Finite Group Databasebeta

← #15872362

Subgroups — #15872362

Order 3328.

1474 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88178C211yesmaximal, characteristic
2#13117219C211yesmaximal, characteristic
3#13115821C214yesmaximal, complemented
4#13115820C214yesmaximal, complemented
5#13114908C214yesmaximal
6C13×#2280C211yesmaximal, characteristic
7C24×C4×C13C2211yescharacteristic
8C23×Dic26C411yescharacteristic, complemented
9C2×C13×#117—21no—
10C22×C22⋊Dic13C2212yes—
11C2×#88180—21no—
12C22×C4⋊Dic13C411yescharacteristic, complemented
13C2×#88178—21no—
14C2×#88178—21no—
15C2×#88178—21no—
16C2×#88178—21no—
17C2×#88178—21no—
18C2×#88178—21no—
19C2×#88178—21no—
20C2×#88178—21no—
21C2×#88178C412yescomplemented
22C2×#88178C412yescomplemented
23C2×#88178C2212yes—
24C2×#88178C2212yes—
25C22×#6101C412yescomplemented
26C13×#381—21no—
27C13×#380—21no—
28C13×#380C2212yes—
29C13×#379C2212yes—
30C4×C13×C22⋊C4—21no—
31C4×C13×C22⋊C4C2212yes—
32#11718908C2212yes—
33#11718873—21no—
34#11718873C2212yes—
35#11718872—21no—
36C4×C22⋊Dic13—21no—
37C4×C22⋊Dic13C2212yes—
38#11718119C22116yes—
39C25×C13C2311yescharacteristic
40C23×C4×C13—44no—
41C23×C4×C13C2×C411yescharacteristic
42C23×C4×C13C2×C411yescharacteristic
43C23×C4×C13C2×C411yescharacteristic
44C23×C4×C13C2×C411yescharacteristic
45C23×C4×C13D411yescharacteristic
46C23×C4×C13D411yescharacteristic
47C23×C4×C13D411yescharacteristic
48C23×C4×C13D411yescharacteristic
49C23×C4×C13D411yescharacteristic
50C23×C4×C13D411yescharacteristic
51C23×C4×C13D411yescharacteristic
52C23×C4×C13D411yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C23×Dic13C2×C412yes—
56C23×Dic13C2×C412yes—
57C22×Dic26—21no—
58C22×Dic26—21no—
59C22×Dic26—21no—
60C22×Dic26—21no—
61C22×Dic26—44no—
62C22×Dic26C2×C412yes—
63C22×Dic26C2×C412yes—
64C13×#117—44no—
65C2×C13×C4⋊C4—22no—
66C2×C13×C22⋊C4—22no—
67C2×C13×C22⋊C4—22no—
68C2×C13×C22⋊C4C2314yes—
69C2×C42×C13—22no—
70C2×C22⋊Dic13—22no—
71C2×C22⋊Dic13—22no—
72C2×C22⋊Dic13—22no—
73C2×C22⋊Dic13—22no—
74C2×C22⋊Dic13—22no—
75C2×C22⋊Dic13—22no—
76C2×C22⋊Dic13C2×C414yes—
77C2×C22⋊Dic13C2314yes—
78C2×C22⋊Dic13C2314yes—
79#88180—44no—
80C2×C4⋊Dic13—21no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13—22no—
85C2×C4⋊Dic13C2×C412yes—
86C2×C4⋊Dic13C2×C412yes—
87#88178—22no—
88#88178—22no—
89#88178—22no—
90#88178—22no—
91#88178—22no—
92#88178—22no—
93#88178—22no—
94#88178—22no—
95#88178—22no—
96#88178—22no—
97#88178—22no—
98#88178—22no—
99#88178—22no—
100#88178—22no—
101#88178—22no—
102#88178—22no—
103C2×#6101—22no—
104C2×#6101—22no—
105C2×#6101—22no—
106C2×#6101—22no—
107C2×#6101C2×C414yes—
108C2×#6101C2×C414yes—
109C2×C4×Dic13—22no—
110C13×#95—22no—
111C13×#95—22no—
112#88071—22no—
113#88071—22no—
114#21825—131nomaximal, Sylow
115C24×C13—24no—
116C24×C13—42no—
117C24×C13—42no—
118C24×C13C22×C411yescharacteristic
119C24×C13C22×C411yescharacteristic
120C24×C13C2×D411yescharacteristic
121C24×C13C2×D411yescharacteristic
