Finite Group Databasebeta

← C2×#13079539 #15624954

Subgroups — C2×#13079539 #15624954

Order 2816.

2414 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
1C2×#10623127C211yesmaximal, characteristic
2C22×#66997C211yesmaximal, characteristic, complemented
3#13079539C2116yesmaximal, direct product factor
4C2×#10622788C212yesmaximal, complemented
5C2×#10622405C212yesmaximal, complemented
6C2×#10622431C212yesmaximal, complemented
7C2×#10622775C212yesmaximal, complemented
8C2×#10622351C211yesmaximal, characteristic, complemented
9C2×#10622840C211yesmaximal, characteristic, complemented
10C2×#10622653C211yesmaximal, characteristic, complemented
11C2×#10622331C211yesmaximal, characteristic, complemented
12C2×C11×#448C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C22×#4341—21no—
15C23×Dic22C2211yescharacteristic
16C22×C11×SD16C2212yes—
17C2×C11×#121C2211yescharacteristic
18C2×#66997—21no—
19C2×#66997—21no—
20C2×#66997—24no—
21C2×#66997C2212yes—
22C2×#66997C2212yes—
23C2×#66997C2218yescomplemented
24C22×#4325C2212yes—
25C2×#66993C2211yescharacteristic
26C2×#66992—21no—
27C2×D4×Dic11C2211yescharacteristic
28C22×#4324C2212yes—
29C2×#66983C2211yescharacteristic
30C22×Dic11⋊C4—21no—
31C22×Dic11⋊C4—21no—
32C22×C4×Dic11C2211yescharacteristic
33C22×#4314C2212yes—
34#10623127—24no—
35#10623127C2218yes—
36C2×#66946C2211yescharacteristic
37C2×#66941C2211yescharacteristic
38C2×#66938—21no—
39C2×(C22⋊D11)⋊C4—21no—
40C11×#448C2218yescomplemented
41C2×C11×#103C2212yes—
42C2×C11×C22⋊C8C2211yescharacteristic
43#10622840C2218yescomplemented
44C2×#66899C2212yes—
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46#10622788C22116yescomplemented
47#10622775C22116yescomplemented
48C2×#66880C2212yes—
49C2×Dic11⋊C8C2212yes—
50C2×C8×Dic11C2212yes—
51#10622653C2218yescomplemented
52C2×#66874C2212yes—
53#10622431C22116yescomplemented
54#10622405C22116yescomplemented
55#10622351C2218yescomplemented
56#10622331C2218yescomplemented
57C22×Q8×C11—21no—
58C22×Q8×C11—22no—
59C22×Q8×C11—44no—
60C22×Q8×C11C2312yes—
61C22×Q8×C11C2314yes—
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—21no—
67C22×C22⋊D11—21no—
68C22×C22⋊D11—21no—
69C23×Dic11—21no—
70C23×Dic11—21no—
71C23×Dic11D411yescharacteristic
72C23×Dic11D411yescharacteristic
73C2×#4341—28no—
74C2×#4341—48no—
75C22×D44C2311yescharacteristic
76C22×C4×D11—21no—
77C22×Dic22—21no—
78C22×Dic22—22no—
79C22×Dic22—21no—
80C22×Dic22—44no—
81C22×Dic22C2312yes—
82C22×Dic22C2314yes—
83C2×C11×SD16—44no—
84C2×C11×SD16C2318yes—
85C22×C8×C11C2312yes—
86C11×#121—22no—
87C11×#121C2314yes—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C22⋊Dic11—21no—
91#66997—24no—
92#66997—24no—
93#66997—28no—
94#66997—28no—
95#66997C2318yes—
96#66997C2318yes—
97C2×#4325—44no—
98C2×#4325C2318yes—
99#66993—22no—
100#66993C2314yes—
101#66992—28no—
102D4×Dic11—22no—
103D4×Dic11C2314yes—
104C2×#4324—44no—
