Finite Group Databasebeta

← C2×#13069734 #14780970

Subgroups — C2×#13069734 #14780970

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×#67004C211yesmaximal, characteristic
2C23×#4326C211yesmaximal, characteristic, complemented
3C22×#66900C211yesmaximal, characteristic, complemented
4C22×#66888C211yesmaximal, characteristic, complemented
5C2×#10622847C211yesmaximal, characteristic
6#13069734C218yesmaximal, direct product factor
7C2×#10622196C211yesmaximal, characteristic, complemented
8C22×C11×#137C211yesmaximal, characteristic
9C22×C11×#41C2211yescharacteristic
10C23×Q8×C11C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C2×C11×#137—22no—
13C2×C11×#137—24no—
14C2×C11×#137—24no—
15C2×C11×#137C2214yes—
16C22×C11×Q16—21no—
17C22×C11×SD16—21no—
18C22×C11×M16C2211yescharacteristic
19C2×#67004—22no—
20C2×#67004—24no—
21C2×#67004—24no—
22C2×#67004C2214yes—
23C22×#4326—24no—
24C22×#4326—21no—
25C22×#4326—24no—
26C22×#4326—22no—
27C22×#4326—22no—
28C22×#4326C2214yescomplemented
29C22×#4324—21no—
30C22×#4318C2211yescharacteristic
31C22×#4318C2211yescharacteristic
32C23×C11⋊C8C2211yescharacteristic
33#10622847—22no—
34#10622847C2214yes—
35C2×#66900—24no—
36C2×#66900C2214yescomplemented
37C2×C22⋊(C11⋊C8)—22no—
38C2×#66888—24no—
39C2×#66888C2214yescomplemented
40#10622196C2214yescomplemented
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41D412yes—
48C2×C11×#41C2312yes—
49C22×Q8×C11—22no—
50C22×Q8×C11—21no—
51C22×Q8×C11—22no—
52C22×Q8×C11—21no—
53C22×Q8×C11—21no—
54C22×Q8×C11—21no—
55C22×Q8×C11—21no—
56C22×Q8×C11—22no—
57C22×Q8×C11D411yescharacteristic
58C22×Q8×C11D414yes—
59C22×Q8×C11C2312yes—
60C22×D4×C11—21no—
61C22×D4×C11D411yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11—21no—
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—21no—
66C22×Dic22—21no—
67C22×Dic22—21no—
68C22×Dic22—21no—
69C22×Dic22—22no—
70C22×Dic22—22no—
71C22×Dic22—21no—
72C22×Dic22—22no—
73C22×Dic22—21no—
74C22×Dic22D414yes—
75C22×Dic22C2312yes—
76C11×#137—216no—
77C11×#137—28no—
78C11×#137—28no—
79C2×C11×Q16—28no—
80C2×C11×Q16—24no—
81C2×C11×SD16—28no—
82C2×C11×SD16—24no—
83C2×C11×M16—22no—
84C2×C11×M16—21no—
85C2×C11×M16D414yes—
86C2×C11×M16C2312yes—
87C22×C8×C11—21no—
88#67004—216no—
89#67004—28no—
90#67004—28no—
91C2×#4326—216no—
92C2×#4326—216no—
93C2×#4326—28no—
94C2×#4326—28no—
95C2×#4326—24no—
96C2×#4326—28no—
97C2×#4326—28no—
98C2×#4324—28no—
99C2×#4324—24no—
100C2×#4318—22no—
101C2×#4318—21no—
102C2×#4318—21no—
103C2×#4318—22no—
104C2×#4318—22no—
105C2×#4318D414yes—
106C2×#4318C2312yes—
107C2×#4318C2312yes—
108C22×C11⋊C8—22no—
109C22×C11⋊C8—22no—
110C22×C11⋊C8—21no—
111C22×C11⋊C8—21no—
112C22×C11⋊C8D412yes—
113C22×C11⋊C8D412yes—
