Finite Group Databasebeta

← #30620188

Subgroups — #30620188

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
1#21462558C211yesmaximal, characteristic, complemented
2C2×#16840759C211yesmaximal, characteristic, complemented
3C2×D61⋊#104C211yesmaximal, characteristic, complemented
4#21462273C211yesmaximal, characteristic, complemented
5#21461983C211yesmaximal, characteristic, complemented
6#21461957C211yesmaximal, characteristic, complemented
7#21461839C211yesmaximal, characteristic, complemented
8#21461837C211yesmaximal, characteristic, complemented
9#21461803C211yesmaximal, characteristic, complemented
10#21461802C211yesmaximal, characteristic, complemented
11#21461694C211yesmaximal, characteristic, complemented
12#21461661C211yesmaximal, characteristic, complemented
13#21461661C211yesmaximal, characteristic, complemented
14#21461583C211yesmaximal, characteristic, complemented
15#21459309C211yesmaximal, characteristic
16C22×#11758213C2211yescharacteristic, complemented
17C2×D61⋊M16C2211yescharacteristic, complemented
18C2×#14519856C2211yescharacteristic, complemented
19C22×C4×#6923C2211yescharacteristic, complemented
20#16840795—21no—
21#16840793—21no—
22#16840792—21no—
23#16840789—21no—
24#16840767C2211yescharacteristic, complemented
25#16840759—24no—
26C2×#14519842C2211yescharacteristic
27C2×#14519842C2211yescharacteristic
28C2×#14519842C2211yescharacteristic
29C2×#14519842C2211yescharacteristic
30D61⋊#104—24no—
31C2×#14519841C2211yescharacteristic, complemented
32C2×#14519841C2211yescharacteristic, complemented
33C2×#14519841C2211yescharacteristic, complemented
34C2×#14519841C2211yescharacteristic, complemented
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
54C2×#41×D61C2211yescharacteristic
55C2×#41×D61C2211yescharacteristic
56Q8×D244C411yescharacteristic, complemented
57#16840419C411yescharacteristic, complemented
58#16840419C411yescharacteristic, complemented
59#16840417—21no—
60#16840417C411yescharacteristic, complemented
61#16840409—21no—
62#16840409—21no—
63#16840409C411yescharacteristic, complemented
64#16840409C411yescharacteristic, complemented
65#16840397—21no—
66#16840397C411yescharacteristic, complemented
67#16840310—21no—
68#16840310C2211yescharacteristic
69#16840272—21no—
70#16840272—21no—
71#16840272C2211yescharacteristic
72#16840272C2211yescharacteristic
73C4×#11758226C2211yescharacteristic
74C4×D4×D61—21no—
75C4×D4×D61C2211yescharacteristic
76C61×#550C411yescharacteristic, complemented
77C23×#6923—21no—
78C2×#11758213—22no—
79C2×#11758213—21no—
80C2×#11758213—41no—
81C2×#11758213C2311yescharacteristic
82C2×#11758213C2311yescharacteristic
83C2×#11758213C2311yescharacteristic
84C2×#11758213C2311yescharacteristic
85D61⋊M16—22no—
86D61⋊M16—41no—
87C2×#11758217—21no—
88C2×D61⋊C8—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
104#14519844—21no—
105#14519844—21no—
106#14519842—22no—
107#14519842—22no—
108#14519842—22no—
109#14519842D414yescomplemented
110#14519841—22no—
111#14519841—22no—
