Finite Group Databasebeta

← C2×#13117670 #16022107

Subgroups — C2×#13117670 #16022107

Order 3328.

5414 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Q8×D13C211yesmaximal, characteristic
2C22×C4×Dic26C211yesmaximal, characteristic, complemented
3C22×#88141C211yesmaximal, characteristic, complemented
4#13117670C2116yesmaximal, direct product factor
5C2×#11718891C211yesmaximal, characteristic, complemented
6C2×#11718307C212yesmaximal, complemented
7C2×#11718307C212yesmaximal, complemented
8C2×#11718328C212yesmaximal
9C2×#11718648C211yesmaximal, characteristic
10C2×C4×#6103C211yesmaximal, characteristic
11C2×#11718327C212yesmaximal
12C2×C13×#391C211yesmaximal, characteristic, complemented
13C23×Q8×C13C2211yescharacteristic
14C22×Q8×D13—28no—
15C22×Q8×D13—28no—
16C22×Q8×D13C4116yescomplemented
17C22×Q8×D13C2218yes—
18C23×C4×D13C2211yescharacteristic
19C23×C4×D13C2212yes—
20C23×Dic26C2212yes—
21C23×Dic26C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C42×C13C2211yescharacteristic
24C22×#6103C2212yes—
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×#6101C2212yes—
29C22×#6101C2212yes—
30C22×C4×Dic13C2212yes—
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2212yes—
33C2×#88141—28no—
34C2×#88141C2218yescomplemented
35C2×C4×Dic26—28no—
36C2×C4×Dic26C2218yescomplemented
37C13×#391C2218yescomplemented
38C2×C13×#95C2212yes—
39C2×C13×#95C2212yes—
40#11718891C2218yescomplemented
41C2×#88071C2212yes—
42C2×#88071C2212yes—
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2212yes—
46#11718648C2218yes—
47C4×#6103C2218yes—
48#11718328C22116yes—
49#11718327C22116yes—
50#11718307C22116yescomplemented
51#11718307C22116yescomplemented
52C24×D13C2311yescharacteristic
53C22×Q8×C13—24no—
54C22×Q8×C13—24no—
55C22×Q8×C13C2×C418yes—
56C22×Q8×C13C2314yes—
57C23×C4×C13C2312yes—
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2312yes—
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×Dic13C2311yescharacteristic
63C23×Dic13C2312yes—
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2312yes—
67C2×Q8×D13—2128no—
68C2×Q8×D13—232no—
69C2×Q8×D13—232no—
70C2×Q8×D13C2×C4164yescomplemented
71C22×C4×D13—24no—
72C22×C4×D13—24no—
73C22×C4×D13—28no—
74C22×C4×D13—28no—
75C22×C4×D13C2×C418yes—
76C22×C4×D13C2×C4116yes—
77C22×C4×D13C2318yes—
78C22×C4×D13C2314yes—
79C22×Dic26—28no—
80C22×Dic26—28no—
81C22×Dic26C2×C4116yes—
82C22×Dic26C2×C418yes—
83C22×Dic26D418yes—
84C22×Dic26D418yes—
85C22×Dic26C2318yes—
86C22×Dic26C2314yes—
87C2×C13×C4⋊C4—24no—
88C2×C13×C4⋊C4C2314yes—
89C2×C42×C13—24no—
90C2×C42×C13C2314yes—
91C2×#6103—28no—
92C2×#6103—24no—
93C2×#6103Q818yescomplemented
94C2×#6103C2318yes—
95C2×#6103C2314yes—
96C2×#6103C2314yes—
97C2×C4⋊Dic13—24no—
98C2×C4⋊Dic13C2314yes—
99C2×#6101—28no—
100C2×#6101—28no—
101C2×#6101C2318yes—
102C2×#6101C2318yes—
103C2×C4×Dic13—24no—
104C2×C4×Dic13—28no—
105C2×C4×Dic13—28no—
106C2×C4×Dic13C2318yes—
