Finite Group Databasebeta

← C2×#13130118 #16792976

Subgroups — C2×#13130118 #16792976

Order 3328.

1066 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×#11719128C211yesmaximal, characteristic, complemented
2C2×#11719119C211yesmaximal, characteristic, complemented
3#13130118C218yesmaximal, direct product factor
4C2×#11718286C212yesmaximal, complemented
5C2×#11718305C212yesmaximal
6C22×#88133C211yesmaximal, characteristic
7C22×C13×C22⋊C4C411yescharacteristic
8C22×C22⋊Dic13C411yescharacteristic
9C22×C22⋊Dic13C2211yescharacteristic
10C22×C4⋊Dic13C411yescharacteristic
11C22×#6101C411yescharacteristic
12C22×#6101C2211yescharacteristic
13C22×C4×Dic13C2211yescharacteristic
14C2×#88133—21no—
15C2×#88133—21no—
16C2×#88133—22no—
17C2×#88133—21no—
18C2×#88133—21no—
19C2×#88133—22no—
20C2×#88133C414yes—
21C2×#88133C2214yes—
22C2×C22⋊#1057C2212yes—
23C2×C22⋊#1057C2212yes—
24#11719128—22no—
25#11719128C2214yescomplemented
26C2×#88112—21no—
27C2×#88110—21no—
28#11719119—22no—
29#11719119C2214yescomplemented
30C2×C4⋊#1057—21no—
31C2×C4×#1057—21no—
32#11718305C2218yes—
33#11718286C2218yescomplemented
34C25×C13C2×C411yescharacteristic
35C23×C4×C13C2×C411yescharacteristic
36C23×C4×C13C2×C411yescharacteristic
37C23×Dic13C2×C411yescharacteristic
38C23×Dic13C2×C411yescharacteristic
39C23×Dic13C2×C411yescharacteristic
40C23×Dic13C2311yescharacteristic
41C22×#1057—22no—
42C22×#1057—22no—
43C2×C13×C22⋊C4—22no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4C2×C414yes—
47C2×C22⋊Dic13—21no—
48C2×C22⋊Dic13—21no—
49C2×C22⋊Dic13—22no—
50C2×C22⋊Dic13—21no—
51C2×C22⋊Dic13—21no—
52C2×C22⋊Dic13—21no—
53C2×C22⋊Dic13—21no—
54C2×C22⋊Dic13C2×C412yes—
55C2×C22⋊Dic13C2×C414yes—
56C2×C22⋊Dic13C2312yes—
57C2×C4⋊Dic13—21no—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13—22no—
60C2×C4⋊Dic13C2×C414yes—
61C2×#6101—22no—
62C2×#6101—21no—
63C2×#6101—21no—
64C2×#6101—21no—
65C2×#6101—21no—
66C2×#6101—21no—
67C2×#6101—21no—
68C2×#6101C2×C412yes—
69C2×#6101C2×C414yes—
70C2×#6101C2312yes—
71C2×C4×Dic13C2×C412yes—
72C2×C4×Dic13D411yescharacteristic
73C2×C4×Dic13D411yescharacteristic
74C2×C4×Dic13D412yes—
75C2×C4×Dic13D411yescharacteristic
76C2×C4×Dic13D411yescharacteristic
77C2×C4×Dic13D412yes—
78C2×C4×Dic13C2312yes—
79#88133—24no—
80#88133—24no—
81#88133—24no—
82#88133—24no—
83#88133—24no—
84#88133—24no—
85#88133—24no—
86#88133—24no—
87C22⋊#1057—22no—
88C22⋊#1057—22no—
89C22⋊#1057C2314yes—
90C22⋊#1057C2314yes—
91#88112—24no—
92#88110—24no—
93C4⋊#1057—24no—
94C4×#1057—24no—
95C2×#1473—131nomaximal, Sylow
96C24×C13—21no—
97C24×C13—21no—
98C24×C13—24no—
99C24×C13—42no—
100C24×C13—42no—
101C24×C13C22×C411yescharacteristic
102C24×C13C22×C412yes—
