Finite Group Databasebeta

← C2×#13067555 #14725950

Subgroups — C2×#13067555 #14725950

Order 2816.

1372 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1372 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×#10623031C211yesmaximal, characteristic, complemented
2C2×#10622831C212yesmaximal
3#13067555C218yesmaximal, direct product factor
4C2×#10622090C212yesmaximal, complemented
5C2×#10622166C211yesmaximal, characteristic, complemented
6C2×C11×#394C211yesmaximal, characteristic
7C23×D4×C11C2211yescharacteristic
8C22×C11×C4⋊C4C2211yescharacteristic
9C22×C11×C22⋊C4—21no—
10C22×C11×C22⋊C4—21no—
11C22×#4324—22no—
12C2×#66979—21no—
13C2×#66977—21no—
14C2×#66977C2212yes—
15#10623031—22no—
16#10623031—24no—
17#10623031C2214yescomplemented
18C2×#66943—22no—
19C2×#66941—22no—
20C11×#394—22no—
21C11×#394C2214yes—
22C2×C11×#95C2211yescharacteristic
23#10622831—24no—
24#10622831C2218yes—
25C2×#66896—22no—
26C2×C22⋊(C11⋊C8)C2212yes—
27#10622166C2214yescomplemented
28#10622090C2218yescomplemented
29C25×C11—21no—
30C22×D4×C11—22no—
31C22×D4×C11—22no—
32C22×D4×C11—21no—
33C22×D4×C11—44no—
34C22×D4×C11C2312yes—
35C23×C4×C11—21no—
36C23×C4×C11D411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C22×Dic22—21no—
40C22×Dic22D412yes—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4D412yes—
44C2×C11×C4⋊C4C2312yes—
45C2×C11×C22⋊C4—24no—
46C2×C11×C22⋊C4—24no—
47C2×C11×C22⋊C4—44no—
48C2×C11×C22⋊C4—44no—
49C2×C22⋊Dic11—22no—
50C2×#4324—28no—
51C2×#4324—48no—
52#66979—24no—
53#66979—24no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11D412yes—
58#66977—24no—
59#66977—22no—
60#66977—22no—
61#66977—24no—
62#66977D414yes—
63#66977C2314yes—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—22no—
66C2×C4×Dic11—22no—
67C22×C11⋊C8—22no—
68#66943—28no—
69#66943—28no—
70#66941—28no—
71#66941—28no—
72C11×#95—21no—
73C11×#95C2312yes—
74#66896—28no—
75C22⋊(C11⋊C8)—22no—
76C22⋊(C11⋊C8)C2314yes—
77C2×#1599—111nomaximal, Sylow
78C24×C11—24no—
79C24×C11—22no—
80C24×C11—42no—
81C24×C11—42no—
82C24×C11—42no—
83C24×C11—41no—
84C24×C11—41no—
85C24×C11—42no—
86C24×C11—42no—
87C24×C11C2×D411yescharacteristic
88C2×D4×C11—28no—
89C2×D4×C11—24no—
90C2×D4×C11—44no—
91C2×D4×C11—44no—
92C2×D4×C11—48no—
93C2×D4×C11—44no—
94C2×D4×C11—42no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—42no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11SD1614yescomplemented
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2411yescharacteristic
113C22×Dic11—22no—
114C22×Dic11—22no—
115C2×Dic22—24no—
116C2×Dic22—22no—
117C2×Dic22—44no—
118C2×Dic22—82no—
119C2×Dic22C2×D414yes—
120C11×C4⋊C4—24no—
121C11×C4⋊C4—24no—
122C11×C22⋊C4—48no—
123C11×C22⋊C4—48no—
124C22⋊Dic11—24no—
125C22⋊Dic11—24no—
126#4324—416no—
127C4⋊Dic11—24no—
128C4⋊Dic11—24no—
129C4⋊Dic11—24no—
130C4⋊Dic11—22no—
131C4⋊Dic11C2×D414yes—
132Dic11⋊C4—28no—
133Dic11⋊C4—24no—
134Dic11⋊C4—24no—
135C4×Dic11—28no—
136C2×C11⋊C8—24no—
137C2×C11⋊C8—44no—
138C2×#544—111no—
139C2×#450—112no—
140C2×#394D1111yescharacteristic
141#1599—118no—
142C2×#328—112no—
143C2×#324—111no—
144C23×C11—22no—
145C23×C11—22no—
