Finite Group Databasebeta

← #15756274

Subgroups — #15756274

Order 3328.

592 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88146C211yesmaximal, characteristic
2#13114813C211yesmaximal, characteristic
3C4×#88060C211yesmaximal, characteristic
4#13112677C211yesmaximal, characteristic, complemented
5#13112676C211yesmaximal, characteristic, complemented
6#13112675C211yesmaximal, characteristic, complemented
7C13×#1279C211yesmaximal, characteristic, complemented
8C2×#88146C411yescharacteristic
9C2×#88146C411yescharacteristic
10C2×C42×D13C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C4×C8×C13C2211yescharacteristic
13C4×C13×C4⋊C4C2211yescharacteristic
14C2×#88060—21no—
15C2×#88060—21no—
16C4⋊C4×Dic13C411yescharacteristic
17C4⋊C4×Dic13C411yescharacteristic
18C4×#6103—21no—
19C4×C4⋊Dic13C2211yescharacteristic
20C42×Dic13—21no—
21C2×C4⋊#1055C2211yescharacteristic
22C2×C4×#1055C2211yescharacteristic
23#11718327—21no—
24#11718309—21no—
25#11718142—21no—
26#11718142—21no—
27C22×C4×D13C2×C411yescharacteristic
28C22×C4×D13D411yescharacteristic
29C22×C4×D13D411yescharacteristic
30C22×C8×C13—21no—
31C22×C8×C13—21no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C42×C13—21no—
35C2×C42×C13C2311yescharacteristic
36C2×#6103—21no—
37C2×#6103—21no—
38C2×C4⋊Dic13C2×C411yescharacteristic
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×C4×Dic13—21no—
41C2×C4×Dic13—21no—
42C2×C4×Dic13—21no—
43C2×C4×Dic13—21no—
44C2×C4×Dic13—21no—
45C2×C4×Dic13C2×C411yescharacteristic
46C2×C4×Dic13D411yescharacteristic
47C2×C4×Dic13D411yescharacteristic
48C22×#1055—21no—
49C22×#1055—21no—
50#88146—22no—
51#88146—22no—
52#88146—22no—
53#88146C814yescomplemented
54C42×D13—21no—
55C42×D13—21no—
56C42×D13—21no—
57C42×D13—21no—
58C13×C4⋊C8—21no—
59C13×C4⋊C8—21no—
60C4×C8×C13—21no—
61C4×C8×C13—21no—
62C13×#95—21no—
63#88071—21no—
64#88071—21no—
65#88071—21no—
66#88060—24no—
67#88060—42no—
68C4⋊#1055—21no—
69C4⋊#1055—21no—
70C4×#1055—21no—
71C4×#1055—21no—
72#8708—131nomaximal, Sylow
73C23×D13C22⋊C411yescharacteristic
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×Dic13—21no—
80C22×Dic13—21no—
81C22×Dic13C22⋊C411yescharacteristic
82C22×Dic13C22⋊C411yescharacteristic
83C22×Dic13C22⋊C411yescharacteristic
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—21no—
95C2×C4×D13—21no—
96C2×C4×D13—22no—
97C2×C4×D13—41no—
98C2×C4×D13C2×C812yes—
99C2×C4×D13M1612yes—
100C2×C8×C13—22no—
101C2×C8×C13—41no—
102C2×C8×C13—41no—
103C2×C8×C13—41no—
104C2×C8×C13—41no—
105C2×C8×C13—41no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4C2×C812yes—
109C13×C4⋊C4M1612yes—
110C42×C13—41no—
111C42×C13—41no—
112C42×C13#4111yescharacteristic
113C42×C13#4111yescharacteristic
114C42×C13#4111yescharacteristic
115C42×C13#4111yescharacteristic
116#6103—24no—
117#6103—24no—
118C4⋊Dic13—21no—
119C4⋊Dic13—21no—
120C4⋊Dic13C2×C812yes—
121C4⋊Dic13M1612yes—
122C4×Dic13—24no—
123C4×Dic13—21no—
124C4×Dic13—21no—
125C4×Dic13—21no—
126C4×Dic13—21no—
127C4×Dic13—21no—
128C4×Dic13—21no—
129C4×Dic13—24no—
130C4×Dic13—42no—
131C4×Dic13—41no—
132C4×Dic13—41no—
133C4×Dic13—42no—
134C2×#1055—22no—
135C2×#1055—41no—
136C2×#1055—41no—
137C2×#1055—41no—
138C2×#1055—41no—
139C2×#1055—41no—
140C4×#117—131no—
141#1797—131no—
142C4×C22⋊C8—131no—
143#1279—131no—
144#1279—131no—
145#1279—131no—
146#1279D1311yescharacteristic, complemented
147C23×C13C2×C22⋊C411yescharacteristic
148C22×D13—21no—
149C22×D13—21no—
150C22×D13—21no—
151C22×D13—21no—
152C22×D13—21no—
153C22×D13—21no—