103C22×C4×C13—24no—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—42no—
107C22×C4×C13C22⋊C412yes—
108C22×C4×C13C22⋊C411yescharacteristic
109C22×C4×C13C22⋊C411yescharacteristic
110C22×C4×C13C22×C412yes—
111C22×C4×C13C22×C412yes—
112C22×Dic13—21no—
113C22×Dic13—21no—
114C22×Dic13—21no—
115C22×Dic13—21no—
116C22×Dic13—24no—
117C22×Dic13—42no—
118C22×Dic13—42no—
119C22×Dic13—42no—
120C22×Dic13C22⋊C411yescharacteristic
121C22×Dic13C22⋊C411yescharacteristic
122C22×Dic13C22⋊C412yes—
123C22×Dic13C22×C412yes—
124C22×Dic13C22×C412yes—
125C22×Dic13C22×C411yescharacteristic
126C22×Dic13C22×C412yes—
127C22×Dic13C2×D411yescharacteristic
128C22×Dic13C2×D411yescharacteristic
129C22×Dic13C2×D411yescharacteristic
130C22×Dic13C2×D411yescharacteristic
131C22×Dic13C2411yescharacteristic
132C2×#1057—24no—
133C2×#1057—24no—
134C2×#1057—44no—
135C2×#1057—44no—
136C13×C22⋊C4—24no—
137C13×C22⋊C4—24no—
138C22⋊Dic13—24no—
139C22⋊Dic13—24no—
140C22⋊Dic13—22no—
141C22⋊Dic13—22no—
142C22⋊Dic13—22no—
143C22⋊Dic13—22no—
144C4⋊Dic13—24no—
145C4⋊Dic13—24no—
146#6101—24no—
147#6101—24no—
148#6101—22no—
149#6101—22no—
150#6101—22no—
151#6101—22no—
152C4×Dic13C22⋊C412yes—
153C4×Dic13C22⋊C412yes—
154C4×Dic13C22⋊C412yes—
155C4×Dic13C22⋊C412yes—
156C4×Dic13C2×D412yes—
157C4×Dic13C2×D412yes—
158C4×Dic13C2×D412yes—
159C4×Dic13C2×D412yes—
160C22×#126—131no—
161C2×#432—131no—
162C2×#431—131no—
163#1473—138no—
164C2×#324—132no—
165C2×#323—132no—
166C23×C13—22no—
167C23×C13—22no—
168C23×C13—22no—
169C23×C13—24no—
170C23×C13—42no—
171C23×C13—42no—
172C23×C13—42no—
173C23×C13—42no—
174C23×C13—42no—
175C23×C13—42no—
176C23×C13—42no—
177C23×C13—42no—
178C23×C13—88no—
179C23×C13C2×C22⋊C411yescharacteristic
180C23×C13C2×C22⋊C411yescharacteristic
181C23×C13#13114yes—
182C23×C13C23×C411yescharacteristic
183C2×C4×C13—24no—
184C2×C4×C13—24no—
185C2×C4×C13—22no—
186C2×C4×C13—22no—
187C2×C4×C13—22no—
188C2×C4×C13—42no—
189C2×C4×C13—42no—
190C2×C4×C13—42no—
191C2×C4×C13C2×C22⋊C412yes—
192C2×C4×C13C2×C22⋊C412yes—
193C2×Dic13—22no—
194C2×Dic13—22no—
195C2×Dic13—22no—
196C2×Dic13—22no—
197C2×Dic13—22no—
198C2×Dic13—22no—
199C2×Dic13—24no—
200C2×Dic13—42no—
201C2×Dic13—41no—
202C2×Dic13—42no—
203C2×Dic13—41no—
204C2×Dic13—41no—
205C2×Dic13—41no—
206C2×Dic13—42no—
207C2×Dic13—42no—
208C2×Dic13—42no—
209C2×Dic13—42no—
210C2×Dic13—42no—
211C2×Dic13C2×C22⋊C411yescharacteristic
212C2×Dic13C2×C22⋊C411yescharacteristic
213C2×Dic13C2×C22⋊C412yes—
214C2×Dic13C2×C22⋊C412yes—
215C2×Dic13C22×D411yescharacteristic
216C2×Dic13C22×D411yescharacteristic
217#1057—44no—
218#1057—44no—
219C2×#126—134no—
220C2×#126—134no—
221C2×#126—261no—
222C2×#126—261no—
223C2×#126—261no—
224C2×#126—261no—
225C2×#126—262no—
226C2×#126—262no—
227C22×C4⋊C4—131no—
