Finite Group Databasebeta

← C2×#13130074 #16792806

Subgroups — C2×#13130074 #16792806

Order 3328.

1826 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊#1057C212yesmaximal, complemented
2#13130074C218yesmaximal, direct product factor
3C2×#11718286C212yesmaximal, complemented
4C2×#11718287C212yesmaximal, complemented
5C22×#88135C211yesmaximal, characteristic
6C23×C22⋊D13C411yescharacteristic
7C24×Dic13C2211yescharacteristic
8C23×C4×D13C411yescharacteristic
9C23×#1057—22no—
10C22×C13×C22⋊C4C411yescharacteristic
11C22×#6103C2211yescharacteristic
12C22×#6101C2211yescharacteristic
13C22×C4×Dic13C411yescharacteristic
14C2×#88135—22no—
15C2×#88135—24no—
16C2×#88135—22no—
17C2×#88135C414yes—
18C2×#88135C2214yes—
19C2×C22⋊#1057—24no—
20C2×C22⋊#1057—22no—
21C2×C22⋊#1057C2214yes—
22C2×C22⋊#1057C2218yescomplemented
23#11718287C2218yescomplemented
24#11718286C2218yescomplemented
25C25×C13C2×C411yescharacteristic
26C24×D13C2×C411yescharacteristic
27C23×C4×C13C2×C411yescharacteristic
28C23×C4×C13C2×C411yescharacteristic
29C22×C22⋊D13—22no—
30C22×C22⋊D13—22no—
31C22×C22⋊D13—24no—
32C22×C22⋊D13C818yescomplemented
33C22×C22⋊D13C2×C414yes—
34C23×Dic13—44no—
35C23×Dic13C2×C411yescharacteristic
36C23×Dic13C2×C411yescharacteristic
37C23×Dic13C2×C412yes—
38C23×Dic13D412yes—
39C23×Dic13D414yes—
40C23×Dic13D412yes—
41C23×Dic13C2311yescharacteristic
42C23×Dic13C2312yes—
43C22×C4×D13—22no—
44C22×C4×D13—21no—
45C22×C4×D13—21no—
46C22×C4×D13—44no—
47C22×C4×D13C2×C414yes—
48C22×#1057—24no—
49C22×#1057—28no—
50C22×#1057—48no—
51C2×C13×C22⋊C4—22no—
52C2×C13×C22⋊C4—22no—
53C2×C13×C22⋊C4C2×C414yes—
54C2×#6103—22no—
55C2×#6103—22no—
56C2×#6103C2×C412yes—
57C2×#6103C2312yes—
58C2×#6101—22no—
59C2×#6101—22no—
60C2×#6101C2×C412yes—
61C2×#6101C2312yes—
62C2×C4×Dic13—22no—
63C2×C4×Dic13—21no—
64C2×C4×Dic13—21no—
65C2×C4×Dic13C2×C414yes—
66#88135—28no—
67#88135—28no—
68#88135—28no—
69#88135—28no—
70C22⋊#1057—24no—
71C22⋊#1057—28no—
72C22⋊#1057C2318yes—
73C2×#1459—131nomaximal, Sylow
74C24×C13—42no—
75C24×C13—42no—
76C24×C13C22⋊C412yes—
77C24×C13C22⋊C412yes—
78C24×C13C2×C814yes—
79C24×C13M1614yes—
80C24×C13C22×C411yescharacteristic
81C24×C13C22×C412yes—
82C23×D13—21no—
83C23×D13—21no—
84C23×D13—22no—
85C23×D13—42no—
86C23×D13—42no—
87C23×D13C2×C814yescomplemented
88C23×D13C22×C412yes—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—42no—
94C22×C4×C13—42no—
95C22×C4×C13C22×C412yes—
96C22×C4×C13C22×C412yes—
97C2×C22⋊D13—216no—
98C2×C22⋊D13—216no—
99C2×C22⋊D13—28no—
100C2×C22⋊D13—28no—
101C2×C22⋊D13C2×C8116yescomplemented
102C22×Dic13—21no—
103C22×Dic13—21no—
104C22×Dic13—22no—
105C22×Dic13—28no—
106C22×Dic13—24no—
107C22×Dic13—44no—
108C22×Dic13—48no—
109C22×Dic13—44no—
110C22×Dic13—44no—
