Finite Group Databasebeta

← C2×#11805 #481828

Subgroups — C2×#11805 #481828

Order 512.

1236 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2618C211yesmaximal, characteristic
2C2×#1821C211yesmaximal, characteristic, complemented
3C2×#1463C211yesmaximal, characteristic, complemented
4#11805C218yesmaximal, direct product factor
5C2×#1346C212yesmaximal, complemented
6C2×#1345C212yesmaximal, complemented
7C22×#123—21no—
8C22×#121C411yescharacteristic
9C23×C4⋊C4C2211yescharacteristic
10C2×#407—21no—
11C2×#407—21no—
12#2618—22no—
13#2618—22no—
14#2618C414yes—
15#2618C2214yes—
16C2×#398C411yescharacteristic
17C2×#398C2211yescharacteristic
18C2×#396—21no—
19C2×#396—21no—
20C2×#394C411yescharacteristic
21C2×#394C2211yescharacteristic
22C2×#386—21no—
23C2×#380C411yescharacteristic
24#1821—22no—
25#1821C2214yescomplemented
26C2×#343—21no—
27C2×#343C2212yes—
28#1463—22no—
29#1463C2214yescomplemented
30C2×#324—21no—
31C2×#324C2212yes—
32#1346C2218yescomplemented
33#1345C2218yescomplemented
34C23×D4—21no—
35C23×D4C2×C411yescharacteristic
36C24×C4C2×C411yescharacteristic
37C24×C4D411yescharacteristic
38C24×C4D411yescharacteristic
39C22×M16—22no—
40C22×M16—41no—
41C2×#123—24no—
42C2×#123—24no—
43C2×#123—48no—
44C2×#121—22no—
45C2×#121—42no—
46C2×#121—41no—
47C2×#121—41no—
48C2×#121C2×C414yes—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—41no—
53C22×C4⋊C4—41no—
54C22×C4⋊C4—42no—
55C22×C4⋊C4C2×C411yescharacteristic
56C22×C4⋊C4C2×C412yes—
57C22×C4⋊C4C2×C411yescharacteristic
58C22×C4⋊C4D412yes—
59C22×C4⋊C4D412yes—
60C22×C4⋊C4D411yescharacteristic
61C22×C4⋊C4D411yescharacteristic
62C22×C4⋊C4C2312yes—
63C22×C4⋊C4C2311yescharacteristic
64C22×C22⋊C4—21no—
65C22×C22⋊C4—21no—
66C22×C22⋊C4—21no—
67C22×C22⋊C4—21no—
68C22×C22⋊C4—21no—
69C22×C22⋊C4—21no—
70#407—24no—
71#407—24no—
72#407—42no—
73#407—42no—
74C2×C22⋊C8—22no—
75C2×C22⋊C8—41no—
76C2×C22⋊C8—41no—
77C2×C22⋊C8—41no—
78#398—22no—
79#398—21no—
80#398—21no—
81#398C2×C412yes—
82#398C2×C414yes—
83#398C2312yes—
84#396—24no—
85#396—24no—
86#396—24no—
87#396—24no—
88#394—22no—
89#394—21no—
90#394—21no—
91#394C2×C412yes—
92#394C2×C414yes—
93#394C2312yes—
94#386—24no—
95#386—24no—
96#380—22no—
97#380C2×C414yes—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95C2×C411yescharacteristic
101C2×#95C2×C411yescharacteristic
102#343—22no—
103#343—24no—
104#343C2314yes—
105#324—24no—
106#324—22no—
107#324C2314yes—
108C25—21no—
109C25C22⋊C411yescharacteristic
110C22×D4—24no—
111C22×D4—21no—
112C22×D4—41no—
113C22×D4—41no—
114C22×D4—44no—
115C22×D4—44no—
116C22×D4—42no—
117C22×D4—41no—
118C22×D4—41no—
119C22×D4—82no—
120C22×D4C22×C412yes—
121C23×C4—21no—
122C23×C4—21no—
123C23×C4—21no—
124C23×C4—22no—
125C23×C4—22no—
126C23×C4—21no—
127C23×C4—21no—
128C23×C4—21no—
129C23×C4—22no—
130C23×C4—24no—
131C23×C4—21no—
132C23×C4—21no—
133C23×C4—21no—
134C23×C4—42no—
135C23×C4—82no—
136C23×C4—82no—
137C23×C4C22⋊C411yescharacteristic
138C23×C4C22⋊C412yes—
139C23×C4C22⋊C411yescharacteristic
