Finite Group Databasebeta

← C2×#13081530 #15634266

Subgroups — C2×#13081530 #15634266

Order 2816.

1854 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623253C211yesmaximal, characteristic, complemented
2C2×#10623074C211yesmaximal, characteristic
3#13081530C2116yesmaximal, direct product factor
4C2×#10622469C212yesmaximal, complemented
5C2×#10622691C211yesmaximal, characteristic, complemented
6C2×#10622470C212yesmaximal, complemented
7C2×#10622463C211yesmaximal, characteristic, complemented
8C2×#10622372C212yesmaximal
9C2×#10622444C211yesmaximal, characteristic, complemented
10C2×#10622370C212yesmaximal
11C2×C4×#4324C211yesmaximal, characteristic
12C2×C11×#476C211yesmaximal, characteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66997—22no—
16C2×D4×Dic11C2212yes—
17C22×#4324C2211yescharacteristic
18C22×C4⋊Dic11—21no—
19C2×#66977—21no—
20#10623253—24no—
21#10623253C2218yescomplemented
22#10623074—24no—
23#10623074C2218yes—
24C2×#66943C2212yes—
25C2×#66941—21no—
26C2×#66941C2212yes—
27C2×#66940—21no—
28C2×#66940C2212yes—
29C2×#66931—22no—
30C2×#66922C2211yescharacteristic
31C2×C4×Dic22C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C11×#476C2218yes—
34C2×C11×#106C2212yes—
35C2×C11×C4⋊C8C2211yescharacteristic
36C2×C11×#102C2212yes—
37C2×#66896C2211yescharacteristic
38C2×#66882C2212yes—
39C2×#66880C2212yes—
40C2×#66879C2212yes—
41C2×Dic11⋊C8C2212yes—
42#10622691C2218yescomplemented
43C4×#4324C2218yes—
44C2×#66874C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66871C2212yes—
47C2×#66871C2212yes—
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622470C22116yescomplemented
50#10622469C22116yescomplemented
51#10622463C2218yescomplemented
52#10622444C2218yescomplemented
53#10622372C22116yes—
54#10622370C22116yes—
55C22×Q8×C11—21no—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C23×Dic11—22no—
59C22×Dic22—21no—
60C22×Dic22—22no—
61C22×Dic22D411yescharacteristic
62C22×Dic22C2311yescharacteristic
63C22×C8×C11C2312yes—
64C11×C4⋊Q8—22no—
65C11×C4⋊Q8C2314yes—
66C4×D4×C11—22no—
67C4×D4×C11C2314yes—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C42×C11C2311yescharacteristic
73C2×C22⋊Dic11—22no—
74#66997—216no—
75D4×Dic11—24no—
76D4×Dic11C2318yes—
77C2×#4324Q818yescomplemented
78C2×#4324C2314yes—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—28no—
82C2×C4⋊Dic11D411yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2312yes—
85#66977—28no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—22no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4D412yes—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—22no—
93C2×C4×Dic11C2312yes—
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96#66943—24no—
97#66943C2318yes—
98#66941—28no—
99#66941—24no—
100#66941C2318yes—
101#66940—28no—
102#66940—24no—
103#66940C2318yes—
104#66931—216no—
105#66922—22no—
106#66922C2314yes—
