Finite Group Databasebeta

← #15757762

Subgroups — #15757762

Order 3328.

540 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124844C211yesmaximal, characteristic
2D4×#6099C211yesmaximal, characteristic
3#13115779C211yesmaximal, characteristic, complemented
4#13113292C211yesmaximal, characteristic, complemented
5#13112739C211yesmaximal, characteristic, complemented
6#13112673C211yesmaximal, characteristic, complemented
7C4×C13×#102C211yesmaximal, characteristic
8C2×C4×D4×C13C2211yescharacteristic
9C22×#6099—21no—
10#11719175C2211yescharacteristic
11C2×C13×#102—21no—
12C2×C4×C8×C13C2211yescharacteristic
13C4×C13×C4⋊C4C2211yescharacteristic
14#11718879—21no—
15#11718868—21no—
16#11718680C411yescharacteristic, complemented
17#11718680C411yescharacteristic, complemented
18C4×#6105—21no—
19C4×#6105—21no—
20#11718673—21no—
21#11718672—22no—
22D4×#1055—21no—
23#11718669C411yescharacteristic, complemented
24#11718669C411yescharacteristic, complemented
25#11718632—21no—
26#11718586C2211yescharacteristic
27#11718585C2211yescharacteristic
28C4×#6099C2211yescharacteristic
29C13×#340—21no—
30#11718115—21no—
31#11718115—21no—
32#11718048—22no—
33C22×D4×C13D411yescharacteristic
34C23×C4×C13—21no—
35C22×C8×C13—21no—
36C4×D4×C13—21no—
37C4×D4×C13—21no—
38C4×D4×C13C2×C411yescharacteristic
39C4×D4×C13C2×C411yescharacteristic
40C4×D4×C13D411yescharacteristic
41C4×D4×C13D411yescharacteristic
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4D411yescharacteristic
44C2×C13×C22⋊C4—21no—
45C2×C42×C13—21no—
46C2×C42×C13C2311yescharacteristic
47C2×#6105—21no—
48C2×#6105—21no—
49#88180—21no—
50#88178—21no—
51#88178—21no—
52C2×#6099—22no—
53C2×#6099—21no—
54C2×#6099—42no—
55C2×#6099—42no—
56C2×#6099D411yescharacteristic
57C2×#6099D411yescharacteristic
58C22×#1055—22no—
59#88124—21no—
60#88123C2×C411yescharacteristic
61#88123C2×C411yescharacteristic
62C4×Dic26—21no—
63C4×Dic26—21no—
64C13×#102—24no—
65C4×C8×C13—21no—
66C4×C8×C13—21no—
67C13×#95—21no—
68#88072—21no—
69#88072—21no—
70C22⋊#1055—22no—
71C22⋊#1055—22no—
72C22⋊#1055—21no—
73#88050—21no—
74#88050—21no—
75#88048—21no—
76#88048—21no—
77C4⋊#1055—21no—
78C4⋊#1055C2×C411yescharacteristic
79C4⋊#1055C2×C411yescharacteristic
80C4⋊#1055D412yes—
81#88043—21no—
82C4×#1055—21no—
83C4×#1055—21no—
84#8989—131nomaximal, Sylow
85C24×C13—21no—
86C2×D4×C13—22no—
87C2×D4×C13—21no—
88C2×D4×C13—41no—
89C2×D4×C13C22⋊C411yescharacteristic
90C2×D4×C13C22⋊C411yescharacteristic
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—41no—
97C22×C4×C13—41no—
98C22×C4×C13—41no—
99C22×C4×C13—41no—
100C22×C4×C13—41no—
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13#4111yescharacteristic
104C2×Dic26—21no—
105C2×Dic26—21no—
106C2×C8×C13—22no—
107C2×C8×C13—41no—
108C2×C8×C13—41no—
109C13×C4⋊C4—21no—
110C13×C4⋊C4—22no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4C22⋊C411yescharacteristic
113C13×C4⋊C4C22⋊C411yescharacteristic
114C13×C22⋊C4—21no—
115C13×C22⋊C4—21no—
116C13×C22⋊C4—21no—
117C13×C22⋊C4—21no—
118C42×C13—41no—
119C42×C13—41no—
120C42×C13C22×C411yescharacteristic
121C42×C13C2×D411yescharacteristic
122C42×C13C2×D411yescharacteristic
123C42×C13#4111yescharacteristic
124C22⋊Dic13—41no—
125#6105—42no—
126#6105—42no—
127C4⋊Dic13—21no—
128C4⋊Dic13—21no—
129C4⋊Dic13—21no—
130C4⋊Dic13—21no—
131#6101—41no—
132#6101—41no—
133C4×Dic13—41no—
134#6099—21no—
135#6099—21no—
