Finite Group Databasebeta

← #15758593

Subgroups — #15758593

Order 3328.

612 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718498C211yesmaximal, characteristic
2#13123189C211yesmaximal, characteristic
3#13114813C211yesmaximal, characteristic
4C2×#11718073C211yesmaximal, characteristic, complemented
5C2×#11718073C211yesmaximal, characteristic, complemented
6#13112719C211yesmaximal, characteristic, complemented
7C13×#1296C211yesmaximal, characteristic, complemented
8C22×#6094—21no—
9C2×#88151C412yes—
10C2×C42×D13C2211yescharacteristic
11C2×#88123C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13C2×C13×C4⋊C8C2211yescharacteristic
14C13×#384C2211yescharacteristic
15C2×#88060—21no—
16C2×#88054—21no—
17#11718648—21no—
18#11718648—21no—
19#11718646—21no—
20#11718646—21no—
21#11718635C412yes—
22C2×C4⋊#1055C2211yescharacteristic
23C2×C4⋊#1055C2211yescharacteristic
24#11718498—22no—
25#11718498—22no—
26#11718142—21no—
27#11718073—22no—
28#11718073—22no—
29C22×C4×D13C2×C411yescharacteristic
30C22×C4×D13D411yescharacteristic
31C22×C4×D13D411yescharacteristic
32C22×Dic26C2×C412yes—
33C22×C8×C13—21no—
34C22×C8×C13—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4C2×C412yes—
38C2×C42×C13C2311yescharacteristic
39C2×#6103—22no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42C2×C4⋊Dic13—22no—
43C2×C4×Dic13C2×C411yescharacteristic
44C2×C4×Dic13D411yescharacteristic
45C2×C4×Dic13D411yescharacteristic
46C22×#1055—21no—
47C22×#1055—21no—
48C2×#6094—24no—
49C2×#6094—42no—
50C2×#6094—42no—
51#88151—44no—
52C42×D13—21no—
53C42×D13—21no—
54C42×D13—21no—
55C42×D13—21no—
56#88123—21no—
57#88123—21no—
58#88123—21no—
59#88123—21no—
60C13×C4⋊C8—21no—
61C13×C4⋊C8—21no—
62C13×C4⋊C8—21no—
63C13×C4⋊C8D412yes—
64#88071—22no—
65#88071—22no—
66#88060—42no—
67#88054—24no—
68C4⋊#1055—21no—
69C4⋊#1055—21no—
70C4⋊#1055—21no—
71C4⋊#1055D412yes—
72#9135—131nomaximal, Sylow
73C23×D13C22⋊C411yescharacteristic
74C22×C4×C13—22no—
75C22×C4×C13C22×C411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×Dic13—22no—
79C22×Dic13C22⋊C411yescharacteristic
80C22×Dic13C22⋊C411yescharacteristic
81C22×Dic13C22⋊C411yescharacteristic
82C2×C4×D13—21no—
83C2×C4×D13—21no—
84C2×C4×D13—21no—
85C2×C4×D13—21no—
86C2×C4×D13—21no—
87C2×C4×D13—21no—
88C2×C4×D13—21no—
89C2×C4×D13—21no—
90C2×C4×D13—21no—
91C2×C4×D13—21no—
92C2×C4×D13—21no—
93C2×C4×D13—21no—
94C2×C4×D13—22no—
95C2×C4×D13—41no—
96C2×C4×D13SD1612yes—
97C2×C4×D13Q1612yes—
98C2×Dic26—22no—
99C2×Dic26—22no—
100C2×Dic26—42no—
101C2×Dic26—42no—
102C2×C8×C13—22no—
103C2×C8×C13—41no—
104C2×C8×C13—41no—
105C2×C8×C13—41no—
106C2×C8×C13—41no—
107C2×C8×C13—41no—
108C13×C4⋊C4—42no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4—41no—
113C42×C13C2×D411yescharacteristic
114C42×C13C2×D411yescharacteristic
115C42×C13#4111yescharacteristic
116C42×C13#4111yescharacteristic
117#6103—44no—
118C4⋊Dic13—41no—
119C4⋊Dic13—41no—
120C4⋊Dic13—41no—
121C4⋊Dic13—41no—
122C4⋊Dic13—44no—
123C4×Dic13—21no—
124C4×Dic13—21no—
125C4×Dic13—21no—
126C4×Dic13—21no—
127C4×Dic13—21no—
128C4×Dic13—21no—
129C2×#1055—22no—
130C2×#1055—41no—
131C2×#1055—41no—
132C2×#1055—41no—
133C2×#1055—41no—
134C2×#1055—41no—
135#6094—48no—
136C2×#423—131no—
137#2857—131no—
138#1797—131no—
139C2×#333—131no—
140C2×#333—131no—
141#1296—131no—
142#1296D1311yescharacteristic, complemented
143C23×C13C2×C22⋊C411yescharacteristic
144C22×D13—21no—
145C22×D13—21no—
146C22×D13—21no—
147C22×D13—21no—
148C22×D13—21no—
149C22×D13—21no—
