Finite Group Databasebeta

← #15755621

Subgroups — #15755621

Order 3328.

568 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117297C211yesmaximal, characteristic
2#13114987C211yesmaximal, 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—
14C2×#88054—21no—
15C2×#88054—21no—
16#11718649C411yescharacteristic
17#11718649C411yescharacteristic
18#11718634C411yescharacteristic
19#11718634C411yescharacteristic
20C4×#6103—21no—
21C42×Dic13C2211yescharacteristic
22C2×C4⋊#1055C2211yescharacteristic
23C2×C4×#1055C2211yescharacteristic
24#11718330—21no—
25#11718330—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—
67#88054—42no—
68#88054—42no—
69C4⋊#1055—21no—
70C4⋊#1055—21no—
71C4×#1055—21no—
72C4×#1055—21no—
73#8567—131nomaximal, Sylow
74C23×D13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×Dic13—21no—
81C22×Dic13C22⋊C411yescharacteristic
82C22×Dic13C22⋊C411yescharacteristic
83C22×Dic13C22⋊C411yescharacteristic
84C22×Dic13C22⋊C411yescharacteristic
85C2×D52—21no—
86C2×D52—21no—
87C2×D52—21no—
88C2×D52—21no—
89C2×D52—21no—
90C2×D52C4⋊C412yes—
91C2×C4×D13—22no—
92C2×C4×D13—22no—
93C2×C4×D13—41no—
94C2×C4×D13—41no—
95C2×C4×D13—41no—
96C2×C4×D13—41no—
97C2×C8×C13—22no—
98C2×C8×C13—41no—
99C2×C8×C13—41no—
100C2×C8×C13—41no—
101C2×C8×C13—41no—
102C2×C8×C13—41no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—21no—
106C13×C4⋊C4—21no—
107C42×C13—41no—
108C42×C13—41no—
109C42×C13C2×D411yescharacteristic
110C42×C13C2×Q811yescharacteristic
111C42×C13#4111yescharacteristic
112C42×C13#4111yescharacteristic
113#6103—22no—
114#6103—22no—
115#6103—42no—
116#6103—42no—
117#6103—42no—
118#6103—42no—
119C4⋊Dic13—21no—
120C4⋊Dic13C4⋊C412yes—
121#6101—42no—
122#6101—42no—
123C4×Dic13—21no—
124C4×Dic13—21no—
125C4×Dic13—21no—
126C4×Dic13—21no—
127C4×Dic13—21no—
128C4×Dic13—21no—
129C4×Dic13—22no—
130C4×Dic13—41no—
131C4×Dic13D812yes—
132C4×Dic13SD1612yes—
133C2×#1055—22no—
134C2×#1055—41no—
135C2×#1055—41no—
136C2×#1055—41no—
137C2×#1055—41no—
138C2×#1055—41no—
139#2293—131no—
140#1842—131no—
141C4×C4⋊C8—131no—
142C2×D4⋊C8—131no—
143C2×D4⋊C8—131no—
144#1279—131no—
145#1279D1311yescharacteristic, complemented
146C23×C13C2×C22⋊C411yescharacteristic
147C22×D13—22no—
148C22×D13—41no—
149C22×D13—41no—
150C22×D13—41no—
151C22×D13—41no—
152C22×D13—41no—
153C22×D13—41no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13C2×C4⋊C411yescharacteristic
163C2×C4×C13#11711yescharacteristic
164C2×C4×C13#12111yescharacteristic
165C2×C4×C13#12111yescharacteristic
166C2×C4×C13C22⋊Q811yescharacteristic
167C2×C4×C13C22⋊Q811yescharacteristic
168C2×C4×C13#13111yescharacteristic
169C2×C4×C13#13111yescharacteristic
170C2×C4×C13#13111yescharacteristic
171C2×C4×C13#13111yescharacteristic
172C2×C4×C13C2×D811yescharacteristic
173C2×C4×C13C2×SD1611yescharacteristic
174C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C13#13711yescharacteristic
176C2×Dic13—21no—
177C2×Dic13—21no—
178C2×Dic13—21no—
179C2×Dic13—21no—
180C2×Dic13—21no—
181C2×Dic13—21no—
182C2×Dic13—22no—
183C2×Dic13—21no—
184C2×Dic13—21no—
185C2×Dic13—21no—
