Finite Group Databasebeta

← #115800

Subgroups — #115800

Order 512.

602 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21954C211yesmaximal, characteristic
2#21835C211yesmaximal, characteristic
3C2×#1506C211yesmaximal, characteristic
4C2×#1497C211yesmaximal, characteristic
5#8022C211yesmaximal, characteristic
6C2×#1287C211yesmaximal, characteristic
7C2×#1274C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C2×#431C2211yescharacteristic
13#2285C2211yescharacteristic
14C2×#376C2211yescharacteristic
15#1990C412yescomplemented
16#1990C412yescomplemented
17#1989—22no—
18#1940—22no—
19#1939—22no—
20#1825—22no—
21#1798—22no—
22#1506—22no—
23#1506—22no—
24C2×#328—22no—
25#1497—22no—
26#1497—22no—
27C2×Q8⋊C8—22no—
28#1294—22no—
29#1287—22no—
30#1274—22no—
31#533—21no—
32#533—21no—
33#533—21no—
34#533—21no—
35#533—21no—
36#533—21no—
37#533D412yes—
38#533Q812yes—
39C2×C4⋊Q8C2×C411yescharacteristic
40C2×C4⋊Q8C2×C411yescharacteristic
41C2×#125—21no—
42C2×C22⋊Q8—21no—
43C2×C22⋊Q8—21no—
44C2×C4×Q8—21no—
45C2×C4×Q8—21no—
46C2×#117—21no—
47C2×#117—21no—
48C22×C42—21no—
49C22×C42C2311yescharacteristic
50#432—21no—
51#432—21no—
52#432—21no—
53#432—21no—
54#432—21no—
55#432—21no—
56#432—21no—
57#432D412yes—
58#431—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63#431—21no—
64#431—21no—
65#431—21no—
66C2×C4⋊C8—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—24no—
71C2×C22⋊C8—21no—
72C2×C22⋊C8—21no—
73C2×C22⋊C8—21no—
74C2×C22⋊C8D412yes—
75C2×#97—21no—
76C2×#97—21no—
77C2×C4×C8C2×C412yes—
78C2×C4×C8D412yes—
79#384C2×C412yes—
80#382—21no—
81#380—21no—
82#380D412yes—
83C4×C4⋊C4—21no—
84C4×C4⋊C4D412yes—
85#376—21no—
86#376—21no—
87#376—21no—
88#376D412yes—
89C2×#95—21no—
90C2×#95—21no—
91#340—24no—
92#340—24no—
93#336—24no—
94#328—28no—
95Q8⋊C8—28no—
96C22×Q8—21no—
97C22×Q8—21no—
98C23×C4—41no—
99C23×C4C2×D411yescharacteristic
100C23×C4C2×D411yescharacteristic
101C23×C4#4111yescharacteristic
102C22×C8—22no—
103C22×C8—22no—
104C22×C8—22no—
105C22×C8—41no—
106C4⋊Q8—21no—
107C4⋊Q8—21no—
108C4⋊Q8—21no—
109C4⋊Q8—21no—
110C4⋊Q8—21no—
111C4⋊Q8—21no—
112C4⋊Q8C4⋊C412yes—
113C4⋊Q8C4⋊C412yes—
114#125—22no—
115#125—22no—
116#125—41no—
117#125—41no—
118C22⋊Q8—22no—
119C22⋊Q8—22no—
120C22⋊Q8—22no—
121C22⋊Q8—22no—
122C22⋊Q8—41no—
123C22⋊Q8—41no—
124C22⋊Q8—41no—
125C22⋊Q8—41no—
126C4×Q8—22no—
127C4×Q8—22no—
128C4×Q8—22no—
129C4×Q8—22no—
130C4×Q8—41no—
131C4×Q8—41no—
132C4×Q8—41no—
133C4×Q8—41no—
134#117—22no—
135#117—22no—
136#117—41no—
137#117—41no—
138#117—82no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—41no—
146C2×C4⋊C4—41no—
147C2×C4⋊C4C22⋊C414yes—
148C2×C22⋊C4—22no—
149C2×C22⋊C4—41no—
150C2×C42—24no—
151C2×C42—22no—
152C2×C42—22no—
153C2×C42—42no—
154C2×C42—41no—
155C2×C42—41no—
156C2×C42C22×C411yescharacteristic
157C2×C42C2×D411yescharacteristic
158C2×C42C2×D411yescharacteristic
159C2×C42C2×D411yescharacteristic
160C2×C42C2×D411yescharacteristic
161C2×C42C2×D411yescharacteristic
162C2×C42C2×Q811yescharacteristic
163C2×C42#4111yescharacteristic
164C2×C42#4111yescharacteristic
165C2×C42#4111yescharacteristic
166C2×C42#4111yescharacteristic
167C2×C42#4111yescharacteristic
168C4⋊C8—22no—
169C4⋊C8—41no—
170C4⋊C8—41no—
171C4⋊C8—41no—
172C4⋊C8—41no—
173C4⋊C8—41no—
174C4⋊C8—41no—
175C4⋊C8—41no—
176C4⋊C8—84no—
177C22⋊C8—22no—
178C22⋊C8—22no—
179C22⋊C8—22no—
180C22⋊C8—41no—
181C22⋊C8—41no—
182C22⋊C8—41no—
183C22⋊C8—41no—
184C22⋊C8—41no—
185#97—22no—
186#97—41no—
187#97—41no—
188#97—41no—
189C4×C8—22no—
190C4×C8—22no—
191C4×C8—22no—
192C4×C8—22no—
193#95—22no—
194#95—22no—
195#95—22no—
196#95—22no—
197#95—41no—
198#95—41no—
