Finite Group Databasebeta

← C2×#13117837 #16022432

Subgroups — C2×#13117837 #16022432

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×#88200C211yesmaximal, characteristic
2C22×C4⋊C4×D13C211yesmaximal, characteristic
3#13117837C2116yesmaximal, direct product factor
4C2×#11718891C211yesmaximal, characteristic, complemented
5C2×#11718589C211yesmaximal, characteristic, complemented
6C2×#11718633C212yesmaximal, complemented
7C2×#11718594C212yesmaximal, complemented
8C2×#11718650C212yesmaximal
9C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
10C2×C4×#6103C211yesmaximal, characteristic
11C2×C4×#6103C212yesmaximal
12C22×C4×Q8×C13C211yesmaximal, characteristic, complemented
13C23×Q8×C13C2211yescharacteristic
14C23×C4×D13C2212yes—
15C23×C4×D13C2211yescharacteristic
16C2×C4×Q8×C13—28no—
17C2×C4×Q8×C13C2218yescomplemented
18C22×C13×C4⋊C4C2212yes—
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C42×C13C2212yes—
21C22×C42×C13C2211yescharacteristic
22C2×#88200C4116yescomplemented
23C2×#88200C2218yes—
24C22×#6103C2211yescharacteristic
25C22×#6103C2212yes—
26C22×#6103C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×#6101C2212yes—
30C22×#6101C2212yes—
31C22×#6101C2212yes—
32C22×C4×Dic13C2211yescharacteristic
33C22×C4×Dic13C2212yes—
34C2×C4⋊C4×D13—28no—
35C2×C4⋊C4×D13C2218yes—
36#11718891C2218yescomplemented
37C2×#88071C2212yes—
38C2×#88071C2212yes—
39C2×#88071C2211yescharacteristic
40C2×#88071C2212yes—
41C2×#88071C2211yescharacteristic
42C2×#88071C2212yes—
43#11718650C22116yes—
44C4⋊C4×Dic13C2218yescomplemented
45#11718633C22116yescomplemented
46C4×#6103C22116yes—
47C4×#6103C2218yes—
48#11718594C22116yescomplemented
49#11718589C2218yescomplemented
50C24×D13C2311yescharacteristic
51C22×Q8×C13—24no—
52C22×Q8×C13—24no—
53C22×Q8×C13C2×C418yescomplemented
54C22×Q8×C13C2314yes—
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2312yes—
57C23×C4×C13C2312yes—
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×Dic13C2311yescharacteristic
61C23×Dic13C2312yes—
62C23×Dic13C2312yes—
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C22×C4×D13—24no—
66C22×C4×D13—24no—
67C22×C4×D13—28no—
68C22×C4×D13—28no—
69C22×C4×D13—44no—
70C22×C4×D13C2×C418yes—
71C22×C4×D13C2318yes—
72C22×C4×D13C2314yes—
73C4×Q8×C13—232no—
74C2×C13×C4⋊C4—28no—
75C2×C13×C4⋊C4D418yes—
76C2×C13×C4⋊C4C2318yes—
77C2×C13×C4⋊C4C2314yes—
78C2×C42×C13—28no—
79C2×C42×C13—24no—
80C2×C42×C13C2314yes—
81C2×C42×C13C2318yes—
82#88200C2×C4164yescomplemented
83C2×#6103—24no—
84C2×#6103C2×C4116yes—
85C2×#6103Q818yescomplemented
86C2×#6103C2314yes—
87C2×#6103C2318yes—
88C2×#6103C2314yes—
89C2×C4⋊Dic13—24no—
90C2×C4⋊Dic13C2×C418yescomplemented
91C2×C4⋊Dic13C2314yes—
92C2×C4⋊Dic13C2314yes—