186C2×Dic13—41no—
187C2×Dic13—41no—
188C2×Dic13#10212yes—
189C2×Dic13#10212yes—
190C2×Dic13#10412yes—
191D52—22no—
192D52—22no—
193D52—41no—
194D52—41no—
195C4×D13—42no—
196C4×D13—42no—
197C4×D13—42no—
198C4×D13—42no—
199C8×C13—42no—
200C8×C13—81no—
201#1055—42no—
202#1055—81no—
203C2×C4×D4—131no—
204C2×#117—261no—
205C2×C4⋊C8—131no—
206C2×C4⋊C8—261no—
207C2×C4⋊C8—261no—
208C2×C4⋊C8—261no—
209C2×C4⋊C8C2×D1311yescharacteristic
210C2×C4×C8—131no—
211C2×C4×C8C2×D1311yescharacteristic
212#390—131no—
213#390—131no—
214#389—131no—
215#389—131no—
216#388—261no—
217#388—261no—
218C4×C4⋊C4C2×D1311yescharacteristic
219C4×C22⋊C4—261no—
220C43—131no—
221#336—261no—
222D4⋊C8—262no—
223D4⋊C8—262no—
224C22×C13#38011yescharacteristic
225C22×C13#40811yescharacteristic
226C22×C13#40811yescharacteristic
227C22×C13C2×#10211yescharacteristic
228C22×C13#41711yescharacteristic
229C22×C13C2×#10411yescharacteristic
230C22×C13#42111yescharacteristic
231C2×D13—42no—
232C2×D13—42no—
233C2×D13—42no—
234C2×D13—81no—
235C2×D13—81no—
236C2×D13—81no—
237C2×D13—81no—
238C4×C13—21no—
239C4×C13—21no—
240C4×C13—81no—
241C4×C13—81no—
242C4×C13#42411yescharacteristic
243C4×C13#42411yescharacteristic
244C4×C13#43311yescharacteristic
245C4×C13#43311yescharacteristic
246C4×C13#45911yescharacteristic
247C4×C13#46111yescharacteristic
248C4×C13#47411yescharacteristic
249C4×C13#47611yescharacteristic
250Dic13—22no—
251Dic13—22no—
252Dic13—22no—
253Dic13—42no—
254Dic13—41no—
255C22×D4—131no—
256C23×C4—261no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—261no—
260C22×C8—261no—
261C4×D4—132no—
262C4×D4—132no—
263C4×D4—261no—
264C4×D4—261no—
265#117—522no—
266#117—522no—
267C2×C4⋊C4—131no—
268C2×C4⋊C4—261no—
269C2×C4⋊C4—261no—
270C2×C4⋊C4C4×D1311yescharacteristic
271C2×C4⋊C4C4×D1311yescharacteristic
272C2×C22⋊C4—261no—
273C2×C22⋊C4—261no—
274C2×C22⋊C4—261no—
275C2×C22⋊C4—261no—
276C2×C22⋊C4—261no—
277C2×C42—21no—
278C2×C42—131no—
279C2×C42—131no—
280C2×C42—131no—
281C2×C42—131no—
282C2×C42—131no—
283C2×C42—131no—
284C2×C42C22×D1311yescharacteristic
285C4⋊C8—21no—
286C4⋊C8—21no—
287C4⋊C8—264no—
288C4⋊C8—261no—
289C4⋊C8—261no—
290C4⋊C8—522no—
291C4⋊C8—522no—
292C4×C8—21no—
293C4×C8—21no—
294C4×C8—261no—
295C4×C8—261no—
296#95—21no—
297#95—261no—
298#95—261no—
299C2×C13#148011yescharacteristic
300C2×C13#148311yescharacteristic
301C2×C13#149211yescharacteristic
302C2×C13#149511yescharacteristic
303C2×C13#179811yescharacteristic
304C2×C13#180211yescharacteristic
305C2×C13#180611yescharacteristic
306D13—82no—
307C24—261no—
308C2×D4—132no—
309C2×D4—261no—
310C2×D4—261no—
311C2×D4—261no—
312C2×D4—261no—
313C2×D4—261no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—131no—
317C22×C4—131no—
318C22×C4—131no—
319C22×C4—131no—
320C22×C4—261no—
321C22×C4—262no—
322C22×C4—262no—
323C22×C4—521no—
324C22×C4—521no—
325C22×C4—521no—
326C22×C4—521no—
327C22×C4C2×C4×D1311yescharacteristic
328C22×C4D4×D1311yescharacteristic
329C22×C4D4×D1311yescharacteristic
330C2×C8—22no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—262no—
337C2×C8—521no—
338C2×C8—521no—
