Finite Group Databasebeta

← #99533

Subgroups — #99533

Order 512.

462 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#22825C211yesmaximal, characteristic
2C4×#462C211yesmaximal, characteristic
3#9870C211yesmaximal, characteristic
4#9865C211yesmaximal, characteristic
5C4×Q8⋊C8C211yesmaximal, characteristic
6#7031C211yesmaximal, characteristic
7#7015C211yesmaximal, characteristic
8C2×#462C411yescharacteristic
9C2×C4×Q16—21no—
10C4×C4⋊Q8C2211yescharacteristic
11C42×Q8C2211yescharacteristic
12#1984—21no—
13#1981C411yescharacteristic
14#1947C411yescharacteristic
15#1928—21no—
16#1917—22no—
17#1878—21no—
18#1842C2211yescharacteristic
19#1831—21no—
20#1803C411yescharacteristic
21#1770—21no—
22#1767—21no—
23C4×C4⋊C8C2211yescharacteristic
24C4×C4⋊C8C2211yescharacteristic
25C4×C4⋊C8C2211yescharacteristic
26C4×#103—21no—
27C42×C8C2211yescharacteristic
28C2×Q8⋊C8—21no—
29#1279—21no—
30#1279—21no—
31#1279—22no—
32#1279—21no—
33C22×Q16—21no—
34C2×C4⋊Q8C2×C411yescharacteristic
35C2×C4×Q8—21no—
36C2×C4×Q8C2×C411yescharacteristic
37C2×C4×Q8D411yescharacteristic
38C2×C4×Q8D411yescharacteristic
39#462—22no—
40#462—22no—
41C4×Q16—42no—
42C4×Q16—42no—
43C2×#107—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8C2×C411yescharacteristic
48C2×C4⋊C8C2×C411yescharacteristic
49C2×C4⋊C8D411yescharacteristic
50C2×C4⋊C8D411yescharacteristic
51C2×C4⋊C8D412yes—
52C2×#103—21no—
53C2×#103—21no—
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#336—22no—
80#336—22no—
81#336—22no—
82#336—21no—
83#336—21no—
84#336—21no—
85Q8⋊C8—24no—
86C22×Q8—21no—
87C22×Q8C22⋊C411yescharacteristic
88C2×Q16—24no—
89C2×Q16—42no—
90C2×Q16—42no—
91C22×C8—21no—
92C22×C8—21no—
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—22no—
96C22×C8—41no—
97C22×C8—41no—
98C4⋊Q8—21no—
99C4⋊Q8—21no—
100C4⋊Q8—21no—
101C4⋊Q8M1612yes—
102C4×Q8—22no—
103C4×Q8—21no—
104C4×Q8—21no—
105C4×Q8—21no—
106C4×Q8—21no—
107C4×Q8—21no—
108C4×Q8—21no—
109C4×Q8—21no—
110C4×Q8—21no—
111C4×Q8—41no—
112C4×Q8—41no—
113C4×Q8—41no—
114C4×Q8—41no—
115C4×Q8—41no—
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—21no—
124C2×C4⋊C4—41no—
125C2×C4⋊C4C22⋊C411yescharacteristic
126C2×C4⋊C4C22⋊C411yescharacteristic
127C2×C4⋊C4C22⋊C411yescharacteristic
128C2×C42—21no—
129C2×C42—21no—
130C2×C42—21no—
131C2×C42—21no—
132C2×C42—21no—
133C2×C42—21no—
134C2×C42—41no—
135C2×C42C22×C411yescharacteristic
136C2×C42C2×D411yescharacteristic
137C2×C42C2×D411yescharacteristic
138C2×C42C2×D411yescharacteristic
139C2×C42C2×D411yescharacteristic
140C2×C42#4111yescharacteristic
141C2×C42#4111yescharacteristic
142#107—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—41no—
153C4⋊C8—41no—
154C4⋊C8—41no—
155C4⋊C8—41no—
156C4⋊C8M1612yes—
157C4⋊C8Q1612yescomplemented
158#103—24no—
159#103—42no—
160#103—42no—
161#103—42no—
162#97—82no—
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—22no—
183C2×Q8—21no—
184C2×Q8—21no—
185C2×Q8—21no—
186C2×Q8—41no—
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8#10412yes—
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
205Q16—48no—
206C2×C8—22no—
207C2×C8—22no—
208C2×C8—42no—
209C2×C8—42no—
210C2×C8—42no—
211C2×C8—41no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—41no—
