Finite Group Databasebeta

← C2×#13069558 #14758253

Subgroups — C2×#13069558 #14758253

Order 2816.

1290 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623048C211yesmaximal, characteristic
2C2×M16×Dic11C211yesmaximal, characteristic
3C2×C4×Dic11⋊C4C211yesmaximal, characteristic
4#13069558C218yesmaximal, direct product factor
5C2×#10622193C211yesmaximal, characteristic
6C2×#10622161C211yesmaximal, characteristic
7C2×#10622170C211yesmaximal, characteristic
8C2×C11×#339C211yesmaximal, characteristic
9C22×C11×M16C2211yescharacteristic
10C2×C11×#117C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C22×Dic11⋊C4—21no—
14C22×C4×Dic11C2211yescharacteristic
15C22×C4×Dic11C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17#10623048—22no—
18#10623048—22no—
19#10623048C414yescomplemented
20#10623048C2214yes—
21C2×#66943C411yescharacteristic, complemented
22C2×#66943C411yescharacteristic, complemented
23C2×#66941C411yescharacteristic, complemented
24C2×#66941C411yescharacteristic, complemented
25C2×#66931—21no—
26C2×#66931—21no—
27C2×C4×Dic22—21no—
28C2×C4×Dic22—21no—
29C2×C11⋊#95—21no—
30M16×Dic11—22no—
31M16×Dic11C2214yes—
32C2×#66879—21no—
33C2×C8×Dic11—21no—
34C4×Dic11⋊C4—22no—
35C4×Dic11⋊C4C2214yes—
36C11×#339C2214yes—
37#10622193C2214yes—
38#10622170C2214yes—
39#10622161C2214yes—
40C23×C4×C11—21no—
41C23×C4×C11C2311yescharacteristic
42C23×Dic11—21no—
43C23×Dic11D411yescharacteristic
44C23×Dic11D411yescharacteristic
45C22×Dic22—21no—
46C22×Dic22—21no—
47C2×C11×M16—21no—
48C2×C11×M16—22no—
49C2×C11×M16Q814yescomplemented
50C2×C11×M16C2312yes—
51C22×C8×C11—21no—
52C11×#117—21no—
53C11×#117—21no—
54C11×#117C2×C412yes—
55C11×#117C2312yes—
56C2×C11×C4⋊C4C2×C411yescharacteristic
57C2×C11×C4⋊C4C2×C411yescharacteristic
58C2×C11×C22⋊C4—21no—
59C2×C42×C11—21no—
60C2×C42×C11—22no—
61C2×C42×C11—22no—
62C2×C42×C11—21no—
63C2×C42×C11C2312yes—
64C2×C22⋊Dic11—21no—
65#66979—21no—
66#66979—21no—
67#66979C2×C412yes—
68#66979C2312yes—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11C2×C411yescharacteristic
72C2×C4⋊Dic11C2×C411yescharacteristic
73C2×Dic11⋊C4—28no—
74C2×Dic11⋊C4—21no—
75C2×Dic11⋊C4—21no—
76C2×Dic11⋊C4—21no—
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—24no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11—22no—
82C2×C4×Dic11—21no—
83C2×C4×Dic11C2×C411yescharacteristic
84C2×C4×Dic11C2×C411yescharacteristic
85C2×C4×Dic11C2×C412yes—
86C2×C4×Dic11D412yes—
87C2×C4×Dic11D412yes—
88C2×C4×Dic11D411yescharacteristic
89C2×C4×Dic11D411yescharacteristic
90C2×C4×Dic11C2312yes—
91C2×C4×Dic11C2312yes—
92C2×#4318—21no—
93C2×#4318—22no—
94C2×#4318Q814yescomplemented
95C2×#4318C2312yes—
96C22×C11⋊C8—21no—
97#66943—22no—
98#66943—22no—
99#66943C2×C414yescomplemented
100#66943C2×C414yescomplemented
101#66941—22no—
102#66941—22no—
103#66941C2×C414yescomplemented
104#66941C2×C414yescomplemented
105#66931—24no—
106#66931—24no—
107#66931—24no—
108#66931—24no—
109C4×Dic22—24no—
110C4×Dic22—24no—
111C4×Dic22—24no—
112C4×Dic22—24no—
113C11⋊#95—24no—
114#66879—24no—
115C8×Dic11—24no—
116C2×#1986—111nomaximal, Sylow
117C24×C11C2×D411yescharacteristic
118C22×C4×C11—24no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11C22×C411yescharacteristic
125C22×C4×C11C22×C411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×Q812yes—
