Finite Group Databasebeta

← C2×#13067609 #14725902

Subgroups — C2×#13067609 #14725902

Order 2816.

1136 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1136 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×#10623014C211yesmaximal, characteristic
2C2×#10622334C212yesmaximal, complemented
3C2×#10622566C211yesmaximal, characteristic
4#13067609C218yesmaximal, direct product factor
5C2×#10622105C212yesmaximal, complemented
6C2×C11×#323C211yesmaximal, characteristic
7C22×C11×C22⋊C4C2211yescharacteristic
8C22×C22⋊Dic11—21no—
9C22×C22⋊Dic11—21no—
10C22×C4⋊Dic11C2211yescharacteristic
11C2×#66977—21no—
12C2×#66977C2212yes—
13#10623014—22no—
14#10623014—24no—
15#10623014C2214yes—
16C2×#66931—22no—
17C2×#66931—22no—
18C2×C11×C22⋊C8C2212yes—
19C2×C11⋊#95—21no—
20C2×C11⋊#95C2211yescharacteristic
21C2×#66881—22no—
22C2×#66880—22no—
23#10622566—22no—
24#10622566C2214yes—
25#10622334—24no—
26#10622334C2218yescomplemented
27C11×#323C2214yes—
28#10622105C2218yescomplemented
29C25×C11D411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C23×C4×C11C2311yescharacteristic
32C23×Dic11—21no—
33C23×Dic11—21no—
34C23×Dic11—21no—
35C23×Dic11—21no—
36C22×Dic22—21no—
37C22×Dic22D412yes—
38C22×C8×C11—22no—
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4D412yes—
42C2×C11×C22⋊C4C2312yes—
43C2×C22⋊Dic11—22no—
44C2×C22⋊Dic11—24no—
45C2×C22⋊Dic11—24no—
46C2×C22⋊Dic11—22no—
47C2×C22⋊Dic11—24no—
48C2×C22⋊Dic11—44no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—22no—
51C2×C4⋊Dic11—22no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11D412yes—
54C2×C4⋊Dic11C2312yes—
55#66977—24no—
56#66977—22no—
57#66977—22no—
58#66977—24no—
59#66977D414yes—
60#66977C2314yes—
61C2×Dic11⋊C4—22no—
62C2×Dic11⋊C4—22no—
63#66931—28no—
64#66931—28no—
65#66931—28no—
66#66931—28no—
67C11×C22⋊C8—22no—
68C11×C22⋊C8C2314yes—
69C11⋊#95—24no—
70C11⋊#95—21no—
71C11⋊#95C2312yes—
72#66881—28no—
73#66880—28no—
74C2×#1608—111nomaximal, Sylow
75C24×C11—21no—
76C24×C11—21no—
77C24×C11—22no—
78C24×C11—42no—
79C24×C11—42no—
80C24×C11SD1614yes—
81C24×C11C2×D411yescharacteristic
82C24×C11C2×D412yes—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—42no—
86C22×C4×C11—42no—
87C22×C4×C11C2×D412yes—
88C22×C4×C11C2×D412yes—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2411yescharacteristic
92C22×Dic11—24no—
93C22×Dic11—24no—
94C22×Dic11—22no—
95C22×Dic11—22no—
96C22×Dic11—22no—
97C22×Dic11—22no—
98C22×Dic11—42no—
99C22×Dic11—42no—
100C22×Dic11—41no—
101C22×Dic11—41no—
102C22×Dic11—42no—
103C22×Dic11—42no—
104C22×Dic11—42no—
105C22×Dic11—82no—
106C22×Dic11—82no—
107C2×Dic22—24no—
108C2×Dic22—22no—
109C2×Dic22—44no—
110C2×Dic22—82no—
111C2×Dic22C2×D414yes—
112C2×C8×C11—24no—
113C2×C8×C11—44no—
114C11×C22⋊C4—24no—
115C11×C22⋊C4—24no—
116C22⋊Dic11—28no—
117C22⋊Dic11—24no—
118C22⋊Dic11—24no—
119C22⋊Dic11—48no—
120C4⋊Dic11—24no—
121C4⋊Dic11—22no—
122C4⋊Dic11—24no—
123C4⋊Dic11—42no—
124C4⋊Dic11C2×D414yes—
125Dic11⋊C4—28no—
