Finite Group Databasebeta

← #16793364

Subgroups — #16793364

Order 3328.

1214 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131512C211yesmaximal, characteristic
2#13131512C211yesmaximal, characteristic
3#13130180C214yesmaximal, complemented
4#13130166C214yesmaximal, complemented
5#13130140C214yesmaximal, complemented
6C22×#88141C211yesmaximal, characteristic
7C23×Dic26C411yescharacteristic
8C22×C13×C4⋊C4C411yescharacteristic
9C22×#6101—21no—
10C22×C4×Dic13—21no—
11C22×C4×Dic13C2211yescharacteristic
12C2×#88141—21no—
13C2×#88141—21no—
14C2×#88141—21no—
15C2×#88141—21no—
16C2×#88141—21no—
17C2×#88141—21no—
18C2×#88141C412yes—
19C2×#88141C412yes—
20C2×#88141C412yes—
21C2×#88141C2212yes—
22C2×#88141C2212yes—
23C2×#88141C2212yes—
24#11719169—21no—
25#11719169—21no—
26#11719130—21no—
27#11719130C2212yes—
28#11719129—21no—
29#11719129C2212yes—
30#11719128—21no—
31#11719128—21no—
32#11719125—21no—
33#11719125C2212yes—
34C4×#6122—21no—
35C4×#6122C2212yes—
36#11719119C2212yes—
37#11719119C2212yes—
38#11718244C22116yescomplemented
39C23×C4×C13—21no—
40C23×C4×C13C2×C411yescharacteristic
41C23×Dic13—21no—
42C23×Dic13D411yescharacteristic
43C23×Dic13D411yescharacteristic
44C22×Dic26—21no—
45C22×Dic26—21no—
46C22×Dic26—21no—
47C22×Dic26—28no—
48C22×Dic26C2×C412yes—
49C22×Dic26C2×C412yes—
50C22×Dic26C2×C412yes—
51C2×#6122—22no—
52C2×#6122—22no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4C2×C412yes—
57C2×C13×C4⋊C4C2×C412yes—
58C2×C13×C4⋊C4C2×C412yes—
59C2×#6101—22no—
60C2×#6101—22no—
61C2×#6101—22no—
62C2×#6101—22no—
63C2×#6101—22no—
64C2×#6101—22no—
65C2×C4×Dic13—22no—
66C2×C4×Dic13—22no—
67C2×C4×Dic13—22no—
68C2×C4×Dic13—22no—
69C2×C4×Dic13—22no—
70C2×C4×Dic13—22no—
71C2×C4×Dic13C2×C411yescharacteristic
72C2×C4×Dic13C2×C411yescharacteristic
73C2×C4×Dic13C2×C411yescharacteristic
74C2×C4×Dic13D411yescharacteristic
75C2×C4×Dic13D411yescharacteristic
76C2×C4×Dic13D411yescharacteristic
77C2×C4×Dic13D411yescharacteristic
78C2×C4×Dic13D411yescharacteristic
79C2×C4×Dic13D411yescharacteristic
80C2×C4×Dic13C2311yescharacteristic
81C2×C4×Dic13C2311yescharacteristic
82C2×C4×Dic13C2311yescharacteristic
83#88141—22no—
84#88141—22no—
85#88141—22no—
86#88141—22no—
87#88141—22no—
88#88141—22no—
89#88141—22no—
90#88141—22no—
91#88141—22no—
92#88141—22no—
93#88141—22no—
94#88141—22no—
95#88141C2×C414yes—
96#88141C2×C414yes—
97#88141C2×C414yes—
98#88141C2314yes—
99C22⋊#1057—22no—
100C22⋊#1057—22no—
101C22⋊#1057—22no—
102C22⋊#1057—22no—
103#88112—22no—
104#88112—22no—
105#88110—22no—
106#88110—22no—
107C4⋊#1057—22no—
108C4⋊#1057C2314yes—
109C4×#1057—22no—
110C4×#1057C2314yes—
111#17449—131nomaximal, Sylow
112C24×C13C22⋊C411yescharacteristic
113C22×C4×C13—24no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—44no—
118C22×C4×C13C22⋊C411yescharacteristic
119C22×C4×C13C22⋊C411yescharacteristic
120C22×C4×C13C22⋊C411yescharacteristic
