Finite Group Databasebeta

← C2×#13067584 #14725944

Subgroups — C2×#13067584 #14725944

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×#10622840C212yesmaximal, complemented
3#13067584C218yesmaximal, direct product factor
4C2×#10622089C212yesmaximal, complemented
5C2×#10622166C211yesmaximal, characteristic, complemented
6C2×C11×#395C211yesmaximal, characteristic, complemented
7C23×Q8×C11C2211yescharacteristic
8C22×#4339—21no—
9C22×C11×C4⋊C4—21no—
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×#4325—22no—
12C2×#66983—21no—
13C2×#66983C2212yes—
14#10623041—22no—
15#10623041—24no—
16#10623041C2214yes—
17C2×#66950—22no—
18C2×#66948—22no—
19C11×#395—22no—
20C11×#395C2214yescomplemented
21C2×C11×#95—21no—
22C2×C11×#95C2211yescharacteristic
23#10622840—24no—
24#10622840C2218yescomplemented
25C2×#66899—22no—
26C2×C22⋊(C11⋊C8)C2212yes—
27#10622166C2214yescomplemented
28#10622089C2218yescomplemented
29C22×Q8×C11—21no—
30C22×Q8×C11—22no—
31C22×Q8×C11—22no—
32C22×Q8×C11—44no—
33C22×Q8×C11C2312yes—
34C23×C4×C11—21no—
35C23×C4×C11—21no—
36C23×C4×C11D411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C22×C22⋊D11—22no—
40C2×#4339—24no—
41C2×#4339—24no—
42C2×#4339—44no—
43C2×#4339—44no—
44C22×D44—21no—
45C22×D44—21no—
46C22×D44D412yes—
47C22×C4×D11—22no—
48C22×Dic22—21no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—24no—
52C2×C11×C4⋊C4—44no—
53C2×C11×C4⋊C4D412yes—
54C2×C11×C4⋊C4C2312yes—
55C2×#4325—28no—
56C2×#4325—48no—
57#66983—24no—
58#66983—22no—
59#66983—22no—
60#66983—24no—
61#66983D414yes—
62#66983C2314yes—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11D412yes—
67C22×C11⋊C8—22no—
68#66950—28no—
69#66950—28no—
70#66948—28no—
71#66948—28no—
72C11×#95—24no—
73C11×#95—21no—
74C11×#95C2312yes—
75#66899—28no—
76C22⋊(C11⋊C8)—22no—
77C22⋊(C11⋊C8)C2314yes—
78C2×#1604—111nomaximal, Sylow
79C24×C11C2×D411yescharacteristic
80C23×D11—22no—
81C2×Q8×C11—28no—
82C2×Q8×C11—24no—
83C2×Q8×C11—44no—
84C2×Q8×C11—44no—
85C2×Q8×C11—44no—
86C2×Q8×C11—48no—
87C2×Q8×C11—42no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—22no—
91C22×C4×C11—24no—
92C22×C4×C11—24no—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11—42no—
98C22×C4×C11—42no—
99C22×C4×C11—42no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11SD1614yescomplemented
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2411yescharacteristic
111C2×C22⋊D11—24no—
112C2×C22⋊D11—24no—
113C2×C22⋊D11—44no—
114C2×C22⋊D11—44no—
115C22×Dic11—22no—
116#4339—48no—
117#4339—416no—
118#4339—48no—
119C2×D44—24no—
120C2×D44—24no—
121C2×D44—22no—
122C2×D44—44no—
123C2×D44—44no—
124C2×D44—82no—
125C2×D44C2×D414yes—
126C2×C4×D11—28no—
127C2×C4×D11—48no—
128C2×Dic22—24no—
129C2×Dic22—44no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—48no—
133#4325—416no—
134(C2×D11)⋊C4—28no—
135(C2×D11)⋊C4—24no—
136(C2×D11)⋊C4—24no—
137C4⋊Dic11—24no—
138C4⋊Dic11—22no—
139C4⋊Dic11C2×D414yes—
140C2×C11⋊C8—24no—
141C2×C11⋊C8—44no—
142C2×#537—111no—
143C2×#448—112no—
144C2×#395D1111yescharacteristic, complemented
145#1604—118no—
146C2×#327—112no—
147C2×#324—111no—
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—
159Q8×C11—28no—
160Q8×C11—48no—
161Q8×C11—44no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—24no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—24no—
168C2×C4×C11—24no—
169C2×C4×C11—22no—
170C2×C4×C11—42no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—48no—
175C2×C4×C11—42no—
176C2×C4×C11—44no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—44no—
181C2×C4×C11—42no—
182C2×C4×C11—81no—
183C2×C4×C11#12012yes—
184C2×C4×C11C2×SD1614yescomplemented
185C2×C4×C11C22×D412yes—
186C22⋊D11—44no—
187C22⋊D11—44no—
188C22⋊D11—48no—
189C2×Dic11—24no—
190C2×Dic11—44no—
191D44—44no—
192D44—48no—
193D44—82no—
194D44—84no—
195C4×D11—416no—
196Dic22—48no—
197C11⋊C8—44no—
198C22×#41—221no—
199C23×Q8C2×D1111yescharacteristic
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—21no—
209C22×C4⋊C4C2×D1111yescharacteristic
210#448—118no—
