Finite Group Databasebeta

← C2×#13070617 #14907802

Subgroups — C2×#13070617 #14907802

Order 2816.

1392 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 1392 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622645C212yesmaximal, complemented
2C2×#10622674C211yesmaximal, characteristic, complemented
3#13070617C218yesmaximal, direct product factor
4C2×#10622179C211yesmaximal, characteristic, complemented
5C2×#10622174C212yesmaximal, complemented
6C2×C11×H(3,𝔽4)C211yesmaximal, characteristic, complemented
7C2×#67037C2211yescharacteristic
8C11×H(3,𝔽4)—22no—
9C11×H(3,𝔽4)—24no—
10C11×H(3,𝔽4)C2214yescomplemented
11C2×C11×#124—21no—
12C2×C11×#124—22no—
13C2×C11×#124—21no—
14C2×C11×#124C2211yescharacteristic
15C2×C11×#120—22no—
16C2×C11×#120C2212yes—
17C2×#67006—22no—
18C2×#66995—21no—
19C2×#66898C2212yes—
20C2×#66897C2211yescharacteristic
21#10622674—22no—
22#10622674C2214yescomplemented
23#10622645—24no—
24#10622645C2218yescomplemented
25C2×#66870—22no—
26C2×#66869—21no—
27#10622179C2214yescomplemented
28#10622174C2218yescomplemented
29C25×C11D412yescomplemented
30C22×Q8×C11—21no—
31C22×Q8×C11D411yescharacteristic, complemented
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11—22no—
35C22×D4×C11C2311yescharacteristic
36C22×C22⋊D11—22no—
37C22×C22⋊D11—42no—
38#67037—21no—
39#67037—22no—
40#67037—42no—
41#67037C2312yes—
42C2×#4341—41no—
43C2×D4×D11—41no—
44C2×#4339—21no—
45C11×#124—28no—
46C11×#124—24no—
47C11×#124—24no—
48C11×#124—24no—
49C11×#124—22no—
50C11×#124—28no—
51C11×#124—24no—
52C11×#124D412yescomplemented
53C11×#124C2312yes—
54C11×#120—28no—
55C11×#120—28no—
56C11×#120—22no—
57C11×#120—22no—
58C11×#120D414yescomplemented
59C11×#120C2314yes—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4D412yescomplemented
65C2×C42×C11—21no—
66C2×C42×C11D411yescharacteristic, complemented
67#67006—28no—
68#67006—44no—
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11—42no—
71C2×#4326—41no—
72#66995—24no—
73#66995—42no—
74C2×#4325—41no—
75C2×#4318—21no—
76#66898—22no—
77#66898C2314yes—
78#66897—21no—
79#66897C2312yes—
80#66870—28no—
81#66869—24no—
82C2×#2199—111nomaximal, Sylow
83C24×C11—22no—
84C24×C11—22no—
85C24×C11—42no—
86C24×C11—42no—
87C24×C11—84no—
88C24×C11C2×D412yes—
89C24×C11C2×D414yescomplemented
90C23×D11—22no—
91C2×Q8×C11—24no—
92C2×Q8×C11—21no—
93C2×Q8×C11—41no—
94C2×Q8×C11—41no—
95C2×Q8×C11—82no—
96C2×Q8×C11C2×D412yescomplemented
97C2×D4×C11—24no—
98C2×D4×C11—24no—
99C2×D4×C11—24no—
100C2×D4×C11—24no—
101C2×D4×C11—41no—
102C2×D4×C11—41no—
103C2×D4×C11—84no—
104C2×D4×C11—82no—
105C2×D4×C11—81no—
106C2×D4×C11—81no—
107C2×D4×C11C2×D412yes—
108C2×D4×C11C2×D411yescharacteristic
109C2×D4×C11C2411yescharacteristic
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11C2×D411yescharacteristic
