Finite Group Databasebeta

← #120932

Subgroups — #120932

Order 512.

446 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21965C211yesmaximal, characteristic
2#10856C211yesmaximal, characteristic
3#8061C211yesmaximal, characteristic
4#8052C211yesmaximal, characteristic
5#7962C211yesmaximal, characteristic
6#7960C211yesmaximal, characteristic
7#7940C211yesmaximal, characteristic
8#2920C2211yescharacteristic
9#2920C2211yescharacteristic
10C2×#423C2211yescharacteristic
11C2×#423C2211yescharacteristic
12#2283C2211yescharacteristic
13#2283C2211yescharacteristic
14C4×#117C2211yescharacteristic
15#1949—21no—
16#1949—21no—
17#1949—21no—
18#1949—21no—
19#1809—21no—
20#1809—21no—
21C2×#344—21no—
22C2×#344—21no—
23#1299C414yescomplemented
24#1297—22no—
25#1286—21no—
26#1286—21no—
27#1286—21no—
28#1286—21no—
29#1284—22no—
30C22×M16—21no—
31C22×M16D411yescharacteristic
32C22×M16D411yescharacteristic
33C2×#117—21no—
34C22×C42C2311yescharacteristic
35#432—21no—
36#432—21no—
37#432—21no—
38#432—21no—
39#431—21no—
40#431—21no—
41#431—21no—
42#431C2×C412yes—
43C2×#107—21no—
44C2×#107—21no—
45C2×#106—21no—
46C2×#106—21no—
47#423—21no—
48#423—21no—
49#423—21no—
50#423—21no—
51#423—21no—
52#423—21no—
53#423—21no—
54#423—21no—
55#423C2×C412yes—
56#423Q812yes—
57C2×C4⋊C8—21no—
58C2×C4⋊C8—21no—
59C2×C4⋊C8—21no—
60C2×C4⋊C8Q812yes—
61#407—21no—
62#407—21no—
63C4×M16—21no—
64C4×M16C2×C412yes—
65#383—21no—
66#383—21no—
67#382D411yescharacteristic
68#382D411yescharacteristic
69#382D411yescharacteristic
70#382D411yescharacteristic
71#381—21no—
72#381—21no—
73#380—21no—
74#380—21no—
75C4×C4⋊C4—21no—
76C4×C4⋊C4—21no—
77C4×C4⋊C4—21no—
78C4×C4⋊C4—21no—
79C4×C22⋊C4—21no—
80C4×C22⋊C4—21no—
81C4×C22⋊C4—21no—
82C4×C22⋊C4D412yes—
83#376—21no—
84#376—21no—
85#376—21no—
86C43—21no—
87#344—42no—
88#344—42no—
89#340—21no—
90#340—21no—
91#340—21no—
92#340—21no—
93C23×C4C2×D411yescharacteristic
94C23×C4C2×D411yescharacteristic
95C23×C4#4111yescharacteristic
96C2×M16—21no—
97C2×M16—21no—
98C2×M16—22no—
99C2×M16—41no—
100C2×M16—41no—
101C2×M16—41no—
102C2×M16—41no—
103C2×M16—41no—
104C2×M16—41no—
105C2×M16—41no—
106C2×M16—41no—
107C2×M16—41no—
108C2×M16—41no—
109C2×M16—41no—
110C2×M16C4⋊C412yes—
111C2×M16C4⋊C412yes—
112C22×C8—21no—
113C22×C8—21no—
114C22×C8—22no—
115#117—22no—
116#117—22no—
117#117—41no—
118#117—41no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—41no—
124C2×C22⋊C4—22no—
125C2×C22⋊C4—41no—
126C2×C22⋊C4—41no—
127C2×C42—22no—
128C2×C42—41no—
129C2×C42—41no—
130C2×C42—41no—
131C2×C42—41no—
132C2×C42C22×C411yescharacteristic
133C2×C42C2×D411yescharacteristic
134C2×C42C2×D411yescharacteristic
135C2×C42C2×Q811yescharacteristic
136C2×C42C2×Q811yescharacteristic
137C2×C42#4111yescharacteristic
138C2×C42#4111yescharacteristic
139C2×C42#4111yescharacteristic
140C2×C42#4111yescharacteristic
141C2×C42#4111yescharacteristic
142C2×C42#4111yescharacteristic
143C2×C42#4111yescharacteristic
144#107—81no—
145#107—81no—
146#106—81no—
147#106—81no—
148C4⋊C8—22no—
149C4⋊C8—22no—
150C4⋊C8—22no—
151C4⋊C8—22no—
152C4⋊C8—22no—
153C4⋊C8—22no—
154C4⋊C8—22no—
155C4⋊C8—41no—
156C4⋊C8—41no—
157C4⋊C8—41no—
158C4⋊C8—41no—
159C4⋊C8—41no—
160C22⋊C8—22no—
161C22⋊C8—41no—
162C22⋊C8—41no—
163C22⋊C8—41no—
164#97—22no—
165#97—41no—
166C4×C8—22no—
167C4×C8—22no—
168#95—21no—
169#95—21no—
170#95—21no—
171#95—21no—
172#95—22no—
173#95—21no—
174#95—21no—
175#95—21no—
176#95—21no—
177#95—41no—
178#95—41no—
179#95—41no—
180#95—41no—
