Finite Group Databasebeta

← #15919925

Subgroups — #15919925

Order 3328.

1072 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718730C211yesmaximal, characteristic, complemented
2C2×#11718680C211yesmaximal, characteristic
3#13120048C211yesmaximal, characteristic, complemented
4#13115984C212yesmaximal, complemented
5#13115974C212yesmaximal, complemented
6#13115794C211yesmaximal, characteristic, complemented
7#13115777C211yesmaximal, characteristic, complemented
8#13115170C212yesmaximal
9#13115170C212yesmaximal
10#13114661C211yesmaximal, characteristic
11C2×C13×#554C211yesmaximal, characteristic
12C13×#554—24no—
13C13×#554—24no—
14C2×C13×C4⋊Q8C2211yescharacteristic
15C2×C13×#125C2211yescharacteristic
16C2×C13×#125C2211yescharacteristic
17C2×C13×C22⋊Q8—21no—
18C2×C13×C22⋊Q8—21no—
19C2×C13×C22⋊Q8—21no—
20C2×C4×Q8×C13C2211yescharacteristic
21C2×C4×D4×C13C2211yescharacteristic
22C2×C4×D4×C13C2211yescharacteristic
23C2×C4×D4×C13C2211yescharacteristic
24C22×C13×C4⋊C4—21no—
25C22×#6105C2212yes—
26C2×#88123C2211yescharacteristic
27#11718891—21no—
28C2×#88072C2212yes—
29#11718730—24no—
30#11718680—24no—
31#11718647—21no—
32#11718647—21no—
33#11718638—21no—
34C2×#88050C2212yes—
35C2×#88050C2212yes—
36C2×#88050C2212yes—
37C4×C4⋊Dic13C2211yescharacteristic
38#11718590C2212yes—
39#11718590C2212yes—
40C2×C4⋊#1055C2211yescharacteristic
41C2×#88043C2211yescharacteristic
42#11718121C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45#11718116C2212yes—
46#11718116C2212yes—
47C22×Q8×C13—21no—
48C22×Q8×C13D411yescharacteristic
49C22×D4×C13C2311yescharacteristic
50C23×C4×C13—21no—
51C23×C4×C13—21no—
52C23×C4×C13—21no—
53C22×Dic26C2312yes—
54C13×C4⋊Q8—22no—
55C13×C4⋊Q8—22no—
56C13×#125—22no—
57C13×#125—22no—
58C13×#125—22no—
59C13×#125D414yes—
60C13×C22⋊Q8—28no—
61C13×C22⋊Q8—28no—
62C13×C22⋊Q8—28no—
63C4×Q8×C13—22no—
64C4×Q8×C13—22no—
65C4×D4×C13—22no—
66C4×D4×C13—22no—
67C4×D4×C13—22no—
68C4×D4×C13—22no—
69C4×D4×C13—22no—
70C4×D4×C13D414yes—
71C2×C13×C4⋊C4—28no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4D411yescharacteristic
78C2×C13×C4⋊C4D411yescharacteristic
79C2×C13×C4⋊C4D411yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4—21no—
85C2×C13×C22⋊C4—21no—
86C2×C42×C13C2311yescharacteristic
87C2×C42×C13C2311yescharacteristic
88C2×C42×C13C2311yescharacteristic
89C2×#6105—24no—
90C2×#6105—28no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13C2312yes—
94C2×C4×Dic13—21no—
95C22×#1055C2312yes—
96C22×#1055C2312yes—
97#88123—22no—
98#88123—22no—
99#88072—24no—
100#88071—22no—
101#88071—22no—
102#88071—22no—
103#88071—22no—
104#88071—21no—
105#88050—24no—
106#88050—24no—
107#88050—24no—
108C4⋊#1055—22no—
109#88043—22no—
