Finite Group Databasebeta

← C2×#13069954 #14781806

Subgroups — C2×#13069954 #14781806

Order 2816.

1238 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66923C211yesmaximal, characteristic
2C22×#66871C211yesmaximal, characteristic
3C22×#66872C211yesmaximal, characteristic
4#13069954C218yesmaximal, direct product factor
5C2×#10622167C211yesmaximal, characteristic
6C2×#10622167C211yesmaximal, characteristic
7C2×#10622162C211yesmaximal, characteristic
8C2×C11×#389C211yesmaximal, characteristic
9C22×C11×C4⋊C4—21no—
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C22×C4⋊Dic11C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×Dic11⋊C4—21no—
16C22×Dic11⋊C4—21no—
17C23×C11⋊C8C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19C2×#66923—22no—
20C2×#66923—24no—
21C2×#66923—24no—
22C2×#66923C2214yes—
23C11×#389—22no—
24C11×#389C2214yes—
25C2×C11×#95—21no—
26C2×#66872—24no—
27C2×#66872C2214yes—
28C2×#66871—24no—
29C2×#66871C2214yes—
30#10622167C2214yes—
31#10622167C2214yes—
32#10622162C2214yes—
33C23×C4×C11—21no—
34C23×C4×C11—21no—
35C23×C4×C11D411yescharacteristic
36C23×C4×C11D411yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C23×Dic11—21no—
39C23×Dic11—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—24no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—44no—
47C2×C11×C4⋊C4Q814yes—
48C2×C11×C4⋊C4C2312yes—
49C2×C11×C4⋊C4C2312yes—
50C2×C42×C11—22no—
51C2×C42×C11—22no—
52C2×C42×C11D412yes—
53C2×C42×C11C2312yes—
54C2×C4⋊Dic11—22no—
55C2×C4⋊Dic11—22no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11D414yes—
59C2×C4⋊Dic11D414yes—
60C2×C4⋊Dic11C2312yes—
61C2×C4⋊Dic11C2312yes—
62C2×Dic11⋊C4—28no—
63C2×Dic11⋊C4—28no—
64C2×Dic11⋊C4—24no—
65C2×Dic11⋊C4—24no—
66C22×C11⋊C8—22no—
67C22×C11⋊C8—22no—
68C22×C11⋊C8—22no—
69C22×C11⋊C8—22no—
70C22×C11⋊C8Q814yes—
71C22×C11⋊C8Q814yes—
72C22×C11⋊C8C2312yes—
73C22×C11⋊C8C2312yes—
74#66923—216no—
75#66923—28no—
76#66923—28no—
77C11×#95—24no—
78#66872—28no—
79#66871—28no—
80C2×#2059—111nomaximal, Sylow
81C24×C11C2×D411yescharacteristic
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—24no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—42no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×Q812yes—
102C22×C4×C11C2×Q812yes—
103C22×C4×C11C2×Q812yes—
104C22×C4×C11#4112yes—
105C22×C4×C11C2411yescharacteristic
106C22×Dic11—24no—
107C22×Dic11—24no—
108C22×Dic11—22no—
109C22×Dic11—22no—
110C22×Dic11—42no—
111C22×Dic11—42no—
112C22×Dic11—42no—
113C22×Dic11—42no—
114C11×C4⋊C4—24no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—48no—
119C11×C4⋊C4—42no—
120C11×C4⋊C4C2×Q814yes—
121C42×C11—24no—
122C42×C11—22no—
123C42×C11—22no—
124C4⋊Dic11—24no—
125C4⋊Dic11—24no—
126C4⋊Dic11—22no—
127C4⋊Dic11—22no—
128C4⋊Dic11C2×D414yes—
129C4⋊Dic11C2×D414yes—
130Dic11⋊C4—216no—
131Dic11⋊C4—216no—
132C2×C11⋊C8—28no—
133C2×C11⋊C8—28no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8C2×Q814yes—
139C2×C11⋊C8C2×Q814yes—
140C22×#125—111no—
141C22×#107—111no—
142C22×#106—111no—
143C2×#389D1111yescharacteristic
144#2059—118no—
145C2×#340—111no—
146C2×#340—111no—
147C2×#336—111no—
148C23×C11#12012yes—
149C23×C11C22⋊Q812yes—
150C23×C11C4⋊Q812yes—
151C23×C11#13512yes—
152C23×C11#13512yes—
