Finite Group Databasebeta

← C2×D13⋊#324 #16792795

Subgroups — C2×D13⋊#324 #16792795

Order 3328.

1806 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13⋊(C22⋊C8)C212yesmaximal
2C2×#11718286C212yesmaximal, complemented
3D13⋊#324C218yesmaximal, direct product factor
4C2×#11718285C212yesmaximal, complemented
5C22×C4⋊C4×D13C211yesmaximal, characteristic
6C23×C4×D13C411yescharacteristic
7C23×C4×D13C411yescharacteristic
8C23×C4×D13C2211yescharacteristic
9C22×D13⋊C8—22no—
10C22×C13×C4⋊C4C411yescharacteristic
11C22×C4⋊Dic13C2211yescharacteristic
12C22×#6101C411yescharacteristic
13C22×#6101C2211yescharacteristic
14C2×C4⋊C4×D13—22no—
15C2×C4⋊C4×D13—22no—
16C2×C4⋊C4×D13—24no—
17C2×C4⋊C4×D13C414yes—
18C2×C4⋊C4×D13C2214yes—
19C2×C22⋊#1057C2214yes—
20D13⋊(C22⋊C8)—24no—
21D13⋊(C22⋊C8)C2218yes—
22C2×#88111—22no—
23#11718286C2218yescomplemented
24#11718285C2218yescomplemented
25C24×D13C2×C411yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C23×C4×C13C2×C411yescharacteristic
28C23×C4×C13C2×C411yescharacteristic
29C23×Dic13C2×C411yescharacteristic
30C23×Dic13C2×C411yescharacteristic
31C23×Dic13C2311yescharacteristic
32C22×C4×D13—22no—
33C22×C4×D13—21no—
34C22×C4×D13—21no—
35C22×C4×D13—24no—
36C22×C4×D13—22no—
37C22×C4×D13—21no—
38C22×C4×D13—21no—
39C22×C4×D13—44no—
40C22×C4×D13—44no—
41C22×C4×D13C818yescomplemented
42C22×C4×D13C2×C414yes—
43C22×C4×D13C2×C414yes—
44C22×C4×D13C2×C412yes—
45C22×C4×D13D412yes—
46C22×C4×D13D412yes—
47C22×C4×D13D414yes—
48C22×C4×D13C2312yes—
49C22×#1057—24no—
50C2×D13⋊C8—28no—
51C2×D13⋊C8—48no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C4⋊C4C2×C414yes—
55C2×C4⋊Dic13—22no—
56C2×C4⋊Dic13—22no—
57C2×C4⋊Dic13C2×C412yes—
58C2×C4⋊Dic13C2312yes—
59C2×#6101—22no—
60C2×#6101—22no—
61C2×#6101—22no—
62C2×#6101—22no—
63C2×#6101C2×C412yes—
64C2×#6101C2×C414yes—
65C2×#6101C2312yes—
66C4⋊C4×D13—28no—
67C4⋊C4×D13—28no—
68C4⋊C4×D13—28no—
69C4⋊C4×D13—28no—
70C22⋊#1057—24no—
71C22⋊#1057C2318yes—
72#88111—28no—
73C22×#324—131nomaximal, Sylow
74C24×C13C22×C411yescharacteristic
75C23×D13—24no—
76C23×D13—24no—
77C23×D13C22⋊C412yes—
78C23×D13C22⋊C411yescharacteristic
79C23×D13C22⋊C411yescharacteristic
80C23×D13C2×C814yes—
81C23×D13M1614yes—
82C23×D13C22×C412yes—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—22no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—42no—
89C22×C4×C13—42no—
90C22×C4×C13C22⋊C412yes—
91C22×C4×C13C22⋊C412yes—
92C22×C4×C13C2×C814yescomplemented
93C22×C4×C13C22×C412yes—
94C22×C4×C13C22×C412yes—
95C22×C4×C13C22×C412yes—
96C22×Dic13—21no—
97C22×Dic13—21no—
98C22×Dic13—22no—
99C22×Dic13—21no—
100C22×Dic13—21no—
101C22×Dic13—42no—
102C22×Dic13—42no—
103C22×Dic13C2×C814yescomplemented
104C22×Dic13C22×C412yes—