107C2×C4×Dic13C2318yes—
108C2×C4×Dic13C2314yes—
109#88141—232no—
110C4×Dic26—232no—
111C13×#95C2318yes—
112C13×#95C2318yes—
113#88071C2314yes—
114#88071C2314yes—
115#88071C2318yes—
116#88071C2318yes—
117#88071C2318yes—
118C2×Q8×C22⋊C4—131nomaximal, Sylow
119C24×C13C2411yescharacteristic
120C23×D13—22no—
121C23×D13—22no—
122C23×D13—22no—
123C23×D13—22no—
124C23×D13C22×C414yes—
125C23×D13C2×Q814yes—
126C23×D13#4114yes—
127C23×D13C2412yes—
128C2×Q8×C13—232no—
129C2×Q8×C13—28no—
130C2×Q8×C13—28no—
131C2×Q8×C13C22×C4116yes—
132C22×C4×C13—22no—
133C22×C4×C13—24no—
134C22×C4×C13—24no—
135C22×C4×C13—22no—
136C22×C4×C13—24no—
137C22×C4×C13—22no—
138C22×C4×C13—24no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—24no—
142C22×C4×C13C22×C418yes—
143C22×C4×C13C22×C414yes—
144C22×C4×C13C2×D414yes—
145C22×C4×C13C2×D414yes—
146C22×C4×C13C2×Q814yescomplemented
147C22×C4×C13C2414yes—
148C22×C4×C13C2412yes—
149C22×C4×C13C2414yes—
150C22×C4×C13C2412yes—
151C22×C4×C13C2412yes—
152C22×Dic13—22no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—24no—
158C22×Dic13—22no—
159C22×Dic13—24no—
160C22×Dic13—24no—
161C22×Dic13—22no—
162C22×Dic13C22×C414yes—
163C22×Dic13C22×C418yes—
164C22×Dic13C2×D418yes—
165C22×Dic13C2×D418yes—
166C22×Dic13C2×Q814yescomplemented
167C22×Dic13C2412yes—
168C22×Dic13C2414yes—
169C22×Dic13C2412yes—
170C22×Dic13C2412yes—
171C22×Dic13C2414yes—
172Q8×D13—2256no—
173C2×C4×D13—232no—
174C2×C4×D13—28no—
175C2×C4×D13—28no—
176C2×C4×D13—264no—
177C2×C4×D13—216no—
178C2×C4×D13—216no—
179C2×C4×D13C22×C4116yes—
180C2×C4×D13C22×C4132yes—
181C2×Dic26—264no—
182C2×Dic26—216no—
183C2×Dic26—216no—
184C2×Dic26C22⋊C4164yescomplemented
185C2×Dic26C22×C4132yes—
186C2×Dic26C22×C4116yes—
187C2×Dic26C2×D4116yes—
188C2×Dic26C2×D4116yes—
189C13×C4⋊C4—28no—
190C42×C13—28no—
191#6103—216no—
192#6103—28no—
193#6103C2×Q8116yescomplemented
194C4⋊Dic13—28no—
195#6101—216no—
196#6101—216no—
197C4×Dic13—28no—
198C4×Dic13—216no—
199C4×Dic13—216no—
200C24×Q8—131no—
201C22×C4×Q8—131no—
202C22×C4×Q8—131no—
203Q8×C22⋊C4—1316no—
204C2×#391—132no—
205C2×#391—132no—
206C2×#391—131no—
207C2×#391D1311yescharacteristic, complemented
208C2×#380—132no—
209C2×#380—131no—
210C2×C4×C22⋊C4—131no—
211C2×C4×C22⋊C4—132no—
212C23×C13C23×C412yes—
213C23×C13C22×D412yes—
214C23×C13C22×D412yes—
215C23×C13C22×Q812yes—
216C23×C13C2×#4112yes—
217C23×C132−1+412yes—
218C23×C132−1+412yes—
219C23×C13C2511yescharacteristic
220C22×D13—28no—
221C22×D13—28no—
222C22×D13—28no—
223C22×D13—28no—
224C22×D13—28no—
225C22×D13—28no—
226C22×D13—22no—
227C22×D13—22no—
228C22×D13—22no—
229C22×D13—22no—
230C22×D13C4×Q8116yescomplemented
231C22×D13C23×C414yes—
232C22×D13C22×Q814yes—
233C22×D13C2×#4114yes—
234Q8×C13—232no—
235C2×C4×C13—216no—
236C2×C4×C13—28no—
237C2×C4×C13—22no—
238C2×C4×C13—24no—
239C2×C4×C13—24no—
240C2×C4×C13—22no—
241C2×C4×C13—24no—
242C2×C4×C13—22no—
243C2×C4×C13—24no—
