Finite Group Databasebeta

← #120441

Subgroups — #120441

Order 512.

528 conjugacy classes of subgroups.

The subgroup lattice has 435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21986C211yesmaximal, characteristic
2C2×#1573C211yesmaximal, characteristic
3#10850C211yesmaximal, characteristic
4#8044C211yesmaximal, characteristic
5#8014C211yesmaximal, characteristic
6C2×#1285C211yesmaximal, characteristic
7#7914C211yesmaximal, characteristic
8C2×#432C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C22×C4⋊C8C2211yescharacteristic
12#2285C2211yescharacteristic
13C2×#382C2211yescharacteristic
14C2×C4×C4⋊C4C2211yescharacteristic
15#1949—21no—
16#1949—21no—
17#1853—21no—
18#1852—21no—
19#1847—21no—
20#1836—21no—
21C2×#340—21no—
22C2×#340—21no—
23#1573—22no—
24#1573C414yescomplemented
25C2×#335—21no—
26C2×#334—21no—
27#1296—21no—
28#1296—21no—
29#1294—22no—
30#1285—22no—
31#1280—22no—
32C23×C8—21no—
33C2×#117—21no—
34C22×C4⋊C4—21no—
35C22×C4⋊C4D411yescharacteristic
36C22×C4⋊C4D411yescharacteristic
37C22×C42—21no—
38C22×C42C2311yescharacteristic
39#432—21no—
40#432—21no—
41#432—21no—
42#432—21no—
43#432—21no—
44#432C2×C412yes—
45#432D412yes—
46#432Q812yes—
47#431—21no—
48#431—21no—
49#431C2×C412yes—
50#431Q812yes—
51C2×#107—21no—
52C2×#107—21no—
53C2×#106—21no—
54C2×#106—21no—
55C2×C4⋊C8—21no—
56C2×C4⋊C8—21no—
57C2×C4⋊C8—21no—
58C2×C4⋊C8—21no—
59C2×C4⋊C8—21no—
60C2×C4⋊C8—21no—
61C2×C4⋊C8—21no—
62C2×C4⋊C8C2×C412yes—
63C2×C4⋊C8D411yescharacteristic
64C2×C4⋊C8D411yescharacteristic
65C2×C22⋊C8—21no—
66C2×C22⋊C8—21no—
67C2×C22⋊C8D412yes—
68C2×#97—21no—
69C2×#97—21no—
70C2×C4×C8—21no—
71#384D411yescharacteristic
72#384D411yescharacteristic
73#382—21no—
74#382—21no—
75#382—21no—
76#382—21no—
77#382—21no—
78#380—21no—
79#380—21no—
80C4×C4⋊C4—21no—
81C4×C4⋊C4—21no—
82C4×C4⋊C4—21no—
83C4×C4⋊C4—21no—
84C4×C4⋊C4—21no—
85C4×C4⋊C4Q812yes—
86C2×#95—21no—
87C2×#95—21no—
88C2×#95—21no—
89#340—21no—
90#340—21no—
91#340—21no—
92#340—21no—
93#340—42no—
94#340—42no—
95#335—24no—
96#334—24no—
97C23×C4—21no—
98C23×C4—21no—
99C23×C4—41no—
100C23×C4C2×D411yescharacteristic
101C23×C4C2×D411yescharacteristic
102C23×C4#4111yescharacteristic
103C22×C8—21no—
104C22×C8—21no—
105C22×C8—22no—
106C22×C8—22no—
107C22×C8—41no—
108C22×C8—41no—
109C22×C8—41no—
110C22×C8—41no—
111C22×C8—41no—
112C22×C8—41no—
113C22×C8—41no—
114#117—81no—
115#117—81no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—22no—
118C2×C4⋊C4—22no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—21no—
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—41no—
130C2×C4⋊C4—41no—
131C2×C4⋊C4—41no—
132C2×C4⋊C4—41no—
133C2×C4⋊C4—41no—
134C2×C4⋊C4—41no—
135C2×C4⋊C4—41no—
136C2×C22⋊C4—41no—
137C2×C42—22no—
138C2×C42—41no—
139C2×C42—41no—
140C2×C42—81no—
141C2×C42—81no—
142C2×C42C22×C411yescharacteristic
143C2×C42C2×D411yescharacteristic
144C2×C42C2×D411yescharacteristic
145C2×C42C2×D411yescharacteristic
146C2×C42C2×Q811yescharacteristic
147C2×C42C2×Q811yescharacteristic
148C2×C42C2×Q811yescharacteristic
149C2×C42#4111yescharacteristic
150C2×C42#4111yescharacteristic
151C2×C42#4111yescharacteristic
152C2×C42#4111yescharacteristic
153C2×C42#4111yescharacteristic
154#107—81no—
155#107—81no—
156#106—81no—
157#106—81no—
158C4⋊C8—22no—
159C4⋊C8—22no—
160C4⋊C8—22no—
161C4⋊C8—22no—
162C4⋊C8—22no—
163C4⋊C8—21no—
164C4⋊C8—21no—
165C4⋊C8—41no—
166C4⋊C8—41no—
167C4⋊C8—41no—
168C4⋊C8C22⋊C412yes—
169C4⋊C8C22⋊C412yes—
170C22⋊C8—22no—
171C22⋊C8—22no—
172C22⋊C8—22no—
173C22⋊C8—22no—
174C22⋊C8—41no—
175C22⋊C8C4⋊C414yes—
176#97—22no—
177#97—22no—
178#97—22no—
179#97—41no—
180C4×C8—22no—
181C4×C8—22no—
182#95—22no—
183#95—41no—
184#95—41no—
185#95—41no—
186#95—41no—
187#95—41no—
188#95—41no—
189#95—41no—
190C24#12111yescharacteristic
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—81no—
213C22×C4—81no—
214C22×C4—81no—