105C22×Dic13C22×C412yes—
106C22×Dic13C22×C411yescharacteristic
107C22×Dic13C2×D412yes—
108C22×Dic13C2×D412yes—
109C22×Dic13C2411yescharacteristic
110C2×C4×D13—28no—
111C2×C4×D13—216no—
112C2×C4×D13—28no—
113C2×C4×D13—28no—
114C2×C4×D13—24no—
115C2×C4×D13—24no—
116C2×C4×D13—28no—
117C2×C4×D13—24no—
118C2×C4×D13—24no—
119C2×C4×D13—44no—
120C2×C4×D13—48no—
121C2×C4×D13—44no—
122C2×C4×D13—44no—
123C2×C4×D13—44no—
124C2×C4×D13—48no—
125C2×C4×D13—44no—
126C2×C4×D13—48no—
127C2×C4×D13C22⋊C414yes—
128C2×C4×D13C22⋊C414yes—
129C2×C4×D13C2×C8116yescomplemented
130C2×C4×D13C2×D414yes—
131C2×C4×D13C2×D414yes—
132C2×#1057—28no—
133C2×#1057—48no—
134D13⋊C8—416no—
135C13×C4⋊C4—28no—
136C4⋊Dic13—24no—
137C4⋊Dic13—24no—
138#6101—28no—
139#6101—24no—
140#6101—24no—
141C23×C4⋊C4—131no—
142C22×C22⋊C8—132no—
143C2×#324—132no—
144C2×#324—138no—
145C2×#324—132no—
146C23×C13—22no—
147C23×C13—22no—
148C23×C13C2×C22⋊C411yescharacteristic
149C23×C13C2×C22⋊C411yescharacteristic
150C23×C13C22×C812yes—
151C23×C13C2×M1612yes—
152C23×C13C23×C411yescharacteristic
153C22×D13—22no—
154C22×D13—22no—
155C22×D13—216no—
156C22×D13—216no—
157C22×D13—24no—
158C22×D13—24no—
159C22×D13—24no—
160C22×D13—24no—
161C22×D13C22⋊C814yes—
162C22×D13C22⋊C818yes—
163C22×D13C22⋊C814yes—
164C22×D13#9914yes—
165C22×D13#10114yes—
166C22×D13C2×C22⋊C412yes—
167C22×D13C2×C22⋊C412yes—
168C22×D13C22×C814yes—
169C22×D13C2×M1614yes—
170C2×C4×C13—22no—
171C2×C4×C13—22no—
172C2×C4×C13—24no—
173C2×C4×C13—24no—
174C2×C4×C13—24no—
175C2×C4×C13—22no—
176C2×C4×C13—42no—
177C2×C4×C13—42no—
178C2×C4×C13—42no—
179C2×C4×C13—42no—
180C2×C4×C13—42no—
181C2×C4×C13C2×C22⋊C414yes—
182C2×C4×C13C22×C814yescomplemented
183C2×Dic13—22no—
184C2×Dic13—22no—
185C2×Dic13—24no—
186C2×Dic13—24no—
187C2×Dic13—24no—
188C2×Dic13—22no—
189C2×Dic13—41no—
190C2×Dic13—42no—
191C2×Dic13—41no—
192C2×Dic13—42no—
193C2×Dic13—42no—
194C2×Dic13—42no—
195C2×Dic13C2×C22⋊C412yes—
196C2×Dic13C22×C814yescomplemented
197C2×Dic13C22×D412yes—
198C4×D13—216no—
199C4×D13—216no—
200C4×D13—28no—
201C4×D13—28no—
202C4×D13—44no—
203C4×D13—44no—
204C4×D13—48no—
205C4×D13—48no—
206#1057—48no—
207C24×C4—131no—
208C24×C4—131no—
209C24×C4—131no—
210C23×C8—262no—
211C22×C4⋊C4—131no—
212C22×C4⋊C4—131no—
213C22×C4⋊C4—131no—
214C22×C4⋊C4—134no—
215C22×C4⋊C4—134no—
216C22×C4⋊C4—262no—
217C22×C4⋊C4—264no—
218C22×C4⋊C4—262no—
219C22×C4⋊C4#26111yescharacteristic
220C2×C22⋊C8—134no—
221C2×C22⋊C8—138no—
222C2×C22⋊C8—262no—
223C2×C22⋊C8—264no—
224#324—138no—
225#324—138no—
226C22×C13—21no—
227C22×C13—21no—
228C22×C13—21no—
229C22×C13—21no—
230C22×C13—24no—
231C22×C13—24no—
232C22×C13C2×C22⋊C812yes—
233C22×C13C2×C22⋊C812yes—
234C22×C13C2×#9912yes—