110#25945—131nomaximal, Sylow
111C24×C13—21no—
112C2×Q8×C13—24no—
113C2×Q8×C13—22no—
114C2×Q8×C13—22no—
115C2×Q8×C13—41no—
116C2×Q8×C13—82no—
117C2×D4×C13—21no—
118C2×D4×C13—22no—
119C2×D4×C13C2×D412yes—
120C2×D4×C13#4114yes—
121C22×C4×C13—24no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—24no—
126C22×C4×C13—24no—
127C22×C4×C13—42no—
128C22×C4×C13—42no—
129C22×C4×C13—82no—
130C22×C4×C13—82no—
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2411yescharacteristic
138C22×Dic13—22no—
139C22×Dic13—22no—
140C2×Dic26—22no—
141C2×Dic26—22no—
142C2×Dic26—24no—
143C2×Dic26—24no—
144C13×C4⋊C4—24no—
145C13×C4⋊C4—24no—
146C13×C4⋊C4—24no—
147C13×C4⋊C4—22no—
148C13×C4⋊C4—24no—
149C13×C4⋊C4—24no—
150C13×C4⋊C4—22no—
151C13×C4⋊C4—22no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4C2×D412yes—
156C13×C4⋊C4C2×D412yes—
157C13×C4⋊C4C2×D412yes—
158C13×C22⋊C4—24no—
159C13×C22⋊C4—24no—
160C13×C22⋊C4—24no—
161C42×C13—21no—
162C42×C13—21no—
163C42×C13—21no—
164C42×C13—21no—
165C42×C13C2×D412yes—
166C42×C13C2×D412yes—
167#6105—48no—
168C4⋊Dic13—22no—
169C4⋊Dic13—22no—
170C4⋊Dic13—42no—
171C4⋊Dic13—42no—
172C4×Dic13—42no—
173C2×#1055—22no—
174C2×#1055—22no—
175C2×#1055—22no—
176C2×#1055—24no—
177C2×#1055—22no—
178C2×#554D1311yescharacteristic
179C2×#491—131no—
180C2×#461—131no—
181#2568—131no—
182#2026—132no—
183#2024—132no—
184#1989—131no—
185#1985—131no—
186#1877—132no—
187#1877—132no—
188#1762—131no—
189C23×C13—22no—
190C23×C13—24no—
191C23×C13—41no—
192C23×C13—41no—
193C23×C13—42no—
194C23×C13C22×D411yescharacteristic
195Q8×C13—44no—
196Q8×C13—84no—
197D4×C13—22no—
198D4×C13—24no—
199D4×C13#12414yes—
200C2×C4×C13—21no—
201C2×C4×C13—21no—
202C2×C4×C13—21no—
203C2×C4×C13—21no—
204C2×C4×C13—22no—
205C2×C4×C13—21no—
206C2×C4×C13—21no—
207C2×C4×C13—21no—
208C2×C4×C13—22no—
209C2×C4×C13—22no—
210C2×C4×C13—22no—
211C2×C4×C13—21no—
212C2×C4×C13—21no—
213C2×C4×C13—22no—
214C2×C4×C13—22no—
215C2×C4×C13—48no—
216C2×C4×C13—41no—
217C2×C4×C13—41no—
218C2×C4×C13—42no—
219C2×C4×C13—42no—
220C2×C4×C13—84no—
221C2×C4×C13—84no—
222C2×C4×C13#12012yes—
223C2×C4×C13#12012yes—
224C2×C4×C13#13712yes—
225C2×C4×C13C22×D411yescharacteristic
226C2×C4×C13C22×D411yescharacteristic
227C2×C4×C13C2×#4112yes—
228C2×C4×C132−1+412yes—
229C2×Dic13—42no—
230C2×Dic13—42no—
231C2×Dic13—44no—
232C2×Dic13—42no—
233C2×Dic13—42no—
234Dic26—42no—
235Dic26—42no—
236Dic26—44no—
237#1055—42no—
238#1055—42no—
239C22×SD16—132no—
240#554—24no—
241#554—24no—
242C2×C4⋊Q8—131no—
243C2×C4⋊Q8C2×D1311yescharacteristic
244C2×#125C2×D1311yescharacteristic
245C2×#125C2×D1311yescharacteristic
246C2×C22⋊Q8—21no—
247C2×C22⋊Q8—21no—
248C2×C22⋊Q8—21no—
249C2×C4×Q8C2×D1311yescharacteristic
