Finite Group Databasebeta

← C2×#13113843 #15835147

Subgroups — C2×#13113843 #15835147

Order 3328.

1028 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1028 conjugacy classes of subgroups — too many to draw. Only its 203 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×#11719205C211yesmaximal, characteristic
2C2×#11718632C212yesmaximal
3#13113843C218yesmaximal, direct product factor
4C2×#11718044C212yesmaximal
5C2×#11718120C211yesmaximal, characteristic
6C2×C13×#398C211yesmaximal, characteristic
7C22×C13×C4⋊C4—21no—
8C22×C13×C4⋊C4C2211yescharacteristic
9C22×C13×C4⋊C4C2211yescharacteristic
10C2×#88180—21no—
11C2×#88178—21no—
12C2×#88178C2212yes—
13#11719205—22no—
14#11719205—24no—
15#11719205C2214yes—
16C2×#88144—22no—
17C2×#88142—22no—
18C13×#398—22no—
19C13×#398C2214yes—
20C2×C13×#95—21no—
21C2×C13×#95C2211yescharacteristic
22C2×C22⋊#1055C2212yes—
23#11718632—24no—
24#11718632C2218yes—
25C2×#88050—22no—
26C2×#88048—22no—
27#11718120C2214yes—
28#11718044C2218yes—
29C23×C4×C13—21no—
30C23×C4×C13—21no—
31C23×C4×C13D411yescharacteristic
32C23×C4×C13D411yescharacteristic
33C23×C4×C13C2311yescharacteristic
34C22×Dic26—21no—
35C22×Dic26D412yes—
36C2×C13×C4⋊C4—22no—
37C2×C13×C4⋊C4—22no—
38C2×C13×C4⋊C4—22no—
39C2×C13×C4⋊C4—22no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—24no—
42C2×C13×C4⋊C4—44no—
43C2×C13×C4⋊C4D412yes—
44C2×C13×C4⋊C4C2312yes—
45C2×C13×C4⋊C4C2312yes—
46C2×C22⋊Dic13—22no—
47#88180—24no—
48#88180—24no—
49C2×C4⋊Dic13—21no—
50C2×C4⋊Dic13—21no—
51C2×C4⋊Dic13—21no—
52C2×C4⋊Dic13D412yes—
53#88178—24no—
54#88178—22no—
55#88178—22no—
56#88178—24no—
57#88178D414yes—
58#88178C2314yes—
59C2×#6101—22no—
60C2×#6101—22no—
61C2×C4×Dic13—22no—
62C22×#1055—22no—
63#88144—28no—
64#88144—28no—
65#88142—28no—
66#88142—28no—
67C13×#95—21no—
68C13×#95—24no—
69C13×#95C2312yes—
70C22⋊#1055—22no—
71C22⋊#1055C2314yes—
72#88050—28no—
73#88048—28no—
74C2×#1611—131nomaximal, Sylow
75C24×C13C2×D411yescharacteristic
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—22no—
79C22×C4×C13—24no—
80C22×C4×C13—21no—
81C22×C4×C13—22no—
82C22×C4×C13—21no—
83C22×C4×C13—22no—
84C22×C4×C13—42no—
85C22×C4×C13—42no—
86C22×C4×C13—42no—
87C22×C4×C13—42no—
88C22×C4×C13—41no—
89C22×C4×C13—41no—
90C22×C4×C13—42no—
91C22×C4×C13—42no—
92C22×C4×C13SD1614yes—
93C22×C4×C13C2×D412yes—
94C22×C4×C13C2×D412yes—
95C22×C4×C13C2×D412yes—
96C22×C4×C13C2×D412yes—
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2411yescharacteristic
99C22×Dic13—22no—
100C22×Dic13—22no—
101C2×Dic26—24no—
102C2×Dic26—22no—
103C2×Dic26—44no—
104C2×Dic26—82no—
105C2×Dic26C2×D414yes—
106C13×C4⋊C4—24no—
107C13×C4⋊C4—24no—
108C13×C4⋊C4—24no—
109C13×C4⋊C4—42no—
110C13×C4⋊C4—48no—
