Finite Group Databasebeta

← #99532

Subgroups — #99532

Order 512.

486 conjugacy classes of subgroups.

The subgroup lattice has 391 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22722C211yesmaximal, characteristic
2C4×#462C211yesmaximal, characteristic
3#9870C211yesmaximal, characteristic
4#9865C211yesmaximal, characteristic
5C4×Q8⋊C8C211yesmaximal, characteristic
6#7031C211yesmaximal, characteristic
7#7015C211yesmaximal, characteristic
8C2×#462C411yescharacteristic
9C2×#446—21no—
10C2×C4×Q16—21no—
11C4×C4⋊Q8C2211yescharacteristic
12C42×Q8C2211yescharacteristic
13#1981C411yescharacteristic
14#1947C411yescharacteristic
15#1940—22no—
16#1939—21no—
17#1928—21no—
18#1878—21no—
19#1842—21no—
20#1842C2211yescharacteristic
21#1803C411yescharacteristic
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—
41#446—42no—
42#446—42no—
43C4×Q16—42no—
44C4×Q16—42no—
45C2×#107—21no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8—22no—
48C2×C4⋊C8—21no—
49C2×C4⋊C8—21no—
50C2×C4⋊C8—22no—
51C2×C4⋊C8C2×C411yescharacteristic
52C2×C4⋊C8C2×C411yescharacteristic
53C2×C4⋊C8D411yescharacteristic
54C2×C4⋊C8D411yescharacteristic
55C2×C4⋊C8D412yes—
56C2×#103—21no—
57C2×#103—21no—
58C2×#103—21no—
59C2×#103—21no—
60C2×#97—22no—
61C2×C4×C8—21no—
62C2×C4×C8—21no—
63C2×C4×C8—21no—
64C2×C4×C8—21no—
65C2×C4×C8—21no—
66C2×C4×C8—21no—
67#391—21no—
68#389—21no—
69#389—21no—
70#384C2×C411yescharacteristic
71C4×C4⋊C4—21no—
72C4×C4⋊C4—21no—
73C4×C4⋊C4—21no—
74C4×C4⋊C4—21no—
75C4×C4⋊C4—21no—
76C4×C4⋊C4C2×C411yescharacteristic
77C4×C4⋊C4D411yescharacteristic
78C4×C4⋊C4D411yescharacteristic
79C43—21no—
80C43C2311yescharacteristic
81#340—21no—
82#340—21no—
83#336—22no—
84#336—21no—
85#336—21no—
86#336—21no—
87Q8⋊C8—24no—
88C22×Q8—21no—
89C22×Q8C22⋊C411yescharacteristic
90C2×Q16—24no—
91C2×Q16—42no—
92C2×Q16—42no—
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—21no—
97C22×C8—22no—
98C22×C8—41no—
99C22×C8—41no—
100C4⋊Q8—21no—
101C4⋊Q8—21no—
102C4⋊Q8—21no—
103C4⋊Q8M1612yes—
104C4×Q8—21no—
105C4×Q8—21no—
106C4×Q8—22no—
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—
116C4×Q8D812yes—
117C4×Q8SD1612yes—
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—21no—
125C2×C4⋊C4—21no—
126C2×C4⋊C4—41no—
127C2×C4⋊C4C22⋊C411yescharacteristic
128C2×C4⋊C4C22⋊C411yescharacteristic
129C2×C4⋊C4C22⋊C411yescharacteristic
130C2×C42—21no—
131C2×C42—21no—
132C2×C42—21no—
133C2×C42—21no—
134C2×C42—21no—
135C2×C42—21no—
136C2×C42—41no—
137C2×C42C22×C411yescharacteristic
138C2×C42C2×D411yescharacteristic
139C2×C42C2×D411yescharacteristic
140C2×C42C2×D411yescharacteristic
141C2×C42C2×D411yescharacteristic
142C2×C42#4111yescharacteristic
143C2×C42#4111yescharacteristic
144#107—42no—
145C4⋊C8—22no—
146C4⋊C8—21no—
147C4⋊C8—21no—
148C4⋊C8—21no—
149C4⋊C8—21no—
150C4⋊C8—21no—
151C4⋊C8—21no—
152C4⋊C8—42no—
153C4⋊C8—41no—
154C4⋊C8—44no—
155C4⋊C8—41no—
156C4⋊C8—41no—
157C4⋊C8—41no—
158C4⋊C8—41no—
159C4⋊C8—82no—
160C4⋊C8M1612yes—
161C4⋊C8Q1612yescomplemented
162#103—24no—
163#103—42no—
164#103—42no—
165#103—42no—
166#97—44no—
167C4×C8—22no—
168C4×C8—22no—
169C4×C8—22no—
170C4×C8—41no—
171C4×C8—41no—
172C4×C8—41no—
173C4×C8—41no—
174C4×C8—41no—
175C4×C8—41no—
176C4×C8—41no—
177C4×C8—41no—
178C4×C8—41no—
179#95—21no—
180#95—21no—
181#95—21no—
182#95—41no—
183#95—41no—
184C2×Q8—21no—
185C2×Q8—21no—
186C2×Q8—22no—
187C2×Q8—21no—
188C2×Q8—21no—
189C2×Q8—21no—
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8—41no—
193C2×Q8—41no—
194C2×Q8—41no—
195C2×Q8#10212yes—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4C2×C22⋊C411yescharacteristic
203C22×C4C4×D411yescharacteristic
