Finite Group Databasebeta

← #196069

Subgroups — #196069

Order 512.

1172 conjugacy classes of subgroups.

The subgroup lattice has 503 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2984C211yesmaximal, characteristic
2C2×#2565C211yesmaximal, characteristic
3#21820C211yesmaximal, characteristic
4C2×#1470C211yesmaximal, characteristic
5C2×#1470C211yesmaximal, characteristic
6#9086C214yesmaximal
7#9082C214yesmaximal
8#7912C211yesmaximal, characteristic
9#7908C211yesmaximal, characteristic
10C22×#125C2211yescharacteristic
11C22×C4×Q8C2211yescharacteristic
12#2984—24no—
13#2984—24no—
14C2×#446—22no—
15C2×#446—21no—
16C2×C8×Q8—21no—
17C2×#432C2211yescharacteristic
18C2×#432C2212yes—
19C2×#432C2211yescharacteristic
20C2×#431C2211yescharacteristic
21C2×#431C2212yes—
22C2×#431C2211yescharacteristic
23#2565—21no—
24#2565—22no—
25#2565—21no—
26#2565—21no—
27#2565—21no—
28#2565—22no—
29C2×#398C414yes—
30C2×#391C411yescharacteristic
31C2×#391C411yescharacteristic
32C2×#387C2214yes—
33C2×#384C411yescharacteristic
34C2×#382C411yescharacteristic
35C2×C4×C4⋊C4C2211yescharacteristic
36#1985—22no—
37#1984—21no—
38#1984—21no—
39#1817C2214yes—
40#1470—24no—
41#1470—24no—
42C2×#324C2212yes—
43C2×#324C2214yes—
44C2×#324C2212yes—
45#1280C2212yes—
46#1280C2214yes—
47#1280C2212yes—
48C23×Q8C2×C411yescharacteristic
49C2×#125—21no—
50C2×#125—21no—
51C2×#125—21no—
52C2×#125—21no—
53C2×#125—22no—
54C2×#125—22no—
55C2×#125—22no—
56C2×#125—22no—
57C2×C4×Q8—22no—
58C2×C4×Q8—22no—
59C2×C4×Q8—22no—
60C2×C4×Q8—22no—
61C2×C4×Q8D411yescharacteristic
62C2×C4×Q8D412yes—
63C2×C4×Q8D411yescharacteristic
64C2×C4×Q8D411yescharacteristic
65C2×C4×Q8D411yescharacteristic
66C2×C4×Q8D412yes—
67C22×C4⋊C4C2×C412yes—
68C22×C4⋊C4C2×C411yescharacteristic
69C22×C4⋊C4C2×C411yescharacteristic
70C22×C4⋊C4C2×C412yes—
71C22×C4⋊C4C2×C414yes—
72C22×C4⋊C4C2×C412yes—
73C22×C4⋊C4C2×C411yescharacteristic
74C22×C4⋊C4C2312yes—
75C22×C42C2×C411yescharacteristic
76C22×C42C2×C411yescharacteristic
77C22×C42C2312yes—
78C22×C42C2311yescharacteristic
79#446—216no—
80#446—28no—
81C8×Q8—28no—
82#432—22no—
83#432—24no—
84#432—24no—
85#432—22no—
86#432—22no—
87#432D414yes—
88#431—22no—
89#431—24no—
90#431—24no—
91#431—22no—
92#431—22no—
93#431D414yes—
94C2×C4⋊C8—22no—
95C2×C4⋊C8—21no—
96C2×C4⋊C8—22no—
97C2×C4⋊C8—21no—
98C2×C4⋊C8—21no—
99C2×C4⋊C8—21no—
100C2×C22⋊C8C2312yes—
101C2×C22⋊C8C2312yes—
102C2×C22⋊C8C2311yescharacteristic
103C2×C22⋊C8C2312yes—
104C2×C22⋊C8C2311yescharacteristic
105C2×#97—22no—
106C2×#97—21no—
107C2×#97—21no—
108C2×C4×C8—22no—
109C2×C4×C8—21no—
110C2×C4×C8—21no—
111#398—24no—
112#398—24no—
113#398—24no—
114#398—24no—
115#391—21no—
116#391—22no—
117#391—21no—
118#391—21no—
119#391—22no—
120#391—21no—
121#387—24no—
122#387—24no—
123#387—24no—
124#387—24no—
125#384—22no—
126#384—21no—
127#384—21no—
128#382—22no—
129#382—21no—
130#382—21no—
131C4×C4⋊C4—21no—
132C4×C4⋊C4—21no—
133C4×C4⋊C4—21no—
134C4×C4⋊C4—21no—
135C2×#95C2×C414yes—
136C2×#95C2×C414yes—
