Finite Group Databasebeta

← #16794474

Subgroups — #16794474

Order 3328.

962 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131512C211yesmaximal, characteristic
2#13131512C211yesmaximal, characteristic
3#13130318C214yesmaximal, complemented
4#13130300C214yesmaximal, complemented
5#13130298C214yesmaximal, complemented
6C22×#88144C211yesmaximal, characteristic
7C22×C13×C4⋊C4C411yescharacteristic
8C22×C4⋊Dic13—21no—
9C22×C4⋊Dic13C411yescharacteristic
10C22×#6101—21no—
11C22×C4×Dic13C2211yescharacteristic
12C2×#88144—21no—
13C2×#88144—21no—
14C2×#88144—21no—
15C2×#88144—21no—
16C2×#88144—21no—
17C2×#88144—21no—
18C2×#88144C412yes—
19C2×#88144C412yes—
20C2×#88144C412yes—
21C2×#88144C2212yes—
22C2×#88144C2212yes—
23C2×#88144C2212yes—
24#11719169—21no—
25#11719169—21no—
26#11719130C2212yes—
27#11719130C2212yes—
28#11719129—21no—
29#11719129—21no—
30#11719128C2212yes—
31#11719128C2212yes—
32#11719125—21no—
33#11719125—21no—
34C4×#6122C2212yes—
35C4×#6122C2212yes—
36#11719119—21no—
37#11719119—21no—
38#11718242C22116yescomplemented
39C23×C4×C13—21no—
40C23×C4×C13C2×C411yescharacteristic
41C23×Dic13—21no—
42C23×Dic13D411yescharacteristic
43C23×Dic13D411yescharacteristic
44C2×#6122—22no—
45C2×#6122—22no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4C2×C412yes—
50C2×C13×C4⋊C4C2×C412yes—
51C2×C13×C4⋊C4C2×C412yes—
52C2×C4⋊Dic13—21no—
53C2×C4⋊Dic13—21no—
54C2×C4⋊Dic13—21no—
55C2×C4⋊Dic13—22no—
56C2×C4⋊Dic13—22no—
57C2×C4⋊Dic13—22no—
58C2×C4⋊Dic13—22no—
59C2×C4⋊Dic13—22no—
60C2×C4⋊Dic13—22no—
61C2×C4⋊Dic13C2×C412yes—
62C2×C4⋊Dic13C2×C412yes—
63C2×C4⋊Dic13C2×C412yes—
64C2×#6101—22no—
65C2×#6101—22no—
66C2×#6101—22no—
67C2×#6101—22no—
68C2×#6101—22no—
69C2×#6101—22no—
70C2×C4×Dic13C2×C411yescharacteristic
71C2×C4×Dic13C2×C411yescharacteristic
72C2×C4×Dic13C2×C411yescharacteristic
73C2×C4×Dic13D411yescharacteristic
74C2×C4×Dic13D411yescharacteristic
75C2×C4×Dic13D411yescharacteristic
76C2×C4×Dic13D411yescharacteristic
77C2×C4×Dic13D411yescharacteristic
78C2×C4×Dic13D411yescharacteristic
79C2×C4×Dic13C2311yescharacteristic
80C2×C4×Dic13C2311yescharacteristic
81C2×C4×Dic13C2311yescharacteristic
82#88144—22no—
83#88144—22no—
84#88144—22no—
85#88144—22no—
86#88144—22no—
87#88144—22no—
88#88144—22no—
89#88144—22no—
90#88144—22no—
91#88144—22no—
92#88144—22no—
93#88144—22no—
94#88144C2×C414yes—
95#88144C2×C414yes—
96#88144C2×C414yes—
97#88144C2314yes—
98C22⋊#1057—22no—
99C22⋊#1057—22no—
100C22⋊#1057—22no—
101C22⋊#1057—22no—
102#88112—22no—
103#88112—22no—
104#88110C2314yes—
105#88110C2314yes—
106C4⋊#1057—22no—
107C4⋊#1057—22no—
108C4×#1057—22no—
109C4×#1057—22no—
110#17667—131nomaximal, Sylow
111C24×C13C22⋊C411yescharacteristic
112C22×C4×C13—24no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—44no—
117C22×C4×C13C22⋊C411yescharacteristic
118C22×C4×C13C22⋊C411yescharacteristic
