Finite Group Databasebeta

← C2×#13112767 #15772017

Subgroups — C2×#13112767 #15772017

Order 3328.

834 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 834 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718649C211yesmaximal, characteristic
2C2×#11718120C211yesmaximal, characteristic, complemented
3#13112767C214yesmaximal, direct product factor
4C2×C13×#324C211yesmaximal, characteristic, complemented
5C23×D52C411yescharacteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C22×#6103—21no—
8C22×#6103—21no—
9C22×C4×Dic13C411yescharacteristic
10C2×C13×C22⋊C8—21no—
11C2×C22⋊#1055—21no—
12#11718649—21no—
13#11718649—21no—
14#11718649C412yes—
15#11718649C2212yes—
16C13×#324—21no—
17C13×#324C2212yescomplemented
18#11718120—21no—
19#11718120C2212yescomplemented
20C24×D13—21no—
21C23×C4×C13C2×C411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×Dic13—21no—
25C22×D52—21no—
26C22×D52—22no—
27C22×D52—41no—
28C22×D52—41no—
29C22×D52—42no—
30C22×D52C814yescomplemented
31C22×D52C2×C412yes—
32C22×C8×C13—41no—
33C2×C13×C4⋊C4—41no—
34C2×C13×C4⋊C4—41no—
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C4⋊C4C2311yescharacteristic
39C2×#6103—22no—
40C2×#6103—22no—
41C2×#6103—22no—
42C2×#6103—22no—
43C2×#6103—44no—
44C2×#6103—44no—
45C2×C4×Dic13—21no—
46C2×C4×Dic13—42no—
47C2×C4×Dic13C2×C412yes—
48C22×#1055—41no—
49C13×C22⋊C8—22no—
50C13×C22⋊C8—41no—
51C22⋊#1055—22no—
52C22⋊#1055—41no—
53C2×#1318—131nomaximal, Sylow
54C24×C13C22⋊C411yescharacteristic
55C23×D13—24no—
56C23×D13—22no—
57C23×D13—42no—
58C23×D13—42no—
59C23×D13—42no—
60C23×D13—42no—
61C23×D13—41no—
62C23×D13—41no—
63C23×D13—42no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—22no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—42no—
72C22×C4×C13—42no—
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C2×C812yes—
77C22×C4×C13M1612yes—
78C22×C4×C13C22×C411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×Dic13—24no—
82C22×Dic13—22no—
83C22×Dic13—42no—
84C22×Dic13—42no—
85C2×D52—24no—
86C2×D52—22no—
87C2×D52—44no—
88C2×D52—44no—
89C2×D52—42no—
90C2×D52—42no—
91C2×D52—44no—
92C2×D52—44no—
93C2×D52—42no—
94C2×D52—42no—
95C2×D52C2×C814yescomplemented
96C2×C8×C13—42no—
97C2×C8×C13—82no—
98C13×C4⋊C4—41no—
99C13×C4⋊C4—41no—
100C13×C4⋊C4—41no—
101C13×C4⋊C4—41no—
102#6103—44no—
103#6103—44no—
104#6103—44no—
105#6103—44no—
106C4×Dic13—42no—
107C4×Dic13—42no—
108C2×#1055—42no—
109C2×#1055—82no—
110C2×#390—131no—
111C2×#324—131no—
112C2×#324D1311yescharacteristic, complemented
113#1318—134no—
114C23×C13—22no—
115C23×C13—22no—
116C23×C13C22⋊C812yes—
117C23×C13#9911yescharacteristic
118C23×C13#9911yescharacteristic
119C23×C13#10012yes—
120C23×C13C2×C22⋊C411yescharacteristic
121C22×D13—24no—
122C22×D13—42no—
123C22×D13—42no—
124C22×D13—48no—
125C22×D13—48no—
126C22×D13—42no—
127C22×D13—42no—
128C22×D13—44no—
129C22×D13—44no—
130C22×D13—42no—
131C22×D13—42no—
132C22×D13—84no—
133C22×D13—84no—
134C22×D13—82no—
135C22×D13—82no—
136C22×D13—82no—
137C22×D13—82no—
138C2×C4×C13—22no—
139C2×C4×C13—22no—
140C2×C4×C13—22no—
141C2×C4×C13—22no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—42no—
151C2×C4×C13—42no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—81no—
157C2×C4×C13—81no—
158C2×C4×C13C22⋊C812yes—
159C2×C4×C13C22×C811yescharacteristic
160C2×C4×C13C2×M1611yescharacteristic
161C2×Dic13—24no—
162C2×Dic13—48no—
163C2×Dic13—42no—
164C2×Dic13—42no—
165D52—48no—
166D52—44no—
167D52—44no—
168C8×C13—82no—
169#1055—82no—
170C23×D4—131no—
171C22×C4⋊C4C2×D1311yescharacteristic
172C22×C22⋊C4—261no—
173C22×C22⋊C4—261no—
174C22×C42—131no—
175C2×C22⋊C8—21no—
176C2×C22⋊C8—261no—
177#390—132no—
178#390—132no—
179#390—261no—
180#390—261no—
181#324—21no—
182#324—132no—
183#324—261no—
184#324C2×D1312yescomplemented
185C22×C13—24no—
186C22×C13—24no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13#32312yes—
192C22×C13#32312yes—
193C22×C13#35312yes—
194C22×C13#35512yes—
195C22×C13C2×C22⋊C811yescharacteristic
196C22×C13C2×#9911yescharacteristic
197C22×C13C2×#10011yescharacteristic
198C2×D13—44no—
199C2×D13—44no—
200C2×D13—44no—
201C2×D13—82no—
202C2×D13—82no—
203C2×D13—88no—
