Finite Group Databasebeta

← C2×#13299 #495414

Subgroups — C2×#13299 #495414

Order 512.

1332 conjugacy classes of subgroups.

The subgroup lattice has 497 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2563C211yesmaximal, characteristic
2C2×#1799C211yesmaximal, characteristic
3C2×C4×#99C211yesmaximal, characteristic
4#13299C218yesmaximal, direct product factor
5C2×#1393C214yesmaximal
6C22×C4⋊Q8C411yescharacteristic, complemented
7C22×C4×D4C2211yescharacteristic
8C22×#99C2212yes—
9C22×#99C2212yes—
10#2563—22no—
11#2563—22no—
12#2563C414yescomplemented
13#2563C2214yes—
14C2×#393—21no—
15C2×#393—21no—
16C2×#390C2212yes—
17C2×#382C412yescomplemented
18C2×#380—21no—
19C2×#380—21no—
20C2×#380—21no—
21C2×C4×C4⋊C4C411yescharacteristic, complemented
22C2×C4×C22⋊C4—21no—
23#1799—22no—
24#1799C2214yes—
25C4×#99—22no—
26C4×#99C2214yes—
27C2×#342—21no—
28C2×#342—21no—
29#1393C22116yes—
30C23×Q8—21no—
31C23×D4C2311yescharacteristic
32C24×C4D411yescharacteristic
33C24×C4D411yescharacteristic
34C2×C4⋊Q8—22no—
35C2×C4⋊Q8—42no—
36C2×C4⋊Q8—41no—
37C2×C4⋊Q8—41no—
38C2×C4⋊Q8C2×C414yescomplemented
39C2×C4×D4—41no—
40C2×C4×D4—41no—
41C2×C4×D4—42no—
42C2×C4×D4C2×C412yes—
43C2×C4×D4D412yes—
44C2×C4×D4D412yes—
45C2×C4×D4C2312yes—
46C22×C4⋊C4—21no—
47C22×C4⋊C4—21no—
48C22×C4⋊C4—41no—
49C22×C4⋊C4C2×C412yes—
50C22×C4⋊C4C2×C411yescharacteristic
51C22×C22⋊C4—22no—
52C22×C22⋊C4—22no—
53C22×C22⋊C4—22no—
54C22×C22⋊C4—22no—
55C22×C22⋊C4D411yescharacteristic
56C22×C22⋊C4D411yescharacteristic
57C22×C42—41no—
58C22×C42C2×C411yescharacteristic
59C22×C42C2×C412yes—
60C2×#99—22no—
61C2×#99—24no—
62C2×#99—28no—
63C2×#99—22no—
64C2×#99Q818yescomplemented
65C2×#99C2314yes—
66C2×#99C2314yes—
67#393—24no—
68#393—24no—
69#393—24no—
70#393—24no—
71#390—22no—
72#390—22no—
73#390C2×C414yes—
74#390C2314yes—
75#382—24no—
76#382C2×C418yescomplemented
77#380—24no—
78#380—24no—
79#380—24no—
80#380—24no—
81#380—24no—
82#380—42no—
83C4×C4⋊C4—22no—
84C4×C4⋊C4C2×C414yescomplemented
85C4×C22⋊C4—24no—
86C4×C22⋊C4—42no—
87C2×#95—21no—
88C2×#95—22no—
89C2×#95—22no—
90C2×#95—41no—
91C2×#95—41no—
92#342—24no—
93#342—24no—
94C25C2×D411yescharacteristic
95C25C2×D411yescharacteristic
96C22×Q8—24no—
97C22×Q8—42no—
98C22×Q8—42no—
99C22×Q8—84no—
100C22×D4—41no—
101C22×D4—41no—
102C22×D4—42no—
103C22×D4C22×C411yescharacteristic
104C22×D4C2×D411yescharacteristic
105C22×D4C2×D411yescharacteristic
106C22×D4C2×Q814yes—
107C22×D4#4114yes—
108C22×D4C2411yescharacteristic
109C23×C4—21no—
110C23×C4—21no—
111C23×C4—21no—
112C23×C4—21no—
113C23×C4—22no—
114C23×C4—22no—
115C23×C4—22no—
116C23×C4—22no—
117C23×C4—44no—
118C23×C4—44no—
119C23×C4—42no—
120C23×C4—42no—
121C23×C4C22⋊C411yescharacteristic
122C23×C4C22⋊C411yescharacteristic
123C23×C4C22⋊C411yescharacteristic
124C23×C4C22⋊C412yes—
125C23×C4C22⋊C412yes—
126C23×C4C22⋊C411yescharacteristic
127C23×C4C22×C411yescharacteristic
128C23×C4C2×D412yes—
129C23×C4C2×D412yes—
130C4⋊Q8—44no—
131C4⋊Q8—44no—
132C4⋊Q8—44no—
133C4⋊Q8—44no—
134C4×D4—42no—
135C4×D4—42no—
136C4×D4—42no—
137C4×D4—42no—
