Finite Group Databasebeta

← #6805981

Subgroups — #6805981

Order 512.

1282 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36598C211yesmaximal, characteristic
2#36563C211yesmaximal, characteristic
3#33289C211yesmaximal, characteristic
4#32315C218yesmaximal
5#30229C212yesmaximal
6#29218C211yesmaximal, characteristic
7#29178C212yesmaximal
8#28688C212yesmaximal
9#28687C211yesmaximal, characteristic
10#26507C214yesmaximal
11#26277C214yesmaximal
12#22246C212yesmaximal
13C4×#500C211yesmaximal, characteristic
14#21339C211yesmaximal, characteristic
15C2×#500C2211yescharacteristic
16C2×#498C2212yes—
17#2868C2211yescharacteristic
18#2868C2211yescharacteristic
19#2862C2212yes—
20#2859C2212yes—
21#2582—21no—
22#2582—21no—
23#2571C2212yes—
24#2570C2214yes—
25#2568—21no—
26#2567C2212yes—
27#2552—21no—
28#2550—22no—
29#2511—22no—
30#2507C2214yes—
31#2451—22no—
32#2446—22no—
33#2369C2212yes—
34#2365—21no—
35#2355—21no—
36#2355—21no—
37#2355C2212yes—
38Q8×C4⋊C4—21no—
39C4×C4⋊Q8C2211yescharacteristic
40C4×C4⋊Q8C2212yes—
41C4×C4⋊Q8C2211yescharacteristic
42C4×C4⋊Q8C2212yes—
43C42×Q8C2211yescharacteristic
44#2101C2218yes—
45#2101C2218yes—
46#2100C2214yes—
47#2086C2218yes—
48#2085C2218yes—
49#2084C2214yes—
50#1990C2212yes—
51#1990C2212yes—
52#1990C2214yes—
53#1990C2212yes—
54#1990C2212yes—
55#1990C2211yescharacteristic
56#1990C2211yescharacteristic
57#1987C2214yes—
58#1984C2212yes—
59#1949C2218yes—
60#1948C2214yes—
61#1942C2214yes—
62#1939C2212yes—
63#1920C2218yes—
64#1919C2218yes—
65#1918C2218yes—
66#1916C2214yes—
67#1845C2211yescharacteristic
68#1834C2214yes—
69#1834C2212yes—
70C4×#107C2214yes—
71C4×C4⋊C8C2211yescharacteristic
72C4×C4⋊C8C2212yes—
73#1744C2212yes—
74C42×C8C2211yescharacteristic
75C2×C4⋊Q8—21no—
76C2×C4⋊Q8—21no—
77C2×C4⋊Q8—21no—
78C2×C4⋊Q8—21no—
79C2×C4⋊Q8C2311yescharacteristic
80C2×C4⋊Q8C2312yes—
81C2×C4⋊Q8C2312yes—
82C2×C4⋊Q8C2311yescharacteristic
83C2×#125—22no—
84C2×C4×Q8—21no—
85C2×C4×Q8—21no—
86C2×C4×Q8—22no—
87C2×C4×Q8—22no—
88C2×C4×Q8D411yescharacteristic
89C2×C4×Q8D411yescharacteristic
90C2×C4×Q8C2311yescharacteristic
91#500—24no—
92#498—28no—
93C2×#107C2314yes—
94C2×#107C2314yes—
95C2×#106C2318yes—
96C2×C4⋊C8C2314yes—
97C2×C4⋊C8C2312yes—
98C2×C4×C8C2312yes—
99C2×C4×C8C2312yes—
100C2×C4×C8C2311yescharacteristic
101C2×C4×C8C2312yes—
102C2×C4×C8C2311yescharacteristic
103#400—24no—
104#400—24no—
105#398—24no—
106#398—24no—
107#398—24no—
108#395—24no—
109#391—22no—
110#391—22no—
111#391—22no—
112#391—22no—
113#391—21no—
114#391—21no—
115#391—22no—
116#391—22no—
117#391—22no—
118#391—22no—
119#391—24no—
120#389—22no—
121#389—22no—
122#389—22no—
123#389—21no—
124#389—21no—
125#389—22no—
126#389—22no—
127#389—22no—
128#389—24no—
129#389C2314yes—
130#389C2312yes—
131#389C2314yes—
132#389C2312yes—
133#389C2314yes—
134#389C2314yes—
135#387—24no—
136#387—24no—
137#387—24no—
138#387—24no—
139#384—22no—
140#384—21no—
141#384—21no—
142#384—21no—