250C2×C4×D4C2×D1311yescharacteristic
251C2×C4×D4C2×D1311yescharacteristic
252C2×C4×D4C2×D1311yescharacteristic
253C22×C4⋊C4—21no—
254#491—264no—
255#461—264no—
256C2×C4⋊C8—131no—
257C2×#103—132no—
258C2×#103—132no—
259C2×#103—132no—
260C2×#102—132no—
261C2×#97—131no—
262#400—261no—
263#400—261no—
264#391—132no—
265#391—132no—
266#391—261no—
267#382—261no—
268C4×C4⋊C4—131no—
269#340—132no—
270#340—132no—
271#340—132no—
272#336—132no—
273#336—132no—
274C22×C13—24no—
275C22×C13—44no—
276C22×C13—44no—
277C22×C13—42no—
278C22×C13—42no—
279C22×C13C2×#12011yescharacteristic
280C22×C13#54812yes—
281C22×C13C2×#13711yescharacteristic
282C22×C13#57511yescharacteristic
283C22×C13#57712yes—
284C4×C13—22no—
285C4×C13—22no—
286C4×C13—22no—
287C4×C13—41no—
288C4×C13—42no—
289C4×C13—41no—
290C4×C13—41no—
291C4×C13—42no—
292C4×C13—42no—
293C4×C13C2×#12411yescharacteristic
294C4×C13#53611yescharacteristic
295C4×C13#54812yes—
296Dic13—82no—
297Dic13—82no—
298C22×Q8—21no—
299C22×Q8—132no—
300C22×Q8C22⋊D1311yescharacteristic
301C22×D4C22×D1311yescharacteristic
302C23×C4—21no—
303C23×C4—21no—
304C23×C4—21no—
305C2×SD16—268no—
306C2×SD16—264no—
307C22×C8—132no—
308C22×C8—132no—
309C4⋊Q8—22no—
310C4⋊Q8—22no—
311C4⋊Q8—262no—
312C4⋊Q8—262no—
313#125—22no—
314#125—22no—
315#125—22no—
316#125C22⋊D1314yes—
317C22⋊Q8—28no—
318C22⋊Q8—28no—
319C22⋊Q8—28no—
320C4×Q8—22no—
321C4×Q8—22no—
322C4×D4—22no—
323C4×D4—22no—
324C4×D4—22no—
325C4×D4—22no—
326C4×D4—22no—
327C4×D4C22⋊D1314yes—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—132no—
335C2×C4⋊C4—261no—
336C2×C4⋊C4—261no—
337C2×C4⋊C4C22⋊D1311yescharacteristic
338C2×C4⋊C4C22⋊D1311yescharacteristic
339C2×C4⋊C4C22⋊D1311yescharacteristic
340C2×C4⋊C4C22×D1311yescharacteristic
341C2×C4⋊C4C22×D1311yescharacteristic
342C2×C4⋊C4C22×D1311yescharacteristic
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C42—261no—
347C2×C42C22×D1311yescharacteristic
348C2×C42C22×D1311yescharacteristic
349C2×C42C22×D1311yescharacteristic
350C4⋊C8—262no—
351#103—264no—
352#103—264no—
353#103—264no—
354#102—264no—
355#97—262no—
356#95—261no—
357#95—262no—
358#95—262no—
359#95—262no—
360#95—262no—
361C2×C13—44no—
362C2×C13#243611yescharacteristic
363C2×C13#300711yescharacteristic
364C2×C13#300911yescharacteristic
365C2×C13#337212yes—
366C2×C13#337612yes—
367C24—21no—
368C2×Q8—24no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—41no—
372C2×Q8—82no—
373C2×Q8—264no—
374C2×Q8—264no—
375C2×Q8—262no—
376C2×Q8—262no—
377C2×D4—22no—
378C2×D4—21no—
379C2×D4#613114yes—
380C2×D4C2×C22⋊D1312yes—
381C22×C4—24no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—82no—
390C22×C4—82no—
391C22×C4—262no—
392C22×C4—262no—
393C22×C4C2×C22⋊D1311yescharacteristic
