Finite Group Databasebeta

← C2×#13118534 #16030745

Subgroups — C2×#13118534 #16030745

Order 3328.

3550 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×#88200C212yesmaximal
2C22×C4⋊C4×D13C211yesmaximal, characteristic
3#13118534C2116yesmaximal, direct product factor
4C2×#11718645C212yesmaximal, complemented
5C2×#11718890C212yesmaximal, complemented
6C2×#11718646C211yesmaximal, characteristic, complemented
7C2×#11718589C211yesmaximal, characteristic, complemented
8C2×#11718650C212yesmaximal
9C2×#11718637C211yesmaximal, characteristic, complemented
10C2×#11718648C211yesmaximal, characteristic
11C2×C4×#6103C211yesmaximal, characteristic
12C22×C13×C4⋊Q8C211yesmaximal, characteristic, complemented
13C23×Q8×C13C2212yes—
14C23×C4×D13C2212yes—
15C23×C4×D13C2211yescharacteristic
16C2×C13×C4⋊Q8—28no—
17C2×C13×C4⋊Q8C2218yescomplemented
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2212yes—
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C42×C13C2211yescharacteristic
22C2×#88200—216no—
23C2×#88200C22116yes—
24C22×#6103C2212yes—
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×C4⋊Dic13C2212yes—
30C22×#6101C2212yes—
31C22×#6101C2212yes—
32C22×#6101C2212yes—
33C22×#6101C2212yes—
34C22×C4×Dic13C2211yescharacteristic
35C2×C4⋊C4×D13—28no—
36C2×C4⋊C4×D13C2218yes—
37#11718890C22116yescomplemented
38C2×#88071C2212yes—
39C2×#88071C2212yes—
40C2×#88071C2212yes—
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43#11718650C22116yes—
44#11718648C2218yes—
45#11718646C2218yescomplemented
46#11718645C22116yescomplemented
47#11718637C2218yescomplemented
48C4×#6103C2218yes—
49#11718589C2218yescomplemented
50C24×D13C2311yescharacteristic
51C22×Q8×C13—28no—
52C22×Q8×C13—28no—
53C22×Q8×C13—44no—
54C22×Q8×C13C2318yes—
55C23×C4×C13C2312yes—
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2312yes—
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×Dic13C2312yes—
61C23×Dic13C2312yes—
62C23×Dic13C2311yescharacteristic
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×D13Q818yescomplemented
71C22×C4×D13C2318yes—
72C22×C4×D13C2314yes—
73C13×C4⋊Q8—232no—
74C2×C13×C4⋊C4—28no—
75C2×C13×C4⋊C4—24no—
76C2×C13×C4⋊C4D418yes—
77C2×C13×C4⋊C4C2314yes—
78C2×C13×C4⋊C4C2318yes—
79C2×C13×C4⋊C4C2314yes—
80C2×C42×C13—24no—
81C2×C42×C13C2314yes—
82#88200—264no—
83C2×#6103—28no—
84C2×#6103D418yes—
85C2×#6103Q818yescomplemented
86C2×#6103C2318yes—
87C2×#6103C2314yes—
88C2×#6103C2314yes—
89C2×C4⋊Dic13—24no—
90C2×C4⋊Dic13—24no—
91C2×C4⋊Dic13—28no—
92C2×C4⋊Dic13C2314yes—
93C2×C4⋊Dic13C2318yes—
94C2×C4⋊Dic13C2314yes—
95C2×#6101—28no—
96C2×#6101—28no—
97C2×#6101—28no—
98C2×#6101—44no—
99C2×#6101C2318yes—
100C2×#6101C2318yes—
101C2×#6101C2318yes—
102C2×#6101C2318yes—
