Finite Group Databasebeta

← #119760

Subgroups — #119760

Order 512.

594 conjugacy classes of subgroups.

The subgroup lattice has 413 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21838C211yesmaximal, characteristic
2C2×#1989C211yesmaximal, characteristic
3C2×#1470C211yesmaximal, characteristic
4#8044C211yesmaximal, characteristic
5#8014C211yesmaximal, characteristic
6C2×#1285C211yesmaximal, characteristic
7#7879C211yesmaximal, characteristic
8C22×#125C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C22×C4⋊C8C2211yescharacteristic
13#2285C2211yescharacteristic
14C2×C4×C4⋊C4C2211yescharacteristic
15#1992—22no—
16#1989—22no—
17#1989—22no—
18#1989C414yescomplemented
19#1824—21no—
20#1823—21no—
21C2×#340—21no—
22C2×#340—21no—
23#1470—22no—
24#1470—22no—
25C2×#324—22no—
26#1296—22no—
27#1294—22no—
28#1285—22no—
29#1277—22no—
30C23×C8—21no—
31C2×#125—21no—
32C2×#125—21no—
33C2×#125—21no—
34C2×#125—21no—
35C2×#125—21no—
36C2×#125—21no—
37C2×#125—21no—
38C2×#125—21no—
39C2×#125—21no—
40C2×#125—21no—
41C2×#125C2×C412yes—
42C2×#125D412yes—
43C2×#117—21no—
44C22×C4⋊C4—21no—
45C22×C4⋊C4—21no—
46C22×C4⋊C4—21no—
47C22×C4⋊C4D411yescharacteristic
48C22×C4⋊C4D411yescharacteristic
49C22×C42—21no—
50C22×C42C2311yescharacteristic
51#432—21no—
52#432—21no—
53#432—21no—
54#432—21no—
55#432—21no—
56#432—21no—
57#432—21no—
58#432D412yes—
59#431—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63C2×C4⋊C8—21no—
64C2×C4⋊C8—21no—
65C2×C4⋊C8—21no—
66C2×C4⋊C8—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8C2×C412yes—
71C2×C4⋊C8D412yes—
72C2×C22⋊C8—21no—
73C2×C22⋊C8—21no—
74C2×C22⋊C8D412yes—
75C2×#97—21no—
76C2×#97—21no—
77C2×C4×C8—21no—
78#384D412yes—
79#382—21no—
80#380—21no—
81#380—21no—
82C4×C4⋊C4—21no—
83C4×C4⋊C4—21no—
84C4×C4⋊C4—21no—
85C4×C4⋊C4—21no—
86C4×C4⋊C4—21no—
87C4×C4⋊C4C2×C412yes—
88C2×#95—21no—
89#340—24no—
90#340—24no—
91#340—24no—
92#340—24no—
93#324—28no—
94C23×C4—21no—
95C23×C4—21no—
96C23×C4—41no—
97C23×C4C2×D411yescharacteristic
98C23×C4C2×D411yescharacteristic
99C23×C4#4111yescharacteristic
100C22×C8—22no—
101C22×C8—22no—
102C22×C8—22no—
103C22×C8—44no—
104C22×C8—41no—
105C22×C8—41no—
106C22×C8—41no—
107#125—22no—
108#125—22no—
109#125—22no—
110#125—22no—
111#125—22no—
112#125—22no—
113#125—22no—
114#125—22no—
115#125—41no—
116#125—41no—
117#125—41no—
118#125—41no—
119#125—41no—
120#125—41no—
121#125—41no—
122#125—41no—
123#117—81no—
124#117—81no—
125C2×C4⋊C4—24no—
126C2×C4⋊C4—22no—
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—22no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—42no—
145C2×C4⋊C4—41no—
146C2×C4⋊C4—41no—
147C2×C4⋊C4—41no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4C22⋊C412yes—
155C2×C4⋊C4C22⋊C412yes—
156C2×C22⋊C4—41no—
157C2×C42—22no—
158C2×C42—41no—
159C2×C42—41no—
160C2×C42—81no—
161C2×C42—81no—
162C2×C42C22×C411yescharacteristic
163C2×C42C2×D411yescharacteristic
164C2×C42C2×D411yescharacteristic
165C2×C42C2×D411yescharacteristic
166C2×C42C2×D411yescharacteristic
167C2×C42#4111yescharacteristic
168C2×C42#4111yescharacteristic
169C2×C42#4111yescharacteristic
170C2×C42#4111yescharacteristic
171C2×C42#4111yescharacteristic
172C2×C42#4111yescharacteristic
173C2×C42#4111yescharacteristic
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8—22no—
177C4⋊C8—22no—
178C4⋊C8—22no—
179C4⋊C8—41no—
180C4⋊C8—41no—
181C4⋊C8—41no—
182C4⋊C8—41no—
183C4⋊C8—41no—
184C22⋊C8—22no—
185C22⋊C8—22no—
186C22⋊C8—22no—
187C22⋊C8—41no—
188C22⋊C8—41no—
189C22⋊C8—41no—
190#97—22no—
191#97—41no—
192#97—41no—
193#97—41no—
194C4×C8—41no—
195C4×C8—41no—
196#95—22no—
197#95—41no—
198#95—41no—
199#95—41no—
200C24#12111yescharacteristic
