Finite Group Databasebeta

← C2×#13119784 #16034695

Subgroups — C2×#13119784 #16034695

Order 3328.

4006 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88142C211yesmaximal, characteristic, complemented
2C22×#88150C212yesmaximal, complemented
3C22×#88132C212yesmaximal, complemented
4C22×#88135C211yesmaximal, characteristic
5#13119784C2116yesmaximal, direct product factor
6C2×#11718338C211yesmaximal, characteristic, complemented
7C2×#11718610C211yesmaximal, characteristic, complemented
8C2×#11718653C211yesmaximal, characteristic, complemented
9C2×#11718618C212yesmaximal
10C2×#11718637C212yesmaximal, complemented
11C2×#11718310C211yesmaximal, characteristic, complemented
12C2×C13×#399C211yesmaximal, characteristic, complemented
13C23×C22⋊D13C2211yescharacteristic
14C24×Dic13C2211yescharacteristic
15C23×C4×D13C2211yescharacteristic
16C23×Dic26C2212yes—
17C22×C13×C4⋊C4C2212yes—
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2212yes—
21C22×C22⋊Dic13C2212yes—
22C22×#6103C2211yescharacteristic
23C22×#6103C2212yes—
24C22×#6103C2212yes—
25C22×C4⋊Dic13C2212yes—
26C22×C4⋊Dic13C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2212yes—
29C22×#6101C2212yes—
30C22×#6101C2212yes—
31C22×#6101C2212yes—
32C22×C4×Dic13C2212yes—
33C22×C4×Dic13C2211yescharacteristic
34C2×#88150—216no—
35C2×#88150C22116yescomplemented
36C2×#88142—28no—
37C2×#88142C2218yescomplemented
38C2×#88135—28no—
39C2×#88135C2218yes—
40C2×#88132—216no—
41C2×#88132C22116yescomplemented
42C13×#399C2218yescomplemented
43C2×C13×#95C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45#11718653C2218yescomplemented
46#11718637C22116yescomplemented
47#11718618C22116yes—
48#11718610C2218yescomplemented
49#11718338C2218yescomplemented
50#11718310C2218yescomplemented
51C25×C13C2311yescharacteristic
52C24×D13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2312yes—
55C23×C4×C13C2312yes—
56C23×C4×C13C2311yescharacteristic
57C22×C22⋊D13—24no—
58C22×C22⋊D13—24no—
59C22×C22⋊D13Q818yescomplemented
60C22×C22⋊D13C2314yes—
61C23×Dic13—28no—
62C23×Dic13—24no—
63C23×Dic13C2314yes—
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2312yes—
66C23×Dic13C2312yes—
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C22×C4×D13—24no—
70C22×C4×D13—28no—
71C22×C4×D13C2314yes—
72C22×Dic26—28no—
73C22×Dic26—28no—
74C22×Dic26—28no—
75C22×Dic26C2318yes—
76C2×C13×C4⋊C4—24no—
77C2×C13×C4⋊C4—28no—
78C2×C13×C4⋊C4C2314yes—
79C2×C13×C4⋊C4C2318yes—
80C2×C13×C22⋊C4—28no—
81C2×C13×C22⋊C4—24no—
82C2×C13×C22⋊C4C2318yes—
83C2×C13×C22⋊C4C2314yes—
84C2×C22⋊Dic13—28no—
85C2×C22⋊Dic13C2318yes—
86C2×#6103—24no—
87C2×#6103—28no—
88C2×#6103—28no—
89C2×#6103C2314yes—
90C2×#6103C2318yes—
91C2×#6103C2318yes—
