Finite Group Databasebeta

← #107159

Subgroups — #107159

Order 512.

1029 conjugacy classes of subgroups.

The subgroup lattice has 535 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34245C211yesmaximal, characteristic
2#21753C211yesmaximal, characteristic
3C2×#1996C211yesmaximal, characteristic
4C2×#1297C211yesmaximal, characteristic
5#8019C211yesmaximal, characteristic
6#7983C211yesmaximal, characteristic
7#7942C211yesmaximal, characteristic
8C22×C22⋊Q8C2211yescharacteristic
9C2×#407C2211yescharacteristic
10C2×#407C2211yescharacteristic
11#2368—22no—
12#2362—22no—
13#2344—21no—
14#2342—22no—
15Q8×C22⋊C4—21no—
16#2332—22no—
17#2313C412yescomplemented
18C4×C22⋊Q8—22no—
19#2280C2211yescharacteristic
20C2×#380C2211yescharacteristic
21#2274C412yescomplemented
22C2×C4×C22⋊C4C2211yescharacteristic
23C2×C4×C22⋊C4C2211yescharacteristic
24#1996—22no—
25#1996C414yescomplemented
26#1901—22no—
27#1901C414yescomplemented
28#1821—21no—
29#1784—21no—
30C2×#342—22no—
31#1297—22no—
32#1294—22no—
33#1289—22no—
34#1284—22no—
35C23×Q8D411yescharacteristic
36C24×C4C2311yescharacteristic
37C22×M16—21no—
38C22×M16C2×C412yes—
39C2×C22⋊Q8—21no—
40C2×C22⋊Q8—21no—
41C2×C22⋊Q8—21no—
42C2×C22⋊Q8—21no—
43C2×C22⋊Q8—21no—
44C2×C22⋊Q8—21no—
45C2×C22⋊Q8—21no—
46C2×C22⋊Q8—21no—
47C2×C22⋊Q8C2×C412yes—
48C2×C22⋊Q8C2×C412yes—
49C2×C22⋊Q8D412yes—
50C2×C22⋊Q8Q812yes—
51C2×C4×Q8—22no—
52C2×#117—22no—
53C2×#117—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4C2×C412yes—
56C22×C4⋊C4D411yescharacteristic
57C22×C22⋊C4—21no—
58C22×C22⋊C4—21no—
59C22×C22⋊C4—21no—
60C22×C22⋊C4D412yes—
61C22×C42—21no—
62C22×C42—21no—
63C2×#101—24no—
64#407—21no—
65#407—21no—
66#407—21no—
67#407—21no—
68#407—21no—
69#407—21no—
70#407—21no—
71#407C2×C412yes—
72C2×C22⋊C8—21no—
73C2×C22⋊C8—21no—
74C2×C22⋊C8—21no—
75C2×C22⋊C8—21no—
76#391—24no—
77#391—22no—
78#389—22no—
79#388—24no—
80#388—24no—
81#387—24no—
82#387—24no—
83#387—24no—
84#385—24no—
85#381—22no—
86#381D412yes—
87#380—22no—
88#380—21no—
89#380—21no—
90#380—21no—
91#380—21no—
92#380C2×C412yes—
93#380D412yes—
94#379—21no—
95C4×C4⋊C4—22no—
96C4×C4⋊C4—24no—
97C4×C4⋊C4—24no—
98C4×C22⋊C4—24no—
99C4×C22⋊C4—22no—
100C4×C22⋊C4—21no—
101C4×C22⋊C4—21no—
102C4×C22⋊C4—21no—
103C4×C22⋊C4—21no—
104C4×C22⋊C4—21no—
105C4×C22⋊C4—21no—
106C4×C22⋊C4C2×C412yes—
107C4×C22⋊C4C2×C411yescharacteristic
108C4×C22⋊C4C2×C412yes—
109C4×C22⋊C4C2×C411yescharacteristic
110C4×C22⋊C4D412yes—
111C2×#95—21no—
112C2×#95—21no—
113C2×#95D412yes—
114#343—24no—
115#342—28no—
116C25C2×D411yescharacteristic
117C22×Q8—21no—
118C22×Q8—21no—
119C22×Q8—21no—
120C22×Q8—21no—
121C22×Q8—82no—
122C22×Q8C22⋊C412yes—
123C22×Q8C4⋊C412yes—
124C23×C4—22no—
125C23×C4—41no—
126C23×C4—41no—
127C23×C4—82no—
128C23×C4C22⋊C412yes—
129C23×C4C22⋊C412yes—
130C23×C4C22×C411yescharacteristic
131C23×C4C22×C411yescharacteristic
132C23×C4C22×C411yescharacteristic
133C23×C4C2×D411yescharacteristic
134C23×C4C2×D411yescharacteristic
135C23×C4C2×D411yescharacteristic
136C23×C4C2×D411yescharacteristic
137C23×C4C2×D411yescharacteristic
138C23×C4C2×D411yescharacteristic
139C23×C4C2×Q811yescharacteristic
140C23×C4#4111yescharacteristic
141C23×C4#4111yescharacteristic
142C23×C4#4111yescharacteristic
143C23×C4#4111yescharacteristic
144C2×M16—22no—