93C2×#6101—28no—
94C2×#6101—44no—
95C2×#6101C2×C4116yescomplemented
96C2×#6101C2318yes—
97C2×#6101C2318yes—
98C2×#6101C2318yes—
99C2×C4×Dic13—24no—
100C2×C4×Dic13—44no—
101C2×C4×Dic13C2314yes—
102C2×C4×Dic13C2318yes—
103C4⋊C4×D13—232no—
104#88071C2318yes—
105#88071C2314yes—
106#88071C2318yes—
107#88071C2318yes—
108#88071C2314yes—
109#88071C2318yes—
110C2×#2360—131nomaximal, Sylow
111C24×C13C2411yescharacteristic
112C23×D13—22no—
113C23×D13—22no—
114C23×D13—22no—
115C23×D13—22no—
116C23×D13C22×C414yes—
117C23×D13C2×Q814yes—
118C23×D13#4114yes—
119C23×D13C2412yes—
120C2×Q8×C13—232no—
121C2×Q8×C13—28no—
122C2×Q8×C13—28no—
123C2×Q8×C13C22×C4116yescomplemented
124C22×C4×C13—22no—
125C22×C4×C13—24no—
126C22×C4×C13—24no—
127C22×C4×C13—24no—
128C22×C4×C13—24no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13C22×C418yes—
134C22×C4×C13C22×C414yes—
135C22×C4×C13C2×D418yes—
136C22×C4×C13C2×D414yes—
137C22×C4×C13C2×Q814yes—
138C22×C4×C13#4114yes—
139C22×C4×C13C2412yes—
140C22×C4×C13C2414yes—
141C22×C4×C13C2414yes—
142C22×C4×C13C2412yes—
143C22×C4×C13C2412yes—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—24no—
149C22×Dic13—24no—
150C22×Dic13—24no—
151C22×Dic13—22no—
152C22×Dic13—22no—
153C22×Dic13—24no—
154C22×Dic13—24no—
155C22×Dic13—22no—
156C22×Dic13C22×C414yes—
157C22×Dic13C22×C418yes—
158C22×Dic13C2×Q814yes—
159C22×Dic13C2412yes—
160C22×Dic13C2414yes—
161C22×Dic13C2414yes—
162C22×Dic13C2412yes—
163C22×Dic13C2412yes—
164C2×C4×D13—232no—
165C2×C4×D13—28no—
166C2×C4×D13—28no—
167C2×C4×D13—216no—
168C2×C4×D13—216no—
169C2×C4×D13—48no—
170C2×C4×D13—432no—
171C2×C4×D13C22×C4116yes—
172C13×C4⋊C4—216no—
173C13×C4⋊C4C2×D4116yes—
174C42×C13—216no—
175C42×C13—28no—
176#6103—28no—
177#6103C22×C4132yes—
178#6103C2×Q8116yescomplemented
179C4⋊Dic13—28no—
180C4⋊Dic13C22×C4116yescomplemented
181#6101—216no—
182#6101—48no—
183#6101C22×C4132yescomplemented
184C4×Dic13—28no—
185C4×Dic13—48no—
186C22×C22⋊Q8—131no—
187C22×C4×Q8D1311yescharacteristic, complemented
188C23×C4⋊C4—131no—
189#2360—1316no—
190C2×#391—131no—
191C2×#389—131no—
192C2×#389—132no—
193C2×#387—132no—
194C2×#385—132no—
195C2×C4×C4⋊C4—131no—
196C2×C4×C22⋊C4—132no—
197C2×C4×C22⋊C4—131no—
198C23×C13C23×C412yes—
199C23×C13C22×D412yes—
200C23×C13C22×Q812yes—
201C23×C13C2×#4112yes—
202C23×C13C2×#4112yes—
203C23×C13H(5,𝔽2)12yes—
204C23×C132−1+412yes—
205C23×C13C2511yescharacteristic
206C22×D13—28no—
207C22×D13—28no—
208C22×D13—28no—
209C22×D13—28no—
210C22×D13—28no—
211C22×D13—28no—
212C22×D13—22no—
213C22×D13—22no—
214C22×D13—22no—
215C22×D13—22no—
216C22×D13C4×Q8116yescomplemented
217C22×D13C23×C414yes—
218C22×D13C22×Q814yes—
219C22×D13C2×#4114yes—
220Q8×C13—232no—
221C2×C4×C13—216no—
