Finite Group Databasebeta

← C2×#13130165 #16793323

Subgroups — C2×#13130165 #16793323

Order 3328.

1282 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719051C211yesmaximal, characteristic
2C2×#11719052C211yesmaximal, characteristic
3#13130165C218yesmaximal, direct product factor
4C2×#11718244C212yesmaximal, complemented
5C2×Q8⋊#1057C212yesmaximal, complemented
6C2×C4×Q8×D13C211yesmaximal, characteristic
7C22×Q8×D13C411yescharacteristic
8C22×#6118—21no—
9C2×C4×Q8×C13C411yescharacteristic
10C2×Q8×Dic13C2211yescharacteristic
11C4×Q8×D13—22no—
12C4×Q8×D13—22no—
13C4×Q8×D13C414yes—
14C4×Q8×D13C2214yes—
15C2×C4⋊C4×D13—21no—
16C2×C4⋊C4×D13C411yescharacteristic
17C2×#88141—21no—
18C2×#88141C2211yescharacteristic
19C2×C42×D13—21no—
20C2×C42×D13C2211yescharacteristic
21C2×C4×Dic26—21no—
22C2×C4×Dic26C411yescharacteristic
23C2×#88111—21no—
24C2×C4⋊#1057—21no—
25C2×C4⋊#1057—21no—
26C2×C4⋊#1057C2212yes—
27C2×C4×#1057C2212yes—
28#11719052—22no—
29#11719052C2214yes—
30#11719051—22no—
31#11719051C2214yes—
32Q8⋊#1057C2218yescomplemented
33#11718244C2218yescomplemented
34C22×Q8×C13C2×C411yescharacteristic
35C2×Q8×D13—24no—
36C2×Q8×D13—22no—
37C2×Q8×D13—24no—
38C2×Q8×D13C2×C414yes—
39C22×C4×D13—21no—
40C22×C4×D13—21no—
41C22×C4×D13C2×C411yescharacteristic
42C22×C4×D13D411yescharacteristic
43C22×C4×D13D411yescharacteristic
44C22×Dic26—21no—
45C22×Dic26C2×C411yescharacteristic
46C22×#1057—22no—
47C22×#1057—22no—
48C2×#6118—24no—
49C2×#6118—44no—
50C4×Q8×C13—22no—
51C4×Q8×C13C2×C414yes—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4C2×C411yescharacteristic
54C2×C42×C13—21no—
55C2×C42×C13C2×C411yescharacteristic
56Q8×Dic13—21no—
57Q8×Dic13—21no—
58Q8×Dic13C2×C412yes—
59Q8×Dic13C2312yes—
60C2×C4⋊Dic13—21no—
61C2×C4⋊Dic13C2×C411yescharacteristic
62C2×#6101—21no—
63C2×#6101—21no—
64C2×#6101—21no—
65C2×C4×Dic13—21no—
66C2×C4×Dic13—21no—
67C2×C4×Dic13—21no—
68C2×C4×Dic13D411yescharacteristic
69C2×C4×Dic13D411yescharacteristic
70C2×C4×Dic13C2311yescharacteristic
71C4⋊C4×D13—24no—
72C4⋊C4×D13—22no—
73C4⋊C4×D13—24no—
74C4⋊C4×D13C2×C414yes—
75#88141—24no—
76#88141—24no—
77#88141—21no—
78#88141—21no—
79#88141C2×C412yes—
80#88141C2312yes—
81C42×D13—24no—
82C42×D13—24no—
83C42×D13C2×C412yes—
84C42×D13D412yes—
85C42×D13D412yes—
86C42×D13C2312yes—
87C4×Dic26—22no—
88C4×Dic26—24no—
89C4×Dic26—24no—
90C4×Dic26C2×C414yes—
91#88111—24no—
92C4⋊#1057—24no—
93C4⋊#1057—22no—
94C4⋊#1057—24no—
95C4⋊#1057C2314yes—
96C4×#1057—22no—
97C4×#1057C2314yes—
98C2×#1487—131nomaximal, Sylow
99C23×D13C22⋊C411yescharacteristic
100C2×Q8×C13—21no—
101C2×Q8×C13—22no—
102C2×Q8×C13M1614yescomplemented
103C2×Q8×C13C22×C412yes—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13C22⋊C411yescharacteristic
107C22×C4×C13C22⋊C411yescharacteristic
108C22×C4×C13C22×C411yescharacteristic