130C22×C4×C11C2×Q812yes—
131C22×C4×C11#4112yes—
132C22×C4×C11#4112yes—
133C22×C4×C11C2411yescharacteristic
134C22×Dic11—24no—
135C22×Dic11—24no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—22no—
139C22×Dic11—42no—
140C22×Dic11—42no—
141C22×Dic11—42no—
142C22×Dic11C22⋊C412yes—
143C22×Dic11C22⋊C411yescharacteristic
144C22×Dic11C22⋊C411yescharacteristic
145C22×Dic11C22⋊C411yescharacteristic
146C22×Dic11C22⋊C412yes—
147C22×Dic11C22⋊C411yescharacteristic
148C22×Dic11C2×D412yes—
149C22×Dic11C2×D412yes—
150C2×Dic22—24no—
151C2×Dic22—24no—
152C2×Dic22—44no—
153C2×Dic22—44no—
154C11×M16—24no—
155C11×M16—22no—
156C11×M16C2×Q814yescomplemented
157C2×C8×C11—24no—
158C2×C8×C11—22no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4C22×C412yes—
162C11×C4⋊C4C22×C412yes—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—22no—
165C42×C11—22no—
166C42×C11—22no—
167C42×C11—22no—
168C42×C11—22no—
169C42×C11—42no—
170C22⋊Dic11—22no—
171C22⋊Dic11—22no—
172C4⋊Dic11—24no—
173C4⋊Dic11—24no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11C22×C412yes—
177C4⋊Dic11C22×C412yes—
178Dic11⋊C4—216no—
179Dic11⋊C4—24no—
180Dic11⋊C4—24no—
181Dic11⋊C4—24no—
182Dic11⋊C4—24no—
183C4×Dic11—22no—
184C4×Dic11—22no—
185C4×Dic11—22no—
186C4×Dic11—22no—
187C4×Dic11—42no—
188C4×Dic11C22⋊C412yes—
189C4×Dic11C22⋊C412yes—
190C4×Dic11C22⋊C412yes—
191C4×Dic11C22⋊C412yes—
192C4×Dic11C22×C412yes—
193C4×Dic11C22×C412yes—
194C4×Dic11C2×D412yes—
195C4×Dic11C2×D412yes—
196#4318—24no—
197#4318—22no—
198#4318C2×Q814yescomplemented
199C2×C11⋊C8—24no—
200C2×C11⋊C8—22no—
201C2×#533—111no—
202C2×C4×M16—111no—
203C2×C4×C4⋊C4—111no—
204#1986—118no—
205C2×#339—111no—
206C2×#339—111no—
207C2×#339—111no—
208C2×#339D1111yescharacteristic
209C23×C11—22no—
210C23×C11—22no—
211C23×C11C2×C22⋊C411yescharacteristic
212C23×C11C2×C22⋊C411yescharacteristic
213C23×C11#12412yes—
214C23×C11C4⋊Q812yes—
215C23×C11C22×D411yescharacteristic
216C2×C4×C11—24no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—42no—
220C2×C4×C11—48no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11C2×C22⋊C411yescharacteristic
225C2×C4×C11C2×C22⋊C411yescharacteristic
226C2×C4×C11C4×Q812yes—
227C2×C4×C11C4×Q812yes—
228C2×C4×C11C4×Q812yes—
229C2×C4×C11C4×Q812yes—
230C2×C4×C11C22⋊Q812yes—
231C2×C4×C11C22⋊Q812yes—
232C2×C4×C11C22⋊Q812yes—
233C2×C4×C11C22⋊Q812yes—
234C2×C4×C11#12412yes—
235C2×C4×C11C4⋊Q812yes—
236C2×C4×C11C23×C411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×Q811yescharacteristic
239C2×C4×C11C22×Q811yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—48no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11#10414yes—
258C2×Dic11C2×C22⋊C412yes—
259C2×Dic11C2×C22⋊C412yes—
260C2×Dic11C2×C22⋊C412yes—
261C2×Dic11C2×C22⋊C412yes—
262Dic22—48no—
263Dic22—48no—
264C8×C11—24no—
265C11⋊C8—24no—
266C22×M16—111no—
267C22×M16C2×D1111yescharacteristic
268#533—114no—
269#533—114no—
270#533—222no—
271#533—222no—
272C2×C4⋊Q8—111no—
273C2×C4⋊Q8—111no—
274C2×#125—111no—
275C2×#125—111no—
276C2×C22⋊Q8—221no—
277C2×C22⋊Q8—221no—
278C2×C4×Q8—221no—
279C2×C4×Q8—221no—
280C2×#117—111no—
281C2×#117C2×D1111yescharacteristic
282C22×C4⋊C4—221no—
283C22×C42—111no—
284C22×C42—111no—
285C22×C42C2×D1111yescharacteristic
286C4×M16—114no—
287C4×M16—222no—
288C2×#97—221no—
289C2×C4×C8—221no—
290C4×C4⋊C4—114no—
