Finite Group Databasebeta

← C2×#11740 #481537

Subgroups — C2×#11740 #481537

Order 512.

926 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2634C211yesmaximal, characteristic
2C2×C4×#101C211yesmaximal, characteristic
3C2×#1461C211yesmaximal, characteristic
4#11740C218yesmaximal, direct product factor
5C2×#1353C212yesmaximal
6C2×#1346C212yesmaximal
7C22×#125C411yescharacteristic
8C22×C4×Q8C2211yescharacteristic
9C2×#431—21no—
10C22×#101—21no—
11C2×C4×M16—21no—
12#2634—22no—
13#2634—22no—
14#2634C414yes—
15#2634C2214yes—
16C2×#400—21no—
17C2×#400C411yescharacteristic
18C2×#400C2211yescharacteristic
19C2×#398C411yescharacteristic
20C2×#398C2211yescharacteristic
21C2×#395—21no—
22C2×#387—21no—
23C2×#387—21no—
24C2×#383C411yescharacteristic
25C4×#101—22no—
26C4×#101C2214yes—
27C2×#343C2212yes—
28#1461—22no—
29#1461C2214yes—
30C2×#324—21no—
31C2×#324C2212yes—
32#1353C2218yes—
33#1346C2218yes—
34C23×Q8D411yescharacteristic
35C22×M16—22no—
36C2×#125—22no—
37C2×#125—42no—
38C2×#125—41no—
39C2×#125—41no—
40C2×#125C2×C414yes—
41C2×C4×Q8—41no—
42C2×C4×Q8—41no—
43C2×C4×Q8—42no—
44C2×C4×Q8C2×C412yes—
45C2×C4×Q8D412yes—
46C2×C4×Q8D412yes—
47C2×C4×Q8C2312yes—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4C2×C411yescharacteristic
53C22×C4⋊C4C2×C411yescharacteristic
54C22×C4⋊C4C2×C411yescharacteristic
55C22×C4⋊C4D411yescharacteristic
56C22×C4⋊C4C2311yescharacteristic
57C22×C42C2×C411yescharacteristic
58C22×C42D411yescharacteristic
59C22×C42D411yescharacteristic
60#431—24no—
61#431—42no—
62C2×C4⋊C8—41no—
63C2×#101—28no—
64C2×#101—24no—
65C2×C22⋊C8—22no—
66C4×M16—24no—
67C4×M16—42no—
68C2×#97—41no—
69C2×C4×C8—41no—
70C2×C4×C8—41no—
71#400—22no—
72#400—24no—
73#400—21no—
74#400—21no—
75#400—24no—
76#400C2×C412yes—
77#400C2×C414yes—
78#400C2312yes—
79#398—22no—
80#398—21no—
81#398—21no—
82#398C2×C412yes—
83#398C2×C414yes—
84#398C2312yes—
85#395—24no—
86#395—24no—
87#387—24no—
88#387—24no—
89#387—24no—
90#387—24no—
91#383—22no—
92#383C2×C414yes—
93C2×#95—21no—
94C2×#95—21no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95—21no—
101C2×#95C2×C411yescharacteristic
102C2×#95C2×C411yescharacteristic
103#343—22no—
104#343C2314yes—
105#324—24no—
106#324—22no—
107#324C2314yes—
108C22×Q8—24no—
109C22×Q8—24no—
110C22×Q8—41no—
111C22×Q8—41no—
112C22×Q8C22⋊C412yes—
113C22×Q8C2×D412yes—
114C23×C4—21no—
115C23×C4—21no—
116C23×C4—21no—
117C23×C4—21no—
118C23×C4C22⋊C411yescharacteristic
119C23×C4C22⋊C411yescharacteristic
120C23×C4C22⋊C411yescharacteristic
121C23×C4C22⋊C411yescharacteristic
122C23×C4C22×C411yescharacteristic
123C23×C4C2×D411yescharacteristic
124C23×C4C2×D411yescharacteristic
125C2×M16—28no—
126C2×M16—24no—
127C2×M16—42no—
128C2×M16—44no—
129C22×C8—42no—
130C22×C8—42no—
131#125—44no—
132#125—44no—
133#125—44no—
134#125—44no—
135C4×Q8—42no—
136C4×Q8—42no—
137C4×Q8—42no—
138C4×Q8—42no—
139C4×Q8—42no—
140C4×Q8—42no—
141C4×Q8—42no—
142C4×Q8—42no—
143C2×C4⋊C4—24no—
144C2×C4⋊C4—24no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—24no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4—41no—
160C2×C4⋊C4—42no—
161C2×C4⋊C4—42no—
162C2×C4⋊C4—42no—
163C2×C4⋊C4—41no—
164C2×C4⋊C4—41no—
165C2×C4⋊C4—44no—
166C2×C4⋊C4—44no—
167C2×C4⋊C4C22⋊C412yes—
168C2×C4⋊C4C22⋊C412yes—
169C2×C4⋊C4C22×C412yes—
170C2×C4⋊C4C22×C412yes—
171C2×C4⋊C4C22×C412yes—
172C2×C4⋊C4C22×C411yescharacteristic
173C2×C4⋊C4C2×D412yes—
174C2×C4⋊C4C2×D411yescharacteristic
