Finite Group Databasebeta

← C2×#13071012 #14912058

Subgroups — C2×#13071012 #14912058

Order 2816.

3246 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D11C211yesmaximal, characteristic
2#13071012C2116yesmaximal, direct product factor
3C2×#10622264C212yesmaximal, complemented
4C2×#10622590C212yesmaximal, complemented
5C2×#10622277C212yesmaximal
6C2×#10622600C212yesmaximal
7C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
8C2×C4×(C2×D11)⋊C4C212yesmaximal
9C2×#10622545C212yesmaximal, complemented
10C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
11C23×C4×D11C2211yescharacteristic
12C23×C4×D11C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C22×C11×C4⋊C4C2212yes—
15C22×C42×C11C2212yes—
16C22×C42×C11C2211yescharacteristic
17C22×(C2×D11)⋊C4C2214yes—
18C22×C4⋊Dic11C2212yes—
19C22×C4×Dic11C2212yes—
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C2×C42×D11C4116yescomplemented
24C2×C42×D11C2218yes—
25C4×C11×C4⋊C4C2218yescomplemented
26C2×C11×#95C2212yes—
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2214yes—
30C2×C11⋊#95C2212yes—
31#10622600C22116yes—
32#10622590C22116yescomplemented
33C4×(C2×D11)⋊C4C22116yes—
34C4×C4⋊Dic11C2218yescomplemented
35#10622545C22116yescomplemented
36#10622277C22116yes—
37#10622264C22116yescomplemented
38C24×D11C2311yescharacteristic
39C23×C4×C11C2314yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×Dic11C2314yes—
44C23×Dic11C2311yescharacteristic
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2311yescharacteristic
47C22×C4×D11—28no—
48C22×C4×D11—28no—
49C22×C4×D11—24no—
50C22×C4×D11—24no—
51C22×C4×D11C2×C418yes—
52C22×C4×D11C2×C418yes—
53C22×C4×D11C2×C418yes—
54C22×C4×D11C2314yes—
55C22×C4×D11C2314yes—
56C22×C4×D11C2314yes—
57C2×C11×C4⋊C4—28no—
58C2×C11×C4⋊C4C2318yes—
59C2×C42×C11—28no—
60C2×C42×C11C2×C418yes—
61C2×C42×C11C2318yes—
62C2×C42×C11C2314yes—
63C2×(C2×D11)⋊C4—216no—
64C2×(C2×D11)⋊C4C23116yes—
65C2×C4⋊Dic11—28no—
66C2×C4⋊Dic11C2318yes—
67C2×C4×Dic11—28no—
68C2×C4×Dic11C2×C418yes—
69C2×C4×Dic11C2×C418yes—
70C2×C4×Dic11C2×C418yes—
71C2×C4×Dic11C2318yes—
72C2×C4×Dic11C2314yes—
73C2×C4×Dic11C2314yes—
74C2×C4×Dic11C2314yes—
75C42×D11C2×C4164yescomplemented
76C11×#95C2318yes—
77C11⋊#95C2318yes—
78C11⋊#95C23116yes—
79C11⋊#95C23116yes—
80C11⋊#95C23116yes—
81C2×#2283—111nomaximal, Sylow
82C24×C11C2411yescharacteristic
83C23×D11—24no—
84C23×D11—22no—
85C23×D11—22no—
86C23×D11C22×C414yes—
87C23×D11#4118yes—
88C23×D11C2412yes—
89C22×C4×C11—24no—
90C22×C4×C11—28no—
91C22×C4×C11—28no—
92C22×C4×C11—28no—
93C22×C4×C11C22×C414yes—
94C22×C4×C11C22×C414yes—
