Finite Group Databasebeta

← C2×#13067587 #14725947

Subgroups — C2×#13067587 #14725947

Order 2816.

1480 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1480 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×#10623041C211yesmaximal, characteristic
2C2×#10622351C212yesmaximal, complemented
3C2×#10622592C211yesmaximal, characteristic, complemented
4#13067587C218yesmaximal, direct product factor
5C2×#10622108C212yesmaximal, complemented
6C2×C11×#324C211yesmaximal, characteristic, complemented
7C22×#4339—21no—
8C23×Dic22C2211yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C2×#66983—21no—
11C2×#66983C2212yes—
12C22×Dic11⋊C4—21no—
13C22×#4314—22no—
14#10623041—22no—
15#10623041—24no—
16#10623041C2214yes—
17C2×#66950—22no—
18C2×#66948—22no—
19C2×C11×C22⋊C8C2212yes—
20C2×C11⋊#95—21no—
21C2×C11⋊#95C2211yescharacteristic
22C2×#66880—22no—
23#10622592—22no—
24#10622592C2214yescomplemented
25#10622351—24no—
26#10622351C2218yescomplemented
27C11×#324C2214yescomplemented
28#10622108C2218yescomplemented
29C23×C4×C11D411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11—22no—
33C23×Dic11—21no—
34C23×Dic11—21no—
35C2×#4339—24no—
36C2×#4339—24no—
37C2×#4339—44no—
38C2×#4339—44no—
39C22×D44—21no—
40C22×D44—21no—
41C22×D44D412yes—
42C22×C4×D11—22no—
43C22×Dic22—22no—
44C22×Dic22—21no—
45C22×Dic22—22no—
46C22×Dic22—21no—
47C22×Dic22—44no—
48C22×Dic22C2312yes—
49C22×C8×C11—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4D412yes—
53C2×C11×C4⋊C4C2312yes—
54#66983—24no—
55#66983—22no—
56#66983—22no—
57#66983—24no—
58#66983D414yes—
59#66983C2314yes—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11D412yes—
64C2×Dic11⋊C4—24no—
65C2×Dic11⋊C4—44no—
66C2×#4314—28no—
67C2×#4314—48no—
68#66950—28no—
69#66950—28no—
70#66948—28no—
71#66948—28no—
72C11×C22⋊C8—22no—
73C11×C22⋊C8C2314yes—
74C11⋊#95—24no—
75C11⋊#95—21no—
76C11⋊#95C2312yes—
77#66880—28no—
78C2×#1604—111nomaximal, Sylow
79C24×C11C2×D411yescharacteristic
80C23×D11—22no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—22no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—42no—
87C22×C4×C11—42no—
88C22×C4×C11SD1614yescomplemented
89C22×C4×C11C2×D412yes—
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D412yes—
94C22×C4×C11C2411yescharacteristic
95C2×C22⋊D11—24no—
96C2×C22⋊D11—24no—
97C2×C22⋊D11—44no—
98C2×C22⋊D11—44no—
99C22×Dic11—24no—
100C22×Dic11—24no—
101C22×Dic11—22no—
102C22×Dic11—22no—
103C22×Dic11—22no—
104C22×Dic11—42no—
105C22×Dic11—42no—
106C22×Dic11—41no—
107C22×Dic11—41no—
108C22×Dic11—42no—
109#4339—48no—
110#4339—416no—
111#4339—48no—
112C2×D44—24no—
113C2×D44—24no—
114C2×D44—22no—
115C2×D44—44no—
116C2×D44—44no—
117C2×D44—82no—
118C2×D44C2×D414yes—
119C2×C4×D11—28no—
120C2×C4×D11—48no—
121C2×Dic22—28no—
122C2×Dic22—24no—
123C2×Dic22—24no—
124C2×Dic22—44no—
125C2×Dic22—44no—
126C2×Dic22—44no—
127C2×Dic22—48no—
128C2×Dic22—44no—
129C2×Dic22—42no—
130C2×C8×C11—24no—
131C2×C8×C11—44no—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—24no—
134(C2×D11)⋊C4—28no—
135(C2×D11)⋊C4—24no—
136(C2×D11)⋊C4—24no—
137C4⋊Dic11—24no—
138C4⋊Dic11—22no—
139C4⋊Dic11C2×D414yes—
140Dic11⋊C4—48no—
141#4314—416no—
142C2×#537—111no—
143C2×#448—112no—
144C2×#395—111no—
145#1604—118no—
