Finite Group Databasebeta

← C2×#11833 #481916

Subgroups — C2×#11833 #481916

Order 512.

1008 conjugacy classes of subgroups.

The subgroup lattice has 479 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2632C211yesmaximal, characteristic
2C2×#1801C211yesmaximal, characteristic, complemented
3C2×#1467C211yesmaximal, characteristic, complemented
4#11833C218yesmaximal, direct product factor
5C2×#1354C212yesmaximal, complemented
6C2×#1345C212yesmaximal
7C22×#124C411yescharacteristic
8C22×C4×Q8C2211yescharacteristic
9C2×#432—21no—
10C2×#423—21no—
11C22×#101—21no—
12#2632—22no—
13#2632—22no—
14#2632C414yes—
15#2632C2214yes—
16C2×#399—21no—
17C2×#395C411yescharacteristic
18C2×#395C2211yescharacteristic
19C2×#394C411yescharacteristic
20C2×#394C2211yescharacteristic
21C2×#393—21no—
22C2×#388—21no—
23C2×#388—21no—
24C2×#383C411yescharacteristic
25#1801—22no—
26#1801C2214yescomplemented
27C2×#343C2212yes—
28#1467—22no—
29#1467C2214yescomplemented
30C2×#324—21no—
31C2×#324C2212yes—
32#1354C2218yescomplemented
33#1345C2218yes—
34C23×Q8C2×C411yescharacteristic
35C23×Q8D411yescharacteristic
36C23×D4C2×C411yescharacteristic
37C22×M16—22no—
38C2×#124—22no—
39C2×#124—42no—
40C2×#124—41no—
41C2×#124—41no—
42C2×#124C2×C414yes—
43C2×C4×Q8—41no—
44C2×C4×Q8—41no—
45C2×C4×Q8—42no—
46C2×C4×Q8C2×C412yes—
47C2×C4×Q8D412yes—
48C2×C4×Q8D412yes—
49C2×C4×Q8C2312yes—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4C2×C411yescharacteristic
53C22×C4⋊C4D411yescharacteristic
54C22×C4⋊C4C2311yescharacteristic
55C22×C22⋊C4—21no—
56C22×C22⋊C4—21no—
57C22×C22⋊C4—21no—
58C22×C22⋊C4—21no—
59C22×C22⋊C4—21no—
60C22×C22⋊C4—21no—
61C22×C42C2×C411yescharacteristic
62C22×C42D411yescharacteristic
63C22×C42D411yescharacteristic
64#432—24no—
65#432—42no—
66#423—24no—
67#423—42no—
68C2×C4⋊C8—41no—
69C2×C4⋊C8—41no—
70C2×C4⋊C8—41no—
71C2×#101—24no—
72C2×#101—44no—
73C2×C22⋊C8—22no—
74C2×#97—41no—
75#399—24no—
76#399—24no—
77#395—22no—
78#395—21no—
79#395—21no—
80#395C2×C412yes—
81#395C2×C414yes—
82#395C2312yes—
83#394—22no—
84#394—21no—
85#394—21no—
86#394C2×C412yes—
87#394C2×C414yes—
88#394C2312yes—
89#393—24no—
90#393—24no—
91#388—24no—
92#388—24no—
93#388—24no—
94#388—24no—
95#383—22no—
96#383C2×C414yes—
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—
108C25—21no—
109C22×Q8—21no—
110C22×Q8—22no—
111C22×Q8—22no—
112C22×Q8—41no—
113C22×Q8—41no—
114C22×Q8—42no—
115C22×Q8—41no—
116C22×Q8—41no—
117C22×Q8—82no—
118C22×Q8C22⋊C412yes—
119C22×Q8C22×C412yes—
120C22×Q8C2×D412yes—
121C22×D4—21no—
122C22×D4—41no—
123C22×D4—41no—
124C22×D4—82no—
125C22×D4C22×C412yes—
126C23×C4—21no—
127C23×C4—21no—
128C23×C4—21no—
