Finite Group Databasebeta

← C2×#13118609 #16030949

Subgroups — C2×#13118609 #16030949

Order 3328.

2550 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88142C211yesmaximal, characteristic
2C22×C4×Dic26C211yesmaximal, characteristic
3#13118609C2116yesmaximal, direct product factor
4C2×#11718319C211yesmaximal, characteristic
5C2×#11718320C211yesmaximal, characteristic
6C2×#11718645C211yesmaximal, characteristic
7C2×#11718644C211yesmaximal, characteristic
8C2×#11718307C211yesmaximal, characteristic
9C2×#11718307C211yesmaximal, characteristic
10C2×#11718307C211yesmaximal, characteristic
11C2×#11718633C211yesmaximal, characteristic
12C2×#11718316C211yesmaximal, characteristic
13C2×#11718594C211yesmaximal, characteristic
14C2×#11718313C211yesmaximal, characteristic
15C2×#11718310C211yesmaximal, characteristic
16C2×C13×#387C211yesmaximal, characteristic
17C23×Dic26C2211yescharacteristic
18C23×Dic26C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C42×C13C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C22×C4⋊Dic13C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C22×C4×Dic13C2211yescharacteristic
36C2×#88142—28no—
37C2×#88142C2218yes—
38C2×C4×Dic26—28no—
39C2×C4×Dic26C2218yes—
40C13×#387C2218yes—
41C2×C13×#95C2211yescharacteristic
42C2×C13×#95C2211yescharacteristic
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57#11718645C2218yes—
58#11718644C2218yes—
59#11718633C2218yes—
60#11718594C2218yes—
61#11718320C2218yes—
62#11718319C2218yes—
63#11718316C2218yes—
64#11718313C2218yes—
65#11718310C2218yes—
66#11718307C2218yes—
67#11718307C2218yes—
68#11718307C2218yes—
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C22×Dic26—24no—
85C22×Dic26—24no—
86C22×Dic26—24no—
87C22×Dic26—24no—
88C22×Dic26—24no—
89C22×Dic26D418yes—
90C22×Dic26C2314yes—
91C22×Dic26C2314yes—
92C2×C13×C4⋊C4—24no—
93C2×C13×C4⋊C4—24no—
94C2×C13×C4⋊C4C2314yes—
95C2×C13×C4⋊C4C2314yes—
96C2×C42×C13—24no—
97C2×C42×C13C2314yes—
98C2×C4⋊Dic13—24no—
99C2×C4⋊Dic13—24no—
100C2×C4⋊Dic13C2314yes—
101C2×C4⋊Dic13C2314yes—
102C2×#6101—24no—
103C2×#6101—24no—
104C2×#6101—24no—
105C2×#6101—24no—
106C2×#6101—24no—
107C2×#6101—24no—
108C2×#6101—24no—
109C2×#6101Q818yescomplemented
110C2×#6101C2314yes—
111C2×#6101C2314yes—
112C2×#6101C2314yes—
113C2×#6101C2314yes—
114C2×#6101C2314yes—
115C2×#6101C2314yes—
116C2×#6101C2314yes—
117C2×#6101C2314yes—
118C2×C4×Dic13—24no—
119C2×C4×Dic13—24no—
120C2×C4×Dic13—24no—
121C2×C4×Dic13—24no—
122C2×C4×Dic13C2314yes—
123C2×C4×Dic13C2314yes—
124C2×C4×Dic13C2314yes—
125C2×C4×Dic13C2314yes—
126#88142—232no—
127C4×Dic26—232no—
128C13×#95C2314yes—
129C13×#95C2314yes—