119C22×C4×C13C22⋊C411yescharacteristic
120C22×C4×C13C22×C411yescharacteristic
121C22×C4×C13C22×C411yescharacteristic
122C22×C4×C13C22×C411yescharacteristic
123C22×Dic13—22no—
124C22×Dic13—22no—
125C22×Dic13—22no—
126C22×Dic13—42no—
127C22×Dic13—42no—
128C22×Dic13—44no—
129C22×Dic13C22⋊C411yescharacteristic
130C22×Dic13C22⋊C411yescharacteristic
131C22×Dic13C22⋊C411yescharacteristic
132C22×Dic13C22⋊C411yescharacteristic
133C22×Dic13C22⋊C411yescharacteristic
134C22×Dic13C22⋊C411yescharacteristic
135C22×Dic13C2×D411yescharacteristic
136C22×Dic13C2×D411yescharacteristic
137C22×Dic13C2×D411yescharacteristic
138C22×Dic13C2×D411yescharacteristic
139C22×Dic13C2×D411yescharacteristic
140C22×Dic13C2×D411yescharacteristic
141#6122—44no—
142#6122—44no—
143C2×#1057—24no—
144C2×#1057—24no—
145C13×C4⋊C4—22no—
146C13×C4⋊C4—22no—
147C13×C4⋊C4—22no—
148C13×C4⋊C4C22×C414yes—
149C4⋊Dic13—22no—
150C4⋊Dic13—22no—
151C4⋊Dic13—22no—
152C4⋊Dic13—24no—
153C4⋊Dic13—24no—
154C4⋊Dic13—24no—
155C4⋊Dic13—24no—
156C4⋊Dic13C22×C414yes—
157#6101—24no—
158#6101—24no—
159#6101—24no—
160#6101—24no—
161C4×Dic13C22⋊C411yescharacteristic
162C4×Dic13C22⋊C411yescharacteristic
163C4×Dic13C22⋊C411yescharacteristic
164C4×Dic13C22⋊C411yescharacteristic
165C4×Dic13C22⋊C411yescharacteristic
166C4×Dic13C22⋊C411yescharacteristic
167C4×Dic13C22×C411yescharacteristic
168C4×Dic13C22×C411yescharacteristic
169C4×Dic13C22×C411yescharacteristic
170C4×Dic13C2×D411yescharacteristic
171C4×Dic13C2×D411yescharacteristic
172C4×Dic13C2×D411yescharacteristic
173C4×Dic13C2×D411yescharacteristic
174C4×Dic13C2×D411yescharacteristic
175C4×Dic13C2×D411yescharacteristic
176C4×Dic13C2411yescharacteristic
177C22×#125—131no—
178#2920—131no—
179#2920—131no—
180#1534—134no—
181#1528—134no—
182#1528—134no—
183C23×C13—22no—
184C23×C13—22no—
185C23×C13—22no—
186C23×C13C2×C22⋊C411yescharacteristic
187C23×C13C2×C22⋊C411yescharacteristic
188C23×C13C2×C22⋊C411yescharacteristic
189C2×C4×C13—22no—
190C2×C4×C13—22no—
191C2×C4×C13—22no—
192C2×C4×C13—22no—
193C2×C4×C13—22no—
194C2×C4×C13—24no—
195C2×C4×C13—44no—
196C2×C4×C13—44no—
197C2×C4×C13—44no—
198C2×C4×C13#10114yes—
199C2×C4×C13C2×C22⋊C411yescharacteristic
200C2×C4×C13C2×C22⋊C411yescharacteristic
201C2×C4×C13C2×C22⋊C411yescharacteristic
202C2×C4×C13C23×C411yescharacteristic
203C2×Dic13—22no—
204C2×Dic13—22no—
205C2×Dic13—22no—
206C2×Dic13—22no—
207C2×Dic13—24no—
208C2×Dic13—41no—
209C2×Dic13—41no—
210C2×Dic13—41no—
211C2×Dic13—41no—
212C2×Dic13—41no—
213C2×Dic13—41no—
214C2×Dic13—41no—
215C2×Dic13—41no—
216C2×Dic13—44no—
217C2×Dic13—44no—
218C2×Dic13—44no—
219C2×Dic13C2×C22⋊C411yescharacteristic
220C2×Dic13C2×C22⋊C411yescharacteristic
221C2×Dic13C2×C22⋊C411yescharacteristic
222C2×Dic13C2×C22⋊C411yescharacteristic
223C2×Dic13C2×C22⋊C411yescharacteristic
224C2×Dic13C2×C22⋊C411yescharacteristic