121C22×C4×C13C22×C411yescharacteristic
122C22×C4×C13C22×C411yescharacteristic
123C22×C4×C13C22×C411yescharacteristic
124C22×Dic13—28no—
125C22×Dic13—22no—
126C22×Dic13—22no—
127C22×Dic13—22no—
128C22×Dic13—24no—
129C22×Dic13—42no—
130C22×Dic13C22⋊C411yescharacteristic
131C22×Dic13C22⋊C411yescharacteristic
132C22×Dic13C22⋊C411yescharacteristic
133C22×Dic13C22⋊C411yescharacteristic
134C22×Dic13C22⋊C411yescharacteristic
135C22×Dic13C22⋊C411yescharacteristic
136C22×Dic13C2×D411yescharacteristic
137C22×Dic13C2×D411yescharacteristic
138C22×Dic13C2×D411yescharacteristic
139C22×Dic13C2×D411yescharacteristic
140C22×Dic13C2×D411yescharacteristic
141C22×Dic13C2×D411yescharacteristic
142C2×Dic26—28no—
143C2×Dic26—28no—
144C2×Dic26—28no—
145C2×Dic26—22no—
146C2×Dic26—22no—
147C2×Dic26—22no—
148C2×Dic26—24no—
149C2×Dic26—28no—
150C2×Dic26—28no—
151C2×Dic26M1618yescomplemented
152C2×Dic26C22×C414yes—
153#6122—44no—
154#6122—44no—
155C2×#1057—24no—
156C2×#1057—24no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4C22×C414yes—
161#6101—24no—
162#6101—24no—
163#6101—24no—
164#6101—24no—
165C4×Dic13—24no—
166C4×Dic13—24no—
167C4×Dic13—24no—
168C4×Dic13—24no—
169C4×Dic13C22⋊C411yescharacteristic
170C4×Dic13C22⋊C411yescharacteristic
171C4×Dic13C22⋊C411yescharacteristic
172C4×Dic13C22⋊C411yescharacteristic
173C4×Dic13C22⋊C411yescharacteristic
174C4×Dic13C22⋊C411yescharacteristic
175C4×Dic13C22×C411yescharacteristic
176C4×Dic13C22×C411yescharacteristic
177C4×Dic13C22×C411yescharacteristic
178C4×Dic13C2×D411yescharacteristic
179C4×Dic13C2×D411yescharacteristic
180C4×Dic13C2×D411yescharacteristic
181C4×Dic13C2×D411yescharacteristic
182C4×Dic13C2×D411yescharacteristic
183C4×Dic13C2×D411yescharacteristic
184C4×Dic13C2411yescharacteristic
185C22×C4×Q8—131no—
186#2920—131no—
187#2920—131no—
188#1491—134no—
189#1487—134no—
190#1479—134no—
191C23×C13—22no—
192C23×C13—22no—
193C23×C13—22no—
194C23×C13C2×C22⋊C411yescharacteristic
195C23×C13C2×C22⋊C411yescharacteristic
196C23×C13C2×C22⋊C411yescharacteristic
197C2×C4×C13—22no—
198C2×C4×C13—22no—
199C2×C4×C13—22no—
200C2×C4×C13—22no—
201C2×C4×C13—22no—
202C2×C4×C13—24no—
203C2×C4×C13—44no—
204C2×C4×C13—44no—
205C2×C4×C13—44no—
206C2×C4×C13C2×C22⋊C411yescharacteristic
207C2×C4×C13C2×C22⋊C411yescharacteristic
208C2×C4×C13C2×C22⋊C411yescharacteristic
209C2×C4×C13C2×M1614yes—
210C2×C4×C13C23×C411yescharacteristic
211C2×Dic13—28no—
212C2×Dic13—28no—
213C2×Dic13—24no—
214C2×Dic13—28no—
215C2×Dic13—22no—
216C2×Dic13—22no—
217C2×Dic13—22no—
218C2×Dic13—22no—
219C2×Dic13—22no—
220C2×Dic13—22no—
221C2×Dic13—22no—
222C2×Dic13—41no—
223C2×Dic13—41no—
224C2×Dic13—41no—
225C2×Dic13—41no—
226C2×Dic13C2×C22⋊C411yescharacteristic
227C2×Dic13C2×C22⋊C411yescharacteristic
228C2×Dic13C2×C22⋊C411yescharacteristic
229C2×Dic13C2×C22⋊C411yescharacteristic
230C2×Dic13C2×C22⋊C411yescharacteristic
231C2×Dic13C2×C22⋊C411yescharacteristic
232C2×Dic13#13714yes—
