Finite Group Databasebeta

← C2×#13071009 #14912055

Subgroups — C2×#13071009 #14912055

Order 2816.

3246 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D11C211yesmaximal, characteristic
2#13071009C2116yesmaximal, direct product factor
3C2×#10622264C212yesmaximal, complemented
4C2×#10622549C211yesmaximal, characteristic, complemented
5C2×#10622277C212yesmaximal
6C2×#10622600C212yesmaximal
7C2×C4⋊C4×Dic11C212yesmaximal, complemented
8C2×#10622279C212yesmaximal
9C2×#10622261C212yesmaximal, complemented
10C2×C11×#382C211yesmaximal, characteristic, complemented
11C23×C4×D11C2211yescharacteristic
12C23×C4×D11C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C22×C11×C4⋊C4C2212yes—
15C22×C42×C11C2211yescharacteristic
16C22×(C2×D11)⋊C4C2214yes—
17C22×C4⋊Dic11C2212yes—
18C22×C4×Dic11C2214yes—
19C22×C4×Dic11C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C2×C42×D11C4116yescomplemented
23C2×C42×D11C2218yes—
24C11×#382C2218yescomplemented
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2214yes—
31#10622600C22116yes—
32C4⋊C4×Dic11C22116yescomplemented
33#10622549C2218yescomplemented
34#10622279C22116yes—
35#10622277C22116yes—
36#10622264C22116yescomplemented
37#10622261C22116yescomplemented
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—24no—
49C22×C4×D11—24no—
50C22×C4×D11—28no—
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×C11C2×C418yes—
60C2×C42×C11C2314yes—
61C2×(C2×D11)⋊C4—216no—
62C2×(C2×D11)⋊C4C23116yes—
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×Dic11C23116yes—
70C2×C4×Dic11C2314yes—
71C2×C4×Dic11C2314yes—
72C2×C4×Dic11C2314yes—
73C42×D11C2×C4164yescomplemented
74C11×#95C2318yes—
75C11×#95C2318yes—
76C11⋊#95C23116yes—
77C11⋊#95C2318yes—
78C11⋊#95C23116yes—
79C11⋊#95C2318yes—
80C2×#2283—111nomaximal, Sylow
81C24×C11C2411yescharacteristic
82C23×D11—22no—
83C23×D11—22no—
84C23×D11—24no—
85C23×D11C22×C414yes—
86C23×D11#4118yes—
87C23×D11C2412yes—
88C22×C4×C11—24no—
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#4114yes—
97C22×C4×C11#4114yes—
98C22×C4×C11C2418yes—
99C22×C4×C11C2412yes—
100C22×C4×C11C2412yes—
101C22×C4×C11C2412yes—
102C22×Dic11—22no—
103C22×Dic11—22no—
104C22×Dic11—24no—
105C22×Dic11—28no—
106C22×Dic11—28no—
107C22×Dic11—28no—
108C22×Dic11C22×C414yes—
109C22×Dic11C22×C414yes—
110C22×Dic11C22×C414yes—
111C22×Dic11#4118yes—
112C22×Dic11C2418yes—
113C22×Dic11C2412yes—
114C22×Dic11C2412yes—
115C22×Dic11C2412yes—
116C2×C4×D11—232no—
117C2×C4×D11—216no—
118C2×C4×D11—232no—
119C2×C4×D11—216no—
120C2×C4×D11—232no—
121C2×C4×D11—28no—
122C2×C4×D11—28no—
123C2×C4×D11C22×C4116yes—
124C2×C4×D11C22×C4116yes—
125C2×C4×D11C22×C4116yes—
126C11×C4⋊C4—216no—
127C42×C11C22×C4116yes—
128(C2×D11)⋊C4—232no—
129C4⋊Dic11—216no—
130C4×Dic11—232no—
131C4×Dic11C22×C4116yes—
132C4×Dic11C22×C4116yes—
133C4×Dic11C22×C4116yes—
134C23×C42—111no—
135#2283—1116no—
136C2×#383—112no—
137C2×#382—111no—
138C2×#382D1111yescharacteristic, complemented
139C2×#381—112no—
140C2×#380—112no—
141C2×C4×C4⋊C4—112no—
142C2×C4×C22⋊C4—112no—
143C2×#376—112no—
144C23×C11C23×C412yes—
145C23×C11C2×#4112yes—
146C23×C11C2×#4112yes—
147C23×C11C2×#4114yes—
