Finite Group Databasebeta

← #121556

Subgroups — #121556

Order 512.

632 conjugacy classes of subgroups.

The subgroup lattice has 455 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21981C211yesmaximal, characteristic
2#21170C211yesmaximal, characteristic
3C2×#1947C211yesmaximal, characteristic
4C2×#1301C211yesmaximal, characteristic
5#8043C211yesmaximal, characteristic
6#7908C211yesmaximal, characteristic
7#7893C211yesmaximal, characteristic
8C2×#431C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#428—21no—
11C22×#107—21no—
12C2×#423C2211yescharacteristic
13C22×C4⋊C8C2211yescharacteristic
14#2285C2211yescharacteristic
15C2×#384C2211yescharacteristic
16C2×C4×C4⋊C4C2211yescharacteristic
17#1949—22no—
18#1948—21no—
19#1948—22no—
20#1947—22no—
21#1947—22no—
22#1947—21no—
23#1853—22no—
24#1844—21no—
25#1834—21no—
26#1736—21no—
27C2×#340—21no—
28#1301C414yescomplemented
29#1296—22no—
30#1280—22no—
31#1279—22no—
32C22×M16—21no—
33C23×C8—21no—
34C2×#117—21no—
35C22×C4⋊C4—21no—
36C22×C4⋊C4—21no—
37C22×C4⋊C4—21no—
38C22×C4⋊C4D411yescharacteristic
39C22×C4⋊C4D411yescharacteristic
40C22×C42—21no—
41C22×C42C2311yescharacteristic
42#431—21no—
43#431—21no—
44#431—21no—
45#431—21no—
46#431—21no—
47#431C2×C412yes—
48#431Q812yes—
49#431Q812yes—
50#428—42no—
51#428—42no—
52C2×#107—24no—
53C2×#107—22no—
54C2×#107—42no—
55C2×#107—42no—
56C2×#106—22no—
57C2×#106—24no—
58#423—21no—
59#423—21no—
60#423C2×C412yes—
61#423Q812yes—
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⋊C8C2×C412yes—
69C2×C4⋊C8D412yes—
70C2×C4⋊C8D412yes—
71C2×C4⋊C8Q812yes—
72C2×C22⋊C8—21no—
73C2×C22⋊C8D412yes—
74C2×C4×C8—21no—
75C2×C4×C8—21no—
76#384—21no—
77#384—21no—
78#384—21no—
79#384D411yescharacteristic
80#384D411yescharacteristic
81#384D412yes—
82#382—21no—
83#380—21no—
84#380—21no—
85C4×C4⋊C4—21no—
86C4×C4⋊C4—21no—
87C4×C4⋊C4—21no—
88C4×C4⋊C4—21no—
89C4×C4⋊C4—21no—
90C4×C4⋊C4—21no—
91C2×#95—21no—
92#340—24no—
93#340—24no—
94#340—22no—
95#340—22no—
96C23×C4—21no—
97C23×C4—21no—
98C23×C4—41no—
99C23×C4C2×D411yescharacteristic
100C23×C4C2×D411yescharacteristic
101C23×C4#4111yescharacteristic
102C2×M16—22no—
103C2×M16—22no—
104C2×M16—41no—
105C2×M16—41no—
106C2×M16—41no—
107C2×M16—41no—
108C22×C8—22no—
109C22×C8—22no—
110C22×C8—22no—
111C22×C8—22no—
112C22×C8—22no—
113C22×C8—41no—
114C22×C8—41no—
115C22×C8—41no—
116C22×C8—41no—
117C22×C8—41no—
118#117—41no—
119#117—41no—
120#117—41no—
121#117—41no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—21no—
126C2×C4⋊C4—21no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—41no—
142C2×C4⋊C4—41no—
143C2×C4⋊C4—41no—
144C2×C4⋊C4—41no—
145C2×C4⋊C4—41no—
146C2×C4⋊C4—41no—
147C2×C4⋊C4—41no—
148C2×C4⋊C4—82no—
149C2×C4⋊C4—82no—
150C2×C4⋊C4SD1612yes—
151C2×C4⋊C4SD1612yes—
152C2×C22⋊C4—41no—
153C2×C42—41no—
154C2×C42—41no—
155C2×C42—41no—
156C2×C42—82no—
157C2×C42C22×C411yescharacteristic
158C2×C42C2×D411yescharacteristic
159C2×C42C2×D411yescharacteristic
160C2×C42C2×D411yescharacteristic
161C2×C42C2×D411yescharacteristic
162C2×C42C2×Q811yescharacteristic
