Finite Group Databasebeta

← C2×#13067640 #14725905

Subgroups — C2×#13067640 #14725905

Order 2816.

1180 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1180 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×#10622583C212yesmaximal, complemented
3#13067640C218yesmaximal, direct product factor
4C2×#10622090C212yesmaximal, complemented
5C2×#10622163C211yesmaximal, characteristic
6C2×C11×#399C211yesmaximal, characteristic
7C22×C11×C4⋊C4—21no—
8C22×C11×C4⋊C4C2211yescharacteristic
9C22×C11×C22⋊C4—21no—
10C22×C11×C22⋊C4C2211yescharacteristic
11C22×C22⋊Dic11—21no—
12C2×#66977—21no—
13C2×#66977C2212yes—
14#10623014—22no—
15#10623014—24no—
16#10623014C2214yes—
17C2×#66931—22no—
18C2×#66931—22no—
19C11×#399—22no—
20C11×#399C2214yes—
21C2×C11×#95C2211yescharacteristic
22C2×C22⋊(C11⋊C8)C2212yes—
23#10622583—24no—
24#10622583C2218yescomplemented
25C2×#66874—22no—
26C2×#66871—22no—
27#10622163C2214yes—
28#10622090C2218yescomplemented
29C25×C11D411yescharacteristic
30C23×C4×C11—21no—
31C23×C4×C11—21no—
32C23×C4×C11D411yescharacteristic
33C23×C4×C11C2311yescharacteristic
34C23×Dic11—21no—
35C23×Dic11—21no—
36C22×Dic22—21no—
37C22×Dic22D412yes—
38C2×C11×C4⋊C4—22no—
39C2×C11×C4⋊C4—22no—
40C2×C11×C4⋊C4—24no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—44no—
43C2×C11×C4⋊C4C2312yes—
44C2×C11×C22⋊C4—22no—
45C2×C11×C22⋊C4—22no—
46C2×C11×C22⋊C4—24no—
47C2×C11×C22⋊C4—44no—
48C2×C11×C22⋊C4D412yes—
49C2×C11×C22⋊C4C2312yes—
50C2×C22⋊Dic11—22no—
51C2×C22⋊Dic11—24no—
52C2×C22⋊Dic11—24no—
53C2×C22⋊Dic11—22no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11D412yes—
56#66977—24no—
57#66977—22no—
58#66977—22no—
59#66977—24no—
60#66977D414yes—
61#66977C2314yes—
62C2×Dic11⋊C4—22no—
63C2×Dic11⋊C4—22no—
64C22×C11⋊C8—22no—
65#66931—28no—
66#66931—28no—
67#66931—28no—
68#66931—28no—
69C11×#95—21no—
70C11×#95C2312yes—
71C22⋊(C11⋊C8)—22no—
72C22⋊(C11⋊C8)C2314yes—
73#66874—28no—
74#66871—28no—
75C2×#1614—111nomaximal, Sylow
76C24×C11—21no—
77C24×C11—21no—
78C24×C11—22no—
79C24×C11—42no—
80C24×C11—42no—
81C24×C11Q1614yes—
82C24×C11C2×D411yescharacteristic
83C24×C11C2×D412yes—
84C22×C4×C11—24no—
85C22×C4×C11—21no—
86C22×C4×C11—22no—
87C22×C4×C11—21no—
88C22×C4×C11—22no—
89C22×C4×C11—42no—
90C22×C4×C11—42no—
91C22×C4×C11—42no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11—42no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2411yescharacteristic
102C22×Dic11—24no—
103C22×Dic11—24no—
104C22×Dic11—22no—
105C22×Dic11—22no—
106C22×Dic11—82no—
107C22×Dic11—82no—
108C2×Dic22—24no—
109C2×Dic22—22no—
110C2×Dic22—44no—
111C2×Dic22—82no—
112C2×Dic22C2×D414yes—
113C11×C4⋊C4—24no—
114C11×C4⋊C4—48no—
115C11×C4⋊C4—42no—
116C11×C22⋊C4—24no—
117C11×C22⋊C4—24no—
118C11×C22⋊C4—48no—
119C22⋊Dic11—28no—
120C22⋊Dic11—24no—
121C22⋊Dic11—24no—
122C4⋊Dic11—24no—
123C4⋊Dic11—22no—
124C4⋊Dic11C2×D414yes—
125Dic11⋊C4—28no—
126Dic11⋊C4—24no—
127Dic11⋊C4—24no—
128C2×C11⋊C8—24no—
