Finite Group Databasebeta

← C2×#13130338 #16794620

Subgroups — C2×#13130338 #16794620

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×#11719125C211yesmaximal, characteristic
2C22×#88112C211yesmaximal, characteristic
3#13130338C218yesmaximal, direct product factor
4C2×#11718303C212yesmaximal, complemented
5C2×#11718245C212yesmaximal, complemented
6C2×#11719327C211yesmaximal, characteristic
7C23×#1057—21no—
8C2×C13×C22⋊Q8C411yescharacteristic
9C2×Q8×Dic13C411yescharacteristic
10C2×#88198C2211yescharacteristic
11C2×#88178C411yescharacteristic
12C22×C4×Dic13C2211yescharacteristic
13#11719327—22no—
14#11719327—22no—
15#11719327C414yes—
16#11719327C2214yes—
17C2×#88143—21no—
18C2×#88142C2211yescharacteristic
19C2×#88141—21no—
20C2×#88141C411yescharacteristic
21C2×#88132—21no—
22C2×#88131—21no—
23C2×C22⋊#1057—21no—
24#11719125—22no—
25#11719125C2214yes—
26C2×#88112—21no—
27C2×#88112—22no—
28C2×#88112C2212yes—
29C2×#88112C2212yes—
30C2×#88112C2214yes—
31C2×C4×#1057—21no—
32#11718303C2218yescomplemented
33#11718245C2218yescomplemented
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—22no—
51Q8×Dic13C2×C414yes—
52#88198—21no—
53#88198—21no—
54#88198C2×C412yes—
55#88198C2312yes—
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—21no—
78#88142—21no—
79#88142C2×C412yes—
80#88142C2312yes—
81#88141—24no—
82#88141—22no—
83#88141—24no—
84#88141C2×C414yes—
85#88132—24no—
86#88132—24no—
87#88131—24no—
88#88131—24no—
89C22⋊#1057—24no—
90#88112—22no—
91#88112—24no—
92#88112—22no—
93#88112C2314yes—
94#88112C2314yes—
95C4×#1057—24no—
96C2×#1542—131nomaximal, Sylow
97C24×C13C22⋊C411yescharacteristic
98C2×Q8×C13—21no—
99C2×Q8×C13—42no—
100C2×Q8×C13C22×C412yes—
101C22×C4×C13—21no—
102C22×C4×C13—21no—
103C22×C4×C13—42no—
104C22×C4×C13C22⋊C411yescharacteristic
105C22×C4×C13C22⋊C412yes—
106C22×C4×C13C22×C411yescharacteristic
107C22×C4×C13C22×C412yes—
108C22×Dic13—24no—
109C22×Dic13—21no—
110C22×Dic13—21no—
111C22×Dic13C22⋊C412yes—
112C22×Dic13C22⋊C411yescharacteristic
113C22×Dic13C22⋊C412yes—
114C22×Dic13C22⋊C411yescharacteristic
115C22×Dic13SD1614yes—
116C22×Dic13Q1614yes—
117C22×Dic13C2×D412yes—
118C22×Dic13C2×D412yes—
119C22×Dic13C2×D411yescharacteristic
120C22×Dic13C2×D411yescharacteristic
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—48no—
130C2×#1057—44no—
131C2×#1057—44no—
132C13×C4⋊C4—21no—
133C13×C4⋊C4—24no—
134C13×C4⋊C4C22×C412yes—
135C13×C22⋊C4—24no—
136C22⋊Dic13—24no—
137C4⋊Dic13—21no—
138C4⋊Dic13—24no—
139C4⋊Dic13C22×C412yes—
140#6101—24no—
141#6101—22no—
142#6101—22no—
143#6101—22no—
144#6101—24no—
145#6101—22no—
146#6101—22no—
147#6101—22no—
148C4×Dic13—24no—
149C4×Dic13—24no—
150C4×Dic13C22⋊C412yes—
151C4×Dic13C22⋊C412yes—
152C4×Dic13C22⋊C412yes—
153C4×Dic13C22×C412yes—
154C4×Dic13C22×C411yescharacteristic
155C4×Dic13C2×D412yes—
156C4×Dic13C2×D411yescharacteristic
157C4×Dic13C2×D411yescharacteristic
158C4×Dic13C2×D412yes—
159C4×Dic13C2411yescharacteristic
160C2×#533—131no—
161C2×#431—131no—
162C22×C4⋊C8—131no—
163#1542—138no—
164C2×#333—132no—
165C2×#332—132no—
166C23×C13—22no—
167C23×C13—22no—
168C23×C13#10314yes—
169C23×C13C2×C22⋊C412yes—
170C23×C13C2×C22⋊C411yescharacteristic
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—42no—
180C2×C4×C13—42no—
181C2×C4×C13C2×C22⋊C412yes—
182C2×C4×C13C2×C22⋊C411yescharacteristic
183C2×C4×C13C23×C411yescharacteristic
184C2×Dic13—22no—
185C2×Dic13—24no—
186C2×Dic13—24no—
187C2×Dic13—22no—
188C2×Dic13—22no—
189C2×Dic13—42no—
190C2×Dic13—42no—
191C2×Dic13#10318yes—
192C2×Dic13#10314yes—
193C2×Dic13C2×C22⋊C412yes—
194C2×Dic13C2×C22⋊C412yes—
195C2×Dic13C2×C22⋊C411yescharacteristic
196C2×Dic13C2×C22⋊C411yescharacteristic
197C2×Dic13C2×SD1614yes—
198C2×Dic13C2×SD1612yes—
199C2×Dic13C2×Q1614yes—
200C2×Dic13C2×Q1612yes—
201C2×Dic13#13514yes—
202C2×Dic13C22×D411yescharacteristic
