Finite Group Databasebeta

← #30620189

Subgroups — #30620189

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×#16840760C211yesmaximal, characteristic, complemented
3C22×#14519841C211yesmaximal, 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#21461693C211yesmaximal, characteristic, complemented
12#21461660C211yesmaximal, characteristic, complemented
13#21461660C211yesmaximal, characteristic, complemented
14#21461582C211yesmaximal, characteristic, complemented
15D4×#11758224C211yesmaximal, 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#16840760—24no—
26C2×#14519841—24no—
27C2×#14519841C2211yescharacteristic
28C2×#14519841C2211yescharacteristic
29C2×#14519841C2211yescharacteristic
30C2×#14519841C2211yescharacteristic
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
54C22×#11758224C2211yescharacteristic
55C22×#11758224C2211yescharacteristic
56#16840432C411yescharacteristic, complemented
57D4×Dic122C411yescharacteristic, complemented
58#16840418C411yescharacteristic, complemented
59#16840418C411yescharacteristic, complemented
60#16840416C411yescharacteristic, complemented
61#16840412—21no—
62#16840406C411yescharacteristic, complemented
63#16840406C411yescharacteristic, complemented
64#16840399—21no—
65#16840399—21no—
66D4×C22⋊D61—21no—
67#16840310C2211yescharacteristic
68#16840307—21no—
69#16840272C2211yescharacteristic
70#16840272C2211yescharacteristic
71#16840268—21no—
72#16840268—21no—
73C4×#11758224C2211yescharacteristic
74C2×D4×Dic61—21no—
75C4×D4×D61C2211yescharacteristic
76D42×C61C411yescharacteristic, 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#14519841—22no—
107#14519841—22no—
108#14519841—22no—
109#14519841—22no—
110#14519841—22no—
111#14519841—22no—
112#14519841—22no—
113#14519841—41no—
114#14519841—41no—
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×#11758224—22no—
130C2×#11758224—22no—
131C2×#11758224—22no—
132C2×#11758224—22no—
133C2×#11758224—21no—
134C2×#11758224—21no—
135C2×#11758224—21no—
136C2×#11758224—21no—
137C2×#11758224—41no—
138C2×#11758224—41no—
139C2×#11758224—41no—
140C2×#11758224—41no—
141C2×#11758224C2×C411yescharacteristic
142C2×#11758224C2×C411yescharacteristic
143C2×#11758224C2×C411yescharacteristic, complemented
144C2×#11758224C2×C411yescharacteristic, complemented
145C2×#11758224C2311yescharacteristic
146C2×#11758224C2311yescharacteristic
147C2×#11758224C2311yescharacteristic
148C22×Dic122C2×C411yescharacteristic
149C22×Dic122C2×C411yescharacteristic, complemented
150C22×C22⋊D61—21no—
151C22×C22⋊D61—21no—
152C2×D4×D61D411yescharacteristic
153C23×Dic61—21no—
154C23×Dic61—21no—
155C22×C4×D61C2311yescharacteristic
156C22×C4×D61C2311yescharacteristic
157#14519777C2×C411yescharacteristic, complemented
158#14519776—21no—
159#14519773—21no—
160#14519764C2×C411yescharacteristic, complemented
161#14519764C2×C411yescharacteristic, complemented
162#14519763—21no—
163#14519763—21no—
164#14519761—21no—
