Finite Group Databasebeta

← C2×#10555 #240940

Subgroups — C2×#10555 #240940

Order 512.

942 conjugacy classes of subgroups.

The subgroup lattice has 503 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3165C211yesmaximal, characteristic
2C2×#1950C211yesmaximal, characteristic
3C2×#1550C211yesmaximal, characteristic
4C2×#1549C211yesmaximal, characteristic
5C22×#333C211yesmaximal, characteristic
6C2×#1481C211yesmaximal, characteristic
7#10555C218yesmaximal, direct product factor
8C2×#1283C211yesmaximal, characteristic
9C2×#533C2211yescharacteristic
10C22×C4⋊Q8C2211yescharacteristic
11#3165—22no—
12#3165—22no—
13#3165—22no—
14#3165C2214yes—
15C2×#501—22no—
16C2×#500—21no—
17C2×#498—21no—
18C2×#431C2211yescharacteristic
19C22×#108—21no—
20C2×#428—21no—
21C2×#428—21no—
22C2×#423C2211yescharacteristic
23C22×C4⋊C8C2211yescharacteristic
24C22×C4⋊C8C2211yescharacteristic
25C2×C4×M16C2211yescharacteristic
26#1950—22no—
27#1950C2214yes—
28C2×#341—21no—
29#1550—22no—
30#1550C2214yes—
31#1549—22no—
32#1549C2214yes—
33C2×#333—22no—
34C2×#333—22no—
35C2×#333—21no—
36C2×#333C2214yes—
37C2×#332—22no—
38C2×#332—21no—
39#1481—22no—
40#1481C2214yes—
41C2×Q8⋊C8—22no—
42#1283C2214yes—
43C23×Q8—21no—
44C22×M16—21no—
45C22×M16D411yescharacteristic
46C22×M16D411yescharacteristic
47C23×C8—21no—
48C23×C8—21no—
49#533—21no—
50#533—21no—
51#533—21no—
52#533—21no—
53#533—21no—
54#533—21no—
55#533D412yes—
56#533C2312yes—
57C2×C4⋊Q8—21no—
58C2×C4⋊Q8—21no—
59C2×C4⋊Q8—21no—
60C2×C4⋊Q8—21no—
61C2×C4⋊Q8—21no—
62C2×C4⋊Q8—21no—
63C2×C4⋊Q8—21no—
64C2×C4⋊Q8—21no—
65C2×C4⋊Q8—21no—
66C2×C4⋊Q8D411yescharacteristic
67C2×C4⋊Q8D412yes—
68C2×C4⋊Q8D411yescharacteristic
69C2×C4⋊Q8D412yes—
70C2×C4⋊Q8C2312yes—
71C2×#125—21no—
72C2×C22⋊Q8—21no—
73C2×C22⋊Q8—21no—
74C2×C4×Q8—21no—
75C2×C4×Q8—21no—
76C2×#117—21no—
77C22×C4⋊C4—21no—
78C22×C4⋊C4—21no—
79C22×C42C2311yescharacteristic
80#501—28no—
81#501—28no—
82#500—24no—
83#500—24no—
84#498—24no—
85#498—24no—
86#431—21no—
87#431—21no—
88#431—21no—
89#431C2312yes—
90C2×#108—24no—
91C2×#108—44no—
92#428—24no—
93#428—24no—
94#428—24no—
95#428—24no—
96C2×#107—22no—
97C2×#107—22no—
98C2×#106—22no—
99C2×#106—22no—
100#423—21no—
101#423—21no—
102#423—21no—
103#423C2312yes—
104C2×C4⋊C8—21no—
105C2×C4⋊C8—21no—
106C2×C4⋊C8—21no—
107C2×C4⋊C8—21no—
108C2×C4⋊C8—21no—
109C2×C4⋊C8—21no—
110C2×C4⋊C8—21no—
111C2×C4⋊C8—21no—
112C2×C4⋊C8—21no—
113C2×C4⋊C8—21no—
114C2×C4⋊C8—21no—
115C2×C4⋊C8D412yes—
116C2×C4⋊C8D412yes—
117C2×C4⋊C8C2312yes—
118C2×C4⋊C8C2312yes—
119C2×C22⋊C8—21no—
120C4×M16—21no—
121C4×M16—21no—
122C4×M16D412yes—
123C4×M16C2312yes—
124C2×#97—21no—
125C2×C4×C8—21no—
126C2×C4×C8—21no—
127#341—24no—
128#333—24no—
129#333—28no—
130#332—28no—
131#332—24no—
132Q8⋊C8—28no—
133C22×Q8—21no—
134C22×Q8—22no—
135C22×Q8—22no—
136C22×Q8—21no—
137C22×Q8—22no—
138C22×Q8—41no—
139C22×Q8—41no—
140C22×Q8—41no—
141C22×Q8—84no—
142C23×C4—41no—
143C23×C4C2×D411yescharacteristic
144C23×C4#4111yescharacteristic
145C23×C4#4111yescharacteristic
146C2×M16—21no—
147C2×M16—21no—
148C2×M16—22no—
149C2×M16—22no—
150C2×M16—22no—
151C2×M16—41no—
152C2×M16—42no—
153C2×M16—42no—
154C2×M16SD1614yes—
155C2×M16Q1614yes—
156C2×M16C2×D412yes—
157C2×M16C2×D412yes—
158C22×C8—21no—
159C22×C8—21no—
160C22×C8—22no—
161C22×C8—22no—
