Finite Group Databasebeta

← C2×#13069736 #14780972

Subgroups — C2×#13069736 #14780972

Order 2816.

1902 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66962C211yesmaximal, characteristic
2C22×#66995C211yesmaximal, characteristic
3C23×#4326C211yesmaximal, characteristic, complemented
4C22×#66888C211yesmaximal, characteristic, complemented
5C2×#10622742C211yesmaximal, characteristic
6#13069736C218yesmaximal, direct product factor
7C2×#10622196C211yesmaximal, characteristic, complemented
8C22×C11×#101C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C22×#4339C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C22×#4326—24no—
15C22×#4326—24no—
16C22×#4326—21no—
17C22×#4326—22no—
18C22×#4326—22no—
19C22×#4326C2214yescomplemented
20C2×#66995—24no—
21C2×#66995—22no—
22C2×#66995—24no—
23C2×#66995C2214yes—
24C22×#4325—21no—
25C22×#4318C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27C2×#66962—22no—
28C2×#66962—24no—
29C2×#66962—24no—
30C2×#66962C2214yes—
31C22×Dic44—21no—
32C22×#4314—21no—
33C2×C11×#101—24no—
34C2×C11×#101C2214yescomplemented
35C2×#66888—24no—
36C2×#66888C2214yescomplemented
37#10622742—22no—
38#10622742C2214yes—
39C2×(C2×D11)⋊C8—22no—
40#10622196C2214yescomplemented
41C22×Q8×C11—22no—
42C22×Q8×C11—21no—
43C22×Q8×C11—21no—
44C22×Q8×C11—21no—
45C22×Q8×C11—22no—
46C22×Q8×C11—22no—
47C22×Q8×C11—21no—
48C22×Q8×C11—21no—
49C22×Q8×C11D414yes—
50C22×Q8×C11C2312yes—
51C23×C4×C11—21no—
52C23×C4×C11C2311yescharacteristic
53C22×C22⋊D11—21no—
54C23×Dic11—21no—
55C2×#4339—21no—
56C2×#4339—21no—
57C2×#4339—22no—
58C2×#4339—22no—
59C2×#4339—22no—
60C2×#4339—22no—
61C2×#4339D412yes—
62C2×#4339C2312yes—
63C22×D44D411yescharacteristic
64C22×C4×D11—21no—
65C22×Dic22—21no—
66C22×Dic22—21no—
67C22×Dic22—22no—
68C22×Dic22—22no—
69C22×Dic22—21no—
70C22×Dic22—21no—
71C22×Dic22—22no—
72C22×Dic22—21no—
73C22×Dic22D411yescharacteristic
74C22×Dic22D414yes—
75C22×Dic22C2312yes—
76C2×C11×M16—22no—
77C2×C11×M16—21no—
78C2×C11×M16—21no—
79C2×C11×M16—22no—
80C2×C11×M16—22no—
81C2×C11×M16D414yes—
82C2×C11×M16C2312yes—
83C2×C11×M16C2312yes—
84C22×C8×C11—21no—
85C22×C8×C11—21no—
86C2×#4326—28no—
87C2×#4326—216no—
88C2×#4326—216no—
89C2×#4326—28no—
90C2×#4326—24no—
91C2×#4326—28no—
92C2×#4326—28no—
93#66995—216no—
94#66995—28no—
95#66995—28no—
96C2×#4325—28no—
97C2×#4325—24no—
98C2×#4318—22no—
99C2×#4318—21no—
100C2×#4318D414yes—
101C2×#4318C2312yes—
102C22×C11⋊C8—22no—
103C22×C11⋊C8—22no—
104C22×C11⋊C8—21no—
105C22×C11⋊C8D412yes—
106C22×C11⋊C8D412yes—
107C22×C11⋊C8C2312yes—
108#66962—216no—
109#66962—28no—
110#66962—28no—
111C2×Dic44—28no—
112C2×Dic44—24no—
113C2×#4314—28no—
114C2×#4314—24no—
115C11×#101—28no—
116#66888—28no—