291C4×C4⋊C4—222no—
292C2×#95—221no—
293#339—114no—
294#339—114no—
295#339—114no—
296#339C2×D1114yes—
297C22×C11—21no—
298C22×C11—21no—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—24no—
302C22×C11—24no—
303C22×C11#39112yes—
304C22×C11#39112yes—
305C22×C11C2×#10412yes—
306C22×C11#42112yes—
307C22×C11C22×C22⋊C411yescharacteristic
308C22×C11C2×#12411yescharacteristic
309C22×C11C2×C4⋊Q811yescharacteristic
310C4×C11—44no—
311C4×C11—42no—
312C4×C11—42no—
313C4×C11#39112yes—
314C4×C11#39112yes—
315C4×C11C2×C4×Q811yescharacteristic
316C4×C11C2×C4×Q811yescharacteristic
317C4×C11C2×C22⋊Q811yescharacteristic
318C4×C11C2×C22⋊Q811yescharacteristic
319Dic11—22no—
320Dic11—22no—
321Dic11—22no—
322Dic11—44no—
323Dic11—42no—
324Dic11—42no—
325Dic11C2×#10414yes—
326C22×Q8—221no—
327C22×Q8—221no—
328C23×C4—21no—
329C23×C4—111no—
330C23×C4—111no—
331C23×C4—221no—
332C23×C4C22×D1111yescharacteristic
333C2×M16—21no—
334C2×M16—22no—
335C2×M16—114no—
336C2×M16—112no—
337C2×M16—222no—
338C2×M16—221no—
339C2×M16Dic2214yescomplemented
340C2×M16C22×D1112yes—
341C22×C8—21no—
342C22×C8—221no—
343C4⋊Q8—114no—
344C4⋊Q8—114no—
345C4⋊Q8—222no—
346C4⋊Q8—222no—
347#125—114no—
348#125—114no—
349#125—222no—
350#125—222no—
351C22⋊Q8—224no—
352C22⋊Q8—224no—
353C22⋊Q8—224no—
354C22⋊Q8—224no—
355C4×Q8—224no—
356C4×Q8—224no—
357C4×Q8—224no—
358C4×Q8—224no—
359#117—21no—
360#117—21no—
361#117—112no—
362#117—112no—
363#117—221no—
364#117—221no—
365#117C4×D1112yes—
366#117C22×D1112yes—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—224no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—228no—
377C2×C4⋊C4C4×D1111yescharacteristic
378C2×C4⋊C4C4×D1111yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—221no—
381C2×C42—21no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—21no—
385C2×C42—111no—
386C2×C42—111no—
387C2×C42—112no—
388C2×C42—112no—
389C2×C42—112no—
390C2×C42—111no—
391C2×C42—111no—
392C2×C42—112no—
393C2×C42—112no—
394C2×C42—221no—
395C2×C42—222no—
396C2×C42—222no—
397C2×C42—221no—
398C2×C42C22×D1112yes—
399#97—224no—
400C4×C8—224no—
401#95—224no—
402C2×C11—21no—
403C2×C11—21no—
404C2×C11—22no—
405C2×C11#198614yescomplemented
406C2×C11C2×#39111yescharacteristic
407C2×C11C22×#10411yescharacteristic
408C2×C11C2×#42111yescharacteristic
409C24D4×D1111yescharacteristic
410C2×Q8—224no—
411C2×Q8—224no—
412C2×Q8—444no—
413C2×Q8—444no—
414C22×C4—24no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—111no—
421C22×C4—111no—
422C22×C4—111no—
423C22×C4—111no—
424C22×C4—112no—
425C22×C4—112no—
426C22×C4—112no—
427C22×C4—112no—
428C22×C4—224no—
429C22×C4—224no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—222no—
433C22×C4—442no—
434C22×C4—442no—
435C22×C4—442no—
436C22×C4C2×Dic2212yes—
437C22×C4C2×C4×D1111yescharacteristic
438C22×C4C2×C4×D1111yescharacteristic
439C22×C4#433912yes—
440C22×C4D4×D1111yescharacteristic
441C22×C4D4×D1111yescharacteristic
442C22×C4D4×D1111yescharacteristic
443C22×C4#434112yes—
444C22×C4Q8×D1112yes—
445C22×C4C23×D1111yescharacteristic
446M16—24no—
447M16—22no—
448M16—114no—
449M16—224no—
450M16—222no—
451M16C2×Dic2214yescomplemented
452C2×C8—24no—
453C2×C8—22no—
454C2×C8—224no—
455C2×C8—222no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—112no—
459C4⋊C4—112no—
460C4⋊C4—224no—
461C4⋊C4—224no—
462C4⋊C4—224no—
