Finite Group Databasebeta

← C2×#13117841 #16022436

Subgroups — C2×#13117841 #16022436

Order 3328.

3614 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88178C211yesmaximal, characteristic
2C22×#88141C211yesmaximal, characteristic, complemented
3#13117841C2116yesmaximal, direct product factor
4C2×#11718635C211yesmaximal, characteristic, complemented
5C2×#11718634C211yesmaximal, characteristic, complemented
6C2×#11718633C212yesmaximal, complemented
7C2×#11718639C212yesmaximal, complemented
8C2×#11718871C212yesmaximal
9C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
10C2×C4×C22⋊Dic13C212yesmaximal
11C2×C4×C22⋊Dic13C211yesmaximal, characteristic
12C23×C13×C4⋊C4C211yesmaximal, characteristic
13C24×C4×C13C2212yes—
14C24×C4×C13C2211yescharacteristic
15C23×Dic26C2211yescharacteristic
16C22×C13×C4⋊C4—28no—
17C22×C13×C4⋊C4C2212yes—
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2218yes—
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2212yes—
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C4⋊Dic13C2211yescharacteristic
25C2×#88178C4116yescomplemented
26C2×#88178C2218yes—
27C22×#6101C2212yes—
28C22×#6101C2212yes—
29C22×#6101C2212yes—
30C22×C4×Dic13C2212yes—
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C22×C4×Dic13C2212yes—
34C2×#88141—28no—
35C2×#88141C2218yescomplemented
36#11718871C22116yes—
37C4×C22⋊Dic13C2218yes—
38C4×C22⋊Dic13C22116yes—
39C2×#88071C2212yes—
40C2×#88071C2212yes—
41C2×#88071C2211yescharacteristic
42C2×#88071C2212yes—
43C2×#88071C2211yescharacteristic
44C2×#88071C2212yes—
45#11718639C22116yescomplemented
46C4⋊C4×Dic13C2218yescomplemented
47#11718635C2218yescomplemented
48#11718634C2218yescomplemented
49#11718633C22116yescomplemented
50C25×C13C2311yescharacteristic
51C23×C4×C13—24no—
52C23×C4×C13—24no—
53C23×C4×C13—28no—
54C23×C4×C13—28no—
55C23×C4×C13—44no—
56C23×C4×C13C2×C418yes—
57C23×C4×C13C2312yes—
58C23×C4×C13C2318yes—
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2314yes—
61C23×C4×C13C2312yes—
62C23×C4×C13C2311yescharacteristic
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2312yes—
66C23×Dic13C2312yes—
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C22×Dic26—24no—
70C22×Dic26—24no—
71C22×Dic26C2×C418yescomplemented
72C22×Dic26C2314yes—
73C2×C13×C4⋊C4—28no—
74C2×C13×C4⋊C4—24no—
75C2×C13×C4⋊C4—232no—
76C2×C13×C4⋊C4D418yes—
77C2×C13×C4⋊C4C2318yes—
78C2×C13×C4⋊C4C2314yes—
79C2×C13×C4⋊C4C2314yes—
80C2×C22⋊Dic13—24no—
81C2×C22⋊Dic13C2×C4116yes—
82C2×C22⋊Dic13Q818yescomplemented
83C2×C22⋊Dic13C2314yes—
84C2×C22⋊Dic13C2318yes—
85C2×C22⋊Dic13C2314yes—
86C2×C4⋊Dic13C2×C418yescomplemented
87C2×C4⋊Dic13C2314yes—
88#88178C2×C4164yescomplemented
89C2×#6101—28no—
90C2×#6101—44no—
91C2×#6101C2×C4116yescomplemented
92C2×#6101C2318yes—
93C2×#6101C2318yes—
94C2×#6101C2318yes—
