Finite Group Databasebeta

← C2×#13130108 #16792956

Subgroups — C2×#13130108 #16792956

Order 3328.

1002 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719128C211yesmaximal, characteristic
2C2×#11719119C211yesmaximal, characteristic
3#13130108C218yesmaximal, direct product factor
4C2×#11718286C212yesmaximal
5C2×#11718285C212yesmaximal
6C22×#88143C211yesmaximal, characteristic
7C22×C13×C4⋊C4C411yescharacteristic
8C22×C4⋊Dic13C2211yescharacteristic
9C22×#6101C411yescharacteristic
10C22×#6101C411yescharacteristic
11C22×#6101C411yescharacteristic
12C22×#6101C2211yescharacteristic
13C22×C4×Dic13C2211yescharacteristic
14C2×#88143—21no—
15C2×#88143—21no—
16C2×#88143—22no—
17C2×#88143—21no—
18C2×#88143—21no—
19C2×#88143—22no—
20C2×#88143C414yes—
21C2×#88143C2214yes—
22C2×C22⋊#1057C2212yes—
23C2×C22⋊#1057C2212yes—
24#11719128—22no—
25#11719128C2214yes—
26C2×#88112—21no—
27C2×#88110—21no—
28#11719119—22no—
29#11719119C2214yes—
30C2×C4⋊#1057—21no—
31C2×C4×#1057—21no—
32#11718286C2218yes—
33#11718285C2218yes—
34C23×C4×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×C4⋊C4—22no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4C2×C414yes—
47C2×C4⋊Dic13—21no—
48C2×C4⋊Dic13—21no—
49C2×C4⋊Dic13—21no—
50C2×C4⋊Dic13—21no—
51C2×C4⋊Dic13C2×C412yes—
52C2×C4⋊Dic13C2312yes—
53C2×#6101—22no—
54C2×#6101—21no—
55C2×#6101—21no—
56C2×#6101—22no—
57C2×#6101—21no—
58C2×#6101—21no—
59C2×#6101—22no—
60C2×#6101—21no—
61C2×#6101—21no—
62C2×#6101—21no—
63C2×#6101—21no—
64C2×#6101—21no—
65C2×#6101—21no—
66C2×#6101C2×C412yes—
67C2×#6101C2×C414yes—
68C2×#6101C2×C414yes—
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#88143—24no—
80#88143—24no—
81#88143—24no—
82#88143—24no—
83#88143—24no—
84#88143—24no—
85#88143—24no—
86#88143—24no—
87C22⋊#1057—22no—
88C22⋊#1057—22no—
89C22⋊#1057C2314yes—
90C22⋊#1057C2314yes—
91#88112—24no—
92#88110—24no—
93C4⋊#1057—24no—
94C4×#1057—24no—
95C2×#1470—131nomaximal, Sylow
96C24×C13C22×C411yescharacteristic
97C22×C4×C13—24no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—24no—
103C22×C4×C13—42no—
104C22×C4×C13C22⋊C412yes—
105C22×C4×C13C22⋊C411yescharacteristic
106C22×C4×C13C22⋊C411yescharacteristic
107C22×C4×C13C22×C412yes—
108C22×C4×C13C22×C412yes—
109C22×C4×C13C22×C412yes—
110C22×Dic13—24no—
111C22×Dic13—21no—
112C22×Dic13—21no—
113C22×Dic13—21no—
114C22×Dic13—21no—
115C22×Dic13—24no—
116C22×Dic13—42no—
117C22×Dic13—42no—
118C22×Dic13C22⋊C411yescharacteristic
119C22×Dic13C22⋊C412yes—
120C22×Dic13C22⋊C411yescharacteristic
121C22×Dic13C22×C412yes—
122C22×Dic13C22×C412yes—
123C22×Dic13C22×C412yes—
124C22×Dic13C22×C411yescharacteristic
125C22×Dic13C2×D411yescharacteristic
126C22×Dic13C2×D411yescharacteristic
127C22×Dic13C2×D411yescharacteristic
128C22×Dic13C2×D411yescharacteristic
129C22×Dic13C2411yescharacteristic
130C2×#1057—24no—
131C2×#1057—24no—
132C2×#1057—44no—
133C2×#1057—44no—
134C13×C4⋊C4—24no—
135C13×C4⋊C4—24no—
136C4⋊Dic13—22no—
137C4⋊Dic13—22no—
138C4⋊Dic13—22no—
139C4⋊Dic13—22no—
140#6101—24no—
141#6101—24no—
142#6101—22no—
143#6101—22no—
144#6101—24no—
145#6101—24no—
146#6101—24no—
147#6101—24no—
148#6101—22no—
149#6101—22no—
150C4×Dic13C22⋊C412yes—