204C22×C4C4×D411yescharacteristic
205C22×C4#12011yescharacteristic
206C22×C4#12111yescharacteristic
207C22×C4#12111yescharacteristic
208C22×C4#12311yescharacteristic
209Q16—48no—
210C2×C8—22no—
211C2×C8—22no—
212C2×C8—42no—
213C2×C8—42no—
214C2×C8—42no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8—42no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8—41no—
223C2×C8—41no—
224C2×C8—42no—
225C2×C8—41no—
226C2×C8—42no—
227C2×C8—42no—
228C2×C8—41no—
229C2×C8—81no—
230C2×C8—81no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—22no—
234C4⋊C4—22no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—22no—
238C4⋊C4—22no—
239C4⋊C4—42no—
240C4⋊C4—42no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—81no—
250C4⋊C4—81no—
251C4⋊C4#10212yes—
252C4⋊C4#10412yes—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—21no—
257C42—22no—
258C42—22no—
259C42—21no—
260C42—21no—
261C42—41no—
262C42—42no—
263C42—41no—
264C42—41no—
265C42—41no—
266C42—41no—
267C42—41no—
268C42—41no—
269C42—81no—
270C42—81no—
271C42—81no—
272C42C2×M1611yescharacteristic
273C42C2×M1611yescharacteristic
274C42#13111yescharacteristic
275C42#13111yescharacteristic
276C42C2×D811yescharacteristic
277C42C2×SD1611yescharacteristic
278C42C2×Q1611yescharacteristic
279C42#13511yescharacteristic
280C42AGL(1,ℤ/8)11yescharacteristic
281C42#13711yescharacteristic
282C42#13711yescharacteristic
283C42#13711yescharacteristic
284C23#38611yescharacteristic
285Q8—22no—
286Q8—22no—
287Q8—41no—
288Q8—41no—
289Q8—42no—
290Q8—42no—
291Q8—81no—
292Q8—81no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4#40711yescharacteristic
321C2×C4#40811yescharacteristic
322C2×C4C2×#10211yescharacteristic
323C2×C4#41711yescharacteristic
324C2×C4C2×#10411yescharacteristic
325C2×C4#42111yescharacteristic
326C2×C4#43511yescharacteristic
327C2×C4#43511yescharacteristic
328C2×C4#43611yescharacteristic
329C2×C4#43611yescharacteristic
330C2×C4C4×Q1611yescharacteristic
331C2×C4#44111yescharacteristic
332C2×C4#44311yescharacteristic
333C2×C4#44411yescharacteristic
334C2×C4#44711yescharacteristic
335C2×C4#44811yescharacteristic
336C2×C4#45111yescharacteristic
337C2×C4#45211yescharacteristic
338C2×C4#45511yescharacteristic
339C2×C4#45611yescharacteristic
340C2×C4#46211yescharacteristic
341C2×C4#46411yescharacteristic
342C2×C4#48011yescharacteristic
343C2×C4#48111yescharacteristic
344C8—44no—
345C8—42no—
346C8—42no—
347C8—82no—
348C8—81no—
349C8—82no—
350C8—81no—
351C22#187011yescharacteristic
352C22#187111yescharacteristic
353C22#187411yescharacteristic
354C22#187611yescharacteristic
355C22#187811yescharacteristic
356C22#188111yescharacteristic
357C22#188211yescharacteristic
358C4—21no—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—41no—
365C4—42no—
366C4—42no—
367C4—42no—
368C4—82no—
369C4—81no—
370C4—161no—
371C4#148611yescharacteristic
372C4#148911yescharacteristic
373C4#149211yescharacteristic
374C4#149511yescharacteristic
375C4#158411yescharacteristic
376C4#158711yescharacteristic
377C4#159111yescharacteristic
378C4#159311yescharacteristic
379C4#164111yescharacteristic
380C4#164511yescharacteristic
381C4#164911yescharacteristic
382C4#165311yescharacteristic
383C2#894411yescharacteristic
384C2#895011yescharacteristic
385C2#895511yescharacteristic
386C2#897111yescharacteristic
387C2#898711yescharacteristic
388C2#899011yescharacteristic
389C2#899511yescharacteristic
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
161. C4⋊C8Q16semidirect

Maximal subgroups

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

subgroupindex
#227222
C4×#4622
#98702
#98652
C4×Q8⋊C82
#70312
#70152