95C2×C4×Dic13—28no—
96C2×C4×Dic13—24no—
97C2×C4×Dic13—24no—
98C2×C4×Dic13—44no—
99C2×C4×Dic13C2314yes—
100C2×C4×Dic13C2318yes—
101C2×C4×Dic13C2314yes—
102C2×C4×Dic13C2318yes—
103#88141—232no—
104#88071C2314yes—
105#88071C2318yes—
106#88071C2318yes—
107#88071C2314yes—
108#88071C2318yes—
109#88071C2318yes—
110C2×#2360—131nomaximal, Sylow
111C24×C13—22no—
112C24×C13—22no—
113C24×C13—22no—
114C24×C13—22no—
115C24×C13C22×C414yes—
116C24×C13C2×Q814yes—
117C24×C13#4114yes—
118C24×C13C2412yes—
119C24×C13C2411yescharacteristic
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—24no—
123C22×C4×C13—24no—
124C22×C4×C13—232no—
125C22×C4×C13—28no—
126C22×C4×C13—28no—
127C22×C4×C13—24no—
128C22×C4×C13—216no—
129C22×C4×C13—24no—
130C22×C4×C13—24no—
131C22×C4×C13—216no—
132C22×C4×C13—48no—
133C22×C4×C13—432no—
134C22×C4×C13C22×C414yes—
135C22×C4×C13C22×C4116yes—
136C22×C4×C13C22×C414yes—
137C22×C4×C13C2×D418yes—
138C22×C4×C13C2×D414yes—
139C22×C4×C13#4114yes—
140C22×C4×C13C2414yes—
141C22×C4×C13C2412yes—
142C22×C4×C13C2414yes—
143C22×C4×C13C2412yes—
144C22×Dic13—22no—
145C22×Dic13—24no—
146C22×Dic13—22no—
147C22×Dic13—24no—
148C22×Dic13—22no—
149C22×Dic13—24no—
150C22×Dic13—24no—
151C22×Dic13—22no—
152C22×Dic13—22no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13C22×C418yes—
159C22×Dic13C22×C418yes—
160C22×Dic13C2×Q814yes—
161C22×Dic13C2×Q814yes—
162C22×Dic13C2412yes—
163C22×Dic13C2412yes—
164C22×Dic13C2414yes—
165C22×Dic13C2414yes—
166C22×Dic13C2412yes—
167C22×Dic13C2412yes—
168C2×Dic26—232no—
169C2×Dic26—28no—
170C2×Dic26—28no—
171C2×Dic26C22×C4116yescomplemented
172C13×C4⋊C4—216no—
173C13×C4⋊C4—28no—
174C13×C4⋊C4C2×D4116yes—
175C22⋊Dic13—28no—
176C22⋊Dic13C22×C4132yes—
177C22⋊Dic13C2×Q8116yescomplemented
178C4⋊Dic13C22×C4116yescomplemented
179#6101—216no—
180#6101—48no—
181#6101C22×C4132yescomplemented
182C4×Dic13—216no—
183C4×Dic13—28no—
184C4×Dic13—28no—
185C4×Dic13—48no—
186C22×C22⋊Q8—131no—
187C22×C4×Q8—131no—
188C23×C4⋊C4D1311yescharacteristic
189#2360—1316no—
190C2×#391—131no—
191C2×#389—132no—
192C2×#389—131no—
193C2×#387—132no—
194C2×#385—132no—
195C2×C4×C4⋊C4—131no—
196C2×C4×C22⋊C4—132no—
197C2×C4×C22⋊C4—131no—
198C23×C13—28no—
199C23×C13—28no—
200C23×C13—28no—
201C23×C13—28no—
202C23×C13—28no—
203C23×C13—28no—
204C23×C13—22no—
205C23×C13—22no—
206C23×C13—22no—
207C23×C13—22no—
208C23×C13C4×Q8116yescomplemented
209C23×C13C23×C414yes—
210C23×C13C23×C412yes—
211C23×C13C22×D412yes—
212C23×C13C22×Q814yes—
213C23×C13C22×Q812yes—
214C23×C13C2×#4114yes—
215C23×C13C2×#4112yes—
216C23×C13C2×#4112yes—
217C23×C13H(5,𝔽2)12yes—
218C23×C132−1+412yes—
219C23×C13C2511yescharacteristic
220C2×C4×C13—28no—
221C2×C4×C13—216no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—24no—
225C2×C4×C13—24no—
226C2×C4×C13—232no—
227C2×C4×C13—24no—
228C2×C4×C13—24no—