151C4×Dic13C22⋊C412yes—
152C4×Dic13C22⋊C412yes—
153C4×Dic13C22⋊C412yes—
154C4×Dic13C2×D412yes—
155C4×Dic13C2×D412yes—
156C4×Dic13C2×D412yes—
157C4×Dic13C2×D412yes—
158C22×#125—131no—
159C2×#432—131no—
160C2×#431—131no—
161#1470—138no—
162C2×#324—132no—
163C2×#324—132no—
164C23×C13—22no—
165C23×C13—22no—
166C23×C13C2×C22⋊C411yescharacteristic
167C23×C13C2×C22⋊C411yescharacteristic
168C23×C13#13114yes—
169C23×C13C23×C411yescharacteristic
170C2×C4×C13—24no—
171C2×C4×C13—24no—
172C2×C4×C13—22no—
173C2×C4×C13—22no—
174C2×C4×C13—22no—
175C2×C4×C13—22no—
176C2×C4×C13—24no—
177C2×C4×C13—42no—
178C2×C4×C13—42no—
179C2×C4×C13—42no—
180C2×C4×C13—42no—
181C2×C4×C13—42no—
182C2×C4×C13C2×C22⋊C412yes—
183C2×C4×C13C2×C22⋊C412yes—
184C2×Dic13—22no—
185C2×Dic13—22no—
186C2×Dic13—22no—
187C2×Dic13—24no—
188C2×Dic13—24no—
189C2×Dic13—22no—
190C2×Dic13—22no—
191C2×Dic13—24no—
192C2×Dic13—41no—
193C2×Dic13—41no—
194C2×Dic13—41no—
195C2×Dic13—41no—
196C2×Dic13—42no—
197C2×Dic13—42no—
198C2×Dic13—42no—
199C2×Dic13—42no—
200C2×Dic13—42no—
201C2×Dic13#10114yes—
202C2×Dic13C2×C22⋊C411yescharacteristic
203C2×Dic13C2×C22⋊C411yescharacteristic
204C2×Dic13C2×C22⋊C412yes—
205C2×Dic13C2×C22⋊C412yes—
206C2×Dic13C22×D411yescharacteristic
207C2×Dic13C22×D411yescharacteristic
208#1057—44no—
209#1057—44no—
210C2×#125—134no—
211C2×#125—134no—
212C2×#125—261no—
213C2×#125—261no—
214C2×#125—261no—
215C2×#125—261no—
216C2×#125—262no—
217C2×#125—262no—
218C22×C4⋊C4—131no—
219C22×C4⋊C4—131no—
220C22×C4⋊C4—131no—
221C22×C4⋊C4—131no—
222C22×C4⋊C4—131no—
223C22×C4⋊C4#26111yescharacteristic
224C22×C42—131no—
225#432—134no—
226#432—262no—
227#431—134no—
228#431—262no—
229C2×C4⋊C8—261no—
230C2×C4⋊C8—261no—
231C2×C22⋊C8—132no—
232C2×C22⋊C8—132no—
233C2×#97—261no—
234C2×C4×C8—261no—
235#324—138no—
236#324—138no—
237C22×C13—21no—
238C22×C13—21no—
239C22×C13—21no—
240C22×C13—21no—
241C22×C13—28no—
242C22×C13#40812yes—
243C22×C13#40812yes—
244C22×C13#41012yes—
245C22×C13C2×#10112yes—
246C22×C13C22×C22⋊C411yescharacteristic
247C22×C13C2×#13112yes—
248C4×C13—22no—
249C4×C13—22no—
250C4×C13—42no—
251C4×C13—42no—
252Dic13—21no—
253Dic13—21no—
254Dic13—21no—
255Dic13—21no—
256Dic13—22no—
257Dic13—42no—
258Dic13—42no—
259Dic13C2×#10114yes—
260C23×C4—131no—
261C23×C4—131no—
262C23×C4—131no—
263C23×C4—131no—
264C23×C4C2×#26111yescharacteristic
265C23×C4C2×#26111yescharacteristic
266C23×C4C2×#26111yescharacteristic
267C22×C8—262no—
268C22×C8—262no—
269#125—264no—
270#125—264no—
271#125—264no—
272#125—264no—
273#125—264no—
274#125—264no—
275#125—264no—
276#125—264no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—132no—
281C2×C4⋊C4—132no—
282C2×C4⋊C4—134no—
283C2×C4⋊C4—134no—
284C2×C4⋊C4—132no—
285C2×C4⋊C4—134no—
286C2×C4⋊C4—132no—
287C2×C4⋊C4—262no—
288C2×C4⋊C4—262no—
289C2×C4⋊C4—261no—
290C2×C4⋊C4—261no—
291C2×C4⋊C4—261no—
292C2×C4⋊C4—261no—
293C2×C4⋊C4—261no—
294C2×C4⋊C4—261no—
295C2×C4⋊C4—261no—
296C2×C4⋊C4—261no—
297C2×C4⋊C4—261no—
298C2×C4⋊C4—261no—
299C2×C4⋊C4—261no—
300C2×C4⋊C4—261no—
301C2×C4⋊C4—262no—
302C2×C4⋊C4—261no—
303C2×C4⋊C4—261no—
304C2×C4⋊C4C2×#26114yes—
305C2×C42—131no—
306C2×C42—131no—
307C2×C42—131no—
308C2×C42—131no—
309C2×C42—132no—
