Finite Group Databasebeta

← C2×#11804 #481826

Subgroups — C2×#11804 #481826

Order 512.

1318 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2392C211yesmaximal, characteristic
2C2×#1822C211yesmaximal, characteristic, complemented
3C2×#1464C211yesmaximal, characteristic, complemented
4#11804C218yesmaximal, direct product factor
5C2×#1346C212yesmaximal, complemented
6C2×#1345C212yesmaximal, complemented
7C22×C4×D4—21no—
8C22×C4×D4C411yescharacteristic
9C22×#117C2211yescharacteristic
10C2×#432—21no—
11C2×#407—21no—
12#2392—22no—
13#2392—22no—
14#2392C414yes—
15#2392C2214yes—
16C2×#398C2211yescharacteristic
17C2×#397C411yescharacteristic
18C2×#396—21no—
19C2×#394—21no—
20C2×#394C2211yescharacteristic
21C2×#392C411yescharacteristic
22C2×C4×C4⋊C4C411yescharacteristic
23C2×C4×C22⋊C4—21no—
24#1822—22no—
25#1822C2214yescomplemented
26C2×#343—21no—
27C2×#343C2212yes—
28#1464—22no—
29#1464C2214yescomplemented
30C2×#324C2212yes—
31C2×#323—21no—
32#1346C2218yescomplemented
33#1345C2218yescomplemented
34C23×D4—21no—
35C23×D4C2×C411yescharacteristic
36C24×C4—21no—
37C24×C4D411yescharacteristic
38C22×M16—22no—
39C2×C4×D4—24no—
40C2×C4×D4—24no—
41C2×C4×D4—22no—
42C2×C4×D4—42no—
43C2×C4×D4—41no—
44C2×C4×D4—41no—
45C2×C4×D4—48no—
46C2×C4×D4C2×C414yes—
47C2×#117—41no—
48C2×#117—41no—
49C2×#117—42no—
50C2×#117C2×C412yes—
51C2×#117D412yes—
52C2×#117D412yes—
53C2×#117C2312yes—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4C2×C411yescharacteristic
57C22×C4⋊C4D411yescharacteristic
58C22×C4⋊C4C2311yescharacteristic
59C22×C22⋊C4—21no—
60C22×C22⋊C4—21no—
61C22×C22⋊C4—21no—
62C22×C22⋊C4—21no—
63C22×C22⋊C4—21no—
64C22×C22⋊C4C2×C411yescharacteristic
65C22×C22⋊C4D411yescharacteristic
66C22×C42—21no—
67C22×C42C2×C411yescharacteristic
68C22×C42D411yescharacteristic
69#432—24no—
70#432—42no—
71C2×C4⋊C8—41no—
72#407—24no—
73#407—42no—
74C2×C22⋊C8—22no—
75C2×C22⋊C8—41no—
76C2×C22⋊C8—41no—
77C2×#97—41no—
78#398—21no—
79#398—21no—
80#398C2×C412yes—
81#398C2312yes—
82#397—22no—
83#397C2×C414yes—
84#396—24no—
85#396—24no—
86#394—21no—
87#394—21no—
88#394—24no—
89#394—24no—
90#394C2×C412yes—
91#394C2312yes—
92#392—22no—
93#392C2×C414yes—
94C4×C4⋊C4—22no—
95C4×C4⋊C4C2×C414yes—
96C4×C22⋊C4—24no—
97C4×C22⋊C4—24no—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95C2×C411yescharacteristic
101C2×#95C2×C411yescharacteristic
102#343—22no—
103#343—24no—
104#343C2314yes—
105#324—22no—
106#324C2314yes—
107#323—24no—
108C25—21no—
109C25C22⋊C411yescharacteristic
110C22×D4—24no—
111C22×D4—21no—
112C22×D4—41no—
113C22×D4—41no—
114C22×D4—44no—
115C22×D4—44no—
116C22×D4—44no—
117C22×D4—44no—
118C22×D4C22×C412yes—
119C23×C4—21no—
120C23×C4—21no—
121C23×C4—21no—
122C23×C4—22no—
123C23×C4—24no—
124C23×C4—21no—
125C23×C4—21no—
126C23×C4—24no—
127C23×C4—42no—
128C23×C4—44no—
129C23×C4—44no—
130C23×C4—42no—
131C23×C4—41no—
132C23×C4—41no—
133C23×C4C22⋊C412yes—
134C23×C4C22⋊C411yescharacteristic
135C23×C4C22⋊C411yescharacteristic
136C23×C4C22⋊C411yescharacteristic
