Finite Group Databasebeta

← C2×#13071011 #14912057

Subgroups — C2×#13071011 #14912057

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
1C23×C4×Dic11C211yesmaximal, characteristic
2#13071011C2116yesmaximal, direct product factor
3C2×#10622264C212yesmaximal, complemented
4C2×#10622590C212yesmaximal, complemented
5C2×#10622556C212yesmaximal
6C2×#10622825C211yesmaximal, characteristic
7C2×C4⋊C4×Dic11C212yesmaximal, complemented
8C2×C22⋊C4×Dic11C212yesmaximal
9C2×#10622261C212yesmaximal, complemented
10C2×C11×#380C211yesmaximal, characteristic
11C24×C4×C11C2211yescharacteristic
12C24×Dic11C2211yescharacteristic
13C24×Dic11C2211yescharacteristic
14C22×C11×C4⋊C4C2212yes—
15C22×C11×C22⋊C4C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×C4⋊Dic11C2212yes—
18C22×C4×Dic11C4116yescomplemented
19C22×C4×Dic11C2214yes—
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C22×C4×Dic11C2218yes—
25C11×#380C2218yes—
26C2×C11×#95C2212yes—
27#10622825C2218yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2214yes—
30C2×C11⋊#95C2214yes—
31C2×C11⋊#95C2214yes—
32#10622590C22116yescomplemented
33C4⋊C4×Dic11C22116yescomplemented
34#10622556C22116yes—
35C22⋊C4×Dic11C22116yes—
36#10622264C22116yescomplemented
37#10622261C22116yescomplemented
38C25×C11C2311yescharacteristic
39C23×C4×C11—28no—
40C23×C4×C11C2×C418yes—
41C23×C4×C11C2314yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2314yes—
44C23×C4×C11C2311yescharacteristic
45C23×Dic11—24no—
46C23×Dic11—24no—
47C23×Dic11—28no—
48C23×Dic11C2×C418yes—
49C23×Dic11C2×C418yes—
50C23×Dic11C2314yes—
51C23×Dic11C2314yes—
52C23×Dic11C2314yes—
53C23×Dic11C2311yescharacteristic
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2311yescharacteristic
56C23×Dic11C2311yescharacteristic
57C2×C11×C4⋊C4—28no—
58C2×C11×C4⋊C4C2318yes—
59C2×C11×C22⋊C4—28no—
60C2×C11×C22⋊C4C2318yes—
61C2×C22⋊Dic11—28no—
62C2×C22⋊Dic11C2318yes—
63C2×C4⋊Dic11—28no—
64C2×C4⋊Dic11C2318yes—
65C2×C4×Dic11—216no—
66C2×C4×Dic11C2×C418yes—
67C2×C4×Dic11C2×C418yes—
68C2×C4×Dic11C2×C418yes—
69C2×C4×Dic11C2×C418yes—
70C2×C4×Dic11C2×C4164yescomplemented
71C2×C4×Dic11C23116yes—
72C2×C4×Dic11C2314yes—
73C2×C4×Dic11C2314yes—
74C2×C4×Dic11C2314yes—
75C2×C4×Dic11C2314yes—
76C11×#95C2318yes—
77C11⋊#95C2318yes—
78C11⋊#95C23116yes—
79C11⋊#95C23116yes—
80C11⋊#95C23116yes—
81C2×#2283—111nomaximal, Sylow
82C24×C11—24no—
83C24×C11—24no—
84C24×C11C22×C414yes—
85C24×C11#4114yes—
86C24×C11#4114yes—
87C24×C11C2412yes—
88C24×C11C2411yescharacteristic
89C22×C4×C11—24no—
90C22×C4×C11—232no—
91C22×C4×C11—216no—
92C22×C4×C11—28no—
93C22×C4×C11—28no—
94C22×C4×C11—28no—
95C22×C4×C11C22×C414yes—
96C22×C4×C11C22×C4116yes—
97C22×C4×C11C22×C414yes—
98C22×C4×C11#4118yes—
99C22×C4×C11C2418yes—
100C22×C4×C11C2412yes—
101C22×C4×C11C2412yes—
102C22×Dic11—232no—
103C22×Dic11—216no—
104C22×Dic11—232no—
105C22×Dic11—28no—
106C22×Dic11—22no—
107C22×Dic11—22no—
108C22×Dic11—28no—
109C22×Dic11—22no—
110C22×Dic11—22no—
111C22×Dic11—24no—
112C22×Dic11—28no—
113C22×Dic11—28no—
114C22×Dic11—28no—
115C22×Dic11C22×C414yes—
116C22×Dic11C22×C414yes—
117C22×Dic11C22×C414yes—
118C22×Dic11C22×C4116yes—
119C22×Dic11C22×C4116yes—
120C22×Dic11C22×C414yes—
121C22×Dic11#4118yes—
122C22×Dic11C2418yes—
123C22×Dic11C2412yes—
124C22×Dic11C2412yes—
125C22×Dic11C2412yes—
