Finite Group Databasebeta

← C2×#13067621 #14725992

Subgroups — C2×#13067621 #14725992

Order 2816.

1308 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1308 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×#10622349C212yesmaximal, complemented
3C2×#10622596C211yesmaximal, characteristic, complemented
4#13067621C218yesmaximal, direct product factor
5C2×#10622108C212yesmaximal, complemented
6C2×C11×#324C211yesmaximal, characteristic, complemented
7C22×#4339—21no—
8C22×C11×C4⋊C4C2211yescharacteristic
9C2×#66983—21no—
10C2×#66983C2212yes—
11C22×C4⋊Dic11C2211yescharacteristic
12C22×Dic11⋊C4—21no—
13#10623041—22no—
14#10623041—24no—
15#10623041C2214yes—
16C2×#66950—22no—
17C2×#66948—22no—
18C2×C11×C22⋊C8C2212yes—
19C2×C11⋊#95—21no—
20C2×C11⋊#95C2211yescharacteristic
21C2×#66885—22no—
22C2×#66882—22no—
23#10622596—22no—
24#10622596C2214yescomplemented
25#10622349—24no—
26#10622349C2218yescomplemented
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—21no—
44C22×C8×C11—22no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4D412yes—
48C2×C11×C4⋊C4C2312yes—
49#66983—24no—
50#66983—22no—
51#66983—22no—
52#66983—24no—
53#66983D414yes—
54#66983C2314yes—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11D412yes—
62C2×C4⋊Dic11C2312yes—
63C2×Dic11⋊C4—24no—
64C2×Dic11⋊C4—44no—
65#66950—28no—
66#66950—28no—
67#66948—28no—
68#66948—28no—
69C11×C22⋊C8—22no—
70C11×C22⋊C8C2314yes—
71C11⋊#95—24no—
72C11⋊#95—21no—
73C11⋊#95C2312yes—
74#66885—28no—
75#66882—28no—
76C2×#1610—111nomaximal, Sylow
77C24×C11C2×D411yescharacteristic
78C23×D11—22no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—22no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—42no—
85C22×C4×C11—42no—
86C22×C4×C11D814yes—
87C22×C4×C11C2×D412yes—
88C22×C4×C11C2×D412yes—
89C22×C4×C11C2×D412yes—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2411yescharacteristic
93C2×C22⋊D11—24no—
94C2×C22⋊D11—24no—
95C2×C22⋊D11—44no—
96C2×C22⋊D11—44no—
97C22×Dic11—24no—
98C22×Dic11—22no—
99C22×Dic11—22no—
100C22×Dic11—22no—
101C22×Dic11—42no—
102C22×Dic11—41no—
103C22×Dic11—41no—
104C22×Dic11—42no—
105C22×Dic11—42no—
106C22×Dic11—42no—
107#4339—48no—
108#4339—416no—
109#4339—48no—
110C2×D44—24no—
111C2×D44—24no—
112C2×D44—22no—
113C2×D44—44no—
114C2×D44—44no—
115C2×D44—82no—
116C2×D44C2×D414yes—
117C2×C4×D11—28no—
118C2×C4×D11—48no—
119C2×Dic22—24no—
120C2×Dic22—44no—
121C2×C8×C11—24no—
122C2×C8×C11—44no—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—24no—
125(C2×D11)⋊C4—28no—
126(C2×D11)⋊C4—24no—
127(C2×D11)⋊C4—24no—
128C4⋊Dic11—24no—
129C4⋊Dic11—22no—
130C4⋊Dic11—24no—
131C4⋊Dic11—42no—
132C4⋊Dic11C2×D414yes—
133Dic11⋊C4—48no—
134C2×#537—111no—
135C2×#480—112no—
136C2×#398—111no—
137#1610—118no—
138C2×#327—112no—
139C2×#324D1111yescharacteristic, complemented
140C23×C11—22no—
141C23×C11—22no—
142C23×C11#12011yescharacteristic
143C23×C11#12011yescharacteristic