92C2×C4⋊Dic13—28no—
93C2×C4⋊Dic13—24no—
94C2×C4⋊Dic13C2318yes—
95C2×C4⋊Dic13C2314yes—
96C2×#6101—28no—
97C2×#6101—24no—
98C2×#6101—28no—
99C2×#6101—28no—
100C2×#6101D4116yescomplemented
101C2×#6101C2318yes—
102C2×#6101C2314yes—
103C2×#6101C2318yes—
104C2×#6101C2318yes—
105C2×#6101C2318yes—
106C2×C4×Dic13—28no—
107C2×C4×Dic13D418yes—
108C2×C4×Dic13C2318yes—
109C2×C4×Dic13C2314yes—
110#88150—264no—
111#88142—232no—
112#88135—232no—
113#88132—264no—
114C13×#95C2314yes—
115#88071C2314yes—
116C2×#2542—131nomaximal, Sylow
117C24×C13—24no—
118C24×C13—22no—
119C24×C13—22no—
120C24×C13—24no—
121C24×C13C2×Q814yes—
122C24×C13C2412yes—
123C24×C13C2411yescharacteristic
124C23×D13—24no—
125C23×D13—22no—
126C23×D13—22no—
127C23×D13—24no—
128C23×D13C2×Q814yes—
129C23×D13C2412yes—
130C22×C4×C13—24no—
131C22×C4×C13—24no—
132C22×C4×C13—24no—
133C22×C4×C13—24no—
134C22×C4×C13—22no—
135C22×C4×C13—24no—
136C22×C4×C13—24no—
137C22×C4×C13—24no—
138C22×C4×C13C2×D414yes—
139C22×C4×C13C2×D418yes—
140C22×C4×C13C2412yes—
141C22×C4×C13C2414yes—
142C22×C4×C13C2412yes—
143C22×C4×C13C2414yes—
144C2×C22⋊D13—232no—
145C2×C22⋊D13—28no—
146C2×C22⋊D13—28no—
147C2×C22⋊D13C2×Q8116yescomplemented
148C22×Dic13—24no—
149C22×Dic13—24no—
150C22×Dic13—24no—
151C22×Dic13—24no—
152C22×Dic13—24no—
153C22×Dic13—22no—
154C22×Dic13—24no—
155C22×Dic13—216no—
156C22×Dic13—28no—
157C22×Dic13—416no—
158C22×Dic13C2×D418yes—
159C22×Dic13C2×D414yes—
160C22×Dic13C2×D414yes—
161C22×Dic13C2×D418yes—
162C22×Dic13C2×Q814yes—
163C22×Dic13#4114yes—
164C22×Dic13C2412yes—
165C22×Dic13C2414yes—
166C22×Dic13C2414yes—
167C22×Dic13C2412yes—
168C22×Dic13C2412yes—
169C2×C4×D13—28no—
170C2×C4×D13—216no—
171C2×C4×D13—416no—
172C2×Dic26—216no—
173C2×Dic26—216no—
174C2×Dic26—216no—
175C2×Dic26—432no—
176C13×C4⋊C4—28no—
177C13×C4⋊C4—216no—
178C13×C22⋊C4—216no—
179C13×C22⋊C4—28no—
180C22⋊Dic13—216no—
181#6103—28no—
182#6103—216no—
183#6103—216no—
184C4⋊Dic13—216no—
185C4⋊Dic13—28no—
186#6101—216no—
187#6101—28no—
188#6101—216no—
189#6101—216no—
190#6101C2×D4132yescomplemented
191C4×Dic13—216no—
192C4×Dic13C2×D4116yes—
193C22×C4⋊Q8—131no—
194C22×C22⋊Q8—132no—
195C22×C22⋊Q8—132no—
196C22×C4×D4—131no—
197#2542—1316no—
198C2×#399—131no—
199C2×#399—131no—
200C2×#399—131no—
201C2×#399D1311yescharacteristic, complemented
202C2×#390—132no—
203C2×#384—132no—
204C2×C4×C4⋊C4—131no—
205C23×C13—28no—
206C23×C13—216no—
207C23×C13—24no—
208C23×C13—22no—
209C23×C13—22no—
210C23×C13—24no—
211C23×C13—44no—
212C23×C13—44no—
213C23×C13—48no—
214C23×C13C22×D412yes—
215C23×C13C22×D414yes—
216C23×C13C22×Q814yes—
217C23×C13C22×Q812yes—
218C23×C13C2×#4112yes—
219C23×C132−1+414yes—
220C23×C13C2511yescharacteristic
