Finite Group Databasebeta

← #16028178

Subgroups — #16028178

Order 3328.

2244 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic26C211yesmaximal, characteristic
2#13118003C214yesmaximal, complemented
3#13117923C212yesmaximal, complemented
4#13117894C211yesmaximal, characteristic, complemented
5#13117863C212yesmaximal, complemented
6#13117808C212yesmaximal
7#13117795C211yesmaximal, characteristic, complemented
8#13117668C212yesmaximal, complemented
9#13117586C214yesmaximal, complemented
10#13117580C212yesmaximal, complemented
11#13117514C212yesmaximal, complemented
12#13117473C212yesmaximal
13#13117420C212yesmaximal, complemented
14#13117403C211yesmaximal, characteristic, complemented
15#13117310C211yesmaximal, characteristic, complemented
16#13117301C211yesmaximal, characteristic
17C13×#2354C211yesmaximal, characteristic
18C23×Dic26C2212yes—
19C2×C4×D4×C13C2211yescharacteristic
20C2×C13×#117C2212yes—
21C2×D4×Dic13C2212yes—
22C2×#88180C2212yes—
23C2×#88178C2212yes—
24D4×Dic26C4116yescomplemented
25C2×#88142C2212yes—
26C2×#88141C2212yes—
27C2×#88141C2212yes—
28C2×#88132C2214yes—
29C2×#88123C2211yescharacteristic
30C2×C4×Dic26C2211yescharacteristic
31C13×#390C2212yes—
32C13×#388C2214yes—
33C13×#384C2211yescharacteristic
34C13×#380C2212yes—
35C4×C13×C4⋊C4C2211yescharacteristic
36C4×C13×C4⋊C4C2212yes—
37#11718882C2211yescharacteristic
38#11718882C2211yescharacteristic
39C4×C22⋊Dic13C2212yes—
40#11718646C2211yescharacteristic
41#11718646C2211yescharacteristic
42#11718639C2214yes—
43#11718638C2212yes—
44C4⋊C4×Dic13C2212yes—
45C4⋊C4×Dic13C2212yes—
46C4⋊C4×Dic13C2212yes—
47C4⋊C4×Dic13C2212yes—
48#11718635C2212yes—
49#11718635C2212yes—
50#11718635C2211yescharacteristic
51#11718635C2211yescharacteristic
52#11718635C2212yes—
53#11718634C2212yes—
54#11718634C2212yes—
55#11718634C2211yescharacteristic
56#11718634C2211yescharacteristic
57#11718612C2212yes—
58#11718612C2212yes—
59#11718606C2214yes—
60#11718606C2214yes—
61#11718605C2214yes—
62#11718605C2214yes—
63#11718604C2214yes—
64#11718604C2214yes—
65#11718603C2214yes—
66C22⋊C4×Dic13C2214yes—
67C4×C4⋊Dic13C2211yescharacteristic
68C4×C4⋊Dic13C2212yes—
69#11718594C2214yes—
70#11718593C2212yes—
71C4×#6101C2212yes—
72C4×#6101C2214yes—
73C42×Dic13C2211yescharacteristic
74#11718590C2214yes—
75#11718590C2214yes—
76#11718589C2212yes—
77#11718316C2214yes—
78#11718314C2214yes—
79#11718313C2212yes—
80#11718313C2212yes—
81#11718308C2214yes—
82#11718307C2214yes—
83#11718307C2214yes—
84C22×D4×C13C2311yescharacteristic
85C23×C4×C13C2312yes—