114C22×C11⋊C8C2312yes—
115#66900—28no—
116C22⋊(C11⋊C8)—28no—
117#66888—28no—
118C2×#2020—111nomaximal, Sylow
119C24×C11—21no—
120C24×C11#4111yescharacteristic
121C11×#41—24no—
122C11×#41—24no—
123C11×#41—22no—
124C11×#41—22no—
125C11×#41—22no—
126C11×#41—22no—
127C11×#41—42no—
128C11×#41—42no—
129C11×#41—42no—
130C11×#41—42no—
131C2×Q8×C11—24no—
132C2×Q8×C11—21no—
133C2×Q8×C11—22no—
134C2×Q8×C11—24no—
135C2×Q8×C11—24no—
136C2×Q8×C11—22no—
137C2×Q8×C11—24no—
138C2×Q8×C11—22no—
139C2×Q8×C11—24no—
140C2×Q8×C11—22no—
141C2×Q8×C11—22no—
142C2×Q8×C11—22no—
143C2×Q8×C11—22no—
144C2×Q8×C11—42no—
145C2×Q8×C11—42no—
146C2×Q8×C11—42no—
147C2×Q8×C11—41no—
148C2×Q8×C11—41no—
149C2×Q8×C11—42no—
150C2×Q8×C11—42no—
151C2×Q8×C11C2×D412yes—
152C2×Q8×C11C2×D414yes—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—22no—
156C2×D4×C11—22no—
157C2×D4×C11—21no—
158C2×D4×C11—42no—
159C2×D4×C11—42no—
160C2×D4×C11C2×D412yes—
161C22×C4×C11—21no—
162C22×C4×C11—24no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—42no—
167C22×C4×C11—41no—
168C22×C4×C11—41no—
169C22×C4×C11—42no—
170C22×C4×C11—42no—
171C22×C4×C11C2×D412yes—
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D412yes—
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D412yes—
178C22×C4×C11C2×D412yes—
179C22×C4×C11#4111yescharacteristic
180C22×C4×C11C2411yescharacteristic
181C22×Dic11—24no—
182C22×Dic11—22no—
183C22×Dic11—42no—
184C22×Dic11—41no—
185C22×Dic11—41no—
186C2×Dic22—24no—
187C2×Dic22—24no—
188C2×Dic22—24no—
189C2×Dic22—24no—
190C2×Dic22—24no—
191C2×Dic22—22no—
192C2×Dic22—22no—
193C2×Dic22—22no—
194C2×Dic22—22no—
195C2×Dic22—22no—
196C2×Dic22—42no—
197C2×Dic22—42no—
198C2×Dic22—41no—
199C2×Dic22—41no—
200C2×Dic22—42no—
201C2×Dic22—42no—
202C2×Dic22—42no—
203C2×Dic22C2×D414yes—
204C11×Q16—216no—
205C11×SD16—216no—
206C11×M16—24no—
207C11×M16—22no—
208C11×M16C2×D414yes—
209C2×C8×C11—24no—
210C2×C8×C11—22no—
211#4326—232no—
212#4326—216no—
213#4324—216no—
214#4318—24no—
215#4318—22no—
216#4318—22no—
217#4318—22no—
218#4318—42no—
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⋊C8—22no—
227C2×C11⋊C8—42no—
228C2×C11⋊C8C2×D414yes—
229C22×#137—111no—
230C22×#137D1111yescharacteristic
231C23×Q16—111no—
232C22×#101—111no—
233C22×#101—111no—
234C2×#408—111no—
235#2020—118no—
236C2×#341—111no—
237C23×C11—24no—
238C23×C11—22no—
239C23×C11—42no—
240C23×C11—44no—
241C23×C11#12112yes—
242C23×C11#12112yes—
243C23×C11#12111yescharacteristic
244C23×C11#12111yescharacteristic
245C23×C11C2×#4111yescharacteristic
246Q8×C11—24no—
247Q8×C11—22no—
248Q8×C11—24no—
249Q8×C11—22no—
250Q8×C11—42no—
251Q8×C11—42no—
252Q8×C11—44no—
253Q8×C11—44no—
254Q8×C11—42no—
255D4×C11—22no—
