Finite Group Databasebeta

← #15756086

Subgroups — #15756086

Order 3328.

454 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×#1055C211yesmaximal, characteristic
2#13114856C211yesmaximal, characteristic
3C4×#88047C211yesmaximal, characteristic, complemented
4#13113594C211yesmaximal, characteristic, complemented
5#13112739C211yesmaximal, characteristic, complemented
6#13112737C211yesmaximal, characteristic, complemented
7C13×#1806C211yesmaximal, characteristic
8C4×C13×#41C2211yescharacteristic
9C13×#423C2211yescharacteristic
10C2×C13×#104—21no—
11C4×C13×C4⋊C4C2211yescharacteristic
12C2×#88077—21no—
13Q8×#1055C411yescharacteristic, complemented
14Q8×#1055C411yescharacteristic, complemented
15D4×#1055—21no—
16D4×#1055—21no—
17D4×#1055C411yescharacteristic, complemented
18D4×#1055C411yescharacteristic, complemented
19C2×#88047—21no—
20C4×C4⋊Dic13C2211yescharacteristic
21#11718586—21no—
22#11718586C2211yescharacteristic
23#11718585C2211yescharacteristic
24C2×C4×#1055—21no—
25C2×C4×#1055C2211yescharacteristic
26C13×#339—21no—
27#11718124—21no—
28#11718121—21no—
29#11718071—21no—
30#11718071—21no—
31C2×C13×#41D411yescharacteristic
32C2×C13×M16—21no—
33C4×Q8×C13C2×C411yescharacteristic
34C4×Q8×C13Q811yescharacteristic
35C4×D4×C13—21no—
36C4×D4×C13—21no—
37C4×D4×C13C2×C411yescharacteristic
38C4×D4×C13Q811yescharacteristic
39C13×#117—21no—
40C13×#117D411yescharacteristic
41C2×C13×C4⋊C4—21no—
42C2×C42×C13—21no—
43C2×C42×C13—21no—
44C2×C42×C13C2311yescharacteristic
45C2×C4⋊Dic13—21no—
46C2×C4×Dic13—21no—
47C2×#6099—21no—
48C22×#1055—21no—
49C22×#1055—21no—
50C22×#1055D411yescharacteristic
51C22×#1055D411yescharacteristic
52C13×C4⋊C8—21no—
53C13×C4⋊C8—21no—
54C13×#104—42no—
55C13×#95—21no—
56#88077—42no—
57#88071—21no—
58C22⋊#1055—21no—
59C22⋊#1055—21no—
60C22⋊#1055—21no—
61#88047—24no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64C4⋊#1055—21no—
65C4⋊#1055—21no—
66C4⋊#1055C2×C411yescharacteristic
67C4⋊#1055C2×C411yescharacteristic
68C4×#1055—21no—
69C4×#1055—21no—
70C4×#1055—21no—
71C4×#1055C2×C411yescharacteristic
72C4×#1055C2×C411yescharacteristic
73C4×#1055D411yescharacteristic
74C4×#1055D411yescharacteristic
75#8667—131nomaximal, Sylow
76C13×#41—21no—
77C13×#41—21no—
78C13×#41D812yes—
79C13×#41Q1612yes—
80C2×Q8×C13C4⋊C411yescharacteristic
81C2×D4×C13—21no—
82C2×D4×C13C4⋊C411yescharacteristic
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—41no—
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13#4111yescharacteristic
90C22×Dic13—41no—
91C13×M16—41no—
92C13×M16—41no—
93C2×C8×C13—41no—
94C13×C4⋊C4—21no—
95C13×C4⋊C4—21no—
96C13×C4⋊C4—22no—
97C13×C4⋊C4—41no—
98C13×C4⋊C4C4⋊C411yescharacteristic
99C13×C4⋊C4C4⋊C411yescharacteristic
100C13×C22⋊C4—21no—
101C13×C22⋊C4—21no—
102C13×C22⋊C4—21no—
103C42×C13—21no—
104C42×C13—21no—
105C42×C13—21no—
106C42×C13—41no—
107C42×C13—41no—
108C42×C13C22×C411yescharacteristic
109C42×C13C2×D411yescharacteristic
110C42×C13C2×Q811yescharacteristic
111C42×C13#4111yescharacteristic
112C4⋊Dic13—22no—
113C4⋊Dic13—41no—
114C4×Dic13—41no—
115C4×Dic13—41no—
116#6099—41no—
117#6099—41no—
118C2×#1055—22no—
119C2×#1055—21no—
120C2×#1055—21no—
121C2×#1055—41no—
122C2×#1055—42no—
123C2×#1055—42no—