235C22×C13C2×#10112yes—
236C22×C13C22×C22⋊C411yescharacteristic
237C22×C13C23×C811yescharacteristic
238C22×C13C22×M1611yescharacteristic
239C2×D13—22no—
240C2×D13—22no—
241C2×D13—28no—
242C2×D13—216no—
243C2×D13—28no—
244C2×D13—28no—
245C2×D13#324116yescomplemented
246C2×D13C2×C22⋊C814yes—
247C2×D13C2×C22⋊C814yes—
248C2×D13C2×#9914yes—
249C2×D13C2×#10114yes—
250C4×C13—24no—
251C4×C13—24no—
252C4×C13—42no—
253Dic13—24no—
254Dic13—22no—
255Dic13—22no—
256Dic13—42no—
257C25—131no—
258C23×C4—131no—
259C23×C4—131no—
260C23×C4—138no—
261C23×C4—132no—
262C23×C4—134no—
263C23×C4—132no—
264C23×C4—134no—
265C23×C4—132no—
266C23×C4—132no—
267C23×C4—131no—
268C23×C4—134no—
269C23×C4—262no—
270C23×C4—261no—
271C23×C4—261no—
272C23×C4—264no—
273C23×C4—262no—
274C23×C4—261no—
275C23×C4—261no—
276C23×C4—524no—
277C23×C4—524no—
278C23×C4C2×#26111yescharacteristic
279C23×C4C2×#26111yescharacteristic
280C23×C4C2×#26111yescharacteristic
281C22×C8—268no—
282C22×C8—264no—
283C22×C8—528no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—132no—
287C2×C4⋊C4—132no—
288C2×C4⋊C4—132no—
289C2×C4⋊C4—134no—
290C2×C4⋊C4—132no—
291C2×C4⋊C4—268no—
292C2×C4⋊C4—268no—
293C2×C4⋊C4—268no—
294C2×C4⋊C4—268no—
295C2×C4⋊C4—262no—
296C2×C4⋊C4—262no—
297C2×C4⋊C4—262no—
298C2×C4⋊C4—262no—
299C2×C4⋊C4—262no—
300C2×C4⋊C4—262no—
301C2×C4⋊C4C2×#26114yes—
302C22⋊C8—138no—
303C22⋊C8—268no—
304C22⋊C8—264no—
305C2×C13—21no—
306C2×C13—21no—
307C2×C13—22no—
308C2×C13C2×#32414yescomplemented
309C2×C13C22×C22⋊C811yescharacteristic
310C2×C13C22×#9911yescharacteristic
311C2×C13C22×#10111yescharacteristic
312D13—24no—
313D13C2×#32418yescomplemented
314C24—131no—
315C24—134no—
316C24—134no—
317C24—132no—
318C24—131no—
319C24—132no—
320C24—264no—
321C24—264no—
322C24C22×#26111yescharacteristic
323C22×C4—22no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—134no—
331C22×C4—132no—
332C22×C4—132no—
333C22×C4—132no—
334C22×C4—131no—
335C22×C4—131no—
336C22×C4—1316no—
337C22×C4—134no—
338C22×C4—134no—
339C22×C4—134no—
340C22×C4—134no—
341C22×C4—132no—
342C22×C4—264no—
343C22×C4—264no—
344C22×C4—268no—
345C22×C4—268no—
346C22×C4—268no—
347C22×C4—2616no—
348C22×C4—268no—
349C22×C4—264no—
350C22×C4—264no—
351C22×C4—262no—
352C22×C4—261no—
353C22×C4—261no—
354C22×C4—261no—
355C22×C4—261no—
356C22×C4—524no—
357C22×C4—528no—
358C22×C4—524no—
359C22×C4—524no—
360C22×C4—524no—
361C22×C4—528no—
362C22×C4—524no—
363C22×C4—528no—
364C22×C4—522no—
365C22×C4—522no—
366C22×C4D13⋊C814yescomplemented
367C22×C4C22⋊#26112yes—
368C22×C4C22⋊#26112yes—
369C22×C4C22×#26112yes—
370C22×C4C22×#26112yes—
371C22×C4C22×#26112yes—
372C2×C8—268no—
373C2×C8—5216no—
374C2×C8—528no—
375C4⋊C4—28no—
376C4⋊C4—264no—
377C4⋊C4—264no—