130C13×#95C2314yes—
131C13×#95C2314yes—
132#88071C2314yes—
133#88071C2314yes—
134#88071C2314yes—
135#88071C2314yes—
136#88071C2314yes—
137#88071C2314yes—
138#88071C2314yes—
139#88071C2314yes—
140#88071C2314yes—
141#88071C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144C2×#2446—131nomaximal, Sylow
145C24×C13C2411yescharacteristic
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13C2×D414yes—
165C22×C4×C13C2×Q814yes—
166C22×C4×C13#4114yes—
167C22×C4×C13C2412yes—
168C22×C4×C13C2412yes—
169C22×C4×C13C2412yes—
170C22×C4×C13C2412yes—
171C22×C4×C13C2412yes—
172C22×C4×C13C2412yes—
173C22×C4×C13C2412yes—
174C22×Dic13—22no—
175C22×Dic13—22no—
176C22×Dic13—22no—
177C22×Dic13—22no—
178C22×Dic13—22no—
179C22×Dic13—22no—
180C22×Dic13—22no—
181C22×Dic13—22no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13C2×D414yes—
193C22×Dic13C2×D414yes—
194C22×Dic13C2×Q814yes—
195C22×Dic13C2×Q814yes—
196C22×Dic13#4114yes—
197C22×Dic13#4114yes—
198C22×Dic13C2412yes—
199C22×Dic13C2412yes—
200C22×Dic13C2412yes—
201C22×Dic13C2412yes—
202C22×Dic13C2412yes—
203C22×Dic13C2412yes—
204C22×Dic13C2412yes—
205C22×Dic13C2412yes—
206C2×Dic26—232no—
207C2×Dic26—28no—
208C2×Dic26—28no—
209C2×Dic26—28no—
210C2×Dic26—28no—
211C2×Dic26—28no—
212C2×Dic26—416no—
213C2×Dic26C2×D4116yes—
214C13×C4⋊C4—28no—
215C13×C4⋊C4—28no—
216C42×C13—28no—
217C4⋊Dic13—28no—
218C4⋊Dic13—28no—
219#6101—28no—
220#6101—28no—
221#6101—28no—
222#6101—28no—
223#6101—28no—
224#6101—28no—
225#6101—28no—
226#6101C2×Q8116yescomplemented
227C4×Dic13—28no—
228C4×Dic13—28no—
229C4×Dic13—28no—
230C4×Dic13—28no—
231C22×C4⋊Q8—131no—
232C22×C4×Q8—131no—
233#2446—1316no—
234C2×#400—131no—
235C2×#400—131no—
236C2×#398—131no—
237C2×#398—131no—
238C2×#391—131no—
239C2×#391—131no—
240C2×#391—131no—
241C2×#389—131no—
242C2×#387—131no—
243C2×#387—131no—
244C2×#387—131no—
245C2×#387D1311yescharacteristic
246C2×C4×C4⋊C4—131no—
247C23×C13C22×D412yes—
248C23×C13C22×Q812yes—
249C23×C13C2×#4112yes—
250C23×C13C2×#4112yes—
251C23×C13C2×#4112yes—
252C23×C132−1+412yes—
253C23×C132−1+412yes—
254C23×C13C2511yescharacteristic
255C2×C4×C13—28no—
256C2×C4×C13—28no—
257C2×C4×C13—28no—
258C2×C4×C13—22no—
259C2×C4×C13—22no—
260C2×C4×C13—22no—
261C2×C4×C13—22no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—22no—
265C2×C4×C13—22no—
266C2×C4×C13—22no—
267C2×C4×C13—22no—
268C2×C4×C13—22no—
269C2×C4×C13—22no—
270C2×C4×C13—22no—
271C2×C4×C13—22no—
272C2×C4×C13—22no—
273C2×C4×C13—22no—
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—44no—
277C2×C4×C13—44no—
278C2×C4×C13—44no—
279C2×C4×C13—44no—
280C2×C4×C13C22×D414yes—