129C2×C11⋊C8—44no—
130C2×#543—111no—
131C2×#484—112no—
132C2×#399D1111yescharacteristic
133#1614—118no—
134C2×#328—112no—
135C2×#323—111no—
136C23×C11—22no—
137C23×C11—22no—
138C23×C11—22no—
139C23×C11—24no—
140C23×C11—22no—
141C23×C11—24no—
142C23×C11—42no—
143C23×C11—48no—
144C23×C11—42no—
145C23×C11—42no—
146C23×C11—42no—
147C23×C11—84no—
148C23×C11—81no—
149C23×C11—81no—
150C23×C11#12011yescharacteristic
151C23×C11#12011yescharacteristic
152C23×C11C2×Q1612yes—
153C23×C11C2×Q1614yes—
154C23×C11#13712yes—
155C23×C11C22×D411yescharacteristic
156C2×C4×C11—24no—
157C2×C4×C11—24no—
158C2×C4×C11—22no—
159C2×C4×C11—42no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—48no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—81no—
171C2×C4×C11—82no—
172C2×C4×C11—82no—
173C2×C4×C11#12012yes—
174C2×C4×C11C22×D412yes—
175C2×Dic11—24no—
176C2×Dic11—24no—
177C2×Dic11—44no—
178C2×Dic11—44no—
179C2×Dic11—84no—
180C2×Dic11—84no—
181Dic22—44no—
182Dic22—82no—
183Dic22—84no—
184C11⋊C8—44no—
185#543—114no—
186#543—224no—
187#543—222no—
188C2×C22⋊Q8—112no—
189C2×C22⋊Q8—222no—
190C2×C22⋊Q8—222no—
191C2×C22⋊Q8—221no—
192C22×C4⋊C4—21no—
193C22×C4⋊C4C2×D1111yescharacteristic
194C22×C22⋊C4—21no—
195C22×C22⋊C4—221no—
196C22×C22⋊C4C2×D1111yescharacteristic
197#484—118no—
198#484—224no—
199C2×#107—222no—
200C2×#103—222no—
201C2×C22⋊C8—112no—
202#399—22no—
203#399C2×D1114yes—
204C2×#95C2×D1111yescharacteristic
205#328—118no—
206#323—114no—
207C22×C11—24no—
208C22×C11—24no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—24no—
214C22×C11—44no—
215C22×C11—48no—
216C22×C11—42no—
217C22×C11—42no—
218C22×C11—82no—
219C22×C11—84no—
220C22×C11#45112yes—
221C22×C11#45112yes—
222C22×C11#45312yes—
223C22×C11#45812yes—
224C22×C11C2×#12011yescharacteristic
225C22×C11C22×Q1611yescharacteristic
226C22×C11C2×#13711yescharacteristic
227C4×C11—22no—
228C4×C11—22no—
229C4×C11—44no—
230C4×C11—42no—
231C4×C11—82no—
232Dic11—44no—
233Dic11—44no—
234C25C22⋊D1111yescharacteristic
235C22×Q8—112no—
236C22×Q8—221no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—221no—
240C23×C4—221no—
241C23×C4C22⋊D1111yescharacteristic
242C23×C4C22×D1111yescharacteristic
243C22×C8—222no—
244C22⋊Q8—114no—
245C22⋊Q8—114no—
246C22⋊Q8—228no—
247C22⋊Q8—228no—
248C22⋊Q8—228no—
249C22⋊Q8—228no—
250C22⋊Q8—224no—
251C22⋊Q8—222no—
252C22⋊Q8—222no—
253C22⋊Q8—224no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—44no—
259C2×C4⋊C4—112no—
260C2×C4⋊C4—222no—
261C2×C4⋊C4—221no—
262C2×C4⋊C4—222no—
263C2×C4⋊C4C22×D1112yes—
264C2×C22⋊C4—22no—
265C2×C22⋊C4—22no—
266C2×C22⋊C4—24no—
267C2×C22⋊C4—44no—
268C2×C22⋊C4—222no—
269C2×C22⋊C4—224no—
270C2×C22⋊C4—222no—
271C2×C22⋊C4—224no—
272C2×C22⋊C4C22⋊D1112yes—
273C2×C22⋊C4C22×D1112yes—
274#107—228no—
275#103—228no—
276C22⋊C8—114no—
277C22⋊C8—222no—
278#95—21no—
279#95C22×D1112yes—
280C2×C11—21no—
281C2×C11—21no—
282C2×C11—22no—
283C2×C11—44no—
