Finite Group Databasebeta

← C2×#13077459 #15617882

Subgroups — C2×#13077459 #15617882

Order 2816.

2730 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66995C211yesmaximal, characteristic
2C2×#10623054C211yesmaximal, characteristic
3#13077459C2116yesmaximal, direct product factor
4C2×#10622643C212yesmaximal, complemented
5C2×#10622639C212yesmaximal, complemented
6C2×C4×#4326C212yesmaximal, complemented
7C2×C4×#4325C212yesmaximal, complemented
8C2×#10622608C211yesmaximal, characteristic, complemented
9C2×#10622615C211yesmaximal, characteristic
10C22×#66899C211yesmaximal, characteristic, complemented
11C2×#10622610C211yesmaximal, characteristic, complemented
12C2×C11×#519C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C11×#519—24no—
16C11×#519C2218yescomplemented
17C2×C4×Q8×C11—21no—
18C2×C4×Q8×C11—21no—
19C2×C4×Q8×C11C2212yes—
20C2×C4×Q8×C11C2212yes—
21C2×C11×#117—22no—
22C2×C11×#117C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C22×#4326C2212yes—
25C2×#66995C4116yescomplemented
26C2×#66995C2218yes—
27C22×#4325C2212yes—
28C22×C4⋊Dic11C2211yescharacteristic
29C22×#4318C2211yescharacteristic
30C23×C11⋊C8C2211yescharacteristic
31#10623054—24no—
32#10623054C2218yes—
33C2×#66945—21no—
34C2×C4⋊C4×D11—21no—
35C2×(C22⋊D11)⋊C4—22no—
36C2×C4×D44C2212yes—
37C2×C4×Dic22C2212yes—
38C2×#66899C2212yes—
39C2×#66899C2212yes—
40C2×#66899C2218yescomplemented
41#10622643C22116yescomplemented
42C4×#4326C22116yescomplemented
43#10622639C22116yescomplemented
44C4×#4325C22116yescomplemented
45#10622615C2218yes—
46#10622610C2218yescomplemented
47#10622608C2218yescomplemented
48C2×#66874C2211yescharacteristic
49C2×#66874C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51C2×#66873C2211yescharacteristic
52C2×#66872C2212yes—
53C2×#66871C2212yes—
54C2×#66867C2212yes—
55C2×C4×C11⋊C8C2212yes—
56C22×Q8×C11—21no—
57C22×Q8×C11—22no—
58C22×Q8×C11—24no—
59C22×Q8×C11C2×C418yescomplemented
60C22×Q8×C11C2312yes—
61C22×Q8×C11C2314yes—
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—21no—
65C23×Dic11—21no—
66C2×#4339—22no—
67C2×#4339—24no—
68C2×#4339C2×C418yes—
69C2×#4339C2314yes—
70C22×D44C2311yescharacteristic
71C22×C4×D11—21no—
72C22×C4×D11—22no—
73C22×Dic22C2311yescharacteristic
74C4×Q8×C11—28no—
75C4×Q8×C11—28no—
76C4×Q8×C11—24no—
77C4×Q8×C11—24no—
78C4×Q8×C11C2318yes—
79C4×Q8×C11C2318yes—
80C11×#117—22no—
81C11×#117—216no—
82C11×#117D414yes—
83C11×#117C2314yes—
84C11×#117C2314yes—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4D411yescharacteristic
88C2×C11×C4⋊C4D411yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4D412yes—
93C2×C42×C11—22no—
94C2×C42×C11—22no—
95C2×C42×C11—21no—
96C2×C42×C11C2312yes—
97C2×#4326C2×C4116yescomplemented
