Finite Group Databasebeta

← C2×#11816 #481864

Subgroups — C2×#11816 #481864

Order 512.

1026 conjugacy classes of subgroups.

The subgroup lattice has 453 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2396C211yesmaximal, characteristic
2C2×#1822C211yesmaximal, characteristic
3C2×#1464C211yesmaximal, characteristic
4#11816C218yesmaximal, direct product factor
5C2×#1354C212yesmaximal, complemented
6C2×#1353C212yesmaximal, complemented
7C22×C4×Q8C411yescharacteristic
8C22×#117C2211yescharacteristic
9C2×#432—21no—
10C2×#407—21no—
11#2396—22no—
12#2396—22no—
13#2396C414yes—
14#2396C2214yes—
15C2×#400C2211yescharacteristic
16C2×#399C411yescharacteristic
17C2×#398—21no—
18C2×#396—21no—
19C2×#395C2211yescharacteristic
20C2×#393C411yescharacteristic
21C2×C4×C4⋊C4—21no—
22C2×C4×C4⋊C4C411yescharacteristic
23C2×C4×C22⋊C4—21no—
24#1822—22no—
25#1822C2214yes—
26C2×#343—21no—
27C2×#343C2212yes—
28#1464—22no—
29#1464C2214yes—
30C2×#324C2212yes—
31C2×#323—21no—
32#1354C2218yescomplemented
33#1353C2218yescomplemented
34C23×Q8C2×C411yescharacteristic
35C24×C4D411yescharacteristic
36C22×M16—22no—
37C2×C4×Q8—22no—
38C2×C4×Q8—42no—
39C2×C4×Q8—41no—
40C2×C4×Q8—41no—
41C2×C4×Q8C2×C414yes—
42C2×#117—41no—
43C2×#117—41no—
44C2×#117—42no—
45C2×#117C2×C412yes—
46C2×#117D412yes—
47C2×#117D412yes—
48C2×#117C2312yes—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4C2×C411yescharacteristic
54C22×C4⋊C4D411yescharacteristic
55C22×C4⋊C4C2311yescharacteristic
56C22×C22⋊C4—21no—
57C22×C22⋊C4—21no—
58C22×C22⋊C4C2×C411yescharacteristic
59C22×C22⋊C4D411yescharacteristic
60C22×C42—21no—
61C22×C42—21no—
62C22×C42C2×C411yescharacteristic
63C22×C42D411yescharacteristic
64#432—24no—
65#432—42no—
66C2×C4⋊C8—41no—
67#407—24no—
68#407—42no—
69C2×C22⋊C8—22no—
70C2×C22⋊C8—41no—
71C2×C22⋊C8—41no—
72C2×#97—41no—
73#400—21no—
74#400—21no—
75#400C2×C412yes—
76#400C2312yes—
77#399—22no—
78#399C2×C414yes—
79#398—24no—
80#398—24no—
81#396—24no—
82#396—24no—
83#395—21no—
84#395—21no—
85#395C2×C412yes—
86#395C2312yes—
87#393—22no—
88#393C2×C414yes—
89C4×C4⋊C4—22no—
90C4×C4⋊C4—24no—
91C4×C4⋊C4—24no—
92C4×C4⋊C4C2×C414yes—
93C4×C22⋊C4—24no—
94C4×C22⋊C4—24no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95C2×C411yescharacteristic
100C2×#95C2×C411yescharacteristic
101#343—22no—
102#343—24no—
103#343C2314yes—
104#324—22no—
105#324C2314yes—
106#323—24no—
107C25C22⋊C411yescharacteristic
108C22×Q8—21no—
109C22×Q8—44no—
110C22×Q8—41no—
111C22×Q8—41no—
112C22×Q8C22×C412yes—
113C23×C4—21no—
114C23×C4—21no—
115C23×C4—21no—
116C23×C4—21no—
117C23×C4—22no—
118C23×C4—24no—
119C23×C4—21no—
120C23×C4—21no—
121C23×C4—42no—
122C23×C4C22⋊C412yes—
123C23×C4C22⋊C411yescharacteristic
124C23×C4C22⋊C411yescharacteristic
125C23×C4C22⋊C411yescharacteristic
126C23×C4C22×C411yescharacteristic
127C23×C4C2×D412yes—
128C23×C4C2×D411yescharacteristic
129C23×C4C2×D411yescharacteristic
130C2×M16—24no—
131C2×M16—42no—
132C2×M16—44no—
133C2×M16—44no—
134C22×C8—42no—
135C22×C8—42no—
136C4×Q8—44no—
137C4×Q8—44no—
138C4×Q8—44no—
139C4×Q8—44no—
140#117—42no—
141#117—42no—
142#117—42no—
143#117—42no—
144#117—42no—
145#117—42no—
146#117—42no—
147#117—42no—
148C2×C4⋊C4—24no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—24no—
151C2×C4⋊C4—24no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—22no—
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—44no—
161C2×C4⋊C4—44no—
162C2×C4⋊C4—44no—
163C2×C4⋊C4—42no—
164C2×C4⋊C4—42no—
165C2×C4⋊C4C22⋊C412yes—
166C2×C4⋊C4C22×C412yes—
167C2×C4⋊C4C22×C411yescharacteristic
168C2×C4⋊C4C2×D412yes—
169C2×C4⋊C4C2×D411yescharacteristic
170C2×C4⋊C4C2×D411yescharacteristic
171C2×C4⋊C4C2411yescharacteristic
172C2×C22⋊C4—24no—
173C2×C22⋊C4—24no—
174C2×C22⋊C4—41no—
175C2×C22⋊C4—41no—
176C2×C22⋊C4—41no—
177C2×C22⋊C4—41no—
178C2×C22⋊C4—44no—
179C2×C22⋊C4—44no—
180C2×C22⋊C4C22⋊C412yes—
181C2×C22⋊C4C22⋊C412yes—
182C2×C22⋊C4C22×C412yes—
183C2×C22⋊C4C2×D412yes—
184C2×C42—22no—
