Finite Group Databasebeta

← #15758573

Subgroups — #15758573

Order 3328.

644 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×C4⋊C8C211yesmaximal, characteristic
2#13123189C211yesmaximal, characteristic
3#13114813C211yesmaximal, characteristic
4C2×#11718074C211yesmaximal, characteristic, complemented
5C2×#11718078C211yesmaximal, characteristic, complemented
6#13112719C211yesmaximal, characteristic, complemented
7C13×#1296C211yesmaximal, characteristic, complemented
8C22×C8×D13—21no—
9C2×#88151—21no—
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#11718648C412yes—
19#11718646—21no—
20#11718646C412yes—
21#11718635—21no—
22C2×C4⋊#1055C2211yescharacteristic
23C2×C4⋊#1055C2211yescharacteristic
24D13×C4⋊C8—22no—
25D13×C4⋊C8—22no—
26#11718142—21no—
27#11718078—22no—
28#11718074—22no—
29C22×C4×D13C2×C411yescharacteristic
30C22×C4×D13D411yescharacteristic
31C22×C4×D13D411yescharacteristic
32C22×Dic26—21no—
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—22no—
42C2×C4⋊Dic13C2×C412yes—
43C2×C4×Dic13C2×C411yescharacteristic
44C2×C4×Dic13D411yescharacteristic
45C2×C4×Dic13D411yescharacteristic
46C22×#1055—21no—
47C22×#1055—21no—
48C2×C8×D13—24no—
49C2×C8×D13—42no—
50C2×C8×D13—42no—
51#88151—42no—
52#88151—42no—
53C42×D13—21no—
54C42×D13—21no—
55C42×D13—21no—
56C42×D13—21no—
57#88123—21no—
58#88123—21no—
59#88123—21no—
60#88123—21no—
61C13×C4⋊C8—21no—
62C13×C4⋊C8—21no—
63C13×C4⋊C8—21no—
64C13×C4⋊C8D412yes—
65#88071—22no—
66#88071—22no—
67#88060—42no—
68#88054—24no—
69C4⋊#1055—21no—
70C4⋊#1055—21no—
71C4⋊#1055—21no—
72C4⋊#1055D412yes—
73#9131—131nomaximal, Sylow
74C23×D13C22⋊C411yescharacteristic
75C22×C4×C13—22no—
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×Dic13—22no—
80C22×Dic13C22⋊C411yescharacteristic
81C22×Dic13C22⋊C411yescharacteristic
82C22×Dic13C22⋊C411yescharacteristic
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—22no—
92C2×C4×D13—21no—
93C2×C4×D13—21no—
94C2×C4×D13—41no—
95C2×C4×D13D812yes—
96C2×C4×D13SD1612yes—
97C2×C4×D13SD1612yes—
98C2×C4×D13Q1612yes—
99C2×Dic26—41no—
100C2×Dic26—41no—
101C2×Dic26—41no—
102C2×Dic26—41no—
103C2×Dic26—41no—
104C2×Dic26—41no—
105C2×C8×C13—22no—
106C2×C8×C13—41no—
107C2×C8×C13—41no—
108C2×C8×C13—41no—
109C2×C8×C13—41no—
110C2×C8×C13—41no—
111C13×C4⋊C4—42no—
112C13×C4⋊C4—41no—
113C13×C4⋊C4—41no—
114C13×C4⋊C4—41no—
115C13×C4⋊C4—41no—
116C42×C13C2×D411yescharacteristic
117C42×C13C2×D411yescharacteristic
118C42×C13#4111yescharacteristic
119C42×C13#4111yescharacteristic
120#6103—44no—
121C4⋊Dic13—22no—
122C4⋊Dic13—22no—
123C4⋊Dic13—41no—
124C4⋊Dic13—41no—
125C4⋊Dic13—44no—
126C4×Dic13—21no—
127C4×Dic13—21no—
128C4×Dic13—21no—
129C4×Dic13—21no—
130C4×Dic13—21no—
131C4×Dic13—21no—
132C2×#1055—22no—
133C2×#1055—41no—
134C2×#1055—41no—
135C2×#1055—41no—
136C2×#1055—41no—
137C2×#1055—41no—
138C8×D13—48no—
139C22×C4⋊C8—131no—
140#2857—131no—
141#1797—131no—
142C2×#332—131no—
143C2×#332—131no—
144#1296—131no—
145#1296D1311yescharacteristic, complemented
146C23×C13C2×C22⋊C411yescharacteristic
147C22×D13—21no—
148C22×D13—21no—
149C22×D13—21no—
150C22×D13—21no—
151C22×D13#10112yes—
152C22×D13#10212yes—
153C22×D13#10312yes—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—42no—
157C2×C4×C13—42no—
158C2×C4×C13—42no—
159C2×C4×C13C4×D411yescharacteristic
160C2×C4×C13C4×D411yescharacteristic
161C2×C4×C13#12011yescharacteristic
162C2×C4×C13#12111yescharacteristic