222C2×C4×C13—216no—
223C2×C4×C13—28no—
224C2×C4×C13—22no—
225C2×C4×C13—24no—
226C2×C4×C13—24no—
227C2×C4×C13—24no—
228C2×C4×C13—24no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
233C2×C4×C13—44no—
234C2×C4×C13C4×D4116yes—
235C2×C4×C13C23×C418yes—
236C2×C4×C13C23×C414yes—
237C2×C4×C13C22×D418yes—
238C2×C4×C13C22×D414yes—
239C2×C4×C13C22×Q814yes—
240C2×C4×C13C2×#4114yes—
241C2×Dic13—28no—
242C2×Dic13—216no—
243C2×Dic13—28no—
244C2×Dic13—22no—
245C2×Dic13—22no—
246C2×Dic13—22no—
247C2×Dic13—22no—
248C2×Dic13—24no—
249C2×Dic13—24no—
250C2×Dic13—24no—
251C2×Dic13—22no—
252C2×Dic13—22no—
253C2×Dic13—24no—
254C2×Dic13—24no—
255C2×Dic13—22no—
256C2×Dic13—48no—
257C2×Dic13—44no—
258C2×Dic13C23×C414yes—
259C2×Dic13C23×C418yes—
260C2×Dic13C22×Q814yes—
261C4×D13—232no—
262C4×D13—432no—
263C23×Q8C2×D1311yescharacteristic
264C24×C4—131no—
265C24×C4—132no—
266C2×C22⋊Q8—1316no—
267C2×C22⋊Q8—138no—
268C2×C4×Q8—28no—
269C2×C4×Q8C2×D1318yescomplemented
270C22×C4⋊C4—132no—
271C22×C4⋊C4—131no—
272C22×C4⋊C4—132no—
273C22×C4⋊C4—131no—
274C22×C4⋊C4—132no—
275C22×C4⋊C4—138no—
276C22×C4⋊C4—268no—
277C22×C4⋊C4C2×D1312yes—
278C22×C4⋊C4C2×D1311yescharacteristic
279C22×C22⋊C4—132no—
280C22×C22⋊C4—131no—
281C22×C22⋊C4—131no—
282C22×C42—131no—
283C22×C42—132no—
284C22×C42C2×D1312yes—
285C22×C42C2×D1311yescharacteristic
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×C13C2×C4×D414yes—
301C22×C13C2×C4×Q814yes—
302C22×C13#52014yes—
303C22×C13#54614yes—
304C22×C13D4×Q814yes—
305C22×C13#55214yes—
306C22×C13#55414yes—
307C22×C13C24×C411yescharacteristic
308C22×C13C23×D411yescharacteristic
309C22×C13C23×Q811yescharacteristic
310C22×C13C22×#4111yescharacteristic
311C22×C13C22×#4111yescharacteristic
312C22×C13C2×H(5,𝔽2)11yescharacteristic
313C22×C13C2×2−1+411yescharacteristic
314C2×D13—232no—
315C2×D13—24no—
316C2×D13—24no—
317C2×D13—24no—
318C2×D13—24no—
319C2×D13—24no—
320C2×D13—24no—
321C2×D13C2×C4×Q818yescomplemented
322C4×C13—28no—
323C4×C13—28no—
324C4×C13—24no—
325C4×C13—42no—
326C4×C13C2×C4×D418yes—
327Dic13—24no—
328Dic13—28no—
329Dic13—24no—
330Dic13—44no—
331Dic13—42no—
332C25—131no—
333C22×Q8—24no—
334C22×Q8—24no—
335C22×Q8C4×D1318yescomplemented
336C22×Q8C22×D1314yes—
337C23×C4—132no—
338C23×C4—131no—
339C23×C4—131no—
340C23×C4—138no—
341C23×C4—134no—
342C23×C4—131no—
343C23×C4—132no—
344C23×C4—138no—
345C23×C4—268no—
346C23×C4—264no—
347C23×C4—264no—
348C23×C4—268no—
349C23×C4—524no—
350C23×C4C22×D1311yescharacteristic
351C23×C4C22×D1312yes—
352C23×C4C22×D1311yescharacteristic
353C23×C4C22×D1312yes—
354C23×C4C22×D1311yescharacteristic
355C22⋊Q8—1364no—
356C4×Q8—232no—
357C2×C4⋊C4—28no—
358C2×C4⋊C4—1316no—
359C2×C4⋊C4—138no—
360C2×C4⋊C4—138no—
361C2×C4⋊C4—134no—
