Finite Group Databasebeta

← C2×#9082 #195921

Subgroups — C2×#9082 #195921

Order 512.

1786 conjugacy classes of subgroups.

The subgroup lattice has 535 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#431C211yesmaximal, characteristic
2C22×#387C211yesmaximal, characteristic
3C2×#1817C211yesmaximal, characteristic
4C22×#324C212yesmaximal
5#9082C218yesmaximal, direct product factor
6C2×#1280C212yesmaximal
7C23×C4⋊C4C411yescharacteristic
8C23×C4⋊C4C2211yescharacteristic
9C23×C42C2211yescharacteristic
10C2×#431—22no—
11C2×#431—28no—
12C2×#431C2214yes—
13C22×C4⋊C8—21no—
14C22×C22⋊C8C2212yes—
15C22×C22⋊C8C2212yes—
16C22×C4×C8—21no—
17C2×#387—22no—
18C2×#387—21no—
19C2×#387—21no—
20C2×#387—22no—
21C2×#387—21no—
22C2×#387—21no—
23C2×#387C414yes—
24C2×#387C2214yes—
25C22×#95C411yescharacteristic
26C22×#95C411yescharacteristic
27C22×#95C411yescharacteristic
28C22×#95C2211yescharacteristic
29#1817—22no—
30#1817C2214yes—
31C2×#336—21no—
32C2×#336—21no—
33C2×#324—28no—
34C2×#324C2218yes—
35#1280C2218yes—
36C24×C4C2×C411yescharacteristic
37C24×C4C2×C411yescharacteristic
38C24×C4C2×C411yescharacteristic
39C24×C4C2×C411yescharacteristic
40C24×C4C2×C411yescharacteristic
41C24×C4C2×C411yescharacteristic
42C24×C4C2311yescharacteristic
43C23×C8—22no—
44C23×C8—22no—
45C22×C4⋊C4—22no—
46C22×C4⋊C4—21no—
47C22×C4⋊C4—21no—
48C22×C4⋊C4—24no—
49C22×C4⋊C4—24no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—24no—
55C22×C4⋊C4C818yescomplemented
56C22×C4⋊C4C2×C412yes—
57C22×C4⋊C4C2×C414yes—
58C22×C4⋊C4C2312yes—
59C22×C42—24no—
60C22×C42—24no—
61C22×C42C2×C412yes—
62C22×C42D412yes—
63C22×C42D411yescharacteristic
64C22×C42D411yescharacteristic
65C22×C42D412yes—
66C22×C42D411yescharacteristic
67C22×C42D411yescharacteristic
68C22×C42C2312yes—
69#431—216no—
70#431—216no—
71C2×C4⋊C8—28no—
72C2×C4⋊C8—24no—
73C2×C22⋊C8—22no—
74C2×C22⋊C8—24no—
75C2×C22⋊C8—24no—
76C2×C22⋊C8—24no—
77C2×C22⋊C8—22no—
78C2×C22⋊C8D418yes—
79C2×C22⋊C8C2314yes—
80C2×C22⋊C8C2314yes—
81C2×C4×C8—28no—
82C2×C4×C8—24no—
83#387—24no—
84#387—24no—
85#387—24no—
86#387—24no—
87#387—24no—
88#387—24no—
89#387—24no—
90#387—24no—
91C2×#95—22no—
92C2×#95—22no—
93C2×#95—21no—
94C2×#95—21no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—22no—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95—21no—
101C2×#95—21no—
102C2×#95—21no—
103C2×#95—21no—
104C2×#95C2×C414yes—
105C2×#95C2×C414yes—
106C2×#95C2×C414yes—
107C2×#95C2×C412yes—
108C2×#95C2312yes—
109#336—24no—
110#336—24no—
111#324—216no—
112C25C22×C411yescharacteristic
113C23×C4—24no—
114C23×C4—24no—
115C23×C4—21no—
116C23×C4—21no—
117C23×C4—21no—
118C23×C4—21no—
119C23×C4—24no—
120C23×C4—24no—
121C23×C4—22no—
122C23×C4—22no—
123C23×C4—24no—
124C23×C4—24no—
125C23×C4—21no—
126C23×C4—21no—
127C23×C4—21no—
128C23×C4—21no—
129C23×C4—24no—
130C23×C4—24no—
131C23×C4—42no—
132C23×C4—42no—
133C23×C4—42no—
134C23×C4—42no—
135C23×C4—42no—
136C23×C4—42no—
137C23×C4—42no—
138C23×C4—42no—
139C23×C4—42no—
140C23×C4C22⋊C411yescharacteristic
141C23×C4C22⋊C412yes—
142C23×C4C22⋊C412yes—
143C23×C4C22⋊C411yescharacteristic
144C23×C4C22⋊C411yescharacteristic
145C23×C4C22⋊C411yescharacteristic
146C23×C4C2×C814yes—
147C23×C4C2×C814yes—
148C23×C4C2×C814yes—
149C23×C4M1614yes—
150C23×C4C22×C412yes—
151C23×C4C22×C412yes—
