Finite Group Databasebeta

← C2×#13067772 #14729508

Subgroups — C2×#13067772 #14729508

Order 2816.

914 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623098C211yesmaximal, characteristic
2C2×#10622694C211yesmaximal, characteristic
3C2×#10622704C211yesmaximal, characteristic
4#13067772C218yesmaximal, direct product factor
5C2×#10622120C211yesmaximal, characteristic
6C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic
7C2×#10622122C211yesmaximal, characteristic
8C2×C11×#477C211yesmaximal, characteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C2×#66997—21no—
12#10623098—22no—
13#10623098—22no—
14#10623098—22no—
15#10623098C2214yes—
16C2×#66942—22no—
17C2×#66940—21no—
18C2×#66923—21no—
19C2×#66922C2211yescharacteristic
20C2×C4×Dic22—21no—
21C2×C4×Dic22C2211yescharacteristic
22C11×#477—22no—
23C11×#477C2214yes—
24C2×C11×#107—21no—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103—21no—
27C2×#66899—22no—
28#10622704—22no—
29#10622704C2214yes—
30#10622694—22no—
31#10622694C2214yes—
32C2×#66874—21no—
33C2×#66871—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36Q8⋊(C11⋊C8)C2214yes—
37#10622122C2214yes—
38#10622120C2214yes—
39C22×Q8×C11—21no—
40C22×Q8×C11D411yescharacteristic
41C22×Dic22—21no—
42C22×Dic22D411yescharacteristic
43C22×C8×C11—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8C2312yes—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C4×Q8×C11D412yes—
51C4×Q8×C11C2312yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C42×C11—21no—
57C2×C42×C11C2311yescharacteristic
58#66997—24no—
59#66997—24no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11D411yescharacteristic
62C2×C4⋊Dic11D412yes—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—21no—
67C2×C4×Dic11—22no—
68C2×C4×Dic11—21no—
69C22×C11⋊C8—21no—
70C22×C11⋊C8—21no—
71#66942—28no—
72#66942—28no—
73#66940—24no—
74#66940—24no—
75#66923—24no—
76#66923—24no—
77#66922—21no—
78#66922—21no—
79#66922D412yes—
80#66922C2312yes—
81C4×Dic22—24no—
82C4×Dic22—24no—
83C4×Dic22—21no—
84C4×Dic22—21no—
85C4×Dic22D412yes—
86C4×Dic22C2312yes—
87C11×#107—24no—
88C11×C4⋊C8—21no—
89C11×C4⋊C8C2312yes—
90C11×#103—24no—
91#66899—28no—
92#66874—24no—
93#66871—24no—
94C4⋊(C11⋊C8)—21no—
95C4⋊(C11⋊C8)C2312yes—
96C4×C11⋊C8—21no—
97C4×C11⋊C8C2312yes—
98C2×#1636—111nomaximal, Sylow
99C2×Q8×C11—21no—
100C2×Q8×C11—22no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11—44no—
104C2×Q8×C11—41no—
105C2×Q8×C11C2×D412yes—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—41no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—22no—
115C2×Dic22—21no—
116C2×Dic22—22no—
117C2×Dic22—22no—
118C2×Dic22—22no—
119C2×Dic22—42no—
120C2×Dic22—42no—
121C2×Dic22Q1614yes—
122C2×Dic22C2×D412yes—
123C2×C8×C11—22no—
124C2×C8×C11—42no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—41no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4C2×D412yes—
133C42×C11—22no—
134C42×C11—22no—
135C42×C11C2×D411yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11C2411yescharacteristic
139C4⋊Dic11—22no—