154C22×D13C22⋊C812yes—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—22no—
158C2×C4×C13—22no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13#11711yescharacteristic
164C2×C4×C13#11711yescharacteristic
165C2×C4×C13#12311yescharacteristic
166C2×C4×C13#12311yescharacteristic
167C2×C4×C13#12311yescharacteristic
168C2×C4×C13#12311yescharacteristic
169C2×C4×C13C22×C811yescharacteristic
170C2×C4×C13C2×M1611yescharacteristic
171C2×C4×C13C2×M1611yescharacteristic
172C2×C4×C13C2×M1611yescharacteristic
173C2×C4×C13#13511yescharacteristic
174C2×C4×C13#13511yescharacteristic
175C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C13#13711yescharacteristic
177C2×Dic13—21no—
178C2×Dic13—21no—
179C2×Dic13—21no—
180C2×Dic13—21no—
181C2×Dic13—21no—
182C2×Dic13—22no—
183C2×Dic13—22no—
184C2×Dic13—21no—
185C2×Dic13—21no—
186C2×Dic13—41no—
187C2×Dic13—41no—
188C2×Dic13—41no—
189C2×Dic13—41no—
190C2×Dic13C22⋊C812yes—
191C2×Dic13#10412yes—
192C4×D13—22no—
193C4×D13—22no—
194C4×D13—22no—
195C4×D13—22no—
196C4×D13—42no—
197C4×D13—42no—
198C4×D13—41no—
199C4×D13—41no—
200C4×D13—41no—
201C4×D13—41no—
202C8×C13—42no—
203C8×C13—81no—
204#1055—42no—
205#1055—81no—
206C2×#117—131no—
207C2×#117—131no—
208C22×C42—131no—
209C2×C4⋊C8—131no—
210C2×C4⋊C8C2×D1311yescharacteristic
211C2×C22⋊C8—261no—
212C2×C22⋊C8—261no—
213C2×C4×C8—131no—
214C2×C4×C8C2×D1311yescharacteristic
215C4×C4⋊C4—131no—
216C4×C4⋊C4—131no—
217C4×C4⋊C4—131no—
218C4×C4⋊C4C2×D1311yescharacteristic
219C4×C22⋊C4—261no—
220C4×C22⋊C4—261no—
221#376—261no—
222C43—261no—
223#336—261no—
224#336—261no—
225C22×C13#38111yescharacteristic
226C22×C13C2×C22⋊C811yescharacteristic
227C22×C13#40711yescharacteristic
228C22×C13#41611yescharacteristic
229C22×C13#41711yescharacteristic
230C22×C13C2×#10411yescharacteristic
231C22×C13#42111yescharacteristic
232C2×D13—22no—
233C2×D13—22no—
234C2×D13—22no—
235C2×D13—41no—
236C2×D13—41no—
237C2×D13—41no—
238C2×D13—41no—
239C4×C13—21no—
240C4×C13—21no—
241C4×C13—42no—
242C4×C13—42no—
243C4×C13#43111yescharacteristic
244C4×C13#43111yescharacteristic
245C4×C13#43211yescharacteristic
246C4×C13#43211yescharacteristic
247C4×C13#48211yescharacteristic
248C4×C13#48211yescharacteristic
249C4×C13#48511yescharacteristic
250C4×C13#48511yescharacteristic
251Dic13—22no—
252Dic13—22no—
253Dic13—41no—
254Dic13—42no—
255Dic13—42no—
256C23×C4—131no—
257C23×C4—131no—
258C23×C4—131no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—261no—
262C22×C8—261no—
263#117—134no—
264#117—262no—
265#117—262no—
266#117—262no—
267C2×C4⋊C4—131no—
268C2×C4⋊C4—131no—
269C2×C4⋊C4C4×D1311yescharacteristic
270C2×C4⋊C4C4×D1311yescharacteristic
271C2×C22⋊C4—261no—
272C2×C22⋊C4—261no—
273C2×C42—21no—
274C2×C42—131no—
275C2×C42—131no—
276C2×C42—131no—
277C2×C42—261no—
278C2×C42—261no—
279C2×C42—261no—
280C2×C42—261no—
281C2×C42—261no—
282C2×C42—261no—
283C2×C42—261no—
284C2×C42—261no—
285C2×C42—261no—
286C2×C42C22×D1311yescharacteristic
287C4⋊C8—21no—
288C4⋊C8—21no—
289C4⋊C8—261no—
290C4⋊C8—261no—
291C22⋊C8—264no—
292C22⋊C8—522no—
293C4×C8—21no—
294C4×C8—21no—
295C4×C8—261no—
296C4×C8—261no—
297#95—21no—
298#95—261no—
299#95—261no—
300#95—261no—
301C2×C13#147611yescharacteristic
302C2×C13#147711yescharacteristic
303C2×C13#148811yescharacteristic
304C2×C13#148911yescharacteristic
305C2×C13#181711yescharacteristic
306C2×C13#182511yescharacteristic
307C2×C13#182611yescharacteristic
308D13—42no—
309C24—131no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—131no—
313C22×C4—131no—
314C22×C4—132no—
315C22×C4—132no—