150C22×D13#10312yes—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—42no—
154C2×C4×C13—42no—
155C2×C4×C13—42no—
156C2×C4×C13C4×D411yescharacteristic
157C2×C4×C13C4×D411yescharacteristic
158C2×C4×C13#12011yescharacteristic
159C2×C4×C13#12111yescharacteristic
160C2×C4×C13#12111yescharacteristic
161C2×C4×C13#12311yescharacteristic
162C2×C4×C13C2×SD1611yescharacteristic
163C2×C4×C13C2×Q1611yescharacteristic
164C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C13#13711yescharacteristic
167C2×C4×C13#13711yescharacteristic
168C2×C4×C13#13711yescharacteristic
169C2×C4×C13#13711yescharacteristic
170C2×Dic13—21no—
171C2×Dic13—21no—
172C2×Dic13—21no—
173C2×Dic13—21no—
174C2×Dic13—21no—
175C2×Dic13—21no—
176C2×Dic13—21no—
177C2×Dic13—42no—
178C2×Dic13—42no—
179C2×Dic13—42no—
180C2×Dic13#10012yes—
181C2×Dic13#10312yes—
182C4×D13—22no—
183C4×D13—22no—
184C4×D13—22no—
185C4×D13—22no—
186C4×D13—42no—
187C4×D13—42no—
188C4×D13—41no—
189C4×D13—41no—
190C4×D13—41no—
191C4×D13—41no—
192Dic26—82no—
193Dic26—82no—
194C8×C13—42no—
195C8×C13—81no—
196#1055—42no—
197#1055—81no—
198C22×M16—261no—
199C2×C4⋊Q8—131no—
200C2×C22⋊Q8—132no—
201C22×C42—131no—
202#423—262no—
203#423—262no—
204C2×C4⋊C8—131no—
205C2×C4⋊C8—131no—
206C2×C4⋊C8—261no—
207C2×C4⋊C8C2×D1311yescharacteristic
208C2×C4⋊C8C2×D1311yescharacteristic
209C2×C22⋊C8—261no—
210#391—132no—
211#389—261no—
212#389—261no—
213#384C2×D1311yescharacteristic
214#380—261no—
215#380—261no—
216#336—261no—
217#333—262no—
218#333—262no—
219C22×C13#38611yescharacteristic
220C22×C13C2×#10011yescharacteristic
221C22×C13#41311yescharacteristic
222C22×C13C2×#10311yescharacteristic
223C22×C13#41711yescharacteristic
224C22×C13#41711yescharacteristic
225C22×C13#41911yescharacteristic
226C2×D13—22no—
227C2×D13—22no—
228C2×D13—22no—
229C2×D13—41no—
230C2×D13—41no—
231C2×D13—41no—
232C2×D13—41no—
233C4×C13—21no—
234C4×C13—21no—
235C4×C13—82no—
236C4×C13#45011yescharacteristic
237C4×C13#45111yescharacteristic
238C4×C13#46811yescharacteristic
239C4×C13#46811yescharacteristic
240C4×C13#47011yescharacteristic
241C4×C13#47011yescharacteristic
242C4×C13#48311yescharacteristic
243C4×C13#48411yescharacteristic
244Dic13—22no—
245Dic13—22no—
246Dic13—41no—
247Dic13—82no—
248C22×Q8—132no—
249C23×C4—131no—
250C23×C4—131no—
251C23×C4—131no—
252C2×M16—264no—
253C2×M16—522no—
254C2×M16—522no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—261no—
258C22×C8—261no—
259C4⋊Q8—261no—
260C4⋊Q8—261no—
261C4⋊Q8—261no—
262C4⋊Q8—261no—
263C22⋊Q8—524no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—262no—
267C2×C4⋊C4—261no—
268C2×C4⋊C4—261no—
269C2×C4⋊C4C4×D1312yes—
270C2×C22⋊C4—262no—
271C2×C42—131no—
272C2×C42—131no—
273C2×C42—131no—
274C2×C42—261no—
275C2×C42—261no—
276C2×C42—261no—
277C2×C42—261no—
278C2×C42C22×D1311yescharacteristic
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—132no—
283C4⋊C8—264no—
284C4⋊C8—261no—
285C4⋊C8—261no—
286C4⋊C8—261no—
287C4⋊C8D5212yes—
288C22⋊C8—522no—
289#95—262no—
290#95—262no—
291C2×C13#154811yescharacteristic
292C2×C13#155011yescharacteristic
293C2×C13#155911yescharacteristic
294C2×C13#156011yescharacteristic
295C2×C13#187211yescharacteristic
296C2×C13#189411yescharacteristic
297C2×C13#190011yescharacteristic
298D13—42no—
299C24—131no—
300C2×Q8—262no—
301C2×Q8—262no—
302C2×Q8—522no—
303C2×Q8—522no—
304C22×C4—22no—
305C22×C4—131no—
306C22×C4—131no—
307C22×C4—132no—
308C22×C4—132no—
309C22×C4—131no—
310C22×C4—262no—
311C22×C4—261no—
