Finite Group Databasebeta

← C2×#9420 #200769

Subgroups — C2×#9420 #200769

Order 512.

1028 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3165C211yesmaximal, characteristic
2C2×#2987C211yesmaximal, characteristic
3C2×#1558C211yesmaximal, characteristic
4C2×#1556C211yesmaximal, characteristic
5C2×#1537C211yesmaximal, characteristic
6#9420C218yesmaximal, direct product factor
7C2×#1291C211yesmaximal, characteristic
8C2×#1291C211yesmaximal, characteristic
9C2×#533C2211yescharacteristic
10C22×C4⋊Q8C2211yescharacteristic
11#3165—22no—
12#3165—22no—
13#3165C414yes—
14#3165C2214yes—
15C2×#501—22no—
16C2×#500C412yes—
17C2×#498C412yes—
18#2987—22no—
19#2987—22no—
20#2987—22no—
21#2987C2214yes—
22C2×#446—22no—
23C2×#446—22no—
24C2×#433—22no—
25C2×#432C2211yescharacteristic
26C2×#432C2211yescharacteristic
27C2×#432C2211yescharacteristic
28C2×#432C2211yescharacteristic
29C2×#428—22no—
30C2×C4×M16C2211yescharacteristic
31#1558—22no—
32#1558C2214yes—
33#1556—22no—
34#1556C2214yes—
35C2×#333—22no—
36C2×#332—22no—
37#1537—22no—
38#1537C2214yes—
39C2×#330—22no—
40#1291C2214yes—
41#1291C2214yes—
42C23×Q8—21no—
43C22×M16—21no—
44#533—21no—
45#533—21no—
46#533—21no—
47#533—21no—
48#533C2×C412yes—
49#533D412yes—
50#533D412yes—
51#533C2312yes—
52C2×C4⋊Q8—21no—
53C2×C4⋊Q8—21no—
54C2×C4⋊Q8—21no—
55C2×C4⋊Q8—21no—
56C2×C4⋊Q8—21no—
57C2×C4⋊Q8—21no—
58C2×C4⋊Q8—21no—
59C2×C4⋊Q8—21no—
60C2×C4⋊Q8—21no—
61C2×C4⋊Q8C2×C412yes—
62C2×C4⋊Q8C2×C412yes—
63C2×C4⋊Q8C2×C411yescharacteristic
64C2×C4⋊Q8C2×C411yescharacteristic
65C2×C4⋊Q8C2312yes—
66C2×#125D412yes—
67C2×C22⋊Q8—21no—
68C2×C22⋊Q8—21no—
69C2×C4×Q8—21no—
70C2×C4×Q8—21no—
71C2×#117D412yes—
72C22×C4⋊C4—21no—
73C22×C4⋊C4—21no—
74C22×C42C2311yescharacteristic
75#501—28no—
76#501—28no—
77#500—24no—
78#500C2×C418yes—
79#498—24no—
80#498C2×C418yes—
81#446—28no—
82#446—28no—
83#446—28no—
84#446—28no—
85#433—28no—
86#433—28no—
87#432—21no—
88#432—21no—
89#432—21no—
90#432—21no—
91#432—21no—
92#432—21no—
93#432—21no—
94#432—21no—
95#432—21no—
96#432—21no—
97#432D412yes—
98#432D412yes—
99#432C2312yes—
100#432C2312yes—
101#432C2312yes—
102#432C2312yes—
103#428—28no—
104#428—28no—
105C2×#107—24no—
106C2×#106—24no—
107C2×C4⋊C8—24no—
108C2×C4⋊C8—21no—
109C2×C4⋊C8—21no—
110C2×C4⋊C8D412yes—
111C2×C4⋊C8D412yes—
112C2×C22⋊C8—21no—
113C2×C22⋊C8—21no—
114C2×C22⋊C8—21no—
115C2×C22⋊C8—21no—
116C4×M16—21no—
117C4×M16—21no—
118C4×M16C2×C412yes—
119C4×M16C2312yes—
120C2×#97—22no—
121C2×#97—21no—
122C2×#97—21no—
123C2×#97—21no—
124C2×#97—21no—
125C2×#97—21no—
126C2×C4×C8—22no—
127C2×C4×C8C2×C412yes—
128#333—28no—
129#332—28no—
130#330—28no—
131C22×Q8—21no—
132C22×Q8—21no—
133C22×Q8—22no—
134C22×Q8—22no—
135C22×Q8—22no—
136C22×Q8—41no—
137C22×Q8—41no—
138C22×Q8—41no—
139C22×Q8—84no—
140C23×C4—41no—
141C23×C4C2×D411yescharacteristic
142C23×C4#4111yescharacteristic
