Finite Group Databasebeta

← #99528

Subgroups — #99528

Order 512.

470 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22722C211yesmaximal, characteristic
2C4×#475C211yesmaximal, characteristic
3#9870C211yesmaximal, characteristic
4#9673C211yesmaximal, characteristic
5C4×Q8⋊C8C211yesmaximal, characteristic
6#7031C211yesmaximal, characteristic
7#7015C211yesmaximal, characteristic
8C2×#475C411yescharacteristic
9C2×#446—21no—
10C4×C4⋊Q8C2211yescharacteristic
11C42×Q8C2211yescharacteristic
12#1988C411yescharacteristic
13#1948C411yescharacteristic
14#1940—22no—
15#1939—21no—
16#1919—21no—
17#1865—21no—
18#1842—21no—
19#1842C2211yescharacteristic
20#1803C411yescharacteristic
21C4×#106—21no—
22#1767—21no—
23C4×C4⋊C8C2211yescharacteristic
24C4×C4⋊C8C2211yescharacteristic
25C4×C4⋊C8C2211yescharacteristic
26C4×#103—21no—
27C42×C8C2211yescharacteristic
28C2×Q8⋊C8—21no—
29C2×Q8⋊C8—21no—
30C2×Q8⋊C8—21no—
31#1279—22no—
32#1279—21no—
33C2×C4⋊Q8C2×C411yescharacteristic
34C2×C4×Q8—21no—
35C2×C4×Q8C2×C411yescharacteristic
36C2×C4×Q8D411yescharacteristic
37C2×C4×Q8D411yescharacteristic
38#475—22no—
39#475—22no—
40#446—42no—
41#446—42no—
42C2×#106—21no—
43C2×#106—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—22no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8—22no—
49C2×C4⋊C8C2×C411yescharacteristic
50C2×C4⋊C8C2×C411yescharacteristic
51C2×C4⋊C8D411yescharacteristic
52C2×C4⋊C8D411yescharacteristic
53C2×C4⋊C8D412yes—
54C2×#103—21no—
55C2×#103—21no—
56C2×#97—22no—
57C2×C4×C8—21no—
58C2×C4×C8—21no—
59C2×C4×C8—21no—
60C2×C4×C8—21no—
61C2×C4×C8—21no—
62C2×C4×C8—21no—
63#391—21no—
64#389—21no—
65#389—21no—
66#384C2×C411yescharacteristic
67C4×C4⋊C4—21no—
68C4×C4⋊C4—21no—
69C4×C4⋊C4—21no—
70C4×C4⋊C4—21no—
71C4×C4⋊C4—21no—
72C4×C4⋊C4C2×C411yescharacteristic
73C4×C4⋊C4D411yescharacteristic
74C4×C4⋊C4D411yescharacteristic
75C43—21no—
76C43C2311yescharacteristic
77#340—21no—
78#340—21no—
79#340—21no—
80#340—21no—
81#336—22no—
82#336—21no—
83#336—21no—
84#336—21no—
85Q8⋊C8—24no—
86Q8⋊C8—42no—
87Q8⋊C8—42no—
88C22×Q8—21no—
89C22×Q8C22⋊C411yescharacteristic
90C22×C8—21no—
91C22×C8—21no—
92C22×C8—21no—
93C22×C8—21no—
94C22×C8—22no—
95C22×C8—41no—
96C22×C8—41no—
97C4⋊Q8—21no—
98C4⋊Q8—21no—
99C4⋊Q8—21no—
100C4⋊Q8M1612yes—
101C4×Q8—21no—
102C4×Q8—21no—
103C4×Q8—22no—
104C4×Q8—21no—
105C4×Q8—21no—
106C4×Q8—21no—
107C4×Q8—21no—
108C4×Q8—41no—
109C4×Q8—41no—
110C4×Q8—41no—
111C4×Q8—41no—
112C4×Q8—41no—
113C4×Q8SD1612yes—
114C4×Q8Q1612yes—
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—21no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—41no—
124C2×C4⋊C4C22⋊C411yescharacteristic
125C2×C4⋊C4C22⋊C411yescharacteristic
126C2×C4⋊C4C22⋊C411yescharacteristic
127C2×C42—21no—
128C2×C42—21no—
129C2×C42—21no—
130C2×C42—21no—
131C2×C42—21no—
132C2×C42—21no—
133C2×C42—41no—
134C2×C42C22×C411yescharacteristic
135C2×C42C2×D411yescharacteristic
136C2×C42C2×D411yescharacteristic
137C2×C42C2×D411yescharacteristic
138C2×C42C2×D411yescharacteristic
139C2×C42#4111yescharacteristic
140C2×C42#4111yescharacteristic
141#106—24no—
142#106—42no—
143C4⋊C8—22no—
144C4⋊C8—21no—
145C4⋊C8—21no—
146C4⋊C8—21no—
147C4⋊C8—21no—
148C4⋊C8—21no—
149C4⋊C8—21no—
150C4⋊C8—42no—
151C4⋊C8—41no—
152C4⋊C8—44no—
153C4⋊C8—41no—
154C4⋊C8—41no—
155C4⋊C8—41no—
156C4⋊C8—41no—
157C4⋊C8—82no—
158C4⋊C8M1612yes—
159C4⋊C8SD1612yes—
160#103—24no—
161#103—42no—
162#97—44no—
163C4×C8—22no—
164C4×C8—22no—
165C4×C8—22no—
166C4×C8—41no—
167C4×C8—41no—
168C4×C8—41no—
169C4×C8—41no—
170C4×C8—41no—
171C4×C8—41no—
172C4×C8—41no—
173C4×C8—41no—
174C4×C8—41no—
175#95—21no—
176#95—21no—
177#95—21no—
178#95—41no—
179#95—41no—
180C2×Q8—21no—
181C2×Q8—21no—
182C2×Q8—21no—
183C2×Q8—21no—
184C2×Q8—21no—