163C2×C42C2×Q811yescharacteristic
164C2×C42C2×Q811yescharacteristic
165C2×C42C2×Q811yescharacteristic
166C2×C42#4111yescharacteristic
167C2×C42#4111yescharacteristic
168C2×C42#4111yescharacteristic
169#107—48no—
170#107—44no—
171#106—44no—
172#106—84no—
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⋊C8C4⋊C414yes—
184C4⋊C8C4⋊C414yes—
185C22⋊C8—22no—
186C22⋊C8—22no—
187C22⋊C8—41no—
188C22⋊C8C4⋊C414yes—
189C4×C8—22no—
190C4×C8—22no—
191C4×C8—22no—
192C4×C8—41no—
193#95—41no—
194#95—41no—
195#95—41no—
196#95—41no—
197C24#12111yescharacteristic
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—42no—
211C22×C4—81no—
212C22×C4—81no—
213C22×C4—81no—
214C22×C4—81no—
215C22×C4—82no—
216C22×C4—82no—
217C22×C4—81no—
218C22×C4—81no—
219C22×C4C2×C4⋊C411yescharacteristic
220C22×C4C4×D411yescharacteristic
221C22×C4C4×Q811yescharacteristic
222C22×C4#12011yescharacteristic
223C22×C4#12011yescharacteristic
224C22×C4#12011yescharacteristic
225C22×C4#12111yescharacteristic
226C22×C4#12111yescharacteristic
227C22×C4C22⋊Q811yescharacteristic
228C22×C4C22⋊Q811yescharacteristic
229C22×C4C22⋊Q811yescharacteristic
230C22×C4#12311yescharacteristic
231C22×C4#12511yescharacteristic
232C22×C4#12511yescharacteristic
233C22×C4#12511yescharacteristic
234C22×C4#12711yescharacteristic
235C22×C4C4⋊Q811yescharacteristic
236C22×C4C4⋊Q811yescharacteristic
237C22×C4C2×SD1611yescharacteristic
238C22×C4C2×SD1611yescharacteristic
239C22×C4#13511yescharacteristic
240C22×C4#13511yescharacteristic
241C22×C4AGL(1,ℤ/8)11yescharacteristic
242C22×C4AGL(1,ℤ/8)11yescharacteristic
243C22×C4#13711yescharacteristic
244C22×C4#13711yescharacteristic
245M16—42no—
246M16—42no—
247M16—42no—
248M16—42no—
249C2×C8—24no—
250C2×C8—24no—
251C2×C8—24no—
252C2×C8—42no—
253C2×C8—42no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—42no—
259C2×C8—42no—
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—42no—
263C2×C8—81no—
264C2×C8—81no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—42no—
270C4⋊C4—44no—
271C4⋊C4—42no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—42no—
278C4⋊C4—41no—
279C4⋊C4—42no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C4⋊C4—82no—
285C4⋊C4—82no—
286C4⋊C4—81no—
287C4⋊C4—81no—
288C4⋊C4—82no—
289C22⋊C4—81no—
290C22⋊C4—81no—
291C42—82no—
292C42—81no—
293C42—81no—
294C42—82no—
295C42C2×C4⋊C411yescharacteristic
296C42C2×C4⋊C411yescharacteristic
297C42C4×D411yescharacteristic
298C42C4×D411yescharacteristic
299C42C22⋊Q811yescharacteristic
300C42C22⋊Q811yescharacteristic
301C42C22⋊Q811yescharacteristic
302C42C22⋊Q811yescharacteristic
303C42C22⋊Q811yescharacteristic
304C42C22⋊Q811yescharacteristic
305C42#12311yescharacteristic
306C42#12311yescharacteristic
307C42C4⋊Q811yescharacteristic
308C42C4⋊Q811yescharacteristic
309C42C4⋊Q811yescharacteristic
310C42C4⋊Q811yescharacteristic
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23#38911yescharacteristic
316C23#39211yescharacteristic
317C23#39811yescharacteristic
318C23#46511yescharacteristic
319C23#46511yescharacteristic
