Finite Group Databasebeta

← #16379

Subgroups — #16379

Order 256.

807 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397C211yesmaximal, characteristic, complemented
2C2×#386C211yesmaximal, characteristic
3#1443C211yesmaximal, characteristic, complemented
4#1443C211yesmaximal, characteristic, complemented
5#1443C211yesmaximal, characteristic, complemented
6#1441C211yesmaximal, characteristic, complemented
7#1440C211yesmaximal, characteristic, complemented
8#1440C211yesmaximal, characteristic, complemented
9#1439C211yesmaximal, characteristic, complemented
10#1439C211yesmaximal, characteristic, complemented
11#1439C211yesmaximal, characteristic, complemented
12#1438C211yesmaximal, characteristic
13#1438C211yesmaximal, characteristic
14C22⋊#95C211yesmaximal, characteristic, complemented
15C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4C2211yescharacteristic
17C24×C4C2211yescharacteristic
18C22×C4⋊C4C2211yescharacteristic
19C22×C4⋊C4C2211yescharacteristic
20C22×C22⋊C4C2211yescharacteristic
21C22×C22⋊C4C2211yescharacteristic
22C22×C22⋊C4C2211yescharacteristic
23C22×C22⋊C4C2211yescharacteristic
24C22×C22⋊C4C2211yescharacteristic
25C22×C22⋊C4C2211yescharacteristic
26C22×C22⋊C4C2211yescharacteristic
27C22×C22⋊C4C2211yescharacteristic
28C22×C22⋊C4C2211yescharacteristic
29C22×C22⋊C4C2211yescharacteristic
30C22×C22⋊C4C2211yescharacteristic
31#397—24no—
32#386—24no—
33C2×#95C2211yescharacteristic
34C2×#95C2211yescharacteristic
35C2×#95C2211yescharacteristic
36C2×#95C2211yescharacteristic
37C2×#95C2211yescharacteristic
38C2×#95C2211yescharacteristic
39C2×#95C2211yescharacteristic
40C2×#95C2211yescharacteristic
41C2×#95C2211yescharacteristic
42C2×#95C2211yescharacteristic
43C2×#95C2211yescharacteristic
44C2×#95C2211yescharacteristic
45C2×#95C2211yescharacteristic
46C2×#95C2211yescharacteristic
47C2×#95C2211yescharacteristic
48C2×#95C2211yescharacteristic
49C2×#95C2211yescharacteristic
50C2×#95C2211yescharacteristic
51C2×#95C2211yescharacteristic
52C2×#95C2211yescharacteristic
53C25C2311yescharacteristic
54C25C2311yescharacteristic
55C22×D4—22no—
56C22×D4—22no—
57C22×D4—22no—
58C22×D4—22no—
59C22×D4—22no—
60C22×D4—41no—
61C22×D4—41no—
62C23×C4—22no—
63C23×C4—22no—
64C23×C4—22no—
65C23×C4—41no—
66C23×C4—41no—
67C23×C4—41no—
68C23×C4—41no—
69C23×C4C2311yescharacteristic
70C23×C4C2311yescharacteristic
71C23×C4C2311yescharacteristic
72C23×C4C2311yescharacteristic
73C23×C4C2311yescharacteristic
74C23×C4C2311yescharacteristic
75C23×C4C2311yescharacteristic
76C23×C4C2311yescharacteristic
77C23×C4C2311yescharacteristic
78C23×C4C2311yescharacteristic
79C23×C4C2311yescharacteristic
80C23×C4C2311yescharacteristic
81C23×C4C2311yescharacteristic
82C2×C4⋊C4—22no—
83C2×C4⋊C4—22no—
84C2×C4⋊C4—41no—
85C2×C4⋊C4—41no—
86C2×C4⋊C4—41no—
87C2×C4⋊C4—41no—
88C2×C22⋊C4—22no—
89C2×C22⋊C4—22no—
90C2×C22⋊C4—22no—
91C2×C22⋊C4—22no—
92C2×C22⋊C4—22no—
93C2×C22⋊C4—22no—
94C2×C22⋊C4—22no—
95C2×C22⋊C4—22no—
96C2×C22⋊C4—22no—
97C2×C22⋊C4—22no—
98C2×C22⋊C4—22no—
99C2×C22⋊C4—22no—
100C2×C22⋊C4—41no—
101C2×C22⋊C4—41no—
102C2×C22⋊C4—41no—
103C2×C22⋊C4—41no—
104C2×C22⋊C4—41no—
105C2×C22⋊C4—41no—
106C2×C22⋊C4—41no—
107C2×C22⋊C4—41no—
108C2×C22⋊C4—41no—
109C2×C22⋊C4—41no—
110C2×C22⋊C4—41no—
111C2×C22⋊C4—41no—
112C2×C22⋊C4—41no—
113C2×C22⋊C4—41no—
114C2×C22⋊C4—41no—
115C2×C22⋊C4—41no—
116C2×C22⋊C4—41no—
117C2×C22⋊C4—41no—
118C2×C22⋊C4—41no—
119C2×C22⋊C4—41no—
120C2×C22⋊C4D414yes—
121#95—22no—
122#95—22no—
123#95—22no—
124#95—22no—
125#95—22no—
126#95—22no—
127#95—22no—
128#95—22no—
129#95—41no—
130#95—41no—
131#95—41no—
132#95—41no—
133#95—41no—
134#95—41no—
135#95—41no—
136#95—41no—
137#95—41no—
138#95—41no—
139#95—41no—
140#95—41no—
141C24—21no—
142C24—21no—
143C24—21no—
144C24—21no—
145C24—21no—
146C24—21no—
147C24—21no—
148C24—21no—
149C24—21no—
150C24—21no—
151C24—21no—
152C24—21no—
153C24—21no—
154C24—21no—
155C24—21no—
156C24—21no—
157C24—21no—
158C24—21no—
159C24—21no—
160C24—21no—
161C24—21no—
162C24—21no—
163C24—21no—
164C24—21no—
165C24—21no—
166C24—21no—
167C24C2×D412yes—
168C24#4112yes—
169C24#4112yes—
170C24#4112yes—
171C24C2411yescharacteristic