185C2×Q8—22no—
186C2×Q8—41no—
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8#10312yes—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4C2×C22⋊C411yescharacteristic
199C22×C4C4×D411yescharacteristic
200C22×C4C4×D411yescharacteristic
201C22×C4#12011yescharacteristic
202C22×C4#12111yescharacteristic
203C22×C4#12111yescharacteristic
204C22×C4#12311yescharacteristic
205C2×C8—22no—
206C2×C8—22no—
207C2×C8—42no—
208C2×C8—42no—
209C2×C8—42no—
210C2×C8—41no—
211C2×C8—41no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—42no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8—42no—
220C2×C8—41no—
221C2×C8—42no—
222C2×C8—42no—
223C2×C8—41no—
224C2×C8—81no—
225C2×C8—81no—
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—22no—
229C4⋊C4—22no—
230C4⋊C4—22no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—22no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—81no—
245C4⋊C4—81no—
246C4⋊C4#10312yes—
247C4⋊C4#10412yes—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—22no—
253C42—22no—
254C42—21no—
255C42—21no—
256C42—41no—
257C42—42no—
258C42—41no—
259C42—41no—
260C42—41no—
261C42—41no—
262C42—41no—
263C42—41no—
264C42—81no—
265C42—81no—
266C42—81no—
267C42C2×M1611yescharacteristic
268C42C2×M1611yescharacteristic
269C42#13111yescharacteristic
270C42#13111yescharacteristic
271C42C2×SD1611yescharacteristic
272C42C2×SD1611yescharacteristic
273C42C2×Q1611yescharacteristic
274C42#13511yescharacteristic
275C42AGL(1,ℤ/8)11yescharacteristic
276C42AGL(1,ℤ/8)11yescharacteristic
277C42#13711yescharacteristic
278C42#13711yescharacteristic
279C23#38611yescharacteristic
280Q8—22no—
281Q8—22no—
282Q8—41no—
283Q8—41no—
284Q8—42no—
285Q8—42no—
286Q8—81no—
287Q8—81no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4#40711yescharacteristic
316C2×C4#40811yescharacteristic
317C2×C4C2×#10311yescharacteristic
318C2×C4#41711yescharacteristic
319C2×C4C2×#10411yescharacteristic
320C2×C4#42111yescharacteristic
321C2×C4#43511yescharacteristic
322C2×C4#43511yescharacteristic
323C2×C4#43611yescharacteristic
324C2×C4#43611yescharacteristic
325C2×C4C4×SD1611yescharacteristic
326C2×C4#44011yescharacteristic
327C2×C4#44311yescharacteristic
328C2×C4#44411yescharacteristic
329C2×C4#44811yescharacteristic
330C2×C4#44911yescharacteristic
331C2×C4#45011yescharacteristic
332C2×C4#45111yescharacteristic
333C2×C4#45511yescharacteristic
334C2×C4#45611yescharacteristic
335C2×C4#46011yescharacteristic
336C2×C4#46411yescharacteristic
337C2×C4#48311yescharacteristic
338C2×C4#48411yescharacteristic
339C8—44no—
340C8—42no—
341C8—42no—
342C8—82no—
343C8—81no—
344C8—82no—
345C8—81no—
346C22#187011yescharacteristic
347C22#187111yescharacteristic
348C22#187211yescharacteristic
349C22#187611yescharacteristic
350C22#188011yescharacteristic
351C22#188111yescharacteristic
352C22#188211yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—41no—
360C4—42no—
361C4—42no—
362C4—42no—
363C4—82no—
364C4—81no—
365C4—161no—
366C4#148711yescharacteristic
367C4#148911yescharacteristic
368C4#149311yescharacteristic
369C4#149511yescharacteristic
370C4#158211yescharacteristic
371C4#158511yescharacteristic
372C4#159011yescharacteristic
373C4#159211yescharacteristic
374C4#164211yescharacteristic
375C4#164511yescharacteristic
376C4#164811yescharacteristic
377C4#165111yescharacteristic
378C2#894211yescharacteristic
379C2#895211yescharacteristic
380C2#895511yescharacteristic
381C2#897111yescharacteristic
382C2#898311yescharacteristic
383C2#899211yescharacteristic
384C2#899311yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
socle, prime radicalC23#386
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#227222
C4×#4752
#98702
#96732
C4×Q8⋊C82
#70312
#70152