111C22×Dic13—42no—
112C22×Dic13C22⋊C414yes—
113C22×Dic13C22⋊C411yescharacteristic
114C22×Dic13C22⋊C412yes—
115C22×Dic13C22⋊C414yes—
116C22×Dic13C22⋊C411yescharacteristic
117C22×Dic13C2×C814yescomplemented
118C22×Dic13C22×C412yes—
119C22×Dic13C22×C412yes—
120C22×Dic13C22×C411yescharacteristic
121C22×Dic13C2×D414yes—
122C22×Dic13C2×D412yes—
123C22×Dic13C2×D414yes—
124C22×Dic13C2×D412yes—
125C22×Dic13C2411yescharacteristic
126C2×C4×D13—24no—
127C2×C4×D13—24no—
128C2×C4×D13—44no—
129C2×C4×D13—48no—
130C2×C4×D13—44no—
131C2×C4×D13—48no—
132C2×#1057—28no—
133C2×#1057—48no—
134C2×#1057—416no—
135C13×C22⋊C4—28no—
136#6103—24no—
137#6103—24no—
138#6101—24no—
139#6101—24no—
140C4×Dic13—24no—
141C4×Dic13—24no—
142C22×C4×D4—131no—
143C22×C22⋊C8—132no—
144#1459—138no—
145C2×#324—132no—
146C2×#323—132no—
147C23×C13—22no—
148C23×C13—24no—
149C23×C13—22no—
150C23×C13—24no—
151C23×C13—42no—
152C23×C13—42no—
153C23×C13—42no—
154C23×C13—48no—
155C23×C13—48no—
156C23×C13—42no—
157C23×C13C22⋊C818yes—
158C23×C13C22⋊C818yes—
159C23×C13C2×C22⋊C414yes—
160C23×C13C2×C22⋊C411yescharacteristic
161C23×C13C2×C22⋊C411yescharacteristic
162C23×C13C22×C812yes—
163C23×C13C22×C814yes—
164C23×C13C2×M1612yes—
165C23×C13C2×M1614yes—
166C23×C13C23×C411yescharacteristic
167C22×D13—22no—
168C22×D13—22no—
169C22×D13—24no—
170C22×D13—24no—
171C22×D13—42no—
172C22×D13—42no—
173C22×D13—48no—
174C22×D13—42no—
175C22×D13—42no—
176C22×D13—42no—
177C22×D13—48no—
178C22×D13—42no—
179C22×D13C22×C814yescomplemented
180C2×C4×C13—22no—
181C2×C4×C13—22no—
182C2×C4×C13—42no—
183C2×C4×C13—42no—
184C2×C4×C13—42no—
185C2×C4×C13—42no—
186C2×C4×C13—42no—
187C2×C4×C13—42no—
188C22⋊D13—232no—
189C2×Dic13—22no—
190C2×Dic13—22no—
191C2×Dic13—24no—
192C2×Dic13—24no—
193C2×Dic13—24no—
194C2×Dic13—22no—
195C2×Dic13—28no—
196C2×Dic13—24no—
197C2×Dic13—24no—
198C2×Dic13—28no—
199C2×Dic13—44no—
200C2×Dic13—41no—
201C2×Dic13—44no—
202C2×Dic13—42no—
203C2×Dic13—41no—
204C2×Dic13#9914yes—
205C2×Dic13C2×C22⋊C412yes—
206C2×Dic13C2×C22⋊C412yes—
207C2×Dic13C2×C22⋊C412yes—
208C2×Dic13C22×C814yescomplemented
209C2×Dic13C22×D412yes—
210C4×D13—48no—
211C4×D13—48no—
212#1057—48no—
213C23×D4—131no—
214C24×C4—131no—
215C24×C4—131no—
216C23×C8—262no—
217C2×C4×D4—134no—
218C2×C4×D4—134no—
219C2×C4×D4—262no—
220C2×C4×D4—264no—
221C2×C4×D4—262no—
222C22×C4⋊C4—131no—
223C22×C22⋊C4—131no—
224C22×C22⋊C4#26111yescharacteristic
225C22×C42—131no—
226C2×C22⋊C8—134no—
227C2×C22⋊C8—138no—
228C2×C22⋊C8—264no—
229C2×C22⋊C8—262no—
230#324—138no—
231#323—138no—
232C22×C13—21no—
233C22×C13—21no—
234C22×C13—24no—
235C22×C13—21no—
236C22×C13—21no—
237C22×C13—24no—
238C22×C13—24no—
239C22×C13—24no—
240C22×C13—216no—
241C22×C13—48no—
242C22×C13—44no—