378C4⋊C4—264no—
379C4⋊C4—264no—
380C4⋊C4—268no—
381C13C22×#32411yescharacteristic, complemented, Sylow
382C23—22no—
383C23—22no—
384C23—132no—
385C23—134no—
386C23—134no—
387C23—134no—
388C23—134no—
389C23—134no—
390C23—132no—
391C23—138no—
392C23—134no—
393C23—264no—
394C23—264no—
395C23—2616no—
396C23—2616no—
397C23—264no—
398C23—264no—
399C23—262no—
400C23—262no—
401C23C2×D13⋊C812yes—
402C23D13⋊M1612yes—
403C23C2×C22⋊#26111yescharacteristic
404C23C2×C22⋊#26111yescharacteristic
405C23C23×#26111yescharacteristic
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—22no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—134no—
418C2×C4—132no—
419C2×C4—132no—
420C2×C4—268no—
421C2×C4—2616no—
422C2×C4—2616no—
423C2×C4—268no—
424C2×C4—262no—
425C2×C4—262no—
426C2×C4—264no—
427C2×C4—264no—
428C2×C4—264no—
429C2×C4—262no—
430C2×C4—524no—
431C2×C4—524no—
432C2×C4—528no—
433C2×C4—528no—
434C2×C4—521no—
435C2×C4—522no—
436C2×C4—521no—
437C2×C4—522no—
438C2×C4—522no—
439C2×C4—522no—
440C2×C4C2×D13⋊C814yescomplemented
441C2×C4C2×C22⋊#26114yes—
442C8—528no—
443C22—24no—
444C22—24no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—1316no—
450C22—134no—
451C22—134no—
452C22—134no—
453C22—134no—
454C22—268no—
455C22—268no—
456C22—2616no—
457C22—268no—
458C22—262no—
459C22—262no—
460C22D13⋊(C22⋊C8)12yes—
461C22D13⋊(C22⋊C8)12yes—
462C22D13⋊#9912yes—
463C22D13⋊#10112yes—
464C22C22×D13⋊C811yescharacteristic
465C22C2×D13⋊M1611yescharacteristic
466C22C22×C22⋊#26111yescharacteristic
467C4—24no—
468C4—24no—
469C4—42no—
470C4—264no—
471C4—262no—
472C4—262no—
473C4—522no—
474C2—21no—
475C2—21no—
476C2—22no—
477C2—138no—
478C2—264no—
479C2D13⋊#32414yesdirect product factor
480C2C2×D13⋊(C22⋊C8)11yescharacteristic
481C2C2×D13⋊#9911yescharacteristic
482C2C2×D13⋊#10111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C13C23×C8
FrattiniC23C23×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC24×D13C2×C4
cosocleC22×Dic13C24
hypercenterC22×C4⋊C4#261
hypocenterC13C22×#324
LCSG ▷ C22×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
2. C2×#11718286C2semidirect
3. D13⋊#324C2direct (N × H)
4. C2×#11718285C2semidirect
23. #11718286C22semidirect
24. #11718285C22semidirect
41. C22×C4×D13C8semidirect
92. C22×C4×C13C2×C8semidirect
103. C22×Dic13C2×C8semidirect
129. C2×C4×D13C2×C8semidirect
182. C2×C4×C13C22×C8semidirect
196. C2×Dic13C22×C8semidirect
245. C2×D13#324semidirect
308. C2×C13C2×#324semidirect
313. D13C2×#324semidirect
366. C22×C4D13⋊C8semidirect
381. C13C22×#324semidirect
440. C2×C4C2×D13⋊C8semidirect
479. C2D13⋊#324direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D13⋊(C22⋊C8)2
C2×#117182862
D13⋊#3242
C2×#117182852
C22×C4⋊C4×D132
C22×#32413