Finite Group Databasebeta

← C2×#13131631 #16808420

Subgroups — C2×#13131631 #16808420

Order 3328.

1938 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
1#13131631C2116yesmaximal, direct product factor
2C2×#11719078C212yesmaximal, complemented
3C2×#11719158C211yesmaximal, characteristic, complemented
4C2×#11719080C211yesmaximal, characteristic, complemented
5C2×#11719080C212yesmaximal, complemented
6C2×#11719074C211yesmaximal, characteristic, complemented
7C2×Q8×#1057C211yesmaximal, characteristic, complemented
8C2×#11719067C212yesmaximal
9C22×C4⋊#1057C211yesmaximal, characteristic
10C2×#11719062C212yesmaximal
11C2×C4×#6122C211yesmaximal, characteristic
12C2×#11719327C211yesmaximal, characteristic
13C22×#6122C2211yescharacteristic
14C22×#6122C2211yescharacteristic
15C23×#1057C2212yes—
16C2×C13×C22⋊Q8C411yescharacteristic
17C2×Q8×Dic13C2211yescharacteristic
18C2×#88198C411yescharacteristic
19C2×#88178C411yescharacteristic
20C22×C4×Dic13C2211yescharacteristic
21#11719327C418yes—
22#11719327C2218yes—
23C2×#88143C412yes—
24C2×#88142C411yescharacteristic
25C2×#88141C2211yescharacteristic
26C2×#88141C2212yes—
27C2×#88132C412yes—
28C2×#88131C2212yes—
29#11719158C2218yescomplemented
30Q8×#1057C2218yescomplemented
31C2×#88112C2212yes—
32C2×#88112C2212yes—
33C4×#6122C2218yes—
34C2×#88110C2211yescharacteristic
35C2×#88110C2212yes—
36C2×#88110C2212yes—
37C2×#88110C2211yescharacteristic
38C2×C4⋊#1057C2211yescharacteristic
39C2×C4⋊#1057C2212yes—
40C2×C4⋊#1057C2212yes—
41C2×C4⋊#1057C2211yescharacteristic
42C2×C4⋊#1057C2212yes—
43C2×C4⋊#1057C2218yes—
44C2×C4×#1057C2211yescharacteristic
45C2×C4×#1057C2212yes—
46C2×C4×#1057C2212yes—
47C2×C4×#1057C2211yescharacteristic
48#11719080C22116yescomplemented
49#11719080C2218yescomplemented
50#11719078C22116yescomplemented
51#11719074C2218yescomplemented
52#11719067C22116yes—
53#11719062C22116yes—
54C22×Q8×C13C2×C411yescharacteristic
55C23×C4×C13C2×C411yescharacteristic
56C23×Dic13C2×C411yescharacteristic
57C23×Dic13C2311yescharacteristic
58C22×Dic26C2×C411yescharacteristic
59C22×Dic26C2×C412yes—
60C2×#6122—24no—
61C2×#6122Q818yescomplemented
62C2×#6122C2314yes—
63C2×#6122C2314yes—
64C22×#1057—28no—
65C22×#1057C2318yes—
66C22×#1057C2312yes—
67C22×#1057C2311yescharacteristic
68C22×#1057C2311yescharacteristic
69C22×#1057C2312yes—
70C22×#1057C2311yescharacteristic
71C22×#1057C2311yescharacteristic
72C13×C22⋊Q8C2×C418yes—
73C2×C13×C4⋊C4C2×C411yescharacteristic
74C2×C13×C4⋊C4C2×C412yes—
75C2×C13×C22⋊C4C2×C412yes—
76C2×C22⋊Dic13C2×C412yes—
77Q8×Dic13C2×C414yes—
78Q8×Dic13C2314yes—
79#88198C2×C418yes—
80C2×C4⋊Dic13C2×C412yes—
81C2×C4⋊Dic13C2×C411yescharacteristic
82#88178C2×C418yes—
83C2×#6101C2×C412yes—
84C2×#6101C2×C412yes—
85C2×#6101C2×C412yes—
86C2×#6101C2×C412yes—
87C2×#6101C2×C412yes—
88C2×C4×Dic13C2×C411yescharacteristic
89C2×C4×Dic13C2×C411yescharacteristic
90C2×C4×Dic13C2×C414yes—
91C2×C4×Dic13C2312yes—
92C2×C4×Dic13C2312yes—
93C2×C4×Dic13C2311yescharacteristic
94C2×C4×Dic13C2311yescharacteristic
