Finite Group Databasebeta

← C2×#13130144 #16793399

Subgroups — C2×#13130144 #16793399

Order 3328.

1066 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719125C211yesmaximal, characteristic
2C22×C4⋊#1057C211yesmaximal, characteristic
3#13130144C218yesmaximal, direct product factor
4C2×#11718244C212yesmaximal, complemented
5C2×Q8⋊#1057C212yesmaximal, complemented
6C2×#11719327C211yesmaximal, characteristic
7C23×#1057—21no—
8C2×C13×C22⋊Q8C411yescharacteristic
9C2×Q8×Dic13C2211yescharacteristic
10C2×#88198C411yescharacteristic
11C2×#88178C411yescharacteristic
12C22×C4×Dic13C2211yescharacteristic
13#11719327—22no—
14#11719327—22no—
15#11719327C414yes—
16#11719327C2214yes—
17C2×#88143—21no—
18C2×#88142C411yescharacteristic
19C2×#88141—21no—
20C2×#88141C2211yescharacteristic
21C2×#88132—21no—
22C2×#88131—21no—
23C2×C22⋊#1057—21no—
24#11719125—22no—
25#11719125C2214yes—
26C2×#88112—21no—
27C2×C4⋊#1057—21no—
28C2×C4⋊#1057—22no—
29C2×C4⋊#1057C2212yes—
30C2×C4⋊#1057C2214yes—
31C2×C4×#1057C2212yes—
32Q8⋊#1057C2218yescomplemented
33#11718244C2218yescomplemented
34C22×Q8×C13C2×C411yescharacteristic
35C23×C4×C13C2×C411yescharacteristic
36C23×Dic13D411yescharacteristic
37C23×Dic13D411yescharacteristic
38C22×Dic26—21no—
39C22×Dic26C2×C411yescharacteristic
40C22×#1057—22no—
41C22×#1057—24no—
42C22×#1057—22no—
43C22×#1057—44no—
44C13×C22⋊Q8—22no—
45C13×C22⋊Q8C2×C414yes—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4C2×C411yescharacteristic
48C2×C13×C22⋊C4—21no—
49C2×C22⋊Dic13—21no—
50Q8×Dic13—21no—
51Q8×Dic13—21no—
52Q8×Dic13C2×C412yes—
53Q8×Dic13C2312yes—
54#88198—22no—
55#88198C2×C414yes—
56C2×C4⋊Dic13—21no—
57C2×C4⋊Dic13C2×C411yescharacteristic
58#88178—22no—
59#88178C2×C414yes—
60C2×#6101—21no—
61C2×#6101—21no—
62C2×#6101—21no—
63C2×#6101—21no—
64C2×#6101—21no—
65C2×C4×Dic13—21no—
66C2×C4×Dic13—21no—
67C2×C4×Dic13C2×C411yescharacteristic
68C2×C4×Dic13C2×C412yes—
69C2×C4×Dic13D411yescharacteristic
70C2×C4×Dic13D411yescharacteristic
71C2×C4×Dic13D412yes—
72C2×C4×Dic13D412yes—
73C2×C4×Dic13C2311yescharacteristic
74C2×C4×Dic13C2312yes—
75#88143—24no—
76#88143—24no—
77#88142—22no—
78#88142C2×C414yes—
79#88141—24no—
80#88141—24no—
81#88141—21no—
82#88141—21no—
83#88141C2×C412yes—
84#88141C2312yes—
85#88132—24no—
86#88132—24no—
87#88131—24no—
88#88131—24no—
89C22⋊#1057—24no—
90#88112—24no—
91C4⋊#1057—24no—
92C4⋊#1057—22no—
93C4⋊#1057C2314yes—
94C4×#1057—22no—
95C4×#1057C2314yes—
96C2×#1481—131nomaximal, Sylow
97C24×C13C22⋊C411yescharacteristic
98C2×Q8×C13—21no—
99C2×Q8×C13—24no—
100C2×Q8×C13C22×C412yes—
