Finite Group Databasebeta

← C2×D13⋊(Q8⋊C8) #16793283

Subgroups — C2×D13⋊(Q8⋊C8) #16793283

Order 3328.

1454 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13⋊(C4⋊C8)C211yesmaximal, characteristic
2C2×C4×D13⋊C8C211yesmaximal, characteristic
3C2×#11718244C212yesmaximal, complemented
4D13⋊(Q8⋊C8)C218yesmaximal, direct product factor
5C2×Q8⋊#1057C212yesmaximal, complemented
6C2×C4×Q8×D13C211yesmaximal, characteristic
7C22×Q8×D13C411yescharacteristic
8C22×D13⋊C8—21no—
9C22×D13⋊C8—21no—
10C2×C4×Q8×C13C411yescharacteristic
11C2×Q8×Dic13C2211yescharacteristic
12C4×Q8×D13—22no—
13C4×Q8×D13—22no—
14C4×Q8×D13C414yes—
15C4×Q8×D13C2214yes—
16C2×C4⋊C4×D13—21no—
17C2×C4⋊C4×D13C411yescharacteristic
18C2×#88141—21no—
19C2×#88141C2211yescharacteristic
20C2×C42×D13—21no—
21C2×C42×D13C2211yescharacteristic
22C2×C4×Dic26—21no—
23C2×C4×Dic26C411yescharacteristic
24C2×#88112—21no—
25C2×C4⋊#1057C2212yes—
26C2×C4×#1057—21no—
27C2×C4×#1057C2212yes—
28D13⋊(C4⋊C8)—22no—
29D13⋊(C4⋊C8)C2214yes—
30C4×D13⋊C8—22no—
31C4×D13⋊C8C2214yes—
32Q8⋊#1057C2218yescomplemented
33#11718244C2218yescomplemented
34C22×Q8×C13C2×C411yescharacteristic
35C2×Q8×D13—22no—
36C2×Q8×D13—24no—
37C2×Q8×D13C818yescomplemented
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×D13⋊C8—28no—
49C2×D13⋊C8—24no—
50C2×D13⋊C8—24no—
51C2×D13⋊C8—44no—
52C4×Q8×C13—22no—
53C4×Q8×C13C2×C414yes—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4C2×C411yescharacteristic
56C2×C42×C13—21no—
57C2×C42×C13C2×C411yescharacteristic
58Q8×Dic13—21no—
59Q8×Dic13—21no—
60Q8×Dic13C2×C412yes—
61Q8×Dic13C2312yes—
62C2×C4⋊Dic13—21no—
63C2×C4⋊Dic13C2×C411yescharacteristic
64C2×#6101—21no—
65C2×#6101—21no—
66C2×#6101—21no—
67C2×C4×Dic13—21no—
68C2×C4×Dic13—21no—
69C2×C4×Dic13—21no—
70C2×C4×Dic13D411yescharacteristic
71C2×C4×Dic13D411yescharacteristic
72C2×C4×Dic13C2311yescharacteristic
73C4⋊C4×D13—24no—
74C4⋊C4×D13—22no—
75C4⋊C4×D13—24no—
76C4⋊C4×D13C2×C414yes—
77#88141—24no—
78#88141—24no—
79#88141—21no—
80#88141—21no—
81#88141C2×C412yes—
82#88141C2312yes—
83C42×D13—24no—
84C42×D13—24no—
85C42×D13C2×C412yes—
86C42×D13D412yes—
87C42×D13D412yes—
88C42×D13C2312yes—
89C4×Dic26—22no—
90C4×Dic26—24no—
91C4×Dic26—24no—
92C4×Dic26C2×C414yes—
93#88112—24no—
94C4⋊#1057—22no—
95C4⋊#1057C2314yes—
96C4×#1057—22no—
97C4×#1057—24no—
98C4×#1057C2314yes—
99C22×Q8⋊C8—131nomaximal, Sylow
100C23×D13C22⋊C411yescharacteristic
101C2×Q8×C13—21no—
102C2×Q8×C13—22no—
103C2×Q8×C13C2×C814yescomplemented
104C2×Q8×C13C22×C412yes—
105C22×C4×C13—21no—
106C22×C4×C13—21no—
107C22×C4×C13C22⋊C411yescharacteristic
108C22×C4×C13C22⋊C411yescharacteristic
109C22×C4×C13C22×C411yescharacteristic
110C22×Dic13—21no—
111C22×Dic13—21no—
112C22×Dic13C22⋊C411yescharacteristic
113C22×Dic13C2×D411yescharacteristic
114C22×Dic13C2×D411yescharacteristic
115Q8×D13—216no—
116Q8×D13—28no—
117Q8×D13C2×C8116yescomplemented
