Finite Group Databasebeta

← C2×#13131490 #16808149

Subgroups — C2×#13131490 #16808149

Order 3328.

2766 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719631C212yesmaximal
2#13131490C2116yesmaximal, direct product factor
3C2×#11719098C216yesmaximal, complemented
4C2×#11719092C213yesmaximal, complemented
5C22×#88101C213yesmaximal, complemented
6C2×D13×#131C211yesmaximal, characteristic
7C2×#41×D13C2211yescharacteristic
8#11719631—28no—
9#11719631C22116yes—
10C2×Q8×#261—22no—
11C2×D4×#261—26no—
12C2×#88237C2216yes—
13C22×C4⋊#261C2216yes—
14C2×C13×#131C411yescharacteristic, complemented
15C2×#88202C411yescharacteristic, complemented
16D13×#131C418yescomplemented
17D13×#131C2218yes—
18C2×#88161C413yescomplemented
19C2×M16×D13C2213yes—
20C2×#88155C413yescomplemented
21C22×C8×D13C2213yes—
22#11719098C22148yescomplemented
23#11719092C22124yescomplemented
24C2×#88102C2216yes—
25C2×#88101C2213yes—
26C2×#88101C2216yes—
27C2×#88101C2211yescharacteristic
28C2×#88101C22124yescomplemented
29C23×#261—26no—
30C2×C13×#41C2×C411yescharacteristic
31#41×D13C2×C414yes—
32#41×D13D414yes—
33#41×D13Q814yes—
34#41×D13C2314yes—
35C2×#6131Q811yescharacteristic
36C2×Q8×D13D411yescharacteristic
37C2×#6129Q813yes—
38C2×D4×D13D413yes—
39C2×#6127C2×C413yes—
40C22×C4×D13C2313yes—
41C2×C22⋊#261—26no—
42Q8×#261—216no—
43D4×#261—248no—
44#88237—212no—
45#88237C23124yes—
46C2×C4⋊#261—26no—
47C2×C4⋊#261—212no—
48C2×C4⋊#261C2316yes—
49C2×C4⋊#261C2312yes—
50C2×C4⋊#261C23124yes—
51C2×C4×#261—26no—
52C13×#131C2×C418yescomplemented
53C2×C13×M16C2×C413yescomplemented
54C22×C8×C13C2×C413yescomplemented
55#88202C2×C418yescomplemented
56C2×#6099C2×C413yescomplemented
57C22×#1055C2×C413yescomplemented
58#88161C2×C4124yescomplemented
59M16×D13C2×C4112yescomplemented
60M16×D13C23112yes—
61#88155C2×C4124yescomplemented
62C2×#6094C2×C416yescomplemented
63C2×C8×D13C2×C4112yescomplemented
64C2×C8×D13C2×C413yescomplemented
65C2×C8×D13C2×C413yescomplemented
66C2×C8×D13C2311yescharacteristic
67C2×C8×D13C2313yes—
68C2×C8×D13C23112yes—
69#88102C23124yes—
70#88101C23112yes—
71#88101C23124yes—
72#88101C2314yes—
73C2×#2912—131nomaximal, Sylow
74C23×D13C2×D413yes—
75C22×#261—22no—
76C22×#261—26no—
77C22×#261—224no—
78C22×#261—812no—
79C13×#41C4⋊C414yes—
80C13×#41C22×C414yes—
81C2×Q8×C13C4⋊C411yescharacteristic
82C2×D4×C13C4⋊C413yes—
83C22×C4×C13C22×C413yes—
84C2×C22⋊D13C4⋊C416yes—
85C22×Dic13C2×Q813yes—
86#6131C4⋊C414yes—
87#6131C2×Q814yes—
88Q8×D13C4⋊C414yes—
89Q8×D13C2×D414yes—
90#6129C4⋊C4112yes—
91#6129C2×Q8112yes—