86C23×Dic13C2314yes—
87C22×Dic26—44no—
88C22×Dic26—44no—
89C22×Dic26C2×C4116yes—
90C22×Dic26C2311yescharacteristic
91C22×Dic26C2312yes—
92C22×Dic26C2314yes—
93C4×D4×C13C2×C418yes—
94C13×#117—44no—
95C2×C13×C4⋊C4C2311yescharacteristic
96C2×C13×C4⋊C4C2312yes—
97C2×C13×C4⋊C4C2311yescharacteristic
98C2×C13×C4⋊C4C2312yes—
99C2×C13×C4⋊C4C2312yes—
100C2×C13×C4⋊C4C2311yescharacteristic
101C2×C13×C22⋊C4C2314yes—
102C2×C13×C22⋊C4C2314yes—
103C2×C13×C22⋊C4C2312yes—
104C2×C42×C13C2312yes—
105C2×C42×C13C2314yes—
106C2×C42×C13C2311yescharacteristic
107C2×C22⋊Dic13C2312yes—
108C2×C22⋊Dic13C2312yes—
109C2×C22⋊Dic13C2312yes—
110C2×C22⋊Dic13C2312yes—
111C2×C22⋊Dic13C2314yes—
112D4×Dic13C2×C4116yes—
113#88180—44no—
114C2×C4⋊Dic13C2311yescharacteristic
115C2×C4⋊Dic13C2311yescharacteristic
116C2×C4⋊Dic13C2312yes—
117C2×C4⋊Dic13C2312yes—
118C2×C4⋊Dic13C2311yescharacteristic
119C2×C4⋊Dic13C2312yes—
120C2×C4⋊Dic13C2312yes—
121#88178C2×C4116yes—
122C2×#6101C2312yes—
123C2×#6101C2314yes—
124C2×#6101C2314yes—
125C2×#6101C2312yes—
126C2×#6101C2312yes—
127C2×#6101C2314yes—
128C2×C4×Dic13C2311yescharacteristic
129C2×C4×Dic13C2312yes—
130C2×C4×Dic13C2311yescharacteristic
131C2×C4×Dic13C2311yescharacteristic
132C2×C4×Dic13C2311yescharacteristic
133C2×C4×Dic13C2311yescharacteristic
134C2×C4×Dic13C2314yes—
135C2×C4×Dic13C2314yes—
136C2×C4×Dic13C2314yes—
137C2×C4×Dic13C2311yescharacteristic
138C2×C4×Dic13C2312yes—
139#88142C2×C4116yes—
140#88141—44no—
141#88141—44no—
142#88132C2×C4132yes—
143#88123C2×C418yes—
144C4×Dic26C2×C418yes—
145C13×#95C2314yes—
146C13×#95C2312yes—
147#88071C2312yes—
148#88071C2312yes—
149#88071C2312yes—
150#88071C2312yes—
151#88071C2314yes—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2312yes—
155#88071C2312yes—
156#88071C2312yes—
157#88071C2312yes—
158#88071C2312yes—
159#88071C2314yes—
160#88071C2314yes—
161#88071C2314yes—
162#88071C2314yes—
163#34487—131nomaximal, Sylow
164C24×C13C2412yes—
165C2×D4×C13—22no—
166C2×D4×C13—22no—
167C2×D4×C13C22×C414yes—
168C22×C4×C13—24no—
169C22×C4×C13—24no—
170C22×C4×C13C22×C418yes—
171C22×C4×C13C2412yes—
172C22×C4×C13C2414yes—
173C22×C4×C13C2412yes—
174C22×C4×C13C2411yescharacteristic
175C22×C4×C13C2412yes—
176C22×C4×C13C2411yescharacteristic
177C22×C4×C13C2411yescharacteristic
178C22×Dic13—44no—
179C22×Dic13—44no—
180C22×Dic13C22×C4116yes—
181C22×Dic13C2412yes—
182C22×Dic13C2411yescharacteristic
183C22×Dic13C2411yescharacteristic
184C22×Dic13C2412yes—
185C22×Dic13C2411yescharacteristic
186C22×Dic13C2412yes—
187C22×Dic13C2412yes—
188C22×Dic13C2414yes—
