Finite Group Databasebeta

← #99428

Subgroups — #99428

Order 512.

490 conjugacy classes of subgroups.

The subgroup lattice has 413 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22287C211yesmaximal, characteristic
2#11322C211yesmaximal, characteristic
3#8937C211yesmaximal, characteristic
4#8830C211yesmaximal, characteristic
5C4×#328C211yesmaximal, characteristic
6#7028C211yesmaximal, characteristic
7#7016C211yesmaximal, characteristic
8C22×C4⋊C8—21no—
9C22×C4⋊C8C2211yescharacteristic
10C4×C22⋊Q8C2211yescharacteristic
11#1984—21no—
12#1939—21no—
13#1916—21no—
14#1916—21no—
15#1850—21no—
16#1797C2211yescharacteristic
17C8×C22⋊C4—21no—
18C4×C22⋊C8C2211yescharacteristic
19C4×C22⋊C8C2211yescharacteristic
20C2×#336—21no—
21C2×#336C2211yescharacteristic
22C2×#334—21no—
23C2×#328C411yescharacteristic
24C2×#328C411yescharacteristic
25C2×Q8⋊C8—21no—
26C4×#95C2211yescharacteristic
27#1294C411yescharacteristic
28#1294C411yescharacteristic
29#1279—21no—
30#1277—21no—
31C23×C8—21no—
32C23×C8D411yescharacteristic
33C23×C8D411yescharacteristic
34C2×C22⋊Q8C2×C411yescharacteristic
35C2×C4×Q8D411yescharacteristic
36C22×C42—21no—
37C22×C42C2311yescharacteristic
38C2×C4⋊C8—21no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—42no—
43C2×C4⋊C8—42no—
44C2×C4⋊C8—42no—
45C2×C4⋊C8—42no—
46C2×C4⋊C8D411yescharacteristic
47C2×C4⋊C8D411yescharacteristic
48C2×C22⋊C8—21no—
49C2×C22⋊C8—21no—
50C2×C22⋊C8C2×C411yescharacteristic
51C2×C22⋊C8C2×C411yescharacteristic
52C2×C4×C8—21no—
53C2×C4×C8—21no—
54C2×C4×C8—21no—
55C2×C4×C8—21no—
56#391Q811yescharacteristic
57#389Q811yescharacteristic
58#387—21no—
59#385—21no—
60#380C2×C411yescharacteristic
61C4×C4⋊C4—21no—
62C4×C4⋊C4D411yescharacteristic
63C4×C22⋊C4—21no—
64C2×#95—21no—
65C2×#95C2×C411yescharacteristic
66C2×#95C2×C411yescharacteristic
67#336—21no—
68#336—21no—
69#336—21no—
70#336—21no—
71#336—21no—
72#336—21no—
73#336—21no—
74#336—21no—
75#336—21no—
76#336—42no—
77#334—42no—
78#328—22no—
79#328C814yescomplemented
80Q8⋊C8—42no—
81C22×Q8C4⋊C411yescharacteristic
82C23×C4—21no—
83C23×C4—21no—
84C23×C4C22×C411yescharacteristic
85C23×C4C2×D411yescharacteristic
86C23×C4#4111yescharacteristic
87C22×C8—21no—
88C22×C8—21no—
89C22×C8—21no—
90C22×C8—22no—
91C22×C8—21no—
92C22×C8—21no—
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—21no—
97C22×C8—41no—
98C22×C8—41no—
99C22×C8—41no—
100C22×C8—41no—
101C22×C8—41no—
102C22×C8—41no—
103C22×C8—41no—
104C22×C8—41no—
105C22×C8—41no—
106C22×C8—41no—
107C22×C8—41no—
108C22×C8SD1612yes—
109C22⋊Q8—21no—
110C22⋊Q8—21no—
111C22⋊Q8C2×C812yes—
112C22⋊Q8M1612yes—
113C4×Q8—41no—
114C4×Q8—41no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4C4⋊C411yescharacteristic
119C2×C4⋊C4C4⋊C411yescharacteristic
120C2×C4⋊C4C4⋊C411yescharacteristic
121C2×C22⋊C4—21no—
122C2×C22⋊C4—21no—
123C2×C42—22no—
124C2×C42—22no—
125C2×C42—21no—
126C2×C42—21no—
127C2×C42—41no—
128C2×C42—41no—
129C2×C42—41no—
130C2×C42—41no—
131C2×C42—41no—
132C2×C42—41no—
133C2×C42C2×D411yescharacteristic
134C2×C42C2×D411yescharacteristic
135C2×C42C2×Q811yescharacteristic
136C2×C42#4111yescharacteristic
137C4⋊C8—22no—
138C4⋊C8—22no—
139C4⋊C8—41no—
140C4⋊C8—41no—
141C4⋊C8—41no—
142C4⋊C8—41no—
143C4⋊C8—48no—
144C4⋊C8—81no—
145C4⋊C8—81no—
146C22⋊C8—21no—
147C22⋊C8—22no—
148C22⋊C8—21no—
149C22⋊C8—21no—
150C22⋊C8—41no—
151C22⋊C8—41no—
152C22⋊C8—41no—
153C22⋊C8C2×C812yes—
154C4×C8—41no—
155C4×C8—41no—
156C4×C8—41no—
157C4×C8—41no—
158C4×C8—81no—
159C4×C8—81no—
160#95—21no—
161#95—21no—
162#95—21no—
163#95—21no—
164#95—21no—
165#95—21no—
166#95—21no—
167#95—21no—
168#95—42no—
169#95C2×C812yes—
170C24C4×D411yescharacteristic
171C2×Q8—21no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8C4⋊C812yescomplemented
