Finite Group Databasebeta

← C2×#11905 #482128

Subgroups — C2×#11905 #482128

Order 512.

976 conjugacy classes of subgroups.

The subgroup lattice has 437 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2581C211yesmaximal, characteristic
2C2×#1801C211yesmaximal, characteristic
3C2×#1461C211yesmaximal, characteristic
4#11905C218yesmaximal, direct product factor
5C2×#1354C212yesmaximal
6C2×#1353C212yesmaximal
7C22×C4×Q8C411yescharacteristic
8C22×C4×Q8C2211yescharacteristic
9C2×#431—21no—
10C2×#423—21no—
11C22×#101—21no—
12#2581—22no—
13#2581—22no—
14#2581C414yes—
15#2581C2214yes—
16C2×#400C411yescharacteristic
17C2×#400C2211yescharacteristic
18C2×#395C411yescharacteristic
19C2×#395C2211yescharacteristic
20C2×#391—21no—
21C2×#389—21no—
22C2×#387—21no—
23C2×#387—21no—
24C2×#382C411yescharacteristic
25#1801—22no—
26#1801C2214yes—
27C2×#343C2212yes—
28#1461—22no—
29#1461C2214yes—
30C2×#324—21no—
31C2×#324C2212yes—
32#1354C2218yes—
33#1353C2218yes—
34C23×Q8C2×C411yescharacteristic
35C23×Q8D411yescharacteristic
36C22×M16—22no—
37C2×C4×Q8—22no—
38C2×C4×Q8—41no—
39C2×C4×Q8—41no—
40C2×C4×Q8—42no—
41C2×C4×Q8—42no—
42C2×C4×Q8—41no—
43C2×C4×Q8—41no—
44C2×C4×Q8C2×C414yes—
45C2×C4×Q8C2×C412yes—
46C2×C4×Q8D412yes—
47C2×C4×Q8D412yes—
48C2×C4×Q8C2312yes—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4C2×C411yescharacteristic
54C22×C4⋊C4C2×C411yescharacteristic
55C22×C4⋊C4D411yescharacteristic
56C22×C4⋊C4C2311yescharacteristic
57C22×C42—21no—
58C22×C42C2×C411yescharacteristic
59C22×C42D411yescharacteristic
60C22×C42D411yescharacteristic
61#431—24no—
62#431—42no—
63#423—24no—
64#423—42no—
65C2×C4⋊C8—41no—
66C2×C4⋊C8—41no—
67C2×C4⋊C8—41no—
68C2×#101—24no—
69C2×#101—44no—
70C2×C22⋊C8—22no—
71C2×C4×C8—41no—
72#400—22no—
73#400—21no—
74#400—21no—
75#400C2×C412yes—
76#400C2×C414yes—
77#400C2312yes—
78#395—22no—
79#395—21no—
80#395—21no—
81#395C2×C412yes—
82#395C2×C414yes—
83#395C2312yes—
84#391—24no—
85#391—24no—
86#389—24no—
87#389—24no—
88#387—24no—
89#387—24no—
90#387—24no—
91#387—24no—
92#382—22no—
93#382C2×C414yes—
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—21no—
109C22×Q8—41no—
110C22×Q8—41no—
111C22×Q8—42no—
112C22×Q8—44no—
113C22×Q8—41no—
114C22×Q8—41no—
115C22×Q8C22⋊C412yes—
116C22×Q8SD1614yes—
117C22×Q8Q1614yes—
118C22×Q8C22×C412yes—
119C22×Q8C2×D412yes—
120C23×C4—21no—
121C23×C4—21no—
122C23×C4—21no—
123C23×C4—21no—
124C23×C4C22⋊C411yescharacteristic
125C23×C4C22⋊C411yescharacteristic
126C23×C4C22⋊C411yescharacteristic
127C23×C4C22⋊C411yescharacteristic
128C23×C4C22×C411yescharacteristic
129C23×C4C2×D411yescharacteristic
130C23×C4C2×D411yescharacteristic
131C2×M16—24no—
132C2×M16—42no—
133C2×M16—44no—
134C2×M16—44no—
135C22×C8—42no—
136C22×C8—42no—
137C4×Q8—42no—
138C4×Q8—42no—
139C4×Q8—42no—
140C4×Q8—42no—
141C4×Q8—42no—
142C4×Q8—42no—
143C4×Q8—42no—
144C4×Q8—42no—
145C4×Q8—44no—
146C4×Q8—44no—
147C4×Q8—44no—
148C4×Q8—44no—
149C2×C4⋊C4—24no—
150C2×C4⋊C4—24no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—24no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4—41no—
160C2×C4⋊C4—41no—
161C2×C4⋊C4—41no—
162C2×C4⋊C4—41no—
163C2×C4⋊C4—44no—
164C2×C4⋊C4—44no—
165C2×C4⋊C4—44no—
166C2×C4⋊C4—42no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—41no—
169C2×C4⋊C4C22⋊C412yes—
170C2×C4⋊C4C22⋊C412yes—
171C2×C4⋊C4C22×C412yes—
172C2×C4⋊C4C22×C412yes—
173C2×C4⋊C4C22×C411yescharacteristic
174C2×C4⋊C4C2×D412yes—
175C2×C4⋊C4C2×D411yescharacteristic
176C2×C4⋊C4C2×D411yescharacteristic
177C2×C4⋊C4C2411yescharacteristic
178C2×C42—22no—
179C2×C42—21no—
180C2×C42—21no—
181C2×C42—21no—
182C2×C42—21no—
183C2×C42—21no—
184C2×C42—21no—
185C2×C42—22no—
186C2×C42—22no—
187C2×C42—24no—
188C2×C42—42no—