243C22×C13—44no—
244C22×C13C2×C22⋊C812yes—
245C22×C13C2×C22⋊C818yes—
246C22×C13C2×C22⋊C812yes—
247C22×C13C2×#9912yes—
248C22×C13#41312yes—
249C22×C13C22×C22⋊C411yescharacteristic
250C22×C13C23×C811yescharacteristic
251C22×C13C22×M1611yescharacteristic
252C2×D13—24no—
253C2×D13—44no—
254C2×D13—48no—
255C2×D13—42no—
256C2×D13—42no—
257C2×D13—48no—
258C2×D13—44no—
259C4×C13—42no—
260C4×C13—42no—
261Dic13—24no—
262Dic13—22no—
263Dic13—22no—
264Dic13—22no—
265Dic13C2×#9914yes—
266C25—131no—
267C25C2×#26111yescharacteristic
268C22×D4—138no—
269C22×D4—134no—
270C22×D4—264no—
271C22×D4—262no—
272C22×D4—262no—
273C23×C4—132no—
274C23×C4—131no—
275C23×C4—131no—
276C23×C4—134no—
277C23×C4—132no—
278C23×C4—131no—
279C23×C4—132no—
280C23×C4—132no—
281C23×C4—134no—
282C23×C4—262no—
283C23×C4—261no—
284C23×C4—261no—
285C23×C4—524no—
286C23×C4—524no—
287C23×C4C2×#26111yescharacteristic
288C23×C4C2×#26111yescharacteristic
289C22×C8—268no—
290C22×C8—264no—
291C22×C8—528no—
292C4×D4—268no—
293C4×D4—268no—
294C4×D4—268no—
295C4×D4—268no—
296C2×C4⋊C4—132no—
297C2×C4⋊C4—132no—
298C2×C4⋊C4—262no—
299C2×C4⋊C4—262no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—132no—
303C2×C22⋊C4—132no—
304C2×C22⋊C4—262no—
305C2×C22⋊C4—262no—
306C2×C22⋊C4C2×#26114yes—
307C2×C42—134no—
308C2×C42—262no—
309C2×C42—261no—
310C2×C42—261no—
311C22⋊C8—138no—
312C22⋊C8—264no—
313C22⋊C8—268no—
314C2×C13—21no—
315C2×C13—21no—
316C2×C13—22no—
317C2×C13—28no—
318C2×C13#145914yescomplemented
319C2×C13C22×C22⋊C811yescharacteristic
320C2×C13C22×#9911yescharacteristic
321C2×C13C2×#41311yescharacteristic
322D13—44no—
323C24—42no—
324C24—42no—
325C24—134no—
326C24—132no—
327C24—262no—
328C24—261no—
329C24—261no—
330C24—522no—
331C24—522no—
332C24D13⋊C814yes—
333C24#611814yes—
334C24C22⋊#26112yes—
335C24C22⋊#26112yes—
336C24C22×#26111yescharacteristic
337C24C22×#26112yes—
338C2×D4—1316no—
339C2×D4—2616no—
340C2×D4—2616no—
341C2×D4—268no—
342C2×D4—268no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—131no—
350C22×C4—134no—
351C22×C4—132no—
352C22×C4—134no—
353C22×C4—134no—
354C22×C4—131no—
355C22×C4—132no—
356C22×C4—132no—
357C22×C4—132no—
358C22×C4—132no—
359C22×C4—134no—
360C22×C4—134no—
361C22×C4—131no—
362C22×C4—131no—
363C22×C4—264no—
364C22×C4—264no—
365C22×C4—268no—
366C22×C4—264no—
367C22×C4—262no—
368C22×C4—261no—
369C22×C4—261no—
370C22×C4—524no—
371C22×C4—528no—
372C22×C4—524no—
373C22×C4—528no—
374C22×C4—524no—
375C22×C4—528no—
376C22×C4—524no—
377C22×C4—522no—
378C22×C4—524no—
379C22×C4C22×#26112yes—
380C22×C4C22×#26112yes—
381C2×C8—268no—
382C2×C8—5216no—
383C2×C8—528no—
384C4⋊C4—264no—
385C4⋊C4—264no—
386C22⋊C4—28no—
387C22⋊C4—264no—
388C22⋊C4—264no—
389C42—264no—
390C42—264no—
