Finite Group Databasebeta

← C2×#24905817 #35370356

Subgroups — C2×#24905817 #35370356

Order 21248.

1002 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581782C211yesmaximal, characteristic
2C2×#19127755C211yesmaximal, characteristic
3C2×#19127751C211yesmaximal, characteristic
4#24905817C218yesmaximal, direct product factor
5C2×#19127427C211yesmaximal, characteristic
6C2×#19127426C211yesmaximal, characteristic
7C2×#19127426C211yesmaximal, characteristic
8C2×#324×C83C211yesmaximal, characteristic
9C2×#14581782—21no—
10C2×#14581782—21no—
11C2×#14581782—21no—
12C2×#14581782—21no—
13C2×#14581782—22no—
14C2×#14581782—22no—
15C2×#14581782C414yes—
16C2×#14581782C2214yes—
17C22×C4⋊Dic83C411yescharacteristic
18C22×Dic83⋊C4C411yescharacteristic
19C22×Dic83⋊C4C411yescharacteristic
20C22×Dic83⋊C4C411yescharacteristic
21C22×Dic83⋊C4C2211yescharacteristic
22C22×C4×Dic83C2211yescharacteristic
23#19127755—22no—
24#19127755C2214yes—
25#19127751—22no—
26#19127751C2214yes—
27C2×Dic83⋊C8—21no—
28C2×Dic83⋊C8—21no—
29C2×C22⋊(C83⋊C8)C2211yescharacteristic
30C2×C22⋊(C83⋊C8)C2211yescharacteristic
31C2×#14581702—21no—
32C2×C8×Dic83—21no—
33#19127427C2214yes—
34#19127426C2214yes—
35#19127426C2214yes—
36C22×C4⋊C4×C83C2211yescharacteristic
37C2×C22⋊C8×C83C2211yescharacteristic
38C2×C22⋊C8×C83C2211yescharacteristic
39#324×C83C2214yes—
40C23×Dic83C2×C411yescharacteristic
41C23×Dic83C2×C411yescharacteristic
42C23×Dic83C2×C411yescharacteristic
43C23×Dic83C2×C411yescharacteristic
44C22×C83⋊C8—21no—
45C22×C83⋊C8—21no—
46#14581782—24no—
47#14581782—24no—
48#14581782—24no—
49#14581782—24no—
50#14581782—24no—
51#14581782—24no—
52#14581782—24no—
53#14581782—24no—
54C2×C4⋊Dic83—22no—
55C2×C4⋊Dic83—21no—
56C2×C4⋊Dic83—21no—
57C2×C4⋊Dic83C2×C414yes—
58C2×Dic83⋊C4—22no—
59C2×Dic83⋊C4—21no—
60C2×Dic83⋊C4—21no—
61C2×Dic83⋊C4—22no—
62C2×Dic83⋊C4—21no—
63C2×Dic83⋊C4—21no—
64C2×Dic83⋊C4—22no—
65C2×Dic83⋊C4—21no—
66C2×Dic83⋊C4—21no—
67C2×Dic83⋊C4—21no—
68C2×Dic83⋊C4—21no—
69C2×Dic83⋊C4—21no—
70C2×Dic83⋊C4—21no—
71C2×Dic83⋊C4C2×C414yes—
72C2×Dic83⋊C4C2×C414yes—
73C2×Dic83⋊C4C2×C414yes—
74C2×Dic83⋊C4C2×C412yes—
75C2×Dic83⋊C4C2312yes—
76C2×C4×Dic83C2×C412yes—
77C2×C4×Dic83D411yescharacteristic
78C2×C4×Dic83D411yescharacteristic
79C2×C4×Dic83D411yescharacteristic
80C2×C4×Dic83D411yescharacteristic
81C2×C4×Dic83D412yes—
82C2×C4×Dic83D412yes—
83C2×C4×Dic83C2312yes—
84Dic83⋊C8—24no—
85Dic83⋊C8—24no—
86C22⋊(C83⋊C8)—21no—
87C22⋊(C83⋊C8)—21no—
88C22⋊(C83⋊C8)C2312yes—
89C22⋊(C83⋊C8)C2312yes—
90#14581702—24no—
91C8×Dic83—24no—
92C23×C4×C83C2×C411yescharacteristic
93C23×C4×C83C2×C411yescharacteristic
94C23×C4×C83C2311yescharacteristic
95C22×C8×C83—21no—
96C22×C8×C83—21no—
97C2×C4⋊C4×C83—21no—
98C2×C4⋊C4×C83—21no—
99C2×C4⋊C4×C83—21no—
100C2×C4⋊C4×C83—21no—
101C2×C4⋊C4×C83C2×C412yes—
102C2×C4⋊C4×C83C2312yes—
103C22⋊C8×C83—21no—
104C22⋊C8×C83—21no—
105C22⋊C8×C83C2312yes—
106C22⋊C8×C83C2312yes—