117(C2×D11)⋊C8—28no—
118C2×#2020—111nomaximal, Sylow
119C24×C11#4111yescharacteristic
120C23×D11—21no—
121C2×Q8×C11—24no—
122C2×Q8×C11—22no—
123C2×Q8×C11—24no—
124C2×Q8×C11—24no—
125C2×Q8×C11—24no—
126C2×Q8×C11—24no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—42no—
132C2×Q8×C11—42no—
133C2×Q8×C11—42no—
134C2×Q8×C11—41no—
135C2×Q8×C11—41no—
136C2×Q8×C11—42no—
137C2×Q8×C11—42no—
138C2×Q8×C11C2×D414yes—
139C22×C4×C11—24no—
140C22×C4×C11—22no—
141C22×C4×C11—42no—
142C22×C4×C11—41no—
143C22×C4×C11—41no—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11#4111yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C2×C22⋊D11—22no—
155C2×C22⋊D11—22no—
156C2×C22⋊D11—42no—
157C2×C22⋊D11—42no—
158C22×Dic11—24no—
159C22×Dic11—21no—
160C22×Dic11—22no—
161C22×Dic11—41no—
162C22×Dic11—41no—
163C22×Dic11—42no—
164#4339—24no—
165#4339—24no—
166#4339—22no—
167#4339—22no—
168#4339—22no—
169#4339—22no—
170#4339—42no—
171#4339—42no—
172#4339—42no—
173#4339—42no—
174C2×D44—22no—
175C2×D44—22no—
176C2×D44—21no—
177C2×D44C2×D412yes—
178C2×C4×D11—22no—
179C2×C4×D11—22no—
180C2×C4×D11—42no—
181C2×C4×D11—42no—
182C2×Dic22—24no—
183C2×Dic22—22no—
184C2×Dic22—24no—
185C2×Dic22—24no—
186C2×Dic22—24no—
187C2×Dic22—22no—
188C2×Dic22—24no—
189C2×Dic22—21no—
190C2×Dic22—22no—
191C2×Dic22—22no—
192C2×Dic22—22no—
193C2×Dic22—22no—
194C2×Dic22—22no—
195C2×Dic22—42no—
196C2×Dic22—42no—
197C2×Dic22—41no—
198C2×Dic22—41no—
199C2×Dic22—42no—
200C2×Dic22—42no—
201C2×Dic22—42no—
202C2×Dic22C2×D412yes—
203C2×Dic22C2×D414yes—
204C11×M16—24no—
205C11×M16—22no—
206C11×M16—22no—
207C11×M16—22no—
208C11×M16—42no—
209C11×M16C2×D414yes—
210C2×C8×C11—24no—
211C2×C8×C11—22no—
212C2×C8×C11—22no—
213C2×C8×C11—42no—
214#4326—216no—
215#4326—232no—
216#4325—216no—
217#4318—24no—
218#4318—22no—
219#4318C2×D414yes—
220C2×C11⋊C8—24no—
221C2×C11⋊C8—24no—
222C2×C11⋊C8—24no—
223C2×C11⋊C8—22no—
224C2×C11⋊C8—22no—
225C2×C11⋊C8—22no—
226C2×C11⋊C8C2×D414yes—
227Dic44—216no—
228#4314—216no—
229C22×#137—111no—
230C22×#137—111no—
231C23×Q16—111no—
232C22×#101—111no—
233C22×#101D1111yescharacteristic, complemented
234C2×#408—111no—
235#2020—118no—
236C2×#341—111no—
237C23×C11—24no—
238C23×C11#12112yes—
239C23×C11#12111yescharacteristic
240C23×C11#12111yescharacteristic
241C23×C11#12112yes—
242C23×C11C2×#4111yescharacteristic
243C22×D11—22no—
244C22×D11—42no—
245C22×D11—44no—
246Q8×C11—24no—
247Q8×C11—24no—
248Q8×C11—42no—
249Q8×C11—42no—
250Q8×C11—44no—
251Q8×C11—44no—
252C2×C4×C11—24no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—44no—
256C2×C4×C11—44no—
257C2×C4×C11#12012yes—
258C2×C4×C11#12012yes—
259C2×C4×C11#12012yes—
260C2×C4×C11#12012yes—
261C2×C4×C11#12012yes—
262C2×C4×C11#12012yes—
