Finite Group Databasebeta

← C2×#13080334 #15629013

Subgroups — C2×#13080334 #15629013

Order 2816.

2806 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67003C212yesmaximal, complemented
2C2×#10623082C211yesmaximal, characteristic, complemented
3#13080334C2116yesmaximal, direct product factor
4C2×#10622705C211yesmaximal, characteristic, complemented
5C2×#10622664C212yesmaximal, complemented
6C2×#10622632C211yesmaximal, characteristic, complemented
7C2×#10622696C211yesmaximal, characteristic, complemented
8C2×#10622852C212yesmaximal, complemented
9C2×#10622660C212yesmaximal, complemented
10C2×C4×#4323C211yesmaximal, characteristic, complemented
11C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
12C2×C11×#547C211yesmaximal, characteristic, complemented
13C22×C11×#41C2212yes—
14C22×#4339C2212yes—
15C11×#547—24no—
16C11×#547C2218yescomplemented
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#123—22no—
19C2×C11×C22⋊Q8C2212yes—
20C2×C11×#121—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C22×C11×C4⋊C4—21no—
24C2×#67003—216no—
25C2×#67003C22116yescomplemented
26C22×#4326C2212yes—
27C22×#4326C2212yes—
28C22×#4325C2212yes—
29C2×#66991—21no—
30C22×#4324C2212yes—
31C22×#4323C2211yescharacteristic
32C2×#66977C2212yes—
33C23×C11⋊C8C2212yes—
34#10623082—24no—
35#10623082C2218yescomplemented
36C2×C4⋊C4×D11—21no—
37C2×#66936—22no—
38C2×C4×D44C2211yescharacteristic
39C2×#66922C2211yescharacteristic
40#10622852C22116yescomplemented
41C2×#66899C2212yes—
42C2×#66896C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2212yes—
44#10622705C2218yescomplemented
45#10622696C2218yescomplemented
46#10622664C22116yescomplemented
47#10622660C22116yescomplemented
48#10622632C2218yescomplemented
49C4×#4323C2218yescomplemented
50D4×C11⋊C8C2218yescomplemented
51C2×#66874C2212yes—
52C2×#66873C2211yescharacteristic
53C2×#66871C2211yescharacteristic
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55C2×C4×C11⋊C8C2211yescharacteristic
56C2×C11×#41—24no—
57C2×C11×#41—28no—
58C2×C11×#41—44no—
59C2×C11×#41C2318yes—
60C22×Q8×C11C2312yes—
61C22×D4×C11—22no—
62C22×D4×C11D411yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11—22no—
66C23×C4×C11C2312yes—
67C22×C22⋊D11—22no—
68C2×#4339—24no—
69C2×#4339—28no—
70C2×#4339—44no—
71C2×#4339C2318yes—
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×C4×D11—22no—
75C22×Dic22C2312yes—
76C11×C4⋊Q8—22no—
77C11×C4⋊Q8C2314yes—
78C11×#123—216no—
79C11×C22⋊Q8—24no—
80C11×C22⋊Q8C2318yes—
81C11×#121—28no—
82C4×D4×C11—22no—
83C4×D4×C11D414yes—
84C4×D4×C11C2314yes—
85C4×D4×C11C2314yes—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—28no—
90C2×C11×C4⋊C4D411yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4D412yes—
95C2×C42×C11C2311yescharacteristic
96C2×C22⋊Dic11—22no—
97#67003—264no—
98C2×#4326—28no—
99C2×#4326—44no—