98C2×#4326C2318yes—
99#66995C2×C4164yescomplemented
100C2×#4325C2×C4116yescomplemented
101C2×#4325C2318yes—
102C2×(C2×D11)⋊C4—22no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11—22no—
105C2×C4⋊Dic11C2312yes—
106C2×C4⋊Dic11C2314yes—
107C2×Dic11⋊C4—22no—
108C2×C4×Dic11—22no—
109C2×#4318C2×C418yescomplemented
110C2×#4318C2314yes—
111C22×C11⋊C8—24no—
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2314yes—
115C22×C11⋊C8C2312yes—
116#66945—28no—
117C4⋊C4×D11—28no—
118(C22⋊D11)⋊C4—216no—
119C4×D44—24no—
120C4×D44C2318yes—
121C4×Dic22—24no—
122C4×Dic22C2318yes—
123#66899C2318yes—
124#66899C2318yes—
125#66874C2314yes—
126#66874C2314yes—
127#66873C2314yes—
128#66873C2314yes—
129#66872C2318yes—
130#66871C2318yes—
131#66867C2318yes—
132C4×C11⋊C8C2318yes—
133C2×#2947—111nomaximal, Sylow
134C24×C11C2×D411yescharacteristic
135C23×D11—21no—
136C2×Q8×C11—28no—
137C2×Q8×C11—216no—
138C2×Q8×C11—24no—
139C2×Q8×C11—22no—
140C2×Q8×C11—24no—
141C2×Q8×C11—28no—
142C2×Q8×C11C22×C418yes—
143C2×Q8×C11C22×C4116yescomplemented
144C2×Q8×C11C2414yes—
145C22×C4×C11—28no—
146C22×C4×C11—22no—
147C22×C4×C11—24no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11C22×C414yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D412yes—
155C22×C4×C11#4114yes—
156C22×C4×C11C2411yescharacteristic
157C22×C4×C11C2412yes—
158C2×C22⋊D11—28no—
159C2×C22⋊D11—24no—
160C22×Dic11—21no—
161C22×Dic11—22no—
162C22×Dic11—24no—
163C22×Dic11—82no—
164#4339—216no—
165#4339—28no—
166#4339C22×C4116yes—
167C2×D44—21no—
168C2×D44—22no—
169C2×D44C22×C414yes—
170C2×D44C2412yes—
171C2×C4×D11—28no—
172C2×C4×D11—24no—
173C2×C4×D11—28no—
174C2×C4×D11—84no—
175C2×Dic22—21no—
176C2×Dic22—22no—
177C2×Dic22C22×C414yes—
178C2×Dic22C2412yes—
179C11×C4⋊C4—28no—
180C11×C4⋊C4—28no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4C2×D414yes—
184C11×C4⋊C4C2×D414yes—
185C11×C4⋊C4C2412yes—
186C11×C4⋊C4C2412yes—
187C11×C22⋊C4—24no—
188C11×C22⋊C4C2×D418yes—
189C42×C11—28no—
190C42×C11—28no—
191C42×C11—24no—
192C42×C11C2×D414yes—
193C42×C11C2414yes—
194#4326C22×C4132yescomplemented
195#4325C22×C4132yescomplemented
196(C2×D11)⋊C4—28no—
197C4⋊Dic11—22no—
198C4⋊Dic11—24no—
199C4⋊Dic11C2414yes—
200Dic11⋊C4—28no—
201C4×Dic11—28no—
202#4318C22×C4116yescomplemented
203C2×C11⋊C8—22no—
204C2×C11⋊C8—22no—
205C2×C11⋊C8—28no—
206C2×C11⋊C8C22×C418yes—
207C2×C11⋊C8C2412yes—
208C2×C11⋊C8C2412yes—
209C2×C11⋊C8C2414yes—
210C22×#137—111no—
211C2×#520—111no—
212C2×#519D1111yescharacteristic, complemented
213#2947—1116no—
214C2×#441—112no—
215C2×#440—112no—
216C2×C4×Q16—112no—
217C2×C4×SD16—112no—
218C2×#428—111no—
219C2×#416—111no—
220C22×#103—111no—
221C2×#405—111no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11C4×D414yes—