165#14519761—21no—
166#14519759—21no—
167#14519759—21no—
168#14519758—21no—
169#14519758—21no—
170#14519757C2×C411yescharacteristic
171#14519757C2×C411yescharacteristic, complemented
172#14519756C2×C411yescharacteristic
173#14519756C2×C411yescharacteristic, complemented
174#14519754—21no—
175#14519754—21no—
176#14519754—21no—
177#14519754—21no—
178#14519751—21no—
179#14519749—21no—
180#14519749—21no—
181#14519749—21no—
182#14519749—21no—
183#14519749—21no—
184#14519749—21no—
185#14519748—21no—
186#14519748—21no—
187#14519748C2×C411yescharacteristic
188#14519748C2×C411yescharacteristic, complemented
189#14519746—21no—
190#14519746—21no—
191#14519745—21no—
192#14519745—21no—
193C4×Dic122C2×C411yescharacteristic, complemented
194#14519742C2×C411yescharacteristic, complemented
195C4×D244C2×C411yescharacteristic
196D4×Dic61—21no—
197D4×Dic61—21no—
198D4×Dic61—21no—
199D4×Dic61—21no—
200D4×Dic61—21no—
201D4×Dic61—21no—
202D4×Dic61—21no—
203D4×Dic61—21no—
204D4×Dic61C2×C411yescharacteristic, complemented
205D4×Dic61D411yescharacteristic
206#14519739D411yescharacteristic
207C4×C22⋊D61—21no—
208C4×C22⋊D61C2×C411yescharacteristic
209C4×C22⋊D61C2×C411yescharacteristic
210#14519737—21no—
211#14519737—21no—
212#14519737—21no—
213#14519737D411yescharacteristic
214#14519737D411yescharacteristic
215#14519735C2311yescharacteristic
216#14519733—21no—
217C2×C4⋊Dic61—21no—
218C4⋊C4×D61D411yescharacteristic
219C2×C22⋊Dic61—21no—
220C2×C22⋊Dic61—21no—
221C22⋊C4×D61D411yescharacteristic
222C22⋊C4×D61D411yescharacteristic
223C2×C4×Dic61—21no—
224C42×D61C2311yescharacteristic
225C22×D4×C61—21no—
226C22×D4×C61C2×C411yescharacteristic
227C22×D4×C61C2×C411yescharacteristic, complemented
228#127×C61C2×C411yescharacteristic, complemented
229#121×C61—21no—
230#121×C61C2×C411yescharacteristic
231#121×C61C2×C411yescharacteristic, complemented
232#120×C61—21no—
233#120×C61—21no—
234C4×D4×C61C2×C411yescharacteristic
235C4×D4×C61C2×C411yescharacteristic, complemented
236C24×C61—21no—
237C24×C61—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—
247C2×D4×C61—22no—
248C2×D4×C61—22no—
249C2×D4×C61—21no—
250C2×D4×C61—21no—
251C2×D4×C61—21no—
252C2×D4×C61—21no—
253C2×D4×C61—21no—
254C2×D4×C61—21no—
255C2×D4×C61—41no—
256C2×D4×C61—41no—
257C2×D4×C61—44no—
258C2×D4×C61C22⋊C411yescharacteristic
259C2×D4×C61C22×C411yescharacteristic
260C2×D4×C61C22×C411yescharacteristic
261C2×D4×C61C22×C411yescharacteristic
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⋊D61—21no—
274C2×C22⋊D61—42no—
275C2×C22⋊D61—42no—
276C2×C22⋊D61—42no—
277C2×C22⋊D61—42no—
278C2×C22⋊D61C22⋊C411yescharacteristic
279C2×C22⋊D61C22⋊C411yescharacteristic
280C22×Dic61—21no—
281C22×Dic61—21no—
282C22×Dic61—21no—
283C22×Dic61—21no—
284C22×Dic61—21no—
285C22×Dic61—21no—
286C22×Dic61—21no—
287C22×Dic61—21no—
288C22×Dic61—21no—
289C22×Dic61—21no—
290C22×Dic61—42no—
291C22×Dic61—42no—
292C22×Dic61—42no—
293C22×Dic61—42no—
294C22×Dic61C2×D411yescharacteristic