112#14519841—22no—
113#14519841—22no—
114#14519841—41no—
115#14519841—41no—
116#14519841—41no—
117#14519841—41no—
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×#11758222—21no—
132C2×#11758222C2×C411yescharacteristic
133C2×#11758222C2×C411yescharacteristic, complemented
134C2×#11758224—21no—
135C2×#11758224—21no—
136C2×#11758224C2311yescharacteristic
137C2×#11758224C2311yescharacteristic
138#41×D61—22no—
139#41×D61—22no—
140#41×D61—22no—
141#41×D61—22no—
142#41×D61—41no—
143#41×D61—41no—
144#41×D61—41no—
145#41×D61—41no—
146C2×Q8×D61C2×C411yescharacteristic
147C2×Q8×D61C2×C411yescharacteristic, complemented
148C2×D4×D61—21no—
149C2×D4×D61—21no—
150C2×D4×D61—21no—
151C2×D4×D61C2×C411yescharacteristic
152C2×D4×D61C2×C411yescharacteristic, complemented
153C2×D4×D61D411yescharacteristic
154C22×C4×D61—21no—
155C22×C4×D61—21no—
156C22×C4×D61C2311yescharacteristic
157C22×C4×D61C2311yescharacteristic
158#14519777—21no—
159#14519777C2×C411yescharacteristic, complemented
160#14519764—21no—
161#14519764—21no—
162#14519764C2×C411yescharacteristic, complemented
163#14519764C2×C411yescharacteristic, complemented
164#14519759—21no—
165#14519759—21no—
166#14519759—21no—
167#14519759—21no—
168#14519759—21no—
169#14519759—21no—
170#14519757—21no—
171#14519757—21no—
172#14519757C2×C411yescharacteristic
173#14519757C2×C411yescharacteristic, complemented
174#14519756—21no—
175#14519756—21no—
176#14519756C2×C411yescharacteristic
177#14519756C2×C411yescharacteristic, complemented
178#14519748—21no—
179#14519748—21no—
180#14519748—21no—
181#14519748—21no—
182#14519748—21no—
183#14519748—21no—
184#14519748—21no—
185#14519748—21no—
186#14519748C2×C411yescharacteristic
187#14519748C2×C411yescharacteristic, complemented
188#14519745—21no—
189#14519745—21no—
190#14519745—21no—
191#14519745—21no—
192#14519745—21no—
193#14519745—21no—
194Q8×Dic61C2×C411yescharacteristic, complemented
195C4×D244—21no—
196C4×D244—21no—
197C4×D244C2×C411yescharacteristic
198C4×D244C2×C411yescharacteristic, complemented
199D4×Dic61—21no—
200D4×Dic61—21no—
201D4×Dic61—21no—
202D4×Dic61—21no—
203D4×Dic61D411yescharacteristic
204#14519739—21no—
205#14519739C2×C411yescharacteristic, complemented
206#14519739D411yescharacteristic
207C4×C22⋊D61—21no—
208C4×C22⋊D61—21no—
209C4×C22⋊D61C2×C411yescharacteristic
210C4×C22⋊D61C2×C411yescharacteristic
211#14519737—21no—
212#14519737—21no—
213#14519737D411yescharacteristic
214#14519737D411yescharacteristic
215#14519735—21no—
216#14519735C2311yescharacteristic
217C4⋊C4×D61—21no—
218C4⋊C4×D61D411yescharacteristic
219C22⋊C4×D61—21no—
220C22⋊C4×D61—21no—
221C22⋊C4×D61D411yescharacteristic
222C22⋊C4×D61D411yescharacteristic
223C42×D61—21no—
224C42×D61C2311yescharacteristic
225C2×#41×C61C2×C411yescharacteristic
226C2×#41×C61C2×C411yescharacteristic, complemented
227#127×C61—21no—
228#127×C61C2×C411yescharacteristic, complemented
229#121×C61—21no—
230#121×C61—21no—
231#121×C61C2×C411yescharacteristic
232#121×C61C2×C411yescharacteristic, complemented