152C23×C4C22×C412yes—
153C23×C4C22×C412yes—
154C23×C4C22×C412yes—
155C23×C4C22×C412yes—
156C23×C4C22×C411yescharacteristic
157C23×C4C2×D411yescharacteristic
158C23×C4C2×D411yescharacteristic
159C23×C4C2×D411yescharacteristic
160C23×C4C2×D411yescharacteristic
161C23×C4C2×D414yes—
162C23×C4#4114yes—
163C23×C4C2411yescharacteristic
164C22×C8—28no—
165C22×C8—24no—
166C22×C8—24no—
167C22×C8—44no—
168C22×C8—44no—
169C22×C8—44no—
170C22×C8—44no—
171C22×C8—44no—
172C2×C4⋊C4—216no—
173C2×C4⋊C4—28no—
174C2×C4⋊C4—28no—
175C2×C4⋊C4—24no—
176C2×C4⋊C4—24no—
177C2×C4⋊C4—28no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—28no—
181C2×C4⋊C4—24no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—24no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4—42no—
187C2×C4⋊C4—44no—
188C2×C4⋊C4—44no—
189C2×C4⋊C4—42no—
190C2×C4⋊C4—42no—
191C2×C4⋊C4C2×C8116yescomplemented
192C2×C42—28no—
193C2×C42—22no—
194C2×C42—22no—
195C2×C42—24no—
196C2×C42—24no—
197C2×C42—24no—
198C2×C42—28no—
199C2×C42—22no—
200C2×C42—22no—
201C2×C42—24no—
202C2×C42—24no—
203C2×C42—24no—
204C2×C42C22⋊C412yes—
205C2×C42C22⋊C412yes—
206C2×C42C22⋊C412yes—
207C2×C42C22⋊C412yes—
208C2×C42C2×D412yes—
209C2×C42C2×D412yes—
210C2×C42C2×D412yes—
211C2×C42C2×D412yes—
212C4⋊C8—216no—
213C22⋊C8—28no—
214C22⋊C8—24no—
215C22⋊C8—24no—
216C22⋊C8—24no—
217C22⋊C8—44no—
218C22⋊C8C2×D418yes—
219C4×C8—216no—
220#95—22no—
221#95—22no—
222#95—24no—
223#95—24no—
224#95—24no—
225#95—24no—
226#95—24no—
227#95—24no—
228#95—22no—
229#95—22no—
230C24—22no—
231C24—22no—
232C24—22no—
233C24—22no—
234C24C2×C22⋊C411yescharacteristic
235C24C2×C22⋊C411yescharacteristic
236C24C4×D414yes—
237C24C22×C812yes—
238C24C2×M1612yes—
239C24#13114yes—
240C24C23×C411yescharacteristic
241C22×C4—24no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—24no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—216no—
256C22×C4—216no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—24no—
260C22×C4—24no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—24no—
264C22×C4—24no—
265C22×C4—22no—
266C22×C4—24no—
267C22×C4—24no—
268C22×C4—24no—
269C22×C4—24no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—216no—
273C22×C4—24no—
274C22×C4—24no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—42no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—42no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—48no—
288C22×C4—48no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—416no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—48no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—48no—
302C22×C4—48no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—88no—
322C22×C4—88no—
323C22×C4C22⋊C818yes—
324C22×C4C22⋊C814yes—
325C22×C4C22⋊C814yes—
326C22×C4#10114yes—
327C22×C4C2×C22⋊C412yes—
328C22×C4C2×C22⋊C411yescharacteristic
329C22×C4C2×C22⋊C411yescharacteristic
330C22×C4C2×C22⋊C412yes—
331C22×C4C2×C22⋊C412yes—
332C22×C4C2×C22⋊C412yes—
333C22×C4C4×D414yes—
334C22×C4#12012yes—
335C22×C4#12012yes—
336C22×C4#12114yes—
337C22×C4#12114yes—
338C22×C4#12312yes—
339C22×C4#12312yes—
340C22×C4C22×C814yes—
341C22×C4C22×C814yes—
342C22×C4C22×C814yes—
343C22×C4C2×M1614yes—
344C22×C4C22×D411yescharacteristic
345C22×C4C22×D411yescharacteristic
346C22×C4C22×D412yes—
347C22×C4C2×#4112yes—