225C2×Dic13C22×D411yescharacteristic
226C2×Dic13C22×D411yescharacteristic
227#1057—44no—
228#1057—44no—
229C2×#125—132no—
230C2×#125—132no—
231C2×#125—132no—
232C2×#125—132no—
233C2×#125—132no—
234C2×#125—132no—
235C2×#125—261no—
236C2×#125—261no—
237C2×#125—261no—
238C2×#125—261no—
239C2×#125—261no—
240C2×#125—261no—
241C22×C4⋊C4—131no—
242C22×C4⋊C4—261no—
243C22×C4⋊C4—261no—
244C22×C4⋊C4#26111yescharacteristic
245C22×C42—131no—
246#432—132no—
247#432—132no—
248#432—132no—
249#432—132no—
250#431—261no—
251#431—261no—
252#431—261no—
253#431—261no—
254#423—261no—
255#423—261no—
256#407—261no—
257#407—261no—
258C4×M16—132no—
259C4×M16—132no—
260#330—1316no—
261C22×C13—28no—
262C22×C13—21no—
263C22×C13—21no—
264C22×C13—21no—
265C22×C13—21no—
266C22×C13—21no—
267C22×C13—21no—
268C22×C13C2×#10112yes—
269C22×C13#42112yes—
270C22×C13#42112yes—
271C22×C13C22×C22⋊C411yescharacteristic
272C4×C13—21no—
273C4×C13—21no—
274C4×C13—44no—
275C4×C13C2×#10112yes—
276C4×C13C2×#10112yes—
277Dic13—21no—
278Dic13—21no—
279Dic13—21no—
280Dic13—21no—
281Dic13—21no—
282Dic13—21no—
283Dic13—21no—
284Dic13—21no—
285Dic13—44no—
286C23×C4—21no—
287C23×C4—131no—
288C23×C4—131no—
289C23×C4—261no—
290C23×C4C2×#26111yescharacteristic
291C2×M16—262no—
292C2×M16—262no—
293#125—134no—
294#125—134no—
295#125—134no—
296#125—134no—
297#125—262no—
298#125—262no—
299#125—262no—
300#125—262no—
301#125—262no—
302#125—262no—
303#125—262no—
304#125—262no—
305#125—262no—
306#125—262no—
307#125—262no—
308#125—262no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—132no—
313C2×C4⋊C4—132no—
314C2×C4⋊C4—132no—
315C2×C4⋊C4—262no—
316C2×C4⋊C4—262no—
317C2×C4⋊C4—262no—
318C2×C4⋊C4—262no—
319C2×C4⋊C4—262no—
320C2×C4⋊C4—262no—
321C2×C4⋊C4—262no—
322C2×C4⋊C4—262no—
323C2×C4⋊C4—262no—
324C2×C4⋊C4—262no—
325C2×C4⋊C4—262no—
326C2×C4⋊C4—262no—
327C2×C4⋊C4—261no—
328C2×C4⋊C4—261no—
329C2×C4⋊C4—261no—
330C2×C4⋊C4C2×#26112yes—
331C2×C4⋊C4C2×#26112yes—
332C2×C4⋊C4C2×#26112yes—
333C2×C42—131no—
334C2×C42—131no—
335C2×C42—131no—
336C2×C42—131no—
337C2×C42—131no—
338C2×C42—131no—
339C2×C42—131no—
340C2×C42—131no—
341C2×C42—131no—
342C2×C42—131no—
343C2×C42—131no—
344C2×C42—131no—
345C4⋊C8—262no—
346C4⋊C8—262no—
347C4⋊C8—262no—
348C4⋊C8—262no—
349C22⋊C8—262no—
350C22⋊C8—262no—
351C22⋊C8—262no—
352C22⋊C8—262no—
353#97—134no—
354#97—134no—
355C4×C8—262no—
356C4×C8—262no—
357C2×C13—22no—
358C2×C13—22no—
359C2×C13—22no—
360C2×C13C22×#10111yescharacteristic
361C2×C13C2×#42111yescharacteristic
362C2×C13C2×#42111yescharacteristic
363C24C22⋊#26111yescharacteristic
364C22×C4—24no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—44no—
369C22×C4—131no—
370C22×C4—131no—
371C22×C4—131no—
372C22×C4—131no—
373C22×C4—131no—
374C22×C4—131no—
375C22×C4—131no—
376C22×C4—131no—
377C22×C4—131no—
378C22×C4—131no—
379C22×C4—131no—
380C22×C4—131no—