122C24×C13C2×D411yescharacteristic
123C24×C13C2×D411yescharacteristic
124C24×C13C2411yescharacteristic
125C22×C4×C13—24no—
126C22×C4×C13—24no—
127C22×C4×C13—24no—
128C22×C4×C13—24no—
129C22×C4×C13—42no—
130C22×C4×C13—42no—
131C22×C4×C13—42no—
132C22×C4×C13—42no—
133C22×C4×C13—42no—
134C22×C4×C13—42no—
135C22×C4×C13—42no—
136C22×C4×C13—42no—
137C22×C4×C13—42no—
138C22×C4×C13—42no—
139C22×C4×C13—42no—
140C22×C4×C13C22⋊C411yescharacteristic
141C22×C4×C13C22⋊C411yescharacteristic
142C22×C4×C13C22⋊C411yescharacteristic
143C22×C4×C13C22⋊C411yescharacteristic
144C22×C4×C13C22⋊C411yescharacteristic
145C22×C4×C13C22⋊C411yescharacteristic
146C22×C4×C13C22⋊C411yescharacteristic
147C22×C4×C13C22⋊C411yescharacteristic
148C22×C4×C13C22⋊C411yescharacteristic
149C22×C4×C13C22⋊C411yescharacteristic
150C22×C4×C13C22⋊C411yescharacteristic
151C22×C4×C13C22⋊C411yescharacteristic
152C22×C4×C13C22⋊C411yescharacteristic
153C22×C4×C13C22⋊C411yescharacteristic
154C22×C4×C13C22⋊C411yescharacteristic
155C22×C4×C13C22⋊C411yescharacteristic
156C22×C4×C13C22×C411yescharacteristic
157C22×C4×C13C22×C411yescharacteristic
158C22×C4×C13C22×C411yescharacteristic
159C22×C4×C13C22×C411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×D411yescharacteristic
162C22×C4×C13C2×D411yescharacteristic
163C22×C4×C13C2×D411yescharacteristic
164C22×C4×C13C2×D411yescharacteristic
165C22×C4×C13C2×D411yescharacteristic
166C22×C4×C13C2×D411yescharacteristic
167C22×C4×C13C2×D411yescharacteristic
168C22×Dic13—22no—
169C22×Dic13—22no—
170C22×Dic13—22no—
171C22×Dic13—22no—
172C22×Dic13—24no—
173C22×Dic13—44no—
174C22×Dic13—44no—
175C22×Dic13C22×C414yes—
176C22×Dic13C22×C414yes—
177C2×Dic26—22no—
178C2×Dic26—22no—
179C2×Dic26—22no—
180C2×Dic26—22no—
181C2×Dic26—44no—
182C2×Dic26—44no—
183C2×Dic26—44no—
184C2×Dic26—44no—
185C2×Dic26—44no—
186C2×Dic26—44no—
187C13×C4⋊C4—44no—
188C13×C22⋊C4—28no—
189C13×C22⋊C4—44no—
190C13×C22⋊C4—44no—
191C42×C13—44no—
192C22⋊Dic13—24no—
193C22⋊Dic13—24no—
194C22⋊Dic13—24no—
195C22⋊Dic13—24no—
196C22⋊Dic13—28no—
197C22⋊Dic13—44no—
198C22⋊Dic13—44no—
199C4⋊Dic13—22no—
200C4⋊Dic13—22no—
201C4⋊Dic13—22no—
202C4⋊Dic13—22no—
203C4⋊Dic13—44no—
204#6101—24no—
205#6101—24no—
206#6101—24no—
207#6101—24no—
208C4×Dic13—44no—
209C22×C22⋊Q8—131no—
210#2280—131no—
211#2280D1311yescharacteristic
212#1996—134no—
213#1996—134no—
214#1819—134no—
215C23×C13—22no—
216C23×C13—22no—
217C23×C13—22no—
218C23×C13—22no—
219C23×C13—22no—
220C23×C13—22no—
221C23×C13—22no—
222C23×C13—22no—
223C23×C13—22no—
224C23×C13—22no—
225C23×C13—22no—
226C23×C13—22no—
227C23×C13—41no—
228C23×C13—41no—
229C23×C13—41no—
230C23×C13—41no—
231C23×C13—41no—
232C23×C13—41no—
233C23×C13—41no—
234C23×C13—41no—
235C23×C13—416no—
236C23×C13C2×C22⋊C411yescharacteristic
237C23×C13C2×C22⋊C411yescharacteristic
238C23×C13C2×C22⋊C411yescharacteristic
239C23×C13C2×C22⋊C411yescharacteristic
240C23×C13C23×C411yescharacteristic