310C2×C42—132no—
311C2×C42—132no—
312C2×C42—132no—
313C4⋊C8—264no—
314C4⋊C8—264no—
315C22⋊C8—134no—
316C22⋊C8—134no—
317C22⋊C8—262no—
318C22⋊C8—262no—
319#97—264no—
320C4×C8—264no—
321C2×C13—22no—
322C2×C13—22no—
323C2×C13#147014yescomplemented
324C2×C13C2×#40811yescharacteristic
325C2×C13C2×#41011yescharacteristic
326C2×C13C22×#10111yescharacteristic
327C24C22×#26111yescharacteristic
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—42no—
335C22×C4—131no—
336C22×C4—132no—
337C22×C4—131no—
338C22×C4—131no—
339C22×C4—131no—
340C22×C4—132no—
341C22×C4—131no—
342C22×C4—131no—
343C22×C4—131no—
344C22×C4—131no—
345C22×C4—132no—
346C22×C4—132no—
347C22×C4—264no—
348C22×C4—264no—
349C22×C4—261no—
350C22×C4—261no—
351C22×C4—261no—
352C22×C4—261no—
353C22×C4—522no—
354C22×C4—522no—
355C22×C4C22⋊#26112yes—
356C22×C4C22⋊#26111yescharacteristic
357C22×C4C22⋊#26111yescharacteristic
358C22×C4C22×#26112yes—
359C22×C4C22×#26112yes—
360C22×C4C22×#26112yes—
361C2×C8—264no—
362C2×C8—264no—
363C2×C8—524no—
364C2×C8—524no—
365C4⋊C4—24no—
366C4⋊C4—24no—
367C4⋊C4—264no—
368C4⋊C4—264no—
369C4⋊C4—262no—
370C4⋊C4—262no—
371C4⋊C4—264no—
372C4⋊C4—262no—
373C4⋊C4—262no—
374C4⋊C4—264no—
375C4⋊C4—262no—
376C4⋊C4—262no—
377C4⋊C4—262no—
378C4⋊C4—262no—
379C4⋊C4—264no—
380C4⋊C4—264no—
381C42—132no—
382C42—132no—
383C42—132no—
384C42—132no—
385C42—132no—
386C42—132no—
387C42—132no—
388C42—132no—
389C13C2×#147011yescharacteristic, complemented, Sylow
390C23—22no—
391C23—22no—
392C23#8823814yes—
393C23C2×C22⋊#26111yescharacteristic
394C23C2×C22⋊#26111yescharacteristic
395C23C23×#26111yescharacteristic
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—24no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—132no—
409C2×C4—134no—
410C2×C4—131no—
411C2×C4—131no—
412C2×C4—131no—
413C2×C4—131no—
414C2×C4—132no—
415C2×C4—264no—
416C2×C4—264no—
417C2×C4—262no—
418C2×C4—262no—
419C2×C4—262no—
420C2×C4—264no—
421C2×C4—262no—
422C2×C4—262no—
423C2×C4—521no—
424C2×C4—521no—
425C2×C4—521no—
426C2×C4—521no—
427C2×C4—522no—
428C2×C4—522no—
429C2×C4—522no—
430C2×C4—522no—
431C2×C4—522no—
432C2×C4C2×C22⋊#26112yes—
433C2×C4C2×C22⋊#26112yes—
434C8—524no—
435C8—524no—
436C22—28no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22#1171911612yes—
442C22#1171914612yes—
443C22#1171914612yes—
444C22D13⋊#10112yes—
445C22C2×#8823812yes—
446C22C22×C22⋊#26111yescharacteristic
447C4—22no—
448C4—22no—
449C4—42no—
450C4—42no—
451C4—134no—
452C4—261no—
453C4—261no—
454C4—261no—
455C4—261no—
456C4—262no—
457C4—522no—
458C4—522no—
459C2—22no—
460C2—22no—
461C2#1313010814yesdirect product factor
462C2C2×#1171914611yescharacteristic
463C2C2×#1171911611yescharacteristic
464C2C2×D13⋊#10111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC23×C13C23×C4
FrattiniC23C23×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22×C4
cosocleC22×Dic13C24
hypercenterC22×C4⋊C4#261
hypocenterC13C2×#1470
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13130108C2direct (N × H)
323. C2×C13#1470semidirect
389. C13C2×#1470semidirect
461. C2#13130108direct (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
#131301082
C2×#117182862
C2×#117182852
C22×#881432
C2×#147013