Finite Group Databasebeta

← C2×#11908 #482124

Subgroups — C2×#11908 #482124

Order 512.

1020 conjugacy classes of subgroups.

The subgroup lattice has 387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2567C211yesmaximal, characteristic
2C2×#1801C211yesmaximal, characteristic
3C2×#1461C211yesmaximal, characteristic
4#11908C218yesmaximal, direct product factor
5C2×#1354C214yesmaximal
6C22×C4⋊Q8C411yescharacteristic
7C22×C4×Q8C2211yescharacteristic
8C2×#431—21no—
9C2×#423—21no—
10C22×#101—21no—
11#2567—22no—
12#2567—22no—
13#2567C414yes—
14#2567C2214yes—
15C2×#395C412yes—
16C2×#395C2212yes—
17C2×#391—21no—
18C2×#389—21no—
19C2×#389—21no—
20C2×#384—21no—
21C2×C4×C4⋊C4C411yescharacteristic
22#1801—22no—
23#1801C2214yes—
24C2×#343C2212yes—
25#1461—22no—
26#1461C2214yes—
27C2×#324—21no—
28C2×#324C2212yes—
29#1354C22116yes—
30C23×Q8C2×C412yes—
31C23×Q8D411yescharacteristic
32C22×M16—22no—
33C2×C4⋊Q8—22no—
34C2×C4⋊Q8—42no—
35C2×C4⋊Q8—41no—
36C2×C4⋊Q8—41no—
37C2×C4⋊Q8C2×C414yes—
38C2×C4×Q8—41no—
39C2×C4×Q8—41no—
40C2×C4×Q8—42no—
41C2×C4×Q8C2×C412yes—
42C2×C4×Q8D412yes—
43C2×C4×Q8D412yes—
44C2×C4×Q8C2312yes—
45C22×C4⋊C4—21no—
46C22×C4⋊C4—21no—
47C22×C4⋊C4—21no—
48C22×C4⋊C4—22no—
49C22×C4⋊C4—22no—
50C22×C4⋊C4C2×C411yescharacteristic
51C22×C4⋊C4D411yescharacteristic
52C22×C4⋊C4C2311yescharacteristic
53C22×C42—21no—
54C22×C42C2×C411yescharacteristic
55C22×C42D411yescharacteristic
56C22×C42D411yescharacteristic
57#431—24no—
58#431—42no—
59#423—24no—
60#423—42no—
61C2×C4⋊C8—41no—
62C2×C4⋊C8—41no—
63C2×C4⋊C8—41no—
64C2×#101—24no—
65C2×#101—44no—
66C2×C22⋊C8—22no—
67C2×C4×C8—41no—
68#395—24no—
69#395—22no—
70#395—22no—
71#395C2×C414yes—
72#395C2×C418yes—
73#395C2314yes—
74#391—24no—
75#391—24no—
76#389—24no—
77#389—24no—
78#389—24no—
79#389—24no—
80#384—24no—
81#384—24no—
82C4×C4⋊C4—22no—
83C4×C4⋊C4C2×C414yes—
84C2×#95—22no—
85C2×#95—22no—
86C2×#95C2×C412yes—
87#343—22no—
88#343C2314yes—
89#324—24no—
90#324—22no—
91#324C2314yes—
92C22×Q8—22no—
93C22×Q8—41no—
94C22×Q8—41no—
95C22×Q8—42no—
96C22×Q8—42no—
97C22×Q8—42no—
98C22×Q8—84no—
99C22×Q8C22⋊C412yes—
100C22×Q8SD1614yes—
101C22×Q8Q1614yes—
102C22×Q8C22×C414yes—
103C22×Q8C2×D412yes—
104C23×C4—22no—
105C23×C4—22no—
106C23×C4C22⋊C411yescharacteristic
107C23×C4C22⋊C411yescharacteristic
108C23×C4C22⋊C411yescharacteristic
109C23×C4C22⋊C411yescharacteristic
110C23×C4C22×C411yescharacteristic
111C23×C4C2×D411yescharacteristic
112C23×C4C2×D411yescharacteristic
113C2×M16—24no—
114C2×M16—42no—
115C2×M16—44no—
116C2×M16—44no—
117C22×C8—42no—
118C22×C8—42no—
119C4⋊Q8—44no—
120C4⋊Q8—44no—
121C4⋊Q8—44no—
122C4⋊Q8—44no—
123C4×Q8—42no—
124C4×Q8—42no—
125C4×Q8—42no—
126C4×Q8—42no—
127C4×Q8—42no—
128C4×Q8—42no—
129C4×Q8—42no—
130C4×Q8—42no—
131C2×C4⋊C4—28no—
132C2×C4⋊C4—24no—
133C2×C4⋊C4—24no—
134C2×C4⋊C4—24no—
135C2×C4⋊C4—24no—
136C2×C4⋊C4—28no—
137C2×C4⋊C4—24no—
138C2×C4⋊C4—41no—
139C2×C4⋊C4—41no—
140C2×C4⋊C4—41no—
141C2×C4⋊C4—41no—
142C2×C4⋊C4—41no—
143C2×C4⋊C4—41no—
144C2×C4⋊C4—42no—
145C2×C4⋊C4—42no—
146C2×C4⋊C4—42no—
147C2×C4⋊C4—41no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—84no—
150C2×C4⋊C4—84no—
151C2×C4⋊C4C22⋊C412yes—
152C2×C4⋊C4C22⋊C412yes—
153C2×C4⋊C4C22×C412yes—
154C2×C4⋊C4C22×C411yescharacteristic
155C2×C4⋊C4C2×D412yes—
156C2×C4⋊C4C2×D411yescharacteristic
157C2×C4⋊C4C2×D411yescharacteristic
158C2×C4⋊C4C2411yescharacteristic
159C2×C42—22no—
160C2×C42—21no—
161C2×C42—21no—
162C2×C42—21no—
163C2×C42—21no—
164C2×C42—21no—
165C2×C42—21no—
166C2×C42—22no—
167C2×C42—22no—
168C2×C42—24no—
169C2×C42—44no—
170C2×C42C22⋊C412yes—