148C23×C11C2×#4114yes—
149C23×C11C2511yescharacteristic
150C22×D11—28no—
151C22×D11—28no—
152C22×D11—216no—
153C22×D11—216no—
154C22×D11—22no—
155C22×D11—22no—
156C22×D11—24no—
157C22×D11#117116yes—
158C22×D11C23×C414yes—
159C22×D11C2×#4118yes—
160C2×C4×C11—28no—
161C2×C4×C11—28no—
162C2×C4×C11—24no—
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×C11C23×C414yes—
170C2×C4×C11C23×C414yes—
171C2×C4×C11C23×C414yes—
172C2×C4×C11C2×#4114yes—
173C2×C4×C11C2×#4114yes—
174C2×Dic11—28no—
175C2×Dic11—28no—
176C2×Dic11—22no—
177C2×Dic11—22no—
178C2×Dic11—24no—
179C2×Dic11—28no—
180C2×Dic11—28no—
181C2×Dic11—28no—
182C2×Dic11—416no—
183C2×Dic11#117116yes—
184C2×Dic11C23×C414yes—
185C2×Dic11C23×C414yes—
186C2×Dic11C23×C414yes—
187C2×Dic11C2×#4118yes—
188C4×D11—232no—
189C4×D11—232no—
190C4×D11—232no—
191C24×C4—111no—
192C24×C4—111no—
193C24×C4—111no—
194C22×C4⋊C4—112no—
195C22×C4⋊C4C2×D1112yes—
196C22×C22⋊C4—114no—
197C22×C42—111no—
198C22×C42—111no—
199C22×C42—111no—
200C22×C42—118no—
201C22×C42—1116no—
202C22×C42—114no—
203C22×C42C2×D1111yescharacteristic
204#383—1116no—
205#382—118no—
206#382C2×D1118yescomplemented
207#381—1116no—
208#380—1116no—
209C4×C4⋊C4—1116no—
210C4×C22⋊C4—1116no—
211#376—1116no—
212C2×#95—114no—
213C2×#95—112no—
214C2×#95—112no—
215C2×#95—114no—
216C2×#95C2×D1112yes—
217C2×#95C2×D1112yes—
218C22×C11C2×#11714yes—
219C22×C11C2×#11714yes—
220C22×C11C2×#11714yes—
221C22×C11#52918yes—
222C22×C11#52918yes—
223C22×C11C24×C411yescharacteristic
224C22×C11C22×#4111yescharacteristic
225C22×C11C22×#4111yescharacteristic
226C22×C11C22×#4112yes—
227C22×C11C22×#4112yes—
228C2×D11—24no—
229C2×D11—24no—
230C2×D11—28no—
231C2×D11—28no—
232C2×D11—232no—
233C2×D11C2×#11718yes—
234C4×C11—24no—
235C4×C11—24no—
236C4×C11—48no—
237C4×C11C2×#11718yes—
238Dic11—24no—
239Dic11—24no—
240Dic11—48no—
241Dic11C2×#11718yes—
242C25—111no—
243C23×C4—111no—
244C23×C4—111no—
245C23×C4—111no—
246C23×C4—118no—
247C23×C4—118no—
248C23×C4—118no—
249C23×C4—114no—
250C23×C4—114no—
251C23×C4—114no—
252C23×C4—114no—
253C23×C4—228no—
254C23×C4—228no—
255C23×C4—224no—
256C23×C4—224no—
257C23×C4C22×D1114yes—
258C23×C4C22×D1111yescharacteristic
259C23×C4C22×D1111yescharacteristic
260C23×C4C22×D1111yescharacteristic
261C2×C4⋊C4—28no—
262C2×C4⋊C4—118no—
263C2×C4⋊C4—228no—
264C2×C4⋊C4C22×D1118yes—
265C2×C22⋊C4—1116no—
266C2×C22⋊C4—2216no—
267C2×C42—118no—
268C2×C42—118no—
269C2×C42—118no—
270C2×C42—114no—
271C2×C42—114no—
272C2×C42—114no—
273C2×C42—1164no—
274C2×C42—1116no—
275C2×C42—2216no—
276C2×C42C4×D1118yes—
277C2×C42C22×D1114yes—
278#95—1116no—
279#95—118no—
280#95—118no—
281#95—1116no—
282#95C22×D1118yes—
283#95C22×D1118yes—
284C2×C11#228318yescomplemented
285C2×C11C22×#11711yescharacteristic
286C2×C11C22×#11711yescharacteristic
287C2×C11C22×#11711yescharacteristic
288C2×C11C2×#52912yes—
289C2×C11C2×#52912yes—
290D11—28no—
291C24—114no—
292C24—118no—
293C24—112no—
294C24—222no—
295C24—222no—
296C24—224no—
297C24C23×D1111yescharacteristic
298C22×C4—24no—
299C22×C4—24no—
300C22×C4—28no—
301C22×C4—28no—
302C22×C4—28no—
303C22×C4—114no—
304C22×C4—118no—
305C22×C4—112no—
306C22×C4—114no—
307C22×C4—114no—
