Finite Group Databasebeta

← C2×#13074000 #14925009

Subgroups — C2×#13074000 #14925009

Order 2816.

2574 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66942C211yesmaximal, characteristic
2C22×#66940C211yesmaximal, characteristic
3#13074000C2116yesmaximal, direct product factor
4C2×#10622593C211yesmaximal, characteristic
5C2×#10622269C211yesmaximal, characteristic
6C2×#10622592C211yesmaximal, characteristic
7C2×#10622260C212yesmaximal
8C2×#10622260C212yesmaximal
9C2×#10622586C212yesmaximal
10C2×#10622585C212yesmaximal
11C2×#10622262C211yesmaximal, characteristic
12C2×C11×#398C211yesmaximal, characteristic
13C23×Dic22C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2212yes—
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4⋊Dic11C2212yes—
19C22×Dic11⋊C4C2211yescharacteristic
20C22×Dic11⋊C4C2211yescharacteristic
21C22×Dic11⋊C4C2211yescharacteristic
22C22×Dic11⋊C4C2211yescharacteristic
23C22×Dic11⋊C4C2212yes—
24C22×Dic11⋊C4C2212yes—
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2212yes—
27C22×C4×Dic11C2212yes—
28C22×C4×Dic11C2212yes—
29C22×C4×Dic11C2211yescharacteristic
30C2×#66942—28no—
31C2×#66942C2218yes—
32C2×#66940—28no—
33C2×#66940C2218yes—
34C11×#398C2218yes—
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622593C2218yes—
42#10622592C2218yes—
43#10622586C22116yes—
44#10622585C22116yes—
45#10622269C2218yes—
46#10622262C2218yes—
47#10622260C22116yes—
48#10622260C22116yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2312yes—
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2311yescharacteristic
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2312yes—
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C22×Dic22—24no—
61C22×Dic22—28no—
62C22×Dic22C2314yes—
63C2×C11×C4⋊C4—24no—
64C2×C11×C4⋊C4—24no—
65C2×C11×C4⋊C4—44no—
66C2×C11×C4⋊C4C2314yes—
67C2×C11×C4⋊C4C2314yes—
68C2×C11×C4⋊C4C2318yes—
69C2×C4⋊Dic11—24no—
70C2×C4⋊Dic11—28no—
71C2×C4⋊Dic11C2314yes—
72C2×C4⋊Dic11C2318yes—
73C2×Dic11⋊C4—24no—
74C2×Dic11⋊C4—28no—
75C2×Dic11⋊C4—24no—
76C2×Dic11⋊C4—24no—
77C2×Dic11⋊C4—24no—
78C2×Dic11⋊C4—28no—
79C2×Dic11⋊C4—44no—
80C2×Dic11⋊C4Q8116yescomplemented
81C2×Dic11⋊C4C2318yes—
82C2×Dic11⋊C4C2314yes—
83C2×Dic11⋊C4C2318yes—
84C2×Dic11⋊C4C2314yes—
85C2×Dic11⋊C4C2314yes—
86C2×Dic11⋊C4C2314yes—
87C2×Dic11⋊C4C2318yes—
88C2×Dic11⋊C4C2318yes—
89C2×C4×Dic11—28no—
90C2×C4×Dic11—44no—
91C2×C4×Dic11D418yes—
92C2×C4×Dic11C2318yes—
93C2×C4×Dic11C2318yes—
94C2×C4×Dic11C2314yes—
95#66942—232no—
96#66940—232no—
97C11×#95C2318yes—
98C11×#95C2314yes—
99C11⋊#95C2318yes—
100C11⋊#95C2318yes—