140C4⋊Dic11—21no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11C2×D412yes—
144C4⋊Dic11C2×D414yes—
145Dic11⋊C4—28no—
146Dic11⋊C4—28no—
147Dic11⋊C4—28no—
148Dic11⋊C4—22no—
149Dic11⋊C4—22no—
150C4×Dic11—28no—
151C4×Dic11—22no—
152C4×Dic11—22no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—42no—
156C2×C11⋊C8—42no—
157C2×#557—111no—
158C2×#487—111no—
159C2×#477—111no—
160C2×#477D1111yescharacteristic
161#1636—118no—
162C2×#332—111no—
163C2×Q8⋊C8—111no—
164C2×Q8⋊C8—111no—
165C23×C11#12011yescharacteristic
166Q8×C11—22no—
167Q8×C11—22no—
168Q8×C11—44no—
169Q8×C11—42no—
170Q8×C11—82no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—82no—
178C2×C4×C11#12011yescharacteristic
179C2×C4×C11#12011yescharacteristic
180C2×C4×C11#12011yescharacteristic
181C2×C4×C11C2×Q1612yes—
182C2×C4×C11#13512yes—
183C2×C4×C11#13712yes—
184C2×C4×C11#13712yes—
185C2×C4×C11C22×D411yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11C22×D411yescharacteristic
188C2×Dic11—22no—
189C2×Dic11—24no—
190C2×Dic11—22no—
191C2×Dic11—24no—
192C2×Dic11—44no—
193C2×Dic11—42no—
194Dic22—22no—
195Dic22—24no—
196Dic22—42no—
197Dic22—42no—
198Dic22—44no—
199Dic22C2×Q1614yes—
200C8×C11—42no—
201C11⋊C8—42no—
202C11⋊C8—42no—
203#557—114no—
204#557—222no—
205#557—222no—
206#557—222no—
207C2×C4⋊Q8—111no—
208C2×C4⋊Q8—221no—
209C2×C4⋊Q8C2×D1111yescharacteristic
210C2×#125—221no—
211C2×#125—222no—
212C2×C4×Q8—111no—
213C2×C4×Q8—221no—
214C2×C4×Q8—221no—
215C2×C4×Q8C2×D1111yescharacteristic
216#487—114no—
217#487—222no—
218#477—22no—
219#477—114no—
220#477—222no—
221#477C2×D1114yes—
222C2×#107—21no—
223C2×#107—221no—
224C2×C4⋊C8—111no—
225C2×C4⋊C8C2×D1111yescharacteristic
226C2×#103—21no—
227C2×#103—221no—
228C2×#103—222no—
229C2×C4×C8—111no—
230#332—114no—
231Q8⋊C8—114no—
232Q8⋊C8—114no—
233C22×C11#45112yes—
234C22×C11#45212yes—
235C22×C11#45412yes—
236C22×C11C2×#12011yescharacteristic
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—42no—
240C4×C11—42no—
241C4×C11—82no—
242C4×C11#45112yes—
243C4×C11#45212yes—
244C4×C11C22×Q1611yescharacteristic
245C4×C11C2×#13511yescharacteristic
246C4×C11C2×#13711yescharacteristic
247C4×C11C2×#13711yescharacteristic
248Dic11—24no—
249Dic11—44no—
250Dic11—42no—
251C22×Q8—21no—
252C22×Q8—111no—
253C22×Q8—221no—
254C22×Q8C22⋊D1111yescharacteristic
255C22×C8—21no—
256C22×C8—221no—
257C22×C8—221no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
261C4⋊Q8—112no—
262C4⋊Q8—112no—
263C4⋊Q8—224no—
264C4⋊Q8—224no—
265C4⋊Q8—221no—
266C4⋊Q8—221no—
267C4⋊Q8C22×D1112yes—
268#125—224no—
269#125—224no—
270#125—228no—
271#125—228no—
272C4×Q8—21no—
273C4×Q8—21no—
274C4×Q8—112no—
275C4×Q8—112no—
276C4×Q8—224no—
277C4×Q8—224no—
278C4×Q8—224no—
279C4×Q8—224no—
280C4×Q8—221no—
281C4×Q8—221no—
282C4×Q8C22⋊D1112yes—
283C4×Q8C22×D1112yes—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—112no—
289C2×C4⋊C4—222no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4—221no—
293C2×C4⋊C4—221no—
294C2×C4⋊C4C22⋊D1111yescharacteristic
295C2×C42—21no—
296C2×C42—222no—
297C2×C42—221no—
298C2×C42C22×D1111yescharacteristic
