Finite Group Databasebeta

← C2×#13130337 #16794618

Subgroups — C2×#13130337 #16794618

Order 3328.

1050 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719049C211yesmaximal, characteristic
2C2×D13⋊(C4⋊C8)C211yesmaximal, characteristic
3#13130337C218yesmaximal, direct product factor
4C2×#11718303C212yesmaximal, complemented
5C2×#11718245C212yesmaximal, complemented
6C2×#11719283C211yesmaximal, characteristic
7C22×D13⋊C8—21no—
8C2×C4×Q8×C13C411yescharacteristic
9C2×#88200C411yescharacteristic
10C2×#88198C2211yescharacteristic
11#11719283—22no—
12#11719283—22no—
13#11719283C414yes—
14#11719283C2214yes—
15C2×#88151C411yescharacteristic
16C2×#88150—21no—
17C2×#88143—21no—
18C2×#88142C2211yescharacteristic
19C2×#88126—21no—
20C2×C42×D13C2211yescharacteristic
21C2×C4×Dic26—21no—
22C2×C4×Dic26C411yescharacteristic
23C2×#88112C2212yes—
24C2×#88112C2212yes—
25C2×#88111—21no—
26C2×C4⋊#1057—21no—
27C2×C4×#1057—21no—
28D13⋊(C4⋊C8)—22no—
29D13⋊(C4⋊C8)C2214yes—
30#11719049—22no—
31#11719049C2214yes—
32#11718303C2218yescomplemented
33#11718245C2218yescomplemented
34C22×Q8×C13C2×C411yescharacteristic
35C22×C4×D13C2×C411yescharacteristic
36C22×C4×D13D411yescharacteristic
37C22×C4×D13D411yescharacteristic
38C22×Dic26—21no—
39C22×Dic26C2×C411yescharacteristic
40C22×#1057—22no—
41C22×#1057—22no—
42C2×D13⋊C8—24no—
43C2×D13⋊C8—44no—
44C4×Q8×C13—22no—
45C4×Q8×C13C2×C414yes—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4C2×C411yescharacteristic
48C2×C42×C13—21no—
49C2×C42×C13C2×C411yescharacteristic
50#88200—22no—
51#88200C2×C414yes—
52#88198—21no—
53#88198—21no—
54#88198C2×C412yes—
55#88198C2312yes—
56C2×#6103—21no—
57C2×#6103—21no—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13C2×C411yescharacteristic
60C2×#6101—21no—
61C2×#6101—21no—
62C2×#6101—21no—
63C2×#6101—21no—
64C2×#6101—21no—
65C2×C4×Dic13—21no—
66C2×C4×Dic13D411yescharacteristic
67C2×C4×Dic13D411yescharacteristic
68C2×C4×Dic13C2311yescharacteristic
69#88151—22no—
70#88151C2×C414yes—
71#88150—24no—
72#88150—24no—
73#88143—24no—
74#88143—24no—
75#88142—21no—
76#88142—21no—
77#88142C2×C412yes—
78#88142C2312yes—
79#88126—24no—
80#88126—24no—
81C42×D13C2×C412yes—
82C42×D13D412yes—
83C42×D13D412yes—
84C42×D13C2312yes—
85C4×Dic26—22no—
86C4×Dic26—24no—
87C4×Dic26—24no—
88C4×Dic26C2×C414yes—
89#88112—22no—
90#88112—22no—
91#88112C2314yes—
92#88112C2314yes—
93#88111—24no—
94C4⋊#1057—24no—
95C4×#1057—24no—
96C2×#1542—131nomaximal, Sylow
97C23×D13C22⋊C411yescharacteristic
98C2×Q8×C13—21no—
99C2×Q8×C13—42no—
100C2×Q8×C13C22×C412yes—