295C22×Dic61C2×D411yescharacteristic
296#11758224—22no—
297#11758224—22no—
298#11758224—21no—
299#11758224—21no—
300#11758224—21no—
301#11758224—21no—
302#11758224—21no—
303#11758224—21no—
304#11758224—21no—
305#11758224—21no—
306#11758224—21no—
307#11758224—21no—
308#11758224—22no—
309#11758224—22no—
310#11758224—41no—
311#11758224—41no—
312#11758224—41no—
313#11758224—41no—
314#11758224—42no—
315#11758224—42no—
316#11758224—42no—
317#11758224—42no—
318#11758224—42no—
319#11758224—42no—
320#11758224—42no—
321#11758224—42no—
322#11758224C2×D412yes—
323#11758224#4112yes—
324D4×D61—42no—
325C2×D244C22⋊C411yescharacteristic
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×D61C22×C411yescharacteristic
335C2×C4×D61C22×C411yescharacteristic
336C2×C4×D61C2×D411yescharacteristic
337C2×C4×D61C2×D411yescharacteristic
338C2×C4×D61C2×D411yescharacteristic
339C2×C4×D61C2×D411yescharacteristic
340C2×C4×D61C2×D411yescharacteristic
341C2×C4×D61C2×D411yescharacteristic
342C2×C4×D61C2411yescharacteristic
343C2×Dic122—22no—
344C2×Dic122—22no—
345C2×Dic122—21no—
346C2×Dic122—21no—
347C2×Dic122—41no—
348C2×Dic122—41no—
349C2×Dic122C22×C411yescharacteristic
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×C61C22⋊C411yescharacteristic
383C4⋊C4×C61C22×C411yescharacteristic
384C22⋊C4×C61—21no—
385C22⋊C4×C61—21no—
386C22⋊C4×C61—21no—
387C22⋊C4×C61C22⋊C411yescharacteristic
388C22⋊C4×C61C22⋊C411yescharacteristic
389C42×C61C22×C411yescharacteristic
390C22⋊Dic61—21no—
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#11758198C22⋊C411yescharacteristic
405#11758198C22⋊C411yescharacteristic
406#11758198C22⋊C411yescharacteristic
407#11758198C22⋊C411yescharacteristic
408C4⋊Dic61—21no—
409C4⋊Dic61—21no—
410C4⋊Dic61—21no—
411C4⋊Dic61—21no—
412C4⋊Dic61C22⋊C411yescharacteristic
413C4⋊Dic61C22×C411yescharacteristic
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—21no—
429C23×C61—42no—
430C23×C61—42no—
431C23×C61—42no—
432C23×C61—42no—
433C23×C61—81no—
434C23×C61—81no—
435C23×C61C2×C22⋊C411yescharacteristic
436C23×C61C2×C22⋊C411yescharacteristic
437C22×D61—22no—
438C22×D61—21no—
439C22×D61—21no—
440C22×D61—21no—
441C22×D61—21no—
442C22×D61—41no—
443C22×D61—41no—
444C22×D61—41no—
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—
461D4×C61—22no—
462D4×C61—21no—
463D4×C61—21no—
464D4×C61—21no—
465D4×C61—21no—
466D4×C61—21no—
467D4×C61—42no—
468D4×C61—42no—
469D4×C61—42no—
470D4×C61—42no—
471D4×C61—42no—
472D4×C61—81no—
473D4×C61C4×D412yes—
474C2×C4×C61—21no—
475C2×C4×C61—21no—
476C2×C4×C61—21no—
477C2×C4×C61—21no—
478C2×C4×C61—21no—
479C2×C4×C61—42no—
480C2×C4×C61C2×C22⋊C411yescharacteristic
481C2×C4×C61C2×C22⋊C411yescharacteristic
482C2×C4×C61C2×C22⋊C411yescharacteristic
483C2×C4×C61C2×C22⋊C411yescharacteristic
484C2×C4×C61C23×C411yescharacteristic
485C22⋊D61—22no—
486C22⋊D61—22no—
487C22⋊D61—22no—
488C22⋊D61—41no—
489C22⋊D61—42no—
490C22⋊D61—42no—
491C22⋊D61—42no—
492C22⋊D61—42no—
