21no—
562C22×C61—21no—
563C22×C61—41no—
564C22×C61—41no—
565C22×C61—41no—
566C22×C61—41no—
567C22×C61—41no—
568C22×C61—84no—
569C22×C61#42112yescomplemented
570C22×C61C22×C22⋊C411yescharacteristic
571C2×D61—21no—
572C2×D61—21no—
573C2×D61—21no—
574C2×D61—21no—
575C2×D61—21no—
576C2×D61—21no—
577C2×D61—21no—
578C2×D61—21no—
579C2×D61—42no—
580C2×D61—42no—
581C2×D61—41no—
582C2×D61—41no—
583C2×D61—41no—
584C2×D61—81no—
585C2×D61—81no—
586C2×D61—84no—
587C2×D61D4211yescharacteristic
588C2×D61#54611yescharacteristic
589#6923—42no—
590#6923—42no—
591#6923—81no—
592#6923—81no—
593C4×C61—21no—
594C4×C61—21no—
595C4×C61—21no—
596C4×C61—21no—
597C4×C61—41no—
598C4×C61—41no—
599C4×C61C2×C4×D411yescharacteristic
600C4×C61#51811yescharacteristic
601Dic61—22no—
602Dic61—21no—
603Dic61—21no—
604Dic61—21no—
605Dic61—21no—
606Dic61—41no—
607Dic61—41no—
608Dic61D4211yescharacteristic
609Dic61#54611yescharacteristic
610D4×#41—611no—
611D4×M16—611no—
612C2×#421—611no—
613C22×#104—611no—
614#2290—611no—
615#1980—611no—
616#1963—611no—
617#1897—611no—
618#1896—611no—
619#1871—611no—
620#1871—611no—
621#1806—611no—
622#1789—611no—
623#1789—611no—
624#1759—611no—
625C2×C61—22no—
626C2×C61—41no—
627C2×C61—42no—
628C2×C61—81no—
629C2×C61D4×C22⋊C411yescharacteristic
630C2×C61C2×#42111yescharacteristic
631C2×C61#290111yescharacteristic
632D61—21no—
633D61—21no—
634D61—41no—
635D61—41no—
636D61—81no—
637C22×#41—611no—
638C22×#41—611no—
639C22×M16—611no—
640C22×M16—611no—
641#550—611no—
642D4×Q8—611no—
643#548—611no—
644#548—611no—
645#547—611no—
646#547—1221no—
647#546—611no—
648#546—1221no—
649#546—1221no—
650#546#692311yescharacteristic, complemented
651D42—611no—
652D42—1221no—
653#532—611no—
654#532—1221no—
655#525—611no—
656#525—611no—
657#525—1221no—
658#525—1221no—
659C4×#41—611no—
660C2×C4×D4—611no—
661C2×C4×D4—1221no—
662C2×#117—611no—
663C22×C42—611no—
664#436—1221no—
665#435—1221no—
666#435—1221no—
667C8×D4—1221no—
668#423—611no—
669#421—1224no—
670C2×#104—611no—
671C2×#104—611no—
672C2×#104—611no—
673C2×#104—611no—
674C2×#104—611no—
675C2×#104—611no—
676C2×#104—611no—
677C2×#104—611no—
678C2×#104—611no—
679C2×#104—611no—
680C2×#104—611no—
681C2×#104—611no—
682C2×#104—1224no—
683#407—611no—
684#407—611no—
685C4×M16—611no—
686#388—1221no—
687#387—1221no—
688#386—1221no—
689#385—1221no—
690C4×C4⋊C4—611no—
691C4×C22⋊C4—611no—
692C4×C22⋊C4—611no—
693#376—611no—
694#339—611no—
695#339—611no—
696#339—611no—
697#339—611no—
698C61#2243411yescharacteristic, complemented, Sylow
699C2×#41—611no—
700C2×#41—611no—
701C2×#41—611no—
702C2×#41—611no—
703C2×#41—611no—
704C2×#41—611no—
705C2×#41—1221no—
706C2×#41—1221no—
707C2×#41—1221no—
708C2×#41—1221no—
709C2×#41—1222no—
710C2×#41—1222no—
711C2×#41—1222no—
712C2×#41—1222no—
713C2×#41—2441no—
714C2×#41—2441no—
715C2×#41—2441no—
716C2×#41—2441no—
717C2×#41C2×#692311yescharacteristic, complemented
718C22×Q8—611no—
719C22×Q8—611no—
720C22×D4—611no—
721C22×D4—611no—
