Finite Group Databasebeta

← C2×#9455 #201187

Subgroups — C2×#9455 #201187

Order 512.

1560 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2973C211yesmaximal, characteristic
2C2×#2542C211yesmaximal, characteristic
3C2×#1556C212yesmaximal, complemented
4C2×#1466C211yesmaximal, characteristic
5#9455C218yesmaximal, direct product factor
6C2×#1285C212yesmaximal, complemented
7C22×C4⋊Q8C2211yescharacteristic
8C22×C22⋊Q8—21no—
9C22×C22⋊Q8—21no—
10C22×C4×D4C2211yescharacteristic
11#2973—24no—
12#2973—22no—
13#2973C2214yes—
14C2×#435—24no—
15C2×#432C2212yes—
16C2×#432C2212yes—
17C2×#407—21no—
18C22×C22⋊C8—21no—
19#2542—22no—
20#2542—22no—
21#2542C414yes—
22#2542C2214yes—
23C2×#399—21no—
24C2×#399—21no—
25C2×#390C412yes—
26C2×#384C412yes—
27C2×C4×C4⋊C4C2211yescharacteristic
28#1556—24no—
29#1556C2218yescomplemented
30C2×#332—24no—
31#1466—22no—
32#1466C2214yes—
33C2×#323—21no—
34C2×#323—21no—
35#1285C2218yescomplemented
36C23×Q8—21no—
37C23×D4C2×C411yescharacteristic
38C24×C4D411yescharacteristic
39C24×C4D411yescharacteristic
40C22×M16—22no—
41C23×C8—22no—
42C2×C4⋊Q8—21no—
43C2×C4⋊Q8—21no—
44C2×C4⋊Q8—22no—
45C2×C4⋊Q8—22no—
46C2×C4⋊Q8—22no—
47C2×C4⋊Q8—22no—
48C2×C4⋊Q8C2×C412yes—
49C2×C4⋊Q8C2312yes—
50C2×C22⋊Q8—24no—
51C2×C22⋊Q8—24no—
52C2×C22⋊Q8—24no—
53C2×C22⋊Q8—24no—
54C2×C22⋊Q8—48no—
55C2×C22⋊Q8—48no—
56C2×C4×D4—22no—
57C2×C4×D4—22no—
58C2×C4×D4—22no—
59C2×C4×D4—22no—
60C2×C4×D4C2×C412yes—
61C2×C4×D4D412yes—
62C2×C4×D4D412yes—
63C2×C4×D4C2312yes—
64C22×C4⋊C4—21no—
65C22×C4⋊C4—22no—
66C22×C4⋊C4—22no—
67C22×C4⋊C4—21no—
68C22×C4⋊C4C2×C412yes—
69C22×C4⋊C4C2×C411yescharacteristic
70C22×C22⋊C4—22no—
71C22×C22⋊C4—22no—
72C22×C22⋊C4D411yescharacteristic
73C22×C22⋊C4D411yescharacteristic
74C22×C42C2×C412yes—
75C22×C42C2311yescharacteristic
76#435—216no—
77#435—216no—
78#432—22no—
79#432—22no—
80#432—22no—
81#432—22no—
82#432—22no—
83#432D414yes—
84#432C2314yes—
85#432C2314yes—
86C2×C4⋊C8—22no—
87C2×C4⋊C8D414yes—
88#407—24no—
89#407—24no—
90C2×C22⋊C8—22no—
91C2×C22⋊C8—24no—
92C2×C22⋊C8—22no—
93C2×C22⋊C8—22no—
94C2×C22⋊C8—24no—
95C2×C22⋊C8—22no—
96C2×#97—22no—
97C2×#97—22no—
98#399—24no—
99#399—24no—
100#399—24no—
101#399—24no—
102#390—24no—
103#390C2×C418yes—
104#384—24no—
105#384C2×C418yes—
106C4×C4⋊C4—21no—
107C4×C4⋊C4—21no—
108C4×C4⋊C4C2×C412yes—
109C4×C4⋊C4C2312yes—
110C2×#95—21no—
111#332—216no—
112#323—24no—
113#323—24no—
114C25C22⋊C411yescharacteristic
115C25C22⋊C411yescharacteristic
116C22×Q8—22no—
117C22×Q8—22no—
118C22×Q8—44no—
119C22×Q8—44no—
120C22×Q8—41no—
121C22×Q8—41no—
122C22×Q8—41no—
123C22×Q8—41no—
124C22×D4—24no—
125C22×D4—22no—
126C22×D4—22no—
127C22×D4—42no—
128C22×D4C22⋊C412yes—
129C22×D4C22×C412yes—
130C23×C4—22no—
131C23×C4—21no—
132C23×C4—21no—
133C23×C4—21no—
134C23×C4—21no—
135C23×C4—21no—
136C23×C4—21no—
137C23×C4—21no—
138C23×C4—21no—
139C23×C4—22no—
140C23×C4—44no—
141C23×C4—44no—
142C23×C4C22⋊C411yescharacteristic
143C23×C4C22⋊C411yescharacteristic
144C23×C4C22⋊C412yes—
145C23×C4C22⋊C412yes—
146C23×C4C22×C411yescharacteristic
147C23×C4C2×D411yescharacteristic
