Finite Group Databasebeta

← C2×#13120246 #16033186

Subgroups — C2×#13120246 #16033186

Order 3328.

2182 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13120246C2116yesmaximal, direct product factor
2C2×#11718322C211yesmaximal, characteristic
3C2×#11718317C211yesmaximal, characteristic
4C2×#11718317C211yesmaximal, characteristic
5C2×#11718640C211yesmaximal, characteristic
6C2×#11718590C211yesmaximal, characteristic
7C2×#11718307C211yesmaximal, characteristic
8C2×#11718307C211yesmaximal, characteristic
9C2×#11718646C211yesmaximal, characteristic
10C2×#11718308C211yesmaximal, characteristic
11C2×#11718642C211yesmaximal, characteristic
12C2×#11718315C211yesmaximal, characteristic
13C2×#11718315C211yesmaximal, characteristic
14C2×C4⋊C4×Dic13C211yesmaximal, characteristic
15C2×C4×C4⋊Dic13C211yesmaximal, 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×C4⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C22×C4×Dic13C2211yescharacteristic
36C13×#387C2218yes—
37C2×C13×#95C2211yescharacteristic
38C2×C13×#95C2211yescharacteristic
39C2×C13×#95C2211yescharacteristic
40C2×C13×#95C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53#11718646C2218yes—
54#11718642C2218yes—
55#11718640C2218yes—
56C4⋊C4×Dic13C2218yes—
57C4×C4⋊Dic13C2218yes—
58#11718590C2218yes—
59#11718322C2218yes—
60#11718317C2218yes—
61#11718317C2218yes—
62#11718315C2218yes—
63#11718315C2218yes—
64#11718308C2218yes—
65#11718307C2218yes—
66#11718307C2218yes—
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C22×Dic26—24no—
83C22×Dic26—24no—
84C22×Dic26—24no—
85C22×Dic26—42no—
86C22×Dic26—42no—
87C22×Dic26—42no—
88C22×Dic26C2314yes—
89C22×Dic26C2314yes—
90C2×C13×C4⋊C4—24no—
91C2×C13×C4⋊C4Q818yescomplemented
92C2×C13×C4⋊C4C2314yes—
93C2×C13×C4⋊C4C2314yes—
94C2×C42×C13—24no—
95C2×C42×C13C2314yes—
96C2×C4⋊Dic13—24no—
97C2×C4⋊Dic13—24no—
98C2×C4⋊Dic13—42no—
99C2×C4⋊Dic13—42no—
100C2×C4⋊Dic13—42no—
101C2×C4⋊Dic13Q818yescomplemented
102C2×C4⋊Dic13C2314yes—
103C2×C4⋊Dic13C2314yes—
104C2×C4⋊Dic13C2314yes—
105C2×C4⋊Dic13C2314yes—
106C2×C4⋊Dic13C2314yes—
107C2×C4⋊Dic13C2314yes—
108C2×#6101—24no—
109C2×#6101—42no—
110C2×#6101—42no—
111C2×#6101—42no—
112C2×#6101C2314yes—
113C2×#6101C2314yes—
114C2×#6101C2314yes—
115C2×#6101C2314yes—
116C2×C4×Dic13—24no—
117C2×C4×Dic13—42no—
118C2×C4×Dic13—42no—
119C2×C4×Dic13—42no—
120C2×C4×Dic13C2314yes—
121C2×C4×Dic13C2314yes—
122C2×C4×Dic13C2314yes—
123C2×C4×Dic13C2314yes—
124C13×#95C2314yes—
125C13×#95C2314yes—
126C13×#95C2314yes—
127C13×#95C2314yes—
128#88071C2314yes—
129#88071C2314yes—
130#88071C2314yes—
131#88071C2314yes—
132#88071C2314yes—
133#88071C2314yes—
134#88071C2314yes—
135#88071C2314yes—
136#88071C2314yes—
137#88071C2314yes—
138#88071C2314yes—
139#88071C2314yes—
140C2×#2586—131nomaximal, Sylow
141C24×C13C2411yescharacteristic
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
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×C13C2×Q814yes—
159C22×C4×C13C2×Q814yes—
160C22×C4×C13C2×Q814yes—
161C22×C4×C13C2×Q814yes—
162C22×C4×C13#4114yes—
163C22×C4×C13C2412yes—
164C22×C4×C13C2412yes—
165C22×C4×C13C2412yes—
166C22×C4×C13C2412yes—
167C22×C4×C13C2412yes—
