Finite Group Databasebeta

← #15778664

Subgroups — #15778664

Order 3328.

876 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13116585C211yesmaximal, characteristic, complemented
2C2×#11718157C211yesmaximal, characteristic, complemented
3#13116572C211yesmaximal, characteristic, complemented
4#13116556C211yesmaximal, characteristic, complemented
5#13116464C211yesmaximal, characteristic, complemented
6#13114890C211yesmaximal, characteristic, complemented
7C2×C13×#578C211yesmaximal, characteristic
8C2×C13×2−1+4—21no—
9C13×#578—22no—
10C13×#578—22no—
11C13×#578—22no—
12C13×#578C414yescomplemented
13C2×C13×#137—22no—
14C2×C13×#137—21no—
15C2×C13×#135—21no—
16C2×C13×#135C2211yescharacteristic
17C22×C13×Q16—21no—
18C22×C13×Q16C2211yescharacteristic
19C2×C13×#131C2211yescharacteristic
20#11718897—21no—
21C2×#88059C2211yescharacteristic
22#11718767C2211yescharacteristic
23C2×#88052C2211yescharacteristic
24C2×#88052C2211yescharacteristic
25#11718158—22no—
26#11718157—22no—
27#11718157—21no—
28#11718156—22no—
29#11718155—21no—
30#11718153—22no—
31#11718151—21no—
32C13×2−1+4—24no—
33C13×2−1+4—24no—
34C13×2−1+4—42no—
35C13×2−1+4—42no—
36C2×C13×#41—22no—
37C2×C13×#41—21no—
38C2×C13×#41—42no—
39C2×C13×#41—41no—
40C2×C13×#41D411yescharacteristic
41C22×Q8×C13—22no—
42C22×Q8×C13—21no—
43C22×Q8×C13—41no—
44C13×#137—24no—
45C13×#137—28no—
46C13×#137—28no—
47C13×#137—24no—
48C13×#135—24no—
49C13×#135—24no—
50C13×#135—21no—
51C13×#135—21no—
52C13×#135C2×C412yes—
53C13×#135D412yes—
54C2×C13×Q16—22no—
55C2×C13×Q16—24no—
56C2×C13×Q16—24no—
57C2×C13×Q16—21no—
58C2×C13×Q16—21no—
59C2×C13×Q16—21no—
60C2×C13×Q16C2×C412yes—
61C2×C13×Q16D412yes—
62C2×C13×Q16D411yescharacteristic
63C2×C13×Q16D412yes—
64C2×C13×SD16—22no—
65C2×C13×SD16—21no—
66C2×C13×D8D411yescharacteristic
67C13×#131—21no—
68C13×#131—21no—
69C13×#131C2×C412yes—
70C13×#131D412yes—
71C2×C13×M16—21no—
72C2×C13×M16D411yescharacteristic
73C22×C8×C13—21no—
74C22×C8×C13C2311yescharacteristic
75#88180—21no—
76C2×#6099—21no—
77#88077—42no—
78#88059—21no—
79#88059—21no—
80#88058—21no—
81#88057—21no—
82#88052—21no—
83#88052—21no—
84#88052—21no—
85#88052—21no—
86C2×#6090—21no—
87C2×#6090—21no—
88#12751—131nomaximal, Sylow
89C13×#41—21no—
90C13×#41—21no—
91C13×#41—28no—
92C13×#41—22no—
93C13×#41—22no—
94C13×#41—44no—
95C13×#41—48no—
96C13×#41—48no—
97C13×#41—44no—
98C13×#41—44no—
99C13×#41—41no—
100C13×#41—41no—
101C13×#41C22⋊C412yes—
102C13×#41D812yes—
103C2×Q8×C13—28no—
104C2×Q8×C13—22no—
105C2×Q8×C13—22no—
106C2×Q8×C13—21no—
107C2×Q8×C13—22no—
108C2×Q8×C13—42no—
109C2×Q8×C13—44no—
110C2×Q8×C13—44no—
111C2×Q8×C13—44no—
112C2×Q8×C13—41no—
113C2×Q8×C13—41no—
114C2×Q8×C13—41no—
115C2×Q8×C13SD1611yescharacteristic
116C2×D4×C13—21no—
117C2×D4×C13—21no—
118C2×D4×C13—42no—
119C2×D4×C13—41no—
120C2×D4×C13SD1611yescharacteristic
121C22×C4×C13—21no—
122C22×C4×C13—42no—
123C22×C4×C13—42no—
124C22×C4×C13—41no—
125C22×C4×C13—41no—
126C22×C4×C13C2×D411yescharacteristic
127C13×Q16—28no—
128C13×Q16—22no—
129C13×Q16—21no—
130C13×Q16—22no—
131C13×Q16—22no—
132C13×Q16C22⋊C412yes—
133C13×Q16C22⋊C414yes—
134C13×SD16—28no—
135C13×SD16—22no—
136C13×SD16—22no—
137C13×D8—21no—
138C13×D8C22⋊C412yes—
139C13×M16—21no—
140C13×M16—22no—
141C13×M16—22no—
142C13×M16C22⋊C412yes—
143C2×C8×C13—21no—
144C2×C8×C13—22no—
145C2×C8×C13—22no—
146C2×C8×C13C22×C411yescharacteristic
147C2×C8×C13C2×D411yescharacteristic