92D4×D13C4⋊C4112yes—
93D4×D13C2×D4112yes—
94#6127C4⋊C4112yes—
95#6127C22×C4112yes—
96C2×D52C4⋊C413yes—
97C2×C4×D13C22×C413yes—
98C2×C4×D13C22×C416yes—
99C2×C4×D13C2×D413yes—
100C2×C4×D13C2×D416yes—
101C2×C4×D13C2×Q813yes—
102C2×C4×D13C2×Q816yes—
103C2×C4×D13C2411yescharacteristic
104C2×C4×D13C2416yes—
105C2×Dic26C4⋊C413yes—
106C22⋊#261—224no—
107C4⋊#261—26no—
108C4⋊#261—224no—
109C4⋊#261—22no—
110C4⋊#261C24112yes—
111C4⋊#261C2414yes—
112C4×#261—224no—
113C13×M16C22×C4112yescomplemented
114C2×C8×C13C22×C411yescharacteristic
115C2×C8×C13C22×C413yes—
116C2×C8×C13C22×C4112yescomplemented
117#6099C22×C4112yescomplemented
118C2×#1055C22×C411yescharacteristic
119C2×#1055C22×C413yes—
120C2×#1055C22×C4112yescomplemented
121#6094C22×C4124yescomplemented
122C8×D13C22×C412yes—
123C8×D13C22×C416yes—
124C8×D13C22×C4112yescomplemented
125C8×D13C22×C4112yescomplemented
126C8×D13C2412yes—
127C8×D13C2416yes—
128C22×#131—131no—
129C2×#520—132no—
130#2912—1316no—
131C2×#428—136no—
132C2×#427—133no—
133C22×#106—133no—
134C23×C13C2×C4⋊C413yes—
135C22×D13—212no—
136C22×D13C2×C4⋊C413yes—
137C22×D13C2×C4⋊C416yes—
138C22×D13C22×D416yes—
139C22×D13C22×D411yescharacteristic
140C2×#261—24no—
141C2×#261—212no—
142C2×#261—44no—
143C2×#261—412no—
144C2×#261—824no—
145Q8×C13C2×C4⋊C414yes—
146D4×C13C2×C4⋊C4112yes—
147C2×C4×C13C2×C4⋊C413yes—
148C2×C4×C13C2×C4⋊C416yes—
149C2×C4×C13C23×C411yescharacteristic
150C2×C4×C13C23×C416yes—
151C22⋊D13C2×C4⋊C4124yes—
152C2×Dic13C2×C4⋊C413yes—
153C2×Dic13C2×C4⋊C416yes—
154C2×Dic13C22×Q811yescharacteristic
155C2×Dic13C22×Q816yes—
156D52C2×C4⋊C4112yes—
157C4×D13C2×C4⋊C416yes—
158C4×D13C2×C4⋊C416yes—
159C4×D13C2×C4⋊C416yes—
160C4×D13C23×C411yescharacteristic
161C4×D13C23×C416yes—
162C4×D13C22×D416yes—
163C4×D13C22×D411yescharacteristic
164C4×D13C22×Q811yescharacteristic
165C4×D13C22×Q816yes—
166C4×D13C2511yescharacteristic
167Dic26C2×C4⋊C4112yes—
168C8×C13C23×C412yes—
169C8×C13C23×C416yes—
170#1055C23×C412yes—
171#1055C23×C416yes—
172C22×#41—131no—
173C2×#131—131no—
174C2×#131—138no—
175C2×#131—138no—
176C2×#131—133no—
177C2×#131—133no—
178C2×#131#26111yescharacteristic, complemented
179C22×M16—133no—
180C23×C8—133no—
181#520—1316no—
182#520—268no—
183C2×C4×Q8—262no—
184C2×C4×D4—266no—
185C2×#117—136no—
186C22×C4⋊C4—136no—
187#428—1348no—
188#427—1324no—
189C2×#107—136no—
190C2×#106—133no—
191C2×#106—136no—
192C2×#106—1324no—
193C2×#106—131no—
194C22×C13—26no—
195C22×C13C22×C4⋊C416yes—
196C22×C13C22×C4⋊C411yescharacteristic
197C2×D13—26no—
198C2×D13—212no—
199C2×D13—212no—