171C2×C42C22⋊C412yes—
172C2×C42C22⋊C412yes—
173C2×C42C22×C412yes—
174C2×C42C2×D412yes—
175C2×C42C2×D412yes—
176C4⋊C8—44no—
177C4⋊C8—44no—
178C4⋊C8—44no—
179#101—48no—
180C22⋊C8—24no—
181C22⋊C8—42no—
182C4×C8—44no—
183#95—24no—
184#95—28no—
185#95—22no—
186#95—24no—
187#95C22×C414yes—
188C24C2×C22⋊C411yescharacteristic
189C2×Q8—42no—
190C2×Q8—42no—
191C2×Q8—42no—
192C2×Q8—44no—
193C2×Q8—44no—
194C2×Q8—44no—
195C2×Q8—44no—
196C2×Q8—42no—
197C2×Q8—44no—
198C2×Q8—44no—
199C2×Q8—84no—
200C2×Q8—84no—
201C2×Q8—88no—
202C2×Q8—88no—
203C2×Q8#10318yes—
204C2×Q8C2×SD1614yes—
205C2×Q8C2×Q1614yes—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—24no—
216C22×C4—28no—
217C22×C4—24no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—24no—
225C22×C4—44no—
226C22×C4—44no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—44no—
231C22×C4—44no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4#9912yes—
235C22×C4#9911yescharacteristic
236C22×C4#9911yescharacteristic
237C22×C4#10314yes—
238C22×C4#10314yes—
239C22×C4C2×C22⋊C412yes—
240C22×C4C2×C22⋊C411yescharacteristic
241C22×C4C2×C22⋊C412yes—
242C22×C4C2×C22⋊C412yes—
243C22×C4C2×C22⋊C411yescharacteristic
244C22×C4C2×C22⋊C411yescharacteristic
245C22×C4C2×C22⋊C412yes—
246C22×C4C2×SD1612yes—
247C22×C4C2×Q1612yes—
248C22×C4C23×C411yescharacteristic
249C22×C4C22×D411yescharacteristic
250C22×C4C22×D411yescharacteristic
251M16—44no—
252M16—44no—
253M16—84no—
254C2×C8—44no—
255C2×C8—44no—
256C2×C8—84no—
257C2×C8—84no—
258C4⋊C4—216no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—41no—
263C4⋊C4—42no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—48no—
268C4⋊C4—44no—
269C4⋊C4—44no—
270C4⋊C4—88no—
271C4⋊C4—84no—
272C4⋊C4—84no—
273C42—22no—
274C42—22no—
275C42—22no—
276C42—22no—
277C42—22no—
278C42—22no—
279C42—22no—
280C42—22no—
281C42—22no—
282C42—22no—
283C42—22no—
284C42—22no—
285C42—48no—
286C23—22no—
287C23—22no—
288C23C2×#9911yescharacteristic
289C23C2×#9911yescharacteristic
290C23C2×#10312yes—
291C23#42112yes—
292C23C22×C22⋊C411yescharacteristic
293Q8—48no—
294Q8—44no—
295Q8—44no—
296Q8—88no—
297Q8—88no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—24no—
312C2×C4—24no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—24no—
316C2×C4—24no—
317C2×C4—28no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—44no—
324C2×C4—416no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—44no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—44no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—84no—
341C2×C4—84no—
342C2×C4#35614yes—
343C2×C4C2×#9912yes—
344C2×C4C2×#9912yes—
345C2×C4C2×#10314yes—
346C2×C4C2×#10314yes—
347C2×C4C2×#10312yes—
348C2×C4C22×SD1611yescharacteristic
349C2×C4C22×Q1611yescharacteristic
350C8—84no—
351C8—84no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—24no—
357C22—24no—
358C22#152012yes—
359C22#152012yes—
360C22#212212yes—
361C22C2×#35612yes—
362C22C22×#9911yescharacteristic
363C22C22×#10311yescharacteristic
364C22C2×#42111yescharacteristic
365C4—22no—
366C4—21no—
367C4—21no—
368C4—24no—
369C4—22no—
370C4—24no—
371C4—48no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—42no—
377C4—84no—
378C4C2×#35614yes—
379C2—21no—
380C2—21no—
381C2—22no—
382C2#1190814yesdirect product factor
383C2C2×#152011yescharacteristic
384C2C2×#212211yescharacteristic
385C2C22×#35611yescharacteristic
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. #11908C2direct (N × H)
382. C2#11908direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25672
C2×#18012
C2×#14612
#119082
C2×#13542