126C22×Dic11C2412yes—
127C11×C4⋊C4—216no—
128C11×C22⋊C4—216no—
129C22⋊Dic11—216no—
130C4⋊Dic11—216no—
131C4×Dic11—232no—
132C4×Dic11C22×C4116yes—
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—111no—
142C2×#380D1111yescharacteristic
143C2×C4×C4⋊C4—112no—
144C2×C4×C22⋊C4—112no—
145C2×#376—112no—
146C23×C11—28no—
147C23×C11—28no—
148C23×C11—216no—
149C23×C11—216no—
150C23×C11—24no—
151C23×C11—24no—
152C23×C11#117116yes—
153C23×C11C23×C414yes—
154C23×C11C23×C412yes—
155C23×C11C2×#4114yes—
156C23×C11C2×#4112yes—
157C23×C11C2×#4114yes—
158C23×C11C2×#4114yes—
159C23×C11C2×#4112yes—
160C23×C11C2×#4114yes—
161C23×C11C2511yescharacteristic
162C2×C4×C11—28no—
163C2×C4×C11—24no—
164C2×C4×C11—232no—
165C2×C4×C11—28no—
166C2×C4×C11—28no—
167C2×C4×C11—28no—
168C2×C4×C11—416no—
169C2×C4×C11#117116yes—
170C2×C4×C11C23×C414yes—
171C2×C4×C11C23×C414yes—
172C2×C4×C11C2×#4118yes—
173C2×Dic11—232no—
174C2×Dic11—28no—
175C2×Dic11—28no—
176C2×Dic11—28no—
177C2×Dic11—22no—
178C2×Dic11—22no—
179C2×Dic11—22no—
180C2×Dic11—22no—
181C2×Dic11—24no—
182C2×Dic11—232no—
183C2×Dic11—28no—
184C2×Dic11—28no—
185C2×Dic11—28no—
186C2×Dic11—416no—
187C2×Dic11#117116yes—
188C2×Dic11C23×C414yes—
189C2×Dic11C23×C414yes—
190C2×Dic11C23×C414yes—
191C2×Dic11C23×C414yes—
192C2×Dic11C2×#4118yes—
193C24×C4—111no—
194C24×C4—111no—
195C24×C4C2×D1111yescharacteristic
196C22×C4⋊C4—112no—
197C22×C4⋊C4C2×D1112yes—
198C22×C22⋊C4—112no—
199C22×C22⋊C4C2×D1112yes—
200C22×C42—111no—
201C22×C42—111no—
202C22×C42—111no—
203C22×C42—111no—
204C22×C42—118no—
205C22×C42—1116no—
206C22×C42—114no—
207#383—1116no—
208#382—1116no—
209#381—1116no—
210#380—118no—
211#380C2×D1118yes—
212C4×C4⋊C4—1116no—
213C4×C22⋊C4—1116no—
214#376—1116no—
215C2×#95—112no—
216C2×#95—114no—
217C2×#95—114no—
218C2×#95—114no—
219C2×#95C2×D1112yes—
220C22×C11—24no—
221C22×C11—24no—
222C22×C11—28no—
223C22×C11—28no—
224C22×C11—232no—
225C22×C11C2×#11714yes—
226C22×C11C2×#11718yes—
227C22×C11C2×#11714yes—
228C22×C11C2×#11714yes—
229C22×C11#52918yes—
230C22×C11#52918yes—
231C22×C11C24×C411yescharacteristic
232C22×C11C22×#4111yescharacteristic
233C22×C11C22×#4112yes—
234C22×C11C22×#4111yescharacteristic
235C22×C11C22×#4112yes—
236C4×C11—24no—
237C4×C11—48no—
238C4×C11C2×#11718yes—
239Dic11—24no—
240Dic11—24no—
241Dic11—24no—
242Dic11—48no—
243Dic11C2×#11718yes—
244C25C22×D1111yescharacteristic
245C23×C4—28no—
246C23×C4—111no—
247C23×C4—118no—
248C23×C4—118no—
249C23×C4—114no—
250C23×C4—114no—
251C23×C4—111no—
252C23×C4—111no—
253C23×C4—111no—
254C23×C4—114no—
255C23×C4—228no—
256C23×C4—224no—
257C23×C4—224no—
258C23×C4C4×D1118yes—
259C23×C4C22×D1114yes—
260C23×C4C22×D1114yes—
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—28no—
268C2×C22⋊C4—118no—
269C2×C22⋊C4—228no—
270C2×C22⋊C4C22×D1118yes—
271C2×C42—118no—
272C2×C42—118no—
273C2×C42—118no—
274C2×C42—118no—
275C2×C42—1164no—
276C2×C42—114no—
277C2×C42—114no—
278C2×C42—114no—
279C2×C42—114no—
280C2×C42—1116no—
281C2×C42—2216no—
282#95—118no—
283#95—1116no—
284#95—1116no—
285#95—1116no—
286#95C22×D1118yes—
287C2×C11—28no—
288C2×C11#228318yescomplemented
289C2×C11C22×#11711yescharacteristic
290C2×C11C22×#11711yescharacteristic
291C2×C11C22×#11711yescharacteristic
292C2×C11C2×#52912yes—
293C2×C11C2×#52912yes—
294C24—24no—
295C24—24no—
296C24C2×C4×D1114yes—