162C22×C8—22no—
163C22×C8—22no—
164C22×C8—42no—
165C22×C8—42no—
166C22×C8—41no—
167C22×C8—41no—
168C22×C8—41no—
169C22×C8—41no—
170C22×C8—82no—
171C4⋊Q8—22no—
172C4⋊Q8—22no—
173C4⋊Q8—21no—
174C4⋊Q8—21no—
175C4⋊Q8—21no—
176C4⋊Q8—22no—
177C4⋊Q8—22no—
178C4⋊Q8—21no—
179C4⋊Q8—22no—
180C4⋊Q8—22no—
181C4⋊Q8—21no—
182C4⋊Q8—21no—
183C4⋊Q8—22no—
184C4⋊Q8—22no—
185C4⋊Q8—22no—
186C4⋊Q8—41no—
187C4⋊Q8—41no—
188C4⋊Q8—41no—
189C4⋊Q8—41no—
190C4⋊Q8—41no—
191C4⋊Q8—41no—
192C4⋊Q8C2×D414yes—
193C4⋊Q8C2×D412yes—
194C4⋊Q8C2×D412yes—
195#125—22no—
196#125—22no—
197#125—41no—
198#125—41no—
199C22⋊Q8—22no—
200C22⋊Q8—22no—
201C22⋊Q8—22no—
202C22⋊Q8—22no—
203C22⋊Q8—41no—
204C22⋊Q8—41no—
205C22⋊Q8—41no—
206C22⋊Q8—41no—
207C4×Q8—22no—
208C4×Q8—22no—
209C4×Q8—22no—
210C4×Q8—22no—
211C4×Q8—41no—
212C4×Q8—41no—
213C4×Q8—41no—
214C4×Q8—41no—
215#117—22no—
216#117—22no—
217#117—41no—
218#117—41no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—41no—
230C2×C4⋊C4—41no—
231C2×C4⋊C4—41no—
232C2×C4⋊C4—41no—
233C2×C4⋊C4—41no—
234C2×C4⋊C4—41no—
235C2×C4⋊C4—41no—
236C2×C4⋊C4—41no—
237C2×C22⋊C4—41no—
238C2×C42—41no—
239C2×C42C2×D411yescharacteristic
240C2×C42C2×D411yescharacteristic
241C2×C42C2×D411yescharacteristic
242C2×C42C2×D411yescharacteristic
243C2×C42C2×D411yescharacteristic
244C2×C42C2×D411yescharacteristic
245C2×C42C2×D411yescharacteristic
246C2×C42#4111yescharacteristic
247C2×C42#4111yescharacteristic
248C2×C42#4111yescharacteristic
249C2×C42#4111yescharacteristic
250C2×C42C2411yescharacteristic
251#108—48no—
252#107—28no—
253#107—28no—
254#106—28no—
255#106—28no—
256C4⋊C8—22no—
257C4⋊C8—22no—
258C4⋊C8—22no—
259C4⋊C8—22no—
260C4⋊C8—22no—
261C4⋊C8—22no—
262C4⋊C8—22no—
263C4⋊C8—22no—
264C4⋊C8—41no—
265C4⋊C8—41no—
266C4⋊C8—41no—
267C4⋊C8—41no—
268C4⋊C8—41no—
269C4⋊C8C2×D414yes—
270C22⋊C8—22no—
271C22⋊C8—41no—
272#97—22no—
273#97—22no—
274C4×C8—22no—
275C4×C8—22no—
276C4×C8—22no—
277C4×C8—41no—
278C24#12411yescharacteristic
279C2×Q8—22no—
280C2×Q8—24no—
281C2×Q8—22no—
282C2×Q8—42no—
283C2×Q8—41no—
284C2×Q8—41no—
285C2×Q8—42no—
286C2×Q8—42no—
287C2×Q8—42no—
288C2×Q8—42no—
289C2×Q8—84no—
290C2×Q8—82no—
291C2×Q8—84no—
292C2×Q8—84no—
293C2×Q8—84no—
294C2×Q8—84no—
295C2×Q8—84no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—42no—
304C22×C4—84no—
305C22×C4#12011yescharacteristic
306C22×C4#12011yescharacteristic
307C22×C4#12111yescharacteristic
308C22×C4#12111yescharacteristic
309C22×C4#12111yescharacteristic
310C22×C4#12111yescharacteristic
311C22×C4#12111yescharacteristic
312C22×C4#12111yescharacteristic
313C22×C4#12311yescharacteristic
314C22×C4#12311yescharacteristic
315C22×C4#12311yescharacteristic
316C22×C4#12311yescharacteristic
317C22×C4#12411yescharacteristic
318C22×C4#12411yescharacteristic
319C22×C4#12411yescharacteristic
320C22×C4C2×SD1612yes—
321C22×C4C2×Q1612yes—
322C22×C4#13712yes—
323C22×C4#13712yes—
324C22×C4C22×D411yescharacteristic
325C22×C4C2×#4111yescharacteristic
326C22×C4C2×#4111yescharacteristic
327M16—22no—
328M16—22no—
329M16—24no—
330M16—24no—
331M16—42no—
332M16—42no—
333M16—82no—
334M16C2×SD1614yes—
335M16C2×Q1614yes—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—24no—
339C2×C8—24no—
340C2×C8—24no—
341C2×C8—42no—
342C2×C8—42no—
343C2×C8—44no—
344C2×C8—44no—
345C2×C8—42no—
