Finite Group Databasebeta

← C2×#10381 #238313

Subgroups — C2×#10381 #238313

Order 512.

882 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2606C211yesmaximal, characteristic
2C2×#1986C211yesmaximal, characteristic
3C2×#1515C211yesmaximal, characteristic
4C2×#1506C211yesmaximal, characteristic
5#10381C218yesmaximal, direct product factor
6C2×#1300C211yesmaximal, characteristic
7C2×#1288C211yesmaximal, characteristic
8C2×#1285C211yesmaximal, characteristic
9C2×#533C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#432C2211yescharacteristic
12C2×C4×M16C2211yescharacteristic
13#2606—22no—
14#2606—22no—
15#2606—22no—
16#2606C2214yes—
17C2×#398—21no—
18C2×#398—21no—
19C2×#389—21no—
20C2×#389—21no—
21C2×#387—21no—
22C2×#387—21no—
23C2×#383C2211yescharacteristic
24C2×C4×C4⋊C4C2211yescharacteristic
25C2×#376C2211yescharacteristic
26#1986—22no—
27#1986C2214yes—
28C2×#339—21no—
29C2×#339—21no—
30#1515—22no—
31#1515C2214yes—
32#1506—22no—
33#1506C2214yes—
34C2×#328—21no—
35C2×#328—21no—
36C2×#328—21no—
37C2×#328—21no—
38#1300C2214yes—
39#1288C2214yes—
40#1285C2214yes—
41C22×M16—21no—
42#533—21no—
43#533—21no—
44#533—21no—
45#533—21no—
46#533—21no—
47#533—21no—
48#533Q812yes—
49#533C2312yes—
50C2×C4⋊Q8Q811yescharacteristic
51C2×C4⋊Q8Q811yescharacteristic
52C2×#125—21no—
53C2×C22⋊Q8—21no—
54C2×C22⋊Q8—21no—
55C2×C4×Q8—21no—
56C2×C4×Q8—21no—
57C2×#117—21no—
58C22×C4⋊C4—21no—
59C22×C4⋊C4—21no—
60C22×C4⋊C4—21no—
61C22×C4⋊C4—21no—
62C22×C4⋊C4—21no—
63C22×C4⋊C4—21no—
64C22×C4⋊C4—21no—
65C22×C42—21no—
66C22×C42D411yescharacteristic
67C22×C42D411yescharacteristic
68C22×C42C2311yescharacteristic
69#432—21no—
70#432—21no—
71#432—21no—
72#432—21no—
73#432—21no—
74#432—21no—
75#432C2312yes—
76#432C2312yes—
77C2×C4⋊C8—21no—
78C2×C4⋊C8—21no—
79C2×C22⋊C8—21no—
80C2×C22⋊C8—21no—
81C4×M16—21no—
82C4×M16—21no—
83C4×M16—21no—
84C4×M16C2312yes—
85C2×#97—21no—
86C2×#97—21no—
87C2×#97—21no—
88C2×C4×C8—21no—
89#398—24no—
90#398—24no—
91#398—24no—
92#398—24no—
93#389—24no—
94#389—24no—
95#389—24no—
96#389—24no—
97#387—24no—
98#387—24no—
99#387—24no—
100#387—24no—
101#383—21no—
102#383—21no—
103#383D412yes—
104#383C2312yes—
105C4×C4⋊C4—21no—
106C4×C4⋊C4—21no—
107C4×C4⋊C4D412yes—
108C4×C4⋊C4C2312yes—
109#376—21no—
110#376—21no—
111#376D412yes—
112#376C2312yes—
113C2×#95—21no—
114C2×#95—21no—
115C2×#95—21no—
116C2×#95—21no—
117C2×#95—21no—
118C2×#95—21no—
119C2×#95D411yescharacteristic
120C2×#95D411yescharacteristic
121C2×#95D411yescharacteristic
122C2×#95D411yescharacteristic
123#339—24no—
124#339—24no—
125#328—24no—
126#328—24no—
127#328—24no—
128#328—24no—
129C22×Q8—21no—
130C22×Q8—21no—
131C23×C4—21no—
132C23×C4—21no—
133C23×C4—21no—
134C23×C4—21no—
135C23×C4—21no—
136C23×C4—21no—
137C23×C4C2×D411yescharacteristic
138C23×C4C2×D411yescharacteristic
139C23×C4C2×D411yescharacteristic
140C2×M16—24no—
141C2×M16—22no—
142C2×M16—42no—