221C22×D13—28no—
222C22×D13—216no—
223C22×D13—24no—
224C22×D13—22no—
225C22×D13—22no—
226C22×D13—24no—
227C22×D13—44no—
228C22×D13—44no—
229C22×D13—48no—
230C22×D13C22×Q814yes—
231C2×C4×C13—28no—
232C2×C4×C13—216no—
233C2×C4×C13—24no—
234C2×C4×C13—24no—
235C2×C4×C13—24no—
236C2×C4×C13—24no—
237C2×C4×C13—22no—
238C2×C4×C13—24no—
239C2×C4×C13—24no—
240C2×C4×C13—24no—
241C2×C4×C13—48no—
242C2×C4×C13—44no—
243C2×C4×C13C22×D414yes—
244C2×C4×C13C22×D418yes—
245C22⋊D13—232no—
246C2×Dic13—216no—
247C2×Dic13—24no—
248C2×Dic13—24no—
249C2×Dic13—24no—
250C2×Dic13—24no—
251C2×Dic13—24no—
252C2×Dic13—22no—
253C2×Dic13—24no—
254C2×Dic13—48no—
255C2×Dic13—44no—
256C2×Dic13—416no—
257C2×Dic13C22⋊Q8116yescomplemented
258C2×Dic13#127116yes—
259C2×Dic13C22×D418yes—
260C2×Dic13C22×D414yes—
261C2×Dic13C22×D414yes—
262C2×Dic13C22×D418yes—
263C2×Dic13C22×Q814yes—
264C2×Dic13C2×#4114yes—
265C4×D13—416no—
266Dic26—432no—
267C23×Q8—132no—
268C23×D4—131no—
269C24×C4—131no—
270C24×C4—131no—
271C2×C4⋊Q8—138no—
272C2×C4⋊Q8—268no—
273C2×C22⋊Q8—1316no—
274C2×C22⋊Q8—1316no—
275C2×C22⋊Q8—2616no—
276C2×C22⋊Q8—2616no—
277C2×C4×D4—138no—
278C2×C4×D4—268no—
279C22×C4⋊C4—132no—
280C22×C4⋊C4—132no—
281C22×C4⋊C4—132no—
282C22×C4⋊C4—131no—
283C22×C4⋊C4—132no—
284C22×C4⋊C4—131no—
285C22×C4⋊C4—132no—
286C22×C4⋊C4C2×D1311yescharacteristic
287C22×C4⋊C4C2×D1312yes—
288C22×C22⋊C4—132no—
289C22×C22⋊C4—131no—
290C22×C22⋊C4—132no—
291C22×C22⋊C4—132no—
292C22×C22⋊C4C2×D1311yescharacteristic
293C22×C22⋊C4C2×D1312yes—
294C22×C42—131no—
295C22×C42—132no—
296#399—138no—
297#399—138no—
298#399—138no—
299#399C2×D1318yescomplemented
300#390—1316no—
301#384—1316no—
302C4×C4⋊C4—138no—
303C2×#95—131no—
304C2×#95C2×D1311yescharacteristic
305C22×C13—24no—
306C22×C13—28no—
307C22×C13—42no—
308C22×C13—42no—
309C22×C13—44no—
310C22×C13—416no—
311C22×C13C2×C22⋊Q814yes—
312C22×C13C2×#12714yes—
313C22×C13#53614yes—
314C22×C13#54718yes—
315C22×C13D4×Q818yes—
316C22×C13C23×D411yescharacteristic
317C22×C13C23×D412yes—
318C22×C13C23×Q811yescharacteristic
319C22×C13C22×#4111yescharacteristic
320C22×C13C2×2−1+412yes—
321C2×D13—24no—
322C2×D13—28no—
323C2×D13—42no—
324C2×D13—42no—
325C2×D13—44no—
326C2×D13—416no—
327C4×C13—24no—
328C4×C13—28no—
329C4×C13—44no—
330C4×C13—42no—
331Dic13—28no—
332Dic13—44no—
333Dic13—42no—
334Dic13C2×C22⋊Q818yescomplemented
335Dic13C2×#12718yes—
336C25—131no—
337C25C22×D1311yescharacteristic
338C22×Q8—138no—
339C22×Q8—268no—
340C22×Q8—268no—
341C22×Q8—268no—
342C22×D4—138no—
343C22×D4—134no—
344C22×D4—264no—
345C22×D4—264no—
346C23×C4—131no—
347C23×C4—131no—
348C23×C4—132no—
349C23×C4—134no—
350C23×C4—132no—
351C23×C4—131no—
352C23×C4—134no—
353C23×C4—264no—
354C23×C4—268no—