105C2×#4324C2318yes—
106#66983—22no—
107#66983C2314yes—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×C4⋊Dic11C2311yescharacteristic
111C2×Dic11⋊C4—21no—
112C2×Dic11⋊C4—22no—
113C2×Dic11⋊C4—22no—
114C2×Dic11⋊C4—22no—
115C2×Dic11⋊C4—22no—
116C2×Dic11⋊C4—28no—
117C2×Dic11⋊C4—28no—
118C2×C4×Dic11D411yescharacteristic
119C2×C4×Dic11D411yescharacteristic
120C2×C4×Dic11D414yes—
121C2×C4×Dic11C2311yescharacteristic
122C2×C4×Dic11C2311yescharacteristic
123C2×C4×Dic11C2314yes—
124C22×C11⋊C8C2312yes—
125C2×#4314—44no—
126C2×#4314C2318yes—
127#66946—22no—
128#66946C2314yes—
129#66941—22no—
130#66941C2314yes—
131#66938—28no—
132(C22⋊D11)⋊C4—28no—
133C11×#103C2318yes—
134C11×C22⋊C8C2314yes—
135#66899C2318yes—
136C22⋊(C11⋊C8)C2314yes—
137#66880C2318yes—
138Dic11⋊C8C2318yes—
139C8×Dic11C2318yes—
140#66874C2318yes—
141C2×#3206—111nomaximal, Sylow
142C24×C11—21no—
143C24×C11C2×D411yescharacteristic
144C23×D11—21no—
145C2×Q8×C11—24no—
146C2×Q8×C11—22no—
147C2×Q8×C11—24no—
148C2×Q8×C11—24no—
149C2×Q8×C11—48no—
150C2×Q8×C11—44no—
151C2×Q8×C11—48no—
152C2×Q8×C11C2414yes—
153C2×D4×C11—24no—
154C2×D4×C11—21no—
155C2×D4×C11—24no—
156C2×D4×C11—44no—
157C2×D4×C11C2412yes—
158C22×C4×C11—24no—
159C22×C4×C11—24no—
160C22×C4×C11—22no—
161C22×C4×C11—21no—
162C22×C4×C11—44no—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2412yes—
166C22×C4×C11C2411yescharacteristic
167C2×C22⋊D11—24no—
168C2×C22⋊D11—24no—
169C2×C22⋊D11—24no—
170C2×C22⋊D11—44no—
171C2×C22⋊D11—44no—
172C2×C22⋊D11—44no—
173C22×Dic11—24no—
174C22×Dic11—24no—
175C22×Dic11—24no—
176C22×Dic11—22no—
177C22×Dic11—21no—
178C22×Dic11—44no—
179C22×Dic11—44no—
180C22×Dic11SD1618yescomplemented
181C22×Dic11C2×D411yescharacteristic
182C22×Dic11C2×D414yes—
183C22×Dic11C2×D411yescharacteristic
184C22×Dic11C2×D411yescharacteristic
185C22×Dic11C2×D414yes—
186C22×Dic11C2×D411yescharacteristic
187#4341—432no—
188C2×D44—21no—
189C2×D44—24no—
190C2×D44C2412yes—
191C2×C4×D11—24no—
192C2×C4×D11—44no—
193C2×Dic22—24no—
194C2×Dic22—24no—
195C2×Dic22—22no—
196C2×Dic22—24no—
197C2×Dic22—24no—
198C2×Dic22—48no—
199C2×Dic22—44no—
200C2×Dic22—48no—
201C2×Dic22—44no—
202C2×Dic22C2414yes—
203C11×SD16—48no—
204C2×C8×C11—24no—
205C2×C8×C11C2414yes—
206C11×C4⋊C4—21no—
207C11×C4⋊C4C2412yes—
208C11×C22⋊C4—24no—
209C22⋊Dic11—24no—
210#4325—48no—
211#4324—48no—
212(C2×D11)⋊C4—24no—
213(C2×D11)⋊C4—24no—
214C4⋊Dic11—21no—
215C4⋊Dic11C2412yes—
216Dic11⋊C4—24no—
217Dic11⋊C4—28no—
218Dic11⋊C4—28no—
219Dic11⋊C4—28no—
220Dic11⋊C4—28no—
221C4×Dic11C2×D414yes—
222C4×Dic11C2×D414yes—
223C4×Dic11C2×D412yes—
224C4×Dic11C2×D412yes—
225C4×Dic11C2412yes—
226C4×Dic11C2412yes—
227C2×C11⋊C8—24no—
228C2×C11⋊C8C2414yes—
229#4314—48no—
230C2×#532—111no—
231C22×C4⋊Q8—111no—
232#3206—1116no—
233C2×#492—112no—
234C2×#487—112no—
235C2×#461—112no—
236C2×#461—112no—
237C2×#448—111no—
238C2×#448—111no—
239C2×#448—111no—