200C2×D13C22×C4⋊C416yes—
201C2×D13C22×C4⋊C411yescharacteristic
202C2×D13#57714yes—
203C2×D13C23×D411yescharacteristic
204#261—44no—
205#261—412no—
206C4×C13C22×C4⋊C416yes—
207C4×C13C22×C4⋊C411yescharacteristic
208C4×C13C24×C411yescharacteristic
209Dic13C22×C4⋊C416yes—
210Dic13C22×C4⋊C411yescharacteristic
211Dic13C23×Q811yescharacteristic
212C2×#41—134no—
213C2×#41—134no—
214C2×#41—134no—
215C2×#41—134no—
216C2×#41—131no—
217C2×#41—133no—
218C2×#41—133no—
219C2×#41C2×#26111yescharacteristic
220C22×Q8—131no—
221C22×D4—133no—
222C23×C4—133no—
223C23×C4—266no—
224#131—138no—
225#131—1324no—
226#131—1324no—
227#131C2×#26118yescomplemented
228C2×M16—133no—
229C2×M16—1312no—
230C2×M16—1312no—
231C2×M16—136no—
232C2×M16C2×#26113yescomplemented
233C22×C8—133no—
234C22×C8—131no—
235C22×C8—133no—
236C22×C8—133no—
237C22×C8—133no—
238C22×C8—1312no—
239C22×C8—1312no—
240C22×C8C2×#26113yescomplemented
241C4×Q8—2616no—
242C4×D4—2648no—
243#117—1324no—
244#117—2612no—
245C2×C4⋊C4—136no—
246C2×C4⋊C4—1324no—
247C2×C4⋊C4—132no—
248C2×C4⋊C4—266no—
249C2×C4⋊C4—2612no—
250C2×C22⋊C4—266no—
251C2×C42—266no—
252#107—1324no—
253#106—1312no—
254#106—1324no—
255#106—134no—
256C2×C13—26no—
257C2×C13#291212yescomplemented
258C2×C13C23×C4⋊C411yescharacteristic
259D13—26no—
260D13#291212yescomplemented
261D13C2×#57712yes—
262C24—133no—
263#41—134no—
264#41—134no—
265#41—1312no—
266#41—1312no—
267#41—1312no—
268#41—1312no—
269#41C4⋊#26114yes—
270#41C22×#26114yes—
271C2×Q8—134no—
272C2×Q8—134no—
273C2×Q8—133no—
274C2×Q8C4⋊#26111yescharacteristic
275C2×D4—136no—
276C2×D4—1312no—
277C2×D4—1312no—
278C2×D4—133no—
279C2×D4C4⋊#26113yes—
280C22×C4—133no—
281C22×C4—133no—
282C22×C4—136no—
283C22×C4—136no—
284C22×C4—133no—
285C22×C4—131no—
286C22×C4—136no—
287C22×C4—136no—
288C22×C4—133no—
289C22×C4—262no—
290C22×C4—266no—
291C22×C4—2624no—
292C22×C4—10412no—
293C22×C4C22×#26113yes—
294M16—1312no—
295M16—1324no—
296M16C22×#261112yescomplemented
297C2×C8—131no—
298C2×C8—133no—
299C2×C8—1312no—
300C2×C8—132no—
301C2×C8—136no—
302C2×C8—132no—
303C2×C8—136no—
304C2×C8—1312no—
305C2×C8—1312no—
306C2×C8C22×#26111yescharacteristic
307C2×C8C22×#26113yes—
308C2×C8C22×#261112yescomplemented
309C4⋊C4—1312no—
310C4⋊C4—134no—
311C4⋊C4—266no—
312C4⋊C4—2624no—
313C4⋊C4—262no—
314C22⋊C4—2624no—
315C42—2624no—
316C13C2×#291211yescharacteristic, complemented, Sylow
317C23—131no—
318C23—136no—
319C23—136no—
320C23—133no—
321C23—2612no—
322C23C2×C4⋊#26113yes—
323Q8—1312no—
324Q8C2×C4⋊#26114yes—
325D4—1324no—
326D4—1312no—