103C2×C4×Dic13—24no—
104C2×C4×Dic13C2314yes—
105C4⋊C4×D13—232no—
106#88071C2318yes—
107#88071C2314yes—
108#88071C2314yes—
109#88071C2318yes—
110#88071C2318yes—
111C2×#2440—131nomaximal, Sylow
112C24×C13C2411yescharacteristic
113C23×D13—22no—
114C23×D13—22no—
115C23×D13—22no—
116C23×D13—22no—
117C23×D13C2×D414yes—
118C23×D13C2×Q814yes—
119C23×D13C2×Q814yes—
120C23×D13C2412yes—
121C2×Q8×C13—216no—
122C2×Q8×C13—216no—
123C2×Q8×C13—48no—
124C2×Q8×C13—432no—
125C22×C4×C13—24no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—24no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—24no—
132C22×C4×C13—24no—
133C22×C4×C13—24no—
134C22×C4×C13C2×D414yes—
135C22×C4×C13C2×D418yes—
136C22×C4×C13C2×D414yes—
137C22×C4×C13C2×Q814yes—
138C22×C4×C13C2×Q814yes—
139C22×C4×C13#4114yes—
140C22×C4×C13C2414yes—
141C22×C4×C13C2412yes—
142C22×C4×C13C2414yes—
143C22×C4×C13C2412yes—
144C22×C4×C13C2412yes—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—24no—
152C22×Dic13—24no—
153C22×Dic13—24no—
154C22×Dic13—24no—
155C22×Dic13—24no—
156C22×Dic13—24no—
157C22×Dic13C2×D414yes—
158C22×Dic13C2×Q814yes—
159C22×Dic13C2×Q814yes—
160C22×Dic13C2414yes—
161C22×Dic13C2414yes—
162C22×Dic13C2412yes—
163C22×Dic13C2412yes—
164C22×Dic13C2412yes—
165C2×C4×D13—232no—
166C2×C4×D13—28no—
167C2×C4×D13—28no—
168C2×C4×D13—216no—
169C2×C4×D13—216no—
170C2×C4×D13—48no—
171C2×C4×D13—432no—
172C2×C4×D13C2×Q8116yescomplemented
173C13×C4⋊C4—216no—
174C13×C4⋊C4—28no—
175C13×C4⋊C4C2×D4116yes—
176C42×C13—28no—
177#6103—216no—
178#6103C2×D4116yes—
179#6103C2×Q8116yescomplemented
180C4⋊Dic13—28no—
181C4⋊Dic13—28no—
182C4⋊Dic13—216no—
183#6101—216no—
184#6101—216no—
185#6101—216no—
186#6101—48no—
187C4×Dic13—28no—
188C22×C4⋊Q8D1311yescharacteristic, complemented
189C22×C22⋊Q8—132no—
190C23×C4⋊C4—131no—
191#2440—1316no—
192C2×#398—132no—
193C2×#395—132no—
194C2×#389—131no—
195C2×#389—131no—
196C2×#385—132no—
197C2×#384—131no—
198C2×#380—131no—
199C2×C4×C22⋊C4—131no—
200C23×C13C22×D412yes—
201C23×C13C22×D412yes—
202C23×C13C22×Q812yes—
203C23×C13C22×Q812yes—
204C23×C13C2×#4112yes—
205C23×C13H(5,𝔽2)12yes—
206C23×C132−1+412yes—
207C23×C13C2511yescharacteristic
208C22×D13—28no—
209C22×D13—28no—
210C22×D13—28no—
211C22×D13—28no—
212C22×D13—28no—
213C22×D13—28no—
214C22×D13—22no—
215C22×D13—22no—
216C22×D13—22no—
217C22×D13—22no—
218C22×D13C4⋊Q8116yescomplemented
219C22×D13C22×D414yes—
220C22×D13C22×Q814yes—
221C22×D13C22×Q814yes—
222Q8×C13—432no—
223C2×C4×C13—216no—
224C2×C4×C13—28no—
225C2×C4×C13—28no—
226C2×C4×C13—24no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—24no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—24no—
233C2×C4×C13—24no—
234C2×C4×C13—24no—
235C2×C4×C13—48no—
