Finite Group Databasebeta

← #120941

Subgroups — #120941

Order 512.

476 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21986C211yesmaximal, characteristic
2#10858C211yesmaximal, characteristic
3#8042C211yesmaximal, characteristic
4#8033C211yesmaximal, characteristic
5#8028C211yesmaximal, characteristic
6C2×#1291C211yesmaximal, characteristic
7#7876C211yesmaximal, characteristic
8C2×#432C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#423C2211yescharacteristic
11C2×C4×M16C2211yescharacteristic
12C2×C4×M16C2211yescharacteristic
13#2285C2211yescharacteristic
14C2×#382C2211yescharacteristic
15#1949—21no—
16#1949—21no—
17#1853—21no—
18#1852—21no—
19#1847—21no—
20#1836—21no—
21C2×#343—21no—
22C2×#343—21no—
23#1296—21no—
24#1296—21no—
25#1295—21no—
26#1295—21no—
27#1295—21no—
28#1295—21no—
29#1291C414yescomplemented
30#1277—21no—
31#1277—21no—
32C22×M16—21no—
33C22×M16—21no—
34C22×M16—21no—
35C2×#117—21no—
36C22×C4⋊C4D411yescharacteristic
37C22×C4⋊C4D411yescharacteristic
38C22×C42C2311yescharacteristic
39#432—21no—
40#432—21no—
41#432—21no—
42#432—21no—
43#432—21no—
44#432C2×C412yes—
45#432C2×C412yes—
46#432Q812yes—
47C2×#107—21no—
48C2×#107—21no—
49C2×#106—21no—
50C2×#106—21no—
51#423—21no—
52#423—21no—
53#423—21no—
54#423Q812yes—
55C2×C4⋊C8—21no—
56C2×C4⋊C8—21no—
57C2×C4⋊C8—21no—
58C2×C4⋊C8D411yescharacteristic
59C2×C4⋊C8D411yescharacteristic
60C2×C22⋊C8—21no—
61C2×C22⋊C8—21no—
62C4×M16—21no—
63C4×M16—21no—
64C4×M16—21no—
65C4×M16—21no—
66C4×M16—21no—
67C4×M16—21no—
68C4×M16—21no—
69C4×M16C2×C412yes—
70C2×#97—21no—
71C2×#97—21no—
72C2×#97—21no—
73C2×#97D411yescharacteristic
74C2×#97D411yescharacteristic
75C2×C4×C8—21no—
76C2×C4×C8—21no—
77#384D411yescharacteristic
78#384D411yescharacteristic
79#382—21no—
80#382—21no—
81#382—21no—
82#382—21no—
83#382—21no—
84#380—21no—
85#380—21no—
86C4×C4⋊C4—21no—
87C4×C4⋊C4—21no—
88C2×#95—21no—
89C2×#95—21no—
90#343—42no—
91#343—42no—
92#340—21no—
93#340—21no—
94#340—21no—
95#340—21no—
96C23×C4—21no—
97C23×C4—21no—
98C23×C4C2×D411yescharacteristic
99C23×C4#4111yescharacteristic
100C23×C4#4111yescharacteristic
101C2×M16—22no—
102C2×M16—22no—
103C2×M16—22no—
104C2×M16—22no—
105C2×M16—42no—
106C2×M16—42no—
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—21no—
119C22×C8—21no—
120C22×C8—21no—
121C22×C8—41no—
122C22×C8—41no—
123C22×C8—41no—
124#117—82no—
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—21no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—41no—
136C2×C4⋊C4—41no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4—41no—
139C2×C22⋊C4—41no—
140C2×C42—41no—
141C2×C42C22×C411yescharacteristic
142C2×C42C2×D411yescharacteristic
143C2×C42C2×D411yescharacteristic
144C2×C42C2×D411yescharacteristic
145C2×C42C2×Q811yescharacteristic
146C2×C42C2×Q811yescharacteristic
147C2×C42#4111yescharacteristic
148C2×C42#4111yescharacteristic
149C2×C42#4111yescharacteristic
150C2×C42#4111yescharacteristic
151C2×C42#4111yescharacteristic
152C2×C42#4111yescharacteristic
153#107—81no—
154#107—81no—
155#106—81no—
156#106—81no—
157C4⋊C8—22no—
158C4⋊C8—22no—
159C4⋊C8—22no—
160C4⋊C8—21no—
161C4⋊C8—21no—
162C4⋊C8—41no—
163C4⋊C8—41no—
164C4⋊C8—41no—
165C4⋊C8C4⋊C412yes—
166C4⋊C8C4⋊C412yes—
167C22⋊C8—22no—
168C22⋊C8—22no—
169C22⋊C8—22no—
170C22⋊C8—41no—
171#97—22no—
172#97—22no—
173#97—22no—
174#97—22no—
175#97—21no—
176#97—21no—
177#97—21no—
178#97—21no—
179#97—41no—
180#97—41no—
181C4×C8—22no—
182C4×C8—41no—
183C4×C8—41no—
184C4×C8—41no—
185#95—41no—
186#95—41no—
187#95—41no—