312C22×C4—261no—
313C22×C4—261no—
314C22×C4—261no—
315C22×C4—261no—
316C22×C4—261no—
317C22×C4—261no—
318C22×C4—261no—
319C22×C4—261no—
320C22×C4—261no—
321C22×C4—261no—
322C22×C4—261no—
323C22×C4—262no—
324C22×C4—521no—
325C22×C4C2×C4×D1311yescharacteristic
326C22×C4D4×D1311yescharacteristic
327C22×C4D4×D1311yescharacteristic
328M16—528no—
329C2×C8—22no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—262no—
336C2×C8—521no—
337C2×C8—521no—
338C2×C8—521no—
339C2×C8—521no—
340C2×C8—521no—
341C4⋊C4—42no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—524no—
347C4⋊C4—521no—
348C4⋊C4—521no—
349C4⋊C4—521no—
350C4⋊C4—521no—
351C22⋊C4—524no—
352C42—261no—
353C42—261no—
354C42—261no—
355C42—261no—
356C42—261no—
357C42—261no—
358C42C2×D5211yescharacteristic
359C42#612711yescharacteristic
360C42D4×D1311yescharacteristic
361C42#613111yescharacteristic
362C13#913511yescharacteristic, complemented, Sylow
363C23—132no—
364C23—261no—
365C23—261no—
366C23—261no—
367C23—261no—
368C23—261no—
369C23—261no—
370C23C22⋊C4×D1311yescharacteristic
371Q8—1042no—
372Q8—1042no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—132no—
379C2×C4—132no—
380C2×C4—261no—
381C2×C4—261no—
382C2×C4—261no—
383C2×C4—261no—
384C2×C4—262no—
385C2×C4—262no—
386C2×C4—262no—
387C2×C4—262no—
388C2×C4—261no—
389C2×C4—261no—
390C2×C4—261no—
391C2×C4—522no—
392C2×C4—522no—
393C2×C4—521no—
394C2×C4—521no—
395C2×C4—521no—
396C2×C4—521no—
397C2×C4—522no—
398C2×C4—522no—
399C2×C4—522no—
400C2×C4C4×D5211yescharacteristic
401C2×C4#8813611yescharacteristic
402C2×C4#8813811yescharacteristic
403C2×C4#8814711yescharacteristic
404C2×C4#8814811yescharacteristic
405C2×C4#8814911yescharacteristic
406C2×C4#8816511yescharacteristic
407C2×C4#8816511yescharacteristic
408C2×C4SD16×D1311yescharacteristic
409C2×C4#8816911yescharacteristic
410C2×C4#8816911yescharacteristic
411C2×C4#8816911yescharacteristic
412C2×C4Q16×D1311yescharacteristic
413C2×C4#8817211yescharacteristic
414C8—42no—
415C8—81no—
416C8—522no—
417C8—1041no—
418C22—262no—
419C22—262no—
420C22—262no—
421C22—521no—
422C22—521no—
423C22—521no—
424C22—521no—
425C22#1171832611yescharacteristic
426C22D13×#10011yescharacteristic
427C22#1171841211yescharacteristic
428C22#1171843211yescharacteristic
429C22#1171843211yescharacteristic
430C22D13×#10311yescharacteristic
431C22#1171846311yescharacteristic
432C4—21no—
433C4—21no—
434C4—82no—
435C4—262no—
436C4—262no—
437C4—521no—
438C4—1042no—
439C4#1171843711yescharacteristic
440C4#1171844111yescharacteristic
441C4#1171846911yescharacteristic
442C4#1171847711yescharacteristic
443C4#1171852311yescharacteristic
444C4#1171852911yescharacteristic
445C4#1171854511yescharacteristic
446C4#1171854711yescharacteristic
447C2—522no—
448C2#1311351511yescharacteristic
449C2#1311352511yescharacteristic
450C2#1311356511yescharacteristic
451C2#1311356811yescharacteristic
452C2#1311514211yescharacteristic
453C2#1311526811yescharacteristic
454C2#1311529811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1296C2
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1296D13
hypocenterC13#9135
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
4. C2×#11718073C2semidirect
5. C2×#11718073C2semidirect
6. #13112719C2semidirect
7. C13×#1296C2semidirect
142. #1296D13semidirect
362. C13#9135semidirect

Maximal subgroups

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

subgroupindex
C2×#117184982
#131231892
#131148132
C2×#117180732
#131127192
C13×#12962
#913513