722C22×D4—1221no—
723C22×D4—1221no—
724C22×D4—1221no—
725C22×D4C2×#692311yescharacteristic
726C23×C4—611no—
727C23×C4—611no—
728C23×C4—1221no—
729C23×C4—1221no—
730C23×C4—1221no—
731C2×M16—611no—
732C2×M16—611no—
733C2×M16—611no—
734C2×M16—611no—
735C2×M16—1221no—
736C2×M16—1221no—
737C2×M16—1222no—
738C2×M16—1222no—
739C2×M16—2441no—
740C2×M16—2441no—
741C22×C8—1221no—
742C22×C8—1221no—
743C4⋊Q8—611no—
744C4⋊Q8—1221no—
745#127—611no—
746#127—1221no—
747#124—611no—
748#124—1221no—
749#124—1221no—
750#124C2×#692311yescharacteristic, complemented
751#123—21no—
752#123—1221no—
753#123—1221no—
754#123—1221no—
755#123—1221no—
756#123—1221no—
757C22⋊Q8—611no—
758C22⋊Q8—611no—
759C22⋊Q8—611no—
760C22⋊Q8—1221no—
761C22⋊Q8—1221no—
762C22⋊Q8—1221no—
763C22⋊Q8—1221no—
764C22⋊Q8C2×#692311yescharacteristic
765#121—21no—
766#121—611no—
767#121—611no—
768#121—611no—
769#121—1221no—
770#121—1221no—
771#121—1221no—
772#121—1221no—
773#121—1221no—
774#121—1221no—
775#121—1221no—
776#121—1221no—
777#121—1221no—
778#121C2×#692311yescharacteristic, complemented
779#120—21no—
780#120—1221no—
781#120—1221no—
782#120—1221no—
783#120—1221no—
784#120—1221no—
785C4×Q8—611no—
786C4×Q8—611no—
787C4×D4—611no—
788C4×D4—611no—
789C4×D4—611no—
790C4×D4—611no—
791C4×D4—611no—
792C4×D4—611no—
793C4×D4—611no—
794C4×D4—611no—
795C4×D4—1221no—
796C4×D4—1221no—
797C4×D4—1221no—
798C4×D4—1221no—
799C4×D4—1221no—
800C4×D4—1221no—
801C4×D4—1221no—
802C4×D4—1221no—
803C4×D4—1221no—
804C4×D4—1221no—
805C4×D4—1221no—
806C4×D4—1221no—
807C4×D4C2×#692311yescharacteristic
808C4×D4C2×#692311yescharacteristic, complemented
809#117—611no—
810#117—1221no—
811#117—1222no—
812#117—2441no—
813C2×C4⋊C4—611no—
814C2×C4⋊C4—1221no—
815C2×C4⋊C4—1221no—
816C2×C4⋊C4—1221no—
817C2×C22⋊C4—21no—
818C2×C22⋊C4—611no—
819C2×C22⋊C4—611no—
820C2×C22⋊C4—1221no—
821C2×C22⋊C4—1221no—
822C2×C22⋊C4—1221no—
823C2×C22⋊C4—1221no—
824C2×C42—611no—
825C2×C42—611no—
826C2×C42—611no—
827C2×C42—611no—
828C2×C42—611no—
829C2×C42—1221no—
830C2×C42—1222no—
831C2×C42—1221no—
832C2×C42—2441no—
833C4⋊C8—1221no—
834C4⋊C8—1221no—
835#104—614no—
836#104—1222no—
837#104—1222no—
838#104—1222no—
839#104—1222no—
840#104—1222no—
841#104—1222no—
842#104—1222no—
843#104—2441no—
844#104—2441no—
845#104—2441no—
846#104—2441no—
847C22⋊C8—1221no—
848C22⋊C8—1221no—
849C22⋊C8—1221no—
850C22⋊C8—1221no—
851#97—1221no—
852C4×C8—1221no—
853#95—1221no—
854#95—1221no—
855#95—1221no—
856#95—1221no—
857#95—1221no—
858C24—21no—
859C24—611no—
860C24—611no—
861C24—1221no—
862#41—22no—
863#41—41no—
864#41—612no—
865#41—612no—
866#41—1222no—
867#41—1221no—
868#41—1221no—
869#41—1221no—
870#41—1221no—
871#41—1221no—
872#41—1221no—
873#41—1221no—
874#41—1221no—
875#41—1221no—
876#41—1221no—
877#41—1222no—
878#41—1222no—
879#41—2441no—
880#41—2442no—
881#41—2442no—
882#41—2442no—
883#41—2442no—
884#41—2442no—
885#41—2442no—
886#41—2441no—
887#41—2441no—
888#41—2442no—
889#41—2442no—