204C2×D13—88no—
205C2×D13—82no—
206C2×D13—82no—
207C4×C13—22no—
208C4×C13—21no—
209C4×C13—21no—
210C4×C13—41no—
211C4×C13—41no—
212C4×C13—41no—
213C4×C13—41no—
214Dic13—44no—
215C25—261no—
216C22×D4—134no—
217C22×D4—132no—
218C22×D4—262no—
219C22×D4—261no—
220C22×D4—521no—
221C22×D4—521no—
222C22×D4—522no—
223C23×C4—261no—
224C23×C4C4×D1311yescharacteristic
225C23×C4D5211yescharacteristic
226C23×C4C22⋊D1311yescharacteristic
227C22×C8—41no—
228C22×C8—521no—
229C2×C4⋊C4—41no—
230C2×C4⋊C4—41no—
231C2×C4⋊C4C4×D1311yescharacteristic
232C2×C4⋊C4D5211yescharacteristic
233C2×C4⋊C4C22⋊D1311yescharacteristic
234C2×C4⋊C4C22×D1311yescharacteristic
235C2×C22⋊C4—262no—
236C2×C22⋊C4—262no—
237C2×C22⋊C4—262no—
238C2×C22⋊C4—262no—
239C2×C22⋊C4—524no—
240C2×C22⋊C4—524no—
241C2×C42—132no—
242C2×C42—261no—
243C2×C42—522no—
244C22⋊C8—22no—
245C22⋊C8—41no—
246C22⋊C8—262no—
247C22⋊C8—521no—
248C2×C13—21no—
249C2×C13—21no—
250C2×C13—22no—
251C2×C13#131814yescomplemented
252C2×C13C2×#32311yescharacteristic
253C2×C13C2×#35311yescharacteristic
254C2×C13C2×#35511yescharacteristic
255D13—84no—
256C24—262no—
257C24—264no—
258C24—522no—
259C24—522no—
260C24—522no—
261C24—522no—
262C24—521no—
263C24—521no—
264C24—522no—
265C24#610311yescharacteristic
266C2×D4—134no—
267C2×D4—262no—
268C2×D4—264no—
269C2×D4—522no—
270C2×D4—524no—
271C2×D4—524no—
272C2×D4—522no—
273C2×D4—522no—
274C2×D4—524no—
275C2×D4—524no—
276C2×D4—522no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—264no—
287C22×C4—262no—
288C22×C4—522no—
289C22×C4—522no—
290C22×C4C8×D1312yes—
291C22×C4#609412yes—
292C22×C4#610311yescharacteristic
293C22×C4#610311yescharacteristic
294C22×C4#610311yescharacteristic
295C22×C4C2×C4×D1311yescharacteristic
296C22×C4C2×D5211yescharacteristic
297C22×C4C2×C22⋊D1311yescharacteristic
298C2×C8—42no—
299C2×C8—82no—
300C2×C8—522no—
301C2×C8—1042no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C22⋊C4—524no—
307C22⋊C4—524no—
308C22⋊C4—524no—
309C22⋊C4—524no—
310C42—522no—
311C42—522no—
312C13C2×#131811yescharacteristic, complemented, Sylow
313C23—22no—
314C23—22no—
315C23—264no—
316C23—522no—
317C23—522no—
318C23—522no—
319C23—522no—
320C23—528no—
321C23—528no—
322C23—522no—
323C23—524no—
324C23—524no—
325C23—522no—
326C23—1042no—
327C23—1042no—
328C23—1044no—
329C23—1044no—
330C23—1042no—
331C23—1042no—
332C23#8804611yescharacteristic
333C23#8804611yescharacteristic
334C23#8806012yes—
335C23#8806312yes—
336C23C2×#610311yescharacteristic
337D4—524no—
338D4—524no—
339D4—528no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—264no—
361C2×C4—522no—
362C2×C4—528no—
363C2×C4—522no—
364C2×C4#8806012yes—
365C2×C4C2×C8×D1311yescharacteristic
366C2×C4C2×#609411yescharacteristic
367C8—82no—
368C8—1042no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—24no—
374C22—24no—
375C22—524no—
376C22—524no—
377C22—524no—
378C22—1042no—
379C22—1042no—
380C22—1048no—
381C22—1042no—
382C22—1042no—
383C22—1048no—
384C22#1171806012yes—
385C22#1171806012yes—
386C22#1171806612yes—
387C22#1171806912yes—
388C22C2×#8804611yescharacteristic
389C22C2×#8806011yescharacteristic
390C22C2×#8806311yescharacteristic
391C4—21no—
392C4—21no—
393C4—22no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—41no—
398C4—524no—
399C2—21no—
400C2—21no—
401C2—22no—
402C2—1044no—
403C2#1311276714yesdirect product factor
404C2C2×#1171806011yescharacteristic
405C2C2×#1171806611yescharacteristic
406C2C2×#1171806911yescharacteristic
subgroupG/H
centerC23#88046
commutatorC2×C4×C13C22×C8
FrattiniC2×C4⋊C4C22×D13
FittingC2×C13×#324C2
socleC23×C13#99
prime radicalC23×D52C4
cosocleC2×C13×C4⋊C4C23
hypercenterC2×#324D13
hypocenterC13C2×#1318
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. C2×#11718120C2semidirect
3. #13112767C2direct (N × H)
4. C2×C13×#324C2semidirect
17. C13×#324C22semidirect
19. #11718120C22semidirect
30. C22×D52C8semidirect
95. C2×D52C2×C8semidirect
112. C2×#324D13semidirect
184. #324C2×D13semidirect
251. C2×C13#1318semidirect
312. C13C2×#1318semidirect
403. C2#13112767direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117186492
C2×#117181202
#131127672
C2×C13×#3242
C2×#131813