256D4×C11—22no—
257D4×C11—42no—
258D4×C11—42no—
259D4×C11—44no—
260D4×C11—42no—
261C2×C4×C11—22no—
262C2×C4×C11—24no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—44no—
267C2×C4×C11—44no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—44no—
271C2×C4×C11#12012yes—
272C2×C4×C11#12012yes—
273C2×C4×C11#12012yes—
274C2×C4×C11#12012yes—
275C2×C4×C11#12012yes—
276C2×C4×C11#12012yes—
277C2×C4×C11#12112yes—
278C2×C4×C11#12111yescharacteristic
279C2×C4×C11#12111yescharacteristic
280C2×C4×C11#12112yes—
281C2×C4×C11#12712yes—
282C2×C4×C11#12712yes—
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C22×D411yescharacteristic
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11C22×D411yescharacteristic
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C22×D411yescharacteristic
289C2×Dic11—24no—
290C2×Dic11—42no—
291C2×Dic11—42no—
292C2×Dic11—44no—
293C2×Dic11—44no—
294Dic22—24no—
295Dic22—24no—
296Dic22—42no—
297Dic22—42no—
298Dic22—44no—
299Dic22—44no—
300C8×C11—24no—
301C11⋊C8—24no—
302C11⋊C8—24no—
303C11⋊C8—42no—
304C22×#41C2×D1111yescharacteristic
305C23×Q8—111no—
306C23×Q8C2×D1111yescharacteristic
307C2×#137—22no—
308C2×#137—24no—
309C2×#137—24no—
310C2×#137—114no—
311C2×#137—224no—
312C2×#137—224no—
313C2×#137—222no—
314C2×#137C2×D1114yes—
315C22×Q16—21no—
316C22×Q16—114no—
317C22×Q16—222no—
318C22×Q16—222no—
319C22×Q16—224no—
320C22×Q16—224no—
321C22×Q16—221no—
322C22×SD16—21no—
323C22×SD16—221no—
324C22×M16—111no—
325C22×M16—111no—
326C22×M16C2×D1111yescharacteristic
327C23×C8—111no—
328C2×#101—114no—
329C2×#101—114no—
330C2×#101—224no—
331C2×#101—224no—
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—42no—
341C22×C11—44no—
342C22×C11—84no—
343C22×C11#39212yes—
344C22×C11#39212yes—
345C22×C11#47314yes—
346C22×C11C2×#12111yescharacteristic
347C22×C11C2×#12111yescharacteristic
348C22×C11C2×#12111yescharacteristic
349C4×C11—42no—
350C4×C11—44no—
351C4×C11#39212yes—
352C4×C11#39212yes—
353C4×C11C2×#12011yescharacteristic
354C4×C11C2×#12011yescharacteristic
355C4×C11C2×#12011yescharacteristic
356C4×C11C2×#12711yescharacteristic
357Dic11—44no—
358C2×#41—21no—
359C2×#41—21no—
360C2×#41—22no—
361C2×#41—22no—
362C2×#41—22no—
363C2×#41—22no—
364C2×#41C22⋊D1112yes—
365C2×#41C22×D1112yes—
366C22×Q8—22no—
367C22×Q8—21no—
368C22×Q8—22no—
369C22×Q8—21no—
370C22×Q8—21no—
371C22×Q8—21no—
372C22×Q8—22no—
373C22×Q8—21no—
374C22×Q8—114no—
375C22×Q8—112no—
376C22×Q8—221no—
377C22×Q8—222no—
378C22×Q8—221no—
379C22×Q8—221no—
380C22×Q8—222no—
381C22×Q8—221no—
382C22×Q8—222no—
383C22×Q8—221no—
384C22×Q8C22⋊D1111yescharacteristic
385C22×Q8C22⋊D1114yes—
386C22×Q8C22×D1112yes—
387C22×D4—21no—
388C22×D4C22⋊D1111yescharacteristic