137C2×#95C2×C414yes—
138C2×#95C2312yes—
139#336—24no—
140#336—24no—
141#324—28no—
142#324—24no—
143#324—24no—
144C22×Q8—24no—
145C22×Q8—22no—
146C22×Q8—22no—
147C22×Q8—42no—
148C22×Q8C22⋊C411yescharacteristic
149C22×Q8C22⋊C412yes—
150C22×Q8C22⋊C411yescharacteristic
151C23×C4C22×C412yes—
152C23×C4C22×C412yes—
153C23×C4C22×C412yes—
154C23×C4C22×C411yescharacteristic
155C23×C4C22×C411yescharacteristic
156C23×C4C22×C412yes—
157C23×C4C22×C412yes—
158C23×C4C22×C412yes—
159C23×C4C2411yescharacteristic
160C22×C8—21no—
161C22×C8—22no—
162C22×C8—21no—
163C22×C8—22no—
164C22×C8—22no—
165#125—42no—
166#125—42no—
167#125—42no—
168#125—42no—
169#125—42no—
170#125—42no—
171#125—42no—
172#125—42no—
173C4×Q8—22no—
174C4×Q8—24no—
175C4×Q8—22no—
176C4×Q8—22no—
177C4×Q8—22no—
178C4×Q8—24no—
179C4×Q8—22no—
180C4×Q8—22no—
181C4×Q8—24no—
182C4×Q8—22no—
183C4×Q8—24no—
184C4×Q8—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—24no—
188C2×C4⋊C4—24no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—24no—
198C2×C4⋊C4—24no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—24no—
202C2×C4⋊C4—24no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—24no—
206C2×C4⋊C4—28no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—42no—
214C2×C4⋊C4—44no—
215C2×C4⋊C4C22⋊C412yes—
216C2×C4⋊C4C22⋊C411yescharacteristic
217C2×C4⋊C4C22⋊C411yescharacteristic
218C2×C4⋊C4C22⋊C412yes—
219C2×C4⋊C4C22⋊C412yes—
220C2×C4⋊C4C22⋊C412yes—
221C2×C4⋊C4C22⋊C412yes—
222C2×C42—22no—
223C2×C42—22no—
224C2×C42—22no—
225C2×C42—22no—
226C2×C42—21no—
227C2×C42—21no—
228C2×C42—21no—
229C2×C42—21no—
230C2×C42—42no—
231C2×C42—42no—
232C2×C42C2×D412yes—
233C2×C42C2×D412yes—
234C2×C42C2×D412yes—
235C2×C42C2×D412yes—
236C2×C42C2×D412yes—
237C2×C42C2×D412yes—
238C2×C42C2×D411yescharacteristic
239C2×C42C2×D411yescharacteristic
240C2×C42C2×D411yescharacteristic
241C2×C42C2×D411yescharacteristic
242C2×C42#4112yes—
243C2×C42#4112yes—
244C4⋊C8—28no—
245C4⋊C8—28no—
246C4⋊C8—24no—
247C4⋊C8—24no—
248C4⋊C8—42no—
249C4⋊C8—42no—
250C22⋊C8—21no—
251C22⋊C8—21no—
252C22⋊C8—22no—
253C22⋊C8—22no—
254C22⋊C8—22no—
255C22⋊C8—22no—
256C22⋊C8—22no—
257C22⋊C8C2×D412yes—
258C22⋊C8C2×D414yes—
259C22⋊C8C2×D412yes—
260#97—28no—
261#97—24no—
262#97—42no—
263C4×C8—28no—
264C4×C8—24no—
265C4×C8—42no—
266#95—24no—
267#95—24no—
268#95—24no—
269#95—24no—
270#95—24no—
271#95—24no—
272#95—22no—
273#95—22no—
274C24C23×C411yescharacteristic
275C2×Q8—22no—
276C2×Q8—24no—
277C2×Q8—22no—
278C2×Q8—24no—
279C2×Q8—22no—
280C2×Q8—22no—
281C2×Q8—22no—
282C2×Q8—42no—
283C2×Q8—48no—
284C2×Q8—48no—
285C2×Q8#10114yes—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—24no—
296C22×C4—22no—
297C22×C4—24no—
298C22×C4—24no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—24no—
305C22×C4—24no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—44no—
316C22×C4—42no—
317C22×C4C2×C22⋊C412yes—
318C22×C4C2×C22⋊C412yes—
319C22×C4C2×C22⋊C412yes—
320C22×C4C2×C22⋊C411yescharacteristic
321C22×C4C2×C22⋊C411yescharacteristic