236C2×C4×C13C22⋊Q8116yescomplemented
237C2×C4×C13C22×D414yes—
238C2×C4×C13C22×D418yes—
239C2×C4×C13C22×D414yes—
240C2×C4×C13C22×Q814yes—
241C2×C4×C13C22×Q814yes—
242C2×C4×C13C2×#4114yes—
243C2×Dic13—28no—
244C2×Dic13—28no—
245C2×Dic13—28no—
246C2×Dic13—22no—
247C2×Dic13—22no—
248C2×Dic13—22no—
249C2×Dic13—22no—
250C2×Dic13—22no—
251C2×Dic13—22no—
252C2×Dic13—24no—
253C2×Dic13—24no—
254C2×Dic13—24no—
255C2×Dic13—24no—
256C2×Dic13—24no—
257C2×Dic13—24no—
258C2×Dic13—48no—
259C2×Dic13—48no—
260C2×Dic13C22×D414yes—
261C2×Dic13C22×Q814yes—
262C2×Dic13C22×Q814yes—
263C4×D13—232no—
264C4×D13—432no—
265C23×Q8C2×D1312yes—
266C24×C4—131no—
267C24×C4—132no—
268C2×C4⋊Q8—28no—
269C2×C4⋊Q8C2×D1318yescomplemented
270C2×C22⋊Q8—1316no—
271C2×C22⋊Q8—2616no—
272C22×C4⋊C4—132no—
273C22×C4⋊C4—132no—
274C22×C4⋊C4—132no—
275C22×C4⋊C4—132no—
276C22×C4⋊C4—131no—
277C22×C4⋊C4—131no—
278C22×C4⋊C4—132no—
279C22×C4⋊C4—138no—
280C22×C4⋊C4—268no—
281C22×C4⋊C4C2×D1312yes—
282C22×C4⋊C4C2×D1311yescharacteristic
283C22×C4⋊C4C2×D1311yescharacteristic
284C22×C22⋊C4—131no—
285C22×C22⋊C4—131no—
286C22×C22⋊C4—132no—
287C22×C42—131no—
288C22×C42C2×D1311yescharacteristic
289#398—1316no—
290#395—1316no—
291#389—138no—
292#389—138no—
293#385—1316no—
294#384—138no—
295#380—138no—
296C4×C22⋊C4—138no—
297C2×#95—131no—
298C2×#95—132no—
299C2×#95—132no—
300C2×#95—131no—
301C2×#95—132no—
302C22×C13C2×C22⋊Q814yes—
303C22×C13C2×C4⋊Q814yes—
304C22×C13#54414yes—
305C22×C13D4214yes—
306C22×C13#54714yes—
307C22×C13D4×Q814yes—
308C22×C13#55414yes—
309C22×C13C23×D411yescharacteristic
310C22×C13C23×D411yescharacteristic
311C22×C13C23×Q811yescharacteristic
312C22×C13C23×Q811yescharacteristic
313C22×C13C22×#4111yescharacteristic
314C22×C13C2×H(5,𝔽2)11yescharacteristic
315C22×C13C2×2−1+411yescharacteristic
316C2×D13—24no—
317C2×D13—24no—
318C2×D13—24no—
319C2×D13—232no—
320C2×D13—24no—
321C2×D13—24no—
322C2×D13—24no—
323C2×D13C2×C4⋊Q818yescomplemented
324C4×C13—28no—
325C4×C13—24no—
326C4×C13—24no—
327C4×C13—44no—
328C4×C13C2×C22⋊Q818yescomplemented
329Dic13—24no—
330Dic13—24no—
331Dic13—24no—
332Dic13—44no—
333Dic13—44no—
334C25—131no—
335C22×Q8—28no—
336C22×Q8—28no—
337C22×Q8—44no—
338C22×Q8C22×D1318yes—
339C23×C4—131no—
340C23×C4—131no—
341C23×C4—131no—
342C23×C4—138no—
343C23×C4—134no—
344C23×C4—132no—
345C23×C4—132no—
346C23×C4—138no—
347C23×C4—268no—
348C23×C4—264no—
349C23×C4—264no—
350C23×C4—268no—
351C23×C4—524no—
352C23×C4C22×D1312yes—
353C23×C4C22×D1311yescharacteristic
354C23×C4C22×D1311yescharacteristic
355C23×C4C22×D1312yes—
356C23×C4C22×D1311yescharacteristic
357C4⋊Q8—232no—
358C22⋊Q8—2664no—
359C2×C4⋊C4—28no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—138no—
362C2×C4⋊C4—134no—