168C22×C4×C13C2412yes—
169C22×C4×C13C2412yes—
170C22×Dic13—22no—
171C22×Dic13—22no—
172C22×Dic13—22no—
173C22×Dic13—22no—
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×Dic13C2×Q814yes—
191C22×Dic13C2×Q814yes—
192C22×Dic13#4114yes—
193C22×Dic13#4114yes—
194C22×Dic13C2412yes—
195C22×Dic13C2412yes—
196C22×Dic13C2412yes—
197C22×Dic13C2412yes—
198C22×Dic13C2412yes—
199C22×Dic13C2412yes—
200C22×Dic13C2412yes—
201C22×Dic13C2412yes—
202C2×Dic26—28no—
203C2×Dic26—28no—
204C2×Dic26—28no—
205C2×Dic26—44no—
206C2×Dic26—44no—
207C2×Dic26—44no—
208C2×Dic26—416no—
209C2×Dic26—416no—
210C13×C4⋊C4—28no—
211C13×C4⋊C4C2×Q8116yescomplemented
212C42×C13—28no—
213C4⋊Dic13—28no—
214C4⋊Dic13—28no—
215C4⋊Dic13—44no—
216C4⋊Dic13—44no—
217C4⋊Dic13—44no—
218C4⋊Dic13C2×Q8116yescomplemented
219#6101—28no—
220#6101—44no—
221#6101—44no—
222#6101—44no—
223C4×Dic13—28no—
224C4×Dic13—44no—
225C4×Dic13—44no—
226C4×Dic13—44no—
227#2586—1316no—
228C2×#398—131no—
229C2×#395—131no—
230C2×#395—131no—
231C2×#395—131no—
232C2×#391—131no—
233C2×#391—131no—
234C2×#391—131no—
235C2×#389—131no—
236C2×#389—131no—
237C2×#387—131no—
238C2×#387—131no—
239C2×#387—131no—
240C2×#387D1311yescharacteristic
241C2×C4×C4⋊C4—131no—
242C2×C4×C4⋊C4—131no—
243C23×C13C22×Q812yes—
244C23×C13C22×Q812yes—
245C23×C13C2×#4112yes—
246C23×C13C2×#4112yes—
247C23×C13C2×#4112yes—
248C23×C13H(5,𝔽2)12yes—
249C23×C13H(5,𝔽2)12yes—
250C23×C13C2511yescharacteristic
251C2×C4×C13—28no—
252C2×C4×C13—28no—
253C2×C4×C13—28no—
254C2×C4×C13—28no—
255C2×C4×C13—28no—
256C2×C4×C13—22no—
257C2×C4×C13—22no—
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—44no—
273C2×C4×C13—44no—
274C2×C4×C13C22×Q814yes—
275C2×C4×C13C22×Q814yes—
276C2×C4×C13C22×Q814yes—
277C2×C4×C13C22×Q814yes—
278C2×C4×C13C2×#4114yes—
279C2×Dic13—28no—
280C2×Dic13—28no—
281C2×Dic13—28no—
282C2×Dic13—28no—
283C2×Dic13—22no—
284C2×Dic13—22no—
285C2×Dic13—22no—
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—44no—
304C2×Dic13—44no—
305C2×Dic13—44no—
306C2×Dic13—44no—
307C2×Dic13C22×Q814yes—
308C2×Dic13C22×Q814yes—
309C2×Dic13C2×#4114yes—
310C2×Dic13C2×#4114yes—
311Dic26—416no—
312Dic26—416no—
313C23×Q8—131no—
314C23×Q8—131no—
315C22×C4⋊C4—131no—
316C22×C4⋊C4—131no—
317C22×C4⋊C4—131no—
318C22×C4⋊C4—131no—
319C22×C4⋊C4—131no—
320C22×C4⋊C4—131no—
321C22×C4⋊C4—131no—
322C22×C4⋊C4—131no—
323C22×C4⋊C4—131no—
324C22×C4⋊C4—131no—
325C22×C4⋊C4C2×D1311yescharacteristic
326C22×C4⋊C4C2×D1311yescharacteristic
327C22×C42—131no—
328C22×C42—131no—
329C22×C42—131no—
330C22×C42—131no—
331C22×C42C2×D1311yescharacteristic
332#398—138no—
333#395—138no—
334#395—138no—
335#395—138no—
336#391—138no—
337#391—138no—
338#391—138no—
339#389—138no—
340#389—138no—
341#387—138no—
342#387—138no—
343#387—138no—
344#387C2×D1318yes—
345C4×C4⋊C4—138no—
346C4×C4⋊C4—138no—
347C2×#95—131no—
348C2×#95—131no—
349C2×#95—131no—
350C2×#95—131no—
351C2×#95—131no—
352C2×#95—131no—
353C2×#95—131no—
354C2×#95—131no—
355C2×#95—131no—
356C2×#95—131no—
357C2×#95—131no—
358C2×#95—131no—
359C2×#95C2×D1311yescharacteristic
360C2×#95C2×D1311yescharacteristic
361C2×#95C2×D1311yescharacteristic
362C2×#95C2×D1311yescharacteristic