153C23×C11AGL(1,ℤ/8)12yes—
154C23×C11#13712yes—
155C23×C11C22×D411yescharacteristic
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—24no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—44no—
166C2×C4×C11—44no—
167C2×C4×C11—48no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—84no—
172C2×C4×C11#12012yes—
173C2×C4×C11C22⋊Q814yes—
174C2×C4×C11C22⋊Q814yes—
175C2×C4×C11C22⋊Q812yes—
176C2×C4×C11C4⋊Q814yes—
177C2×C4×C11C4⋊Q814yes—
178C2×C4×C11C4⋊Q812yes—
179C2×C4×C11C22×D411yescharacteristic
180C2×C4×C11C22×D411yescharacteristic
181C2×C4×C11C22×Q811yescharacteristic
182C2×C4×C11C22×Q811yescharacteristic
183C2×C4×C11C22×Q811yescharacteristic
184C2×C4×C11C2×#4111yescharacteristic
185C2×Dic11—24no—
186C2×Dic11—24no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—48no—
192C2×Dic11—48no—
193C11⋊C8—24no—
194C11⋊C8—24no—
195C23×C8—111no—
196C23×C8—111no—
197C2×#125—114no—
198C2×#125—224no—
199C2×#125—224no—
200C2×#125—222no—
201C22×C4⋊C4—21no—
202C22×C4⋊C4—111no—
203C22×C4⋊C4—111no—
204C22×C4⋊C4—221no—
205C22×C4⋊C4—221no—
206C22×C4⋊C4C2×D1111yescharacteristic
207C22×C4⋊C4C2×D1111yescharacteristic
208C22×C42C2×D1111yescharacteristic
209C2×#107—114no—
210C2×#107—224no—
211C2×#106—114no—
212C2×#106—224no—
213#389—22no—
214#389C2×D1114yes—
215C2×#95—21no—
216#340—114no—
217#340—114no—
218#336—114no—
219C22×C11#39514yes—
220C22×C11#44914yes—
221C22×C11#45214yes—
222C22×C11#47814yes—
223C22×C11#47914yes—
224C22×C11#49914yes—
225C22×C11#50114yes—
226C22×C11C2×#12011yescharacteristic
227C22×C11C2×C22⋊Q811yescharacteristic
228C22×C11C2×C4⋊Q811yescharacteristic
229C22×C11C2×#13511yescharacteristic
230C22×C11C2×#13511yescharacteristic
231C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
232C22×C11C2×#13711yescharacteristic
233C4×C11—44no—
234C4×C11—42no—
235C4×C11—42no—
236C4×C11—82no—
237C4×C11#39514yes—
238C4×C11C2×C22⋊Q811yescharacteristic
239C4×C11C2×C22⋊Q811yescharacteristic
240C4×C11C2×C4⋊Q811yescharacteristic
241C4×C11C2×C4⋊Q811yescharacteristic
242Dic11—44no—
243Dic11—44no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—221no—
247C23×C4—221no—
248C23×C4C22⋊D1111yescharacteristic
249C23×C4C22⋊D1111yescharacteristic
250C23×C4C22×D1111yescharacteristic
251C22×C8—114no—
252C22×C8—114no—
253C22×C8—112no—
254C22×C8—112no—
255C22×C8—222no—
256C22×C8—222no—
257C22×C8—222no—
258C22×C8—222no—
259#125—228no—
260#125—228no—
261#125—2216no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—44no—
269C2×C4⋊C4—114no—
270C2×C4⋊C4—114no—
271C2×C4⋊C4—112no—
272C2×C4⋊C4—112no—
273C2×C4⋊C4—228no—
274C2×C4⋊C4—228no—
275C2×C4⋊C4—222no—
276C2×C4⋊C4—222no—
277C2×C4⋊C4—221no—
278C2×C4⋊C4—221no—
279C2×C4⋊C4—224no—
280C2×C4⋊C4—224no—
281C2×C4⋊C4Dic2214yes—
282C2×C4⋊C4C22×D1112yes—
283C2×C4⋊C4C22×D1112yes—
284C2×C42—22no—
285C2×C42—22no—
286C2×C42C22⋊D1112yes—
287C2×C42C22×D1112yes—
288#107—228no—
289#106—228no—
290#95—24no—
291C2×C11#205918yescomplemented
292C2×C11C2×#39511yescharacteristic
293C2×C11C2×#44911yescharacteristic
294C2×C11C2×#45211yescharacteristic
295C2×C11C2×#47811yescharacteristic
296C2×C11C2×#47911yescharacteristic
297C2×C11C2×#49911yescharacteristic
298C2×C11C2×#50111yescharacteristic
299C24C2×C22⋊D1111yescharacteristic