308C22×C4—112no—
309C22×C4—112no—
310C22×C4—1116no—
311C22×C4—1116no—
312C22×C4—1116no—
313C22×C4—118no—
314C22×C4—2232no—
315C22×C4—2216no—
316C22×C4—2232no—
317C22×C4—2216no—
318C22×C4—222no—
319C22×C4—222no—
320C22×C4—224no—
321C22×C4—2232no—
322C22×C4—228no—
323C22×C4—228no—
324C22×C4—228no—
325C22×C4—228no—
326C22×C4—228no—
327C22×C4C2×C4×D1114yes—
328C22×C4C2×C4×D1114yes—
329C22×C4C2×C4×D1114yes—
330C22×C4#434114yes—
331C22×C4#434314yes—
332C22×C4C23×D1118yes—
333C22×C4C23×D1112yes—
334C22×C4C23×D1112yes—
335C22×C4C23×D1112yes—
336C4⋊C4—216no—
337C4⋊C4—2216no—
338C22⋊C4—2232no—
339C42—1116no—
340C42—1116no—
341C42—1116no—
342C42—2232no—
343C42C2×C4×D11116yes—
344C11C2×#228311yescharacteristic, complemented, Sylow
345C23—1116no—
346C23—114no—
347C23—118no—
348C23—228no—
349C23—228no—
350C23—222no—
351C23—222no—
352C23—224no—
353C23—2216no—
354C23—2216no—
355C23C22×C4×D1112yes—
356C23C2×#434112yes—
357C23C2×#434312yes—
358C23#41×D1114yes—
359C23#41×D1114yes—
360C23C24×D1111yescharacteristic
361C2×C4—28no—
362C2×C4—28no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—28no—
366C2×C4—28no—
367C2×C4—28no—
368C2×C4—416no—
369C2×C4—1116no—
370C2×C4—114no—
371C2×C4—118no—
372C2×C4—114no—
373C2×C4—114no—
374C2×C4—2232no—
375C2×C4—2232no—
376C2×C4—228no—
377C2×C4—228no—
378C2×C4—222no—
379C2×C4—222no—
380C2×C4—224no—
381C2×C4—2232no—
382C2×C4—228no—
383C2×C4—228no—
384C2×C4—228no—
385C2×C4—4416no—
386C2×C4#66945116yes—
387C2×C4C22×C4×D1114yes—
388C2×C4C22×C4×D1114yes—
389C2×C4C22×C4×D1114yes—
390C2×C4C2×#434114yes—
391C2×C4C2×#434314yes—
392C22—118no—
393C22—228no—
394C22—228no—
395C22—2232no—
396C22—224no—
397C22—224no—
398C22C2×#6694514yes—
399C22D11×#11714yes—
400C22D11×#11714yes—
401C22#1062321118yes—
402C22#1062322218yes—
403C22C23×C4×D1111yescharacteristic
404C22C22×#434111yescharacteristic
405C22C22×#434311yescharacteristic
406C22C2×#41×D1112yes—
407C22C2×#41×D1112yes—
408C4—24no—
409C4—24no—
410C4—48no—
411C4—118no—
412C4—224no—
413C4—224no—
414C4—448no—
415C4C2×#6694518yes—
416C2—228no—
417C2#1307100918yesdirect product factor
418C2C2×D11×#11711yescharacteristic
419C2C2×D11×#11711yescharacteristic
420C2C22×#6694511yescharacteristic
421C2C2×#1062321112yes—
422C2C2×#1062322212yes—
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#382C2
socleC24×C11C24
prime radicalC24×D11C23
cosocleC23×C11C25
hypercenterC2×#382D11
hypocenterC11C2×#2283
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
2. #13071009C2direct (N × H)
3. C2×#10622264C2semidirect
4. C2×#10622549C2semidirect
7. C2×C4⋊C4×Dic11C2semidirect
9. C2×#10622261C2semidirect
10. C2×C11×#382C2semidirect
22. C2×C42×D11C4semidirect
24. C11×#382C22semidirect
32. C4⋊C4×Dic11C22semidirect
33. #10622549C22semidirect
36. #10622264C22semidirect
37. #10622261C22semidirect
73. C42×D11C2×C4semidirect
138. C2×#382D11semidirect
206. #382C2×D11semidirect
284. C2×C11#2283semidirect
344. C11C2×#2283semidirect
417. C2#13071009direct (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
#130710092
C2×#106222642
C2×#106225492
C2×#106222772
C2×#106226002
C2×C4⋊C4×Dic112
C2×#106222792
C2×#106222612
C2×C11×#3822
C2×#228311