Finite Group Databasebeta

← #16799532

Subgroups — #16799532

Order 3328.

1518 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719125C211yesmaximal, characteristic, complemented
2C22×C4×#1057C211yesmaximal, characteristic, complemented
3#13131007C212yesmaximal, complemented
4#13130959C212yesmaximal, complemented
5#13130811C212yesmaximal, complemented
6#13130809C212yesmaximal, complemented
7C4×#88111C212yesmaximal, complemented
8C4×C22⋊#1057C212yesmaximal, complemented
9C2×C4×#6129C211yesmaximal, characteristic
10C22×#6129C411yescharacteristic
11C23×#1057C2212yes—
12C2×C4×D4×C13C411yescharacteristic
13C2×D4×Dic13C2211yescharacteristic
14C2×C4×C22⋊D13C411yescharacteristic
15C2×C4×C22⋊D13C411yescharacteristic
16C22×C4×Dic13C2211yescharacteristic
17C22×C4×Dic13C2211yescharacteristic
18C4×#6129—24no—
19C4×#6129—24no—
20C2×#88146C411yescharacteristic
21C2×#88141C2211yescharacteristic
22C2×#88135C2211yescharacteristic
23C2×#88135C2211yescharacteristic
24C2×#88131C411yescharacteristic
25C2×#88131C411yescharacteristic
26C2×C42×D13C2211yescharacteristic
27C2×C4×Dic26C411yescharacteristic
28C2×C22⋊#1057C2212yes—
29C2×C22⋊#1057C2214yes—
30#11719125—24no—
31C2×#88112C2212yes—
32C2×#88111C2214yes—
33C2×C4×#1057—24no—
34C2×C4×#1057C2212yes—
35C2×C4×#1057C2212yes—
36C2×C4×#1057C2212yes—
37#11718290C2214yes—
38#11718290C2214yes—
39C22×D4×C13C2×C411yescharacteristic
40C23×C4×C13C2×C411yescharacteristic
41C23×C4×C13C2×C411yescharacteristic
42C22×C22⋊D13C2×C411yescharacteristic
43C22×C22⋊D13C2×C411yescharacteristic
44C23×Dic13C2×C411yescharacteristic
45C23×Dic13C2×C411yescharacteristic
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2311yescharacteristic
48C2×#6129—24no—
49C2×#6129—24no—
50C2×#6129C818yescomplemented
51C22×C4×D13C2×C411yescharacteristic
52C22×C4×D13C2×C411yescharacteristic
53C22×C4×D13C2311yescharacteristic
54C22×Dic26C2×C411yescharacteristic
55C22×#1057—24no—
56C22×#1057—28no—
57C22×#1057C2314yes—
58C22×#1057C2314yes—
59C4×D4×C13—24no—
60C2×C13×C4⋊C4C2×C411yescharacteristic
61C2×C13×C22⋊C4C2×C411yescharacteristic
62C2×C13×C22⋊C4C2×C411yescharacteristic
63C2×C42×C13C2×C411yescharacteristic
64C2×C22⋊Dic13C2×C411yescharacteristic
65C2×C22⋊Dic13C2×C411yescharacteristic
66D4×Dic13—22no—
67D4×Dic13—22no—
68C4×C22⋊D13—24no—
69C4×C22⋊D13—24no—
70C2×#6103C2×C411yescharacteristic
71C2×#6103C2×C411yescharacteristic
72C2×C4⋊Dic13C2×C411yescharacteristic
73C2×#6101C2×C411yescharacteristic
74C2×#6101C2×C411yescharacteristic
75C2×#6101C2×C411yescharacteristic
76C2×#6101C2×C411yescharacteristic
77C2×C4×Dic13—22no—
78C2×C4×Dic13—22no—
79C2×C4×Dic13C2×C411yescharacteristic
80C2×C4×Dic13C2×C411yescharacteristic
81C2×C4×Dic13C2×C411yescharacteristic
82C2×C4×Dic13C2×C411yescharacteristic