348C2×C8—28no—
349C2×C8—44no—
350C2×C8—44no—
351C2×C8—416no—
352C2×C8—44no—
353C2×C8—44no—
354C2×C8—44no—
355C2×C8—88no—
356C4⋊C4—216no—
357C4⋊C4—216no—
358C4⋊C4—42no—
359C4⋊C4—44no—
360C4⋊C4—42no—
361C4⋊C4—44no—
362C4⋊C4—44no—
363C42—22no—
364C42—22no—
365C42—24no—
366C42—24no—
367C42—22no—
368C42—22no—
369C42—24no—
370C42—24no—
371C42—24no—
372C42—24no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—28no—
382C23—28no—
383C23—24no—
384C23—24no—
385C23—24no—
386C23—24no—
387C23—28no—
388C23—28no—
389C23#38612yes—
390C23#38612yes—
391C23C2×C22⋊C812yes—
392C23C2×C22⋊C812yes—
393C23#40812yes—
394C23#40812yes—
395C23#41012yes—
396C23#41012yes—
397C23C2×#10112yes—
398C23#41312yes—
399C23C8×D418yes—
400C23#43518yes—
401C23C22×C22⋊C411yescharacteristic
402C23C2×C4×D412yes—
403C23C23×C811yescharacteristic
404C23C22×M1611yescharacteristic
405C23C2×#13112yes—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—216no—
418C2×C4—28no—
419C2×C4—28no—
420C2×C4—24no—
421C2×C4—28no—
422C2×C4—24no—
423C2×C4—28no—
424C2×C4—28no—
425C2×C4—28no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—28no—
434C2×C4—22no—
435C2×C4—44no—
436C2×C4—42no—
437C2×C4—44no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—48no—
442C2×C4—48no—
443C2×C4—44no—
444C2×C4—48no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—48no—
449C2×C4—48no—
450C2×C4—44no—
451C2×C4—44no—
452C2×C4—48no—
453C2×C4—42no—
454C2×C4—44no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—84no—
462C2×C4—84no—
463C2×C4—84no—
464C2×C4—84no—
465C2×C4—84no—
466C2×C4—84no—
467C2×C4#38612yes—
468C2×C4#38612yes—
469C2×C4C2×C22⋊C814yes—
470C2×C4C2×C22⋊C814yes—
471C2×C4C2×#10114yes—
472C2×C4C2×#12011yescharacteristic
473C2×C4C2×#12112yes—
474C2×C4C2×#12311yescharacteristic
475C8—48no—
476C8—84no—
477C22—216no—
478C22—216no—
479C22—21no—
480C22—21no—
481C22—22no—
482C22—21no—
483C22—21no—
484C22—22no—
485C22—22no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22—22no—
493C22#145814yes—
494C22#146114yes—
495C22#147014yes—
496C22#147314yes—
497C22#186914yes—
498C22#186914yes—
499C22#189914yes—
500C22#190114yes—
501C22C2×#38611yescharacteristic
502C22C22×C22⋊C811yescharacteristic
503C22C2×#40811yescharacteristic
504C22C2×#41011yescharacteristic
505C22C2×#41011yescharacteristic
506C22C22×#10111yescharacteristic
507C22C2×#41311yescharacteristic
508C22C2×C8×D412yes—
509C22C2×#43512yes—
510C4—24no—
511C4—24no—
512C4—21no—
513C4—22no—
514C4—21no—
515C4—22no—
516C4—22no—
517C4—24no—
518C4—44no—
519C4—44no—
520C4—42no—
521C4—82no—
522C4—82no—
523C2—24no—
524C2—22no—
525C2—22no—
526C2#908218yesdirect product factor
527C2C2×#145811yescharacteristic
528C2C2×#146111yescharacteristic
529C2C2×#147011yescharacteristic
530C2C2×#147311yescharacteristic
531C2C2×#186911yescharacteristic
532C2C2×#189911yescharacteristic
533C2C2×#190111yescharacteristic
subgroupG/H
center, socleC24C2×C22⋊C4
commutatorC23C23×C8
Frattini, cosocleC23×C4C24
prime radicalC25C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C23×C42 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
5. #9082C2direct (N × H)
55. C22×C4⋊C4C8semidirect
191. C2×C4⋊C4C2×C8semidirect
526. C2#9082direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4312
C22×#3872
C2×#18172
C22×#3242
#90822
C2×#12802