Finite Group Databasebeta

← #192045

Subgroups — #192045

Order 512.

956 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60282C211yesmaximal, characteristic
2#21977C212yesmaximal, complemented
3#21847C211yesmaximal, characteristic
4#20723C211yesmaximal, characteristic
5#8852C214yesmaximal, complemented
6#8851C214yesmaximal, complemented
7#7926C212yesmaximal, complemented
8C2×C4×#41C2211yescharacteristic
9#2990—22no—
10#2990—22no—
11#2983—21no—
12#2973—21no—
13#2973C2212yes—
14#2972C2212yes—
15#2970—24no—
16#2920—21no—
17C2×#432—21no—
18C2×#432C2212yes—
19C2×#431C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21#2283C2212yes—
22#1984—21no—
23#1954—21no—
24#1940—24no—
25#1869C2212yes—
26#1869C2212yes—
27#1850C2218yes—
28#1843—22no—
29#1832—22no—
30#1820C412yes—
31#1799C412yes—
32#1799C412yes—
33#1797—21no—
34#1797—21no—
35#1782C412yes—
36C4×#99C2212yes—
37C4×#99C2212yes—
38#1282C2218yes—
39C22×#41C2×C411yescharacteristic
40C23×C8C2312yes—
41C4×#41—22no—
42C4×#41—22no—
43C4×#41—22no—
44C4×#41—22no—
45C2×C4×Q8D411yescharacteristic
46C2×C4×Q8Q811yescharacteristic
47C2×C4×D4C2×C411yescharacteristic
48C2×C4×D4C2×C411yescharacteristic
49C2×C4×D4D411yescharacteristic
50C2×C4×D4Q811yescharacteristic
51C2×C4×D4C2311yescharacteristic
52C2×C4×D4C2311yescharacteristic
53C2×#117C2×C411yescharacteristic
54C2×#117Q811yescharacteristic
55C2×#117Q811yescharacteristic
56C22×C42D411yescharacteristic
57C22×C42D411yescharacteristic
58C22×C42C2311yescharacteristic
59#446—24no—
60#446—24no—
61#435—24no—
62#435—24no—
63#435—24no—
64#435—24no—
65C8×D4—24no—
66C8×D4—24no—
67#432—22no—
68#432—22no—
69#432—22no—
70#432—22no—
71#432—22no—
72#432—22no—
73#432—22no—
74#432—22no—
75#431—22no—
76#431—22no—
77#431—22no—
78#431—22no—
79#423—21no—
80#423—21no—
81C2×C4⋊C8—21no—
82C2×C4⋊C8—21no—
83C2×C4⋊C8—21no—
84C2×C4⋊C8—21no—
85C2×C4⋊C8—22no—
86C2×C4⋊C8—22no—
87C2×C4⋊C8—21no—
88C2×C4⋊C8—28no—
89C2×C4⋊C8D412yes—
90C2×C4⋊C8D412yes—
91C2×#99C2×C414yes—
92C2×#99C2×C414yes—
93#407—22no—
94C2×C22⋊C8—22no—
95C2×C22⋊C8—22no—
96C2×C22⋊C8—22no—
97C2×C22⋊C8C2312yes—
98C2×C22⋊C8C2314yes—
99C4×M16—22no—
100C2×#97—22no—
101C2×#97D414yes—
102C2×C4×C8—21no—
103#383—22no—
104#382—22no—
105#381C2×C414yes—
106#380C2×C414yes—
107C4×C4⋊C4—22no—
108C4×C22⋊C4C2314yes—
109#376—22no—
110#342C2×C414yes—
111#342C2×C414yes—
112#336—28no—
113#336—22no—
114#336—22no—
115C2×#41—24no—
116C2×#41—22no—
117C2×#41—22no—
118C2×#41—42no—
119C22×Q8C4⋊C411yescharacteristic
120C22×D4C4⋊C411yescharacteristic
121C22×D4C22×C411yescharacteristic
122C22×D4C22×C411yescharacteristic
123C23×C4C4⋊C411yescharacteristic
124C23×C4C4⋊C411yescharacteristic
125C23×C4C4⋊C411yescharacteristic
126C23×C4C4⋊C411yescharacteristic
127C23×C4C22×C411yescharacteristic
128C23×C4C22×C411yescharacteristic
129C23×C4C2×D411yescharacteristic
130C23×C4C2×D411yescharacteristic
131C23×C4C2411yescharacteristic
132C2×M16—22no—
133C2×M16—22no—
134C22×C8—22no—