145C2×M16—22no—
146C2×M16—22no—
147C2×M16—41no—
148C2×M16—82no—
149C2×M16—82no—
150C22×C8—22no—
151C22×C8—41no—
152C22⋊Q8—22no—
153C22⋊Q8—22no—
154C22⋊Q8—22no—
155C22⋊Q8—22no—
156C22⋊Q8—22no—
157C22⋊Q8—22no—
158C22⋊Q8—22no—
159C22⋊Q8—22no—
160C22⋊Q8—22no—
161C22⋊Q8—22no—
162C22⋊Q8—22no—
163C22⋊Q8—22no—
164C22⋊Q8—22no—
165C22⋊Q8—22no—
166C22⋊Q8—22no—
167C22⋊Q8—22no—
168C4×Q8—84no—
169#117—48no—
170#117—82no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—24no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—24no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—41no—
184C2×C4⋊C4—82no—
185C2×C4⋊C4C4214yes—
186C2×C4⋊C4C22⋊C412yes—
187C2×C4⋊C4C4⋊C414yes—
188C2×C4⋊C4C4⋊C412yes—
189C2×C22⋊C4—21no—
190C2×C22⋊C4—22no—
191C2×C22⋊C4—22no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—24no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—21no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4—22no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—44no—
203C2×C22⋊C4—42no—
204C2×C22⋊C4—41no—
205C2×C22⋊C4—44no—
206C2×C22⋊C4—41no—
207C2×C22⋊C4C22⋊C414yes—
208C2×C22⋊C4C4⋊C414yes—
209C2×C42—24no—
210C2×C42—22no—
211C2×C42—24no—
212C2×C42—22no—
213C2×C42—21no—
214C2×C42—21no—
215C2×C42—22no—
216C2×C42—41no—
217C2×C42—82no—
218C2×C42—82no—
219#101—84no—
220C22⋊C8—22no—
221C22⋊C8—22no—
222C22⋊C8—41no—
223C22⋊C8—41no—
224C22⋊C8—41no—
225C22⋊C8—41no—
226C22⋊C8—41no—
227C22⋊C8—41no—
228#95—24no—
229#95—24no—
230#95—24no—
231#95—24no—
232#95—22no—
233#95—22no—
234#95—22no—
235#95—22no—
236#95—41no—
237#95—41no—
238#95C22⋊C412yes—
239#95C22⋊C412yes—
240#95C22⋊C414yes—
241C24—22no—
242C24—22no—
243C24—42no—
244C24—81no—
245C24C2×C22⋊C411yescharacteristic
246C24C2×C22⋊C411yescharacteristic
247C24C2×C4⋊C411yescharacteristic
248C24#12011yescharacteristic
249C24#12011yescharacteristic
250C24#12311yescharacteristic
251C24#12311yescharacteristic
252C2×Q8—22no—
253C2×Q8—22no—
254C2×Q8—22no—
255C2×Q8—22no—
256C2×Q8—44no—
257C2×Q8—44no—
258C2×Q8—82no—
259C2×Q8—82no—
260C2×Q8—82no—
261C2×Q8—82no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—24no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—44no—
277C22×C4—44no—
278C22×C4—44no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—81no—
284C22×C4—81no—
285C22×C4—81no—
286C22×C4—81no—
287C22×C4—81no—
288C22×C4—81no—
289C22×C4—81no—
290C22×C4—82no—
291C22×C4—82no—
292C22×C4—82no—
293C22×C4—82no—
294C22×C4—82no—
295C22×C4—82no—
296C22×C4—82no—
297C22×C4#9514yes—
298C22×C4#9514yes—
299C22×C4C2×C4211yescharacteristic
300C22×C4C2×C22⋊C411yescharacteristic
301C22×C4C2×C22⋊C411yescharacteristic
302C22×C4C2×C22⋊C411yescharacteristic
303C22×C4C2×C4⋊C411yescharacteristic
304C22×C4C2×C4⋊C411yescharacteristic
305C22×C4#11711yescharacteristic
306C22×C4#11711yescharacteristic
307C22×C4C4×D411yescharacteristic
308C22×C4C4×D411yescharacteristic
309C22×C4C4×D411yescharacteristic
310C22×C4C4×D411yescharacteristic
311C22×C4C4×D411yescharacteristic
312C22×C4C4×D411yescharacteristic
313C22×C4C4×D411yescharacteristic
314C22×C4C4×D411yescharacteristic
315C22×C4#12011yescharacteristic
316C22×C4#12011yescharacteristic
317C22×C4#12111yescharacteristic
318C22×C4#12111yescharacteristic
319C22×C4#12111yescharacteristic
320C22×C4#12111yescharacteristic