148C2×C8×C13C2×D411yescharacteristic
149C2×C8×C13C2×D411yescharacteristic
150C2×C8×C13C2×D411yescharacteristic
151C2×C8×C13C2×D411yescharacteristic
152C22⋊Dic13—41no—
153C4⋊Dic13—41no—
154C4×Dic13—41no—
155#6099—41no—
156#6099—41no—
157C2×#1055—41no—
158#6090—41no—
159#6090—41no—
160C2×#578D1311yescharacteristic
161#2148—131no—
162C2×#362—131no—
163#2145—131no—
164#2141—131no—
165#2117—131no—
166#1814—131no—
167C23×C13—21no—
168C23×C13—41no—
169C23×C13AGL(1,ℤ/8)11yescharacteristic
170Q8×C13—21no—
171Q8×C13—24no—
172Q8×C13—22no—
173Q8×C13—48no—
174Q8×C13—42no—
175Q8×C13—41no—
176Q8×C13—42no—
177Q8×C13—42no—
178Q8×C13#10212yes—
179D4×C13—22no—
180D4×C13—22no—
181D4×C13—22no—
182D4×C13—21no—
183D4×C13—48no—
184D4×C13—42no—
185D4×C13—42no—
186D4×C13—41no—
187D4×C13#10212yes—
188C2×C4×C13—21no—
189C2×C4×C13—22no—
190C2×C4×C13—22no—
191C2×C4×C13—48no—
192C2×C4×C13—48no—
193C2×C4×C13—42no—
194C2×C4×C13—42no—
195C2×C4×C13—42no—
196C2×C4×C13—41no—
197C2×C4×C13—42no—
198C2×C4×C13—42no—
199C2×C4×C13C2×C22⋊C411yescharacteristic
200C2×C4×C13#12011yescharacteristic
201C2×C4×C13#12011yescharacteristic
202C2×C4×C13C2×D811yescharacteristic
203C2×C4×C13C2×SD1611yescharacteristic
204C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
205C2×Dic13—81no—
206C8×C13—22no—
207C8×C13C2×C22⋊C411yescharacteristic
208C8×C13C2×C22⋊C411yescharacteristic
209C8×C13#12011yescharacteristic
210C8×C13#12011yescharacteristic
211#1055—81no—
212C2×2−1+4—21no—
213#578—22no—
214#578—22no—
215#578—22no—
216#578Dic1314yescomplemented
217C2×#137—22no—
218C2×#137—21no—
219C2×#135—21no—
220C2×#135C2×D1311yescharacteristic
221C22×Q16—21no—
222C22×Q16C2×D1311yescharacteristic
223C2×#131C2×D1311yescharacteristic
224C2×M32—131no—
225C2×M32—131no—
226C2×#108—131no—
227#427—131no—
228#421—261no—
229#362—262no—
230#362—261no—
231#361—261no—
232#360—262no—
233#358—262no—
234#350—262no—
235#344—261no—
236C22×C13—22no—
237C22×C13—41no—
238C22×C13—42no—
239C22×C13—42no—
240C22×C13—82no—
241C22×C13#41811yescharacteristic
242C22×C13#44711yescharacteristic
243C22×C13#45011yescharacteristic
244C4×C13—22no—
245C4×C13—44no—
246C4×C13—42no—
247C4×C13#37911yescharacteristic
248C4×C13C2×#10211yescharacteristic
249C4×C13#44711yescharacteristic
250C4×C13#45011yescharacteristic
251Dic13—161no—
2522−1+4—24no—
2532−1+4—24no—
2542−1+4—42no—
2552−1+4—42no—
256C2×#41—22no—
257C2×#41—21no—
258C2×#41—42no—
259C2×#41—41no—
260C2×#41C22⋊D1311yescharacteristic
261C22×Q8—22no—
262C22×Q8—21no—
263C22×Q8—41no—
264#137—24no—
265#137—28no—
266#137—28no—
267#137—24no—
268#135—24no—
269#135—24no—
270#135—21no—
271#135—21no—
272#135C2×Dic1312yes—
273#135C22⋊D1312yes—
274C2×Q16—22no—
275C2×Q16—24no—
276C2×Q16—24no—
277C2×Q16—21no—
278C2×Q16—21no—
279C2×Q16—21no—
280C2×Q16C2×Dic1312yes—
281C2×Q16C22⋊D1311yescharacteristic
282C2×Q16C22⋊D1312yes—
283C2×Q16C22⋊D1312yes—
284C2×SD16—22no—
285C2×SD16—21no—
286C2×D8C22⋊D1311yescharacteristic
287#131—21no—
288#131—21no—
289#131C2×Dic1312yes—
290#131C22⋊D1312yes—
291C2×M16—21no—
292C2×M16—261no—
293C2×M16C22⋊D1311yescharacteristic
294C22×C8—21no—
295C22×C8C22×D1311yescharacteristic
296#117—261no—
297M32—261no—
298M32—261no—
299M32—261no—
300M32—261no—
301C2×C16—261no—
302C2×C16—261no—
303#108—261no—
304#108—261no—
305#107—261no—
306#106—261no—
307#104—522no—
308C2×C13—21no—
309C2×C13—21no—
310C2×C13—21no—
311C2×C13—42no—
