Finite Group Databasebeta

← #107643

Subgroups — #107643

Order 512.

829 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34239C211yesmaximal, characteristic
2C2×#1528C211yesmaximal, characteristic
3C2×#1528C211yesmaximal, characteristic
4C4×#344C211yesmaximal, characteristic
5#8073C211yesmaximal, characteristic
6#7972C211yesmaximal, characteristic
7#7930C211yesmaximal, characteristic
8C22×#125C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×C4×M16C2211yescharacteristic
12C2×C4×M16C2211yescharacteristic
13#2371—22no—
14#2370—22no—
15#2345C412yes—
16#2344—22no—
17#2344C412yes—
18#2336—22no—
19#2313—21no—
20C4×#125—22no—
21#2283C2211yescharacteristic
22#2274—21no—
23C4×#117C2211yescharacteristic
24C2×#344—22no—
25#1528—22no—
26#1528—22no—
27#1528—22no—
28#1528C414yescomplemented
29C2×#330—22no—
30C2×#330C414yescomplemented
31#1300—22no—
32#1288—22no—
33#1282—21no—
34#1282—21no—
35C22×M16—21no—
36C22×M16—21no—
37C2×#125—21no—
38C2×#125—21no—
39C2×#125—21no—
40C2×#125—21no—
41C2×#125—21no—
42C2×#125—21no—
43C2×#125C2×C412yes—
44C2×#125C2×C412yes—
45C2×#125D412yes—
46C2×#125D412yes—
47C2×#125D412yes—
48C2×#125Q812yes—
49C2×#117—22no—
50C2×#117D412yes—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4C2×C411yescharacteristic
54C22×C4⋊C4C2×C411yescharacteristic
55C22×C42C2311yescharacteristic
56#432—21no—
57#432—21no—
58#432—21no—
59#432—21no—
60#432—21no—
61#432—21no—
62#432—21no—
63#432C2×C412yes—
64C2×C4⋊C8—21no—
65C2×C4⋊C8—21no—
66C2×C22⋊C8—21no—
67C2×C22⋊C8—21no—
68C4×M16—21no—
69C4×M16—21no—
70C4×M16—21no—
71C4×M16—21no—
72C4×M16—21no—
73C4×M16—21no—
74C4×M16—21no—
75C4×M16C2×C412yes—
76C2×#97—21no—
77C2×#97—21no—
78C2×#97C2×C412yes—
79C2×#97C2×C412yes—
80C2×C4×C8—21no—
81C2×C4×C8—21no—
82#389—24no—
83#389—22no—
84#389—22no—
85#387—24no—
86#387—24no—
87#387—24no—
88#387—24no—
89#387—24no—
90#387—24no—
91#383D412yes—
92#382—21no—
93#381—21no—
94#381—22no—
95#380—22no—
96#380C2×C412yes—
97C4×C4⋊C4—24no—
98C4×C4⋊C4—24no—
99C4×C4⋊C4—24no—
100C4×C4⋊C4—22no—
101C4×C4⋊C4—22no—
102C4×C4⋊C4—21no—
103C4×C4⋊C4—21no—
104C4×C4⋊C4—21no—
105C4×C22⋊C4—21no—
106C4×C22⋊C4—22no—
107C4×C22⋊C4C2×C412yes—
108C4×C22⋊C4D411yescharacteristic
109C4×C22⋊C4D411yescharacteristic
110#376—21no—
111#376D412yes—
112C43—21no—
113#344—28no—
114#330—28no—
115#330—28no—
116C23×C4—21no—
117C23×C4—21no—
118C23×C4C22×C411yescharacteristic
119C23×C4C2×D411yescharacteristic
120C23×C4C2×D411yescharacteristic
121C2×M16—24no—
122C2×M16—24no—
123C2×M16—22no—
124C2×M16—42no—
125C2×M16—42no—
126C2×M16—41no—
127C2×M16—41no—
128C2×M16—41no—
129C22×C8—22no—
130C22×C8—22no—
131C22×C8—41no—
132C22×C8—41no—
133#125—22no—
134#125—22no—
135#125—22no—
136#125—22no—
137#125—22no—
138#125—22no—
139#125—22no—
140#125—22no—
141#125—22no—
142#125—22no—
143#125—22no—
144#125—22no—
145#125C22⋊C414yes—
146#125C22⋊C414yes—
147#125C4⋊C414yes—
148#125C4⋊C414yes—
149#117—24no—
150#117—42no—
151#117—44no—
152#117—44no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—24no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—24no—
175C2×C4⋊C4C4212yes—
176C2×C4⋊C4C4212yes—
177C2×C4⋊C4C22⋊C412yes—
178C2×C4⋊C4C22⋊C412yes—
179C2×C4⋊C4C4⋊C412yes—
180C2×C4⋊C4C4⋊C412yes—
181C2×C22⋊C4—22no—
182C2×C22⋊C4C22⋊C412yes—
183C2×C22⋊C4C22⋊C412yes—
184C2×C42—24no—
185C2×C42—22no—
186C2×C42—22no—
187C2×C42—24no—
188C2×C42—21no—
189C2×C42—21no—
190C2×C42—22no—
191C2×C42C22×C411yescharacteristic
192C2×C42C22×C411yescharacteristic
193C2×C42C2×D411yescharacteristic
194C2×C42C2×D411yescharacteristic
195C2×C42C2×D411yescharacteristic
196C2×C42C2×D411yescharacteristic
197C2×C42C2×D411yescharacteristic
198C2×C42C2×Q811yescharacteristic
199C2×C42#4111yescharacteristic
200C2×C42#4111yescharacteristic
201C2×C42#4111yescharacteristic
202C2×C42#4111yescharacteristic
203C4⋊C8—22no—
204C4⋊C8—41no—
205C4⋊C8—41no—
206C4⋊C8—41no—
207C22⋊C8—22no—
208C22⋊C8—41no—
209C22⋊C8—41no—
210C22⋊C8—41no—
211#97—22no—
212#97—22no—
213#97—22no—
214#97—22no—
