Finite Group Databasebeta

← C2×#7763 #165694

Subgroups — C2×#7763 #165694

Order 512.

1083 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2726C211yesmaximal, characteristic
2C2×#2057C211yesmaximal, characteristic
3C2×#2057C211yesmaximal, characteristic
4C2×#2043C211yesmaximal, characteristic
5#7763C218yesmaximal, direct product factor
6C2×#1271C211yesmaximal, characteristic
7C2×#1271C211yesmaximal, characteristic
8C2×#1271C211yesmaximal, characteristic
9C22×C4⋊Q8C2211yescharacteristic
10C22×#125—21no—
11C22×#107—21no—
12C22×#107—21no—
13C22×#103—21no—
14C22×#103—21no—
15#2726—22no—
16#2726—22no—
17#2726—22no—
18#2726C2214yes—
19C2×#398—21no—
20C2×#398—21no—
21C2×#398—21no—
22C2×#389—21no—
23C2×#389C2211yescharacteristic
24C2×#389C2211yescharacteristic
25C2×#389C2211yescharacteristic
26C2×#387—21no—
27#2057—22no—
28#2057—22no—
29#2057C2214yes—
30#2057C2214yes—
31#2043—22no—
32#2043C2214yes—
33C2×#340—21no—
34C2×#340—21no—
35C2×#336C2211yescharacteristic
36C2×#336C2211yescharacteristic
37C2×#336C2211yescharacteristic
38#1271C2214yes—
39#1271C2214yes—
40#1271C2214yes—
41C23×Q8—21no—
42C23×C8—21no—
43C23×C8—21no—
44C23×C8—21no—
45C2×C4⋊Q8—21no—
46C2×C4⋊Q8—21no—
47C2×C4⋊Q8—21no—
48C2×C4⋊Q8—44no—
49C2×C4⋊Q8C2312yes—
50C2×#125—24no—
51C2×#125—24no—
52C2×#125—44no—
53C2×#125—44no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4—21no—
57C22×C4⋊C4—21no—
58C22×C4⋊C4—21no—
59C22×C4⋊C4—21no—
60C22×C4⋊C4—21no—
61C22×C4⋊C4—21no—
62C22×C4⋊C4—21no—
63C22×C4⋊C4D411yescharacteristic
64C22×C4⋊C4D411yescharacteristic
65C22×C4⋊C4D411yescharacteristic
66C22×C4⋊C4D411yescharacteristic
67C22×C4⋊C4D411yescharacteristic
68C22×C4⋊C4D411yescharacteristic
69C22×C42—21no—
70C22×C42C2311yescharacteristic
71C2×#107—24no—
72C2×#107—24no—
73C2×#107—44no—
74C2×#107—44no—
75C2×#103—24no—
76C2×#103—24no—
77C2×#103—44no—
78C2×#103—44no—
79#398—24no—
80#398—24no—
81#398—24no—
82#398—24no—
83#398—24no—
84#398—24no—
85#389—24no—
86#389—24no—
87#389—21no—
88#389—21no—
89#389—21no—
90#389—21no—
91#389—21no—
92#389—21no—
93#389D412yes—
94#389D412yes—
95#389D412yes—
96#389C2312yes—
97#389C2312yes—
98#389C2312yes—
99#387—24no—
100#387—24no—
101C2×#95—21no—
102C2×#95—21no—
103C2×#95—21no—
104C2×#95—21no—
105C2×#95—21no—
106C2×#95—21no—
107#340—24no—
108#340—24no—
109#336—21no—
110#336—21no—
111#336—21no—
112#336C2312yes—
113#336C2312yes—
114#336C2312yes—
115C22×Q8—24no—
116C22×Q8—22no—
117C22×Q8—42no—
118C22×Q8—42no—
119C22×Q8—42no—
120C22×Q8—41no—
121C22×Q8—42no—
122C22×Q8—42no—
123C23×C4—21no—
124C23×C4—21no—
125C23×C4—21no—
126C23×C4—21no—
127C23×C4—21no—
128C23×C4—21no—
129C23×C4—41no—
130C23×C4C2×D411yescharacteristic
131C23×C4C2×D411yescharacteristic
132C23×C4C2×D411yescharacteristic
133C22×C8—24no—
134C22×C8—24no—
135C22×C8—22no—
136C22×C8—22no—
137C22×C8—22no—
138C22×C8—42no—
139C22×C8—42no—
140C22×C8—42no—
141C22×C8—42no—
142C22×C8—42no—
143C22×C8—42no—
144C22×C8—42no—
145C4⋊Q8—44no—
146C4⋊Q8—44no—
147C4⋊Q8—44no—
148C4⋊Q8—44no—
149#125—48no—
150#125—416no—
151#125—48no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—24no—
157C2×C4⋊C4—24no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—24no—
163C2×C4⋊C4—24no—
164C2×C4⋊C4—24no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—24no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—44no—
177C2×C4⋊C4—44no—
178C2×C4⋊C4—44no—
179C2×C4⋊C4—42no—
180C2×C4⋊C4—42no—
181C2×C4⋊C4—41no—
182C2×C4⋊C4—41no—
183C2×C4⋊C4—42no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4—42no—
187C2×C4⋊C4—42no—
188C2×C4⋊C4—42no—
189C2×C4⋊C4—42no—
190C2×C4⋊C4—42no—
191C2×C4⋊C4—42no—
192C2×C4⋊C4—82no—
193C2×C4⋊C4D814yes—
194C2×C4⋊C4Q1614yes—
195C2×C4⋊C4C2×D412yes—
196C2×C4⋊C4C2×D412yes—
197C2×C4⋊C4C2×D412yes—
198C2×C4⋊C4C2×D412yes—
199C2×C4⋊C4C2×D412yes—
200C2×C4⋊C4C2×D412yes—
201C2×C42—24no—
