Finite Group Databasebeta

← #119403

Subgroups — #119403

Order 512.

534 conjugacy classes of subgroups.

The subgroup lattice has 387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21839C211yesmaximal, characteristic
2#21821C211yesmaximal, characteristic
3C2×#1552C211yesmaximal, characteristic
4#8031C211yesmaximal, characteristic
5C2×#1290C211yesmaximal, characteristic
6C2×#1287C211yesmaximal, characteristic
7#7893C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#432C2211yescharacteristic
12C2×#431C2211yescharacteristic
13C22×C4⋊C8C2211yescharacteristic
14#2285C2211yescharacteristic
15#1992C414yes—
16#1988—21no—
17#1987—21no—
18#1985—22no—
19#1984—22no—
20#1825—22no—
21#1818—22no—
22#1552—22no—
23#1552—22no—
24C2×#332—21no—
25C2×#332—21no—
26#1295—22no—
27#1290—22no—
28#1287—22no—
29#1279—22no—
30C23×C8—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×#125C2×C412yes—
42C2×C22⋊Q8—21no—
43C2×C22⋊Q8—21no—
44C2×C4×Q8—21no—
45C2×C4×Q8—21no—
46C2×#117—21no—
47C2×#117D412yes—
48C22×C42C2311yescharacteristic
49#432—21no—
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#432D412yes—
61#431—21no—
62#431—21no—
63#431—21no—
64#431—21no—
65C2×C4⋊C8—21no—
66C2×C4⋊C8—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—21no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74C2×C4⋊C8D412yes—
75C2×C22⋊C8—21no—
76C2×C22⋊C8—21no—
77C2×C22⋊C8—21no—
78C2×C22⋊C8—21no—
79C2×#97—21no—
80C2×#97C2×C412yes—
81C2×#97D412yes—
82C2×C4×C8D412yes—
83#384C2×C412yes—
84#382—21no—
85#380—21no—
86#380—21no—
87C4×C4⋊C4—21no—
88C4×C4⋊C4—21no—
89#340—24no—
90#340—24no—
91#336—28no—
92#332—24no—
93#332—24no—
94C22×Q8—21no—
95C22×Q8—21no—
96C23×C4C2×D411yescharacteristic
97C23×C4#4111yescharacteristic
98C23×C4#4111yescharacteristic
99C22×C8—22no—
100C22×C8—22no—
101C22×C8—22no—
102C22×C8—22no—
103C22×C8—41no—
104C22×C8—41no—
105C22×C8—41no—
106C22×C8—81no—
107C22×C8—81no—
108C4⋊Q8—21no—
109C4⋊Q8—21no—
110C4⋊Q8—21no—
111C4⋊Q8—21no—
112C4⋊Q8—21no—
113C4⋊Q8—21no—
114C4⋊Q8—21no—
115C4⋊Q8—21no—
116#125—22no—
117#125—22no—
118#125—22no—
119#125—22no—
120C22⋊Q8—41no—
121C22⋊Q8—41no—
122C22⋊Q8—41no—
123C22⋊Q8—41no—
124C22⋊Q8—41no—
125C22⋊Q8—41no—
126C22⋊Q8—41no—
127C22⋊Q8—41no—
128C4×Q8—41no—
129C4×Q8—41no—
130C4×Q8—41no—
131C4×Q8—41no—
132C4×Q8—41no—
133C4×Q8—41no—
134C4×Q8—41no—
135C4×Q8—41no—
136#117—22no—
137#117—22no—
138#117—22no—
139#117—22no—
140#117—81no—
141#117—81no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4C22⋊C412yes—
150C2×C4⋊C4C22⋊C412yes—
151C2×C22⋊C4—22no—
152C2×C22⋊C4—41no—
153C2×C42—22no—
154C2×C42—41no—
155C2×C42C22×C411yescharacteristic
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
167C4⋊C8—22no—
168C4⋊C8—22no—
169C4⋊C8—22no—
170C4⋊C8—41no—
171C4⋊C8—41no—
172C4⋊C8—41no—
173C4⋊C8—41no—
174C4⋊C8—41no—
175C4⋊C8—41no—
176C4⋊C8—41no—
177C4⋊C8—41no—
178C4⋊C8—41no—
179C22⋊C8—22no—
180C22⋊C8—41no—
181C22⋊C8—41no—
182C22⋊C8—41no—
183C22⋊C8—41no—
184C22⋊C8—41no—
185C22⋊C8—41no—
186C22⋊C8—41no—
187#97—22no—
188#97—22no—
189#97—22no—
190#97—22no—
191#97—22no—
192#97—41no—
193C4×C8—22no—
194C4×C8—22no—
195#95—41no—
196#95—41no—
197C24#12311yescharacteristic
198C2×Q8—41no—
199C2×Q8—41no—
200C2×Q8—41no—
201C2×Q8—41no—
202C2×Q8—41no—
203C2×Q8—41no—
204C2×Q8—41no—
205C2×Q8—41no—
206C2×Q8—82no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4C2×C22⋊C411yescharacteristic