493C22⋊D61—41no—
494C22⋊D61—41no—
495C22⋊D61—41no—
496C22⋊D61—41no—
497C22⋊D61—81no—
498C22⋊D61—81no—
499C2×Dic61—21no—
500C2×Dic61—21no—
501C2×Dic61—21no—
502C2×Dic61—22no—
503C2×Dic61—21no—
504C2×Dic61—21no—
505C2×Dic61—22no—
506C2×Dic61—21no—
507C2×Dic61—21no—
508C2×Dic61—21no—
509C2×Dic61—42no—
510C2×Dic61—42no—
511C2×Dic61—42no—
512C2×Dic61—42no—
513C2×Dic61—42no—
514C2×Dic61—42no—
515C2×Dic61—41no—
516C2×Dic61—41no—
517C2×Dic61—41no—
518C2×Dic61—41no—
519C2×Dic61—81no—
520C2×Dic61C2×C22⋊C411yescharacteristic
521C2×Dic61C2×C22⋊C411yescharacteristic
522C2×Dic61C2×C22⋊C411yescharacteristic
523C2×Dic61C2×C22⋊C411yescharacteristic
524C2×Dic61C22×D411yescharacteristic
525D244—41no—
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—21no—
537C4×D61—21no—
538C4×D61—41no—
539C4×D61—41no—
540C4×D61C22×D411yescharacteristic
541C4×D61C2×#4111yescharacteristic
542C4×D61H(5,𝔽2)11yescharacteristic
543C4×D61H(5,𝔽2)11yescharacteristic
544Dic122—21no—
545Dic122—21no—
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—41no—
569C22×C61—41no—
570C22×C61—41no—
571C22×C61—84no—
572C22×C61—84no—
573C22×C61#42112yescomplemented
574C22×C61C22×C22⋊C411yescharacteristic
575C2×D61—21no—
576C2×D61—21no—
577C2×D61—21no—
578C2×D61—21no—
579C2×D61—21no—
580C2×D61—21no—
581C2×D61—21no—
582C2×D61—21no—
583C2×D61—42no—
584C2×D61—42no—
585C2×D61—81no—
586C2×D61—81no—
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×C61C2×C4×D411yescharacteristic
599C4×C61#51811yescharacteristic
600Dic61—22no—
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—22no—
626C2×C61—41no—
627C2×C61—42no—
628C2×C61—81no—
629C2×C61—81no—
630C2×C61D4×C22⋊C411yescharacteristic
631C2×C61C2×#42111yescharacteristic
632C2×C61#290111yescharacteristic
633D61—21no—
634D61—21no—
635D61—41no—
636D61—41no—
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—611no—
649#546—1221no—
650#546—1221no—
651D42—1221no—
652D42#692311yescharacteristic, complemented
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—611no—
706C2×#41—1221no—
707C2×#41—1221no—
708C2×#41—1221no—
709C2×#41—1221no—
710C2×#41—1222no—
711C2×#41—1222no—
712C2×#41—1222no—
713C2×#41—1222no—
714C2×#41—2441no—
715C2×#41—2441no—
716C2×#41—2441no—
717C2×#41—2441no—
718C22×Q8—611no—
719C22×Q8—611no—
720C22×D4—21no—
721C22×D4—611no—
722C22×D4—1221no—
723C22×D4—1221no—
724C22×D4C2×#692311yescharacteristic
725C22×D4C2×#692311yescharacteristic, complemented
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—1221no—
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—611no—
767#121—611no—
768#121—1221no—
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—21no—
780#120—21no—
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—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—21no—
859C24—21no—
860C24—611no—
861C24—611no—
862#41—612no—
863#41—612no—
864#41—1221no—
865#41—1221no—
866#41—1221no—
867#41—1221no—
868#41—1221no—
869#41—1221no—
870#41—1221no—