202C2×C42—42no—
203C2×C42—44no—
204C2×C42C2×D411yescharacteristic
205C2×C42C2×D411yescharacteristic
206C2×C42C2×D411yescharacteristic
207C2×C42C2411yescharacteristic
208#107—48no—
209#107—48no—
210#103—48no—
211#103—48no—
212#95—24no—
213#95—24no—
214#95—24no—
215#95—22no—
216#95—22no—
217#95—22no—
218#95—22no—
219#95—22no—
220#95—22no—
221C24#12011yescharacteristic
222C2×Q8—24no—
223C2×Q8—42no—
224C2×Q8—44no—
225C2×Q8—48no—
226C2×Q8—48no—
227C2×Q8—42no—
228C2×Q8—42no—
229C2×Q8—42no—
230C2×Q8—42no—
231C2×Q8—84no—
232C2×Q8—84no—
233C2×Q8—82no—
234C2×Q8—82no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—24no—
244C22×C4—24no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—44no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—82no—
268C22×C4—82no—
269C22×C4#12011yescharacteristic
270C22×C4#12011yescharacteristic
271C22×C4#12011yescharacteristic
272C22×C4C2×D812yes—
273C22×C4C2×Q1612yes—
274C22×C4#13512yes—
275C22×C4AGL(1,ℤ/8)12yes—
276C22×C4#13712yes—
277C22×C4#13712yes—
278C22×C4C22×D411yescharacteristic
279C22×C4C22×D411yescharacteristic
280C22×C4C22×D411yescharacteristic
281C2×C8—24no—
282C2×C8—24no—
283C2×C8—42no—
284C2×C8—42no—
285C2×C8—48no—
286C2×C8—48no—
287C2×C8—42no—
288C2×C8—42no—
289C2×C8—42no—
290C2×C8—42no—
291C2×C8—42no—
292C2×C8—84no—
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—24no—
296C4⋊C4—24no—
297C4⋊C4—24no—
298C4⋊C4—24no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—42no—
302C4⋊C4—42no—
303C4⋊C4—42no—
304C4⋊C4—48no—
305C4⋊C4—48no—
306C4⋊C4—48no—
307C4⋊C4—42no—
308C4⋊C4—42no—
309C4⋊C4—44no—
310C4⋊C4—44no—
311C4⋊C4—42no—
312C4⋊C4—42no—
313C4⋊C4—42no—
314C4⋊C4—42no—
315C4⋊C4—42no—
316C4⋊C4—42no—
317C4⋊C4—44no—
318C4⋊C4—44no—
319C4⋊C4—42no—
320C4⋊C4—44no—
321C4⋊C4—81no—
322C4⋊C4—81no—
323C4⋊C4—81no—
324C4⋊C4—84no—
325C4⋊C4C2×D814yes—
326C4⋊C4C2×Q1614yes—
327C42—41no—
328C42—41no—
329C42—41no—
330C42—41no—
331C42—48no—
332C23#44712yes—
333C23#45112yes—
334C23#45212yes—
335C23#45412yes—
336C23#45612yes—
337C23#45612yes—
338C23B(4,𝔽2)12yes—
339C23C2×#12011yescharacteristic
340Q8—44no—
341Q8—44no—
342Q8—82no—
343Q8—82no—
344Q8—88no—
345C2×C4—24no—
346C2×C4—24no—
347C2×C4—24no—
348C2×C4—24no—
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—48no—
366C2×C4—48no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—44no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—84no—
385C2×C4—84no—
386C2×C4—88no—
387C2×C4—84no—
388C2×C4—84no—
389C2×C4—82no—
390C2×C4—82no—
391C2×C4#44712yes—
392C2×C4#45112yes—
393C2×C4#45212yes—
394C2×C4C22×D811yescharacteristic
395C2×C4C22×Q1611yescharacteristic
396C2×C4C2×#13511yescharacteristic
397C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
398C2×C4C2×#13711yescharacteristic
399C2×C4C2×#13711yescharacteristic
400C8—44no—
401C8—44no—
402C8—82no—
403C22#159814yes—
404C22#160314yes—
405C22#160514yes—
406C22#163614yes—
407C22#164714yes—
408C22#164914yes—
409C22#166314yes—
410C22C2×#44711yescharacteristic
411C22C2×#45111yescharacteristic
412C22C2×#45211yescharacteristic
413C22C2×#45411yescharacteristic
414C22C2×#45611yescharacteristic
415C22C2×#45611yescharacteristic
416C22C2×B(4,𝔽2)11yescharacteristic
417C4—21no—
418C4—21no—
419C4—22no—
420C4—21no—
421C4—21no—
422C4—22no—
423C4—21no—
424C4—21no—
425C4—22no—
426C4—44no—
427C4—44no—
428C4—82no—
429C4—82no—
430C4—82no—
431C4—82no—
432C4—84no—
433C2#776318yesdirect product factor
434C2C2×#160311yescharacteristic
435C2C2×#159811yescharacteristic
436C2C2×#160511yescharacteristic
437C2C2×#163611yescharacteristic
438C2C2×#164711yescharacteristic
439C2C2×#164911yescharacteristic
440C2C2×#166311yescharacteristic
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. #7763C2direct (N × H)
433. C2#7763direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#27262
C2×#20572
C2×#20432
#77632
C2×#12712