Finite Group Databasebeta

← #15755631

Subgroups — #15755631

Order 3328.

548 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
1#13117297C211yesmaximal, characteristic
2#13114952C211yesmaximal, characteristic, complemented
3C4×#88054C211yesmaximal, characteristic, complemented
4C2×#11718051C211yesmaximal, characteristic
5C2×#11718075C211yesmaximal, characteristic
6#13112677C211yesmaximal, characteristic, complemented
7C13×#1279C211yesmaximal, characteristic, complemented
8C2×C4×D52C2211yescharacteristic
9C2×#88126—21no—
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×C4×C8×C13C2211yescharacteristic
12C4×C13×C4⋊C4C2211yescharacteristic
13C2×#88054—21no—
14#11718649C411yescharacteristic
15#11718649C411yescharacteristic
16#11718634C411yescharacteristic
17#11718634C411yescharacteristic
18C4×#6103—21no—
19C42×Dic13C2211yescharacteristic
20C2×C4⋊#1055C2211yescharacteristic
21C2×C4×#1055C2211yescharacteristic
22#11718330—21no—
23#11718330—21no—
24#11718142—21no—
25#11718142—21no—
26#11718142—21no—
27#11718075—22no—
28#11718051—22no—
29C22×D52C2×C411yescharacteristic
30C22×C4×D13—21no—
31C22×C8×C13—21no—
32C22×C8×C13—21no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C42×C13—21no—
36C2×C42×C13C2311yescharacteristic
37C2×#6103—21no—
38C2×#6103—21no—
39C2×#6103—21no—
40C2×#6103—21no—
41C2×#6103—21no—
42C2×C4⋊Dic13C2×C411yescharacteristic
43C2×#6101—21no—
44C2×#6101—21no—
45C2×C4×Dic13C2×C411yescharacteristic
46C2×C4×Dic13C2×C411yescharacteristic
47C2×C4×Dic13D411yescharacteristic
48C2×C4×Dic13D411yescharacteristic
49C2×C4×Dic13D411yescharacteristic
50C2×C4×Dic13D411yescharacteristic
51C22×#1055—21no—
52C22×#1055—21no—
53C4×D52—21no—
54C4×D52—21no—
55C4×D52D412yes—
56C4×D52Q812yes—
57#88126—42no—
58#88126—42no—
59C13×C4⋊C8—21no—
60C13×C4⋊C8—21no—
61C4×C8×C13—21no—
62C4×C8×C13—21no—
63C13×#95—21no—
64#88071—21no—
65#88071—21no—
66#88054—24no—
67C4⋊#1055—21no—
68C4⋊#1055—21no—
69C4×#1055—21no—
70C4×#1055—21no—
71#8569—131nomaximal, Sylow
72C23×D13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13C22×C411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×Dic13—21no—
79C22×Dic13C22⋊C411yescharacteristic
80C22×Dic13C22⋊C411yescharacteristic
81C22×Dic13C22⋊C411yescharacteristic
82C22×Dic13C22⋊C411yescharacteristic
83C2×D52—21no—
84C2×D52—21no—
85C2×D52—21no—
86C2×D52—21no—
87C2×D52—21no—
88C2×D52C4⋊C412yes—
89C2×C4×D13—22no—
90C2×C4×D13—22no—
91C2×C4×D13—41no—
92C2×C4×D13—41no—
93C2×C4×D13—41no—
94C2×C4×D13—41no—
95C2×C8×C13—22no—
96C2×C8×C13—41no—
97C2×C8×C13—41no—
98C2×C8×C13—41no—
99C2×C8×C13—41no—
100C2×C8×C13—41no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—21no—
105C42×C13—41no—
106C42×C13—41no—
107C42×C13C2×D411yescharacteristic
108C42×C13C2×Q811yescharacteristic
109C42×C13#4111yescharacteristic
110C42×C13#4111yescharacteristic
111#6103—22no—
112#6103—22no—
113#6103—42no—
114#6103—42no—
115#6103—42no—
116#6103—42no—
117C4⋊Dic13—21no—
118C4⋊Dic13C4⋊C412yes—
119#6101—42no—
120#6101—42no—
121C4×Dic13—21no—
122C4×Dic13—21no—
123C4×Dic13—21no—
124C4×Dic13—21no—
125C4×Dic13—21no—
126C4×Dic13—21no—
127C4×Dic13—21no—
128C4×Dic13—21no—
129C4×Dic13—22no—
130C4×Dic13—41no—
131C2×#1055—22no—
132C2×#1055—41no—
133C2×#1055—41no—
134C2×#1055—41no—
135C2×#1055—41no—
136C2×#1055—41no—
137#2293—131no—
138#1831—131no—
139C4×C4⋊C8—131no—
140C2×D4⋊C8—131no—
141C2×D4⋊C8—131no—
142#1279—131no—
143#1279D1311yescharacteristic, complemented
144C23×C13C2×C22⋊C411yescharacteristic
145C22×D13—22no—
146C22×D13—41no—
147C22×D13—41no—
148C22×D13—41no—