136#6099—21no—
137#6099—44no—
138#6099—41no—
139#6099—41no—
140#6099SD1612yescomplemented
141C2×#1055—21no—
142C2×#1055—21no—
143C2×#1055—21no—
144C2×#1055—21no—
145C2×#1055—22no—
146C2×#1055—44no—
147#3101—131no—
148D4×M16—131no—
149#1986—131no—
150C4×#102D1311yescharacteristic
151#1493—131no—
152#1303—131no—
153#1278—131no—
154C23×C13—21no—
155C23×C13—21no—
156C23×C13—42no—
157C23×C13—41no—
158C23×C13—41no—
159C23×C13—81no—
160C23×C13#12111yescharacteristic
161D4×C13—21no—
162D4×C13—21no—
163D4×C13—21no—
164D4×C13—42no—
165D4×C13#10412yes—
166C2×C4×C13—21no—
167C2×C4×C13—21no—
168C2×C4×C13—21no—
169C2×C4×C13—21no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—42no—
182C2×C4×C13—81no—
183C2×C4×C13—81no—
184C2×C4×C13C2×C22⋊C411yescharacteristic
185C2×C4×C13C4×D411yescharacteristic
186C2×C4×C13C4×D411yescharacteristic
187C2×C4×C13#12011yescharacteristic
188C2×C4×C13#12111yescharacteristic
189C2×C4×C13#12311yescharacteristic
190C2×C4×C13C2×SD1611yescharacteristic
191C2×C4×C13#13511yescharacteristic
192C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
193C2×C4×C13#13711yescharacteristic
194C2×Dic13—41no—
195C2×Dic13—41no—
196Dic26—42no—
197Dic26—41no—
198Dic26—41no—
199C8×C13—42no—
200#1055—22no—
201#1055—41no—
202#1055—41no—
203#1055—42no—
204#1055—41no—
205C22×M16—261no—
206#533—131no—
207C2×C4×D4C2×D1311yescharacteristic
208#483—261no—
209#476—131no—
210#476—131no—
211#461—131no—
212#461—131no—
213#450—261no—
214C4×SD16—261no—
215C4×SD16—261no—
216#436—261no—
217#435—262no—
218C8×D4—261no—
219#431—131no—
220#423—131no—
221C2×#102—21no—
222#407—261no—
223C4×M16—131no—
224C2×C4×C8C2×D1311yescharacteristic
225C4×C4⋊C4C2×D1311yescharacteristic
226#340—21no—
227#339—261no—
228#339—261no—
229Q8⋊C8—262no—
230C22×C13—21no—
231C22×C13—21no—
232C22×C13—22no—
233C22×C13—41no—
234C22×C13—41no—
235C22×C13—41no—
236C22×C13—41no—
237C22×C13—41no—
238C22×C13—82no—
239C22×C13—82no—
240C22×C13#38611yescharacteristic
241C22×C13#46111yescharacteristic
242C22×C13#46311yescharacteristic
243C4×C13—21no—
244C4×C13—21no—
245C4×C13—21no—
246C4×C13—41no—
247C4×C13—41no—
248C4×C13—82no—
249C4×C13C2×#10411yescharacteristic
250C4×C13#42111yescharacteristic
251C4×C13C4×SD1611yescharacteristic
252C4×C13#44011yescharacteristic
253C4×C13#45011yescharacteristic
254C4×C13#45211yescharacteristic
255Dic13—81no—
256Dic13—81no—
257C22×D4C22⋊D1311yescharacteristic
258C23×C4—21no—
259C2×SD16—261no—
260C2×SD16—261no—
261C2×M16—131no—
262C2×M16—131no—
263C2×M16—262no—
264C2×M16—261no—
265C2×M16—522no—
266C2×M16—522no—
267C22×C8—21no—
268C22×C8—262no—
269C4⋊Q8—131no—
270C4⋊Q8—131no—
271#125—261no—
272C22⋊Q8—261no—
273C22⋊Q8—261no—
274C4×Q8—261no—
275C4×Q8—261no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4C4×D1311yescharacteristic
279C4×D4C4×D1311yescharacteristic
280C4×D4D5211yescharacteristic
281C4×D4D5211yescharacteristic
282#117—261no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4C22⋊D1311yescharacteristic
285C2×C22⋊C4—21no—
286C2×C42—21no—
287C2×C42C22×D1311yescharacteristic
288#106—261no—
289#106—261no—
290C4⋊C8—131no—
291C4⋊C8—131no—
292C4⋊C8—132no—
293C4⋊C8—261no—
294#103—261no—
295#103—261no—
296#102—24no—
297#102—261no—
298#102—261no—
299C22⋊C8—262no—
300C22⋊C8—262no—
301C22⋊C8—261no—
302#97—261no—
303C4×C8—21no—
304C4×C8—21no—
305C4×C8—261no—
306C4×C8—261no—
307#95—21no—
308C2×C13—21no—