109C22×Dic13—21no—
110C22×Dic13—21no—
111C22×Dic13C22⋊C411yescharacteristic
112C22×Dic13C2×D411yescharacteristic
113C22×Dic13C2×D411yescharacteristic
114Q8×D13—216no—
115Q8×D13—28no—
116Q8×D13—28no—
117C2×C4×D13—28no—
118C2×C4×D13—24no—
119C2×C4×D13—22no—
120C2×C4×D13—22no—
121C2×C4×D13—24no—
122C2×C4×D13—42no—
123C2×C4×D13—44no—
124C2×C4×D13C22⋊C412yes—
125C2×C4×D13C22⋊C412yes—
126C2×C4×D13C22⋊C412yes—
127C2×C4×D13SD1614yes—
128C2×C4×D13Q1614yes—
129C2×C4×D13C22×C412yes—
130C2×C4×D13C2×D412yes—
131C2×C4×D13C2×D412yes—
132C2×Dic26—28no—
133C2×Dic26—21no—
134C2×Dic26—22no—
135C2×Dic26—24no—
136C2×Dic26M1614yescomplemented
137C2×Dic26C22×C412yes—
138C2×#1057—24no—
139C2×#1057—24no—
140C2×#1057—44no—
141C2×#1057—44no—
142#6118—48no—
143C13×C4⋊C4—24no—
144C13×C4⋊C4—21no—
145C13×C4⋊C4C22×C412yes—
146C42×C13—24no—
147C42×C13C22⋊C412yes—
148C42×C13C22×C412yes—
149C4⋊Dic13—21no—
150C4⋊Dic13—22no—
151C4⋊Dic13—22no—
152C4⋊Dic13C22×C412yes—
153#6101—24no—
154#6101—24no—
155#6101—22no—
156#6101—22no—
157C4×Dic13—24no—
158C4×Dic13—22no—
159C4×Dic13—22no—
160C4×Dic13—22no—
161C4×Dic13—22no—
162C4×Dic13C22⋊C412yes—
163C4×Dic13C22⋊C412yes—
164C4×Dic13C22×C411yescharacteristic
165C4×Dic13C2×D411yescharacteristic
166C4×Dic13C2×D412yes—
167C4×Dic13C2×D411yescharacteristic
168C4×Dic13C2×D412yes—
169C4×Dic13C2411yescharacteristic
170C22×C4×Q8—131no—
171C2×#431—131no—
172C2×#423—131no—
173#1487—138no—
174C2×Q8⋊C8—132no—
175C2×Q8⋊C8—132no—
176C23×C13C2×C22⋊C411yescharacteristic
177C22×D13—22no—
178C22×D13—22no—
179C22×D13#10314yes—
180C22×D13C2×C22⋊C412yes—
181Q8×C13—22no—
182Q8×C13—24no—
183Q8×C13C2×M1614yescomplemented
184C2×C4×C13—22no—
185C2×C4×C13—24no—
186C2×C4×C13—22no—
187C2×C4×C13—22no—
188C2×C4×C13—42no—
189C2×C4×C13#10314yes—
190C2×C4×C13C2×C22⋊C412yes—
191C2×C4×C13C2×C22⋊C411yescharacteristic
192C2×C4×C13C2×C22⋊C412yes—
193C2×C4×C13C2×M1612yes—
194C2×C4×C13C2×M1612yes—
195C2×C4×C13C23×C411yescharacteristic
196C2×Dic13—22no—
197C2×Dic13—22no—
198C2×Dic13—24no—
199C2×Dic13—22no—
200C2×Dic13—22no—
201C2×Dic13—42no—
202C2×Dic13C2×C22⋊C411yescharacteristic
203C2×Dic13C2×C22⋊C412yes—
204C2×Dic13C2×C22⋊C411yescharacteristic
205C2×Dic13C2×SD1612yes—
206C2×Dic13C2×Q1612yes—
207C2×Dic13C22×D411yescharacteristic
208C2×Dic13C22×D411yescharacteristic
209C4×D13—216no—
210C4×D13—22no—
211C4×D13—22no—
212C4×D13—24no—
213C4×D13—42no—
214C4×D13—42no—
215C4×D13—48no—
216C4×D13#10318yes—
217C4×D13C2×SD1614yes—
218C4×D13C2×Q1614yes—
219Dic26—216no—
220Dic26—22no—
221Dic26—24no—
222Dic26C2×M1614yescomplemented
223#1057—44no—
224#1057—44no—
225C23×Q8—131no—
226C22×M16—261no—
227C2×C4×Q8—131no—
228C2×C4×Q8—134no—
229C2×C4×Q8—134no—
230C2×C4×Q8—131no—
231C2×C4×Q8—131no—
232C2×C4×Q8—261no—
233C2×C4×Q8—261no—
234C2×C4×Q8—262no—
235C2×C4×Q8—262no—
236C2×C4×Q8#26111yescharacteristic