111C22⋊Dic13—24no—
112C22⋊Dic13—24no—
113C4⋊Dic13—24no—
114C4⋊Dic13—24no—
115C4⋊Dic13—24no—
116C4⋊Dic13—22no—
117C4⋊Dic13C2×D414yes—
118#6101—28no—
119#6101—24no—
120#6101—24no—
121C4×Dic13—28no—
122C2×#1055—24no—
123C2×#1055—44no—
124C2×#544—131no—
125C2×#483—132no—
126C2×#398D1311yescharacteristic
127#1611—138no—
128C2×#328—132no—
129C2×#324—131no—
130C23×C13—22no—
131C23×C13—22no—
132C23×C13#12011yescharacteristic
133C23×C13#12011yescharacteristic
134C23×C13C2×SD1612yes—
135C23×C13#13712yes—
136C23×C13C22×D411yescharacteristic
137C2×C4×C13—22no—
138C2×C4×C13—22no—
139C2×C4×C13—24no—
140C2×C4×C13—24no—
141C2×C4×C13—24no—
142C2×C4×C13—24no—
143C2×C4×C13—22no—
144C2×C4×C13—42no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—48no—
148C2×C4×C13—42no—
149C2×C4×C13—42no—
150C2×C4×C13—42no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13—42no—
154C2×C4×C13—42no—
155C2×C4×C13—81no—
156C2×C4×C13—82no—
157C2×C4×C13—82no—
158C2×C4×C13#12012yes—
159C2×C4×C13C2×SD1614yes—
160C2×C4×C13C22×D412yes—
161C2×Dic13—24no—
162C2×Dic13—24no—
163C2×Dic13—44no—
164C2×Dic13—44no—
165Dic26—44no—
166Dic26—82no—
167Dic26—84no—
168#1055—44no—
169#544—134no—
170#544—264no—
171#544—262no—
172C2×C4⋊Q8—262no—
173C2×#125—262no—
174C2×C22⋊Q8—132no—
175C2×C22⋊Q8—261no—
176C2×#117—261no—
177C22×C4⋊C4—21no—
178C22×C4⋊C4C2×D1311yescharacteristic
179C22×C4⋊C4C2×D1311yescharacteristic
180#483—138no—
181#483—264no—
182C2×#106—262no—
183C2×#103—262no—
184C2×C22⋊C8—132no—
185#398—22no—
186#398C2×D1314yes—
187C2×#95—21no—
188C2×#95C2×D1311yescharacteristic
189#328—138no—
190#324—134no—
191C22×C13—24no—
192C22×C13—24no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13#44812yes—
198C22×C13#44812yes—
199C22×C13#45612yes—
200C22×C13#45812yes—
201C22×C13C2×#12011yescharacteristic
202C22×C13C22×SD1611yescharacteristic
203C22×C13C2×#13711yescharacteristic
204C4×C13—24no—
205C4×C13—22no—
206C4×C13—22no—
207C4×C13—44no—
208C4×C13—42no—
209C4×C13—82no—
210Dic13—44no—
211Dic13—44no—
212C22×Q8—132no—
213C22×Q8—261no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4C22⋊D1311yescharacteristic
217C23×C4C22⋊D1311yescharacteristic
218C23×C4C22×D1311yescharacteristic
219C22×C8—262no—
220C4⋊Q8—268no—
221C4⋊Q8—268no—
222#125—268no—
223#125—268no—
224C22⋊Q8—134no—
225C22⋊Q8—134no—
226C22⋊Q8—264no—
227C22⋊Q8—262no—
228C22⋊Q8—262no—
229C22⋊Q8—264no—
230#117—264no—
231#117—264no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—24no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—44no—
239C2×C4⋊C4—132no—
240C2×C4⋊C4—261no—
241C2×C4⋊C4—261no—
242C2×C4⋊C4—261no—
243C2×C4⋊C4—262no—
244C2×C4⋊C4—262no—
245C2×C4⋊C4C22⋊D1312yes—
246C2×C4⋊C4C22×D1312yes—
247C2×C4⋊C4C22×D1312yes—