389C23×C4—21no—
390C23×C4—21no—
391C23×C4—221no—
392C23×C4C22×D1111yescharacteristic
393#137—216no—
394#137—28no—
395#137—28no—
396#137—228no—
397#137—228no—
398#137—2216no—
399C2×Q16—28no—
400C2×Q16—24no—
401C2×Q16—228no—
402C2×Q16—228no—
403C2×Q16—2216no—
404C2×Q16—2216no—
405C2×Q16—228no—
406C2×Q16—228no—
407C2×Q16—224no—
408C2×SD16—28no—
409C2×SD16—24no—
410C2×SD16—228no—
411C2×SD16—224no—
412C2×M16—22no—
413C2×M16—21no—
414C2×M16—114no—
415C2×M16—112no—
416C2×M16—112no—
417C2×M16—222no—
418C2×M16—221no—
419C2×M16—221no—
420C2×M16—222no—
421C2×M16—222no—
422C2×M16C22⋊D1114yes—
423C2×M16C22×D1112yes—
424C22×C8—21no—
425C22×C8—112no—
426C22×C8—112no—
427C22×C8—112no—
428C22×C8—222no—
429C22×C8—222no—
430C22×C8—221no—
431C22×C8—221no—
432#101—228no—
433#101—228no—
434C22⋊C8—228no—
435C2×C11—21no—
436C2×C11—21no—
437C2×C11—22no—
438C2×C11—82no—
439C2×C11#202014yescomplemented
440C2×C11C2×#39211yescharacteristic
441C2×C11C2×#47312yes—
442C24—21no—
443C24#434111yescharacteristic
444#41—24no—
445#41—24no—
446#41—22no—
447#41—22no—
448#41—22no—
449#41—22no—
450#41—42no—
451#41—42no—
452#41—42no—
453#41—42no—
454C2×Q8—24no—
455C2×Q8—21no—
456C2×Q8—22no—
457C2×Q8—24no—
458C2×Q8—24no—
459C2×Q8—22no—
460C2×Q8—24no—
461C2×Q8—22no—
462C2×Q8—24no—
463C2×Q8—22no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—42no—
468C2×Q8—42no—
469C2×Q8—42no—
470C2×Q8—41no—
471C2×Q8—41no—
472C2×Q8—42no—
473C2×Q8—42no—
474C2×Q8—114no—
475C2×Q8—224no—
476C2×Q8—222no—
477C2×Q8—224no—
478C2×Q8—224no—
479C2×Q8—224no—
480C2×Q8—224no—
481C2×Q8—222no—
482C2×Q8—222no—
483C2×Q8—222no—
484C2×Q8—222no—
485C2×Q8—441no—
486C2×Q8—441no—
487C2×Q8—442no—
488C2×Q8—442no—
489C2×Q8—442no—
490C2×Q8—442no—
491C2×Q8—442no—
492C2×Q8C2×C22⋊D1112yes—
493C2×Q8C2×C22⋊D1114yes—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—21no—
498C2×D4—22no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4C2×C22⋊D1112yes—
502C22×C4—24no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—42no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—224no—
513C22×C4—222no—
514C22×C4—442no—
515C22×C4—441no—
516C22×C4—441no—
517C22×C4D4×D1112yes—
518C22×C4D4×D1111yescharacteristic
519C22×C4D4×D1112yes—
520C22×C4D4×D1111yescharacteristic
521C22×C4#434111yescharacteristic
522C22×C4C2×C22⋊D1112yes—
523C22×C4C2×C22⋊D1111yescharacteristic
524C22×C4C2×C22⋊D1111yescharacteristic
525C22×C4C2×C22⋊D1112yes—
526C22×C4C23×D1111yescharacteristic
527Q16—216no—
528Q16—2232no—
529Q16—2216no—
530SD16—216no—
531SD16—2216no—
532M16—24no—
533M16—22no—
534M16—114no—
535M16—224no—
536M16—222no—
537M16—222no—
538M16—222no—
539M16—442no—
540M16C2×C22⋊D1114yes—
541C2×C8—24no—
542C2×C8—22no—
543C2×C8—114no—