229C2×C4×C13—24no—
230C2×C4×C13—432no—
231C2×C4×C13—48no—
232C2×C4×C13C4×D4116yes—
233C2×C4×C13C23×C414yes—
234C2×C4×C13C23×C414yes—
235C2×C4×C13C22×D418yes—
236C2×C4×C13C22×D414yes—
237C2×C4×C13C2×#4114yes—
238C2×Dic13—216no—
239C2×Dic13—216no—
240C2×Dic13—28no—
241C2×Dic13—28no—
242C2×Dic13—22no—
243C2×Dic13—24no—
244C2×Dic13—22no—
245C2×Dic13—24no—
246C2×Dic13—22no—
247C2×Dic13—24no—
248C2×Dic13—24no—
249C2×Dic13—22no—
250C2×Dic13—22no—
251C2×Dic13—22no—
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—22no—
255C2×Dic13—22no—
256C2×Dic13—44no—
257C2×Dic13—44no—
258C2×Dic13C23×C418yes—
259C2×Dic13C23×C418yes—
260C2×Dic13C22×Q814yes—
261C2×Dic13C22×Q814yes—
262Dic26—232no—
263C23×Q8—131no—
264C24×C4C2×D1312yes—
265C24×C4C2×D1311yescharacteristic
266C2×C22⋊Q8—1316no—
267C2×C22⋊Q8—138no—
268C2×C4×Q8—138no—
269C2×C4×Q8—268no—
270C22×C4⋊C4—28no—
271C22×C4⋊C4—132no—
272C22×C4⋊C4—131no—
273C22×C4⋊C4—132no—
274C22×C4⋊C4—132no—
275C22×C4⋊C4C2×D1318yes—
276C22×C4⋊C4C2×D1312yes—
277C22×C4⋊C4C2×D1311yescharacteristic
278C22×C4⋊C4C2×D1311yescharacteristic
279C22×C22⋊C4—132no—
280C22×C22⋊C4—131no—
281C22×C22⋊C4—131no—
282C22×C42—132no—
283C22×C42—131no—
284C22×C42—131no—
285C22×C42—132no—
286#391—138no—
287#389—1316no—
288#389—138no—
289#387—1316no—
290#385—1316no—
291C4×C4⋊C4—138no—
292C4×C22⋊C4—138no—
293C4×C22⋊C4—1316no—
294C2×#95—131no—
295C2×#95—132no—
296C2×#95—131no—
297C2×#95—132no—
298C2×#95—132no—
299C2×#95—132no—
300C22×C13—232no—
301C22×C13—24no—
302C22×C13—24no—
303C22×C13—24no—
304C22×C13—24no—
305C22×C13—24no—
306C22×C13—24no—
307C22×C13C2×C4×D414yes—
308C22×C13C2×C4×Q814yes—
309C22×C13C2×C4×Q818yescomplemented
310C22×C13#52014yes—
311C22×C13#54614yes—
312C22×C13D4×Q814yes—
313C22×C13#55214yes—
314C22×C13#55414yes—
315C22×C13C24×C411yescharacteristic
316C22×C13C23×D411yescharacteristic
317C22×C13C23×Q811yescharacteristic
318C22×C13C22×#4111yescharacteristic
319C22×C13C22×#4111yescharacteristic
320C22×C13C2×H(5,𝔽2)11yescharacteristic
321C22×C13C2×2−1+411yescharacteristic
322C4×C13—24no—
323C4×C13—28no—
324C4×C13—44no—
325C4×C13C2×C4×D418yes—
326Dic13—28no—
327Dic13—28no—
328Dic13—24no—
329Dic13—24no—
330Dic13—42no—
331Dic13—42no—
332C25C22×D1311yescharacteristic
333C22×Q8—138no—
334C22×Q8—134no—
335C22×Q8—264no—
336C22×Q8—264no—
337C23×C4—24no—
338C23×C4—24no—
339C23×C4—28no—
340C23×C4—28no—
341C23×C4—44no—
342C23×C4—132no—
343C23×C4—132no—
344C23×C4—131no—
345C23×C4—131no—
346C23×C4—131no—
347C23×C4—131no—
348C23×C4C4×D1318yes—
349C23×C4C22×D1312yes—
350C23×C4C22×D1318yes—
351C23×C4C22×D1314yes—
352C23×C4C22×D1311yescharacteristic
353C23×C4C22×D1312yes—
354C23×C4C22×D1311yescharacteristic
355C22⋊Q8—1364no—
356C4×Q8—2632no—
357C2×C4⋊C4—28no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—232no—
360C2×C4⋊C4—1316no—
361C2×C4⋊C4—138no—