263C2×C4×C11#12112yes—
264C2×C4×C11#12111yescharacteristic
265C2×C4×C11#12111yescharacteristic
266C2×C4×C11#12112yes—
267C2×C4×C11#12712yes—
268C2×C4×C11#12712yes—
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
275C22⋊D11—42no—
276C22⋊D11—42no—
277C22⋊D11—44no—
278C2×Dic11—24no—
279C2×Dic11—22no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—44no—
283C2×Dic11—44no—
284C2×Dic11—42no—
285D44—22no—
286D44—22no—
287D44—42no—
288C4×D11—42no—
289C4×D11—42no—
290C4×D11—44no—
291Dic22—24no—
292Dic22—22no—
293Dic22—24no—
294Dic22—22no—
295Dic22—42no—
296Dic22—42no—
297Dic22—44no—
298Dic22—44no—
299Dic22—42no—
300C8×C11—24no—
301C8×C11—42no—
302C11⋊C8—24no—
303C11⋊C8—24no—
304C22×#41—111no—
305C23×Q8—111no—
306C23×Q8C2×D1111yescharacteristic
307C2×#137—114no—
308C2×#137—114no—
309C2×#137—224no—
310C2×#137—222no—
311C2×#137—224no—
312C2×#137—222no—
313C2×#137—224no—
314C2×#137—224no—
315C22×Q16—114no—
316C22×Q16—221no—
317C22×Q16—222no—
318C22×Q16—222no—
319C22×Q16—224no—
320C22×Q16—221no—
321C22×Q16—224no—
322C22×SD16—221no—
323C22×SD16—221no—
324C22×M16—111no—
325C22×M16C2×D1111yescharacteristic
326C22×M16C2×D1111yescharacteristic
327C23×C8—111no—
328C2×#101—24no—
329C2×#101—114no—
330C2×#101—224no—
331C2×#101C2×D1114yescomplemented
332#408—114no—
333#408—222no—
334C2×C22⋊C8—222no—
335#341—114no—
336C22×C11—24no—
337C22×C11—24no—
338C22×C11—22no—
339C22×C11—22no—
340C22×C11#39212yes—
341C22×C11#39212yes—
342C22×C11#47314yes—
343C22×C11C2×#12111yescharacteristic
344C22×C11C2×#12111yescharacteristic
345C22×C11C2×#12111yescharacteristic
346C2×D11—42no—
347C2×D11—44no—
348C2×D11—84no—
349C4×C11—44no—
350C4×C11#39212yes—
351C4×C11#39212yes—
352C4×C11C2×#12011yescharacteristic
353C4×C11C2×#12011yescharacteristic
354C4×C11C2×#12011yescharacteristic
355C4×C11C2×#12711yescharacteristic
356Dic11—44no—
357Dic11—42no—
358C2×#41—112no—
359C2×#41—112no—
360C2×#41—221no—
361C2×#41—221no—
362C2×#41—222no—
363C2×#41—222no—
364C2×#41—222no—
365C2×#41—222no—
366C22×Q8—21no—
367C22×Q8—22no—
368C22×Q8—21no—
369C22×Q8—22no—
370C22×Q8—21no—
371C22×Q8—21no—
372C22×Q8—21no—
373C22×Q8—22no—
374C22×Q8—111no—
375C22×Q8—114no—
376C22×Q8—112no—
377C22×Q8—221no—
378C22×Q8—222no—
379C22×Q8—222no—
380C22×Q8—221no—
381C22×Q8—221no—
382C22×Q8—221no—
383C22×Q8—221no—
384C22×Q8—222no—
385C22×Q8D4414yes—
386C22×Q8C22×D1112yes—
387C22×D4—111no—
388C22×D4—221no—
389C23×C4—21no—
390C23×C4—221no—
391C23×C4—221no—
392C23×C4C22×D1111yescharacteristic
393#137—228no—
394#137—2216no—
395#137—228no—
396#137—2216no—
397#137—228no—
398#137—228no—
399C2×Q16—224no—
400C2×Q16—228no—
401C2×Q16—228no—
402C2×Q16—228no—
403C2×Q16—224no—
404C2×Q16—2216no—
405C2×Q16—2216no—
406C2×Q16—228no—
