Finite Group Databasebeta

← C2×#11794 #481645

Subgroups — C2×#11794 #481645

Order 512.

992 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2568C211yesmaximal, characteristic
2C2×C4×#101C211yesmaximal, characteristic
3C2×#1467C211yesmaximal, characteristic
4#11794C218yesmaximal, direct product factor
5C2×#1353C214yesmaximal
6C22×C4⋊Q8C411yescharacteristic
7C22×C4×Q8C2211yescharacteristic
8C2×#432—21no—
9C22×#101—21no—
10C2×C4×M16—21no—
11#2568—22no—
12#2568—22no—
13#2568C414yes—
14#2568C2214yes—
15C2×#400C412yes—
16C2×#400C2212yes—
17C2×#391—21no—
18C2×#391—21no—
19C2×#391—21no—
20C2×#382—21no—
21C2×C4×C4⋊C4C411yescharacteristic
22C4×#101—22no—
23C4×#101C2214yes—
24C2×#343C2212yes—
25#1467—22no—
26#1467C2214yes—
27C2×#324—21no—
28C2×#324C2212yes—
29#1353C22116yes—
30C23×Q8—21no—
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⋊C4C2×C412yes—
48C22×C4⋊C4C2×C411yescharacteristic
49C22×C4⋊C4D411yescharacteristic
50C22×C4⋊C4C2311yescharacteristic
51C22×C42—21no—
52C22×C42C2×C411yescharacteristic
53C22×C42D411yescharacteristic
54C22×C42D411yescharacteristic
55#432—24no—
56#432—42no—
57C2×C4⋊C8—41no—
58C2×#101—28no—
59C2×#101—24no—
60C2×C22⋊C8—22no—
61C4×M16—24no—
62C4×M16—42no—
63C2×#97—41no—
64C2×#97—41no—
65C2×C4×C8—41no—
66#400—24no—
67#400—22no—
68#400—22no—
69#400C2×C414yes—
70#400C2×C418yes—
71#400C2314yes—
72#391—24no—
73#391—24no—
74#391—24no—
75#391—24no—
76#391—24no—
77#391—24no—
78#382—24no—
79#382—24no—
80C4×C4⋊C4—22no—
81C4×C4⋊C4C2×C414yes—
82C2×#95—22no—
83C2×#95—22no—
84C2×#95—22no—
85C2×#95—22no—
86C2×#95C2×C412yes—
87#343—22no—
88#343C2314yes—
89#324—24no—
90#324—22no—
91#324C2314yes—
92C22×Q8—24no—
93C22×Q8—24no—
94C22×Q8—24no—
95C22×Q8—41no—
96C22×Q8—41no—
97C22×Q8—48no—
98C22×Q8—42no—
99C22×Q8—41no—
100C22×Q8—41no—
101C22×Q8C22⋊C412yes—
102C22×Q8C2×D412yes—
103C23×C4—22no—
104C23×C4—22no—
105C23×C4C22⋊C411yescharacteristic
106C23×C4C22⋊C411yescharacteristic
107C23×C4C22⋊C411yescharacteristic
108C23×C4C22⋊C411yescharacteristic
109C23×C4C22×C411yescharacteristic
110C23×C4C2×D411yescharacteristic
111C23×C4C2×D411yescharacteristic
112C2×M16—28no—
113C2×M16—24no—
114C2×M16—42no—
115C2×M16—44no—
116C22×C8—42no—
117C22×C8—42no—
118C4⋊Q8—44no—
119C4⋊Q8—44no—
120C4⋊Q8—44no—
121C4⋊Q8—44no—
122C4×Q8—42no—
123C4×Q8—42no—
124C4×Q8—42no—
125C4×Q8—42no—
126C4×Q8—42no—
127C4×Q8—42no—
128C4×Q8—42no—
129C4×Q8—42no—
130C2×C4⋊C4—24no—
131C2×C4⋊C4—24no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—41no—
134C2×C4⋊C4—41no—
135C2×C4⋊C4—41no—
136C2×C4⋊C4—41no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4—41no—
139C2×C4⋊C4—42no—
140C2×C4⋊C4—42no—
141C2×C4⋊C4—44no—
142C2×C4⋊C4—42no—
143C2×C4⋊C4—42no—
144C2×C4⋊C4C22⋊C412yes—
145C2×C4⋊C4C22⋊C412yes—
146C2×C4⋊C4C22×C414yes—
147C2×C4⋊C4C22×C412yes—
148C2×C4⋊C4C22×C411yescharacteristic
149C2×C4⋊C4C2×D412yes—
150C2×C4⋊C4C2×D411yescharacteristic
151C2×C4⋊C4C2×D411yescharacteristic
152C2×C4⋊C4C2411yescharacteristic
153C2×C42—22no—
154C2×C42—21no—
155C2×C42—21no—
156C2×C42—21no—
157C2×C42—21no—
158C2×C42—21no—
159C2×C42—22no—
160C2×C42—21no—
161C2×C42—22no—
162C2×C42—24no—
163C2×C42—44no—
164C2×C42C22⋊C412yes—
165C2×C42C22⋊C412yes—