114C2×C22⋊D11—24no—
115C2×C22⋊D11—24no—
116C2×C22⋊D11—48no—
117C2×C22⋊D11—42no—
118C2×C22⋊D11—42no—
119C2×C22⋊D11—41no—
120C2×C22⋊D11—42no—
121C2×C22⋊D11—88no—
122C22×Dic11—22no—
123C22×Dic11—42no—
124#4341—42no—
125#4341—42no—
126#4341—44no—
127D4×D11—42no—
128D4×D11—44no—
129D4×D11—42no—
130#4339—22no—
131#4339—22no—
132#4339—41no—
133#4339—41no—
134C2×D44—21no—
135C2×C4×D11—41no—
136C2×Dic22—21no—
137C11×C22⋊C4—28no—
138C11×C22⋊C4—28no—
139C11×C22⋊C4—24no—
140C11×C22⋊C4—22no—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—24no—
143C11×C22⋊C4—24no—
144C11×C22⋊C4C2×D414yescomplemented
145C42×C11—24no—
146C42×C11—21no—
147C42×C11C2×D412yescomplemented
148C22⋊Dic11—24no—
149C22⋊Dic11—42no—
150C22⋊Dic11—48no—
151#4326—44no—
152#4325—44no—
153#4318—22no—
154#4318—41no—
155C2×C11⋊C8—41no—
156C2×H(3,𝔽4)D1111yescharacteristic, complemented
157C2×B(4,𝔽2)—112no—
158C2×#455—111no—
159#2199—118no—
160C2×#354—111no—
161C2×AΣL(1,𝔽16)—112no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11—24no—
165C23×C11—44no—
166C23×C11—44no—
167C23×C11—44no—
168C23×C11—44no—
169C23×C11—48no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11—82no—
173C23×C11—84no—
174C23×C11—84no—
175C23×C11—84no—
176C23×C11—88no—
177C23×C11#12012yes—
178C23×C11#12011yescharacteristic
179C23×C11C22×D412yes—
180C22×D11—24no—
181C22×D11—41no—
182C22×D11—42no—
183C22×D11—84no—
184Q8×C11—42no—
185Q8×C11—81no—
186Q8×C11—84no—
187D4×C11—42no—
188D4×C11—41no—
189D4×C11—41no—
190D4×C11—84no—
191D4×C11—84no—
192D4×C11—84no—
193D4×C11—84no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—22no—
199C2×C4×C11—44no—
200C2×C4×C11—42no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11#12011yescharacteristic
204C2×C4×C11C22×D411yescharacteristic
205C22⋊D11—44no—
206C22⋊D11—44no—
207C22⋊D11—42no—
208C22⋊D11—42no—
209C22⋊D11—816no—
210C2×Dic11—24no—
211C2×Dic11—42no—
212C2×Dic11—41no—
213C2×Dic11—44no—
214C2×Dic11—84no—
215D44—22no—
216D44—41no—
217C4×D11—42no—
218C4×D11—42no—
219Dic22—22no—
220Dic22—41no—
221C11⋊C8—42no—
222C2×H(5,𝔽2)—111no—
223C2×#137—221no—
224H(3,𝔽4)—22no—
225H(3,𝔽4)—24no—
226H(3,𝔽4)C2×D1114yescomplemented
227C2×#124—21no—
228C2×#124—22no—
229C2×#124—21no—
230C2×#124C2×D1111yescharacteristic
231C2×#120—22no—
232C2×#120—222no—
233C2×#120C2×D1112yes—
234B(4,𝔽2)—118no—
235B(4,𝔽2)—224no—
236#455—114no—
237#455—222no—
238C2×#104—221no—
239C2×#100—111no—
240C2×#99—112no—
241C2×#99—222no—
242#354—114no—
243AΣL(1,𝔽16)—118no—
244C22×C11—22no—
245C22×C11—22no—
246C22×C11—22no—
247C22×C11—42no—
248C22×C11—42no—
249C22×C11—44no—
250C22×C11—44no—
251C22×C11—44no—
252C22×C11—48no—
253C22×C11—44no—
254C22×C11—82no—
255C22×C11—84no—
256C22×C11—84no—
257C22×C11—88no—
258C22×C11—84no—
259C22×C11B(4,𝔽2)11yescharacteristic
260C22×C11B(4,𝔽2)11yescharacteristic