233C4×Q8×C61C2×C411yescharacteristic, complemented
234C4×D4×C61—21no—
235C4×D4×C61C2×C411yescharacteristic
236C23×D61—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—22no—
249#41×C61—41no—
250#41×C61—41no—
251C2×Q8×C61C22×C411yescharacteristic
252C2×D4×C61—21no—
253C2×D4×C61—21no—
254C2×D4×C61—21no—
255C2×D4×C61—21no—
256C2×D4×C61—21no—
257C2×D4×C61—21no—
258C2×D4×C61C22⋊C411yescharacteristic
259C2×D4×C61C22×C411yescharacteristic
260C2×D4×C61C22×C411yescharacteristic
261C22×C4×C61—21no—
262C22×C4×C61—21no—
263C22×C4×C61C22×C411yescharacteristic
264C22×C4×C61C22×C411yescharacteristic
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—21no—
273C2×C22⋊D61C22⋊C411yescharacteristic
274C2×C22⋊D61C22⋊C411yescharacteristic
275C22×Dic61—21no—
276C22×Dic61—21no—
277C22×Dic61C2×D411yescharacteristic
278C22×Dic61C2×D411yescharacteristic
279#11758226—21no—
280#11758226—21no—
281#11758226C2×D412yes—
282#11758226#4112yes—
283Q8×D61—22no—
284Q8×D61—22no—
285Q8×D61—41no—
286Q8×D61—41no—
287#11758224—21no—
288#11758224—21no—
289#11758224—21no—
290#11758224—21no—
291#11758224—21no—
292#11758224—21no—
293#11758224—21no—
294#11758224—21no—
295#11758224—42no—
296#11758224—42no—
297#11758224—42no—
298#11758224—42no—
299D4×D61—22no—
300D4×D61—22no—
301D4×D61—41no—
302D4×D61—41no—
303D4×D61—42no—
304D4×D61—42no—
305D4×D61—42no—
306D4×D61—42no—
307D4×D61—42no—
308D4×D61—44no—
309#11758222—22no—
310#11758222—22no—
311#11758222—41no—
312#11758222—41no—
313#11758222—42no—
314#11758222—42no—
315#11758222—42no—
316#11758222—42no—
317C2×D244—21no—
318C2×D244C22⋊C411yescharacteristic
319C2×D244C22×C411yescharacteristic
320C2×C4×D61—21no—
321C2×C4×D61—21no—
322C2×C4×D61—21no—
323C2×C4×D61—21no—
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×D61—42no—
338C2×C4×D61—42no—
339C2×C4×D61C22×C411yescharacteristic
340C2×C4×D61C22×C411yescharacteristic
341C2×C4×D61C2×D411yescharacteristic
342C2×C4×D61C2×D411yescharacteristic
343C2×C4×D61C2×D411yescharacteristic
344C2×C4×D61C2×D411yescharacteristic
345C2×C4×D61C2×D411yescharacteristic
346C2×C4×D61C2×D411yescharacteristic
347C2×C4×D61C2411yescharacteristic
348C2×Dic122—21no—
349C2×Dic122—21no—
350C2×Dic122C22×C411yescharacteristic
351C2×Dic122C22×C411yescharacteristic
352C22⋊#6923—42no—
353C22⋊#6923—42no—
354C22⋊#6923—42no—
355#11758217—42no—
356C2×#92420—21no—
357C2×#92420—21no—
358C2×#92420—21no—
359C2×#92420—21no—
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#11758213C2×D412yescomplemented
381D61⋊C8—42no—
382C4⋊C4×C61—21no—
383C4⋊C4×C61C22⋊C411yescharacteristic
384C4⋊C4×C61C22×C411yescharacteristic
385C22⋊C4×C61—21no—
386C22⋊C4×C61—21no—
387C22⋊C4×C61C22⋊C411yescharacteristic
388C22⋊C4×C61C22⋊C411yescharacteristic
389C42×C61—21no—
390C42×C61C22×C411yescharacteristic
391C22⋊Dic61—21no—
392C22⋊Dic61—21no—
393C22⋊Dic61—21no—
394C22⋊Dic61—21no—
395C22⋊Dic61—21no—
396C22⋊Dic61—21no—
397C22⋊Dic61—21no—
398C22⋊Dic61—21no—
399C22⋊Dic61C22⋊C411yescharacteristic