166C2×C42C22⋊C412yes—
167C2×C42C22×C412yes—
168C2×C42C2×D412yes—
169C2×C42C2×D412yes—
170C4⋊C8—44no—
171#101—216no—
172C22⋊C8—24no—
173C22⋊C8—42no—
174#97—44no—
175#97—44no—
176C4×C8—44no—
177#95—24no—
178#95—28no—
179#95—28no—
180#95—24no—
181#95—22no—
182#95—24no—
183#95—24no—
184#95C22×C414yes—
185C24C2×C22⋊C411yescharacteristic
186C2×Q8—24no—
187C2×Q8—24no—
188C2×Q8—24no—
189C2×Q8—24no—
190C2×Q8—42no—
191C2×Q8—42no—
192C2×Q8—48no—
193C2×Q8—48no—
194C2×Q8—416no—
195C2×Q8—44no—
196C2×Q8—44no—
197C2×Q8—84no—
198C2×Q8—88no—
199C2×Q8—84no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—24no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—24no—
218C22×C4—24no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—44no—
223C22×C4—44no—
224C22×C4—48no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—44no—
228C22×C4#9912yes—
229C22×C4#9911yescharacteristic
230C22×C4#9911yescharacteristic
231C22×C4#10414yes—
232C22×C4C2×C22⋊C412yes—
233C22×C4C2×C22⋊C412yes—
234C22×C4C2×C22⋊C411yescharacteristic
235C22×C4C2×C22⋊C412yes—
236C22×C4C2×C22⋊C411yescharacteristic
237C22×C4C2×C22⋊C412yes—
238C22×C4C2×C22⋊C411yescharacteristic
239C22×C4#13714yes—
240C22×C4C23×C411yescharacteristic
241C22×C4C22×D411yescharacteristic
242C22×C4C22×D411yescharacteristic
243M16—28no—
244M16—48no—
245M16—44no—
246C2×C8—44no—
247C2×C8—48no—
248C2×C8—44no—
249C2×C8—84no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—41no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—44no—
259C4⋊C4—48no—
260C4⋊C4—48no—
261C4⋊C4—44no—
262C42—22no—
263C42—22no—
264C42—22no—
265C42—22no—
266C42—22no—
267C42—22no—
268C42—22no—
269C42—22no—
270C42—22no—
271C42—22no—
272C42—22no—
273C42—22no—
274C42—48no—
275C23—22no—
276C23—22no—
277C23C2×#9911yescharacteristic
278C23C2×#9911yescharacteristic
279C23#41912yes—
280C23C2×#10412yes—
281C23C22×C22⋊C411yescharacteristic
282Q8—48no—
283Q8—48no—
284Q8—88no—
285Q8—88no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—24no—
294C2×C4—24no—
295C2×C4—24no—
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—24no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—44no—
319C2×C4—44no—
320C2×C4—48no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—88no—
326C2×C4—84no—
327C2×C4—84no—
328C2×C4#35514yes—
329C2×C4C2×#9912yes—
330C2×C4C2×#9912yes—
331C2×C4#41912yes—
332C2×C4C2×#10414yes—
333C2×C4C2×#13712yes—
334C8—48no—
335C8—84no—
336C22—24no—
337C22—24no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22#150812yes—
343C22#150812yes—
344C22#212312yes—
345C22C2×#35512yes—
346C22C22×#9911yescharacteristic
347C22C2×#41911yescharacteristic
348C22C22×#10411yescharacteristic
349C4—22no—
350C4—22no—
351C4—22no—
352C4—24no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—42no—
358C4—42no—
359C4—84no—
360C4—84no—
361C4C2×#35514yes—
362C2—21no—
363C2—21no—
364C2—22no—
365C2#1179414yesdirect product factor
366C2C2×#150811yescharacteristic
367C2C2×#212311yescharacteristic
368C2C22×#35511yescharacteristic
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. #11794C2direct (N × H)
365. C2#11794direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25682
C2×C4×#1012
C2×#14672
#117942
C2×#13532