101C11⋊#95C2314yes—
102C11⋊#95C2318yes—
103C2×#2584—111nomaximal, Sylow
104C24×C11C2411yescharacteristic
105C22×C4×C11—24no—
106C22×C4×C11—24no—
107C22×C4×C11—24no—
108C22×C4×C11—24no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—24no—
112C22×C4×C11—24no—
113C22×C4×C11—22no—
114C22×C4×C11—24no—
115C22×C4×C11—22no—
116C22×C4×C11C2×D414yes—
117C22×C4×C11C2×Q818yes—
118C22×C4×C11C2412yes—
119C22×C4×C11C2414yes—
120C22×C4×C11C2412yes—
121C22×C4×C11C2412yes—
122C22×C4×C11C2414yes—
123C22×Dic11—24no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—24no—
127C22×Dic11—24no—
128C22×Dic11—24no—
129C22×Dic11—22no—
130C22×Dic11—24no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11C2×D414yes—
135C22×Dic11C2×D414yes—
136C22×Dic11C2×Q818yes—
137C22×Dic11C2×Q818yes—
138C22×Dic11#4118yes—
139C22×Dic11C2412yes—
140C22×Dic11C2412yes—
141C22×Dic11C2412yes—
142C22×Dic11C2414yes—
143C22×Dic11C2414yes—
144C22×Dic11C2412yes—
145C2×Dic22—232no—
146C2×Dic22—216no—
147C2×Dic22—28no—
148C11×C4⋊C4—28no—
149C11×C4⋊C4—28no—
150C11×C4⋊C4—48no—
151C4⋊Dic11—28no—
152C4⋊Dic11—216no—
153Dic11⋊C4—216no—
154Dic11⋊C4—28no—
155Dic11⋊C4—28no—
156Dic11⋊C4—28no—
157Dic11⋊C4—216no—
158Dic11⋊C4—28no—
159Dic11⋊C4—48no—
160Dic11⋊C4C2×Q8132yescomplemented
161C4×Dic11—216no—
162C4×Dic11—48no—
163C4×Dic11C2×D4116yes—
164C22×#125—111no—
165C22×C4×Q8—111no—
166#2584—1116no—
167C2×#398—111no—
168C2×#398D1111yescharacteristic
169C2×#395—111no—
170C2×#395—111no—
171C2×#389—112no—
172C2×#389—112no—
173C2×#389—112no—
174C2×#389—112no—
175C2×C4×C4⋊C4—111no—
176C23×C11C22×D412yes—
177C23×C11C22×Q814yes—
178C23×C11C2×#4114yes—
179C23×C11H(5,𝔽2)12yes—
180C23×C112−1+412yes—
181C23×C11C2511yescharacteristic
182C2×C4×C11—28no—
183C2×C4×C11—216no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—24no—
191C2×C4×C11—24no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—24no—
195C2×C4×C11—44no—
196C2×C4×C11—48no—
197C2×C4×C11—44no—
198C2×C4×C11C22×D414yes—
199C2×C4×C11C22×Q818yes—
200C2×Dic11—216no—
201C2×Dic11—28no—
202C2×Dic11—216no—
203C2×Dic11—24no—
204C2×Dic11—24no—
205C2×Dic11—24no—
206C2×Dic11—22no—
207C2×Dic11—24no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—24no—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—44no—
215C2×Dic11—44no—
216C2×Dic11C4⋊Q8116yes—
217C2×Dic11C22×D414yes—
218C2×Dic11C22×D414yes—
219C2×Dic11C22×Q818yes—
220C2×Dic11C22×Q818yes—
221C2×Dic11C2×#4118yes—
222Dic22—232no—
223C23×Q8—111no—
224C2×#125—118no—
225C2×#125—228no—
226C2×C4×Q8—118no—
227C2×C4×Q8—228no—
228C22×C4⋊C4—112no—
229C22×C4⋊C4—111no—
230C22×C4⋊C4—112no—