215#97—22no—
216#97—22no—
217#97—41no—
218#97—41no—
219C4×C8—22no—
220C4×C8—41no—
221C4×C8—41no—
222C4×C8—41no—
223#95—24no—
224#95—24no—
225#95—24no—
226#95—24no—
227#95—22no—
228#95—21no—
229#95—21no—
230#95—22no—
231#95—22no—
232#95—22no—
233#95C22⋊C414yes—
234C24C2×C22⋊C411yescharacteristic
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—24no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—81no—
250C22×C4—82no—
251C22×C4C2×C4211yescharacteristic
252C22×C4C2×C22⋊C411yescharacteristic
253C22×C4C2×C22⋊C411yescharacteristic
254C22×C4C2×C4⋊C411yescharacteristic
255C22×C4#11711yescharacteristic
256C22×C4#11711yescharacteristic
257C22×C4C4×D411yescharacteristic
258C22×C4C4×D411yescharacteristic
259C22×C4C4×D411yescharacteristic
260C22×C4C4×D411yescharacteristic
261C22×C4#12011yescharacteristic
262C22×C4#12011yescharacteristic
263C22×C4#12011yescharacteristic
264C22×C4#12011yescharacteristic
265C22×C4#12111yescharacteristic
266C22×C4#12111yescharacteristic
267C22×C4C22⋊Q811yescharacteristic
268C22×C4C22⋊Q811yescharacteristic
269M16—24no—
270M16—44no—
271M16—44no—
272M16—42no—
273M16—44no—
274C2×C8—24no—
275C2×C8—42no—
276C2×C8—44no—
277C2×C8—42no—
278C2×C8—42no—
279C2×C8—42no—
280C2×C8—42no—
281C2×C8—82no—
282C2×C8—82no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—24no—
290C4⋊C4—24no—
291C4⋊C4—24no—
292C4⋊C4—24no—
293C4⋊C4—24no—
294C4⋊C4—24no—
295C4⋊C4—24no—
296C4⋊C4—24no—
297C4⋊C4—44no—
298C4⋊C4—44no—
299C4⋊C4—48no—
300C4⋊C4—84no—
301C4⋊C4#9514yes—
302C4⋊C4#9514yes—
303C22⋊C4—22no—
304C22⋊C4—22no—
305C22⋊C4—22no—
306C22⋊C4—42no—
307C22⋊C4—42no—
308C22⋊C4#10414yes—
309C42—44no—
310C42—44no—
311C42—48no—
312C42—81no—
313C42—82no—
314C42—81no—
315C42—84no—
316C42C2×C22⋊C411yescharacteristic
317C42C2×C22⋊C411yescharacteristic
318C42C2×C4⋊C411yescharacteristic
319C42C2×C4⋊C411yescharacteristic
320C42C4×D411yescharacteristic
321C42C4×D411yescharacteristic
322C42C4×D411yescharacteristic
323C42C4×D411yescharacteristic
324C42#12111yescharacteristic
325C42#12111yescharacteristic
326C42C22⋊Q811yescharacteristic
327C42C22⋊Q811yescharacteristic
328C42#12311yescharacteristic
329C42#12311yescharacteristic
330C42#12311yescharacteristic
331C42#12311yescharacteristic
332C23—41no—
333C23—41no—
334C23C4×C22⋊C411yescharacteristic
335C23#37911yescharacteristic
336C23#38011yescharacteristic
337C23C2×#10412yes—
338C23#42112yes—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—24no—
351C2×C4—24no—
352C2×C4—24no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—44no—
365C2×C4—44no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—44no—
372C2×C4—42no—
373C2×C4—44no—
374C2×C4—42no—
375C2×C4—44no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4C2×#9511yescharacteristic
379C2×C4C4×C22⋊C411yescharacteristic
380C2×C4#38011yescharacteristic
381C2×C4#38111yescharacteristic
382C2×C4#38511yescharacteristic
383C2×C4#38511yescharacteristic
384C2×C4#38511yescharacteristic
385C2×C4#38511yescharacteristic
386C2×C4#38611yescharacteristic
387C2×C4#38611yescharacteristic
388C2×C4#38611yescharacteristic
389C2×C4#38611yescharacteristic
390C8—44no—
391C8—44no—
392C8—82no—
393C8—82no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—42no—
401C22—42no—
402C22C22⋊#9511yescharacteristic
403C22C4×#10411yescharacteristic
404C22#175911yescharacteristic
405C22#178912yes—
406C22#180612yes—
407C4—21no—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—44no—
419C4—44no—
420C4—44no—
421C4—82no—
422C4—84no—
423C4#183012yes—
424C2—22no—
425C2—22no—
426C2—21no—
427C2—21no—
428C2#1077011yescharacteristic
429C2#1078311yescharacteristic
430C2#1079011yescharacteristic
subgroupG/H
center, socleC22C22⋊#95
commutatorC22×C4C2×C42
Frattini, cosocleC22×C42C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
28. #1528C4semidirect
30. C2×#330C4semidirect

Maximal subgroups

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

subgroupindex
#342392
C2×#15282
C4×#3442
#80732
#79722
#79302