149C22×D13—41no—
150C22×D13—41no—
151C22×D13—41no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13C2×C4⋊C411yescharacteristic
161C2×C4×C13#11711yescharacteristic
162C2×C4×C13#12111yescharacteristic
163C2×C4×C13#12111yescharacteristic
164C2×C4×C13C22⋊Q811yescharacteristic
165C2×C4×C13C22⋊Q811yescharacteristic
166C2×C4×C13#13111yescharacteristic
167C2×C4×C13#13111yescharacteristic
168C2×C4×C13#13111yescharacteristic
169C2×C4×C13#13111yescharacteristic
170C2×C4×C13#13511yescharacteristic
171C2×C4×C13#13511yescharacteristic
172C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
174C2×Dic13—21no—
175C2×Dic13—21no—
176C2×Dic13—22no—
177C2×Dic13—21no—
178C2×Dic13—21no—
179C2×Dic13—21no—
180C2×Dic13—21no—
181C2×Dic13—21no—
182C2×Dic13—21no—
183C2×Dic13—21no—
184C2×Dic13—21no—
185C2×Dic13—21no—
186C2×Dic13—41no—
187C2×Dic13—41no—
188C2×Dic13#10412yes—
189D52—22no—
190D52—22no—
191D52—41no—
192D52—41no—
193C4×D13—42no—
194C4×D13—42no—
195C4×D13—42no—
196C4×D13—42no—
197C8×C13—42no—
198C8×C13—81no—
199#1055—42no—
200#1055—81no—
201C2×C4×D4—131no—
202C2×#117—261no—
203C2×C4⋊C8—131no—
204C2×C4⋊C8—261no—
205C2×C4⋊C8C2×D1311yescharacteristic
206C2×C4×C8—131no—
207C2×C4×C8C2×D1311yescharacteristic
208#390—131no—
209#390—131no—
210#389—131no—
211#389—131no—
212#388—261no—
213#388—261no—
214C4×C4⋊C4C2×D1311yescharacteristic
215C4×C22⋊C4—261no—
216C43—131no—
217#336—261no—
218#336—261no—
219#336—261no—
220D4⋊C8—262no—
221D4⋊C8—262no—
222C22×C13#38011yescharacteristic
223C22×C13#40811yescharacteristic
224C22×C13#40811yescharacteristic
225C22×C13#41611yescharacteristic
226C22×C13#41811yescharacteristic
227C22×C13C2×#10411yescharacteristic
228C22×C13#42111yescharacteristic
229C2×D13—42no—
230C2×D13—42no—
231C2×D13—42no—
232C2×D13—81no—
233C2×D13—81no—
234C2×D13—81no—
235C2×D13—81no—
236C4×C13—21no—
237C4×C13—21no—
238C4×C13—81no—
239C4×C13—81no—
240C4×C13#42411yescharacteristic
241C4×C13#42411yescharacteristic
242C4×C13#43311yescharacteristic
243C4×C13#43311yescharacteristic
244C4×C13#46311yescharacteristic
245C4×C13#46311yescharacteristic
246C4×C13#47811yescharacteristic
247C4×C13#47811yescharacteristic
248Dic13—22no—
249Dic13—42no—
250Dic13—41no—
251Dic13—41no—
252Dic13—41no—
253C22×D4—131no—
254C23×C4—261no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—261no—
258C22×C8—261no—
259C4×D4—132no—
260C4×D4—132no—
261C4×D4—261no—
262C4×D4—261no—
263#117—522no—
264#117—522no—
265C2×C4⋊C4—131no—
266C2×C4⋊C4—261no—
267C2×C4⋊C4—261no—
268C2×C4⋊C4C4×D1311yescharacteristic
269C2×C4⋊C4C4×D1311yescharacteristic
270C2×C22⋊C4—261no—
271C2×C22⋊C4—261no—
272C2×C22⋊C4—261no—
273C2×C22⋊C4—261no—
274C2×C22⋊C4—261no—
275C2×C42—21no—
276C2×C42—131no—
277C2×C42—131no—
278C2×C42—131no—
279C2×C42—131no—
280C2×C42—131no—
281C2×C42—131no—
282C2×C42C22×D1311yescharacteristic
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8—264no—
286C4⋊C8—261no—
287C4⋊C8—261no—
288C4×C8—21no—
289C4×C8—21no—
290C4×C8—261no—
291C4×C8—261no—
292#95—21no—
293#95—261no—
294#95—261no—
295C2×C13#148211yescharacteristic
296C2×C13#148411yescharacteristic
297C2×C13#149411yescharacteristic
298C2×C13#149611yescharacteristic
299C2×C13#179811yescharacteristic
300C2×C13#180411yescharacteristic
301C2×C13#180611yescharacteristic
302D13—82no—
303C24—261no—
304C2×D4—132no—
305C2×D4—261no—
306C2×D4—261no—
307C2×D4—261no—
308C2×D4—261no—
309C2×D4—261no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—131no—
313C22×C4—131no—
314C22×C4—131no—
315C22×C4—131no—
316C22×C4—261no—
317C22×C4—262no—
318C22×C4—262no—