95C22×C4×C11C22×C414yes—
96C22×C4×C11#4118yes—
97C22×C4×C11#4114yes—
98C22×C4×C11#4114yes—
99C22×C4×C11C2418yes—
100C22×C4×C11C2412yes—
101C22×C4×C11C2412yes—
102C22×C4×C11C2412yes—
103C22×Dic11—24no—
104C22×Dic11—22no—
105C22×Dic11—22no—
106C22×Dic11—24no—
107C22×Dic11—28no—
108C22×Dic11—28no—
109C22×Dic11—28no—
110C22×Dic11C22×C414yes—
111C22×Dic11C22×C414yes—
112C22×Dic11C22×C414yes—
113C22×Dic11C2418yes—
114C22×Dic11C2412yes—
115C22×Dic11C2412yes—
116C22×Dic11C2412yes—
117C2×C4×D11—232no—
118C2×C4×D11—216no—
119C2×C4×D11—232no—
120C2×C4×D11—232no—
121C2×C4×D11—216no—
122C2×C4×D11—28no—
123C2×C4×D11—28no—
124C2×C4×D11C22×C4116yes—
125C2×C4×D11C22×C4116yes—
126C2×C4×D11C22×C4116yes—
127C11×C4⋊C4—216no—
128C42×C11—216no—
129C42×C11C22×C4116yes—
130(C2×D11)⋊C4—232no—
131C4⋊Dic11—216no—
132C4×Dic11—216no—
133C4×Dic11C22×C4116yes—
134C4×Dic11C22×C4116yes—
135C4×Dic11C22×C4116yes—
136C23×C42—111no—
137#2283—1116no—
138C2×#383—112no—
139C2×#382—112no—
140C2×#381—112no—
141C2×#380—112no—
142C2×C4×C4⋊C4—111no—
143C2×C4×C4⋊C4D1111yescharacteristic, complemented
144C2×C4×C22⋊C4—112no—
145C2×#376—112no—
146C23×C11C23×C412yes—
147C23×C11C2×#4114yes—
148C23×C11C2×#4112yes—
149C23×C11C2×#4112yes—
150C23×C11C2×#4114yes—
151C23×C11C2511yescharacteristic
152C22×D11—28no—
153C22×D11—28no—
154C22×D11—216no—
155C22×D11—216no—
156C22×D11—24no—
157C22×D11—22no—
158C22×D11—22no—
159C22×D11#117116yes—
160C22×D11C23×C414yes—
161C22×D11C2×#4118yes—
162C2×C4×C11—28no—
163C2×C4×C11—24no—
164C2×C4×C11—28no—
165C2×C4×C11—28no—
166C2×C4×C11—28no—
167C2×C4×C11—416no—
168C2×C4×C11#117116yes—
169C2×C4×C11#117116yes—
170C2×C4×C11C23×C414yes—
171C2×C4×C11C23×C414yes—
172C2×C4×C11C23×C414yes—
173C2×C4×C11C2×#4118yes—
174C2×C4×C11C2×#4114yes—
175C2×C4×C11C2×#4114yes—
176C2×Dic11—28no—
177C2×Dic11—28no—
178C2×Dic11—28no—
179C2×Dic11—24no—
180C2×Dic11—22no—
181C2×Dic11—22no—
182C2×Dic11—24no—
183C2×Dic11—28no—
184C2×Dic11—28no—
185C2×Dic11—28no—
186C2×Dic11—416no—
187C2×Dic11C23×C414yes—
188C2×Dic11C23×C414yes—
189C2×Dic11C23×C414yes—
190C4×D11—232no—
191C4×D11—232no—
192C4×D11—232no—
193C24×C4—111no—
194C24×C4—111no—
195C24×C4—111no—
196C22×C4⋊C4—112no—
197C22×C4⋊C4C2×D1112yes—
198C22×C22⋊C4—114no—
199C22×C42—111no—
200C22×C42—111no—
201C22×C42—111no—
202C22×C42—118no—
203C22×C42—1116no—
204C22×C42—112no—
205C22×C42C2×D1112yes—
206C22×C42C2×D1111yescharacteristic
207#383—1116no—
208#382—1116no—
209#381—1116no—
210#380—1116no—
211C4×C4⋊C4—118no—
212C4×C4⋊C4C2×D1118yescomplemented
213C4×C22⋊C4—1116no—
214#376—1116no—
215C2×#95—114no—