146C2×#327—112no—
147C2×#324D1111yescharacteristic, complemented
148C23×C11—22no—
149C23×C11—22no—
150C23×C11#12011yescharacteristic
151C23×C11#12011yescharacteristic
152C23×C11C2×SD1612yes—
153C23×C11AGL(1,ℤ/8)12yes—
154C23×C11C22×D411yescharacteristic
155C22×D11—24no—
156C22×D11—44no—
157C22×D11—44no—
158C22×D11—44no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—24no—
162C2×C4×C11—24no—
163C2×C4×C11—24no—
164C2×C4×C11—22no—
165C2×C4×C11—41no—
166C2×C4×C11—42no—
167C2×C4×C11—41no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—81no—
171C2×C4×C11#12012yes—
172C2×C4×C11C2×SD1614yescomplemented
173C2×C4×C11C22×D412yes—
174C22⋊D11—44no—
175C22⋊D11—44no—
176C22⋊D11—48no—
177C2×Dic11—24no—
178C2×Dic11—24no—
179C2×Dic11—24no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182C2×Dic11—44no—
183C2×Dic11—48no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—44no—
187C2×Dic11—44no—
188D44—44no—
189D44—48no—
190D44—82no—
191D44—84no—
192C4×D11—416no—
193Dic22—28no—
194Dic22—48no—
195Dic22—44no—
196Dic22—48no—
197C8×C11—44no—
198C22×#41—221no—
199C23×Q8—111no—
200C22×SD16—222no—
201#537—114no—
202#537—224no—
203#537—222no—
204C2×C22⋊Q8—222no—
205C2×#121—112no—
206C2×#121—222no—
207C2×#121—221no—
208C22×C4⋊C4—221no—
209C22×C4⋊C4C2×D1111yescharacteristic
210#448—118no—
211#448—224no—
212C2×#103—222no—
213C2×C22⋊C8C2×D1112yes—
214#395—114no—
215#395—222no—
216C2×#95—111no—
217C2×#95—221no—
218#327—118no—
219#324C2×D1114yescomplemented
220C22×C11—24no—
221C22×C11—24no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11#45012yes—
227C22×C11#45012yes—
228C22×C11#45612yes—
229C22×C11B(4,𝔽2)12yes—
230C22×C11C2×#12011yescharacteristic
231C22×C11C22×SD1611yescharacteristic
232C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
233C2×D11—44no—
234C2×D11—44no—
235C2×D11—44no—
236C2×D11—88no—
237C4×C11—24no—
238C4×C11—22no—
239C4×C11—22no—
240C4×C11—42no—
241Dic11—44no—
242Dic11—44no—
243Dic11—44no—
244C2×#41—224no—
245C2×#41—224no—
246C2×#41—444no—
247C2×#41—444no—
248C22×Q8—112no—
249C22×Q8—221no—
250C22×Q8—221no—
251C22×Q8—222no—
252C22×Q8—222no—
253C22×Q8—444no—
254C22×D4—112no—
255C22×D4—221no—
256C22×D4—221no—
257C22×D4—222no—
258C23×C4—222no—
259C23×C4—221no—
260C23×C4—221no—
261C23×C4D4411yescharacteristic
262C23×C4D4411yescharacteristic
263C23×C4C22×D1111yescharacteristic
264C2×SD16—228no—
265C2×SD16—448no—
266C22×C8—22no—
267C22⋊Q8—228no—
268C22⋊Q8—228no—
269#121—114no—
270#121—114no—
271#121—228no—
272#121—228no—
273#121—224no—
274#121—222no—
275#121—224no—
276#121—222no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—112no—
280C2×C4⋊C4—221no—
281C2×C4⋊C4—224no—
282C2×C4⋊C4—444no—
283C2×C4⋊C4D4412yes—
284C2×C4⋊C4C22×D1112yes—
285C2×C22⋊C4—222no—
286C2×C22⋊C4—222no—
287#103—228no—
288C22⋊C8—22no—
289C22⋊C8C22×D1114yes—
290#95—112no—
291#95—221no—
292#95—224no—
293C2×C11—21no—
294C2×C11—21no—
295C2×C11—22no—
296C2×C11#160414yescomplemented
297C2×C11C2×#45011yescharacteristic
298C2×C11C2×#45611yescharacteristic
299C2×C11C2×B(4,𝔽2)11yescharacteristic
300D11—84no—
301C24—222no—
302C24C2×D4411yescharacteristic
303#41—448no—
304#41—4416no—
305#41—448no—
306C2×Q8—224no—
307C2×Q8—228no—
308C2×Q8—224no—
309C2×Q8—444no—
310C2×Q8—444no—