143C2×M16—41no—
144C22×C8—41no—
145C22×C8—41no—
146C22×C8—41no—
147C4⋊Q8—21no—
148C4⋊Q8—21no—
149C4⋊Q8—21no—
150C4⋊Q8—21no—
151C4⋊Q8—21no—
152C4⋊Q8—21no—
153C4⋊Q8C2×Q812yes—
154C4⋊Q8C2×Q812yes—
155#125—22no—
156#125—22no—
157#125—41no—
158#125—41no—
159C22⋊Q8—22no—
160C22⋊Q8—22no—
161C22⋊Q8—22no—
162C22⋊Q8—22no—
163C22⋊Q8—41no—
164C22⋊Q8—41no—
165C22⋊Q8—41no—
166C22⋊Q8—41no—
167C4×Q8—22no—
168C4×Q8—22no—
169C4×Q8—22no—
170C4×Q8—22no—
171C4×Q8—41no—
172C4×Q8—41no—
173C4×Q8—41no—
174C4×Q8—41no—
175#117—22no—
176#117—22no—
177#117—41no—
178#117—41no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—24no—
184C2×C4⋊C4—24no—
185C2×C4⋊C4—24no—
186C2×C4⋊C4—24no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—24no—
190C2×C4⋊C4—24no—
191C2×C4⋊C4—44no—
192C2×C4⋊C4—44no—
193C2×C4⋊C4—44no—
194C2×C4⋊C4—44no—
195C2×C4⋊C4—44no—
196C2×C4⋊C4—41no—
197C2×C4⋊C4—41no—
198C2×C4⋊C4—82no—
199C2×C4⋊C4—82no—
200C2×C22⋊C4—41no—
201C2×C42—22no—
202C2×C42—22no—
203C2×C42—21no—
204C2×C42—21no—
205C2×C42—44no—
206C2×C42—41no—
207C2×C42—42no—
208C2×C42—42no—
209C2×C42C2×D412yes—
210C2×C42C2×D412yes—
211C2×C42C2×D411yescharacteristic
212C2×C42C2×D411yescharacteristic
213C2×C42C2×D411yescharacteristic
214C2×C42C2×Q811yescharacteristic
215C2×C42C2×Q811yescharacteristic
216C2×C42#4111yescharacteristic
217C2×C42#4111yescharacteristic
218C2×C42#4111yescharacteristic
219C2×C42#4111yescharacteristic
220C2×C42#4111yescharacteristic
221C2×C42#4111yescharacteristic
222C2×C42C2411yescharacteristic
223C4⋊C8—22no—
224C4⋊C8—22no—
225C4⋊C8—41no—
226C4⋊C8—41no—
227C22⋊C8—22no—
228C22⋊C8—22no—
229C22⋊C8—41no—
230C22⋊C8—41no—
231#97—22no—
232#97—22no—
233#97—22no—
234#97—41no—
235#97—41no—
236#97—41no—
237C4×C8—22no—
238C4×C8—41no—
239#95—24no—
240#95—24no—
241#95—22no—
242#95—22no—
243#95—22no—
244#95—22no—
245#95—21no—
246#95—21no—
247#95—21no—
248#95—21no—
249#95—22no—
250#95—22no—
251#95—22no—
252#95—22no—
253#95C2×D412yes—
254#95C2×D412yes—
255#95C2×D412yes—
256#95C2×D412yes—
257C24#12011yescharacteristic
258C2×Q8—22no—
259C2×Q8—22no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×Q8—82no—
263C2×Q8—82no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—24no—
267C22×C4—24no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4#12011yescharacteristic
295C22×C4#12011yescharacteristic
296C22×C4#12011yescharacteristic
297C22×C4C22⋊Q811yescharacteristic
298C22×C4C22⋊Q811yescharacteristic
299C22×C4C22⋊Q811yescharacteristic
300C22×C4C22⋊Q811yescharacteristic
301C22×C4C22⋊Q811yescharacteristic
302C22×C4C22⋊Q811yescharacteristic
303C22×C4#12411yescharacteristic
304C22×C4#12411yescharacteristic
305C22×C4#12411yescharacteristic
306C22×C4#12411yescharacteristic
307C22×C4#12411yescharacteristic
308C22×C4#12411yescharacteristic
309C22×C4C22×D411yescharacteristic
310C22×C4C22×D411yescharacteristic
311C22×C4C22×D411yescharacteristic
312M16—24no—