83C2×C4×Dic13C2×C411yescharacteristic
84C2×C4×Dic13D414yes—
85C2×C4×Dic13D414yes—
86C2×C4×Dic13C2311yescharacteristic
87C2×C4×Dic13C2311yescharacteristic
88C2×C4×Dic13C2311yescharacteristic
89C2×C4×Dic13C2311yescharacteristic
90#88146—24no—
91#88141—22no—
92#88141—22no—
93#88135—22no—
94#88135—22no—
95#88135—22no—
96#88135—22no—
97#88131—24no—
98#88131—24no—
99C42×D13—22no—
100C42×D13—22no—
101C4×Dic26—24no—
102C22⋊#1057—24no—
103C22⋊#1057—28no—
104#88112—24no—
105#88111—28no—
106C4×#1057—24no—
107C4×#1057—24no—
108C4×#1057—24no—
109#21373—131nomaximal, Sylow
110C24×C13C22×C411yescharacteristic
111C24×C13C22×C411yescharacteristic
112C23×D13C22×C411yescharacteristic
113C2×D4×C13—22no—
114C2×D4×C13—22no—
115C2×D4×C13C2×C814yes—
116C22×C4×C13—24no—
117C22×C4×C13—22no—
118C22×C4×C13—24no—
119C22×C4×C13C22⋊C414yes—
120C22×C4×C13C22×C411yescharacteristic
121C22×C4×C13C22×C411yescharacteristic
122C22×C4×C13C22×C411yescharacteristic
123C22×C4×C13C22×C411yescharacteristic
124C22×C4×C13C22×C411yescharacteristic
125C2×C22⋊D13—22no—
126C2×C22⋊D13—22no—
127C2×C22⋊D13—22no—
128C2×C22⋊D13—22no—
129C2×C22⋊D13C2×C814yes—
130C2×C22⋊D13C2×C814yescomplemented
131C22×Dic13—22no—
132C22×Dic13—22no—
133C22×Dic13—24no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—24no—
137C22×Dic13C22⋊C414yes—
138C22×Dic13C2×C814yes—
139C22×Dic13C2×C814yescomplemented
140C22×Dic13M1614yes—
141C22×Dic13C22×C411yescharacteristic
142C22×Dic13C22×C411yescharacteristic
143C22×Dic13C22×C411yescharacteristic
144C22×Dic13C22×C411yescharacteristic
145C22×Dic13C22×C411yescharacteristic
146C22×Dic13C22×C411yescharacteristic
147C22×Dic13C2×D412yes—
148C22×Dic13C2×D412yes—
149C22×Dic13C2411yescharacteristic
150#6129—232no—
151C2×C4×D13—22no—
152C2×C4×D13—22no—
153C2×C4×D13—22no—
154C2×C4×D13—24no—
155C2×C4×D13—21no—
156C2×C4×D13—21no—
157C2×C4×D13—24no—
158C2×C4×D13C2×C814yescomplemented
159C2×Dic26—22no—
160C2×Dic26—22no—
161C2×Dic26C2×C814yescomplemented
162C2×#1057—216no—
163C2×#1057—24no—
164C2×#1057—24no—
165C2×#1057—24no—
166C2×#1057—24no—
167C2×#1057—24no—
168C2×#1057#4118yescomplemented
169C13×C4⋊C4—22no—
170C13×C22⋊C4—22no—
171C13×C22⋊C4—22no—
172C42×C13—22no—
173C22⋊Dic13—22no—
174C22⋊Dic13—22no—
175#6103—22no—
176#6103—22no—
177C4⋊Dic13—22no—
178#6101—22no—
179#6101—22no—
180#6101—22no—
181#6101—22no—
182C4×Dic13—22no—
183C4×Dic13—22no—
184C4×Dic13—22no—
185C4×Dic13—21no—
186C4×Dic13—21no—
187C4×Dic13—21no—
188C4×Dic13—21no—
189C4×Dic13C22⋊C414yes—
190C4×Dic13C22⋊C414yes—
191C4×Dic13C2×D412yes—
192C4×Dic13C2×D412yes—
193C4×Dic13C2×D412yes—
194C4×Dic13C2×D412yes—
195C2×C4×#41—131no—
196C2×#431—131no—
197C22×C4×C8—131no—
198#1984—132no—
199#1954—132no—
200#1869—132no—
201#1869—132no—
202C4×C22⋊C8—132no—
203C4×C22⋊C8—132no—
204C23×C13—22no—
205C23×C13—22no—