890C2×Q8—611no—
891C2×Q8—611no—
892C2×Q8—1221no—
893C2×Q8—1222no—
894C2×Q8—1221no—
895C2×Q8—1222no—
896C2×Q8—2441no—
897C2×Q8—2441no—
898C2×Q8C22×#692311yescharacteristic
899C2×D4—22no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—41no—
904C2×D4—611no—
905C2×D4—611no—
906C2×D4—611no—
907C2×D4—611no—
908C2×D4—1221no—
909C2×D4—1221no—
910C2×D4—1221no—
911C2×D4—1221no—
912C2×D4—1221no—
913C2×D4—1221no—
914C2×D4—1222no—
915C2×D4—1221no—
916C2×D4—1221no—
917C2×D4—1221no—
918C2×D4—1221no—
919C2×D4—1221no—
920C2×D4—1221no—
921C2×D4—2441no—
922C2×D4—2442no—
923C2×D4—2442no—
924C2×D4—2442no—
925C2×D4—2442no—
926C2×D4—2442no—
927C2×D4—2444no—
928C2×D4C22⋊#692311yescharacteristic
929C2×D4C22×#692311yescharacteristic
930C2×D4C22×#692311yescharacteristic
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—611no—
934C22×C4—611no—
935C22×C4—611no—
936C22×C4—611no—
937C22×C4—611no—
938C22×C4—611no—
939C22×C4—611no—
940C22×C4—611no—
941C22×C4—611no—
942C22×C4—611no—
943C22×C4—611no—
944C22×C4—1221no—
945C22×C4—1221no—
946C22×C4—1221no—
947C22×C4—1221no—
948C22×C4—1221no—
949C22×C4—1221no—
950C22×C4—1221no—
951C22×C4—1221no—
952C22×C4—1221no—
953C22×C4—1221no—
954C22×C4—1221no—
955C22×C4—1221no—
956C22×C4—1221no—
957C22×C4—1221no—
958C22×C4—1221no—
959C22×C4—1221no—
960C22×C4—1221no—
961C22×C4—1221no—
962C22×C4—1221no—
963C22×C4—1221no—
964C22×C4—1221no—
965C22×C4—2442no—
966C22×C4—2442no—
967C22×C4—2442no—
968C22×C4—2442no—
969C22×C4—2442no—
970C22×C4—2442no—
971C22×C4—2442no—
972C22×C4C22×#692311yescharacteristic
973C22×C4C22×#692311yescharacteristic
974M16—612no—
975M16—1221no—
976M16—1221no—
977M16—1221no—
978M16—1221no—
979M16—1221no—
980M16—1221no—
981M16—1221no—
982M16—2442no—
983M16—2442no—
984C2×C8—1221no—
985C2×C8—1221no—
986C2×C8—1221no—
987C2×C8—1221no—
988C2×C8—2442no—
989C2×C8—2442no—
990C4⋊C4—21no—
991C4⋊C4—611no—
992C4⋊C4—611no—
993C4⋊C4—611no—
994C4⋊C4—611no—
995C4⋊C4—1221no—
996C4⋊C4—1221no—
997C4⋊C4—1221no—
998C4⋊C4—1221no—
999C4⋊C4—1221no—
1000C4⋊C4—1221no—
1001C4⋊C4—1221no—
1002C4⋊C4—2442no—
1003C4⋊C4—2442no—
1004C4⋊C4C22⋊#692311yescharacteristic
1005C4⋊C4C22×#692311yescharacteristic
1006C22⋊C4—21no—
1007C22⋊C4—21no—
1008C22⋊C4—21no—
1009C22⋊C4—21no—
1010C22⋊C4—21no—
1011C22⋊C4—611no—
1012C22⋊C4—611no—
1013C22⋊C4—611no—
1014C22⋊C4—611no—
1015C22⋊C4—611no—
1016C22⋊C4—611no—
1017C22⋊C4—1221no—
1018C22⋊C4—1221no—
1019C22⋊C4—1221no—
1020C22⋊C4—1221no—
1021C22⋊C4—1221no—
1022C22⋊C4—1221no—
1023C22⋊C4—1221no—
1024C22⋊C4—1221no—
1025C22⋊C4—1221no—
1026C22⋊C4—1221no—
1027C22⋊C4—2442no—
1028C22⋊C4—2442no—
1029C22⋊C4—2442no—
1030C22⋊C4C22⋊#692311yescharacteristic
1031C22⋊C4C22⋊#692311yescharacteristic
1032C42—611no—
1033C42—611no—
1034C42—611no—
1035C42—612no—
1036C42—1221no—
1037C42—1221no—
1038C42—1221no—
1039C42—1221no—
1040C42—1221no—
1041C42—1221no—
1042C42—1221no—
1043C42—1221no—
1044C42—1221no—
1045C42—1221no—
1046C42—2442no—
1047C42C22×#692311yescharacteristic
1048C23—21no—
