Finite Group Databasebeta

← C2×#7579 #160447

Subgroups — C2×#7579 #160447

Order 512.

1598 conjugacy classes of subgroups.

The subgroup lattice has 457 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2296C211yesmaximal, characteristic
2C2×#1817C211yesmaximal, characteristic
3C22×#336C211yesmaximal, characteristic
4#7579C218yesmaximal, direct product factor
5C2×#1271C212yesmaximal, complemented
6C2×#1271C212yesmaximal, complemented
7C24×C8—21no—
8C22×#117C411yescharacteristic
9C22×#117C411yescharacteristic
10C23×C42C2211yescharacteristic
11C22×C22⋊C8—21no—
12#2296—22no—
13#2296—22no—
14#2296C414yes—
15#2296C2214yes—
16C2×#389C411yescharacteristic
17C2×#389C411yescharacteristic
18C2×#389C2211yescharacteristic
19C2×#389C2211yescharacteristic
20C2×#385—21no—
21C2×#385—21no—
22C2×C4×C4⋊C4—21no—
23C2×C4×C4⋊C4—21no—
24#1817—22no—
25#1817C2214yes—
26C2×#336—21no—
27C2×#336—22no—
28C2×#336—21no—
29C2×#336C2212yes—
30C2×#336C2214yes—
31C2×#336C2212yes—
32#1271C2218yescomplemented
33#1271C2218yescomplemented
34C24×C4C2×C411yescharacteristic
35C24×C4D411yescharacteristic
36C24×C4D411yescharacteristic
37C23×C8—28no—
38C23×C8—24no—
39C23×C8—22no—
40C23×C8—22no—
41C23×C8—44no—
42C23×C8—44no—
43C2×#117—22no—
44C2×#117—24no—
45C2×#117—22no—
46C2×#117—44no—
47C2×#117C818yescomplemented
48C2×#117C2×C414yes—
49C2×#117C2×C414yes—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4C2×C411yescharacteristic
55C22×C4⋊C4C2×C411yescharacteristic
56C22×C4⋊C4C2×C411yescharacteristic
57C22×C4⋊C4C2×C411yescharacteristic
58C22×C22⋊C4—21no—
59C22×C22⋊C4—21no—
60C22×C42—21no—
61C22×C42—21no—
62C22×C42—44no—
63C22×C42C2×C411yescharacteristic
64C22×C42C2×C412yes—
65C22×C42D412yes—
66C22×C42D411yescharacteristic
67C22×C42D411yescharacteristic
68C22×C42D412yes—
69C22×C42C2312yes—
70C22×C42C2311yescharacteristic
71C2×C22⋊C8—24no—
72C2×C22⋊C8—44no—
73#389—22no—
74#389—22no—
75#389—21no—
76#389—21no—
77#389—21no—
78#389—21no—
79#389C2×C414yes—
80#389C2×C414yes—
81#389C2×C412yes—
82#389C2×C412yes—
83#389C2312yes—
84#389C2312yes—
85#385—24no—
86#385—24no—
87#385—24no—
88#385—24no—
89C4×C4⋊C4—24no—
90C4×C4⋊C4—24no—
91C4×C4⋊C4—24no—
92C4×C4⋊C4—24no—
93C2×#95—21no—
94C2×#95—21no—
95C2×#95—21no—
96C2×#95—21no—
97#336—22no—
98#336—24no—
99#336—24no—
100#336—22no—
101#336C2314yes—
102#336C2314yes—
103C25C22⋊C411yescharacteristic
104C23×C4—24no—
105C23×C4—24no—
106C23×C4—24no—
107C23×C4—24no—
108C23×C4—22no—
109C23×C4—22no—
110C23×C4—24no—
111C23×C4—21no—
112C23×C4—21no—
113C23×C4—24no—
114C23×C4—21no—
115C23×C4—21no—
116C23×C4—42no—
117C23×C4C22⋊C412yes—
118C23×C4C22⋊C411yescharacteristic
119C23×C4C22⋊C412yes—
120C23×C4C22⋊C412yes—
121C23×C4C22⋊C411yescharacteristic
122C23×C4C22⋊C411yescharacteristic
123C23×C4C2×C814yes—
124C23×C4M1614yes—
125C23×C4C22×C412yes—
126C23×C4C22×C411yescharacteristic
127C23×C4C2×D412yes—
128C23×C4C2×D412yes—
129C23×C4C2×D411yescharacteristic
130C23×C4C2×D411yescharacteristic
131C22×C8—28no—
132C22×C8—216no—
133C22×C8—24no—
134C22×C8—24no—
135C22×C8—432no—
136C22×C8—48no—
137C22×C8—44no—
138C22×C8—48no—