217C22×C4C4×D411yescharacteristic
218C22×C4C4×D411yescharacteristic
219C22×C4#12011yescharacteristic
220C22×C4#12111yescharacteristic
221C22×C4#12111yescharacteristic
222C22×C4#12111yescharacteristic
223C22×C4#12111yescharacteristic
224C22×C4#12311yescharacteristic
225C22×C4#12311yescharacteristic
226C22×C4#12311yescharacteristic
227C22×C4#12311yescharacteristic
228C22×C4#12411yescharacteristic
229C22×C4#12411yescharacteristic
230C22×C4#12611yescharacteristic
231C22×C4#12611yescharacteristic
232C22×C4#12611yescharacteristic
233C22×C4#12611yescharacteristic
234C2×C8—44no—
235C2×C8—44no—
236C2×C8—44no—
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—82no—
243C2×C8—82no—
244C2×C8—81no—
245C2×C8—81no—
246C2×C8—82no—
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—44no—
252C4⋊C4—44no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C4⋊C4—42no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—82no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C22⋊C4—82no—
265C42—42no—
266C42—42no—
267C42—81no—
268C42—81no—
269C42#11711yescharacteristic
270C42#11711yescharacteristic
271C42C4×D411yescharacteristic
272C42C4×D411yescharacteristic
273C42#12011yescharacteristic
274C42#12111yescharacteristic
275C42#12111yescharacteristic
276C42#12111yescharacteristic
277C42#12111yescharacteristic
278C42#12311yescharacteristic
279C42#12311yescharacteristic
280C42#12311yescharacteristic
281C42#12311yescharacteristic
282C42#12311yescharacteristic
283C42#12411yescharacteristic
284C42#12411yescharacteristic
285C23—22no—
286C23—21no—
287C23—21no—
288C23—22no—
289C23#38611yescharacteristic
290C23#39711yescharacteristic
291C23#39711yescharacteristic
292Q8—82no—
293Q8—82no—
294Q8—81no—
295Q8—81no—
296Q8—81no—
297Q8—81no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—22no—
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—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—44no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4#38111yescharacteristic
329C2×C4#38611yescharacteristic
330C2×C4#38811yescharacteristic
331C2×C4#38811yescharacteristic
332C2×C4#38811yescharacteristic
333C2×C4#38811yescharacteristic
334C2×C4#39411yescharacteristic
335C2×C4#39411yescharacteristic
336C2×C4#39411yescharacteristic
337C2×C4#39411yescharacteristic
338C2×C4#39711yescharacteristic
339C2×C4#39711yescharacteristic
340C2×C4#47111yescharacteristic
341C2×C4#47111yescharacteristic
342C2×C4#47211yescharacteristic
343C2×C4#47311yescharacteristic
344C8—82no—
345C8—82no—
346C8—82no—
347C8—82no—
348C8—82no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—42no—
356C22—42no—
357C22#144011yescharacteristic
358C22#188112yes—
359C22#190711yescharacteristic
360C22#190811yescharacteristic
361C22#191212yes—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—82no—
373C4—82no—
374C4—162no—
375C4#205111yescharacteristic
376C4#205211yescharacteristic
377C4#207811yescharacteristic
378C4#207911yescharacteristic
379C2—41no—
380C2—41no—
381C2#937212yes—
382C2#937412yes—
383C2#1115611yescharacteristic
384C2#1119211yescharacteristic
385C2#1119411yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#123
LCSG ▷ C2×C42 ▷ 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
#218392
#218212
C2×#15522
#80312
C2×#12902
C2×#12872
#78932