233C2×Dic13C22×D411yescharacteristic
234C2×Dic13C22×D411yescharacteristic
235Dic26—28no—
236Dic26—28no—
237Dic26—24no—
238Dic26—28no—
239Dic26C2×M1618yes—
240#1057—44no—
241#1057—44no—
242C23×Q8—131no—
243C2×C4×Q8—132no—
244C2×C4×Q8—132no—
245C2×C4×Q8—132no—
246C2×C4×Q8—132no—
247C2×C4×Q8—132no—
248C2×C4×Q8—132no—
249C2×C4×Q8—261no—
250C2×C4×Q8—261no—
251C2×C4×Q8—261no—
252C2×C4×Q8—261no—
253C2×C4×Q8—261no—
254C2×C4×Q8—261no—
255C22×C4⋊C4—261no—
256C22×C4⋊C4#26111yescharacteristic
257C22×C42—131no—
258C22×C42—261no—
259#432—132no—
260#432—261no—
261#432—261no—
262#432—261no—
263#431—132no—
264#431—132no—
265#431—132no—
266#431—261no—
267#423—132no—
268#423—261no—
269#407—261no—
270#407—261no—
271C4×M16—132no—
272C4×M16—261no—
273Q8⋊C8—1316no—
274C22×C13—28no—
275C22×C13—21no—
276C22×C13—21no—
277C22×C13—21no—
278C22×C13—21no—
279C22×C13—21no—
280C22×C13—21no—
281C22×C13#40712yes—
282C22×C13#41912yes—
283C22×C13#42112yes—
284C22×C13C22×C22⋊C411yescharacteristic
285C4×C13—21no—
286C4×C13—21no—
287C4×C13—44no—
288C4×C13#40712yes—
289C4×C13C22×M1612yes—
290Dic13—28no—
291Dic13—21no—
292Dic13—21no—
293Dic13—21no—
294Dic13—21no—
295Dic13—21no—
296Dic13—21no—
297Dic13#41912yes—
298Dic13C2×#13712yes—
299C22×Q8—132no—
300C22×Q8—132no—
301C22×Q8—132no—
302C22×Q8—268no—
303C22×Q8—261no—
304C22×Q8—261no—
305C22×Q8—261no—
306C23×C4—21no—
307C23×C4—131no—
308C23×C4—131no—
309C23×C4—261no—
310C23×C4C2×#26111yescharacteristic
311C2×M16—262no—
312C2×M16—262no—
313C4×Q8—134no—
314C4×Q8—134no—
315C4×Q8—134no—
316C4×Q8—134no—
317C4×Q8—262no—
318C4×Q8—262no—
319C4×Q8—262no—
320C4×Q8—262no—
321C4×Q8—262no—
322C4×Q8—262no—
323C4×Q8—262no—
324C4×Q8—262no—
325C4×Q8—262no—
326C4×Q8—262no—
327C4×Q8—262no—
328C4×Q8—262no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—262no—
333C2×C4⋊C4—262no—
334C2×C4⋊C4—262no—
335C2×C4⋊C4—262no—
336C2×C4⋊C4—262no—
337C2×C4⋊C4—262no—
338C2×C4⋊C4C2×#26112yes—
339C2×C4⋊C4C2×#26112yes—
340C2×C4⋊C4C2×#26112yes—
341C2×C42—131no—
342C2×C42—131no—
343C2×C42—131no—
344C2×C42—131no—
345C2×C42—131no—
346C2×C42—131no—
347C2×C42—131no—
348C2×C42—131no—
349C2×C42—131no—
350C2×C42—131no—
351C2×C42—131no—
352C2×C42—131no—
353C2×C42—262no—
354C2×C42—262no—
355C2×C42—262no—
356C2×C42—262no—
357C2×C42—262no—
358C2×C42—262no—
359C4⋊C8—134no—
360C4⋊C8—262no—
361C4⋊C8—262no—
362C4⋊C8—262no—
363C22⋊C8—262no—
364C22⋊C8—262no—
365C22⋊C8—262no—
366C22⋊C8—262no—
367#97—262no—
368#97—262no—
369C4×C8—134no—
370C4×C8—262no—
371C2×C13—22no—
372C2×C13—22no—
373C2×C13—22no—
374C2×C13C2×#40711yescharacteristic
375C2×C13C2×#41911yescharacteristic
376C2×C13C2×#42111yescharacteristic
377C24C22⋊#26111yescharacteristic
378C2×Q8—138no—
379C2×Q8—134no—
380C2×Q8—268no—
381C2×Q8—268no—
382C2×Q8—268no—
383C2×Q8—268no—
384C2×Q8—268no—
385C2×Q8—264no—
386C2×Q8—262no—
387C2×Q8—262no—
388C2×Q8—262no—
389C22×C4—24no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—44no—