143#384—21no—
144#384C2311yescharacteristic
145#384C2312yes—
146#384C2311yescharacteristic
147#384C2312yes—
148#384C2312yes—
149#384C2312yes—
150#382—22no—
151#382—22no—
152#382C2314yes—
153#382C2314yes—
154C4×C4⋊C4—22no—
155C4×C4⋊C4—22no—
156C4×C4⋊C4—21no—
157C4×C4⋊C4—22no—
158C4×C4⋊C4—22no—
159C4×C4⋊C4—21no—
160C4×C4⋊C4D411yescharacteristic
161C4×C4⋊C4D411yescharacteristic
162C4×C4⋊C4D412yes—
163C4×C4⋊C4D412yes—
164C4×C4⋊C4C2312yes—
165C4×C4⋊C4C2314yes—
166C4×C4⋊C4C2312yes—
167C4×C4⋊C4C2314yes—
168C4×C4⋊C4C2312yes—
169C4×C4⋊C4C2311yescharacteristic
170C43C2312yes—
171C43C2311yescharacteristic
172#340C2318yes—
173#340C2318yes—
174#340C2318yes—
175#340C2318yes—
176#340C2318yes—
177#340C2314yes—
178#340C2314yes—
179#336C2312yes—
180#336C2314yes—
181#336C2314yes—
182#336C2314yes—
183C22×Q8—21no—
184C22×Q8—22no—
185C22×Q8—21no—
186C22×Q8—22no—
187C22×Q8C2×D411yescharacteristic
188C22×C8C2412yes—
189C22×C8C2414yes—
190C22×C8C2412yes—
191C4⋊Q8—24no—
192C4⋊Q8—22no—
193C4⋊Q8—22no—
194C4⋊Q8—28no—
195C4⋊Q8—22no—
196C4⋊Q8—24no—
197C4⋊Q8—44no—
198C4⋊Q8—82no—
199C4⋊Q8—82no—
200C4⋊Q8—82no—
201C4⋊Q8#4114yes—
202#125—84no—
203C4×Q8—24no—
204C4×Q8—24no—
205C4×Q8—24no—
206C4×Q8—44no—
207C4×Q8—44no—
208C4×Q8—84no—
209C4×Q8—84no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—24no—
225C2×C4⋊C4—24no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—24no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4C2×D411yescharacteristic
233C2×C4⋊C4C2×D412yes—
234C2×C4⋊C4C2×D411yescharacteristic
235C2×C4⋊C4C2×D412yes—
236C2×C4⋊C4C2×D411yescharacteristic
237C2×C4⋊C4C2×D412yes—
238C2×C4⋊C4C2414yes—
239C2×C4⋊C4C2412yes—
240C2×C4⋊C4C2414yes—
241C2×C4⋊C4C2412yes—
242C2×C4⋊C4C2412yes—
243C2×C4⋊C4C2412yes—
244C2×C42—22no—
245C2×C42—22no—
246C2×C42—24no—
247C2×C42—24no—
248C2×C42C2×D412yes—
249C2×C42C2×D412yes—
250C2×C42C2×D412yes—
251C2×C42C2×D412yes—
252C2×C42C2×D411yescharacteristic
253C2×C42C2×D411yescharacteristic
254C2×C42C2×D411yescharacteristic
255C2×C42C2×D411yescharacteristic
256C2×C42C2412yes—
257C2×C42C2412yes—
258C2×C42C2411yescharacteristic
259C2×C42C2411yescharacteristic
260C2×C42C2411yescharacteristic
261#107—28no—
262#107—28no—
263#106—216no—
264C4⋊C8—28no—
265C4⋊C8—24no—
266C4×C8—24no—
267C4×C8—24no—
268C4×C8—22no—
269C4×C8—24no—
270C4×C8—22no—
271#95—24no—
272#95—24no—
273#95—24no—
274#95—22no—
275#95—22no—
276#95—24no—
277#95—22no—
278#95—24no—
279#95—24no—
280#95—22no—
281#95—24no—
282#95—24no—
283#95—24no—
284#95—24no—
285#95C2×D412yes—
286#95C2×D412yes—
287#95C2×D412yes—
288C2×Q8—22no—
289C2×Q8—24no—
290C2×Q8—22no—
291C2×Q8—22no—
292C2×Q8—44no—
293C2×Q8—42no—
294C2×Q8—44no—
295C2×Q8—42no—
296C2×Q8—42no—
297C2×Q8—44no—
298C2×Q8—44no—
299C2×Q8—42no—
300C2×Q8—42no—
301C2×Q8—82no—
302C2×Q8—82no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—24no—
308C22×C4—24no—
309C22×C4C22×D412yes—
310C22×C4C22×D412yes—
311C22×C4C22×D412yes—
312C22×C4C22×D412yes—