463C4⋊C4—224no—
464C4⋊C4—224no—
465C4⋊C4—224no—
466C4⋊C4—2216no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4C2×C4×D1112yes—
470C4⋊C4C2×C4×D1112yes—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—222no—
474C22⋊C4—222no—
475C42—22no—
476C42—22no—
477C42—22no—
478C42—22no—
479C42—42no—
480C42—112no—
481C42—112no—
482C42—112no—
483C42—112no—
484C42—112no—
485C42—112no—
486C42—112no—
487C42—112no—
488C42—222no—
489C42—222no—
490C42—222no—
491C42—222no—
492C42—442no—
493C11C2×#198611yescharacteristic, complemented, Sylow
494C23—22no—
495C23—22no—
496C23C22⋊C4×D1111yescharacteristic
497C23C22⋊C4×D1111yescharacteristic
498C23#6693812yes—
499C23#6694112yes—
500C23C2×D4×D1111yescharacteristic
501Q8—448no—
502Q8—448no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—42no—
507C2×C4—48no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—112no—
512C2×C4—114no—
513C2×C4—112no—
514C2×C4—112no—
515C2×C4—112no—
516C2×C4—224no—
517C2×C4—224no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—222no—
521C2×C4—224no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—448no—
528C2×C4—442no—
529C2×C4—442no—
530C2×C4—442no—
531C2×C4C4×Dic2212yes—
532C2×C4C4×Dic2212yes—
533C2×C4#6693112yes—
534C2×C4#6693112yes—
535C2×C4C22⋊C4×D1111yescharacteristic
536C2×C4C22⋊C4×D1111yescharacteristic
537C2×C4#6693812yes—
538C2×C4#6694012yes—
539C2×C4#6694012yes—
540C2×C4#6694112yes—
541C2×C4#6694912yes—
542C2×C4#6694912yes—
543C2×C4C22×Dic2211yescharacteristic
544C2×C4C22×C4×D1111yescharacteristic
545C2×C4C2×#433911yescharacteristic
546C2×C4C2×D4×D1111yescharacteristic
547C2×C4C2×#434111yescharacteristic
548C2×C4C2×Q8×D1111yescharacteristic
549C8—24no—
550C8—224no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—24no—
556C22—24no—
557C22#1062225912yes—
558C22#1062225912yes—
559C22D11×#10412yes—
560C22#1062243412yes—
561C22C2×C22⋊C4×D1111yescharacteristic
562C22C2×#6693811yescharacteristic
563C22C2×#6694111yescharacteristic
564C4—44no—
565C4—42no—
566C4—42no—
567C4—114no—
568C4—222no—
569C4—222no—
570C4—222no—
571C4—444no—
572C4—442no—
573C4—442no—
574C4#1062225912yes—
575C4#1062225912yes—
576C4C2×C4×Dic2211yescharacteristic
577C4C2×#6693111yescharacteristic
578C4C2×#6694011yescharacteristic
579C4C2×#6694911yescharacteristic
580C2—21no—
581C2—22no—
582C2—21no—
583C2#1306955814yesdirect product factor
584C2C2×#1062225911yescharacteristic
585C2C2×D11×#10411yescharacteristic
586C2C2×#1062243411yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#339C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#339D11
hypocenterC11C2×#1986
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. #13069558C2direct (N × H)
19. #10623048C4semidirect
21. C2×#66943C4semidirect
22. C2×#66943C4semidirect
23. C2×#66941C4semidirect
24. C2×#66941C4semidirect
49. C2×C11×M16Q8semidirect
94. C2×#4318Q8semidirect
99. #66943C2×C4semidirect
100. #66943C2×C4semidirect
103. #66941C2×C4semidirect
104. #66941C2×C4semidirect
156. C11×M16C2×Q8semidirect
198. #4318C2×Q8semidirect
339. C2×M16Dic22semidirect
405. C2×C11#1986semidirect
451. M16C2×Dic22semidirect
493. C11C2×#1986semidirect
583. C2#13069558direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230482
C2×M16×Dic112
C2×C4×Dic11⋊C42
#130695582
C2×#106221932
C2×#106221612
C2×#106221702
C2×C11×#3392
C2×#198611