355C23×C4—264no—
356C23×C4—268no—
357C23×C4C22×D1312yes—
358C23×C4C22×D1311yescharacteristic
359C23×C4C22×D1312yes—
360C23×C4C22×D1311yescharacteristic
361C4⋊Q8—2632no—
362C22⋊Q8—2664no—
363C22⋊Q8—2664no—
364C4×D4—2632no—
365C2×C4⋊C4—28no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—1316no—
368C2×C4⋊C4—138no—
369C2×C4⋊C4—134no—
370C2×C4⋊C4—138no—
371C2×C4⋊C4—138no—
372C2×C4⋊C4—138no—
373C2×C4⋊C4—138no—
374C2×C4⋊C4—134no—
375C2×C4⋊C4—264no—
376C2×C4⋊C4—268no—
377C2×C4⋊C4—268no—
378C2×C4⋊C4—268no—
379C2×C4⋊C4—268no—
380C2×C4⋊C4—264no—
381C2×C4⋊C4C22×D1318yes—
382C2×C4⋊C4C22×D1314yes—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—138no—
386C2×C22⋊C4—134no—
387C2×C22⋊C4—138no—
388C2×C22⋊C4—138no—
389C2×C22⋊C4—268no—
390C2×C22⋊C4—268no—
391C2×C22⋊C4—264no—
392C2×C22⋊C4—268no—
393C2×C22⋊C4C22×D1314yes—
394C2×C22⋊C4C22×D1318yes—
395C2×C42—138no—
396C2×C42—134no—
397C2×C42—138no—
398C2×C42—268no—
399#95—134no—
400#95C22×D1314yes—
401C2×C13—44no—
402C2×C13#254218yescomplemented
403C2×C13C22×C22⋊Q811yescharacteristic
404C2×C13C22×#12711yescharacteristic
405C2×C13C2×#53611yescharacteristic
406C2×C13C2×#54712yes—
407C2×C13C2×D4×Q812yes—
408D13—44no—
409C24—24no—
410C24—22no—
411C24—22no—
412C24—24no—
413C24—134no—
414C24—132no—
415C24—264no—
416C24—262no—
417C24—262no—
418C24—264no—
419C24Q8×D1314yes—
420C24C23×D1312yes—
421C24C23×D1311yescharacteristic
422C2×Q8—2616no—
423C2×Q8—2616no—
424C2×Q8—2616no—
425C2×Q8—5232no—
426C2×D4—1316no—
427C2×D4—268no—
428C2×D4—2632no—
429C2×D4—268no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—134no—
439C22×C4—134no—
440C22×C4—138no—
441C22×C4—134no—
442C22×C4—134no—
443C22×C4—132no—
444C22×C4—132no—
445C22×C4—138no—
446C22×C4—134no—
447C22×C4—134no—
448C22×C4—132no—
449C22×C4—268no—
450C22×C4—2616no—
451C22×C4—268no—
452C22×C4—2616no—
453C22×C4—264no—
454C22×C4—264no—
455C22×C4—262no—
456C22×C4—264no—
457C22×C4—264no—
458C22×C4—264no—
459C22×C4—264no—
460C22×C4—5216no—
461C22×C4—5216no—
462C22×C4D4×D1314yes—
463C22×C4D4×D1318yes—
464C22×C4C23×D1314yes—
465C22×C4C23×D1312yes—
466C22×C4C23×D1312yes—
467C22×C4C23×D1314yes—
468C4⋊C4—216no—
469C4⋊C4—28no—
470C4⋊C4—1332no—
471C4⋊C4—268no—
472C4⋊C4—2616no—
473C4⋊C4—2616no—
474C4⋊C4—2616no—
475C4⋊C4—2616no—
476C4⋊C4—268no—
477C22⋊C4—28no—
478C22⋊C4—216no—
479C22⋊C4—2616no—
480C22⋊C4—2616no—
481C22⋊C4—268no—
482C22⋊C4—2616no—
483C42—1316no—
484C42—2616no—
485C13C2×#254211yescharacteristic, complemented, Sylow
486C23—28no—
487C23—216no—
488C23—24no—
489C23—22no—
490C23—22no—
491C23—24no—
492C23—44no—
493C23—48no—
494C23—44no—
495C23—134no—
496C23—268no—
497C23—2616no—
498C23—264no—
499C23—262no—
500C23—262no—
501C23—264no—
502C23—524no—