362C2×C4⋊C4—138no—
363C2×C4⋊C4—134no—
364C2×C4⋊C4—138no—
365C2×C4⋊C4—268no—
366C2×C4⋊C4—264no—
367C2×C4⋊C4—2632no—
368C2×C4⋊C4—524no—
369C2×C4⋊C4C22⋊D1318yes—
370C2×C4⋊C4C22×D1318yes—
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—28no—
379C2×C42—24no—
380C2×C42—134no—
381C2×C42—138no—
382C2×C42—264no—
383C2×C42—524no—
384C2×C42C22×D1318yes—
385C2×C42C22×D1314yes—
386#95—134no—
387#95—138no—
388#95—134no—
389#95—138no—
390#95—138no—
391#95—138no—
392C2×C13#236018yescomplemented
393C2×C13C22×C4×D411yescharacteristic
394C2×C13C22×C4×Q811yescharacteristic
395C2×C13C2×#52011yescharacteristic
396C2×C13C2×#54611yescharacteristic
397C2×C13C2×D4×Q811yescharacteristic
398C2×C13C2×#55211yescharacteristic
399C2×C13C2×#55411yescharacteristic
400D13—28no—
401C24—134no—
402C24—134no—
403C24—134no—
404C24—132no—
405C24—262no—
406C24—262no—
407C24—262no—
408C24—262no—
409C24C23×D1311yescharacteristic
410C2×Q8—232no—
411C2×Q8—28no—
412C2×Q8—28no—
413C2×Q8C2×C4×D13116yescomplemented
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—138no—
424C22×C4—134no—
425C22×C4—134no—
426C22×C4—132no—
427C22×C4—134no—
428C22×C4—132no—
429C22×C4—1316no—
430C22×C4—132no—
431C22×C4—134no—
432C22×C4—2616no—
433C22×C4—262no—
434C22×C4—262no—
435C22×C4—264no—
436C22×C4—262no—
437C22×C4—264no—
438C22×C4—262no—
439C22×C4—2632no—
440C22×C4—268no—
441C22×C4—268no—
442C22×C4—262no—
443C22×C4—262no—
444C22×C4—262no—
445C22×C4—264no—
446C22×C4—264no—
447C22×C4—264no—
448C22×C4—2616no—
449C22×C4—528no—
450C22×C4—5232no—
451C22×C4C2×C4×D1318yes—
452C22×C4C2×C4×D1314yes—
453C22×C4#612714yes—
454C22×C4Q8×D1314yes—
455C22×C4C2×C22⋊D1318yes—
456C22×C4C2×C22⋊D1314yes—
457C22×C4C23×D1312yes—
458C22×C4C23×D1314yes—
459C22×C4C23×D1312yes—
460C22×C4C23×D1314yes—
461C22×C4C23×D1312yes—
462C4⋊C4—216no—
463C4⋊C4—1332no—
464C4⋊C4—1316no—
465C4⋊C4—2616no—
466C4⋊C4—268no—
467C4⋊C4—528no—
468C4⋊C4C2×C22⋊D13116yes—
469C22⋊C4—1332no—
470C22⋊C4—1316no—
471C22⋊C4—268no—
472C42—216no—
473C42—28no—
474C42—268no—
475C42—528no—
476C13C2×#236011yescharacteristic, complemented, Sylow
477C23—1316no—
478C23—134no—
479C23—134no—
480C23—134no—
481C23—268no—
482C23—268no—
483C23—268no—
484C23—268no—
485C23—268no—
486C23—268no—
487C23—262no—
488C23—262no—
489C23—262no—
490C23—262no—
491C23C22×C4×D1312yes—
492C23C2×#612712yes—
493C23C2×Q8×D1312yes—
494C23#8825412yes—
495C23#41×D1312yes—
496C23#8825612yes—
497C23C22×C22⋊D1312yes—
498C23C24×D1311yescharacteristic
499Q8—232no—
500C2×C4—216no—
501C2×C4—28no—
502C2×C4—216no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—44no—
513C2×C4—138no—
514C2×C4—134no—
515C2×C4—134no—
516C2×C4—268no—
517C2×C4—2616no—
518C2×C4—268no—
519C2×C4—262no—
520C2×C4—262no—