362C2×C4⋊C4—138no—
363C2×C4⋊C4—134no—
364C2×C4⋊C4—138no—
365C2×C4⋊C4—138no—
366C2×C4⋊C4—268no—
367C2×C4⋊C4—524no—
368C2×C4⋊C4C22⋊D1318yes—
369C2×C4⋊C4C22×D1318yes—
370C2×C4⋊C4C22×D1314yes—
371C2×C4⋊C4C22×D1314yes—
372C2×C22⋊C4—1316no—
373C2×C22⋊C4—138no—
374C2×C22⋊C4—138no—
375C2×C22⋊C4—134no—
376C2×C22⋊C4—134no—
377C2×C22⋊C4—264no—
378C2×C42—138no—
379C2×C42—134no—
380C2×C42—134no—
381C2×C42—138no—
382C2×C42—264no—
383C2×C42—268no—
384C2×C42—264no—
385C2×C42—524no—
386#95—134no—
387#95—138no—
388#95—134no—
389#95—138no—
390#95—138no—
391#95—138no—
392C2×C13—28no—
393C2×C13#236018yescomplemented
394C2×C13C22×C4×D411yescharacteristic
395C2×C13C22×C4×Q811yescharacteristic
396C2×C13C2×#52011yescharacteristic
397C2×C13C2×#54611yescharacteristic
398C2×C13C2×D4×Q811yescharacteristic
399C2×C13C2×#55211yescharacteristic
400C2×C13C2×#55411yescharacteristic
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24C2×C4×D1314yes—
406C24#612914yes—
407C24Q8×D1314yes—
408C24C23×D1312yes—
409C24C23×D1311yescharacteristic
410C2×Q8—1316no—
411C2×Q8—2632no—
412C2×Q8—268no—
413C2×Q8—268no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—232no—
419C22×C4—28no—
420C22×C4—28no—
421C22×C4—216no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—216no—
426C22×C4—48no—
427C22×C4—432no—
428C22×C4—138no—
429C22×C4—138no—
430C22×C4—134no—
431C22×C4—134no—
432C22×C4—132no—
433C22×C4—132no—
434C22×C4—134no—
435C22×C4—134no—
436C22×C4—132no—
437C22×C4—132no—
438C22×C4—262no—
439C22×C4—264no—
440C22×C4—262no—
441C22×C4—264no—
442C22×C4—264no—
443C22×C4—262no—
444C22×C4—262no—
445C22×C4—264no—
446C22×C4—262no—
447C22×C4—262no—
448C22×C4—262no—
449C22×C4—262no—
450C22×C4—262no—
451C22×C4—262no—
452C22×C4C2×C4×D1314yes—
453C22×C4C2×C4×D13116yes—
454C22×C4C2×C4×D1314yes—
455C22×C4#612714yes—
456C22×C4C2×C22⋊D1318yes—
457C22×C4C2×C22⋊D1314yes—
458C22×C4C23×D1314yes—
459C22×C4C23×D1312yes—
460C22×C4C23×D1314yes—
461C22×C4C23×D1312yes—
462C4⋊C4—216no—
463C4⋊C4—28no—
464C4⋊C4—1332no—
465C4⋊C4—1316no—
466C4⋊C4—2616no—
467C4⋊C4—528no—
468C4⋊C4C2×C22⋊D13116yes—
469C22⋊C4—1332no—
470C22⋊C4—1316no—
471C22⋊C4—268no—
472C42—268no—
473C42—2616no—
474C42—268no—
475C42—528no—
476C13C2×#236011yescharacteristic, complemented, Sylow
477C23—28no—
478C23—28no—
479C23—28no—
480C23—28no—
481C23—28no—
482C23—28no—
483C23—22no—
484C23—22no—
485C23—22no—
486C23—22no—
487C23#88141116yescomplemented
488C23C22×C4×D1314yes—
489C23C22×C4×D1312yes—
490C23C2×#612712yes—
491C23C2×#612914yes—
492C23C2×#612912yes—
493C23#8825112yes—
494C23C2×Q8×D1314yes—
495C23C2×Q8×D1312yes—
496C23#8825412yes—
497C23C22×C22⋊D1312yes—
498C23C24×D1311yescharacteristic
499Q8—2632no—
500C2×C4—28no—
501C2×C4—216no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—232no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—432no—