181#95—41no—
182C24#12111yescharacteristic
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—42no—
188C22×C4—41no—
189C22×C4—41no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4—81no—
193C22×C4—81no—
194C22×C4C2×C4⋊C411yescharacteristic
195C22×C4C4×D411yescharacteristic
196C22×C4C4×Q811yescharacteristic
197C22×C4#12011yescharacteristic
198C22×C4#12111yescharacteristic
199C22×C4#12111yescharacteristic
200C22×C4C22⋊Q811yescharacteristic
201C22×C4#12311yescharacteristic
202C22×C4#12311yescharacteristic
203C22×C4#12311yescharacteristic
204C22×C4#12311yescharacteristic
205C22×C4#12311yescharacteristic
206C22×C4#12411yescharacteristic
207C22×C4#12411yescharacteristic
208C22×C4#12511yescharacteristic
209C22×C4#12611yescharacteristic
210C22×C4#12611yescharacteristic
211C22×C4C4⋊Q811yescharacteristic
212M16—42no—
213M16—42no—
214M16—81no—
215M16—81no—
216M16—81no—
217M16—81no—
218M16—82no—
219M16—81no—
220M16—81no—
221M16—82no—
222C2×C8—22no—
223C2×C8—22no—
224C2×C8—41no—
225C2×C8—41no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8—42no—
229C2×C8—42no—
230C2×C8—42no—
231C2×C8—42no—
232C2×C8—42no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C22⋊C4—24no—
244C22⋊C4—42no—
245C22⋊C4—82no—
246C22⋊C4—82no—
247C42—42no—
248C42—42no—
249C42—82no—
250C42—82no—
251C42—82no—
252C42—82no—
253C42#11711yescharacteristic
254C42#11711yescharacteristic
255C42C4×D411yescharacteristic
256C42C4×D411yescharacteristic
257C42C22⋊Q811yescharacteristic
258C42C22⋊Q811yescharacteristic
259C42C22⋊Q811yescharacteristic
260C42C22⋊Q811yescharacteristic
261C42#12411yescharacteristic
262C42#12411yescharacteristic
263C42#12511yescharacteristic
264C42#12511yescharacteristic
265C42#12511yescharacteristic
266C42#12511yescharacteristic
267C42#12611yescharacteristic
268C42#12611yescharacteristic
269C23—21no—
270C23—21no—
271C23—41no—
272C23—41no—
273C23#38911yescharacteristic
274C23#39411yescharacteristic
275C23#39711yescharacteristic
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—44no—
299C2×C4—82no—
300C2×C4—82no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4#38211yescharacteristic
314C2×C4#38511yescharacteristic
315C2×C4#38711yescharacteristic
316C2×C4#38711yescharacteristic
317C2×C4#38811yescharacteristic
318C2×C4#38811yescharacteristic
319C2×C4#39311yescharacteristic
320C2×C4#39811yescharacteristic
321C2×C4#39811yescharacteristic
322C2×C4#40011yescharacteristic
323C2×C4#40011yescharacteristic
324C2×C4#40011yescharacteristic
325C2×C4#45311yescharacteristic
326C2×C4#45411yescharacteristic
327C2×C4#45511yescharacteristic
328C2×C4#45611yescharacteristic
329C8—42no—
330C8—42no—
331C8—82no—
332C8—82no—
333C8—82no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—81no—
343C22—81no—
344C22#144211yescharacteristic
345C22#203911yescharacteristic
346C22#204011yescharacteristic
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—84no—
358C4—161no—
359C4—161no—
360C4—161no—
361C4—161no—
362C4#185611yescharacteristic
363C4#185711yescharacteristic
364C4#202711yescharacteristic
365C4#202811yescharacteristic
366C2—21no—
367C2—21no—
368C2—41no—
369C2—41no—
370C2#1126511yescharacteristic
371C2#1127711yescharacteristic
372C2#1129611yescharacteristic
subgroupG/H
center, socleC22#1442
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
23. #1299C4semidirect

Maximal subgroups

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

subgroupindex
#219652
#108562
#80612
#80522
#79622
#79602
#79402