1049C23—21no—
1050C23—42no—
1051C23—42no—
1052C23—81no—
1053C23—611no—
1054C23—611no—
1055C23—611no—
1056C23—1221no—
1057C23—1221no—
1058C23—1221no—
1059C23—1221no—
1060C23—1222no—
1061C23—1221no—
1062C23—4881no—
1063C23—2441no—
1064C23—2441no—
1065C23—2441no—
1066C23—2442no—
1067C23—2442no—
1068C23C2×C22⋊#692311yescharacteristic
1069C23C2×C22⋊#692311yescharacteristic
1070Q8—21no—
1071Q8—21no—
1072Q8—612no—
1073Q8—1221no—
1074Q8—1221no—
1075Q8—1221no—
1076Q8—2442no—
1077Q8—2442no—
1078D4—22no—
1079D4—21no—
1080D4—21no—
1081D4—21no—
1082D4—42no—
1083D4—42no—
1084D4—81no—
1085D4—1222no—
1086D4—1222no—
1087D4—1222no—
1088D4—1221no—
1089D4—1221no—
1090D4—4881no—
1091D4—4881no—
1092D4—2441no—
1093D4—2441no—
1094D4—2441no—
1095D4—2441no—
1096D4—2442no—
1097D4—2442no—
1098D4—2442no—
1099D4—2442no—
1100D4—2442no—
1101D4—2441no—
1102D4—2441no—
1103D4—2442no—
1104D4—2442no—
1105D4D4×#692312yes—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—42no—
1113C2×C4—81no—
1114C2×C4—611no—
1115C2×C4—611no—
1116C2×C4—611no—
1117C2×C4—611no—
1118C2×C4—611no—
1119C2×C4—611no—
1120C2×C4—611no—
1121C2×C4—611no—
1122C2×C4—611no—
1123C2×C4—1221no—
1124C2×C4—1221no—
1125C2×C4—1221no—
1126C2×C4—1221no—
1127C2×C4—1221no—
1128C2×C4—1221no—
1129C2×C4—1221no—
1130C2×C4—1221no—
1131C2×C4—1221no—
1132C2×C4—1221no—
1133C2×C4—1221no—
1134C2×C4—1221no—
1135C2×C4—1222no—
1136C2×C4—1222no—
1137C2×C4—1221no—
1138C2×C4—1221no—
1139C2×C4—1221no—
1140C2×C4—1221no—
1141C2×C4—1221no—
1142C2×C4—1222no—
1143C2×C4—1222no—
1144C2×C4—1221no—
1145C2×C4—1221no—
1146C2×C4—2441no—
1147C2×C4—2441no—
1148C2×C4—2442no—
1149C2×C4—2441no—
1150C2×C4—2441no—
1151C2×C4—2442no—
1152C2×C4—2441no—
1153C2×C4—2441no—
1154C2×C4—2442no—
1155C2×C4—2442no—
1156C2×C4—2442no—
1157C2×C4—2442no—
1158C2×C4—2441no—
1159C2×C4—2441no—
1160C2×C4—2441no—
1161C2×C4—2441no—
1162C2×C4—2441no—
1163C2×C4—2441no—
1164C2×C4—2441no—
1165C2×C4—2441no—
1166C2×C4—2441no—
1167C2×C4—2441no—
1168C2×C4—2448no—
1169C2×C4C2×C22⋊#692311yescharacteristic
1170C2×C4C2×C22⋊#692311yescharacteristic
1171C2×C4C2×C22⋊#692311yescharacteristic
1172C2×C4C2×C22⋊#692311yescharacteristic
1173C2×C4C23×#692311yescharacteristic
1174C8—1222no—
1175C8—2441no—
1176C8—2441no—
1177C8—2441no—
1178C22—21no—
1179C22—21no—
1180C22—21no—
1181C22—22no—
1182C22—21no—
1183C22—21no—
1184C22—41no—
1185C22—41no—
1186C22—41no—
1187C22—41no—
1188C22—41no—
1189C22—84no—
1190C22—611no—
1191C22—611no—
1192C22—1221no—
1193C22—1221no—
1194C22—1221no—
1195C22—1221no—
1196C22—1221no—
1197C22—1221no—
1198C22—1221no—
1199C22—1221no—
1200C22—4881no—
1201C22—4881no—
1202C22—4884no—
1203C22—2442no—
1204C22—2442no—
1205C22—2441no—
1206C22—2441no—
1207C22—2441no—
1208C22#1684075912yescomplemented
1209C22C22×C22⋊#692311yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—21no—
1213C4—21no—
1214C4—41no—
1215C4—41no—
1216C4—611no—
1217C4—611no—
1218C4—1221no—
1219C4—1221no—
1220C4—1222no—
1221C4—1221no—
1222C4—1221no—