124C2×#1055—41no—
125C2×#1055C22⋊C411yescharacteristic
126C2×#1055C22⋊C411yescharacteristic
127C2×#1055C22⋊C411yescharacteristic
128C2×#1055C22⋊C411yescharacteristic
129C8×#41—131no—
130#1806—131no—
131#1806D1311yescharacteristic
132C4×#107—131no—
133#1567—131no—
134#1303—131no—
135#1303—131no—
136C23×C13—21no—
137C23×C13#12111yescharacteristic
138Q8×C13—21no—
139Q8×C13#10712yescomplemented
140D4×C13—22no—
141D4×C13—22no—
142D4×C13—21no—
143D4×C13#10712yescomplemented
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—22no—
148C2×C4×C13—22no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—41no—
152C2×C4×C13—42no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—42no—
156C2×C4×C13—81no—
157C2×C4×C13—81no—
158C2×C4×C13C2×C22⋊C411yescharacteristic
159C2×C4×C13C2×C4⋊C411yescharacteristic
160C2×C4×C13#11711yescharacteristic
161C2×C4×C13#12111yescharacteristic
162C2×C4×C13C22⋊Q811yescharacteristic
163C2×C4×C13C22⋊Q811yescharacteristic
164C2×C4×C13C2×D811yescharacteristic
165C2×C4×C13C2×Q1611yescharacteristic
166C2×C4×C13#13511yescharacteristic
167C2×C4×C13#13511yescharacteristic
168C2×Dic13—42no—
169C2×Dic13—81no—
170C2×Dic13—81no—
171C8×C13—81no—
172#1055—21no—
173#1055—21no—
174#1055—21no—
175#1055—41no—
176#1055—41no—
177#1055—81no—
178#1055#10412yescomplemented
179C4×#41C2×D1311yescharacteristic
180C8×Q8—131no—
181C8×Q8—131no—
182C8×D4—131no—
183C8×D4—131no—
184C8×D4—261no—
185C8×D4—261no—
186#431—131no—
187#431—261no—
188C2×#107—261no—
189#423—131no—
190#423C2×D1311yescharacteristic
191C2×#104—21no—
192C2×#104—261no—
193C2×C4×C8—131no—
194C2×C4×C8—261no—
195C4×C4⋊C4—131no—
196C4×C4⋊C4C2×D1311yescharacteristic
197#340—261no—
198#339—21no—
199#339—261no—
200#335—261no—
201#335—261no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—22no—
205C22×C13—41no—
206C22×C13—41no—
207C22×C13#38011yescharacteristic
208C22×C13#46611yescharacteristic
209C22×C13#46711yescharacteristic
210C4×C13—21no—
211C4×C13—22no—
212C4×C13—21no—
213C4×C13—21no—
214C4×C13—41no—
215C4×C13—41no—
216C4×C13—82no—
217C4×C13C2×#10411yescharacteristic
218C4×C13#42111yescharacteristic
219C4×C13C2×#10711yescharacteristic
220C4×C13#42711yescharacteristic
221C4×C13#46611yescharacteristic
222C4×C13#46711yescharacteristic
223Dic13—82no—
224C2×#41C22⋊D1311yescharacteristic
225C2×M16—21no—
226C2×M16—261no—
227C22×C8—131no—
228C22×C8—131no—
229C22×C8—261no—
230C22×C8—261no—
231C4×Q8Dic2611yescharacteristic
232C4×Q8C4×D1311yescharacteristic
233C4×D4—21no—
234C4×D4—21no—
235C4×D4Dic2611yescharacteristic
236C4×D4C4×D1311yescharacteristic
237#117—21no—
238#117C22⋊D1311yescharacteristic
239C2×C4⋊C4—21no—
240C2×C4⋊C4—261no—
241C2×C42—21no—
242C2×C42—21no—
243C2×C42—261no—
244C2×C42C22×D1311yescharacteristic
245#107—264no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—131no—
249C4⋊C8—131no—
250C4⋊C8—261no—
251C4⋊C8—261no—
252C4⋊C8—261no—
253C4⋊C8—261no—
254#104—42no—
255#104—522no—
256C22⋊C8—261no—
257C22⋊C8—261no—
258C22⋊C8—261no—
259C4×C8—131no—
260C4×C8—131no—
261C4×C8—131no—
262C4×C8—131no—
263C4×C8—261no—
264C4×C8—261no—
265C4×C8—261no—
266#95—21no—
267#95—261no—
268C2×C13—21no—
269C2×C13—21no—
270C2×C13—42no—
271C2×C13#180611yescharacteristic
