Finite Group Databasebeta

← C2×#13117049 #16017802

Subgroups — C2×#13117049 #16017802

Order 3328.

604 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718820C211yesmaximal, characteristic
2C2×#11718554C211yesmaximal, characteristic, complemented
3#13117049C218yesmaximal, direct product factor
4C2×#11718086C211yesmaximal, characteristic, complemented
5C2×#11718105C211yesmaximal, characteristic, complemented
6C2×#11718155C211yesmaximal, characteristic, complemented
7C2×#11718106C211yesmaximal, characteristic, complemented
8C2×C13×#361C211yesmaximal, characteristic, complemented
9C22×C13×D8C2211yescharacteristic
10C2×#88192—21no—
11C2×M16×D13—21no—
12C22×#6094C2211yescharacteristic
13C2×C13×M32C2211yescharacteristic
14C2×C13×#108C2211yescharacteristic
15C2×#88072—21no—
16#11718820—22no—
17#11718820C2214yes—
18C2×#88062—21no—
19C2×#88059C2211yescharacteristic
20C2×#88057C2211yescharacteristic
21C2×#88052C2211yescharacteristic
22#11718554—22no—
23#11718554C2214yescomplemented
24C13×#361C2214yescomplemented
25#11718155C2214yescomplemented
26#11718106C2214yescomplemented
27#11718105C2214yescomplemented
28#11718086C2214yescomplemented
29C22×D4×C13—21no—
30C22×C22⋊D13—41no—
31C22×C4×D13D411yescharacteristic
32C2×C13×D8—21no—
33C2×C13×D8—21no—
34C2×C13×D8—21no—
35C2×C13×D8—21no—
36C2×C13×D8—21no—
37C2×C13×D8C2312yes—
38C2×C13×M16—21no—
39C22×C8×C13C2311yescharacteristic
40C2×C22⋊Dic13—41no—
41#88192—24no—
42#88192—42no—
43C2×C4⋊Dic13—21no—
44C2×#6099—21no—
45C22×#1055D411yescharacteristic
46M16×D13—24no—
47M16×D13—42no—
48C2×#6094—21no—
49C2×#6094—21no—
50C2×#6094—21no—
51C2×#6094—21no—
52C2×#6094—41no—
53C2×#6094D412yes—
54C2×#6094C2312yes—
55C2×C8×D13—41no—
56C13×M32—21no—
57C13×M32C2312yes—
58C2×C13×C16—21no—
59C13×#108—21no—
60C13×#108C2312yes—
61#88072—24no—
62#88062—24no—
63#88059—21no—
64#88059C2312yes—
65#88057—21no—
66#88057C2312yes—
67#88052—21no—
68#88052C2312yes—
69C2×#6090—21no—
70C2×#2238—131nomaximal, Sylow
71C24×C13—41no—
72C23×D13SD1611yescharacteristic
73C2×D4×C13—22no—
74C2×D4×C13—41no—
75C2×D4×C13—41no—
76C2×D4×C13—41no—
77C2×D4×C13—41no—
78C2×D4×C13—41no—
79C22×C4×C13C2×D411yescharacteristic
80C2×C22⋊D13—44no—
81C2×C22⋊D13—84no—
82C22×Dic13—41no—
83C22×Dic13SD1611yescharacteristic
84C2×C4×D13—21no—
85C2×C4×D13—21no—
86C2×C4×D13—21no—
87C2×C4×D13—21no—
88C2×C4×D13SD1612yes—
89C2×C4×D13C2×D412yes—
90C13×D8—22no—
91C13×D8—22no—
92C13×D8—41no—
93C13×D8—41no—
94C13×M16—22no—
95C13×M16—41no—
96C2×C8×C13—41no—
97C2×C8×C13C2×D411yescharacteristic
98C2×C8×C13#4111yescharacteristic
99C2×C8×C13#4111yescharacteristic
100C2×C8×C13#4111yescharacteristic
101C2×C8×C13#4111yescharacteristic
102C2×C8×C13C2411yescharacteristic
103C22⋊Dic13—44no—
104C4⋊Dic13—22no—
105C4⋊Dic13—41no—
106#6099—22no—
107#6099—41no—
108C2×#1055—21no—
109C2×#1055—21no—
110C2×#1055—41no—
111C2×#1055C2×D412yes—
112#6094—22no—
113#6094—22no—
114#6094—22no—
115#6094—22no—
116#6094—44no—
117C8×D13—44no—