363C22×C13#53314yes—
364C22×C13#53314yes—
365C22×C13#53814yes—
366C22×C13#55114yes—
367C22×C13#55414yes—
368C22×C13#55414yes—
369C22×C13Q8214yes—
370C22×C13C23×Q811yescharacteristic
371C22×C13C23×Q811yescharacteristic
372C22×C13C22×#4111yescharacteristic
373C22×C13C22×#4111yescharacteristic
374C22×C13C22×#4111yescharacteristic
375C22×C13C2×H(5,𝔽2)11yescharacteristic
376C22×C13C2×H(5,𝔽2)11yescharacteristic
377C4×C13—24no—
378C4×C13—24no—
379C4×C13—24no—
380C4×C13—24no—
381C4×C13—24no—
382C4×C13—42no—
383C4×C13—42no—
384Dic13—24no—
385Dic13—24no—
386Dic13—24no—
387Dic13—24no—
388Dic13—42no—
389Dic13—42no—
390Dic13—42no—
391Dic13—42no—
392C22×Q8—134no—
393C22×Q8—134no—
394C22×Q8—264no—
395C22×Q8—264no—
396C22×Q8—264no—
397C22×Q8—522no—
398C22×Q8—522no—
399C22×Q8—522no—
400C23×C4—131no—
401C23×C4—131no—
402C23×C4—131no—
403C23×C4—131no—
404C23×C4—131no—
405C23×C4—131no—
406C23×C4—131no—
407C23×C4—131no—
408C23×C4C22×D1311yescharacteristic
409C23×C4C22×D1311yescharacteristic
410C23×C4C22×D1311yescharacteristic
411C23×C4C22×D1311yescharacteristic
412C23×C4C22×D1311yescharacteristic
413C23×C4C22×D1311yescharacteristic
414C23×C4C22×D1311yescharacteristic
415C2×C4⋊C4—24no—
416C2×C4⋊C4—138no—
417C2×C4⋊C4—134no—
418C2×C4⋊C4—134no—
419C2×C4⋊C4—134no—
420C2×C4⋊C4—134no—
421C2×C4⋊C4—134no—
422C2×C4⋊C4—134no—
423C2×C4⋊C4—134no—
424C2×C4⋊C4—134no—
425C2×C4⋊C4—134no—
426C2×C4⋊C4—134no—
427C2×C4⋊C4—264no—
428C2×C4⋊C4—264no—
429C2×C4⋊C4—264no—
430C2×C4⋊C4—522no—
431C2×C4⋊C4—522no—
432C2×C4⋊C4—522no—
433C2×C4⋊C4—522no—
434C2×C4⋊C4—522no—
435C2×C4⋊C4—522no—
436C2×C4⋊C4Dic2618yescomplemented
437C2×C4⋊C4C22×D1314yes—
438C2×C4⋊C4C22×D1314yes—
439C2×C42—24no—
440C2×C42—134no—
441C2×C42—134no—
442C2×C42—134no—
443C2×C42—134no—
444C2×C42—264no—
445C2×C42—522no—
446C2×C42—522no—
447C2×C42—522no—
448C2×C42C22×D1314yes—
449#95—134no—
450#95—134no—
451#95—134no—
452#95—134no—
453#95—134no—
454#95—134no—
455#95—134no—
456#95—134no—
457#95—134no—
458#95—134no—
459#95—134no—
460#95—134no—
461#95C22×D1314yes—
462#95C22×D1314yes—
463#95C22×D1314yes—
464#95C22×D1314yes—
465C2×C13#258618yescomplemented
466C2×C13C2×#53311yescharacteristic
467C2×C13C2×#53311yescharacteristic
468C2×C13C2×#53811yescharacteristic
469C2×C13C2×#55111yescharacteristic
470C2×C13C2×#55411yescharacteristic
471C2×C13C2×#55411yescharacteristic
472C2×C13C2×Q8211yescharacteristic
473C24C23×D1311yescharacteristic
474C2×Q8—268no—
475C2×Q8—268no—
476C2×Q8—268no—
477C2×Q8—524no—
478C2×Q8—524no—
479C2×Q8—524no—
480C2×Q8—5216no—
481C2×Q8—5216no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
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—134no—
499C22×C4—134no—
500C22×C4—134no—
501C22×C4—134no—
502C22×C4—132no—
503C22×C4—132no—
504C22×C4—132no—
505C22×C4—132no—
506C22×C4—132no—
507C22×C4—132no—
508C22×C4—132no—
509C22×C4—132no—
510C22×C4—262no—
511C22×C4—262no—
512C22×C4—262no—
513C22×C4—262no—
514C22×C4—262no—
515C22×C4—262no—
516C22×C4—262no—
517C22×C4—262no—
518C22×C4—262no—
519C22×C4—262no—
520C22×C4—262no—
521C22×C4—262no—
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×C4C2×Dic2614yes—
531C22×C4C2×Dic2614yes—
532C22×C4C2×Dic2614yes—