244C2×C4×C13—22no—
245C2×C4×C13—22no—
246C2×C4×C13—24no—
247C2×C4×C13—44no—
248C2×C4×C13—48no—
249C2×C4×C13C2×C22⋊C4116yes—
250C2×C4×C13C23×C418yes—
251C2×C4×C13C23×C414yes—
252C2×C4×C13C22×D414yes—
253C2×C4×C13C22×D414yes—
254C2×C4×C13C22×Q814yescomplemented
255C2×Dic13—28no—
256C2×Dic13—28no—
257C2×Dic13—22no—
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—22no—
261C2×Dic13—22no—
262C2×Dic13—24no—
263C2×Dic13—22no—
264C2×Dic13—24no—
265C2×Dic13—24no—
266C2×Dic13—22no—
267C2×Dic13—48no—
268C2×Dic13—44no—
269C2×Dic13C2×C22⋊C4132yes—
270C2×Dic13C23×C414yes—
271C2×Dic13C23×C418yes—
272C2×Dic13C22×D418yes—
273C2×Dic13C22×D418yes—
274C2×Dic13C22×Q814yescomplemented
275C4×D13—232no—
276C4×D13—264no—
277Dic26—264no—
278Dic26C2×C22⋊C4164yescomplemented
279C23×Q8—1316no—
280C23×Q8—138no—
281C23×Q8—131no—
282C23×Q8—132no—
283C23×Q8—268no—
284C23×Q8—268no—
285C23×Q8C2×D1311yescharacteristic
286C24×C4—132no—
287C24×C4—131no—
288C2×C4×Q8—138no—
289C2×C4×Q8—138no—
290C2×C4×Q8—268no—
291C2×C4×Q8—268no—
292C22×C4⋊C4—132no—
293C22×C4⋊C4—132no—
294C22×C4⋊C4—131no—
295C22×C4⋊C4C2×D1311yescharacteristic
296C22×C22⋊C4—131no—
297C22×C22⋊C4—131no—
298C22×C22⋊C4—132no—
299C22×C42—132no—
300C22×C42—132no—
301C22×C42—131no—
302C22×C42C2×D1311yescharacteristic
303#391—138no—
304#391—1316no—
305#391—1316no—
306#391C2×D1318yescomplemented
307#380—138no—
308#380—1316no—
309C4×C22⋊C4—138no—
310C4×C22⋊C4—1316no—
311C2×#95—131no—
312C2×#95—132no—
313C2×#95—131no—
314C2×#95—132no—
315C2×#95—132no—
316C2×#95C2×D1312yes—
317C2×#95C2×D1312yes—
318C22×C13C22×C22⋊C414yes—
319C22×C13C2×C4×Q814yes—
320C22×C13#51914yes—
321C22×C13#54814yes—
322C22×C13#54814yes—
323C22×C13D4×Q814yes—
324C22×C13D4×Q814yes—
325C22×C13C24×C411yescharacteristic
326C22×C13C23×D411yescharacteristic
327C22×C13C23×D411yescharacteristic
328C22×C13C23×Q811yescharacteristic
329C22×C13C22×#4111yescharacteristic
330C22×C13C2×2−1+411yescharacteristic
331C22×C13C2×2−1+411yescharacteristic
332C2×D13—232no—
333C2×D13—24no—
334C2×D13—24no—
335C2×D13—24no—
336C2×D13—24no—
337C2×D13—24no—
338C2×D13—24no—
339C2×D13C2×C4×Q818yescomplemented
340C4×C13—28no—
341C4×C13—24no—
342C4×C13—44no—
343C4×C13—42no—
344C4×C13C22×C22⋊C418yes—
345Dic13—24no—
346Dic13—24no—
347Dic13—42no—
348Dic13—44no—
349Dic13C22×C22⋊C4116yes—
350C25—131no—
351C22×Q8—24no—
352C22×Q8—24no—
353C22×Q8—1364no—
354C22×Q8—138no—
355C22×Q8—1316no—
356C22×Q8—138no—
357C22×Q8—138no—
358C22×Q8—134no—
359C22×Q8—138no—
360C22×Q8—268no—
361C22×Q8—268no—
362C22×Q8—26128no—
363C22×Q8—2632no—
364C22×Q8—2632no—
365C22×Q8C4×D1318yes—
366C22×Q8C22×D1314yes—
367C23×C4—132no—
368C23×C4—131no—
369C23×C4—131no—
370C23×C4—1316no—
371C23×C4—138no—
372C23×C4—138no—
373C23×C4—134no—
374C23×C4—132no—
375C23×C4—131no—
376C23×C4—268no—
377C23×C4—268no—
378C23×C4—264no—
379C23×C4—264no—
380C23×C4C22×D1311yescharacteristic
381C23×C4C22×D1312yes—
