Finite Group Databasebeta

← C2×#13130185 #16793479

Subgroups — C2×#13130185 #16793479

Order 3328.

1150 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719052C211yesmaximal, characteristic
2C2×C4×D13⋊C8C211yesmaximal, characteristic
3#13130185C218yesmaximal, direct product factor
4C2×Q8⋊#1057C214yesmaximal, complemented
5C2×#11719433C211yesmaximal, characteristic
6C22×#6118—21no—
7C22×D13⋊C8—21no—
8C2×C13×C4⋊Q8C411yescharacteristic
9C2×#88200C412yes—
10C2×Q8×Dic13C2212yes—
11#11719433—22no—
12#11719433—22no—
13#11719433C414yes—
14#11719433C2214yes—
15C2×#88151—21no—
16C2×#88146—21no—
17C2×#88144—21no—
18C2×#88141—21no—
19C2×C42×D13C2211yescharacteristic
20C2×#88123C411yescharacteristic
21C2×C4⋊#1057—21no—
22C2×C4⋊#1057C2212yes—
23C2×C4×#1057—21no—
24C2×C4×#1057C2212yes—
25#11719052—22no—
26#11719052C2214yes—
27C4×D13⋊C8—22no—
28C4×D13⋊C8C2214yes—
29Q8⋊#1057C22116yescomplemented
30C22×Q8×C13C2×C412yes—
31C22×C4×D13C2×C411yescharacteristic
32C22×C4×D13D411yescharacteristic
33C22×C4×D13D411yescharacteristic
34C22×Dic26—21no—
35C22×#1057—22no—
36C22×#1057—22no—
37C2×#6118—24no—
38C2×#6118—44no—
39C2×D13⋊C8—28no—
40C2×D13⋊C8—24no—
41C13×C4⋊Q8—22no—
42C13×C4⋊Q8C2×C414yes—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C42×C13C2×C411yescharacteristic
46#88200—24no—
47#88200C2×C418yes—
48Q8×Dic13—22no—
49Q8×Dic13—22no—
50Q8×Dic13C2×C414yes—
51Q8×Dic13C2314yes—
52C2×#6103—22no—
53C2×C4⋊Dic13—21no—
54C2×C4⋊Dic13—22no—
55C2×C4⋊Dic13C2×C412yes—
56C2×#6101—22no—
57C2×C4×Dic13—22no—
58C2×C4×Dic13D411yescharacteristic
59C2×C4×Dic13D411yescharacteristic
60C2×C4×Dic13C2311yescharacteristic
61#88151—24no—
62#88151—24no—
63#88146—24no—
64#88146—24no—
65#88144—24no—
66#88144—24no—
67#88141—24no—
68#88141—24no—
69C42×D13C2×C412yes—
70C42×D13D412yes—
71C42×D13D412yes—
72C42×D13C2312yes—
73#88123—22no—
74#88123C2×C414yes—
75C4⋊#1057—22no—
76C4⋊#1057—24no—
77C4⋊#1057C2314yes—
78C4×#1057—22no—
79C4×#1057—24no—
80C4×#1057C2314yes—
81C2×#1493—131nomaximal, Sylow
82C23×D13C22⋊C411yescharacteristic
83C2×Q8×C13—22no—
84C2×Q8×C13—28no—
85C2×Q8×C13C22×C414yes—
86C22×C4×C13—22no—
87C22×C4×C13C22⋊C411yescharacteristic
88C22×C4×C13C22⋊C411yescharacteristic
89C22×C4×C13C22×C411yescharacteristic
90C22×Dic13—22no—
91C22×Dic13C22⋊C411yescharacteristic
92C22×Dic13C2×D411yescharacteristic
93C22×Dic13C2×D411yescharacteristic
94C2×C4×D13—24no—
95C2×C4×D13—24no—
96C2×C4×D13C22⋊C412yes—
97C2×C4×D13C22⋊C412yes—
98C2×C4×D13C22⋊C412yes—
99C2×C4×D13SD1614yes—
100C2×C4×D13Q1614yes—
101C2×C4×D13C22×C412yes—
102C2×C4×D13C2×D412yes—
103C2×C4×D13C2×D412yes—
104C2×Dic26—24no—
105C2×Dic26—44no—
106C2×#1057—28no—
107C2×#1057—24no—
108C2×#1057—24no—
109C2×#1057—44no—
110#6118—48no—
111D13⋊C8—216no—
112C13×C4⋊C4—24no—
113C13×C4⋊C4—24no—
114C42×C13C22⋊C412yes—
115C42×C13C22×C412yes—
116#6103—28no—
117C4⋊Dic13—22no—
118C4⋊Dic13—24no—
119C4⋊Dic13—24no—
120C4⋊Dic13—24no—
121C4⋊Dic13C22×C414yes—