199C24#12111yescharacteristic
200C2×Q8—22no—
201C2×Q8—22no—
202C2×Q8—41no—
203C2×Q8—41no—
204C2×Q8—42no—
205C2×Q8—42no—
206C2×Q8—81no—
207C2×Q8—81no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—24no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—42no—
214C22×C4—44no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—42no—
218C22×C4—81no—
219C22×C4—81no—
220C22×C4—82no—
221C22×C4C2×C22⋊C411yescharacteristic
222C22×C4C4×D411yescharacteristic
223C22×C4C4×D411yescharacteristic
224C22×C4#12011yescharacteristic
225C22×C4#12011yescharacteristic
226C22×C4#12111yescharacteristic
227C22×C4#12111yescharacteristic
228C22×C4#12111yescharacteristic
229C22×C4#12111yescharacteristic
230C22×C4#12111yescharacteristic
231C22×C4C22⋊Q811yescharacteristic
232C22×C4C22⋊Q811yescharacteristic
233C22×C4C22⋊Q811yescharacteristic
234C22×C4#12311yescharacteristic
235C22×C4#12311yescharacteristic
236C22×C4#12311yescharacteristic
237C22×C4#12411yescharacteristic
238C22×C4#12611yescharacteristic
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—44no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—82no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—44no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C4⋊C4—82no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C22⋊C4—82no—
268C42—24no—
269C42—44no—
270C42—44no—
271C42—42no—
272C42—42no—
273C42—42no—
274C42C2×C4⋊C411yescharacteristic
275C42#11711yescharacteristic
276C42C4×D411yescharacteristic
277C42C4×D411yescharacteristic
278C42#12011yescharacteristic
279C42#12111yescharacteristic
280C42#12111yescharacteristic
281C42C22⋊Q811yescharacteristic
282C42C22⋊Q811yescharacteristic
283C42C22⋊Q811yescharacteristic
284C42#12311yescharacteristic
285C42#12311yescharacteristic
286C42#12411yescharacteristic
287C42#12411yescharacteristic
288C42#12611yescharacteristic
289C42#12711yescharacteristic
290C23—22no—
291C23—21no—
292C23—21no—
293C23—22no—
294C23#38611yescharacteristic
295C23#39411yescharacteristic
296C23#39611yescharacteristic
297Q8—44no—
298Q8—82no—
299Q8—82no—
300Q8—81no—
301Q8—81no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—44no—
324C2×C4—44no—
325C2×C4—44no—
326C2×C4—44no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4—84no—
332C2×C4—84no—
333C2×C4—82no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4#38011yescharacteristic
337C2×C4#38511yescharacteristic
338C2×C4#38511yescharacteristic
339C2×C4#38811yescharacteristic
340C2×C4#38811yescharacteristic
341C2×C4#39011yescharacteristic
342C2×C4#39211yescharacteristic
343C2×C4#39311yescharacteristic
344C2×C4#39411yescharacteristic
345C2×C4#39611yescharacteristic
346C2×C4#39711yescharacteristic
347C2×C4#39911yescharacteristic
348C2×C4#44312yes—
349C2×C4#44412yes—
350C8—82no—
351C8—82no—
352C8—82no—
353C8—82no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—42no—
361C22—42no—
362C22#143911yescharacteristic
363C22#187612yes—
364C22#190411yescharacteristic
365C22#190511yescharacteristic
366C22#190912yes—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—84no—
378C4—82no—
379C4—82no—
380C4—84no—
381C4#186612yes—
382C4#193711yescharacteristic
383C4#193811yescharacteristic
384C2—41no—
385C2—41no—
386C2#927912yes—
387C2#928012yes—
388C2#1105711yescharacteristic
389C2#1106811yescharacteristic
390C2#1107411yescharacteristic
subgroupG/H
center, socleC23#386
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
15. #1990C4semidirect
16. #1990C4semidirect

Maximal subgroups

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

subgroupindex
#219542
#218352
C2×#15062
C2×#14972
#80222
C2×#12872
C2×#12742