1223C4—4881no—
1224C4—4881no—
1225C4—2442no—
1226C4—2442no—
1227C4—2441no—
1228C4—2441no—
1229C4C2×D4×#692311yescharacteristic
1230C4#1684082911yescharacteristic
1231C2—22no—
1232C2—41no—
1233C2—42no—
1234C2—81no—
1235C2—1221no—
1236C2—1221no—
1237C2—4881no—
1238C2—2441no—
1239C2—2441no—
1240C2D4×C22⋊#692311yescharacteristic
1241C2C2×#1684075911yescharacteristic
1242C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#546C4
socleC22×C61C22×C22⋊C4
prime radical#21459303C2
cosocleC2×C4×D61C24
hypercenter#546#6923
hypocenterC61#22434
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. D4×#11758213C2semidirect
2. C2×#16840759C2semidirect
3. C22×#14519841C2semidirect
4. #21462273C2semidirect
5. #21461984C2semidirect
6. #21461956C2semidirect
7. #21461839C2semidirect
8. #21461836C2semidirect
9. #21461802C2semidirect
10. #21461800C2semidirect
11. #21461691C2semidirect
12. #21461661C2semidirect
13. #21461660C2semidirect
14. #21461582C2semidirect
16. C22×#11758213C22semidirect
17. C22×#11758213C22semidirect
18. C2×#14519856C22semidirect
19. C22×C4×#6923C22semidirect
24. #16840766C22semidirect
26. C2×#14519842C22semidirect
27. C2×#14519842C22semidirect
28. C2×#14519842C22semidirect
29. C2×#14519842C22semidirect
35. C2×#14519841C22semidirect
36. C2×#14519841C22semidirect
37. C2×#14519841C22semidirect
38. C2×#14519841C22semidirect
39. #16840733C22semidirect
40. #16840733C22semidirect
41. C4×#11758213C22semidirect
46. C4×C4⋊#6923C22semidirect
47. C4×C22⋊#6923C22semidirect
48. C4×C22⋊#6923C22semidirect
49. #16840698C22semidirect
50. #16840632C22semidirect
51. #16840632C22semidirect
52. #16840632C22semidirect
53. #16840632C22semidirect
56. #16840430C4semidirect
57. #16840425C4semidirect
58. #16840421C4semidirect
59. #16840420C4semidirect
60. #16840411C4semidirect
62. #16840407C4semidirect
65. D4×C22⋊D61C4semidirect
76. C61×#546C4semidirect
117. #14519841D4semidirect
131. C2×#11758222C2×C4semidirect
148. C2×Q8×D61C2×C4semidirect
152. C2×D4×D61C2×C4semidirect
159. #14519775C2×C4semidirect
161. #14519773C2×C4semidirect
162. #14519765C2×C4semidirect
170. #14519757C2×C4semidirect
171. #14519756C2×C4semidirect
188. #14519748C2×C4semidirect
194. C4×Dic122C2×C4semidirect
195. #14519742C2×C4semidirect
198. D4×Dic61C2×C4semidirect
225. C2×#41×C61C2×C4semidirect
227. #124×C61C2×C4semidirect
231. #121×C61C2×C4semidirect
234. C4×D4×C61C2×C4semidirect
371. C4×#6923C2×D4semidirect
381. #11758213C2×D4semidirect
569. C22×C61#421semidirect
650. #546#6923semidirect
698. C61#22434semidirect
717. C2×#41C2×#6923semidirect
750. #124C2×#6923semidirect
778. #121C2×#6923semidirect
808. C4×D4C2×#6923semidirect
1208. C22#16840759semidirect

Maximal subgroups

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

subgroupindex
D4×#117582132
C2×#168407592
C22×#145198412
#214622732
#214619842
#214619562
#214618392
#214618362
#214618022
#214618002
#214616912
#214616612
#214616602
#214615822
#214593032
#2243461