339C2×C8—521no—
340C2×C8—521no—
341C2×C8—521no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—132no—
347C4⋊C4—261no—
348C4⋊C4—522no—
349C4⋊C4—522no—
350C22⋊C4—262no—
351C22⋊C4—262no—
352C22⋊C4—522no—
353C22⋊C4—522no—
354C22⋊C4—522no—
355C22⋊C4—522no—
356C42—41no—
357C42—41no—
358C42—132no—
359C42—132no—
360C42—262no—
361C42—261no—
362C42—261no—
363C42—261no—
364C42—261no—
365C42—261no—
366C42—261no—
367C42—521no—
368C42#612711yescharacteristic
369C42#612711yescharacteristic
370C42D4×D1311yescharacteristic
371C42Q8×D1311yescharacteristic
372C13#856711yescharacteristic, complemented, Sylow
373C23—262no—
374C23—521no—
375C23—521no—
376C23—521no—
377C23—521no—
378C23—521no—
379C23—521no—
380C23C22⋊C4×D1311yescharacteristic
381D4—262no—
382D4—262no—
383D4—521no—
384D4—521no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—132no—
394C2×C4—132no—
395C2×C4—132no—
396C2×C4—261no—
397C2×C4—261no—
398C2×C4—261no—
399C2×C4—261no—
400C2×C4—261no—
401C2×C4—261no—
402C2×C4—261no—
403C2×C4—261no—
404C2×C4—262no—
405C2×C4—261no—
406C2×C4—521no—
407C2×C4—521no—
408C2×C4—522no—
409C2×C4—522no—
410C2×C4—522no—
411C2×C4—522no—
412C2×C4#8812611yescharacteristic
413C2×C4#8813811yescharacteristic
414C2×C4#8813811yescharacteristic
415C2×C4C4⋊C4×D1311yescharacteristic
416C2×C4#8815011yescharacteristic
417C2×C4#8815011yescharacteristic
418C2×C4#8815511yescharacteristic
419C2×C4#8815511yescharacteristic
420C2×C4#8816111yescharacteristic
421C2×C4#8816111yescharacteristic
422C2×C4D8×D1311yescharacteristic
423C2×C4SD16×D1311yescharacteristic
424C2×C4#8816811yescharacteristic
425C2×C4#8817211yescharacteristic
426C8—42no—
427C8—81no—
428C8—522no—
429C8—1041no—
430C22—522no—
431C22—522no—
432C22—522no—
433C22—1041no—
434C22—1041no—
435C22—1041no—
436C22—1041no—
437C22#1171832811yescharacteristic
438C22#1171838811yescharacteristic
439C22#1171838811yescharacteristic
440C22D13×#10211yescharacteristic
441C22#1171846411yescharacteristic
442C22D13×#10411yescharacteristic
443C22#1171848211yescharacteristic
444C4—21no—
445C4—21no—
446C4—81no—
447C4—81no—
448C4—262no—
449C4—262no—
450C4—262no—
451C4—522no—
452C4—521no—
453C4#1171835111yescharacteristic
454C4#1171837011yescharacteristic
455C4#1171844711yescharacteristic
456C4#1171847911yescharacteristic
457C4#1171850011yescharacteristic
458C4#1171850011yescharacteristic
459C4#1171853111yescharacteristic
460C4#1171855111yescharacteristic
461C2—1042no—
462C2#1311323311yescharacteristic
463C2#1311324811yescharacteristic
464C2#1311328511yescharacteristic
465C2#1311330011yescharacteristic
466C2#1311481911yescharacteristic
467C2#1311483511yescharacteristic
468C2#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#8567
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. #13114987C2semidirect
3. C4×#88054C2semidirect
6. #13112677C2semidirect
7. C13×#1279C2semidirect
145. #1279D13semidirect
372. C13#8567semidirect

Maximal subgroups

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

subgroupindex
#131172972
#131149872
C4×#880542
C2×#117180512
C2×#117180752
#131126772
C13×#12792
#856713