Finite Group Databasebeta

← #99864

Subgroups — #99864

Order 512.

448 conjugacy classes of subgroups.

The subgroup lattice has 381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#475C211yesmaximal, characteristic
2#21339C211yesmaximal, characteristic
3#9637C211yesmaximal, characteristic
4#8564C211yesmaximal, characteristic
5#7570C211yesmaximal, characteristic
6#7031C211yesmaximal, characteristic
7#7015C211yesmaximal, characteristic
8C2×#475C411yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10C42×Q8C2211yescharacteristic
11#1988C411yescharacteristic
12#1984—21no—
13#1948C411yescharacteristic
14#1939—21no—
15#1919—21no—
16#1916—22no—
17#1865—21no—
18#1842C2211yescharacteristic
19#1803C411yescharacteristic
20C4×#106—21no—
21C4×C4⋊C8—21no—
22C4×C4⋊C8C2211yescharacteristic
23C4×C4⋊C8C2211yescharacteristic
24C4×C4⋊C8C2211yescharacteristic
25C4×#103—21no—
26#1744—21no—
27C42×C8C2211yescharacteristic
28C2×Q8⋊C8—21no—
29C2×Q8⋊C8—21no—
30C2×Q8⋊C8—21no—
31#1279—21no—
32#1271—22no—
33C2×C4⋊Q8C2×C411yescharacteristic
34C2×C4×Q8—21no—
35C2×C4×Q8C2×C411yescharacteristic
36C2×C4×Q8D411yescharacteristic
37C2×C4×Q8D411yescharacteristic
38#475—22no—
39#475C814yescomplemented
40C2×#106—21no—
41C2×#106—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—22no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8C2×C411yescharacteristic
49C2×C4⋊C8C2×C411yescharacteristic
50C2×#103—21no—
51C2×#103—21no—
52C2×C4×C8—21no—
53C2×C4×C8—21no—
54C2×C4×C8—21no—
55C2×C4×C8—21no—
56C2×C4×C8—21no—
57C2×C4×C8D411yescharacteristic
58C2×C4×C8D411yescharacteristic
59#391—21no—
60#389—21no—
61#389—21no—
62#384C2×C411yescharacteristic
63C4×C4⋊C4—21no—
64C4×C4⋊C4—21no—
65C4×C4⋊C4—21no—
66C4×C4⋊C4—21no—
67C4×C4⋊C4—21no—
68C4×C4⋊C4C2×C411yescharacteristic
69C4×C4⋊C4D411yescharacteristic
70C4×C4⋊C4D411yescharacteristic
71C43—21no—
72C43C2311yescharacteristic
73#340—21no—
74#340—21no—
75#340—21no—
76#340—21no—
77#336—22no—
78#336—22no—
79#336—22no—
80#336—21no—
81#336—21no—
82#336D412yes—
83Q8⋊C8—42no—
84Q8⋊C8—42no—
85Q8⋊C8—42no—
86C22×Q8—21no—
87C22×Q8C22⋊C411yescharacteristic
88C22×C8—21no—
89C22×C8—21no—
90C22×C8—21no—
91C22×C8—21no—
92C22×C8—22no—
93C22×C8—41no—
94C22×C8—41no—
95C4⋊Q8—21no—
96C4⋊Q8—21no—
97C4⋊Q8—21no—
98C4⋊Q8C2×C812yes—
99C4×Q8—21no—
100C4×Q8—21no—
101C4×Q8—21no—
102C4×Q8—21no—
103C4×Q8—21no—
104C4×Q8—21no—
105C4×Q8—41no—
106C4×Q8—41no—
107C4×Q8—41no—
108C4×Q8—41no—
109C4×Q8—41no—
110C4×Q8—41no—
111C4×Q8C2×C812yes—
112C4×Q8M1612yes—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4C22⋊C411yescharacteristic
123C2×C4⋊C4C22⋊C411yescharacteristic
124C2×C4⋊C4C22⋊C411yescharacteristic
125C2×C42—21no—
126C2×C42—21no—
127C2×C42—21no—
128C2×C42—21no—
129C2×C42—21no—
130C2×C42—21no—
131C2×C42—41no—
132C2×C42C22×C411yescharacteristic
133C2×C42C2×D411yescharacteristic
134C2×C42C2×D411yescharacteristic
135C2×C42C2×D411yescharacteristic
136C2×C42C2×D411yescharacteristic
137C2×C42#4111yescharacteristic
138C2×C42#4111yescharacteristic
139#106—24no—
140#106—42no—
141C4⋊C8—22no—
142C4⋊C8—21no—
143C4⋊C8—21no—
144C4⋊C8—21no—
145C4⋊C8—41no—
146C4⋊C8—41no—
147C4⋊C8—41no—
148C4⋊C8—44no—
149C4⋊C8—41no—
150C4⋊C8—41no—
151C4⋊C8—41no—
152C4⋊C8—41no—
153C4⋊C8—81no—
154C4⋊C8C2×C812yes—
155#103—24no—
156#103—42no—
157C4×C8—21no—
158C4×C8—21no—
159C4×C8—21no—
160C4×C8—41no—
161C4×C8—41no—
162C4×C8—42no—
163C4×C8—41no—
164C4×C8—41no—
165C4×C8—41no—
166C4×C8—41no—
167C4×C8—41no—
168C4×C8—41no—
169C4×C8SD1612yes—
170#95—21no—
171#95—21no—
172#95—21no—
173#95—41no—
174#95—41no—
175C2×Q8—21no—
176C2×Q8—21no—
177C2×Q8—21no—
178C2×Q8—21no—
179C2×Q8—21no—
180C2×Q8—22no—
181C2×Q8—41no—
182C2×Q8—41no—
183C2×Q8—41no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8C22⋊C812yes—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4C2×C22⋊C411yescharacteristic