135C22×C8—22no—
136C22×C8—22no—
137C22×C8—24no—
138C22×C8—22no—
139C22×C8—82no—
140C22×C8C2×D414yes—
141C22×C8C2×D414yes—
142C4×Q8—22no—
143C4×Q8—22no—
144C4×Q8—22no—
145C4×Q8—22no—
146C4×D4—22no—
147C4×D4—22no—
148C4×D4—22no—
149C4×D4—22no—
150C4×D4—22no—
151C4×D4—22no—
152C4×D4—22no—
153C4×D4—22no—
154C4×D4—22no—
155C4×D4—22no—
156C4×D4—22no—
157C4×D4—22no—
158#117—22no—
159#117—22no—
160#117—22no—
161#117—22no—
162#117—22no—
163#117—22no—
164C2×C4⋊C4—24no—
165C2×C4⋊C4C4⋊C411yescharacteristic
166C2×C4⋊C4C4⋊C411yescharacteristic
167C2×C4⋊C4C4⋊C411yescharacteristic
168C2×C4⋊C4C4⋊C411yescharacteristic
169C2×C4⋊C4C2×Q811yescharacteristic
170C2×C4⋊C4C2×Q811yescharacteristic
171C2×C22⋊C4C4⋊C411yescharacteristic
172C2×C22⋊C4C4⋊C411yescharacteristic
173C2×C22⋊C4C22×C418yes—
174C2×C22⋊C4C22×C411yescharacteristic
175C2×C22⋊C4C22×C411yescharacteristic
176C2×C22⋊C4C2×Q811yescharacteristic
177C2×C22⋊C4C2×Q811yescharacteristic
178C2×C42—21no—
179C2×C42—21no—
180C2×C42—21no—
181C2×C42—21no—
182C2×C42—21no—
183C2×C42—21no—
184C2×C42—21no—
185C2×C42—21no—
186C2×C42—24no—
187C2×C42C4⋊C411yescharacteristic
188C2×C42C4⋊C411yescharacteristic
189C2×C42C4⋊C411yescharacteristic
190C2×C42C4⋊C411yescharacteristic
191C2×C42C2×D411yescharacteristic
192C2×C42C2×D411yescharacteristic
193C2×C42C2×D412yes—
194C2×C42C2×D412yes—
195C2×C42C2×D411yescharacteristic
196C2×C42C2×D411yescharacteristic
197C2×C42C2×Q811yescharacteristic
198C2×C42C2×Q811yescharacteristic
199C2×C42#4112yes—
200C2×C42#4112yes—
201C4⋊C8—22no—
202C4⋊C8—22no—
203C4⋊C8—22no—
204C4⋊C8—22no—
205C4⋊C8—22no—
206C4⋊C8—22no—
207C4⋊C8—22no—
208C4⋊C8—22no—
209C4⋊C8—41no—
210C4⋊C8—42no—
211C4⋊C8—41no—
212C4⋊C8—41no—
213C4⋊C8—41no—
214C4⋊C8—88no—
215#99—28no—
216#99—44no—
217C22⋊C8—24no—
218C22⋊C8—24no—
219C22⋊C8—24no—
220C22⋊C8—24no—
221C22⋊C8—24no—
222C22⋊C8—82no—
223C22⋊C8—82no—
224#97—24no—
225#97—24no—
226#97—24no—
227C4×C8—24no—
228C4×C8—42no—
229#95—24no—
230#95—24no—
231#95—24no—
232#95—24no—
233C24C2×C4⋊C411yescharacteristic
234C24C2×C4⋊C411yescharacteristic
235C24C23×C411yescharacteristic
236#41—48no—
237#41—48no—
238C2×Q8—22no—
239C2×Q8—22no—
240C2×Q8—41no—
241C2×D4—22no—
242C2×D4—22no—
243C2×D4—22no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—22no—
247C2×D4—22no—
248C2×D4—41no—
249C2×D4#13114yes—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—28no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—81no—
276C22×C4—81no—
277C22×C4—81no—
278C22×C4C2×C4⋊C411yescharacteristic
279C22×C4C2×C4⋊C411yescharacteristic
280C22×C4C2×C4⋊C411yescharacteristic
281C22×C4C2×C4⋊C411yescharacteristic
282C22×C4C2×C4⋊C411yescharacteristic
283C22×C4C2×C4⋊C411yescharacteristic
284C22×C4C2×C4⋊C411yescharacteristic
285C22×C4C2×C4⋊C411yescharacteristic
286C22×C4C2×C4⋊C411yescharacteristic
287C22×C4C2×C4⋊C411yescharacteristic
288C22×C4C4×D412yes—
289C22×C4C4×D412yes—
290C22×C4C4×D412yes—
291C22×C4C4×D412yes—
292C22×C4C22×D412yes—