138C4×D4—42no—
139C4×D4—42no—
140C4×D4—42no—
141C4×D4—42no—
142C2×C4⋊C4—24no—
143C2×C4⋊C4—24no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—41no—
146C2×C4⋊C4—41no—
147C2×C4⋊C4—42no—
148C2×C4⋊C4—42no—
149C2×C4⋊C4—44no—
150C2×C4⋊C4—42no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—44no—
154C2×C4⋊C4—84no—
155C2×C4⋊C4C22⋊C412yes—
156C2×C4⋊C4C22×C414yes—
157C2×C4⋊C4C22×C412yes—
158C2×C22⋊C4—28no—
159C2×C22⋊C4—24no—
160C2×C22⋊C4—24no—
161C2×C22⋊C4—24no—
162C2×C22⋊C4—24no—
163C2×C22⋊C4—24no—
164C2×C22⋊C4—24no—
165C2×C22⋊C4—41no—
166C2×C22⋊C4—41no—
167C2×C22⋊C4—41no—
168C2×C22⋊C4—41no—
169C2×C22⋊C4—44no—
170C2×C22⋊C4—42no—
171C2×C22⋊C4—44no—
172C2×C22⋊C4—44no—
173C2×C22⋊C4—42no—
174C2×C22⋊C4—84no—
175C2×C22⋊C4—84no—
176C2×C22⋊C4C22⋊C412yes—
177C2×C22⋊C4C22⋊C412yes—
178C2×C22⋊C4C2×D412yes—
179C2×C22⋊C4C2×D412yes—
180C2×C42—22no—
181C2×C42—21no—
182C2×C42—21no—
183C2×C42—22no—
184C2×C42—44no—
185C2×C42—44no—
186C2×C42—84no—
187C2×C42C22⋊C412yes—
188C2×C42C22×C412yes—
189C2×C42C22×C414yes—
190#99—28no—
191#99—24no—
192#99—28no—
193#99—44no—
194#99C2×Q818yescomplemented
195#95—24no—
196#95—28no—
197#95—28no—
198#95—44no—
199#95—44no—
200C24—21no—
201C24—21no—
202C24—21no—
203C24—21no—
204C24—22no—
205C24—22no—
206C24—42no—
207C24—42no—
208C24—42no—
209C24—42no—
210C24C2×C22⋊C411yescharacteristic
211C24C2×C22⋊C411yescharacteristic
212C24C2×C22⋊C411yescharacteristic
213C24C22⋊Q814yes—
214C24#12412yes—
215C24C4⋊Q812yes—
216C24C22×D411yescharacteristic
217C24C22×D411yescharacteristic
218C2×Q8—48no—
219C2×Q8—88no—
220C2×Q8—88no—
221C2×Q8—88no—
222C2×D4—41no—
223C2×D4—41no—
224C2×D4—41no—
225C2×D4—41no—
226C2×D4—41no—
227C2×D4—41no—
228C2×D4—41no—
229C2×D4—44no—
230C2×D4—44no—
231C2×D4—44no—
232C2×D4—44no—
233C2×D4—41no—
234C2×D4C4×Q814yes—
235C2×D4C22⋊Q814yes—
236C2×D4#12412yes—
237C2×D4C4⋊Q812yes—
238C2×D4C22×Q812yes—
239C2×D4C2×#4112yes—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—22no—
243C22×C4—24no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—24no—
259C22×C4—24no—
260C22×C4—44no—
261C22×C4—44no—
262C22×C4—44no—
263C22×C4—44no—
264C22×C4—44no—
265C22×C4—44no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—44no—
270C22×C4—48no—
271C22×C4—44no—
272C22×C4—44no—
273C22×C4—44no—
274C22×C4—44no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—44no—
278C22×C4—44no—
279C22×C4—84no—
280C22×C4—84no—
281C22×C4—82no—
282C22×C4—82no—
283C22×C4—84no—
284C22×C4—84no—
285C22×C4—84no—
286C22×C4—84no—
287C22×C4—84no—
288C22×C4#9912yes—
289C22×C4#9911yescharacteristic
290C22×C4#9911yescharacteristic
291C22×C4C2×C22⋊C411yescharacteristic
292C22×C4C2×C22⋊C412yes—
293C22×C4C2×C22⋊C412yes—
294C22×C4C2×C22⋊C412yes—
295C22×C4C2×C22⋊C412yes—
296C22×C4C4×Q814yes—
297C22×C4C23×C411yescharacteristic
298C4⋊C4—42no—
299C4⋊C4—42no—
300C4⋊C4—44no—
301C4⋊C4—48no—
302C4⋊C4—44no—
303C4⋊C4—44no—
304C4⋊C4—44no—
305C4⋊C4—88no—
306C22⋊C4—28no—
307C22⋊C4—42no—
308C22⋊C4—42no—
309C22⋊C4—42no—
310C22⋊C4—42no—
311C22⋊C4—44no—
312C22⋊C4—48no—
313C22⋊C4—44no—
314C22⋊C4—44no—