216C2×#95—114no—
217C2×#95—114no—
218C2×#95—112no—
219C2×#95C2×D1112yes—
220C22×C11C2×#11714yes—
221C22×C11C2×#11714yes—
222C22×C11C2×#11714yes—
223C22×C11#52918yes—
224C22×C11#52918yes—
225C22×C11C24×C411yescharacteristic
226C22×C11C22×#4112yes—
227C22×C11C22×#4111yescharacteristic
228C22×C11C22×#4111yescharacteristic
229C22×C11C22×#4112yes—
230C2×D11—24no—
231C2×D11—24no—
232C2×D11—28no—
233C2×D11—28no—
234C2×D11—232no—
235C2×D11C2×#11718yes—
236C4×C11—24no—
237C4×C11—48no—
238C4×C11C2×#11718yes—
239C4×C11C2×#11718yes—
240Dic11—24no—
241Dic11—24no—
242Dic11—24no—
243Dic11—48no—
244C25—111no—
245C23×C4—111no—
246C23×C4—111no—
247C23×C4—111no—
248C23×C4—118no—
249C23×C4—118no—
250C23×C4—118no—
251C23×C4—114no—
252C23×C4—114no—
253C23×C4—114no—
254C23×C4—114no—
255C23×C4—228no—
256C23×C4—228no—
257C23×C4—224no—
258C23×C4—224no—
259C23×C4C22×D1114yes—
260C23×C4C22×D1111yescharacteristic
261C23×C4C22×D1111yescharacteristic
262C23×C4C22×D1111yescharacteristic
263C2×C4⋊C4—28no—
264C2×C4⋊C4—118no—
265C2×C4⋊C4—228no—
266C2×C4⋊C4C22×D1118yes—
267C2×C22⋊C4—1116no—
268C2×C22⋊C4—2216no—
269C2×C42—28no—
270C2×C42—118no—
271C2×C42—118no—
272C2×C42—118no—
273C2×C42—114no—
274C2×C42—114no—
275C2×C42—114no—
276C2×C42—1164no—
277C2×C42—118no—
278C2×C42—228no—
279C2×C42C4×D1118yes—
280C2×C42C22×D1118yes—
281C2×C42C22×D1114yes—
282#95—1116no—
283#95—1116no—
284#95—1116no—
285#95—118no—
286#95C22×D1118yes—
287C2×C11#228318yescomplemented
288C2×C11C22×#11711yescharacteristic
289C2×C11C22×#11711yescharacteristic
290C2×C11C22×#11711yescharacteristic
291C2×C11C2×#52912yes—
292C2×C11C2×#52912yes—
293D11—28no—
294C24—114no—
295C24—118no—
296C24—112no—
297C24—224no—
298C24—222no—
299C24—222no—
300C24C23×D1111yescharacteristic
301C22×C4—24no—
302C22×C4—28no—
303C22×C4—28no—
304C22×C4—28no—
305C22×C4—114no—
306C22×C4—114no—
307C22×C4—114no—
308C22×C4—112no—
309C22×C4—112no—
310C22×C4—112no—
311C22×C4—1116no—
312C22×C4—1116no—
313C22×C4—1116no—
314C22×C4—118no—
315C22×C4—2232no—
316C22×C4—2216no—
317C22×C4—224no—
318C22×C4—222no—
319C22×C4—222no—
320C22×C4—224no—
321C22×C4—2232no—
322C22×C4—2232no—
323C22×C4—2216no—
324C22×C4—228no—
325C22×C4—228no—
326C22×C4—228no—
327C22×C4—228no—
328C22×C4—228no—
329C22×C4C2×C4×D1114yes—
330C22×C4C2×C4×D1114yes—
331C22×C4C2×C4×D1114yes—
332C22×C4#433918yes—
333C22×C4#434114yes—
334C22×C4#434314yes—
335C22×C4C23×D1118yes—
336C22×C4C23×D1112yes—
337C22×C4C23×D1112yes—
338C22×C4C23×D1112yes—
339C4⋊C4—216no—
340C4⋊C4—2216no—
341C22⋊C4—2232no—
342C42—216no—
343C42—1116no—
344C42—1116no—
345C42—1116no—