144C23×C11C2×D812yes—
145C23×C11AGL(1,ℤ/8)12yes—
146C23×C11C22×D411yescharacteristic
147C22×D11—24no—
148C22×D11—44no—
149C22×D11—44no—
150C22×D11—44no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—24no—
154C2×C4×C11—24no—
155C2×C4×C11—24no—
156C2×C4×C11—22no—
157C2×C4×C11—41no—
158C2×C4×C11—42no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—81no—
163C2×C4×C11#12012yes—
164C2×C4×C11C2×D814yes—
165C2×C4×C11C22×D412yes—
166C22⋊D11—44no—
167C22⋊D11—44no—
168C22⋊D11—48no—
169C2×Dic11—24no—
170C2×Dic11—24no—
171C2×Dic11—48no—
172C2×Dic11—42no—
173C2×Dic11—42no—
174C2×Dic11—44no—
175C2×Dic11—42no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—82no—
179C2×Dic11—82no—
180D44—44no—
181D44—48no—
182D44—82no—
183D44—84no—
184C4×D11—416no—
185Dic22—48no—
186C8×C11—44no—
187C22×#41—221no—
188#537—114no—
189#537—224no—
190#537—222no—
191C2×C22⋊Q8—222no—
192C2×#121—112no—
193C2×#121—222no—
194C2×#121—221no—
195C22×C4⋊C4—111no—
196C22×C4⋊C4—221no—
197C22×C4⋊C4C2×D1111yescharacteristic
198#480—118no—
199#480—224no—
200C2×#107—222no—
201C2×#102—222no—
202C2×C22⋊C8C2×D1112yes—
203#398—114no—
204#398—222no—
205C2×#95—111no—
206C2×#95—221no—
207#327—118no—
208#324C2×D1114yescomplemented
209C22×C11—24no—
210C22×C11—24no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11#44712yes—
216C22×C11#44712yes—
217C22×C11#45612yes—
218C22×C11#45812yes—
219C22×C11C2×#12011yescharacteristic
220C22×C11C22×D811yescharacteristic
221C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
222C2×D11—44no—
223C2×D11—44no—
224C2×D11—44no—
225C2×D11—88no—
226C4×C11—24no—
227C4×C11—22no—
228C4×C11—22no—
229C4×C11—42no—
230Dic11—44no—
231Dic11—44no—
232Dic11—82no—
233C2×#41—224no—
234C2×#41—224no—
235C2×#41—444no—
236C2×#41—444no—
237C22×Q8—221no—
238C22×D4—112no—
239C22×D4—221no—
240C22×D4—221no—
241C22×D4—222no—
242C23×C4—222no—
243C23×C4—221no—
244C23×C4—221no—
245C23×C4D4411yescharacteristic
246C23×C4D4411yescharacteristic
247C23×C4C22×D1111yescharacteristic
248C22×C8—22no—
249C22⋊Q8—228no—
250C22⋊Q8—228no—
251#121—114no—
252#121—114no—
253#121—228no—
254#121—228no—
255#121—224no—
256#121—222no—
257#121—224no—
258#121—222no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—112no—
262C2×C4⋊C4—112no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4—222no—
265C2×C4⋊C4—222no—
266C2×C4⋊C4—221no—
267C2×C4⋊C4—224no—
268C2×C4⋊C4—444no—
269C2×C4⋊C4D4412yes—
270C2×C4⋊C4C22×D1112yes—
271C2×C22⋊C4—222no—
272C2×C22⋊C4—222no—
273#107—228no—
274#102—228no—
275C22⋊C8—22no—
276C22⋊C8C22×D1114yes—
277#95—112no—
278#95—221no—
279#95—224no—
280C2×C11—21no—
281C2×C11—21no—
282C2×C11—22no—
283C2×C11#161014yescomplemented
284C2×C11C2×#44711yescharacteristic
285C2×C11C2×#45611yescharacteristic
286C2×C11C2×#45811yescharacteristic
287D11—84no—
288C24—222no—
289C24C2×D4411yescharacteristic
290#41—448no—
291#41—4416no—
292#41—448no—
293C2×Q8—224no—