281C2×C4×C13C22×Q814yes—
282C2×C4×C13C2×#4114yes—
283C2×Dic13—28no—
284C2×Dic13—28no—
285C2×Dic13—28no—
286C2×Dic13—22no—
287C2×Dic13—22no—
288C2×Dic13—22no—
289C2×Dic13—22no—
290C2×Dic13—22no—
291C2×Dic13—22no—
292C2×Dic13—22no—
293C2×Dic13—22no—
294C2×Dic13—22no—
295C2×Dic13—22no—
296C2×Dic13—22no—
297C2×Dic13—22no—
298C2×Dic13—22no—
299C2×Dic13—22no—
300C2×Dic13—22no—
301C2×Dic13—22no—
302C2×Dic13—22no—
303C2×Dic13—22no—
304C2×Dic13—44no—
305C2×Dic13—44no—
306C2×Dic13—44no—
307C2×Dic13—44no—
308C2×Dic13#123116yes—
309C2×Dic13C22×D414yes—
310C2×Dic13C22×D414yes—
311C2×Dic13C22×Q814yes—
312C2×Dic13C22×Q814yes—
313C2×Dic13C2×#4114yes—
314C2×Dic13C2×#4114yes—
315Dic26—232no—
316Dic26—416no—
317C23×Q8—131no—
318C23×Q8—131no—
319C2×C4⋊Q8—138no—
320C2×C4⋊Q8—268no—
321C2×C4×Q8—138no—
322C2×C4×Q8—268no—
323C22×C4⋊C4—131no—
324C22×C4⋊C4—131no—
325C22×C4⋊C4—131no—
326C22×C4⋊C4—131no—
327C22×C4⋊C4—131no—
328C22×C4⋊C4—131no—
329C22×C4⋊C4—131no—
330C22×C4⋊C4—131no—
331C22×C4⋊C4—131no—
332C22×C4⋊C4—131no—
333C22×C4⋊C4C2×D1311yescharacteristic
334C22×C4⋊C4C2×D1311yescharacteristic
335C22×C42—131no—
336C22×C42—131no—
337C22×C42—131no—
338C22×C42—131no—
339C22×C42C2×D1311yescharacteristic
340#400—138no—
341#400—138no—
342#398—138no—
343#398—138no—
344#391—138no—
345#391—138no—
346#391—138no—
347#389—138no—
348#387—138no—
349#387—138no—
350#387—138no—
351#387C2×D1318yes—
352C4×C4⋊C4—138no—
353C2×#95—131no—
354C2×#95—131no—
355C2×#95—131no—
356C2×#95—131no—
357C2×#95—131no—
358C2×#95—131no—
359C2×#95—131no—
360C2×#95—131no—
361C2×#95—131no—
362C2×#95—131no—
363C2×#95—131no—
364C2×#95—131no—
365C2×#95C2×D1311yescharacteristic
366C2×#95C2×D1311yescharacteristic
367C2×#95C2×D1311yescharacteristic
368C2×#95C2×D1311yescharacteristic
369C22×C13C2×#12314yes—
370C22×C13#53314yes—
371C22×C13#54114yes—
372C22×C13#54814yes—
373C22×C13D4×Q814yes—
374C22×C13#55614yes—
375C22×C13#55714yes—
376C22×C13C23×D411yescharacteristic
377C22×C13C23×Q811yescharacteristic
378C22×C13C22×#4111yescharacteristic
379C22×C13C22×#4111yescharacteristic
380C22×C13C22×#4111yescharacteristic
381C22×C13C2×2−1+411yescharacteristic
382C22×C13C2×2−1+411yescharacteristic
383C4×C13—24no—
384C4×C13—24no—
385C4×C13—24no—
386C4×C13—42no—
387C4×C13—42no—
388C4×C13—42no—
389C4×C13—42no—
390Dic13—24no—
391Dic13—24no—
392Dic13—24no—
393Dic13—42no—
394Dic13—42no—
395Dic13—42no—
396Dic13—42no—
397Dic13C2×#12318yes—
398C22×Q8—138no—
399C22×Q8—134no—
400C22×Q8—134no—
401C22×Q8—264no—
402C22×Q8—264no—
403C22×Q8—264no—
404C22×Q8—264no—
405C22×Q8—264no—
406C23×C4—131no—
407C23×C4—131no—
408C23×C4—131no—
409C23×C4—131no—
410C23×C4—131no—