107C4×Dic22—22no—
108C4×Dic22D414yes—
109C4×Dic22C2314yes—
110C4×Dic22C2314yes—
111C11×#106C2318yes—
112C11×C4⋊C8C2314yes—
113C11×#102C2318yes—
114#66896C2314yes—
115#66882C2318yes—
116#66880C2318yes—
117#66879C2318yes—
118Dic11⋊C8C2318yes—
119#66874C2314yes—
120#66872C2314yes—
121#66871C2318yes—
122#66871C2318yes—
123C4×C11⋊C8C2314yes—
124C2×#3385—111nomaximal, Sylow
125C24×C11—21no—
126C2×Q8×C11—24no—
127C2×Q8×C11—82no—
128C2×D4×C11—21no—
129C2×D4×C11—22no—
130C2×D4×C11C2×Q814yes—
131C2×D4×C11C2412yes—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—24no—
135C22×C4×C11—44no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—28no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—22no—
143C22×Dic11—84no—
144C22×Dic11C2×D412yes—
145C22×Dic11C2×D412yes—
146C2×Dic22—28no—
147C2×Dic22—24no—
148C2×Dic22—21no—
149C2×Dic22—24no—
150C2×Dic22—22no—
151C2×Dic22—82no—
152C2×Dic22—84no—
153C2×Dic22C2×D414yes—
154C2×Dic22C2×Q814yes—
155C2×Dic22C2412yes—
156C2×C8×C11—24no—
157C2×C8×C11C2414yes—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4C2414yes—
162C11×C4⋊C4C2412yes—
163C11×C22⋊C4—24no—
164C42×C11C2×D412yes—
165C42×C11C2412yes—
166C22⋊Dic11—28no—
167#4324C2×Q8116yescomplemented
168C4⋊Dic11—28no—
169C4⋊Dic11—21no—
170C4⋊Dic11—22no—
171C4⋊Dic11—24no—
172C4⋊Dic11C2×D414yes—
173C4⋊Dic11C2414yes—
174C4⋊Dic11C2412yes—
175Dic11⋊C4—28no—
176Dic11⋊C4—28no—
177Dic11⋊C4—28no—
178Dic11⋊C4—24no—
179Dic11⋊C4C2×D418yes—
180C4×Dic11—28no—
181C4×Dic11—24no—
182C4×Dic11C2×D414yes—
183C4×Dic11C2414yes—
184C2×C11⋊C8—22no—
185C2×C11⋊C8C2×Q814yes—
186C2×C11⋊C8C2412yes—
187C2×C11⋊C8C2412yes—
188C2×Q82—111no—
189C2×#554—111no—
190#3385—1116no—
191C2×#501—112no—
192C2×#500—111no—
193C2×#479—112no—
194C2×#477—111no—
195C2×#476D1111yescharacteristic
196C2×#474—112no—
197C2×#446—111no—
198C2×#440—112no—
199C2×C4×SD16—111no—
200C23×C11—24no—
201C23×C11—22no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11C22×D411yescharacteristic
205Q8×C11—84no—
206D4×C11—24no—
207D4×C11—22no—
208D4×C11C22×Q814yes—
209C2×C4×C11—22no—
210C2×C4×C11—24no—
211C2×C4×C11—22no—
212C2×C4×C11—42no—
213C2×C4×C11—44no—
214C2×C4×C11—48no—
215C2×C4×C11#13714yes—
216C2×C4×C11C22×D412yes—
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×D412yes—
219C2×C4×C11C22×Q812yes—
220C2×C4×C112−1+412yes—
221C2×C4×C11C2511yescharacteristic
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—24no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—24no—
228C2×Dic11—42no—
229C2×Dic11—44no—
230C2×Dic11—88no—
231C2×Dic11C22×D414yes—
232C2×Dic11C22×D414yes—
233Dic22—24no—
234Dic22—28no—
235Dic22—22no—
236Dic22—88no—
237Dic22—84no—
238Dic22C22×Q814yes—
239C8×C11—24no—
240C11⋊C8—22no—
241C11⋊C8C22×Q814yes—
242C22×SD16—111no—
243Q82—118no—
244Q82—224no—
245#554—118no—
246#554—224no—
247C2×C4⋊Q8—112no—
248C2×C4⋊Q8—111no—
249C2×C4⋊Q8—221no—
250C2×C4⋊Q8—222no—