382C23×C4C22×D1312yes—
383C23×C4C22×D1311yescharacteristic
384C23×C4C22×D1311yescharacteristic
385C4×Q8—2632no—
386C4×Q8—2632no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—138no—
389C2×C4⋊C4—138no—
390C2×C4⋊C4—134no—
391C2×C4⋊C4—268no—
392C2×C4⋊C4—268no—
393C2×C4⋊C4—264no—
394C2×C4⋊C4C22×D1314yes—
395C2×C22⋊C4—138no—
396C2×C22⋊C4—134no—
397C2×C22⋊C4—138no—
398C2×C22⋊C4—134no—
399C2×C22⋊C4—264no—
400C2×C22⋊C4—268no—
401C2×C42—24no—
402C2×C42—138no—
403C2×C42—138no—
404C2×C42—134no—
405C2×C42—268no—
406C2×C42—268no—
407C2×C42—264no—
408C2×C42C22×D1314yes—
409#95—134no—
410#95—134no—
411#95—138no—
412#95—138no—
413#95—138no—
414#95C22×D1318yes—
415#95C22×D1318yes—
416C2×C13Q8×C22⋊C418yescomplemented
417C2×C13C23×C22⋊C411yescharacteristic
418C2×C13C22×C4×Q811yescharacteristic
419C2×C13C2×#51911yescharacteristic
420C2×C13C2×#54811yescharacteristic
421C2×C13C2×#54811yescharacteristic
422C2×C13C2×D4×Q811yescharacteristic
423C2×C13C2×D4×Q811yescharacteristic
424D13—28no—
425C24—134no—
426C24—134no—
427C24—134no—
428C24—132no—
429C24—262no—
430C24—262no—
431C24—262no—
432C24—262no—
433C24C23×D1311yescharacteristic
434C2×Q8—232no—
435C2×Q8—28no—
436C2×Q8—28no—
437C2×Q8—1364no—
438C2×Q8—1316no—
439C2×Q8—1332no—
440C2×Q8—1316no—
441C2×Q8—1316no—
442C2×Q8—2664no—
443C2×Q8—2616no—
444C2×Q8—2616no—
445C2×Q8—26256no—
446C2×Q8C2×C4×D13116yes—
447C22×C4—22no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—24no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—138no—
458C22×C4—138no—
459C22×C4—138no—
460C22×C4—134no—
461C22×C4—134no—
462C22×C4—134no—
463C22×C4—132no—
464C22×C4—132no—
465C22×C4—1332no—
466C22×C4—1316no—
467C22×C4—134no—
468C22×C4—132no—
469C22×C4—2664no—
470C22×C4—2616no—
471C22×C4—2616no—
472C22×C4—262no—
473C22×C4—262no—
474C22×C4—262no—
475C22×C4—262no—
476C22×C4—2632no—
477C22×C4—268no—
478C22×C4—268no—
479C22×C4—264no—
480C22×C4—262no—
481C22×C4—264no—
482C22×C4—264no—
483C22×C4—262no—
484C22×C4—262no—
485C22×C4C2×C4×D1318yes—
486C22×C4C2×C4×D1314yes—
487C22×C4D4×D1314yes—
488C22×C4D4×D1314yes—
489C22×C4Q8×D1314yescomplemented
490C22×C4C23×D1314yes—
491C22×C4C23×D1312yes—
492C22×C4C23×D1314yes—
493C22×C4C23×D1312yes—
494C22×C4C23×D1312yes—
495C4⋊C4—28no—
496C4⋊C4—2616no—
497C4⋊C4—2616no—
498C4⋊C4—268no—
499C22⋊C4—1316no—
500C22⋊C4—2616no—
501C22⋊C4—268no—
502C42—28no—
503C42—2616no—
504C42—2616no—
505C42—268no—
506C13C2×Q8×C22⋊C411yescharacteristic, complemented, Sylow
507C23—1316no—
508C23—134no—
509C23—134no—
510C23—134no—
511C23—268no—
512C23—268no—
513C23—268no—
514C23—268no—
515C23—268no—
516C23—268no—
517C23—262no—
518C23—262no—
519C23—262no—
520C23—262no—
521C23C22×C4×D1312yes—
522C23C2×D4×D1312yes—
523C23C2×D4×D1312yes—
524C23C2×Q8×D1312yes—
525C23#8825412yes—
526C23#41×D1312yes—
527C23#8825712yes—
528C23C24×D1311yescharacteristic
529Q8—232no—
530Q8—1364no—
531Q8—2664no—
532C2×C4—216no—
533C2×C4—28no—