315C22⋊C4—84no—
316C22⋊C4—84no—
317C22⋊C4—84no—
318C22⋊C4—84no—
319C22⋊C4—84no—
320C42—22no—
321C42—22no—
322C42—22no—
323C42—22no—
324C42—44no—
325C42—44no—
326C42—88no—
327C23—22no—
328C23—22no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—24no—
334C23—22no—
335C23—22no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—24no—
341C23—22no—
342C23—22no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—48no—
352C23—44no—
353C23—44no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—42no—
358C23—81no—
359C23—81no—
360C23—81no—
361C23—81no—
362C23—84no—
363C23—84no—
364C23#39112yes—
365C23#39112yes—
366C23#39112yes—
367C23C2×#9911yescharacteristic
368C23C2×#9911yescharacteristic
369C23#41012yes—
370C23C22×C22⋊C411yescharacteristic
371C23C2×C22⋊Q812yes—
372C23C2×#12411yescharacteristic
373C23C2×C4⋊Q811yescharacteristic
374Q8—816no—
375D4—44no—
376D4—44no—
377D4—42no—
378D4—42no—
379D4—42no—
380D4—42no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—22no—
386C2×C4—24no—
387C2×C4—24no—
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—44no—
398C2×C4—44no—
399C2×C4—44no—
400C2×C4—44no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—48no—
405C2×C4—44no—
406C2×C4—44no—
407C2×C4—44no—
408C2×C4—44no—
409C2×C4—44no—
410C2×C4—44no—
411C2×C4—82no—
412C2×C4—82no—
413C2×C4—82no—
414C2×C4—82no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—88no—
418C2×C4—84no—
419C2×C4—84no—
420C2×C4—84no—
421C2×C4—816no—
422C2×C4—84no—
423C2×C4—84no—
424C2×C4—84no—
425C2×C4—84no—
426C2×C4—168no—
427C2×C4#35414yes—
428C2×C4#39112yes—
429C2×C4C2×#9912yes—
430C2×C4C2×#9912yes—
431C2×C4C2×C4×Q812yes—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—24no—
437C22—24no—
438C22—22no—
439C22—21no—
440C22—21no—
441C22—22no—
442C22—22no—
443C22—42no—
444C22—41no—
445C22—41no—
446C22—42no—
447C22—42no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—48no—
457C22—44no—
458C22—44no—
459C22—81no—
460C22—81no—
461C22—81no—
462C22—81no—
463C22—84no—
464C22—82no—
465C22—82no—
466C22#199612yes—
467C22#199612yes—
468C22C2×#35412yes—
469C22#212812yes—
470C22C2×#39111yescharacteristic
471C22C22×#9911yescharacteristic
472C22C2×#41011yescharacteristic
473C4—22no—
474C4—22no—
475C4—22no—
476C4—42no—
477C4—42no—
478C4—42no—
479C4—84no—
480C4—88no—
481C4—84no—
482C4—164no—
483C4C2×#35414yes—
484C2—21no—
485C2—21no—
486C2—22no—
487C2—42no—
488C2—41no—
489C2—41no—
490C2—42no—
491C2—42no—
492C2#1329914yesdirect product factor
493C2C2×#199611yescharacteristic
494C2C22×#35411yescharacteristic
495C2C2×#212811yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC22×D4C24
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #13299C2direct (N × H)
6. C22×C4⋊Q8C4semidirect
12. #2563C4semidirect
17. C2×#382C4semidirect
21. C2×C4×C4⋊C4C4semidirect
38. C2×C4⋊Q8C2×C4semidirect
64. C2×#99Q8semidirect
76. #382C2×C4semidirect
84. C4×C4⋊C4C2×C4semidirect
194. #99C2×Q8semidirect
492. C2#13299direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25632
C2×#17992
C2×C4×#992
#132992
C2×#13932