272C2×C13#180811yescharacteristic
273C2×C13#181411yescharacteristic
274#41—21no—
275#41—21no—
276#41#610412yes—
277#41#610712yes—
278C2×Q8#610111yescharacteristic
279C2×D4—21no—
280C2×D4#610111yescharacteristic
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—41no—
285C22×C4—521no—
286C22×C4D4×D1311yescharacteristic
287C22×C4#612911yescharacteristic
288C22×C4C2×C22⋊D1311yescharacteristic
289M16—41no—
290M16—41no—
291M16—521no—
292M16—521no—
293C2×C8—41no—
294C2×C8—131no—
295C2×C8—131no—
296C2×C8—131no—
297C2×C8—131no—
298C2×C8—262no—
299C2×C8—261no—
300C2×C8—261no—
301C2×C8—522no—
302C2×C8—521no—
303C2×C8—522no—
304C2×C8—521no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—22no—
308C4⋊C4—41no—
309C4⋊C4—262no—
310C4⋊C4—521no—
311C4⋊C4#610111yescharacteristic
312C4⋊C4#610111yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C42—21no—
317C42—21no—
318C42—21no—
319C42—41no—
320C42—41no—
321C42—521no—
322C42—521no—
323C42C2×Dic2611yescharacteristic
324C42C2×C4×D1311yescharacteristic
325C42D4×D1311yescharacteristic
326C42#612911yescharacteristic
327C13#866711yescharacteristic, complemented, Sylow
328C23—21no—
329C23#8819311yescharacteristic
330Q8—21no—
331Q8#8804712yescomplemented
332D4—22no—
333D4—22no—
334D4—21no—
335D4#8804712yescomplemented
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—522no—
351C2×C4—1041no—
352C2×C4—1041no—
353C2×C4#8813111yescharacteristic
354C2×C4#8813211yescharacteristic
355C2×C4#8813211yescharacteristic
356C2×C4C22⋊C4×D1311yescharacteristic
357C2×C4C2×#610111yescharacteristic
358C2×C4C2×#610411yescharacteristic
359C2×C4#8819311yescharacteristic
360C2×C4C2×#610711yescharacteristic
361C2×C4#8820411yescharacteristic
362C2×C4#8820411yescharacteristic
363C8—81no—
364C8—132no—
365C8—261no—
366C8—261no—
367C8—261no—
368C8—521no—
369C8—521no—
370C8—1041no—
371C22—21no—
372C22—21no—
373C22—22no—
374C22—41no—
375C22—41no—
376C22#1171860311yescharacteristic
377C22#1171869911yescharacteristic
378C22#1171871211yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—22no—
383C4—41no—
384C4—41no—
385C4—82no—
386C4—1042no—
387C4D13×#10411yescharacteristic
388C4#1171848211yescharacteristic
389C4C2×#8804711yescharacteristic
390C4#1171865911yescharacteristic
391C4#1171869911yescharacteristic
392C4#1171871211yescharacteristic
393C2—21no—
394C2—21no—
395C2—42no—
396C2#1311485411yescharacteristic
397C2#1311486311yescharacteristic
398C2#1311488811yescharacteristic
subgroupG/H
centerC2×C4#88193
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1806C2
socleC22×C13#380
prime radicalC2×C13×#41D4
cosocleC2×C42×C13C23
hypercenter#1806D13
hypocenterC13#8667
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
3. C4×#88047C2semidirect
4. #13113594C2semidirect
5. #13112739C2semidirect
6. #13112737C2semidirect
13. Q8×#1055C4semidirect
14. Q8×#1055C4semidirect
17. D4×#1055C4semidirect
18. D4×#1055C4semidirect
139. Q8×C13#107semidirect
143. D4×C13#107semidirect
178. #1055#104semidirect
327. C13#8667semidirect
331. Q8#88047semidirect
335. D4#88047semidirect

Maximal subgroups

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

subgroupindex
#41×#10552
#131148562
C4×#880472
#131135942
#131127392
#131127372
C13×#18062
#866713