Finite Group Databasebeta

← #480765

Subgroups — #480765

Order 512.

914 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35279C211yesmaximal, characteristic
2#17363C211yesmaximal, characteristic
3#17363C211yesmaximal, characteristic
4#11576C214yesmaximal, complemented
5#11575C214yesmaximal, complemented
6#11520C214yesmaximal, complemented
7C22×C4⋊Q8C411yescharacteristic
8C2×C4×#41C2211yescharacteristic
9C2×#432—21no—
10C2×#432—21no—
11#2857—21no—
12#2857—21no—
13#2628—21no—
14#2628—21no—
15#2568—21no—
16#2567—21no—
17#2563—21no—
18#2542—21no—
19#2487C412yes—
20#2487C2212yes—
21#2409C412yes—
22#2409C2212yes—
23#2317C2212yes—
24#2311C412yes—
25#2285C411yescharacteristic
26#1467—21no—
27#1467—21no—
28#1466C2212yes—
29#1466C2212yes—
30#1464—21no—
31#1464—21no—
32#1464C2212yes—
33#1464C2212yes—
34#1459—21no—
35#1459—21no—
36#1459C2212yes—
37#1459C2212yes—
38#1326C22116yes—
39C22×#41C2×C411yescharacteristic
40C23×Q8C2×C412yes—
41C2×C4⋊Q8—21no—
42C2×C4⋊Q8—21no—
43C2×C4⋊Q8—21no—
44C2×C4⋊Q8—21no—
45C2×C4⋊Q8—41no—
46C2×C4⋊Q8—41no—
47C2×C4⋊Q8—41no—
48C2×C4⋊Q8—41no—
49C2×C22⋊Q8—22no—
50C2×C22⋊Q8—22no—
51C4×#41—41no—
52C4×#41—41no—
53C4×#41—41no—
54C4×#41—41no—
55C2×C4×Q8D411yescharacteristic
56C2×C4×Q8D411yescharacteristic
57C2×C4×D4C2×C411yescharacteristic
58C2×C4×D4C2×C411yescharacteristic
59C2×C4×D4D411yescharacteristic
60C2×C4×D4D411yescharacteristic
61C2×C4×D4C2311yescharacteristic
62C2×C4×D4C2311yescharacteristic
63C2×#117C2×C412yes—
64C2×#117D411yescharacteristic
65C2×#117D411yescharacteristic
66C2×#117C2311yescharacteristic
67C22×C4⋊C4C2×C412yes—
68C22×C4⋊C4C2×C412yes—
69C22×C42C2×C411yescharacteristic
70C22×C42D411yescharacteristic
71C22×C42D411yescharacteristic
72#432—22no—
73#432—22no—
74#432—22no—
75#432—22no—
76#432—41no—
77#432—41no—
78#432—41no—
79#432—41no—
80C2×C4⋊C8—41no—
81C2×C4⋊C8—41no—
82C2×C22⋊C8—22no—
83C2×C22⋊C8—22no—
84C2×#97—41no—
85C2×#97—41no—
86#400—22no—
87#400—22no—
88#399—22no—
89#399—22no—
90#395—22no—
91#395—22no—
92#393—22no—
93#393—22no—
94#391—22no—
95#391—22no—
96#391—22no—
97#390—22no—
98#389—22no—
99#389—22no—
100#389—22no—
101#389—22no—
102#386C2×C414yes—
103#386C2×C414yes—
104#385C2×C414yes—
105#385C2314yes—
106#384—22no—
107#384—21no—
108#382—22no—
109#382—21no—
110#380—22no—
111#380—22no—
112#380—22no—
113#380—22no—
114#380C2×C412yes—
115#380C2×C412yes—
116C4×C4⋊C4—21no—
117C4×C4⋊C4—21no—
118#324—22no—
119#324—22no—
120#324—22no—
121#324—22no—
122#323—22no—
123#323—22no—
124#323C2314yes—
125#323C2314yes—
126C2×#41—24no—
127C2×#41—41no—
128C2×#41—41no—
129C2×#41—42no—
130C22×Q8—22no—
131C22×Q8—22no—
132C22×Q8—42no—
133C22×Q8—42no—
134C22×Q8—84no—
135C22×Q8C22⋊C411yescharacteristic
136C22×D4C22⋊C411yescharacteristic
137C22×D4C22×C411yescharacteristic
138C22×D4C22×C411yescharacteristic
139C23×C4C22⋊C411yescharacteristic
140C23×C4C22⋊C411yescharacteristic
141C23×C4C22⋊C411yescharacteristic