189C2×C42—42no—
190C2×C42C22⋊C412yes—
191C2×C42C22⋊C412yes—
192C2×C42C22⋊C412yes—
193C2×C42C22×C412yes—
194C2×C42C2×D412yes—
195C2×C42C2×D412yes—
196C4⋊C8—44no—
197C4⋊C8—44no—
198C4⋊C8—44no—
199#101—48no—
200C22⋊C8—24no—
201C22⋊C8—42no—
202C4×C8—44no—
203#95—24no—
204#95—22no—
205#95—24no—
206#95—22no—
207#95—24no—
208#95—22no—
209#95—24no—
210#95—21no—
211#95—21no—
212#95—22no—
213#95—22no—
214#95—22no—
215#95C22×C412yes—
216#95C22×C412yes—
217C24C2×C22⋊C411yescharacteristic
218C2×Q8—42no—
219C2×Q8—42no—
220C2×Q8—42no—
221C2×Q8—44no—
222C2×Q8—44no—
223C2×Q8—44no—
224C2×Q8—44no—
225C2×Q8—42no—
226C2×Q8—44no—
227C2×Q8—42no—
228C2×Q8—44no—
229C2×Q8—42no—
230C2×Q8—48no—
231C2×Q8—44no—
232C2×Q8—44no—
233C2×Q8#10318yes—
234C2×Q8C2×SD1614yes—
235C2×Q8C2×Q1614yes—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—24no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—44no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4#9911yescharacteristic
273C22×C4#9911yescharacteristic
274C22×C4#9912yes—
275C22×C4#10314yes—
276C22×C4#10314yes—
277C22×C4C2×C22⋊C411yescharacteristic
278C22×C4C2×C22⋊C412yes—
279C22×C4C2×C22⋊C412yes—
280C22×C4C2×C22⋊C411yescharacteristic
281C22×C4C2×C22⋊C411yescharacteristic
282C22×C4C2×C22⋊C412yes—
283C22×C4C2×C22⋊C412yes—
284C22×C4C2×SD1612yes—
285C22×C4C2×Q1612yes—
286C22×C4C23×C411yescharacteristic
287C22×C4C22×D411yescharacteristic
288C22×C4C22×D411yescharacteristic
289M16—44no—
290M16—44no—
291M16—84no—
292C2×C8—44no—
293C2×C8—44no—
294C2×C8—84no—
295C2×C8—84no—
296C4⋊C4—42no—
297C4⋊C4—42no—
298C4⋊C4—42no—
299C4⋊C4—41no—
300C4⋊C4—42no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—42no—
305C4⋊C4—48no—
306C4⋊C4—48no—
307C4⋊C4—44no—
308C4⋊C4—44no—
309C4⋊C4—42no—
310C4⋊C4—44no—
311C4⋊C4—44no—
312C42—22no—
313C42—22no—
314C42—22no—
315C42—22no—
316C42—22no—
317C42—22no—
318C42—22no—
319C42—22no—
320C42—22no—
321C42—22no—
322C42—22no—
323C42—22no—
324C42—48no—
325C23—22no—
326C23—22no—
327C23C2×#9911yescharacteristic
328C23C2×#9911yescharacteristic
329C23C2×#10312yes—
330C23#42112yes—
331C23C22×C22⋊C411yescharacteristic
332Q8—48no—
333Q8—44no—
334Q8—44no—
335Q8—44no—
336Q8—44no—
337Q8—48no—
338C2×C4—22no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—24no—
351C2×C4—24no—
352C2×C4—24no—
353C2×C4—24no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—24no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—22no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—44no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—44no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—44no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—84no—
388C2×C4—84no—
389C2×C4—82no—
390C2×C4—82no—
391C2×C4C2×#9912yes—
392C2×C4C2×#9912yes—
393C2×C4C2×#10314yes—
394C2×C4C2×#10314yes—
395C2×C4C2×#10312yes—
396C2×C4C22×SD1611yescharacteristic
397C2×C4C22×Q1611yescharacteristic
398C8—84no—
399C8—84no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—24no—
405C22—24no—
406C22#152012yes—
407C22#152012yes—
408C22#212012yes—
409C22#213312yes—
410C22C22×#9911yescharacteristic
411C22C22×#10311yescharacteristic
412C22C2×#42111yescharacteristic
413C4—22no—
414C4—22no—
415C4—21no—
416C4—21no—
417C4—24no—
418C4—22no—
419C4—24no—
420C4—41no—
421C4—44no—
422C4—41no—
423C4—41no—
424C4—41no—
425C4—42no—
426C4—82no—
427C4—82no—
428C4—82no—
429C2—21no—
430C2—21no—
431C2—22no—
432C2#1190514yesdirect product factor
433C2C2×#152011yescharacteristic
434C2C2×#212011yescharacteristic
435C2C2×#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. #11905C2direct (N × H)
432. C2#11905direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25812
C2×#18012
C2×#14612
#119052
C2×#13542
C2×#13532