Finite Group Databasebeta

← #15759387

Subgroups — #15759387

Order 3328.

750 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718888C211yesmaximal, characteristic
2#13115672C211yesmaximal, characteristic
3#13114771C211yesmaximal, characteristic, complemented
4#13113403C211yesmaximal, characteristic
5#13112703C211yesmaximal, characteristic, complemented
6#13112684C211yesmaximal, characteristic, complemented
7Q8×C13×C22⋊C4C211yesmaximal, characteristic, complemented
8C23×Q8×C13C2211yescharacteristic
9C2×C4×Q8×C13—21no—
10C22×#6106C412yescomplemented
11C2×#88184C2211yescharacteristic
12C13×#391—21no—
13C13×#391—22no—
14C13×#380—21no—
15C13×#380C2211yescharacteristic
16C4×C13×C22⋊C4—21no—
17C4×C13×C22⋊C4C2211yescharacteristic
18#11718888—22no—
19#11718888—21no—
20#11718888—21no—
21C2×#88075—22no—
22C2×#88075C412yescomplemented
23#11718873C2211yescharacteristic
24C2×C22⋊#1055C2211yescharacteristic
25C2×C22⋊#1055C2211yescharacteristic
26C2×#88046—21no—
27C2×#88046—21no—
28#11718043—22no—
29C22×Q8×C13—21no—
30C22×Q8×C13—21no—
31C22×Q8×C13—21no—
32C22×Q8×C13—44no—
33C22×Q8×C13C2×C412yes—
34C22×Q8×C13D412yes—
35C22×Q8×C13D411yescharacteristic
36C22×Q8×C13D411yescharacteristic
37C23×C4×C13—21no—
38C23×C4×C13C2311yescharacteristic
39C22×C22⋊D13—21no—
40C22×D52C2×C411yescharacteristic
41C4×Q8×C13—44no—
42C2×C13×C4⋊C4—22no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4D411yescharacteristic
46C2×C13×C22⋊C4D411yescharacteristic
47C2×C42×C13—22no—
48C2×C42×C13—21no—
49C2×C22⋊Dic13—21no—
50C2×#6106—22no—
51C2×#6106—22no—
52C2×#6106—44no—
53#88184—21no—
54#88184—21no—
55#88184—21no—
56#88184—21no—
57C2×#6103—21no—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13C2×C411yescharacteristic
60C22×#1055—21no—
61C22×#1055C2×C412yes—
62C13×#95—22no—
63C13×#95—22no—
64C13×#95—21no—
65C13×#95D412yes—
66#88075—22no—
67#88075—22no—
68#88075—44no—
69#88071—21no—
70C22⋊#1055—21no—
71C22⋊#1055—21no—
72C22⋊#1055—21no—
73C22⋊#1055—21no—
74#88046—42no—
75#88046—42no—
76#9262—131nomaximal, Sylow
77C24×C13C2×D411yescharacteristic
78C23×D13—21no—
79C2×Q8×C13—24no—
80C2×Q8×C13—22no—
81C2×Q8×C13—22no—
82C2×Q8×C13—21no—
83C2×Q8×C13—21no—
84C2×Q8×C13—24no—
85C2×Q8×C13—24no—
86C2×Q8×C13—42no—
87C2×Q8×C13—42no—
88C2×Q8×C13—42no—
89C2×Q8×C13—44no—
90C2×Q8×C13—44no—
91C2×Q8×C13—44no—
92C2×Q8×C13C22⋊C412yes—
93C2×Q8×C13C22⋊C412yes—
94C22×C4×C13—21no—
95C22×C4×C13—22no—
96C22×C4×C13—21no—
97C22×C4×C13—21no—
98C22×C4×C13—22no—
99C22×C4×C13—21no—
100C22×C4×C13—22no—
101C22×C4×C13—42no—
102C22×C4×C13—44no—
103C22×C4×C13C22×C411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13#4111yescharacteristic