100C2×#4326C2318yes—
101C2×#4326C2318yes—
102C2×#4325—28no—
103C2×#4325C2318yes—
104#66991—28no—
105C2×#4324—28no—
106C2×#4324C2318yes—
107C2×#4323D418yescomplemented
108C2×#4323C2314yes—
109C2×(C2×D11)⋊C4—21no—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11—21no—
112C2×C4⋊Dic11C2311yescharacteristic
113#66977—24no—
114#66977C2318yes—
115C2×Dic11⋊C4—22no—
116C22×C11⋊C8—28no—
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2312yes—
119C22×C11⋊C8C2318yes—
120C22×C11⋊C8C2311yescharacteristic
121C4⋊C4×D11—28no—
122#66936—216no—
123C4×D44—22no—
124C4×D44C2314yes—
125#66922—22no—
126#66922C2314yes—
127#66899C2318yes—
128#66896C2314yes—
129C22⋊(C11⋊C8)C2318yes—
130#66874C2318yes—
131#66873C2314yes—
132#66871C2314yes—
133C4⋊(C11⋊C8)C2314yes—
134C4×C11⋊C8C2314yes—
135C2×#3283—111nomaximal, Sylow
136C24×C11—21no—
137C24×C11C2×D412yes—
138C23×D11—21no—
139C11×#41—216no—
140C11×#41—48no—
141C11×#41—416no—
142C2×Q8×C11—22no—
143C2×Q8×C11—24no—
144C2×Q8×C11—24no—
145C2×Q8×C11C2414yes—
146C2×D4×C11—28no—
147C2×D4×C11—24no—
148C2×D4×C11—21no—
149C2×D4×C11—22no—
150C2×D4×C11—48no—
151C2×D4×C11C2×D414yes—
152C2×D4×C11C2×D414yes—
153C2×D4×C11C2412yes—
154C22×C4×C11—24no—
155C22×C4×C11—24no—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—24no—
159C22×C4×C11—28no—
160C22×C4×C11—48no—
161C22×C4×C11—44no—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D414yes—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2414yes—
167C22×C4×C11C2411yescharacteristic
168C2×C22⋊D11—28no—
169C2×C22⋊D11—48no—
170C22×Dic11—21no—
171C22×Dic11—22no—
172#4339—216no—
173#4339—48no—
174#4339—416no—
175C2×D44—21no—
176C2×D44—22no—
177C2×D44C2×D414yes—
178C2×D44C2412yes—
179C2×C4×D11—24no—
180C2×C4×D11—28no—
181C2×C4×D11—48no—
182C2×C4×D11—44no—
183C2×Dic22—24no—
184C2×Dic22—22no—
185C2×Dic22—24no—
186C2×Dic22C2414yes—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—28no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4C2×D414yes—
192C11×C4⋊C4C2412yes—
193C11×C22⋊C4—28no—
194C11×C22⋊C4—24no—
195C11×C22⋊C4C2×D418yes—
196C42×C11C2×D412yes—
197C42×C11C2412yes—
198C22⋊Dic11—28no—
199#4326—216no—
200#4326—48no—
201#4325—216no—
202#4324—216no—
203#4323C2×D4116yescomplemented
204(C2×D11)⋊C4—24no—
205C4⋊Dic11—24no—
206C4⋊Dic11—24no—
207C4⋊Dic11—21no—
208C4⋊Dic11C2412yes—
209Dic11⋊C4—28no—
210C2×C11⋊C8—216no—
211C2×C11⋊C8—24no—
212C2×C11⋊C8—22no—
213C2×C11⋊C8C2×D414yes—
214C2×C11⋊C8C2412yes—
215C2×C11⋊C8C2414yes—
216C2×C11⋊C8C2412yes—
217C22×#135—112no—
218C2×#547—111no—
219C2×#547D1111yescharacteristic, complemented
220#3283—1116no—
221C2×#494—111no—
222C2×#467—112no—
223C2×#461—111no—
224C2×#461—111no—
225C2×#452—112no—
226C2×#452—112no—
227C2×C4×D8—111no—
228C2×C8×D4—111no—
229C23×C11—24no—
230C23×C11—24no—
231C23×C11—24no—
232C23×C11—24no—