148C23×C4C2×D412yes—
149C23×C4C2×D412yes—
150C23×C4C2×D411yescharacteristic
151C2×M16—28no—
152C2×M16—84no—
153C22×C8—24no—
154C22×C8—28no—
155C22×C8—42no—
156C22×C8—84no—
157C4⋊Q8—24no—
158C4⋊Q8—24no—
159C4⋊Q8—24no—
160C4⋊Q8—24no—
161C4⋊Q8—42no—
162C4⋊Q8—42no—
163C4⋊Q8—42no—
164C4⋊Q8—42no—
165C22⋊Q8—416no—
166C22⋊Q8—416no—
167C22⋊Q8—416no—
168C22⋊Q8—416no—
169C4×D4—24no—
170C4×D4—24no—
171C4×D4—24no—
172C4×D4—24no—
173C4×D4—24no—
174C4×D4—24no—
175C4×D4—24no—
176C4×D4—24no—
177C2×C4⋊C4—28no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—24no—
183C2×C4⋊C4—24no—
184C2×C4⋊C4—28no—
185C2×C4⋊C4—28no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—48no—
190C2×C4⋊C4—48no—
191C2×C4⋊C4—42no—
192C2×C4⋊C4—42no—
193C2×C4⋊C4C22⋊C412yes—
194C2×C4⋊C4C22×C414yes—
195C2×C4⋊C4C22×C412yes—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4—22no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—28no—
201C2×C22⋊C4—28no—
202C2×C22⋊C4—48no—
203C2×C22⋊C4—48no—
204C2×C22⋊C4C22⋊C412yes—
205C2×C22⋊C4C22⋊C412yes—
206C2×C22⋊C4C2×D412yes—
207C2×C22⋊C4C2×D412yes—
208C2×C42—22no—
209C2×C42—44no—
210C2×C42C22×C414yes—
211C2×C42C22×C411yescharacteristic
212C2×C42C2×D412yes—
213C2×C42C2×D412yes—
214C2×C42C2×D411yescharacteristic
215C2×C42C2×D411yescharacteristic
216C2×C42#4112yes—
217C2×C42#4112yes—
218C2×C42C2411yescharacteristic
219C4⋊C8—24no—
220C4⋊C8—24no—
221C4⋊C8—42no—
222C4⋊C8C2×D418yes—
223C22⋊C8—28no—
224C22⋊C8—28no—
225C22⋊C8—24no—
226C22⋊C8—24no—
227C22⋊C8—24no—
228C22⋊C8—42no—
229#97—24no—
230#97—24no—
231#97—24no—
232#97—42no—
233#95—22no—
234#95—22no—
235C24—21no—
236C24—21no—
237C24—22no—
238C24—21no—
239C24—22no—
240C24—21no—
241C24—22no—
242C24—42no—
243C24—42no—
244C24—42no—
245C24—42no—
246C24#10114yes—
247C24C2×C22⋊C411yescharacteristic
248C24C2×C22⋊C412yes—
249C24C2×C22⋊C412yes—
250C2×Q8—44no—
251C2×Q8—44no—
252C2×Q8—44no—
253C2×Q8—44no—
254C2×Q8—42no—
255C2×Q8—42no—
256C2×Q8—42no—
257C2×Q8—42no—
258C2×Q8—84no—
259C2×Q8—84no—
260C2×Q8—84no—
261C2×Q8—84no—
262C2×D4—24no—
263C2×D4—24no—
264C2×D4—24no—
265C2×D4—24no—
266C2×D4—42no—
267C2×D4—42no—
268C2×D4—48no—
269C2×D4—48no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—24no—
273C22×C4—28no—
274C22×C4—24no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—24no—
288C22×C4—42no—
289C22×C4—44no—
290C22×C4—44no—
291C22×C4—44no—
292C22×C4—44no—
293C22×C4—44no—
294C22×C4—44no—
295C22×C4—44no—
296C22×C4—44no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—44no—
300C22×C4—44no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—82no—
304C22×C4—82no—
305C22×C4—82no—
306C22×C4—82no—
307C22×C4—82no—
308C22×C4—82no—
309C22×C4C2×C22⋊C411yescharacteristic
310C22×C4C2×C22⋊C411yescharacteristic
311C22×C4C2×C22⋊C412yes—
312C22×C4C2×C22⋊C412yes—
313C22×C4C2×C22⋊C411yescharacteristic
314C22×C4C4×D412yes—
315C22×C4C4×D412yes—
316C22×C4#12011yescharacteristic
317C22×C4#12011yescharacteristic
318C22×C4#12112yes—
319C22×C4#12112yes—
320C22×C4#12311yescharacteristic
321C22×C4#12311yescharacteristic
322C22×C4C23×C411yescharacteristic
323C22×C4C22×D411yescharacteristic