108C22×C4×C13#4111yescharacteristic
109C2×C22⋊D13—41no—
110C2×C22⋊D13—41no—
111C2×C22⋊D13—41no—
112C2×C22⋊D13—41no—
113C2×C22⋊D13—41no—
114C2×C22⋊D13—41no—
115C22×Dic13—21no—
116C22×Dic13—41no—
117C2×D52—21no—
118C2×D52—21no—
119C2×D52—42no—
120C13×C4⋊C4—44no—
121C13×C4⋊C4—42no—
122C13×C22⋊C4—21no—
123C13×C22⋊C4—21no—
124C13×C22⋊C4—21no—
125C13×C22⋊C4—41no—
126C13×C22⋊C4—41no—
127C13×C22⋊C4SD1612yescomplemented
128C42×C13—44no—
129C42×C13—42no—
130C22⋊Dic13—41no—
131C22⋊Dic13—41no—
132#6106—44no—
133#6106—44no—
134#6103—41no—
135#6103—41no—
136C4⋊Dic13—21no—
137C4⋊Dic13—21no—
138C4⋊Dic13—42no—
139C2×#1055—22no—
140C2×#1055—42no—
141C2×#1055—42no—
142C2×#1055—41no—
143C2×#448—131no—
144Q8×C22⋊C4D1311yescharacteristic, complemented
145#1964—131no—
146#1787—131no—
147#1519—131no—
148#1289—131no—
149#1282—131no—
150C23×C13—41no—
151C23×C13—41no—
152C23×C13C4×D411yescharacteristic
153C23×C13#12011yescharacteristic
154C23×C13#12111yescharacteristic
155C23×C13C2×SD1611yescharacteristic
156C23×C13#13511yescharacteristic
157C23×C13AGL(1,ℤ/8)11yescharacteristic
158C23×C13#13711yescharacteristic
159C22×D13—41no—
160C22×D13—41no—
161C22×D13—41no—
162C22×D13—81no—
163C22×D13—81no—
164Q8×C13—24no—
165Q8×C13—22no—
166Q8×C13—22no—
167Q8×C13—22no—
168Q8×C13—44no—
169Q8×C13—44no—
170Q8×C13—42no—
171Q8×C13#9914yescomplemented
172C2×C4×C13—24no—
173C2×C4×C13—22no—
174C2×C4×C13—22no—
175C2×C4×C13—22no—
176C2×C4×C13—22no—
177C2×C4×C13—22no—
178C2×C4×C13—22no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13—44no—
183C2×C4×C13—44no—
184C2×C4×C13—41no—
185C2×C4×C13—41no—
186C2×C4×C13—42no—
187C2×C4×C13—41no—
188C2×C4×C13—42no—
189C2×C4×C13—41no—
190C2×C4×C13—42no—
191C2×C4×C13—41no—
192C2×C4×C13—42no—
193C2×C4×C13C2×C22⋊C411yescharacteristic
194C2×C4×C13C4×D411yescharacteristic
195C2×C4×C13#12111yescharacteristic
196C2×C4×C13#12311yescharacteristic
197C22⋊D13—81no—
198C22⋊D13—81no—
199C22⋊D13—81no—
200C22⋊D13—81no—
201C2×Dic13—41no—
202C2×Dic13—41no—
203C2×Dic13—41no—
204C2×Dic13—81no—
205C2×Dic13—81no—
206C2×Dic13—81no—
207D52—42no—
208D52—81no—
209#1055—42no—
210#1055—81no—
211C23×Q8C2×D1311yescharacteristic
212C22×SD16—132no—
213C2×#121—131no—
214C2×C4×Q8—21no—
215#448—262no—
216#448—261no—
217#448—261no—
218C2×#103—132no—
219C2×#103—262no—
220C2×#99—261no—
221C2×#99—261no—
222C2×C22⋊C8—131no—
223C2×C22⋊C8—131no—
224#391—21no—
225#391—22no—
226#380—21no—
227#380—131no—
228#380C2×D1311yescharacteristic
229C4×C22⋊C4—21no—
230C4×C22⋊C4C2×D1311yescharacteristic
231#327—262no—
232C22×C13—21no—
233C22×C13—21no—
234C22×C13—21no—
235C22×C13—21no—
236C22×C13—21no—
237C22×C13—21no—