194C22×C4C4×D411yescharacteristic
195C22×C4C4×D411yescharacteristic
196C22×C4#12011yescharacteristic
197C22×C4#12111yescharacteristic
198C22×C4#12111yescharacteristic
199C22×C4#12311yescharacteristic
200C2×C8—22no—
201C2×C8—22no—
202C2×C8—22no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8—42no—
210C2×C8—42no—
211C2×C8—42no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—41no—
215C2×C8—42no—
216C2×C8—81no—
217C2×C8—81no—
218C2×C8—81no—
219C2×C8—81no—
220C2×C8—81no—
221C4⋊C4—21no—
222C4⋊C4—22no—
223C4⋊C4—22no—
224C4⋊C4—22no—
225C4⋊C4—21no—
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—22no—
230C4⋊C4—42no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—81no—
240C4⋊C4—81no—
241C4⋊C4—81no—
242C4⋊C4C22⋊C812yes—
243C42—21no—
244C42—21no—
245C42—22no—
246C42—22no—
247C42—21no—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—41no—
252C42—42no—
253C42—42no—
254C42—41no—
255C42—41no—
256C42—41no—
257C42—41no—
258C42—41no—
259C42—41no—
260C42—81no—
261C42—81no—
262C42C22×C811yescharacteristic
263C42C2×M1611yescharacteristic
264C42#13111yescharacteristic
265C42#13111yescharacteristic
266C42C2×SD1611yescharacteristic
267C42#13511yescharacteristic
268C42AGL(1,ℤ/8)11yescharacteristic
269C42AGL(1,ℤ/8)11yescharacteristic
270C42#13711yescharacteristic
271C42#13711yescharacteristic
272C42#13711yescharacteristic
273C42#13711yescharacteristic
274C23#38611yescharacteristic
275Q8—22no—
276Q8—22no—
277Q8—41no—
278Q8—41no—
279Q8—42no—
280Q8—42no—
281Q8—81no—
282Q8—81no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4C2×C22⋊C811yescharacteristic
311C2×C4#40811yescharacteristic
312C2×C4#41711yescharacteristic
313C2×C4#41911yescharacteristic
314C2×C4#42111yescharacteristic
315C2×C4#42111yescharacteristic
316C2×C4C8×D411yescharacteristic
317C2×C4C8×D411yescharacteristic
318C2×C4#43511yescharacteristic
319C2×C4#43511yescharacteristic
320C2×C4C4×SD1611yescharacteristic
321C2×C4#44011yescharacteristic
322C2×C4#44311yescharacteristic
323C2×C4#44411yescharacteristic
324C2×C4#44811yescharacteristic
325C2×C4#44911yescharacteristic
326C2×C4#46011yescharacteristic
327C2×C4#46411yescharacteristic
328C2×C4#46811yescharacteristic
329C2×C4#46811yescharacteristic
330C2×C4#47011yescharacteristic
331C2×C4#47011yescharacteristic
332C2×C4#47111yescharacteristic
333C2×C4#47311yescharacteristic
334C8—42no—
335C8—42no—
336C8—42no—
337C8—82no—
338C8—82no—
339C8—81no—
340C8—161no—
341C22#186911yescharacteristic
342C22#187611yescharacteristic
343C22#188011yescharacteristic
344C22#189411yescharacteristic
345C22#189711yescharacteristic
346C22#190611yescharacteristic
347C22#190811yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—42no—
355C4—42no—
356C4—41no—
357C4—82no—
358C4—81no—
359C4—81no—
360C4—161no—
361C4#147711yescharacteristic
362C4#147911yescharacteristic
363C4#149511yescharacteristic
364C4#149711yescharacteristic
365C4C8×SD1611yescharacteristic
366C4SD16⋊C811yescharacteristic
367C4#158311yescharacteristic
368C4#158811yescharacteristic
369C4#168611yescharacteristic
370C4#169011yescharacteristic
371C4#170011yescharacteristic
372C4#170411yescharacteristic
373C2#894811yescharacteristic
374C2#907311yescharacteristic
375C2#909611yescharacteristic
376C2#920911yescharacteristic
377C2#921411yescharacteristic
378C2#922811yescharacteristic
379C2#923811yescharacteristic
subgroupG/H
centerC22×C4#121
commutatorC42C22×C8
Frattini, cosocleC43C23
socle, prime radicalC23#386
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
39. #475C8semidirect

Maximal subgroups

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

subgroupindex
C4×#4752
#213392
#96372
#85642
#75702
#70312
#70152