139C22×C8—44no—
140C22×C8—44no—
141C22×C8—44no—
142C22×C8—44no—
143#117—216no—
144#117—28no—
145#117—48no—
146#117—48no—
147#117C2×C8116yescomplemented
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—24no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—24no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—42no—
161C2×C4⋊C4—42no—
162C2×C4⋊C4—44no—
163C2×C4⋊C4—44no—
164C2×C4⋊C4—44no—
165C2×C4⋊C4—42no—
166C2×C4⋊C4—42no—
167C2×C4⋊C4C2×C814yescomplemented
168C2×C4⋊C4C2×C814yescomplemented
169C2×C4⋊C4C22×C412yes—
170C2×C4⋊C4C22×C412yes—
171C2×C4⋊C4C22×C412yes—
172C2×C4⋊C4C22×C412yes—
173C2×C22⋊C4—28no—
174C2×C22⋊C4—24no—
175C2×C22⋊C4—24no—
176C2×C22⋊C4—44no—
177C2×C42—28no—
178C2×C42—24no—
179C2×C42—24no—
180C2×C42—42no—
181C2×C42—44no—
182C2×C42—42no—
183C2×C42—42no—
184C2×C42—44no—
185C2×C42—44no—
186C2×C42—42no—
187C2×C42—44no—
188C2×C42—44no—
189C2×C42C22⋊C412yes—
190C2×C42C22⋊C412yes—
191C2×C42C22⋊C412yes—
192C2×C42C22×C412yes—
193C2×C42C22×C411yescharacteristic
194C2×C42C2×D412yes—
195C2×C42C2×D412yes—
196C2×C42C2×D411yescharacteristic
197C2×C42C2×D411yescharacteristic
198C2×C42C2411yescharacteristic
199C22⋊C8—48no—
200#95—24no—
201#95—22no—
202#95—22no—
203#95—24no—
204#95—22no—
205#95—22no—
206C24—22no—
207C24—22no—
208C24—22no—
209C24—22no—
210C24C22⋊C814yes—
211C24#9914yes—
212C24#10114yes—
213C24C2×C22⋊C412yes—
214C24C2×C22⋊C411yescharacteristic
215C22×C4—216no—
216C22×C4—216no—
217C22×C4—216no—
218C22×C4—216no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—24no—
222C22×C4—24no—
223C22×C4—24no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—24no—
227C22×C4—22no—
228C22×C4—24no—
229C22×C4—22no—
230C22×C4—24no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—24no—
238C22×C4—24no—
239C22×C4—24no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4—24no—
245C22×C4—24no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—24no—
250C22×C4—24no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—416no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4C22⋊C814yes—
267C22×C4C22⋊C818yes—
268C22×C4#10414yes—
269C22×C4C2×C22⋊C412yes—
270C22×C4C2×C22⋊C412yes—
271C22×C4C2×C22⋊C411yescharacteristic
272C22×C4C2×C22⋊C411yescharacteristic
273C22×C4C2×C22⋊C411yescharacteristic
274C22×C4C2×C22⋊C412yes—
275C22×C4C22×C812yes—
276C22×C4C22×C814yes—
277C22×C4C2×M1612yes—
278C22×C4C2×M1614yes—
279C22×C4#13514yes—
280C22×C4AGL(1,ℤ/8)12yes—
281C22×C4#13712yes—
282C22×C4C23×C411yescharacteristic
283C22×C4C22×D411yescharacteristic
284C22×C4C22×D411yescharacteristic
285C2×C8—28no—
286C2×C8—432no—
287C2×C8—44no—
288C2×C8—416no—
289C2×C8—44no—
290C2×C8—44no—
291C2×C8—44no—
292C2×C8—44no—
293C2×C8—88no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—24no—
297C4⋊C4—24no—
298C4⋊C4—42no—
299C4⋊C4—42no—
300C4⋊C4—48no—
301C4⋊C4—42no—
302C4⋊C4—42no—
303C4⋊C4—44no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—44no—
307C4⋊C4—44no—
308C4⋊C4—48no—
309C4⋊C4C22×C814yescomplemented
310C4⋊C4C22×C814yescomplemented
311C22⋊C4—216no—
312C22⋊C4—48no—
313C42—216no—
314C42—42no—
315C42—42no—
