Finite Group Databasebeta

← #120467

Subgroups — #120467

Order 512.

584 conjugacy classes of subgroups.

The subgroup lattice has 467 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21170C211yesmaximal, characteristic
2C2×#1566C211yesmaximal, characteristic
3#10847C211yesmaximal, characteristic
4#8045C211yesmaximal, characteristic
5C2×#1292C211yesmaximal, characteristic
6#7897C211yesmaximal, characteristic
7C2×#1279C211yesmaximal, characteristic
8C2×#428—21no—
9C2×#423C2211yescharacteristic
10C2×#423C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C22×C4⋊C8C2211yescharacteristic
13C22×C4×C8C2211yescharacteristic
14#2285C2211yescharacteristic
15C2×C4×C4⋊C4C2211yescharacteristic
16#1949—22no—
17#1948—21no—
18#1947—21no—
19C2×#343—21no—
20C2×#343—21no—
21#1736—21no—
22#1566—22no—
23#1566C414yescomplemented
24C2×#334—22no—
25#1296—21no—
26#1296—21no—
27#1292—22no—
28#1279—21no—
29#1279—21no—
30#1279—21no—
31#1279—21no—
32C22×M16—21no—
33C22×M16—21no—
34C22×M16—21no—
35C23×C8—21no—
36C23×C8—21no—
37C2×#117—21no—
38C22×C4⋊C4D411yescharacteristic
39C22×C4⋊C4D411yescharacteristic
40C22×C42—21no—
41C22×C42C2311yescharacteristic
42#428—42no—
43#428—42no—
44C2×#107—22no—
45C2×#106—22no—
46#423—21no—
47#423—21no—
48#423—21no—
49#423—21no—
50#423—21no—
51#423—21no—
52#423—21no—
53#423—21no—
54#423C2×C412yes—
55#423C2×C412yes—
56#423D412yes—
57#423Q812yes—
58C2×C4⋊C8—21no—
59C2×C4⋊C8—21no—
60C2×C4⋊C8—21no—
61C2×C4⋊C8—21no—
62C2×C4⋊C8—21no—
63C2×C4⋊C8—21no—
64C2×C4⋊C8—21no—
65C2×C4⋊C8—21no—
66C2×C4⋊C8—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8D412yes—
69C2×C4⋊C8Q812yes—
70C2×C4×C8—21no—
71C2×C4×C8—21no—
72C2×C4×C8—21no—
73C2×C4×C8C2×C412yes—
74C2×C4×C8D411yescharacteristic
75C2×C4×C8D411yescharacteristic
76C2×C4×C8Q812yes—
77#384D411yescharacteristic
78#384D411yescharacteristic
79#382—21no—
80#380—21no—
81#380—21no—
82C4×C4⋊C4—21no—
83C4×C4⋊C4—21no—
84C4×C4⋊C4—21no—
85C4×C4⋊C4—21no—
86C4×C4⋊C4—21no—
87C4×C4⋊C4—21no—
88C2×#95—21no—
89#343—42no—
90#343—42no—
91#340—22no—
92#340—22no—
93#334—28no—
94C23×C4—21no—
95C23×C4—21no—
96C23×C4C2×D411yescharacteristic
97C23×C4#4111yescharacteristic
98C23×C4#4111yescharacteristic
99C2×M16—22no—
100C2×M16—22no—
101C2×M16—22no—
102C2×M16—22no—
103C2×M16—41no—
104C2×M16—41no—
105C2×M16—41no—
106C2×M16—41no—
107C2×M16—41no—
108C2×M16—41no—
109C2×M16—41no—
110C2×M16—41no—
111C2×M16—41no—
112C2×M16—41no—
113C2×M16—41no—
114C2×M16—41no—
115C2×M16—41no—
116C2×M16—41no—
117C22×C8—21no—
118C22×C8—22no—
119C22×C8—22no—
120C22×C8—21no—
121C22×C8—22no—
122C22×C8—22no—
123C22×C8—42no—
124C22×C8—42no—
125C22×C8—41no—
126C22×C8—41no—
127C22×C8—41no—
128C22×C8—41no—
129C22×C8—81no—
130C22×C8—81no—
131#117—41no—
132#117—41no—
133#117—41no—
134#117—41no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4SD1612yes—
152C2×C4⋊C4SD1612yes—
153C2×C22⋊C4—41no—
154C2×C42—41no—
155C2×C42—41no—
156C2×C42—41no—
157C2×C42—81no—
158C2×C42—81no—
159C2×C42C22×C411yescharacteristic
160C2×C42C2×D411yescharacteristic
161C2×C42C2×D411yescharacteristic