107C22×Dic83—22no—
108C22×Dic83—22no—
109C22×Dic83—24no—
110C22×Dic83—21no—
111C22×Dic83—21no—
112C22×Dic83—21no—
113C22×Dic83—21no—
114C22×Dic83—22no—
115C22×Dic83—22no—
116C22×Dic83—42no—
117C22×Dic83C22⋊C412yes—
118C22×Dic83C22⋊C411yescharacteristic
119C22×Dic83C22⋊C412yes—
120C22×Dic83C22⋊C411yescharacteristic
121C22×Dic83C22⋊C411yescharacteristic
122C22×Dic83C22⋊C411yescharacteristic
123C22×Dic83C22×C412yes—
124C22×Dic83C22×C412yes—
125C22×Dic83C22×C412yes—
126C22×Dic83C22×C412yes—
127C2×C83⋊C8—22no—
128C2×C83⋊C8—22no—
129C2×C83⋊C8—42no—
130C2×C83⋊C8—42no—
131C4⋊Dic83—24no—
132C4⋊Dic83—24no—
133Dic83⋊C4—22no—
134Dic83⋊C4—22no—
135Dic83⋊C4—22no—
136Dic83⋊C4—22no—
137Dic83⋊C4—24no—
138Dic83⋊C4—24no—
139Dic83⋊C4—24no—
140Dic83⋊C4—24no—
141Dic83⋊C4—24no—
142Dic83⋊C4—24no—
143C4×Dic83C22⋊C412yes—
144C4×Dic83C22⋊C412yes—
145C4×Dic83C22⋊C412yes—
146C4×Dic83C22⋊C412yes—
147C4×Dic83C2×D412yes—
148C4×Dic83C2×D412yes—
149C4×Dic83C2×D412yes—
150C4×Dic83C2×D412yes—
151C24×C83C22×C411yescharacteristic
152C22×C4×C83—21no—
153C22×C4×C83—21no—
154C22×C4×C83—21no—
155C22×C4×C83—21no—
156C22×C4×C83—22no—
157C22×C4×C83—22no—
158C22×C4×C83—42no—
159C22×C4×C83—42no—
160C22×C4×C83C22×C412yes—
161C22×C4×C83C22×C412yes—
162C22×C4×C83C22×C411yescharacteristic
163C22×C4×C83C2×D411yescharacteristic
164C22×C4×C83C2×D411yescharacteristic
165C22×C4×C83C2×D411yescharacteristic
166C22×C4×C83C2×D411yescharacteristic
167C22×C4×C83C2411yescharacteristic
168C2×C8×C83—22no—
169C2×C8×C83—22no—
170C2×C8×C83—42no—
171C2×C8×C83—42no—
172C4⋊C4×C83—22no—
173C4⋊C4×C83—22no—
174C4⋊C4×C83—22no—
175C4⋊C4×C83—22no—
176C23×C83—22no—
177C23×C83—22no—
178C23×C83C2×C22⋊C411yescharacteristic
179C23×C83C2×C22⋊C411yescharacteristic
180C23×C83#13112yes—
181C23×C83#13112yes—
182C23×C83C23×C411yescharacteristic
183C2×C4×C83—22no—
184C2×C4×C83—22no—
185C2×C4×C83—22no—
186C2×C4×C83—22no—
187C2×C4×C83—22no—
188C2×C4×C83—22no—
189C2×C4×C83—41no—
190C2×C4×C83—41no—
191C2×C4×C83—41no—
192C2×C4×C83—41no—
193C2×C4×C83—42no—
194C2×C4×C83—42no—
195C2×C4×C83—42no—
196C2×C4×C83—42no—
197C2×C4×C83—42no—
198C2×C4×C83C2×C22⋊C411yescharacteristic
199C2×C4×C83C2×C22⋊C411yescharacteristic
200C2×C4×C83C22×D411yescharacteristic
201C2×C4×C83C22×D411yescharacteristic
202C2×Dic83—22no—
203C2×Dic83—22no—
204C2×Dic83—24no—
205C2×Dic83—22no—
206C2×Dic83—22no—
207C2×Dic83—22no—
208C2×Dic83—24no—
209C2×Dic83—24no—
210C2×Dic83—22no—
211C2×Dic83—22no—
212C2×Dic83—22no—
213C2×Dic83—22no—
214C2×Dic83—42no—
215C2×Dic83—42no—
216C2×Dic83—42no—
217C2×Dic83—42no—
218C2×Dic83—42no—
219C2×Dic83#10114yes—
220C2×Dic83C2×C22⋊C412yes—
221C2×Dic83C2×C22⋊C412yes—
222C2×Dic83C2×C22⋊C412yes—
223C2×Dic83C2×C22⋊C412yes—
224C8×C83—42no—
225C8×C83—42no—
226C83⋊C8—42no—
227C83⋊C8—42no—
228C22×C83—21no—
229C22×C83—21no—
230C22×C83—21no—
231C22×C83—21no—
232C22×C83—24no—
233C22×C83—24no—
234C22×C83#40812yes—
235C22×C83#40812yes—
236C22×C83#41012yes—