411C23×C4—131no—
412C23×C4—131no—
413C23×C4—131no—
414C23×C4C22×D1311yescharacteristic
415C23×C4C22×D1311yescharacteristic
416C23×C4C22×D1311yescharacteristic
417C23×C4C22×D1311yescharacteristic
418C23×C4C22×D1311yescharacteristic
419C23×C4C22×D1311yescharacteristic
420C23×C4C22×D1311yescharacteristic
421C4⋊Q8—2632no—
422C4×Q8—2632no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—138no—
426C2×C4⋊C4—134no—
427C2×C4⋊C4—134no—
428C2×C4⋊C4—134no—
429C2×C4⋊C4—134no—
430C2×C4⋊C4—134no—
431C2×C4⋊C4—134no—
432C2×C4⋊C4—134no—
433C2×C4⋊C4—134no—
434C2×C4⋊C4—134no—
435C2×C4⋊C4—134no—
436C2×C4⋊C4—264no—
437C2×C4⋊C4—264no—
438C2×C4⋊C4—264no—
439C2×C4⋊C4—264no—
440C2×C4⋊C4—264no—
441C2×C4⋊C4—264no—
442C2×C4⋊C4—264no—
443C2×C4⋊C4—264no—
444C2×C4⋊C4—264no—
445C2×C4⋊C4C22×D1314yes—
446C2×C4⋊C4C22×D1314yes—
447C2×C42—24no—
448C2×C42—134no—
449C2×C42—134no—
450C2×C42—134no—
451C2×C42—134no—
452C2×C42—264no—
453C2×C42—264no—
454C2×C42—264no—
455C2×C42—264no—
456C2×C42C22×D1314yes—
457#95—134no—
458#95—134no—
459#95—134no—
460#95—134no—
461#95—134no—
462#95—134no—
463#95—134no—
464#95—134no—
465#95—134no—
466#95—134no—
467#95—134no—
468#95—134no—
469#95C22×D1314yes—
470#95C22×D1314yes—
471#95C22×D1314yes—
472#95C22×D1314yes—
473C2×C13#244618yescomplemented
474C2×C13C22×#12311yescharacteristic
475C2×C13C2×#53311yescharacteristic
476C2×C13C2×#54111yescharacteristic
477C2×C13C2×#54811yescharacteristic
478C2×C13C2×D4×Q811yescharacteristic
479C2×C13C2×#55611yescharacteristic
480C2×C13C2×#55711yescharacteristic
481C24C23×D1311yescharacteristic
482C2×Q8—1316no—
483C2×Q8—2632no—
484C2×Q8—268no—
485C2×Q8—268no—
486C2×Q8—268no—
487C2×Q8—268no—
488C2×Q8—268no—
489C2×Q8—5216no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—134no—
509C22×C4—134no—
510C22×C4—134no—
511C22×C4—132no—
512C22×C4—134no—
513C22×C4—134no—
514C22×C4—134no—
515C22×C4—132no—
516C22×C4—132no—
517C22×C4—132no—
518C22×C4—132no—
519C22×C4—132no—
520C22×C4—132no—
521C22×C4—132no—
522C22×C4—262no—
523C22×C4—262no—
524C22×C4—262no—
525C22×C4—262no—
526C22×C4—262no—
527C22×C4—262no—
528C22×C4—262no—
529C22×C4—262no—
530C22×C4—262no—
531C22×C4—262no—
532C22×C4—262no—
533C22×C4—262no—
534C22×C4—262no—
535C22×C4—262no—
536C22×C4—262no—
537C22×C4—262no—
538C22×C4—262no—
539C22×C4—262no—
540C22×C4#612714yes—
541C22×C4D4×D1314yes—
542C22×C4Q8×D1314yes—
543C22×C4C23×D1312yes—
544C22×C4C23×D1312yes—
545C22×C4C23×D1312yes—
546C22×C4C23×D1312yes—
547C22×C4C23×D1312yes—
548C22×C4C23×D1312yes—
549C22×C4C23×D1312yes—
550C4⋊C4—28no—
551C4⋊C4—28no—
552C4⋊C4—1316no—
553C4⋊C4—268no—
554C4⋊C4—268no—
555C4⋊C4—268no—
556C4⋊C4—268no—
