Finite Group Databasebeta

← C2×#7807 #165790

Subgroups — C2×#7807 #165790

Order 512.

909 conjugacy classes of subgroups.

The subgroup lattice has 415 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2805C211yesmaximal, characteristic
2C2×#2096C211yesmaximal, characteristic
3C2×#2084C211yesmaximal, characteristic
4C2×#2083C211yesmaximal, characteristic
5#7807C218yesmaximal, direct product factor
6C2×#1272C211yesmaximal, characteristic
7C2×#1271C211yesmaximal, characteristic
8C2×#1271C211yesmaximal, characteristic
9C22×#107—21no—
10C22×#106—21no—
11C22×#106—21no—
12C22×#103—21no—
13#2805—22no—
14#2805—22no—
15#2805—22no—
16#2805C2214yes—
17C2×#400—21no—
18C2×#400—21no—
19C2×#395—21no—
20C2×#391C2211yescharacteristic
21C2×#389—21no—
22C2×#389C2211yescharacteristic
23C2×#389C2211yescharacteristic
24C2×#387—21no—
25C2×#387—21no—
26C2×#384C2211yescharacteristic
27#2096—22no—
28#2096C2214yes—
29#2084—22no—
30#2084C2214yes—
31#2083—22no—
32#2083C2214yes—
33C2×#340—21no—
34C2×#340—21no—
35C2×#336C2211yescharacteristic
36C2×#336C2211yescharacteristic
37C2×#336C2211yescharacteristic
38#1272C2214yes—
39#1271C2214yes—
40#1271C2214yes—
41C23×Q8D411yescharacteristic
42C23×C8—21no—
43C23×C8—21no—
44C23×C8—21no—
45C22×C4⋊C4—21no—
46C22×C4⋊C4—21no—
47C22×C4⋊C4—21no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4D411yescharacteristic
53C22×C4⋊C4D411yescharacteristic
54C22×C4⋊C4D411yescharacteristic
55C22×C4⋊C4D411yescharacteristic
56C22×C4⋊C4D411yescharacteristic
57C22×C42—21no—
58C22×C42C2311yescharacteristic
59C2×#107—24no—
60C2×#107—44no—
61C2×#106—24no—
62C2×#106—24no—
63C2×#106—44no—
64C2×#106—44no—
65C2×#103—24no—
66C2×#103—44no—
67#400—24no—
68#400—24no—
69#400—24no—
70#400—24no—
71#395—24no—
72#395—24no—
73#391—21no—
74#391—21no—
75#391D412yes—
76#391C2312yes—
77#389—24no—
78#389—24no—
79#389—21no—
80#389—21no—
81#389—21no—
82#389—21no—
83#389D412yes—
84#389D412yes—
85#389C2312yes—
86#389C2312yes—
87#387—24no—
88#387—24no—
89#387—24no—
90#387—24no—
91#384—21no—
92#384—21no—
93#384—21no—
94#384C2312yes—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95—21no—
101C2×#95—21no—
102C2×#95—21no—
103C2×#95—21no—
104#340—24no—
105#340—24no—
106#336—21no—
107#336—21no—
108#336—21no—
109#336C2312yes—
110#336C2312yes—
111#336C2312yes—
112C22×Q8—21no—
113C22×Q8—22no—
114C22×Q8—22no—
115C22×Q8—42no—
116C22×Q8—42no—
117C22×Q8C2×D412yes—
118C23×C4—21no—
119C23×C4—21no—
120C23×C4—21no—
121C23×C4—21no—
122C23×C4—21no—
123C23×C4—21no—
124C23×C4—41no—
125C23×C4C2×D411yescharacteristic
126C23×C4C2×D411yescharacteristic
127C23×C4C2×D411yescharacteristic
128C22×C8—24no—
129C22×C8—24no—
130C22×C8—24no—
131C22×C8—22no—
132C22×C8—22no—
133C22×C8—22no—
134C22×C8—42no—
135C22×C8—42no—
136C22×C8—42no—
137C22×C8—42no—
138C22×C8—42no—
139C22×C8—42no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—24no—
153C2×C4⋊C4—24no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—42no—
158C2×C4⋊C4—42no—
159C2×C4⋊C4—42no—
160C2×C4⋊C4—42no—
161C2×C4⋊C4—42no—
162C2×C4⋊C4—42no—
163C2×C4⋊C4—42no—
164C2×C4⋊C4—42no—
165C2×C4⋊C4—42no—
166C2×C4⋊C4—42no—
167C2×C4⋊C4—42no—
168C2×C4⋊C4—42no—
169C2×C4⋊C4—42no—
170C2×C4⋊C4—41no—
171C2×C4⋊C4—41no—
172C2×C4⋊C4—41no—
173C2×C4⋊C4—82no—
174C2×C4⋊C4—82no—
175C2×C4⋊C4SD1614yes—
176C2×C4⋊C4C2×D412yes—
177C2×C4⋊C4C2×D412yes—
178C2×C4⋊C4C2×D412yes—
179C2×C4⋊C4C2×D412yes—
180C2×C4⋊C4C2×D412yes—
181C2×C42—24no—
182C2×C42—42no—
183C2×C42—82no—
184C2×C42C2×D411yescharacteristic
185C2×C42C2×D411yescharacteristic
186C2×C42C2×D411yescharacteristic
187C2×C42C2411yescharacteristic
