Finite Group Databasebeta

← C2×#9297 #199050

Subgroups — C2×#9297 #199050

Order 512.

1208 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3209C211yesmaximal, characteristic
2C2×#2331C211yesmaximal, characteristic
3C2×#1995C211yesmaximal, characteristic
4C2×#1548C211yesmaximal, characteristic
5C2×#1518C211yesmaximal, characteristic
6#9297C218yesmaximal, direct product factor
7C2×#1286C211yesmaximal, characteristic
8C2×#1274C211yesmaximal, characteristic
9C2×#533C2211yescharacteristic
10C22×C4⋊Q8C2211yescharacteristic
11#3209—22no—
12#3209—22no—
13#3209C414yescomplemented
14#3209C2214yes—
15C2×#494C412yescomplemented
16C2×#487C412yescomplemented
17C2×#462—22no—
18C2×#451—22no—
19C2×#431C2211yescharacteristic
20C2×#431C2211yescharacteristic
21C2×#423C2211yescharacteristic
22#2331—22no—
23#2331—22no—
24#2331—22no—
25#2331C2214yes—
26C2×#391—22no—
27C2×#389—21no—
28C2×#387—22no—
29C2×#382C2211yescharacteristic
30C2×C4×C4⋊C4—21no—
31C2×#376C2211yescharacteristic
32#1995—22no—
33#1995C2214yes—
34C2×#339—21no—
35C2×#339—21no—
36#1548—22no—
37#1548C2214yes—
38C2×#333—22no—
39#1518—22no—
40#1518C2214yes—
41C2×#328—22no—
42#1286C2214yes—
43#1274C2214yes—
44C23×Q8D412yes—
45C22×Q16—24no—
46C22×M16—21no—
47#533—21no—
48#533—21no—
49#533—21no—
50#533—21no—
51#533—21no—
52#533—21no—
53#533C2×C412yes—
54#533C2312yes—
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×C411yescharacteristic
62C2×C4⋊Q8C2×C411yescharacteristic
63C2×C4⋊Q8C2×C412yes—
64C2×C4⋊Q8C2×C412yes—
65C2×C4⋊Q8D412yes—
66C2×C4⋊Q8D412yes—
67C2×C4⋊Q8D412yes—
68C2×C4⋊Q8C2312yes—
69C2×#125—21no—
70C2×C22⋊Q8—21no—
71C2×C22⋊Q8—21no—
72C2×C4×Q8—21no—
73C2×C4×Q8—21no—
74C2×#117—21no—
75C22×C4⋊C4—21no—
76C22×C4⋊C4—21no—
77C22×C4⋊C4—21no—
78C22×C4⋊C4—22no—
79C22×C42—22no—
80C22×C42D411yescharacteristic
81C22×C42D411yescharacteristic
82C22×C42C2311yescharacteristic
83#494—24no—
84#494C2×C418yescomplemented
85#487—24no—
86#487C2×C418yescomplemented
87#462—28no—
88#462—28no—
89#451—28no—
90#451—28no—
91#431—21no—
92#431—21no—
93#431—21no—
94#431—21no—
95#431—21no—
96#431C2×C412yes—
97#431C2312yes—
98#431C2312yes—
99#423—21no—
100#423—21no—
101#423—21no—
102#423C2312yes—
103C2×C4⋊C8—21no—
104C2×C4⋊C8—21no—
105C2×C4⋊C8—21no—
106C2×C4⋊C8—21no—
107C2×#103—24no—
108C2×C22⋊C8—21no—
109C2×C22⋊C8—21no—
110C2×C4×C8—21no—
111C2×C4×C8C2×C412yes—
112#391—28no—
113#391—28no—
114#389—24no—
115#389—24no—
116#387—28no—
117#387—28no—
118#382—21no—
119#382—21no—
120#382D412yes—
121#382C2312yes—
122C4×C4⋊C4—24no—
123C4×C4⋊C4—24no—
124#376—21no—
125#376—21no—
126#376D412yes—
127#376C2312yes—
128C2×#95—22no—
129C2×#95—22no—
130C2×#95—21no—
131C2×#95—21no—
132C2×#95—21no—
133C2×#95D412yes—
134#339—24no—
135#339—24no—
136#333—28no—
137#328—28no—
138C22×Q8—22no—
139C22×Q8—22no—
140C22×Q8—22no—
141C22×Q8—21no—
142C22×Q8—21no—
143C22×Q8—84no—
144C22×Q8C22⋊C414yes—
145C22×Q8C22⋊C414yes—
146C22×Q8C2×D414yes—
147C23×C4—22no—
148C23×C4—21no—
149C23×C4—21no—
150C23×C4—22no—
151C23×C4C2×D411yescharacteristic
152C23×C4C2×D411yescharacteristic
153C23×C4C2×D411yescharacteristic
154C2×Q16—216no—
155C2×Q16—88no—
156C2×M16—22no—
157C2×M16—41no—
158C2×M16—42no—
159C2×M16—42no—
160C22×C8—22no—
161C22×C8—41no—
162C22×C8—41no—
163C4⋊Q8—21no—
164C4⋊Q8—21no—
165C4⋊Q8—22no—
166C4⋊Q8—22no—
167C4⋊Q8—22no—
168C4⋊Q8—22no—
169C4⋊Q8—21no—
170C4⋊Q8—21no—
171C4⋊Q8—21no—
172C4⋊Q8—21no—
173C4⋊Q8—22no—
174C4⋊Q8—22no—
175C4⋊Q8—22no—
176C4⋊Q8—22no—
177C4⋊Q8—22no—