400C22⋊Dic61C22⋊C411yescharacteristic
401#11758198—21no—
402#11758198—21no—
403#11758198—21no—
404#11758198—21no—
405#11758198—21no—
406#11758198C22⋊C411yescharacteristic
407#11758198C22⋊C411yescharacteristic
408#11758198C22⋊C411yescharacteristic
409#11758198C22⋊C411yescharacteristic
410C4⋊Dic61—21no—
411C4⋊Dic61—21no—
412C4⋊Dic61—21no—
413C4⋊Dic61—21no—
414C4⋊Dic61—21no—
415C4⋊Dic61C22⋊C411yescharacteristic
416C4⋊Dic61C22×C411yescharacteristic
417#11758196—21no—
418#11758196—21no—
419#11758196C22⋊C411yescharacteristic
420#11758196C22⋊C411yescharacteristic
421C4×Dic61—21no—
422C4×Dic61—21no—
423C4×Dic61C22×C411yescharacteristic
424C4×Dic61C2×D411yescharacteristic
425C4×Dic61C2×D411yescharacteristic
426C23×C61—21no—
427C23×C61—21no—
428C23×C61C2×C22⋊C411yescharacteristic
429C23×C61C2×C22⋊C411yescharacteristic
430C22×D61—21no—
431C22×D61—21no—
432C22×D61—21no—
433C22×D61—22no—
434C22×D61—21no—
435C22×D61—21no—
436C22×D61—41no—
437C22×D61—41no—
438C22×D61—41no—
439C22×D61—42no—
440C22×D61—42no—
441C22×D61—42no—
442C22×D61—42no—
443C22×D61—81no—
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×C61C4×D412yes—
463D4×C61—21no—
464D4×C61—21no—
465D4×C61—21no—
466D4×C61—21no—
467D4×C61—41no—
468D4×C61—42no—
469D4×C61—42no—
470D4×C61—42no—
471D4×C61—81no—
472D4×C61—81no—
473D4×C61—81no—
474C2×C4×C61—21no—
475C2×C4×C61—21no—
476C2×C4×C61—21no—
477C2×C4×C61—21no—
478C2×C4×C61—21no—
479C2×C4×C61—21no—
480C2×C4×C61—42no—
481C2×C4×C61—42no—
482C2×C4×C61C2×C22⋊C411yescharacteristic
483C2×C4×C61C2×C22⋊C411yescharacteristic
484C2×C4×C61C2×C22⋊C411yescharacteristic
485C2×C4×C61C2×C22⋊C411yescharacteristic
486C2×C4×C61C23×C411yescharacteristic
487C22⋊D61—22no—
488C22⋊D61—41no—
489C22⋊D61—42no—
490C22⋊D61—42no—
491C22⋊D61—42no—
492C22⋊D61—42no—
493C22⋊D61—42no—
494C22⋊D61—41no—
495C22⋊D61—41no—
496C22⋊D61—41no—
497C22⋊D61—41no—
498C22⋊D61—42no—
499C2×Dic61—21no—
500C2×Dic61—21no—
501C2×Dic61—21no—
502C2×Dic61—21no—
503C2×Dic61—21no—
504C2×Dic61—21no—
505C2×Dic61—21no—
506C2×Dic61—41no—
507C2×Dic61—41no—
508C2×Dic61—41no—
509C2×Dic61—41no—
510C2×Dic61C2×C22⋊C411yescharacteristic
511C2×Dic61C2×C22⋊C411yescharacteristic
512C2×Dic61C2×C22⋊C411yescharacteristic
513C2×Dic61C2×C22⋊C411yescharacteristic
514C2×Dic61C22×D411yescharacteristic
515D244—22no—
516D244—22no—
517D244—22no—
518D244—21no—
519D244C4×D412yes—
520C4×D61—21no—
521C4×D61—21no—
522C4×D61—21no—
523C4×D61—21no—
524C4×D61—21no—
525C4×D61—21no—
526C4×D61—21no—
527C4×D61—21no—
528C4×D61—21no—
529C4×D61—21no—
530C4×D61—22no—
531C4×D61—21no—
532C4×D61—21no—
533C4×D61—22no—
534C4×D61—41no—
535C4×D61—41no—
536C4×D61—42no—
537C4×D61—42no—
538C4×D61—42no—
539C4×D61—42no—
540C4×D61—42no—
541C4×D61—81no—
542C4×D61C22×D411yescharacteristic
543C4×D61C2×#4111yescharacteristic
544C4×D61H(5,𝔽2)11yescharacteristic
545C4×D61H(5,𝔽2)11yescharacteristic
546Dic122—21no—
547Dic122—21no—
548Dic122—21no—
549Dic122—21no—
550Dic122—42no—
551Dic122—42no—
552#92420—22no—
553#92420—41no—
554#92420—41no—
555#92420—41no—