394C22×C4C2×C22⋊D1311yescharacteristic
395C22×C4C2×C22⋊D1311yescharacteristic
396C22×C4C2×C22⋊D1311yescharacteristic
397C22×C4C2×C22⋊D1311yescharacteristic
398C22×C4C2×C22⋊D1311yescharacteristic
399C22×C4C23×D1311yescharacteristic
400SD16—528no—
401C2×C8—262no—
402C2×C8—264no—
403C2×C8—262no—
404C2×C8—262no—
405C2×C8—262no—
406C4⋊C4—24no—
407C4⋊C4—24no—
408C4⋊C4—24no—
409C4⋊C4—22no—
410C4⋊C4—24no—
411C4⋊C4—24no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—262no—
418C4⋊C4—262no—
419C4⋊C4—522no—
420C4⋊C4—522no—
421C4⋊C4C2×C22⋊D1312yes—
422C4⋊C4C2×C22⋊D1312yes—
423C4⋊C4C2×C22⋊D1312yes—
424C22⋊C4—24no—
425C22⋊C4—24no—
426C22⋊C4—24no—
427C42—21no—
428C42—21no—
429C42—21no—
430C42—21no—
431C42—522no—
432C42C2×C22⋊D1312yes—
433C42C2×C22⋊D1312yes—
434C13#2594511yescharacteristic, complemented, Sylow
435C23—24no—
436C23—22no—
437C23—41no—
438C23—41no—
439C23—42no—
440C23C22×C22⋊D1311yescharacteristic
441Q8—44no—
442Q8—84no—
443Q8—522no—
444Q8—522no—
445Q8—524no—
446D4—22no—
447D4—24no—
448D4#8820114yes—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—22no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—48no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—84no—
470C2×C4—84no—
471C2×C4—522no—
472C2×C4—524no—
473C2×C4—522no—
474C2×C4—522no—
475C2×C4—522no—
476C2×C4#8820512yes—
477C2×C4#8820712yes—
478C2×C4#8820712yes—
479C2×C4C2×#613112yes—
480C2×C4#8825412yes—
481C2×C4C22×C22⋊D1311yescharacteristic
482C2×C4C22×C22⋊D1311yescharacteristic
483C8—522no—
484C8—522no—
485C22—24no—
486C22—42no—
487C22—42no—
488C22—44no—
489C22—44no—
490C22#1171952212yes—
491C22#1171952711yescharacteristic
492C22C2×#8820511yescharacteristic
493C22#1171954112yes—
494C22C2×#8820711yescharacteristic
495C4—22no—
496C4—22no—
497C4—22no—
498C4—41no—
499C4—42no—
500C4—41no—
501C4—41no—
502C4—42no—
503C4—42no—
504C4—1042no—
505C4—1042no—
506C4C2×#8820111yescharacteristic
507C4#1171952111yescharacteristic
508C4#1171952212yes—
509C2—44no—
510C2#1311849011yescharacteristic
511C2#1312409611yescharacteristic
512C2#1312411311yescharacteristic
513C2#1312761712yes—
514C2#1312766312yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#554C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenterC2×#554D13
hypocenterC13#25945
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#11718730C2semidirect
3. #13120048C2semidirect
4. #13115984C2semidirect
5. #13115974C2semidirect
6. #13115794C2semidirect
7. #13115777C2semidirect
434. C13#25945semidirect

Maximal subgroups

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

subgroupindex
C2×#117187302
C2×#117186802
#131200482
#131159842
#131159742
#131157942
#131157772
#131151702
#131146612
C2×C13×#5542
#2594513