237C22×C4⋊C4—131no—
238C22×C4⋊C4—261no—
239C22×C42—131no—
240C22×C42—261no—
241#431—134no—
242#431—262no—
243#423—134no—
244#423—262no—
245C2×C4⋊C8—132no—
246C2×C4⋊C8—261no—
247C2×C4⋊C8—261no—
248C2×C22⋊C8—261no—
249C2×C4×C8—132no—
250Q8⋊C8—138no—
251Q8⋊C8—138no—
252C22×C13#40712yes—
253C22×C13C2×#10312yes—
254C22×C13#42112yes—
255C22×C13C22×C22⋊C411yescharacteristic
256C2×D13—22no—
257C2×D13—22no—
258C2×D13—28no—
259C2×D13C2×#10314yes—
260C4×C13—24no—
261C4×C13—22no—
262C4×C13—42no—
263C4×C13#40712yes—
264C4×C13C2×#10314yes—
265C4×C13C22×M1611yescharacteristic
266C4×C13C22×M1611yescharacteristic
267Dic13—22no—
268Dic13—24no—
269Dic13—21no—
270Dic13—21no—
271Dic13—42no—
272Dic13C2×#10312yes—
273Dic13C22×SD1611yescharacteristic
274Dic13C22×Q1611yescharacteristic
275C22×Q8—134no—
276C22×Q8—131no—
277C22×Q8—261no—
278C22×Q8—262no—
279C22×Q8—264no—
280C22×Q8—264no—
281C22×Q8C2×#26111yescharacteristic
282C23×C4—131no—
283C23×C4—131no—
284C23×C4—131no—
285C23×C4—261no—
286C23×C4—261no—
287C2×M16—264no—
288C2×M16—524no—
289C22×C8—262no—
290C22×C8—262no—
291C4×Q8—22no—
292C4×Q8—132no—
293C4×Q8—132no—
294C4×Q8—132no—
295C4×Q8—132no—
296C4×Q8—134no—
297C4×Q8—264no—
298C4×Q8—264no—
299C4×Q8—261no—
300C4×Q8—264no—
301C4×Q8—261no—
302C4×Q8—264no—
303C4×Q8—261no—
304C4×Q8—261no—
305C4×Q8—262no—
306C4×Q8C2×#26114yes—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—131no—
309C2×C4⋊C4—134no—
310C2×C4⋊C4—262no—
311C2×C4⋊C4—264no—
312C2×C4⋊C4—264no—
313C2×C4⋊C4—261no—
314C2×C4⋊C4—261no—
315C2×C4⋊C4—261no—
316C2×C4⋊C4—261no—
317C2×C4⋊C4C2×#26111yescharacteristic
318C2×C42—21no—
319C2×C42—131no—
320C2×C42—131no—
321C2×C42—131no—
322C2×C42—132no—
323C2×C42—132no—
324C2×C42—132no—
325C2×C42—132no—
326C2×C42—264no—
327C2×C42—264no—
328C2×C42—261no—
329C2×C42—261no—
330C2×C42—261no—
331C2×C42C2×#26111yescharacteristic
332C4⋊C8—134no—
333C4⋊C8—262no—
334C4⋊C8—264no—
335C4⋊C8—264no—
336C22⋊C8—264no—
337C4×C8—134no—
338C4×C8—262no—
339C2×C13#148714yescomplemented
340C2×C13C2×#40711yescharacteristic
341C2×C13C22×#10311yescharacteristic
342C2×C13C2×#42111yescharacteristic
343D13—24no—
344C24—131no—
345C2×Q8—22no—
346C2×Q8—21no—
347C2×Q8—134no—
348C2×Q8—132no—
349C2×Q8—264no—
350C2×Q8—268no—
351C2×Q8—268no—
352C2×Q8—2616no—
353C2×Q8—268no—
354C2×Q8—262no—
355C2×Q8—261no—
356C2×Q8#611814yescomplemented
357C2×Q8C22×#26112yes—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—131no—
361C22×C4—134no—
362C22×C4—134no—
363C22×C4—132no—
364C22×C4—132no—
365C22×C4—131no—
366C22×C4—131no—
367C22×C4—132no—
368C22×C4—132no—
369C22×C4—132no—
370C22×C4—132no—
371C22×C4—264no—
372C22×C4—268no—
373C22×C4—264no—
374C22×C4—261no—
375C22×C4—262no—
376C22×C4—262no—
377C22×C4—261no—
378C22×C4—522no—
379C22×C4—524no—
380C22×C4C22⋊#26111yescharacteristic