95C2×C4×Dic13C2314yes—
96#88143C2×C4116yes—
97#88142C2×C418yes—
98#88141C2×C414yes—
99#88141C2×C418yes—
100#88141C2314yes—
101#88141C2318yes—
102#88132C2×C4116yes—
103#88131C2×C418yes—
104#88131C2318yes—
105#88112C2318yes—
106#88112C2318yes—
107#88110C2318yes—
108#88110C2318yes—
109#88110C2314yes—
110#88110C2314yes—
111C4⋊#1057C2318yes—
112C4⋊#1057C2318yes—
113C4⋊#1057C2314yes—
114C4⋊#1057C2318yes—
115C4⋊#1057C2314yes—
116C4×#1057C2318yes—
117C4×#1057C2318yes—
118C4×#1057C2314yes—
119C4×#1057C2314yes—
120C2×#2962—131nomaximal, Sylow
121C24×C13C22×C411yescharacteristic
122C2×Q8×C13—24no—
123C2×Q8×C13C22×C414yes—
124C22×C4×C13—24no—
125C22×C4×C13C22×C411yescharacteristic
126C22×C4×C13C22×C414yes—
127C22×C4×C13C22×C412yes—
128C22×C4×C13C22×C412yes—
129C22×C4×C13C22×C411yescharacteristic
130C22×Dic13—42no—
131C22×Dic13C22×C411yescharacteristic
132C22×Dic13C22×C411yescharacteristic
133C22×Dic13C22×C412yes—
134C22×Dic13C22×C412yes—
135C22×Dic13C22×C414yes—
136C22×Dic13C22×C412yes—
137C22×Dic13C22×C411yescharacteristic
138C22×Dic13C2×Q814yes—
139C22×Dic13#4114yes—
140C22×Dic13C2412yes—
141C22×Dic13C2411yescharacteristic
142C2×Dic26—24no—
143C2×Dic26—44no—
144C2×Dic26C22×C414yes—
145C2×Dic26C22×C418yes—
146#6122—28no—
147#6122C2×Q8116yescomplemented
148C2×#1057—24no—
149C2×#1057—24no—
150C2×#1057—216no—
151C2×#1057—22no—
152C2×#1057—22no—
153C2×#1057C2×Q814yes—
154C2×#1057C2×Q814yes—
155C2×#1057C2414yes—
156C2×#1057C2412yes—
157C2×#1057C2412yes—
158C2×#1057C2414yes—
159C2×#1057C2412yes—
160C2×#1057C2412yes—
161C13×C4⋊C4C22×C414yes—
162C13×C4⋊C4C22×C418yes—
163C13×C22⋊C4C22×C418yes—
164C22⋊Dic13C22×C418yes—
165C4⋊Dic13C22×C418yes—
166C4⋊Dic13C22×C414yes—
167#6101C22×C418yes—
168#6101C22×C418yes—
169#6101C22×C418yes—
170#6101C22×C418yes—
171#6101C22×C418yes—
172C4×Dic13C22×C414yes—
173C4×Dic13C22×C414yes—
174C4×Dic13C22×C412yes—
175C4×Dic13C22×C412yes—
176C4×Dic13C22×C414yes—
177C4×Dic13C22×C414yes—
178C4×Dic13C2412yes—
179C4×Dic13C2414yes—
180C4×Dic13C2414yes—
181C4×Dic13C2412yes—
182C2×#533—131no—
183#2962—1316no—
184C2×#446—131no—
185C2×#446—132no—
186C2×#446—131no—
187C2×#446—132no—
188C2×C8×Q8—131no—
189C2×C8×Q8—131no—
190C2×#424—132no—
191C22×C4⋊C8—131no—
192C2×#405—132no—
193C2×C4×M16—131no—
194C23×C13—22no—
195C23×C13—22no—
196C23×C13C4×Q814yes—
197C23×C13C23×C412yes—
198C23×C13C23×C411yescharacteristic
199Q8×C13—28no—
200C2×C4×C13—22no—
201C2×C4×C13—24no—
202C2×C4×C13—24no—
203C2×C4×C13—28no—
204C2×C4×C13#13114yes—
205C2×C4×C13C23×C412yes—
206C2×C4×C13C23×C414yes—
207C2×C4×C13C23×C414yes—
208C2×C4×C13C23×C412yes—
209C2×Dic13—24no—
210C2×Dic13—22no—
211C2×Dic13—24no—
212C2×Dic13—22no—
213C2×Dic13—44no—
214C2×Dic13C4×Q818yes—
215C2×Dic13C4×Q814yes—
216C2×Dic13C23×C412yes—
217C2×Dic13C23×C412yes—
218C2×Dic13C23×C414yes—
219C2×Dic13C23×C414yes—
220C2×Dic13C23×C411yescharacteristic
221C2×Dic13C23×C412yes—
222C2×Dic13C22×Q812yes—
223C2×Dic13C22×Q814yes—
224C2×Dic13C2×#4112yes—
225C2×Dic13C2×#4114yes—
226C2×Dic13C2511yescharacteristic