363C2×C4⋊C4—138no—
364C2×C4⋊C4—138no—
365C2×C4⋊C4—138no—
366C2×C4⋊C4—134no—
367C2×C4⋊C4—138no—
368C2×C4⋊C4—268no—
369C2×C4⋊C4—268no—
370C2×C4⋊C4—268no—
371C2×C4⋊C4—264no—
372C2×C4⋊C4—268no—
373C2×C4⋊C4—264no—
374C2×C4⋊C4—2632no—
375C2×C4⋊C4—524no—
376C2×C4⋊C4C22⋊D1318yes—
377C2×C4⋊C4C22×D1314yes—
378C2×C4⋊C4C22×D1318yes—
379C2×C4⋊C4C22×D1314yes—
380C2×C22⋊C4—138no—
381C2×C22⋊C4—138no—
382C2×C22⋊C4—134no—
383C2×C22⋊C4—134no—
384C2×C22⋊C4—138no—
385C2×C22⋊C4—268no—
386C2×C42—24no—
387C2×C42—134no—
388C2×C42—264no—
389C2×C42C22×D1314yes—
390#95—134no—
391#95—134no—
392#95—138no—
393#95—138no—
394#95—138no—
395C2×C13#244018yescomplemented
396C2×C13C22×C22⋊Q811yescharacteristic
397C2×C13C22×C4⋊Q811yescharacteristic
398C2×C13C2×#54411yescharacteristic
399C2×C13C2×D4211yescharacteristic
400C2×C13C2×#54711yescharacteristic
401C2×C13C2×D4×Q811yescharacteristic
402C2×C13C2×#55411yescharacteristic
403D13—28no—
404C24—134no—
405C24—134no—
406C24—134no—
407C24—132no—
408C24—262no—
409C24—262no—
410C24—262no—
411C24—262no—
412C24C23×D1311yescharacteristic
413C2×Q8—216no—
414C2×Q8—216no—
415C2×Q8—48no—
416C2×Q8—432no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—134no—
427C22×C4—134no—
428C22×C4—134no—
429C22×C4—132no—
430C22×C4—132no—
431C22×C4—132no—
432C22×C4—1316no—
433C22×C4—134no—
434C22×C4—134no—
435C22×C4—2616no—
436C22×C4—262no—
437C22×C4—262no—
438C22×C4—262no—
439C22×C4—262no—
440C22×C4—262no—
441C22×C4—262no—
442C22×C4—2632no—
443C22×C4—268no—
444C22×C4—268no—
445C22×C4—264no—
446C22×C4—264no—
447C22×C4—264no—
448C22×C4—264no—
449C22×C4—264no—
450C22×C4—264no—
451C22×C4—2616no—
452C22×C4—528no—
453C22×C4—5232no—
454C22×C4D4×D1314yes—
455C22×C4Q8×D1314yes—
456C22×C4Q8×D1314yes—
457C22×C4#613114yes—
458C22×C4C2×C22⋊D1318yes—
459C22×C4C2×C22⋊D1314yes—
460C22×C4C23×D1314yes—
461C22×C4C23×D1312yes—
462C22×C4C23×D1312yes—
463C22×C4C23×D1314yes—
464C22×C4C23×D1312yes—
465C4⋊C4—216no—
466C4⋊C4—28no—
467C4⋊C4—2616no—
468C4⋊C4—2616no—
469C4⋊C4—2616no—
470C4⋊C4—268no—
471C4⋊C4—2616no—
472C4⋊C4—268no—
473C4⋊C4—528no—
474C4⋊C4C2×C22⋊D13116yes—
475C22⋊C4—1316no—
476C22⋊C4—1316no—
477C22⋊C4—2616no—
478C42—28no—
479C42—268no—
480C13C2×#244011yescharacteristic, complemented, Sylow
481C23—1316no—
482C23—134no—
483C23—134no—
484C23—134no—
485C23—268no—
486C23—268no—
487C23—268no—
488C23—268no—
489C23—268no—
490C23—268no—
491C23—262no—
492C23—262no—
493C23—262no—
494C23—262no—
495C23C2×D4×D1312yes—
496C23#8825112yes—
497C23C2×Q8×D1312yes—
498C23C2×Q8×D1312yes—
499C23C2×#613112yes—
500C23#8825412yes—
501C23C22×C22⋊D1312yes—
502C23C24×D1311yescharacteristic
503Q8—432no—
504C2×C4—216no—
505C2×C4—28no—
506C2×C4—28no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—48no—