871#41—1221no—
872#41—1221no—
873#41—1221no—
874#41—1222no—
875#41—1222no—
876#41—1222no—
877#41—1222no—
878#41—2442no—
879#41—2442no—
880#41—2442no—
881#41—2442no—
882#41—2441no—
883#41—2441no—
884#41—2441no—
885#41—2441no—
886#41—2442no—
887#41—2442no—
888#41—2442no—
889#41—2442no—
890C2×Q8—611no—
891C2×Q8—611no—
892C2×Q8—611no—
893C2×Q8—1222no—
894C2×Q8—1222no—
895C2×Q8—1221no—
896C2×Q8—1221no—
897C2×Q8—2441no—
898C2×Q8—2441no—
899C2×D4—22no—
900C2×D4—22no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—41no—
908C2×D4—41no—
909C2×D4—44no—
910C2×D4—611no—
911C2×D4—611no—
912C2×D4—611no—
913C2×D4—1221no—
914C2×D4—1221no—
915C2×D4—1221no—
916C2×D4—1221no—
917C2×D4—1221no—
918C2×D4—1221no—
919C2×D4—1221no—
920C2×D4—1221no—
921C2×D4—1221no—
922C2×D4—2442no—
923C2×D4—2442no—
924C2×D4—2442no—
925C2×D4—2442no—
926C2×D4—2442no—
927C2×D4C22⋊#692311yescharacteristic
928C2×D4C22×#692311yescharacteristic
929C2×D4C22×#692311yescharacteristic
930C2×D4C22×#692311yescharacteristic
931C22×C4—21no—
932C22×C4—611no—
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—1221no—
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—611no—
991C4⋊C4—611no—
992C4⋊C4—611no—
993C4⋊C4—611no—
994C4⋊C4—1221no—
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—611no—
1010C22⋊C4—611no—
1011C22⋊C4—611no—
1012C22⋊C4—611no—
1013C22⋊C4—611no—
1014C22⋊C4—611no—
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—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—21no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—81no—
1056C23—81no—
1057C23—611no—
1058C23—611no—
1059C23—611no—
1060C23—1221no—
1061C23—1221no—
1062C23—1221no—
1063C23—1221no—
1064C23—1222no—
1065C23—2441no—
1066C23—2441no—
1067C23—2441no—
1068C23C2×C22⋊#692311yescharacteristic
1069C23C2×C22⋊#692311yescharacteristic
1070Q8—612no—
1071Q8—1221no—
1072Q8—1221no—
1073Q8—1221no—
1074Q8—1221no—
1075Q8—1221no—
1076Q8—2442no—
1077Q8—2442no—
1078D4—22no—
1079D4—21no—
1080D4—21no—
1081D4—21no—
1082D4—21no—
1083D4—21no—
1084D4—42no—
1085D4—42no—
1086D4—42no—
1087D4—42no—
1088D4—42no—
1089D4—81no—
1090D4—1222no—
1091D4—1222no—
1092D4—1222no—
1093D4—4881no—
1094D4—4881no—
1095D4—2441no—
1096D4—2441no—
1097D4—2442no—
1098D4—2442no—
1099D4—2442no—
1100D4—2442no—
1101D4—2441no—
1102D4—2441no—
1103D4—2441no—
1104D4—2441no—
1105D4D4×#692312yes—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—42no—
1112C2×C4—611no—
1113C2×C4—611no—
1114C2×C4—611no—
1115C2×C4—611no—
1116C2×C4—611no—
1117C2×C4—611no—
1118C2×C4—611no—
1119C2×C4—611no—
1120C2×C4—611no—
1121C2×C4—1221no—
1122C2×C4—1221no—
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—1222no—
1134C2×C4—1222no—
1135C2×C4—1221no—
1136C2×C4—1221no—
1137C2×C4—1221no—
1138C2×C4—1221no—
1139C2×C4—1221no—
1140C2×C4—1222no—
1141C2×C4—1222no—
1142C2×C4—1221no—
1143C2×C4—1221no—
1144C2×C4—1221no—
1145C2×C4—4881no—
1146C2×C4—2441no—
1147C2×C4—2441no—
1148C2×C4—2441no—
1149C2×C4—2441no—
1150C2×C4—2441no—