143C23×C4#4111yescharacteristic
144C2×M16—28no—
145C2×M16—22no—
146C2×M16—22no—
147C22×C8—22no—
148C22×C8—22no—
149C22×C8—22no—
150C22×C8—41no—
151C22×C8—41no—
152C4⋊Q8—22no—
153C4⋊Q8—22no—
154C4⋊Q8—21no—
155C4⋊Q8—21no—
156C4⋊Q8—21no—
157C4⋊Q8—21no—
158C4⋊Q8—22no—
159C4⋊Q8—22no—
160C4⋊Q8—22no—
161C4⋊Q8—22no—
162C4⋊Q8—22no—
163C4⋊Q8—22no—
164C4⋊Q8—22no—
165C4⋊Q8—41no—
166C4⋊Q8—41no—
167C4⋊Q8—41no—
168C4⋊Q8—41no—
169C4⋊Q8—41no—
170C4⋊Q8—41no—
171C4⋊Q8C22⋊C412yes—
172C4⋊Q8C22⋊C412yes—
173C4⋊Q8C22×C414yes—
174C4⋊Q8C22×C412yes—
175C4⋊Q8C22×C412yes—
176#125—22no—
177#125—22no—
178#125C22⋊C414yes—
179#125C2×D414yes—
180C22⋊Q8—22no—
181C22⋊Q8—22no—
182C22⋊Q8—22no—
183C22⋊Q8—22no—
184C22⋊Q8—22no—
185C22⋊Q8—22no—
186C22⋊Q8—22no—
187C22⋊Q8—22no—
188C4×Q8—22no—
189C4×Q8—22no—
190C4×Q8—22no—
191C4×Q8—22no—
192C4×Q8—22no—
193C4×Q8—22no—
194C4×Q8—22no—
195C4×Q8—22no—
196#117—22no—
197#117—22no—
198#117C22⋊C414yes—
199#117C2×D414yes—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—41no—
211C2×C4⋊C4—41no—
212C2×C4⋊C4—41no—
213C2×C4⋊C4—41no—
214C2×C4⋊C4—41no—
215C2×C4⋊C4—41no—
216C2×C4⋊C4C22⋊C412yes—
217C2×C4⋊C4C22⋊C412yes—
218C2×C22⋊C4—22no—
219C2×C42—22no—
220C2×C42C22×C411yescharacteristic
221C2×C42C22×C411yescharacteristic
222C2×C42C2×D411yescharacteristic
223C2×C42C2×D411yescharacteristic
224C2×C42C2×D411yescharacteristic
225C2×C42C2×D411yescharacteristic
226C2×C42C2×D411yescharacteristic
227C2×C42C2×D411yescharacteristic
228C2×C42C2×D411yescharacteristic
229C2×C42#4111yescharacteristic
230C2×C42#4111yescharacteristic
231C2×C42C2411yescharacteristic
232#107—216no—
233#106—216no—
234C4⋊C8—216no—
235C4⋊C8—22no—
236C4⋊C8—22no—
237C4⋊C8—22no—
238C4⋊C8—22no—
239C4⋊C8—41no—
240C4⋊C8—41no—
241C4⋊C8C2×D414yes—
242C4⋊C8C2×D414yes—
243C22⋊C8—22no—
244C22⋊C8—22no—
245C22⋊C8—22no—
246C22⋊C8—22no—
247C22⋊C8—22no—
248C22⋊C8—22no—
249C22⋊C8—41no—
250C22⋊C8—41no—
251#97—28no—
252#97—22no—
253#97—22no—
254#97—22no—
255#97—22no—
256#97—22no—
257#97—22no—
258#97—22no—
259#97—22no—
260#97—41no—
261#97—41no—
262C4×C8—28no—
263C4×C8—22no—
264C4×C8C22×C414yes—
265C24#12311yescharacteristic
266C2×Q8—22no—
267C2×Q8—22no—
268C2×Q8—22no—
269C2×Q8—22no—
270C2×Q8—24no—
271C2×Q8—42no—
272C2×Q8—42no—
273C2×Q8—42no—
274C2×Q8—82no—
275C2×Q8—82no—
276C2×Q8—84no—
277C2×Q8—84no—
278C2×Q8—84no—
279C2×Q8—84no—
280C2×Q8—84no—
281C2×Q8—84no—
282C22×C4—24no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—84no—
291C22×C4C2×C22⋊C411yescharacteristic
292C22×C4C2×C22⋊C411yescharacteristic
293C22×C4C4×D411yescharacteristic
294C22×C4C4×D411yescharacteristic
295C22×C4C4×D411yescharacteristic
296C22×C4C4×D411yescharacteristic
297C22×C4#12011yescharacteristic
298C22×C4#12011yescharacteristic
299C22×C4#12111yescharacteristic
300C22×C4#12111yescharacteristic
301C22×C4#12111yescharacteristic
302C22×C4#12111yescharacteristic
