Finite Group Databasebeta

← #120827

Subgroups — #120827

Order 512.

504 conjugacy classes of subgroups.

The subgroup lattice has 431 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21986C211yesmaximal, characteristic
2#10850C211yesmaximal, characteristic
3#8044C211yesmaximal, characteristic
4#8014C211yesmaximal, characteristic
5C2×#1285C211yesmaximal, characteristic
6#7914C211yesmaximal, characteristic
7#7879C211yesmaximal, 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#1296—21no—
24#1296—21no—
25#1294—22no—
26#1285C414yescomplemented
27#1280—22no—
28#1277—21no—
29#1277—21no—
30C23×C8—21no—
31C2×#117—21no—
32C22×C4⋊C4—21no—
33C22×C4⋊C4D411yescharacteristic
34C22×C4⋊C4D411yescharacteristic
35C22×C42—21no—
36C22×C42C2311yescharacteristic
37#432—21no—
38#432—21no—
39#432—21no—
40#432—21no—
41#432—21no—
42#432C2×C412yes—
43#432C2×C412yes—
44#432Q812yes—
45#431—21no—
46#431—21no—
47#431—21no—
48#431—21no—
49C2×#107—21no—
50C2×#107—21no—
51C2×#106—21no—
52C2×#106—21no—
53C2×C4⋊C8—21no—
54C2×C4⋊C8—21no—
55C2×C4⋊C8—21no—
56C2×C4⋊C8—21no—
57C2×C4⋊C8—21no—
58C2×C4⋊C8—21no—
59C2×C4⋊C8—21no—
60C2×C4⋊C8D411yescharacteristic
61C2×C4⋊C8D411yescharacteristic
62C2×C4⋊C8Q812yes—
63C2×C22⋊C8—21no—
64C2×C22⋊C8—21no—
65C2×C22⋊C8D412yes—
66C2×#97—21no—
67C2×#97—21no—
68C2×C4×C8—21no—
69#384D411yescharacteristic
70#384D411yescharacteristic
71#382—21no—
72#382—21no—
73#382—21no—
74#382—21no—
75#382—21no—
76#380—21no—
77#380—21no—
78C4×C4⋊C4—21no—
79C4×C4⋊C4—21no—
80C4×C4⋊C4—21no—
81C4×C4⋊C4—21no—
82C4×C4⋊C4—21no—
83C4×C4⋊C4C2×C412yes—
84C2×#95—21no—
85C2×#95—21no—
86C2×#95—21no—
87#340—21no—
88#340—21no—
89#340—21no—
90#340—21no—
91#340—42no—
92#340—42no—
93C23×C4—21no—
94C23×C4—21no—
95C23×C4—41no—
96C23×C4C2×D411yescharacteristic
97C23×C4C2×D411yescharacteristic
98C23×C4#4111yescharacteristic
99C22×C8—21no—
100C22×C8—21no—
101C22×C8—22no—
102C22×C8—22no—
103C22×C8—41no—
104C22×C8—41no—
105C22×C8—41no—
106C22×C8—41no—
107C22×C8—41no—
108C22×C8—41no—
109C22×C8—41no—
110#117—81no—
111#117—81no—
112C2×C4⋊C4—22no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4—22no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
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—41no—
126C2×C4⋊C4—41no—
127C2×C4⋊C4—41no—
128C2×C4⋊C4—41no—
129C2×C4⋊C4—41no—
130C2×C4⋊C4—41no—
131C2×C4⋊C4—41no—
132C2×C22⋊C4—41no—
133C2×C42—22no—
134C2×C42—41no—
135C2×C42—41no—
136C2×C42—81no—
137C2×C42—81no—
138C2×C42C22×C411yescharacteristic
139C2×C42C2×D411yescharacteristic
140C2×C42C2×D411yescharacteristic
141C2×C42C2×Q811yescharacteristic
142C2×C42C2×Q811yescharacteristic
143C2×C42#4111yescharacteristic
144C2×C42#4111yescharacteristic
145C2×C42#4111yescharacteristic
146C2×C42#4111yescharacteristic
147C2×C42#4111yescharacteristic
148C2×C42#4111yescharacteristic
149C2×C42#4111yescharacteristic
150#107—81no—
151#107—81no—
152#106—81no—
153#106—81no—
154C4⋊C8—22no—
155C4⋊C8—22no—
156C4⋊C8—22no—
157C4⋊C8—21no—
158C4⋊C8—21no—
159C4⋊C8—41no—
160C4⋊C8—41no—
161C4⋊C8—41no—
162C4⋊C8—41no—
163C4⋊C8—41no—
164C4⋊C8C4⋊C412yes—
165C4⋊C8C4⋊C412yes—
166C22⋊C8—22no—
167C22⋊C8—22no—
168C22⋊C8—22no—
169C22⋊C8—22no—
170C22⋊C8—22no—
171C22⋊C8—41no—
172#97—22no—
173#97—22no—
174#97—22no—
175#97—41no—
176C4×C8—41no—
177C4×C8—41no—
178#95—22no—
179#95—41no—
180#95—41no—
181#95—41no—
182#95—41no—
183#95—41no—
184#95—41no—
185#95—41no—
186C24#12111yescharacteristic
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—42no—
198C22×C4—42no—
199C22×C4—42no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—81no—
209C22×C4—81no—
210C22×C4—81no—
211C22×C4—81no—
212C22×C4—81no—
213C22×C4—81no—
214C22×C4—81no—
215C22×C4—81no—
216C22×C4#11711yescharacteristic
217C22×C4C4×D411yescharacteristic