137C23×C4C22×C411yescharacteristic
138C23×C4C2×D412yes—
139C23×C4C2×D411yescharacteristic
140C23×C4C2×D411yescharacteristic
141C2×M16—24no—
142C2×M16—42no—
143C2×M16—44no—
144C2×M16—44no—
145C22×C8—42no—
146C22×C8—42no—
147C4×D4—44no—
148C4×D4—44no—
149C4×D4—44no—
150C4×D4—44no—
151C4×D4—416no—
152C4×D4—416no—
153#117—42no—
154#117—42no—
155#117—42no—
156#117—42no—
157#117—42no—
158#117—42no—
159#117—42no—
160#117—42no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—24no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—41no—
166C2×C4⋊C4—41no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—41no—
169C2×C4⋊C4—41no—
170C2×C4⋊C4—41no—
171C2×C4⋊C4—44no—
172C2×C4⋊C4—44no—
173C2×C4⋊C4C22⋊C412yes—
174C2×C4⋊C4C22×C412yes—
175C2×C4⋊C4C22×C411yescharacteristic
176C2×C4⋊C4C2×D412yes—
177C2×C4⋊C4C2×D411yescharacteristic
178C2×C4⋊C4C2×D411yescharacteristic
179C2×C4⋊C4C2411yescharacteristic
180C2×C22⋊C4—24no—
181C2×C22⋊C4—22no—
182C2×C22⋊C4—24no—
183C2×C22⋊C4—24no—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—41no—
188C2×C22⋊C4—41no—
189C2×C22⋊C4—41no—
190C2×C22⋊C4—41no—
191C2×C22⋊C4—44no—
192C2×C22⋊C4—42no—
193C2×C22⋊C4—42no—
194C2×C22⋊C4—44no—
195C2×C22⋊C4—44no—
196C2×C22⋊C4—44no—
197C2×C22⋊C4C22⋊C412yes—
198C2×C22⋊C4C22⋊C412yes—
199C2×C22⋊C4C22×C412yes—
200C2×C22⋊C4C2×D412yes—
201C2×C42—22no—
202C2×C42—21no—
203C2×C42—21no—
204C2×C42—21no—
205C2×C42—21no—
206C2×C42—22no—
207C2×C42—24no—
208C2×C42—44no—
209C2×C42C22⋊C412yes—
210C2×C42C22⋊C412yes—
211C2×C42C22×C412yes—
212C2×C42C2×D412yes—
213C4⋊C8—44no—
214C22⋊C8—24no—
215C22⋊C8—42no—
216C22⋊C8—44no—
217C22⋊C8—44no—
218#97—44no—
219#95—22no—
220#95—24no—
221#95—21no—
222#95—21no—
223#95—22no—
224#95C22×C412yes—
225#95C22×C412yes—
226C24—24no—
227C24—22no—
228C24—21no—
229C24—22no—
230C24—21no—
231C24—22no—
232C24—42no—
233C24—42no—
234C24—42no—
235C24—42no—
236C24—42no—
237C24—41no—
238C24—41no—
239C24—42no—
240C24—42no—
241C24C2×C22⋊C411yescharacteristic
242C24C2×C22⋊C412yes—
243C2×D4—42no—
244C2×D4—42no—
245C2×D4—48no—
246C2×D4—48no—
247C2×D4—48no—
248C2×D4—44no—
249C2×D4—44no—
250C2×D4—48no—
251C2×D4—432no—
252C2×D4—44no—
253C2×D4—44no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—24no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—24no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—24no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—44no—
280C22×C4—44no—
281C22×C4—48no—
282C22×C4—48no—
283C22×C4—48no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—44no—
298C22×C4—44no—
299C22×C4—88no—
300C22×C4—84no—
301C22×C4—84no—
302C22×C4#9912yes—
303C22×C4#9911yescharacteristic
304C22×C4#9911yescharacteristic
305C22×C4C2×C22⋊C412yes—
306C22×C4C2×C22⋊C411yescharacteristic
307C22×C4C2×C22⋊C411yescharacteristic
308C22×C4C2×C22⋊C411yescharacteristic
309C22×C4C2×C22⋊C412yes—
310C22×C4C2×C22⋊C412yes—
311C22×C4AGL(1,ℤ/8)14yes—
312C22×C4C23×C411yescharacteristic
313C22×C4C22×D411yescharacteristic
314C22×C4C22×D411yescharacteristic
315M16—44no—