312C2×C13—82no—
313C2×C13#178611yescharacteristic
314#41—21no—
315#41—21no—
316#41—28no—
317#41—22no—
318#41—22no—
319#41—44no—
320#41—48no—
321#41—48no—
322#41—44no—
323#41—44no—
324#41—41no—
325#41—41no—
326#41#610412yes—
327#41C22⋊Dic1312yes—
328C2×Q8—28no—
329C2×Q8—22no—
330C2×Q8—22no—
331C2×Q8—21no—
332C2×Q8—22no—
333C2×Q8—42no—
334C2×Q8—44no—
335C2×Q8—44no—
336C2×Q8—44no—
337C2×Q8—41no—
338C2×Q8—41no—
339C2×Q8—41no—
340C2×Q8#610511yescharacteristic
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—42no—
344C2×D4—41no—
345C2×D4#610511yescharacteristic
346C22×C4—21no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4C2×C22⋊D1311yescharacteristic
352Q16—28no—
353Q16—22no—
354Q16—21no—
355Q16—22no—
356Q16—22no—
357Q16C22⋊Dic1312yes—
358Q16C22⋊Dic1314yes—
359SD16—28no—
360SD16—22no—
361SD16—22no—
362D8—21no—
363D8C22⋊Dic1312yes—
364M16—21no—
365M16—22no—
366M16—22no—
367M16—521no—
368M16—521no—
369M16C22⋊Dic1312yes—
370C2×C8—21no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—521no—
374C2×C8C22×Dic1311yescharacteristic
375C2×C8C2×C22⋊D1311yescharacteristic
376C2×C8C2×C22⋊D1311yescharacteristic
377C2×C8C2×C22⋊D1311yescharacteristic
378C2×C8C2×C22⋊D1311yescharacteristic
379C2×C8C2×C22⋊D1311yescharacteristic
380C4⋊C4—521no—
381C22⋊C4—521no—
382C42—521no—
383C16—521no—
384C16—521no—
385C13#1275111yescharacteristic, complemented, Sylow
386C23—21no—
387C23—41no—
388C23#8818611yescharacteristic
389Q8—21no—
390Q8—24no—
391Q8—22no—
392Q8—48no—
393Q8—42no—
394Q8—41no—
395Q8—42no—
396Q8—42no—
397Q8#8807212yes—
398D4—22no—
399D4—22no—
400D4—21no—
401D4—22no—
402D4—48no—
403D4—42no—
404D4—42no—
405D4—41no—
406D4#8807212yes—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—48no—
411C2×C4—48no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—1041no—
419C2×C4C2×#610411yescharacteristic
420C2×C4#8818611yescharacteristic
421C2×C4C2×#610511yescharacteristic
422C2×C4C2×C22⋊Dic1311yescharacteristic
423C2×C4#8820711yescharacteristic
424C2×C4#8820711yescharacteristic
425C8—22no—
426C8—1041no—
427C8C2×C22⋊Dic1311yescharacteristic
428C8C2×C22⋊Dic1311yescharacteristic
429C8#8820711yescharacteristic
430C8#8820711yescharacteristic
431C22—22no—
432C22—41no—
433C22—42no—
434C22—42no—
435C22—82no—
436C22#1171887611yescharacteristic
437C22#1171887811yescharacteristic
438C22#1171887911yescharacteristic
439C4—22no—
440C4—44no—
441C4—42no—
442C4—2081no—
443C4C2×#8807211yescharacteristic
444C4#1171887811yescharacteristic
445C4#1171887911yescharacteristic
446C4#1171890811yescharacteristic
447C2—21no—
448C2—21no—
449C2—21no—
450C2—42no—
451C2—82no—
452C2#1311476711yescharacteristic
subgroupG/H
centerC2#13114767
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
Fitting, prime radicalC2×C13×#578C2
socleC2×C13#1786
cosocleC22×C8×C13C23
hypercenterC2×#578D13
hypocenterC13#12751
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ C2×#578

Complements

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

NH ≅ G/Ntype
1. #13116585C2semidirect
2. C2×#11718157C2semidirect
3. #13116572C2semidirect
4. #13116556C2semidirect
5. #13116464C2semidirect
6. #13114890C2semidirect
12. C13×#578C4semidirect
216. #578Dic13semidirect
385. C13#12751semidirect

Maximal subgroups

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

subgroupindex
#131165852
C2×#117181572
#131165722
#131165562
#131164642
#131148902
C2×C13×#5782
#1275113