Finite Group Databasebeta

← C2×#13123402 #16726544

Subgroups — C2×#13123402 #16726544

Order 3328.

2810 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88202C211yesmaximal, characteristic
2C2×#41×Dic13C211yesmaximal, characteristic
3#13123402C2116yesmaximal, direct product factor
4C2×#11718780C213yesmaximal, complemented
5C2×#11718763C213yesmaximal, complemented
6C2×#11718779C213yesmaximal, complemented
7C22×#88054C213yesmaximal, complemented
8C22×C13×#131C211yesmaximal, characteristic
9C22×C13×#41C2211yescharacteristic
10C2×C13×#131—28no—
11C2×C13×#131C2218yes—
12C22×C13×M16C2213yes—
13C23×C8×C13C2213yes—
14#41×Dic13C418yes—
15#41×Dic13C2218yes—
16C2×#88202—28no—
17C2×#88202C2218yes—
18C2×Q8×Dic13C411yescharacteristic
19C2×Q8×Dic13C411yescharacteristic
20C2×D4×Dic13C413yes—
21C2×D4×Dic13C413yes—
22C2×#88180C2213yes—
23C22×C4×Dic13C2213yes—
24C22×#6099C2213yes—
25C23×#1055C2213yes—
26#11718780C22124yescomplemented
27#11718779C22124yescomplemented
28#11718763C22124yescomplemented
29C2×#88054C2211yescharacteristic
30C2×#88054C2213yes—
31C2×#88054C2213yes—
32C2×#88054C2213yes—
33C2×#88054C2216yes—
34C2×#88054C22124yescomplemented
35C2×C13×#41C2×C414yes—
36C2×C13×#41D418yes—
37C2×C13×#41Q818yes—
38C2×C13×#41C2314yes—
39C22×Q8×C13C2×C411yescharacteristic
40C22×D4×C13C2×C413yes—
41C23×C4×C13C2313yes—
42C23×Dic13C2×C413yes—
43C23×Dic13C2×C413yes—
44C13×#131—232no—
45C2×C13×M16—212no—
46C2×C13×M16C23112yes—
47C22×C8×C13—212no—
48C22×C8×C13C2311yescharacteristic
49C22×C8×C13C2313yes—
50C22×C8×C13C23112yes—
51C2×C22⋊Dic13C2×C416yes—
52#88202—232no—
53Q8×Dic13C2×C418yes—
54Q8×Dic13C2×C418yes—
55D4×Dic13C2×C4124yes—
56D4×Dic13C2×C4124yes—
57#88180C2×C4112yes—
58#88180C23112yes—
59C2×C4⋊Dic13C2×C413yes—
60C2×C4⋊Dic13C2×C413yes—
61C2×C4×Dic13C2×C413yes—
62C2×C4×Dic13C2×C413yes—
63C2×C4×Dic13C2×C4112yes—
64C2×C4×Dic13C2311yescharacteristic
65C2×C4×Dic13C2313yes—
66C2×C4×Dic13C23112yes—
67C2×#6099—212no—
68C2×#6099C23112yes—
69C22×#1055—212no—
70C22×#1055C2311yescharacteristic
71C22×#1055C2313yes—
72C22×#1055C23112yes—
73#88054C2314yes—
74#88054C23112yes—
75#88054C23112yes—
76#88054C23112yes—
77#88054C23124yes—
78C2×#2906—131nomaximal, Sylow
79C24×C13C22×C413yes—
80C13×#41C4⋊C4132yes—
81C13×#41C2×D4116yes—
82C13×#41C2×Q8116yes—
83C2×Q8×C13C4⋊C418yes—
84C2×Q8×C13C22×C414yes—
85C2×D4×C13C4⋊C4124yes—
86C2×D4×C13C22×C4112yes—
87C22×C4×C13C22×C413yes—
88C22×C4×C13C22×C416yes—
89C22×C4×C13C2×D4112yes—
90C22×C4×C13C2×Q8112yes—
91C22×C4×C13C2416yes—
92C22×C4×C13C2411yescharacteristic
93C22×Dic13—212no—
94C22×Dic13—46no—
95C22×Dic13C22×C411yescharacteristic
96C22×Dic13C22×C413yes—
97C22×Dic13C22×C413yes—
98C22×Dic13C22×C4112yes—
99C22×Dic13C22×C4112yes—
100C22×Dic13C22×C411yescharacteristic
101C13×M16—224no—
102C2×C8×C13—22no—
103C2×C8×C13—26no—
104C2×C8×C13—224no—
105C2×C8×C13C2412yes—
106C2×C8×C13C2416yes—
107C22⋊Dic13C22×C4124yes—
108C4⋊Dic13C22×C4112yes—
109C4⋊Dic13C22×C4112yes—
