Finite Group Databasebeta

← C2×#13067604 #14725890

Subgroups — C2×#13067604 #14725890

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×#10623024C211yesmaximal, characteristic
2C2×#10622349C212yesmaximal, complemented
3C2×#10622566C211yesmaximal, characteristic, complemented
4#13067604C218yesmaximal, direct product factor
5C2×#10622108C212yesmaximal, complemented
6C2×C11×#323C211yesmaximal, characteristic, complemented
7C23×C22⋊D11—21no—
8C22×C11×C22⋊C4C2211yescharacteristic
9C22×C22⋊Dic11—21no—
10C2×#66983—21no—
11C2×#66983C2212yes—
12C22×C4⋊Dic11C2211yescharacteristic, complemented
13#10623024—22no—
14#10623024—24no—
15#10623024C2214yes—
16C2×#66939—22no—
17C2×#66935—22no—
18C2×C11×C22⋊C8C2212yescomplemented
19C2×C11⋊#95—21no—
20C2×C11⋊#95C2211yescharacteristic, complemented
21C2×#66885—22no—
22C2×#66882—22no—
23#10622566—22no—
24#10622566C2214yescomplemented
25#10622349—24no—
26#10622349C2218yescomplemented
27C11×#323C2214yescomplemented
28#10622108C2218yescomplemented
29C25×C11D411yescharacteristic
30C24×D11—21no—
31C23×C4×C11D411yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C22×C22⋊D11—22no—
34C22×C22⋊D11—24no—
35C22×C22⋊D11—24no—
36C22×C22⋊D11—22no—
37C22×C22⋊D11—44no—
38C22×C22⋊D11—44no—
39C23×Dic11—21no—
40C23×Dic11—21no—
41C23×Dic11—21no—
42C22×D44—21no—
43C22×D44D412yes—
44C22×C8×C11—22no—
45C2×C11×C22⋊C4—22no—
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4D412yes—
48C2×C11×C22⋊C4C2312yes—
49C2×C22⋊Dic11—24no—
50C2×C22⋊Dic11—44no—
51#66983—24no—
52#66983—22no—
53#66983—22no—
54#66983—24no—
55#66983D414yes—
56#66983C2314yes—
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—22no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11D412yes—
64C2×C4⋊Dic11C2312yescomplemented
65#66939—28no—
66#66939—28no—
67#66935—28no—
68#66935—28no—
69C11×C22⋊C8—22no—
70C11×C22⋊C8C2314yescomplemented
71C11⋊#95—24no—
72C11⋊#95—21no—
73C11⋊#95C2312yescomplemented
74#66885—28no—
75#66882—28no—
76C2×#1607—111nomaximal, Sylow
77C24×C11—21no—
78C24×C11—21no—
79C24×C11—22no—
80C24×C11—42no—
81C24×C11—42no—
82C24×C11D814yes—
83C24×C11C2×D411yescharacteristic
84C24×C11C2×D412yes—
85C23×D11—22no—
86C23×D11—24no—
87C23×D11—44no—
88C23×D11—82no—
89C23×D11—82no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2411yescharacteristic
99C2×C22⋊D11—28no—
100C2×C22⋊D11—24no—
101C2×C22⋊D11—24no—
102C2×C22⋊D11—48no—
103C2×C22⋊D11—416no—
104C2×C22⋊D11—48no—
105C2×C22⋊D11—48no—
106C2×C22⋊D11—44no—
107C2×C22⋊D11—44no—
108C22×Dic11—24no—
109C22×Dic11—22no—
110C22×Dic11—22no—
111C22×Dic11—22no—
112C22×Dic11—44no—
113C22×Dic11—42no—
114C22×Dic11—42no—
115C22×Dic11—41no—
116C22×Dic11—41no—
117C22×Dic11—42no—
118C22×Dic11—42no—
119C22×Dic11—42no—
120C2×D44—24no—
121C2×D44—22no—
122C2×D44—44no—
123C2×D44—82no—
124C2×D44C2×D414yes—
125C2×C8×C11—24no—
126C2×C8×C11—44no—
127C11×C22⋊C4—24no—
128C11×C22⋊C4—24no—
129C22⋊Dic11—48no—
130(C2×D11)⋊C4—28no—
131(C2×D11)⋊C4—24no—
132(C2×D11)⋊C4—24no—
133C4⋊Dic11—24no—
134C4⋊Dic11—22no—
135C4⋊Dic11—24no—
136C4⋊Dic11—42no—
137C4⋊Dic11C2×D414yes—
138C2×#534—111no—
139C2×#480—112no—
140C2×#397—111no—
141#1607—118no—
142C2×#327—112no—
143C2×#323D1111yescharacteristic, complemented
144C23×C11—22no—
145C23×C11—22no—
146C23×C11—22no—
147C23×C11—24no—
148C23×C11—22no—
149C23×C11—24no—
150C23×C11—48no—