327D4C2×C4⋊#261112yes—
328C2×C4—136no—
329C2×C4—136no—
330C2×C4—133no—
331C2×C4—131no—
332C2×C4—136no—
333C2×C4—131no—
334C2×C4—136no—
335C2×C4—136no—
336C2×C4—136no—
337C2×C4—131no—
338C2×C4—136no—
339C2×C4—131no—
340C2×C4—131no—
341C2×C4—136no—
342C2×C4—264no—
343C2×C4—2612no—
344C2×C4—5212no—
345C2×C4—524no—
346C2×C4—10424no—
347C2×C4C2×C4⋊#26116yes—
348C2×C4C2×C4⋊#26113yes—
349C2×C4C23×#26116yes—
350C2×C4C23×#26111yescharacteristic
351C8—132no—
352C8—136no—
353C8C23×#26112yes—
354C8C23×#26116yes—
355C22—26no—
356C22—131no—
357C22—131no—
358C22—134no—
359C22—136no—
360C22—2612no—
361C22—2612no—
362C22—266no—
363C22C22×C4⋊#26116yes—
364C22C22×C4⋊#26111yescharacteristic
365C4—131no—
366C4—136no—
367C4—131no—
368C4—524no—
369C4—5212no—
370C4C22×C4⋊#26111yescharacteristic
371C4C22×C4⋊#26116yes—
372C4C24×#26111yescharacteristic
373C2—26no—
374C2—132no—
375C2—132no—
376C2—266no—
377C2#1313149012yesdirect product factor
378C2C23×C4⋊#26111yescharacteristic
subgroupG/H
centerC22C22×C4⋊#261
commutatorC4×C13C24×C4
FrattiniC4C24×#261
FittingC2×C13×#131C4
socleC22×C13C22×C4⋊C4
prime radicalC2×#41×D13C22
cosocleC4×D13C25
hypercenterC2×#131#261
hypocenterC13C2×#2912
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
2. #13131490C2direct (N × H)
3. C2×#11719098C2semidirect
4. C2×#11719092C2semidirect
5. C22×#88101C2semidirect
14. C2×C13×#131C4semidirect
15. C2×#88202C4semidirect
16. D13×#131C4semidirect
18. C2×#88161C4semidirect
20. C2×#88155C4semidirect
22. #11719098C22semidirect
23. #11719092C22semidirect
28. C2×#88101C22semidirect
52. C13×#131C2×C4semidirect
53. C2×C13×M16C2×C4semidirect
54. C22×C8×C13C2×C4semidirect
55. #88202C2×C4semidirect
56. C2×#6099C2×C4semidirect
57. C22×#1055C2×C4semidirect
58. #88161C2×C4semidirect
59. M16×D13C2×C4semidirect
61. #88155C2×C4semidirect
62. C2×#6094C2×C4semidirect
63. C2×C8×D13C2×C4semidirect
64. C2×C8×D13C2×C4semidirect
65. C2×C8×D13C2×C4semidirect
113. C13×M16C22×C4semidirect
116. C2×C8×C13C22×C4semidirect
117. #6099C22×C4semidirect
120. C2×#1055C22×C4semidirect
121. #6094C22×C4semidirect
124. C8×D13C22×C4semidirect
125. C8×D13C22×C4semidirect
178. C2×#131#261semidirect
227. #131C2×#261semidirect
232. C2×M16C2×#261semidirect
240. C22×C8C2×#261semidirect
257. C2×C13#2912semidirect
260. D13#2912semidirect
296. M16C22×#261semidirect
308. C2×C8C22×#261semidirect
316. C13C2×#2912semidirect
377. C2#13131490direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117196312
#131314902
C2×#117190982
C2×#117190922
C22×#881012
C2×D13×#1312
C2×#291213