533C22×C4#612914yes—
534C22×C4Q8×D1314yes—
535C22×C4C23×D1312yes—
536C22×C4C23×D1312yes—
537C22×C4C23×D1312yes—
538C22×C4C23×D1312yes—
539C22×C4C23×D1312yes—
540C22×C4C23×D1312yes—
541C22×C4C23×D1312yes—
542C4⋊C4—28no—
543C4⋊C4—1316no—
544C4⋊C4—268no—
545C4⋊C4—268no—
546C4⋊C4—268no—
547C4⋊C4—524no—
548C4⋊C4—524no—
549C4⋊C4—524no—
550C4⋊C4—524no—
551C4⋊C4—524no—
552C4⋊C4—524no—
553C4⋊C4C2×Dic26116yescomplemented
554C42—28no—
555C42—268no—
556C42—524no—
557C42—524no—
558C42—524no—
559C13C2×#258611yescharacteristic, complemented, Sylow
560C23C22×Dic2612yes—
561C23C2×#612912yes—
562C23C2×Q8×D1312yes—
563C23#41×D1312yes—
564C23#41×D1312yes—
565C23#8825612yes—
566C23#8825612yes—
567C23C24×D1311yescharacteristic
568Q8—5216no—
569Q8—5216no—
570C2×C4—28no—
571C2×C4—28no—
572C2×C4—28no—
573C2×C4—28no—
574C2×C4—28no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
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—44no—
592C2×C4—44no—
593C2×C4—134no—
594C2×C4—134no—
595C2×C4—134no—
596C2×C4—134no—
597C2×C4—268no—
598C2×C4—262no—
599C2×C4—262no—
600C2×C4—262no—
601C2×C4—262no—
602C2×C4—262no—
603C2×C4—262no—
604C2×C4—262no—
605C2×C4—262no—
606C2×C4—268no—
607C2×C4—268no—
608C2×C4—268no—
609C2×C4—262no—
610C2×C4—262no—
611C2×C4—262no—
612C2×C4—262no—
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—524no—
622C2×C4—524no—
623C2×C4—524no—
624C2×C4—524no—
625C2×C4C22×Dic2614yes—
626C2×C4C22×Dic2614yes—
627C2×C4C22×Dic2614yes—
628C2×C4C2×#612914yes—
629C2×C4C2×Q8×D1314yes—
630C22#1171922214yes—
631C22#1171924814yes—
632C22Q8×Dic2614yes—
633C22#1171932714yes—
634C22#1171936314yes—
635C22#1171939514yes—
636C22#1171940914yes—
637C22C23×Dic2611yescharacteristic
638C22C22×#612911yescharacteristic
639C22C22×Q8×D1311yescharacteristic
640C22C2×#41×D1311yescharacteristic
641C22C2×#41×D1311yescharacteristic
642C22C2×#8825611yescharacteristic
643C22C2×#8825611yescharacteristic
644C4—24no—
645C4—24no—
646C4—24no—
647C4—24no—
648C4—24no—
649C4—42no—
650C4—42no—
651C4—264no—
652C4—264no—
653C4—264no—
654C4—264no—
655C4—522no—
656C4—522no—
657C4—522no—
658C4—522no—
659C2#1312024618yesdirect product factor
660C2C2×#1171932711yescharacteristic
661C2C2×#1171922211yescharacteristic
662C2C2×#1171940911yescharacteristic
663C2C2×#1171936311yescharacteristic
664C2C2×#1171939511yescharacteristic
665C2C2×#1171924811yescharacteristic
666C2C2×Q8×Dic2611yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#387C2
socle, prime radicalC24×C13C24
hypercenterC2×#387D13
hypocenterC13C2×#2586
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. #13120246C2direct (N × H)
91. C2×C13×C4⋊C4Q8semidirect
101. C2×C4⋊Dic13Q8semidirect
211. C13×C4⋊C4C2×Q8semidirect
218. C4⋊Dic13C2×Q8semidirect
436. C2×C4⋊C4Dic26semidirect
465. C2×C13#2586semidirect
553. C4⋊C4C2×Dic26semidirect
559. C13C2×#2586semidirect
659. C2#13120246direct (N × H)

Maximal subgroups

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

subgroupindex
#131202462
C2×#117183222
C2×#117183172
C2×#117186402
C2×#117185902
C2×#117183072
C2×#117186462
C2×#117183082
C2×#117186422
C2×#117183152
C2×C4⋊C4×Dic132
C2×C4×C4⋊Dic132
C2×C13×#3872
C2×#258613