140C23×C4C22⋊C411yescharacteristic
141C23×C4C22⋊C412yes—
142C23×C4C22⋊C412yes—
143C23×C4C22×C411yescharacteristic
144C23×C4C22×C412yes—
145C23×C4C2×D412yes—
146C23×C4C2×D411yescharacteristic
147C23×C4C2×D411yescharacteristic
148C23×C4C2×D412yes—
149C2×M16—24no—
150C2×M16—42no—
151C2×M16—44no—
152C2×M16—44no—
153C2×M16—44no—
154C2×M16—84no—
155C22×C8—42no—
156C22×C8—42no—
157#123—416no—
158#123—416no—
159#121—44no—
160#121—44no—
161#121—44no—
162#121—44no—
163C2×C4⋊C4—24no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—24no—
168C2×C4⋊C4—41no—
169C2×C4⋊C4—42no—
170C2×C4⋊C4—42no—
171C2×C4⋊C4—41no—
172C2×C4⋊C4—41no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4—42no—
175C2×C4⋊C4—42no—
176C2×C4⋊C4—41no—
177C2×C4⋊C4—42no—
178C2×C4⋊C4—42no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4—41no—
182C2×C4⋊C4—42no—
183C2×C4⋊C4—42no—
184C2×C4⋊C4—41no—
185C2×C4⋊C4—41no—
186C2×C4⋊C4—44no—
187C2×C4⋊C4—44no—
188C2×C4⋊C4—82no—
189C2×C4⋊C4C22⋊C412yes—
190C2×C4⋊C4C22⋊C412yes—
191C2×C4⋊C4C22⋊C412yes—
192C2×C4⋊C4C22×C412yes—
193C2×C4⋊C4C22×C412yes—
194C2×C4⋊C4C22×C411yescharacteristic
195C2×C4⋊C4C2×D411yescharacteristic
196C2×C4⋊C4C2×D412yes—
197C2×C4⋊C4C2×D411yescharacteristic
198C2×C4⋊C4C2×D412yes—
199C2×C4⋊C4C2411yescharacteristic
200C2×C22⋊C4—24no—
201C2×C22⋊C4—24no—
202C2×C22⋊C4—24no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4—24no—
206C2×C22⋊C4—22no—
207C2×C22⋊C4—22no—
208C2×C22⋊C4—42no—
209C2×C22⋊C4—42no—
210C2×C22⋊C4—44no—
211C2×C22⋊C4—44no—
212C2×C22⋊C4—44no—
213C2×C22⋊C4—82no—
214C2×C22⋊C4—82no—
215C22⋊C8—24no—
216C22⋊C8—42no—
217C22⋊C8—44no—
218C22⋊C8—44no—
219C22⋊C8—44no—
220#95—24no—
221#95—22no—
222#95—21no—
223#95—21no—
224#95—22no—
225#95C22×C412yes—
226#95C22×C412yes—
227C24—22no—
228C24—22no—
229C24—22no—
230C24—42no—
231C24—42no—
232C24—42no—
233C24—42no—
234C24—42no—
235C24—42no—
236C24—41no—
237C24—41no—
238C24—42no—
239C24—42no—
240C24#9911yescharacteristic
241C24#9911yescharacteristic
242C24#9912yes—
243C24C2×C22⋊C411yescharacteristic
244C24C2×C22⋊C412yes—
245C2×D4—42no—
246C2×D4—42no—
247C2×D4—48no—
248C2×D4—48no—
249C2×D4—44no—
250C2×D4—44no—
251C2×D4—82no—
252C2×D4—84no—
253C2×D4—84no—
254C2×D4—82no—
255C2×D4—88no—
256C2×D4—84no—
257C2×D4—84no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—24no—
286C22×C4—24no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—44no—
293C22×C4—44no—
294C22×C4—48no—
295C22×C4—44no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—82no—
311C22×C4—82no—
312C22×C4—82no—
313C22×C4—82no—
314C22×C4—82no—
315C22×C4—84no—
316C22×C4—84no—
317C22×C4—82no—
318C22×C4—82no—
319C22×C4C2×C22⋊C412yes—
320C22×C4C2×C22⋊C411yescharacteristic
321C22×C4C2×C22⋊C412yes—
322C22×C4C2×C22⋊C411yescharacteristic
323C22×C4C2×C22⋊C411yescharacteristic
324C22×C4C2×C22⋊C412yes—
325C22×C4AGL(1,ℤ/8)14yes—
326C22×C4C23×C411yescharacteristic
327C22×C4C22×D411yescharacteristic
328C22×C4C22×D411yescharacteristic
329M16—44no—
330M16—44no—
331M16—84no—
332M16—88no—
333C2×C8—44no—