188#107—48no—
189#106—48no—
190#106—48no—
191#103—48no—
192#95—24no—
193#95—24no—
194#95—24no—
195#95—24no—
196#95—24no—
197#95—22no—
198#95—22no—
199#95—22no—
200#95—22no—
201#95—22no—
202#95—22no—
203#95—22no—
204#95—22no—
205C24#12011yescharacteristic
206C2×Q8—22no—
207C2×Q8—22no—
208C2×Q8—42no—
209C2×Q8—42no—
210C2×Q8—48no—
211C2×Q8—42no—
212C2×Q8—81no—
213C2×Q8—81no—
214C2×Q8—84no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—24no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—82no—
247C22×C4—82no—
248C22×C4—82no—
249C22×C4#12011yescharacteristic
250C22×C4#12011yescharacteristic
251C22×C4#12011yescharacteristic
252C22×C4C2×SD1612yes—
253C22×C4#13512yes—
254C22×C4#13512yes—
255C22×C4AGL(1,ℤ/8)12yes—
256C22×C4#13712yes—
257C22×C4#13712yes—
258C22×C4C22×D411yescharacteristic
259C22×C4C22×D411yescharacteristic
260C22×C4C22×D411yescharacteristic
261C2×C8—24no—
262C2×C8—24no—
263C2×C8—24no—
264C2×C8—48no—
265C2×C8—48no—
266C2×C8—48no—
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—42no—
272C2×C8—42no—
273C4⋊C4—22no—
274C4⋊C4—24no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C4⋊C4—42no—
285C4⋊C4—42no—
286C4⋊C4—42no—
287C4⋊C4—44no—
288C4⋊C4—44no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C4⋊C4—42no—
292C4⋊C4—42no—
293C4⋊C4—81no—
294C4⋊C4—81no—
295C4⋊C4—81no—
296C4⋊C4—82no—
297C4⋊C4—84no—
298C4⋊C4—84no—
299C4⋊C4—82no—
300C4⋊C4—82no—
301C4⋊C4C2×SD1614yes—
302C42—41no—
303C42—41no—
304C42—41no—
305C42—41no—
306C42—84no—
307C23#44812yes—
308C23#44912yes—
309C23#45212yes—
310C23#45312yes—
311C23#45612yes—
312C23#45612yes—
313C23#45812yes—
314C23C2×#12011yescharacteristic
315Q8—44no—
316Q8—82no—
317Q8—84no—
318C2×C4—24no—
319C2×C4—24no—
320C2×C4—24no—
321C2×C4—24no—
322C2×C4—24no—
323C2×C4—24no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—24no—
337C2×C4—48no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—84no—
356C2×C4—84no—
357C2×C4—84no—
358C2×C4—84no—
359C2×C4—84no—
360C2×C4—82no—
361C2×C4—82no—
362C2×C4—82no—
363C2×C4—164no—
364C2×C4#44812yes—
365C2×C4#44912yes—
366C2×C4#45212yes—
367C2×C4C22×SD1611yescharacteristic
368C2×C4C2×#13511yescharacteristic
369C2×C4C2×#13511yescharacteristic
370C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
371C2×C4C2×#13711yescharacteristic
372C2×C4C2×#13711yescharacteristic
373C8—44no—
374C8—44no—
375C8—44no—
376C22#160914yes—
377C22#161114yes—
378C22#161814yes—
379C22#162214yes—
380C22#165014yes—
381C22#165314yes—
382C22#166014yes—
383C22C2×#44811yescharacteristic
384C22C2×#44911yescharacteristic
385C22C2×#45211yescharacteristic
386C22C2×#45311yescharacteristic
387C22C2×#45611yescharacteristic
388C22C2×#45611yescharacteristic
389C22C2×#45811yescharacteristic
390C4—21no—
391C4—21no—
392C4—22no—
393C4—21no—
394C4—21no—
395C4—22no—
396C4—21no—
397C4—21no—
398C4—22no—
399C4—44no—
400C4—82no—
401C4—82no—
402C4—82no—
403C4—82no—
404C4—82no—
405C4—162no—
406C2#780718yesdirect product factor
407C2C2×#160911yescharacteristic
408C2C2×#161111yescharacteristic
409C2C2×#161811yescharacteristic
410C2C2×#162211yescharacteristic
411C2C2×#165311yescharacteristic
412C2C2×#165011yescharacteristic
413C2C2×#166011yescharacteristic
subgroupG/H
center, socle, prime radicalC24#120
commutator, Frattini, cosocleC2×C42C24
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ C22×C42 ◁ G
LECSG ▷ C2×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
5. #7807C2direct (N × H)
406. C2#7807direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#28052
C2×#20962
C2×#20842
C2×#20832
#78072
C2×#12722
C2×#12712