211#448—224no—
212C2×#103—222no—
213C2×C22⋊C8—112no—
214#395—22no—
215#395C2×D1114yescomplemented
216C2×#95—21no—
217C2×#95C2×D1111yescharacteristic
218#327—118no—
219#324—114no—
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—44no—
241C4×C11—44no—
242C4×C11—42no—
243Dic11—44no—
244C2×#41—224no—
245C2×#41—224no—
246C2×#41—444no—
247C2×#41—444no—
248C22×Q8—21no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—44no—
252C22×Q8—221no—
253C22×Q8C22×D1112yes—
254C22×D4—112no—
255C22×D4—221no—
256C22×D4—221no—
257C22×D4—222no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—222no—
261C23×C4C22⋊D1111yescharacteristic
262C23×C4C22⋊D1111yescharacteristic
263C23×C4C22×D1111yescharacteristic
264C2×SD16—228no—
265C2×SD16—448no—
266C22×C8—222no—
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—222no—
276#121—224no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—44no—
281C2×C4⋊C4—112no—
282C2×C4⋊C4—221no—
283C2×C4⋊C4C22⋊D1112yes—
284C2×C4⋊C4C22×D1112yes—
285C2×C22⋊C4—222no—
286C2×C22⋊C4—222no—
287#103—228no—
288C22⋊C8—114no—
289C22⋊C8—222no—
290#95—24no—
291#95—21no—
292#95C22×D1112yes—
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×C22⋊D1111yescharacteristic
303#41—448no—
304#41—4416no—
305#41—448no—
306C2×Q8—28no—
307C2×Q8—24no—
308C2×Q8—44no—
309C2×Q8—44no—
310C2×Q8—44no—
311C2×Q8—48no—
312C2×Q8—42no—
313C2×Q8—224no—
314C2×Q8—444no—
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—24no—
330C22×C4—24no—
331C22×C4—21no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—228no—
343C22×C4—222no—
344C22×C4—448no—
345C22×C4#432514yescomplemented
346C22×C4D4×D1112yes—
347C22×C4D4×D1112yes—
348C22×C4C2×C22⋊D1112yes—
349C22×C4C2×C22⋊D1112yes—
350C22×C4C2×C22⋊D1111yescharacteristic
351C22×C4C23×D1111yescharacteristic
352SD16—4416no—
353C2×C8—224no—
354C2×C8—444no—
355C4⋊C4—24no—
356C4⋊C4—24no—
357C4⋊C4—48no—
358C4⋊C4—114no—
359C4⋊C4—224no—
360C4⋊C4—222no—
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#6699011yescharacteristic
372C23#6699011yescharacteristic
373C23C2×#432512yes—
374C23#6700212yes—
375C23C22×C22⋊D1111yescharacteristic
376Q8—28no—
377Q8—44no—
378Q8—48no—
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—24no—
393C2×C4—24no—
394C2×C4—22no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—48no—
400C2×C4—42no—
401C2×C4—44no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—44no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—81no—
408C2×C4—224no—
409C2×C4—4416no—
410C2×C4—444no—
411C2×C4#6699012yes—
412C2×C4C2×#432514yescomplemented
413C2×C4C2×D4×D1112yes—
414C8—444no—
415C22—24no—
416C22—24no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—444no—
422C22—444no—
423C22—444no—
424C22—888no—
425C22#1062264512yes—
426C22#1062265912yes—
427C22#1062265912yes—
428C22#1062270812yes—
429C22C2×#6699011yescharacteristic
430C22C22×#432511yescharacteristic
431C22C2×#6700211yescharacteristic
432C4—24no—
433C4—22no—
434C4—22no—
435C4—44no—
436C4—44no—
437C4—42no—
438C4—444no—
439C2—21no—
440C2—21no—
441C2—22no—
442C2—884no—
443C2#1306758414yesdirect product factor
444C2C2×#1062265911yescharacteristic
445C2C2×#1062270811yescharacteristic
446C2C2×#1062264511yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#395C2
socleC23×C11#120
prime radicalC2×#10623041C2
hypercenterC2×#395D11
hypocenterC11C2×#1604
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
2. C2×#10622840C2semidirect
3. #13067584C2direct (N × H)
4. C2×#10622089C2semidirect
5. C2×#10622166C2semidirect
6. C2×C11×#395C2semidirect
20. C11×#395C22semidirect
24. #10622840C22semidirect
27. #10622166C22semidirect
28. #10622089C22semidirect
104. C22×C4×C11SD16semidirect
144. C2×#395D11semidirect
184. C2×C4×C11C2×SD16semidirect
215. #395C2×D11semidirect
296. C2×C11#1604semidirect
345. C22×C4#4325semidirect
364. C11C2×#1604semidirect
412. C2×C4C2×#4325semidirect
443. C2#13067584direct (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×#106228402
#130675842
C2×#106220892
C2×#106221662
C2×C11×#3952
C2×#160411