126Dic11⋊C4—24no—
127Dic11⋊C4—24no—
128C2×#543—111no—
129C2×#483—112no—
130C2×#397—111no—
131#1608—118no—
132C2×#328—112no—
133C2×#323D1111yescharacteristic
134C23×C11—22no—
135C23×C11—22no—
136C23×C11—22no—
137C23×C11—24no—
138C23×C11—22no—
139C23×C11—24no—
140C23×C11—48no—
141C23×C11—42no—
142C23×C11—42no—
143C23×C11—42no—
144C23×C11—42no—
145C23×C11—84no—
146C23×C11—81no—
147C23×C11—81no—
148C23×C11#12011yescharacteristic
149C23×C11#12011yescharacteristic
150C23×C11C2×SD1612yes—
151C23×C11C2×SD1614yes—
152C23×C11#13712yes—
153C23×C11C22×D411yescharacteristic
154C2×C4×C11—24no—
155C2×C4×C11—22no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—81no—
162C2×C4×C11#12012yes—
163C2×C4×C11C22×D412yes—
164C2×Dic11—24no—
165C2×Dic11—24no—
166C2×Dic11—44no—
167C2×Dic11—44no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172C2×Dic11—42no—
173C2×Dic11—42no—
174C2×Dic11—84no—
175C2×Dic11—84no—
176C2×Dic11—84no—
177C2×Dic11—82no—
178C2×Dic11—82no—
179Dic22—44no—
180Dic22—82no—
181Dic22—84no—
182C8×C11—44no—
183#543—114no—
184#543—224no—
185#543—222no—
186C2×C22⋊Q8—112no—
187C2×C22⋊Q8—222no—
188C2×C22⋊Q8—222no—
189C2×C22⋊Q8—221no—
190C22×C4⋊C4—111no—
191C22×C22⋊C4—221no—
192C22×C22⋊C4—221no—
193C22×C22⋊C4C2×D1111yescharacteristic
194#483—118no—
195#483—224no—
196C2×#106—222no—
197C2×#103—222no—
198C2×C22⋊C8C2×D1112yes—
199#397—114no—
200#397—222no—
201C2×#95—111no—
202C2×#95—221no—
203#328—118no—
204#323C2×D1114yes—
205C22×C11—24no—
206C22×C11—24no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—24no—
212C22×C11—44no—
213C22×C11—48no—
214C22×C11—42no—
215C22×C11—42no—
216C22×C11—82no—
217C22×C11—84no—
218C22×C11#44812yes—
219C22×C11#44812yes—
220C22×C11#45512yes—
221C22×C11#45812yes—
222C22×C11C2×#12011yescharacteristic
223C22×C11C22×SD1611yescharacteristic
224C22×C11C2×#13711yescharacteristic
225C4×C11—22no—
226C4×C11—22no—
227C4×C11—42no—
228Dic11—44no—
229Dic11—44no—
230Dic11—82no—
231Dic11—82no—
232C25D4411yescharacteristic
233C22×Q8—112no—
234C22×Q8—221no—
235C23×C4—221no—
236C23×C4—221no—
237C23×C4—221no—
238C23×C4—221no—
239C23×C4D4411yescharacteristic
240C23×C4C22×D1111yescharacteristic
241C22×C8—22no—
242C22⋊Q8—114no—
243C22⋊Q8—114no—
244C22⋊Q8—228no—
245C22⋊Q8—228no—
246C22⋊Q8—228no—
247C22⋊Q8—228no—
248C22⋊Q8—224no—
249C22⋊Q8—222no—
250C22⋊Q8—224no—
251C22⋊Q8—222no—
252C2×C4⋊C4—112no—
253C2×C4⋊C4—112no—
254C2×C4⋊C4—222no—
255C2×C4⋊C4—221no—
256C2×C4⋊C4—222no—
257C2×C4⋊C4—222no—
258C2×C4⋊C4—222no—
259C2×C4⋊C4—221no—
260C2×C22⋊C4—22no—
261C2×C22⋊C4—22no—
262C2×C22⋊C4—222no—
263C2×C22⋊C4—224no—
264C2×C22⋊C4—222no—
265C2×C22⋊C4—224no—
266C2×C22⋊C4—224no—
267C2×C22⋊C4—444no—
268C2×C22⋊C4D4412yes—
269C2×C22⋊C4C22×D1112yes—
270#106—228no—
271#103—228no—
272C22⋊C8—22no—
273C22⋊C8C22×D1114yes—
274#95—112no—
275#95—221no—
276#95—224no—
277C2×C11—21no—
278C2×C11—21no—
279C2×C11—22no—
280C2×C11—44no—
281C2×C11#160814yescomplemented
282C2×C11C2×#44811yescharacteristic