320C23#46811yescharacteristic
321C23#46811yescharacteristic
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—82no—
339C2×C4—82no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—82no—
345C2×C4—82no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—82no—
349C2×C4—82no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—82no—
354C2×C4—81no—
355C2×C4—162no—
356C2×C4—162no—
357C2×C4#38411yescharacteristic
358C2×C4#38511yescharacteristic
359C2×C4#38511yescharacteristic
360C2×C4#38511yescharacteristic
361C2×C4#38911yescharacteristic
362C2×C4#38911yescharacteristic
363C2×C4#39511yescharacteristic
364C2×C4#39511yescharacteristic
365C2×C4#39511yescharacteristic
366C2×C4#39811yescharacteristic
367C2×C4#39811yescharacteristic
368C2×C4#39911yescharacteristic
369C2×C4C4×SD1611yescharacteristic
370C2×C4C4×SD1611yescharacteristic
371C2×C4#44111yescharacteristic
372C2×C4#44211yescharacteristic
373C2×C4#44811yescharacteristic
374C2×C4#44811yescharacteristic
375C2×C4#44911yescharacteristic
376C2×C4#44911yescharacteristic
377C2×C4#45011yescharacteristic
378C2×C4#45011yescharacteristic
379C2×C4#45211yescharacteristic
380C2×C4#45211yescharacteristic
381C2×C4#47212yes—
382C2×C4#47312yes—
383C2×C4#47511yescharacteristic
384C2×C4#47511yescharacteristic
385C2×C4#47611yescharacteristic
386C2×C4#47611yescharacteristic
387C2×C4#47811yescharacteristic
388C2×C4#47811yescharacteristic
389C2×C4#47911yescharacteristic
390C2×C4#47911yescharacteristic
391C2×C4#49811yescharacteristic
392C2×C4#49911yescharacteristic
393C2×C4#50111yescharacteristic
394C2×C4#50111yescharacteristic
395C8—44no—
396C8—44no—
397C8—44no—
398C8—82no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22#144411yescharacteristic
412C22#194111yescharacteristic
413C22#194311yescharacteristic
414C22#200011yescharacteristic
415C22#200011yescharacteristic
416C22#200811yescharacteristic
417C22#200911yescharacteristic
418C22#201811yescharacteristic
419C22#202011yescharacteristic
420C22#208811yescharacteristic
421C22#208811yescharacteristic
422C4—21no—
423C4—21no—
424C4—21no—
425C4—21no—
426C4—21no—
427C4—21no—
428C4—82no—
429C4—82no—
430C4—162no—
431C4—161no—
432C4—161no—
433C4#186411yescharacteristic
434C4#186411yescharacteristic
435C4#186511yescharacteristic
436C4#186511yescharacteristic
437C4#195212yes—
438C4#205811yescharacteristic
439C4#205811yescharacteristic
440C4#205911yescharacteristic
441C4#205911yescharacteristic
442C4#208912yes—
443C2—21no—
444C2—21no—
445C2—21no—
446C2—21no—
447C2#1017811yescharacteristic
448C2#1018111yescharacteristic
449C2#1018711yescharacteristic
450C2#1018811yescharacteristic
451C2#1132711yescharacteristic
452C2#1133111yescharacteristic
453C2#1133311yescharacteristic
subgroupG/H
center, socleC23#392
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#121
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
28. #1301C4semidirect

Maximal subgroups

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

subgroupindex
#219812
#211702
C2×#19472
C2×#13012
#80432
#79082
#78932