319C22×C4—521no—
320C22×C4—521no—
321C22×C4—521no—
322C22×C4—521no—
323C22×C4C2×C4×D1311yescharacteristic
324C22×C4D4×D1311yescharacteristic
325C22×C4D4×D1311yescharacteristic
326C2×C8—22no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—262no—
333C2×C8—521no—
334C2×C8—521no—
335C2×C8—521no—
336C2×C8—521no—
337C2×C8—521no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—132no—
343C4⋊C4—261no—
344C4⋊C4—522no—
345C4⋊C4—522no—
346C22⋊C4—262no—
347C22⋊C4—262no—
348C22⋊C4—522no—
349C22⋊C4—522no—
350C22⋊C4—522no—
351C22⋊C4—522no—
352C42—41no—
353C42—41no—
354C42—262no—
355C42—261no—
356C42—261no—
357C42—261no—
358C42—261no—
359C42—261no—
360C42—261no—
361C42—261no—
362C42—261no—
363C42—521no—
364C42#612711yescharacteristic
365C42#612711yescharacteristic
366C42D4×D1311yescharacteristic
367C42Q8×D1311yescharacteristic
368C13#856911yescharacteristic, complemented, Sylow
369C23—262no—
370C23—521no—
371C23—521no—
372C23—521no—
373C23—521no—
374C23—521no—
375C23—521no—
376C23C22⋊C4×D1311yescharacteristic
377D4—262no—
378D4—262no—
379D4—521no—
380D4—521no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—132no—
390C2×C4—261no—
391C2×C4—261no—
392C2×C4—261no—
393C2×C4—261no—
394C2×C4—261no—
395C2×C4—261no—
396C2×C4—261no—
397C2×C4—261no—
398C2×C4—262no—
399C2×C4—261no—
400C2×C4—261no—
401C2×C4—261no—
402C2×C4—521no—
403C2×C4—521no—
404C2×C4—522no—
405C2×C4—522no—
406C2×C4—522no—
407C2×C4—522no—
408C2×C4#8812611yescharacteristic
409C2×C4#8813811yescharacteristic
410C2×C4#8813811yescharacteristic
411C2×C4C4⋊C4×D1311yescharacteristic
412C2×C4#8815011yescharacteristic
413C2×C4#8815011yescharacteristic
414C2×C4#8815511yescharacteristic
415C2×C4#8815511yescharacteristic
416C2×C4#8816111yescharacteristic
417C2×C4#8816111yescharacteristic
418C2×C4#8816511yescharacteristic
419C2×C4#8816811yescharacteristic
420C2×C4#8817011yescharacteristic
421C2×C4#8817311yescharacteristic
422C8—42no—
423C8—81no—
424C8—522no—
425C8—1041no—
426C22—522no—
427C22—522no—
428C22—522no—
429C22—1041no—
430C22—1041no—
431C22—1041no—
432C22—1041no—
433C22#1171832811yescharacteristic
434C22#1171838811yescharacteristic
435C22#1171838811yescharacteristic
436C22#1171843111yescharacteristic
437C22#1171846511yescharacteristic
438C22D13×#10411yescharacteristic
439C22#1171848211yescharacteristic
440C4—21no—
441C4—21no—
442C4—81no—
443C4—81no—
444C4—262no—
445C4—521no—
446C4—521no—
447C4—521no—
448C4—522no—
449C4#1171835111yescharacteristic
450C4#1171837011yescharacteristic
451C4#1171844811yescharacteristic
452C4#1171848011yescharacteristic
453C4#1171850011yescharacteristic
454C4#1171850011yescharacteristic
455C4#1171853211yescharacteristic
456C4#1171855211yescharacteristic
457C2—1042no—
458C2#1311324311yescharacteristic
459C2#1311325111yescharacteristic
460C2#1311329511yescharacteristic
461C2#1311330311yescharacteristic
462C2#1311481911yescharacteristic
463C2#1311484511yescharacteristic
464C2#1311485511yescharacteristic
subgroupG/H
centerC22×C4D4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1279C2
socleC23×C13C2×C22⋊C4
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenter#1279D13
hypocenterC13#8569
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
2. #13114952C2semidirect
3. C4×#88054C2semidirect
6. #13112677C2semidirect
7. C13×#1279C2semidirect
143. #1279D13semidirect
368. C13#8569semidirect

Maximal subgroups

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

subgroupindex
#131172972
#131149522
C4×#880542
C2×#117180512
C2×#117180752
#131126772
C13×#12792
#856913