534C2×C4—22no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—44no—
545C2×C4—48no—
546C2×C4—1332no—
547C2×C4—138no—
548C2×C4—138no—
549C2×C4—138no—
550C2×C4—134no—
551C2×C4—134no—
552C2×C4—2664no—
553C2×C4—268no—
554C2×C4—268no—
555C2×C4—262no—
556C2×C4—262no—
557C2×C4—262no—
558C2×C4—262no—
559C2×C4—2632no—
560C2×C4—262no—
561C2×C4—264no—
562C2×C4—264no—
563C2×C4—262no—
564C2×C4—264no—
565C2×C4—262no—
566C2×C4—528no—
567C2×C4—524no—
568C2×C4C22⋊C4×D13116yes—
569C2×C4C22×C4×D1318yes—
570C2×C4C22×C4×D1314yes—
571C2×C4C2×D4×D1314yes—
572C2×C4C2×D4×D1314yes—
573C2×C4C2×Q8×D1314yescomplemented
574C22—138no—
575C22—264no—
576C22—264no—
577C22—264no—
578C22—264no—
579C22—264no—
580C22—264no—
581C22—2632no—
582C22C2×C22⋊C4×D1314yes—
583C22C4×Q8×D1314yes—
584C22#1171927714yes—
585C22#1171933714yes—
586C22#1171933814yes—
587C22#1171938214yes—
588C22#1171943214yes—
589C22C23×C4×D1311yescharacteristic
590C22C22×D4×D1311yescharacteristic
591C22C22×D4×D1311yescharacteristic
592C22C22×Q8×D1311yescharacteristic
593C22C2×#8825411yescharacteristic
594C22C2×#41×D1311yescharacteristic
595C22C2×#8825711yescharacteristic
596C4—28no—
597C4—24no—
598C4—44no—
599C4—42no—
600C4—1316no—
601C4—264no—
602C4—264no—
603C4—522no—
604C4—524no—
605C4C2×C22⋊C4×D1318yes—
606C2—268no—
607C2#1311767018yesdirect product factor
608C2C22×C22⋊C4×D1311yescharacteristic
609C2C2×C4×Q8×D1311yescharacteristic
610C2C2×#1171927711yescharacteristic
611C2C2×#1171938211yescharacteristic
612C2C2×#1171933811yescharacteristic
613C2C2×#1171933711yescharacteristic
614C2C2×#1171943211yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#391C2
socleC24×C13C24
prime radicalC24×D13C23
cosocleC23×C13C25
hypercenterC2×#391D13
hypocenterC13C2×Q8×C22⋊C4
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic26C2semidirect
3. C22×#88141C2semidirect
4. #13117670C2direct (N × H)
5. C2×#11718891C2semidirect
6. C2×#11718307C2semidirect
7. C2×#11718307C2semidirect
12. C2×C13×#391C2semidirect
16. C22×Q8×D13C4semidirect
34. C2×#88141C22semidirect
36. C2×C4×Dic26C22semidirect
37. C13×#391C22semidirect
40. #11718891C22semidirect
50. #11718307C22semidirect
51. #11718307C22semidirect
70. C2×Q8×D13C2×C4semidirect
93. C2×#6103Q8semidirect
146. C22×C4×C13C2×Q8semidirect
166. C22×Dic13C2×Q8semidirect
184. C2×Dic26C22⋊C4semidirect
193. #6103C2×Q8semidirect
207. C2×#391D13semidirect
230. C22×D13C4×Q8semidirect
254. C2×C4×C13C22×Q8semidirect
274. C2×Dic13C22×Q8semidirect
278. Dic26C2×C22⋊C4semidirect
306. #391C2×D13semidirect
339. C2×D13C2×C4×Q8semidirect
416. C2×C13Q8×C22⋊C4semidirect
489. C22×C4Q8×D13semidirect
506. C13C2×Q8×C22⋊C4semidirect
573. C2×C4C2×Q8×D13semidirect
607. C2#13117670direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Q8×D132
C22×C4×Dic262
C22×#881412
#131176702
C2×#117188912
C2×#117183072
C2×#117183282
C2×#117186482
C2×C4×#61032
C2×#117183272
C2×C13×#3912
C2×Q8×C22⋊C413