110C4×Dic13C22×C412yes—
111C4×Dic13C22×C416yes—
112C4×Dic13C22×C4112yes—
113C4×Dic13C22×C4112yes—
114C4×Dic13C2412yes—
115C4×Dic13C2416yes—
116#6099—224no—
117C2×#1055—22no—
118C2×#1055—26no—
119C2×#1055—224no—
120C2×#1055C2412yes—
121C2×#1055C2416yes—
122C22×#131—131no—
123C22×#131D1311yescharacteristic
124C2×C4×#41—131no—
125#2906—1316no—
126C2×#424—133no—
127C2×#424—133no—
128C2×#423—133no—
129C22×C4⋊C8—133no—
130C23×C13—26no—
131C23×C13—26no—
132C23×C13C2×C4⋊C4112yes—
133C23×C13C23×C416yes—
134C23×C13C23×C411yescharacteristic
135Q8×C13C2×C4⋊C4116yes—
136D4×C13C2×C4⋊C4148yes—
137C2×C4×C13C2×C4⋊C4112yes—
138C2×C4×C13C2×C4⋊C4124yes—
139C2×C4×C13C23×C411yescharacteristic
140C2×C4×C13C23×C416yes—
141C2×C4×C13C22×D412yes—
142C2×C4×C13C22×D4112yes—
143C2×C4×C13C22×Q812yes—
144C2×C4×C13C22×Q8112yes—
145C2×C4×C13C2511yescharacteristic
146C2×Dic13—26no—
147C2×Dic13—22no—
148C2×Dic13—26no—
149C2×Dic13—224no—
150C2×Dic13—412no—
151C2×Dic13#13114yescomplemented
152C2×Dic13C23×C412yes—
153C2×Dic13C23×C416yes—
154C2×Dic13C23×C416yes—
155C2×Dic13C23×C412yes—
156C8×C13—22no—
157C8×C13—26no—
158#1055—22no—
159#1055—26no—
160C22×#41C2×D1311yescharacteristic
161C2×#131—28no—
162C2×#131—138no—
163C2×#131—268no—
164C2×#131C2×D1318yes—
165C22×M16—133no—
166C22×M16C2×D1313yes—
167C23×C8—133no—
168C23×C8C2×D1313yes—
169C4×#41—138no—
170C4×#41—138no—
171C2×C4×Q8—131no—
172C2×C4×Q8—131no—
173C2×C4×D4—133no—
174C2×C4×D4—133no—
175C2×#117—133no—
176C22×C42—133no—
177#424—1324no—
178#424—1324no—
179#423—1324no—
180C2×C4⋊C8—131no—
181C2×C4⋊C8—133no—
182C2×C4⋊C8—133no—
183C2×C4⋊C8—133no—
184C2×C4⋊C8—1324no—
185C2×C4⋊C8—136no—
186C22×C13—224no—
187C22×C13—26no—
188C22×C13—26no—
189C22×C13C22×C4⋊C4112yes—
190C22×C13C22×C4⋊C412yes—
191C22×C13C2×#13112yes—
192C22×C13#56812yes—
193C22×C13C24×C411yescharacteristic
194C4×C13C22×C4⋊C412yes—
195C4×C13C22×C4⋊C4112yes—
196C4×C13C23×D411yescharacteristic
197C4×C13C23×Q811yescharacteristic
198Dic13—26no—
199Dic13—22no—
200Dic13—26no—
201Dic13C2×#13114yescomplemented
202C2×#41Dic2618yes—
203C2×#41C4×D1314yes—
204C2×#41C22⋊D1318yes—
205C2×#41C22×D1314yes—
206C22×Q8C4×D1311yescharacteristic
207C22×D4C4×D1313yes—
208C23×C4—133no—
209C23×C4—133no—
210C23×C4C22×D1313yes—
211#131—232no—
212#131—2632no—
213C2×M16—212no—
214C2×M16—1312no—
215C2×M16—2612no—
216C2×M16C22×D13112yes—
217C22×C8—212no—
218C22×C8—1312no—
219C22×C8—131no—
220C22×C8—133no—
221C22×C8—2612no—
222C22×C8C22×D13112yes—
223C22×C8C22×D1311yescharacteristic
224C22×C8C22×D1313yes—
225C4×Q8—138no—
226C4×Q8—138no—
227C4×D4—1324no—
228C4×D4—1324no—
229#117—1312no—
230#117—1312no—
231C2×C4⋊C4—133no—
232C2×C4⋊C4—133no—
233C2×C22⋊C4—136no—
234C2×C42—133no—
235C2×C42—133no—
236C2×C42—1312no—
237C2×C42—1312no—
238C2×C42—133no—
239C2×C42—131no—
240C4⋊C8—134no—
241C4⋊C8—1312no—
242C4⋊C8—1312no—
243C4⋊C8—1312no—
244C4⋊C8—1324no—
245C2×C13—212no—
246C2×C13#290614yescomplemented
247C2×C13C23×C4⋊C411yescharacteristic