225C23×C11C22×D412yes—
226C23×C11C22×D411yescharacteristic
227C22×D11—24no—
228C22×D11—22no—
229C22×D11—42no—
230C22×D11—42no—
231Q8×C11—28no—
232Q8×C11—216no—
233Q8×C11—24no—
234Q8×C11C23×C418yes—
235C2×C4×C11—28no—
236C2×C4×C11—216no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11C4×D414yes—
245C2×C4×C11C4×D418yes—
246C2×C4×C11C23×C412yes—
247C2×C4×C11C23×C414yes—
248C2×C4×C11C22×D414yes—
249C2×C4×C11C22×D414yes—
250C2×C4×C11C22×D412yes—
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C2×#4112yes—
253C2×C4×C11C2×#4114yes—
254C2×C4×C11C2511yescharacteristic
255C22⋊D11—216no—
256C2×Dic11—24no—
257C2×Dic11—22no—
258C2×Dic11—24no—
259C2×Dic11—44no—
260C2×Dic11—84no—
261D44—24no—
262D44—22no—
263D44C23×C414yes—
264C4×D11—216no—
265C4×D11—88no—
266Dic22—24no—
267Dic22—22no—
268Dic22C23×C414yes—
269C11⋊C8—22no—
270C11⋊C8—22no—
271C11⋊C8C23×C418yes—
272C22×#41—111no—
273C23×Q8C2×D1111yescharacteristic
274C2×#137—118no—
275C2×#137—1116no—
276C22×Q16—112no—
277C22×SD16—112no—
278C22×M16—111no—
279C23×C8—111no—
280#520—118no—
281#520—224no—
282#519—24no—
283#519C2×D1118yescomplemented
284C2×C4×Q8—21no—
285C2×C4×Q8—21no—
286C2×C4×Q8—112no—
287C2×C4×Q8C2×D1112yes—
288C2×C4×Q8C2×D1112yes—
289C2×C4×D4—112no—
290C2×C4×D4—222no—
291C2×#117—22no—
292C2×#117—221no—
293C2×#117C2×D1111yescharacteristic
294C2×#117C2×D1111yescharacteristic
295C22×C4⋊C4—111no—
296C22×C4⋊C4—221no—
297#441—1116no—
298#440—1116no—
299C4×Q16—1116no—
300C4×SD16—1116no—
301#428—118no—
302C2×#107—112no—
303C2×#106—112no—
304#416—118no—
305C2×#103—112no—
306C2×#103—112no—
307C2×#103—118no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#102—111no—
311C2×#102—111no—
312#405—118no—
313C2×#97—112no—
314C2×C4×C8—112no—
315C22×C11—28no—
316C22×C11—22no—
317C22×C11—22no—
318C22×C11C2×C4×D414yes—
319C22×C11C2×C4×D412yes—
320C22×C11#57712yes—
321C22×C11#57812yes—
322C22×C11C23×D411yescharacteristic
323C2×D11—24no—
324C2×D11—48no—
325C2×D11—42no—
326C2×D11—42no—
327C4×C11—28no—
328C4×C11—24no—
329C4×C11—24no—
330C4×C11—42no—
331C4×C11—42no—
332C4×C11C2×C4×D412yes—
333C4×C11C2×C4×D414yes—
334C4×C11C24×C411yescharacteristic
335C4×C11C22×#4111yescharacteristic
336Dic11—24no—
337Dic11—44no—
338C2×#41—118no—
339C2×#41—114no—
340C2×#41—224no—
341C2×#41—222no—
342C22×Q8—24no—
343C22×Q8—21no—
344C22×Q8—22no—
345C22×Q8—111no—
346C22×Q8C4×D1118yescomplemented
347C22×Q8C22×D1112yes—
348C22×Q8C22×D1114yes—
349C22×D4—111no—
350C22×D4—221no—
351C23×C4—21no—
352C23×C4—221no—
353C23×C4—221no—
354C23×C4—222no—
355C23×C4C22×D1111yescharacteristic
356#137—1164no—
357C2×Q16—1116no—
358C2×Q16—118no—
359C2×SD16—1116no—
360C2×SD16—118no—
361C2×M16—118no—
362C2×M16—114no—
363C22×C8—112no—
364C22×C8—111no—