227Dic26—28no—
228Dic26—48no—
229#1057—24no—
230#1057—24no—
231#1057—22no—
232#1057—22no—
233#1057C22×Q814yes—
234#1057C22×Q814yes—
235C22×M16—131no—
236C22×M16—131no—
237C23×C8—132no—
238#533—138no—
239#533—138no—
240C2×C4⋊Q8—131no—
241C2×C4⋊Q8—131no—
242C2×#125—132no—
243C2×C22⋊Q8—131no—
244C2×C22⋊Q8—132no—
245C2×C22⋊Q8#26111yescharacteristic
246C2×C4×Q8—131no—
247C2×C4×Q8—131no—
248C2×C4×Q8—132no—
249C2×#117—132no—
250C22×C42—131no—
251#446—1316no—
252#446—138no—
253#446—1316no—
254#446—138no—
255C8×Q8—138no—
256C8×Q8—138no—
257#424—1316no—
258C2×C4⋊C8—131no—
259C2×C4⋊C8—131no—
260C2×C4⋊C8—132no—
261C2×C4⋊C8—138no—
262C2×C4⋊C8—132no—
263C2×C4⋊C8—132no—
264C2×C4⋊C8—132no—
265C2×C4⋊C8—132no—
266#405—1316no—
267C4×M16—138no—
268C2×#97—131no—
269C2×#97—131no—
270C2×#97—132no—
271C2×#97—132no—
272C2×C4×C8—131no—
273C2×C4×C8—131no—
274C2×C4×C8—132no—
275C2×C4×C8—132no—
276C22×C13—28no—
277C22×C13—22no—
278C22×C13—22no—
279C22×C13C2×C4×Q814yes—
280C22×C13C2×C4×Q812yes—
281C22×C13C2×#13112yes—
282C22×C13#56812yes—
283C22×C13C24×C411yescharacteristic
284C4×C13—22no—
285C4×C13—24no—
286C4×C13—24no—
287C4×C13C2×#13114yes—
288Dic13—24no—
289Dic13—22no—
290Dic13—24no—
291Dic13—22no—
292Dic13C2×C4×Q812yes—
293Dic13C2×C4×Q814yes—
294Dic13C23×Q811yescharacteristic
295Dic13C22×#4111yescharacteristic
296C22×Q8—131no—
297C22×Q8—132no—
298C22×Q8C2×#26111yescharacteristic
299C23×C4—131no—
300C23×C4—131no—
301C23×C4C2×#26111yescharacteristic
302C2×M16—134no—
303C2×M16—138no—
304C2×M16—134no—
305C2×M16—264no—
306C22×C8—131no—
307C22×C8—131no—
308C22×C8—132no—
309C22×C8—132no—
310C22×C8—138no—
311C22×C8—131no—
312C22×C8—131no—
313C22×C8—268no—
314C4⋊Q8—138no—
315C4⋊Q8—138no—
316#125—1316no—
317C22⋊Q8—138no—
318C22⋊Q8—1316no—
319C22⋊Q8C2×#26118yes—
320C4×Q8—134no—
321C4×Q8—134no—
322C4×Q8—134no—
323C4×Q8—138no—
324C4×Q8—134no—
325C4×Q8—138no—
326#117—138no—
327#117—138no—
328C2×C4⋊C4—132no—
329C2×C4⋊C4—132no—
330C2×C4⋊C4—132no—
331C2×C4⋊C4—132no—
332C2×C4⋊C4—132no—
333C2×C4⋊C4—132no—
334C2×C4⋊C4—131no—
335C2×C4⋊C4C2×#26112yes—
336C2×C4⋊C4C2×#26111yescharacteristic
337C2×C22⋊C4—132no—
338C2×C22⋊C4C2×#26112yes—
339C2×C42—132no—
340C2×C42—132no—
341C2×C42—131no—
342C2×C42—131no—
343C2×C42—131no—
344C2×C42—131no—
345C2×C42—134no—
346C2×C42—134no—
347C4⋊C8—134no—
348C4⋊C8—134no—
349C4⋊C8—138no—
350C4⋊C8—138no—
351C4⋊C8—138no—
352C4⋊C8—138no—
353C4⋊C8—138no—
354#97—134no—
355#97—134no—
356#97—138no—
357#97—138no—
358C4×C8—134no—
359C4×C8—134no—
360C4×C8—138no—
361C4×C8—138no—
362C2×C13—24no—
363C2×C13#296214yescomplemented
364C2×C13C22×C4×Q811yescharacteristic
365C2×C13C22×#13111yescharacteristic
366C2×C13C2×#56811yescharacteristic
367C24C22×#26111yescharacteristic
368C2×Q8—24no—
369C2×Q8—134no—
370C2×Q8—138no—
371C2×Q8—264no—
372C2×Q8—524no—
373C2×Q8C22×#26114yes—
374C22×C4—24no—
375C22×C4—134no—
376C22×C4—134no—
377C22×C4—132no—
378C22×C4—132no—
379C22×C4—131no—
380C22×C4—131no—
381C22×C4—131no—
382C22×C4—131no—
383C22×C4—132no—
384C22×C4—132no—