321C22×C4C22⋊Q811yescharacteristic
322C22×C4C22⋊Q811yescharacteristic
323C22×C4C22⋊Q811yescharacteristic
324C22×C4C22⋊Q811yescharacteristic
325C22×C4#12311yescharacteristic
326C22×C4#12311yescharacteristic
327M16—44no—
328M16—44no—
329M16—82no—
330M16—82no—
331C2×C8—42no—
332C2×C8—42no—
333C2×C8—82no—
334C2×C8—82no—
335C4⋊C4—24no—
336C4⋊C4—24no—
337C4⋊C4—24no—
338C4⋊C4—24no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—48no—
344C4⋊C4—44no—
345C4⋊C4—82no—
346C4⋊C4—84no—
347C4⋊C4—82no—
348C22⋊C4—24no—
349C22⋊C4—24no—
350C22⋊C4—24no—
351C22⋊C4—24no—
352C22⋊C4—24no—
353C22⋊C4—24no—
354C22⋊C4—44no—
355C22⋊C4—44no—
356C22⋊C4—42no—
357C22⋊C4—42no—
358C22⋊C4—44no—
359C22⋊C4—42no—
360C22⋊C4—42no—
361C22⋊C4—44no—
362C22⋊C4—82no—
363C22⋊C4—82no—
364C42—44no—
365C42—48no—
366C42—82no—
367C42—81no—
368C42—81no—
369C42—82no—
370C42—84no—
371C42—82no—
372C23—22no—
373C23—22no—
374C23—22no—
375C23—22no—
376C23—22no—
377C23—21no—
378C23—21no—
379C23—22no—
380C23—22no—
381C23—21no—
382C23—21no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—84no—
395C23—84no—
396C23C2×#9511yescharacteristic
397C23#37911yescharacteristic
398C23#38111yescharacteristic
399C23#38511yescharacteristic
400C23#38511yescharacteristic
401C23#38611yescharacteristic
402C23#38611yescharacteristic
403C23#45412yes—
404C23#45612yes—
405Q8—44no—
406Q8—44no—
407Q8—82no—
408Q8—82no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—24no—
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—42no—
441C2×C4—42no—
442C2×C4—44no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—44no—
446C2×C4—44no—
447C2×C4—44no—
448C2×C4—42no—
449C2×C4—44no—
450C2×C4—44no—
451C2×C4—44no—
452C2×C4—42no—
453C2×C4—44no—
454C2×C4—42no—
455C2×C4—82no—
456C2×C4—84no—
457C2×C4—84no—
458C2×C4—82no—
459C2×C4—82no—
460C2×C4—88no—
461C2×C4—82no—
462C2×C4—82no—
463C2×C4—82no—
464C2×C4—164no—
465C2×C4C4×C22⋊C411yescharacteristic
466C2×C4C4×C22⋊C411yescharacteristic
467C2×C4#38011yescharacteristic
468C2×C4#38011yescharacteristic
469C2×C4#38511yescharacteristic
470C2×C4#38511yescharacteristic
471C2×C4#38611yescharacteristic
472C2×C4#38611yescharacteristic
473C8—82no—
474C8—82no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—42no—
493C22—42no—
494C22—44no—
495C22—42no—
496C22—44no—
497C22—42no—
498C22—82no—
499C22—81no—
500C22—82no—
501C22—81no—
502C22C22⋊#9511yescharacteristic
503C22#179312yes—
504C22#182712yes—
505C22#185712yes—
506C22#188611yescharacteristic
507C22#188811yescharacteristic
508C4—21no—
509C4—21no—
510C4—21no—
511C4—21no—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—44no—
516C4—44no—
517C4—44no—
518C4—84no—
519C4—82no—
520C4—84no—
521C4—162no—
522C4#191312yes—
523C2—22no—
524C2—21no—
525C2—22no—
526C2—22no—
527C2—21no—
528C2—41no—
529C2—41no—
530C2—41no—
531C2#1075011yescharacteristic
532C2#1075411yescharacteristic
533C2#1075811yescharacteristic
subgroupG/H
center, socleC22C22⋊#95
commutatorC22×C4C2×C42
Frattini, cosocleC24×C4C23
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
17. #2313C4semidirect
21. #2274C4semidirect
25. #1996C4semidirect
27. #1901C4semidirect

Maximal subgroups

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

subgroupindex
#342452
#217532
C2×#19962
C2×#12972
#80192
#79832
#79422