237C22×C83C2×#10112yes—
238C22×C83C22×C22⋊C411yescharacteristic
239C22×C83C2×#13111yescharacteristic
240C22×C83C2×#13111yescharacteristic
241C4×C83—21no—
242C4×C83—21no—
243C4×C83—21no—
244C4×C83—21no—
245C4×C83—42no—
246C4×C83—42no—
247Dic83—22no—
248Dic83—22no—
249Dic83—22no—
250Dic83—42no—
251Dic83—42no—
252Dic83C2×#10114yes—
253C2×#1470—831nomaximal, Sylow
254C2×C83—21no—
255C2×C83—21no—
256C2×C83—22no—
257C2×C83#147014yescomplemented
258C2×C83C2×#40811yescharacteristic
259C2×C83C2×#41011yescharacteristic
260C2×C83C22×#10111yescharacteristic
261C22×#125—831no—
262C2×#432—831no—
263C2×#431—831no—
264#1470—838no—
265C2×#324—831no—
266C2×#324—831no—
267C2×#324—831no—
268C2×#324D8311yescharacteristic
269C83C2×#147011yescharacteristic, complemented, Sylow
270C2×#125—834no—
271C2×#125—834no—
272C2×#125—1661no—
273C2×#125—1661no—
274C2×#125—1661no—
275C2×#125—1661no—
276C2×#125—1662no—
277C2×#125—1662no—
278C22×C4⋊C4—831no—
279C22×C4⋊C4—831no—
280C22×C4⋊C4—831no—
281C22×C4⋊C4—831no—
282C22×C4⋊C4—831no—
283C22×C4⋊C4C2×D8311yescharacteristic
284C22×C42—831no—
285#432—834no—
286#432—1662no—
287#431—834no—
288#431—1662no—
289C2×C4⋊C8—1661no—
290C2×C4⋊C8—1661no—
291C2×C22⋊C8—831no—
292C2×C22⋊C8—831no—
293C2×C22⋊C8C2×D8311yescharacteristic
294C2×C22⋊C8C2×D8311yescharacteristic
295C2×#97—1661no—
296C2×C4×C8—1661no—
297#324—834no—
298#324—834no—
299#324—834no—
300#324C2×D8314yes—
301C23×C4—831no—
302C23×C4—831no—
303C23×C4—831no—
304C23×C4—831no—
305C23×C4C4×D8311yescharacteristic
306C23×C4C4×D8311yescharacteristic
307C23×C4C22×D8311yescharacteristic
308C22×C8—21no—
309C22×C8—21no—
310C22×C8—1661no—
311C22×C8—1661no—
312#125—1664no—
313#125—1664no—
314#125—1664no—
315#125—1664no—
316#125—1664no—
317#125—1664no—
318#125—1664no—
319#125—1664no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—834no—
325C2×C4⋊C4—834no—
326C2×C4⋊C4—834no—
327C2×C4⋊C4—832no—
328C2×C4⋊C4—834no—
329C2×C4⋊C4—832no—
330C2×C4⋊C4—1662no—
331C2×C4⋊C4—1662no—
332C2×C4⋊C4—1662no—
333C2×C4⋊C4—1661no—
334C2×C4⋊C4—1661no—
335C2×C4⋊C4—1661no—
336C2×C4⋊C4—1661no—
337C2×C4⋊C4—1661no—
338C2×C4⋊C4—1661no—
339C2×C4⋊C4—1662no—
340C2×C4⋊C4—1661no—
341C2×C4⋊C4—1661no—
342C2×C4⋊C4—1661no—
343C2×C4⋊C4—1661no—
344C2×C4⋊C4—1661no—
345C2×C4⋊C4—1661no—
346C2×C4⋊C4C4×D8312yes—
347C2×C4⋊C4C22×D8312yes—
348C2×C42—832no—
349C2×C42—831no—
350C2×C42—831no—
351C2×C42—831no—
352C2×C42—831no—
353C2×C42—832no—
354C2×C42—832no—
355C2×C42—832no—
356C4⋊C8—1664no—
357C4⋊C8—1664no—
358C22⋊C8—21no—
359C22⋊C8—21no—
360C22⋊C8—832no—
361C22⋊C8—832no—
362C22⋊C8—1661no—
363C22⋊C8—1661no—
364C22⋊C8C22×D8312yes—
365C22⋊C8C22×D8312yes—
366#97—1664no—
367C4×C8—1664no—
368C24C2×C4×D8311yescharacteristic
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—3322no—
378C22×C4—832no—
379C22×C4—831no—
380C22×C4—832no—
381C22×C4—832no—
382C22×C4—832no—
383C22×C4—832no—
384C22×C4—831no—
385C22×C4—831no—
386C22×C4—831no—
