Finite Group Databasebeta

← #196055

Subgroups — #196055

Order 512.

1208 conjugacy classes of subgroups.

The subgroup lattice has 491 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2984C211yesmaximal, characteristic
2C2×#2581C211yesmaximal, characteristic
3#21820C211yesmaximal, characteristic
4C2×#1467C211yesmaximal, characteristic
5C2×#1461C211yesmaximal, characteristic
6#9086C214yesmaximal
7#9082C214yesmaximal
8#7914C211yesmaximal, characteristic
9#7914C211yesmaximal, characteristic
10C22×C4×Q8C2211yescharacteristic
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#2581—21no—
24#2581—21no—
25#2581—22no—
26#2581—21no—
27#2581—21no—
28#2581—22no—
29C2×#400C412yes—
30C2×#395C412yes—
31C2×#391C412yes—
32C2×#389C412yes—
33C2×#387C2214yes—
34C2×#382C2211yescharacteristic
35#1985—22no—
36#1984—21no—
37#1984—21no—
38#1817C2214yes—
39#1467—24no—
40#1461—24no—
41C2×#324C2212yes—
42C2×#324C2214yes—
43C2×#324C2212yes—
44#1280C2212yes—
45#1280C2214yes—
46#1280C2212yes—
47C23×Q8C2×C411yescharacteristic
48C23×Q8C2×C411yescharacteristic
49C2×C4×Q8—22no—
50C2×C4×Q8—22no—
51C2×C4×Q8—21no—
52C2×C4×Q8—21no—
53C2×C4×Q8—21no—
54C2×C4×Q8—21no—
55C2×C4×Q8—22no—
56C2×C4×Q8—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×C411yescharacteristic
68C22×C4⋊C4C2×C414yes—
69C22×C4⋊C4C2×C412yes—
70C22×C4⋊C4C2×C411yescharacteristic
71C22×C4⋊C4C2×C412yes—
72C22×C4⋊C4C2312yes—
73C22×C42C2×C412yes—
74C22×C42C2312yes—
75C22×C42C2311yescharacteristic
76#446—216no—
77#446—28no—
78C8×Q8—28no—
79#432—22no—
80#432—24no—
81#432—24no—
82#432—22no—
83#432—22no—
84#432D414yes—
85#431—22no—
86#431—24no—
87#431—24no—
88#431—22no—
89#431—22no—
90#431D414yes—
91C2×C4⋊C8—22no—
92C2×C4⋊C8—21no—
93C2×C4⋊C8—22no—
94C2×C4⋊C8—21no—
95C2×C4⋊C8—21no—
96C2×C4⋊C8—21no—
97C2×C22⋊C8C2312yes—
98C2×C22⋊C8C2312yes—
99C2×C22⋊C8C2311yescharacteristic
100C2×C22⋊C8C2312yes—
101C2×C22⋊C8C2311yescharacteristic
102C2×#97—22no—
103C2×#97—21no—
104C2×#97—21no—
105C2×C4×C8—22no—
106C2×C4×C8—21no—
107C2×C4×C8—21no—
108#400—22no—
109#400—22no—
110#400—22no—
111#400—22no—
112#395—22no—
113#395—22no—
114#395—22no—
115#395—22no—
116#391—22no—
117#391—24no—
118#391—22no—
119#389—24no—
120#389—22no—
121#389—22no—
122#387—24no—
123#387—24no—
124#387—24no—
125#387—24no—
126#382—21no—
127#382—21no—
128#382—21no—
129#382—21no—
130C2×#95C2×C412yes—
131C2×#95C2×C414yes—
132C2×#95C2×C414yes—
133C2×#95C2×C414yes—
134C2×#95C2312yes—
135#336—24no—
136#336—24no—
137#324—24no—
138#324—24no—
139#324—28no—
140C22×Q8—24no—
141C22×Q8—21no—
142C22×Q8—21no—
143C22×Q8—22no—
144C22×Q8—22no—
145C22×Q8—22no—
146C22×Q8—22no—
147C22×Q8—24no—
148C22×Q8—42no—
149C22×Q8—42no—
150C22×Q8C22⋊C411yescharacteristic
151C22×Q8C22⋊C412yes—
152C22×Q8C22⋊C411yescharacteristic
153C23×C4C22×C412yes—
154C23×C4C22×C412yes—