189C22×Dic13C2411yescharacteristic
190C2×Dic26—24no—
191C2×Dic26—24no—
192C2×Dic26—22no—
193C2×Dic26—22no—
194C2×Dic26—432no—
195C2×Dic26—44no—
196C2×Dic26—44no—
197C2×Dic26C22×C414yes—
198C2×Dic26C22×C418yes—
199C2×Dic26C22×C4116yes—
200C13×C4⋊C4—22no—
201C13×C4⋊C4—24no—
202C13×C4⋊C4—22no—
203C13×C4⋊C4—24no—
204C13×C4⋊C4—42no—
205C13×C4⋊C4C22×C414yes—
206C13×C22⋊C4—44no—
207C13×C22⋊C4—44no—
208C13×C22⋊C4C22×C418yes—
209C42×C13—24no—
210C42×C13—44no—
211C42×C13C22×C414yes—
212C22⋊Dic13—24no—
213C22⋊Dic13—42no—
214C22⋊Dic13—42no—
215C22⋊Dic13—42no—
216C22⋊Dic13C22×C4116yes—
217C4⋊Dic13—22no—
218C4⋊Dic13—22no—
219C4⋊Dic13—42no—
220C4⋊Dic13—42no—
221C4⋊Dic13C22×C414yes—
222C4⋊Dic13C22×C418yes—
223C4⋊Dic13C22×C418yes—
224#6101—24no—
225#6101—44no—
226#6101—44no—
227#6101—42no—
228#6101C22×C418yes—
229#6101C22×C4116yes—
230C4×Dic13—22no—
231C4×Dic13—24no—
232C4×Dic13—22no—
233C4×Dic13—22no—
234C4×Dic13—22no—
235C4×Dic13—22no—
236C4×Dic13—44no—
237C4×Dic13—44no—
238C4×Dic13—44no—
239C4×Dic13—41no—
240C4×Dic13C22×C418yes—
241C2×D4×Q8—131no—
242#2378—134no—
243#2369—132no—
244#2365—131no—
245#2362—132no—
246#2357—132no—
247#2355—131no—
248#2354D1311yescharacteristic
249Q8×C22⋊C4—132no—
250#2332—134no—
251#2331—132no—
252#2323—132no—
253#2319—132no—
254#2310—132no—
255C4×C4⋊Q8—131no—
256#2295—131no—
257#2293—131no—
258C23×C13—22no—
259C23×C13—22no—
260C23×C13—22no—
261C23×C13—22no—
262C23×C13—22no—
263C23×C13—22no—
264C23×C13C23×C414yes—
265C23×C13C2511yescharacteristic
266D4×C13—28no—
267C2×C4×C13—22no—
268C2×C4×C13—22no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—216no—
272C2×C4×C13—22no—
273C2×C4×C13—24no—
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—22no—
277C2×C4×C13—22no—
278C2×C4×C13—24no—
279C2×C4×C13—24no—
280C2×C4×C13—22no—
281C2×C4×C13C23×C412yes—
282C2×C4×C13C23×C414yes—
283C2×C4×C13C23×C412yes—
284C2×C4×C13C23×C412yes—
285C2×C4×C13H(5,𝔽2)12yes—
286C2×C4×C13H(5,𝔽2)12yes—
287C2×C4×C132−1+412yes—
288C2×C4×C132−1+412yes—
289C2×Dic13—21no—
290C2×Dic13—24no—
291C2×Dic13—24no—
292C2×Dic13—22no—
293C2×Dic13—22no—
294C2×Dic13—21no—
295C2×Dic13—22no—
296C2×Dic13—22no—
297C2×Dic13—22no—
298C2×Dic13—21no—
299C2×Dic13—22no—
300C2×Dic13—21no—
301C2×Dic13—21no—
302C2×Dic13—21no—
303C2×Dic13—21no—
304C2×Dic13—21no—
305C2×Dic13—21no—
306C2×Dic13—22no—
307C2×Dic13—22no—
308C2×Dic13—22no—
309C2×Dic13—22no—
310C2×Dic13—21no—
311C2×Dic13—21no—
312C2×Dic13—416no—
313C2×Dic13C23×C414yes—
314C2×Dic13C23×C414yes—
315C2×Dic13C23×C418yes—
316C2×Dic132−1+412yes—
317Dic26—28no—