101C22×C4×C13—21no—
102C22×C4×C13—21no—
103C22×C4×C13C22⋊C411yescharacteristic
104C22×C4×C13C22⋊C411yescharacteristic
105C22×C4×C13C22×C411yescharacteristic
106C22×Dic13—21no—
107C22×Dic13—21no—
108C22×Dic13C22⋊C411yescharacteristic
109C22×Dic13C2×D411yescharacteristic
110C22×Dic13C2×D411yescharacteristic
111C2×C4×D13—24no—
112C2×C4×D13—42no—
113C2×C4×D13C22⋊C412yes—
114C2×C4×D13C22⋊C412yes—
115C2×C4×D13C22⋊C412yes—
116C2×C4×D13SD1614yes—
117C2×C4×D13Q1614yes—
118C2×C4×D13C22×C412yes—
119C2×C4×D13C2×D412yes—
120C2×C4×D13C2×D412yes—
121C2×Dic26—21no—
122C2×Dic26—22no—
123C2×Dic26—22no—
124C2×Dic26—44no—
125C2×Dic26—42no—
126C2×Dic26C22×C412yes—
127C2×#1057—24no—
128C2×#1057—24no—
129C2×#1057—44no—
130C2×#1057—44no—
131D13⋊C8—48no—
132C13×C4⋊C4—21no—
133C13×C4⋊C4—24no—
134C13×C4⋊C4C22×C412yes—
135C42×C13—24no—
136C42×C13C22⋊C412yes—
137C42×C13C22×C412yes—
138#6103—24no—
139#6103—24no—
140C4⋊Dic13—21no—
141C4⋊Dic13—24no—
142C4⋊Dic13C22×C412yes—
143#6101—24no—
144#6101—24no—
145#6101—22no—
146#6101—22no—
147#6101—22no—
148#6101—22no—
149#6101—22no—
150#6101—22no—
151C4×Dic13—24no—
152C4×Dic13C22⋊C412yes—
153C4×Dic13C22⋊C412yes—
154C4×Dic13C22×C411yescharacteristic
155C4×Dic13C2×D412yes—
156C4×Dic13C2×D412yes—
157C4×Dic13C2×D411yescharacteristic
158C4×Dic13C2×D411yescharacteristic
159C4×Dic13C2411yescharacteristic
160C2×#533—131no—
161C2×#431—131no—
162C22×C4⋊C8—131no—
163#1542—138no—
164C2×#333—132no—
165C2×#332—132no—
166C23×C13C2×C22⋊C411yescharacteristic
167C22×D13—22no—
168C22×D13—22no—
169C22×D13#10314yes—
170C22×D13C2×C22⋊C412yes—
171Q8×C13—42no—
172Q8×C13—42no—
173C2×C4×C13—22no—
174C2×C4×C13—22no—
175C2×C4×C13—22no—
176C2×C4×C13—22no—
177C2×C4×C13—42no—
178C2×C4×C13—42no—
179C2×C4×C13#10314yes—
180C2×C4×C13C2×C22⋊C412yes—
181C2×C4×C13C2×C22⋊C411yescharacteristic
182C2×C4×C13C2×C22⋊C412yes—
183C2×C4×C13C23×C411yescharacteristic
184C2×Dic13—22no—
185C2×Dic13—22no—
186C2×Dic13—22no—
187C2×Dic13—42no—
188C2×Dic13—42no—
189C2×Dic13C2×C22⋊C412yes—
190C2×Dic13C2×C22⋊C411yescharacteristic
191C2×Dic13C2×C22⋊C411yescharacteristic
192C2×Dic13C2×SD1612yes—
193C2×Dic13C2×Q1612yes—
194C2×Dic13#13514yes—
195C2×Dic13C22×D411yescharacteristic
196C2×Dic13C22×D411yescharacteristic
197C4×D13—24no—
198C4×D13—24no—
199C4×D13—42no—
200C4×D13—42no—
201C4×D13#10318yes—
202C4×D13C2×SD1614yes—
203C4×D13C2×Q1614yes—
204Dic26—42no—
205Dic26—44no—
206Dic26—44no—
207Dic26—42no—
208#1057—44no—
209#1057—44no—
210C23×C8—261no—
211#533—134no—
212#533—134no—
213#533—262no—
214#533—262no—
215C2×C4⋊Q8—131no—