297C24#434114yes—
298C24#434314yes—
299C24C23×D1112yes—
300C24C23×D1111yescharacteristic
301C22×C4—24no—
302C22×C4—232no—
303C22×C4—216no—
304C22×C4—28no—
305C22×C4—28no—
306C22×C4—28no—
307C22×C4—114no—
308C22×C4—118no—
309C22×C4—112no—
310C22×C4—1116no—
311C22×C4—1116no—
312C22×C4—114no—
313C22×C4—114no—
314C22×C4—114no—
315C22×C4—112no—
316C22×C4—112no—
317C22×C4—112no—
318C22×C4—118no—
319C22×C4—2232no—
320C22×C4—2216no—
321C22×C4—2232no—
322C22×C4—228no—
323C22×C4—222no—
324C22×C4—222no—
325C22×C4—228no—
326C22×C4—222no—
327C22×C4—222no—
328C22×C4—224no—
329C22×C4—228no—
330C22×C4—228no—
331C22×C4—228no—
332C22×C4C2×C4×D1114yes—
333C22×C4C2×C4×D11116yes—
334C22×C4C2×C4×D1114yes—
335C22×C4#434118yes—
336C22×C4C23×D1118yes—
337C22×C4C23×D1112yes—
338C22×C4C23×D1112yes—
339C4⋊C4—216no—
340C4⋊C4—2216no—
341C22⋊C4—216no—
342C22⋊C4—2216no—
343C42—1116no—
344C42—1116no—
345C42—1116no—
346C42—1116no—
347C42—2232no—
348C11C2×#228311yescharacteristic, complemented, Sylow
349C23—28no—
350C23—28no—
351C23—216no—
352C23—216no—
353C23—24no—
354C23—24no—
355C23#66945116yes—
356C23C22×C4×D1114yes—
357C23C22×C4×D1112yes—
358C23C2×#434114yes—
359C23C2×#434114yes—
360C23C2×#434112yes—
361C23C2×#434314yes—
362C23C2×#434312yes—
363C23#41×D1114yes—
364C23C24×D1111yescharacteristic
365C2×C4—28no—
366C2×C4—24no—
367C2×C4—232no—
368C2×C4—28no—
369C2×C4—28no—
370C2×C4—28no—
371C2×C4—416no—
372C2×C4—1116no—
373C2×C4—114no—
374C2×C4—118no—
375C2×C4—114no—
376C2×C4—114no—
377C2×C4—114no—
378C2×C4—2232no—
379C2×C4—2232no—
380C2×C4—228no—
381C2×C4—228no—
382C2×C4—228no—
383C2×C4—222no—
384C2×C4—222no—
385C2×C4—222no—
386C2×C4—222no—
387C2×C4—224no—
388C2×C4—228no—
389C2×C4—228no—
390C2×C4—228no—
391C2×C4—4416no—
392C2×C4#66930116yes—
393C2×C4C22×C4×D1114yes—
394C2×C4C22×C4×D1114yes—
395C2×C4C2×#434118yes—
396C22—28no—
397C22—28no—
398C22—232no—
399C22—24no—
400C22—24no—
401C22C2×#6693014yes—
402C22C2×#6694518yes—
403C22C2×#6694514yes—
404C22D11×#11714yes—
405C22#1062313118yes—
406C22#1062315518yes—
407C22C23×C4×D1111yescharacteristic
408C22C22×#434111yescharacteristic
409C22C22×#434112yes—
410C22C22×#434311yescharacteristic
411C22C2×#41×D1112yes—
412C4—24no—
413C4—48no—
414C4—118no—
415C4—224no—
416C4—224no—
417C4—224no—
418C4—448no—
419C4C2×#6693018yes—
420C2—28no—
421C2#1307101118yesdirect product factor
422C2C2×D11×#11711yescharacteristic
423C2C22×#6693011yescharacteristic
424C2C22×#6694511yescharacteristic
425C2C2×#1062313112yes—
426C2C2×#1062315512yes—
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#380C2
socleC24×C11C24
prime radicalC25×C11C23
cosocleC23×C11C25
hypercenterC2×#380D11
hypocenterC11C2×#2283
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. #13071011C2direct (N × H)
3. C2×#10622264C2semidirect
4. C2×#10622590C2semidirect
7. C2×C4⋊C4×Dic11C2semidirect
9. C2×#10622261C2semidirect
18. C22×C4×Dic11C4semidirect
32. #10622590C22semidirect
33. C4⋊C4×Dic11C22semidirect
36. #10622264C22semidirect
37. #10622261C22semidirect
70. C2×C4×Dic11C2×C4semidirect
288. C2×C11#2283semidirect
348. C11C2×#2283semidirect
421. C2#13071011direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4×Dic112
#130710112
C2×#106222642
C2×#106225902
C2×#106225562
C2×#106228252
C2×C4⋊C4×Dic112
C2×C22⋊C4×Dic112
C2×#106222612
C2×C11×#3802
C2×#228311