231C22×C4⋊C4—112no—
232C22×C4⋊C4—111no—
233C22×C4⋊C4—111no—
234C22×C4⋊C4—111no—
235C22×C4⋊C4—112no—
236C22×C4⋊C4—111no—
237C22×C4⋊C4—112no—
238C22×C4⋊C4C2×D1111yescharacteristic
239C22×C4⋊C4C2×D1111yescharacteristic
240C22×C4⋊C4C2×D1112yes—
241C22×C42—111no—
242C22×C42—112no—
243C22×C42—112no—
244#398—118no—
245#398C2×D1118yes—
246#395—118no—
247#395—118no—
248#389—1116no—
249#389—1116no—
250#389—1116no—
251#389—1116no—
252C4×C4⋊C4—118no—
253C2×#95—111no—
254C2×#95—112no—
255C2×#95—112no—
256C2×#95—112no—
257C2×#95C2×D1111yescharacteristic
258C2×#95C2×D1112yes—
259C22×C11#52514yes—
260C22×C11C2×C4⋊Q814yes—
261C22×C11#53714yes—
262C22×C11#55418yes—
263C22×C11#55718yes—
264C22×C11C23×D411yescharacteristic
265C22×C11C23×Q812yes—
266C22×C11C22×#4112yes—
267C22×C11C2×H(5,𝔽2)11yescharacteristic
268C22×C11C2×2−1+411yescharacteristic
269C4×C11—24no—
270C4×C11—28no—
271C4×C11—42no—
272C4×C11—44no—
273C4×C11—42no—
274Dic11—28no—
275Dic11—24no—
276Dic11—28no—
277Dic11—42no—
278Dic11—42no—
279Dic11C2×C4⋊Q818yes—
280C22×Q8—114no—
281C22×Q8—228no—
282C22×Q8—224no—
283C23×C4—111no—
284C23×C4—111no—
285C23×C4—112no—
286C23×C4—112no—
287C23×C4—111no—
288C23×C4—111no—
289C23×C4C22×D1111yescharacteristic
290C23×C4C22×D1111yescharacteristic
291C23×C4C22×D1112yes—
292C23×C4C22×D1111yescharacteristic
293C23×C4C22×D1112yes—
294#125—2232no—
295C4×Q8—2232no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4—1116no—
300C2×C4⋊C4—118no—
301C2×C4⋊C4—118no—
302C2×C4⋊C4—114no—
303C2×C4⋊C4—114no—
304C2×C4⋊C4—114no—
305C2×C4⋊C4—114no—
306C2×C4⋊C4—114no—
307C2×C4⋊C4—118no—
308C2×C4⋊C4—118no—
309C2×C4⋊C4—118no—
310C2×C4⋊C4—228no—
311C2×C4⋊C4—224no—
312C2×C4⋊C4—224no—
313C2×C4⋊C4—224no—
314C2×C4⋊C4—224no—
315C2×C4⋊C4—228no—
316C2×C4⋊C4—228no—
317C2×C4⋊C4—224no—
318C2×C4⋊C4—444no—
319C2×C4⋊C4C22×D1114yes—
320C2×C4⋊C4C22×D1114yes—
321C2×C4⋊C4C22×D1118yes—
322C2×C42—118no—
323C2×C42—114no—
324C2×C42—118no—
325C2×C42—118no—
326C2×C42—228no—
327C2×C42—444no—
328#95—114no—
329#95—118no—
330#95—118no—
331#95—118no—
332#95C22×D1114yes—
333#95C22×D1118yes—
334C2×C11#258418yescomplemented
335C2×C11C2×#52511yescharacteristic
336C2×C11C22×C4⋊Q811yescharacteristic
337C2×C11C2×#53711yescharacteristic
338C2×C11C2×#55412yes—
339C2×C11C2×#55712yes—
340C24C23×D1111yescharacteristic
341C2×Q8—2216no—
342C2×Q8—2232no—
343C2×Q8—228no—
344C22×C4—24no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—22no—
354C22×C4—24no—
355C22×C4—114no—
356C22×C4—118no—
357C22×C4—112no—
358C22×C4—114no—
359C22×C4—118no—
360C22×C4—118no—
361C22×C4—114no—
362C22×C4—114no—
