Finite Group Databasebeta

← #118492

Subgroups — #118492

Order 512.

574 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21836C211yesmaximal, characteristic
2#21314C211yesmaximal, characteristic
3#17809C211yesmaximal, characteristic
4#17394C211yesmaximal, characteristic
5#8092C211yesmaximal, characteristic
6#7962C211yesmaximal, characteristic
7#7940C211yesmaximal, characteristic
8C22×#125C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C2×#423C2211yescharacteristic
13#2283C2211yescharacteristic
14C4×#117C2211yescharacteristic
15#1991—22no—
16#1989—22no—
17#1989—21no—
18#1989—21no—
19#1989—22no—
20#1824—21no—
21#1823—21no—
22#1736—21no—
23#1736—21no—
24#1574—22no—
25#1571—21no—
26#1570—21no—
27#1565—22no—
28#1470—22no—
29#1470C414yescomplemented
30#1463—22no—
31#1303—22no—
32#1286—22no—
33#1284—22no—
34C22×M16—21no—
35C2×#125—21no—
36C2×#125—21no—
37C2×#125—21no—
38C2×#125—21no—
39C2×#125—21no—
40C2×#125—21no—
41C2×#125—21no—
42C2×#125—21no—
43C2×#125—21no—
44C2×#125—21no—
45C2×#125C2×C412yes—
46C2×#125Q812yes—
47C2×#117—21no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4D411yescharacteristic
51C22×C4⋊C4D411yescharacteristic
52C22×C42C2311yescharacteristic
53#432—21no—
54#432—21no—
55#432—21no—
56#432C2×C412yes—
57#431—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63#431C2×C412yes—
64#431D412yes—
65#423—21no—
66#423—21no—
67#423—21no—
68#423—21no—
69#423—21no—
70#423—21no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8D412yes—
73C2×C4⋊C8D411yescharacteristic
74C2×C4⋊C8D411yescharacteristic
75#407—21no—
76#407D412yes—
77C2×C22⋊C8—21no—
78C4×M16—21no—
79C4×M16—21no—
80C2×C4×C8—21no—
81#383—21no—
82#382D412yes—
83#381—21no—
84#380—21no—
85C4×C4⋊C4—21no—
86C4×C4⋊C4—21no—
87C4×C4⋊C4D412yes—
88C4×C22⋊C4—21no—
89C4×C22⋊C4—21no—
90C4×C22⋊C4—21no—
91#376—21no—
92#376—21no—
93C43—21no—
94#340—22no—
95#340—22no—
96#340—22no—
97#340—22no—
98#340—24no—
99#340—24no—
100#335—24no—
101#334—24no—
102#324—28no—
103C23×C4—21no—
104C23×C4—21no—
105C23×C4C2×D411yescharacteristic
106C23×C4C2×D411yescharacteristic
107C23×C4#4111yescharacteristic
108C2×M16—22no—
109C2×M16—44no—
110C2×M16—41no—
111C2×M16—41no—
112C2×M16—41no—
113C22×C8—22no—
114C22×C8—21no—
115C22×C8—21no—
116#125—22no—
117#125—22no—
118#125—22no—
119#125—22no—
120#125—22no—
121#125—22no—
122#125—22no—
123#125—22no—
124#125—41no—
125#125—41no—
126#125—41no—
127#125—41no—
128#125—41no—
129#125—41no—
130#125—41no—
131#125—41no—
132#117—24no—
133#117—42no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—22no—
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—21no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4C4⋊C412yes—
159C2×C4⋊C4C4⋊C412yes—
160C2×C22⋊C4—41no—
161C2×C22⋊C4—41no—
162C2×C42—22no—
163C2×C42—41no—
164C2×C42—41no—
165C2×C42—41no—
166C2×C42C22×C411yescharacteristic
167C2×C42C2×D411yescharacteristic
168C2×C42C2×D411yescharacteristic
169C2×C42C2×D411yescharacteristic
170C2×C42C2×D411yescharacteristic
171C2×C42C2×D411yescharacteristic
172C2×C42C2×Q811yescharacteristic
173C2×C42#4111yescharacteristic
174C2×C42#4111yescharacteristic
175C2×C42#4111yescharacteristic
176C2×C42#4111yescharacteristic
177C2×C42#4111yescharacteristic
178C4⋊C8—22no—
179C4⋊C8—22no—
180C4⋊C8—21no—
181C4⋊C8—22no—
182C4⋊C8—21no—
183C4⋊C8—22no—
184C4⋊C8—21no—
185C4⋊C8—21no—
186C4⋊C8—22no—
187C4⋊C8—41no—
188C4⋊C8—41no—
189C4⋊C8—41no—
190C22⋊C8—22no—