233C23×C11—22no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11C22×D414yes—
237C23×C11C22×D411yescharacteristic
238C22×D11—24no—
239C22×D11—22no—
240C22×D11—42no—
241C22×D11—42no—
242Q8×C11—24no—
243Q8×C11—24no—
244Q8×C11—44no—
245D4×C11—24no—
246D4×C11—28no—
247D4×C11—22no—
248D4×C11—416no—
249D4×C11C22×D414yes—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—28no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—22no—
256C2×C4×C11—24no—
257C2×C4×C11—416no—
258C2×C4×C11—44no—
259C2×C4×C11—42no—
260C2×C4×C11—48no—
261C2×C4×C11#13514yescomplemented
262C2×C4×C11C22×D412yes—
263C2×C4×C11C22×D414yes—
264C2×C4×C11C22×D412yes—
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×D412yes—
267C2×C4×C11H(5,𝔽2)12yes—
268C2×C4×C11C2511yescharacteristic
269C22⋊D11—416no—
270C2×Dic11—22no—
271C2×Dic11—24no—
272C2×Dic11—44no—
273C2×Dic11—42no—
274D44—24no—
275D44—22no—
276D44C22×D414yes—
277C4×D11—416no—
278C4×D11—48no—
279Dic22—24no—
280Dic22—24no—
281Dic22—44no—
282C11⋊C8—24no—
283C11⋊C8—22no—
284C11⋊C8C22×D414yes—
285C22×#41—112no—
286C22×#41C2×D1112yes—
287C2×#135—1116no—
288C2×#135—2216no—
289C22×Q16—112no—
290C22×Q16—112no—
291C22×SD16—112no—
292C22×SD16—112no—
293C22×D8—111no—
294C23×C8—112no—
295#547—24no—
296#547—118no—
297#547—224no—
298#547C2×D1118yescomplemented
299C2×C4⋊Q8—111no—
300C2×C4⋊Q8C2×D1111yescharacteristic
301C2×#123—22no—
302C2×#123—222no—
303C2×C22⋊Q8—112no—
304C2×C22⋊Q8C2×D1112yes—
305C2×#121—21no—
306C2×#121—221no—
307C2×C4×D4—111no—
308C2×C4×D4C2×D1111yescharacteristic
309C2×C4×D4C2×D1111yescharacteristic
310C22×C4⋊C4—21no—
311C22×C4⋊C4—221no—
312#494—118no—
313#467—1116no—
314#461—118no—
315#461—118no—
316#452—1116no—
317#452—1116no—
318C4×D8—118no—
319C8×D4—118no—
320C2×#107—111no—
321C2×C4⋊C8—111no—
322C2×#103—112no—
323C2×#103—112no—
324C2×#102—111no—
325C2×#102—111no—
326C2×C22⋊C8—112no—
327C2×C4×C8—111no—
328C22×C11—24no—
329C22×C11—24no—
330C22×C11—24no—
331C22×C11—24no—
332C22×C11—48no—
333C22×C11—48no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11D4212yes—
337C22×C11C2×#13512yes—
338C22×C11#57812yes—
339C22×C11C23×D411yescharacteristic
340C2×D11—24no—
341C2×D11—48no—
342C2×D11—42no—
343C2×D11—42no—
344C4×C11—24no—
345C4×C11—22no—
346C4×C11—44no—
347C4×C11—42no—
348C4×C11D4212yes—
349C4×C11C2×#13514yescomplemented
350C4×C11C23×D411yescharacteristic
351C4×C11C2×H(5,𝔽2)11yescharacteristic
352Dic11—44no—
353Dic11—42no—
354C2×#41—24no—
355C2×#41—28no—
356C2×#41—44no—
357C2×#41—118no—
358C2×#41—228no—
359C2×#41—224no—
360C2×#41—444no—
361C2×#41C22×D1118yes—
362C22×Q8—112no—
363C22×Q8C22×D1112yes—
364C22×D4—22no—
365C22×D4—111no—
366C22×D4—222no—
367C22×D4C22⋊D1111yescharacteristic
368C22×D4C22×D1111yescharacteristic
369C23×C4—21no—
370C23×C4—22no—
371C23×C4—221no—
372C23×C4—222no—
373C23×C4C22×D1112yes—
374#135—2264no—
375C2×Q16—118no—
376C2×Q16—118no—