155C23×C4C22×C412yes—
156C23×C4C22×C411yescharacteristic
157C23×C4C22×C411yescharacteristic
158C23×C4C22×C414yes—
159C23×C4C22×C412yes—
160C23×C4C2411yescharacteristic
161C22×C8—21no—
162C22×C8—22no—
163C22×C8—21no—
164C22×C8—22no—
165C22×C8—22no—
166C4×Q8—22no—
167C4×Q8—24no—
168C4×Q8—22no—
169C4×Q8—22no—
170C4×Q8—22no—
171C4×Q8—24no—
172C4×Q8—22no—
173C4×Q8—22no—
174C4×Q8—24no—
175C4×Q8—22no—
176C4×Q8—24no—
177C4×Q8—22no—
178C4×Q8—42no—
179C4×Q8—42no—
180C4×Q8—42no—
181C4×Q8—42no—
182C4×Q8—42no—
183C4×Q8—42no—
184C4×Q8—42no—
185C4×Q8—42no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—24no—
189C2×C4⋊C4—24no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—24no—
195C2×C4⋊C4—24no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—28no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—44no—
206C2×C4⋊C4—44no—
207C2×C4⋊C4C22⋊C412yes—
208C2×C4⋊C4C22⋊C411yescharacteristic
209C2×C4⋊C4C22⋊C411yescharacteristic
210C2×C4⋊C4C22⋊C412yes—
211C2×C4⋊C4C22⋊C412yes—
212C2×C4⋊C4C22⋊C412yes—
213C2×C4⋊C4C22⋊C412yes—
214C2×C42—22no—
215C2×C42—22no—
216C2×C42—22no—
217C2×C42—22no—
218C2×C42—22no—
219C2×C42—22no—
220C2×C42—24no—
221C2×C42—24no—
222C2×C42C2×D412yes—
223C2×C42C2×D412yes—
224C2×C42C2×D412yes—
225C2×C42C2×D412yes—
226C2×C42C2×D412yes—
227C2×C42C2×D412yes—
228C2×C42C2×D411yescharacteristic
229C2×C42C2×D411yescharacteristic
230C2×C42C2×D411yescharacteristic
231C2×C42C2×D411yescharacteristic
232C2×C42#4112yes—
233C2×C42#4112yes—
234C4⋊C8—28no—
235C4⋊C8—28no—
236C4⋊C8—24no—
237C4⋊C8—24no—
238C4⋊C8—42no—
239C4⋊C8—42no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242C22⋊C8—22no—
243C22⋊C8—22no—
244C22⋊C8—22no—
245C22⋊C8—22no—
246C22⋊C8—22no—
247C22⋊C8C2×D412yes—
248C22⋊C8C2×D414yes—
249C22⋊C8C2×D412yes—
250#97—28no—
251#97—24no—
252#97—42no—
253C4×C8—28no—
254C4×C8—24no—
255C4×C8—42no—
256#95—22no—
257#95—22no—
258#95—24no—
259#95—24no—
260#95—24no—
261#95—24no—
262#95—24no—
263#95—24no—
264#95—22no—
265#95—22no—
266C24C23×C411yescharacteristic
267C2×Q8—28no—
268C2×Q8—22no—
269C2×Q8—24no—
270C2×Q8—22no—
271C2×Q8—24no—
272C2×Q8—22no—
273C2×Q8—22no—
274C2×Q8—22no—
275C2×Q8—42no—
276C2×Q8—44no—
277C2×Q8—44no—
278C2×Q8—48no—
279C2×Q8—48no—
280C2×Q8—48no—
281C2×Q8—44no—
282C2×Q8—42no—
283C2×Q8—42no—
284C2×Q8#10114yes—
285C22×C4—22no—
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—22no—
296C22×C4—24no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—24no—
300C22×C4—22no—
301C22×C4—24no—
302C22×C4—24no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—24no—
307C22×C4—24no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—44no—
311C22×C4—44no—
312C22×C4—44no—
313C22×C4C2×C22⋊C412yes—
314C22×C4C2×C22⋊C412yes—
315C22×C4C2×C22⋊C412yes—
316C22×C4C2×C22⋊C411yescharacteristic
317C22×C4C2×C22⋊C411yescharacteristic