316M16—44no—
317M16—84no—
318C2×C8—44no—
319C2×C8—44no—
320C2×C8—84no—
321C2×C8—84no—
322C4⋊C4—42no—
323C4⋊C4—41no—
324C4⋊C4—42no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—42no—
329C4⋊C4—48no—
330C4⋊C4—42no—
331C4⋊C4—44no—
332C4⋊C4—44no—
333C22⋊C4—42no—
334C22⋊C4—42no—
335C22⋊C4—42no—
336C22⋊C4—42no—
337C22⋊C4—48no—
338C22⋊C4—48no—
339C22⋊C4—44no—
340C22⋊C4—44no—
341C22⋊C4—48no—
342C22⋊C4—44no—
343C22⋊C4—44no—
344C42—22no—
345C42—22no—
346C42—22no—
347C42—22no—
348C42—22no—
349C42—22no—
350C42—22no—
351C42—22no—
352C42—48no—
353C23—22no—
354C23—22no—
355C23—24no—
356C23—22no—
357C23—22no—
358C23—22no—
359C23—42no—
360C23—42no—
361C23—42no—
362C23—48no—
363C23—48no—
364C23—42no—
365C23—44no—
366C23—42no—
367C23—48no—
368C23—42no—
369C23—44no—
370C23—42no—
371C23—42no—
372C23—42no—
373C23—42no—
374C23—42no—
375C23—42no—
376C23—81no—
377C23—81no—
378C23—84no—
379C23—84no—
380C23—84no—
381C23—82no—
382C23—82no—
383C23—82no—
384C23—82no—
385C23C2×#9911yescharacteristic
386C23C2×#9911yescharacteristic
387C23#41812yes—
388C23#42112yes—
389C23C22×C22⋊C411yescharacteristic
390D4—44no—
391D4—432no—
392D4—44no—
393D4—48no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—22no—
397C2×C4—21no—
398C2×C4—22no—
399C2×C4—21no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—24no—
406C2×C4—22no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—22no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—44no—
416C2×C4—42no—
417C2×C4—48no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—88no—
438C2×C4—88no—
439C2×C4—81no—
440C2×C4—81no—
441C2×C4—84no—
442C2×C4—82no—
443C2×C4—82no—
444C2×C4C2×#9912yes—
445C2×C4C2×#9912yes—
446C2×C4#41812yes—
447C2×C4C2×AGL(1,ℤ/8)12yes—
448C8—84no—
449C8—84no—
450C22—24no—
451C22—24no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—44no—
457C22—44no—
458C22—44no—
459C22—44no—
460C22—42no—
461C22—42no—
462C22—42no—
463C22—82no—
464C22—82no—
465C22—82no—
466C22—84no—
467C22—88no—
468C22—84no—
469C22—88no—
470C22—82no—
471C22—82no—
472C22#151012yes—
473C22#151012yes—
474C22#212012yes—
475C22#213212yes—
476C22C22×#9911yescharacteristic
477C22C2×#41811yescharacteristic
478C22C2×#42111yescharacteristic
479C4—22no—
480C4—22no—
481C4—22no—
482C4—22no—
483C4—44no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—41no—
488C4—42no—
489C4—42no—
490C4—82no—
491C4—82no—
492C2—21no—
493C2—21no—
494C2—22no—
495C2—82no—
496C2—84no—
497C2#1180414yesdirect product factor
498C2C2×#151011yescharacteristic
499C2C2×#212011yescharacteristic
500C2C2×#213211yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC2×#392C4
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
2. C2×#1822C2semidirect
3. C2×#1464C2semidirect
4. #11804C2direct (N × H)
5. C2×#1346C2semidirect
6. C2×#1345C2semidirect
25. #1822C22semidirect
29. #1464C22semidirect
32. #1346C22semidirect
33. #1345C22semidirect
497. C2#11804direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#23922
C2×#18222
C2×#14642
#118042
C2×#13462
C2×#13452