163C2×C4×C13#12111yescharacteristic
164C2×C4×C13#12311yescharacteristic
165C2×C4×C13C2×D811yescharacteristic
166C2×C4×C13C2×SD1611yescharacteristic
167C2×C4×C13C2×SD1611yescharacteristic
168C2×C4×C13C2×Q1611yescharacteristic
169C2×C4×C13#13511yescharacteristic
170C2×C4×C13#13511yescharacteristic
171C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C13#13711yescharacteristic
173C2×Dic13—21no—
174C2×Dic13—21no—
175C2×Dic13—21no—
176C2×Dic13—21no—
177C2×Dic13—21no—
178C2×Dic13—21no—
179C2×Dic13—21no—
180C2×Dic13—42no—
181C2×Dic13—42no—
182C2×Dic13—42no—
183C2×Dic13#10212yes—
184C2×Dic13#10312yes—
185C4×D13—22no—
186C4×D13—22no—
187C4×D13—22no—
188C4×D13—22no—
189C4×D13—22no—
190C4×D13—22no—
191C4×D13—22no—
192C4×D13—22no—
193C4×D13—42no—
194C4×D13—42no—
195Dic26—81no—
196Dic26—81no—
197Dic26—81no—
198Dic26—81no—
199C8×C13—42no—
200C8×C13—81no—
201#1055—42no—
202#1055—81no—
203C23×C8—261no—
204C2×C4⋊Q8—131no—
205C2×C22⋊Q8—261no—
206C22×C42—131no—
207C2×C4⋊C8—131no—
208C2×C4⋊C8—131no—
209C2×C4⋊C8—262no—
210C2×C4⋊C8—261no—
211C2×C4⋊C8—262no—
212C2×C4⋊C8C2×D1311yescharacteristic
213C2×C4⋊C8C2×D1311yescharacteristic
214C2×C22⋊C8—261no—
215#391—261no—
216#389—132no—
217#389—261no—
218#384C2×D1311yescharacteristic
219#380—132no—
220#380—261no—
221#336—261no—
222#332—262no—
223#332—262no—
224C22×C13#38611yescharacteristic
225C22×C13C2×#10111yescharacteristic
226C22×C13#41311yescharacteristic
227C22×C13C2×#10211yescharacteristic
228C22×C13C2×#10311yescharacteristic
229C22×C13#41611yescharacteristic
230C22×C13#41711yescharacteristic
231C2×D13—22no—
232C2×D13—22no—
233C2×D13—22no—
234C2×D13—22no—
235C2×D13—22no—
236C2×D13—22no—
237C2×D13#33214yescomplemented
238C4×C13—21no—
239C4×C13—21no—
240C4×C13—82no—
241C4×C13#44711yescharacteristic
242C4×C13#44811yescharacteristic
243C4×C13#46511yescharacteristic
244C4×C13#46511yescharacteristic
245C4×C13#46711yescharacteristic
246C4×C13#46711yescharacteristic
247C4×C13#48011yescharacteristic
248C4×C13#48111yescharacteristic
249Dic13—22no—
250Dic13—22no—
251Dic13—41no—
252Dic13—82no—
253C22×Q8—261no—
254C23×C4—131no—
255C23×C4—131no—
256C23×C4—131no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—264no—
260C22×C8—261no—
261C22×C8—261no—
262C22×C8—522no—
263C22×C8—522no—
264C4⋊Q8—261no—
265C4⋊Q8—261no—
266C4⋊Q8—261no—
267C4⋊Q8—261no—
268C22⋊Q8—522no—
269C22⋊Q8—522no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—132no—
273C2×C4⋊C4—262no—
274C2×C4⋊C4—261no—
275C2×C4⋊C4C4×D1312yes—
276C2×C22⋊C4—262no—
277C2×C42—131no—
278C2×C42—131no—
279C2×C42—131no—
280C2×C42—261no—
281C2×C42—261no—
282C2×C42—261no—
283C2×C42—261no—
284C2×C42C22×D1311yescharacteristic
285C4⋊C8—21no—
286C4⋊C8—21no—
287C4⋊C8—21no—
288C4⋊C8—132no—
289C4⋊C8—264no—
290C4⋊C8—261no—
291C4⋊C8—261no—
292C4⋊C8—261no—
293C4⋊C8D5212yes—
294C22⋊C8—522no—
295#95—262no—
296#95—262no—
297C2×C13C2×#33211yescharacteristic
298C2×C13#154011yescharacteristic
299C2×C13#155011yescharacteristic
300C2×C13#155211yescharacteristic
301C2×C13#187411yescharacteristic
302C2×C13#189211yescharacteristic
303C2×C13#190111yescharacteristic
304D13—24no—
305C24—131no—
306C2×Q8—521no—
307C2×Q8—521no—
308C2×Q8—521no—
309C2×Q8—521no—
310C2×Q8—521no—
311C2×Q8—521no—
312C22×C4—22no—
313C22×C4—131no—
314C22×C4—131no—
315C22×C4—132no—
316C22×C4—132no—
317C22×C4—132no—
318C22×C4—132no—
319C22×C4—131no—
320C22×C4—262no—
321C22×C4—261no—
322C22×C4—261no—
323C22×C4—261no—