556#22434—611nomaximal, Sylow
557C22×C61—21no—
558C22×C61—21no—
559C22×C61—21no—
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—41no—
569C22×C61C22×C22⋊C411yescharacteristic
570C2×D61—21no—
571C2×D61—21no—
572C2×D61—21no—
573C2×D61—21no—
574C2×D61—21no—
575C2×D61—22no—
576C2×D61—21no—
577C2×D61—21no—
578C2×D61—42no—
579C2×D61—42no—
580C2×D61—41no—
581C2×D61—41no—
582C2×D61—81no—
583C2×D61—81no—
584C2×D61—84no—
585C2×D61—84no—
586C2×D61#42112yescomplemented
587C2×D61D4211yescharacteristic
588C2×D61#54611yescharacteristic
589#6923—42no—
590#6923—42no—
591#6923—81no—
592#6923—81no—
593C4×C61—22no—
594C4×C61—21no—
595C4×C61—21no—
596C4×C61—21no—
597C4×C61—21no—
598C4×C61—41no—
599C4×C61C2×C4×D411yescharacteristic
600C4×C61#51811yescharacteristic
601Dic61—21no—
602Dic61—21no—
603Dic61—21no—
604Dic61—21no—
605Dic61—41no—
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—41no—
626C2×C61—41no—
627C2×C61—81no—
628C2×C61—81no—
629C2×C61D4×C22⋊C411yescharacteristic
630C2×C61C2×#42111yescharacteristic
631C2×C61#290111yescharacteristic
632D61—21no—
633D61—21no—
634D61—22no—
635D61—41no—
636D61—42no—
637C22×#41—611no—
638C22×#41—611no—
639C22×M16—611no—
640C22×M16—611no—
641#550#692311yescharacteristic, complemented
642D4×Q8—611no—
643#548—611no—
644#548—611no—
645#547—611no—
646#547—1221no—
647#546—611no—
648#546—611no—
649#546—1221no—
650#546—1221no—
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—1221no—
705C2×#41—1221no—
706C2×#41—1221no—
707C2×#41—1221no—
708C2×#41—1222no—
709C2×#41—1222no—
710C2×#41—1222no—
711C2×#41—1222no—
712C2×#41—2441no—
713C2×#41—2441no—
714C2×#41—2441no—
715C2×#41—2441no—
716C2×#41C2×#692311yescharacteristic
717C2×#41C2×#692311yescharacteristic, complemented
718C22×Q8—611no—
719C22×Q8—611no—
720C22×D4—611no—
721C22×D4—611no—
722C22×D4—611no—
723C22×D4—1221no—
724C22×D4—1221no—
725C22×D4—1221no—
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—21no—
746#127C2×#692311yescharacteristic, complemented
747#124—611no—
748#124—611no—
749#124—1221no—
750#124—1221no—
751#123—1221no—
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—611no—
761C22⋊Q8—1221no—
762C22⋊Q8—1221no—
763C22⋊Q8—1221no—
764C22⋊Q8—1221no—
765#121—21no—
766#121—21no—
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#121C2×#692311yescharacteristic
778#121C2×#692311yescharacteristic, complemented
779#120—1221no—
780#120—1221no—
781#120—1221no—
782#120—1221no—
783#120—1221no—
784#120—1221no—
785C4×Q8—611no—
786C4×Q8C2×#692311yescharacteristic, complemented
787C4×D4—21no—
788C4×D4—611no—
789C4×D4—611no—
790C4×D4—611no—
791C4×D4—611no—
792C4×D4—611no—
793C4×D4—611no—
794C4×D4—611no—
795C4×D4—611no—
796C4×D4—611no—
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×D4—1221no—
808C4×D4C2×#692311yescharacteristic
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—611no—
818C2×C22⋊C4—611no—
819C2×C22⋊C4—1221no—
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—611no—
859C24—611no—
860C24—1221no—
861C24—1221no—