178C4⋊Q8—22no—
179C4⋊Q8—22no—
180C4⋊Q8—22no—
181C4⋊Q8C22⋊C414yes—
182C4⋊Q8C22⋊C414yes—
183C4⋊Q8C22×C412yes—
184C4⋊Q8C22×C412yes—
185C4⋊Q8C22×C414yes—
186C4⋊Q8C2×D414yes—
187#125—22no—
188#125—22no—
189#125—41no—
190#125—41no—
191C22⋊Q8—22no—
192C22⋊Q8—22no—
193C22⋊Q8—22no—
194C22⋊Q8—22no—
195C22⋊Q8—41no—
196C22⋊Q8—41no—
197C22⋊Q8—41no—
198C22⋊Q8—41no—
199C4×Q8—22no—
200C4×Q8—22no—
201C4×Q8—22no—
202C4×Q8—22no—
203C4×Q8—41no—
204C4×Q8—41no—
205C4×Q8—41no—
206C4×Q8—41no—
207#117—22no—
208#117—22no—
209#117—41no—
210#117—41no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—28no—
230C2×C4⋊C4—41no—
231C2×C4⋊C4—41no—
232C2×C4⋊C4—42no—
233C2×C4⋊C4—42no—
234C2×C4⋊C4—84no—
235C2×C22⋊C4—41no—
236C2×C42—21no—
237C2×C42—22no—
238C2×C42—22no—
239C2×C42—22no—
240C2×C42—21no—
241C2×C42—28no—
242C2×C42—41no—
243C2×C42—84no—
244C2×C42Q1614yescomplemented
245C2×C42C22×C411yescharacteristic
246C2×C42C22×C411yescharacteristic
247C2×C42C2×D412yes—
248C2×C42C2×D412yes—
249C2×C42C2×D411yescharacteristic
250C2×C42C2×D411yescharacteristic
251C2×C42C2×D411yescharacteristic
252C2×C42C2×D411yescharacteristic
253C2×C42C2×D411yescharacteristic
254C2×C42#4111yescharacteristic
255C2×C42#4111yescharacteristic
256C2×C42#4111yescharacteristic
257C2×C42#4111yescharacteristic
258C2×C42C2411yescharacteristic
259C4⋊C8—22no—
260C4⋊C8—22no—
261C4⋊C8—22no—
262C4⋊C8—22no—
263C4⋊C8—22no—
264C4⋊C8—41no—
265C4⋊C8—41no—
266C4⋊C8—41no—
267#103—216no—
268C22⋊C8—22no—
269C22⋊C8—22no—
270C22⋊C8—22no—
271C22⋊C8—41no—
272C4×C8—22no—
273C4×C8—22no—
274C4×C8—41no—
275C4×C8C22×C414yes—
276#95—28no—
277#95—28no—
278#95—22no—
279#95—22no—
280#95—22no—
281#95—22no—
282#95—22no—
283#95—22no—
284#95—22no—
285#95C2×D414yes—
286C24#12011yescharacteristic
287C2×Q8—24no—
288C2×Q8—24no—
289C2×Q8—24no—
290C2×Q8—22no—
291C2×Q8—22no—
292C2×Q8—48no—
293C2×Q8—44no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×Q8—84no—
297C2×Q8—82no—
298C2×Q8—84no—
299C2×Q8—84no—
300C2×Q8—84no—
301C2×Q8—84no—
302C2×Q8C2×C22⋊C418yes—
303C22×C4—22no—
304C22×C4—24no—
305C22×C4—24no—
306C22×C4—24no—
307C22×C4—24no—
308C22×C4—22no—
309C22×C4—24no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—44no—
314C22×C4—44no—
315C22×C4—42no—
316C22×C4—44no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—44no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—42no—
323C22×C4—44no—
324C22×C4C2×C22⋊C411yescharacteristic
325C22×C4C2×C22⋊C411yescharacteristic
326C22×C4C4×D411yescharacteristic
327C22×C4C4×D411yescharacteristic
328C22×C4C4×D411yescharacteristic
329C22×C4C4×D411yescharacteristic
330C22×C4#12011yescharacteristic
331C22×C4#12011yescharacteristic
332C22×C4#12011yescharacteristic
333C22×C4#12111yescharacteristic
334C22×C4#12111yescharacteristic
335C22×C4#12111yescharacteristic
336C22×C4#12111yescharacteristic
337C22×C4#12311yescharacteristic
338C22×C4#12311yescharacteristic
339C22×C4C2×Q1612yes—
340C22×C4#13512yes—
341C22×C4#13712yes—
342C22×C4#13712yes—
343C22×C4C22×D411yescharacteristic
344C22×C4C22×D411yescharacteristic
345C22×C4C22×D411yescharacteristic
346Q16—816no—
347M16—42no—
348M16—42no—
349M16—82no—
350C2×C8—24no—
351C2×C8—44no—
352C2×C8—42no—
353C2×C8—42no—
354C2×C8—82no—
355C2×C8—82no—
356C4⋊C4—24no—
357C4⋊C4—24no—
358C4⋊C4—24no—
359C4⋊C4—24no—
360C4⋊C4—24no—
361C4⋊C4—24no—
362C4⋊C4—24no—
363C4⋊C4—24no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—42no—
369C4⋊C4—42no—
370C4⋊C4—42no—