241C23×C13C22×D411yescharacteristic
242C23×C13C22×D411yescharacteristic
243C23×C132−1+414yes—
244C2×C4×C13—22no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—22no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—22no—
251C2×C4×C13—22no—
252C2×C4×C13—22no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—22no—
256C2×C4×C13—22no—
257C2×C4×C13—22no—
258C2×C4×C13—22no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—44no—
272C2×C4×C13—44no—
273C2×C4×C13—44no—
274C2×C4×C13#9914yes—
275C2×C4×C13C2×C22⋊C411yescharacteristic
276C2×C4×C13C2×C22⋊C411yescharacteristic
277C2×C4×C13C2×C22⋊C411yescharacteristic
278C2×C4×C13C2×C22⋊C411yescharacteristic
279C2×C4×C13C2×C22⋊C411yescharacteristic
280C2×C4×C13C2×C22⋊C411yescharacteristic
281C2×C4×C13C2×C22⋊C411yescharacteristic
282C2×C4×C13C2×C22⋊C411yescharacteristic
283C2×Dic13—24no—
284C2×Dic13—24no—
285C2×Dic13—44no—
286C2×Dic13—44no—
287C2×Dic13—44no—
288C2×Dic13—44no—
289C2×Dic13—44no—
290C2×Dic13—44no—
291C2×Dic13—44no—
292C2×Dic13—44no—
293C2×Dic13—44no—
294Dic26—44no—
295Dic26—44no—
296Dic26—44no—
297Dic26—44no—
298C23×Q8—131no—
299C24×C4C2×D1311yescharacteristic
300C2×C22⋊Q8—132no—
301C2×C22⋊Q8—132no—
302C2×C22⋊Q8—132no—
303C2×C22⋊Q8—132no—
304C2×C22⋊Q8—261no—
305C2×C22⋊Q8—261no—
306C2×C22⋊Q8—261no—
307C2×C22⋊Q8—261no—
308C2×C22⋊Q8—261no—
309C2×C22⋊Q8—261no—
310C2×C22⋊Q8—261no—
311C2×C22⋊Q8—261no—
312C2×#117—21no—
313C2×#117—261no—
314C22×C4⋊C4—132no—
315C22×C4⋊C4—131no—
316C22×C22⋊C4—132no—
317#381—21no—
318#381—261no—
319#380—21no—
320#380—132no—
321#380—261no—
322#380C2×D1312yes—
323#379—132no—
324#379C2×D1312yes—
325C4×C22⋊C4—21no—
326C4×C22⋊C4—132no—
327C4×C22⋊C4—261no—
328C4×C22⋊C4C2×D1312yes—
329#342—1316no—
330C22×C13—28no—
331C22×C13—21no—
332C22×C13—21no—
333C22×C13—21no—
334C22×C13—21no—
335C22×C13—21no—
336C22×C13—21no—
337C22×C13—21no—
338C22×C13—21no—
339C22×C13—21no—
340C22×C13—21no—
341C22×C13—21no—
342C22×C13—21no—
343C22×C13—21no—
344C22×C13—21no—
345C22×C13—21no—
346C22×C13—21no—
347C22×C13—44no—
348C22×C13—44no—
349C22×C13—44no—
350C22×C13—44no—
351C22×C13—44no—
352C22×C13—44no—
353C22×C13C2×#9912yes—
354C22×C13#41012yes—
355C22×C13C22×C22⋊C411yescharacteristic
356C22×C13#51912yes—
357C22×C13#53612yes—
358C22×C13#53612yes—
359C4×C13—21no—
360C4×C13—21no—
361C4×C13—21no—
362C4×C13—21no—
363C4×C13—21no—
364C4×C13—21no—
365C4×C13—84no—
366C4×C13C2×#9912yes—
367C4×C13C2×#9912yes—
368Dic13—44no—
369Dic13—44no—
370Dic13—84no—
371C25C22×D1311yescharacteristic
372C22×Q8—132no—
373C22×Q8—132no—
374C22×Q8—261no—
375C22×Q8—261no—
376C22×Q8—261no—
377C22×Q8—261no—
378C22×Q8—524no—
379C23×C4—44no—
380C23×C4—132no—
381C23×C4—132no—
382C23×C4C4×D1311yescharacteristic
383C23×C4C4×D1311yescharacteristic
384C23×C4C4×D1311yescharacteristic
385C23×C4C4×D1311yescharacteristic
386C23×C4D5211yescharacteristic
387C23×C4D5211yescharacteristic
388C23×C4D5211yescharacteristic
389C23×C4D5211yescharacteristic