1151C2×C4—2441no—
1152C2×C4—2442no—
1153C2×C4—2442no—
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—41no—
1190C22—41no—
1191C22—41no—
1192C22—84no—
1193C22—84no—
1194C22—611no—
1195C22—611no—
1196C22—1221no—
1197C22—1221no—
1198C22—1221no—
1199C22—1221no—
1200C22—1221no—
1201C22—1221no—
1202C22—1221no—
1203C22—1221no—
1204C22—4881no—
1205C22—4881no—
1206C22—2442no—
1207C22—2442no—
1208C22#1684076012yescomplemented
1209C22C22×C22⋊#692311yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—21no—
1213C4—21no—
1214C4—41no—
1215C4—611no—
1216C4—611no—
1217C4—1221no—
1218C4—1221no—
1219C4—1222no—
1220C4—1221no—
1221C4—1221no—
1222C4—4881no—
1223C4—4881no—
1224C4—2442no—
1225C4—2442no—
1226C4—2441no—
1227C4—2441no—
1228C4—2441no—
1229C4C2×D4×#692311yescharacteristic
1230C4#1684082911yescharacteristic
1231C2—22no—
1232C2—41no—
1233C2—42no—
1234C2—81no—
1235C2—81no—
1236C2—1221no—
1237C2—1221no—
1238C2—2441no—
1239C2—2441no—
1240C2D4×C22⋊#692311yescharacteristic
1241C2C2×#1684076011yescharacteristic
1242C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingD42×C61C4
socleC22×C61C22×C22⋊C4
prime radicalD4×#11758224C2
cosocleC2×C4×D61C24
hypercenterD42#6923
hypocenterC61#22434
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #21462558C2semidirect
2. C2×#16840760C2semidirect
3. C22×#14519841C2semidirect
4. #21462273C2semidirect
5. #21461983C2semidirect
6. #21461957C2semidirect
7. #21461839C2semidirect
8. #21461837C2semidirect
9. #21461803C2semidirect
10. #21461802C2semidirect
11. #21461693C2semidirect
12. #21461660C2semidirect
13. #21461660C2semidirect
14. #21461582C2semidirect
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. #16840432C4semidirect
57. D4×Dic122C4semidirect
58. #16840418C4semidirect
59. #16840418C4semidirect
60. #16840416C4semidirect
62. #16840406C4semidirect
63. #16840406C4semidirect
76. D42×C61C4semidirect
117. #14519841D4semidirect
143. C2×#11758224C2×C4semidirect
144. C2×#11758224C2×C4semidirect
149. C22×Dic122C2×C4semidirect
157. #14519777C2×C4semidirect
160. #14519764C2×C4semidirect
161. #14519764C2×C4semidirect
171. #14519757C2×C4semidirect
173. #14519756C2×C4semidirect
188. #14519748C2×C4semidirect
193. C4×Dic122C2×C4semidirect
194. #14519742C2×C4semidirect
204. D4×Dic61C2×C4semidirect
227. C22×D4×C61C2×C4semidirect
228. #127×C61C2×C4semidirect
231. #121×C61C2×C4semidirect
235. C4×D4×C61C2×C4semidirect
371. C4×#6923C2×D4semidirect
380. #11758213C2×D4semidirect
573. C22×C61#421semidirect
652. D42#6923semidirect
698. C61#22434semidirect
725. C22×D4C2×#6923semidirect
746. #127C2×#6923semidirect
778. #121C2×#6923semidirect
808. C4×D4C2×#6923semidirect
1208. C22#16840760semidirect

Maximal subgroups

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

subgroupindex
#214625582
C2×#168407602
C22×#145198412
#214622732
#214619832
#214619572
#214618392
#214618372
#214618032
#214618022
#214616932
#214616602
#214615822
D4×#117582242
#2243461