101C22×C4×C13—24no—
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13C22⋊C411yescharacteristic
105C22×C4×C13C22⋊C412yes—
106C22×C4×C13C22×C412yes—
107C22×C4×C13C22×C411yescharacteristic
108C22×Dic13—21no—
109C22×Dic13—21no—
110C22×Dic13—42no—
111C22×Dic13C22⋊C411yescharacteristic
112C22×Dic13C22⋊C412yes—
113C22×Dic13C22⋊C412yes—
114C22×Dic13C22⋊C411yescharacteristic
115C22×Dic13SD1614yes—
116C22×Dic13Q1614yes—
117C22×Dic13C2×D411yescharacteristic
118C22×Dic13C2×D412yes—
119C22×Dic13C2×D412yes—
120C22×Dic13C2×D411yescharacteristic
121C2×Dic26—24no—
122C2×Dic26—21no—
123C2×Dic26—24no—
124C2×Dic26—44no—
125C2×Dic26C22×C412yes—
126C2×#1057—24no—
127C2×#1057—24no—
128C2×#1057—44no—
129C2×#1057—48no—
130C2×#1057—44no—
131C13×C4⋊C4—21no—
132C13×C4⋊C4—24no—
133C13×C4⋊C4C22×C412yes—
134C13×C22⋊C4—24no—
135C22⋊Dic13—24no—
136C4⋊Dic13—21no—
137C4⋊Dic13—22no—
138C4⋊Dic13—22no—
139C4⋊Dic13C22×C412yes—
140#6101—24no—
141#6101—24no—
142#6101—24no—
143#6101—24no—
144#6101—22no—
145#6101—22no—
146C4×Dic13—22no—
147C4×Dic13—22no—
148C4×Dic13—22no—
149C4×Dic13—22no—
150C4×Dic13C22⋊C412yes—
151C4×Dic13C22⋊C412yes—
152C4×Dic13C22⋊C412yes—
153C4×Dic13C22×C411yescharacteristic
154C4×Dic13C22×C412yes—
155C4×Dic13C2×D411yescharacteristic
156C4×Dic13C2×D412yes—
157C4×Dic13C2×D411yescharacteristic
158C4×Dic13C2×D412yes—
159C4×Dic13C2411yescharacteristic
160C2×#533—131no—
161C2×#431—131no—
162C22×C4⋊C8—131no—
163#1481—138no—
164C2×Q8⋊C8—132no—
165C2×Q8⋊C8—132no—
166C23×C13—22no—
167C23×C13—22no—
168C23×C13#10314yes—
169C23×C13C2×C22⋊C412yes—
170C23×C13C2×C22⋊C411yescharacteristic
171Q8×C13—24no—
172Q8×C13—42no—
173C2×C4×C13—22no—
174C2×C4×C13—24no—
175C2×C4×C13—24no—
176C2×C4×C13—22no—
177C2×C4×C13—22no—
178C2×C4×C13—42no—
179C2×C4×C13—42no—
180C2×C4×C13C2×C22⋊C412yes—
181C2×C4×C13C2×C22⋊C411yescharacteristic
182C2×C4×C13#13114yes—
183C2×C4×C13C23×C411yescharacteristic
184C2×Dic13—22no—
185C2×Dic13—22no—
186C2×Dic13—22no—
187C2×Dic13—22no—
188C2×Dic13—42no—
189C2×Dic13—42no—
190C2×Dic13—42no—
191C2×Dic13—42no—
192C2×Dic13#10318yes—
193C2×Dic13#10314yes—
194C2×Dic13C2×C22⋊C411yescharacteristic
195C2×Dic13C2×C22⋊C412yes—
196C2×Dic13C2×C22⋊C411yescharacteristic
197C2×Dic13C2×C22⋊C412yes—
198C2×Dic13C2×SD1614yes—
199C2×Dic13C2×SD1612yes—
200C2×Dic13C2×Q1614yes—
201C2×Dic13C2×Q1612yes—
202C2×Dic13C22×D411yescharacteristic
203C2×Dic13C22×D411yescharacteristic
204Dic26—24no—
205Dic26—48no—
206Dic26—42no—
207#1057—44no—
208#1057—44no—
209C23×C8—261no—
210#533—134no—
211#533—134no—
212#533—262no—
213#533—262no—
214C2×C4⋊Q8—131no—