390C23×C4C22⋊D1311yescharacteristic
391C23×C4C22⋊D1311yescharacteristic
392C23×C4C22⋊D1311yescharacteristic
393C23×C4C22⋊D1311yescharacteristic
394C23×C4C22×D1311yescharacteristic
395C23×C4C22×D1311yescharacteristic
396C22⋊Q8—262no—
397C22⋊Q8—262no—
398C22⋊Q8—262no—
399C22⋊Q8—262no—
400C22⋊Q8—262no—
401C22⋊Q8—262no—
402C22⋊Q8—262no—
403C22⋊Q8—262no—
404C22⋊Q8—262no—
405C22⋊Q8—262no—
406C22⋊Q8—262no—
407C22⋊Q8—262no—
408C22⋊Q8—262no—
409C22⋊Q8—262no—
410C22⋊Q8—262no—
411C22⋊Q8—262no—
412#117—44no—
413#117—524no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—134no—
416C2×C4⋊C4—134no—
417C2×C4⋊C4—132no—
418C2×C4⋊C4—132no—
419C2×C4⋊C4—262no—
420C2×C4⋊C4—262no—
421C2×C4⋊C4—262no—
422C2×C4⋊C4—262no—
423C2×C4⋊C4—261no—
424C2×C4⋊C4—261no—
425C2×C4⋊C4—261no—
426C2×C4⋊C4—261no—
427C2×C4⋊C4—262no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—134no—
431C2×C22⋊C4—134no—
432C2×C22⋊C4—134no—
433C2×C22⋊C4—262no—
434C2×C22⋊C4—262no—
435C2×C22⋊C4—262no—
436C2×C22⋊C4—262no—
437C2×C22⋊C4—262no—
438C2×C22⋊C4—262no—
439C2×C22⋊C4C22×D1314yes—
440C2×C42—22no—
441C2×C42—262no—
442#95—22no—
443#95—22no—
444#95—262no—
445#95—262no—
446C2×C13—22no—
447C2×C13—22no—
448C2×C13—22no—
449C2×C13—22no—
450C2×C13—22no—
451C2×C13—41no—
452C2×C13—41no—
453C2×C13#231011yescharacteristic
454C2×C13C22×#9911yescharacteristic
455C2×C13C2×#41011yescharacteristic
456C24—24no—
457C24—42no—
458C24—42no—
459C24C2×C4×D1311yescharacteristic
460C24C2×C4×D1311yescharacteristic
461C24C2×D5211yescharacteristic
462C24C2×D5211yescharacteristic
463C24C2×C22⋊D1311yescharacteristic
464C24C2×C22⋊D1311yescharacteristic
465C24C23×D1311yescharacteristic
466C2×Q8—262no—
467C2×Q8—262no—
468C2×Q8—262no—
469C2×Q8—262no—
470C2×Q8—524no—
471C2×Q8—524no—
472C2×Q8—524no—
473C2×Q8—524no—
474C2×Q8—524no—
475C2×Q8—524no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—134no—
492C22×C4—134no—
493C22×C4—262no—
494C22×C4—262no—
495C22×C4—262no—
496C22×C4—262no—
497C22×C4—264no—
498C22×C4—524no—
499C22×C4—524no—
500C22×C4#610311yescharacteristic
501C22×C4#610311yescharacteristic
502C22×C4#610311yescharacteristic
503C22×C4#610311yescharacteristic
504C22×C4#610311yescharacteristic
505C22×C4#610311yescharacteristic
506C22×C4#610311yescharacteristic
507C22×C4#610311yescharacteristic
508C22×C4#610311yescharacteristic
509C22×C4#610311yescharacteristic
510C22×C4#610311yescharacteristic
511C22×C4#610311yescharacteristic
512C22×C4#610311yescharacteristic
513C22×C4#610311yescharacteristic
514C22×C4#610311yescharacteristic
515C22×C4#610311yescharacteristic
516C22×C4C2×C4×D1311yescharacteristic
517C22×C4C2×C4×D1311yescharacteristic
518C22×C4C2×C4×D1311yescharacteristic
519C22×C4C2×C4×D1311yescharacteristic
520C22×C4C2×D5211yescharacteristic
521C22×C4C2×D5211yescharacteristic
522C22×C4C2×D5211yescharacteristic
523C22×C4C2×D5211yescharacteristic
524C22×C4C2×C22⋊D1311yescharacteristic
525C22×C4C2×C22⋊D1311yescharacteristic
526C22×C4C2×C22⋊D1311yescharacteristic