503C23—528no—
504C23—524no—
505C23C2×D4×D1312yes—
506C23C2×D4×D1314yes—
507C23C2×Q8×D1314yes—
508C23C2×Q8×D1312yes—
509C23#41×D1312yes—
510C23#8825714yes—
511C23C24×D1311yescharacteristic
512Q8—5232no—
513D4—2632no—
514C2×C4—28no—
515C2×C4—216no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—44no—
525C2×C4—48no—
526C2×C4—1316no—
527C2×C4—134no—
528C2×C4—134no—
529C2×C4—138no—
530C2×C4—134no—
531C2×C4—134no—
532C2×C4—1316no—
533C2×C4—138no—
534C2×C4—2616no—
535C2×C4—264no—
536C2×C4—264no—
537C2×C4—262no—
538C2×C4—264no—
539C2×C4—264no—
540C2×C4—264no—
541C2×C4—264no—
542C2×C4—5216no—
543C2×C4—5216no—
544C2×C4—524no—
545C2×C4—528no—
546C2×C4C2×D4×D1314yes—
547C2×C4C2×D4×D1318yes—
548C22—28no—
549C22—24no—
550C22—416no—
551C22—44no—
552C22—42no—
553C22—42no—
554C22—268no—
555C22—264no—
556C22—5216no—
557C22—524no—
558C22—522no—
559C22—522no—
560C22D13×C22⋊Q814yes—
561C22#1171933718yes—
562C22#1171935314yes—
563C22#1171936018yes—
564C22D13×#12714yes—
565C22C22×D4×D1312yes—
566C22C22×D4×D1311yescharacteristic
567C22C22×Q8×D1311yescharacteristic
568C22C2×#41×D1311yescharacteristic
569C22C2×#8825712yes—
570C4—28no—
571C4—24no—
572C4—42no—
573C4—44no—
574C4—138no—
575C4—138no—
576C4—268no—
577C4—522no—
578C4—524no—
579C2—44no—
580C2—524no—
581C2#1311978418yesdirect product factor
582C2C2×D13×C22⋊Q811yescharacteristic
583C2C2×D13×#12711yescharacteristic
584C2C2×#1171935311yescharacteristic
585C2C2×#1171936012yes—
586C2C2×#1171933712yes—
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#399C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC2×#399D13
hypocenterC13C2×#2542
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×#88142C2semidirect
2. C22×#88150C2semidirect
3. C22×#88132C2semidirect
5. #13119784C2direct (N × H)
6. C2×#11718338C2semidirect
7. C2×#11718610C2semidirect
8. C2×#11718653C2semidirect
10. C2×#11718637C2semidirect
11. C2×#11718310C2semidirect
12. C2×C13×#399C2semidirect
35. C2×#88150C22semidirect
37. C2×#88142C22semidirect
41. C2×#88132C22semidirect
42. C13×#399C22semidirect
45. #11718653C22semidirect
46. #11718637C22semidirect
48. #11718610C22semidirect
49. #11718338C22semidirect
50. #11718310C22semidirect
59. C22×C22⋊D13Q8semidirect
100. C2×#6101D4semidirect
147. C2×C22⋊D13C2×Q8semidirect
190. #6101C2×D4semidirect
201. C2×#399D13semidirect
257. C2×Dic13C22⋊Q8semidirect
299. #399C2×D13semidirect
334. Dic13C2×C22⋊Q8semidirect
402. C2×C13#2542semidirect
485. C13C2×#2542semidirect
581. C2#13119784direct (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×#881502
C22×#881322
C22×#881352
#131197842
C2×#117183382
C2×#117186102
C2×#117186532
C2×#117186182
C2×#117186372
C2×#117183102
C2×C13×#3992
C2×#254213