381C22×C4—262no—
382C22×C4—262no—
383C22×C4—262no—
384C22×C4—522no—
385C22×C4—522no—
386C22×C4—524no—
387C22×C4C22⋊#26111yescharacteristic
388C22×C4C22⋊#26111yescharacteristic
389C22×C4C22⋊#26111yescharacteristic
390C22×C4C22×#26111yescharacteristic
391C22×C4C22×#26111yescharacteristic
392C22×C4C22×#26111yescharacteristic
393M16—524no—
394M16—524no—
395C2×C8—264no—
396C2×C8—264no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—134no—
401C4⋊C4—264no—
402C4⋊C4—264no—
403C4⋊C4—264no—
404C4⋊C4—264no—
405C4⋊C4—264no—
406C4⋊C4—264no—
407C4⋊C4—264no—
408C4⋊C4—264no—
409C4⋊C4—262no—
410C4⋊C4—262no—
411C4⋊C4—262no—
412C4⋊C4C22×#26114yes—
413C42—131no—
414C42—131no—
415C42—131no—
416C42—131no—
417C42—131no—
418C42—131no—
419C42—131no—
420C42—131no—
421C42—131no—
422C42—131no—
423C42—131no—
424C42—131no—
425C42—131no—
426C42—131no—
427C42—131no—
428C42—131no—
429C13#1766711yescharacteristic, complemented, Sylow
430C23—22no—
431C23—22no—
432C23—22no—
433C23C2×C22⋊#26111yescharacteristic
434C23C2×C22⋊#26111yescharacteristic
435C23C2×C22⋊#26111yescharacteristic
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—24no—
442C2×C4—44no—
443C2×C4—44no—
444C2×C4—44no—
445C2×C4—131no—
446C2×C4—131no—
447C2×C4—131no—
448C2×C4—131no—
449C2×C4—131no—
450C2×C4—131no—
451C2×C4—131no—
452C2×C4—131no—
453C2×C4—262no—
454C2×C4—262no—
455C2×C4—262no—
456C2×C4—262no—
457C2×C4—264no—
458C2×C4—521no—
459C2×C4—521no—
460C2×C4—521no—
461C2×C4—521no—
462C2×C4—521no—
463C2×C4—521no—
464C2×C4—521no—
465C2×C4—521no—
466C2×C4—524no—
467C2×C4—524no—
468C2×C4—524no—
469C2×C4#8811314yes—
470C2×C4C2×C22⋊#26111yescharacteristic
471C2×C4C2×C22⋊#26111yescharacteristic
472C2×C4C2×C22⋊#26111yescharacteristic
473C2×C4C23×#26111yescharacteristic
474C8—524no—
475C8—524no—
476C22—28no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22C2×#8811312yes—
484C22#1171914012yes—
485C22#1171915512yes—
486C22C22×C22⋊#26111yescharacteristic
487C4—21no—
488C4—21no—
489C4—44no—
490C4—261no—
491C4—261no—
492C4—261no—
493C4—261no—
494C4—261no—
495C4—261no—
496C4—261no—
497C4—261no—
498C4—524no—
499C4C2×#8811312yes—
500C4C2×#8811312yes—
501C2—22no—
502C2—22no—
503C2—22no—
504C2C22×#8811311yescharacteristic
505C2C2×#1171914011yescharacteristic
506C2C2×#1171915511yescharacteristic
subgroupG/H
centerC22C22×C22⋊#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC22×C13×C4⋊C4C4
socleC22×C13C22×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC4×Dic13C24
hypercenterC22×C4⋊C4#261
hypocenterC13#17667
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13130318C2semidirect
4. #13130300C2semidirect
5. #13130298C2semidirect
38. #11718242C22semidirect
429. C13#17667semidirect

Maximal subgroups

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

subgroupindex
#131315122
#131303182
#131303002
#131302982
C22×#881442
#1766713