228C22×C4⋊C4—131no—
229C22×C4⋊C4—131no—
230C22×C22⋊C4—131no—
231C22×C22⋊C4—131no—
232C22×C22⋊C4#26111yescharacteristic
233C22×C42—131no—
234#432—134no—
235#432—262no—
236#431—134no—
237#431—262no—
238C2×C4⋊C8—261no—
239C2×C4⋊C8—261no—
240C2×C22⋊C8—132no—
241C2×C22⋊C8—132no—
242C2×#97—261no—
243C2×C4×C8—261no—
244#324—138no—
245#323—138no—
246C22×C13—21no—
247C22×C13—21no—
248C22×C13—21no—
249C22×C13—21no—
250C22×C13—28no—
251C22×C13—42no—
252C22×C13—42no—
253C22×C13—42no—
254C22×C13—84no—
255C22×C13—84no—
256C22×C13—84no—
257C22×C13#40812yes—
258C22×C13#40812yes—
259C22×C13#41012yes—
260C22×C13#41312yes—
261C22×C13C22×C22⋊C411yescharacteristic
262C22×C13C2×#13112yes—
263C4×C13—22no—
264C4×C13—22no—
265C4×C13—42no—
266Dic13—21no—
267Dic13—21no—
268Dic13—21no—
269Dic13—21no—
270Dic13—22no—
271Dic13—22no—
272Dic13—42no—
273Dic13—42no—
274C25C2×#26111yescharacteristic
275C23×C4—131no—
276C23×C4—131no—
277C23×C4—131no—
278C23×C4—131no—
279C23×C4C2×#26111yescharacteristic
280C23×C4C2×#26111yescharacteristic
281C22×C8—262no—
282C22×C8—262no—
283#126—264no—
284#126—264no—
285#126—264no—
286#126—264no—
287#126—264no—
288#126—264no—
289#126—264no—
290#126—264no—
291C2×C4⋊C4—132no—
292C2×C4⋊C4—132no—
293C2×C4⋊C4—134no—
294C2×C4⋊C4—134no—
295C2×C4⋊C4—261no—
296C2×C4⋊C4—261no—
297C2×C4⋊C4—261no—
298C2×C4⋊C4—261no—
299C2×C4⋊C4—262no—
300C2×C4⋊C4—261no—
301C2×C4⋊C4—261no—
302C2×C4⋊C4—262no—
303C2×C4⋊C4—261no—
304C2×C4⋊C4—261no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—132no—
309C2×C22⋊C4—134no—
310C2×C22⋊C4—132no—
311C2×C22⋊C4—261no—
312C2×C22⋊C4—261no—
313C2×C22⋊C4—261no—
314C2×C22⋊C4—261no—
315C2×C22⋊C4—261no—
316C2×C22⋊C4—261no—
317C2×C22⋊C4—262no—
318C2×C22⋊C4C2×#26114yes—
319C2×C42—131no—
320C2×C42—131no—
321C2×C42—131no—
322C2×C42—131no—
323C2×C42—132no—
324C2×C42—132no—
325C2×C42—132no—
326C2×C42—132no—
327C4⋊C8—264no—
328C4⋊C8—264no—
329C22⋊C8—134no—
330C22⋊C8—134no—
331C22⋊C8—262no—
332C22⋊C8—262no—
333#97—264no—
334C4×C8—264no—
335C2×C13—22no—
336C2×C13—22no—
337C2×C13—82no—
338C2×C13#147314yescomplemented
339C2×C13C2×#40811yescharacteristic
340C2×C13C2×#41011yescharacteristic
341C2×C13C2×#41311yescharacteristic
342C24—21no—
343C24—21no—
344C24—24no—
345C24—42no—
346C24—42no—
347C24C22×#26111yescharacteristic
348C24C22×#26112yes—
349C22×C4—24no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—42no—
353C22×C4—131no—
354C22×C4—131no—
355C22×C4—131no—
356C22×C4—131no—
357C22×C4—131no—
358C22×C4—131no—
359C22×C4—132no—
360C22×C4—131no—
361C22×C4—131no—
362C22×C4—132no—
363C22×C4—132no—
364C22×C4—132no—
365C22×C4—264no—
366C22×C4—261no—
367C22×C4—261no—
368C22×C4—261no—
369C22×C4—261no—
370C22×C4—522no—
371C22×C4—522no—
372C22×C4—522no—