300C22×C4—24no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—224no—
315C22×C4—224no—
316C22×C4—222no—
317C22×C4—222no—
318C22×C4—442no—
319C22×C4—442no—
320C22×C4—442no—
321C22×C4—442no—
322C22×C4C2×Dic2212yes—
323C22×C4#433912yes—
324C22×C4D4×D1112yes—
325C22×C4D4×D1112yes—
326C22×C4Q8×D1112yes—
327C22×C4Q8×D1112yes—
328C22×C4C2×C22⋊D1112yes—
329C22×C4C2×C22⋊D1112yes—
330C22×C4C2×C22⋊D1111yescharacteristic
331C22×C4C23×D1111yescharacteristic
332C2×C8—114no—
333C2×C8—114no—
334C2×C8—228no—
335C2×C8—228no—
336C2×C8—222no—
337C2×C8—222no—
338C2×C8—222no—
339C2×C8—222no—
340C4⋊C4—24no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—48no—
345C4⋊C4—42no—
346C4⋊C4—114no—
347C4⋊C4—114no—
348C4⋊C4—2216no—
349C4⋊C4—2216no—
350C4⋊C4—224no—
351C4⋊C4—224no—
352C4⋊C4—222no—
353C4⋊C4—222no—
354C4⋊C4C2×Dic2214yes—
355C42—24no—
356C42—22no—
357C42—22no—
358C11C2×#205911yescharacteristic, complemented, Sylow
359C23#6697712yes—
360C23#6698512yes—
361C23#6699012yes—
362C23#6699512yes—
363C23#6699712yes—
364C23#6700312yes—
365C23#6700312yes—
366C23C22×C22⋊D1111yescharacteristic
367C2×C4—24no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—48no—
377C2×C4—44no—
378C2×C4—44no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—84no—
383C2×C4—224no—
384C2×C4—224no—
385C2×C4—442no—
386C2×C4—442no—
387C2×C4—442no—
388C2×C4—442no—
389C2×C4—448no—
390C2×C4—448no—
391C2×C4#6694114yes—
392C2×C4#6694114yes—
393C2×C4#6694914yes—
394C2×C4#6694914yes—
395C2×C4#6697712yes—
396C2×C4#6699012yes—
397C2×C4#6699712yes—
398C2×C4C22×Dic2211yescharacteristic
399C2×C4C2×#433911yescharacteristic
400C2×C4C2×D4×D1111yescharacteristic
401C2×C4C2×D4×D1111yescharacteristic
402C2×C4C2×Q8×D1111yescharacteristic
403C2×C4C2×Q8×D1111yescharacteristic
404C8—224no—
405C8—224no—
406C22#1062259214yes—
407C22#1062262214yes—
408C22#1062263514yes—
409C22#1062265014yes—
410C22#1062266014yes—
411C22#1062267714yes—
412C22#1062269314yes—
413C22C2×#6697711yescharacteristic
414C22C2×#6698511yescharacteristic
415C22C2×#6699011yescharacteristic
416C22C2×#6699511yescharacteristic
417C22C2×#6699711yescharacteristic
418C22C2×#6700311yescharacteristic
419C22C2×#6700311yescharacteristic
420C4—42no—
421C4—42no—
422C4—44no—
423C4—82no—
424C4—444no—
425C4—444no—
426C4#1062259214yes—
427C4C2×#6694111yescharacteristic
428C4C2×#6694111yescharacteristic
429C4C2×#6694911yescharacteristic
430C4C2×#6694911yescharacteristic
431C2#1306995418yesdirect product factor
432C2C2×#1062259211yescharacteristic
433C2C2×#1062265011yescharacteristic
434C2C2×#1062266011yescharacteristic
435C2C2×#1062262211yescharacteristic
436C2C2×#1062263511yescharacteristic
437C2C2×#1062267711yescharacteristic
438C2C2×#1062269311yescharacteristic
subgroupG/H
centerC24C2×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#389C2
socle, prime radicalC24×C11C2×D4
hypercenterC2×#389D11
hypocenterC11C2×#2059
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
4. #13069954C2direct (N × H)
291. C2×C11#2059semidirect
358. C11C2×#2059semidirect
431. C2#13069954direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669232
C22×#668712
C22×#668722
#130699542
C2×#106221672
C2×#106221622
C2×C11×#3892
C2×#205911