118C13×C16—22no—
119#6090—22no—
120C2×#469—131no—
121C2×#430—131no—
122#2238—138no—
123C2×#365—131no—
124C2×#365—131no—
125C2×#361—131no—
126C2×#361D1311yescharacteristic, complemented
127C2×#349—131no—
128C23×C13—42no—
129C23×C13—82no—
130C23×C13—82no—
131C23×C13—81no—
132C23×C13—81no—
133C23×C13C2×SD1611yescharacteristic
134C22×D13—21no—
135C22×D13—21no—
136C22×D13—42no—
137C22×D13C2×SD1612yes—
138D4×C13—42no—
139D4×C13—42no—
140D4×C13—81no—
141D4×C13—81no—
142C2×C4×C13#12311yescharacteristic
143C2×C4×C13#12311yescharacteristic
144C2×C4×C13C2×SD1611yescharacteristic
145C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C13C22×D411yescharacteristic
148C22⋊D13—88no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—42no—
152C2×Dic13—82no—
153C2×Dic13C2×SD1612yes—
154C4×D13—22no—
155C4×D13—22no—
156C4×D13—22no—
157C4×D13—22no—
158C8×C13—42no—
159C8×C13#12311yescharacteristic
160C8×C13#12311yescharacteristic
161C8×C13C2×#4111yescharacteristic
162C8×C13C2×#4111yescharacteristic
163#1055—22no—
164#1055—42no—
165C22×D8C2×D1311yescharacteristic
166C22×M16—131no—
167C22×M16—261no—
168C2×#121—261no—
169C2×M32—131no—
170C2×M32C2×D1311yescharacteristic
171#469—134no—
172#469—262no—
173#430—134no—
174#430—262no—
175C2×#108—131no—
176C2×#108—261no—
177C2×#108C2×D1311yescharacteristic
178C2×#106—131no—
179C2×#102—261no—
180#365—134no—
181#365—134no—
182#361—134no—
183#361C2×D1314yescomplemented
184#349—134no—
185C22×C13—22no—
186C22×C13—82no—
187C22×C13—82no—
188C22×C13—82no—
189C22×C13—162no—
190C22×C13—162no—
191C22×C13#48111yescharacteristic
192C22×C13#48111yescharacteristic
193C22×C13C22×SD1611yescharacteristic
194C2×D13—22no—
195C2×D13—42no—
196C2×D13—42no—
197C2×D13—81no—
198C4×C13#48111yescharacteristic
199C4×C13#48111yescharacteristic
200C4×C13C2×#12311yescharacteristic
201C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
202Dic13—22no—
203Dic13—82no—
204C22×D4—21no—
205C22×D4—521no—
206C23×C4—131no—
207C2×D8—21no—
208C2×D8—21no—
209C2×D8—21no—
210C2×D8—21no—
211C2×D8—21no—
212C2×D8C22×D1312yes—
213C2×M16—21no—
214C2×M16—132no—
215C2×M16—132no—
216C2×M16—261no—
217C2×M16—261no—
218C2×M16—261no—
219C2×M16—261no—
220C2×M16—264no—
221C2×M16—261no—
222C2×M16—521no—
223C2×M16—522no—
224C22×C8—131no—
225C22×C8—521no—
226C22×C8C22×D1311yescharacteristic
227#121—264no—
228#121—522no—
229C2×C4⋊C4—261no—
230C2×C22⋊C4—521no—
231M32—21no—
232M32—132no—
233M32—261no—
234M32C22×D1312yes—
235C2×C16—21no—
236C2×C16—261no—
237#108—21no—
238#108—132no—
239#108—264no—
240#108—261no—
241#108C22×D1312yes—
242#106—132no—
243#106—261no—
244#102—264no—
245C2×C13—21no—
246C2×C13—21no—
247C2×C13—162no—
248C2×C13#223812yescomplemented
249C2×C13C2×#48111yescharacteristic
250D13—42no—
251C24—41no—
252C24—131no—
253C2×D4—22no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—524no—
260C2×D4—1044no—
261C22×C4—131no—
262C22×C4—132no—
263C22×C4—132no—
264C22×C4—261no—
265C22×C4—261no—
266C22×C4—261no—