162C2×C42C2×D411yescharacteristic
163C2×C42C2×D411yescharacteristic
164C2×C42C2×Q811yescharacteristic
165C2×C42C2×Q811yescharacteristic
166C2×C42C2×Q811yescharacteristic
167C2×C42#4111yescharacteristic
168C2×C42#4111yescharacteristic
169C2×C42#4111yescharacteristic
170C2×C42#4111yescharacteristic
171#107—44no—
172#106—44no—
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8—22no—
177C4⋊C8—22no—
178C4⋊C8—22no—
179C4⋊C8—22no—
180C4⋊C8—22no—
181C4⋊C8—22no—
182C4⋊C8—41no—
183C4⋊C8—41no—
184C4⋊C8—41no—
185C4⋊C8—41no—
186C4⋊C8—41no—
187C4⋊C8—41no—
188C4⋊C8C22⋊C414yes—
189C4×C8—22no—
190C4×C8—21no—
191C4×C8—21no—
192C4×C8—22no—
193C4×C8C4⋊C412yes—
194C4×C8C4⋊C412yes—
195#95—41no—
196#95—41no—
197#95—41no—
198#95—41no—
199C24#12311yescharacteristic
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—81no—
215C22×C4—81no—
216C22×C4—81no—
217C22×C4—81no—
218C22×C4#11711yescharacteristic
219C22×C4C4×D411yescharacteristic
220C22×C4C4×Q811yescharacteristic
221C22×C4#12011yescharacteristic
222C22×C4#12111yescharacteristic
223C22×C4#12111yescharacteristic
224C22×C4#12111yescharacteristic
225C22×C4#12111yescharacteristic
226C22×C4C22⋊Q811yescharacteristic
227C22×C4C22⋊Q811yescharacteristic
228C22×C4C22⋊Q811yescharacteristic
229C22×C4#12311yescharacteristic
230C22×C4#12411yescharacteristic
231C22×C4#12511yescharacteristic
232C22×C4#12511yescharacteristic
233C22×C4#12511yescharacteristic
234C22×C4#12611yescharacteristic
235C22×C4C4⋊Q811yescharacteristic
236C22×C4C2×SD1611yescharacteristic
237C22×C4C2×SD1611yescharacteristic
238C22×C4#13511yescharacteristic
239C22×C4#13511yescharacteristic
240C22×C4AGL(1,ℤ/8)11yescharacteristic
241C22×C4AGL(1,ℤ/8)11yescharacteristic
242C22×C4#13711yescharacteristic
243C22×C4#13711yescharacteristic
244M16—42no—
245M16—42no—
246M16—42no—
247M16—42no—
248M16—42no—
249M16—42no—
250M16—42no—
251M16—42no—
252M16—81no—
253M16—81no—
254M16—81no—
255M16—81no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—24no—
261C2×C8—44no—
262C2×C8—44no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—42no—
266C2×C8—42no—
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—82no—
271C2×C8—81no—
272C2×C8—81no—
273C2×C8—81no—
274C2×C8—81no—
275C2×C8—81no—
276C2×C8—81no—
277C2×C8—82no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—81no—
295C4⋊C4—81no—
296C22⋊C4—81no—
297C22⋊C4—81no—
298C42—82no—
299C42—81no—
300C42—81no—
301C42—81no—
302C42—81no—
303C42C2×C22⋊C411yescharacteristic
304C42C2×C4⋊C411yescharacteristic
305C42C4×D411yescharacteristic
306C42C4×Q811yescharacteristic
307C42#12111yescharacteristic
308C42#12111yescharacteristic
309C42C22⋊Q811yescharacteristic
310C42C22⋊Q811yescharacteristic
311C42C22⋊Q811yescharacteristic
312C42C22⋊Q811yescharacteristic
313C42C22⋊Q811yescharacteristic
314C42#12311yescharacteristic
315C42#12511yescharacteristic
316C42#12611yescharacteristic
317C42C4⋊Q811yescharacteristic
318C42C4⋊Q811yescharacteristic
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23#38711yescharacteristic
324C23#39411yescharacteristic
325C23#39811yescharacteristic