294C2×Q8—444no—
295C2×D4—114no—
296C2×D4—224no—
297C2×D4—224no—
298C2×D4—224no—
299C2×D4—224no—
300C2×D4—222no—
301C2×D4—444no—
302C2×D4—444no—
303C2×D4—444no—
304C2×D4—444no—
305C2×D4—882no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—22no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—228no—
314C22×C4—224no—
315C22×C4—222no—
316C22×C4—222no—
317C22×C4—222no—
318C22×C4—448no—
319C22×C4—442no—
320C22×C4—442no—
321C22×C4—441no—
322C22×C4—441no—
323C22×C4—442no—
324C22×C4—442no—
325C22×C4D8814yes—
326C22×C4C2×D4412yes—
327C22×C4C2×D4412yes—
328C22×C4C2×D4411yescharacteristic
329C22×C4D4×D1112yes—
330C22×C4D4×D1112yes—
331C22×C4C23×D1111yescharacteristic
332C2×C8—24no—
333C2×C8—44no—
334C4⋊C4—24no—
335C4⋊C4—24no—
336C4⋊C4—114no—
337C4⋊C4—224no—
338C4⋊C4—222no—
339C4⋊C4—224no—
340C4⋊C4—442no—
341C4⋊C4—448no—
342C22⋊C4—228no—
343C22⋊C4—224no—
344C22⋊C4—224no—
345C11C2×#161011yescharacteristic, complemented, Sylow
346C23—22no—
347C23—22no—
348C23—224no—
349C23—444no—
350C23—444no—
351C23—444no—
352C23#6693511yescharacteristic
353C23#6693511yescharacteristic
354C23C2×D8812yes—
355C23#6696112yes—
356C23C22×D4411yescharacteristic
357Q8—448no—
358D4—444no—
359D4—448no—
360D4—444no—
361D4—444no—
362D4—448no—
363D4—882no—
364D4—884no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—81no—
377C2×C4—224no—
378C2×C4—224no—
379C2×C4—4416no—
380C2×C4—448no—
381C2×C4—442no—
382C2×C4—442no—
383C2×C4—444no—
384C2×C4—442no—
385C2×C4—442no—
386C2×C4—442no—
387C2×C4—882no—
388C2×C4—882no—
389C2×C4#6693512yes—
390C2×C4C2×D8814yes—
391C2×C4C2×D4×D1112yes—
392C8—44no—
393C22—24no—
394C22—24no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—444no—
400C22—444no—
401C22—444no—
402C22—888no—
403C22#1062234512yes—
404C22#1062234512yes—
405C22#1062235512yes—
406C22#1062236512yes—
407C22C2×#6693511yescharacteristic
408C22C22×D8811yescharacteristic
409C22C2×#6696111yescharacteristic
410C4—24no—
411C4—22no—
412C4—22no—
413C4—42no—
414C4—444no—
415C4—444no—
416C4—882no—
417C2—21no—
418C2—21no—
419C2—22no—
420C2—884no—
421C2#1306762114yesdirect product factor
422C2C2×#1062234511yescharacteristic
423C2C2×#1062236511yescharacteristic
424C2C2×#1062235511yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#324C2
socleC23×C11#120
prime radicalC2×#10623041C2
hypercenterC2×#324D11
hypocenterC11C2×#1610
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×#10622349C2semidirect
3. C2×#10622596C2semidirect
4. #13067621C2direct (N × H)
5. C2×#10622108C2semidirect
6. C2×C11×#324C2semidirect
24. #10622596C22semidirect
26. #10622349C22semidirect
27. C11×#324C22semidirect
28. #10622108C22semidirect
139. C2×#324D11semidirect
208. #324C2×D11semidirect
283. C2×C11#1610semidirect
345. C11C2×#1610semidirect
421. C2#13067621direct (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×#106223492
C2×#106225962
#130676212
C2×#106221082
C2×C11×#3242
C2×#161011