261C22×C11C2×#12011yescharacteristic
262C2×D11—42no—
263C2×D11—82no—
264C2×D11—84no—
265C2×D11—162no—
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—44no—
269C4×C11—42no—
270C4×C11—42no—
271Dic11—42no—
272Dic11—84no—
273C25C22⋊D1112yescomplemented
274H(5,𝔽2)—112no—
275H(5,𝔽2)—222no—
276H(5,𝔽2)—221no—
277H(5,𝔽2)—442no—
278C2×#41—221no—
279C2×#41—441no—
280C22×Q8—21no—
281C22×Q8C22⋊D1111yescharacteristic, complemented
282C22×D4—21no—
283C22×D4—21no—
284C22×D4—22no—
285C22×D4—222no—
286C22×D4—441no—
287C22×D4—442no—
288C22×D4C22×D1111yescharacteristic
289#137—224no—
290#137—442no—
291C2×Q16—441no—
292C2×SD16—441no—
293C2×M16—221no—
294#124—28no—
295#124—24no—
296#124—24no—
297#124—24no—
298#124—22no—
299#124—28no—
300#124—24no—
301#124C22⋊D1112yescomplemented
302#124C22×D1112yes—
303#120—28no—
304#120—28no—
305#120—22no—
306#120—22no—
307#120—228no—
308#120—444no—
309#120C22⋊D1114yescomplemented
310#120C22×D1114yes—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—222no—
316C2×C22⋊C4—442no—
317C2×C22⋊C4C22⋊D1112yescomplemented
318C2×C42—21no—
319C2×C42C22⋊D1111yescharacteristic, complemented
320#104—224no—
321#100—112no—
322#100—221no—
323#99—114no—
324#99—222no—
325#99—228no—
326C2×C11—21no—
327C2×C11—21no—
328C2×C11—42no—
329C2×C11—42no—
330C2×C11—84no—
331C2×C11#219912yescomplemented
332C2×C11C2×B(4,𝔽2)11yescharacteristic
333D11—82no—
334C24—22no—
335C24—22no—
336C24—42no—
337C24—42no—
338C24—84no—
339C24—222no—
340C24C2×C22⋊D1112yes—
341C24C2×C22⋊D1114yescomplemented
342#41—222no—
343#41—222no—
344#41—441no—
345#41—442no—
346#41—444no—
347#41—442no—
348#41—441no—
349C2×Q8—24no—
350C2×Q8—21no—
351C2×Q8—41no—
352C2×Q8—41no—
353C2×Q8—82no—
354C2×Q8—221no—
355C2×Q8C2×C22⋊D1112yescomplemented
356C2×D4—24no—
357C2×D4—24no—
358C2×D4—24no—
359C2×D4—24no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—84no—
363C2×D4—82no—
364C2×D4—81no—
365C2×D4—81no—
366C2×D4—221no—
367C2×D4—224no—
368C2×D4—224no—
369C2×D4—442no—
370C2×D4—442no—
371C2×D4—444no—
372C2×D4—442no—
373C2×D4—442no—
374C2×D4—442no—
375C2×D4—441no—
376C2×D4—448no—
377C2×D4—888no—
378C2×D4C2×C22⋊D1112yes—
379C2×D4C2×C22⋊D1111yescharacteristic
380C2×D4C23×D1111yescharacteristic
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—21no—
384C22×C4—222no—
385C22×C4—441no—
386C22×C4—442no—
387C22×C4C2×C22⋊D1111yescharacteristic
388Q16—444no—
389SD16—444no—
390M16—222no—
391M16—441no—
392C2×C8—441no—
393C22⋊C4—28no—
394C22⋊C4—28no—
395C22⋊C4—24no—
396C22⋊C4—22no—
397C22⋊C4—24no—
398C22⋊C4—24no—
399C22⋊C4—24no—
400C22⋊C4—224no—
401C22⋊C4—448no—
402C22⋊C4—442no—
403C22⋊C4C2×C22⋊D1114yescomplemented
404C42—24no—
405C42—21no—
406C42C2×C22⋊D1112yescomplemented
407C11C2×#219911yescharacteristic, complemented, Sylow
408C23—22no—
409C23—22no—
410C23—24no—
411C23—44no—