118C2×C4×D13—28no—
119C2×C4×D13—24no—
120C2×C4×D13—24no—
121C2×C4×D13—24no—
122C2×C4×D13—44no—
123C2×C4×D13C22⋊C412yes—
124C2×C4×D13C22⋊C412yes—
125C2×C4×D13C22⋊C412yes—
126C2×C4×D13C2×C814yes—
127C2×C4×D13M1614yes—
128C2×C4×D13SD1614yes—
129C2×C4×D13Q1614yes—
130C2×C4×D13C22×C412yes—
131C2×C4×D13C2×D412yes—
132C2×C4×D13C2×D412yes—
133C2×Dic26—21no—
134C2×Dic26—22no—
135C2×Dic26—28no—
136C2×Dic26—24no—
137C2×Dic26C2×C814yescomplemented
138C2×Dic26C22×C412yes—
139C2×#1057—28no—
140C2×#1057—24no—
141C2×#1057—24no—
142C2×#1057—44no—
143D13⋊C8—216no—
144D13⋊C8—48no—
145C13×C4⋊C4—24no—
146C13×C4⋊C4—21no—
147C13×C4⋊C4C22×C412yes—
148C42×C13—24no—
149C42×C13C22⋊C412yes—
150C42×C13C22×C412yes—
151C4⋊Dic13—21no—
152C4⋊Dic13—22no—
153C4⋊Dic13—22no—
154C4⋊Dic13C22×C412yes—
155#6101—24no—
156#6101—24no—
157#6101—22no—
158#6101—22no—
159C4×Dic13—24no—
160C4×Dic13—22no—
161C4×Dic13—22no—
162C4×Dic13—22no—
163C4×Dic13—22no—
164C4×Dic13C22⋊C412yes—
165C4×Dic13C22⋊C412yes—
166C4×Dic13C22×C411yescharacteristic
167C4×Dic13C2×D412yes—
168C4×Dic13C2×D411yescharacteristic
169C4×Dic13C2×D411yescharacteristic
170C4×Dic13C2×D412yes—
171C4×Dic13C2411yescharacteristic
172C22×C4×Q8—131no—
173C22×C4⋊C8—131no—
174C22×C4×C8—131no—
175C2×Q8⋊C8—132no—
176C2×Q8⋊C8—138no—
177C2×Q8⋊C8—132no—
178C23×C13C2×C22⋊C411yescharacteristic
179C22×D13C22⋊C814yes—
180C22×D13#10314yes—
181C22×D13#10414yes—
182C22×D13C2×C22⋊C412yes—
183Q8×C13—22no—
184Q8×C13—24no—
185Q8×C13C22×C814yescomplemented
186C2×C4×C13—22no—
187C2×C4×C13—24no—
188C2×C4×C13—22no—
189C2×C4×C13—22no—
190C2×C4×C13—42no—
191C2×C4×C13#10314yes—
192C2×C4×C13C2×C22⋊C412yes—
193C2×C4×C13C2×C22⋊C411yescharacteristic
194C2×C4×C13C2×C22⋊C412yes—
195C2×C4×C13C22×C812yes—
196C2×C4×C13C2×M1612yes—
197C2×C4×C13C23×C411yescharacteristic
198C2×Dic13—22no—
199C2×Dic13—24no—
200C2×Dic13—22no—
201C2×Dic13—22no—
202C2×Dic13—42no—
203C2×Dic13C22⋊C814yes—
204C2×Dic13C2×C22⋊C411yescharacteristic
205C2×Dic13C2×C22⋊C412yes—
206C2×Dic13C2×C22⋊C411yescharacteristic
207C2×Dic13C2×SD1612yes—
208C2×Dic13C2×Q1612yes—
209C2×Dic13C22×D411yescharacteristic
210C2×Dic13C22×D411yescharacteristic
211C4×D13—216no—
212C4×D13—24no—
213C4×D13—24no—
214C4×D13—48no—
215C4×D13C22⋊C818yes—
216C4×D13#10318yes—
217C4×D13C22×C814yes—
218C4×D13C2×M1614yes—
219C4×D13C2×SD1614yes—
220C4×D13C2×Q1614yes—
221Dic26—22no—
222Dic26—24no—
223Dic26—216no—
224Dic26C22×C814yescomplemented
225#1057—28no—
226#1057—44no—
227C23×Q8—131no—
228C23×C8—261no—
229C23×C8—261no—
230C2×C4×Q8—131no—
231C2×C4×Q8—134no—
232C2×C4×Q8—134no—
233C2×C4×Q8—131no—
234C2×C4×Q8—131no—
235C2×C4×Q8—261no—
236C2×C4×Q8—261no—
237C2×C4×Q8—262no—
238C2×C4×Q8—262no—
239C2×C4×Q8#26111yescharacteristic
240C22×C4⋊C4—131no—
241C22×C4⋊C4—261no—
242C22×C42—131no—
243C22×C42—261no—
244C2×C4⋊C8—134no—
245C2×C4⋊C8—132no—
246C2×C4⋊C8—262no—
247C2×C4⋊C8—261no—
248C2×C4×C8—134no—