313C22×C4C22×D411yescharacteristic
314C22×C4C22×D411yescharacteristic
315C22×C4C22×D411yescharacteristic
316C22×C4C22×D411yescharacteristic
317C22×C4C22×D411yescharacteristic
318C22×C4C22×D411yescharacteristic
319C22×C4C2511yescharacteristic
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—24no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—24no—
327C2×C8—24no—
328C2×C82−1+414yes—
329C4⋊C4—22no—
330C4⋊C4—24no—
331C4⋊C4—24no—
332C4⋊C4—22no—
333C4⋊C4—24no—
334C4⋊C4—22no—
335C4⋊C4—24no—
336C4⋊C4—22no—
337C4⋊C4—24no—
338C4⋊C4—22no—
339C4⋊C4—24no—
340C4⋊C4—24no—
341C4⋊C4—28no—
342C4⋊C4—22no—
343C4⋊C4—24no—
344C4⋊C4—44no—
345C4⋊C4—44no—
346C4⋊C4—42no—
347C4⋊C4—44no—
348C4⋊C4—42no—
349C4⋊C4—42no—
350C4⋊C4—44no—
351C4⋊C4—44no—
352C4⋊C4—44no—
353C4⋊C4—42no—
354C4⋊C4—42no—
355C4⋊C4—44no—
356C4⋊C4—44no—
357C4⋊C4—84no—
358C4⋊C4—84no—
359C4⋊C4—84no—
360C4⋊C4—84no—
361C4⋊C4—82no—
362C4⋊C4—82no—
363C4⋊C4—82no—
364C4⋊C4—82no—
365C4⋊C4C2×#4114yes—
366C42—24no—
367C42—24no—
368C42—24no—
369C42—22no—
370C42—24no—
371C42—22no—
372C42—22no—
373C42—24no—
374C42—24no—
375C42—44no—
376C42—44no—
377C42—84no—
378C42—84no—
379C42#13514yes—
380C42#13714yes—
381C42C2×#4112yes—
382C422−1+414yes—
383C422−1+412yes—
384C23C23×D411yescharacteristic
385Q8—48no—
386Q8—44no—
387Q8—84no—
388Q8—88no—
389Q8—164no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—24no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—44no—
412C2×C4—42no—
413C2×C4—44no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—44no—
420C2×C4—42no—
421C2×C4—44no—
422C2×C4—42no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4—42no—
426C2×C4#53612yes—
427C2×C4#53612yes—
428C2×C4#54812yes—
429C2×C4#54812yes—
430C2×C4C2×#13512yes—
431C2×C4C2×#13512yes—
432C2×C4C2×#13512yes—
433C2×C4C2×#13712yes—
434C2×C4C2×#13712yes—
435C2×C4C2×#13712yes—
436C2×C4#57612yes—
437C2×C4#57712yes—
438C2×C4C22×#4111yescharacteristic
439C2×C4C2×2−1+412yes—
440C2×C4C2×2−1+412yes—
441C2×C4C2×2−1+411yescharacteristic
442C8—24no—
443C8—44no—
444C8—42no—
445C22C2×#53611yescharacteristic
446C22C2×#54811yescharacteristic
447C22#349911yescharacteristic
448C22C22×#13511yescharacteristic
449C22C22×#13711yescharacteristic
450C22C2×#57611yescharacteristic
451C22C2×#57711yescharacteristic
452C4—22no—
453C4—22no—
454C4—22no—
455C4—42no—
456C4—42no—
457C4—44no—
458C4—42no—
459C4—42no—
460C4—82no—
461C4—82no—
462C4—82no—
463C4—84no—
464C4—84no—
465C4#323114yes—
466C4#336014yes—
467C4#337514yes—
468C4#352312yes—
469C4#355612yes—
470C2#3917011yescharacteristic
471C2C2×#323111yescharacteristic
472C2#6087711yescharacteristic
473C2C2×#336011yescharacteristic
474C2C2×#337511yescharacteristic
475C2#6247411yescharacteristic
476C2#6247811yescharacteristic
subgroupG/H
center, socle, prime radicalC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#365982
#365632
#332892
#323152
#302292
#292182
#291782
#286882
#286872
#265072
#262772
#222462
C4×#5002
#213392