326C23#48111yescharacteristic
327C23#48211yescharacteristic
328C23#48311yescharacteristic
329C23#48511yescharacteristic
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—82no—
357C2×C4—82no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4#38011yescharacteristic
365C2×C4#38611yescharacteristic
366C2×C4#38711yescharacteristic
367C2×C4#38911yescharacteristic
368C2×C4#38911yescharacteristic
369C2×C4#39111yescharacteristic
370C2×C4#39511yescharacteristic
371C2×C4#39611yescharacteristic
372C2×C4#39611yescharacteristic
373C2×C4#39811yescharacteristic
374C2×C4#39811yescharacteristic
375C2×C4#40011yescharacteristic
376C2×C4C4×SD1611yescharacteristic
377C2×C4C4×SD1611yescharacteristic
378C2×C4#44011yescharacteristic
379C2×C4#44011yescharacteristic
380C2×C4#44811yescharacteristic
381C2×C4#44911yescharacteristic
382C2×C4#45011yescharacteristic
383C2×C4#45211yescharacteristic
384C2×C4#46011yescharacteristic
385C2×C4#46111yescharacteristic
386C2×C4#46311yescharacteristic
387C2×C4#46411yescharacteristic
388C2×C4#46511yescharacteristic
389C2×C4#46511yescharacteristic
390C2×C4#46911yescharacteristic
391C2×C4#47011yescharacteristic
392C2×C4#47111yescharacteristic
393C2×C4#47111yescharacteristic
394C2×C4#47211yescharacteristic
395C2×C4#47311yescharacteristic
396C2×C4#47511yescharacteristic
397C2×C4#47611yescharacteristic
398C2×C4#47811yescharacteristic
399C2×C4#47911yescharacteristic
400C2×C4#49811yescharacteristic
401C2×C4#49911yescharacteristic
402C2×C4#50111yescharacteristic
403C2×C4#50111yescharacteristic
404C8—24no—
405C8—42no—
406C8—44no—
407C8—82no—
408C8—82no—
409C8—82no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22#144111yescharacteristic
423C22#191911yescharacteristic
424C22#192011yescharacteristic
425C22#203411yescharacteristic
426C22#203511yescharacteristic
427C22#205011yescharacteristic
428C22#205011yescharacteristic
429C22#205111yescharacteristic
430C22#205211yescharacteristic
431C22#208411yescharacteristic
432C22#208511yescharacteristic
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—82no—
440C4—82no—
441C4—161no—
442C4—161no—
443C4#187711yescharacteristic
444C4#188011yescharacteristic
445C4#194111yescharacteristic
446C4#194411yescharacteristic
447C4#195111yescharacteristic
448C4#195211yescharacteristic
449C4#205811yescharacteristic
450C4#205911yescharacteristic
451C4#206311yescharacteristic
452C4#206411yescharacteristic
453C4#206511yescharacteristic
454C4#206611yescharacteristic
455C2—21no—
456C2—21no—
457C2—21no—
458C2—21no—
459C2#1045711yescharacteristic
460C2#1045911yescharacteristic
461C2#1046011yescharacteristic
462C2#1046211yescharacteristic
463C2#1122011yescharacteristic
464C2#1124311yescharacteristic
465C2#1124911yescharacteristic
subgroupG/H
center, socleC23#394
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#123
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
23. #1566C4semidirect

Maximal subgroups

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

subgroupindex
#211702
C2×#15662
#108472
#80452
C2×#12922
#78972
C2×#12792