249C2×C4×C8—132no—
250C2×C4×C8—262no—
251C2×C4×C8—261no—
252Q8⋊C8—138no—
253Q8⋊C8—138no—
254C22×C13C2×C22⋊C812yes—
255C22×C13C2×#10312yes—
256C22×C13C2×#10412yes—
257C22×C13C22×C22⋊C411yescharacteristic
258C2×D13Q8⋊C8116yescomplemented
259C2×D13C2×C22⋊C814yes—
260C2×D13C2×#10314yes—
261C2×D13C2×#10414yes—
262C4×C13—24no—
263C4×C13—22no—
264C4×C13—42no—
265C4×C13C2×C22⋊C812yes—
266C4×C13C2×#10314yes—
267C4×C13C23×C811yescharacteristic
268C4×C13C22×M1611yescharacteristic
269Dic13—24no—
270Dic13—21no—
271Dic13—21no—
272Dic13—42no—
273Dic13C2×C22⋊C814yes—
274Dic13C2×#10312yes—
275Dic13C22×SD1611yescharacteristic
276Dic13C22×Q1611yescharacteristic
277C22×Q8—138no—
278C22×Q8—134no—
279C22×Q8—131no—
280C22×Q8—261no—
281C22×Q8—262no—
282C22×Q8—264no—
283C22×Q8C2×#26111yescharacteristic
284C23×C4—131no—
285C23×C4—131no—
286C23×C4—131no—
287C23×C4—261no—
288C23×C4—261no—
289C22×C8—264no—
290C22×C8—262no—
291C22×C8—268no—
292C22×C8—264no—
293C22×C8—262no—
294C22×C8—524no—
295C4×Q8—22no—
296C4×Q8—132no—
297C4×Q8—132no—
298C4×Q8—132no—
299C4×Q8—132no—
300C4×Q8—134no—
301C4×Q8—264no—
302C4×Q8—264no—
303C4×Q8—261no—
304C4×Q8—264no—
305C4×Q8—261no—
306C4×Q8—264no—
307C4×Q8—261no—
308C4×Q8—261no—
309C4×Q8—262no—
310C4×Q8C2×#26114yes—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—131no—
313C2×C4⋊C4—134no—
314C2×C4⋊C4—262no—
315C2×C4⋊C4—264no—
316C2×C4⋊C4—264no—
317C2×C4⋊C4—261no—
318C2×C4⋊C4—261no—
319C2×C4⋊C4—261no—
320C2×C4⋊C4—261no—
321C2×C4⋊C4C2×#26111yescharacteristic
322C2×C42—21no—
323C2×C42—131no—
324C2×C42—131no—
325C2×C42—131no—
326C2×C42—132no—
327C2×C42—132no—
328C2×C42—132no—
329C2×C42—132no—
330C2×C42—264no—
331C2×C42—264no—
332C2×C42—261no—
333C2×C42—261no—
334C2×C42—261no—
335C2×C42C2×#26111yescharacteristic
336C4⋊C8—134no—
337C4⋊C8—262no—
338C4⋊C8—264no—
339C4×C8—134no—
340C4×C8—262no—
341C4×C8—264no—
342C2×C13C2×Q8⋊C814yescomplemented
343C2×C13C22×C22⋊C811yescharacteristic
344C2×C13C22×#10311yescharacteristic
345C2×C13C22×#10411yescharacteristic
346D13C2×Q8⋊C818yescomplemented
347C24—131no—
348C2×Q8—22no—
349C2×Q8—21no—
350C2×Q8—1316no—
351C2×Q8—134no—
352C2×Q8—132no—
353C2×Q8—264no—
354C2×Q8—268no—
355C2×Q8—268no—
356C2×Q8—2616no—
357C2×Q8—262no—
358C2×Q8—261no—
359C2×Q8D13⋊C814yescomplemented
360C2×Q8C22×#26112yes—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—131no—
364C22×C4—131no—
365C22×C4—134no—
366C22×C4—134no—
367C22×C4—134no—
368C22×C4—134no—
369C22×C4—132no—
370C22×C4—132no—
371C22×C4—132no—
372C22×C4—132no—
373C22×C4—131no—
374C22×C4—132no—
375C22×C4—132no—
376C22×C4—264no—
377C22×C4—264no—
378C22×C4—268no—
379C22×C4—264no—
380C22×C4—261no—
381C22×C4—261no—
382C22×C4—524no—
383C22×C4C22⋊#26111yescharacteristic
384C22×C4C22⋊#26111yescharacteristic
385C22×C4C22×#26111yescharacteristic
386C2×C8—264no—
387C2×C8—2616no—
388C2×C8—268no—
389C2×C8—264no—
390C2×C8—528no—