146C23×C11—24no—
147C23×C11—42no—
148C23×C11—44no—
149C23×C11—48no—
150C23×C11—48no—
151C23×C11—42no—
152C23×C11—42no—
153C23×C11—42no—
154C23×C11—42no—
155C23×C11—42no—
156C23×C11—44no—
157C23×C11—84no—
158C23×C11—84no—
159C23×C11—82no—
160C23×C11—82no—
161C23×C11—82no—
162C23×C11—82no—
163C23×C11#12011yescharacteristic
164C23×C11#12011yescharacteristic
165C23×C11C2×SD1612yes—
166C23×C11#13712yes—
167C23×C11C22×D411yescharacteristic
168D4×C11—28no—
169D4×C11—48no—
170D4×C11—44no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11—22no—
177C2×C4×C11—42no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—81no—
186C2×C4×C11—84no—
187C2×C4×C11#12012yes—
188C2×C4×C11C2×SD1614yescomplemented
189C2×C4×C11C22×D412yes—
190C2×Dic11—24no—
191C2×Dic11—24no—
192C2×Dic11—44no—
193C2×Dic11—44no—
194Dic22—44no—
195Dic22—82no—
196Dic22—84no—
197C11⋊C8—44no—
198C23×D4C2×D1111yescharacteristic
199C22×SD16—222no—
200#544—114no—
201#544—224no—
202#544—222no—
203C2×C4⋊Q8—222no—
204C2×#125—222no—
205C2×C22⋊Q8—112no—
206C2×C22⋊Q8—221no—
207C2×#117—221no—
208C22×C4⋊C4C2×D1111yescharacteristic
209C22×C22⋊C4—21no—
210C22×C22⋊C4—21no—
211#450—118no—
212#450—224no—
213C2×#102—222no—
214C2×C22⋊C8—112no—
215#394—22no—
216#394C2×D1114yes—
217C2×#95C2×D1111yescharacteristic
218#328—118no—
219#324—114no—
220C22×C11—24no—
221C22×C11—24no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—44no—
227C22×C11—44no—
228C22×C11—44no—
229C22×C11—82no—
230C22×C11—82no—
231C22×C11—88no—
232C22×C11—88no—
233C22×C11—82no—
234C22×C11—82no—
235C22×C11#44812yes—
236C22×C11#44812yes—
237C22×C11#45412yes—
238C22×C11B(4,𝔽2)12yes—
239C22×C11C2×#12011yescharacteristic
240C22×C11C22×SD1611yescharacteristic
241C22×C11C2×#13711yescharacteristic
242C4×C11—24no—
243C4×C11—22no—
244C4×C11—22no—
245C4×C11—42no—
246C4×C11—82no—
247Dic11—44no—
248Dic11—44no—
249C25—21no—
250C22×Q8—112no—
251C22×Q8—221no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—21no—
255C22×D4—44no—
256C22×D4C22×D1112yes—
257C23×C4—21no—
258C23×C4C22⋊D1111yescharacteristic
259C23×C4C22⋊D1111yescharacteristic
260C23×C4C22×D1111yescharacteristic
261C2×SD16—228no—
262C2×SD16—448no—
263C22×C8—222no—
264C4⋊Q8—228no—
265C4⋊Q8—228no—
266#125—228no—
267#125—228no—
268C22⋊Q8—114no—
269C22⋊Q8—114no—
270C22⋊Q8—224no—
271C22⋊Q8—222no—
272C22⋊Q8—222no—
273C22⋊Q8—224no—
274#117—224no—
275#117—224no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—112no—
279C2×C4⋊C4—221no—
280C2×C4⋊C4—221no—
281C2×C4⋊C4—221no—
282C2×C4⋊C4—222no—
283C2×C4⋊C4—222no—
284C2×C4⋊C4C22⋊D1112yes—
285C2×C4⋊C4C22×D1112yes—
286C2×C22⋊C4—24no—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—44no—
289C2×C22⋊C4—44no—
290C2×C22⋊C4—222no—
291C2×C42—222no—
292#102—228no—
293C22⋊C8—114no—
294C22⋊C8—222no—
295#95—21no—
296#95C22×D1112yes—
297C2×C11—21no—
298C2×C11—21no—
299C2×C11—22no—
300C2×C11—84no—
301C2×C11#159914yescomplemented
302C2×C11C2×#44811yescharacteristic
303C2×C11C2×#45411yescharacteristic
304C2×C11C2×B(4,𝔽2)11yescharacteristic
305C24—24no—
306C24—22no—
307C24—42no—
308C24—42no—
309C24—42no—
310C24—42no—
311C24—41no—
312C24—41no—