175C2×C4⋊C4C2×D411yescharacteristic
176C2×C4⋊C4C2411yescharacteristic
177C2×C42—22no—
178C2×C42—21no—
179C2×C42—21no—
180C2×C42—21no—
181C2×C42—21no—
182C2×C42—21no—
183C2×C42—22no—
184C2×C42—21no—
185C2×C42—22no—
186C2×C42C22⋊C412yes—
187C2×C42C22⋊C412yes—
188C2×C42C22⋊C412yes—
189C2×C42C22×C412yes—
190C2×C42C2×D412yes—
191C2×C42C2×D412yes—
192C4⋊C8—44no—
193#101—216no—
194C22⋊C8—24no—
195C22⋊C8—42no—
196#97—44no—
197C4×C8—44no—
198C4×C8—44no—
199#95—24no—
200#95—24no—
201#95—22no—
202#95—24no—
203#95—22no—
204#95—24no—
205#95—22no—
206#95—24no—
207#95—21no—
208#95—21no—
209#95—22no—
210#95—22no—
211#95—22no—
212#95C22×C412yes—
213#95C22×C412yes—
214C24C2×C22⋊C411yescharacteristic
215C2×Q8—24no—
216C2×Q8—24no—
217C2×Q8—24no—
218C2×Q8—24no—
219C2×Q8—42no—
220C2×Q8—42no—
221C2×Q8—48no—
222C2×Q8—48no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—44no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4#9911yescharacteristic
261C22×C4#9911yescharacteristic
262C22×C4#9912yes—
263C22×C4#10414yes—
264C22×C4C2×C22⋊C412yes—
265C22×C4C2×C22⋊C411yescharacteristic
266C22×C4C2×C22⋊C412yes—
267C22×C4C2×C22⋊C411yescharacteristic
268C22×C4C2×C22⋊C412yes—
269C22×C4C2×C22⋊C411yescharacteristic
270C22×C4C2×C22⋊C412yes—
271C22×C4#13514yes—
272C22×C4C23×C411yescharacteristic
273C22×C4C22×D411yescharacteristic
274C22×C4C22×D411yescharacteristic
275M16—28no—
276M16—48no—
277M16—44no—
278C2×C8—44no—
279C2×C8—48no—
280C2×C8—44no—
281C2×C8—84no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C4⋊C4—42no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—42no—
289C4⋊C4—41no—
290C4⋊C4—42no—
291C4⋊C4—42no—
292C4⋊C4—42no—
293C4⋊C4—42no—
294C4⋊C4—48no—
295C4⋊C4—44no—
296C4⋊C4—44no—
297C4⋊C4—44no—
298C4⋊C4—44no—
299C4⋊C4—48no—
300C42—22no—
301C42—22no—
302C42—22no—
303C42—22no—
304C42—22no—
305C42—22no—
306C42—22no—
307C42—22no—
308C42—22no—
309C42—22no—
310C42—22no—
311C42—22no—
312C23—22no—
313C23—22no—
314C23C2×#9911yescharacteristic
315C23C2×#9911yescharacteristic
316C23#41612yes—
317C23C2×#10412yes—
318C23C22×C22⋊C411yescharacteristic
319Q8—48no—
320Q8—48no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—22no—
340C2×C4—22no—
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—41no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—44no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—84no—
368C2×C4—84no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4—82no—
372C2×C4—82no—
373C2×C4C2×#9912yes—
374C2×C4C2×#9912yes—
375C2×C4#41612yes—
376C2×C4C2×#10414yes—
377C2×C4C2×#13512yes—
378C8—48no—
379C8—84no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—24no—
385C22—24no—
386C22#150112yes—
387C22#150112yes—
388C22#212312yes—
389C22#213312yes—
390C22C22×#9911yescharacteristic
391C22C2×#41611yescharacteristic
392C22C22×#10411yescharacteristic
393C4—22no—
394C4—22no—
395C4—22no—
396C4—22no—
397C4—24no—
398C4—41no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—42no—
403C4—42no—
404C4—82no—
405C4—82no—
406C4—82no—
407C4—82no—
408C2—21no—
409C2—21no—
410C2—22no—
411C2#1174014yesdirect product factor
412C2C2×#150111yescharacteristic
413C2C2×#212311yescharacteristic
414C2C2×#213311yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC24C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #11740C2direct (N × H)
411. C2#11740direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#26342
C2×C4×#1012
C2×#14612
#117402
C2×#13532
C2×#13462