218C22×C4C4×D411yescharacteristic
219C22×C4#12011yescharacteristic
220C22×C4#12111yescharacteristic
221C22×C4#12111yescharacteristic
222C22×C4C22⋊Q811yescharacteristic
223C22×C4C22⋊Q811yescharacteristic
224C22×C4#12311yescharacteristic
225C22×C4#12311yescharacteristic
226C22×C4#12311yescharacteristic
227C22×C4#12311yescharacteristic
228C22×C4#12411yescharacteristic
229C22×C4#12411yescharacteristic
230C22×C4#12511yescharacteristic
231C22×C4#12511yescharacteristic
232C22×C4#12611yescharacteristic
233C22×C4C4⋊Q811yescharacteristic
234C2×C8—22no—
235C2×C8—22no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—81no—
248C2×C8—81no—
249C2×C8—81no—
250C2×C8—81no—
251C2×C8—81no—
252C2×C8—81no—
253C4⋊C4—24no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C4⋊C4—42no—
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—
271C22⋊C4—81no—
272C22⋊C4—81no—
273C42—82no—
274C42—82no—
275C42—82no—
276C42C2×C4⋊C411yescharacteristic
277C42#11711yescharacteristic
278C42C4×D411yescharacteristic
279C42C4×Q811yescharacteristic
280C42C22⋊Q811yescharacteristic
281C42C22⋊Q811yescharacteristic
282C42C22⋊Q811yescharacteristic
283C42#12311yescharacteristic
284C42#12411yescharacteristic
285C42#12411yescharacteristic
286C42#12511yescharacteristic
287C42#12511yescharacteristic
288C42#12511yescharacteristic
289C42#12611yescharacteristic
290C42#12611yescharacteristic
291C42#12611yescharacteristic
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23#38811yescharacteristic
297C23#39411yescharacteristic
298C23#39811yescharacteristic
299C23#47111yescharacteristic
300C23#47111yescharacteristic
301C23#47211yescharacteristic
302C23#47311yescharacteristic
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—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—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—44no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—82no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
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—161no—
353C2×C4—161no—
354C2×C4—161no—
355C2×C4—161no—
356C2×C4#38211yescharacteristic
357C2×C4#38511yescharacteristic
358C2×C4#38711yescharacteristic
359C2×C4#38711yescharacteristic
360C2×C4#38811yescharacteristic
361C2×C4#38911yescharacteristic
362C2×C4#39311yescharacteristic
363C2×C4#39711yescharacteristic
364C2×C4#39811yescharacteristic
365C2×C4#40011yescharacteristic
366C2×C4#40011yescharacteristic
367C2×C4#40011yescharacteristic
368C2×C4#45311yescharacteristic
369C2×C4#45411yescharacteristic
370C2×C4#45511yescharacteristic
371C2×C4#45611yescharacteristic
372C8—42no—
373C8—42no—
374C8—82no—
375C8—82no—
376C8—82no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22#144211yescharacteristic
390C22#193011yescharacteristic
391C22#193111yescharacteristic
392C22#203711yescharacteristic
393C22#203811yescharacteristic
394C22#205111yescharacteristic
395C22#205211yescharacteristic
396C22#205311yescharacteristic
397C22#205311yescharacteristic
398C22#208911yescharacteristic
399C22#209011yescharacteristic
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—21no—
410C4—84no—
411C4—161no—
412C4—161no—
413C4—161no—
414C4—161no—
415C4#185911yescharacteristic
416C4#186011yescharacteristic
417C4#202711yescharacteristic
418C4#202811yescharacteristic
419C2—21no—
420C2—21no—
421C2—21no—
422C2—21no—
423C2#1050811yescharacteristic
424C2#1050911yescharacteristic
425C2#1051011yescharacteristic
426C2#1051111yescharacteristic
427C2#1127611yescharacteristic
428C2#1128511yescharacteristic
429C2#1129011yescharacteristic
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
26. #1285C4semidirect

Maximal subgroups

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

subgroupindex
#219862
#108502
#80442
#80142
C2×#12852
#79142
#78792