151C23×C11—42no—
152C23×C11—42no—
153C23×C11—42no—
154C23×C11—42no—
155C23×C11—84no—
156C23×C11—81no—
157C23×C11—81no—
158C23×C11#12011yescharacteristic
159C23×C11#12011yescharacteristic
160C23×C11C2×D812yes—
161C23×C11C2×D814yes—
162C23×C11AGL(1,ℤ/8)12yes—
163C23×C11C22×D411yescharacteristic
164C22×D11—24no—
165C22×D11—48no—
166C22×D11—44no—
167C22×D11—44no—
168C22×D11—44no—
169C22×D11—84no—
170C22×D11—84no—
171C22×D11—816no—
172C2×C4×C11—24no—
173C2×C4×C11—22no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—81no—
180C2×C4×C11#12012yes—
181C2×C4×C11C22×D412yes—
182C22⋊D11—416no—
183C22⋊D11—44no—
184C22⋊D11—44no—
185C22⋊D11—48no—
186C2×Dic11—24no—
187C2×Dic11—48no—
188C2×Dic11—44no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—84no—
196C2×Dic11—82no—
197C2×Dic11—82no—
198D44—44no—
199D44—82no—
200D44—84no—
201C8×C11—44no—
202C23×D4—221no—
203#534—114no—
204#534—224no—
205#534—222no—
206C2×#123—222no—
207C2×#121—112no—
208C2×#121—221no—
209C2×#120—222no—
210C22×C4⋊C4—111no—
211C22×C22⋊C4—221no—
212C22×C22⋊C4C2×D1111yescharacteristic
213#480—118no—
214#480—224no—
215C2×#107—222no—
216C2×#102—222no—
217C2×C22⋊C8C2×D1112yescomplemented
218#397—114no—
219#397—222no—
220C2×#95—111no—
221C2×#95—221no—
222#327—118no—
223#323C2×D1114yescomplemented
224C22×C11—24no—
225C22×C11—24no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—24no—
231C22×C11—44no—
232C22×C11—48no—
233C22×C11—42no—
234C22×C11—42no—
235C22×C11—82no—
236C22×C11—84no—
237C22×C11#44712yes—
238C22×C11#44712yes—
239C22×C11#45512yes—
240C22×C11#45812yes—
241C22×C11C2×#12011yescharacteristic
242C22×C11C22×D811yescharacteristic
243C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
244C2×D11—44no—
245C2×D11—44no—
246C2×D11—44no—
247C2×D11—816no—
248C2×D11—88no—
249C4×C11—22no—
250C4×C11—22no—
251C4×C11—42no—
252Dic11—44no—
253Dic11—82no—
254Dic11—82no—
255C25—221no—
256C25D4411yescharacteristic
257C22×D4—112no—
258C22×D4—221no—
259C22×D4—222no—
260C22×D4—224no—
261C22×D4—222no—
262C22×D4—224no—
263C22×D4—444no—
264C22×D4—444no—
265C23×C4—221no—
266C23×C4—221no—
267C23×C4—221no—
268C23×C4D4411yescharacteristic
269C23×C4C22×D1111yescharacteristic
270C22×C8—22no—
271#123—228no—
272#123—228no—
273#121—114no—
274#121—114no—
275#121—224no—
276#121—222no—
277#121—224no—
278#121—222no—
279#120—228no—
280#120—228no—
281C2×C4⋊C4—112no—
282C2×C4⋊C4—112no—
283C2×C4⋊C4—221no—
284C2×C4⋊C4—222no—
285C2×C4⋊C4—222no—
286C2×C4⋊C4—221no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—222no—
290C2×C22⋊C4—222no—
291C2×C22⋊C4—224no—
292C2×C22⋊C4—444no—
293C2×C22⋊C4D4412yes—
294C2×C22⋊C4C22×D1112yes—
295#107—228no—
296#102—228no—
297C22⋊C8—22no—
298C22⋊C8C22×D1114yescomplemented
299#95—112no—
300#95—221no—
301#95—224no—
302C2×C11—21no—
303C2×C11—21no—
304C2×C11—22no—
305C2×C11—44no—
306C2×C11#160714yescomplemented
307C2×C11C2×#44711yescharacteristic
308C2×C11C2×#45511yescharacteristic
309C2×C11C2×#45811yescharacteristic
310D11—84no—
311C24—21no—
312C24—21no—
313C24—22no—
314C24—42no—
315C24—42no—
316C24—224no—
317C24—222no—
318C24—444no—
319C24—882no—
320C24—882no—
321C24D8814yes—
322C24C2×D4411yescharacteristic
323C24C2×D4412yes—
324C2×D4—114no—
325C2×D4—224no—
326C2×D4—228no—
327C2×D4—224no—
328C2×D4—224no—
329C2×D4—222no—
330C2×D4—444no—
331C2×D4—448no—