206C23×C13—21no—
207C23×C13—22no—
208C23×C13—21no—
209C23×C13—22no—
210C23×C13C2×C22⋊C412yes—
211C23×C13C22×C812yes—
212C23×C13C22×C812yes—
213C23×C13C2×M1612yes—
214C23×C13C23×C411yescharacteristic
215C22×D13—21no—
216C22×D13—22no—
217C22×D13—21no—
218C22×D13—22no—
219C22×D13C22×C812yes—
220D4×C13—28no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—22no—
224C2×C4×C13—28no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—44no—
230C2×C4×C13C2×C22⋊C412yes—
231C2×C4×C13C2×C22⋊C412yes—
232C2×C4×C13C22×C812yes—
233C2×C4×C13#13114yes—
234C22⋊D13—28no—
235C22⋊D13—28no—
236C2×Dic13—21no—
237C2×Dic13—22no—
238C2×Dic13—21no—
239C2×Dic13—24no—
240C2×Dic13—24no—
241C2×Dic13—28no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—22no—
245C2×Dic13—22no—
246C2×Dic13—42no—
247C2×Dic13—42no—
248C2×Dic13C22⋊C8116yescomplemented
249C2×Dic13C2×C22⋊C412yes—
250C2×Dic13C2×C22⋊C412yes—
251C2×Dic13C2×C22⋊C412yes—
252C2×Dic13C22×C812yes—
253C2×Dic13C22×C812yes—
254C2×Dic13C22×C812yes—
255C2×Dic13C2×M1612yes—
256C2×Dic13C2×M1612yes—
257C2×Dic13C22×D411yescharacteristic
258C2×Dic13C22×D411yescharacteristic
259C2×Dic13C2×#4114yes—
260C4×D13—28no—
261C4×D13—44no—
262C4×D13—42no—
263C4×D13—42no—
264Dic26—28no—
265#1057—28no—
266#1057—44no—
267C22×#41—131no—
268C23×C8—132no—
269C4×#41—264no—
270C4×#41—264no—
271C2×C4×Q8—131no—
272C2×C4×Q8—131no—
273C2×C4×D4—131no—
274C2×C4×D4—131no—
275C2×C4×D4—131no—
276C2×C4×D4—131no—
277C2×C4×D4—131no—
278C2×C4×D4#26111yescharacteristic
279C2×#117—131no—
280C2×#117—131no—
281C2×#117—131no—
282C22×C42—131no—
283C22×C42—131no—
284C22×C42—131no—
285#431—264no—
286C2×C4⋊C8—132no—
287C2×C22⋊C8—132no—
288C2×C22⋊C8—134no—
289C2×C22⋊C8—134no—
290C2×C4×C8—132no—
291C2×C4×C8—132no—
292C2×C4×C8—132no—
293C2×C4×C8—264no—
294#336—134no—
295#336—134no—
296C22×C13—22no—
297C22×C13—24no—
298C22×C13—24no—
299C22×C13—22no—
300C22×C13—22no—
301C22×C13—24no—
302C22×C13—41no—
303C22×C13—42no—
304C22×C13—41no—
305C22×C13C2×C22⋊C814yes—
306C22×C13C22×C22⋊C411yescharacteristic
307C22×C13C4×#4112yes—
308C22×C13C23×C811yescharacteristic
309C22×C13C22×M1611yescharacteristic
310C22×C13C2×#13112yes—
311C2×D13—22no—
312C2×D13—24no—
313C2×D13—41no—
314C2×D13—42no—
315C2×D13—41no—
316C4×C13—22no—
317C4×C13—22no—
318C4×C13—41no—
319C4×C13—41no—
320C4×C13#40814yes—
321Dic13—22no—
322Dic13—22no—
323Dic13—41no—
324Dic13—41no—
325Dic13C2×C22⋊C814yes—
326Dic13C2×C22⋊C814yes—
327Dic13#52512yes—
328Dic13#53212yes—
329C2×#41—138no—
330C2×#41—264no—
331C2×#41—264no—
332C22×Q8—131no—
333C22×D4—131no—
334C22×D4—131no—
335C22×D4C2×#26111yescharacteristic
336C23×C4—131no—
337C23×C4—131no—
338C23×C4—131no—
339C23×C4—131no—
340C23×C4—131no—
341C23×C4—131no—
342C23×C4—131no—
343C23×C4C2×#26111yescharacteristic