216C2×C4⋊Q8—131no—
217C2×#125—261no—
218C2×C22⋊Q8—131no—
219C2×C22⋊Q8—131no—
220C2×C22⋊Q8—261no—
221C2×C4×Q8—131no—
222C2×C4×Q8—261no—
223C2×C4×Q8#26111yescharacteristic
224C2×#117—261no—
225C22×C42—131no—
226#431—134no—
227#431—262no—
228C2×C4⋊C8—132no—
229C2×C4⋊C8—132no—
230C2×C4⋊C8—134no—
231C2×C4⋊C8—262no—
232C2×C4⋊C8—261no—
233C2×C22⋊C8—261no—
234C2×C4×C8—261no—
235#333—138no—
236#332—138no—
237C22×C13#41312yes—
238C22×C13C2×#10312yes—
239C22×C13#41612yes—
240C22×C13C22×C22⋊C411yescharacteristic
241C2×D13—28no—
242C2×D13—22no—
243C2×D13—22no—
244C2×D13C2×#10314yes—
245C4×C13—21no—
246C4×C13—21no—
247C4×C13—22no—
248C4×C13—42no—
249C4×C13—42no—
250C4×C13C2×#10314yes—
251Dic13—22no—
252Dic13—42no—
253Dic13—42no—
254Dic13C2×#10312yes—
255Dic13#41612yes—
256Dic13C22×SD1611yescharacteristic
257Dic13C22×Q1611yescharacteristic
258Dic13C2×#13512yes—
259C22×Q8—131no—
260C22×Q8—261no—
261C22×Q8C2×#26111yescharacteristic
262C23×C4—131no—
263C23×C4—131no—
264C23×C4—131no—
265C22×C8—264no—
266C22×C8—262no—
267C22×C8—262no—
268C22×C8—524no—
269C4⋊Q8—132no—
270C4⋊Q8—132no—
271C4⋊Q8—132no—
272C4⋊Q8—132no—
273C4⋊Q8—261no—
274C4⋊Q8—261no—
275C4⋊Q8—261no—
276C4⋊Q8—261no—
277#125—264no—
278#125—264no—
279C22⋊Q8—134no—
280C22⋊Q8—134no—
281C22⋊Q8—262no—
282C22⋊Q8—264no—
283C22⋊Q8—264no—
284C22⋊Q8—262no—
285C4×Q8—22no—
286C4×Q8—134no—
287C4×Q8—264no—
288C4×Q8—264no—
289C4×Q8—262no—
290C4×Q8C2×#26114yes—
291#117—264no—
292#117—264no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—131no—
295C2×C4⋊C4—261no—
296C2×C4⋊C4—261no—
297C2×C4⋊C4—261no—
298C2×C4⋊C4—261no—
299C2×C4⋊C4—261no—
300C2×C4⋊C4—261no—
301C2×C4⋊C4C2×#26111yescharacteristic
302C2×C22⋊C4—261no—
303C2×C22⋊C4—261no—
304C2×C42—21no—
305C2×C42—131no—
306C2×C42—131no—
307C2×C42—131no—
308C2×C42—132no—
309C2×C42—132no—
310C2×C42—132no—
311C2×C42—132no—
312C2×C42—261no—
313C2×C42C2×#26111yescharacteristic
314C4⋊C8—134no—
315C4⋊C8—134no—
316C4⋊C8—264no—
317C4⋊C8—262no—
318C4⋊C8—262no—
319C22⋊C8—264no—
320C4×C8—264no—
321C2×C13#154214yescomplemented
322C2×C13C2×#41311yescharacteristic
323C2×C13C22×#10311yescharacteristic
324C2×C13C2×#41611yescharacteristic
325D13—24no—
326C24—131no—
327C2×Q8—21no—
328C2×Q8—42no—
329C2×Q8—132no—
330C2×Q8—262no—
331C2×Q8—262no—
332C2×Q8—261no—
333C2×Q8—522no—
334C2×Q8—524no—
335C2×Q8C22×#26112yes—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—131no—
339C22×C4—131no—
340C22×C4—134no—
341C22×C4—134no—
342C22×C4—132no—
343C22×C4—132no—
344C22×C4—131no—
345C22×C4—132no—
346C22×C4—132no—