391C13C2×#145911yescharacteristic, complemented, Sylow
392C23—22no—
393C23—24no—
394C23—22no—
395C23—24no—
396C23—42no—
397C23—42no—
398C23—48no—
399C23—48no—
400C23—42no—
401C23—42no—
402C23—134no—
403C23—262no—
404C23—264no—
405C23—264no—
406C23—262no—
407C23—522no—
408C23—528no—
409C23—522no—
410C23—522no—
411C23—528no—
412C23—522no—
413C23—522no—
414C23—522no—
415C23#8811118yes—
416C23#8811118yes—
417C23C2×D13⋊C812yes—
418C23C2×D13⋊C814yes—
419C23C2×#611812yes—
420C23C2×#611814yes—
421C23C2×C22⋊#26114yes—
422C23C2×C22⋊#26111yescharacteristic
423C23C2×C22⋊#26111yescharacteristic
424C23C23×#26111yescharacteristic
425D4—2632no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—132no—
435C2×C4—134no—
436C2×C4—134no—
437C2×C4—132no—
438C2×C4—132no—
439C2×C4—132no—
440C2×C4—268no—
441C2×C4—268no—
442C2×C4—264no—
443C2×C4—264no—
444C2×C4—262no—
445C2×C4—264no—
446C2×C4—264no—
447C2×C4—262no—
448C2×C4—264no—
449C2×C4—262no—
450C2×C4—528no—
451C2×C4—528no—
452C2×C4—521no—
453C2×C4—522no—
454C2×C4—524no—
455C2×C4—521no—
456C2×C4—524no—
457C8—528no—
458C22—24no—
459C22—24no—
460C22—216no—
461C22—21no—
462C22—21no—
463C22—24no—
464C22—21no—
465C22—21no—
466C22—24no—
467C22—48no—
468C22—44no—
469C22—44no—
470C22—264no—
471C22—524no—
472C22—524no—
473C22—528no—
474C22—528no—
475C22—522no—
476C22—522no—
477C22C2×#8811112yes—
478C22C2×#8811118yes—
479C22C2×#8811112yes—
480C22D13⋊#9912yes—
481C22#1171914812yes—
482C22C22×D13⋊C811yescharacteristic
483C22C22×#611811yescharacteristic
484C22C22×C22⋊#26111yescharacteristic
485C4—42no—
486C4—42no—
487C4—134no—
488C4—264no—
489C4—262no—
490C4—262no—
491C4—262no—
492C2—21no—
493C2—21no—
494C2—22no—
495C2—28no—
496C2—524no—
497C2#1313007414yesdirect product factor
498C2C22×#8811111yescharacteristic
499C2C2×D13⋊#9911yescharacteristic
500C2C2×#1171914811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C13C23×C8
FrattiniC23C23×#261
FittingC22×C13×C22⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC23×C22⋊D13C4
cosocleC22×Dic13C24
hypercenterC22×C22⋊C4#261
hypocenterC13C2×#1459
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C25 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊#1057C2semidirect
2. #13130074C2direct (N × H)
3. C2×#11718286C2semidirect
4. C2×#11718287C2semidirect
22. C2×C22⋊#1057C22semidirect
23. #11718287C22semidirect
24. #11718286C22semidirect
32. C22×C22⋊D13C8semidirect
87. C23×D13C2×C8semidirect
101. C2×C22⋊D13C2×C8semidirect
117. C22×Dic13C2×C8semidirect
179. C22×D13C22×C8semidirect
208. C2×Dic13C22×C8semidirect
318. C2×C13#1459semidirect
391. C13C2×#1459semidirect
497. C2#13130074direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C22⋊#10572
#131300742
C2×#117182862
C2×#117182872
C22×#881352
C2×#145913