142C23×C4C22⋊C411yescharacteristic
143C23×C4C22×C411yescharacteristic
144C23×C4C22×C411yescharacteristic
145C23×C4C22×C411yescharacteristic
146C23×C4C22×C414yes—
147C23×C4C2×D411yescharacteristic
148C23×C4C2×D411yescharacteristic
149C22×C8—42no—
150C22×C8—42no—
151C4⋊Q8—42no—
152C4⋊Q8—42no—
153C4⋊Q8—42no—
154C4⋊Q8—42no—
155C4⋊Q8—42no—
156C4⋊Q8—42no—
157C4⋊Q8—41no—
158C4⋊Q8—41no—
159C4⋊Q8—41no—
160C4⋊Q8—41no—
161C22⋊Q8—84no—
162C22⋊Q8—84no—
163C4×Q8—41no—
164C4×Q8—41no—
165C4×Q8—41no—
166C4×Q8—41no—
167C4×D4—41no—
168C4×D4—41no—
169C4×D4—41no—
170C4×D4—41no—
171C4×D4—41no—
172C4×D4—41no—
173C4×D4—41no—
174C4×D4—41no—
175C4×D4—41no—
176C4×D4—41no—
177C4×D4—41no—
178C4×D4—41no—
179#117—41no—
180#117—41no—
181#117—41no—
182#117—41no—
183#117—41no—
184#117—41no—
185#117—44no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—24no—
194C2×C4⋊C4—24no—
195C2×C4⋊C4—42no—
196C2×C4⋊C4—42no—
197C2×C4⋊C4—42no—
198C2×C4⋊C4—42no—
199C2×C4⋊C4C22⋊C411yescharacteristic
200C2×C4⋊C4C22⋊C411yescharacteristic
201C2×C4⋊C4C2×D411yescharacteristic
202C2×C4⋊C4C2×D411yescharacteristic
203C2×C4⋊C4C2×D411yescharacteristic
204C2×C4⋊C4C2×D411yescharacteristic
205C2×C22⋊C4—24no—
206C2×C22⋊C4—24no—
207C2×C22⋊C4C22⋊C411yescharacteristic
208C2×C22⋊C4C22⋊C411yescharacteristic
209C2×C22⋊C4C22×C414yes—
210C2×C22⋊C4C22×C411yescharacteristic
211C2×C22⋊C4C2×D411yescharacteristic
212C2×C22⋊C4C2×D411yescharacteristic
213C2×C22⋊C4C2411yescharacteristic
214C2×C42—21no—
215C2×C42—21no—
216C2×C42—21no—
217C2×C42—21no—
218C2×C42—21no—
219C2×C42—21no—
220C2×C42—21no—
221C2×C42—21no—
222C2×C42—21no—
223C2×C42—21no—
224C2×C42—21no—
225C2×C42—21no—
226C2×C42—22no—
227C2×C42C22⋊C411yescharacteristic
228C2×C42C22⋊C411yescharacteristic
229C2×C42C22⋊C411yescharacteristic
230C2×C42C22⋊C411yescharacteristic
231C2×C42C22⋊C411yescharacteristic
232C2×C42C22⋊C411yescharacteristic
233C2×C42C2×D411yescharacteristic
234C2×C42C2×D411yescharacteristic
235C2×C42C2×D411yescharacteristic
236C2×C42C2×D411yescharacteristic
237C4⋊C8—42no—
238C4⋊C8—42no—
239C4⋊C8—42no—
240C4⋊C8—42no—
241C22⋊C8—24no—
242C22⋊C8—24no—
243C22⋊C8—42no—
244C22⋊C8—42no—
245#97—42no—
246#97—42no—
247#97—42no—
248#97—42no—
249#95—22no—
250#95—22no—
251#95—24no—
252#95—24no—
253#95—24no—
254#95—24no—
255C24C2×C22⋊C411yescharacteristic
256C24C2×C22⋊C411yescharacteristic
257C24C23×C411yescharacteristic
258#41—48no—
259#41—48no—
260C2×Q8—22no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—44no—
264C2×Q8—44no—
265C2×Q8—44no—
266C2×Q8—42no—
267C2×Q8—42no—
268C2×Q8—84no—
269C2×Q8—88no—
270C2×Q8—88no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—22no—
274C2×D4—22no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4#10114yes—
280C22×C4—22no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—24no—
303C22×C4—24no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—44no—
313C22×C4—84no—
314C22×C4C2×C22⋊C411yescharacteristic