248C2×C22⋊C4—262no—
249C2×C42—262no—
250#106—268no—
251#103—268no—
252C22⋊C8—134no—
253C22⋊C8—262no—
254#95—24no—
255#95—21no—
256#95C22×D1312yes—
257C2×C13—21no—
258C2×C13—21no—
259C2×C13—22no—
260C2×C13#161114yescomplemented
261C2×C13C2×#44811yescharacteristic
262C2×C13C2×#45611yescharacteristic
263C2×C13C2×#45811yescharacteristic
264C24C2×C22⋊D1311yescharacteristic
265C2×Q8—134no—
266C2×Q8—264no—
267C2×Q8—262no—
268C2×Q8—524no—
269C2×Q8—1042no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—24no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—42no—
286C22×C4—262no—
287C22×C4—262no—
288C22×C4#610514yes—
289C22×C4D4×D1312yes—
290C22×C4D4×D1312yes—
291C22×C4C2×C22⋊D1312yes—
292C22×C4C2×C22⋊D1312yes—
293C22×C4C2×C22⋊D1311yescharacteristic
294C22×C4C23×D1311yescharacteristic
295C2×C8—264no—
296C2×C8—524no—
297C4⋊C4—24no—
298C4⋊C4—24no—
299C4⋊C4—24no—
300C4⋊C4—48no—
301C4⋊C4—42no—
302C4⋊C4—134no—
303C4⋊C4—264no—
304C4⋊C4—264no—
305C4⋊C4—264no—
306C4⋊C4—268no—
307C4⋊C4—262no—
308C4⋊C4—264no—
309C4⋊C4—264no—
310C22⋊C4—264no—
311C22⋊C4—264no—
312C42—268no—
313C13C2×#161111yescharacteristic, complemented, Sylow
314C23—22no—
315C23—22no—
316C23C2×#610512yes—
317C23#8819111yescharacteristic
318C23#8819111yescharacteristic
319C23#8820512yes—
320C23C22×C22⋊D1311yescharacteristic
321Q8—524no—
322Q8—1042no—
323Q8—1044no—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—24no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—24no—
330C2×C4—22no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—48no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—264no—
346C2×C4—264no—
347C2×C4—524no—
348C2×C4—524no—
349C2×C4C2×#610514yes—
350C2×C4#8819112yes—
351C2×C4C2×D4×D1312yes—
352C8—524no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—24no—
358C22—24no—
359C22#1171870112yes—
360C22#1171870112yes—
361C22#1171871412yes—
362C22#1171875612yes—
363C22C22×#610511yescharacteristic
364C22C2×#8819111yescharacteristic
365C22C2×#8820511yescharacteristic
366C4—22no—
367C4—22no—
368C4—24no—
369C4—44no—
370C4—42no—
371C4—82no—
372C4—524no—
373C4—524no—
374C2—21no—
375C2—22no—
376C2—21no—
377C2#1311384314yesdirect product factor
378C2C2×#1171870111yescharacteristic
379C2C2×#1171875611yescharacteristic
380C2C2×#1171871411yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#398C2
socleC23×C13#120
prime radicalC24×C13C2×D4
hypercenterC2×#398D13
hypocenterC13C2×#1611
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
3. #13113843C2direct (N × H)
260. C2×C13#1611semidirect
313. C13C2×#1611semidirect
377. C2#13113843direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192052
C2×#117186322
#131138432
C2×#117180442
C2×#117181202
C2×C13×#3982
C2×#161113