251C2×C4⋊Q8C2×D1111yescharacteristic
252C2×#125—112no—
253C2×C22⋊Q8—222no—
254C2×C22⋊Q8—221no—
255C2×C4×Q8—111no—
256C2×C4×Q8—112no—
257C2×C4×Q8—111no—
258C2×C4×Q8—221no—
259C2×C4×D4—112no—
260C2×C4×D4C2×D1111yescharacteristic
261C22×C4⋊C4—221no—
262#501—1116no—
263#500—118no—
264#479—1116no—
265#477—118no—
266#476C2×D1118yes—
267#474—1116no—
268#446—118no—
269#440—1116no—
270C4×SD16—118no—
271C2×#107—112no—
272C2×#107—112no—
273C2×#107—112no—
274C2×#106—111no—
275C2×#106C2×D1112yes—
276C2×C4⋊C8—112no—
277C2×C4⋊C8C2×D1111yescharacteristic
278C2×#103—112no—
279C2×#103—111no—
280C2×#102—111no—
281C2×#102C2×D1112yes—
282C2×#97—112no—
283C2×C4×C8—111no—
284C22×C11—24no—
285C22×C11—48no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11D4×Q812yes—
289C22×C11C2×#13712yes—
290C22×C11#57612yes—
291C22×C11C23×D411yescharacteristic
292C4×C11—22no—
293C4×C11—42no—
294C4×C11—44no—
295C4×C11D4×Q812yes—
296C4×C11C2×#13714yes—
297C4×C11C23×Q811yescharacteristic
298C4×C11C2×2−1+411yescharacteristic
299Dic11—24no—
300Dic11—24no—
301Dic11—24no—
302Dic11—42no—
303Dic11—44no—
304C22×Q8—21no—
305C22×Q8—111no—
306C22×Q8—111no—
307C22×Q8—222no—
308C22×Q8—221no—
309C22×D4C22×D1111yescharacteristic
310C23×C4—21no—
311C23×C4—222no—
312C2×SD16—118no—
313C2×SD16—114no—
314C22×C8—111no—
315C22×C8—111no—
316C22×C8C22×D1112yes—
317C4⋊Q8—22no—
318C4⋊Q8—118no—
319C4⋊Q8—114no—
320C4⋊Q8—224no—
321C4⋊Q8—228no—
322C4⋊Q8—2216no—
323C4⋊Q8—222no—
324C4⋊Q8C22×D1114yes—
325#125—118no—
326#125—224no—
327C22⋊Q8—2216no—
328C22⋊Q8—228no—
329C4×Q8—114no—
330C4×Q8—114no—
331C4×Q8—118no—
332C4×Q8—114no—
333C4×Q8—224no—
334C4×Q8—228no—
335C4×Q8—222no—
336C4×D4—22no—
337C4×D4—118no—
338C4×D4—224no—
339C4×D4C22×D1114yes—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—111no—
342C2×C4⋊C4—112no—
343C2×C4⋊C4—112no—
344C2×C4⋊C4—111no—
345C2×C4⋊C4—228no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4—221no—
352C2×C4⋊C4C22×D1111yescharacteristic
353C2×C4⋊C4C22×D1112yes—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—222no—
356C2×C42—112no—
357C2×C42—222no—
358C2×C42—221no—
359C2×C42C22×D1111yescharacteristic
360#107—118no—
361#107—118no—
362#107—118no—
363#106—114no—
364#106C22×D1118yes—
365C4⋊C8—118no—
366C4⋊C8C22×D1114yes—
367#103—118no—
368#103—114no—
369#102—114no—
370#102C22×D1118yes—
371#97—118no—
372C4×C8—114no—
373C2×C11—44no—
374C2×C11#338514yescomplemented
375C2×C11C2×D4×Q811yescharacteristic
376C2×C11C22×#13711yescharacteristic
377C2×C11C2×#57611yescharacteristic
378C24—21no—
379C2×Q8—24no—
380C2×Q8—82no—
381C2×Q8—114no—
382C2×Q8—114no—
383C2×Q8—112no—
384C2×Q8—228no—
385C2×Q8—224no—
386C2×Q8—221no—
387C2×Q8—224no—
388C2×Q8—222no—
389C2×Q8—882no—
390C2×Q8—884no—
391C2×D4—21no—
392C2×D4—22no—
393C2×D4Q8×D1114yes—
394C2×D4C23×D1112yes—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—24no—
398C22×C4—44no—
399C22×C4—112no—
400C22×C4—112no—
401C22×C4—228no—