318Dic26—216no—
319Dic26—416no—
320C23×Q8—132no—
321D4×Q8—1316no—
322C2×C4⋊Q8—132no—
323C2×C4⋊Q8—131no—
324C2×C22⋊Q8—132no—
325C2×C22⋊Q8—134no—
326C2×C4×Q8—132no—
327C2×C4×Q8—132no—
328C2×C4×Q8—131no—
329C2×C4×D4—132no—
330C2×C4×D4C2×D1311yescharacteristic
331C2×#117—132no—
332C2×#117C2×D1312yes—
333#391—132no—
334#391—131no—
335#391—132no—
336#391—132no—
337#391—131no—
338#391—134no—
339#391—134no—
340#391—134no—
341#391—134no—
342#390—131no—
343#390—131no—
344#390C2×D1312yes—
345#389—132no—
346#389—132no—
347#389—131no—
348#389—131no—
349#389—131no—
350#389—131no—
351#389—132no—
352#389—134no—
353#388—134no—
354#388—134no—
355#388—134no—
356#388—132no—
357#388—134no—
358#388—132no—
359#388C2×D1314yes—
360#387—134no—
361#387—134no—
362#387—134no—
363#387—132no—
364#387—134no—
365#387—132no—
366#384C2×D1311yescharacteristic
367#382—132no—
368#381—134no—
369#381—134no—
370#380—134no—
371#380C2×D1312yes—
372C4×C4⋊C4—132no—
373C4×C4⋊C4—132no—
374C4×C4⋊C4—132no—
375C4×C4⋊C4—132no—
376C4×C4⋊C4—132no—
377C4×C4⋊C4—134no—
378C4×C4⋊C4—131no—
379C4×C4⋊C4—132no—
380C4×C4⋊C4C2×D1312yes—
381C4×C4⋊C4C2×D1311yescharacteristic
382C4×C22⋊C4—132no—
383C4×C22⋊C4—134no—
384#376—132no—
385C43—131no—
386C22×C13—24no—
387C22×C13—24no—
388C22×C13—24no—
389C22×C13—42no—
390C22×C13—42no—
391C22×C13—42no—
392C22×C13—42no—
393C22×C13C24×C411yescharacteristic
394C22×C13C2×H(5,𝔽2)11yescharacteristic
395C22×C13C2×H(5,𝔽2)11yescharacteristic
396C22×C13C2×2−1+411yescharacteristic
397C22×C13C2×2−1+411yescharacteristic
398C22×C13C2×2−1+411yescharacteristic
399C22×C13#58511yescharacteristic
400C4×C13—24no—
401C4×C13—22no—
402C4×C13—42no—
403C4×C13—42no—
404C4×C13—44no—
405C4×C13#51814yes—
406C4×C13#51914yes—
407Dic13—24no—
408Dic13—28no—
409Dic13—24no—
410Dic13—22no—
411Dic13—42no—
412Dic13—41no—
413Dic13—42no—
414Dic13—41no—
415Dic13—41no—
416C22×Q8—1316no—
417C22×Q8—132no—
418C22×Q8—131no—
419C22×Q8—134no—
420C22×Q8—524no—
421C22×Q8—524no—
422C22×D4C22×D1311yescharacteristic
423C23×C4—134no—
424C23×C4C22×D1312yes—
425C4⋊Q8—1316no—
426C4⋊Q8—138no—
427C22⋊Q8—1316no—
428C22⋊Q8—1332no—
429C4×Q8—138no—
430C4×Q8—524no—
431C4×Q8—524no—
432C4×D4—1316no—
433C4×D4C4×D1318yes—
434#117—44no—
435#117—524no—
436C2×C4⋊C4—132no—
437C2×C4⋊C4—132no—
438C2×C4⋊C4—131no—
439C2×C4⋊C4—134no—
440C2×C4⋊C4—132no—
441C2×C4⋊C4—132no—
442C2×C4⋊C4—131no—
443C2×C4⋊C4—131no—
444C2×C4⋊C4—132no—
445C2×C4⋊C4—132no—
446C2×C4⋊C4—134no—
447C2×C4⋊C4—134no—
448C2×C4⋊C4—132no—
449C2×C4⋊C4C22×D1311yescharacteristic
450C2×C4⋊C4C22×D1312yes—