283C2×C11C2×#45511yescharacteristic
284C2×C11C2×#45811yescharacteristic
285C24—21no—
286C24—21no—
287C24—22no—
288C24—42no—
289C24—42no—
290C24#431414yes—
291C24C2×D4411yescharacteristic
292C24C2×D4412yes—
293C2×Q8—114no—
294C2×Q8—224no—
295C2×Q8—222no—
296C2×Q8—444no—
297C2×Q8—882no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—222no—
303C22×C4—222no—
304C22×C4—224no—
305C22×C4—224no—
306C22×C4—222no—
307C22×C4—222no—
308C22×C4—442no—
309C22×C4—442no—
310C22×C4—441no—
311C22×C4—441no—
312C22×C4—442no—
313C22×C4—442no—
314C22×C4—442no—
315C22×C4—882no—
316C22×C4—882no—
317C22×C4C2×D4412yes—
318C22×C4C2×D4411yescharacteristic
319C22×C4D4×D1112yes—
320C22×C4D4×D1112yes—
321C22×C4C23×D1111yescharacteristic
322C2×C8—24no—
323C2×C8—44no—
324C4⋊C4—114no—
325C4⋊C4—228no—
326C4⋊C4—224no—
327C4⋊C4—222no—
328C4⋊C4—224no—
329C4⋊C4—224no—
330C4⋊C4—224no—
331C4⋊C4—442no—
332C22⋊C4—24no—
333C22⋊C4—24no—
334C22⋊C4—228no—
335C22⋊C4—224no—
336C22⋊C4—224no—
337C22⋊C4—448no—
338C11C2×#160811yescharacteristic, complemented, Sylow
339C23—22no—
340C23—22no—
341C23—22no—
342C23—24no—
343C23—22no—
344C23—24no—
345C23—48no—
346C23—42no—
347C23—42no—
348C23—42no—
349C23—42no—
350C23—84no—
351C23—81no—
352C23—81no—
353C23#6693511yescharacteristic
354C23#6693511yescharacteristic
355C23C2×#431412yes—
356C23C2×#431414yes—
357C23#6696212yes—
358C23C22×D4411yescharacteristic
359Q8—444no—
360Q8—882no—
361Q8—884no—
362C2×C4—24no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—81no—
370C2×C4—224no—
371C2×C4—224no—
372C2×C4—444no—
373C2×C4—444no—
374C2×C4—442no—
375C2×C4—442no—
376C2×C4—442no—
377C2×C4—442no—
378C2×C4—442no—
379C2×C4—442no—
380C2×C4—884no—
381C2×C4—884no—
382C2×C4—884no—
383C2×C4—882no—
384C2×C4—882no—
385C2×C4#6693512yes—
386C2×C4C2×D4×D1112yes—
387C8—44no—
388C22—24no—
389C22—24no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—24no—
395C22—44no—
396C22—48no—
397C22—42no—
398C22—42no—
399C22—82no—
400C22—84no—
401C22#1062235112yes—
402C22#1062235112yes—
403C22#1062235512yes—
404C22#1062235912yes—
405C22C2×#6693511yescharacteristic
406C22C22×#431411yescharacteristic
407C22C2×#6696211yescharacteristic
408C4—22no—
409C4—22no—
410C4—42no—
411C4—444no—
412C4—444no—
413C4—882no—
414C4—882no—
415C2—21no—
416C2—21no—
417C2—22no—
418C2—44no—
419C2#1306760914yesdirect product factor
420C2C2×#1062235111yescharacteristic
421C2C2×#1062235911yescharacteristic
422C2C2×#1062235511yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#323C2
socleC23×C11#120
prime radicalC25×C11D4
hypercenterC2×#323D11
hypocenterC11C2×#1608
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. C2×#10622334C2semidirect
4. #13067609C2direct (N × H)
5. C2×#10622105C2semidirect
26. #10622334C22semidirect
28. #10622105C22semidirect
281. C2×C11#1608semidirect
338. C11C2×#1608semidirect
419. C2#13067609direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230142
C2×#106223342
C2×#106225662
#130676092
C2×#106221052
C2×C11×#3232
C2×#160811