346C42—2216no—
347C42C2×C4×D11116yes—
348C11C2×#228311yescharacteristic, complemented, Sylow
349C23—1116no—
350C23—114no—
351C23—118no—
352C23—228no—
353C23—228no—
354C23—2216no—
355C23—2216no—
356C23—224no—
357C23—222no—
358C23—222no—
359C23C22×C4×D1112yes—
360C23C2×#433914yes—
361C23C2×#434112yes—
362C23C2×#434312yes—
363C23#41×D1114yes—
364C23C24×D1111yescharacteristic
365C2×C4—28no—
366C2×C4—24no—
367C2×C4—28no—
368C2×C4—28no—
369C2×C4—28no—
370C2×C4—416no—
371C2×C4—114no—
372C2×C4—114no—
373C2×C4—114no—
374C2×C4—2232no—
375C2×C4—228no—
376C2×C4—228no—
377C2×C4—228no—
378C2×C4—224no—
379C2×C4—222no—
380C2×C4—222no—
381C2×C4—224no—
382C2×C4—2232no—
383C2×C4—2232no—
384C2×C4—228no—
385C2×C4—228no—
386C2×C4—228no—
387C2×C4—4416no—
388C2×C4#66925116yes—
389C2×C4#66945116yes—
390C2×C4C22×C4×D1114yes—
391C2×C4C22×C4×D1114yes—
392C2×C4C22×C4×D1114yes—
393C2×C4C2×#433918yes—
394C2×C4C2×#434114yes—
395C2×C4C2×#434314yes—
396C22—118no—
397C22—228no—
398C22—228no—
399C22—2232no—
400C22—224no—
401C22—224no—
402C22C2×#6692514yes—
403C22C2×#6694514yes—
404C22D11×#11714yes—
405C22#1062308818yes—
406C22#1062311118yes—
407C22C23×C4×D1111yescharacteristic
408C22C22×#433912yes—
409C22C22×#434111yescharacteristic
410C22C22×#434311yescharacteristic
411C22C2×#41×D1112yes—
412C4—24no—
413C4—48no—
414C4—224no—
415C4—224no—
416C4—224no—
417C4—448no—
418C4C2×#6692518yes—
419C4C2×#6694518yes—
420C2—228no—
421C2#1307101218yesdirect product factor
422C2C2×D11×#11711yescharacteristic
423C2C22×#6692511yescharacteristic
424C2C22×#6694511yescharacteristic
425C2C2×#1062308812yes—
426C2C2×#1062311112yes—
subgroupG/H
centerC23×C4C22×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C4×C11×C4⋊C4C2
socleC24×C11C24
prime radicalC24×D11C23
cosocleC23×C11C25
hypercenterC2×C4×C4⋊C4D11
hypocenterC11C2×#2283
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13071012C2direct (N × H)
3. C2×#10622264C2semidirect
4. C2×#10622590C2semidirect
7. C2×C4×C4⋊Dic11C2semidirect
9. C2×#10622545C2semidirect
10. C2×C4×C11×C4⋊C4C2semidirect
23. C2×C42×D11C4semidirect
25. C4×C11×C4⋊C4C22semidirect
32. #10622590C22semidirect
34. C4×C4⋊Dic11C22semidirect
35. #10622545C22semidirect
37. #10622264C22semidirect
75. C42×D11C2×C4semidirect
143. C2×C4×C4⋊C4D11semidirect
212. C4×C4⋊C4C2×D11semidirect
287. C2×C11#2283semidirect
348. C11C2×#2283semidirect
421. C2#13071012direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C42×D112
#130710122
C2×#106222642
C2×#106225902
C2×#106222772
C2×#106226002
C2×C4×C4⋊Dic112
C2×C4×(C2×D11)⋊C42
C2×#106225452
C2×C4×C11×C4⋊C42
C2×#228311