527C22×C4C2×C22⋊D1311yescharacteristic
528C4⋊C4—44no—
529C4⋊C4—264no—
530C4⋊C4—264no—
531C4⋊C4—264no—
532C4⋊C4—264no—
533C4⋊C4—262no—
534C4⋊C4—262no—
535C4⋊C4—262no—
536C4⋊C4—262no—
537C4⋊C4—524no—
538C22⋊C4—28no—
539C22⋊C4—44no—
540C22⋊C4—44no—
541C22⋊C4—264no—
542C22⋊C4—264no—
543C22⋊C4—264no—
544C22⋊C4—264no—
545C22⋊C4—268no—
546C22⋊C4—524no—
547C22⋊C4—524no—
548C42—44no—
549C42—524no—
550C13#2182511yescharacteristic, complemented, Sylow
551C23—22no—
552C23—22no—
553C23—22no—
554C23—22no—
555C23—22no—
556C23—22no—
557C23—22no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—416no—
572C23C2×#610311yescharacteristic
573C23C2×#610311yescharacteristic
574C23C2×#610311yescharacteristic
575C23C2×#610311yescharacteristic
576C23C22×C4×D1311yescharacteristic
577C23C22×D5211yescharacteristic
578C23#8825714yes—
579C23C22×C22⋊D1311yescharacteristic
580Q8—524no—
581Q8—524no—
582Q8—524no—
583Q8—524no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—44no—
612C2×C4—44no—
613C2×C4—44no—
614C2×C4—264no—
615C2×C4—264no—
616C2×C4—524no—
617C2×C4—524no—
618C2×C4—524no—
619C2×C4—524no—
620C2×C4—524no—
621C2×C4—524no—
622C2×C4—524no—
623C2×C4—524no—
624C2×C4—524no—
625C2×C4#8804614yes—
626C2×C4C2×#610311yescharacteristic
627C2×C4C2×#610311yescharacteristic
628C2×C4C2×#610311yescharacteristic
629C2×C4C2×#610311yescharacteristic
630C2×C4C2×#610311yescharacteristic
631C2×C4C2×#610311yescharacteristic
632C2×C4C2×#610311yescharacteristic
633C2×C4C2×#610311yescharacteristic
634C22—28no—
635C22—21no—
636C22—21no—
637C22—21no—
638C22—21no—
639C22—21no—
640C22—21no—
641C22—21no—
642C22—21no—
643C22—21no—
644C22—21no—
645C22—21no—
646C22—21no—
647C22—21no—
648C22—21no—
649C22—21no—
650C22—21no—
651C22—44no—
652C22—44no—
653C22—44no—
654C22—44no—
655C22—44no—
656C22—44no—
657C22C2×#8804612yes—
658C22#1171866712yes—
659C22#1171922112yes—
660C22#1171923112yes—
661C22C22×#610311yescharacteristic
662C22#1171953012yes—
663C4—21no—
664C4—21no—
665C4—21no—
666C4—21no—
667C4—21no—
668C4—21no—
669C4—84no—
670C4—524no—
671C4—524no—
672C4—1044no—
673C4C2×#8804612yes—
674C4C2×#8804612yes—
675C2—22no—
676C2—22no—
677C2—22no—
678C2—22no—
679C2—22no—
680C2—41no—
681C2—41no—
682C2#1311742011yescharacteristic
683C2C22×#8804611yescharacteristic
684C2C2×#1171866711yescharacteristic
subgroupG/H
centerC22C22×#6103
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC13×#2280C2
socleC22×C13C22×C22⋊C4
prime radicalC25×C13C23
cosocleC24×C13C24
hypercenter#2280D13
hypocenterC13#21825
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
3. #13115821C2semidirect
4. #13115820C2semidirect
8. C23×Dic26C4semidirect
12. C22×C4⋊Dic13C4semidirect
21. C2×#88178C4semidirect
22. C2×#88178C4semidirect
25. C22×#6101C4semidirect
550. C13#21825semidirect

Maximal subgroups

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

subgroupindex
C22×#881782
#131172192
#131158212
#131158202
#131149082
C13×#22802
#2182513