391C2×C8—524no—
392C4⋊C4—24no—
393C4⋊C4—21no—
394C4⋊C4—132no—
395C4⋊C4—264no—
396C4⋊C4—262no—
397C4⋊C4—262no—
398C4⋊C4—262no—
399C4⋊C4—262no—
400C4⋊C4—261no—
401C4⋊C4—264no—
402C4⋊C4C22×#26112yes—
403C42—24no—
404C42—131no—
405C42—132no—
406C42—132no—
407C42—131no—
408C42—132no—
409C42—132no—
410C42—131no—
411C42—131no—
412C42—262no—
413C42—262no—
414C42—262no—
415C42—262no—
416C42—264no—
417C42C22⋊#26112yes—
418C42C22×#26112yes—
419C13C22×Q8⋊C811yescharacteristic, complemented, Sylow
420C23—132no—
421C23—134no—
422C23—134no—
423C23—134no—
424C23C2×C22⋊#26111yescharacteristic
425Q8—22no—
426Q8—24no—
427Q8—134no—
428Q8—2616no—
429Q8—262no—
430Q8—264no—
431Q8C2×D13⋊C814yescomplemented
432C2×C4—22no—
433C2×C4—24no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—42no—
437C2×C4—131no—
438C2×C4—131no—
439C2×C4—132no—
440C2×C4—134no—
441C2×C4—132no—
442C2×C4—132no—
443C2×C4—134no—
444C2×C4—134no—
445C2×C4—138no—
446C2×C4—134no—
447C2×C4—138no—
448C2×C4—134no—
449C2×C4—131no—
450C2×C4—131no—
451C2×C4—264no—
452C2×C4—264no—
453C2×C4—2616no—
454C2×C4—262no—
455C2×C4—264no—
456C2×C4—262no—
457C2×C4—262no—
458C2×C4—528no—
459C2×C4—522no—
460C2×C4#8811714yes—
461C2×C4C2×D13⋊C812yes—
462C2×C4D13⋊M1612yes—
463C2×C4C2×C22⋊#26112yes—
464C2×C4C2×C22⋊#26111yescharacteristic
465C2×C4C2×C22⋊#26112yes—
466C2×C4C23×#26111yescharacteristic
467C8—268no—
468C8—524no—
469C22—1316no—
470C22—134no—
471C22—134no—
472C22—134no—
473C22D13⋊(C22⋊C8)12yes—
474C22C2×#8811712yes—
475C22D13⋊#10412yes—
476C22C22×C22⋊#26111yescharacteristic
477C4—24no—
478C4—22no—
479C4—42no—
480C4—134no—
481C4—131no—
482C4—131no—
483C4—132no—
484C4—264no—
485C4—261no—
486C4—261no—
487C4—522no—
488C4D13⋊(C22⋊C8)12yes—
489C4C2×#8811714yes—
490C4C22×D13⋊C811yescharacteristic
491C4C2×D13⋊M1611yescharacteristic
492C2—138no—
493C2D13⋊(Q8⋊C8)14yesdirect product factor
494C2C2×D13⋊(C22⋊C8)11yescharacteristic
495C2C22×#8811711yescharacteristic
496C2C2×D13⋊#10411yescharacteristic
subgroupG/H
centerC22×C4C22⋊#261
commutatorC4×C13C23×C8
FrattiniC2×C4C23×#261
FittingC2×C4×Q8×C13C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC4×Dic13C24
hypercenterC2×C4×Q8#261
hypocenterC13C22×Q8⋊C8
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. C2×#11718244C2semidirect
4. D13⋊(Q8⋊C8)C2direct (N × H)
5. C2×Q8⋊#1057C2semidirect
32. Q8⋊#1057C22semidirect
33. #11718244C22semidirect
37. C2×Q8×D13C8semidirect
103. C2×Q8×C13C2×C8semidirect
117. Q8×D13C2×C8semidirect
137. C2×Dic26C2×C8semidirect
185. Q8×C13C22×C8semidirect
224. Dic26C22×C8semidirect
258. C2×D13Q8⋊C8semidirect
342. C2×C13C2×Q8⋊C8semidirect
346. D13C2×Q8⋊C8semidirect
359. C2×Q8D13⋊C8semidirect
419. C13C22×Q8⋊C8semidirect
431. Q8C2×D13⋊C8semidirect
493. C2D13⋊(Q8⋊C8)direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D13⋊(C4⋊C8)2
C2×C4×D13⋊C82
C2×#117182442
D13⋊(Q8⋊C8)2
C2×Q8⋊#10572
C2×C4×Q8×D132
C22×Q8⋊C813