299#107—24no—
300#107—224no—
301C4⋊C8—21no—
302C4⋊C8—112no—
303C4⋊C8—221no—
304C4⋊C8C22×D1112yes—
305#103—24no—
306#103—224no—
307#103—228no—
308C4×C8—112no—
309C4×C8—221no—
310C2×C11#163614yescomplemented
311C2×C11C2×#45111yescharacteristic
312C2×C11C2×#45211yescharacteristic
313C2×C11C2×#45411yescharacteristic
314C2×Q8—21no—
315C2×Q8—22no—
316C2×Q8—22no—
317C2×Q8—22no—
318C2×Q8—44no—
319C2×Q8—41no—
320C2×Q8—114no—
321C2×Q8—112no—
322C2×Q8—222no—
323C2×Q8—221no—
324C2×Q8—222no—
325C2×Q8—222no—
326C2×Q8—442no—
327C2×Q8—442no—
328C2×Q8C2×C22⋊D1112yes—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—41no—
332C22×C4—221no—
333C22×C4—221no—
334C22×C4—222no—
335C22×C4D4×D1111yescharacteristic
336C22×C4D4×D1111yescharacteristic
337C22×C4C2×C22⋊D1111yescharacteristic
338C2×C8—22no—
339C2×C8—42no—
340C2×C8—222no—
341C2×C8—222no—
342C2×C8—442no—
343C2×C8—442no—
344C4⋊C4—22no—
345C4⋊C4—21no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—114no—
352C4⋊C4—112no—
353C4⋊C4—228no—
354C4⋊C4—228no—
355C4⋊C4—228no—
356C4⋊C4—221no—
357C4⋊C4—222no—
358C4⋊C4—222no—
359C4⋊C4—222no—
360C4⋊C4—222no—
361C4⋊C4—222no—
362C4⋊C4C2×C22⋊D1112yes—
363C42—22no—
364C42—22no—
365C42—228no—
366C42—222no—
367C42—222no—
368C42D4×D1111yescharacteristic
369C42D4×D1111yescharacteristic
370C42C2×C22⋊D1111yescharacteristic
371C42C23×D1111yescharacteristic
372C11C2×#163611yescharacteristic, complemented, Sylow
373C23#6699011yescharacteristic
374Q8—22no—
375Q8—22no—
376Q8—44no—
377Q8—42no—
378Q8—82no—
379Q8—114no—
380Q8—222no—
381Q8—224no—
382Q8—442no—
383Q8—442no—
384Q8—444no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—82no—
392C2×C4—224no—
393C2×C4—222no—
394C2×C4—222no—
395C2×C4—224no—
396C2×C4—442no—
397C2×C4—444no—
398C2×C4Q16×D1112yes—
399C2×C4#6697112yes—
400C2×C4#6699011yescharacteristic
401C2×C4#6699011yescharacteristic
402C2×C4#6699011yescharacteristic
403C2×C4#6699512yes—
404C2×C4#6700312yes—
405C2×C4C2×D4×D1111yescharacteristic
406C2×C4C2×D4×D1111yescharacteristic
407C2×C4C22×C22⋊D1111yescharacteristic
408C8—42no—
409C8—442no—
410C8—442no—
411C22#1062266012yes—
412C22#1062279912yes—
413C22#1062281412yes—
414C22C2×#6699011yescharacteristic
415C4—21no—
416C4—21no—
417C4—42no—
418C4—42no—
419C4—82no—
420C4—224no—
421C4—444no—
422C4—442no—
423C4#1062266012yes—
424C4#1062279912yes—
425C4C2×Q16×D1111yescharacteristic
426C4C2×#6697111yescharacteristic
427C4C2×#6699511yescharacteristic
428C4C2×#6700311yescharacteristic
429C2#1306777214yesdirect product factor
430C2C2×#1062279911yescharacteristic
431C2C2×#1062266011yescharacteristic
432C2C2×#1062281411yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#477C2
socle, prime radicalC23×C11#120
hypercenterC2×#477D11
hypocenterC11C2×#1636
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
4. #13067772C2direct (N × H)
310. C2×C11#1636semidirect
372. C11C2×#1636semidirect
429. C2#13067772direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230982
C2×#106226942
C2×#106227042
#130677722
C2×#106221202
C2×Q8⋊(C11⋊C8)2
C2×#106221222
C2×C11×#4772
C2×#163611