188#95—41no—
189#95—41no—
190#95—41no—
191C24#12311yescharacteristic
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—81no—
207C22×C4—81no—
208C22×C4—81no—
209C22×C4—81no—
210C22×C4#11711yescharacteristic
211C22×C4C4×D411yescharacteristic
212C22×C4C4×Q811yescharacteristic
213C22×C4#12011yescharacteristic
214C22×C4#12111yescharacteristic
215C22×C4#12111yescharacteristic
216C22×C4#12111yescharacteristic
217C22×C4C22⋊Q811yescharacteristic
218C22×C4C22⋊Q811yescharacteristic
219C22×C4#12311yescharacteristic
220C22×C4#12411yescharacteristic
221C22×C4#12411yescharacteristic
222C22×C4#12511yescharacteristic
223C22×C4#12511yescharacteristic
224C22×C4#12511yescharacteristic
225C22×C4#12611yescharacteristic
226C22×C4#12611yescharacteristic
227C22×C4#12611yescharacteristic
228M16—24no—
229M16—42no—
230M16—42no—
231M16—42no—
232M16—44no—
233M16—44no—
234M16—42no—
235M16—42no—
236M16—81no—
237M16—81no—
238C2×C8—22no—
239C2×C8—22no—
240C2×C8—22no—
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—42no—
254C2×C8—42no—
255C2×C8—81no—
256C2×C8—81no—
257C2×C8—81no—
258C2×C8—81no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—81no—
268C4⋊C4—81no—
269C4⋊C4—81no—
270C4⋊C4—81no—
271C4⋊C4—81no—
272C4⋊C4—81no—
273C22⋊C4—82no—
274C42—82no—
275C42C2×C4⋊C411yescharacteristic
276C42#11711yescharacteristic
277C42C4×D411yescharacteristic
278C42C4×D411yescharacteristic
279C42C22⋊Q811yescharacteristic
280C42C22⋊Q811yescharacteristic
281C42C22⋊Q811yescharacteristic
282C42#12311yescharacteristic
283C42#12311yescharacteristic
284C42#12311yescharacteristic
285C42#12411yescharacteristic
286C42#12411yescharacteristic
287C42#12511yescharacteristic
288C42#12511yescharacteristic
289C42#12611yescharacteristic
290C42C4⋊Q811yescharacteristic
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23#38711yescharacteristic
298C23#39411yescharacteristic
299C23#40011yescharacteristic
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—162no—
339C2×C4—162no—
340C2×C4#38211yescharacteristic
341C2×C4#38511yescharacteristic
342C2×C4#38711yescharacteristic
343C2×C4#38811yescharacteristic
344C2×C4#38811yescharacteristic
345C2×C4#38911yescharacteristic
346C2×C4#39311yescharacteristic
347C2×C4#39711yescharacteristic
348C2×C4#39811yescharacteristic
349C2×C4#39811yescharacteristic
350C2×C4#40011yescharacteristic
351C2×C4#40011yescharacteristic
352C2×C4#45311yescharacteristic
353C2×C4#45411yescharacteristic
354C2×C4#45511yescharacteristic
355C2×C4#45611yescharacteristic
356C8—42no—
357C8—42no—
358C8—44no—
359C8—42no—
360C8—42no—
361C8—82no—
362C8—82no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22#144211yescharacteristic
374C22#203711yescharacteristic
375C22#203811yescharacteristic
376C22#204811yescharacteristic
377C22#204911yescharacteristic
378C22#205011yescharacteristic
379C22#205011yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—161no—
391C4—161no—
392C4—161no—
393C4—161no—
394C4#185911yescharacteristic
395C4#186011yescharacteristic
396C4#202711yescharacteristic
397C4#202811yescharacteristic
398C2—41no—
399C2—41no—
400C2#1049611yescharacteristic
401C2#1049711yescharacteristic
402C2#1049811yescharacteristic
403C2#1049911yescharacteristic
404C2#1127411yescharacteristic
405C2#1127611yescharacteristic
406C2#1129411yescharacteristic
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
29. #1291C4semidirect

Maximal subgroups

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

subgroupindex
#219862
#108582
#80422
#80332
#80282
C2×#12912
#78762