215C2×C8—42no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8—41no—
220C2×C8—42no—
221C2×C8—41no—
222C2×C8—42no—
223C2×C8—42no—
224C2×C8—41no—
225C2×C8—81no—
226C2×C8—81no—
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—22no—
234C4⋊C4—22no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—81no—
248C4⋊C4—81no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—41no—
256C42—42no—
257C42—41no—
258C42—41no—
259C42—41no—
260C42—41no—
261C42—41no—
262C42—41no—
263C42—41no—
264C42—41no—
265C42—81no—
266C42—81no—
267C42—81no—
268C42C2×M1611yescharacteristic
269C42C2×M1611yescharacteristic
270C42#13111yescharacteristic
271C42#13111yescharacteristic
272C42C2×Q1611yescharacteristic
273C42#13511yescharacteristic
274C42#13511yescharacteristic
275C42#13511yescharacteristic
276C42AGL(1,ℤ/8)11yescharacteristic
277C42AGL(1,ℤ/8)11yescharacteristic
278C42#13711yescharacteristic
279C42#13711yescharacteristic
280C23#38611yescharacteristic
281Q8—22no—
282Q8—22no—
283Q8—41no—
284Q8—41no—
285Q8—42no—
286Q8—42no—
287Q8—81no—
288Q8—81no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4#40711yescharacteristic
317C2×C4#40811yescharacteristic
318C2×C4#41611yescharacteristic
319C2×C4#41811yescharacteristic
320C2×C4C2×#10411yescharacteristic
321C2×C4#42111yescharacteristic
322C2×C4#43511yescharacteristic
323C2×C4#43511yescharacteristic
324C2×C4#43611yescharacteristic
325C2×C4#43611yescharacteristic
326C2×C4C4×Q1611yescharacteristic
327C2×C4#44111yescharacteristic
328C2×C4#44311yescharacteristic
329C2×C4#44411yescharacteristic
330C2×C4#44911yescharacteristic
331C2×C4#44911yescharacteristic
332C2×C4#45111yescharacteristic
333C2×C4#45211yescharacteristic
334C2×C4#45511yescharacteristic
335C2×C4#45611yescharacteristic
336C2×C4#46211yescharacteristic
337C2×C4#46411yescharacteristic
338C2×C4#48211yescharacteristic
339C2×C4#48211yescharacteristic
340C8—44no—
341C8—42no—
342C8—42no—
343C8—82no—
344C8—82no—
345C8—81no—
346C8—81no—
347C22#187011yescharacteristic
348C22#187111yescharacteristic
349C22#187511yescharacteristic
350C22#187611yescharacteristic
351C22#187811yescharacteristic
352C22#188111yescharacteristic
353C22#188211yescharacteristic
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—42no—
362C4—81no—
363C4—81no—
364C4—82no—
365C4—81no—
366C4—161no—
367C4#148811yescharacteristic
368C4#149011yescharacteristic
369C4#149411yescharacteristic
370C4#149611yescharacteristic
371C4#158411yescharacteristic
372C4#158711yescharacteristic
373C4#159111yescharacteristic
374C4#159311yescharacteristic
375C4#164011yescharacteristic
376C4#164411yescharacteristic
377C4#164811yescharacteristic
378C4#165211yescharacteristic
379C2#894311yescharacteristic
380C2#895011yescharacteristic
381C2#895511yescharacteristic
382C2#897211yescharacteristic
383C2#898611yescharacteristic
384C2#899011yescharacteristic
385C2#899611yescharacteristic
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

Complements

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

NH ≅ G/Ntype
157. C4⋊C8Q16semidirect

Maximal subgroups

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

subgroupindex
#228252
C4×#4622
#98702
#98652
C4×Q8⋊C82
#70312
#70152