313M16—42no—
314M16—44no—
315C2×C8—44no—
316C2×C8—42no—
317C2×C8—42no—
318C2×C8—42no—
319C2×C8—82no—
320C2×C8—82no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—48no—
326C4⋊C4—48no—
327C4⋊C4—44no—
328C4⋊C4—44no—
329C4⋊C4—48no—
330C4⋊C4—48no—
331C4⋊C4—42no—
332C4⋊C4—42no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—42no—
338C4⋊C4—42no—
339C4⋊C4—84no—
340C4⋊C4—84no—
341C22⋊C4—42no—
342C22⋊C4—42no—
343C42—42no—
344C42—42no—
345C42—44no—
346C42—44no—
347C42—42no—
348C42—42no—
349C42—81no—
350C42—81no—
351C42C22⋊Q811yescharacteristic
352C42C22⋊Q811yescharacteristic
353C42C22⋊Q811yescharacteristic
354C42C22⋊Q811yescharacteristic
355C42C22⋊Q811yescharacteristic
356C42C22⋊Q811yescharacteristic
357C42#12411yescharacteristic
358C42#12411yescharacteristic
359C42#12411yescharacteristic
360C42#12411yescharacteristic
361C42#12411yescharacteristic
362C42#12411yescharacteristic
363C42C22×Q811yescharacteristic
364C42C2×#4111yescharacteristic
365C42C2×#4111yescharacteristic
366C42C2×#4111yescharacteristic
367C23—22no—
368C23—22no—
369C23#39311yescharacteristic
370C23#39311yescharacteristic
371C23#45512yes—
372C23#45612yes—
373C23C2×#12011yescharacteristic
374Q8—82no—
375Q8—82no—
376Q8—82no—
377Q8—82no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—24no—
391C2×C4—24no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—48no—
403C2×C4—48no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—84no—
421C2×C4—84no—
422C2×C4—84no—
423C2×C4—84no—
424C2×C4—82no—
425C2×C4—82no—
426C2×C4#39311yescharacteristic
427C2×C4#39311yescharacteristic
428C2×C4#39311yescharacteristic
429C2×C4#39311yescharacteristic
430C2×C4#39311yescharacteristic
431C2×C4#39311yescharacteristic
432C2×C4C2×C22⋊Q811yescharacteristic
433C2×C4C2×C22⋊Q811yescharacteristic
434C2×C4C2×C22⋊Q811yescharacteristic
435C2×C4C2×#12411yescharacteristic
436C2×C4C2×#12411yescharacteristic
437C2×C4C2×#12411yescharacteristic
438C8—44no—
439C8—82no—
440C8—82no—
441C22—24no—
442C22—24no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22#202812yes—
448C22#202812yes—
449C22#203112yes—
450C22#203112yes—
451C22C2×#39311yescharacteristic
452C22C2×#45511yescharacteristic
453C22C2×#45611yescharacteristic
454C4—21no—
455C4—21no—
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—44no—
467C4—44no—
468C4—82no—
469C4—82no—
470C4—82no—
471C4—82no—
472C4—82no—
473C4—82no—
474C2—21no—
475C2—21no—
476C2—22no—
477C2#1038114yesdirect product factor
478C2C2×#202811yescharacteristic
479C2C2×#203111yescharacteristic
480C2C2×#203111yescharacteristic
subgroupG/H
center, socleC23#393
commutator, Frattini, cosocleC2×C42C24
prime radicalC24#120
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
5. #10381C2direct (N × H)
477. C2#10381direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#26062
C2×#19862
C2×#15152
C2×#15062
#103812
C2×#13002
C2×#12882
C2×#12852