407C2×Q16—228no—
408C2×SD16—224no—
409C2×SD16—228no—
410C2×SD16—224no—
411C2×SD16—228no—
412C2×M16—22no—
413C2×M16—21no—
414C2×M16—21no—
415C2×M16—22no—
416C2×M16—22no—
417C2×M16—114no—
418C2×M16—112no—
419C2×M16—222no—
420C2×M16—221no—
421C2×M16C22⋊D1114yes—
422C2×M16C22×D1112yes—
423C2×M16C22×D1112yes—
424C22×C8—21no—
425C22×C8—21no—
426C22×C8—112no—
427C22×C8—112no—
428C22×C8—112no—
429C22×C8—222no—
430C22×C8—222no—
431C22×C8—221no—
432#101—28no—
433#101—228no—
434C22⋊C8—228no—
435C2×C11—21no—
436C2×C11—21no—
437C2×C11—22no—
438C2×C11#202014yescomplemented
439C2×C11C2×#39211yescharacteristic
440C2×C11C2×#47312yes—
441D11—82no—
442C24—221no—
443C24#433911yescharacteristic
444#41—224no—
445#41—224no—
446#41—222no—
447#41—222no—
448#41—222no—
449#41—222no—
450#41—442no—
451#41—442no—
452#41—442no—
453#41—442no—
454C2×Q8—24no—
455C2×Q8—22no—
456C2×Q8—24no—
457C2×Q8—24no—
458C2×Q8—24no—
459C2×Q8—24no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—41no—
465C2×Q8—41no—
466C2×Q8—42no—
467C2×Q8—42no—
468C2×Q8—42no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—112no—
472C2×Q8—114no—
473C2×Q8—224no—
474C2×Q8—221no—
475C2×Q8—222no—
476C2×Q8—224no—
477C2×Q8—224no—
478C2×Q8—222no—
479C2×Q8—224no—
480C2×Q8—222no—
481C2×Q8—224no—
482C2×Q8—222no—
483C2×Q8—222no—
484C2×Q8—222no—
485C2×Q8—222no—
486C2×Q8—442no—
487C2×Q8—442no—
488C2×Q8—441no—
489C2×Q8—441no—
490C2×Q8—442no—
491C2×Q8—442no—
492C2×Q8—442no—
493C2×Q8C2×D4414yes—
494C2×D4—112no—
495C2×D4—222no—
496C2×D4—222no—
497C2×D4—222no—
498C2×D4—221no—
499C2×D4—222no—
500C2×D4—442no—
501C2×D4—442no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—42no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—224no—
508C22×C4—221no—
509C22×C4—222no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—441no—
513C22×C4—441no—
514C22×C4—442no—
515C22×C4—442no—
516C22×C4—442no—
517C22×C4C2×D4412yes—
518C22×C4#433911yescharacteristic
519C22×C4D4×D1112yes—
520C22×C4D4×D1111yescharacteristic
521C22×C4D4×D1111yescharacteristic
522C22×C4D4×D1111yescharacteristic
523C22×C4D4×D1112yes—
524C22×C4D4×D1111yescharacteristic
525C22×C4C2×C22⋊D1112yes—
526C22×C4C23×D1111yescharacteristic
527Q16—2216no—
528Q16—2232no—
529Q16—2216no—
530SD16—2216no—
531SD16—2216no—
532M16—24no—
533M16—22no—
534M16—22no—
535M16—22no—
536M16—42no—
537M16—114no—
538M16—224no—
539M16—222no—
540M16C2×C22⋊D1114yes—
541C2×C8—24no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—42no—
545C2×C8—114no—
546C2×C8—224no—
547C2×C8—224no—
548C2×C8—224no—
549C2×C8—222no—
550C2×C8—222no—
551C2×C8—222no—
552C11C2×#202011yescharacteristic, complemented, Sylow
553C23—24no—
554C23—222no—
555C23—442no—
556C23—444no—
557C23#6693712yes—