347C22×C4—132no—
348C22×C4—132no—
349C22×C4—264no—
350C22×C4—261no—
351C22×C4—261no—
352C22×C4—522no—
353C22×C4C22⋊#26111yescharacteristic
354C22×C4C22⋊#26111yescharacteristic
355C22×C4C22×#26111yescharacteristic
356C2×C8—264no—
357C2×C8—264no—
358C2×C8—528no—
359C2×C8—524no—
360C2×C8—524no—
361C4⋊C4—24no—
362C4⋊C4—21no—
363C4⋊C4—132no—
364C4⋊C4—262no—
365C4⋊C4—262no—
366C4⋊C4—262no—
367C4⋊C4—262no—
368C4⋊C4—264no—
369C4⋊C4—264no—
370C4⋊C4—262no—
371C4⋊C4—262no—
372C4⋊C4—261no—
373C4⋊C4—264no—
374C4⋊C4C22×#26112yes—
375C22⋊C4—264no—
376C22⋊C4—264no—
377C42—24no—
378C42—132no—
379C42—132no—
380C42—131no—
381C42—131no—
382C42—132no—
383C42—132no—
384C42—131no—
385C42—131no—
386C42—264no—
387C42C22⋊#26112yes—
388C42C22×#26112yes—
389C13C2×#154211yescharacteristic, complemented, Sylow
390C23—132no—
391C23—134no—
392C23—262no—
393C23—262no—
394C23C2×C22⋊#26111yescharacteristic
395Q8—42no—
396Q8—42no—
397Q8—522no—
398Q8—522no—
399Q8—524no—
400Q8—524no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—131no—
408C2×C4—131no—
409C2×C4—131no—
410C2×C4—131no—
411C2×C4—132no—
412C2×C4—132no—
413C2×C4—134no—
414C2×C4—134no—
415C2×C4—138no—
416C2×C4—134no—
417C2×C4—132no—
418C2×C4—264no—
419C2×C4—264no—
420C2×C4—262no—
421C2×C4—262no—
422C2×C4—262no—
423C2×C4—522no—
424C2×C4—522no—
425C2×C4—522no—
426C2×C4—522no—
427C2×C4#8811714yes—
428C2×C4C2×C22⋊#26111yescharacteristic
429C2×C4C2×C22⋊#26112yes—
430C2×C4C2×C22⋊#26112yes—
431C2×C4C23×#26111yescharacteristic
432C8—524no—
433C8—524no—
434C22—134no—
435C22—268no—
436C22—262no—
437C22—262no—
438C22#1171913212yes—
439C22C2×#8811712yes—
440C22#1171916512yes—
441C22C22×C22⋊#26111yescharacteristic
442C4—21no—
443C4—21no—
444C4—22no—
445C4—42no—
446C4—42no—
447C4—131no—
448C4—131no—
449C4—132no—
450C4—132no—
451C4—132no—
452C4—262no—
453C4—522no—
454C4—522no—
455C4C2×#8811714yes—
456C2—264no—
457C2#1313033714yesdirect product factor
458C2C2×#1171913211yescharacteristic
459C2C22×#8811711yescharacteristic
460C2C2×#1171916511yescharacteristic
subgroupG/H
centerC22×C4C22⋊#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×#1542
LCSG ▷ C2×C4×C13 ▷ C22×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. #13130337C2direct (N × H)
4. C2×#11718303C2semidirect
5. C2×#11718245C2semidirect
32. #11718303C22semidirect
33. #11718245C22semidirect
321. C2×C13#1542semidirect
389. C13C2×#1542semidirect
457. C2#13130337direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117190492
C2×D13⋊(C4⋊C8)2
#131303372
C2×#117183032
C2×#117182452
C2×#117192832
C2×#154213