240C2×#448D1111yescharacteristic, complemented
241C2×#431—111no—
242C23×C11—22no—
243C23×C11—22no—
244C23×C11—22no—
245C23×C11—42no—
246C23×C11—42no—
247C23×C11—42no—
248C23×C11C2×SD1614yes—
249C23×C11C22×D412yes—
250C23×C11C22×D411yescharacteristic
251C22×D11—22no—
252C22×D11—42no—
253C22×D11—42no—
254C22×D11—42no—
255Q8×C11—24no—
256Q8×C11—24no—
257Q8×C11—48no—
258Q8×C11—44no—
259D4×C11—24no—
260D4×C11—48no—
261D4×C11—42no—
262C2×C4×C11—22no—
263C2×C4×C11—24no—
264C2×C4×C11—24no—
265C2×C4×C11—24no—
266C2×C4×C11—22no—
267C2×C4×C11—48no—
268C2×C4×C11—44no—
269C2×C4×C11—42no—
270C2×C4×C11C22×D412yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11H(5,𝔽2)14yes—
273C2×C4×C11C2511yescharacteristic
274C22⋊D11—48no—
275C22⋊D11—48no—
276C22⋊D11—48no—
277C2×Dic11—22no—
278C2×Dic11—28no—
279C2×Dic11—24no—
280C2×Dic11—22no—
281C2×Dic11—48no—
282C2×Dic11—44no—
283C2×Dic11—42no—
284C2×Dic11—48no—
285C2×Dic11C2×SD1614yes—
286C2×Dic11C2×SD1614yes—
287C2×Dic11C2×SD16116yescomplemented
288C2×Dic11#13714yes—
289C2×Dic11C22×D412yes—
290C2×Dic11C22×D412yes—
291C2×Dic11C22×D412yes—
292C2×Dic11C22×D412yes—
293D44—24no—
294D44—42no—
295C4×D11—48no—
296Dic22—24no—
297Dic22—24no—
298Dic22—48no—
299Dic22—44no—
300Dic22—48no—
301C8×C11—24no—
302C11⋊C8—24no—
303C22×#41—221no—
304C23×Q8—111no—
305C23×Q8C2×D1111yescharacteristic
306C22×SD16—112no—
307C22×SD16—112no—
308C22×SD16—112no—
309C22×SD16C2×D1112yes—
310#532—118no—
311#532—224no—
312C2×C4⋊Q8—111no—
313C2×C4⋊Q8—112no—
314C2×C4⋊Q8—112no—
315C2×C4⋊Q8—118no—
316C2×C4⋊Q8—221no—
317C2×C4⋊Q8—221no—
318C2×C4⋊Q8—224no—
319C2×#127—111no—
320C2×#124—221no—
321C2×#121—111no—
322C2×#121—221no—
323C2×#121C2×D1111yescharacteristic
324C2×C4×D4—111no—
325C2×C4×D4—111no—
326C2×C4×D4—221no—
327C22×C4⋊C4—221no—
328C22×C4⋊C4—221no—
329C22×C42—111no—
330#492—1116no—
331#487—1116no—
332#461—1116no—
333#461—1116no—
334#448—118no—
335#448—118no—
336#448—118no—
337#448C2×D1118yescomplemented
338#431—118no—
339C2×C4⋊C8—112no—
340C2×#103—112no—
341C2×#103—112no—
342C2×#103—112no—
343C2×#103C2×D1112yes—
344C2×C22⋊C8—111no—
345C2×C22⋊C8C2×D1111yescharacteristic
346C2×C4×C8—112no—
347C22×C11—22no—
348C22×C11—28no—
349C22×C11—22no—
350C22×C11—42no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—84no—
354C22×C11#53512yes—
355C22×C11C22×SD1614yes—
356C22×C11C22×SD1612yes—
357C22×C11C2×#13712yes—
358C22×C11C23×D411yescharacteristic
359C2×D11—42no—
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—84no—
363C4×C11—22no—
364C4×C11—44no—
365C4×C11—42no—
366C4×C11#53512yes—
367C4×C11C2×H(5,𝔽2)12yes—
368Dic11—22no—
369Dic11—44no—
370Dic11—42no—
371Dic11C22×SD1614yes—
372Dic11C22×SD1614yes—
373Dic11C2×#13714yes—
374C2×#41—228no—
375C2×#41—448no—
376C22×Q8—22no—
377C22×Q8—21no—
378C22×Q8—44no—
379C22×Q8—112no—
380C22×Q8—114no—
381C22×Q8—221no—
382C22×Q8—222no—
383C22×Q8—221no—
384C22×Q8—444no—
385C22×Q8C22×D1112yes—
386C22×Q8C22×D1114yes—
