Finite Group Databasebeta

← #119321

Subgroups — #119321

Order 512.

574 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21821C211yesmaximal, characteristic
2#21394C211yesmaximal, characteristic
3C2×#1559C211yesmaximal, characteristic
4C2×#1307C211yesmaximal, characteristic
5C2×#1287C211yesmaximal, characteristic
6#7912C211yesmaximal, characteristic
7#7901C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#432C2211yescharacteristic
12C2×#431C2211yescharacteristic
13C2×#423C2211yescharacteristic
14C2×C4×C4⋊C4C2211yescharacteristic
15#1988—21no—
16#1985—22no—
17#1984—22no—
18#1981—21no—
19#1872C414yes—
20#1818—22no—
21#1763—22no—
22#1559—22no—
23#1559—22no—
24C2×#333—21no—
25C2×#332—21no—
26#1307—22no—
27#1287—22no—
28#1280—22no—
29#1279—22no—
30C22×M16—21no—
31#533—21no—
32#533—21no—
33#533—21no—
34#533—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38#533—21no—
39C2×C4⋊Q8D411yescharacteristic
40C2×C4⋊Q8D411yescharacteristic
41C2×#125—21no—
42C2×C22⋊Q8—21no—
43C2×C22⋊Q8C2×C412yes—
44C2×C4×Q8—21no—
45C2×C4×Q8D412yes—
46C2×#117—21no—
47C22×C4⋊C4C2×C412yes—
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#432—21no—
58#432—21no—
59#432—21no—
60#432—21no—
61#432D412yes—
62#431—21no—
63#431—21no—
64#431—21no—
65#431—21no—
66#423—21no—
67#423—21no—
68#423—21no—
69#423D412yes—
70C2×C4⋊C8—21no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74C2×C4⋊C8—21no—
75C2×C4⋊C8—21no—
76C2×#103—24no—
77C2×C22⋊C8—21no—
78C2×C22⋊C8—21no—
79C2×C22⋊C8C2×C412yes—
80C2×C22⋊C8D412yes—
81C2×#97—21no—
82C2×#97—21no—
83C2×#97—21no—
84C2×C4×C8D412yes—
85C4×C4⋊C4—21no—
86C4×C4⋊C4—21no—
87C4×C4⋊C4—21no—
88C4×C4⋊C4—21no—
89C2×#95—21no—
90#340—24no—
91#336—28no—
92#333—24no—
93#332—24no—
94C22×Q8—21no—
95C22×Q8C22⋊C412yes—
96C23×C4—22no—
97C23×C4C22×C411yescharacteristic
98C23×C4C2×D411yescharacteristic
99C23×C4#4111yescharacteristic
100C2×M16—22no—
101C2×M16—41no—
102C2×M16—81no—
103C2×M16—81no—
104C22×C8—22no—
105C22×C8—22no—
106C22×C8—22no—
107C22×C8—41no—
108C22×C8—41no—
109C4⋊Q8—21no—
110C4⋊Q8—21no—
111C4⋊Q8—21no—
112C4⋊Q8—21no—
113C4⋊Q8—21no—
114C4⋊Q8—21no—
115C4⋊Q8—21no—
116C4⋊Q8—21no—
117#125—41no—
118#125—41no—
119#125—41no—
120#125—41no—
121C22⋊Q8—22no—
122C22⋊Q8—22no—
123C22⋊Q8—22no—
124C22⋊Q8—22no—
125C22⋊Q8—41no—
126C22⋊Q8—41no—
127C22⋊Q8—41no—
128C22⋊Q8—41no—
129C4×Q8—22no—
130C4×Q8—22no—
131C4×Q8—22no—
132C4×Q8—22no—
133C4×Q8—41no—
134C4×Q8—41no—
135C4×Q8—41no—
136C4×Q8—41no—
137#117—41no—
138#117—41no—
139#117—41no—
140#117—41no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—44no—
149C2×C4⋊C4C22⋊C412yes—
150C2×C22⋊C4—22no—
151C2×C42—22no—
152C2×C42—41no—
153C2×C42—41no—
154C2×C42—81no—
155C2×C42—81no—
156C2×C42C2×D411yescharacteristic
157C2×C42C2×D411yescharacteristic
158C2×C42C2×D411yescharacteristic
159C2×C42C2×D411yescharacteristic
160C2×C42C2×D411yescharacteristic
161C2×C42#4111yescharacteristic
162C2×C42#4111yescharacteristic
163C2×C42#4111yescharacteristic
164C2×C42#4111yescharacteristic
165C2×C42#4111yescharacteristic
166C2×C42#4111yescharacteristic
167C2×C42#4111yescharacteristic
168C4⋊C8—22no—
169C4⋊C8—22no—
170C4⋊C8—22no—
171C4⋊C8—41no—
172C4⋊C8—41no—
173C4⋊C8—41no—
174C4⋊C8—41no—
175C4⋊C8—41no—
176C4⋊C8—41no—
177C4⋊C8—41no—
178C4⋊C8—41no—
179C4⋊C8—41no—
180#103—48no—
181C22⋊C8—22no—
182C22⋊C8—22no—
183C22⋊C8—22no—
184C22⋊C8—22no—
185C22⋊C8—22no—
186C22⋊C8—41no—
187C22⋊C8—41no—
188C22⋊C8—41no—
189#97—22no—
190#97—41no—
191#97—41no—
192#97—41no—
193#97—41no—
194#97—41no—
195C4×C8—22no—
196C4×C8—22no—
197#95—41no—