129C23×C4C22⋊C411yescharacteristic
130C23×C4C22⋊C411yescharacteristic
131C23×C4C22⋊C411yescharacteristic
132C23×C4C22⋊C411yescharacteristic
133C23×C4C22×C411yescharacteristic
134C23×C4C2×D411yescharacteristic
135C23×C4C2×D411yescharacteristic
136C2×M16—24no—
137C2×M16—42no—
138C2×M16—44no—
139C2×M16—44no—
140C22×C8—42no—
141C22×C8—42no—
142#124—44no—
143#124—44no—
144#124—44no—
145#124—44no—
146C4×Q8—42no—
147C4×Q8—42no—
148C4×Q8—42no—
149C4×Q8—42no—
150C4×Q8—42no—
151C4×Q8—42no—
152C4×Q8—42no—
153C4×Q8—42no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—24no—
156C2×C4⋊C4—22no—
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—82no—
164C2×C4⋊C4—82no—
165C2×C4⋊C4C22⋊C412yes—
166C2×C4⋊C4C22⋊C412yes—
167C2×C4⋊C4C22×C412yes—
168C2×C4⋊C4C22×C411yescharacteristic
169C2×C4⋊C4C2×D412yes—
170C2×C4⋊C4C2×D411yescharacteristic
171C2×C4⋊C4C2×D411yescharacteristic
172C2×C4⋊C4C2411yescharacteristic
173C2×C22⋊C4—24no—
174C2×C22⋊C4—24no—
175C2×C22⋊C4—24no—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—24no—
180C2×C22⋊C4—22no—
181C2×C22⋊C4—44no—
182C2×C22⋊C4—42no—
183C2×C22⋊C4—42no—
184C2×C22⋊C4—42no—
185C2×C22⋊C4—41no—
186C2×C22⋊C4—41no—
187C2×C22⋊C4—42no—
188C2×C22⋊C4—42no—
189C2×C22⋊C4—82no—
190C2×C22⋊C4—82no—
191C2×C42—22no—
192C2×C42—21no—
193C2×C42—21no—
194C2×C42—21no—
195C2×C42—21no—
196C2×C42—21no—
197C2×C42—21no—
198C2×C42—22no—
199C2×C42—22no—
200C2×C42C22⋊C412yes—
201C2×C42C22⋊C412yes—
202C2×C42C22⋊C412yes—
203C2×C42C22×C412yes—
204C2×C42C2×D412yes—
205C2×C42C2×D412yes—
206C4⋊C8—44no—
207C4⋊C8—44no—
208C4⋊C8—44no—
209#101—48no—
210C22⋊C8—24no—
211C22⋊C8—42no—
212#97—44no—
213#95—24no—
214#95—24no—
215#95—24no—
216#95—22no—
217#95—21no—
218#95—21no—
219#95—22no—
220#95C22×C412yes—
221#95C22×C412yes—
222C24—22no—
223C24—42no—
224C24—42no—
225C24—42no—
226C24—42no—
227C24—41no—
228C24—41no—
229C24—42no—
230C24—42no—
231C24C2×C22⋊C411yescharacteristic
232C2×Q8—22no—
233C2×Q8—22no—
234C2×Q8—24no—
235C2×Q8—42no—
236C2×Q8—42no—
237C2×Q8—42no—
238C2×Q8—42no—
239C2×Q8—44no—
240C2×Q8—44no—
241C2×Q8—44no—
242C2×Q8—44no—
243C2×Q8—42no—
244C2×Q8—42no—
245C2×Q8—82no—
246C2×Q8—82no—
247C2×Q8—84no—
248C2×Q8—84no—
249C2×D4—42no—
250C2×D4—42no—
251C2×D4—82no—
252C2×D4—84no—
253C2×D4—84no—
254C2×D4—82no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—22no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4#9911yescharacteristic
290C22×C4#9911yescharacteristic
291C22×C4#9912yes—
292C22×C4C2×C22⋊C412yes—
293C22×C4C2×C22⋊C412yes—
294C22×C4C2×C22⋊C411yescharacteristic
295C22×C4C2×C22⋊C411yescharacteristic
296C22×C4C2×C22⋊C411yescharacteristic
297C22×C4C2×C22⋊C412yes—
298C22×C4C2×C22⋊C412yes—