381C22×C4C22⋊#26111yescharacteristic
382C22×C4C22×#26111yescharacteristic
383M16—528no—
384C2×C8—264no—
385C2×C8—264no—
386C2×C8—524no—
387C2×C8—524no—
388C4⋊C4—24no—
389C4⋊C4—21no—
390C4⋊C4—132no—
391C4⋊C4—264no—
392C4⋊C4—262no—
393C4⋊C4—262no—
394C4⋊C4—262no—
395C4⋊C4—262no—
396C4⋊C4—261no—
397C4⋊C4—264no—
398C4⋊C4C22×#26112yes—
399C42—24no—
400C42—131no—
401C42—131no—
402C42—132no—
403C42—132no—
404C42—132no—
405C42—132no—
406C42—131no—
407C42—131no—
408C42—262no—
409C42—262no—
410C42—262no—
411C42—262no—
412C42—264no—
413C42C22⋊#26112yes—
414C42C22×#26112yes—
415C13C2×#148711yescharacteristic, complemented, Sylow
416C23—132no—
417C23—134no—
418C23—262no—
419C23—262no—
420C23C2×C22⋊#26111yescharacteristic
421Q8—22no—
422Q8—24no—
423Q8—134no—
424Q8—2616no—
425Q8—262no—
426Q8—264no—
427Q8C2×#611814yescomplemented
428C2×C4—22no—
429C2×C4—24no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—42no—
433C2×C4—131no—
434C2×C4—131no—
435C2×C4—132no—
436C2×C4—132no—
437C2×C4—134no—
438C2×C4—138no—
439C2×C4—134no—
440C2×C4—131no—
441C2×C4—131no—
442C2×C4—132no—
443C2×C4—2616no—
444C2×C4—262no—
445C2×C4—262no—
446C2×C4—264no—
447C2×C4—262no—
448C2×C4—262no—
449C2×C4—262no—
450C2×C4—264no—
451C2×C4—262no—
452C2×C4—522no—
453C2×C4—522no—
454C2×C4—528no—
455C2×C4—522no—
456C2×C4#8811714yes—
457C2×C4C2×#611812yes—
458C2×C4D13⋊M1612yes—
459C2×C4C2×C22⋊#26112yes—
460C2×C4C2×C22⋊#26111yescharacteristic
461C2×C4C2×C22⋊#26112yes—
462C2×C4C23×#26111yescharacteristic
463C8—524no—
464C8—524no—
465C22—134no—
466C22—262no—
467C22—268no—
468C22—262no—
469C22#1171912712yes—
470C22C2×#8811712yes—
471C22#1171916612yes—
472C22C22×C22⋊#26111yescharacteristic
473C4—24no—
474C4—22no—
475C4—42no—
476C4—131no—
477C4—131no—
478C4—132no—
479C4—262no—
480C4—264no—
481C4—261no—
482C4—261no—
483C4—522no—
484C4#1171912712yes—
485C4C2×#8811714yes—
486C4C22×#611811yescharacteristic
487C4C2×D13⋊M1611yescharacteristic
488C2—264no—
489C2#1313016514yesdirect product factor
490C2C2×#1171912711yescharacteristic
491C2C22×#8811711yescharacteristic
492C2C2×#1171916611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C4×Q8×C13C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC4×Dic13C24
hypercenterC2×C4×Q8#261
hypocenterC13C2×#1487
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #13130165C2direct (N × H)
4. C2×#11718244C2semidirect
5. C2×Q8⋊#1057C2semidirect
32. Q8⋊#1057C22semidirect
33. #11718244C22semidirect
102. C2×Q8×C13M16semidirect
136. C2×Dic26M16semidirect
183. Q8×C13C2×M16semidirect
222. Dic26C2×M16semidirect
339. C2×C13#1487semidirect
356. C2×Q8#6118semidirect
415. C13C2×#1487semidirect
427. Q8C2×#6118semidirect
489. C2#13130165direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117190512
C2×#117190522
#131301652
C2×#117182442
C2×Q8⋊#10572
C2×C4×Q8×D132
C2×#148713