365C22×C8—111no—
366C22×C8—114no—
367C22×C8—224no—
368C4×Q8—28no—
369C4×Q8—28no—
370C4×Q8—24no—
371C4×Q8—24no—
372C4×Q8—118no—
373C4×Q8—224no—
374C4×Q8C22×D1118yes—
375C4×Q8C22×D1118yes—
376C4×D4—118no—
377C4×D4—2216no—
378C4×D4—224no—
379#117—22no—
380#117—216no—
381#117—228no—
382#117C22⋊D1114yes—
383#117C22×D1114yes—
384#117C22×D1114yes—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—112no—
388C2×C4⋊C4—114no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—222no—
392C2×C4⋊C4—228no—
393C2×C4⋊C4C22⋊D1111yescharacteristic
394C2×C4⋊C4C22⋊D1111yescharacteristic
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C4⋊C4C22×D1111yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—222no—
399C2×C22⋊C4C22⋊D1112yes—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—21no—
403C2×C42—222no—
404C2×C42C22×D1112yes—
405#107—118no—
406#106—118no—
407#103—118no—
408#103—118no—
409#103—114no—
410#103—114no—
411#102—114no—
412#102—114no—
413#97—118no—
414C4×C8—118no—
415C2×C11—24no—
416C2×C11#294714yescomplemented
417C2×C11C22×C4×D411yescharacteristic
418C2×C11C2×#57711yescharacteristic
419C2×C11C2×#57811yescharacteristic
420D11—44no—
421C24—221no—
422C24C2×C22⋊D1111yescharacteristic
423#41—1116no—
424#41—2216no—
425#41—228no—
426C2×Q8—28no—
427C2×Q8—216no—
428C2×Q8—24no—
429C2×Q8—28no—
430C2×Q8—24no—
431C2×Q8—22no—
432C2×Q8—114no—
433C2×Q8—112no—
434C2×Q8—222no—
435C2×Q8—221no—
436C2×Q8C2×C4×D1118yes—
437C2×Q8C2×C4×D11116yescomplemented
438C2×Q8C23×D1114yes—
439C2×D4—114no—
440C2×D4—112no—
441C2×D4—228no—
442C2×D4—224no—
443C2×D4—222no—
444C2×D4—221no—
445C22×C4—28no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—221no—
451C22×C4—228no—
452C22×C4—224no—
453C22×C4—222no—
454C22×C4—224no—
455C22×C4—228no—
456C22×C4—884no—
457C22×C4—882no—
458C22×C4C2×C4×D1114yes—
459C22×C4#433914yes—
460C22×C4C2×C22⋊D1112yes—
461C22×C4C2×C22⋊D1112yes—
462C22×C4C2×C22⋊D1112yes—
463C22×C4C2×C22⋊D1111yescharacteristic
464C22×C4C23×D1112yes—
465C22×C4C23×D1111yescharacteristic
466Q16—1132no—
467SD16—1132no—
468M16—1116no—
469C2×C8—118no—
470C2×C8—114no—
471C2×C8—112no—
472C2×C8—112no—
473C2×C8—222no—
474C2×C8—222no—
475C2×C8—228no—
476C4⋊C4—28no—
477C4⋊C4—28no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—114no—
481C4⋊C4—224no—
482C4⋊C4—222no—
483C4⋊C4—228no—
484C4⋊C4C2×C22⋊D1114yes—
485C4⋊C4C2×C22⋊D1114yes—
486C4⋊C4C23×D1112yes—
487C4⋊C4C23×D1112yes—
488C22⋊C4—24no—
489C22⋊C4—228no—
490C22⋊C4C2×C22⋊D1118yes—
491C42—28no—
492C42—28no—
493C42—24no—
494C42—228no—
495C42C2×C22⋊D1114yes—
496C42C23×D1114yes—
497C11C2×#294711yescharacteristic, complemented, Sylow
498C23—22no—
499C23—22no—
500C23—224no—
501C23—222no—
502C23—442no—
503C23—442no—
504C23C4×C22⋊D1114yes—