324C22×C4—261no—
325C22×C4—261no—
326C22×C4—261no—
327C22×C4—261no—
328C22×C4—261no—
329C22×C4—261no—
330C22×C4—261no—
331C22×C4—262no—
332C22×C4—521no—
333C22×C4C2×C4×D1311yescharacteristic
334C22×C4D4×D1311yescharacteristic
335C22×C4D4×D1311yescharacteristic
336C2×C8—22no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—262no—
343C2×C8—528no—
344C2×C8—521no—
345C2×C8—521no—
346C2×C8—521no—
347C2×C8—521no—
348C2×C8—521no—
349C4⋊C4—42no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—262no—
355C4⋊C4—262no—
356C4⋊C4—524no—
357C4⋊C4—521no—
358C4⋊C4—521no—
359C22⋊C4—524no—
360C42—261no—
361C42—261no—
362C42—261no—
363C42—261no—
364C42—261no—
365C42—261no—
366C42C2×D5211yescharacteristic
367C42#612711yescharacteristic
368C42D4×D1311yescharacteristic
369C42#613111yescharacteristic
370C13#913111yescharacteristic, complemented, Sylow
371C23—132no—
372C23—132no—
373C23—132no—
374C23—261no—
375C23—261no—
376C23—261no—
377C23—261no—
378C23C22⋊C4×D1311yescharacteristic
379Q8—1041no—
380Q8—1041no—
381Q8—1041no—
382Q8—1041no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—132no—
389C2×C4—132no—
390C2×C4—261no—
391C2×C4—261no—
392C2×C4—261no—
393C2×C4—261no—
394C2×C4—262no—
395C2×C4—262no—
396C2×C4—262no—
397C2×C4—262no—
398C2×C4—262no—
399C2×C4—262no—
400C2×C4—262no—
401C2×C4—262no—
402C2×C4—261no—
403C2×C4—261no—
404C2×C4—261no—
405C2×C4—522no—
406C2×C4—522no—
407C2×C4—522no—
408C2×C4—522no—
409C2×C4—522no—
410C2×C4C4×D5211yescharacteristic
411C2×C4#8813611yescharacteristic
412C2×C4#8813811yescharacteristic
413C2×C4#8814711yescharacteristic
414C2×C4#8814811yescharacteristic
415C2×C4#8814911yescharacteristic
416C2×C4D8×D1311yescharacteristic
417C2×C4#8816611yescharacteristic
418C2×C4SD16×D1311yescharacteristic
419C2×C4SD16×D1311yescharacteristic
420C2×C4#8816811yescharacteristic
421C2×C4#8817011yescharacteristic
422C2×C4Q16×D1311yescharacteristic
423C2×C4#8817211yescharacteristic
424C8—42no—
425C8—81no—
426C8—522no—
427C8—1041no—
428C22—134no—
429C22—262no—
430C22—262no—
431C22—262no—
432C22—262no—
433C22—262no—
434C22—262no—
435C22#1171832611yescharacteristic
436C22#1171840611yescharacteristic
437C22D13×#10111yescharacteristic
438C22D13×#10211yescharacteristic
439C22#1171843311yescharacteristic
440C22D13×#10311yescharacteristic
441C22#1171846411yescharacteristic
442C4—21no—
443C4—21no—
444C4—82no—
445C4—262no—
446C4—262no—
447C4—521no—
448C4—1042no—
449C4#1171843411yescharacteristic
450C4#1171843911yescharacteristic
451C4#1171846711yescharacteristic
452C4#1171847411yescharacteristic
453C4#1171852411yescharacteristic
454C4#1171852511yescharacteristic
455C4#1171854311yescharacteristic
456C4#1171854811yescharacteristic
457C2—264no—
458C2D13×#33211yescharacteristic
459C2#1311348211yescharacteristic
460C2#1311352311yescharacteristic
461C2#1311353311yescharacteristic
462C2#1311515211yescharacteristic
463C2#1311525811yescharacteristic
464C2#1311530311yescharacteristic
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#9131
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×#11718074C2semidirect
5. C2×#11718078C2semidirect
6. #13112719C2semidirect
7. C13×#1296C2semidirect
145. #1296D13semidirect
237. C2×D13#332semidirect
370. C13#9131semidirect

Maximal subgroups

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

subgroupindex
C2×D13×C4⋊C82
#131231892
#131148132
C2×#117180742
C2×#117180782
#131127192
C13×#12962
#913113