387C22×C4—832no—
388C22×C4—1662no—
389C22×C4—1662no—
390C22×C4—1661no—
391C22×C4—1661no—
392C22×C4—1661no—
393C22×C4—1661no—
394C22×C4—1664no—
395C22×C4—1662no—
396C22×C4—1662no—
397C22×C4C2×C4×D8312yes—
398C22×C4C2×C4×D8312yes—
399C22×C4C2×C4×D8311yescharacteristic
400C22×C4D4×D8311yescharacteristic
401C22×C4D4×D8311yescharacteristic
402C22×C4D4×D8311yescharacteristic
403C22×C4D4×D8311yescharacteristic
404C22×C4C23×D8311yescharacteristic
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—42no—
408C2×C8—42no—
409C2×C8—3322no—
410C2×C8—3322no—
411C2×C8—1662no—
412C2×C8—1662no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—1664no—
418C4⋊C4—1664no—
419C4⋊C4—1664no—
420C4⋊C4—1664no—
421C4⋊C4—1664no—
422C4⋊C4—1664no—
423C4⋊C4—1664no—
424C4⋊C4—1664no—
425C4⋊C4—1662no—
426C4⋊C4—1662no—
427C4⋊C4—1662no—
428C4⋊C4—1662no—
429C42—832no—
430C42—832no—
431C42—832no—
432C42—832no—
433C42—832no—
434C42—832no—
435C42—832no—
436C42—832no—
437C23—22no—
438C23—22no—
439C23C22⋊C4×D8311yescharacteristic
440C23C22⋊C4×D8311yescharacteristic
441C23#1458179812yes—
442C23#1458180012yes—
443C23C22×C4×D8311yescharacteristic
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—3322no—
460C2×C4—3322no—
461C2×C4—3322no—
462C2×C4—3322no—
463C2×C4—3322no—
464C2×C4—832no—
465C2×C4—834no—
466C2×C4—832no—
467C2×C4—832no—
468C2×C4—832no—
469C2×C4—1662no—
470C2×C4—1662no—
471C2×C4—1662no—
472C2×C4—1662no—
473C2×C4—1664no—
474C2×C4—1664no—
475C2×C4—1664no—
476C2×C4—1662no—
477C2×C4—1662no—
478C2×C4—1662no—
479C2×C4—1662no—
480C2×C4—1662no—
481C2×C4C22⋊C4×D8311yescharacteristic
482C2×C4C22⋊C4×D8311yescharacteristic
483C2×C4C2×D4×D8311yescharacteristic
484C2×C4C2×D4×D8311yescharacteristic
485C8—42no—
486C8—42no—
487C8—3322no—
488C8—3322no—
489C22—24no—
490C22—24no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22#1912766612yes—
496C22#1912766612yes—
497C22#1912767312yes—
498C22#101×D8312yes—
499C22C2×C22⋊C4×D8311yescharacteristic
500C22C2×#1458179811yescharacteristic
501C22C2×#1458180011yescharacteristic
502C4—21no—
503C4—21no—
504C4—21no—
505C4—21no—
506C4—42no—
507C4—42no—
508C4—3322no—
509C4—3322no—
510C4—834no—
511C4—1662no—
512C4—1662no—
513C4—1662no—
514C2—22no—
515C2—21no—
516C2—21no—
517C2#2490581714yesdirect product factor
518C2C2×#1912766611yescharacteristic
519C2C2×#1912767311yescharacteristic
520C2C2×#101×D8311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D83
commutatorC23×C83C23×C4
FrattiniC22×C4C23×D83
FittingC2×#324×C83C2
socleC23×C83C2×C22⋊C4
prime radicalC24×C83C22×C4
cosocleC22×C4×C83C24
hypercenterC2×#324D83
hypocenterC83C2×#1470
LCSG ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
4. #24905817C2direct (N × H)
257. C2×C83#1470semidirect
269. C83C2×#1470semidirect
517. C2#24905817direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817822
C2×#191277552
C2×#191277512
#249058172
C2×#191274272
C2×#191274262
C2×#324×C832
C2×#147083