316C22×C4—131no—
317C22×C4—262no—
318C22×C4—261no—
319C22×C4—261no—
320C22×C4—261no—
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—261no—
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—521no—
344C2×C8—521no—
345C2×C8—521no—
346C2×C8—521no—
347C2×C8—521no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—132no—
351C4⋊C4—132no—
352C4⋊C4—261no—
353C4⋊C4—261no—
354C4⋊C4C8×D1312yes—
355C4⋊C4#609412yes—
356C22⋊C4—264no—
357C22⋊C4—264no—
358C42—41no—
359C42—41no—
360C42—264no—
361C42—264no—
362C42—261no—
363C42—261no—
364C42—261no—
365C42—261no—
366C42—261no—
367C42—261no—
368C42—522no—
369C42—522no—
370C42—521no—
371C42—521no—
372C42#612711yescharacteristic
373C42#612711yescharacteristic
374C42#612911yescharacteristic
375C42#613111yescharacteristic
376C13#870811yescharacteristic, complemented, Sylow
377C23—132no—
378C23—261no—
379C23—261no—
380C23—261no—
381C23—261no—
382C23—261no—
383C23—261no—
384C23C22⋊C4×D1311yescharacteristic
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—132no—
394C2×C4—132no—
395C2×C4—261no—
396C2×C4—261no—
397C2×C4—261no—
398C2×C4—261no—
399C2×C4—262no—
400C2×C4—262no—
401C2×C4—262no—
402C2×C4—262no—
403C2×C4—261no—
404C2×C4—261no—
405C2×C4—261no—
406C2×C4—262no—
407C2×C4—262no—
408C2×C4—522no—
409C2×C4—522no—
410C2×C4—521no—
411C2×C4—521no—
412C2×C4—521no—
413C2×C4—521no—
414C2×C4—521no—
415C2×C4—521no—
416C2×C4—521no—
417C2×C4—521no—
418C2×C4#8812611yescharacteristic
419C2×C4#8813711yescharacteristic
420C2×C4#8813711yescharacteristic
421C2×C4#8814611yescharacteristic
422C2×C4#8814811yescharacteristic
423C2×C4#8814811yescharacteristic
424C2×C4C2×C8×D1311yescharacteristic
425C2×C4C2×#609411yescharacteristic
426C2×C4M16×D1311yescharacteristic
427C2×C4M16×D1311yescharacteristic
428C2×C4#8816511yescharacteristic
429C2×C4#8816911yescharacteristic
430C2×C4#8817011yescharacteristic
431C2×C4#8817311yescharacteristic
432C8—42no—
433C8—81no—
434C8—522no—
435C8—1041no—
436C22—262no—
437C22—262no—
438C22—262no—
439C22—521no—
440C22—521no—
441C22—521no—
442C22—521no—
443C22#1171832511yescharacteristic
444C22D13×C22⋊C811yescharacteristic
445C22#1171838711yescharacteristic
446C22#1171843211yescharacteristic
447C22#1171846511yescharacteristic
448C22D13×#10411yescharacteristic
449C22#1171848211yescharacteristic
450C4—21no—
451C4—21no—
452C4—42no—
453C4—42no—
454C4—262no—
455C4—262no—
456C4—521no—
457C4—522no—
458C4—522no—
459C4#1171834611yescharacteristic
460C4#1171836611yescharacteristic
461C4#1171844011yescharacteristic
462C4#1171847511yescharacteristic
463C4#1171849411yescharacteristic
464C4#1171849611yescharacteristic
465C4#1171852811yescharacteristic
466C4#1171854611yescharacteristic
467C2—522no—
468C2#1311321711yescharacteristic
469C2#1311322011yescharacteristic
470C2#1311326911yescharacteristic
471C2#1311327211yescharacteristic
472C2#1311490311yescharacteristic
473C2#1311493011yescharacteristic
474C2#1311493411yescharacteristic
subgroupG/H
centerC22×C4D4×D13
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1279C2
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1279D13
hypocenterC13#8708
LCSG ▷ C2×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
4. #13112677C2semidirect
5. #13112676C2semidirect
6. #13112675C2semidirect
7. C13×#1279C2semidirect
53. #88146C8semidirect
146. #1279D13semidirect
376. C13#8708semidirect

Maximal subgroups

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

subgroupindex
C4×#881462
#131148132
C4×#880602
#131126772
#131126762
#131126752
C13×#12792
#870813