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—42no—
210C22×C4—44no—
211C22×C4—42no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—41no—
220C22×C4—42no—
221C22×C4—82no—
222C22×C4—81no—
223C22×C4—81no—
224C22×C4—82no—
225C22×C4C2×C22⋊C411yescharacteristic
226C22×C4C4×D411yescharacteristic
227C22×C4C4×D411yescharacteristic
228C22×C4#12011yescharacteristic
229C22×C4#12011yescharacteristic
230C22×C4#12111yescharacteristic
231C22×C4#12111yescharacteristic
232C22×C4#12111yescharacteristic
233C22×C4#12311yescharacteristic
234C22×C4#12311yescharacteristic
235C22×C4#12311yescharacteristic
236C22×C4#12311yescharacteristic
237C22×C4#12311yescharacteristic
238C22×C4#12311yescharacteristic
239C22×C4#12411yescharacteristic
240C22×C4#12411yescharacteristic
241C22×C4#12611yescharacteristic
242C22×C4#12611yescharacteristic
243C2×C8—44no—
244C2×C8—44no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—82no—
252C2×C8—82no—
253C2×C8—82no—
254C4⋊C4—24no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—42no—
260C4⋊C4—44no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—82no—
276C4⋊C4—82no—
277C22⋊C4—81no—
278C22⋊C4—81no—
279C42—82no—
280C42—82no—
281C42—82no—
282C42#11711yescharacteristic
283C42#11711yescharacteristic
284C42C4×D411yescharacteristic
285C42C4×D411yescharacteristic
286C42#12111yescharacteristic
287C42#12111yescharacteristic
288C42#12111yescharacteristic
289C42#12111yescharacteristic
290C42#12311yescharacteristic
291C42#12311yescharacteristic
292C42#12311yescharacteristic
293C42#12311yescharacteristic
294C42#12411yescharacteristic
295C42#12411yescharacteristic
296C42#12611yescharacteristic
297C42#12611yescharacteristic
298C23—22no—
299C23—22no—
300C23#38611yescharacteristic
301C23#39411yescharacteristic
302C23#39711yescharacteristic
303C23#47111yescharacteristic
304C23#47111yescharacteristic
305C23#47211yescharacteristic
306C23#47311yescharacteristic
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—22no—
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—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—44no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—84no—
338C2×C4—84no—
339C2×C4—82no—
340C2×C4—82no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—82no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—82no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4#38111yescharacteristic
352C2×C4#38611yescharacteristic
353C2×C4#38811yescharacteristic
354C2×C4#38811yescharacteristic
355C2×C4#38811yescharacteristic
356C2×C4#38811yescharacteristic
357C2×C4#39411yescharacteristic
358C2×C4#39411yescharacteristic
359C2×C4#39411yescharacteristic
360C2×C4#39711yescharacteristic
361C2×C4#39711yescharacteristic
362C2×C4#39711yescharacteristic
363C2×C4#45412yes—
364C2×C4#45612yes—
365C8—82no—
366C8—82no—
367C8—82no—
368C8—82no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22#144011yescharacteristic
378C22#190711yescharacteristic
379C22#190811yescharacteristic
380C22#203812yes—
381C22#205111yescharacteristic
382C22#205211yescharacteristic
383C22#205312yes—
384C22#207811yescharacteristic
385C22#207911yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—84no—
397C4—82no—
398C4—82no—
399C4—162no—
400C4#188611yescharacteristic
401C4#188811yescharacteristic
402C4#203812yes—
403C2—21no—
404C2—21no—
405C2—21no—
406C2—21no—
407C2#1050912yes—
408C2#1051112yes—
409C2#1116211yescharacteristic
410C2#1117611yescharacteristic
411C2#1119211yescharacteristic
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
18. #1989C4semidirect

Maximal subgroups

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

subgroupindex
#218382
C2×#19892
C2×#14702
#80442
#80142
C2×#12852
#78792