332C2×D4—4416no—
333C2×D4—448no—
334C2×D4—448no—
335C2×D4—444no—
336C2×D4—444no—
337C2×D4—882no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—224no—
343C22×C4—222no—
344C22×C4—222no—
345C22×C4—222no—
346C22×C4—444no—
347C22×C4—442no—
348C22×C4—442no—
349C22×C4—441no—
350C22×C4—441no—
351C22×C4—442no—
352C22×C4—442no—
353C22×C4—442no—
354C22×C4C2×D4412yes—
355C22×C4C2×D4411yescharacteristic
356C22×C4D4×D1112yes—
357C22×C4D4×D1112yes—
358C22×C4C23×D1111yescharacteristic
359C2×C8—24no—
360C2×C8—44no—
361C4⋊C4—114no—
362C4⋊C4—224no—
363C4⋊C4—222no—
364C4⋊C4—224no—
365C4⋊C4—442no—
366C22⋊C4—24no—
367C22⋊C4—24no—
368C22⋊C4—228no—
369C22⋊C4—224no—
370C22⋊C4—224no—
371C22⋊C4—448no—
372C11C2×#160711yescharacteristic, complemented, Sylow
373C23—22no—
374C23—22no—
375C23—22no—
376C23—24no—
377C23—22no—
378C23—24no—
379C23—48no—
380C23—42no—
381C23—42no—
382C23—42no—
383C23—42no—
384C23—84no—
385C23—81no—
386C23—81no—
387C23—224no—
388C23—448no—
389C23—444no—
390C23—444no—
391C23—444no—
392C23—884no—
393C23—884no—
394C23—8816no—
395C23#6693511yescharacteristic
396C23#6693511yescharacteristic
397C23C2×D8812yes—
398C23C2×D8814yes—
399C23#6696112yes—
400C23C22×D4411yescharacteristic
401D4—444no—
402D4—4416no—
403D4—444no—
404D4—444no—
405D4—448no—
406D4—882no—
407D4—884no—
408C2×C4—24no—
409C2×C4—22no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—81no—
416C2×C4—224no—
417C2×C4—448no—
418C2×C4—444no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4—442no—
422C2×C4—442no—
423C2×C4—442no—
424C2×C4—442no—
425C2×C4—884no—
426C2×C4—882no—
427C2×C4—882no—
428C2×C4#6693512yes—
429C2×C4C2×D4×D1112yes—
430C8—44no—
431C22—24no—
432C22—24no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—24no—
438C22—44no—
439C22—48no—
440C22—42no—
441C22—42no—
442C22—82no—
443C22—84no—
444C22—444no—
445C22—444no—
446C22—444no—
447C22—8816no—
448C22—888no—
449C22#1062234512yes—
450C22#1062234512yes—
451C22#1062235512yes—
452C22#1062235912yes—
453C22C2×#6693511yescharacteristic
454C22C22×D8811yescharacteristic
455C22C2×#6696111yescharacteristic
456C4—22no—
457C4—22no—
458C4—42no—
459C4—444no—
460C4—882no—
461C4—882no—
462C2—21no—
463C2—21no—
464C2—22no—
465C2—44no—
466C2—884no—
467C2#1306760414yesdirect product factor
468C2C2×#1062234511yescharacteristic
469C2C2×#1062235911yescharacteristic
470C2C2×#1062235511yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#323C2
socleC23×C11#120
prime radicalC2×#10623024C2
hypercenterC2×#323D11
hypocenterC11C2×#1607
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. C2×#10622349C2semidirect
3. C2×#10622566C2semidirect
4. #13067604C2direct (N × H)
5. C2×#10622108C2semidirect
6. C2×C11×#323C2semidirect
12. C22×C4⋊Dic11C22semidirect
18. C2×C11×C22⋊C8C22semidirect
20. C2×C11⋊#95C22semidirect
24. #10622566C22semidirect
26. #10622349C22semidirect
27. C11×#323C22semidirect
28. #10622108C22semidirect
64. C2×C4⋊Dic11C23semidirect
70. C11×C22⋊C8C23semidirect
73. C11⋊#95C23semidirect
143. C2×#323D11semidirect
217. C2×C22⋊C8C2×D11semidirect
223. #323C2×D11semidirect
298. C22⋊C8C22×D11semidirect
306. C2×C11#1607semidirect
372. C11C2×#1607semidirect
467. C2#13067604direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230242
C2×#106223492
C2×#106225662
#130676042
C2×#106221082
C2×C11×#3232
C2×#160711