172C2×D4—28no—
173C2×D4—44no—
174C2×D4—44no—
175C2×D4—44no—
176C2×D4—44no—
177C2×D4—44no—
178C2×D4—44no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—44no—
266C22×C4—44no—
267C22×C4—44no—
268C22×C4—44no—
269C22×C4—44no—
270C22×C4—44no—
271C22×C4—44no—
272C22×C4C2×D412yes—
273C22×C4C2×D412yes—
274C22×C4#4112yes—
275C22×C4#4112yes—
276C22×C4#4112yes—
277C4⋊C4—44no—
278C4⋊C4—44no—
279C22⋊C4—44no—
280C22⋊C4—44no—
281C22⋊C4—44no—
282C22⋊C4—44no—
283C22⋊C4—44no—
284C22⋊C4—44no—
285C22⋊C4—44no—
286C22⋊C4—44no—
287C22⋊C4—44no—
288C22⋊C4—44no—
289C22⋊C4—44no—
290C23—22no—
291C23—22no—
292C23—22no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—22no—
297C23—22no—
298C23—22no—
299C23—22no—
300C23—22no—
301C23—22no—
302C23—22no—
303C23—22no—
304C23—22no—
305C23—22no—
306C23—22no—
307C23—22no—
308C23—22no—
309C23—22no—
310C23—22no—
311C23—22no—
312C23—22no—
313C23—22no—
314C23—22no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23#12614yes—
360C23C22×D411yescharacteristic
361C23C2×#4111yescharacteristic
362C23C2×#4111yescharacteristic
363C23C2×#4111yescharacteristic
364C23C2×#4111yescharacteristic
365C23C2×#4111yescharacteristic
366C23C2×#4111yescharacteristic
367C23H(5,𝔽2)11yescharacteristic
368C23H(5,𝔽2)11yescharacteristic
369C23H(5,𝔽2)11yescharacteristic
370C23H(5,𝔽2)11yescharacteristic
371C23H(5,𝔽2)11yescharacteristic
372C23H(5,𝔽2)11yescharacteristic
373C23H(5,𝔽2)11yescharacteristic
374C232−1+411yescharacteristic
375D4—416no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—416no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C22—24no—
469C22—24no—
470C22—24no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—42no—
478C22—42no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—42no—
488C22—42no—
489C22—42no—
490C22—81no—
491C22—81no—
492C22—81no—
493C22—81no—
494C22—81no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22#52511yescharacteristic
499C22C2×#12611yescharacteristic
500C22#52911yescharacteristic
501C22#53411yescharacteristic
502C22#53711yescharacteristic
503C22#53811yescharacteristic
504C22#53811yescharacteristic
505C22#53811yescharacteristic
506C22#53811yescharacteristic
507C22#53811yescharacteristic
508C22#53811yescharacteristic
509C22#53911yescharacteristic
510C22#53911yescharacteristic
511C22#53911yescharacteristic
512C22#53911yescharacteristic
513C22#54011yescharacteristic
514C22#54011yescharacteristic
515C22#54211yescharacteristic
516C22#54211yescharacteristic
517C22#54611yescharacteristic
518C22#54611yescharacteristic
519C22#54611yescharacteristic
520C22#54611yescharacteristic
521C22#55111yescharacteristic
522C22#55111yescharacteristic
523C22#55111yescharacteristic
524C22#55111yescharacteristic
525C22#55311yescharacteristic
526C22#55311yescharacteristic
527C22#55511yescharacteristic
528C22#55911yescharacteristic
529C22#56011yescharacteristic
530C22#56011yescharacteristic
531C22#56011yescharacteristic
532C22#56011yescharacteristic
533C4—42no—
534C4—42no—
535C4—42no—
536C4—42no—
537C4—42no—
538C4—81no—
539C4—81no—
540C4—81no—
541C4—81no—
542C4—81no—
543C4—81no—
544C4—81no—
545C4—81no—
546C2—44no—
547C2—82no—
548C2#245911yescharacteristic
549C2#248011yescharacteristic
550C2#251011yescharacteristic
551C2#263011yescharacteristic
552C2#264311yescharacteristic
553C2#264911yescharacteristic
554C2#268811yescharacteristic
555C2#269111yescharacteristic
556C2#269311yescharacteristic
557C2#269711yescharacteristic
558C2#273711yescharacteristic
559C2#275211yescharacteristic
560C2#275611yescharacteristic
561C2#279611yescharacteristic
562C2#282511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C24
prime radicalC23×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#397C2semidirect
3. #1443C2semidirect
4. #1443C2semidirect
5. #1443C2semidirect
6. #1441C2semidirect
7. #1440C2semidirect
8. #1440C2semidirect
9. #1439C2semidirect
10. #1439C2semidirect
11. #1439C2semidirect
14. C22⋊#95C2semidirect
15. C22⋊#95C2semidirect

Maximal subgroups

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

subgroupindex
C2×#3972
C2×#3862
#14432
#14412
#14402
#14392
#14382
C22⋊#952