557C4⋊C4—268no—
558C4⋊C4—268no—
559C4⋊C4—268no—
560C4⋊C4—268no—
561C4⋊C4—268no—
562C42—28no—
563C42—268no—
564C42—268no—
565C42—268no—
566C42—268no—
567C13C2×#244611yescharacteristic, complemented, Sylow
568C23C2×#612712yes—
569C23C2×D4×D1312yes—
570C23C2×Q8×D1312yes—
571C23#41×D1312yes—
572C23#41×D1312yes—
573C23#8825712yes—
574C23#8825712yes—
575C23C24×D1311yescharacteristic
576Q8—2632no—
577Q8—5216no—
578C2×C4—28no—
579C2×C4—28no—
580C2×C4—28no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—44no—
600C2×C4—44no—
601C2×C4—44no—
602C2×C4—44no—
603C2×C4—1316no—
604C2×C4—134no—
605C2×C4—134no—
606C2×C4—134no—
607C2×C4—134no—
608C2×C4—134no—
609C2×C4—134no—
610C2×C4—268no—
611C2×C4—268no—
612C2×C4—268no—
613C2×C4—262no—
614C2×C4—262no—
615C2×C4—262no—
616C2×C4—262no—
617C2×C4—262no—
618C2×C4—262no—
619C2×C4—262no—
620C2×C4—262no—
621C2×C4—262no—
622C2×C4—262no—
623C2×C4—262no—
624C2×C4—262no—
625C2×C4—262no—
626C2×C4—262no—
627C2×C4—262no—
628C2×C4—262no—
629C2×C4—262no—
630C2×C4—262no—
631C2×C4—524no—
632C2×C4—524no—
633C2×C4—524no—
634C2×C4—524no—
635C2×C4C2×#612714yes—
636C2×C4C2×D4×D1314yes—
637C2×C4C2×Q8×D1314yes—
638C22#1171923814yes—
639C22#1171925714yes—
640C22#1171928314yes—
641C22#1171933714yes—
642C22D13×#12314yes—
643C22#1171939014yes—
644C22#1171940614yes—
645C22C22×#612711yescharacteristic
646C22C22×D4×D1311yescharacteristic
647C22C22×Q8×D1311yescharacteristic
648C22C2×#41×D1311yescharacteristic
649C22C2×#41×D1311yescharacteristic
650C22C2×#8825711yescharacteristic
651C22C2×#8825711yescharacteristic
652C4—24no—
653C4—24no—
654C4—24no—
655C4—42no—
656C4—42no—
657C4—42no—
658C4—42no—
659C4—138no—
660C4—264no—
661C4—264no—
662C4—264no—
663C4—522no—
664C4—522no—
665C4—522no—
666C4—522no—
667C2#1311860918yesdirect product factor
668C2C2×D13×#12311yescharacteristic
669C2C2×#1171928311yescharacteristic
670C2C2×#1171940611yescharacteristic
671C2C2×#1171925711yescharacteristic
672C2C2×#1171933711yescharacteristic
673C2C2×#1171923811yescharacteristic
674C2C2×#1171939011yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#387C2
socle, prime radicalC24×C13C24
hypercenterC2×#387D13
hypocenterC13C2×#2446
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. #13118609C2direct (N × H)
109. C2×#6101Q8semidirect
226. #6101C2×Q8semidirect
473. C2×C13#2446semidirect
567. C13C2×#2446semidirect
667. C2#13118609direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881422
C22×C4×Dic262
#131186092
C2×#117183192
C2×#117183202
C2×#117186452
C2×#117186442
C2×#117183072
C2×#117186332
C2×#117183162
C2×#117185942
C2×#117183132
C2×#117183102
C2×C13×#3872
C2×#244613