324C22×C4C22×D411yescharacteristic
325M16—88no—
326C2×C8—28no—
327C2×C8—48no—
328C2×C8—44no—
329C2×C8—88no—
330C2×C8—84no—
331C4⋊C4—28no—
332C4⋊C4—28no—
333C4⋊C4—24no—
334C4⋊C4—24no—
335C4⋊C4—28no—
336C4⋊C4—416no—
337C4⋊C4—416no—
338C4⋊C4—44no—
339C4⋊C4—44no—
340C4⋊C4—44no—
341C22⋊C4—24no—
342C22⋊C4—24no—
343C22⋊C4—24no—
344C22⋊C4—24no—
345C22⋊C4—416no—
346C22⋊C4—416no—
347C42—44no—
348C42—44no—
349C42C4×D412yes—
350C42C4×D412yes—
351C42#12012yes—
352C42#12112yes—
353C42#12112yes—
354C42#12312yes—
355C42C22×D412yes—
356C42C2×#4112yes—
357C23—22no—
358C23—22no—
359C23—24no—
360C23—22no—
361C23—22no—
362C23—24no—
363C23—22no—
364C23—22no—
365C23—22no—
366C23—42no—
367C23—42no—
368C23—48no—
369C23—42no—
370C23—42no—
371C23—48no—
372C23—42no—
373C23—42no—
374C23—42no—
375C23—42no—
376C23—42no—
377C23—42no—
378C23—81no—
379C23—81no—
380C23—81no—
381C23—81no—
382C23—84no—
383C23—84no—
384C23#38611yescharacteristic
385C23#38611yescharacteristic
386C23C2×#10112yes—
387C23C2×#10114yes—
388C23#41312yes—
389C23C22×C22⋊C411yescharacteristic
390Q8—84no—
391Q8—84no—
392Q8—84no—
393Q8—84no—
394D4—48no—
395D4—48no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—22no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—28no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—44no—
415C2×C4—416no—
416C2×C4—44no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—44no—
420C2×C4—44no—
421C2×C4—44no—
422C2×C4—44no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—44no—
426C2×C4—44no—
427C2×C4—44no—
428C2×C4—82no—
429C2×C4—82no—
430C2×C4—82no—
431C2×C4—82no—
432C2×C4—81no—
433C2×C4—81no—
434C2×C4—84no—
435C2×C4—84no—
436C2×C4#38612yes—
437C2×C4#38611yescharacteristic
438C2×C4#38612yes—
439C2×C4#38611yescharacteristic
440C2×C4#45314yes—
441C2×C4C2×C4×D412yes—
442C2×C4C2×#12011yescharacteristic
443C2×C4C2×#12112yes—
444C2×C4C2×#12311yescharacteristic
445C8—48no—
446C8—84no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—24no—
452C22—24no—
453C22—24no—
454C22—44no—
455C22—44no—
456C22—42no—
457C22—42no—
458C22—48no—
459C22—42no—
460C22—42no—
461C22—42no—
462C22—82no—
463C22—84no—
464C22—82no—
465C22—84no—
466C22—84no—
467C22#188712yes—
468C22#190112yes—
469C22#190112yes—
470C22#190912yes—
471C22C2×#38611yescharacteristic
472C22C22×#10111yescharacteristic
473C22C2×#41311yescharacteristic
474C4—22no—
475C4—22no—
476C4—21no—
477C4—21no—
478C4—22no—
479C4—22no—
480C4—48no—
481C4—42no—
482C4—42no—
483C4—84no—
484C4#188712yes—
485C4C2×#45312yes—
486C2—21no—
487C2—21no—
488C2—22no—
489C2—44no—
490C2—82no—
491C2#945514yesdirect product factor
492C2C2×#188711yescharacteristic
493C2C2×#190111yescharacteristic
494C2C2×#190911yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radicalC23×D4C2×C4
LCSG ▷ C22×C4 ▷ 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
3. C2×#1556C2semidirect
5. #9455C2direct (N × H)
6. C2×#1285C2semidirect
29. #1556C22semidirect
35. #1285C22semidirect
491. C2#9455direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#29732
C2×#25422
C2×#15562
C2×#14662
#94552
C2×#12852