198#95—41no—
199C24C4×D411yescharacteristic
200C2×Q8—22no—
201C2×Q8—22no—
202C2×Q8—44no—
203C2×Q8—41no—
204C2×Q8—41no—
205C2×Q8—41no—
206C2×Q8—41no—
207C2×Q8—41no—
208C2×Q8—41no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—24no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—82no—
221C22×C4—82no—
222C22×C4C2×C22⋊C411yescharacteristic
223C22×C4#11711yescharacteristic
224C22×C4#11711yescharacteristic
225C22×C4C4×D411yescharacteristic
226C22×C4C4×D411yescharacteristic
227C22×C4C4×D411yescharacteristic
228C22×C4#12011yescharacteristic
229C22×C4#12111yescharacteristic
230C22×C4#12111yescharacteristic
231C22×C4#12111yescharacteristic
232C22×C4#12111yescharacteristic
233C22×C4#12311yescharacteristic
234C22×C4#12311yescharacteristic
235C22×C4#12311yescharacteristic
236C22×C4#12411yescharacteristic
237C22×C4#12411yescharacteristic
238C22×C4#12611yescharacteristic
239C22×C4#12611yescharacteristic
240M16—82no—
241M16—82no—
242C2×C8—44no—
243C2×C8—44no—
244C2×C8—44no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—82no—
251C2×C8—81no—
252C2×C8—81no—
253C4⋊C4—24no—
254C4⋊C4—24no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—41no—
269C22⋊C4—42no—
270C22⋊C4—42no—
271C42—42no—
272C42—42no—
273C42—82no—
274C42—81no—
275C42—81no—
276C42#12011yescharacteristic
277C42#12111yescharacteristic
278C42#12111yescharacteristic
279C42#12111yescharacteristic
280C42#12111yescharacteristic
281C42#12311yescharacteristic
282C42#12311yescharacteristic
283C42#12311yescharacteristic
284C42#12311yescharacteristic
285C42#12311yescharacteristic
286C42#12311yescharacteristic
287C42#12311yescharacteristic
288C42#12411yescharacteristic
289C42#12411yescharacteristic
290C42#12611yescharacteristic
291C42#12611yescharacteristic
292C23—22no—
293C23—22no—
294C23—21no—
295C23—21no—
296C23#38611yescharacteristic
297C23#38811yescharacteristic
298C23#38811yescharacteristic
299Q8—44no—
300Q8—82no—
301Q8—81no—
302Q8—81no—
303Q8—81no—
304Q8—81no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
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—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—44no—
328C2×C4—44no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—84no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—84no—
337C2×C4#38111yescharacteristic
338C2×C4#38611yescharacteristic
339C2×C4#38811yescharacteristic
340C2×C4#38811yescharacteristic
341C2×C4#39411yescharacteristic
342C2×C4#39411yescharacteristic
343C2×C4#39411yescharacteristic
344C2×C4#39411yescharacteristic
345C2×C4#39711yescharacteristic
346C2×C4#39711yescharacteristic
347C2×C4#39711yescharacteristic
348C2×C4#39711yescharacteristic
349C2×C4#47111yescharacteristic
350C2×C4#47111yescharacteristic
351C2×C4#47211yescharacteristic
352C2×C4#47311yescharacteristic
353C8—82no—
354C8—82no—
355C8—82no—
356C8—82no—
357C8—82no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—42no—
365C22—42no—
366C22#144011yescharacteristic
367C22#189112yes—
368C22#190512yes—
369C22#190711yescharacteristic
370C22#190811yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—84no—
382C4—82no—
383C4—82no—
384C4#205111yescharacteristic
385C4#205211yescharacteristic
386C4#207811yescharacteristic
387C4#207911yescharacteristic
388C2—41no—
389C2—41no—
390C2#952812yes—
391C2#953012yes—
392C2#1117511yescharacteristic
393C2#1118411yescharacteristic
394C2#1119211yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C4×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#218212
#213942
C2×#15592
C2×#13072
C2×#12872
#79122
#79012