322C22×C4C2×C22⋊C411yescharacteristic
323C22×C4C2×C22⋊C412yes—
324C22×C4C2×C22⋊C411yescharacteristic
325C22×C4C4×D412yes—
326C22×C4C4×D412yes—
327C22×C4C4×D412yes—
328C22×C4C4×D412yes—
329C22×C4#13114yes—
330C22×C4C22×D411yescharacteristic
331C22×C4C22×D411yescharacteristic
332C22×C4C22×D411yescharacteristic
333C22×C4C22×D411yescharacteristic
334C22×C4C2×#4111yescharacteristic
335C22×C4C2×#4111yescharacteristic
336C2×C8—22no—
337C2×C8—24no—
338C2×C8—22no—
339C2×C8—42no—
340C2×C8—44no—
341C2×C8—42no—
342C2×C8—44no—
343C2×C8—44no—
344C2×C8—42no—
345C2×C8—42no—
346C4⋊C4—24no—
347C4⋊C4—24no—
348C4⋊C4—24no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—24no—
352C4⋊C4—24no—
353C4⋊C4—44no—
354C4⋊C4—44no—
355C4⋊C4—48no—
356C4⋊C4—48no—
357C4⋊C4—42no—
358C4⋊C4—42no—
359C4⋊C4—42no—
360C4⋊C4—42no—
361C4⋊C4—44no—
362C4⋊C4—44no—
363C4⋊C4—42no—
364C4⋊C4—42no—
365C4⋊C4—42no—
366C4⋊C4—42no—
367C42—22no—
368C42—22no—
369C42—22no—
370C42—22no—
371C42—22no—
372C42—22no—
373C42—22no—
374C42—22no—
375C42—42no—
376C42—42no—
377C42—42no—
378C42—42no—
379C42#12012yes—
380C42#12012yes—
381C42#12112yes—
382C42#12112yes—
383C42#12112yes—
384C42#12112yes—
385C42#12312yes—
386C42#12312yes—
387C23—22no—
388C23—21no—
389C23—21no—
390C23C22×C22⋊C411yescharacteristic
391C23C2×C4×D411yescharacteristic
392C23C2×C4×D411yescharacteristic
393C23C2×#13112yes—
394C23#56812yes—
395Q8—28no—
396Q8—48no—
397Q8—44no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—24no—
408C2×C4—22no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4—44no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—44no—
431C2×C4—44no—
432C2×C4—42no—
433C2×C4—44no—
434C2×C4—42no—
435C2×C4—44no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—44no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—82no—
443C2×C4—82no—
444C2×C4—82no—
445C2×C4—82no—
446C2×C4#38612yes—
447C2×C4#38612yes—
448C2×C4#38612yes—
449C2×C4#38612yes—
450C2×C4C2×#10114yes—
451C2×C4C2×#10112yes—
452C2×C4#41312yes—
453C2×C4C2×#12011yescharacteristic
454C2×C4C2×#12111yescharacteristic
455C2×C4C2×#12111yescharacteristic
456C2×C4C2×#12311yescharacteristic
457C8—42no—
458C8—44no—
459C8—42no—
460C8—82no—
461C8—82no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22C2×#38611yescharacteristic
471C22#288012yes—
472C22#288412yes—
473C22C22×#10111yescharacteristic
474C22C2×#41311yescharacteristic
475C22#293111yescharacteristic
476C22#293211yescharacteristic
477C22#293512yes—
478C4—22no—
479C4—22no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—22no—
485C4—24no—
486C4—44no—
487C4—42no—
488C4—42no—
489C4—42no—
490C4—82no—
491C4—82no—
492C4—82no—
493C4#190114yes—
494C2—21no—
495C2—21no—
496C2—22no—
497C2#1742312yes—
498C2#1743012yes—
499C2#2090011yescharacteristic
500C2#2098611yescharacteristic
501C2C2×#190111yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutator, prime radicalC24C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#29842
C2×#25652
#218202
C2×#14702
#90862
#90822
#79122
#79082