505C23C22×C22⋊D1112yes—
506C23C22×C22⋊D1111yescharacteristic
507Q8—28no—
508Q8—216no—
509Q8—24no—
510Q8—114no—
511Q8—224no—
512Q8—222no—
513Q8C22×C4×D1118yes—
514D4—114no—
515D4—2216no—
516D4—224no—
517D4—222no—
518C2×C4—28no—
519C2×C4—216no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—224no—
528C2×C4—222no—
529C2×C4—2216no—
530C2×C4—224no—
531C2×C4—444no—
532C2×C4—888no—
533C2×C4—884no—
534C2×C4C4×C22⋊D1114yes—
535C2×C4C4×C22⋊D1118yes—
536C2×C4C22×C4×D1112yes—
537C2×C4C22×C4×D1114yes—
538C2×C4C2×#433912yes—
539C2×C4C2×#433914yes—
540C2×C4C22×C22⋊D1114yes—
541C2×C4C22×C22⋊D1114yes—
542C2×C4C22×C22⋊D1112yes—
543C2×C4C22×C22⋊D1111yescharacteristic
544C2×C4C24×D1111yescharacteristic
545C8—118no—
546C8—222no—
547C8—222no—
548C22—28no—
549C22—22no—
550C22—22no—
551C22—224no—
552C22—448no—
553C22—442no—
554C22—442no—
555C22C2×C4×C22⋊D1114yes—
556C22C2×C4×C22⋊D1112yes—
557C22#1062336812yes—
558C22#1062336912yes—
559C22C23×C22⋊D1111yescharacteristic
560C4—28no—
561C4—24no—
562C4—24no—
563C4—42no—
564C4—42no—
565C4—224no—
566C4—444no—
567C4C2×C4×C22⋊D1114yes—
568C4C2×C4×C22⋊D1112yes—
569C4C23×C4×D1111yescharacteristic
570C4C22×#433911yescharacteristic
571C2—24no—
572C2—444no—
573C2#1307745914yesdirect product factor
574C2C22×C4×C22⋊D1111yescharacteristic
575C2C2×#1062336811yescharacteristic
576C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#519C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC2×C4×C11C25
hypercenterC2×#519D11
hypocenterC11C2×#2947
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
3. #13077459C2direct (N × H)
4. C2×#10622643C2semidirect
5. C2×#10622639C2semidirect
6. C2×C4×#4326C2semidirect
7. C2×C4×#4325C2semidirect
8. C2×#10622608C2semidirect
10. C22×#66899C2semidirect
11. C2×#10622610C2semidirect
12. C2×C11×#519C2semidirect
16. C11×#519C22semidirect
25. C2×#66995C4semidirect
40. C2×#66899C22semidirect
41. #10622643C22semidirect
42. C4×#4326C22semidirect
43. #10622639C22semidirect
44. C4×#4325C22semidirect
46. #10622610C22semidirect
47. #10622608C22semidirect
59. C22×Q8×C11C2×C4semidirect
97. C2×#4326C2×C4semidirect
99. #66995C2×C4semidirect
100. C2×#4325C2×C4semidirect
109. C2×#4318C2×C4semidirect
143. C2×Q8×C11C22×C4semidirect
194. #4326C22×C4semidirect
195. #4325C22×C4semidirect
202. #4318C22×C4semidirect
212. C2×#519D11semidirect
283. #519C2×D11semidirect
346. C22×Q8C4×D11semidirect
416. C2×C11#2947semidirect
437. C2×Q8C2×C4×D11semidirect
497. C11C2×#2947semidirect
573. C2#13077459direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669952
C2×#106230542
#130774592
C2×#106226432
C2×#106226392
C2×C4×#43262
C2×C4×#43252
C2×#106226082
C2×#106226152
C22×#668992
C2×#106226102
C2×C11×#5192
C2×#294711