344C23×C4C2×#26111yescharacteristic
345C22×C8—134no—
346C22×C8—134no—
347C22×C8—268no—
348C22×C8—264no—
349C4×Q8—264no—
350C4×Q8—262no—
351C4×Q8—262no—
352C4×D4—24no—
353C4×D4—262no—
354C4×D4—262no—
355C4×D4—264no—
356C4×D4—262no—
357C4×D4—262no—
358C4×D4—262no—
359C4×D4—262no—
360C4×D4—264no—
361#117—264no—
362#117—264no—
363#117—264no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—131no—
366C2×C4⋊C4—131no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—131no—
369C2×C4⋊C4C2×#26111yescharacteristic
370C2×C22⋊C4—131no—
371C2×C22⋊C4—131no—
372C2×C22⋊C4—131no—
373C2×C22⋊C4—131no—
374C2×C22⋊C4C2×#26111yescharacteristic
375C2×C22⋊C4C2×#26111yescharacteristic
376C2×C42—134no—
377C2×C42—134no—
378C2×C42—131no—
379C2×C42—131no—
380C2×C42—131no—
381C2×C42—131no—
382C2×C42—131no—
383C2×C42—131no—
384C2×C42—131no—
385C2×C42—131no—
386C2×C42—131no—
387C2×C42—262no—
388C2×C42—262no—
389C2×C42—262no—
390C2×C42—262no—
391C2×C42C2×#26111yescharacteristic
392C4⋊C8—264no—
393C22⋊C8—268no—
394C22⋊C8—268no—
395C22⋊C8—264no—
396C4×C8—264no—
397C4×C8—264no—
398C4×C8—264no—
399C2×C13—24no—
400C2×C13—42no—
401C2×C13#229711yescharacteristic
402C2×C13C22×C22⋊C811yescharacteristic
403C2×C13C2×#40811yescharacteristic
404C2×C13C8×#4112yes—
405C2×C13#296512yes—
406D13—42no—
407C24—131no—
408C24C22×#26111yescharacteristic
409C24C22×#26111yescharacteristic
410#41—2632no—
411C2×Q8—134no—
412C2×Q8—262no—
413C2×Q8—262no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—134no—
417C2×D4—134no—
418C2×D4—262no—
419C2×D4—262no—
420C2×D4—262no—
421C2×D4—262no—
422C2×D4D13⋊C814yes—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—134no—
427C22×C4—134no—
428C22×C4—134no—
429C22×C4—131no—
430C22×C4—131no—
431C22×C4—131no—
432C22×C4—134no—
433C22×C4—132no—
434C22×C4—132no—
435C22×C4—131no—
436C22×C4—131no—
437C22×C4—134no—
438C22×C4—131no—
439C22×C4—131no—
440C22×C4—262no—
441C22×C4—262no—
442C22×C4—264no—
443C22×C4—261no—
444C22×C4—261no—
445C22×C4—262no—
446C22×C4—264no—
447C22×C4—262no—
448C22×C4—264no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—264no—
452C22×C4—262no—
453C22×C4C22⋊#26114yes—
454C22×C4C22×#26111yescharacteristic
455C22×C4C22×#26111yescharacteristic
456C22×C4C22×#26111yescharacteristic
457C22×C4C22×#26111yescharacteristic
458C22×C4C22×#26111yescharacteristic
459C2×C8—138no—
460C2×C8—264no—
461C2×C8—264no—
462C2×C8—2616no—
463C2×C8—264no—
464C2×C8—264no—
465C2×C8—264no—
466C4⋊C4—22no—
467C4⋊C4—262no—
468C4⋊C4—262no—
469C4⋊C4—262no—
470C4⋊C4—262no—
471C4⋊C4—262no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—262no—
475C22⋊C4—262no—
476C22⋊C4—262no—
477C22⋊C4—262no—
478C42—22no—
479C42—132no—
480C42—132no—
481C42—132no—
482C42—132no—
483C42—134no—
484C42—134no—
485C42—262no—
486C42—262no—
487C42—261no—