385C22×C4—134no—
386C22×C4—522no—
387C22×C4C22×#26114yes—
388C22×C4C22×#26111yescharacteristic
389C22×C4C22×#26112yes—
390C22×C4C22×#26112yes—
391C22×C4C22×#26111yescharacteristic
392M16—1316no—
393M16—268no—
394C2×C8—132no—
395C2×C8—132no—
396C2×C8—134no—
397C2×C8—134no—
398C2×C8—134no—
399C2×C8—132no—
400C2×C8—132no—
401C2×C8—134no—
402C2×C8—264no—
403C2×C8—264no—
404C2×C8—2616no—
405C2×C8—262no—
406C2×C8—262no—
407C4⋊C4—138no—
408C4⋊C4—138no—
409C4⋊C4—138no—
410C4⋊C4—138no—
411C4⋊C4—138no—
412C4⋊C4—138no—
413C4⋊C4—134no—
414C4⋊C4C22×#26118yes—
415C4⋊C4C22×#26114yes—
416C22⋊C4—138no—
417C22⋊C4C22×#26118yes—
418C42—132no—
419C42—134no—
420C42—134no—
421C42—132no—
422C42—132no—
423C42—132no—
424C42—134no—
425C42—134no—
426C42—134no—
427C42—134no—
428C13C2×#296211yescharacteristic, complemented, Sylow
429C23—22no—
430C23—22no—
431C23Q8×#26114yes—
432C23C23×#26112yes—
433C23C23×#26111yescharacteristic
434Q8—28no—
435Q8—268no—
436Q8—528no—
437C2×C4—22no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—28no—
441C2×C4—132no—
442C2×C4—132no—
443C2×C4—134no—
444C2×C4—134no—
445C2×C4—138no—
446C2×C4—134no—
447C2×C4—131no—
448C2×C4—131no—
449C2×C4—132no—
450C2×C4—132no—
451C2×C4—132no—
452C2×C4—134no—
453C2×C4—134no—
454C2×C4—264no—
455C2×C4—262no—
456C2×C4—262no—
457C2×C4—264no—
458C2×C4—524no—
459C2×C4#8823814yes—
460C2×C4C23×#26112yes—
461C2×C4C23×#26114yes—
462C2×C4C23×#26114yes—
463C2×C4C23×#26112yes—
464C8—134no—
465C8—134no—
466C8—264no—
467C8—264no—
468C8—262no—
469C8—262no—
470C22—22no—
471C22—22no—
472C22—28no—
473C22C2×#8823812yes—
474C22C2×Q8×#26114yes—
475C22C2×Q8×#26112yes—
476C22#1171962912yes—
477C22C24×#26111yescharacteristic
478C4—22no—
479C4—24no—
480C4—24no—
481C4—132no—
482C4—134no—
483C4—131no—
484C4—131no—
485C4—264no—
486C4—262no—
487C4—262no—
488C4—264no—
489C4C2×#8823814yes—
490C2—24no—
491C2#1313163114yesdirect product factor
492C2C22×Q8×#26111yescharacteristic
493C2C22×#8823811yescharacteristic
494C2C2×#1171962911yescharacteristic
subgroupG/H
centerC23C23×#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC2×C13×C22⋊Q8C4
socleC23×C13C23×C4
prime radicalC24×C13C22×C4
cosocleC2×Dic13C25
hypercenterC2×C22⋊Q8#261
hypocenterC13C2×#2962
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #13131631C2direct (N × H)
2. C2×#11719078C2semidirect
3. C2×#11719158C2semidirect
4. C2×#11719080C2semidirect
5. C2×#11719080C2semidirect
6. C2×#11719074C2semidirect
7. C2×Q8×#1057C2semidirect
29. #11719158C22semidirect
30. Q8×#1057C22semidirect
48. #11719080C22semidirect
49. #11719080C22semidirect
50. #11719078C22semidirect
51. #11719074C22semidirect
61. C2×#6122Q8semidirect
147. #6122C2×Q8semidirect
363. C2×C13#2962semidirect
428. C13C2×#2962semidirect
491. C2#13131631direct (N × H)

Maximal subgroups

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

subgroupindex
#131316312
C2×#117190782
C2×#117191582
C2×#117190802
C2×#117190742
C2×Q8×#10572
C2×#117190672
C22×C4⋊#10572
C2×#117190622
C2×C4×#61222
C2×#117193272
C2×#296213