316C42—42no—
317C42—41no—
318C42—42no—
319C42—42no—
320C42—42no—
321C42—41no—
322C42—41no—
323C42—41no—
324C42—48no—
325C23—28no—
326C23—22no—
327C23—22no—
328C23—22no—
329C23—22no—
330C23—28no—
331C23—28no—
332C23—28no—
333C23—28no—
334C23—28no—
335C23#324116yes—
336C23C2×C22⋊C814yes—
337C23C2×C22⋊C812yes—
338C23C2×#9914yes—
339C23C2×#9912yes—
340C23C2×#10114yes—
341C23C2×#10112yes—
342C23#41612yes—
343C23#41712yes—
344C23C2×#10412yes—
345C23#42112yes—
346C23C22×C22⋊C411yescharacteristic
347C2×C4—28no—
348C2×C4—28no—
349C2×C4—216no—
350C2×C4—22no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—22no—
357C2×C4—21no—
358C2×C4—22no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—22no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—216no—
367C2×C4—28no—
368C2×C4—28no—
369C2×C4—24no—
370C2×C4—28no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—28no—
374C2×C4—24no—
375C2×C4—28no—
376C2×C4—24no—
377C2×C4—24no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—48no—
382C2×C4—48no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—48no—
388C2×C4—48no—
389C2×C4—44no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—84no—
397C2×C4—84no—
398C2×C4C2×C22⋊C814yes—
399C2×C4C2×C22⋊C812yes—
400C2×C4#41612yes—
401C2×C4#41712yes—
402C2×C4C2×#10414yes—
403C2×C4C23×C811yescharacteristic
404C2×C4C22×M1611yescharacteristic
405C2×C4C2×#13512yes—
406C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
407C2×C4C2×#13711yescharacteristic
408C8—48no—
409C8—84no—
410C22—24no—
411C22—24no—
412C22—24no—
413C22—24no—
414C22—232no—
415C22—24no—
416C22—24no—
417C22C2×#32418yes—
418C22C2×#32414yes—
419C22#147614yes—
420C22#147714yes—
421C22#150414yes—
422C22#151614yes—
423C22#153114yes—
424C22#155214yes—
425C22C22×C22⋊C811yescharacteristic
426C22C22×#9911yescharacteristic
427C22C22×#10111yescharacteristic
428C22C2×#41611yescharacteristic
429C22C2×#41711yescharacteristic
430C22C22×#10411yescharacteristic
431C22C2×#42111yescharacteristic
432C4—21no—
433C4—21no—
434C4—22no—
435C4—24no—
436C4—22no—
437C4—22no—
438C4—21no—
439C4—21no—
440C4—24no—
441C4—22no—
442C4—44no—
443C4—44no—
444C4—42no—
445C4—82no—
446C4—82no—
447C2—28no—
448C2#757918yesdirect product factor
449C2C22×#32411yescharacteristic
450C2C2×#147611yescharacteristic
451C2C2×#147711yescharacteristic
452C2C2×#150411yescharacteristic
453C2C2×#151611yescharacteristic
454C2C2×#153111yescharacteristic
455C2C2×#155211yescharacteristic
subgroupG/H
center, socleC24C2×C22⋊C4
commutatorC2×C4C23×C8
Frattini, cosocleC2×C42C24
prime radicalC25C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C24 ◁ C23×C42 ◁ G
LECSG ▷ C2×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #7579C2direct (N × H)
5. C2×#1271C2semidirect
6. C2×#1271C2semidirect
32. #1271C22semidirect
33. #1271C22semidirect
47. C2×#117C8semidirect
147. #117C2×C8semidirect
167. C2×C4⋊C4C2×C8semidirect
168. C2×C4⋊C4C2×C8semidirect
309. C4⋊C4C22×C8semidirect
310. C4⋊C4C22×C8semidirect
448. C2#7579direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#22962
C2×#18172
C22×#3362
#75792
C2×#12712