394C22×C4—131no—
395C22×C4—131no—
396C22×C4—131no—
397C22×C4—131no—
398C22×C4—131no—
399C22×C4—131no—
400C22×C4—131no—
401C22×C4—131no—
402C22×C4—131no—
403C22×C4—131no—
404C22×C4—131no—
405C22×C4—131no—
406C22×C4—264no—
407C22×C4—268no—
408C22×C4—262no—
409C22×C4—262no—
410C22×C4—262no—
411C22×C4—522no—
412C22×C4C22⋊#26111yescharacteristic
413C22×C4C22⋊#26111yescharacteristic
414C22×C4C22⋊#26111yescharacteristic
415C22×C4C22×#26111yescharacteristic
416C22×C4C22×#26111yescharacteristic
417C22×C4C22×#26111yescharacteristic
418M16—524no—
419M16—524no—
420C2×C8—264no—
421C2×C8—264no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—264no—
426C4⋊C4—264no—
427C4⋊C4—264no—
428C4⋊C4—264no—
429C4⋊C4C22×#26114yes—
430C42—131no—
431C42—131no—
432C42—131no—
433C42—131no—
434C42—131no—
435C42—131no—
436C42—131no—
437C42—131no—
438C42—131no—
439C42—131no—
440C42—131no—
441C42—131no—
442C42—131no—
443C42—131no—
444C42—131no—
445C42—131no—
446C42—264no—
447C42—264no—
448C42—264no—
449C42—264no—
450C13#1744911yescharacteristic, complemented, Sylow
451C23—22no—
452C23—22no—
453C23—22no—
454C23C2×C22⋊#26111yescharacteristic
455C23C2×C22⋊#26111yescharacteristic
456C23C2×C22⋊#26111yescharacteristic
457Q8—138no—
458Q8—268no—
459Q8—268no—
460Q8—264no—
461Q8—268no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—44no—
469C2×C4—44no—
470C2×C4—44no—
471C2×C4—131no—
472C2×C4—131no—
473C2×C4—134no—
474C2×C4—131no—
475C2×C4—131no—
476C2×C4—131no—
477C2×C4—131no—
478C2×C4—131no—
479C2×C4—131no—
480C2×C4—262no—
481C2×C4—262no—
482C2×C4—262no—
483C2×C4—262no—
484C2×C4—268no—
485C2×C4—268no—
486C2×C4—264no—
487C2×C4—268no—
488C2×C4—262no—
489C2×C4—262no—
490C2×C4—262no—
491C2×C4—521no—
492C2×C4—521no—
493C2×C4—521no—
494C2×C4—521no—
495C2×C4D13⋊M1614yes—
496C2×C4C2×C22⋊#26111yescharacteristic
497C2×C4C2×C22⋊#26111yescharacteristic
498C2×C4C2×C22⋊#26111yescharacteristic
499C2×C4C23×#26111yescharacteristic
500C8—524no—
501C8—524no—
502C22—28no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22#1171912612yes—
510C22#1171914012yes—
511C22#1171915312yes—
512C22C22×C22⋊#26111yescharacteristic
513C4—21no—
514C4—21no—
515C4—44no—
516C4—132no—
517C4—132no—
518C4—268no—
519C4—261no—
520C4—261no—
521C4—261no—
522C4—261no—
523C4—261no—
524C4—261no—
525C4#1171912612yes—
526C4C2×D13⋊M1612yes—
527C2—22no—
528C2—22no—
529C2—22no—
530C2C2×#1171912611yescharacteristic
531C2C2×#1171915311yescharacteristic
532C2C2×#1171914011yescharacteristic
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#17449
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13130180C2semidirect
4. #13130166C2semidirect
5. #13130140C2semidirect
38. #11718244C22semidirect
151. C2×Dic26M16semidirect
450. C13#17449semidirect

Maximal subgroups

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

subgroupindex
#131315122
#131301802
#131301662
#131301402
C22×#881412
#1744913