313C24—42no—
314C24C2×C22⋊D1111yescharacteristic
315C2×Q8—114no—
316C2×Q8—224no—
317C2×Q8—222no—
318C2×Q8—444no—
319C2×Q8—882no—
320C2×D4—28no—
321C2×D4—24no—
322C2×D4—44no—
323C2×D4—44no—
324C2×D4—48no—
325C2×D4—44no—
326C2×D4—42no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—22no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—22no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—222no—
339C22×C4—222no—
340C22×C4#432414yescomplemented
341C22×C4D4×D1112yes—
342C22×C4D4×D1112yes—
343C22×C4C2×C22⋊D1112yes—
344C22×C4C2×C22⋊D1112yes—
345C22×C4C2×C22⋊D1111yescharacteristic
346C22×C4C23×D1111yescharacteristic
347SD16—4416no—
348C2×C8—224no—
349C2×C8—444no—
350C4⋊C4—24no—
351C4⋊C4—24no—
352C4⋊C4—114no—
353C4⋊C4—224no—
354C4⋊C4—224no—
355C4⋊C4—224no—
356C4⋊C4—228no—
357C4⋊C4—222no—
358C4⋊C4—224no—
359C4⋊C4—224no—
360C22⋊C4—48no—
361C22⋊C4—48no—
362C22⋊C4—224no—
363C22⋊C4—224no—
364C42—228no—
365C11C2×#159911yescharacteristic, complemented, Sylow
366C23—22no—
367C23—22no—
368C23—24no—
369C23—42no—
370C23—44no—
371C23—48no—
372C23—48no—
373C23—42no—
374C23—42no—
375C23—42no—
376C23—42no—
377C23—42no—
378C23—44no—
379C23—84no—
380C23—84no—
381C23—82no—
382C23—82no—
383C23—82no—
384C23—82no—
385C23C2×#432412yes—
386C23#6699011yescharacteristic
387C23#6699011yescharacteristic
388C23#6700412yes—
389C23C22×C22⋊D1111yescharacteristic
390Q8—444no—
391Q8—882no—
392Q8—884no—
393D4—28no—
394D4—44no—
395D4—48no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—22no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—81no—
411C2×C4—84no—
412C2×C4—224no—
413C2×C4—224no—
414C2×C4—444no—
415C2×C4—444no—
416C2×C4C2×#432414yescomplemented
417C2×C4#6699012yes—
418C2×C4C2×D4×D1112yes—
419C8—444no—
420C22—24no—
421C22—24no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—44no—
427C22—44no—
428C22—44no—
429C22—82no—
430C22—82no—
431C22—88no—
432C22—88no—
433C22—82no—
434C22—82no—
435C22#1062264512yes—
436C22#1062265312yes—
437C22#1062265312yes—
438C22#1062267512yes—
439C22C22×#432411yescharacteristic
440C22C2×#6699011yescharacteristic
441C22C2×#6700411yescharacteristic
442C4—24no—
443C4—22no—
444C4—22no—
445C4—42no—
446C4—82no—
447C4—444no—
448C4—444no—
449C2—21no—
450C2—21no—
451C2—22no—
452C2—84no—
453C2#1306755514yesdirect product factor
454C2C2×#1062265311yescharacteristic
455C2C2×#1062267511yescharacteristic
456C2C2×#1062264511yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#394C2
socleC23×C11#120
prime radicalC23×D4×C11C22
hypercenterC2×#394D11
hypocenterC11C2×#1599
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C2×#10623031C2semidirect
3. #13067555C2direct (N × H)
4. C2×#10622090C2semidirect
5. C2×#10622166C2semidirect
17. #10623031C22semidirect
27. #10622166C22semidirect
28. #10622090C22semidirect
106. C22×C4×C11SD16semidirect
188. C2×C4×C11C2×SD16semidirect
301. C2×C11#1599semidirect
340. C22×C4#4324semidirect
365. C11C2×#1599semidirect
416. C2×C4C2×#4324semidirect
453. C2#13067555direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230312
C2×#106228312
#130675552
C2×#106220902
C2×#106221662
C2×C11×#3942
C2×#159911