387C22×D4—21no—
388C22×D4—111no—
389C22×D4—221no—
390C22×D4—221no—
391C22×D4—221no—
392C22×D4C22×D1111yescharacteristic
393C23×C4—21no—
394C23×C4—111no—
395C23×C4—111no—
396C23×C4—221no—
397C23×C4—221no—
398C23×C4—221no—
399C23×C4C22×D1111yescharacteristic
400C2×SD16—44no—
401C2×SD16—118no—
402C2×SD16—118no—
403C2×SD16—118no—
404C2×SD16—444no—
405C2×SD16—444no—
406C2×SD16—444no—
407C2×SD16C22×D1118yes—
408C22×C8—112no—
409C22×C8C22×D1112yes—
410C4⋊Q8—114no—
411C4⋊Q8—118no—
412C4⋊Q8—118no—
413C4⋊Q8—222no—
414C4⋊Q8—224no—
415C4⋊Q8—228no—
416C4⋊Q8—228no—
417C4⋊Q8—224no—
418#127—114no—
419#127—222no—
420#124—228no—
421#121—22no—
422#121—114no—
423#121—228no—
424#121—222no—
425#121C22×D1114yes—
426C4×D4—114no—
427C4×D4—114no—
428C4×D4—228no—
429C4×D4—222no—
430C4×D4—222no—
431C2×C4⋊C4—111no—
432C2×C4⋊C4—228no—
433C2×C4⋊C4—228no—
434C2×C4⋊C4—222no—
435C2×C4⋊C4—222no—
436C2×C4⋊C4—222no—
437C2×C4⋊C4—222no—
438C2×C4⋊C4—221no—
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C22⋊C4—21no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C42—111no—
445C2×C42—111no—
446C2×C42—114no—
447C2×C42—111no—
448C2×C42—111no—
449C2×C42—114no—
450C4⋊C8—118no—
451#103—118no—
452#103—118no—
453#103—118no—
454#103C22×D1118yes—
455C22⋊C8—114no—
456C22⋊C8C22×D1114yes—
457C4×C8—118no—
458C2×C11—24no—
459C2×C11—82no—
460C2×C11#320614yescomplemented
461C2×C11C2×#53511yescharacteristic
462C2×C11C23×SD1611yescharacteristic
463C2×C11C22×#13711yescharacteristic
464D11—82no—
465C24—21no—
466C24—221no—
467C24D4×D1111yescharacteristic
468#41—4432no—
469C2×Q8—24no—
470C2×Q8—22no—
471C2×Q8—24no—
472C2×Q8—24no—
473C2×Q8—48no—
474C2×Q8—44no—
475C2×Q8—48no—
476C2×Q8—114no—
477C2×Q8—224no—
478C2×Q8—224no—
479C2×Q8—222no—
480C2×Q8—224no—
481C2×Q8—224no—
482C2×Q8—448no—
483C2×Q8—444no—
484C2×Q8—448no—
485C2×Q8—444no—
486C2×Q8C23×D1114yes—
487C2×D4—24no—
488C2×D4—21no—
489C2×D4—24no—
490C2×D4—44no—
491C2×D4—112no—
492C2×D4—224no—
493C2×D4—224no—
494C2×D4—224no—
495C2×D4—221no—
496C2×D4—224no—
497C2×D4—444no—
498C2×D4—444no—
499C2×D4—444no—
500C2×D4C23×D1112yes—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—44no—
506C22×C4—118no—
507C22×C4—114no—
508C22×C4—111no—
509C22×C4—111no—
510C22×C4—111no—
511C22×C4—114no—
512C22×C4—111no—
513C22×C4—224no—
514C22×C4—224no—
515C22×C4—224no—
516C22×C4—224no—
517C22×C4—221no—
518C22×C4—222no—
519C22×C4—444no—
520C22×C4—444no—
521C22×C4—444no—
522C22×C4D4×D1112yes—
523C22×C4D4×D1111yescharacteristic
524C22×C4C23×D1112yes—
525C22×C4C23×D1111yescharacteristic
526SD16—48no—
527SD16—448no—
528SD16—448no—
529SD16—448no—
530C2×C8—24no—
531C2×C8—114no—
532C2×C8—224no—
533C2×C8C23×D1114yes—
534C4⋊C4—21no—
535C4⋊C4—112no—
536C4⋊C4—228no—
537C4⋊C4—228no—
538C4⋊C4—228no—
539C4⋊C4—228no—
540C4⋊C4—224no—
541C4⋊C4—221no—
542C4⋊C4C23×D1112yes—
543C22⋊C4—24no—
544C22⋊C4—224no—
545C22⋊C4—224no—
546C22⋊C4—224no—
547C42—114no—