311C2×Q8—444no—
312C2×Q8—444no—
313C2×Q8—448no—
314C2×Q8—442no—
315C2×D4—114no—
316C2×D4—224no—
317C2×D4—224no—
318C2×D4—224no—
319C2×D4—224no—
320C2×D4—222no—
321C2×D4—444no—
322C2×D4—444no—
323C2×D4—444no—
324C2×D4—444no—
325C2×D4—882no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—22no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4—228no—
334C22×C4—224no—
335C22×C4—224no—
336C22×C4—222no—
337C22×C4—222no—
338C22×C4—222no—
339C22×C4—448no—
340C22×C4—442no—
341C22×C4—442no—
342C22×C4—441no—
343C22×C4—441no—
344C22×C4—442no—
345C22×C4#431414yescomplemented
346C22×C4C2×D4412yes—
347C22×C4C2×D4412yes—
348C22×C4C2×D4411yescharacteristic
349C22×C4D4×D1112yes—
350C22×C4D4×D1112yes—
351C22×C4C23×D1111yescharacteristic
352SD16—4416no—
353C2×C8—24no—
354C2×C8—44no—
355C4⋊C4—24no—
356C4⋊C4—24no—
357C4⋊C4—114no—
358C4⋊C4—224no—
359C4⋊C4—222no—
360C4⋊C4—448no—
361C22⋊C4—228no—
362C22⋊C4—224no—
363C22⋊C4—224no—
364C11C2×#160411yescharacteristic, complemented, Sylow
365C23—22no—
366C23—22no—
367C23—224no—
368C23—444no—
369C23—444no—
370C23—444no—
371C23#6693511yescharacteristic
372C23#6693511yescharacteristic
373C23C2×#431412yes—
374C23#6696112yes—
375C23C22×D4411yescharacteristic
376Q8—228no—
377Q8—444no—
378Q8—448no—
379Q8—448no—
380D4—444no—
381D4—448no—
382D4—444no—
383D4—444no—
384D4—448no—
385D4—882no—
386D4—884no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—24no—
390C2×C4—24no—
391C2×C4—24no—
392C2×C4—22no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—81no—
399C2×C4—224no—
400C2×C4—224no—
401C2×C4—224no—
402C2×C4—4416no—
403C2×C4—442no—
404C2×C4—442no—
405C2×C4—444no—
406C2×C4—448no—
407C2×C4—442no—
408C2×C4—442no—
409C2×C4—444no—
410C2×C4—444no—
411C2×C4#6693512yes—
412C2×C4C2×#431414yescomplemented
413C2×C4C2×D4×D1112yes—
414C8—44no—
415C22—24no—
416C22—24no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—444no—
422C22—444no—
423C22—444no—
424C22—888no—
425C22#1062234412yes—
426C22#1062234412yes—
427C22#1062235412yes—
428C22#1062236512yes—
429C22C2×#6693511yescharacteristic
430C22C22×#431411yescharacteristic
431C22C2×#6696111yescharacteristic
432C4—24no—
433C4—22no—
434C4—22no—
435C4—42no—
436C4—444no—
437C4—444no—
438C4—444no—
439C2—21no—
440C2—21no—
441C2—22no—
442C2—884no—
443C2#1306758714yesdirect product factor
444C2C2×#1062234411yescharacteristic
445C2C2×#1062236511yescharacteristic
446C2C2×#1062235411yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#324C2
socleC23×C11#120
prime radicalC2×#10623041C2
hypercenterC2×#324D11
hypocenterC11C2×#1604
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. C2×#10622351C2semidirect
3. C2×#10622592C2semidirect
4. #13067587C2direct (N × H)
5. C2×#10622108C2semidirect
6. C2×C11×#324C2semidirect
24. #10622592C22semidirect
26. #10622351C22semidirect
27. C11×#324C22semidirect
28. #10622108C22semidirect
88. C22×C4×C11SD16semidirect
147. C2×#324D11semidirect
172. C2×C4×C11C2×SD16semidirect
219. #324C2×D11semidirect
296. C2×C11#1604semidirect
345. C22×C4#4314semidirect
364. C11C2×#1604semidirect
412. C2×C4C2×#4314semidirect
443. C2#13067587direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230412
C2×#106223512
C2×#106225922
#130675872
C2×#106221082
C2×C11×#3242
C2×#160411