122#6101—28no—
123C4×Dic13—24no—
124C4×Dic13—24no—
125C4×Dic13C22⋊C412yes—
126C4×Dic13C22⋊C412yes—
127C4×Dic13C22×C411yescharacteristic
128C4×Dic13C2×D411yescharacteristic
129C4×Dic13C2×D412yes—
130C4×Dic13C2×D411yescharacteristic
131C4×Dic13C2×D412yes—
132C4×Dic13C2411yescharacteristic
133C2×#533—131no—
134C2×#423—131no—
135C22×C4×C8—131no—
136#1493—138no—
137C2×Q8⋊C8—134no—
138C23×C13C2×C22⋊C411yescharacteristic
139C22×D13—22no—
140C22×D13—22no—
141C22×D13#10314yes—
142C22×D13C2×C22⋊C412yes—
143Q8×C13—28no—
144Q8×C13—44no—
145C2×C4×C13—24no—
146C2×C4×C13—44no—
147C2×C4×C13#10314yes—
148C2×C4×C13#10414yes—
149C2×C4×C13C2×C22⋊C411yescharacteristic
150C2×C4×C13C2×C22⋊C412yes—
151C2×C4×C13C2×C22⋊C412yes—
152C2×C4×C13#13114yes—
153C2×C4×C13C23×C411yescharacteristic
154C2×Dic13—22no—
155C2×Dic13—22no—
156C2×Dic13—24no—
157C2×Dic13—44no—
158C2×Dic13C2×C22⋊C411yescharacteristic
159C2×Dic13C2×C22⋊C412yes—
160C2×Dic13C2×C22⋊C411yescharacteristic
161C2×Dic13C2×SD1612yes—
162C2×Dic13C2×Q1612yes—
163C2×Dic13C22×D411yescharacteristic
164C2×Dic13C22×D411yescharacteristic
165C4×D13—24no—
166C4×D13—24no—
167C4×D13—24no—
168C4×D13—24no—
169C4×D13#10318yes—
170C4×D13C2×SD1614yes—
171C4×D13C2×Q1614yes—
172Dic26—48no—
173#1057—28no—
174#1057—44no—
175C22×M16—261no—
176C23×C8—261no—
177#533—134no—
178#533—134no—
179#533—262no—
180#533—262no—
181C2×C4⋊Q8—131no—
182C2×C4⋊Q8#26111yescharacteristic
183C2×#125—261no—
184C2×C22⋊Q8—132no—
185C2×C22⋊Q8—261no—
186C2×C4×Q8—132no—
187C2×C4×Q8—261no—
188C2×#117—261no—
189C22×C42—131no—
190#423—134no—
191#423—262no—
192C2×C4⋊C8—132no—
193C2×C4⋊C8—261no—
194C2×C4×C8—134no—
195C2×C4×C8—132no—
196C2×C4×C8—262no—
197C2×C4×C8—261no—
198Q8⋊C8—1316no—
199C22×C13#40812yes—
200C22×C13C2×#10312yes—
201C22×C13C2×#10412yes—
202C22×C13C22×C22⋊C411yescharacteristic
203C2×D13—22no—
204C2×D13—22no—
205C2×D13—28no—
206C2×D13C2×#10314yes—
207C4×C13—44no—
208C4×C13#40812yes—
209C4×C13C2×#10314yes—
210C4×C13C2×#10414yes—
211C4×C13C2×#13112yes—
212Dic13—22no—
213Dic13—21no—
214Dic13—21no—
215Dic13—44no—
216Dic13C2×#10312yes—
217Dic13C22×SD1611yescharacteristic
218Dic13C22×Q1611yescharacteristic
219C22×Q8—261no—
220C22×Q8C2×#26112yes—
221C23×C4—131no—
222C23×C4—131no—
223C23×C4—131no—
224C2×M16—264no—
225C2×M16—524no—
226C22×C8—264no—
227C22×C8—262no—
228C22×C8—268no—
229C22×C8—262no—
230C4⋊Q8—22no—
231C4⋊Q8—134no—
232C4⋊Q8—262no—
233C4⋊Q8C2×#26114yes—
234#125—264no—
235#125—264no—
236C22⋊Q8—138no—
237C22⋊Q8—264no—
238C22⋊Q8—264no—
239C22⋊Q8—264no—
240C4×Q8—134no—
241C4×Q8—134no—
242C4×Q8—264no—
243C4×Q8—264no—
244C4×Q8—262no—
245C4×Q8—262no—
246#117—264no—
247#117—264no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—132no—
251C2×C4⋊C4—262no—
252C2×C4⋊C4—262no—
253C2×C4⋊C4—261no—
254C2×C22⋊C4—262no—
255C2×C42—131no—
256C2×C42—131no—
257C2×C42—131no—
258C2×C42—132no—
259C2×C42—132no—
260C2×C42—132no—
261C2×C42—132no—
262C2×C42—262no—