377C2×Q16—228no—
378C2×Q16—444no—
379C2×SD16—118no—
380C2×SD16—118no—
381C2×SD16—228no—
382C2×SD16—228no—
383C2×D8—118no—
384C2×D8—114no—
385C22×C8—111no—
386C22×C8—112no—
387C22×C8—118no—
388C22×C8—111no—
389C22×C8—228no—
390C4⋊Q8—22no—
391C4⋊Q8—114no—
392C4⋊Q8—222no—
393C4⋊Q8C22×D1114yes—
394#123—216no—
395#123—2216no—
396C22⋊Q8—24no—
397C22⋊Q8—118no—
398C22⋊Q8—224no—
399C22⋊Q8C22×D1118yes—
400#121—28no—
401#121—228no—
402C4×D4—22no—
403C4×D4—114no—
404C4×D4—222no—
405C4×D4C22⋊D1114yes—
406C4×D4C22×D1114yes—
407C4×D4C22×D1114yes—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—28no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—222no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—228no—
417C2×C4⋊C4C22⋊D1111yescharacteristic
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C22⋊C4—22no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—222no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4C22⋊D1112yes—
424C2×C42C22×D1111yescharacteristic
425#107—114no—
426C4⋊C8—114no—
427#103—118no—
428#103—118no—
429#102—114no—
430#102—114no—
431C22⋊C8—118no—
432C4×C8—114no—
433C2×C11—44no—
434C2×C11—44no—
435C2×C11#328314yescomplemented
436C2×C11C2×D4211yescharacteristic
437C2×C11C22×#13511yescharacteristic
438C2×C11C2×#57811yescharacteristic
439D11—44no—
440C24—21no—
441C24—221no—
442C24C2×C22⋊D1112yes—
443#41—216no—
444#41—48no—
445#41—416no—
446#41—2216no—
447#41—448no—
448#41—4416no—
449C2×Q8—22no—
450C2×Q8—24no—
451C2×Q8—24no—
452C2×Q8—114no—
453C2×Q8—222no—
454C2×Q8—224no—
455C2×Q8—224no—
456C2×Q8C23×D1114yes—
457C2×D4—28no—
458C2×D4—24no—
459C2×D4—22no—
460C2×D4—21no—
461C2×D4—48no—
462C2×D4—114no—
463C2×D4—112no—
464C2×D4—228no—
465C2×D4—222no—
466C2×D4—221no—
467C2×D4—448no—
468C2×D4D4×D1114yes—
469C2×D4C2×C22⋊D1114yes—
470C2×D4C23×D1112yes—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—28no—
477C22×C4—48no—
478C22×C4—44no—
479C22×C4—221no—
480C22×C4—222no—
481C22×C4—224no—
482C22×C4—228no—
483C22×C4—448no—
484C22×C4—444no—
485C22×C4C2×C22⋊D1114yes—
486C22×C4C2×C22⋊D1111yescharacteristic
487C22×C4C2×C22⋊D1112yes—
488C22×C4C2×C22⋊D1111yescharacteristic
489C22×C4C23×D1114yes—
490C22×C4C23×D1111yescharacteristic
491Q16—2216no—
492Q16—448no—
493SD16—2216no—
494SD16—2216no—
495D8—1116no—
496C2×C8—114no—
497C2×C8—112no—
498C2×C8—112no—
499C2×C8—114no—
500C2×C8—2216no—
501C2×C8—224no—
502C2×C8—222no—
503C4⋊C4—24no—
504C4⋊C4—28no—
505C4⋊C4—24no—
506C4⋊C4—21no—
507C4⋊C4—112no—
508C4⋊C4—221no—
509C4⋊C4—224no—
510C4⋊C4—228no—
511C4⋊C4—224no—
512C4⋊C4C2×C22⋊D1114yes—
513C4⋊C4C23×D1112yes—
514C22⋊C4—28no—
515C22⋊C4—24no—
516C22⋊C4—228no—
517C22⋊C4—224no—
518C22⋊C4C2×C22⋊D1118yes—
519C42C2×C22⋊D1112yes—
520C42C23×D1112yes—
521C11C2×#328311yescharacteristic, complemented, Sylow
522C23—24no—
523C23—24no—
524C23—24no—
525C23—24no—