238C22×C13—41no—
239C22×C13—41no—
240C22×C13—41no—
241C22×C13—41no—
242C22×C13#38611yescharacteristic
243C22×C13C4×SD1611yescharacteristic
244C22×C13#44011yescharacteristic
245C22×C13#44811yescharacteristic
246C22×C13#44911yescharacteristic
247C22×C13#46011yescharacteristic
248C22×C13#46411yescharacteristic
249C2×D13—81no—
250C2×D13—81no—
251C2×D13—81no—
252C2×D13—161no—
253C2×D13—161no—
254C4×C13—21no—
255C4×C13—21no—
256C4×C13—24no—
257C4×C13—21no—
258C4×C13—42no—
259C4×C13—42no—
260C4×C13—81no—
261C4×C13—82no—
262C4×C13C2×#9912yes—
263Dic13—81no—
264Dic13—161no—
265C22×Q8—21no—
266C22×Q8—21no—
267C22×Q8—21no—
268C22×Q8—44no—
269C22×Q8C4×D1312yes—
270C22×Q8D5212yes—
271C22×Q8C22⋊D1311yescharacteristic
272C22×Q8C22⋊D1311yescharacteristic
273C22×D4—131no—
274C22×D4—261no—
275C23×C4—21no—
276C23×C4C22×D1311yescharacteristic
277C2×SD16—262no—
278C2×SD16—262no—
279C2×SD16—524no—
280C22×C8—132no—
281C22×C8—261no—
282#121—261no—
283#121—261no—
284#121—261no—
285#121—261no—
286C4×Q8—44no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—131no—
290C2×C4⋊C4—261no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—261no—
293C2×C22⋊C4—261no—
294C2×C22⋊C4C22⋊D1311yescharacteristic
295C2×C22⋊C4C22⋊D1311yescharacteristic
296C2×C42—22no—
297C2×C42—21no—
298#103—262no—
299#103—262no—
300#103—524no—
301#99—522no—
302#99—522no—
303C22⋊C8—261no—
304C22⋊C8—261no—
305C22⋊C8—261no—
306C22⋊C8—261no—
307#95—22no—
308#95—22no—
309#95—21no—
310#95—261no—
311#95C22⋊D1312yes—
312C2×C13—21no—
313C2×C13—21no—
314C2×C13—21no—
315C2×C13—21no—
316C2×C13—21no—
317C2×C13—21no—
318C2×C13#188011yescharacteristic
319C2×C13#189811yescharacteristic
320C2×C13#190511yescharacteristic
321D13—161no—
322C24—261no—
323C24C2×C22⋊D1311yescharacteristic
324C2×Q8—24no—
325C2×Q8—22no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8—22no—
329C2×Q8—24no—
330C2×Q8—24no—
331C2×Q8—42no—
332C2×Q8—42no—
333C2×Q8—42no—
334C2×Q8—44no—
335C2×Q8—44no—
336C2×Q8—44no—
337C2×Q8#610312yes—
338C2×Q8#610312yes—
339C2×D4—261no—
340C2×D4—261no—
341C2×D4—522no—
342C2×D4—521no—
343C2×D4—521no—
344C2×D4—521no—
345C2×D4—521no—
346C2×D4—521no—
347C2×D4—521no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—42no—
356C22×C4—44no—
357C22×C4—261no—
358C22×C4—521no—
359C22×C4C2×C4×D1311yescharacteristic
360C22×C4C2×D5211yescharacteristic
361C22×C4#612711yescharacteristic
362C22×C4#612711yescharacteristic
363C22×C4C2×C22⋊D1311yescharacteristic
364C22×C4C2×C22⋊D1311yescharacteristic
365SD16—524no—
366SD16—524no—
367C2×C8—262no—
368C2×C8—522no—
369C2×C8—522no—
370C2×C8—521no—
371C4⋊C4—44no—
372C4⋊C4—42no—
373C4⋊C4—261no—
374C4⋊C4—261no—