267C22×C4—261no—
268C22×C4—521no—
269C22×C4D4×D1311yescharacteristic
270D8—22no—
271D8—22no—
272D8—41no—
273D8—41no—
274M16—22no—
275M16—41no—
276M16—262no—
277M16—262no—
278M16—262no—
279M16—262no—
280M16—262no—
281M16—524no—
282M16—521no—
283C2×C8—41no—
284C2×C8—132no—
285C2×C8—261no—
286C2×C8—261no—
287C2×C8—524no—
288C2×C8—521no—
289C2×C8#612711yescharacteristic
290C2×C8#612711yescharacteristic
291C2×C8D4×D1311yescharacteristic
292C2×C8#612911yescharacteristic
293C2×C8#612911yescharacteristic
294C2×C8C23×D1311yescharacteristic
295C4⋊C4—262no—
296C4⋊C4—521no—
297C22⋊C4—524no—
298C16—22no—
299C16—262no—
300C13C2×#223811yescharacteristic, complemented, Sylow
301C23—42no—
302C23—82no—
303C23—82no—
304C23—81no—
305C23—81no—
306C23—132no—
307C23—261no—
308C23—261no—
309C23—522no—
310C23SD16×D1311yescharacteristic
311D4—42no—
312D4—42no—
313D4—81no—
314D4—81no—
315D4—1048no—
316C2×C4—132no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—262no—
320C2×C4—262no—
321C2×C4—262no—
322C2×C4—262no—
323C2×C4—522no—
324C2×C4—1042no—
325C2×C4#8813711yescharacteristic
326C2×C4#8813711yescharacteristic
327C2×C4#8816511yescharacteristic
328C2×C4#8816511yescharacteristic
329C2×C4SD16×D1311yescharacteristic
330C2×C4C2×D4×D1311yescharacteristic
331C8—42no—
332C8—262no—
333C8—522no—
334C8#8813711yescharacteristic
335C8#8813711yescharacteristic
336C8C2×#612711yescharacteristic
337C8C2×#612911yescharacteristic
338C22—22no—
339C22—82no—
340C22—82no—
341C22—82no—
342C22—162no—
343C22—162no—
344C22—262no—
345C22—522no—
346C22—522no—
347C22—1041no—
348C22#1171843811yescharacteristic
349C22#1171843811yescharacteristic
350C22C2×SD16×D1311yescharacteristic
351C4—262no—
352C4—1042no—
353C4#1171843811yescharacteristic
354C4#1171843811yescharacteristic
355C4C2×#8813711yescharacteristic
356C4C2×#8816511yescharacteristic
357C2—21no—
358C2—21no—
359C2—162no—
360C2—522no—
361C2#1311704912yesdirect product factor
362C2C2×#1171843811yescharacteristic
subgroupG/H
centerC22#11718438
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC2×C13×#361C2
socleC22×C13#481
prime radicalC2×#11718820C2
hypercenterC2×#361D13
hypocenterC13C2×#2238
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

Complements

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

NH ≅ G/Ntype
2. C2×#11718554C2semidirect
3. #13117049C2direct (N × H)
4. C2×#11718086C2semidirect
5. C2×#11718105C2semidirect
6. C2×#11718155C2semidirect
7. C2×#11718106C2semidirect
8. C2×C13×#361C2semidirect
23. #11718554C22semidirect
24. C13×#361C22semidirect
25. #11718155C22semidirect
26. #11718106C22semidirect
27. #11718105C22semidirect
28. #11718086C22semidirect
126. C2×#361D13semidirect
183. #361C2×D13semidirect
248. C2×C13#2238semidirect
300. C13C2×#2238semidirect
361. C2#13117049direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117188202
C2×#117185542
#131170492
C2×#117180862
C2×#117181052
C2×#117181552
C2×#117181062
C2×C13×#3612
C2×#223813