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—22no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—22no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—41no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4C2×C4⋊C411yescharacteristic
204C22×C4C4×D411yescharacteristic
205C22×C4#12011yescharacteristic
206C22×C4C22⋊Q811yescharacteristic
207C22×C4C22⋊Q811yescharacteristic
208C22×C4#12311yescharacteristic
209C22×C4C22×C811yescharacteristic
210C22×C4C2×M1611yescharacteristic
211C22×C4#13111yescharacteristic
212C22×C4#13111yescharacteristic
213C22×C4C2×SD1611yescharacteristic
214C22×C4#13511yescharacteristic
215C22×C4#13711yescharacteristic
216C22×C4#13711yescharacteristic
217C2×C8—22no—
218C2×C8—22no—
219C2×C8—41no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8—41no—
223C2×C8—42no—
224C2×C8—41no—
225C2×C8—42no—
226C2×C8—42no—
227C2×C8—41no—
228C2×C8—42no—
229C2×C8—42no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—42no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—81no—
242C2×C8—81no—
243C2×C8—81no—
244C2×C8—81no—
245C2×C8—81no—
246C2×C8—81no—
247C2×C8—81no—
248C2×C8—81no—
249C4⋊C4—21no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—81no—
255C4⋊C4—81no—
256C4⋊C4C4⋊C812yescomplemented
257C22⋊C4—22no—
258C22⋊C4—22no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C42—21no—
262C42—21no—
263C42—21no—
264C42—21no—
265C42—41no—
266C42—41no—
267C42—42no—
268C42—42no—
269C42—42no—
270C42—42no—
271C42—41no—
272C42—41no—
273C42—41no—
274C42—41no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23#38511yescharacteristic
280C23C8×D411yescharacteristic
281C23#43511yescharacteristic
282C23C4×SD1611yescharacteristic
283C23#44111yescharacteristic
284C23#44311yescharacteristic
285C23#44411yescharacteristic
286Q8—42no—
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—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—24no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4C2×C4⋊C811yescharacteristic
341C2×C4#42411yescharacteristic
342C2×C4C8×D411yescharacteristic
343C2×C4#43511yescharacteristic
344C2×C4#44811yescharacteristic
345C2×C4#45211yescharacteristic
346C2×C4#45311yescharacteristic
347C2×C4#45611yescharacteristic
348C2×C4B(4,𝔽2)11yescharacteristic
349C2×C4#45811yescharacteristic
350C2×C4#47511yescharacteristic
351C2×C4#47911yescharacteristic
352C8—42no—
353C8—42no—
354C8—81no—
355C8—82no—
356C8—82no—
357C8—81no—
358C8—81no—
359C8—81no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22C8×SD1611yescharacteristic
373C22#157911yescharacteristic
374C22#158311yescharacteristic
375C22#158711yescharacteristic
376C22#185011yescharacteristic
377C22#185911yescharacteristic
378C22#186111yescharacteristic
379C22#186511yescharacteristic
380C22#186611yescharacteristic
381C22#186711yescharacteristic
382C22#186811yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—44no—
390C4—42no—
391C4—42no—
392C4—41no—
393C4—41no—
394C4—82no—
395C4—81no—
396C4—81no—
397C4#159611yescharacteristic
398C4#160311yescharacteristic
399C4#161111yescharacteristic
400C4#161811yescharacteristic
401C2—21no—
402C2—21no—
403C2—21no—
404C2—21no—
405C2#883911yescharacteristic
406C2#884611yescharacteristic
407C2#885111yescharacteristic
408C2#887111yescharacteristic
409C2#887411yescharacteristic
410C2#887611yescharacteristic
411C2#888111yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC22×C4C22×C8
Frattini, cosocleC22×C42C23
socleC23#385
prime radicalC24C4×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
79. #328C8semidirect
174. C2×Q8C4⋊C8semidirect
256. C4⋊C4C4⋊C8semidirect

Maximal subgroups

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

subgroupindex
#222872
#113222
#89372
#88302
C4×#3282
#70282
#70162