375C4⋊C4—522no—
376C22⋊C4—21no—
377C22⋊C4—21no—
378C22⋊C4—21no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—521no—
382C22⋊C4—521no—
383C22⋊C4—521no—
384C22⋊C4—521no—
385C22⋊C4#610612yescomplemented
386C42—44no—
387C42—42no—
388C13#926211yescharacteristic, complemented, Sylow
389C23—41no—
390C23—41no—
391C23—521no—
392C23—521no—
393C23—521no—
394C23—1041no—
395C23—1041no—
396C23C4×C22⋊D1311yescharacteristic
397C23#8818411yescharacteristic
398C23C2×#610611yescharacteristic
399C23#8819611yescharacteristic
400C23#8820311yescharacteristic
401C23#8820411yescharacteristic
402C23#8820711yescharacteristic
403Q8—24no—
404Q8—22no—
405Q8—22no—
406Q8—22no—
407Q8—44no—
408Q8—44no—
409Q8—42no—
410Q8#8804614yescomplemented
411D4—522no—
412D4—1041no—
413D4—1041no—
414D4—1041no—
415D4—1041no—
416D4—1041no—
417C2×C4—24no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—44no—
428C2×C4—44no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—521no—
439C2×C4—521no—
440C2×C4—521no—
441C2×C4—1041no—
442C2×C4—1041no—
443C2×C4—1041no—
444C2×C4C2×#610311yescharacteristic
445C2×C4C4×C22⋊D1311yescharacteristic
446C2×C4#8818311yescharacteristic
447C2×C4#8818411yescharacteristic
448C8—522no—
449C8—1041no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—1041no—
461C22—1041no—
462C22—1041no—
463C22—2081no—
464C22—2081no—
465C22C4×#610611yescharacteristic
466C22#1171868711yescharacteristic
467C22#1171868811yescharacteristic
468C22#1171868911yescharacteristic
469C22#1171887411yescharacteristic
470C22#1171888811yescharacteristic
471C22#1171889911yescharacteristic
472C4—21no—
473C4—24no—
474C4—21no—
475C4—21no—
476C4—42no—
477C4—42no—
478C4—81no—
479C4—82no—
480C4—1041no—
481C4—2081no—
482C4C2×#8804612yes—
483C2—21no—
484C2—21no—
485C2—21no—
486C2—21no—
487C2—21no—
488C2—21no—
489C2—2081no—
490C2#1311519111yescharacteristic
491C2#1311528911yescharacteristic
492C2#1311533011yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingQ8×C13×C22⋊C4C2
socleC22×C13#386
prime radicalC2×#88184C22
cosocleC23×C4×C13C23
hypercenterQ8×C22⋊C4D13
hypocenterC13#9262
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #13114771C2semidirect
5. #13112703C2semidirect
6. #13112684C2semidirect
7. Q8×C13×C22⋊C4C2semidirect
10. C22×#6106C4semidirect
22. C2×#88075C4semidirect
127. C13×C22⋊C4SD16semidirect
144. Q8×C22⋊C4D13semidirect
171. Q8×C13#99semidirect
385. C22⋊C4#6106semidirect
388. C13#9262semidirect
410. Q8#88046semidirect

Maximal subgroups

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

subgroupindex
C2×#117188882
#131156722
#131147712
#131134032
#131127032
#131126842
Q8×C13×C22⋊C42
#926213