402C22×C4—221no—
403C22×C4—221no—
404C22×C4—222no—
405C22×C4—884no—
406C22×C4D4×D1111yescharacteristic
407C22×C4D4×D1111yescharacteristic
408C22×C4C23×D1111yescharacteristic
409SD16—1116no—
410C2×C8—24no—
411C2×C8—114no—
412C2×C8—112no—
413C2×C8—112no—
414C2×C8—222no—
415C2×C8C23×D1114yes—
416C4⋊C4—24no—
417C4⋊C4—21no—
418C4⋊C4—22no—
419C4⋊C4—114no—
420C4⋊C4—118no—
421C4⋊C4—112no—
422C4⋊C4—114no—
423C4⋊C4—228no—
424C4⋊C4—228no—
425C4⋊C4—228no—
426C4⋊C4—228no—
427C4⋊C4—222no—
428C4⋊C4—221no—
429C4⋊C4—224no—
430C4⋊C4—224no—
431C4⋊C4C23×D1114yes—
432C4⋊C4C23×D1112yes—
433C22⋊C4—24no—
434C22⋊C4—228no—
435C42—114no—
436C42—114no—
437C42—228no—
438C42—224no—
439C42D4×D1112yes—
440C42C23×D1112yes—
441C11C2×#338511yescharacteristic, complemented, Sylow
442C23—24no—
443C23—22no—
444C23—42no—
445C23—42no—
446C23C2×D4×D1111yescharacteristic
447Q8—84no—
448Q8—114no—
449Q8—228no—
450Q8—224no—
451Q8—222no—
452Q8—884no—
453Q8—888no—
454D4—24no—
455D4—22no—
456D4C2×Q8×D1114yes—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—42no—
461C2×C4—44no—
462C2×C4—48no—
463C2×C4—114no—
464C2×C4—114no—
465C2×C4—224no—
466C2×C4—224no—
467C2×C4—224no—
468C2×C4—222no—
469C2×C4—222no—
470C2×C4—224no—
471C2×C4—444no—
472C2×C4—442no—
473C2×C4—888no—
474C2×C4#6696814yes—
475C2×C4C2×D4×D1112yes—
476C2×C4C2×D4×D1112yes—
477C2×C4C2×D4×D1111yescharacteristic
478C2×C4C2×Q8×D1112yes—
479C2×C4#6704312yes—
480C2×C4C24×D1111yescharacteristic
481C8—24no—
482C8—114no—
483C8—222no—
484C22—24no—
485C22—48no—
486C22—42no—
487C22—42no—
488C22#1062316312yes—
489C22C2×#6696812yes—
490C22#1062330512yes—
491C22C22×D4×D1111yescharacteristic
492C4—22no—
493C4—42no—
494C4—44no—
495C4—224no—
496C4—224no—
497C4—224no—
498C4—444no—
499C4—442no—
500C4#1062316312yes—
501C4C2×#6696814yes—
502C4C22×Q8×D1111yescharacteristic
503C4C2×#6704311yescharacteristic
504C2—44no—
505C2#1308153014yesdirect product factor
506C2C2×#1062316311yescharacteristic
507C2C22×#6696811yescharacteristic
508C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#476C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#476D11
hypocenterC11C2×#3385
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#10623253C2semidirect
3. #13081530C2direct (N × H)
4. C2×#10622469C2semidirect
5. C2×#10622691C2semidirect
6. C2×#10622470C2semidirect
7. C2×#10622463C2semidirect
9. C2×#10622444C2semidirect
21. #10623253C22semidirect
42. #10622691C22semidirect
49. #10622470C22semidirect
50. #10622469C22semidirect
51. #10622463C22semidirect
52. #10622444C22semidirect
77. C2×#4324Q8semidirect
167. #4324C2×Q8semidirect
374. C2×C11#3385semidirect
441. C11C2×#3385semidirect
505. C2#13081530direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232532
C2×#106230742
#130815302
C2×#106224692
C2×#106226912
C2×#106224702
C2×#106224632
C2×#106223722
C2×#106224442
C2×#106223702
C2×C4×#43242
C2×C11×#4762
C2×#338511