526C23—22no—
527C23—42no—
528C23—42no—
529C23—224no—
530C23—222no—
531C23—442no—
532C23—442no—
533C23C22×C22⋊D1114yes—
534C23C22×C22⋊D1111yescharacteristic
535Q8—24no—
536Q8—24no—
537Q8—44no—
538Q8—224no—
539Q8—224no—
540Q8—444no—
541D4—24no—
542D4—28no—
543D4—22no—
544D4—416no—
545D4—114no—
546D4—224no—
547D4—222no—
548D4—4416no—
549D4C2×D4×D1114yes—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—28no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—416no—
558C2×C4—44no—
559C2×C4—42no—
560C2×C4—48no—
561C2×C4—222no—
562C2×C4—224no—
563C2×C4—4416no—
564C2×C4—444no—
565C2×C4—442no—
566C2×C4—448no—
567C2×C4#6700314yescomplemented
568C2×C4C2×D4×D1112yes—
569C2×C4#6703712yes—
570C2×C4C22×C22⋊D1112yes—
571C2×C4C22×C22⋊D1114yes—
572C2×C4C22×C22⋊D1111yescharacteristic
573C2×C4C22×C22⋊D1112yes—
574C2×C4C24×D1111yescharacteristic
575C8—114no—
576C8—224no—
577C8—222no—
578C22—24no—
579C22—24no—
580C22—24no—
581C22—24no—
582C22—48no—
583C22—48no—
584C22—42no—
585C22—42no—
586C22—224no—
587C22—448no—
588C22—442no—
589C22—442no—
590C22D4×C22⋊D1112yes—
591C22C2×#6700312yes—
592C22#1062336912yes—
593C22C23×C22⋊D1111yescharacteristic
594C4—24no—
595C4—22no—
596C4—44no—
597C4—42no—
598C4—444no—
599C4—442no—
600C4D4×C22⋊D1112yes—
601C4C2×#6700314yescomplemented
602C4C22×D4×D1111yescharacteristic
603C4C2×#6703711yescharacteristic
604C2—44no—
605C2—44no—
606C2—444no—
607C2#1308033414yesdirect product factor
608C2C2×D4×C22⋊D1111yescharacteristic
609C2C22×#6700311yescharacteristic
610C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#547C2
socleC23×C11C22×D4
hypercenterC2×#547D11
hypocenterC11C2×#3283
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C22×#67003C2semidirect
2. C2×#10623082C2semidirect
3. #13080334C2direct (N × H)
4. C2×#10622705C2semidirect
5. C2×#10622664C2semidirect
6. C2×#10622632C2semidirect
7. C2×#10622696C2semidirect
8. C2×#10622852C2semidirect
9. C2×#10622660C2semidirect
10. C2×C4×#4323C2semidirect
11. C2×D4×C11⋊C8C2semidirect
12. C2×C11×#547C2semidirect
16. C11×#547C22semidirect
25. C2×#67003C22semidirect
35. #10623082C22semidirect
40. #10622852C22semidirect
44. #10622705C22semidirect
45. #10622696C22semidirect
46. #10622664C22semidirect
47. #10622660C22semidirect
48. #10622632C22semidirect
49. C4×#4323C22semidirect
50. D4×C11⋊C8C22semidirect
107. C2×#4323D4semidirect
203. #4323C2×D4semidirect
219. C2×#547D11semidirect
261. C2×C4×C11#135semidirect
298. #547C2×D11semidirect
349. C4×C11C2×#135semidirect
435. C2×C11#3283semidirect
521. C11C2×#3283semidirect
567. C2×C4#67003semidirect
601. C4C2×#67003semidirect
607. C2#13080334direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670032
C2×#106230822
#130803342
C2×#106227052
C2×#106226642
C2×#106226322
C2×#106226962
C2×#106228522
C2×#106226602
C2×C4×#43232
C2×D4×C11⋊C82
C2×C11×#5472
C2×#328311