451C2×C4⋊C4C22×D1311yescharacteristic
452C2×C4⋊C4C22×D1312yes—
453C2×C4⋊C4C22×D1312yes—
454C2×C4⋊C4C22×D1311yescharacteristic
455C2×C22⋊C4—134no—
456C2×C22⋊C4—132no—
457C2×C22⋊C4—132no—
458C2×C22⋊C4—132no—
459C2×C22⋊C4—132no—
460C2×C22⋊C4C22×D1314yes—
461C2×C22⋊C4C22×D1314yes—
462C2×C22⋊C4C22×D1312yes—
463C2×C42—132no—
464C2×C42—131no—
465C2×C42—132no—
466C2×C42—131no—
467C2×C42—131no—
468C2×C42—131no—
469C2×C42—131no—
470C2×C42—134no—
471C2×C42—134no—
472C2×C42—131no—
473C2×C42—134no—
474C2×C42C22×D1312yes—
475C2×C42C22×D1314yes—
476C2×C42C22×D1311yescharacteristic
477#95—132no—
478#95—132no—
479#95—132no—
480#95—132no—
481#95—132no—
482#95—132no—
483#95—134no—
484#95—132no—
485#95—134no—
486#95—132no—
487#95—134no—
488#95—134no—
489#95—134no—
490#95—134no—
491#95—134no—
492#95—132no—
493#95C22×D1314yes—
494#95C22×D1312yes—
495C2×C13—44no—
496C2×C13C2×#51811yescharacteristic
497C2×C13C2×#51911yescharacteristic
498C2×C13C4×2−1+411yescharacteristic
499C2×C13#354711yescharacteristic
500C2×C13#355011yescharacteristic
501C2×C13#355211yescharacteristic
502C2×C13#355411yescharacteristic
503C24C23×D1312yes—
504C2×Q8—134no—
505C2×Q8—138no—
506C2×Q8—1316no—
507C2×Q8—264no—
508C2×Q8—262no—
509C2×Q8—264no—
510C2×Q8—262no—
511C2×Q8—524no—
512C2×Q8—524no—
513C2×Q8—5232no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4C2×C4×D1314yes—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—132no—
520C22×C4—131no—
521C22×C4—132no—
522C22×C4—134no—
523C22×C4—1316no—
524C22×C4—132no—
525C22×C4—131no—
526C22×C4—131no—
527C22×C4—131no—
528C22×C4—132no—
529C22×C4—524no—
530C22×C4—524no—
531C22×C4C2×C4×D1318yes—
532C22×C4C23×D1312yes—
533C22×C4C23×D1314yes—
534C22×C4C23×D1312yes—
535C22×C4C23×D1311yescharacteristic
536C22×C4C23×D1312yes—
537C22×C4C23×D1311yescharacteristic
538C22×C4C23×D1311yescharacteristic
539C4⋊C4—22no—
540C4⋊C4—24no—
541C4⋊C4—22no—
542C4⋊C4—24no—
543C4⋊C4—42no—
544C4⋊C4—138no—
545C4⋊C4—138no—
546C4⋊C4—134no—
547C4⋊C4—1316no—
548C4⋊C4—138no—
549C4⋊C4—264no—
550C4⋊C4—262no—
551C4⋊C4—262no—
552C4⋊C4—522no—
553C4⋊C4—522no—
554C4⋊C4—524no—
555C4⋊C4—524no—
556C4⋊C4—522no—
557C4⋊C4C2×C4×D1314yes—
558C22⋊C4—44no—
559C22⋊C4—44no—
560C22⋊C4—1316no—
561C22⋊C4—264no—
562C22⋊C4—522no—
563C22⋊C4—522no—
564C22⋊C4—522no—
565C22⋊C4C2×C4×D1318yes—
566C42—24no—
567C42—44no—
568C42—138no—
569C42—262no—
570C42—262no—
571C42—262no—
572C42—264no—
573C42—262no—
574C42—262no—
575C42—524no—
576C42—524no—
577C42—521no—
578C42—524no—
579C42C2×C4×D1314yes—
580C13#3448711yescharacteristic, complemented, Sylow