215C2×C4⋊Q8—131no—
216C2×#125—261no—
217C2×C22⋊Q8—131no—
218C2×C22⋊Q8—261no—
219C2×C22⋊Q8#26111yescharacteristic
220C2×C4×Q8—131no—
221C2×C4×Q8—131no—
222C2×C4×Q8—261no—
223C2×#117—261no—
224C22×C42—131no—
225#431—134no—
226#431—262no—
227C2×C4⋊C8—132no—
228C2×C4⋊C8—134no—
229C2×C4⋊C8—261no—
230C2×C4⋊C8—262no—
231C2×C4⋊C8—261no—
232C2×C22⋊C8—261no—
233C2×C4×C8—132no—
234Q8⋊C8—138no—
235Q8⋊C8—138no—
236C22×C13—22no—
237C22×C13—22no—
238C22×C13—28no—
239C22×C13#40812yes—
240C22×C13C2×#10314yes—
241C22×C13C2×#10312yes—
242C22×C13#42112yes—
243C22×C13C22×C22⋊C411yescharacteristic
244C4×C13—22no—
245C4×C13—42no—
246C4×C13—42no—
247C4×C13#40812yes—
248C4×C13C2×#13112yes—
249Dic13—21no—
250Dic13—22no—
251Dic13—21no—
252Dic13—42no—
253Dic13—42no—
254Dic13C2×#10312yes—
255Dic13C2×#10314yes—
256Dic13C22×SD1611yescharacteristic
257Dic13C22×Q1611yescharacteristic
258C22×Q8—131no—
259C22×Q8—261no—
260C22×Q8C2×#26111yescharacteristic
261C23×C4—131no—
262C23×C4—131no—
263C23×C4C2×#26111yescharacteristic
264C22×C8—264no—
265C22×C8—262no—
266C22×C8—262no—
267C22×C8—524no—
268C4⋊Q8—134no—
269C4⋊Q8—134no—
270C4⋊Q8—262no—
271C4⋊Q8—262no—
272#125—264no—
273#125—264no—
274C22⋊Q8—22no—
275C22⋊Q8—134no—
276C22⋊Q8—264no—
277C22⋊Q8—264no—
278C22⋊Q8—262no—
279C22⋊Q8C2×#26114yes—
280C4×Q8—132no—
281C4×Q8—132no—
282C4×Q8—132no—
283C4×Q8—132no—
284C4×Q8—261no—
285C4×Q8—261no—
286C4×Q8—264no—
287C4×Q8—264no—
288C4×Q8—261no—
289C4×Q8—261no—
290#117—264no—
291#117—264no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—131no—
294C2×C4⋊C4—261no—
295C2×C4⋊C4—261no—
296C2×C4⋊C4—261no—
297C2×C4⋊C4—261no—
298C2×C4⋊C4—261no—
299C2×C4⋊C4—261no—
300C2×C4⋊C4C2×#26111yescharacteristic
301C2×C22⋊C4—21no—
302C2×C22⋊C4—261no—
303C2×C42—131no—
304C2×C42—131no—
305C2×C42—132no—
306C2×C42—132no—
307C2×C42—131no—
308C2×C42—131no—
309C2×C42—132no—
310C2×C42—132no—
311C2×C42—261no—
312C2×C42—261no—
313C4⋊C8—134no—
314C4⋊C8—262no—
315C4⋊C8—264no—
316C4⋊C8—264no—
317C22⋊C8—264no—
318C4×C8—134no—
319C4×C8—262no—
320C2×C13—24no—
321C2×C13#148114yescomplemented
322C2×C13C2×#40811yescharacteristic
323C2×C13C22×#10311yescharacteristic
324C2×C13C2×#42111yescharacteristic
325C24C22⋊#26111yescharacteristic
326C2×Q8—21no—
327C2×Q8—24no—
328C2×Q8—132no—
329C2×Q8—264no—
330C2×Q8—261no—
331C2×Q8—264no—
332C2×Q8—524no—
333C2×Q8C22×#26112yes—
334C22×C4—24no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—134no—
338C22×C4—134no—
339C22×C4—132no—
340C22×C4—132no—
341C22×C4—131no—
342C22×C4—131no—
343C22×C4—131no—
344C22×C4—131no—
345C22×C4—132no—