371C4⋊C4—42no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—42no—
377C4⋊C4—42no—
378C4⋊C4—44no—
379C4⋊C4—88no—
380C22⋊C4—42no—
381C22⋊C4—42no—
382C42—22no—
383C42—24no—
384C42—22no—
385C42—22no—
386C42—42no—
387C42—42no—
388C42—42no—
389C42—88no—
390C42C2×C22⋊C411yescharacteristic
391C42C2×C22⋊C411yescharacteristic
392C42C4×D411yescharacteristic
393C42C4×D411yescharacteristic
394C42C4×D411yescharacteristic
395C42C4×D411yescharacteristic
396C42#12111yescharacteristic
397C42#12111yescharacteristic
398C42#12111yescharacteristic
399C42#12111yescharacteristic
400C42#12311yescharacteristic
401C42#12311yescharacteristic
402C42C2×Q1614yescomplemented
403C42C23×C411yescharacteristic
404C42C22×D411yescharacteristic
405C42C2×#4111yescharacteristic
406C42C2×#4111yescharacteristic
407C23—22no—
408C23—22no—
409C23#38611yescharacteristic
410C23#38611yescharacteristic
411C23#45112yes—
412C23#45212yes—
413C23C2×#12011yescharacteristic
414Q8—48no—
415Q8—44no—
416Q8—84no—
417Q8—84no—
418Q8—84no—
419Q8—82no—
420Q8—82no—
421Q8—82no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—24no—
427C2×C4—28no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—44no—
438C2×C4—44no—
439C2×C4—42no—
440C2×C4—48no—
441C2×C4—48no—
442C2×C4—48no—
443C2×C4—44no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—44no—
447C2×C4—42no—
448C2×C4—44no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—88no—
452C2×C4—84no—
453C2×C4—82no—
454C2×C4—82no—
455C2×C4#38611yescharacteristic
456C2×C4#38611yescharacteristic
457C2×C4#38611yescharacteristic
458C2×C4#38611yescharacteristic
459C2×C4#38611yescharacteristic
460C2×C4#38611yescharacteristic
461C2×C4C4×Q1612yes—
462C2×C4C4×Q1612yes—
463C2×C4#44112yes—
464C2×C4#44112yes—
465C2×C4#45112yes—
466C2×C4#45212yes—
467C2×C4#46212yes—
468C2×C4#46212yes—
469C2×C4#46412yes—
470C2×C4#46412yes—
471C2×C4C22×C22⋊C411yescharacteristic
472C2×C4C2×C4×D411yescharacteristic
473C2×C4C2×C4×D411yescharacteristic
474C2×C4C2×#12111yescharacteristic
475C2×C4C2×#12111yescharacteristic
476C2×C4C2×#12311yescharacteristic
477C2×C4C22×Q1611yescharacteristic
478C2×C4C2×#13511yescharacteristic
479C2×C4C2×#13711yescharacteristic
480C2×C4C2×#13711yescharacteristic
481C8—44no—
482C8—82no—
483C8—82no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—24no—
489C22—24no—
490C22#187812yes—
491C22#187812yes—
492C22#190512yes—
493C22#191112yes—
494C22C2×#38611yescharacteristic
495C22C2×#45111yescharacteristic
496C22C2×#45211yescharacteristic
497C4—21no—
498C4—21no—
499C4—21no—
500C4—21no—
501C4—21no—
502C4—21no—
503C4—21no—
504C4—21no—
505C4—44no—
506C4—48no—
507C4—84no—
508C4—82no—
509C4—82no—
510C4—82no—
511C4#187812yes—
512C4#187812yes—
513C4C2×C4×Q1611yescharacteristic
514C4C2×#44111yescharacteristic
515C4C2×#46211yescharacteristic
516C4C2×#46411yescharacteristic
517C2—21no—
518C2—21no—
519C2—22no—
520C2#929714yesdirect product factor
521C2C2×#187811yescharacteristic
522C2C2×#190511yescharacteristic
523C2C2×#191111yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC42C23×C4
Frattini, cosocleC2×C42C24
prime radicalC24#120
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. #9297C2direct (N × H)
13. #3209C4semidirect
15. C2×#494C4semidirect
16. C2×#487C4semidirect
84. #494C2×C4semidirect
86. #487C2×C4semidirect
244. C2×C42Q16semidirect
402. C42C2×Q16semidirect
520. C2#9297direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#32092
C2×#23312
C2×#19952
C2×#15482
C2×#15182
#92972
C2×#12862
C2×#12742