284C2×C11#161414yescomplemented
285C2×C11C2×#45111yescharacteristic
286C2×C11C2×#45311yescharacteristic
287C2×C11C2×#45811yescharacteristic
288C24—21no—
289C24—21no—
290C24—22no—
291C24—42no—
292C24—42no—
293C24#432614yes—
294C24C2×C22⋊D1111yescharacteristic
295C24C2×C22⋊D1112yes—
296C2×Q8—114no—
297C2×Q8—224no—
298C2×Q8—222no—
299C2×Q8—444no—
300C2×Q8—882no—
301C22×C4—24no—
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—222no—
315C22×C4—222no—
316C22×C4—224no—
317C22×C4—224no—
318C22×C4—882no—
319C22×C4—882no—
320C22×C4D4×D1112yes—
321C22×C4D4×D1112yes—
322C22×C4C2×C22⋊D1112yes—
323C22×C4C2×C22⋊D1111yescharacteristic
324C22×C4C23×D1111yescharacteristic
325C2×C8—224no—
326C2×C8—444no—
327C4⋊C4—24no—
328C4⋊C4—48no—
329C4⋊C4—42no—
330C4⋊C4—114no—
331C4⋊C4—228no—
332C4⋊C4—224no—
333C4⋊C4—222no—
334C4⋊C4—224no—
335C4⋊C4—224no—
336C22⋊C4—24no—
337C22⋊C4—24no—
338C22⋊C4—48no—
339C22⋊C4—228no—
340C22⋊C4—224no—
341C22⋊C4—224no—
342C11C2×#161411yescharacteristic, complemented, Sylow
343C23—22no—
344C23—22no—
345C23—22no—
346C23—24no—
347C23—22no—
348C23—24no—
349C23—42no—
350C23—48no—
351C23—42no—
352C23—42no—
353C23—42no—
354C23—84no—
355C23—81no—
356C23—81no—
357C23#6699011yescharacteristic
358C23#6699011yescharacteristic
359C23C2×#432612yes—
360C23C2×#432614yes—
361C23#6700412yes—
362C23C22×C22⋊D1111yescharacteristic
363Q8—444no—
364Q8—882no—
365Q8—884no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—22no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—48no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—81no—
381C2×C4—82no—
382C2×C4—82no—
383C2×C4—224no—
384C2×C4—224no—
385C2×C4—444no—
386C2×C4—444no—
387C2×C4—884no—
388C2×C4—884no—
389C2×C4#6699012yes—
390C2×C4C2×D4×D1112yes—
391C8—444no—
392C22—24no—
393C22—24no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—24no—
399C22—44no—
400C22—48no—
401C22—42no—
402C22—42no—
403C22—82no—
404C22—84no—
405C22#1062266312yes—
406C22#1062266312yes—
407C22#1062266612yes—
408C22#1062269012yes—
409C22C2×#6699011yescharacteristic
410C22C22×#432611yescharacteristic
411C22C2×#6700411yescharacteristic
412C4—22no—
413C4—22no—
414C4—44no—
415C4—42no—
416C4—82no—
417C4—444no—
418C4—444no—
419C2—21no—
420C2—21no—
421C2—22no—
422C2—44no—
423C2#1306764014yesdirect product factor
424C2C2×#1062266311yescharacteristic
425C2C2×#1062269011yescharacteristic
426C2C2×#1062266611yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#399C2
socleC23×C11#120
prime radicalC25×C11D4
hypercenterC2×#399D11
hypocenterC11C2×#1614
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
2. C2×#10622583C2semidirect
3. #13067640C2direct (N × H)
4. C2×#10622090C2semidirect
24. #10622583C22semidirect
28. #10622090C22semidirect
284. C2×C11#1614semidirect
342. C11C2×#1614semidirect
423. C2#13067640direct (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×#106225832
#130676402
C2×#106220902
C2×#106221632
C2×C11×#3992
C2×#161411