412C23—44no—
413C23—44no—
414C23—44no—
415C23—48no—
416C23—42no—
417C23—42no—
418C23—82no—
419C23—84no—
420C23—84no—
421C23—84no—
422C23—88no—
423C23—224no—
424C23—442no—
425C23—441no—
426C23—884no—
427C23#6700612yes—
428C23#6700611yescharacteristic
429C23C22×C22⋊D1112yes—
430Q8—42no—
431Q8—81no—
432Q8—84no—
433Q8—222no—
434Q8—441no—
435D4—41no—
436D4—42no—
437D4—41no—
438D4—84no—
439D4—84no—
440D4—84no—
441D4—84no—
442D4—222no—
443D4—441no—
444D4—444no—
445D4—444no—
446D4—442no—
447D4—442no—
448D4—8816no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—44no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—224no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—441no—
463C2×C4—444no—
464C2×C4—884no—
465C2×C4#6700611yescharacteristic
466C2×C4C22×C22⋊D1111yescharacteristic
467C8—442no—
468C22—22no—
469C22—22no—
470C22—22no—
471C22—42no—
472C22—42no—
473C22—44no—
474C22—44no—
475C22—44no—
476C22—48no—
477C22—44no—
478C22—82no—
479C22—84no—
480C22—84no—
481C22—88no—
482C22—84no—
483C22—442no—
484C22—884no—
485C22—882no—
486C22—1762no—
487C22#1062285711yescharacteristic
488C22#1062285711yescharacteristic
489C22C2×#6700611yescharacteristic
490C4—21no—
491C4—21no—
492C4—44no—
493C4—42no—
494C4—42no—
495C4—442no—
496C4—884no—
497C2—21no—
498C2—21no—
499C2—42no—
500C2—42no—
501C2—84no—
502C2—882no—
503C2#1307061712yesdirect product factor
504C2C2×#1062285711yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×D4×C11C24
FrattiniC2×D4C23×D11
FittingC2×C11×H(3,𝔽4)C2
socleC22×C11B(4,𝔽2)
hypercenterC2×H(3,𝔽4)D11
hypocenterC11C2×#2199
LCSG ▷ C2×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. C2×#10622645C2semidirect
2. C2×#10622674C2semidirect
3. #13070617C2direct (N × H)
4. C2×#10622179C2semidirect
5. C2×#10622174C2semidirect
6. C2×C11×H(3,𝔽4)C2semidirect
10. C11×H(3,𝔽4)C22semidirect
22. #10622674C22semidirect
24. #10622645C22semidirect
27. #10622179C22semidirect
28. #10622174C22semidirect
29. C25×C11D4semidirect
31. C22×Q8×C11D4semidirect
52. C11×#124D4semidirect
58. C11×#120D4semidirect
64. C2×C11×C22⋊C4D4semidirect
66. C2×C42×C11D4semidirect
89. C24×C11C2×D4semidirect
96. C2×Q8×C11C2×D4semidirect
144. C11×C22⋊C4C2×D4semidirect
147. C42×C11C2×D4semidirect
156. C2×H(3,𝔽4)D11semidirect
226. H(3,𝔽4)C2×D11semidirect
273. C25C22⋊D11semidirect
281. C22×Q8C22⋊D11semidirect
301. #124C22⋊D11semidirect
309. #120C22⋊D11semidirect
317. C2×C22⋊C4C22⋊D11semidirect
319. C2×C42C22⋊D11semidirect
331. C2×C11#2199semidirect
341. C24C2×C22⋊D11semidirect
355. C2×Q8C2×C22⋊D11semidirect
403. C22⋊C4C2×C22⋊D11semidirect
406. C42C2×C22⋊D11semidirect
407. C11C2×#2199semidirect
503. C2#13070617direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226452
C2×#106226742
#130706172
C2×#106221792
C2×#106221742
C2×C11×H(3,𝔽4)2
C2×#219911