511C2×C4—48no—
512C2×C4—138no—
513C2×C4—138no—
514C2×C4—134no—
515C2×C4—134no—
516C2×C4—2616no—
517C2×C4—268no—
518C2×C4—2616no—
519C2×C4—268no—
520C2×C4—262no—
521C2×C4—264no—
522C2×C4—262no—
523C2×C4—264no—
524C2×C4—264no—
525C2×C4—262no—
526C2×C4—262no—
527C2×C4—264no—
528C2×C4—262no—
529C2×C4—262no—
530C2×C4—262no—
531C2×C4—262no—
532C2×C4—262no—
533C2×C4—262no—
534C2×C4—524no—
535C2×C4—524no—
536C2×C4C4×C22⋊D13116yes—
537C2×C4C22×C4×D1314yes—
538C2×C4C22×C4×D1314yes—
539C2×C4C2×#612714yes—
540C2×C4C22×C22⋊D1318yes—
541C2×C4C22×C22⋊D1314yes—
542C22—24no—
543C22—24no—
544C22—24no—
545C22—24no—
546C22—232no—
547C22—24no—
548C22—24no—
549C22C2×#8814114yes—
550C22C2×#8814118yescomplemented
551C22#1171920914yes—
552C22#1171921614yes—
553C22#1171921814yes—
554C22C2×C4×C22⋊D1314yes—
555C22#1171951114yes—
556C22Q8×C22⋊D1314yes—
557C22C23×C4×D1311yescharacteristic
558C22C22×#612711yescharacteristic
559C22C22×#612911yescharacteristic
560C22C2×#8825111yescharacteristic
561C22C22×Q8×D1311yescharacteristic
562C22C2×#8825411yescharacteristic
563C22C23×C22⋊D1311yescharacteristic
564C4—24no—
565C4—28no—
566C4—44no—
567C4—268no—
568C4—268no—
569C4—264no—
570C4—264no—
571C4—522no—
572C4—522no—
573C4C2×C4×C22⋊D1318yes—
574C2—28no—
575C2#1311784118yesdirect product factor
576C2C22×C4×C22⋊D1311yescharacteristic
577C2C22×#8814111yescharacteristic
578C2C2×#1171920911yescharacteristic
579C2C2×#1171951111yescharacteristic
580C2C2×Q8×C22⋊D1311yescharacteristic
581C2C2×#1171921811yescharacteristic
582C2C2×#1171921611yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC23×C13×C4⋊C4C2
socleC24×C13C24
prime radicalC25×C13C23
cosocleC23×C13C25
hypercenterC23×C4⋊C4D13
hypocenterC13C2×#2360
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#88141C2semidirect
3. #13117841C2direct (N × H)
4. C2×#11718635C2semidirect
5. C2×#11718634C2semidirect
6. C2×#11718633C2semidirect
7. C2×#11718639C2semidirect
9. C2×C4⋊C4×Dic13C2semidirect
25. C2×#88178C4semidirect
35. C2×#88141C22semidirect
45. #11718639C22semidirect
46. C4⋊C4×Dic13C22semidirect
47. #11718635C22semidirect
48. #11718634C22semidirect
49. #11718633C22semidirect
71. C22×Dic26C2×C4semidirect
82. C2×C22⋊Dic13Q8semidirect
86. C2×C4⋊Dic13C2×C4semidirect
88. #88178C2×C4semidirect
91. C2×#6101C2×C4semidirect
171. C2×Dic26C22×C4semidirect
177. C22⋊Dic13C2×Q8semidirect
178. C4⋊Dic13C22×C4semidirect
181. #6101C22×C4semidirect
208. C23×C13C4×Q8semidirect
309. C22×C13C2×C4×Q8semidirect
393. C2×C13#2360semidirect
476. C13C2×#2360semidirect
487. C23#88141semidirect
550. C22C2×#88141semidirect
575. C2#13117841direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881782
C22×#881412
#131178412
C2×#117186352
C2×#117186342
C2×#117186332
C2×#117186392
C2×#117188712
C2×C4⋊C4×Dic132
C2×C4×C22⋊Dic132
C23×C13×C4⋊C42
C2×#236013