862#41—22no—
863#41—22no—
864#41—41no—
865#41—41no—
866#41—612no—
867#41—612no—
868#41—1222no—
869#41—1222no—
870#41—1221no—
871#41—1221no—
872#41—1221no—
873#41—1221no—
874#41—1221no—
875#41—1221no—
876#41—1221no—
877#41—1221no—
878#41—1221no—
879#41—1221no—
880#41—2441no—
881#41—2441no—
882#41—2442no—
883#41—2442no—
884#41—2442no—
885#41—2442no—
886#41—2442no—
887#41—2442no—
888#41—2442no—
889#41—2442no—
890C2×Q8—611no—
891C2×Q8—611no—
892C2×Q8—1221no—
893C2×Q8—1221no—
894C2×Q8—1222no—
895C2×Q8—1222no—
896C2×Q8—2441no—
897C2×Q8—2441no—
898C2×Q8C22×#692311yescharacteristic
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—611no—
906C2×D4—611no—
907C2×D4—611no—
908C2×D4—611no—
909C2×D4—1221no—
910C2×D4—1221no—
911C2×D4—1221no—
912C2×D4—1222no—
913C2×D4—1222no—
914C2×D4—1221no—
915C2×D4—1221no—
916C2×D4—1221no—
917C2×D4—1221no—
918C2×D4—1221no—
919C2×D4—1221no—
920C2×D4—2441no—
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—611no—
1009C22⋊C4—611no—
1010C22⋊C4—611no—
1011C22⋊C4—611no—
1012C22⋊C4—611no—
1013C22⋊C4—611no—
1014C22⋊C4—1221no—
1015C22⋊C4—1221no—
1016C22⋊C4—1221no—
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—21no—
1033C42—611no—
1034C42—611no—
1035C42—611no—
1036C42—612no—
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—611no—
1051C23—611no—
1052C23—611no—
1053C23—1221no—
1054C23—1221no—
1055C23—1222no—
1056C23—1221no—
1057C23—1221no—
1058C23—1221no—
1059C23—4881no—
1060C23—4881no—
1061C23—2441no—
1062C23—2441no—
1063C23—2441no—
1064C23—2442no—
1065C23—2442no—
1066C23—2442no—
1067C23—2442no—
1068C23C2×C22⋊#692311yescharacteristic
1069C23C2×C22⋊#692311yescharacteristic
1070Q8—21no—
1071Q8—1221no—
1072Q8—1221no—
1073Q8—1221no—
1074Q8—1221no—
1075Q8—2442no—
1076Q8—2442no—
1077Q8D4×#692312yes—
1078D4—21no—
1079D4—21no—
1080D4—21no—
1081D4—21no—
1082D4—41no—
1083D4—42no—
1084D4—42no—
1085D4—42no—
1086D4—81no—
1087D4—81no—
1088D4—81no—
1089D4—612no—
1090D4—1222no—
1091D4—1222no—
1092D4—1222no—
1093D4—1222no—
1094D4—1221no—
1095D4—2441no—
1096D4—2442no—
1097D4—2442no—
1098D4—2442no—
1099D4—2442no—
1100D4—2442no—
1101D4—2441no—
1102D4—2441no—
1103D4—2441no—
1104D4—2441no—
1105D4—2442no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—42no—
1113C2×C4—42no—
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—1222no—
1128C2×C4—1222no—
1129C2×C4—1221no—
1130C2×C4—1221no—
1131C2×C4—1221no—
1132C2×C4—1221no—
1133C2×C4—1221no—
1134C2×C4—1221no—
1135C2×C4—1221no—
1136C2×C4—1221no—
1137C2×C4—1221no—
1138C2×C4—1221no—
1139C2×C4—1221no—
1140C2×C4—1221no—
1141C2×C4—1222no—
1142C2×C4—1222no—
1143C2×C4—1221no—
1144C2×C4—1221no—
1145C2×C4—1221no—
1146C2×C4—4881no—
1147C2×C4—2441no—
1148C2×C4—2441no—
1149C2×C4—2442no—
1150C2×C4—2442no—
1151C2×C4—2442no—
1152C2×C4—2442no—
1153C2×C4—2442no—
1154C2×C4—2441no—
1155C2×C4—2441no—
1156C2×C4—2441no—
1157C2×C4—2441no—
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—21no—
1182C22—21no—
1183C22—21no—
1184C22—41no—
1185C22—41no—
1186C22—41no—
1187C22—41no—