203C2×Dic13C22×D411yescharacteristic
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—261no—
220C2×C22⋊Q8#26111yescharacteristic
221C2×C4×Q8—131no—
222C2×C4×Q8—131no—
223C2×C4×Q8—261no—
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—261no—
232C2×C4⋊C8—262no—
233C2×C22⋊C8—261no—
234C2×C4×C8—261no—
235#333—138no—
236#332—138no—
237C22×C13—28no—
238C22×C13—22no—
239C22×C13—22no—
240C22×C13#41312yes—
241C22×C13C2×#10314yes—
242C22×C13C2×#10312yes—
243C22×C13#41612yes—
244C22×C13C22×C22⋊C411yescharacteristic
245C4×C13—21no—
246C4×C13—21no—
247C4×C13—22no—
248C4×C13—42no—
249C4×C13—42no—
250Dic13—22no—
251Dic13—42no—
252Dic13—42no—
253Dic13C2×#10314yes—
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×C4C2×#26111yescharacteristic
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—22no—
280C22⋊Q8—134no—
281C22⋊Q8—264no—
282C22⋊Q8—264no—
283C22⋊Q8—262no—
284C22⋊Q8C2×#26114yes—
285C4×Q8—134no—
286C4×Q8—134no—
287C4×Q8—262no—
288C4×Q8—264no—
289C4×Q8—264no—
290C4×Q8—262no—
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—21no—
303C2×C22⋊C4—261no—
304C2×C42—131no—
305C2×C42—131no—
306C2×C42—132no—
307C2×C42—132no—
308C2×C42—131no—
309C2×C42—131no—
310C2×C42—132no—
311C2×C42—132no—
312C2×C42—261no—
313C2×C42—261no—
314C4⋊C8—134no—
315C4⋊C8—134no—
316C4⋊C8—264no—
317C4⋊C8—262no—
318C4⋊C8—262no—
319C22⋊C8—264no—
320C4×C8—264no—
321C2×C13—24no—
322C2×C13#154214yescomplemented
323C2×C13C2×#41311yescharacteristic
324C2×C13C22×#10311yescharacteristic
325C2×C13C2×#41611yescharacteristic
326C24C22⋊#26111yescharacteristic
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—42no—
339C22×C4—134no—
340C22×C4—134no—
341C22×C4—132no—
342C22×C4—132no—
343C22×C4—131no—
344C22×C4—131no—
345C22×C4—131no—
346C22×C4—132no—
347C22×C4—132no—
348C22×C4—131no—
349C22×C4—264no—
350C22×C4—261no—
351C22×C4—261no—
352C22×C4C22⋊#26111yescharacteristic
353C22×C4C22⋊#26112yes—
354C22×C4C22×#26111yescharacteristic
355C22×C4C22×#26112yes—
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—24no—
376C22⋊C4—264no—
377C42—132no—
378C42—132no—
379C42—131no—
380C42—131no—
381C42—132no—
382C42—132no—
383C42—132no—
384C42—131no—
385C42—132no—
386C42—131no—
387C42—264no—
388C42—264no—
389C13C2×#154211yescharacteristic, complemented, Sylow
390C23—22no—
391C23—22no—
392C23#8811714yes—
393C23C2×C22⋊#26112yes—
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—42no—
408C2×C4—42no—
409C2×C4—132no—
410C2×C4—131no—
411C2×C4—131no—
412C2×C4—131no—
413C2×C4—131no—
414C2×C4—134no—
415C2×C4—132no—
416C2×C4—138no—
417C2×C4—134no—
418C2×C4—134no—
419C2×C4—132no—
420C2×C4—134no—
421C2×C4—132no—
422C2×C4—264no—
423C2×C4—264no—
424C2×C4—262no—
425C2×C4—262no—
426C2×C4—262no—
427C2×C4—522no—
428C2×C4—522no—
429C2×C4C2×C22⋊#26112yes—
430C2×C4C2×C22⋊#26111yescharacteristic
431C2×C4C23×#26111yescharacteristic
432C8—524no—
433C8—524no—
434C22—28no—
435C22—22no—
436C22—22no—
437C22#1171914812yes—
438C22C2×#8811714yes—
439C22C2×#8811712yes—
440C22#1171916512yes—
441C22C22×C22⋊#26111yescharacteristic
442C4—22no—
443C4—21no—
444C4—21no—
445C4—42no—
446C4—42no—
447C4—131no—
448C4—131no—
449C4—134no—
450C4—132no—
451C4—132no—
452C4—132no—
453C4—262no—
454C4—522no—
455C4—522no—
456C2—24no—
457C2#1313033814yesdirect product factor
458C2C2×#1171914811yescharacteristic
459C2C22×#8811711yescharacteristic
460C2C2×#1171916511yescharacteristic
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×#1542
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13130338C2direct (N × H)
4. C2×#11718303C2semidirect
5. C2×#11718245C2semidirect
32. #11718303C22semidirect
33. #11718245C22semidirect
322. C2×C13#1542semidirect
389. C13C2×#1542semidirect
457. C2#13130338direct (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×#881122
#131303382
C2×#117183032
C2×#117182452
C2×#117193272
C2×#154213