346C22×C4—132no—
347C22×C4—261no—
348C22×C4—261no—
349C22×C4—522no—
350C22×C4C22⋊#26112yes—
351C22×C4C22⋊#26111yescharacteristic
352C22×C4C22×#26112yes—
353C22×C4C22×#26111yescharacteristic
354C2×C8—264no—
355C2×C8—264no—
356C2×C8—528no—
357C2×C8—524no—
358C2×C8—524no—
359C4⋊C4—24no—
360C4⋊C4—21no—
361C4⋊C4—132no—
362C4⋊C4—264no—
363C4⋊C4—264no—
364C4⋊C4—262no—
365C4⋊C4—262no—
366C4⋊C4—262no—
367C4⋊C4—262no—
368C4⋊C4—264no—
369C4⋊C4—261no—
370C4⋊C4—264no—
371C4⋊C4C22×#26112yes—
372C22⋊C4—24no—
373C22⋊C4—264no—
374C42—131no—
375C42—131no—
376C42—132no—
377C42—132no—
378C42—132no—
379C42—132no—
380C42—132no—
381C42—131no—
382C42—131no—
383C42—132no—
384C42—262no—
385C42—262no—
386C42—262no—
387C42—262no—
388C13C2×#148111yescharacteristic, complemented, Sylow
389C23—22no—
390C23—22no—
391C23#8811714yes—
392C23C2×C22⋊#26112yes—
393C23C2×C22⋊#26111yescharacteristic
394Q8—24no—
395Q8—42no—
396Q8—264no—
397Q8—528no—
398Q8—522no—
399C2×C4—22no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—131no—
407C2×C4—131no—
408C2×C4—132no—
409C2×C4—134no—
410C2×C4—132no—
411C2×C4—138no—
412C2×C4—134no—
413C2×C4—134no—
414C2×C4—132no—
415C2×C4—131no—
416C2×C4—131no—
417C2×C4—132no—
418C2×C4—262no—
419C2×C4—262no—
420C2×C4—262no—
421C2×C4—262no—
422C2×C4—522no—
423C2×C4—522no—
424C2×C4—522no—
425C2×C4—522no—
426C2×C4#8823814yes—
427C2×C4C2×C22⋊#26112yes—
428C2×C4C2×C22⋊#26111yescharacteristic
429C2×C4C23×#26111yescharacteristic
430C8—524no—
431C8—524no—
432C22—22no—
433C22—28no—
434C22—22no—
435C22#1171914612yes—
436C22C2×#8811714yes—
437C22C2×#8811712yes—
438C22#1171916612yes—
439C22C22×C22⋊#26111yescharacteristic
440C4—22no—
441C4—42no—
442C4—42no—
443C4—131no—
444C4—131no—
445C4—132no—
446C4—134no—
447C4—261no—
448C4—261no—
449C4—262no—
450C4—522no—
451C4—522no—
452C4#1171914612yes—
453C4C2×#8823812yes—
454C2—24no—
455C2#1313014414yesdirect product factor
456C2C2×#1171914611yescharacteristic
457C2C22×#8811711yescharacteristic
458C2C2×#1171916611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C13×C22⋊Q8C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC4×Dic13C24
hypercenterC2×C22⋊Q8#261
hypocenterC13C2×#1481
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13130144C2direct (N × H)
4. C2×#11718244C2semidirect
5. C2×Q8⋊#1057C2semidirect
32. Q8⋊#1057C22semidirect
33. #11718244C22semidirect
321. C2×C13#1481semidirect
388. C13C2×#1481semidirect
455. C2#13130144direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117191252
C22×C4⋊#10572
#131301442
C2×#117182442
C2×Q8⋊#10572
C2×#117193272
C2×#148113