363C22×C4—112no—
364C22×C4—112no—
365C22×C4—112no—
366C22×C4—224no—
367C22×C4—222no—
368C22×C4—224no—
369C22×C4—224no—
370C22×C4—224no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—222no—
374C22×C4—222no—
375C22×C4—224no—
376C22×C4—222no—
377C22×C4D4×D1114yes—
378C22×C4Q8×D1118yes—
379C22×C4C23×D1112yes—
380C22×C4C23×D1114yes—
381C22×C4C23×D1112yes—
382C22×C4C23×D1112yes—
383C22×C4C23×D1114yes—
384C4⋊C4—28no—
385C4⋊C4—28no—
386C4⋊C4—48no—
387C4⋊C4—1132no—
388C4⋊C4—2216no—
389C4⋊C4—228no—
390C4⋊C4—228no—
391C4⋊C4—228no—
392C4⋊C4—228no—
393C4⋊C4—2216no—
394C4⋊C4—2216no—
395C4⋊C4—228no—
396C4⋊C4—448no—
397C42—1116no—
398C42—2216no—
399C42—448no—
400C11C2×#258411yescharacteristic, complemented, Sylow
401C23C2×D4×D1112yes—
402C23#6703712yes—
403C23C2×Q8×D1114yes—
404C23#41×D1114yes—
405C23#6704312yes—
406C23C24×D1111yescharacteristic
407Q8—2232no—
408C2×C4—216no—
409C2×C4—28no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—22no—
420C2×C4—24no—
421C2×C4—48no—
422C2×C4—44no—
423C2×C4—44no—
424C2×C4—1116no—
425C2×C4—114no—
426C2×C4—118no—
427C2×C4—114no—
428C2×C4—118no—
429C2×C4—118no—
430C2×C4—228no—
431C2×C4—2216no—
432C2×C4—2216no—
433C2×C4—224no—
434C2×C4—222no—
435C2×C4—224no—
436C2×C4—224no—
437C2×C4—224no—
438C2×C4—222no—
439C2×C4—222no—
440C2×C4—222no—
441C2×C4—222no—
442C2×C4—224no—
443C2×C4—222no—
444C2×C4—444no—
445C2×C4—444no—
446C2×C4C2×D4×D1114yes—
447C2×C4C2×Q8×D1118yes—
448C22#1062313914yes—
449C22#1062316718yes—
450C22#1062318714yes—
451C22#1062321618yes—
452C22D11×C4⋊Q814yes—
453C22C22×D4×D1111yescharacteristic
454C22C2×#6703711yescharacteristic
455C22C22×Q8×D1112yes—
456C22C2×#41×D1112yes—
457C22C2×#6704311yescharacteristic
458C4—28no—
459C4—24no—
460C4—44no—
461C4—42no—
462C4—42no—
463C4—118no—
464C4—228no—
465C4—224no—
466C4—228no—
467C4—442no—
468C4—442no—
469C2#1307400018yesdirect product factor
470C2C2×#1062318711yescharacteristic
471C2C2×D11×C4⋊Q811yescharacteristic
472C2C2×#1062313911yescharacteristic
473C2C2×#1062316712yes—
474C2C2×#1062321612yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#398C2
socle, prime radicalC24×C11C24
hypercenterC2×#398D11
hypocenterC11C2×#2584
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
3. #13074000C2direct (N × H)
80. C2×Dic11⋊C4Q8semidirect
160. Dic11⋊C4C2×Q8semidirect
334. C2×C11#2584semidirect
400. C11C2×#2584semidirect
469. C2#13074000direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669422
C22×#669402
#130740002
C2×#106225932
C2×#106222692
C2×#106225922
C2×#106222602
C2×#106225862
C2×#106225852
C2×#106222622
C2×C11×#3982
C2×#258411