548C42—112no—
549C42—114no—
550C42—112no—
551C42—112no—
552C42—112no—
553C11C2×#320611yescharacteristic, complemented, Sylow
554C23—22no—
555C23—22no—
556C23—22no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—222no—
561C23—442no—
562C23—442no—
563C23—442no—
564C23SD16×D1114yes—
565C23C2×D4×D1112yes—
566C23C2×D4×D1111yescharacteristic
567Q8—24no—
568Q8—24no—
569Q8—48no—
570Q8—44no—
571Q8—224no—
572Q8—224no—
573Q8—448no—
574Q8—448no—
575Q8—444no—
576D4—24no—
577D4—48no—
578D4—42no—
579D4—224no—
580D4—448no—
581D4—448no—
582D4—448no—
583D4—442no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—48no—
590C2×C4—42no—
591C2×C4—44no—
592C2×C4—114no—
593C2×C4—114no—
594C2×C4—1116no—
595C2×C4—114no—
596C2×C4—112no—
597C2×C4—112no—
598C2×C4—112no—
599C2×C4—112no—
600C2×C4—228no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—224no—
604C2×C4—448no—
605C2×C4—448no—
606C2×C4—448no—
607C2×C4—442no—
608C2×C4—444no—
609C2×C4C2×D4×D1112yes—
610C2×C4C2×D4×D1111yescharacteristic
611C2×C4#6703714yes—
612C2×C4C24×D1111yescharacteristic
613C8—24no—
614C8—224no—
615C22—22no—
616C22—22no—
617C22—28no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—84no—
622C22—442no—
623C22—442no—
624C22—442no—
625C22—884no—
626C22#1062312312yes—
627C22C2×SD16×D1114yes—
628C22C2×SD16×D1112yes—
629C22D11×#13712yes—
630C22C22×D4×D1111yescharacteristic
631C4—22no—
632C4—44no—
633C4—42no—
634C4—114no—
635C4—114no—
636C4—114no—
637C4—222no—
638C4—444no—
639C4—442no—
640C4#1062312312yes—
641C4C2×#6703712yes—
642C2—24no—
643C2—82no—
644C2—882no—
645C2#1307953914yesdirect product factor
646C2C2×#1062312311yescharacteristic
647C2C22×SD16×D1111yescharacteristic
648C2C2×D11×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#448C2
socleC23×C11C22×D4
prime radicalC2×#10623127C2
hypercenterC2×#448D11
hypocenterC11C2×#3206
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
2. C22×#66997C2semidirect
3. #13079539C2direct (N × H)
4. C2×#10622788C2semidirect
5. C2×#10622405C2semidirect
6. C2×#10622431C2semidirect
7. C2×#10622775C2semidirect
8. C2×#10622351C2semidirect
9. C2×#10622840C2semidirect
10. C2×#10622653C2semidirect
11. C2×#10622331C2semidirect
12. C2×C11×#448C2semidirect
23. C2×#66997C22semidirect
40. C11×#448C22semidirect
43. #10622840C22semidirect
46. #10622788C22semidirect
47. #10622775C22semidirect
51. #10622653C22semidirect
53. #10622431C22semidirect
54. #10622405C22semidirect
55. #10622351C22semidirect
56. #10622331C22semidirect
180. C22×Dic11SD16semidirect
240. C2×#448D11semidirect
287. C2×Dic11C2×SD16semidirect
337. #448C2×D11semidirect
460. C2×C11#3206semidirect
553. C11C2×#3206semidirect
645. C2#13079539direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231272
C22×#669972
#130795392
C2×#106227882
C2×#106224052
C2×#106224312
C2×#106227752
C2×#106223512
C2×#106228402
C2×#106226532
C2×#106223312
C2×C11×#4482
C2×#320611