334C2×C8—44no—
335C2×C8—84no—
336C2×C8—84no—
337C4⋊C4—42no—
338C4⋊C4—42no—
339C4⋊C4—42no—
340C4⋊C4—41no—
341C4⋊C4—42no—
342C4⋊C4—42no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—42no—
346C4⋊C4—41no—
347C4⋊C4—42no—
348C4⋊C4—42no—
349C4⋊C4—48no—
350C4⋊C4—44no—
351C4⋊C4—44no—
352C4⋊C4—84no—
353C22⋊C4—48no—
354C22⋊C4—48no—
355C22⋊C4—48no—
356C22⋊C4—44no—
357C22⋊C4—44no—
358C22⋊C4—84no—
359C22⋊C4—82no—
360C22⋊C4—82no—
361C23—22no—
362C23—22no—
363C23—22no—
364C23—22no—
365C23—22no—
366C23—22no—
367C23—22no—
368C23—22no—
369C23—24no—
370C23—22no—
371C23—22no—
372C23—42no—
373C23—42no—
374C23—42no—
375C23—42no—
376C23—48no—
377C23—48no—
378C23—42no—
379C23—42no—
380C23—42no—
381C23—42no—
382C23—42no—
383C23—42no—
384C23—42no—
385C23—82no—
386C23—84no—
387C23—84no—
388C23—84no—
389C23—84no—
390C23—82no—
391C23—82no—
392C23—82no—
393C23—82no—
394C23—82no—
395C23C2×#9912yes—
396C23C2×#9912yes—
397C23C2×#9911yescharacteristic
398C23C2×#9911yescharacteristic
399C23#41812yes—
400C23#42112yes—
401C23C22×C22⋊C411yescharacteristic
402D4—84no—
403D4—84no—
404D4—88no—
405D4—88no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—22no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—44no—
422C2×C4—44no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4—44no—
426C2×C4—44no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—81no—
451C2×C4—81no—
452C2×C4—82no—
453C2×C4—82no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4—82no—
457C2×C4—82no—
458C2×C4—84no—
459C2×C4—84no—
460C2×C4—82no—
461C2×C4—82no—
462C2×C4#41812yes—
463C2×C4C2×AGL(1,ℤ/8)12yes—
464C8—84no—
465C8—84no—
466C22—24no—
467C22—24no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—22no—
473C22—22no—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—22no—
478C22—44no—
479C22—44no—
480C22—48no—
481C22—44no—
482C22—44no—
483C22—82no—
484C22—82no—
485C22—82no—
486C22—82no—
487C22—82no—
488C22—82no—
489C22—82no—
490C22—164no—
491C22—164no—
492C22#151012yes—
493C22#151012yes—
494C22#212112yes—
495C22#213312yes—
496C22C22×#9911yescharacteristic
497C22C2×#41811yescharacteristic
498C22C2×#42111yescharacteristic
499C4—22no—
500C4—22no—
501C4—41no—
502C4—42no—
503C4—41no—
504C4—42no—
505C4—41no—
506C4—41no—
507C4—42no—
508C4—82no—
509C4—82no—
510C4—82no—
511C2—21no—
512C2—21no—
513C2—22no—
514C2—42no—
515C2—42no—
516C2—162no—
517C2#1180514yesdirect product factor
518C2C2×#151011yescharacteristic
519C2C2×#212111yescharacteristic
520C2C2×#213311yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC22×#121C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C25 ◁ C23×C4⋊C4 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1821C2semidirect
3. C2×#1463C2semidirect
4. #11805C2direct (N × H)
5. C2×#1346C2semidirect
6. C2×#1345C2semidirect
25. #1821C22semidirect
29. #1463C22semidirect
32. #1346C22semidirect
33. #1345C22semidirect
517. C2#11805direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#26182
C2×#18212
C2×#14632
#118052
C2×#13462
C2×#13452