558C23#6693711yescharacteristic
559C23#6693711yescharacteristic
560C23#6698312yes—
561C23C2×#433911yescharacteristic
562Q8—24no—
563Q8—24no—
564Q8—42no—
565Q8—42no—
566Q8—44no—
567Q8—44no—
568Q8—224no—
569Q8—222no—
570Q8—224no—
571Q8—222no—
572Q8—442no—
573Q8—442no—
574Q8—444no—
575Q8—444no—
576Q8—442no—
577D4—222no—
578D4—222no—
579D4—442no—
580D4—442no—
581D4—444no—
582D4—442no—
583C2×C4—24no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—44no—
587C2×C4—44no—
588C2×C4—222no—
589C2×C4—224no—
590C2×C4—442no—
591C2×C4—442no—
592C2×C4—442no—
593C2×C4—444no—
594C2×C4—444no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—444no—
598C2×C4#6693512yes—
599C2×C4#6693512yes—
600C2×C4#6693512yes—
601C2×C4#6693512yes—
602C2×C4#6693711yescharacteristic
603C2×C4#6693711yescharacteristic
604C2×C4#6693712yes—
605C2×C4#6698312yes—
606C2×C4#6699012yes—
607C2×C4#6699012yes—
608C2×C4#6699312yes—
609C2×C4#6699312yes—
610C2×C4C22×D4411yescharacteristic
611C2×C4C2×D4×D1111yescharacteristic
612C2×C4C2×D4×D1111yescharacteristic
613C2×C4C2×D4×D1111yescharacteristic
614C2×C4C2×D4×D1111yescharacteristic
615C2×C4C22×C22⋊D1111yescharacteristic
616C8—24no—
617C8—42no—
618C8—224no—
619C8—224no—
620C22—22no—
621C22—22no—
622C22—24no—
623C22—24no—
624C22—444no—
625C22—442no—
626C22—884no—
627C22#1062236814yes—
628C22#1062257312yes—
629C22#1062257312yes—
630C22C2×#6693711yescharacteristic
631C22C2×#6693711yescharacteristic
632C22C2×#6698311yescharacteristic
633C4—44no—
634C4—442no—
635C4—444no—
636C4#1062257312yes—
637C4#1062257312yes—
638C4C2×#6693511yescharacteristic
639C4C2×#6693511yescharacteristic
640C4C2×#6699011yescharacteristic
641C4C2×#6699311yescharacteristic
642C2—21no—
643C2—21no—
644C2—22no—
645C2—882no—
646C2#1306973614yesdirect product factor
647C2C2×#1062257311yescharacteristic
648C2C2×#1062236812yes—
subgroupG/H
centerC23#66937
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#101C2
socleC23×C11#121
prime radicalC22×#4339C22
hypercenterC22×#101D11
hypocenterC11C2×#2020
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#101

Complements

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

NH ≅ G/Ntype
3. C23×#4326C2semidirect
4. C22×#66888C2semidirect
6. #13069736C2direct (N × H)
7. C2×#10622196C2semidirect
8. C22×C11×#101C2semidirect
19. C22×#4326C22semidirect
34. C2×C11×#101C22semidirect
36. C2×#66888C22semidirect
40. #10622196C22semidirect
233. C22×#101D11semidirect
331. C2×#101C2×D11semidirect
438. C2×C11#2020semidirect
552. C11C2×#2020semidirect
646. C2#13069736direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669622
C22×#669952
C23×#43262
C22×#668882
C2×#106227422
#130697362
C2×#106221962
C22×C11×#1012
C2×#202011