346C2×C8—42no—
347C2×C8—42no—
348C2×C8—82no—
349C2×C8—82no—
350C2×C8—82no—
351C2×C8—82no—
352C2×C8—82no—
353C4⋊C4—22no—
354C4⋊C4—24no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—24no—
358C4⋊C4—22no—
359C4⋊C4—42no—
360C4⋊C4—42no—
361C4⋊C4—42no—
362C4⋊C4—42no—
363C4⋊C4—42no—
364C4⋊C4—42no—
365C4⋊C4—42no—
366C4⋊C4—42no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—42no—
372C4⋊C4—42no—
373C22⋊C4—42no—
374C22⋊C4—42no—
375C42—42no—
376C42—42no—
377C42#12011yescharacteristic
378C42#12011yescharacteristic
379C42#12111yescharacteristic
380C42#12111yescharacteristic
381C42#12111yescharacteristic
382C42#12111yescharacteristic
383C42#12111yescharacteristic
384C42#12111yescharacteristic
385C42#12311yescharacteristic
386C42#12311yescharacteristic
387C42#12311yescharacteristic
388C42#12311yescharacteristic
389C42C22×D411yescharacteristic
390C42C22×D411yescharacteristic
391C42C22×D411yescharacteristic
392C42C2×#4111yescharacteristic
393C23—22no—
394C23—22no—
395C23#39411yescharacteristic
396C23#39411yescharacteristic
397C23#48712yes—
398C23#49112yes—
399C23C2×#12411yescharacteristic
400Q8—42no—
401Q8—42no—
402Q8—82no—
403Q8—84no—
404Q8—82no—
405Q8—84no—
406Q8—84no—
407Q8—84no—
408Q8—82no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—44no—
425C2×C4—84no—
426C2×C4—84no—
427C2×C4—84no—
428C2×C4—82no—
429C2×C4—82no—
430C2×C4#39411yescharacteristic
431C2×C4#39411yescharacteristic
432C2×C4#39411yescharacteristic
433C2×C4#39411yescharacteristic
434C2×C4#39411yescharacteristic
435C2×C4#39411yescharacteristic
436C2×C4#44812yes—
437C2×C4#44812yes—
438C2×C4#45112yes—
439C2×C4#45112yes—
440C2×C4#46112yes—
441C2×C4#46112yes—
442C2×C4#46212yes—
443C2×C4#46212yes—
444C2×C4#47112yes—
445C2×C4#47312yes—
446C2×C4#48712yes—
447C2×C4#49112yes—
448C2×C4C2×#12011yescharacteristic
449C2×C4C2×#12111yescharacteristic
450C2×C4C2×#12111yescharacteristic
451C2×C4C2×#12111yescharacteristic
452C2×C4C2×#12311yescharacteristic
453C2×C4C2×#12311yescharacteristic
454C2×C4C22×SD1611yescharacteristic
455C2×C4C22×Q1611yescharacteristic
456C2×C4C2×#13711yescharacteristic
457C2×C4C2×#13711yescharacteristic
458C8—24no—
459C8—24no—
460C8—44no—
461C8—82no—
462C8—82no—
463C8—82no—
464C22—24no—
465C22—24no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22#204312yes—
471C22#204312yes—
472C22#204812yes—
473C22#205212yes—
474C22C2×#39411yescharacteristic
475C22C2×#48711yescharacteristic
476C22C2×#49111yescharacteristic
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—84no—
484C4—82no—
485C4—82no—
486C4#204312yes—
487C4#204312yes—
488C4#205212yes—
489C4C2×#44811yescharacteristic
490C4C2×#45111yescharacteristic
491C4C2×#46111yescharacteristic
492C4C2×#46211yescharacteristic
493C4C2×#47111yescharacteristic
494C4C2×#47311yescharacteristic
495C2—21no—
496C2—21no—
497C2—22no—
498C2#1055514yesdirect product factor
499C2C2×#204311yescharacteristic
500C2C2×#204811yescharacteristic
501C2C2×#205211yescharacteristic
subgroupG/H
center, socleC23#394
commutator, Frattini, cosocleC2×C42C24
prime radicalC24#124
LCSG ▷ C2×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
7. #10555C2direct (N × H)
498. C2#10555direct (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×#19502
C2×#15502
C2×#15492
C22×#3332
C2×#14812
#105552
C2×#12832