544C2×C8—224no—
545C2×C8—224no—
546C2×C8—224no—
547C2×C8—222no—
548C2×C8—222no—
549C2×C8—222no—
550C2×C8—222no—
551C2×C8—442no—
552C11C2×#202011yescharacteristic, complemented, Sylow
553C23—24no—
554C23—22no—
555C23—44no—
556C23—42no—
557C23#6699112yes—
558C23#6699212yes—
559C23#6699211yescharacteristic
560C23#6699211yescharacteristic
561C23C2×#434111yescharacteristic
562Q8—24no—
563Q8—22no—
564Q8—24no—
565Q8—22no—
566Q8—42no—
567Q8—42no—
568Q8—44no—
569Q8—44no—
570Q8—42no—
571Q8—224no—
572Q8—224no—
573Q8—442no—
574Q8—444no—
575Q8—444no—
576Q8—442no—
577D4—22no—
578D4—22no—
579D4—42no—
580D4—42no—
581D4—44no—
582D4—42no—
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—44no—
593C2×C4—224no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4—444no—
597C2×C4—444no—
598C2×C4#6699012yes—
599C2×C4#6699012yes—
600C2×C4#6699012yes—
601C2×C4#6699012yes—
602C2×C4#6699112yes—
603C2×C4#6699211yescharacteristic
604C2×C4#6699211yescharacteristic
605C2×C4#6699212yes—
606C2×C4#6699312yes—
607C2×C4#6699312yes—
608C2×C4#6700612yes—
609C2×C4#6700612yes—
610C2×C4C2×D4×D1111yescharacteristic
611C2×C4C2×D4×D1111yescharacteristic
612C2×C4C2×D4×D1111yescharacteristic
613C2×C4C22×C22⋊D1111yescharacteristic
614C2×C4C22×C22⋊D1111yescharacteristic
615C2×C4C22×C22⋊D1111yescharacteristic
616C8—24no—
617C8—224no—
618C8—224no—
619C8—442no—
620C22—22no—
621C22—22no—
622C22—24no—
623C22—24no—
624C22—44no—
625C22—42no—
626C22—84no—
627C22#1062281714yes—
628C22#1062283612yes—
629C22#1062283612yes—
630C22C2×#6699111yescharacteristic
631C22C2×#6699211yescharacteristic
632C22C2×#6699211yescharacteristic
633C4—42no—
634C4—44no—
635C4—444no—
636C4#1062283612yes—
637C4#1062283612yes—
638C4C2×#6699011yescharacteristic
639C4C2×#6699011yescharacteristic
640C4C2×#6699311yescharacteristic
641C4C2×#6700611yescharacteristic
642C2—21no—
643C2—21no—
644C2—22no—
645C2—82no—
646C2#1306973414yesdirect product factor
647C2C2×#1062283611yescharacteristic
648C2C2×#1062281712yes—
subgroupG/H
centerC23#66992
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#137C2
socleC23×C11#121
prime radicalC22×C11×#41C22
hypercenterC22×#137D11
hypocenterC11C2×#2020
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
2. C23×#4326C2semidirect
3. C22×#66900C2semidirect
4. C22×#66888C2semidirect
6. #13069734C2direct (N × H)
7. C2×#10622196C2semidirect
28. C22×#4326C22semidirect
36. C2×#66900C22semidirect
39. C2×#66888C22semidirect
40. #10622196C22semidirect
439. C2×C11#2020semidirect
552. C11C2×#2020semidirect
646. C2#13069734direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670042
C23×#43262
C22×#669002
C22×#668882
C2×#106228472
#130697342
C2×#106221962
C22×C11×#1372
C2×#202011