315C22×C4C2×C22⋊C411yescharacteristic
316C22×C4C2×C22⋊C411yescharacteristic
317C22×C4C2×C22⋊C411yescharacteristic
318C22×C4C2×C22⋊C411yescharacteristic
319C22×C4C2×C22⋊C411yescharacteristic
320C22×C4C2×C22⋊C411yescharacteristic
321C22×C4C2×C22⋊C411yescharacteristic
322C22×C4C2×C22⋊C411yescharacteristic
323C22×C4C2×C22⋊C411yescharacteristic
324C22×C4C22×D411yescharacteristic
325C22×C4C22×D411yescharacteristic
326C2×C8—44no—
327C2×C8—44no—
328C2×C8—84no—
329C2×C8—84no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—44no—
337C4⋊C4—44no—
338C4⋊C4—44no—
339C4⋊C4—44no—
340C4⋊C4—44no—
341C4⋊C4—42no—
342C4⋊C4—42no—
343C4⋊C4—42no—
344C4⋊C4—42no—
345C4⋊C4—84no—
346C4⋊C4—84no—
347C22⋊C4—28no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—84no—
355C22⋊C4—84no—
356C42—21no—
357C42—21no—
358C42—21no—
359C42—21no—
360C42—21no—
361C42—21no—
362C42—21no—
363C42—21no—
364C42—21no—
365C42—21no—
366C42—21no—
367C42—21no—
368C42—21no—
369C42—21no—
370C42—21no—
371C42—21no—
372C42—21no—
373C42—21no—
374C42—44no—
375C42#9911yescharacteristic
376C42#9911yescharacteristic
377C42#9911yescharacteristic
378C42#9911yescharacteristic
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23C2×#10112yes—
392C23C2×#10112yes—
393C23C22×C22⋊C411yescharacteristic
394C23#56812yes—
395Q8—44no—
396Q8—84no—
397Q8—88no—
398Q8—84no—
399D4—44no—
400D4—44no—
401D4—44no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—44no—
441C2×C4—44no—
442C2×C4—44no—
443C2×C4—44no—
444C2×C4—44no—
445C2×C4—44no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—81no—
449C2×C4—81no—
450C2×C4—88no—
451C2×C4C2×#9911yescharacteristic
452C2×C4C2×#9911yescharacteristic
453C2×C4C2×#9911yescharacteristic
454C2×C4C2×#9911yescharacteristic
455C2×C4C2×#9911yescharacteristic
456C2×C4C2×#9911yescharacteristic
457C2×C4C2×#10112yes—
458C8—84no—
459C8—84no—
460C22—21no—
461C22—21no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—42no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—41no—
474C22—41no—
475C22—81no—
476C22—81no—
477C22#287911yescharacteristic
478C22C22×#9911yescharacteristic
479C22C22×#10111yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—22no—
485C4—41no—
486C4—41no—
487C4—41no—
488C4—41no—
489C4—41no—
490C4—41no—
491C4—41no—
492C4—41no—
493C4—84no—
494C4—84no—
495C4#212212yes—
496C4#212312yes—
497C2—21no—
498C2—21no—
499C2—42no—
500C2—42no—
501C2—42no—
502C2#1739711yescharacteristic
503C2C2×#212211yescharacteristic
504C2C2×#212311yescharacteristic
subgroupG/H
center, socleC22C22×#99
commutatorC24C23×C4
Frattini, cosocleC2×C22⋊C4C24
prime radicalC22×#41C2×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×#41 ◁ G
LECSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #11576C2semidirect
5. #11575C2semidirect
6. #11520C2semidirect

Maximal subgroups

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

subgroupindex
#352792
#173632
#115762
#115752
#115202