299C22×C4AGL(1,ℤ/8)12yes—
300C22×C4#13712yes—
301C22×C4C23×C411yescharacteristic
302C22×C4C22×D411yescharacteristic
303C22×C4C22×D411yescharacteristic
304M16—44no—
305M16—44no—
306M16—84no—
307C2×C8—44no—
308C2×C8—44no—
309C2×C8—84no—
310C2×C8—84no—
311C4⋊C4—42no—
312C4⋊C4—42no—
313C4⋊C4—41no—
314C4⋊C4—42no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—42no—
318C4⋊C4—41no—
319C4⋊C4—84no—
320C4⋊C4—82no—
321C4⋊C4—82no—
322C22⋊C4—48no—
323C22⋊C4—48no—
324C22⋊C4—42no—
325C22⋊C4—42no—
326C22⋊C4—44no—
327C22⋊C4—44no—
328C22⋊C4—44no—
329C22⋊C4—84no—
330C22⋊C4—82no—
331C22⋊C4—82no—
332C42—22no—
333C42—22no—
334C42—22no—
335C42—22no—
336C42—22no—
337C42—22no—
338C42—22no—
339C42—22no—
340C42—22no—
341C42—22no—
342C42—22no—
343C42—22no—
344C23—22no—
345C23—22no—
346C23—42no—
347C23—42no—
348C23—42no—
349C23—42no—
350C23—42no—
351C23—42no—
352C23—42no—
353C23—82no—
354C23—84no—
355C23—84no—
356C23—84no—
357C23—84no—
358C23—82no—
359C23—82no—
360C23—82no—
361C23—82no—
362C23—82no—
363C23C2×#9911yescharacteristic
364C23C2×#9911yescharacteristic
365C23#41712yes—
366C23#42112yes—
367C23C22×C22⋊C411yescharacteristic
368Q8—44no—
369Q8—44no—
370Q8—48no—
371Q8—84no—
372Q8—84no—
373D4—84no—
374D4—84no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—84no—
423C2×C4—84no—
424C2×C4—82no—
425C2×C4—82no—
426C2×C4C2×#9912yes—
427C2×C4C2×#9912yes—
428C2×C4#41712yes—
429C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
430C2×C4C2×#13711yescharacteristic
431C8—84no—
432C8—84no—
433C22—24no—
434C22—24no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—82no—
440C22—82no—
441C22—82no—
442C22—82no—
443C22—82no—
444C22—82no—
445C22—82no—
446C22—164no—
447C22—164no—
448C22#151312yes—
449C22#151312yes—
450C22#212212yes—
451C22#213312yes—
452C22C22×#9911yescharacteristic
453C22C2×#41711yescharacteristic
454C22C2×#42111yescharacteristic
455C4—22no—
456C4—22no—
457C4—21no—
458C4—21no—
459C4—22no—
460C4—41no—
461C4—41no—
462C4—41no—
463C4—41no—
464C4—42no—
465C4—42no—
466C4—42no—
467C4—82no—
468C4—82no—
469C4—82no—
470C2—21no—
471C2—21no—
472C2—22no—
473C2—162no—
474C2#1183314yesdirect product factor
475C2C2×#151311yescharacteristic
476C2C2×#212211yescharacteristic
477C2C2×#213311yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC23×D4C2×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
2. C2×#1801C2semidirect
3. C2×#1467C2semidirect
4. #11833C2direct (N × H)
5. C2×#1354C2semidirect
26. #1801C22semidirect
29. #1467C22semidirect
32. #1354C22semidirect
474. C2#11833direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#26322
C2×#18012
C2×#14672
#118332
C2×#13542
C2×#13452