1188C22—41no—
1189C22—41no—
1190C22—611no—
1191C22—611no—
1192C22—612no—
1193C22—1221no—
1194C22—1221no—
1195C22—1221no—
1196C22—1221no—
1197C22—1221no—
1198C22—1222no—
1199C22—1221no—
1200C22—1221no—
1201C22—4881no—
1202C22—4881no—
1203C22—4884no—
1204C22—4884no—
1205C22—2442no—
1206C22—2442no—
1207C22—2441no—
1208C22—2441no—
1209C22C22×C22⋊#692311yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—22no—
1213C4—21no—
1214C4—21no—
1215C4—41no—
1216C4—611no—
1217C4—611no—
1218C4—1221no—
1219C4—1221no—
1220C4—1221no—
1221C4—1221no—
1222C4—4881no—
1223C4—4881no—
1224C4—2442no—
1225C4—2442no—
1226C4—2441no—
1227C4—2441no—
1228C4—2441no—
1229C4C2×D4×#692311yescharacteristic
1230C4#1684082911yescharacteristic
1231C2—41no—
1232C2—41no—
1233C2—81no—
1234C2—81no—
1235C2—1221no—
1236C2—1221no—
1237C2—1222no—
1238C2—2441no—
1239C2—2442no—
1240C2D4×C22⋊#692311yescharacteristic
1241C2D61⋊#42111yescharacteristic
1242C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#550C4
socleC22×C61C22×C22⋊C4
prime radical#21459309C2
cosocleC2×C4×D61C24
hypercenter#550#6923
hypocenterC61#22434
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #21462558C2semidirect
2. C2×#16840759C2semidirect
3. C2×D61⋊#104C2semidirect
4. #21462273C2semidirect
5. #21461983C2semidirect
6. #21461957C2semidirect
7. #21461839C2semidirect
8. #21461837C2semidirect
9. #21461803C2semidirect
10. #21461802C2semidirect
11. #21461694C2semidirect
12. #21461661C2semidirect
13. #21461661C2semidirect
14. #21461583C2semidirect
16. C22×#11758213C22semidirect
17. C2×D61⋊M16C22semidirect
18. C2×#14519856C22semidirect
19. C22×C4×#6923C22semidirect
24. #16840767C22semidirect
31. C2×#14519841C22semidirect
32. C2×#14519841C22semidirect
33. C2×#14519841C22semidirect
34. C2×#14519841C22semidirect
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. Q8×D244C4semidirect
57. #16840419C4semidirect
58. #16840419C4semidirect
60. #16840417C4semidirect
63. #16840409C4semidirect
64. #16840409C4semidirect
66. #16840397C4semidirect
76. C61×#550C4semidirect
109. #14519842D4semidirect
133. C2×#11758222C2×C4semidirect
147. C2×Q8×D61C2×C4semidirect
152. C2×D4×D61C2×C4semidirect
159. #14519777C2×C4semidirect
162. #14519764C2×C4semidirect
163. #14519764C2×C4semidirect
173. #14519757C2×C4semidirect
177. #14519756C2×C4semidirect
187. #14519748C2×C4semidirect
194. Q8×Dic61C2×C4semidirect
198. C4×D244C2×C4semidirect
205. #14519739C2×C4semidirect
226. C2×#41×C61C2×C4semidirect
228. #127×C61C2×C4semidirect
232. #121×C61C2×C4semidirect
233. C4×Q8×C61C2×C4semidirect
371. C4×#6923C2×D4semidirect
380. #11758213C2×D4semidirect
586. C2×D61#421semidirect
641. #550#6923semidirect
698. C61#22434semidirect
717. C2×#41C2×#6923semidirect
746. #127C2×#6923semidirect
778. #121C2×#6923semidirect
786. C4×Q8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214625582
C2×#168407592
C2×D61⋊#1042
#214622732
#214619832
#214619572
#214618392
#214618372
#214618032
#214618022
#214616942
#214616612
#214615832
#214593092
#2243461