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23C22×C4×D1314yes—
588C23C24×D1311yescharacteristic
589Q8—2616no—
590Q8—268no—
591Q8—5216no—
592D4—28no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—216no—
598C2×C4—22no—
599C2×C4—24no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—134no—
608C2×C4—134no—
609C2×C4—138no—
610C2×C4—132no—
611C2×C4—261no—
612C2×C4—264no—
613C2×C4—262no—
614C2×C4—264no—
615C2×C4—262no—
616C2×C4—261no—
617C2×C4—262no—
618C2×C4—262no—
619C2×C4—261no—
620C2×C4—262no—
621C2×C4—261no—
622C2×C4—261no—
623C2×C4—262no—
624C2×C4—261no—
625C2×C4—261no—
626C2×C4—261no—
627C2×C4—262no—
628C2×C4—262no—
629C2×C4—262no—
630C2×C4—261no—
631C2×C4—261no—
632C2×C4—261no—
633C2×C4—262no—
634C2×C4—5216no—
635C2×C4C22×C4×D1312yes—
636C2×C4C22×C4×D1314yes—
637C2×C4C22×C4×D1312yes—
638C2×C4C22×C4×D1312yes—
639C2×C4#8825112yes—
640C2×C4#8825612yes—
641C2×C4#8825712yes—
642C2×C4#8825712yes—
643C22—24no—
644C22—24no—
645C22—24no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22C23×C4×D1311yescharacteristic
651C22C2×#8825111yescharacteristic
652C22C2×#8825611yescharacteristic
653C22C2×#8825711yescharacteristic
654C22C2×#8825711yescharacteristic
655C22#1171965011yescharacteristic
656C22D13×2−1+411yescharacteristic
657C4—24no—
658C4—22no—
659C4—42no—
660C4—42no—
661C4—44no—
662C4—262no—
663C4—264no—
664C4—268no—
665C4—264no—
666C4—521no—
667C4—522no—
668C4—522no—
669C4—521no—
670C4—521no—
671C4#1171922114yes—
672C4#1171925014yes—
673C2—44no—
674C2C2×#1171925011yescharacteristic
675C2C2×#1171922111yescharacteristic
676C2#1312804711yescharacteristic
677C2#1312922811yescharacteristic
678C2#1312924911yescharacteristic
679C2#1312927411yescharacteristic
680C2#1312930311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC13×#2354C2
socle, cosocleC23×C13C25
prime radicalC22×D4×C13C23
hypercenter#2354D13
hypocenterC13#34487
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. #13118003C2semidirect
3. #13117923C2semidirect
4. #13117894C2semidirect
5. #13117863C2semidirect
7. #13117795C2semidirect
8. #13117668C2semidirect
9. #13117586C2semidirect
10. #13117580C2semidirect
11. #13117514C2semidirect
13. #13117420C2semidirect
14. #13117403C2semidirect
15. #13117310C2semidirect
24. D4×Dic26C4semidirect
580. C13#34487semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic262
#131180032
#131179232
#131178942
#131178632
#131178082
#131177952
#131176682
#131175862
#131175802
#131175142
#131174732
#131174202
#131174032
#131173102
#131173012
C13×#23542
#3448713