521C2×C4—264no—
522C2×C4—262no—
523C2×C4—264no—
524C2×C4—262no—
525C2×C4—2632no—
526C2×C4—262no—
527C2×C4—262no—
528C2×C4—262no—
529C2×C4—264no—
530C2×C4—264no—
531C2×C4—264no—
532C2×C4—5232no—
533C2×C4—528no—
534C2×C4—524no—
535C2×C4C4×C22⋊D13116yes—
536C2×C4C22×C4×D1318yes—
537C2×C4C22×C4×D1314yes—
538C2×C4C2×#612714yes—
539C2×C4C2×Q8×D1314yes—
540C2×C4C22×C22⋊D1318yes—
541C2×C4C22×C22⋊D1314yes—
542C22—138no—
543C22—264no—
544C22—264no—
545C22—264no—
546C22—264no—
547C22—2632no—
548C22—264no—
549C22—264no—
550C22C4×Q8×D1314yes—
551C22#1171927914yes—
552C22#1171928414yes—
553C22#1171928614yes—
554C22C2×C4×C22⋊D1314yes—
555C22Q8×C22⋊D1314yes—
556C22#1171953414yes—
557C22C23×C4×D1311yescharacteristic
558C22C22×#612711yescharacteristic
559C22C22×Q8×D1311yescharacteristic
560C22C2×#8825411yescharacteristic
561C22C2×#41×D1311yescharacteristic
562C22C2×#8825611yescharacteristic
563C22C23×C22⋊D1311yescharacteristic
564C4—28no—
565C4—28no—
566C4—24no—
567C4—42no—
568C4—264no—
569C4—268no—
570C4—264no—
571C4—524no—
572C4—522no—
573C4C2×C4×C22⋊D1318yes—
574C2—268no—
575C2#1311783718yesdirect product factor
576C2C22×C4×C22⋊D1311yescharacteristic
577C2C2×C4×Q8×D1311yescharacteristic
578C2C2×#1171927911yescharacteristic
579C2C2×#1171953411yescharacteristic
580C2C2×Q8×C22⋊D1311yescharacteristic
581C2C2×#1171928611yescharacteristic
582C2C2×#1171928411yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC22×C4×Q8×C13C2
socleC24×C13C24
prime radicalC24×D13C23
cosocleC23×C13C25
hypercenterC22×C4×Q8D13
hypocenterC13C2×#2360
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #13117837C2direct (N × H)
4. C2×#11718891C2semidirect
5. C2×#11718589C2semidirect
6. C2×#11718633C2semidirect
7. C2×#11718594C2semidirect
9. C2×C4⋊C4×Dic13C2semidirect
12. C22×C4×Q8×C13C2semidirect
17. C2×C4×Q8×C13C22semidirect
22. C2×#88200C4semidirect
36. #11718891C22semidirect
44. C4⋊C4×Dic13C22semidirect
45. #11718633C22semidirect
48. #11718594C22semidirect
49. #11718589C22semidirect
53. C22×Q8×C13C2×C4semidirect
82. #88200C2×C4semidirect
85. C2×#6103Q8semidirect
90. C2×C4⋊Dic13C2×C4semidirect
95. C2×#6101C2×C4semidirect
123. C2×Q8×C13C22×C4semidirect
178. #6103C2×Q8semidirect
180. C4⋊Dic13C22×C4semidirect
183. #6101C22×C4semidirect
187. C22×C4×Q8D13semidirect
216. C22×D13C4×Q8semidirect
269. C2×C4×Q8C2×D13semidirect
321. C2×D13C2×C4×Q8semidirect
335. C22×Q8C4×D13semidirect
392. C2×C13#2360semidirect
413. C2×Q8C2×C4×D13semidirect
476. C13C2×#2360semidirect
575. C2#13117837direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#882002
C22×C4⋊C4×D132
#131178372
C2×#117188912
C2×#117185892
C2×#117186332
C2×#117185942
C2×#117186502
C2×C4⋊C4×Dic132
C2×C4×#61032
C22×C4×Q8×C132
C2×#236013