215C22×C4—81no—
216C22×C4—81no—
217C22×C4—81no—
218C22×C4—81no—
219C22×C4—81no—
220C22×C4C2×C4⋊C411yescharacteristic
221C22×C4C4×D411yescharacteristic
222C22×C4C4×Q811yescharacteristic
223C22×C4#12011yescharacteristic
224C22×C4#12111yescharacteristic
225C22×C4#12111yescharacteristic
226C22×C4#12111yescharacteristic
227C22×C4#12111yescharacteristic
228C22×C4C22⋊Q811yescharacteristic
229C22×C4C22⋊Q811yescharacteristic
230C22×C4C22⋊Q811yescharacteristic
231C22×C4C22⋊Q811yescharacteristic
232C22×C4#12311yescharacteristic
233C22×C4#12311yescharacteristic
234C22×C4#12411yescharacteristic
235C22×C4#12511yescharacteristic
236C22×C4#12611yescharacteristic
237C22×C4C4⋊Q811yescharacteristic
238C2×C8—24no—
239C2×C8—22no—
240C2×C8—22no—
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—81no—
252C2×C8—81no—
253C2×C8—81no—
254C2×C8—81no—
255C2×C8—81no—
256C2×C8—81no—
257C4⋊C4—24no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—81no—
272C4⋊C4—81no—
273C4⋊C4—81no—
274C4⋊C4—81no—
275C22⋊C4—81no—
276C22⋊C4—81no—
277C42—82no—
278C42—82no—
279C42—82no—
280C42C2×C22⋊C411yescharacteristic
281C42#11711yescharacteristic
282C42C4×D411yescharacteristic
283C42C4×Q811yescharacteristic
284C42#12111yescharacteristic
285C42C22⋊Q811yescharacteristic
286C42C22⋊Q811yescharacteristic
287C42C22⋊Q811yescharacteristic
288C42C22⋊Q811yescharacteristic
289C42#12311yescharacteristic
290C42#12511yescharacteristic
291C42#12511yescharacteristic
292C42#12511yescharacteristic
293C42#12611yescharacteristic
294C42C4⋊Q811yescharacteristic
295C42C4⋊Q811yescharacteristic
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23#38911yescharacteristic
301C23#39411yescharacteristic
302C23#39611yescharacteristic
303C23#47111yescharacteristic
304C23#47111yescharacteristic
305C23#47211yescharacteristic
306C23#47311yescharacteristic
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—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—44no—
338C2×C4—82no—
339C2×C4—82no—
340C2×C4—82no—
341C2×C4—82no—
342C2×C4—82no—
343C2×C4—82no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—161no—
357C2×C4—161no—
358C2×C4—161no—
359C2×C4—161no—
360C2×C4#38011yescharacteristic
361C2×C4#38611yescharacteristic
362C2×C4#38711yescharacteristic
363C2×C4#38711yescharacteristic
364C2×C4#38911yescharacteristic
365C2×C4#39111yescharacteristic
366C2×C4#39511yescharacteristic
367C2×C4#39611yescharacteristic
368C2×C4#39811yescharacteristic
369C2×C4#39811yescharacteristic
370C2×C4#39811yescharacteristic
371C2×C4#40011yescharacteristic
372C2×C4#45311yescharacteristic
373C2×C4#45411yescharacteristic
374C2×C4#45511yescharacteristic
375C2×C4#45611yescharacteristic
376C8—44no—
377C8—42no—
378C8—42no—
379C8—82no—
380C8—82no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22#144111yescharacteristic
394C22#195111yescharacteristic
395C22#195211yescharacteristic
396C22#203711yescharacteristic
397C22#203811yescharacteristic
398C22#205111yescharacteristic
399C22#205211yescharacteristic
400C22#205311yescharacteristic
401C22#205311yescharacteristic
402C22#206311yescharacteristic
403C22#206411yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—84no—
415C4—161no—
416C4—161no—
417C4—161no—
418C4—161no—
419C4#188211yescharacteristic
420C4#188311yescharacteristic
421C4#206011yescharacteristic
422C4#206111yescharacteristic
423C2—21no—
424C2—21no—
425C2—21no—
426C2—21no—
427C2#1050811yescharacteristic
428C2#1050911yescharacteristic
429C2#1051011yescharacteristic
430C2#1051111yescharacteristic
431C2#1121711yescharacteristic
432C2#1123611yescharacteristic
433C2#1124911yescharacteristic
subgroupG/H
center, socleC23#394
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
24. #1573C4semidirect

Maximal subgroups

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

subgroupindex
#219862
C2×#15732
#108502
#80442
#80142
C2×#12852
#79142