303C22×C4#12311yescharacteristic
304C22×C4#12311yescharacteristic
305C22×C4#12311yescharacteristic
306C22×C4C22×D411yescharacteristic
307C22×C4C2×#4111yescharacteristic
308C22×C4C2×#4111yescharacteristic
309M16—28no—
310M16—28no—
311C2×C8—28no—
312C2×C8—24no—
313C2×C8—24no—
314C2×C8—24no—
315C2×C8—44no—
316C2×C8—44no—
317C2×C8—42no—
318C2×C8—42no—
319C2×C8—82no—
320C2×C8—82no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—24no—
324C4⋊C4—24no—
325C4⋊C4—24no—
326C4⋊C4—24no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—24no—
332C4⋊C4—24no—
333C4⋊C4—42no—
334C4⋊C4—42no—
335C4⋊C4—42no—
336C4⋊C4—42no—
337C4⋊C4—42no—
338C4⋊C4—42no—
339C4⋊C4C2×C22⋊C414yes—
340C4⋊C4C2×C22⋊C414yes—
341C22⋊C4—24no—
342C22⋊C4—24no—
343C42—24no—
344C42—24no—
345C42C2×C22⋊C411yescharacteristic
346C42C2×C22⋊C411yescharacteristic
347C42C4×D411yescharacteristic
348C42C4×D411yescharacteristic
349C42C4×D411yescharacteristic
350C42C4×D411yescharacteristic
351C42#12011yescharacteristic
352C42#12011yescharacteristic
353C42#12111yescharacteristic
354C42#12111yescharacteristic
355C42#12111yescharacteristic
356C42#12111yescharacteristic
357C42C23×C411yescharacteristic
358C42C22×D411yescharacteristic
359C42C22×D411yescharacteristic
360C42C22×D411yescharacteristic
361C23—22no—
362C23—22no—
363C23—22no—
364C23#38611yescharacteristic
365C23#38611yescharacteristic
366C23C2×#12311yescharacteristic
367Q8—82no—
368Q8—82no—
369Q8—82no—
370Q8—82no—
371Q8—84no—
372Q8—84no—
373Q8—84no—
374Q8—84no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—44no—
395C2×C4—44no—
396C2×C4—44no—
397C2×C4—84no—
398C2×C4—84no—
399C2×C4—84no—
400C2×C4#38611yescharacteristic
401C2×C4#38611yescharacteristic
402C2×C4#38611yescharacteristic
403C2×C4#38611yescharacteristic
404C2×C4#38611yescharacteristic
405C2×C4#38611yescharacteristic
406C2×C4#45614yes—
407C2×C4C22×C22⋊C411yescharacteristic
408C2×C4C2×C4×D411yescharacteristic
409C2×C4C2×C4×D411yescharacteristic
410C2×C4C2×#12011yescharacteristic
411C2×C4C2×#12111yescharacteristic
412C2×C4C2×#12111yescharacteristic
413C8—28no—
414C8—44no—
415C8—44no—
416C8—82no—
417C8—82no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—44no—
425C22#188612yes—
426C22#190212yes—
427C22#190312yes—
428C22C2×#38611yescharacteristic
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—44no—
440C4—44no—
441C4—84no—
442C4#188612yes—
443C4C2×#45612yes—
444C2—41no—
445C2—41no—
446C2#942014yesdirect product factor
447C2C2×#188611yescharacteristic
448C2C2×#190211yescharacteristic
449C2C2×#190311yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC42C23×C4
Frattini, cosocleC2×C42C24
prime radicalC24#123
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
6. #9420C2direct (N × H)
446. C2#9420direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#31652
C2×#29872
C2×#15582
C2×#15562
C2×#15372
#94202
C2×#12912