318C22×C4C2×C22⋊C411yescharacteristic
319C22×C4C2×C22⋊C412yes—
320C22×C4C2×C22⋊C411yescharacteristic
321C22×C4C4×D412yes—
322C22×C4C4×D412yes—
323C22×C4C4×D412yes—
324C22×C4C4×D412yes—
325C22×C4#13114yes—
326C22×C4C22×D411yescharacteristic
327C22×C4C22×D411yescharacteristic
328C22×C4C22×D411yescharacteristic
329C22×C4C22×D411yescharacteristic
330C22×C4C2×#4111yescharacteristic
331C22×C4C2×#4111yescharacteristic
332C2×C8—22no—
333C2×C8—24no—
334C2×C8—22no—
335C2×C8—42no—
336C2×C8—44no—
337C2×C8—42no—
338C2×C8—44no—
339C2×C8—44no—
340C2×C8—42no—
341C2×C8—42no—
342C4⋊C4—24no—
343C4⋊C4—24no—
344C4⋊C4—24no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—24no—
348C4⋊C4—24no—
349C4⋊C4—48no—
350C4⋊C4—48no—
351C4⋊C4—44no—
352C4⋊C4—42no—
353C4⋊C4—42no—
354C4⋊C4—42no—
355C4⋊C4—42no—
356C4⋊C4—42no—
357C4⋊C4—42no—
358C4⋊C4—44no—
359C42—22no—
360C42—22no—
361C42—22no—
362C42—22no—
363C42—22no—
364C42—22no—
365C42—22no—
366C42—22no—
367C42—44no—
368C42—44no—
369C42#12012yes—
370C42#12012yes—
371C42#12112yes—
372C42#12112yes—
373C42#12112yes—
374C42#12112yes—
375C42#12312yes—
376C42#12312yes—
377C23—22no—
378C23—21no—
379C23—21no—
380C23C22×C22⋊C411yescharacteristic
381C23C2×C4×D411yescharacteristic
382C23C2×C4×D411yescharacteristic
383C23C2×#13112yes—
384C23#56812yes—
385Q8—28no—
386Q8—48no—
387Q8—48no—
388Q8—48no—
389Q8—44no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—24no—
400C2×C4—22no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—44no—
418C2×C4—44no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—44no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—44no—
427C2×C4—44no—
428C2×C4—44no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—84no—
432C2×C4—84no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4#38612yes—
436C2×C4#38612yes—
437C2×C4#38612yes—
438C2×C4#38612yes—
439C2×C4C2×#10114yes—
440C2×C4C2×#10112yes—
441C2×C4#41312yes—
442C2×C4C2×#12011yescharacteristic
443C2×C4C2×#12111yescharacteristic
444C2×C4C2×#12111yescharacteristic
445C2×C4C2×#12311yescharacteristic
446C8—42no—
447C8—44no—
448C8—42no—
449C8—82no—
450C8—82no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22C2×#38611yescharacteristic
460C22#288012yes—
461C22#288412yes—
462C22C22×#10111yescharacteristic
463C22C2×#41311yescharacteristic
464C22#292911yescharacteristic
465C22#293011yescharacteristic
466C22#293312yes—
467C4—22no—
468C4—22no—
469C4—21no—
470C4—21no—
471C4—21no—
472C4—21no—
473C4—22no—
474C4—24no—
475C4—42no—
476C4—42no—
477C4—44no—
478C4—42no—
479C4—84no—
480C4—82no—
481C4#190114yes—
482C2—21no—
483C2—21no—
484C2—22no—
485C2#1742812yes—
486C2#1743012yes—
487C2#2089911yescharacteristic
488C2#2098611yescharacteristic
489C2C2×#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×#25812
#218202
C2×#14672
C2×#14612
#90862
#90822
#79142