185C2×C42—21no—
186C2×C42—21no—
187C2×C42—21no—
188C2×C42—21no—
189C2×C42—22no—
190C2×C42—24no—
191C2×C42—24no—
192C2×C42—44no—
193C2×C42—42no—
194C2×C42—41no—
195C2×C42—41no—
196C2×C42C22⋊C412yes—
197C2×C42C22⋊C412yes—
198C2×C42C22×C412yes—
199C2×C42C2×D412yes—
200C4⋊C8—44no—
201C22⋊C8—24no—
202C22⋊C8—42no—
203C22⋊C8—44no—
204C22⋊C8—44no—
205#97—44no—
206#95—22no—
207#95—22no—
208#95—24no—
209#95—22no—
210#95—21no—
211#95—21no—
212#95—22no—
213#95—22no—
214#95—22no—
215#95C22×C412yes—
216#95C22×C412yes—
217C24—21no—
218C24—22no—
219C24—21no—
220C24—22no—
221C24—42no—
222C24—42no—
223C24C2×C22⋊C411yescharacteristic
224C24C2×C22⋊C412yes—
225C2×Q8—44no—
226C2×Q8—42no—
227C2×Q8—44no—
228C2×Q8—42no—
229C2×Q8—48no—
230C2×Q8—44no—
231C2×Q8—44no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—24no—
238C22×C4—24no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—24no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—24no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—44no—
260C22×C4—44no—
261C22×C4—48no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—42no—
278C22×C4#9912yes—
279C22×C4#9911yescharacteristic
280C22×C4#9911yescharacteristic
281C22×C4C2×C22⋊C412yes—
282C22×C4C2×C22⋊C411yescharacteristic
283C22×C4C2×C22⋊C411yescharacteristic
284C22×C4C2×C22⋊C411yescharacteristic
285C22×C4C2×C22⋊C412yes—
286C22×C4C2×C22⋊C412yes—
287C22×C4#13714yes—
288C22×C4C23×C411yescharacteristic
289C22×C4C22×D411yescharacteristic
290C22×C4C22×D411yescharacteristic
291M16—44no—
292M16—44no—
293M16—84no—
294C2×C8—44no—
295C2×C8—44no—
296C2×C8—84no—
297C2×C8—84no—
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—48no—
310C4⋊C4—42no—
311C22⋊C4—42no—
312C22⋊C4—42no—
313C22⋊C4—42no—
314C22⋊C4—42no—
315C22⋊C4—48no—
316C22⋊C4—48no—
317C42—22no—
318C42—22no—
319C42—22no—
320C42—22no—
321C42—22no—
322C42—22no—
323C42—22no—
324C42—22no—
325C42—48no—
326C42—44no—
327C42—44no—
328C23—22no—
329C23—22no—
330C23—22no—
331C23—22no—
332C23—22no—
333C23—42no—
334C23—42no—
335C23—48no—
336C23—42no—
337C23—42no—
338C23—42no—
339C23—42no—
340C23—81no—
341C23—81no—
342C23—84no—
343C23C2×#9911yescharacteristic
344C23C2×#9911yescharacteristic
345C23#41912yes—
346C23#42112yes—
347C23C22×C22⋊C411yescharacteristic
348Q8—44no—
349Q8—44no—
350Q8—48no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—24no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—22no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—44no—
371C2×C4—44no—
372C2×C4—44no—
373C2×C4—44no—
374C2×C4—42no—
375C2×C4—48no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—44no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—44no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—84no—
402C2×C4—82no—
403C2×C4—82no—
404C2×C4C2×#9912yes—
405C2×C4C2×#9912yes—
406C2×C4#41912yes—
407C2×C4C2×#13712yes—
408C8—84no—
409C8—84no—
410C22—24no—
411C22—24no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—44no—
417C22—42no—
418C22—42no—
419C22—42no—
420C22—82no—
421C22—84no—
422C22—84no—
423C22#151112yes—
424C22#151112yes—
425C22#212012yes—
426C22#213212yes—
427C22C22×#9911yescharacteristic
428C22C2×#41911yescharacteristic
429C22C2×#42111yescharacteristic
430C4—22no—
431C4—22no—
432C4—22no—
433C4—22no—
434C4—44no—
435C4—41no—
436C4—44no—
437C4—41no—
438C4—41no—
439C4—41no—
440C4—42no—
441C4—42no—
442C4—82no—
443C4—82no—
444C2—21no—
445C2—21no—
446C2—22no—
447C2—82no—
448C2#1181614yesdirect product factor
449C2C2×#151111yescharacteristic
450C2C2×#212011yescharacteristic
451C2C2×#213211yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC25C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#117 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #11816C2direct (N × H)
5. C2×#1354C2semidirect
6. C2×#1353C2semidirect
32. #1354C22semidirect
33. #1353C22semidirect
448. C2#11816direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#23962
C2×#18222
C2×#14642
#118162
C2×#13542
C2×#13532