373C22×C4C22⋊#26112yes—
374C22×C4C22⋊#26111yescharacteristic
375C22×C4C22⋊#26111yescharacteristic
376C22×C4C22×#26112yes—
377C22×C4C22×#26112yes—
378C2×C8—264no—
379C2×C8—264no—
380C2×C8—524no—
381C2×C8—524no—
382C4⋊C4—262no—
383C4⋊C4—262no—
384C4⋊C4—262no—
385C4⋊C4—262no—
386C4⋊C4—264no—
387C4⋊C4—264no—
388C4⋊C4—264no—
389C4⋊C4—264no—
390C22⋊C4—24no—
391C22⋊C4—24no—
392C22⋊C4—262no—
393C22⋊C4—262no—
394C22⋊C4—262no—
395C22⋊C4—262no—
396C22⋊C4—264no—
397C22⋊C4—264no—
398C42—132no—
399C42—132no—
400C42—132no—
401C42—132no—
402C42—132no—
403C42—132no—
404C42—132no—
405C42—132no—
406C13C2×#147311yescharacteristic, complemented, Sylow
407C23—22no—
408C23—22no—
409C23—22no—
410C23—24no—
411C23—42no—
412C23—42no—
413C23—42no—
414C23—42no—
415C23—42no—
416C23—42no—
417C23—42no—
418C23—42no—
419C23—88no—
420C23#8823814yes—
421C23C2×C22⋊#26111yescharacteristic
422C23C2×C22⋊#26111yescharacteristic
423C23C23×#26111yescharacteristic
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—131no—
433C2×C4—131no—
434C2×C4—131no—
435C2×C4—131no—
436C2×C4—132no—
437C2×C4—132no—
438C2×C4—262no—
439C2×C4—262no—
440C2×C4—262no—
441C2×C4—262no—
442C2×C4—264no—
443C2×C4—262no—
444C2×C4—262no—
445C2×C4—521no—
446C2×C4—521no—
447C2×C4—521no—
448C2×C4—521no—
449C2×C4—522no—
450C2×C4—522no—
451C2×C4—522no—
452C2×C4—522no—
453C2×C4—522no—
454C2×C4—522no—
455C2×C4—522no—
456C2×C4C2×C22⋊#26112yes—
457C2×C4C2×C22⋊#26112yes—
458C8—524no—
459C8—524no—
460C22—28no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—84no—
469C22—84no—
470C22—84no—
471C22#1171913212yes—
472C22#1171914212yes—
473C22#1171914612yes—
474C22#1171914612yes—
475C22C2×#8823812yes—
476C22C22×C22⋊#26111yescharacteristic
477C4—22no—
478C4—22no—
479C4—42no—
480C4—261no—
481C4—261no—
482C4—261no—
483C4—261no—
484C4—262no—
485C4—262no—
486C4—522no—
487C4—522no—
488C2—22no—
489C2—22no—
490C2—82no—
491C2#1313011814yesdirect product factor
492C2C2×#1171914611yescharacteristic
493C2C2×#1171914211yescharacteristic
494C2C2×#1171913211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC23×C13C23×C4
FrattiniC23C23×#261
FittingC22×C13×C22⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC25×C13C2×C4
cosocleC22×Dic13C24
hypercenterC22×C22⋊C4#261
hypocenterC13C2×#1473
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11719128C2semidirect
2. C2×#11719119C2semidirect
3. #13130118C2direct (N × H)
4. C2×#11718286C2semidirect
25. #11719128C22semidirect
29. #11719119C22semidirect
33. #11718286C22semidirect
338. C2×C13#1473semidirect
406. C13C2×#1473semidirect
491. C2#13130118direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117191282
C2×#117191192
#131301182
C2×#117182862
C2×#117183052
C22×#881332
C2×#147313