517C2×C4—134no—
518C2×C4—134no—
519C2×C4—134no—
520C2×C4—268no—
521C2×C4—268no—
522C2×C4—268no—
523C2×C4—262no—
524C2×C4—262no—
525C2×C4—262no—
526C2×C4—262no—
527C2×C4—262no—
528C2×C4—262no—
529C2×C4—2632no—
530C2×C4—264no—
531C2×C4—264no—
532C2×C4—264no—
533C2×C4—264no—
534C2×C4—264no—
535C2×C4—264no—
536C2×C4—5232no—
537C2×C4—528no—
538C2×C4—528no—
539C2×C4#88200116yescomplemented
540C2×C4C2×D4×D1314yes—
541C2×C4C2×Q8×D1314yes—
542C2×C4C2×Q8×D1314yes—
543C2×C4C2×#613114yes—
544C2×C4C22×C22⋊D1318yes—
545C2×C4C22×C22⋊D1314yes—
546C22—138no—
547C22—264no—
548C22—2632no—
549C22—264no—
550C22—264no—
551C22—264no—
552C22—264no—
553C22—264no—
554C22D13×C4⋊Q814yes—
555C22#1171943114yes—
556C22#1171943414yes—
557C22#1171943514yes—
558C22D4×C22⋊D1314yes—
559C22C2×#8820014yes—
560C22Q8×C22⋊D1314yes—
561C22C22×D4×D1311yescharacteristic
562C22C2×#8825111yescharacteristic
563C22C22×Q8×D1311yescharacteristic
564C22C22×Q8×D1311yescharacteristic
565C22C22×#613111yescharacteristic
566C22C2×#8825411yescharacteristic
567C22C23×C22⋊D1311yescharacteristic
568C4—28no—
569C4—24no—
570C4—24no—
571C4—44no—
572C4—264no—
573C4—264no—
574C4—264no—
575C4—524no—
576C4—524no—
577C4C2×#8820018yescomplemented
578C2—268no—
579C2#1311853418yesdirect product factor
580C2C22×#8820011yescharacteristic
581C2C2×D13×C4⋊Q811yescharacteristic
582C2C2×#1171943411yescharacteristic
583C2C2×D4×C22⋊D1311yescharacteristic
584C2C2×#1171943111yescharacteristic
585C2C2×Q8×C22⋊D1311yescharacteristic
586C2C2×#1171943511yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×C4⋊Q8C2
socleC24×C13C24
prime radicalC24×D13C23
hypercenterC22×C4⋊Q8D13
hypocenterC13C2×#2440
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13118534C2direct (N × H)
4. C2×#11718645C2semidirect
5. C2×#11718890C2semidirect
6. C2×#11718646C2semidirect
7. C2×#11718589C2semidirect
9. C2×#11718637C2semidirect
12. C22×C13×C4⋊Q8C2semidirect
17. C2×C13×C4⋊Q8C22semidirect
37. #11718890C22semidirect
45. #11718646C22semidirect
46. #11718645C22semidirect
47. #11718637C22semidirect
49. #11718589C22semidirect
70. C22×C4×D13Q8semidirect
85. C2×#6103Q8semidirect
172. C2×C4×D13C2×Q8semidirect
179. #6103C2×Q8semidirect
188. C22×C4⋊Q8D13semidirect
218. C22×D13C4⋊Q8semidirect
236. C2×C4×C13C22⋊Q8semidirect
269. C2×C4⋊Q8C2×D13semidirect
323. C2×D13C2×C4⋊Q8semidirect
328. C4×C13C2×C22⋊Q8semidirect
395. C2×C13#2440semidirect
480. C13C2×#2440semidirect
539. C2×C4#88200semidirect
577. C4C2×#88200semidirect
579. C2#13118534direct (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
#131185342
C2×#117186452
C2×#117188902
C2×#117186462
C2×#117185892
C2×#117186502
C2×#117186372
C2×#117186482
C2×C4×#61032
C22×C13×C4⋊Q82
C2×#244013