293C22×C4C22×D411yescharacteristic
294C22×C4C22×Q811yescharacteristic
295C22×C4C2×#4112yes—
296M16—82no—
297M16—82no—
298C2×C8—24no—
299C2×C8—24no—
300C2×C8—44no—
301C2×C8—44no—
302C2×C8—42no—
303C2×C8—42no—
304C2×C8—42no—
305C2×C8—48no—
306C2×C8—42no—
307C2×C8—42no—
308C2×C8—42no—
309C2×C8—82no—
310C2×C8—82no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—84no—
318C22⋊C4—22no—
319C22⋊C4—22no—
320C22⋊C4—22no—
321C22⋊C4—22no—
322C22⋊C4—22no—
323C22⋊C4—22no—
324C22⋊C4—28no—
325C22⋊C4—28no—
326C42—21no—
327C42—21no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42—21no—
332C42—21no—
333C42—21no—
334C42—21no—
335C42—21no—
336C42—21no—
337C42—21no—
338C42—44no—
339C42—44no—
340C42#12011yescharacteristic
341C42#12012yes—
342C42#12011yescharacteristic
343C42C22⋊Q812yes—
344C42C22⋊Q812yes—
345C42C22⋊Q812yes—
346C42C22⋊Q812yes—
347C42#12312yes—
348C42#12311yescharacteristic
349C42#12311yescharacteristic
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23#42412yes—
362C23C22×C4⋊C411yescharacteristic
363C23C2×C4×D412yes—
364C23C2×#13112yes—
365C23#56812yes—
366Q8—44no—
367D4—28no—
368D4—44no—
369D4—44no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—24no—
376C2×C4—24no—
377C2×C4—21no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—22no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—42no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—48no—
410C2×C4—48no—
411C2×C4—48no—
412C2×C4—81no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4—81no—
416C2×C4#38511yescharacteristic
417C2×C4#38511yescharacteristic
418C2×C4#38511yescharacteristic
419C2×C4#38511yescharacteristic
420C2×C4#38512yes—
421C2×C4#38512yes—
422C2×C4#42412yes—
423C2×C4C2×#12011yescharacteristic
424C2×C4C2×C22⋊Q812yes—
425C2×C4C2×#12311yescharacteristic
426C8—44no—
427C8—44no—
428C8—82no—
429C8—82no—
430C22—22no—
431C22—21no—
432C22—22no—
433C22—21no—
434C22—22no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22—42no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—81no—
445C22—81no—
446C22C2×#38511yescharacteristic
447C22C2×#42411yescharacteristic
448C22#290511yescharacteristic
449C22#293314yes—
450C4—21no—
451C4—21no—
452C4—22no—
453C4—22no—
454C4—21no—
455C4—22no—
456C4—21no—
457C4—21no—
458C4—22no—
459C4—41no—
460C4—41no—
461C4—41no—
462C4—41no—
463C4—41no—
464C4—88no—
465C4#302711yescharacteristic
466C4#302811yescharacteristic
467C2—24no—
468C2—21no—
469C2—21no—
470C2—42no—
471C2—81no—
472C2#2083611yescharacteristic
473C2#2089011yescharacteristic
474C2#2089211yescharacteristic
subgroupG/H
centerC2×C4C2×#120
commutatorC24C23×C4
Frattini, cosocleC23×C4C24
socleC22C2×#385
prime radicalC22×#41C2×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #21977C2semidirect
5. #8852C2semidirect
6. #8851C2semidirect
7. #7926C2semidirect

Maximal subgroups

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

subgroupindex
#602822
#219772
#218472
#207232
#88522
#88512
#79262