309C2×C13—21no—
310C2×C13—42no—
311C2×C13—81no—
312C2×C13#187111yescharacteristic
313C2×C13#187711yescharacteristic
314C2×C13#188111yescharacteristic
315C24—21no—
316C2×Q8—261no—
317C2×Q8—261no—
318C2×D4—22no—
319C2×D4—21no—
320C2×D4—41no—
321C2×D4#610311yescharacteristic
322C2×D4#610311yescharacteristic
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4D4×D1311yescharacteristic
334C22×C4#612911yescharacteristic
335C22×C4C2×C22⋊D1311yescharacteristic
336SD16—522no—
337SD16—522no—
338M16—132no—
339M16—261no—
340M16—261no—
341M16—261no—
342M16—524no—
343M16—521no—
344M16—521no—
345C2×C8—22no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—261no—
349C2×C8—261no—
350C2×C8—262no—
351C2×C8—261no—
352C2×C8—261no—
353C2×C8—524no—
354C4⋊C4—21no—
355C4⋊C4—22no—
356C4⋊C4—41no—
357C4⋊C4—261no—
358C4⋊C4—261no—
359C4⋊C4—261no—
360C4⋊C4—261no—
361C4⋊C4—521no—
362C4⋊C4—521no—
363C4⋊C4#610311yescharacteristic
364C4⋊C4#610311yescharacteristic
365C22⋊C4—21no—
366C22⋊C4—21no—
367C22⋊C4—21no—
368C22⋊C4—21no—
369C22⋊C4—521no—
370C42—41no—
371C42—41no—
372C42—521no—
373C42C2×C4×D1311yescharacteristic
374C42C2×D5211yescharacteristic
375C42D4×D1311yescharacteristic
376C42#612911yescharacteristic
377C13#898911yescharacteristic, complemented, Sylow
378C23—21no—
379C23—21no—
380C23—42no—
381C23—41no—
382C23—41no—
383C23—81no—
384C23#8819311yescharacteristic
385Q8—522no—
386Q8—521no—
387Q8—521no—
388D4—21no—
389D4—21no—
390D4—21no—
391D4—42no—
392D4#8804512yes—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—81no—
410C2×C4—81no—
411C2×C4—521no—
412C2×C4—521no—
413C2×C4#8813511yescharacteristic
414C2×C4#8813511yescharacteristic
415C2×C4#8813611yescharacteristic
416C2×C4#8814011yescharacteristic
417C2×C4#8816511yescharacteristic
418C2×C4#8816611yescharacteristic
419C2×C4SD16×D1311yescharacteristic
420C2×C4#8816911yescharacteristic
421C2×C4C2×#610311yescharacteristic
422C2×C4#8819311yescharacteristic
423C8—42no—
424C8—262no—
425C8—521no—
426C8—522no—
427C8—521no—
428C8—521no—
429C22—21no—
430C22—21no—
431C22—22no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—82no—
438C22—82no—
439C22#1171861911yescharacteristic
440C22#1171881411yescharacteristic
441C22#1171882311yescharacteristic
442C4—21no—
443C4—21no—
444C4—21no—
445C4—41no—
446C4—41no—
447C4—82no—
448C4—1041no—
449C4—1041no—
450C4#1171841811yescharacteristic
451C4#1171841911yescharacteristic
452C4#1171843711yescharacteristic
453C4#1171844411yescharacteristic
454C4C2×#8804511yescharacteristic
455C4#1171866611yescharacteristic
456C2—21no—
457C2—21no—
458C2—42no—
459C2—81no—
460C2#1311513611yescharacteristic
461C2#1311516811yescharacteristic
462C2#1311519611yescharacteristic
subgroupG/H
centerC2×C4#88136
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC4×C13×#102C2
socleC22×C13#386
prime radicalC22×D4×C13D4
cosocleC2×C42×C13C23
hypercenterC4×#102D13
hypocenterC13#8989
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
3. #13115779C2semidirect
4. #13113292C2semidirect
5. #13112739C2semidirect
6. #13112673C2semidirect
16. #11718680C4semidirect
17. #11718680C4semidirect
23. #11718669C4semidirect
24. #11718669C4semidirect
140. #6099SD16semidirect
377. C13#8989semidirect

Maximal subgroups

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

subgroupindex
#131248442
D4×#60992
#131157792
#131132922
#131127392
#131126732
C4×C13×#1022
#898913