191C22⋊C8—22no—
192C22⋊C8—41no—
193C22⋊C8—41no—
194C22⋊C8—41no—
195C22⋊C8C22⋊C414yes—
196#97—22no—
197#97—41no—
198C4×C8—22no—
199C4×C8—22no—
200C4×C8—41no—
201C4×C8—41no—
202#95—22no—
203#95—22no—
204#95—22no—
205#95—41no—
206#95—41no—
207#95—41no—
208C24#12111yescharacteristic
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—42no—
220C22×C4—81no—
221C22×C4—82no—
222C22×C4—82no—
223C22×C4C2×C22⋊C411yescharacteristic
224C22×C4C2×C4⋊C411yescharacteristic
225C22×C4#11711yescharacteristic
226C22×C4#12011yescharacteristic
227C22×C4#12011yescharacteristic
228C22×C4#12111yescharacteristic
229C22×C4#12111yescharacteristic
230C22×C4#12111yescharacteristic
231C22×C4#12111yescharacteristic
232C22×C4#12111yescharacteristic
233C22×C4C22⋊Q811yescharacteristic
234C22×C4C22⋊Q811yescharacteristic
235C22×C4#12311yescharacteristic
236C22×C4#12311yescharacteristic
237C22×C4#12311yescharacteristic
238C22×C4#12311yescharacteristic
239C22×C4#12411yescharacteristic
240C22×C4#12411yescharacteristic
241M16—44no—
242M16—82no—
243M16—82no—
244M16—82no—
245C2×C8—24no—
246C2×C8—44no—
247C2×C8—42no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—42no—
253C4⋊C4—24no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C22⋊C4—44no—
274C22⋊C4—82no—
275C42—44no—
276C42—82no—
277C42—82no—
278C42—82no—
279C42C4×D411yescharacteristic
280C42C4×D411yescharacteristic
281C42C4×D411yescharacteristic
282C42C4×D411yescharacteristic
283C42#12011yescharacteristic
284C42#12111yescharacteristic
285C42#12111yescharacteristic
286C42C22⋊Q811yescharacteristic
287C42C22⋊Q811yescharacteristic
288C42C22⋊Q811yescharacteristic
289C42C22⋊Q811yescharacteristic
290C42#12311yescharacteristic
291C42#12411yescharacteristic
292C42#12611yescharacteristic
293C42#12611yescharacteristic
294C42#12711yescharacteristic
295C23—22no—
296C23—22no—
297C23—41no—
298C23#38011yescharacteristic
299C23#39411yescharacteristic
300C23#39411yescharacteristic
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
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—44no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—82no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4#38511yescharacteristic
335C2×C4#38511yescharacteristic
336C2×C4#38611yescharacteristic
337C2×C4#38811yescharacteristic
338C2×C4#38811yescharacteristic
339C2×C4#39011yescharacteristic
340C2×C4#39211yescharacteristic
341C2×C4#39311yescharacteristic
342C2×C4#39611yescharacteristic
343C2×C4#39611yescharacteristic
344C2×C4#39711yescharacteristic
345C2×C4#39911yescharacteristic
346C2×C4#45412yes—
347C2×C4#45612yes—
348C8—44no—
349C8—82no—
350C8—81no—
351C8—82no—
352C8—81no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—44no—
361C22#143911yescharacteristic
362C22#203812yes—
363C22#205312yes—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—84no—
375C4—82no—
376C4—82no—
377C4—162no—
378C4#185712yes—
379C4#200311yescharacteristic
380C4#200511yescharacteristic
381C2—22no—
382C2—22no—
383C2—41no—
384C2#1109211yescharacteristic
385C2#1111011yescharacteristic
386C2#1113611yescharacteristic
subgroupG/H
center, socleC22#1439
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#121
LCSG ▷ C2×C42 ▷ 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
29. #1470C4semidirect

Maximal subgroups

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

subgroupindex
#218362
#213142
#178092
#173942
#80922
#79622
#79402