248C2×C13C22×#13111yescharacteristic
249C2×C13C2×#56811yescharacteristic
250C24C2×C4×D1313yes—
251#41#6101132yes—
252#41C2×Dic26116yes—
253#41C2×C22⋊D13116yes—
254C2×Q8#610118yes—
255C2×Q8C2×C4×D1314yes—
256C2×D4#6101124yes—
257C2×D4C2×C4×D13112yes—
258C22×C4—131no—
259C22×C4—131no—
260C22×C4—133no—
261C22×C4—133no—
262C22×C4—1312no—
263C22×C4—1312no—
264C22×C4—2612no—
265C22×C4—526no—
266C22×C4C2×Dic26112yes—
267C22×C4C2×C4×D1313yes—
268C22×C4C2×C4×D1316yes—
269C22×C4C2×C22⋊D13112yes—
270C22×C4C23×D1316yes—
271C22×C4C23×D1311yescharacteristic
272M16—224no—
273M16—2624no—
274C2×C8—22no—
275C2×C8—26no—
276C2×C8—224no—
277C2×C8—132no—
278C2×C8—136no—
279C2×C8—262no—
280C2×C8—266no—
281C2×C8—2624no—
282C2×C8C23×D1312yes—
283C2×C8C23×D1316yes—
284C4⋊C4—1312no—
285C4⋊C4—1312no—
286C22⋊C4—1324no—
287C42—132no—
288C42—136no—
289C42—1312no—
290C42—1312no—
291C42—132no—
292C42—136no—
293C13C2×#290611yescharacteristic, complemented, Sylow
294C23—26no—
295C23—26no—
296C23C2×#6101112yes—
297C23C22×C4×D1316yes—
298C23C22×C4×D1311yescharacteristic
299Q8C2×#6101116yes—
300D4C2×#6101148yes—
301C2×C4—134no—
302C2×C4—132no—
303C2×C4—132no—
304C2×C4—136no—
305C2×C4—136no—
306C2×C4—2624no—
307C2×C4—266no—
308C2×C4—266no—
309C2×C4—262no—
310C2×C4—5212no—
311C2×C4C2×#6101112yes—
312C2×C4C2×#6101124yes—
313C2×C4C22×Dic2612yes—
314C2×C4C22×Dic26112yes—
315C2×C4C22×C4×D1311yescharacteristic
316C2×C4C22×C4×D1316yes—
317C2×C4C22×C22⋊D1312yes—
318C2×C4C22×C22⋊D13112yes—
319C2×C4C24×D1311yescharacteristic
320C8—22no—
321C8—26no—
322C8—262no—
323C8—266no—
324C22—26no—
325C22—26no—
326C22—224no—
327C22D13×#13112yes—
328C22#1171945512yes—
329C22C22×#6101112yes—
330C22C22×#610112yes—
331C22C23×C4×D1311yescharacteristic
332C4—134no—
333C4—266no—
334C4—266no—
335C4—262no—
336C4C22×#610112yes—
337C4C22×#6101112yes—
338C4C23×Dic2611yescharacteristic
339C4C23×C22⋊D1311yescharacteristic
340C2—212no—
341C2#1312340214yesdirect product factor
342C2C23×#610111yescharacteristic
343C2C2×D13×#13111yescharacteristic
344C2C2×#1171945511yescharacteristic
subgroupG/H
centerC22×C4C23×D13
commutatorC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC22×C13×#131C2
socleC23×C13C23×C4
prime radicalC22×C13×#41C22
cosocleC2×C4×C13C25
hypercenterC22×#131D13
hypocenterC13C2×#2906
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×#131

Complements

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

NH ≅ G/Ntype
3. #13123402C2direct (N × H)
4. C2×#11718780C2semidirect
5. C2×#11718763C2semidirect
6. C2×#11718779C2semidirect
7. C22×#88054C2semidirect
26. #11718780C22semidirect
27. #11718779C22semidirect
28. #11718763C22semidirect
34. C2×#88054C22semidirect
151. C2×Dic13#131semidirect
201. Dic13C2×#131semidirect
246. C2×C13#2906semidirect
293. C13C2×#2906semidirect
341. C2#13123402direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#882022
C2×#41×Dic132
#131234022
C2×#117187802
C2×#117187632
C2×#117187792
C22×#880542
C22×C13×#1312
C2×#290613