263C2×C42C2×#26111yescharacteristic
264C4⋊C8—134no—
265C4⋊C8—262no—
266C4⋊C8—264no—
267C4×C8—134no—
268C4×C8—262no—
269C4×C8—264no—
270C2×C13#149314yescomplemented
271C2×C13C2×#40811yescharacteristic
272C2×C13C22×#10311yescharacteristic
273C2×C13C22×#10411yescharacteristic
274D13—24no—
275C24—131no—
276C2×Q8—22no—
277C2×Q8—28no—
278C2×Q8—264no—
279C2×Q8—524no—
280C2×Q8C22×#26114yes—
281C22×C4—22no—
282C22×C4—131no—
283C22×C4—134no—
284C22×C4—134no—
285C22×C4—132no—
286C22×C4—132no—
287C22×C4—131no—
288C22×C4—131no—
289C22×C4—132no—
290C22×C4—132no—
291C22×C4—132no—
292C22×C4—132no—
293C22×C4—264no—
294C22×C4—264no—
295C22×C4—262no—
296C22×C4C22⋊#26111yescharacteristic
297C22×C4C22⋊#26111yescharacteristic
298C22×C4C22×#26111yescharacteristic
299M16—528no—
300C2×C8—264no—
301C2×C8—2616no—
302C2×C8—268no—
303C2×C8—264no—
304C2×C8—524no—
305C4⋊C4—24no—
306C4⋊C4—24no—
307C4⋊C4—134no—
308C4⋊C4—264no—
309C4⋊C4—264no—
310C4⋊C4—268no—
311C4⋊C4—262no—
312C4⋊C4—264no—
313C22⋊C4—268no—
314C42—131no—
315C42—132no—
316C42—131no—
317C42—132no—
318C42—132no—
319C42—132no—
320C42—131no—
321C42—131no—
322C42—264no—
323C42—264no—
324C42C22⋊#26112yes—
325C42C22×#26112yes—
326C13C2×#149311yescharacteristic, complemented, Sylow
327C23—132no—
328C23—134no—
329C23—262no—
330C23—262no—
331C23C2×C22⋊#26111yescharacteristic
332Q8—28no—
333Q8—44no—
334Q8—528no—
335C2×C4—24no—
336C2×C4—44no—
337C2×C4—131no—
338C2×C4—131no—
339C2×C4—132no—
340C2×C4—132no—
341C2×C4—134no—
342C2×C4—138no—
343C2×C4—134no—
344C2×C4—131no—
345C2×C4—132no—
346C2×C4—131no—
347C2×C4—262no—
348C2×C4—262no—
349C2×C4—264no—
350C2×C4—264no—
351C2×C4—264no—
352C2×C4—264no—
353C2×C4—264no—
354C2×C4—524no—
355C2×C4#8811714yes—
356C2×C4#8811814yes—
357C2×C4#8823814yes—
358C2×C4C2×C22⋊#26111yescharacteristic
359C2×C4C2×C22⋊#26112yes—
360C2×C4C2×C22⋊#26112yes—
361C2×C4C23×#26111yescharacteristic
362C8—268no—
363C8—524no—
364C22—134no—
365C22—262no—
366C22—262no—
367C22—268no—
368C22#1171914712yes—
369C22C2×#8811712yes—
370C22C2×#8811812yes—
371C22C22×C22⋊#26111yescharacteristic
372C4—44no—
373C4—131no—
374C4—131no—
375C4—132no—
376C4—262no—
377C4—261no—
378C4—261no—
379C4—524no—
380C4#1171914712yes—
381C4C2×#8811714yes—
382C4C2×#8811814yes—
383C4C2×#8823812yes—
384C2—264no—
385C2#1313018514yesdirect product factor
386C2C2×#1171914711yescharacteristic
387C2C22×#8811711yescharacteristic
388C2C22×#8811811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C13×C4⋊Q8C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC4×Dic13C24
hypercenterC2×C4⋊Q8#261
hypocenterC13C2×#1493
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13130185C2direct (N × H)
4. C2×Q8⋊#1057C2semidirect
29. Q8⋊#1057C22semidirect
270. C2×C13#1493semidirect
326. C13C2×#1493semidirect
385. C2#13130185direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117190522
C2×C4×D13⋊C82
#131301852
C2×Q8⋊#10572
C2×#117194332
C2×#149313