488C42—261no—
489C42—261no—
490C42—261no—
491C42—262no—
492C13#2137311yescharacteristic, complemented, Sylow
493C23—22no—
494C23—22no—
495C23—21no—
496C23—22no—
497C23—22no—
498C23—21no—
499C23—132no—
500C23—261no—
501C23—262no—
502C23—262no—
503C23—261no—
504C23C2×D13⋊C812yes—
505C23C2×D13⋊C812yes—
506C23D13⋊M1612yes—
507C23C2×C22⋊#26112yes—
508C23C23×#26111yescharacteristic
509Q8—268no—
510D4—28no—
511D4—268no—
512D4—268no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—28no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—44no—
522C2×C4—132no—
523C2×C4—132no—
524C2×C4—132no—
525C2×C4—132no—
526C2×C4—134no—
527C2×C4—131no—
528C2×C4—131no—
529C2×C4—132no—
530C2×C4—132no—
531C2×C4—1316no—
532C2×C4—132no—
533C2×C4—132no—
534C2×C4—268no—
535C2×C4—264no—
536C2×C4—264no—
537C2×C4—268no—
538C2×C4—261no—
539C2×C4—262no—
540C2×C4—261no—
541C2×C4—262no—
542C2×C4—262no—
543C2×C4—261no—
544C2×C4—261no—
545C2×C4—522no—
546C2×C4—522no—
547C2×C4—522no—
548C2×C4—522no—
549C2×C4—524no—
550C2×C4C2×D13⋊C812yes—
551C2×C4#8823814yes—
552C2×C4C2×C22⋊#26112yes—
553C2×C4C2×C22⋊#26112yes—
554C8—268no—
555C8—524no—
556C22—22no—
557C22—24no—
558C22—24no—
559C22—22no—
560C22—24no—
561C22—22no—
562C22—41no—
563C22—42no—
564C22—41no—
565C22—264no—
566C22—262no—
567C22—521no—
568C22—522no—
569C22—521no—
570C22D13⋊(C22⋊C8)14yes—
571C22C22×D13⋊C811yescharacteristic
572C22C2×D13⋊M1611yescharacteristic
573C22C2×#8823812yes—
574C22#41×#26112yes—
575C22C22×C22⋊#26111yescharacteristic
576C4—22no—
577C4—22no—
578C4—41no—
579C4—41no—
580C4—132no—
581C4—132no—
582C4—134no—
583C4—134no—
584C4—262no—
585C4—262no—
586C4—521no—
587C4—521no—
588C4#1171914614yes—
589C2—24no—
590C2—42no—
591C2—522no—
592C2#1313129711yescharacteristic
593C2C2×D13⋊(C22⋊C8)11yescharacteristic
594C2C2×#1171914611yescharacteristic
595C2#1313164112yes—
596C2#1313164612yes—
subgroupG/H
centerC22×C4C22×#261
commutatorC22×C13C23×C8
FrattiniC23C23×#261
FittingC2×C4×D4×C13C4
socleC23×C13C23×C4
prime radicalC22×#6129C4
cosocleC22×Dic13C24
hypercenterC2×C4×D4#261
hypocenterC13#21373
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#11719125C2semidirect
2. C22×C4×#1057C2semidirect
3. #13131007C2semidirect
4. #13130959C2semidirect
5. #13130811C2semidirect
6. #13130809C2semidirect
7. C4×#88111C2semidirect
8. C4×C22⋊#1057C2semidirect
50. C2×#6129C8semidirect
130. C2×C22⋊D13C2×C8semidirect
139. C22×Dic13C2×C8semidirect
158. C2×C4×D13C2×C8semidirect
161. C2×Dic26C2×C8semidirect
168. C2×#1057#41semidirect
248. C2×Dic13C22⋊C8semidirect
492. C13#21373semidirect

Maximal subgroups

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

subgroupindex
C2×#117191252
C22×C4×#10572
#131310072
#131309592
#131308112
#131308092
C4×#881112
C4×C22⋊#10572
C2×C4×#61292
#2137313